Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

ANALYZING FRICTION in the DESIGN of RUBBER PRODUCTS and Their PAIRED SURFACES

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ANALYZING FRICTION in the DESIGN of RUBBER PRODUCTS and Their PAIRED SURFACES Robert Horigan Smith

Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

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CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487‑2742 © 2008 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid‑free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number‑13: 978‑0‑8493‑8136‑2 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the conse‑ quences of their use. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978‑750‑8400. CCC is a not‑for‑profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Smith, Robert Horigan. Analyzing friction in the design of rubber products and their paired surfaces / Robert Horigan Smith. p. cm. Includes bibliographical references and index. ISBN‑13: 978‑0‑8493‑8136‑2 (hardcover : alk. paper) ISBN‑10: 0‑8493‑8136‑3 (hardcover : alk. paper) 1. Rubber. 2. Friction. I. Title. TJ1105.S55 2008 620.1’9492‑‑dc22

2007041283

Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

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Dedication To Joseph Dennis Horigan, my father 129th Field Artillery, 35th Division Missouri National Guard World War I

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Contents Preface...................................................................................................... xxiii About the Author......................................................................................xxv 1

Introduction......................................................................................... 1 1.1 Historical Background..........................................................................1 1.2 Purposes of the Book............................................................................. 1 1.3 The Unified Theory of Rubber Friction..............................................2 1.4 Surface Deformation Hysteresis in Rubber........................................ 2 1.5 Differences between Metallic and Rubber Friction Mechanisms............................................................................................ 3 1.6 Consequences Stemming from Use of the Traditional Metallic-Friction Approach to Rubber Friction Analysis................. 3 1.7 Approach to the Subject........................................................................ 4 1.8 Organization of the Book......................................................................4 1.9 Chapter Review......................................................................................5 References........................................................................................................ 6

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Metallic Coefficient of Friction......................................................... 7 2.1 Introduction............................................................................................7 2.2 Smooth-Metal Friction........................................................................... 7 2.2.1 Friction Mechanism between Smooth-Metal Surfaces......... 7 2.2.2 Real Area of Surface-to-Surface Contact in Metallic Friction......................................................................................... 8 2.2.3 Friction Force between Smooth-Metal Surfaces Independent of Apparent Contact Area..................................8 2.2.4 Constant Coefficient of Metallic Friction Equation............... 9 2.3 Adhesion Theory of Smooth-Metal Friction......................................9 2.3.1 Initial Friction Force Posits........................................................ 9 2.3.2 Smooth-Metal Friction Theory............................................... 10 2.4 Origin of the Friction Force between Smooth Metals.................... 10 2.4.1 Surface Energy and the Energy of Adhesion....................... 10 2.4.2 Evidence Supporting the Adhesion Theory of Metallic Friction........................................................................ 11 2.4.3 Metallic Coefficient of Adhesion............................................ 11 2.5 Rough-Metal Friction.......................................................................... 12 2.6 Laws of Metallic Friction.................................................................... 12 2.7 Chapter Review.................................................................................... 12 References...................................................................................................... 13

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Rubber Friction Mechanisms........................................................... 15 3.1 Introduction.......................................................................................... 15 vii

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Contents 3.2 3.3 3.4 3.5 3.6 3.7 3.8

Rubber Friction Coefficient Decreases with Increasing Load...... 15 Adhesion as a Rubber Friction Mechanism..................................... 18 Linking Rubber Friction to the Real Area of Contact..................... 19 Hertz Equation.....................................................................................22 Bulk Deformation Hysteresis in Rubber........................................... 25 Concurrently Acting Rubber Friction Mechanisms....................... 26 van der Waals’ Adhesion and Surface Deformation Hysteresis in Rubber............................................................................ 28 3.9 Adhesion, Bulk Deformation Hysteresis, and Wear in Sliding Rubber...................................................................................... 28 3.10 Expressions for Bulk Deformation Hysteresis in Rubber.............. 31 3.11 Modified Hertz Equation.................................................................... 32 3.12 Schallamach Waves.............................................................................34 3.13 Elastomeric Friction............................................................................. 36 3.14 Microhysteretic Contributions to Wet-Rubber Friction.................. 37 3.15 Chapter Review....................................................................................38 3.15.1 Rubber Coefficient of Friction Decreases with Increasing Load........................................................................38 3.15.2 Adhesion as a Rubber Friction Mechanism.......................... 39 3.15.3 Linking Rubber Friction to the Real Area of Contact......... 40 3.15.4 Bulk Deformation Hysteresis in Rubber............................... 40 3.15.5 Concurrently Acting Rubber Friction Mechanisms............ 41 3.15.6 Adhesion and Surface Deformation in Rubber....................42 3.15.7 Schallamach Waves..................................................................42 3.15.8 Adhesion, Bulk Deformation Hysteresis, and Wear in Sliding Rubber..........................................................................43 References...................................................................................................... 43 4

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Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber............................................................................................ 45 4.1 Introduction..........................................................................................45 4.2 Coefficient of Rubber Friction on Dry, Smooth Surfaces................45 4.2.1 Walking-Surface Slip-Resistance Testing with a Pendulum Device..................................................................... 45 4.2.2 Industrial Rubber Belting........................................................ 47 4.2.3 Rubber Friction on Steel and Aluminum Surfaces.............. 49 4.2.4 Aircraft Tire Friction on Different Portland Cement Concrete Finishes: Smooth Surface........................................ 51 4.2.4.1 Ambient-Temperature Testing.................................. 53 4.2.4.2 High-Temperature Testing..........................................54 4.2.5 Rubber Adhesion on Smooth Solids Increases with Surface Free Energy................................................................. 56 4.2.6 ANOVA Slip-Resistance Testing of Dry, Elastomeric Shoe Heels................................................................................. 62 4.2.7 Friction of Natural and Synthetic Tire-Tread Rubber on Ice..........................................................................................63

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4.3 Coefficient of Rubber Friction on Dry, Textured Surfaces.............65 4.3.1 Aircraft Tire Friction on Different Portland Cement Concrete Finishes: Textured Surfaces.................................... 65 4.3.1.1 Ambient-Temperature Testing..................................66 4.3.1.2 High-Temperature Testing......................................... 66 4.3.2 Bias-Ply and Radial-Belted Aircraft Tire Friction on an Ungrooved, Portland Cement Concrete Runway........... 67 4.3.3 Rubber Friction on Gritted Floor Tile.................................... 73 4.4 Coefficient of Rubber Friction on Wet, Smooth Surfaces............... 74 4.4.1 Rubber Friction on Oil-Coated Surfaces............................... 74 4.4.1.1 Testing with Smooth Rubber Specimens................. 75 4.4.1.2 Testing with Roughened Rubber Specimens.......... 76 4.4.2 Walking-Surface Slip-Resistance Testing of Wet Work Boots...........................................................................................80 4.4.3 Walking-Surface Slip-Resistance Testing of Wet Safety Shoes...............................................................................80 4.4.4 ANOVA Slip-Resistance Testing of Wet, Elastomeric Shoe Heels................................................................................. 81 4.5 Coefficient of Rubber Friction on Wet, Textured Surfaces.............84 4.5.1 Smooth-Rubber Friction Testing on Roughened, OilCoated Surfaces........................................................................84 4.5.2 Tire Friction Testing with a Skid-Test Trailer in Wet Conditions................................................................................. 86 4.5.3 Bias-Ply and Radial-Belted Aircraft Tire Friction on a Wet, Ungrooved, Portland Cement Concrete Runway....... 89 4.5.4 Lubricated-Rubber Friction Testing with Smooth Spheres....................................................................................... 91 4.5.4.1 Slow-Speed Testing with Lubricated Smooth Spheres......................................................................... 91 4.5.4.2 High-Speed Testing with Lubricated Smooth Spheres......................................................................... 94 4.5.5 Lubricated-Rubber Friction Testing with Smooth Cones.......................................................................................... 94 4.6 Constant (Metallic) Coefficient-of-Friction Equation Not Applicable to Rubber........................................................................... 96 4.6.1 Review of the Analyzed Data................................................. 96 4.6.2 Deformational and Constitutive Differences between Rigid Metals and Visco-Elastic Rubber................................. 98 4.7 Chapter Review....................................................................................99 References...................................................................................................... 99 5

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A Unified Theory of Rubber Friction........................................... 101 5.1 Introduction........................................................................................ 101 5.2 Rubber Microhysteresis Development on Macroscopically Smooth Surfaces................................................................................. 101 5.2.1 Roth, Driscoll, and Holt......................................................... 101

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Contents 5.2.2 Thirion..................................................................................... 106 5.2.3 Schallamach............................................................................ 110 5.2.4 Bartenev and Lavrentjev....................................................... 117 5.2.5 Sigler, Geib, and Boone.......................................................... 121 5.2.6 Mori et al.................................................................................. 123 5.3 Rubber Microhysteresis Development on Macroscopically Rough Surfaces................................................................................... 128 5.3.1 Sigler, Geib, and Boone.......................................................... 128 5.3.2 Chang....................................................................................... 129 5.4 Characteristics of the Rubber Microhysteresis Mechanism........ 133 5.4.1 Rubber Microhysteresis Mechanism................................... 133 5.4.2 Independence of the Rubber Microhysteresis Force......... 134 5.4.3 Dependence of the Rubber Microhysteretic Force............. 136 5.4.4 Relevance of the Intercept-Indicated Friction Force — . Hurry and Prock..................................................................... 137 5.5 No-Load Adhesion Hypothesis....................................................... 137 5.5.1 Use of the No-Load Adhesion Hypothesis in Rubber Friction Analysis..................................................................... 137 5.5.2 Residence Time Considerations........................................... 139 5.5.3 No-Load Adhesion in Sliding Rubber................................. 139 5.6 Rubber Surface Deformation Hysteresis Testing.......................... 140 5.6.1 Kummer: Dry Testing............................................................ 140 5.6.2 Kummer: Wet Testing............................................................ 141 5.6.3 Yandell: Dry Testing............................................................... 142 5.6.4 Yandell: Wet Testing............................................................... 149 5.7 A Unified Theory of Rubber Friction.............................................. 150 5.8 Chapter Review.................................................................................. 151 References.................................................................................................... 153

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The Rubber Adhesion Transition Phenomenon.......................... 155 6.1 Introduction........................................................................................ 155 6.2 Further Aspects of the Rubber Adhesive Friction Mechanism.......................................................................................... 155 6.2.1 Arnold, Roberts, and Taylor.................................................. 155 6.2.1.1 Testing Protocols....................................................... 156 6.2.1.2 Arnold et al.’s Interpretations of Their Test Data............................................................................. 157 6.2.1.3 Additional Interpretations of the Arnold et al. Data............................................................................. 159 6.2.1.4 Rubber Microhysteresis and Schallamach Waves.......................................................................... 159 6.3 Adhesive Friction of Metal and Non-Elastomeric Plastics in the Elastic Loading Range................................................................ 160 6.4 Determinants Controlling the Value of PNt.................................... 161 6.4.1 Thirion’s Adhesion Data........................................................ 161 6.4.2 Schallamach’s Adhesion Data............................................... 162

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6.5 Controlling Adhesion Transition Pressure to Optimize Friction Development........................................................................ 162 6.6 “Low” μA Values in the Low-Loading Range................................ 164 6.7 Chapter Review.................................................................................. 165 References.................................................................................................... 166

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Microhysteretic Friction in Dry Rubber Products...................... 167 7.1 Introduction........................................................................................ 167 7.2 Microhysteresis in Automotive Tire Rubber in Dry Conditions.....168 7.3 Microhysteresis in Dry Aircraft Tires............................................. 170 7.3.1 B-29 Tire Rubber on Dry Concrete....................................... 170 7.3.1.1 Testing on Smooth Concrete................................... 170 7.3.1.2 High-Pressure Testing on Textured Concrete...... 175 7.3.1.3 Additional Hample Test Results............................. 178 7.3.2 Commercial Aircraft Tires on Dry, Textured Concrete.... 178 7.4 Rubber Microhysteresis in Dry Footwear Materials..................... 180 7.4.1 Shoe Heels on Dry, Smooth Floors...................................... 180 7.4.2 A Rubber Test Foot on in-Service Floors............................. 182 7.5 Microhysteresis in Dry Rubber Belting.......................................... 183 7.6 Rubber Adhesion-Transition-Pressure Phenomenon on Macroscopically Rough Surfaces..................................................... 184 7.6.1 Development of the Adhesion-Transition-Pressure Phenomenon in Hample’s Testing of Rough Portland Cement Concrete.................................................................... 184 7.6.1.1 Accounting for Inertial Bias in Hample’s Testing........................................................................ 184 7.6.1.2 Adhesion-Development Issues in Hample’s Testing........................................................................ 184 7.6.1.3 Transition Pressure Mechanisms in Hample’s Testing........................................................................ 185 7.6.2 Quantifying Inertial Bias in Hample’s Testing.................. 186 7.7 Chapter Review.................................................................................. 188 References.................................................................................................... 189

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Microhysteresis in Wet Rubber Products..................................... 191 8.1 Introduction........................................................................................ 191 8.2 Effects of Wet Lubricants on the Rubber Adhesion Mechanism.......................................................................................... 191 8.2.1 Wet-Lubricant Investigations in Friction Testing.............. 191 8.2.2 Rubber Friction in “Dry” and Wet Conditions.................. 192 8.3 Microhysteresis in Automotive Tire Rubber under Wet Conditions........................................................................................... 193 8.3.1 Dependence of Wet-Tire Traction on Rubber Microhysteresis....................................................................... 193 8.3.2 Rubber Microhysteresis in Tire-Tread Test Specimens in Wet Conditions................................................................... 194

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Contents 8.4 Microhysteresis in Wet Aircraft Tires............................................. 196 8.5 Rubber Microhysteresis in Wet Footwear Outsoles...................... 199 8.5.1 Rubber Microhysteresis in Wet Work Shoe Outsoles........ 199 8.5.2 Rubber Microhysteresis in Wet Safety Shoe Outsoles...... 199 8.5.3 Microhysteresis in Wet ANOVA Testing of Elastomeric Shoe Outsoles.................................................... 202 8.6 Ramifications of the Presence of Microhysteresis in Wet Rubber Products................................................................................. 204 8.7 Rubber Adhesion-Transition Phenomenon on Wet Surfaces....... 206 8.7.1 Automobile Tire-Tread Rubber............................................. 206 8.7.2 Aircraft Tires........................................................................... 208 8.7.3 Footwear Outsoles.................................................................. 209 8.7.3.1 Work Shoes................................................................ 209 8.7.3.2 Safety Shoes............................................................... 209 8.7.4 Ramifications of the Presence of the AdhesionTransition Phenomenon in Wet Rubber Products............. 211 8.8 Chapter Review.................................................................................. 212 References.................................................................................................... 213

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Rubber Microhysteresis in Static-Friction Testing..................... 215 9.1 Introduction........................................................................................ 215 9.2 Does Static Friction in Rubber Exist?.............................................. 215 9.2.1 Hurry and Prock’s Position................................................... 215 9.2.2 Kummer’s Position................................................................. 216 9.3 Two Portable Static-Friction Testing Devices................................. 217 9.4 Definition of Static Friction............................................................... 219 9.5 Rubber Microhysteresis in Static-Friction Testing........................ 220 9.5.1 Findings of the Powers et al. Testing................................... 220 9.5.2 Adhesion and Rubber Microhysteresis in PIAST Testing...................................................................................... 220 9.6 Independence of the Rubber Microhysteresis Force in StaticFriction Testing...................................................................................223 9.7 Adhesion and Rubber Microhysteresis in VIT Testing................223 9.8 Chapter Review..................................................................................225 References.................................................................................................... 226

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Inertial, Residence-Time, Adhesion-Transition, and Contact-Time Bias in Portable Walking-Surface SlipResistance Testers............................................................................ 227 10.1 Introduction........................................................................................ 227 10.2 Remediable Inertial Bias in Portable Walking-Surface SlipResistance Testers............................................................................... 229 10.2.1 Quantifying Inertial Forces in Static-Friction Testing Using the Hoechst Device..................................................... 229 10.2.2 Inertial Bias in VIT Testing................................................... 230

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10.2.2.1 Static-Friction Testing Utilizing the VIT Device.........................................................................230 10.2.2.2 Correcting for Inertial Bias in Dry VIT StaticFriction Testing.......................................................... 232 10.2.2.3 Inertial Bias in the VIT When Used as a Dynamic-Friction Tester..........................................234 10.2.3 Inertial Bias in the PIAST When Used as a DynamicFriction Tester.......................................................................... 236 10.2.4 Inertial Bias in the HPS When Used as a StaticFriction Tester.......................................................................... 237 10.3 Irremediable Inertial Bias in Portable Walking-Surface SlipResistance Testers............................................................................... 238 10.3.1 Irremediable Inertial Bias in the HP-M............................... 239 10.3.2 Irremediable Inertial Bias in Other Manually Operated Pull-Meter Testers................................................. 240 10.4 Remediable Residence-Time Bias in Static-Friction Testing........ 241 10.4.1 Quantifying Residence-Time Bias Using the Hoechst Device....................................................................................... 241 10.4.2 Demonstrating the Residence-Time Effect Using the VIT............................................................................................ 242 10.4.3 Remedying Residence-Time Bias in Portable SlipResistance Testers................................................................... 242 10.5 Irremediable Adhesion-Transition Bias in Portable WalkingSurface Slip-Resistance Testers........................................................ 242 10.5.1 Irremediable Adhesion-Transition Bias in VIT Testing.... 242 10.5.2 Irremediable Adhesion-Transition Bias in PIAST Testing...................................................................................... 244 10.6 Contact-Time Bias for Tribometer Comparability......................... 245 10.7 Chapter Review.................................................................................. 246 10.7.1 Inertial Bias............................................................................. 246 10.7.2 Residence-Time Bias............................................................... 247 10.7.3 Adhesion-Transition Bias...................................................... 247 10.7.4 Test Foot Contact-Time Bias for Tribometer Comparability......................................................................... 247 References.................................................................................................... 248 11

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Nonscientific Application of the Laws of Metallic Friction to Rubber Tires Operated on Pavements...................................... 249 11.1 Introduction........................................................................................ 249 11.2 Comparing the Characteristics of Rubber Friction to Metallic Friction.................................................................................250 11.3 Effects of the Development of Microhysteretic Forces on Tire-Friction Analysis........................................................................ 251 11.3.1 Development of the Constant Microhysteretic Friction Force in Rubber Tires............................................................. 251

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Contents 11.3.2 Development of the Adhesion-Transition Phenomenon in Rubber Tires............................................... 252 11.3.3 Development of the Macrohysteresis Friction Force in Rubber Tires............................................................................ 253 11.3.4 Application of a Unified Theory of Rubber Friction to Analysis of Tire-Roadway Traction-Testing Results.......... 253 11.4 Comparability of Rubber-Friction Testing Data............................254 11.5 Inadvertent Misapplication of the Laws of Metallic Friction to Rubber Tires in ASTM Test Standards....................................... 257 11.5.1 ASTM Test Standards with an “E” Designation................ 258 11.5.1.1 ASTM E 274 – 06, Standard Test Method for Skid Resistance of Paved Surfaces Using a Full-Scale Tire............................................................ 258 11.5.1.2 ASTM E 445/E 445M – 88 (Reapproved 2001), Standard Test Method for Stopping Distance on Paved Surfaces Using a Passenger Vehicle Equipped with Full-Scale Tires.............................. 259 11.5.1.3 ASTM E 503/E 503M – 88 (Reapproved 2004), Standard Test Methods for Measurement of Skid Resistance on Paved Surfaces Using a Passenger Vehicle Diagonal Braking Technique..... 260 11.5.1.4 ASTM E 670 – 94 (Reapproved 2000), Standard Test Method for Side Friction Force on Paved Surfaces Using the Mu-Meter.................................. 260 11.5.1.5 ASTM E 1337 – 90 (Reapproved 2002), Standard Test Method for Determining Longitudinal Peak Braking Coefficient of Paved Surfaces Using a Standard Reference Tire.................................261 11.5.1.6 ASTM E 1859 – 97 (Reapproved 2006), Standard Test Method for Friction Coefficient Measurements between Tire and Pavement Using a Variable Slip Technique............................. 261 11.5.1.7 ASTM E 1890 – 01 (Reapproved 2006), Standard Guide for Validating New Area Reference Skid Measurement Systems and Equipment.................................................................. 262 11.5.1.8 ASTM E 1911 – 98 (Reapproved 2002), Standard Test Method for Measuring Paved Surface Frictional Properties Using the Dynamic Friction Tester........................................... 262 11.5.1.9 ASTM E 1960 – 03, Standard Practice for Calculating International Friction Index of a Pavement Surface...................................................... 263 11.5.1.10 ASTM E 2100 – 04, Standard Practice for Calculating the International Runway Friction Index............................................................ 263

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11.5.2 ASTM Test Standards with an “F” Designation................264 11.5.2.1 ASTM F 403 – 98, Standard Test Method for Tires for Wet Traction in Straight-Ahead Braking, Using Highway Vehicles.......................... 264 11.5.2.2 ASTM F 408 – 99, Standard Test Method for Tires for Wet Traction in Straight-Ahead Braking, Using a Towed Trailer.............................. 265 11.5.2.3 ASTM F 538 – 03, Standard Terminology Relating to the Characteristics and Performance of Tires................................................ 266 11.5.2.4 ASTM F 1649 – 96 (Reapproved 2003), Standard Test Methods for Evaluating Wet Braking Traction Performance of Passenger Car Tires on Vehicles Equipped with AntiLock Braking Systems.............................................. 266 11.5.2.5 ASTM F 1805 – 00, Standard Test Method for Single-Wheel-Driving Traction in a Straight Line on Snow- and Ice-Covered Surfaces.............. 267 11.6 Inadvertent Misapplication of the Laws of Metallic Friction to Rubber Tires in Motor Vehicle Accident Reconstruction........ 267 11.6.1 Background............................................................................. 267 11.6.2 Traditional Use of Newton’s Second Law of Motion in Accident Reconstruction....................................................... 268 11.6.2.1 Use of Newton’s Second Law of Motion When Only the Rubber Adhesion and Microhysteresis Mechanisms are Present............. 269 11.6.2.2 Use of Newton’s Second Law of Motion When the Rubber Macrohysteresis Mechanism is Present........................................................................ 269 11.6.2.3 Use of Newton’s Second Law of Motion When the Rubber Cohesion-Loss Friction Mechanism is Present.............................................. 270 11.6.2.4 Use of Newton’s Second Law of Motion When Tread Temperatures Change................................... 270 11.6.2.5 Traditional Use of Newton’s Second Law of Motion When Dynamic Load Transfer Occurs.... 271 11.6.2.6 Equations of Motion Utilized in Accident Reconstruction in Which a μ Term May Not be Substituted for an a Term................................... 272 11.6.3 Drag Factors............................................................................ 274 11.6.3.1 Use of Drag Factors in Tire-Traction-Related Motor Vehicle Accident Reconstruction................ 274 11.6.3.2 Use of Drag Factors in Motorcycle Accident Reconstruction.......................................................... 274 11.6.4 Definition of the Maximum Braking Force in Motor Vehicle Accident Reconstruction......................................... 275

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Contents 11.6.5 Traditional Use of Energy Methods in Motor Vehicle Accident Reconstruction....................................................... 275 11.7 Inadvertent Misapplication of the Laws of Metallic Friction to Rubber Tires in the Geometric Design of Roadways............... 276 11.7.1 Background............................................................................. 276 11.7.2 Braking Distance on Horizontal Pavement........................ 277 11.7.2.1 Macroscopically Smooth Pavements...................... 277 11.7.2.2 Macroscopically Rough Pavements........................ 278 11.7.3 Braking Distance on Up- or Down-Grades........................ 279 11.7.4 Side Friction Factor................................................................. 279 11.7.5 Superelevation........................................................................280 11.7.6 Superelevation Runoff Length..............................................280 11.7.7 Maximum Degree of Curvature........................................... 281 11.7.8 Minimum Radius of Curvature........................................... 281 11.8 Chapter Review.................................................................................. 282 11.8.1 Comparing Rubber Friction to Metallic Friction............... 282 11.8.2 Aspects of Microhysteretic Friction Force Development in Rubber......................................................... 283 11.8.3 Comparability of Tire-Friction Test Results........................ 284 11.8.4 Related ASTM Test Standards.............................................. 285 11.8.5 Motor Vehicle Accident Reconstruction.............................. 286 11.8.6 Geometric Design of Roadways........................................... 287 References.................................................................................................... 287

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Friction Analysis in the Design of Rubber Tires and Their Contacted Pavements...................................................................... 289 12.1 Introduction........................................................................................ 289 12.2 Importance of Tire Microhysteresis on Wet Pavements............... 289 12.2.1 Three-Lubrication-Zones Concept....................................... 290 12.2.2 Traditional Wet Roadway Microtexture Analysis............. 291 12.2.3 Importance of Aircraft Tire Microhysteresis on Wet Pavement.................................................................................. 293 12.2.4 Quantifying Tire Microhysteresis on Wet Pavement Using the Unified Theory of Rubber Friction.................... 293 12.2.5 Corroboration for the Three-Lubrication-Zones Concept.................................................................................... 294 12.3 Reformulation of the Traditional Friction Force vs. Tire Slip Relationship........................................................................................ 295 12.4 Measuring Tire Microhysteresis on Wet Pavements in the Design Process.................................................................................... 297 12.4.1 Using the British Pendulum Tester for Microhysteresis Measurements............................................ 297 12.4.1.1 Background................................................................ 297 12.4.1.2 Back-Calculation Analysis of Yandell’s BPT Test Results................................................................ 299

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12.4.2 Using the North Carolina State University Variable-Speed Friction Tester for Microhysteresis Measurements.........................................................................300 12.5 Application of the Unified Theory to Analysis of Friction in the Design of Tire-Pavement Systems............................................. 301 12.5.1 Potential Benefits from Application of the Unified Theory to Friction Analysis.................................................. 301 12.5.2 Rubber Macrohysteresis Mechanisms................................. 302 12.5.2.1 Adhesion-Assisted Macrohysteresis on Dry Surfaces...................................................................... 302 12.5.2.2 Adhesion-Assisted Macrohysteresis in Wet Conditions.................................................................. 307 12.5.2.3 Nonadhesion-Assisted Macrohysteresis on Fully Wetted Surfaces..............................................309 12.5.3 The Load Dependence of Tire-Tread Rubber Friction....... 312 12.5.4 Use of the Unified Theory for Friction Analysis in Design of Tire-Pavement Systems........................................ 313 12.5.4.1 Process Brief............................................................... 314 12.5.4.2 Process Specifications............................................... 314 12.5.4.3 Action Item Concept Design................................... 315 12.5.4.4 Action Item Detail Design....................................... 316 12.6 Chapter Review.................................................................................. 316 12.6.1 Importance of Tire Microhysteresis on Wet Pavements................................................................................ 317 12.6.1.1 Three-Lubrication-Zones Concept.......................... 317 12.6.1.2 Traditional Wet-Roadway Texture Analysis......... 317 12.6.1.3 Importance of Aircraft Tire Microhysteresis on Wet Pavement....................................................... 318 12.6.1.4 Quantifying Tire Microhysteresis on Wet Pavement Using the Unified Theory of Rubber Friction.......................................................... 318 12.6.1.5 Corroboration for the Three-LubricationZones Concept........................................................... 318 12.6.2 Reformulation of the Friction Force vs. Tire-Slip Relationship............................................................................. 318 12.6.3 Measuring Tire Microhysteresis on Wet Pavements in the Design Process................................................................. 319 12.6.4 Application of the Unified Theory to Analysis of Friction in the Design of Tire-Pavement Systems.............. 319 12.6.4.1 Potential Benefits from Application of the Unified Theory to Friction Analysis...................... 319 12.6.4.2 Rubber Macrohysteresis Mechanisms................... 320 12.6.5 The Load Dependence of Rubber Tire-Tread Friction....... 321 12.6.6 Use of the Unified Theory for Friction Analysis in Design of Tire-Pavement Systems........................................ 322 12.6.6.1 Process Brief............................................................... 322

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Contents 12.6.6.2 Process Specifications............................................... 322 References.................................................................................................... 323

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Nonscientific Application of the Laws of Metallic Friction to Footwear Outsole-Walking Surface Pairings.......................... 325 13.1 Introduction........................................................................................ 325 13.2 Comparing the Characteristics of Rubber Friction to Metallic Friction................................................................................. 326 13.3 Effects of the Development of Microhysteretic SlipResistance Forces on Rubber-Friction Analysis............................. 327 13.3.1 Development of the Microhysteretic Slip-Resistance Force in Pedestrian Ambulation.......................................... 327 13.3.2 Development of the Adhesion Transition Phenomenon in Pedestrian Ambulation............................. 327 13.3.3 Development of the Macrohysteresis Slip-Resistance Force in Pedestrian Ambulation.......................................... 328 13.3.4 Application of the Unified Theory of Rubber Friction to Analysis of Footwear Outsole-Walking Surface Slip-Resistance Testing.......................................................... 330 13.4 Comparability of Slip-Resistance Testing Data............................. 331 13.5 Inadvertent Misapplication of the Laws of Metallic Friction in ASTM Slip-Resistance Testing Methods.................................... 333 13.5.1 Irremediable Bias in Slip-Resistance Testers with Active ASTM Test Standards................................................333 13.5.1.1 ASTM D 2047 – 04, Standard Test Method for Static Coefficient of Friction of Polish-Coated Flooring Surfaces as Measured by the James Machine......................................................................334 13.5.1.2 Irremediable Inertial and Residence-Time Bias in the James Machine.......................................334 13.5.2 ASTM F 1646 – 05, Standard Terminology Relating to Safety and Traction for Footwear......................................... 336 13.6 Inadvertent Misapplication of the Laws of Metallic Friction by Slip-Resistance Testing Devices That are Not the Subject of Active ASTM Standards............................................................... 336 13.6.1 Irremediable Bias in Slip-Resistance Testers That are Not the Subject of Active ASTM Test Standards............... 336 13.6.2 Misapplication of the Laws of Metallic Friction in the PIAST and VIT When Used as Static-Friction Testers....... 337 13.6.3 Misapplication of the Laws of Metallic Friction in the PIAST and VIT When Used as Dynamic-Friction Testers....................................................................................... 337 13.6.4 ASM 825 Digital Slip Meter................................................... 338 13.6.5 Portable Articulated Strut Slip Tester (PAST)..................... 338 13.6.6 Technical Products Corporation Model 80 Tester.............. 338

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13.7 Irremediable Inertial and Residence-Time Bias in SlipResistance-Testing Devices That are Not the Subject of ASTM Standards................................................................................ 338 13.7.1 Irremediable Inertial and Residence-Time Bias in the ASM 825 Digital Slip Meter................................................... 339 13.7.2 Irremediable Inertial and Residence-Time Bias in the Technical Products Corporation Model 80 Tester.............. 339 13.8 Chapter Review.................................................................................. 339 13.8.1 Comparing the Characteristics of Rubber Friction to Metallic Friction......................................................................340 13.8.2 Effects of the Development of Microhysteretic SlipResistance Forces on Rubber-Friction Analysis................. 341 13.8.2.1 Development of the Microhysteretic SlipResistance Force in Pedestrian Ambulation......... 341 13.8.2.2 Development of the Adhesion-Transition Phenomenon in Pedestrian Ambulation............... 341 13.8.2.3 Development of the Macrohysteresis SlipResistance Force in Pedestrian Ambulation on Rough Walking Surfaces..........................................342 13.8.3 Application of the Unified Theory of Rubber Friction to Analysis of Footwear Outsole-Walking Surface Slip-Resistance Testing..........................................................342 13.8.4 Comparability of Slip-Resistance Testing Data..................343 13.8.5 Inadvertent Misapplication of the Laws of Metallic Friction in ASTM Slip-Resistance Testing Methods..........344 13.8.6 Inadvertent Misapplication of the Laws of Metallic Friction by Slip-Resistance Testing Devices That are Not the Subject of Active ASTM Standards.......................344 References....................................................................................................344 14

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Slip-Resistance Analysis in the Design of Footwear Outsoles and Their Paired Walking Surfaces............................. 345 14.1 Introduction........................................................................................345 14.2 Importance of Footwear Outsole Microhysteresis in Wet Conditions...........................................................................................345 14.2.1 Three-Lubrication-Zones Concept.......................................346 14.2.2 Traditional Wet Roadway Microtexture Analysis.............346 14.2.3 Importance of Aircraft Tire Microhysteresis on Wet Pavement..................................................................................347 14.2.4 Corroboration for the Three-Lubrication-Zones Concept as Applied to Walking-Surface Slip . Resistance................................................................................348 14.2.4.1 Tisserand’s Testing....................................................348 14.2.4.2 Grönqvist’s Testing...................................................348 14.2.4.3 Redfern and Bidanda’s Testing............................... 349 14.3 Reformulating the Traditional Approach to Walking-Surface Slip-Resistance Testing...................................................................... 350

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xx

Contents 14.3.1 Test Results from the ASTM F-13 Bucknell University Workshop................................................................................. 350 14.3.1.1 Effect from Inadvertent Misapplication of the Laws of Metallic Friction to Rubber Friction........ 351 14.3.1.2 Effect from the Presence of Test-Foot-Area Bias on Test Measurements..................................... 351 14.3.1.3 Effect from the Presence of Inertial Forces in Test Measurements................................................... 351 14.3.1.4 Effect from the Presence of Contact-Time Bias on Test Measurements.............................................. 352 14.3.2 Conclusions from the ASTM F-13 Bucknell Workshop: Sticktion................................................................................... 353 14.3.3 Exemplifying Inertial and Residence-Time Bias in an ASTM F-13 Workshop Pull-Meter........................................ 355 14.3.3.1 Inertial Bias................................................................ 355 14.3.3.2 Contact-Time Bias..................................................... 356 14.3.4 Developments Arising from the ASTM F-13 Workshop Conclusions.......................................................... 357 14.4 Measuring Footwear Outsole Microhysteresis on Wet Walking Surfaces in the Design Process........................................ 357 14.4.1 Using the British Pendulum Tester for Microhysteresis Measurements on Rough Walking Surfaces.................................................................................... 358 14.4.1.1 Background................................................................ 358 14.4.1.2 Back-Calculation Analysis of Yandell’s BPT Test Results................................................................ 359 14.4.2 Using the Sigler Pendulum Tester for Microhysteresis Measurements on Smooth Walking Surfaces..................... 360 14.5 Application of the Unified Theory to Analysis of Slip Resistance in the Design of Footwear Outsole-Walking Surface Pairings.................................................................................. 361 14.5.1 Potential Benefits from Application of the Unified Theory to Friction Analysis.................................................. 361 14.5.2 Rubber Outsole Macrohysteresis Mechanisms.................. 362 14.5.2.1 Adhesion-Assisted Macrohysteresis on Dry Surfaces...................................................................... 362 14.5.2.2 Adhesion-Assisted Macrohysteresis in Wet Conditions.................................................................. 366 14.5.2.3 Nonadhesion-Assisted Macrohysteresis on Fully Wetted Surfaces.............................................. 369 14.5.3 Use of the Unified Theory for Slip-Resistance Analysis in Design of Footwear Outsoles and Their Paired Walking Surfaces....................................................... 372 14.5.3.1 Process Brief............................................................... 373 14.5.3.2 Process Specifications............................................... 373 14.5.3.3 Action Item Concept Design................................... 374

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14.5.3.4 Action Item Detail Design....................................... 375 14.6 Chapter Review.................................................................................. 375 14.6.1 Importance of Rubber Microhysteresis in Wet Conditions............................................................................... 376 14.6.1.1 Three-Lubrication-Zones Concept.......................... 376 14.6.1.2 Traditional Wet-Roadway Texture Analysis......... 376 14.6.1.3 Importance of Aircraft Tire Microhysteresis on Wet Pavement....................................................... 377 14.6.1.4 Corroboration for the Three-LubricationZones Concept as Applied to Walking-Surface Slip Resistance........................................................... 377 14.6.2 Reformulating the Traditional Approach to WalkingSurface Slip-Resistance Testing............................................ 377 14.6.2.1 Test Results from the ASTM F-13 Bucknell University Workshop............................................... 378 14.6.2.2 Effect from Inadvertent Misapplication of the Laws of Metallic Friction to Rubber Friction........ 378 14.6.2.3 Effect from the Presence of Unquantified Inertial Forces in Workshop Test Measurements 379 14.6.2.4 Effect from the Presence of Contact-Time Bias in Workshop Test Measurements........................... 379 14.6.2.5 Effect from the Presence of Test-Foot-Area Bias in Test Measurements...................................... 379 14.6.3 Conclusions from the ASTM F-13 Bucknell Workshop: Sticktion................................................................................... 380 14.6.4 Measuring Footwear Outsole Microhysteresis on Wet Walking Surfaces in the Design Process............................. 381 14.6.4.1 Using the British Pendulum Tester for Outsole Microhysteresis Measurements on Rough Walking Surfaces...................................................... 381 14.6.4.2 Using the Sigler Pendulum Tester for Microhysteresis Measurements on Smooth Walking Surfaces...................................................... 382 14.6.5 Application of the Unified Theory to Analysis of Slip Resistance in the Design of Footwear OutsoleWalking Surface Pairings...................................................... 382 14.6.5.1 Potential Benefits from Application of the Unified Theory to Slip-Resistance Analysis......... 382 14.6.5.2 Rubber Outsole Macrohysteresis Mechanisms in Wet and Dry Conditions..................................... 383 14.6.5.3 Use of the Unified Theory for Slip-Resistance Analysis in Design of Footwear Outsoles and Their Paired Walking Surfaces............................... 385 References.................................................................................................... 385 Index........................................................................................................... 387

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Preface As a civil engineer, my professional involvement in matters associated with the practical friction characteristics of rubber tires began in 1962, in connection with the geometric design of an arterial roadway and a local connectorinterstate highway interchange. This was followed by activities in roadway construction supervision. In 1976, I entered private practice as a forensic engineer, focusing on motor vehicle accident reconstruction and highway design. My practice transitioned in 1983 to the specialty of walking-surface slip resistance and the investigation of pedestrian slip-and-fall incidents. Such investigations usually involve the friction characteristics of rubberlike footwear heels and soles (outsoles). Until 1999, when a chance office conversation concerning the friction of metals raised doubts in my mind, I had believed that the laws of metal friction learned as an undergraduate applied to just about all solids. During this conversation, a question arose: How could it possibly be proper to apply the laws of rigid-metal friction to rubber footwear outsoles? Many engineers, including myself, had been doing just that. Thus commenced a personal quest to understand the basic nature of rubber friction; that is, what is rubber friction from an engineering viewpoint, and why does it behave the way it does? The inquiry began with a reading of a 1976 overview of walking-surface slip resistance by Robert J. Brungraber, to whom much is owed. Examination of the references provided in his report demonstrated that scientific unanimity on a unified theory of rubber friction had not yet been achieved. Further study of the literature revealed that such unanimity is still not attained. It became clear that engineers have been inadvertently misapplying the laws of metallic friction to rubber. Formulation of a scientifically grounded, unified theory would allow the analysis of friction in the design of rubber products and their paired surfaces to be carried out on a more accurate, predictive basis than is currently being done. It is hoped that the newly developed theory of rubber friction detailed in this book will assist in accomplishing that goal. This book is intended to be an applied engineering handbook in which the presented concepts are illustrated in graphical form. The associated quantifying equations have been kept as simple as possible, restricted to those encountered in laboratory courses taken in the first two years of an undergraduate engineering education. Because most of the applicable productrelated rubber-friction-test results reported in the literature were obtained from tires and footwear outsoles, the book emphasizes these uses of rubber; nevertheless, the mechanistic, intuitively consistent theory of rubber friction  Brungraber, R.J., An Overview of Floor Slip-Resistance Research with Annotated Bibliography, U.S. National Bureau of Standards, Washington, D.C., 1976.

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xxiv

Preface

discussed in this work applies to all elastomeric products where friction is an issue. This book is written for two audiences: (1) technical and (2) nontechnical professionals. Reviews at the end of each chapter are simplified reiterations of the chapters’ contents, intended for the nontechnical reader. It is a pleasure to express my thanks to the staff of CRC Press, particularly Allison Shatkin and Marsha Pronin, for their guidance, patience, and courtesy during the preparation of this book. Special thanks are also due to Brendan Rodgers, Michaelinda Kaestner, and B.J. Clark. Without their invaluable assistance, this book could not have been written. Robert Horigan Smith Orcas Island, Washington

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About the Author Robert Horigan Smith, Ph.D., is both a civil engineer and safety engineer. He earned a B.S. degree in civil engineering from the University of Buffalo in 1962, specializing in the properties of engineering materials. In 1964, Dr. Smith was awarded the Diploma of Membership of the Imperial College (D.I.C.) in Concrete Structures and Technology. He earned an M.S. degree in civil engineering in 1965 from the University of Buffalo, specializing in the properties of engineering materials. He then earned a Ph.D. from the University of Calgary, Canada, in 1971, specializing in silicate and aluminate chemistry (portland cement hydration products, microstructure, crystallography, and surface chemistry). He authored a number of peer-reviewed papers on these and related subjects during the early portion of his career. Since 1976, Dr. Smith has provided forensic consultation to the legal and insurance professions — principally in pedestrian walking-surface safety — specializing in the scientific investigation of approximately 500 slip-andfall incidents. In an effort to contribute to the walking-surface safety field, he researched a number of the critical, empirically approached issues in walking-surface slip resistance and, commencing in 2001, authored peer-reviewed articles addressing some of these matters.

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1 Introduction

1.1

Historical Background

Because of the historical importance of metal machinery in industry, many of the initial scientific studies of friction focused on contact between metal surfaces. Traditional, scientifically based metallic friction theory, formulated in the 1940s and 1950s, is now generally accepted. Introductory physics courses in colleges and universities present the laws of metallic friction in a simple, straightforward manner, utilizing the metallic coefficient-of-friction equation in practical applications. Unfortunately, many introductory physics textbooks do not emphasize to the reader that the laws of metallic friction are for metal on metal only and have no scientific applicability to other engineering materials, including rubber. As a consequence, the laws of metallic friction have been inadvertently adopted by many engineers as their technical basis for all friction calculations, regardless of the materials involved. The metallic-friction equation is routinely utilized to quantify rubber friction. This has resulted in an unnecessary empirical, consensus approach to the subject. At present, engineering analysis and design of the friction characteristics of rubber products and their paired surfaces are seldom carried out scientifically. While research on metallic friction has predominated, considerable scientific investigation of the resistance to movement of sliding rubber was conducted in the 1940s, 1950s, and 1960s, in both the United States and Europe. The results of these studies are well known to involved scientists, but they have not usually made their way into post-secondary educational institutions. The engineering community has suffered from this delay.

1.2

Purposes of the Book

A principal purpose of this book is to assemble, discuss, and exemplify the engineering and scientific evidence demonstrating that the laws of metallic friction do not apply to rubber. The second principal purpose of this book 

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Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

is to present a newly developed, scientifically based, unified theory of rubber friction. Although the newly developed theory is applicable to all rubber products for which friction is an issue, use of the theory will be exemplified by focusing on the following important fields: • Analysis of friction in the design of rubber tires and their contacted pavements, • Geometric design of roadways, • Motor vehicle accident reconstruction, and • Analysis of heel and sole slip resistance in the design of footwear and their contacted walking surfaces.

1.3

The Unified Theory of Rubber Friction

It is traditionally accepted in scientific circles that three basic rubber friction forces generated by three different mechanisms can arise when rubber products slide on harder materials in dry or wet conditions. In 1966, Kummer [1] summarized the three mechanisms as: • The combined adhesion between the rubber surface and the contacted surface, • Resistance to bulk deformation in rubber when sliding on rough surfaces, and • Wear of the rubber product’s surface by physical means. The newly developed theory incorporates a fourth basic friction force produced by sliding contact of a rubber product: surface deformation resistance. This force adds a fourth mechanism to the above list. As demonstrated in Chapters 5 and 6 presenting the scientific basis for the new theory, including a surface deformation force in the analysis of friction for the design of rubber products and their paired surfaces can have a profound correcting effect on the bases for the results of such computations. Although the newly developed theory requires further verification beyond that presented in this book, the theory’s application will assist in allowing a scientific approach to rubber friction to supplant traditional empiricism.

1.4

Surface Deformation Hysteresis in Rubber

The existence of a rubber surface deformation force was first hypothesized by Savkoor [2] in 1965 but the subject has received insufficient attention since then. Because sliding involves repetitive exposure of the rubber surface to

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Introduction

the microscopic surface texture of the paired material, the generated friction force is considered hysteretic and the mechanism involved is termed “surface deformation hysteresis,” or “microhysteresis.” In addition to Kummer [1], this microhysteretic friction mechanism has been examined by Moore [3], Yandell [4], and Golden. [5] Their analyses, however, incorporated few test results from other investigators. Consequently, not all aspects of the microhysteresis mechanism came to light, and the existence of surface deformation hysteresis in rubber is not widely accepted. The unified theory of rubber friction presented in this volume is based on the analysis of many test findings — findings from studies specifically seeking to illuminate the friction mechanisms arising in rubber and test results that provided this benefit because of the research procedures involved.

1.5

Differences between Metallic and Rubber Friction Mechanisms

Scientific research showed that the reason for the differences between metallic and rubber friction is that their force-producing mechanisms are different. In metallic friction, contacting points on the two metal surfaces are usually in the plastic loading range; that is, the contacting metal deforms locally under pressure in a flowing, plastic manner. Rubber in contact with its paired surfaces remains elastic. Subsequent confirmatory studies of metal and rubber friction have been carried out but the early work is useful for the present purposes because of its phenomenological emphasis that mechanistically differentiates most clearly between the behavior of metal and the behavior of rubber. Thus, the early work has an important role to play in this book.

1.6

Consequences Stemming from Use of the Traditional Metallic-Friction Approach to Rubber Friction Analysis

Current engineering practices frequently mix forces produced by adhesion and the other rubber friction-generating mechanisms together by inadvertently misapplying the laws of metallic friction to rubber through use of the metallic coefficient-of-friction equation. Results obtained from this misapplication are then compared to other similarly determined rubber friction quantities or standard values to arrive at conclusions. Unfortunately, such results and standards are often not scientifically comparable because more than one rubber friction mechanism is present.

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Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Such inadvertent mechanism mixing can arise, for example, when calculating friction forces to predict traction provided by rubber and a contacted surface. A vehicle tire, or a footwear heel and sole, experiences the total friction force arising from whatever rubber friction mechanisms develop in the given circumstances. When two or more different mechanisms concurrently contribute to traction, the different forces produced may well respond differently to changes in the conditions encountered. When this occurs, correct calculation of the traction developed requires that equations expressing the friction mechanisms actually present be utilized in the computations. In such situations, the metallic friction expression must be replaced by equations appropriate to each different rubber force involved.

1.7

Approach to the Subject

While the traditional empirical approach to rubber friction analysis provides guidance, it is desirable to utilize scientifically based friction equations where possible. The phenomenological emphasis in this book assists in keeping the different rubber friction mechanisms separate so as to facilitate engineering analysis and design that produces comparable findings for both wet and dry conditions. The mechanistic approach taken by this book to explain rubber friction emphasizes the relevant physical behavior of rubber as it slides — or attempts to slide, as in walking-surface slip resistance — on harder, paired materials. This tack allows the forces produced by the mechanisms that develop to be quantified using nothing more complicated than simple equations of the type commonly found in engineering practice. In discussing rubber friction test procedures, this book employs the term “dry” to mean contacting surfaces to which no liquid has been applied by the investigator for purposes of the test. “Wet” means a condition in which a liquid has been interposed intentionally between the paired surfaces by the researcher to assess its effects on rubber friction.

1.8

Organization of the Book

This book is intended for two audiences: (1) technical professionals interested in the physics and chemistry of rubber friction and their practical applications, and (2) nontechnical professionals wishing to gain an understanding of rubber friction that will allow effective communication with engineers specializing in the field. If the unified theory is to replace the inadvertent

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Introduction



misapplication of the laws of metallic friction to rubber in an expeditious manner, effective interaction between these two groups is necessary. To facilitate the use of this book by nontechnical professionals wanting to know what rubber friction really is, a simplified reiteration, in the form of a chapter review written specifically for such individuals, is located at the end of each chapter. For example, reliance on equations in these reviews is kept to a minimum. In addition, technical terminology, which is defined as it is introduced, is limited to those terms necessary for the subject at hand.

1.9

Chapter Review

This chapter presented a historical synopsis of the teaching of metallic friction in college and university physics courses and its effects, expressed through the use of the metallic-friction equation in engineering practice. Because of the lack of clarity in some textbooks, many engineers inadvertently misapply the laws of metallic friction to rubber, resulting in a consensus approach to the subject that is not scientifically based. The purposes of the book are to: • Demonstrate that the laws of metallic do not apply to rubber. • Present, exemplify, and apply a new, unified theory of rubber friction incorporating a fourth basic rubber friction force: surface deformation hysteresis, the existence of which was first hypothesized in 1965. Although the newly developed theory is applicable to all rubber products for which friction is an issue, use of the theory will be exemplified by focusing on the following important fields: • Analysis of friction in the design of rubber tires and their contacted pavements, • Geometric design of roadways, • Motor vehicle accident reconstruction, and • Analysis of heel and sole slip resistance in the design of footwear and their contacted walking surfaces. The chapter also introduced some of the differences between metallic and rubber friction and discussed consequences stemming from the application of the constant coefficient-of-friction equation to rubber. One of these consequences involves mixing forces generated by the different rubber friction mechanisms together and comparing such results to standard values to arrive at conclusions, when the results and standards are not scientifically comparable.

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Analyzing Friction in the Design of Rubber Products and Their Paired

This book is intended for two audiences: (1) technical professionals interested in the physics and chemistry of rubber friction and their practical applications, and (2) nontechnical professionals wishing to gain an understanding of rubber friction that will allow effective communication with engineers specializing in the field. If the unified theory is to replace the inadvertent misapplication of the laws of metallic friction to rubber in an expeditious manner, effective interaction between these two groups is necessary. To facilitate use of this book by nontechnical professionals wanting to know what rubber friction really is and why it behaves the way it does, the summaries of each chapter are written specifically for these individuals.

References

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1. Kummer, H.W., Unified Theory of Rubber and Tire Friction, Engineering Research Bulletin B-94, The Pennsylvania State University, University College, PA, 1966. 2. Savkoor, A.R., On the friction of rubber, Wear, 8, 222, 1965. 3. Moore, D.F., The Friction and Lubrication of Elastomers, Pergamon Press, Oxford, 1972. 4. Yandell, W.O., A new theory of hysteretic sliding friction, Wear, 17, 229, 1971. 5. Golden, J.M., Hysteresis and lubricated rubber friction, Wear, 65, 1980.

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2 Metallic Coefficient of Friction

2.1

Introduction

This chapter presents the rational bases for quantifying friction between smooth metal surfaces so that the movement-resisting mechanisms arising in these conditions can be compared to those that develop in rubber. Early investigations by Amontons [1] and Coulomb [2] of sliding resistance between contacting metals indicated that the friction force is directly proportional to the applied normal load and independent of the apparent (nominal) contact area. Division of the measured friction force by the applied load gave an approximately constant value. Subsequent empirical research by others confirmed this as true in most smooth metals over a wide loading range, giving rise to the familiar constant coefficient-of-metallic-friction (µm) equation: µm = Friction force developed between two smooth metal surfaces Normal load applied to those surfaces

(2.1)

In recent times, scientifically controlled studies revealed the true nature of smooth-metal friction, and Equation 2.1 became the rational relationship describing this behavior.

2.2

Smooth-Metal Friction

2.2.1 Friction Mechanism between Smooth-Metal Surfaces Bowden and Tabor [3, 4] and Rabinowicz [5] conducted extensive research into the friction mechanisms at work between contacting, macroscopically smooth metal surfaces experiencing relative movement. The following is a synopsis of their findings. When two macroscopically smooth metal solids are in relative sliding contact under compression, actual contact is made by their microscopic surface asperities. Under the loading conditions typically found in engineering prac

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Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

tice, the tips of most of these asperities quickly reach the plastic range, after which they deform plastically without giving additional resistance. When further loading is applied, the segments of the contacting asperities still in the elastic range compress proportionally in accordance with their stressstrain curves. Those that become completely plastic during the increased loading cease contributing additional deformational resistance as more stress is assumed by the remaining elastic asperities. 2.2.2 Real Area of Surface-to-Surface Contact in Metallic Friction Bowden and Tabor [3] hypothesized that the mean stress experienced by the plastic asperity tips will remain unchanged under loading and equal to a constant times the yield stress of the asperity metal, or

σm = cσy.

(2.2)

Here, σm is the mean asperity tip stress, c is a constant of proportionality, and σy is the yield stress of the asperity metal involved. They found that the constant c depends on the size and shape of the asperities, and σy encompasses both annealed and work-hardened metal. Bowden and Tabor [3] also determined that the area over which plastic flow occurs is directly proportional to the load on the gross apparent contact area. They hypothesized that for most practical applications, the total area of actual asperity-to-asperity contact is equal to the total applied load on the gross contact area divided by the mean stress in the plastic tips, or

Ar = FN/σm,

(2.3)

where Ar is the total real area of surface-to-surface contact and FN is the applied normal load. Equation 2.3 was verified using hardness-type indentation experiments, electrical resistance testing during which measured currents were made to flow through contacting asperities, examination of the permanently deformed metal surfaces with a profile meter, and by optical microscopy. 2.2.3 Friction Force between Smooth-Metal Surfaces Independent of Apparent Contact Area Bowden and Tabor [3] explained Amontons’s [1] finding that friction forces between smooth metals are independent of apparent contact areas. They considered that the real areas of asperity contact constitute metallic junctions. Because contact is made only at these junctions, the forces that resist relative, constant-velocity (no momentum change involved) shearing between the two metal solids must reside in these locations. The tangent force is therefore given by

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Metallic Coefficient of Friction FSm = Arσs,



(2.4)

where FSm is the friction force between smooth metals and σs is the mean tangential shearing stress in the junctions. Thus, friction between smooth metal surfaces is directly proportional to the real area of contact Ar and independent of the apparent contact area. 2.2.4 Constant Coefficient of Metallic Friction Equation One can see from Equation 2.3 that Ar depends only on the applied normal load. Bowden and Tabor [3] derived the rational coefficient of friction expression for metals by substituting Ar from Equation 2.3 into Equation 2.4. This yields FSm = FNσs/σm.



(2.5)

Bowden and Tabor [3] and Rabinowicz [5] found that shearing of the junctions usually takes place in the softer of the two metals involved. In practice, σs is the shear strength and σm is the yield strength in compression (shearing and compressive resistance to plastic flow) of the softer metal. Both of these are material properties, and the σs/σm ratio is represented by µ in Equation 2.1. Consequently, the constant coefficient of metallic friction, µm, is a material property of the metal pairing, where

µm = FSm/FN.

(2.6)

When the metallic coefficient is considered as µm = FSm/FN = σs/σm = Bulk shearing strength of weaker metal , (2.7) å°“ Bulk yield strength of weaker metal in compression an instructive phenomenological model is evident. As we shall see, however, this is not a rubber friction mechanism. When rubber friction test results are expressed as developed friction forces divided by applied normal loads, such ratios are not material properties, but rather mechanistic performance indicators.

2.3

Adhesion Theory of Smooth-Metal Friction

2.3.1

Initial Friction Force Posits

Amontons [1] assumed that resistance to movement by interlocking surface asperities was responsible for the development of the metallic-friction force. Subsequent researchers, including Coulomb [2], also posited this belief. In

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10 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 1892, Ewing [6], on the basis of his work in electromagnetic fields, posited that the breaking of bonds generated by force fields between two contacting metals gave rise to a surface friction force. In 1928, Tomlinson [7], when interpreting results of his investigations, assumed that friction arose from surface force field adhesion. 2.3.2 Smooth-Metal Friction Theory Subsequent work demonstrated that friction between smooth metal surfaces principally arises from adhesive force fields acting within the junctions of the contacting asperities. Rabinowicz [5] characterizes the force fields as atomto-atom in strength and sphere of influence. They can be very strong, but are significant only over a short distance. Bowden and Tabor [3,4] found that this adhesion depends on three principal factors: (1) the real area of solid contact discussed above (Ar), (2) the bulk material properties of the metals involved, and (3) the nature of any contaminants present. The findings of Bowden and Tabor [3,4] and Rabinowicz [5] led to the acceptance of this model by most workers in the field where it comprises the traditional adhesion theory of metallic friction. The work done, or reported, by Bowden and Tabor [3,4] was carried out in the 1940s and 1950s. In 1995, Rabinowicz [5] reviewed additional adhesion research conducted at that time. He opined that both the empirical and rational bases for the theory had been strengthened. Such adhesion is considered by Rabinowicz [5] to be a direct form of cold welding effectuated by the surface energy forces inherent in the metals in contact.

2.4

Origin of the Friction Force between Smooth Metals

2.4.1

Surface Energy and the Energy of Adhesion

Solids and liquids possess surface free energy. The atoms and molecules well within the body of substances are subjected to attractive forces from their neighbors in all possible directions, while those at the surfaces are not. As a consequence, the free energy of a molecule or atom at the surface is greater, and its surrounding force field extends outward beyond the surface [8]. Surface tension, a manifestation of surface free energy, is observable in liquids through menisci development. The tension of a liquid is equal in value to its surface free energy when comparable units are employed. Rabinowicz [5] emphasized the surface free energy of solids γ. The surface free energy of a metal solid will be somewhat greater than that of the same metal in the liquid state. Surface free energies are important in determining whether friction in metals is mild or severe. When dissimilar metals of low adhesional affinity are in contact, friction will be relatively low. Rabinow-

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11

Metallic Coefficient of Friction

icz [5] presented an expression representing the energy of adhesion, Wab, between two contacting solids:

Wab = γa + γb − γab.

(2.8)

In this relationship, Wab represents the energy that must be applied to separate a unit area of the junction interface between two solids a and b. In doing so, two surfaces of surface free energy γa and γb must be created. Concurrently, junctions possessing interfacial energy of the amount γab are destroyed. The needed net energy to separate a junction can be supplied during the frictional resistance process with relative tangential movement. 2.4.2 Evidence Supporting the Adhesion Theory of Metallic Friction Bowden and Tabor [3,4] described the different approaches utilized in basic studies on metallic friction adhesion. It was found that if one copper surface was rendered radioactive and then made to contact another copper surface in compression, minute radioactive fragments were transferred so as to cover the other surface. This demonstrated that adhesion bonding in the metallic junctions was strong enough such that one surface could pluck out fragments from another. It was further demonstrated that this effect greatly increased if frictional sliding was induced. When copper was slid on steel, the steel plucked out copper fragments through adhesion. Microscopic examination of cross-sections revealed that localized areas of the steel surface had been permanently deformed outward by the plucking mechanism. Metallic adhesion can vary considerably as a result of the oxide films present on most metal surfaces. Bowden and Tabor [4] described experiments in which oxide surface films were excluded. This had a profound effect on adhesion and, therefore, friction. The testing involved outgassing at elevated temperatures in a high vacuum. After cooling, the surfaces were placed together in compression. Complete adhesional seizure developed, preventing relative movement between the surfaces. Their cold-welded strength exceeded the capacity of the testing device within the vacuum apparatus. When frictional resistance of the specimens was determined after removal, coefficients exceeding 50 and 100 were sometimes measured. These values corresponded to the bulk shearing strength of the weaker of the two metals involved. 2.4.3 Metallic Coefficient of Adhesion McFarlane and Tabor [9] carried out experiments with a hard, clean, steel sphere and a flat block of indium, a very soft metal. When the steel sphere was pressed into the indium, considerable adhesion developed. This was measured by the tensile force needed to separate them. McFarlane and Tabor [9] utilized the concept of a coefficient of adhesion in analogy to the coefficient of friction. The coefficient of adhesion was defined as the ratio of the adhesive force measured to the original compressive load applied. This ratio

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12 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces was found to be approximately unity between indium and steel. Moore and Tabor [10] also measured a coefficient of unity between indium and tungsten carbide, iron, cadmium, zinc, copper, silver, platinum, and gold.

2.5

Rough-Metal Friction

When two dissimilar metals are in sliding contact and the harder one is rough, its asperities can dig into the surface of the softer metal. This is often called “plowing.” In these conditions, the developed friction force may not be directly proportional to the applied normal load, and the resulting coefficient of friction may not be constant. One should keep in mind that the coefficient of metallic friction is generally constant only when both surfaces are smooth [5].

2.6

Laws of Metallic Friction

Two traditional laws of metallic friction as applied to smooth metal on smooth metal can be stated as follows [11,12]:

1. The developed friction force is directly proportional to the applied normal load.



2. The coefficient of metallic friction, µm, is independent of the apparent area of contact.

As stated in Chapter 1, these laws of metallic friction do not apply to rubber.

2.7

Chapter Review

This chapter presented a scientific basis for quantifying frictional resistance between smooth metal sliding on smooth metal. It was shown that the widely employed coefficient-of-metallic friction, µm, can be expressed as Equation 2.6:

8136.indb 12

µm = FSm/FN.

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Metallic Coefficient of Friction

13

In this expression, FSm is the friction force developed when one smooth metal surface slides on another, and FN is the load applied to the two objects experiencing such relative movement. Two laws of metallic friction as applied to smooth metal sliding on smooth metal can be stated as follows:

1. The developed friction force is directly proportional to the applied load. 2. The coefficient of metallic friction, µm, is independent of the apparent area of contact of the two surfaces.

As stated in Chapter 1, these laws of metallic friction do not apply to rubber. This book indicates why this is so.

References

8136.indb 13

1. Amontons, G., Histoire de l’Academie Royale des Sciences avec les Mémoires de Mathematique et de Physique, 1699. 2. Coulomb, C.A., Histoire de l’Academie des Sciences, 1785. 3. Bowden, F.P. and Tabor, D., The Friction and Lubrication of Solids, 2nd ed., Clarendon Press, Oxford, 2001. 4. Bowden, F.P and Tabor, D., The adhesion of solids, in The Structure and Properties of Solid Surfaces, Gomer, R. and Smith, C.S., Eds., The University of Chicago Press, Chicago, 1953, chap. 6. 5. Rabinowicz, E., Friction and Wear of Materials, 2nd ed., J. Wiley & Sons, New York, 1995. 6. Ewing, J.A., The atom-to-atom process in magnetic induction, Proc. Roy. Inst., 3, 387–401, 1891. 7. Tomlinson, G.A., Atom-to-atom cohesion, Phil. Mag., 6 (37), 697–712, 1928. 8. Brunauer, S. and Copeland, L.E., Physical adsorption of gases and vapors on solids, in Proc. Symp. Properties of Surfaces, ASTM STP 340, Philadelphia, 1963, p. 59–79. 9. McFarlane, J. and Tabor, D., Adhesion of solids and the effect of surface films, Proc. Roy. Soc., A202, 224–244, 1950. 10. Moore, A.C. and Tabor, D., Some mechanical and adhesive properties of indium, Br. J. App. Phys., 3, 299–301, 1952. 11. Moore, D.F., The Friction of Pneumatic Tyres, Elsevier, New York, 1995. 12. Hutchings, I.M., Tribology: Friction and Wear of Engineering Materials, CRC Press, Boca Raton, FL, 1992.

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3 Rubber Friction Mechanisms

3.1

Introduction

This chapter summarizes early scientific research carried out to understand the basic mechanisms of rubber friction. Relevant findings of the investigations are presented that led to the current acceptance of three distinct friction forces that develop when rubber slides on a harder surface: (1) adhesion, (2) bulk deformation hysteresis, and (3) wear. Included in the studies discussed in this chapter are three investigations designed to determine the variation of the rubber friction force with increasing pressure. Chapter 4 presents other such studies that, together with those in this chapter, demonstrate that the laws of metallic friction do not apply to rubber.

3.2

Rubber Friction Coefficient Decreases with Increasing Load

The first laboratory-controlled investigation of the basic nature of rubber friction was conducted at the U.S. National Bureau of Standards by Roth, Driscoll, and Holt [1] and reported in 1942. Prior research on the frictional properties of rubber had dealt with specific kinds of products, such as tires, power-transmission belts, shoe heels and soles, and flooring. In these product studies, the experimental conditions were those under which the goods were commonly used. In the Roth et al. work, the rubber specimens and testing surfaces were prepared in the laboratory. This made it possible to employ a wide range of experimental conditions and to control rubber specimen composition and the nature of the contacted surfaces. Roth et al.’s dynamic (sliding) friction study focused on soft rubber compounds of the type used in tire treads. Figure€3.1 depicts one of the testing arrangements used by Roth et al. In some of their tests, the rubber specimens were affixed to a carriage that was towed along a smooth, horizontal glass test track at constant speed by means 15

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16 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Wire supports

Steel ring

Weights

Specimen carriage Tow wire

Dial gage

Specimen

Drum driven by motor and reduction gears

Horizontal Track

Tow wires Specimen End view of specimen carriage

Figure€3.1 Schematic diagram of testing arrangement used by Roth et al. to determine coefficients of rubber friction. (From Roth, F.L., Driscoll, R.L., and Holt, W.L., J. Res. Nat. Bur. Stds., 28, 439, 1942.)

of a motor and reduction gears. The resistance to movement of the carriage was determined by measuring the force required to hold the suspended test track at rest while the specimen was towed on it. The coefficient of rubber friction was taken as the ratio of this measured force to the total weight on the specimen. Roth et al. [1] had to refine their testing protocol until reproducible results were obtained. In a number of sliding conditions used during procedure development, specimens exhibited noticeable vibration, or chattering. One of the steps taken to prevent chattering was to limit the sliding speed to a maximum of 0.1 cm/sec (0.04 in./sec). Surface preparation also proved crucial. Roth et al. initially utilized a smooth specimen surface by molding the rubber against plate glass. Test results employing this preparation technique differed greatly among specimens and from any given specimen. It was necessary to texture their surfaces to obtain reproducibility. This was accomplished by forming the rubber in a glass mold that had itself been roughened with 150-mesh abrasive. The investigation was conducted before adhesion was generally recognized as one of the principal components of rubber friction. Roth et al. did not discuss possible mechanisms for the friction they measured. Their initial chattering difficulties most likely arose from adhesion between the optically smooth glass test track and the smooth rubber surface, as well as the possible production of Schallamach waves (discussed later in this chapter). Texturing the rubber surfaces by employing the roughened mold produced a rougher asperity configuration on the specimens. This likely reduced their frictional

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17

Rubber Friction Mechanisms

resistance to sliding on the very smooth glass, allowing reproducible results to be obtained. Figure€3.2(a) presents data selected by Roth et al. as typical of their coefficient of friction (μ) results obtained by varying normal loads in horizontal tests of sliding specimens molded on glass roughened with 150-mesh abrasive. The ratios decreased with increasing pressure, PN. While the authors mentioned the decreases in the coefficients, they did not suggest a possible mechanism for the reductions. Figure€3.2(b) depicts recalculated Roth et al.

Coefficient of Friction–µ

4

3

Large specim en

Small s pecime

n

2

1

0

Horizontal glass track specimens type 150 speed of slide 0.1 cm/sec 0

10

20 Pressure-lb/sq in a

30

40

0.35

Figure€3.2 (a) Coefficient of rubber friction (μ) vs. applied pressure; and (b) coefficient of rubber friction (μ) vs. applied normal force. (From Roth, F.L., Driscoll, R.L., and Holt, W.L., J. Res. Nat. Bur. Stds., 28, 439, 1942.)

Coefficient of Friction–µ

0.30 0.25

= Small specimen = Large specimen

0.20 0.15 0.10 0.05 0

0

5 10 15 20 Applied Normal Force (FN)–lb b

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18 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces [1] data to express μ vs. FN, the applied normal force. As observed, μ also declines with increasing FN. Further note that the two different specimen sizes exhibit different friction coefficients at the same values of PN or FN, except at the crossover point in the FN plot. In these tests, μ appears to depend on the area.

3.3

Adhesion as a Rubber Friction Mechanism

Thirion [2] reported friction test results obtained by sliding two gum rubber specimens of different sizes on smooth glass. He was apparently the first published laboratory investigator to postulate that the friction mechanism developed between rubber and a smooth surface is adhesion. Figure€3.3(a )presents a generalized depiction of Thirion’s findings. The author experienced chattering in his initial tests and reduced sliding speed to 0.0176 cm/ sec to yield reproducible results. As seen in Figure€3.3(a), Thirion observed that the two specimen plots were coincident when expressed in terms of PN, and that the coefficients of rubber friction decreased hyperbolically with increasing pressure. He took an inverse approach to explain his results, proposing the following equation:

1/µ = cPN + b,

(3.1)

where c is a constant and b is a y-axis intercept as indicated in Figure€3.3(a). Thirion adduced that rubber friction may be expressed using two constants by extrapolating the straight-line portion (L–H) of the plotted data to zero pressure on the y-axis to obtain the y-intercept value b, together with the slope of line-segment L–H, c. Ignoring the small curved segment of his plotted data, Thirion assumed that a linear relationship between 1/µ and PN existed at low values of PN. Thirion postulated that the left side of Equation 3.1 indicates the inverse of µ at zero pressure, while the right side of the equation represents the linearly developing rubber friction adhesion force on smooth surfaces as the pressure increases to infinity. Figure€3.3(b) presents Thirion’s data recalculated to express µ vs. FN, which again produces a hyperbolic relationship. Like the Roth et al. results, Thirion’s measurements indicate that the coefficients of rubber friction for the two samples are different at the same values of applied normal load. The developed friction also appears to be area dependent in Thirion’s tests.

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19

Rubber Friction Mechanisms

µ 1/µ H 1/µ

b

L

Applied Normal Pressure (PN) a 2.5

Coefficient of Friction–µ

2.0

Large specimen

1.5 Small specimen

1.0

0.5

0

0

10 20 30 40 Applied Normal Force (FN)–kg

50

b Figure€3.3 Generalized depiction of Thirion’s inverse rubber coefficient of friction (μ) approach. (Based on Thirion, P., Rev. Gén. Caoutch., 23, 101, 1946.) (b) Coefficient of friction (μ) vs. applied normal force. (Calculated from Thirion, P., Rev. Gén. Caoutch., 23, 101, 1946.)

3.4

Linking Rubber Friction to the Real Area of Contact

In 1952, Schallamach [3] reported on the friction forces developed by sliding molded-rubber drag sleds on a smooth glass track. The sleds’ runners were roughened to preclude chattering. Schallamach [3] cited the work of Roth et al. [1] and focused on their finding that the coefficient of rubber friction decreases with increasing normal load. Schallamach [3] also investigated the

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20 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces possibility that, analogously to metals, the friction force developed by rubber is proportional to the real area of asperity contact with the paired surface. It is common in engineering analysis to simplify calculations and the conceptual approach used when complex physical shapes interact by idealizing their configurations. Schallamach [3] idealized the asperities on his drag sled runners by assuming that they were hemispherical and that the glass track was perfectly flat. At the suggestion of Bowden [4], Schallamach [3] employed the Hertz [5] equation — discussed in Section 3.5 —as the empirical relationship approximating the real area of rubber contact with the glass. The equation can take the form µ = c(FN)−1/3. Apparently, this was the first time that the Hertz equation had been applied to the examination of rubber friction. To quantify the deformation of the sled’s asperities, Schallamach [3] molded soft, medium, and hard rubber hemispheres of 3.8 cm (1.5 in.) diameter. These were compressed against a glass plate on which a measuring scale had been engraved. The areas of apparent or nominal contact at various loads were determined. (The term “apparent” is employed here because the true, microscopic rubber-asperity to glass-asperity contact area was unknown.) The radii r of the apparent contact areas between the three rubber hemispheres and the glass scale were found to be proportional to FN1/3. This suggested that the rubber friction force is proportional to FN1/3. Schallamach’s [3] compressed-rubber findings were consistent with Bowden’s [4] suggestion because the Hertz [5] relationship can also be expressed as r = c(FN)−1/3. Figure€3.4(a) presents Schallamach’s [3] coefficient of friction results. The three coefficients decreased hyperbolically with increasing pressure. The sliding speed was 0.0022 cm/sec (0.0009 in./sec). The empirical, Hertz-like equations expressing the frictions coefficients were as follows.

Soft rubber: µ = 1.90(PN)−1/3

(3.2)



Medium rubber: µ = 2.20(PN)−1/3

(3.3)



Hard rubber: µ = 2.39(PN)−1/3

(3.4)

Schallamach [3] considered that the Hertz [5] equation fits results from the two softer rubber compounds reasonably well and noted that the hard rubber did not conform to the Hertz expression in the low loading range. As observed in Figure€3.4(a), the hard rubber curve mirrors the other test results only at higher loads. Schallamach [3] opined that the Hertz equation represented interaction of rubber asperities with the glass track, not the sled runner’s entire bottom surface. Schallamach [3] postulated that the observed frictional behavior of the hard rubber formulation was attributable to the certainty of a statistical distribution in asperity size and further opined that the tallest asperities should compress against the track first, thus providing the initial real areas of

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21

Rubber Friction Mechanisms 4 Hard rubber Medium rubber Soft rubber 3 µ 2

1

0

1

kg/cm2

2

3

a 3.5 Medium rubber

3.0

Coefficient of Friction–µ

2.5

2.0

Soft rubber

Hard rubber

1.5

1.0

0.5

0

0

1

2

3

4 5 6 FN – kg

7

8

9 10

b Figure€3.4 (a) Coefficient of rubber friction (μ) vs. applied pressure, (From Schallamach, A., Proc. Phys. Soc. Sec. Lon. B, 65, 657, 1952. With permission.) (b) Coefficient of rubber friction (μ) vs. applied pressure (Calculated from Schallamach, A., Proc. Phys. Soc. Sec. Lon. B, 65, 657, 1952.)

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22 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces contact. As such, the developed friction force would be smaller until greater loading produced contact between the shorter asperities and the glass. In assessing the role of asperities, Schallamach [3] postulated that because they cannot continuously deform in compression even at the highest loadings, the developed rubber adhesive friction force must eventually become asymptotically constant under such conditions. Figure€3.4(b) presents recalculated Schallamach [3] data expressing µ vs. FN. In this form, three hyperbolic relationships can be seen.

3.5

Hertz Equation

In 1886, Hertz [5] (see also Timoshenko [6]) derived rational equations for contact areas produced during elastic deformation in certain smooth solids pressed together. Hertz verified his equations experimentally by microscopic examination of two glass spheres in compression. His work focused on the stress regimes brought about from such interactions, it was not concerned with friction. Nevertheless, the expressions have appeal in rubber friction metrology because they relate the apparent contact areas developed under elastic compression to the applied normal load. This is useful because the adhesional component of rubber friction arises in the real areas of surfaceto-surface contact. The Hertz equation with perhaps the greatest applicability in rubber friction analysis is the case of a sphere contacting a flat surface as depicted FN in Figure€3.5. The sphere’s lower Z hemisphere can constitute an idealized rubber asperity on a paired material. The derivation associated R with Figure€3.5 assumes involvement r of semi-infinite bodies. In this way, only the local geometrical boundary m Z O conditions must be considered. The n equation also assumes that, before the application of FN, contact is made at a point 0. The distance m–n in Figure€3.5 Derivation of the Hertz equation for deformation Figure€3.5 from the plane tangent to of elastic spheres and planes in contact. (From the surfaces at O to a point such as Timoshenko, S., Theory of Elasticity, McGrawm on the sphere is Z. The distance r Hill, New York, 1934. With permission.)  This is not always strictly true in rubber friction metrology since some degree of adhesional interaction can occur when at least one elastomeric solid is involved. The surface-free energy forces tend to draw the solids together, producing a finite real area of contact. The modified Hertz [5] equation accounting for this phenomenon is discussed in Section 3.11.

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23

Rubber Friction Mechanisms

from the z-axis is assumed to be very small when two rigid solids are compressed together. When the two bodies in Figure€3.5 are pressed together by a normal force FN, the distance m–n goes to zero. Both bodies are assumed to deform during compression. Assuming completely elastic deformation, a surface of contact with a circular boundary is produced. Hertz showed that the radius r of this contact circle can be expressed as:

r = {0.75 FNR[(1 − ν12)/E1 + (1 − ν22)/E2]}1/3,

(3.5)

where: R = radius of the sphere, E1, E2 = Young’s moduli of the sphere and the flat surface materials, and ν1, ν2 = corresponding values of Poisson’s ratio for the two materials. Letting k = [(1 − ν12)/E1 + (1 − ν22)/E2], then r = (0.75FNRk)1/3 or r = c(FN)1/3, where c is a constant, the idealized, circular contact area can be readily calculated as

AH = πr2 = π[c( FN)1/3]2 = cM(FN)2/3,

(3.6)

where AH is the Hertz contact area of a sphere compressed against a plane under the applied normal load FN, and cM is the associated constant for the two materials involved. Because adhesive forces in rubber friction arise in the real areas of contact, AH can be replaced by FA, the adhesive force developed between the two solids; and cM is replaced by cA, the adhesional constant for the two surfaces in contact. Thus,

FA = cA(FN)2/3.

(3.7)

This is the Hertz equation expressed in a form convenient for calculating areas of contact of elastic materials when the normal force is involved. Because the adhesional rubber friction mechanism does not always conform to the Hertz model [5], generalization of Equation 3.7 is desirable as

FA = cA(FN)m,

(3.8)

where m is the exponent equaling the slope of the FA vs. FN plot when rectified on logarithmic coordinates. In Equation 3.8, m usually ranges between 2/3 and nearly unity. If use of a friction ratio (coefficient) is appropriate, both sides of Equation 3.7 can be divided by FN, yielding

8136.indb 23

µA = cA(FN)−1/3,

(3.9)

2/13/08 3:01:20 PM

24 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces where μA is an adhesional rubber friction ratio. To avoid confusion with the metallic coefficient of friction, μm, μA will not be referred to as a coefficient. Equation 3.9 can also be generalized as µA = cA(FN)−m,



(3.10)

where m is the exponent equaling the slope of the µA vs. FN plot when rectified on logarithmic coordinates. Because the slopes of the Equation 3.9 and Equation 3.10 plots when rectified will be downward, m is negative in both instances. Applying the conceptually straightforward Hertz [5] equation allows calculation of circular contact areas between surfaces with complex configurations that have been idealized. When the expression for the idealized contact area is divided by FN to obtain a friction ratio, the parabolic Hertz relationship (Figure€3.6a) becomes hyperbolic (Figure€3.6b). The hyperbolic form fits test data from processes in which something is decreasing while another something is increasing, such as the coefficient of rubber friction µ with FN. It is not surprising that Equation 3.10 is of this form. Hyperbolic equations, with their negative exponents, are one of the small number of relatively simple types that often represent scientific and engineering data quite well [7]. While the Hertz equation is useful in rubber friction metrology, its limitations should be recognized. For example, the pressure within the Hertz circular contact area is not constant [8]; it varies from a maximum at the center to zero on the circumference. Because the real area of contact of rubber asperities with another solid varies with FN, and pressure, the real area of contact will vary within the circle, as will the developed adhesion force. Yet, Equation 3.7 assumes a constant adhesion force within the Hertz circle that is intended to represent the real area of contact.

µA

FA FA = cA(FN)m

0

0

µA = cA(FN)–m

0 FN (a) Parabolic: m < 1

0

FN (b) Hyperbolic: m < 0

Figure€3.6 The generalized Hertz equation: (a) parabolic (Equation 3.8) and (b) hyperbolic (Equation 3.10).

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Rubber Friction Mechanisms

3.6

25

Bulk Deformation Hysteresis in Rubber

In 1955, Tabor [9] reported findings of investigations into the friction mechanism developed when smooth steel cylinders and spheres are rolled on rubber. Previous researchers had attributed rolling resistance in configurations of this kind to adhesion. Tabor [9] pointed out, however, that generation of a significant adhesive force was inconsistent with some of the earlier data. In those situations, lubricants appeared to have little or no effect on reducing frictional resistance. This suggested the presence of a bulk hysteresis loss component. Tabor [9] designed a test that allowed isolation and control of the specific variables involved. He first rolled a 1.27-cm (½ in.) diameter steel sphere over a flat, clean block of rubber. The rubber surface was then lubricated with glycerin and the experiment repeated. A substantially identical, hysteresis-like frictional resistance was found present under both conditions. Tabor [9] also rolled steel spheres of other diameters on the flat rubber blocks. He derived a theoretical expression for the elastic work done in overcoming rubber friction under these conditions and examined whether hysteresis losses for the rubber involved would remain constant when the different sphere diameters were taken into account. They did, and agreement between the experimental results and his theoretical calculations was considered satisfactory. Various sizes of steel spheres were then rolled in dry, clean, preformed rubber grooves of different radii where no interfacial slip was allowed. When the tests were repeated in lubricated grooves, no perceptible reduction in rolling friction was evident. Tabor [9] concluded that the questioned rolling resistance occurring in these investigations stemmed from hysteresis in the rubber. What has since come to be called “bulk deformation hysteresis” arose when the rolling cylinders or spheres compressed or stretched the rubber elastically. The rubber then experienced elastic release as the rolling objects moved out of contact. Such compression or extension resulted in energy losses, constituting a hysteretic deformational friction component. Because a portion of the bulk of the rubber was involved, bulk deformation hysteresis was the operative mechanism. The bulk hysteretic losses elucidated by Tabor [9] constitute a basic friction force developed in rubber. When this rolling or sliding mechanism is experienced by rubber in contact with smooth surfaces, it is often seen that negligible permanent deformation occurs. Consequently, such deformation can take place without significant wear. When wear in a rubber material does occur, the friction associated with it is ascribed to another basis mechanism: cohesion losses. Section 3.9 addresses cohesion losses.

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26 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

3.7

Concurrently Acting Rubber Friction Mechanisms

Furthering Tabor’s [9] bulk deformation work, Grosch [10] carried out dynamic friction studies that involved sliding various surfaces at different speeds on five types of rubber. Flat rubber specimens were pressed into the moving surfaces by dead loads suspended beneath them. The surfaces included smooth, gently wavy glass and abrasive silicon carbide paper. Wavy glass, instead of flat glass, was used to reduce friction and obtain acceptable reproducibility. To prevent frictional heating of specimens that would complicate interpretation of results, Grosch [10] limited the sliding speed of the testing surfaces to less that 3 cm/sec (1.2 in./sec). In an attempt to ensure comparability, each silicon carbide surface was used only once. The testing assembly employed by Grosch controlled the temperatures of both the rubber specimens and sliding surfaces. They were kept constant and equal to each other for the individual test runs. Grosch took a “master curve” approach with his results, involving a reference-temperature transform. Plotting the measured rubber coefficients of friction (μ) against testing surface sliding speed produced peaks. The recorded resistance combined forces from all friction mechanisms present in a test. This was intended to be beneficial. For example, by first testing with smooth wavy glass, adhesional friction was thought to predominate. The sliding speed at which this mechanism exhibited a maximum coefficient of rubber friction peak, or hump, could be identified. If this coefficient peak was evident in results from testing a silicon carbide surface where bulk deformation hysteresis occurred, the presence of both mechanisms would be suggested. As we will see in Chapter 4, however, the coefficient of rubber friction (μ) is calculated by inadvertent misapplication of the laws of metallic friction to rubber friction. Nevertheless, Grosch’s findings are of interest and are summarized here. Grosch [10] reported that when smooth, wavy glass is slid on the rubber specimens at controlled speeds and constant temperatures, μ increased to a particular maximum and then decreased, giving the desired indicator peak. All plots were nearly symmetrical about these peaks, of varying amplitudes, and exhibiting a bell-curve-like friction coefficient distribution. Grosch then dusted a fine magnesium oxide powder on the glass surface and repeated the tests. Frictional resistance fell markedly to an essentially constant value over the whole speed range for all rubber specimens. This was attributed to embedment of magnesia in the rubber surfaces, separating them from the glass. Loss of contact with the glass eliminated the adhesion between it and the rubber, and identified which peak was produced by this friction mechanism. Grosch then carried out silicon carbide testing. An asymmetrical, bulk deformation peak was always produced, usually at a higher speed than the rubber specimen’s peak on the glass surface. With some specimens, a lower

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27

Rubber Friction Mechanisms

Coefficient of Friction–µ

SiC

Adhesion hump

Dusted SiC

Adhesion on glass

f(Sliding speed) SiC = Silicon carbide Figure€3.7 Generalized master curves showing concurrent development of adhesion and bulk deformation hysteresis in rubber samples. (Based on Grosch, K.A., Proc. Roy. Soc. A, 274, 21, 1963.)

hump at the same speed as the peak on the glass was also observed. Dusting the abrasive surface with magnesia invariably reduced the higher peak and eliminated the adhesion hump if it had been present. Figure€3.7 depicts these general findings. A reference surface of dusted silicon carbide was employed to ensure a common density and uniformity of the magnesia particles. Photoelectric reflectivity was used to quantify these properties. The average silicon carbide particle size was 0.01 cm (0.004 in.). Grosch’s test results implied that rubber friction on the dusted, abrasive surfaces was primarily bulk deformation hysteresis. The indicated adhesion hump in the abrasive testing, and its elimination after dusting with magnesia, supported the hypothesis that adhesive and bulk deformation hysteresis friction could develop concurrently in rubber. Subsequent testing by others has allowed this posit to advance to the theory stage [11]. In motor vehicle tires, a mechanism producing hysteresis has been called “draping” [12].

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28 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

3.8

van der Waals’ Adhesion and Surface Deformation Hysteresis in Rubber

By the 1960s, it had been widely accepted that two distinguishable friction mechanisms develop in rubber: (1) adhesion (FA) and (2) bulk deformation hysteresis (FHb). It was also observed that, unlike metallic friction, rubber friction is not necessarily associated with abrasion. Often, no evidence of rubber wear — a third basic friction mechanism — is seen even after a sample slides several times on a smooth, harder surface. In earlier studies, some friction investigators took a complicated analytical approach involving molecular-kinetic activation processes. Savkoor [13] employed a different, simplifying tack using a phenomenological focus, suggesting that consideration of the likely physical mechanisms giving rise to frictional resistance would be more readily and accurately applicable to realworld conditions. Savkoor posited that the real area of sliding rubber contact with a paired surface at low loads is a small fraction of the apparent contact area. Only at high loads does the true contact area approach the full dimensions of the specimen. Savkoor agreed with Bartenev and Lavrentjev [14] that adhesion in rubber arises almost totally from van der Waals’ forces. These forces are far weaker than the atom-to-atom adhesion found in metals discussed in Chapter 2. Savkoor formulated equations expressing the adhesive force component of rubber friction based on the energy required to break the van der Waals’ bonds. Savkoor postulated the existence of a fourth distinct energy loss mechanism arising when rubber slides on a harder material: surface deformation hysteresis, or FHs. He accepted that macroscopically smooth surfaces, such as polished glass, can be microscopically rough. He based his surface hysteresis posit on the supposition that rubber asperities in contact with asperities on harder, smooth surfaces can mechanically interlock with each other, providing deformational resistance. When the paired surface is rough, micro-asperity interlocking still takes place, while bulk deformation hysteresis concurrently develops. If van der Waals’ adhesion is present, the three mechanisms would act simultaneously. Savkoor did not offer experimental evidence indicating the existence of a surface deformation phenomenon.

3.9

Adhesion, Bulk Deformation Hysteresis, and Wear in Sliding Rubber

As part of a program of analysis and testing of friction between motor vehicle tires and roadways, Kummer [12] formulated a generalized friction

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29

Rubber Friction Mechanisms

model for sliding tires. The model encompasses the resistance forces developed by adhesion, bulk deformation hysteresis, and cohesion loss (wear) mechanisms. As seen in Figure€3.8, Kummer [12] depicted the adhesion (Fai) and bulk hysteresis (Fhi) forces associated with a stone chip (i) in the roadway and a tire sliding at velocity V. Adhesional draping of the rubber over the chip accounts for the real area of contact. Kummer [12] considered the friction force F at any instant from all contacted chips to be approximately equal to the sum of the Fa and Fh totals. In dry conditions, Kummer’s [12] model for tires takes the following form:

FT = FA + FHb + FC, p

(3.11)

Friction

Rubber

F ≈ Fa + Fh V i

Stone chip Binder

V

Adhesion Fa

Fai

V Hysteresis Fh Fhi

Figure€3.8 Bulk deformation hysteresis and van der Waals’ adhesion forces developed between rubber tires and a road surface. (Based on Kummer, H.W., Unified Theory of Rubber and Tire Friction, The Pennsylvania State University, 1966.)

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30 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces where: FT = total frictional resistance developed between a sliding tire and dry pavement, FA = frictional contribution from combined van der Waals’ adhesion of the two surfaces, FHb = frictional contribution from bulk deformation hysteresis in the rubber, and FC = cohesion loss contribution from rubber wear. Kummer [12] postulated that FA and FHb are not entirely independent of each other because adhesion can increase the extent of rubber draping over a chip beyond what FN would produce. He also noted that each term in Equation 3.11 can be divided by FN to obtain friction ratios, but pointed out that relating friction forces to applied loads is not always meaningful and cautioned that it should be done only when it is completely justified. Kummer [12] characterized cohesion-loss friction in rubber as “intrinsic” because it occurs when molecular bonds within the material are ruptured. Perhaps counter-intuitively, the effective van der Waals’ adhesion energy of rubber can be much larger than its bonding energy. Consequently, estimates for the cohesion loss when rubber is slid on a smooth surface in controlled laboratory testing indicate it can account for only a fraction of 1% of the total friction force developed. On rough surfaces, when adhesion is reduced and wear naturally increases, the relative cohesion loss contribution can become larger, approximately 2% in those conditions. Kummer [12] reported that frictional resistance from wear due to nonemergency automobile braking is less than 1%. Kummer [15] cited the tread life of passenger car tires, which ranged from 27,800 km to 55,600 km (15,000 to 30,000 miles) at that time (that is, in 1966), and showed that a 1815-kg (4,000 lb) car, making a 0.4 g stop from 80 km/h (50 mph), would have to experience removal of over half the tread rubber on a new set of tires to provide enough frictional resistance for one stop in this situation. He theorized that, because such stops do not cause significant wear, the other rubber friction mechanisms predominate. Kummer [12] cited Savkoor [13] and addressed the possible existence of a surface hysteresis friction mechanism in rubber involving cyclic deformation of its microscopic asperities on the micro-roughness of the harder material. Kummer [12] designated the mechanism “microhysteresis” but chose not to include a separate term for it in Equation 3.11. Kummer [12] hypothesized that the surface hysteresis friction force is implicitly measured in adhesion testing of sliding rubber. He presented what he considered evidence for the presence of microhysteresis in wet testing of rubber on different roadway surface materials. This evidence is discussed in Chapter 5.

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31

Rubber Friction Mechanisms

3.10

Expressions for Bulk Deformation Hysteresis in Rubber

One area in which utilization of rubber friction ratios can be justified is in the analysis of lubricated sliding, in which only bulk deformation hysteresis (macrohysteresis) develops. It is desirable to formulate scientifically based expressions for macrohysteresis to quantify the FHb term in Equation 3.11. Bowden and Tabor [16] formulated a ratio expression by equating friction produced in soap-lubricated sliding on rubber to rolling friction on the same material. They hypothesized that if lubricated sliding conditions are such that adhesion is reduced to negligible proportions (physical contact of the two solids is effectively prevented), and the lubricant’s viscous resistance is also negligible, the only significant friction present would arise from macrohysteresis in the rubber. If this were so, macrohysteretic resistance in a given lubricated rubber specimen would be essentially equal when generated either by sliding or rolling spheres of identical size and material properties. Bowden and Tabor [16] discussed testing that involved rolling and sliding steel spheres on soap-lubricated rubber at speeds on the order of a few millimeters per second, and derived an equation for the rolling frictional force developed by spheres, FR:

FR = c(FN)4/3.

(3.12)

For convenience, they then expressed this relationship in ratio form to obtain the ratio of rolling friction (μRHb) for spheres when only macrohysteresis is present. This is readily achieved by dividing both sides of Equation 3.12 by FN,

μRHb = FR/FN = [c(FN)4/3]/FN or



μRHb = c(FN)1/3.

(3.13)

The lubricated testing utilized 0.32-cm (1/8-in.) and 0.64-cm (1/4-in.) diameter steel spheres on high hysteresis rubber. It was found that, up to a pressure of about 2760 kPa (400 psi), frictional resistance values for sliding and rolling were in close agreement. Above this pressure, however, measurements diverged, apparently because of breakdown of the lubricating soap film, allowing an adhesion contribution to develop as a result of contact between the steel and the rubber. We are now in a position to theorize macrohysteretic expressions for spheres sliding on rubber related to the FHb term in Equation 3.12. Under the conditions stated above,

8136.indb 31



FHb = c(FN)4/3 and

(3.14)



μHb = c(FN)1/3.

(3.15)

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32 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

3.11

Modified Hertz Equation

Johnson, Kendall, and Roberts [17] investigated experimental contradictions to the Hertz [5] equation quantifying the size of contact areas between smooth elastic bodies in compression. Their surface-free-energy related experiments with rubber spheres had previously determined that, at low values of FN, the contact areas were considerably larger than predicted by the Hertz expression. The same studies produced results in close agreement with the Hertz equation at higher loads. The Johnson et al. work provides a number of insights into the mechanics of rubber adhesion that are relevant in the present context. These are discussed subsequently where appropriate. The Johnson et al. testing utilized rubber spheres molded to exhibit optical smoothness. Their surface asperities were estimated to be about 20 nm (8 × 10−7 in.) in height. The rubber employed possessed a low elastic modulus, allowing the surface free energy acting between the specimens to flatten these asperities and provide maximum contact. Johnson et al. found that under zero load, the two rubber spheres in contact would adhere, deform, and reach configurational equilibrium. The surface energy lost by the paring balanced the stored elastic energy of deformation. Figure€3.9 presents a generalized depiction of their findings involving hemispheres of radii R1 and R2. The inner (Hertz) circle of radius r assumes the absence of surface adhesion forces. The actual contact radius rM is larger in accordance with the summation of FN and the combined surface free enerFN

R1

r rM

Modified circular contact area

r rM

R2

Figure€3.9 Generalized depiction of contact between hemispherical elastic solids under an applied normal load, F N, both in the presence and absence of surface adhesion forces. (Based on Johnson, K.L., Kendall, K., and Roberts, A.D., Proc. Roy. Soc. A, 324, 301, 1971.)

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33

Rubber Friction Mechanisms

gies (γ) of the spheres. Because contact between them is maintained over an enlarged area by surface adhesion, the stresses are tensile at the contact circle periphery. They are compressive within the annulus of the tensile ring. This regime was verified by the investigators using optical interferometry [17]. Through a rigorous analysis of the energies involved when two rubber spheres in contact attain configurational equilibrium under an applied compressive load, Johnson et al. modified the Hertz equation to take surface adhesion forces into account. Values calculated from this rational relationship were in good agreement with their experimental results up to the testing limit of 10 gm (0.022 lb). Johnson et al. showed that within this loading range, the magnitudes of FN and the surface attractive forces are comparable for the rubber involved. Johnson et al. also investigated the accuracy of the modified Hertz expression when the applied load was negative. These studies found reasonable agreement between the modified equation and measured pull-off loads in the range 0.3 gm (0.007 lb) to the testing limit of 5 gm (0.011 lb). Equation 3.16 is a rational expression derived by Johnson et al.:

FNm = FN + 3γπR + [6γπRFN + (3γπR)2]1/2

(3.16)

that quantifies a fictitious normal force (FNm) involving two elastic hemispheres of different radii in compression. It is the apparent value above the force calculated using the unmodified Hertz equation needed to produce the additional deformation arising from surface adhesion between the two spheres. In this relationship, R = R1R2/(R1 + R2). The fact that FNm is greater than FN serves as a consistency check on the expression and the Johnson et al. derivation. Equation 3.17 is the Hertz relationship modified by Johnson et al.

rM = {cM(RFN + 3γπR2) + [6γπRFN + (3γπR)2]}1/3

(3.17)

accounting for surface adhesion. The constant cM relates to the bulk elastic properties of the two materials. When the effects of surface energy are made negligible by greater magnitudes of FN, γ can be taken as zero, and Equation 3.17 reverts to a form of the Hertz relationship, Equation 3.5:

r = c(FN)1/3.

Another determination made by Johnson et al. relevant to rubber friction was that adhesion between convex surfaces does not depend on the elastic moduli of the two materials in contact. While the moduli influence the contact radius rM, the amount of surface free energy involved, adhesive forces developed and elastic work expended vary with rM2. Because the adhesive forces are independent of rM, they are also independent of the elastic moduli of the rubber spheres.

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34 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

3.12

Schallamach Waves

In 1971, Schallamach [18] reported his studies on the friction mechanism involved during the sliding of rubber on smooth surfaces. A consensus had developed that friction arises through the breaking and remaking of van der Waals’ adhesive bonds between rubber asperities and the test track. If the sliding rubber surface was too smooth, however, chattering occurred. This required roughening of the rubber to lower its adhesive friction potential to eliminate chattering and allow reproducible test results to be obtained. Schallamach’s [18] investigations produced a considerable body of evidence of a wave-like mechanism that could account for the chattering. Schallamach [18] visually examined sliding rubber by imposing movement between a hemispherical specimen and a transparent, smooth plastic (polymethyl methacrylate) track. This allowed direct observation of their contact areas. Narrow bands across the rubber specimen were seen moving oppositely to the direction of sliding at rates greatly exceeding the gross specimen speed. Stereoscopic microscopy revealed that these bands were detached, having lost optimal contact with the plastic surface. Maximum adhesion occurred only in the contacting segments between the detached areas. No relative motion in the rubber could be observed in these adhering segments. Schallamach [18] referred to the moving bands as “waves of detachment,” which is likened to a caterpillar traveling on a leaf, so this movement does not constitute true sliding. Observation indicated that the detached regions were folds in the rubber surface. The test specimens were polyisoprene and butyl and natural rubber. Figure€3.10 presents the model employed by Schallamach [18] as a substitute for the rubber surface. The contacting strips of rubber between the waves are replaced by equidistant, vertical ridges connected by springs. The ridges are assumed to deform in simple shear against the track, obeying Hooke’s law, as do the springs. To simplify matters, Schallamach [18] also assumed the coefficient of rubber friction (μ) to be constant. Figure€3.11 presents Schallamach’s [18] tangential displacement model for deflection of the rubber in and around the (shaded) area of contact between X

Figure€3.10 Model used by Schallamach as a substitute for a moving rubber surface. (Reprinted from Wear, 17, Schallamach, A., How does rubber slide?, 301, Copyright 1971, with permission from Elsevier.)

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35

Rubber Friction Mechanisms 0.5 0.4

–2.0

0.3 ky/µpm 0.2 2a 0.1 –1.0 0

1.0

x/a 2.0

Movement 2a Figure€3.11 Tangential displacement model used by Schallamach for the wave-like deflection of moving rubber. (Reprinted from Wear, 17, Schallamach, A., How does rubber slide?, 301, Copyright 1971, with permission from Elsevier.)

the waves. As the specimen moves to the right, the rubber surface distorts, reducing the distance between the originally equidistant imaginary lines defining sections in the contact surface. The slope of the dotted lines connecting the surface to the displacement plot is taken as proportional to the local shear strain. Crowding of the sections near the front of the contact area indicates compression in this region. Because the theory predicts that the total contact length, 2a, is unchanged by movement, a tensile strain occurs, producing widening of the rear sections. In the figure, k is the shear stiffness of the rubber, y is the horizontal deflection along the x-axis from the undeformed position, and pm is the pressure near the center of the contacting segment. Schallamach [18] verified visually the acceptability of his model by molding a transparent rubber track on which a square lattice with a 2-mm (0.78-in.) spacing had been marked. The track was composed of an unfilled, peroxidecured vulcanizate of synthetic polyisoprene. A hard, hemispherical slider of 19-mm (0.74-in.) radius was slid on the track. A substantial similarity between the deformed lattice configuration and the mathematical model of Figure€3.11 was observed. In a third testing protocol, Schallamach [18] slid a glass meniscus lens of 25-mm (0.98-in.) radius on the tracks of the rubber compounds. Detached wave patterns also developed on these track surfaces. All observations in the testing protocols were made with constant compression of the moving rubber hemispheres or constant indentation of the fixed rubber tracks. Test speeds for the hemispheres ranged from 0.02 to 0.23 cm/sec (0.008 to 0.09 in./sec). Friction forces were not measured. Although most waveforms were generally similar, exact pattern reproducibility was not obtained. The behavior of dust particles inadvertently caught between rubber specimens and their paired surfaces provided confirmatory evidence of waves with adhering segments between them. Such dust particles were

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36 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces buffeted by passing waves, but remained motionless in the intervening areas. Schallamach [18] emphasized, however, that it was not possible to rule out the existence of undetected true sliding in these segments. Schallamach [18] found that in all of his testing protocol-specimen combinations, only one failed to exhibit detachment waves — that of butyl rubber sliding on the plastic track. He postulated that, when movement is imposed between rubber specimens and another surface, development of detached waves or true sliding depends on which mechanism requires less energy expenditure. Schallamach [18] hypothesized that, for butyl rubber, which is highly hysteretic, true sliding imposes less resistance to motion. Briggs and Briscoe [19,20] further studied the detachment wave mechanism and found that the friction force developed may be accounted for in terms of the energy expenditure required to peel apart the adhering contact segments from the paired surface in front of the traversing dislocations. Either an energy balance or stress distribution method of analysis may be applied with this approach. Briggs and Briscoe [19,20] included the effects of roughness in their investigations, finding that the developed friction was not changed much by sandblasting the polymethyl methacrylate track employed in their testing. Berger and Heinrich [21] generalized the Schallamach [18] model by formulating a theory predicting buckling effects and tangential stress gradients as the driving forces for wave development. The theory allows a varying μ as it changes with pressure. Numerical solutions can be obtained for both symmetrical and nonsymmetrical pressure distributions in the rubber.

3.13

Elastomeric Friction

Moore [11] generalized rubber friction theory by extending it to encompass all elastomers. He addressed the friction mechanisms of van der Waals’ adhesion, bulk deformation hysteresis, and wear or cohesion loss. Citing Kummer [12] and Savkoor [13], Moore [11] discussed surface hysteresis forces in elastomeric friction under dry conditions. Moore acknowledged the existence of microscopic roughness on most harder contacted surfaces and hypothesized that deformation of a sliding elastomer must arise from such roughness. Moore postulated that the frictional resistance thereby developed can be mechanistically attributed to adhesion if the micro asperities are sufficiently small, or to bulk deformation hysteresis if they are sufficiently large. Moore did not report any test results supporting his posit. Persson [22] utilized many of the same analytical approaches taken by, Moore and also characterized dry elastomeric adhesion as van der Waals’ attraction. Persson emphasized the importance of the real area of contact and confirmed that, at room temperature, rubber can slide on smooth, harder surfaces with very little wear.

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37

Rubber Friction Mechanisms

3.14

Microhysteretic Contributions to Wet-Rubber Friction

Because of the extreme practical importance of adequate tire traction on wet roadways, the nature of the possible contribution of pavement micro-roughness to rubber friction on such lubricated surfaces began to receive attention in the 1950s. Kummer [15] hypothesized that a pavement’s microtexture can penetrate the water film and thereby provide limited dry contact with the tire, allowing temporary adhesive bonding to develop between the two materials. Yandell [23] took another approach to the microroughness contribution to vehicle traction, theorizing that what Kummer [12] considered to be dry adhesive contact in wet conditions between microasperities and rubber is, in reality, a lubricated hysteretic mechanism, developed because of high-frequency microhysteresis experienced by sliding tires. Yandell [23] carried out a mathematical mechano-lattice analysis of the wet, sliding tire-road system, applying his results to postulated macrohysteresis and microhysteresis mechanisms in which adhesion can play no part. As shown in Figure€3.12, Yandell [23] analyzed the macro- and microhysteretic contributions of an idealized roadway surface to wet traction by assuming that the two associated hysteretic friction coefficients are additive. He theorized that while a small interaction exists between the two contributions, it can be ignored within engineering accuracy. The total coefficient of hysteretic friction, μHt, is therefore simply the sum of the coefficients from the two components, the bulk macrohysteresis coefficient, μHb, and the surficial microhysteresis coefficient, μHs. This yields

μHt = μHb + μHs.

(3.18)

Yandell’s [23] analysis indicated that approximately 80% of the hysteretic energy dissipated occurs in the volumes represented by the hatching observed in Figure€3.12. He concluded that the coefficient of hysteretic friction of the two textural components can be predicted reasonably well by the Total Texture Rubber

Coarse Texture Rubber

Fine Texture

Rubber

Asperity

Asperity

Asperities

Figure€3.12 Phenomenological approach taken by Yandell to model both rubber macrohysteresis and rubber microhysteresis. Hatched areas postulated to represent volumes of rubber in which about 80% of hysteretic energy is dissipated. (Reprinted from Wear, 17, Yandell, W.O., A new theory of hysteretic sliding friction, 229, Copyright 1971, with permission from Elsevier.)

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38 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces average slope of their contacted surfaces in the direction of sliding. Yandell also theorized that the load dependence of rubber μ values obtained from dry testing of smooth surfaces where it is usually considered that adhesion predominates could be attributed to a hysteretic mechanism involving the microroughness of a smooth, paired material. Golden [24] also considered whether the so-called adhesive component of tire friction in wet conditions is actually lubricated microhysteresis. He examined the issue theoretically by scaling down the macroroughness of a roadway’s surface to a microroughness texture to assist in answering this question. Golden intended that the theoretical expressions he derived be applied in experimental testing to measure coefficients of hysteretic friction with velocity as the independent variable, holding the nominal area of rubber contact and FN constant. His theoretical analysis indicated that the magnitude of the coefficient of hysteretic rubber friction is not affected by scaling down the roughness of surfaces of interest to microscopic levels. He did find, however, that such scaling shifts the μHt vs. velocity dependence to lower velocity values.

3.15

Chapter Review

This chapter summarized early scientific research carried out to understand the basic mechanisms of rubber friction. Relevant findings of these investigations led to the current acceptance of three distinct friction forces that develop when rubber slides on a harder surface: (1) adhesion (FA); (2) bulk deformation hysteresis, or macrohysteresis (FHb); and (3) wear, sometimes termed cohesion losses (FC). 3.15.1 Rubber Coefficient of Friction Decreases with Increasing Load The first laboratory-controlled investigation of the basic nature of rubber friction was conducted at the U.S. National Bureau of Standards by Roth et al. [1] and reported in 1942. The previous research on rubber friction had dealt with specific kinds of products, such as tires, power-transmission belts, shoe heels, and soles and flooring. In these product studies, the experimental conditions were those under which the goods were commonly used. In Roth et al.’s work, the rubber specimens and testing surfaces were prepared in the laboratory. This made it possible to employ a wide range of experimental conditions and to control rubber specimen composition and the nature of the contacted surfaces. Roth et al.’s dynamic (sliding) friction study focused on soft rubber compounds of the type used in tire treads. These researchers had to refine their testing protocol until reproducible results were obtained. In a number of sliding conditions used during procedure development, specimens exhibited noticeable vibration, or chattering.

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39

Rubber Friction Mechanisms

One of the steps taken to prevent chattering was to limit the sliding speed to a maximum of 0.1 cm/sec (0.04 in./sec). Surface preparation also proved crucial. Roth et al. initially utilized a smooth specimen surface by molding the rubber against plate glass. Test results employing this preparation technique differed greatly among specimens. It was necessary to texture their surfaces to obtain reproducibility. This was accomplished by forming the rubber in a glass mold that had itself been roughened with abrasive. The initial chattering difficulties likely arose from adhesion between the smooth glass test track and the smooth rubber surface, and possibly from the production of Schallamach waves. Texturing the rubber surfaces by employing a roughened glass mold produced rougher specimens. This reduced their frictional resistance to sliding on the very smooth glass, allowing reproducible results to be obtained. Most subsequent rubber-friction investigators also employed a specimen-roughening approach. Figure€3.2(a) presents data selected by Roth et al. as typical of their rubber coefficient of friction results obtained by varying applied loads on sliding specimens molded on roughened glass. The y-axis represents the coefficient of rubber friction μ, defined as

μ = F T/FN,

(3.19)

where FT is the total measured friction force and FN is the perpendicular force applied to the rubber specimens during testing. The μ ratios decreased with increasing pressure. It should be further noted that the two different specimen sizes exhibited different friction coefficients at the same pressure values; thus, in these tests, μ is specimen-area dependent. 3.15.2 Adhesion as a Rubber Friction Mechanism Thirion [2] reported friction test results obtained by sliding two gum rubber specimens of different sizes on smooth glass. He was apparently the first published laboratory investigator to postulate that the friction mechanism developed between rubber and a smooth surface is adhesion. Figure€3.3(a) presents a generalized depiction of Thirion’s findings. The author experienced chattering in his initial tests and reduced sliding speed to yield reproducible results. In Figure€3.3(a), the upper curve represents Thirion’s [2] coefficient-of-friction test values from both specimens. He observed that the two specimen plots were coincident when expressed in terms of μ vs. pressure, and that the coefficients decreased with increasing pressure. Figure€3.3(b) presents Thirion’s data recalculated to express μ vs. the applied perpendicular force, FN, which again produces decreasing relationships. Like the Roth et al. results, Thirion’s measurements indicate that the coefficient of rubber friction is different at the same values of applied force for the differently sized specimens. Developed friction was also area dependent in Thirion’s tests.

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40 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 3.15.3 Linking Rubber Friction to the Real Area of Contact In 1952, Schallamach [3] reported friction coefficients developed by sliding three molded-rubber drag sleds on a smooth glass track. The sleds’ rubber runners were roughened to preclude chattering. He cited the work of Roth et al. [1] and focused on their finding that the coefficient of rubber friction decreases with increasing applied load. Schallamach [3] also investigated the possibility that, analogously to metals, the friction force developed by rubber depends on the real area of contact with the paired material. The surface of a rubber product is not perfectly flat. The roughened portions of such surfaces are often termed “asperities.” When a rubber product is first placed on another solid without additional loading — such as on glass in this case — the size of each microscopic area of contact in which rubber asperities touch the glass surface is unknown. This total unknown area is considered the real area of contact. Figure€3.4(a) presents Schallamach’s [3] coefficient-of-rubber-friction test results. Like the Roth et al. [1] and Thirion [2] results, the coefficients decreased with increased loading. Figure€3.4(b) presents Schallamach’s [3] data recalculated to express μ vs. the applied force, FN, which again produces decreasing relationships. In nearly all dry rubber-friction testing to be addressed in this book, μ was found to decrease with increasing loads. Schallamach [3] opined that the rubber-friction plots in Figure€3.4(a) represent interaction of rubber asperities with the glass track, not the sled runner’s entire bottom surface. While Schallamach [3] apparently misapplied the laws of metallic friction to rubber in his analysis, there is little doubt that the magnitude of the developed adhesive friction force depends on the real area of rubber asperity contact with the paired material. 3.15.4 Bulk Deformation Hysteresis in Rubber In 1955, Tabor [9] reported findings of investigations into the friction mechanism developed when smooth steel spheres are rolled on rubber. Previous researchers had attributed rolling resistance in configurations of this kind to adhesion. Tabor [9] pointed out, however, that generation of a significant adhesive force was inconsistent with some of the earlier data. In those situations, lubricants appeared to have little or no effect on reducing frictional resistance. This suggested the presence of a bulk hysteresis loss component. Tabor [9] rolled steel spheres of various diameters on flat, clean rubber blocks. He derived a theoretical expression for these conditions and examined whether hysteresis losses for the rubber involved would remain constant when the different sphere diameters were taken into account. They did, and agreement between the experimental results and his theoretical calculations was considered satisfactory. Various sizes of steel spheres were then rolled in dry, clean, preformed rubber grooves of different radii. When the tests were repeated in lubricated grooves, no perceptible reduction in rolling friction was evident. Tabor [9]

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Rubber Friction Mechanisms

41

concluded that the questioned rolling resistance occurring in these investigations stemmed from hysteresis in the rubber. What has since come to be called bulk deformation hysteresis arose when the rolling spheres compressed or stretched the rubber elastically. The rubber then experienced elastic release in both wet and dry conditions as the rolling spheres moved out of contact. Such compression or extension resulted in energy losses, constituting a hysteretic deformational friction component. Because a portion of the bulk of the rubber was involved, bulk deformation hysteresis was the operative mechanism. The bulk hysteretic losses elucidated by Tabor [9] constitute a basic friction force that can develop in rubber. 3.15.5 Concurrently Acting Rubber Friction Mechanisms Furthering Tabor’s [9] bulk deformation work, Grosch [10] carried out dynamic friction studies that involved sliding various surfaces at different speeds on five types of rubber. Flat rubber specimens were pressed into the moving surfaces by loads suspended beneath them. The moving surfaces included smooth, gently wavy glass and rough silicon carbide paper. Wavy glass, instead of flat glass, was used to reduce friction and obtain acceptable reproducibility. Grosch [10] took a “master curve” approach with his results. Plotting the measured rubber coefficients of friction (μ) against testing surface sliding speed produced peaks. The recorded resistance combined forces from all friction mechanisms present in a test. This was intended to be beneficial. For example, by first testing with smooth wavy glass, adhesional friction was thought to predominate. The sliding speed at which this mechanism exhibited a maximum coefficient of rubber friction peak, or hump, could be identified. If this coefficient peak was evident in results from testing a rough silicon carbide surface where bulk deformation hysteresis occurred, the presence of both mechanisms would be indicated. In these tests [10], the coefficient of rubber friction, μ, was calculated by inadvertent misapplication of the laws of metallic friction to rubber friction. In addition, the possible presence of surface deformation hysteresis in the testing was not considered; nevertheless, the findings are instructive [10]. Grosch reported that when smooth, wavy glass was slid on the rubber specimens at controlled speeds and constant temperatures, μ increased to a particular maximum and then decreased, giving the desired indicator peak. Grosch then dusted a fine powder on the glass surface and repeated the tests. Frictional resistance of this surface fell markedly to an essentially constant value over the whole speed range for all rubber specimens. This was attributed to separation of the rubber from the glass by the powder. Loss of contact with the glass eliminated the adhesion between it and the rubber. Grosch then carried out rough silicon carbide testing. A bulk deformation peak was always produced. Dusting the abrasive surface with powder invariably reduced the bulk deformation peak and eliminated the adhesion hump if it had been present. These general findings are depicted in Figure€3.7.

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42 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Grosch’s test results indicated that rubber friction on the dusted surfaces was primarily bulk deformation hysteresis. The adhesion hump and its elimination after dusting supported the hypothesis that adhesive and bulk deformation hysteresis friction could develop concurrently in rubber. 3.15.6 Adhesion and Surface Deformation in Rubber By the 1960s, it had been widely accepted that two distinguishable friction mechanisms develop in rubber: (1) adhesion (FA) and (2) bulk deformation hysteresis (FHb). In earlier studies, some friction investigators took a complicated analytical approach involving molecular-kinetic activation processes. Savkoor [13] employed a different, simplifying tack using a phenomenological focus, suggesting that consideration of the likely physical mechanisms giving rise to frictional resistance would be more readily and accurately applicable to real-world conditions. Savkoor hypothesized that the real area of sliding rubber contact with a paired surface at low loads is a small fraction of the apparent contact area. Only at high loads does the true contact area approach the full dimensions of the specimen. Savkoor agreed with Bartenev and Lavrentjev [14] that adhesion in rubber arises almost totally from forces that are far weaker than the “cold welding” adhesion found in metals discussed in Chapter 2. Savkoor postulated the existence of a fourth distinct friction mechanism arising when rubber slides on a harder material: surface deformation hysteresis (FHs). He directed attention to the fact that smooth surfaces, such as polished glass, can be microscopically rough. Savkoor’s surface hysteresis posit was based on the supposition that rubber asperities in contact with asperities on harder, smooth surfaces can mechanically interlock with each other, providing deformational resistance. When the paired surface is rough, asperity interlocking still takes place, while bulk deformation hysteresis concurrently develops. If adhesion is also present, the three mechanisms would act simultaneously. The analyses beginning in Chapter 5 of this book provide corroboration for Savkoor’s hypotheses. 3.15.7 Schallamach Waves Schallamach [18] visually showed that, in certain circumstances, rubber can move on a smooth surface utilizing a mechanism involving waves of detachment from that surface. He likened this movement, which does not constitute true sliding, to a caterpillar traveling on a leaf. This mechanism was verified by others and became known as “Schallamach waves.” Care must be taken when conducting rubber friction tests to preclude the development of Schallamach waves, unless they are desired for some purpose.

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43

Rubber Friction Mechanisms 3.15.8 Adhesion, Bulk Deformation Hysteresis, and Wear in Sliding Rubber

As part of a program of analysis and testing of traction between motor vehicle tires and roadways, Kummer [12] formulated a generalized friction model for sliding tires. The model encompasses the resistance forces developed by adhesion, bulk deformation hysteresis, and cohesion loss (wear) mechanisms. As observed in Figure€3.8, Kummer depicted the adhesion (Fai) and bulk hysteresis (Fhi) forces associated with a stone chip (i) in the roadway and a tire sliding at velocity V. Adhesional draping of the rubber over the chip accounts for the real area of contact. Kummer [12] considered the friction force F at any instant from all contacted chips as approximately equal to the sum of the Fa and Fh totals. Kummer [12] proposed a unified theory of rubber friction for tires expressed by Equation 3.11:

FT = FA + FHb + FC,

where: FT = total frictional resistance developed between a sliding tire and the pavement, FA = frictional contribution from combined adhesion of the two surfaces, FHb = frictional contribution from bulk deformation hysteresis in the rubber, and FC = cohesion loss contribution from rubber wear. Kummer [12] presented reasons for believing that short-term automobile tire wear was not significant in ordinary driving and that the FC term could be ignored when applying this equation to that time period. However, the frictional contribution from wear may not be insignificant in emergency situations where braking produces rubber skid marks.

References

8136.indb 43

1. Roth, F.L., Driscoll, R.L., and Holt, W.L., Frictional properties of rubber, J. Res. Nat. Bur. Stds. 28, 439, 1942. 2. Thirion, P., Les coefficients d’adhérence du caoutchouc, Rev. Gén. Caoutch., 23, 101, 1946. 3. Schallamach, A., The load dependence of rubber friction, Proc. Phys. Soc. Sec. Lond. B, 65, 657, 1952. 4. Bowden, F.P. International Conference on Abrasion and Wear, Eng., 172, 724, 1951. 5. Hertz, H.R., Miscellaneous Papers, MacMillian, London, 1896.

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44 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

8136.indb 44

6. Timoshenko, S., Theory of Elasticity, McGraw-Hill, New York, 1934. 7. Fogel, C.M., Introduction to Engineering Computations, International Textbook Company, Scranton, PA, 1962. 8. Tabor, D., The Hardness of Metals, Clarendon Press, Oxford, 2000. 9. Tabor, D., The mechanism of rolling friction, Proc. Roy. Soc. A, 229, 198, 1955. 10. Grosch, K.A., The relation between the friction and visco-elastic properties of rubber, Proc. Roy. Soc. A, 274, 21, 1963. 11. Moore, D.F., The Friction and Lubrication of Elastomers, Pergamon Press, Oxford, 1972. 12. Kummer, H.W., Unified Theory of Rubber and Tire Friction, Engineering Research Bulletin B-94, The Pennsylvania State University, University College, 1966. 13. Savkoor, A.R., On the friction of rubber, Wear, 8, 222, 1965. 14. Bartenev, G.M. and Lavrentjev, V.V., The law of vulcanized rubber friction, Wear, 4, 154, 1961. 15. Kummer, H.W., Lubricated friction of rubber, Rubber Chem. Tech., 41, 895, 1968. 16. Bowden, F.P. and Tabor, D., The Friction and Lubrication of Solids, Part II, Clarendon Press, Oxford, 1964. 17. Johnson, K.L., Kendall, K., and Roberts, A.D., Surface energy and the contact of elastic solids, Proc. Roy. Soc. A, 324, 301, 1971. 18. Schallamach, A., How does rubber slide?, Wear, 17, 301, 1971. 19. Briggs, G.A.D. and Briscoe, B.J., How rubber slips and grips, Schallamach waves and the friction of elastomers, Phil. Mag. A, 38, 387, 1978. 20. Briggs, G.A.D. and Briscoe, B.J., Surface roughness and the friction and adhesion of elastomers, Wear, 57, 269, 1979. 21. Berger, H.R. and Heinrich, G., Friction effects in the contact area of sliding rubber: a generalized Schallamach model, Int. J. Pol. Mat., 4, 200, 2000. 22. Persson, B.N.J., Sliding Friction, Physical Principles and Applications, Springer-Verlag, Berlin, 2000. 23. Yandell, W.O., A new theory of hysteretic sliding friction, Wear, 17, 229, 1970. 24. Golden, J.M., Hysteresis and lubricated rubber friction, Wear, 65, 75, 1980.

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4 Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber

4.1

Introduction

Chapter 2 presented the rational basis for quantifying the constant coefficient of friction between smooth metal surfaces so that the friction mechanisms arising in such circumstances can be compared to those occurring in rubber. Chapter 3 discussed laboratory-controlled, coefficient-of-rubber-friction testing conducted by Roth et al. [1], Thirion [2], and Schallamach [3]. In all their tests, carried out in dry conditions on macroscopically smooth surfaces, the coefficient of rubber friction, µ, decreased with increasing values of PN. Their findings contrast with the constant-coefficient behavior of smooth metals under increasing loading. This chapter considers additional rubber coefficient-of-friction test results, some obtained on dry and wet, smooth surfaces, and some acquired on dry and wet, textured materials. A number of these protocols employed outside-the-laboratory friction-testing devices. Findings from this examination will allow the formulation of a general statement: in practice, the constant (metallic) coefficient-of-friction equation does not apply to rubber. This is so because the laws of metallic friction do not apply to rubber friction. Furthermore, the friction-force-producing mechanisms in metals and rubber are physically and chemically different.

4.2

Coefficient of Rubber Friction on Dry, Smooth Surfaces

4.2.1

Walking-Surface Slip-Resistance Testing with a Pendulum Device

In 1948, Sigler et al. [4] described the development and use of a portable floor slip-resistance tester of the pendulum impact type that came to be known as the National Bureau of Standards (NBS), or Sigler, device. The measured residual energy (as determined from the maximum height of the pendulum’s 45

8136.indb 45

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46 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces center of mass during upswing after floor contact) is subtracted from the known potential energy of the pendulum before release. The result is considered to equal the work done during sliding of a 3.8-cm2 (1.5-in.2) test foot over the floor surface. This work is equal to the average friction force developed during sliding, multiplied by the observed contact distance. An “antislip coefficient” is determined by dividing this calculated average slip-resistance force by a preset, average vertical force applied by the pendulum’s mechanical heel. Sigler et al employed a rubber test foot conforming to U.S. Federal specification ZZ-R-601a. Their rubber test foot was abraded using No. 3/0 abrasive paper and brushed clean before each use to maintain a uniform roughness condition. Sigler et al. carried out calibration testing to determine the optimum, preset average vertical force to be applied through the mechanical heel using a spring. A variation in antislip coefficient values at different contact pressures was observed. Table€4.1 presents these results for the rubber test foot sliding on five macroscopically smooth floors in actual service. The three springs used in the calibration testing exerted the average forces presented in the table. These forces represent an approximate applied pressure during contact of 274 kPa (40 psi), 496 kPa (72 psi), and 827 kPa (120 psi). The pendulum stalled under the highest applied normal load on the Tennessee marble and asphalt tiles. As a consequence, no reading was obtained. The antislip coefficient decreased with increasing pressure in all pairings. Sigler et al. commented on the coefficient decreases with increases in average FN↜渀屮, but did not hypothesize a reason for them. Figure€4.1 presents a plot of the antislip coefficients vs. FN for the rubber test foot on the five macroscopically smooth flooring products. Two of the plots are dashed because only two data points were obtained in those tests. These two plots are also considered curved. Table€4.1 NBS Pendulum Tester Antislip Coefficients for a Rubber Test Foot under Different Applied Loads on Five Smooth Floors and One Gritted Floor in Service Applied Force Floor

3.7 lb

6.7 lb Antislip Coefficients

11.2 lb

Tennessee marble 0.81 0.75 (*) Asphalt tile 0.99 0.93 (*) 0.81 0.69 Rubber tile 0.94 0.69 Gritted rubber tile 0.88 0.81 Linoleum 0.95 0.84 0.69 0.74 0.60 Cellulose nitrate tile 0.86 (*) Pendulum stalled on floor surface. Source: Sigler, P.A., Geib, M.N., and Boone, T.H., Measurement of the slipperiness of walkway surfaces, J. Res. Nat. Bur. Stds., 40, 339, 1948.

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Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber

1.0

47

Asphalt tile

Antislip Coefficient

0.9 Linoleum 0.8

Tennessee marble

0.7 Cellulose nitrate tile 0.6 ∆ = Rubber tile 0.5 0

1

2

3

4

5

6

7

8

9 10 11 12

Applied Normal Load (FN)–lbs Figure€4.1 Variable load testing with a rubber test foot on various used flooring surfaces using the NBS pendulumimpact tester. (From Sigler, P.A., Geib, M.N., and Boone, T.H., J. Res. Nat. Bur. Stds., 28, 439, 1942.)

4.2.2 Industrial Rubber Belting Referencing the work of Roth et al. [1], Hurry and Prock [5] conducted rubber friction investigations of three representative types of industrial belting. While neither the specific belt types nor their compositions were mentioned, all samples were likely composed of natural rubber with appropriate reinforcing. In variable normal load testing, the samples were pulled at a velocity of 1.5 cm/min (0.59 in./min), a slow speed at which frictional heating of the contacting surfaces was presumably negligible. Testing was conducted in a controlled laboratory environment of 20°C (68°F) and 25% relative humidity. The test track was polished steel with an RMS roughness of 3 × 10−5 cm (11.8 μin.). A modification to the Roth et al. setup permitted the addition and removal of weights from the loading unit while the specimens remained in onedirectional sliding contact with the track. This allowed Hurry and Prock to increase the normal force to a maximum and then decrease it, providing two friction readings at each loading except the highest. Their maximum pressure was about 48.3 kPa (7 psi). To investigate the effects of rubber wear on friction, samples taken from unused belts were broken in under identical conditions before testing. Details of the wearing process were not reported. The breaking-in periods were 5 min, 1 h, 24 h, and 96 h. One specimen from each of the three belt types was conditioned for each period. A set of the three belt types was left unworn.

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48 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 40

FT– bs

30 20

FT = 0.49FN + 1.50

10 10

20

30

40 FN–lbs

50

60

70

Figure€4.2 Variable-load friction testing of unworn rubber belting on polished steel. (From Hurry, J.A. and Prock, J.D., India Rubber World, 128, 619, 1953. With permission.)

Figure€4.2 presents the Hurry and Prock results (relabeled for consistency with the present nomenclature) for one of the unworn belt types, plotted as FT (total measured friction) vs. FN. In the figure, a pair of data points is seen for each of the applied normal loads except the maximum. A least-squares fit line falls between the paired points. Although not stated specifically by Hurry and Prock, the loading portion of the testing cycle appears to be represented by the points below the least-squares line. The single, highest friction value is in that position. Hurry and Prock found that the simple, least-squares straight line equation

y = cx + b

fit their data. In this case, b represents the y-intercept. For the unworn belting, b equaled 0.68 kg (1.5 lb). The equations for the four data sets reported by them were: c b

Wearing Period

FT = 0.49FN + 1.50

None

FT = 0.33FN + 0.07

5 min

FT = 0.28FN + 0.47

1h

FT = 0.30FN + 0.76

96 h

Hurry and Prock considered that the c values in their equations represented the coefficient of rubber friction µ, but did not postulate a mechanism potentially explaining development of the friction force in this ratio. They did not comment on possible explanations for the always-present y-intercept, although they postulated that it represented a constant friction force. Nei-

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Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber

49

ther did they address the noticeably larger c values for the unworn belt (0.45) compared to the three worn specimens (0.33, 0.28, and 0.30). Hurry and Prock did not suggest a reason for the inequalities between their loading and unloading friction measurements at each FN value. Because their readings were taken at constant velocity (i.e., no inertial force variations), these differences likely arose from differences in the real area of contact between the rubber belt asperities and the polished steel track. Roth et al. [1], Thirion [2], and Schallamach [3] all reported that the coefficient of rubber friction decreases from the very beginning of load application in testing. Hurry and Prock, however, drew different conclusions: except for the unworn rubber, they theorized that the measured friction force increases in direct proportion to FN, the coefficient of rubber friction is constant, and the y-intercept values could be ignored. 4.2.3 Rubber Friction on Steel and Aluminum Surfaces Bartenev and Lavrentjev [6] measured the coefficient of friction of vulcanized rubber “according to the methods of Roth, Driscoll, and Holt [1]” but utilized steel and aluminum testing surfaces instead of glass to further the understanding of the frictional behavior of rubber on different materials. Furthermore, in accordance with their intention that a contacted surface microroughness not mechanically interlock with sliding rubber, the steel and aluminum plates were polished to a smoothness of 10−5 to 10−6 cm (3.9 × 10−6 to 3.9 × 10−7 in.). Bartenev and Lavrentjev were attempting to carry out their testing so that adhesion between the sliding metal surfaces and the rubber specimens was the only independent variable. Figure€4.3 presents the Bartenev and Lavrentjev steel-track results employing constant sliding velocities at a controlled testing temperature of 23°C. As indicated by the y-axis scale in the figure, Bartenev and Lavrentjev chose to 50

10

100

150

200

1/µ

2 5

1

0

50

0 Pressure–kg/cm2

50

100

Figure€4.3 Dependence of inverse friction coefficient μ of vulcanized rubber sliding on polished steel. (Reprinted from Wear, 4, Bartenev, G.M. and Lavrentjev, V.V. The law of vulcanized rubber friction, 154, copyright 1961, with permission from Elsevier.)

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50 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces present their coefficient of friction results as the inverse of that value, 1/µ. The data in curve 1 were obtained at a velocity of 0.025 mm/min (9.8 × 10−4 in./min), while curve 2 represents static friction testing. The curved shapes of the plots in the low-loading range indicate that µ was not initially constant. In this range, μ decreases as PN increases. Figure€4.4 presents the Bartenev and Lavrentjev friction measurements for vulcanized rubber having a Shore hardness of 68 sliding at constant speed on the aluminum track at two temperatures: 23°C (73.4°F) and 65°C (149°F). The data are again expressed as the inverse of µ. In the low-loading range, μ decreases as PN increases. Bartenev and Lavrentjev were interested in relating the adhesion of rubber to its real area of contact with the harder material. They hypothesized that the deviation downward of the plotted points in the lower loading range from the straight lines arose because of a small, but finite, adhesion-produced real area of contact between the rubber specimens and metal surfaces at zero load. This potential explanation will be termed the “no-load adhesion hypothesis.” Bartenev and Lavrentjev further hypothesized that the extent of this noload real area of contact depended on the degree of rubber roughening, the time of preliminary contact before commencement of sliding (3 minutes in their protocols) between the paired surfaces and other unspecified factors. They postulated that the adhesive force arising from this no-load contact was represented by extrapolating 1/μ vs. PN plots to the y-intercept. Bartenev and Lavrentjev did not provide any laboratory test results in support of their yintercept-related postulate.

10

1/µ

65°C

5 23°C

0

50 100 Pressure–kg/cm2

150

Figure€4.4 Dependence of inverse friction coefficient μ of vulcanized rubber sliding on polished aluminum at 23°C and 65°C. (Reprinted from Wear, 4, Bartenev, G.M. and Lavrentjev, V.V. The law of vulcanized rubber friction, 154, copyright 1961, with permission from Elsevier.)

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51

4.2.4 Aircraft Tire Friction on Different Portland Cement Concrete Finishes: Smooth Surface In 1955, the U.S. National Advisory Committee for Aeronautics (NACA), the forerunner of the National Aeronautics and Space Administration (NASA), published results of coefficient-of-friction tests on segments of rubber B-29 tires carried out by Hample [7] at the Boeing Aircraft Company. Typical (circular) tread samples were cut from the thickest portion of a worn, ten-ply, nose-wheel tire in storage for at least 18 months after use in flight. Hample noted that “checks” in the rubber surface existed over most of the tread. Figure€4.5 indicates the area on the tire from which the specimens were taken. Hample stated that, prior to his study, there had been some doubt as to the validity of previously utilized static friction data obtained from Rubber material testing without taking temperature Ply material 1.75'' Diameter effects into account. It was realized that rapid changes in pressure and CL temperature during aircraft wheel spin-up occurred while landing. The purpose of his investigations was to gain insight into these effects, which 1.75'' Diameter can produce nearly molten tire specimens cut rubber when landing on portland from CL row of cement concrete runways. “Diamonds” Three different types of concrete finishes were selected for test usage. These were a smooth surface obtained by conventional troweling with a metal blade, a broom-swept rough surface, and a “semi-smooth” surface produced by finishing the placed concrete with a 2 × 4 piece of construction lumber. The latter two (textured) surfaces are discussed briefly in this section and then in greater detail later in this chapter. Hample’s testing involved measuring the maximum force developed when a 4.45-cm (1.75-in.) diameter rubber specimen was pulled CL 2.54 cm (1 in.) horizontally on the concrete surfaces starting from an Figure€4.5 at-rest state. Two test setups were Area of B-29 tires from which Hample obtained employed. Three (averaged) test test samples. (From Hample, W.G., Friction Study runs were carried out for each load. of Aircraft Tire Material on Concrete, National Figure€4.6 depicts the high-pressure Advisory Committee for Aeronautics, Washington, D.C., 1955.)

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52 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces +

Support structure Jack pivot point

95 lb Plunger counterweight 10-Ton jack model RC 377

Support structure 3-Ton jack assy.

Spring dynamometer 0-500 lb, 0-2,000 lb

Floor line

Specimen mounting block

1.37 .12

Tension strap

Concrete specimen

110

Rubber specimen

Support structure

Concrete from tie

Figure€4.6 Hample’s high-normal-load testing configuration. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

configuration, covering a high-normal-load range of 345 kPa to 7.58 MPa (50 to 1,100 psi). Vertical loads were applied by a hinged, long-stroke hydraulic jack in 690-kPa (100-psi) increments. Movement of the specimens was induced using a smaller, floor-mounted hydraulic jack connected through a spring dynamometer to the sample holder. Residence time of the rubber specimens on the concrete surfaces prior to commencement of vertical loading was not reported. Although not mentioned, and apparently not quantitatively accounted for by Hample, some inertial resistance to initiation of movement of the specimen, as well as that of the suspended hinged jack, sample holder, and dynamometer, undoubtedly arose. Before break-away of the rubber from the concrete could take place, the friction force developed during loading first had to be overcome. Then, as the movable components of the configuration began to accelerate, inertial resistance was generated. The maximum measured force during the 2.54-cm (1-in.) movement of the specimen was the sum of the dynamic frictional resistance of the rubber and the maximum inertial force developed during this period. Because the rate of horizontal force application by the floor-mounted jack was not reported, it is not possible to quantify the F = ma force. While the inertial component of the measurements given by the dynamometer cannot be differentiated from frictional resistance with available data, analysis of Hample’s findings is nevertheless instructive.

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Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber 40

– Column pivot point

Beam

Counterweight

Support structure 3-Ton jack assy.

Pipe column

32

1.60 (Typ.)

90 lb

Support structure

126 Weight source

Specimen mounting block Spring dynamometer 0-500 lb

53

1.37

1,000 lb Floor line

Concrete specimen Form stop (6'' channel) (Encased in form of 10'' channel, 24'' long)

0.12 Rubber specimen

Figure€4.7 Hample’s low-normal-load testing configuration. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

Figure€4.7 depicts Hample’s low-pressure configuration. Pressure was applied by a weight-loading device in 138-kPa (20-psi) increments. The majority of the testing in Hample’s investigation involved this setup. Its range, 172 kPa to 2.14 MPa (25 to 310 psi), simulated the then-present-day aircraft tire pressures. Associated and unaccounted-for inertial forces also developed in these tests. 4.2.4.1 Ambient-Temperature Testing Initial high-pressure testing of the three concrete surfaces was conducted at room temperature, about 24°C (75°F). Figure€4.8 presents these results. It may be seen that, for all three surfaces, the coefficient of rubber friction decreased with increasing pressure, and the smooth-surface data fell between the measurements from the other two concrete finishes. Hample remarked on this behavior, reporting that the results had been checked, but no suitable explanation for the possible anomaly could be found. As we will see in Chapter 7, the presence of two different friction mechanisms appears to have caused the semi-smooth plot’s positioning. Figure€4.9 further depicts Hample’s high-pressure results from the smooth concrete. It shows averages for each of the three test runs, providing an indication of data scatter. Hample also conducted low-normal-load testing at ambient temperature. Figure€4.10 presents his results from the smooth concrete finish, including averages from each of the three test runs. The coefficient of rubber friction is again seen to decrease with increasing pressure.

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54 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 1.60 1.40

Coefficient of Friction–µ

1.20 1.00 0.80 0.60

Rough surface

Smooth surface Semismooth surface

0.40 0.20

0

200

400 600 800 Normal Pressure, psi

1,000

1,200

Figure€4.8 Hample’s high-pressure testing results in ambient conditions for the three concrete surfaces. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

4.2.4.2 High-Temperature Testing High-temperature friction measurements on the smooth concrete obtained with the high-pressure configuration were carried out at 149°C (300°F). The temperatures of the rubber specimens were not raised to higher values before testing, but rather the concrete surfaces were slowly heated with an oxyacetylene torch. A portable thermocouple was used to measure the temperature of the concrete immediately before and immediately after each friction test. The reported values are averages of the two readings. Figure€4.11 presents Hample’s results for this protocol, showing averages for the three test runs. In this case, µ falls with increasing normal loads. High-temperature testing utilizing the low-pressure configuration was also conducted. Because the high-pressure testing was done first, the concrete also utilized in the low-pressure tests had previously been heated to 149°C (300°F) — that is, above the boiling point of water. This procedure may have altered the physical and chemical characteristics of the concrete surfaces. Different tire rubber specimens were employed with each change in testing temperature, and each sample was used repeatedly throughout a temperature increment until worn out. “Worn-out” was defined as having had

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Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber

55

1.40 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

Coefficient of Friction–µ

1.20 1.00 0.80 0.60 0.40 0.20 0

0

200

400 600 800 Normal Pressure, psi

1,000

1,200

Figure€4.9 Hample’s high-pressure testing results in ambient conditions for the smooth concrete indicating data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.) 1.4

Coefficient of Friction–µ

1.2 1.0 0.8 0.6 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

0.4 0.2 0

40

80

120 160 200 240 Normal Pressure, psi

280

320

Figure€4.10 Hample’s low-pressure testing results in ambient conditions for the smooth concrete indicating data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

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56 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 1.40

Coefficient of Friction–µ

1.20 1.00 0.80 0.60 0.40 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

0.20

0

200

400 600 800 Normal Pressure, psi

1,000

1,200

Figure€4.11 Hample’s high-pressure testing results at 300°F for the smooth concrete indicating data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

sufficient material removed during sliding such that further wear would allow the specimen mounting plate to bear on the concrete surface. As a result, a cohesion-loss friction component was present in some measurements. Further, as seen in Figure€4.5, depicting the tire’s construction, this definition permitted some testing to be carried out with tire ply material, rather than tread rubber, as the tested surface. Coefficient of rubber friction values from low-pressure tests were obtained at 149°C (300°F), 205°C (400°F), 260°C (500°F), 315°C (600°F), and 372°C (700°F). These are presented in Figure€4.12 through Figure€4.16, respectively. The coefficient decreased with increasing pressure at all temperatures. 4.2.5 Rubber Adhesion on Smooth Solids Increases with Surface Free Energy In 1994, Mori et al. [8] reported dynamic friction test results from acrylonitrile butadiene (NBR) and styrene butadiene (SBR) rubber in contact with macroscopically smooth aluminum and Teflon sliders at 20°C (68°F) and 55 to 60% relative humidity. The vulcanized specimens were formed in specially fabricated molds exhibiting different surface free energies. As a result, the NBR and SBR samples possessed “designed” surface free energies, while

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Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber

57

1.4 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

Coefficient of Friction–µ

1.2 1.0 0.8 0.6 0.4 0.2 0

40

80

120 160 200 240 Normal Pressure, psi

280

320

Figure€4.12 Hample’s low-pressure testing results at 300°F for the smooth concrete indicating data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

1.4 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

Coefficient of Friction–µ

1.2 1.0 0.8 0.6 0.4 0.2 0

40

80

120 160 200 240 Normal Pressure, psi

280

320

Figure€4.13 Hample’s low-pressure testing results at 400°F for the smooth concrete indicating data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

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58 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 1.4 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

Coefficient of Friction–µ

1.2 1.0 0.8 0.6 0.4 0.2 0

40

80

120 160 200 240 Normal Pressure, psi

280

320

Figure€4.14 Hample’s low-pressure testing results at 500°F for the smooth concrete indicating data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

1.4 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

Coefficient of Friction–µ

1.2 1.0 0.8 0.6 0.4 0.2 0

40

80

120 160 200 240 Normal Pressure, psi

280

320

Figure€4.15 Hample’s low-pressure testing results at 600°F for the smooth concrete indicating data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

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59

1.4 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

Coefficient of Friction–µ

1.2 1.0 0.8 0.6 0.4 0.2 0

40

80

120 160 200 240 Normal Pressure, psi

280

320

Figure€4.16 Hample’s low-pressure testing results at 700°F for the smooth concrete indicating data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

each retained its inherent bulk deformation properties. Use of low-surfacefree-energy Teflon molds produced specimens with surfaces containing correspondingly low-surface-free-energy butadiene groups. A mold with many polar groups, polyethylene terephthalate (a packaging film), yielded rubber surfaces with numerous high-surface-free-energy nitrile groups. Mori et al. also employed a chrome-plated stainless steel mold to obtain intermediate surface-free-energy test samples. A focus of the Mori et al. investigation was to clarify the effects of an elastomer’s surface free energy on its property of adhesion. It is to be expected that this property increases with surface free energy. Bowden and Tabor [9] had hypothesized that friction developed between sliding rubber and a paired, macroscopically smooth material could be expressed as the sum of the work of deformation at the real areas of contact and the work of adhesion involving surface free energy at the interfacial layers. Previous investigators found that increasing the surface free energy of a test track increased the coefficient of friction of rubber-track pairings. In attempting to assess the contribution of the work of adhesion to friction, however, difficulties arose because of inherent differences in the bulk deformation properties of the tested elastomers. Mori et al. attempted to overcome this problem by keeping the bulk elastic characteristics (i.e., tensile strength, elongation and hardness) of the NBR and SBR constant using the specially designed molds. Controlling the work of deformation during sliding allowed the adhesion contribution to be varied and potentially isolated for subsequent analysis.

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60 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Mori et al. intended to exclude all but the van der Waals’ adhesion mechanism in their testing, in which 8 the rubber samples slid on the Teflon High adhesion NBR and aluminum surfaces at a rate of 0.5 cm/sec (0.2 in./sec). The alumi6 num exhibited a microroughness of 2.5 × 10−5 cm (1 × 10−5 in.) while that of the Teflon was 2.1 × 10−5 cm (0.83 4 × 10−5 in.). Medium adhesion NBR Figure€4.17 presents the test results 2 for aluminum sliding on NBR. All Low adhesion NBR three specimens showed an initial decrease in the coefficient of fric0 tion followed by a constant segment. 0 2 4 6 Mori et al. concluded that the coefApplied Normal Load (FN)–N ficient increased with increased surface free energy, as did the FN value Figure€4.17 at which it became constant. Coefficient of friction testing of aluminum sliding Figure€4.18 depicts the SBR-Tefon acrylonitrile butadiene rubber (NBR) specimens of varying adhesion propensities. (From lon data. Mori et al. concluded that Mori, K. et al., Rubber Chem. Techn., 67, 797, the relationship between the fric1994. Reproduced with permission from Rubber tion coefficients and FN for the SBR Chemistry and Technology © 1994, Rubber Diviresults was essentially the same as sion. American Chemical Society, Inc.) for the NBR-aluminum parings. The five instances of coefficient decrease in the low loading range illustrated in the two figures were ascribed to an “enhancement” in the rubber adhesion forces involved produced by the higher surface free energies of these samples. Mori et al. postulated that the constant coefficient of friction at all loads in the lowest-adhesion SBR-Teflon plot seen in Figure€4.18 could be attributed to the combinative effect of the surface free energies of the Teflon and the SBR specimen. Their total was the lowest of the six mated surfaces tested. Mori et al. did not hypothesize a physical mechanism potentially explaining why the five pairings with the highest combined surface free energies exhibited decreasing coefficients at the lowest loads, while the coefficient for the pairing with the lowest combined surface free energies remained constant. Figure€4.19 presents the Mori et al. plots of their FT vs. FN values for NBR and aluminum. This is the same type of representation (Figure€4.2) given by Hurry and Prock [5] for their two-direction testing. Mori et al. theorized that the slopes of the lines in Figure€4.19 represent the coefficients of adhesive friction for the three pairings. They extrapolated these lines to the FT axis noting that intercept values were produced, and postulated that the existence of measurable adhesive friction forces at zero load was therefore demonstrated. They theorized that these no-load forces arose from the combinative effect of the surface free energies of the two materials involved. Mori et al. cited

Coefficient of Friction–µ

10

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61

Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber

Figure€4.18 Coefficient of friction testing of Teflon® sliding on styrene butadiene rubber (SBR) specimens of varying adhesion propensities. (From Mori, K. et al., Rubber Chem. Techn., 67, 797, 1994. Reproduced with permission from Rubber Chemistry and Technology © 1994, Rubber Division. American Chemical Society, Inc.)

5

4

3

2

Low adhesion SBR

1

0

= Medium adhesion SBR

0

2 4 Applied Normal Load (FN)–N

Figure€4.19 Measured friction force vs. applied normal load for aluminum sliding on acrylonitrile butadiene rubber (NBR) specimens of varying adhesion propensities. (From Mori, K. et al., Rubber Chem. Techn., 67, 797, 1994. Reproduced with permission from Rubber Chemistry and Technology © 1994, Rubber Division. American Chemical Society, Inc.)

6

20 Measured Friction Force (FT)–N

Coefficient of Friction–µ

High adhesion SBR

High adhesion NBR 15

Medium adhesion NBR

10

Low adhesion NBR

5

0

0

2 4 Applied Normal Load (FN)–N

6

the rubber adhesion pull-off test findings of Johnson et al. [10] discussed in Chapter 3, apparently in support of the no-load, adhesion hypothesis used as a basis for this theory.

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62 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 4.2.6 ANOVA Slip-Resistance Testing of Dry, Elastomeric Shoe Heels Slip-resistance measurements are commonly used in the walking surface safety field as a means of quantifying the traction required by pedestrians to prevent a slip and fall. While this approach is widely employed, two opposing groups of safety specialists have developed. One group advocates the use of static friction testing devices, while the other believes that dynamic friction measurements are more appropriate. Redfern and Bidanda [11] developed the Programmable Slip Resistance Tester (PSRT), which measures the dynamic coefficient of friction (µ) arising between a sliding shoe and a flooring surface of interest. The coefficient is defined in the usual manner:

µ = FT/FN.

(4.1)

Redfern and Bidanda selected six independent variables for testing thought to be of principal interest in walking-surface slip-resistance metrology: (1) the shoe bottoms (outsoles), (2) the flooring, (3) the shoe angle to the floor at heel strike, (4) any contaminants present, (5) the shoe’s likely sliding velocity that must be stopped, (6) and the applied normal load. They chose a number of different test samples and protocols representing these independent variables so that an analysis of variance (ANOVA) could be carried out to determine their effects on µ. For example, four smooth flooring surfaces were utilized: (1) untreated vinyl tile, (2) vinyl tile waxed and buffed, (3) stainless steel, and (4) sealed portland cement concrete. There were three types of elastomeric shoe bottoms: (1) hard PVC, durometer 83, no tread pattern; (2) soft urethane, durometer 34, no tread pattern; and (3) rubber, durometer 60, with a typical work boot tread pattern. These were tested dry and in three wet conditions on the four flooring surfaces, utilizing two vertical loads at three different sliding velocities and two heel strike angles. Five repeated test runs were carried out for each possible combination, producing 2880 measurements. Redfern and Bidanda reported their test data by shoe-bottom type due to the large differences in µ ratios between shoes. Values of µ were calculated over the other independent variables. Our focus here is the effect of changes in FN on µ for the three shoe-bottom materials under dry conditions. In this case, Redfern and Bidanda averaged over floor type, heel strike angle, and sliding velocity. While the effects of these three independent variables on µ arising from changes in FN could not be differentiated using the reported data, the ANOVA results are of interest. Figure€4.20 presents the calculated Redfern and Bidanda results for their dry coefficient-of-friction testing. The rubber, urethane, and PVC heels all experienced decreases in µ with increasing normal force. The curved lines between the paired data points are dashed. Based on the µ vs. FN plots reviewed so far, and further analysis to be presented in Chapter 5, we can generally expect that a hyperbolic friction curve will be evidenced for rubber in contact with a smooth paired surface if three or more different loadings are employed and decreasing coefficients develop.

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63

Rubber

1.0

Coefficient of Friction–µ

0.9 0.8 0.7 0.6

Urethane

0.5 0.4

PVC

0.3 0.2 0.1 0

0

1 2 3 4 5 6 7 Applied Normal Force (FN)–kg

8

Figure€4.20 Coefficient of rubber friction (μ) vs. applied normal force from dry ANOVA testing of three shoe heel compositions. (Data taken from Redfern, M.S. and Bidanda, B., Ergonomics, 37, 511, 1994.)

4.2.7 Friction of Natural and Synthetic Tire-Tread Rubber on Ice During the period following World War II, it was realized that the synthetic rubber tires of that time were more likely to slip on ice than were those with treads composed of natural rubber (NR). Pfalzner [12] carried out a comparison coefficient-of-friction testing of these two general types of rubber to assist in improving the traction characteristics of synthetic tires. He selected formulations of Hycar (acrylonitrile butadiene), GR-S (styrene butadiene), and neoprene for this purpose. Pfalzner prepared 6.45 cm2 by 0.61 cm (1 in.2 by 0.25 in.) and 1.6 cm2 by 0.61 cm (0.25 in.2 by 0.25 in.) samples of the four rubber substances and affixed them to the underside of wood blocks that also served as loading platforms. A calibrated steel spring was attached to the blocks in the plane of the loaded block-rubber specimen’s center of mass to measure friction forces without inducing a vertical moment in the carriage. The large and small specimens were loaded up to 290 kPa (42 psi) and 690 kPa (100 psi), respectively. The µ vs. FN testing was carried out at −4°C (+20°F) in a laboratory coldroom capable of controlling temperatures between 0°C (+32°F) and −29°C (−10°F). Pfalzner constructed a circular track on an electrically driven turntable into which water was poured and frozen. Freezing was done in such a manner that the surface of the ice was smooth. This dynamic testing, with the turntable rotating at a constant speed of

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64 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 5.24 rad/sec (50 rpm), may be considered to have been conducted in dry conditions. Pfalzner carried out an initial investigation to determine the effect of turntable speed on the measured friction values. Except at very low speeds where the carriage evidenced a jerky motion, which was subsequently avoided, he found that no discernable difference in µ vs. speed was detected. The maximum relative speed experienced by the spring-restrained specimens was 12.9 km/h (8 mph). As in the testing undertaken by Hurry and Prock [5] discussed in Section 4.2.2, Pfalzner added weights incrementally to the loading platforms and then removed them incrementally during an unloading portion of the protocol. The reported FT values were averages of the two corresponding readings. These reported averages were used in the present analysis to calculate the measured coefficients of rubber friction. Figure€4.21 presents plots of the calculated µ values vs. FN for Pfalzner’s 1.6-cm2 (0.25-in.2) samples of the four different rubber compositions loaded up to 689 kPa (100 psi). It is observed that µ values decreased with increased loading for the NR, GR-S, and Hycar specimens; however, the neoprene 0.200 0.175

Coefficient of Friction–µ

0.150 0.125 0.100 0.075

Natural rubber GR-S (styrene butadiene) Hycar (acrylonitrile butadiene) Neoprene

0.050 0.025 0

0

5 10 15 20 Applied Normal Force (FN)–lbs

25

Figure€4.21 Coefficient of rubber friction (μ) vs. applied normal force test results from four, ¼-in.2 tire tread specimens on ice at 20°F. (Data taken from Pfalzner, P.M., Can. J. Res. F, 28, 468, 1950.)

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65

0.45

0.40

Coefficient of Friction–µ

0.35 Natural rubber GR-S (styrene butadiene) Hycar (acrylonitrile butadiene) Neoprene

0.30

0.25

0.20

0.15

0.10 0

0

10

20 30 40 Applied Normal Force (FN)–lbs

50

Figure€4.22 Coefficient of rubber friction (μ) vs. applied normal force test results from four, 1-in.2 tire tread specimens on ice at 20°F. (Data taken from Pfalzner, P.M., Can, J. Res. F, 28, 468, 1950.)

sample, with the lowest indicated traction potential, exhibited a different behavior: the coefficient first increased and then decreased. The calculated 6.45-cm2 (1-in.2) data, from testing up to 287.7 kPa (42 psi), is depicted in Figure€4.22. In this case, the NR and GR-S coefficients decreased with increased loading, while the formulations with the lowest indicated traction potential, Hycar and neoprene, first showed increasing and then decreasing µ values.

4.3

Coefficient of Rubber Friction on Dry, Textured Surfaces

4.3.1

Aircraft Tire Friction on Different Portland Cement Concrete Finishes: Textured Surfaces

As discussed in Section 4.2.4, Hample [7] carried out aircraft tire friction testing on three different concrete surfaces: (1) smooth; (2) semi-smooth,

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66 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces finishing the placed concrete with a two-by-four; and (3) rough, or broomswept. We focus here on the latter two types. All three finishes were tested utilizing the high- and low-pressure setups described in Section 4.2.4. 4.3.1.1 Ambient-Temperature Testing Initial high-pressure friction testing of the two textured finishes was conducted at room temperature, about 20.4°C (75°F). Figure€4.8 presents these results. Sliding tire samples on the semi-smooth and rough surfaces produced values for the coefficient of rubber friction that decreased with increasing pressure. Figures€4.23 and 4.24 further depict Hample’s high-pressure results from the semi-smooth and rough concrete, respectively, providing an indication of data scatter in ambient conditions. Hample also conducted low-pressure testing of the rough concrete at ambient temperature. Figure€4.25 presents his results indicating data scatter. Again, the measured µ values diminished with increasing normal load. 4.3.1.2 High-Temperature Testing High-temperature friction measurements on the smooth, semi-smooth, and rough surfaces obtained at 140.9°C (300°F) with the high-pressure setup are 1.40

Coefficient of Friction–µ

1.20 Run No. 1 Run No. 2 Run No. 3 Run No. 4 Arithmetical average

1.00 0.80 0.60 0.40 0.20

0

200

400 600 800 Normal Pressure, psi

1,000

1,200

Figure€4.23 Hample’s high-pressure testing results in ambient conditions for the semi-smooth concrete surface. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

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67

1.60 1.40

Coefficient of Friction–µ

1.20 1.00 0.80 0.60 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

0.40 0.20

0

200

400 600 800 Normal Pressure, psi

1,000

1,200

Figure€4.24 Hample’s high-pressure testing results in ambient conditions for the rough concrete surface. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

depicted in Figure€4.26. An overall reduction in µ values, compared to those seen in Figure€4.8, appears to have occurred. Further, in contrast to the corresponding ambient temperature results seen in Figure€4.8, there seems little or no difference between the tire-rubber friction values of the three surfaces at this higher temperature. Figure€4.27 and Figure€4.28 depict data-scatter at 140.9°C (300°F) for the semi-smooth and rough concrete, respectively. As above, the friction coefficients decreased with increasing PN. Hample carried out low-pressure testing of the rough concrete surface at 140.9°C (300°F), 204.5°C (400°F), and 260°C (500°F). His data-scatter results for these studies are presented in Figures€4.29 through 4.31. Reductions in µ values with increasing temperature and increasing pressure are evident. 4.3.2 Bias-Ply and Radial-Belted Aircraft Tire Friction on an Ungrooved, Portland Cement Concrete Runway In 1990, Yager et al. [13] presented an overview of the initial test results developed in the Surface Traction and Radial Tire (START) Program being carried

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68 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 1.6 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

Coefficient of Friction–µ

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0

40

80

120 160 200 240 Normal Pressure, psi

280

320

Figure€4.25 Hample’s low-pressure testing results in ambient conditions for rough concrete surface. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.) 1.40

Coefficient of Friction–µ

1.20 1.00 Rough Smooth Semi-smooth Arithmetical average

0.80 0.60 0.40 0.20

0

200

400 600 800 Normal Pressure, psi

1,000

1,200

Figure€4.26 Hample’s high-pressure testing results at 300°F for rough, semi-smooth and smooth concrete. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

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69

1.40

Coefficient of Friction–µ

1.20 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

1.00 0.80 0.60 0.40 0.20

0

200

400 600 800 Normal Pressure, psi

1,000

1,200

Figure€4.27 Hample’s high-pressure testing results at 300°F for the semi-smooth concrete showing data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.) 1.60 1.40

Coefficient of Friction–µ

1.20 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

1.00 0.80 0.60 0.40 0.20

0

200

400 600 800 Normal Pressure, psi

1,000

1,200

Figure€4.28 Hample’s high-pressure testing results at 300°F for rough concrete showing data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

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70 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 1.4 Run No. 1 Run No. 2 Run No. 3 Arithmetical average

Coefficient of Friction–µ

1.2 1.0 0.8 0.6 0.4 0.2 0

40

80

120 160 200 240 Normal Pressure, psi

280

320

Figure€4.29 Hample’s low-pressure testing results at 300°F for rough concrete showing data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

1.4

Coefficient of Friction–µ

1.2

Run No. 1 Run No. 2 Run No. 3 Arithmetical average

1.0 0.8 0.6 0.4 0.2 0

40

80

120 160 200 240 Normal Pressure, psi

280

320

Figure€4.30 Hample’s low-pressure testing results at 400°F for rough concrete showing data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

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1.4

Coefficient of Friction–µ

1.2

Run No. 1 Run No. 2 Run No. 3 Arithmetical average

1.0 0.8 0.6 0.4 0.2 0

40

80

120 160 200 240 Normal Pressure, psi

280

320

Figure€4.31 Hample’s low-pressure testing results at 500°F for rough concrete showing data scatter. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

out as a joint effort by the National Aeronautics and Space Administration (NASA), the Federal Aviation Administration (FAA), and the aircraft industry. The program focused on evaluation of the rolling resistance, braking, and cornering performance of three different tire types encompassing the ground operational speed range for commercial aircraft. Bias-ply, radialbelted, and H-type 40 × 14 size tires were tested. Bias-ply tires had been used on aircraft since shortly after the 1903 Wright brothers’ flight. Beginning in the mid-1970s, tire engineers turned their attention to radial-belted tires for aircraft use because of the potential for operational and economic advantages over bias-ply construction. Early radial-belted tire testing suggested the possibility of improvements in cornering performance, reduced rolling resistance, and greater tread life, as well as other benefits. A purpose of the START Program was to gain a better understanding of both the benefits and possible disadvantages of radialbelted vs. bias-ply aircraft tires. The testing program was conducted at NASA Langley’s Aircraft Landing Dynamics Facility, which features an 853-m (2,800-ft) long portland cement concrete test track runway. The concrete’s macrotexture was determined to have an average surface roughness depth of 0.0129 cm (0.0051 in.), as measured by the NASA grease sample technique [14]. The three types of tires were tested for cornering performance on a dry runway surface employing a 5.44 × 104-kg (60-ton) carriage operating at a speed of 185 km/h (100 knots). The carriage was capable of applying normal loads of up to 111 kN (25,000 lb) and was instrumented to measure the

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72 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces total side friction force (FS) developed at various tire yaw angles of interest. Application of yaw angles by the pilot is necessary both for steering and to counter a crosswind. Tire performance was assessed using the side coefficient of rubber friction (µS), defined as µS = FS/FN.



(4.2)

The three tire types had tread compounds of equal Shore hardness (69), but had different tread patterns. Their possible differences in rubber compounding, and thus adhesion propensity, were not reported. Five values of FN were applied to each of the three tire types in the dry testing: 22.2 kN (5,000 lb), 44.5 kN (10,000 lb), 66.7 kN (15,000 lb), 89.0 kN (20,000 lb), and 111.2 kN (25,000 lb). Figure€4.32 presents plots of µS values vs. applied normal loads at six different yaw angles for the bias-ply design, calculated from the data presented in the Yager et al. [13] article. Figure€4.33 presents plots of µS values vs. applied 0.8

0.7

Side Coefficient of Friction–µs

0.6

0.5

Yaw angle 12°

0.4

9° 7°

0.3

5°

0.2

0.1

0

2° 1°

0 10 20 30 40 50 60 70 80 90 100 110 120 Applied Normal Force (FN)–kN

Figure€4.32 Side coefficient of friction testing of bias-ply tires at six yaw angles on a dry, portland cement concrete runway. (From Yager, T.J, Stubbs, S.M., and Davis, P.M., Paper 901931, Emerging Technologies in Aircraft Landing Gear, SAE International, Warrendale, PA, 1997.)

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73

0.8

0.7

Side Coefficient of Friction–µs

0.6

0.5 Yaw angle

0.4

9° 7°

0.3

5° 0.2 3° 0.1

0

2° 1° 0 10 20 30 40 50 60 70 80 90 100 110 120 Applied Normal Force (FN)–kN

Figure€4.33 Side coefficient of friction testing of radial-belted tires at six yaw angles on a dry, portland cement concrete runway. (From Yager, T.J, Stubbs, S.M., and Davis, P.M., Paper 901931, Emerging Technologies in Aircraft Landing Gear, SAE International, Warrendale, PA, 1997.)

normal load at six different yaw angles for the radial-belted tires, calculated in the same manner. Figure€4.34 presents plots of µS values vs. the applied normal load at five different yaw angles for the H-type tires, also calculated from the subject article. It is seen in these figures that at each yaw angle for all tire types, µS decreased as FN increased. 4.3.3 Rubber Friction on Gritted Floor Tile In addition to testing smooth floors with the NBS pendulum device, Sigler et al. [4] also used this tester to obtain antislip coefficients on dry floor tile containing Alundum® grit, a fused-alumina product. Figure€4.35 depicts the results of this test. The antislip coefficient diminished with increasing values of FN. Table 4.1 presents the gritted-tile data.  Registered trademark of Norton Company, Worcester, MA.

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74 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 0.7

0.6

Side Coefficient of Friction–µs

Yaw angle 0.5

9° 7°

0.4

5°

0.3

0.2

2° 1°

0.1

0

0 10 20 30 40 50 60 70 80 90 100 110 120 Applied Normal Force (FN)–kN

Figure€4.34 Side coefficient of friction testing of H-type tires at five yaw angles on a dry, portland cement concrete runway. (From Yager, T.J, Stubbs, S.M., and Davis, P.M., Paper 901931, Emerging Technologies in Aircraft Landing Gear, SAE International, Warrendale, PA, 1997.)

4.4

Coefficient of Rubber Friction on Wet, Smooth Surfaces

4.4.1

Rubber Friction on Oil-Coated Surfaces

In 1953, Denny [15] published the results of a large-scale, laboratory-controlled, coefficient-of-rubber-friction investigation involving wet surfaces. He was particularly interested in the effects of pressure increase on the real area of adhesive contact developed in such conditions, carrying out dynamic testing with nine different rubber formulations over a five-orders-of-magnitude loading range. All of Denny’s specimens were molded against smooth, polished steel and slid at a constant velocity of 0.01 cm/sec (0.025 in./sec). To encompass the desired range of applied pressures available in the laboratory testing device, Denny varied the areas of the rectangular specimens from 0.08 to 100 cm2 (0.012 to 1.55 in.2), with a maximum loading of 50 kg (110 lb). In most of the testing, these flat specimens were bonded to the underside of a flat metal plate to which the loads were applied from above. In the very high pressure range, exceeding 100 kg/cm2 (1422 psi), it was found convenient to use cylindrical specimens enclosed in recesses in the loading plate,

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75

1.0

Antislip Coefficient

0.9

0.8

0.7

0.6

0.5 0

1

2

3 4 5 6 7 8 9 10 11 12 Applied Normal Load (FN)–lbs

Figure€4.35 Variable-load testing with a rubber test foot on a rubber tile containing fused alumina grit using the NBS pendulum-impact tester. (Taken from Sigler, P.A., Geib, M.N., and Boone, T.H., J. Res. Nat. Bur. Stds., 28, 439, 1942.)

so that about 0.01 cm (0.0254 in.) of the rubber sample protruded. This was done because Denny considered that any detectable increase in the apparent contact area of his specimens, when compressed against the track, should be avoided. (In preliminary very-high-pressure testing, Denny decreased the thickness of the rectangular specimens as much as practicable, but found that an increase in apparent contact area still occurred.) 4.4.1.1 Testing with Smooth Rubber Specimens In the largest portion of his study, producing more than 150 measured friction values, Denny employed a polished steel track coated with olive oil. A generalized depiction of the findings from this portion is presented in Figure€4.36. This testing thus included the following independent, or potentially independent, variables: • Applied normal load, • Rubber specimen thickness, • Rubber specimen shape, and • Rubber specimen size.

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Log of Coefficient of Friction (µ) Times A Constant (A)

76 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Log of Applied Normal Pressure Divided by Compression Modulus of Rubber–(PN/E0) Figure€4.36 Generalized depiction of results from Denny’s coefficient of rubber friction (μ) testing on a polished steel track coated with olive oil. (Based on Denny, D.F., Proc. Phys. Soc. London, 66, 9 – B, 721, 1953.)

Denny found that, in all of this testing with the above independent, or potentially independent, variables, the coefficient of rubber friction “decreased markedly” with increased pressure. Citing Roth et al. [1], Thirion [2], and Schallamach [3], Denny concluded that Thirion’s equation apparently applies to rubber over the pressure range 0.96 kPa (0.014 psi) to above 9.88 MPa (1,422 psi). The curve in Figure€4.36 represents Thirion’s equation, which Denny formulated as:

1/µ = A(1 + BPN/ E0),

(4.3)

where A is a coefficient that depends on the conditions of testing that ranged in value from 1 to 8, B is a coefficient Denny found equal to about 15 in all cases, and E0 is the compression modulus for the rubber formulation involved. Equation 4.3 was utilized to back-calculate the µ values reported by Denny for the following rubber compounds, including their nominal hardness; neoprene 90, mixed reclaim 80, silicone 80, silicone 60, natural 60, Hycar 90, Hycar 75, and Hycar 60. Figure€4.37(a) presents the calculated µ vs. PN curves for the neoprene 90, natural 60, Hycar 60, and silicone 60 formulations. Figure€4.37(b) depicts the corresponding plots for Denny’s other specimens. As Denny noted, the friction coefficients decrease with increasing pressure. 4.4.1.2 Testing with Roughened Rubber Specimens To test the effects on friction development from roughening rubber surfaces, Denny abraded smooth-molded Hycar 75 specimens with emery cloth and slid them on a smooth, ploy-(methyl methacrylate) track coated with a light mineral oil lubricant. Figure€4.38 presents a generalized depiction of

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Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber a)

77

0.60

0.50 Coefficient of Friction–µ

Hycar 60 0.40

0.30

0.20

0.10 Silicone 60 0

b)

Neoprene 90

Natural 60 0 10 20 30 40 50 60 70 80 90 100 110 120 Applied Normal Pressure (PN)–kg/cm2

0.40

0.35

Coefficient of Friction–µ

0.30

0.25

Hycar 90

0.20

0.15 Hycar 75

0.10 Silicone 80

0.05

0

0

Reclaim 80

10 20 30 40 50 Applied Normal Pressure (PN)–kg/cm2

Figure€4.37 (a) Coefficient of rubber friction testing on a polished steel track coated with olive oil; and (b) coefficient of rubber friction testing on a polished steel track coated with olive oil. (From Denny, D.F., Proc. Phys. Soc. London, 66, 9 – B, 721, 1953.)

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78 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Smooth rubber

Log-Coefficient of Friction–µ

a

a Rough rubber

b

b

Log of Applied Normal Pressure (PN) Figure€4.38 Generalized depiction of results from Denny’s coefficient of friction testing on a smooth, poly-(methyl methacrylate) track coated with light mineral oil showing effect of roughness of rubber surface. (Based on Denny, D.F., Proc. Phys. Soc. London, 66, 9 – B, 721, 1953.)

his findings with this protocol. It is seen that, in the lower loading range, roughening the tested rubber surface diminished the measured µ values in comparison to the smooth-molded samples. At higher pressures, the plots are coincident. This finding on a wet surface is consistent with our Chapter 3 discussions of the rubber friction mechanisms arising in dry conditions: roughening a rubber surface in constant-velocity sliding on a smooth material can decrease frictional resistance to motion, apparently because of a reduction in the real area of adhesive contact between the two solids. Denny considered that the friction measured in his wet studies involving smooth tracks arose from partial adhesion over this real area of contact. The straight-line segments, a–a (low pressure) and b–b (high pressure), of the curves in Figure€4.38 were used to back-calculate Denny’s reported measurements from this portion of his investigation. Figure€4.39 presents these calculated values for the low-pressure testing range. As with his smoothmolded specimens slid on a polished steel track lubricated with olive oil, the coefficient of rubber friction for the roughened Hycar 75 specimens wetted with light mineral oil diminished with increasing pressure. We can also note that the µ values for the abraded Hycar 75 samples are lower than those for the smooth-molded rubber. Figure€4.40 presents the calculated results from Denny’s high-pressure testing (straight-line segment b–b) for the smooth and abraded Hycar 75. In this case, the plots are coincident. The inverse friction coefficient ¹/µ vs. PN relationship is observed again.

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79

0.80

Coefficient of Friction–µ

0.75

Smooth rubber

0.70 0.65 Roughened rubber 0.60 0.55 0

0

0.1 0.2 0.3 0.4 0.5 Applied Normal Pressure (PN)–kg/cm2

0.6

Figure€4.39 Coefficient of rubber friction testing on a smooth, poly-(methyl methacrylate) track coated with light mineral oil showing effect of roughness of rubber surface. (From Denny, D.F., Proc. Phys. Soc. London, 66, 9 – B, 721, 1953.)

0.1 0.09 Coefficient of Friction–µ

0.08 0.07

Smooth rubber and Roughened rubber

0.06 0.05 0.04 0.03 0.02 0.01 0

0

50 100 150 Applied Normal Pressure (PN)–kg/cm2

200

Figure€4.40 High-pressure coefficient of friction testing on a smooth, poly-(methyl methacrylate) track coated with a light mineral oil depicting coincidence of smooth and roughened rubber plots. (From Denny, D.F., Proc. Phys. Soc. London, 66, 9 – B, 721, 1953.)

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80 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 4.4.2 Walking-Surface Slip-Resistance Testing of Wet Work Boots Determining that wide differences in the slip-resistance characteristics of footwear had been reported over a long period of time, Tisserand carried out an analysis of various factors that can contribute to pedestrian slips and falls. These included the character of the floor surface, smooth or rough, and contaminant-related factors such as the viscosity and depth of liquid films present. Tisserand was also concerned with the tractive properties of shoe sole and heel materials, the potential benefits of their different tread patterns, and the long-term effects of wear on such patterns. Assuming that any concurrent contribution to slip resistance from wear can be ignored for a particular slip-and-fall incident, Tisserand concluded that friction developed between dry or wet walking surfaces and an elastomeric shoe heel or sole can be expressed as

FT = FA + FHb.

(4.4)

Tisserand realized that relatively few pedestrian slip-and-fall incidents occur on dry, horizontal floors; and because liquid contaminants can reduce the magnitude of the FA term, he concluded that laboratory footwear slipresistance testing should be carried out on wet surfaces. Further analyses led him to the opinion that, by 1977, considerable progress had been made by manufacturers of safety shoes in providing adequate traction. His studies of work-shoe traction, however, led him to the opposite conclusion, and he undertook slip-resistance testing of this footwear type. Tisserand conducted his traction investigations utilizing the dynamic INRS (Institut National de Recherche et de Sécurité) whole-shoe testing device that allows application of a normal load to be made inside a horizontal shoe at the heel and toe positions by employing an artificial foot. He selected a sliding velocity of 20 cm/sec (7.9 in./sec). Figure€4.41 presents a generalized depiction of his µ vs. FN results for two selected work shoes sliding on stainless steel coated with ordinary engine oil. In both cases, the coefficient of rubber friction decreased with increasing applied normal load. 4.4.3 Walking-Surface Slip-Resistance Testing of Wet Safety Shoes In 1995, Grönqvist [17] reported findings from a walking-surface slip-resistance study of three types of new and used safety shoes with dissimilar tread patterns. The study encompassed various testing parameters and environmental conditions. Its protocol employed an artificial foot device of his own design, an apparatus that operates dynamically and is capable of controlled variation of shoe (heel) contact angle, sliding speed, and applied normal load. As part of this investigation, Grönqvist examined the variation of μ vs. PN obtained from new samples of five different molded shoe sole materials: thermoplastic (TP), nitrile rubber (NR), styrene rubber (SR), polyurethane (PU), and polyvinylchloride (PVC). Three tread patterns were involved: (1) rectan-

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Coefficient of Friction–µ

Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber

81

Work shoe A

Work shoe B

Applied Normal Force (FN) Figure€4.41 Generalized depiction of results from Tisserand’s coefficient of rubber friction (μ) testing of two unidentified work shoes. (Based on Tisserand, M., Ergonomics, 7, 1027, 1985.)

gular, (2) waveform, and (3) triangular. The rectangular pattern was formed with asperities possessing an arithmetic average roughness (Ra) of 9 × 10−4 cm (3.54 × 10−4 in.). Both the waveform and triangular patterns were molded to exhibit a smooth surface with a Ra equal to 2 × 10−4 cm (7.87 × 10−5 in.). All of the μ-versus-PN testing was carried out at room temperature on a smooth stainless steel floor lubricated with glycerol having a viscosity of 200 cP (89% by weight). Grönqvist considered this combination to represent “very slippery” walking conditions. The sample contact angle with the steel flooring was 0° (flat), with a horizontal sliding speed of 0.4 m/sec (1.31 ft./sec). Like Denny [15], Grönqvist utilized differently sized samples for testing. Only one size (1,000 mm2, 155 in.2) was tested at more than one PN value. This discussion of the variation of the rubber coefficient of friction with applied normal load will be limited to Grönqvist’s data obtained from the 1,000-mm2 (155-in.2) specimens. Figure€4.42 presents Grönqvist’s μ-versus-PN results for the nitrile rubber with waveform (NRw) and triangular (NRt) tread patterns and the styrene specimens with the same patterns, SRw and SRt. Figure€4.43 illustrates the variation of μ with PN for the thermoplastic rubber (TR), polyvinylchloride (PVC), and polyurethane (PU), all with rectangular tread patterns. As seen in the two figures, all parings exhibit reductions in μ with increasing PN. 4.4.4 ANOVA Slip-Resistance Testing of Wet, Elastomeric Shoe Heels In addition to carrying out analysis-of-variance slip-resistance testing of dry, elastomeric shoe heels, Redfern and Bidanda [11] (see Section 4.2.6) also conducted an ANOVA investigation assessing the effects on μ of three floor lubricants — water, SAE 10 oil, and SAE 30 oil. As in their dry studies, they averaged the slip-resistance results over floor type, heel strike angle, and sliding velocity.

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82 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

0.25

SRw

Coefficient of Friction–µ

0.20

SRt

0.15 NRt 0.10

NRw NRt = Nitrile rubber with triangular tread pattern NRw = Nitrile rubber with waveform tread pattern SRt = Styrene rubber with triangular tread pattern SRw = Styrene rubber with waveform tread pattern

0.05

0

0

250

500 750 1000 1250 Applied Normal Pressure (PN)–kPa

1500

Figure€4.42 Coefficient of friction vs. applied normal pressure test results from nitrile and styrene rubber shoe materials with different tread patterns sliding on stainless steel flooring lubricated with glycerol. (Data from Grönqvist, R., Ergonomics, 38, 224, 1995.)

1.0 Coefficient of Friction–µ

0.9 0.8

PU

0.7

PVC

0.6 0.5 0.4 0.3

TR = Thermoplastic rubber PVC = Polyvinylchloride PU = Polyurethane

0.2 0.1 0

0

250

TR

500 750 1000 1250 Applied Normal Pressure (PN)–kPa

1500

Figure€4.43 Coefficient of friction vs. applied normal pressure test results from thermoplastic rubber, PVC, and polyurethane shoe materials with rectangular tread patterns sliding on stainless steel flooring lubricated with glycerol. (Data from Grönqvist, R., Ergonomics, 38, 224, 1995.)

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83

Figures€4.44 through 4.46 present the Redfern and Bidanda measurements obtained with water, SAE 10 oil, and SAE 30 oil lubricants, respectively, paired with rubber, urethane, and PVC heels. For all nine wet-data sets, μ diminishes with increasing FN. Because of an analysis to be detailed in Chapter 5, we can expect that hyperbolic curves for these test results would be evidenced if three or more values of FN had been applied. For this reason, the curved lines between the corresponding data points in the figures are dashed. 1.0 Coefficient of Friction–µ

0.9

Lubricants Water

0.8 0.7 0.6 0.5 0.4

SAE 10 oil

0.3

SAE 30 oil

0.2 0.1 0

0

1

2 3 4 5 6 Applied Normal Force (FN)–kg

7

8

Figure€4.44 Coefficient of friction vs. applied normal force from ANOVA testing of a rubber shoe heel wetted by three lubricants. (Data taken from Redfern, M.S. and Bidanda, B., Ergonomics, 37, 511, 1994.)

Lubricants

Coefficient of Friction–µ

0.4

Water

0.3

SAE 10 oil

0.2

SAE 30 oil

0.1 0

0

1

2 3 4 5 6 Applied Normal Force (FN)–kg

7

8

Figure€4.45 Coefficient of friction vs. applied normal force from ANOVA testing of a urethane shoe heel wetted by three lubricants. (Data taken from Redfern, M.S. and Bidanda, B., Ergonomics, 37, 511, 1994.)

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84 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Coefficient of Friction–µ

0.4

Lubricants Water

0.3 SAE 10 oil

0.2

SAE 30 oil 0.1 0

0

1

2 3 4 5 6 Applied Normal Force (FN)–kg

7

8

Figure€4.46 Coefficient of friction vs. applied normal force from ANOVA testing of a PVC shoe heel wetted by three lubricants. (Data taken from Redfern, M.S. and Bidanda, B., Ergonomics, 37, 511, 1994.)

4.5

Coefficient of Rubber Friction on Wet, Textured Surfaces

4.5.1

Smooth-Rubber Friction Testing on Roughened, Oil-Coated Surfaces

To test the effects on smooth-molded rubber friction in lubricated conditions from roughening the contacted surface, Denny [15] transversely abraded four smooth poly-(methyl methacrylate) tracks with various grades of emery cloth and then coated them with a light mineral oil. He slid Hycar 90 specimens on these tracks at a constant speed of 0.01 cm/sec (0.0039 in./sec). The desired nominal pressures were obtained as described in Section 4.4.1. This testing thus included the following independent, or potentially independent, variables: • Applied normal load, • Rubber specimen thickness, • Rubber specimen shape, and • Rubber specimen size. Figure€4.47 presents a generalized depiction of Denny’s findings with this protocol. On logarithmic coordinates, the plots were nearly parallel under low pressures. At the highest pressures, however, the apparent effects of track roughness became more noticeable. As exemplified in Section 4.4.1, Equation 4.3 was utilized to calculate Denny’s reported μ values. Figure€4.48 presents these measurements from the low-pressure testing. The roughest tracks produced the highest coefficients

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85

Increasing Track Roughness

Log of Coefficient of Friction–µ

Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber

Log of Applied Normal Pressure (PN) Figure€4.47 Generalized depiction of results from Denny’s coefficient of friction testing of smooth Hycar 90 rubber on roughened poly-(methyl methacrylate) tracks coated with light mineral oil. (Based on Denny, D.F., Proc. Phys. Soc. London, 66, 9 – B, 721, 1953.)

0.95

Centerline average track roughness 1.62 µm

Coefficient of Friction–µ

0.90

0.85 1.37 µm 0.80

0.75

0.70

0.38 µm

Coincident plots for 0.25 µm and 0.01 µm

0.65 0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Applied Normal Pressure (PN)–kg/cm2

Figure€4.48 Low-pressure coefficient of friction testing on a roughened, poly-(methyl methacrylate) track coated with a light mineral oil depicting effects of different centerline average track roughness. (Data from Denny, D.F., Proc. Phys. Soc. London, 66, 9 – B, 721, 1953.)

8136.indb 85

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86 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces of rubber friction. The center-line-average roughness for the five surfaces were 10−6, 2.5 × 10−5, 3.8 × 10−5, 1.37 × 10−4, and 1.62 × 10−4 cm (3.94 × 10−7, 9.75 × 10−6, 1.5 × 10−5, 5.4 × 10−5, and 6.38 × 10−5 in.), respectively. There was no difference in the measured coefficients between the A and B tracks in Figure€4.48 — they are coincident. In all four plots seen in the figure, μ decreases with increasing PN. Figure€4.49 illustrates the calculated coefficients from Denny’s high-pressure testing. In this case, the A and B curves are differentiated. Like the lowpressure μ values, their values all diminished under increasing pressure. 4.5.2 Tire Friction Testing with a Skid-Test Trailer in Wet Conditions In 1951, the state of Tennessee designed and constructed a two-wheeled trailer for evaluating tire friction forces developed on roadways possessing various texture characteristics [18]. Figure€4.50 depicts the trailer’s basic configuration. As seen in the figure, the left wheel was equipped with an air brake so it could be locked during skid testing. The skid-test trailer accom0.60

Coefficient of Friction–(µ)

0.50

Center line average track roughness 1.62 µm

0.40 1.37 µm 0.30

0.20

0.38 µm

0.10

0.25 µm 0.01 µm

0

0

50 100 150 200 Applied Normal Pressure (PN)–kg/cm2

250

Figure€4.49 High-pressure coefficient of friction testing on a roughened, poly-(methyl methacrylate) track coated with a light mineral oil depicting effects of different centerline average track roughness. (From Denny, D.F., Proc. Phys. Soc. London, 66, 9 – B, 721, 1953.)

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87

Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber

RPM generator

5'–2''

2'-2''

Auxiliary drawbar Test drawbar

Free rolling wheel

Air brake Speed & drawbar force recorder

Static Weight

On test wheel On free rolling wheel On drawbar at hitch Total trailer weight

871 lb. 870 lb. 199 lb. 1940 lb.

Test Wheel PLAN Removable weights

Bourdon pressure gauge Drawbar hitch 1'–1½''

+ L = 5'-8'' Side View

4'-2'' Rear View

Figure€4.50 Configuration of trailer designed by the State of Tennessee for measurement of tire friction forces developed on roadway surfaces. (From Clayton, J.H., An Investigation and Modification of a Pavement SkidTest Trailer, MS thesis, The University of Tennessee, Knoxville, 1962.)

modated removable weights for applying normal loads. The towing vehicle was usually a 1,814-kg (2-ton) truck. Because pavements are usually much more skid-resistant when dry than when wet, roadway surfaces are often traction-tested in the wet condition. In the Tennessee design, the towing vehicle carried an 1,892-L (500-gallon) tank with an air-operated, quick-opening valve controlling water flow from a sprinkler bar located at the rear of the truck. The skid-test trailer results reported by Clayton [18] to be discussed below were obtained on asphaltic concrete roads wetted in this manner. The towing vehicle was driven so that the test wheel tracked in the usual path of the left wheels of typically sized automobiles. Clayton chose to examine a worst-case skidding scenario by employing smooth tires (670-15) throughout his investigation. Some skid-test trailers are equipped with a drawbar instrumented to measure the force required to tow the trailer when the test wheel is locked. In the Tennessee arrangement, the other forces of interest included those arising from the static weight on the test wheel, the static weight on the free-rolling wheel, and the static weight on the drawbar at the hitch. By definition, the pavement-tire coefficient of friction (μ) was assumed equal to FT divided by FN, where FT is the total horizontal tire-pavement friction force at the contact patch during a skid, and FN is the vertical reaction on the tire in this nominal area.

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88 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

T

W P

H

Point m

L

FT

FN

Figure€4.51 Configuration of truck and trailer designed by the State of Tennessee for measurement of tire friction forces developed on roadway surfaces. (From Clayton, J.H., An Investigation and Modification of a Pavement Skid-Test Trailer, MS thesis, The University of Tennessee, Knoxville, 1962.)

The coefficient μ for skid-test trailers of this configuration may be quantified by taking a summation of moments about the hitch point m in Figure€4.51. Thus, (L)(W) − (L)(FN) − (H)( FT) = 0

or

(L)(W) − (L)(FT/μ) − (H)(FT) = 0,

where: L = the distance from the skid-test trailer hitch to the center of the test wheel axle, H = the distance from the pavement to the hitch, and W = the static normal load on the skid tire. This may be expressed as

W − FT/μ −H/L = 0.

Solving for μ, one obtains

μ = FT/[W − (H/L)(FT,)].

(4.5)

If we assume that P, the drawbar force needed to tow the trailer during a skid, is equal to FT, then

μ = P/[W − (H/L)(P)].

(4.6)

Figure€4.52 presents the results of Clayton’s studies to determine the effect on μ from increases in tire inflation pressure at four different test speeds. In all cases, μ decreased with increasing tire pressure.

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89

Pavement-Tire Coefficient of Friction–µ

1.0 10 mph

0.8

0.6

20 mph 30 mph

0.4

40 mph

0.2

0.0 20

25

30 35 40 Tire Pressure (PSIG)

45

50

Figure€4.52 Results of skid-test studies to determine the effect on the coefficient of friction μ from increases in tire pressure at four different test speeds. (From Clayton, J.H., An Investigation and Modification of a Pavement Skid-Test Trailer, MS thesis, The University of Tennessee, Knoxville, 1962.)

4.5.3 Bias-Ply and Radial-Belted Aircraft Tire Friction on a Wet, Ungrooved, Portland Cement Concrete Runway As part of the NASA START Program discussed in Section 4.3.2, Yager et al. [13] conducted radial-belted tire evaluations on the Langley test facility concrete runway when it was wetted with water. Tire performance was again assessed using the side coefficient of rubber friction, µS. The same three tire designs compared in the dry study — bias-ply, radial-belted, and H-type — were employed in the wet investigation. The desired degree of runway wetness was provided by a water sprinkler system installed alongside 548 m (1800 ft.) of the test section. Figure€4.53 presents plots of µS vs. applied normal load at five different yaw angles for the bias-ply design, calculated from the data presented in the Yager et al. article. Unlike the magnitude of the dry bias-ply results of Figure€4.32, which are in rank order of increasing yaw angle, the coefficients for the two largest yaw angle plots in Figure€4.53, 7° and 9°, fell below the μ values of the 5° yaw test. Additionally, all the yaw-angle relationships depicted in Figure€4.53 are horizontal; that is, the side coefficient of rubber friction for the tested bias-ply design appears to be constant for the given conditions. The measured coefficients in one of the (dry) Mori et al. [8] rubber-friction test results obtained on Teflon discussed in Section 4.2.5 were also constant. Hypothesized explanations for the constant coefficients found by Yager et al. and Mori et al. will be

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90 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

0.09

Yaw angle 5°

Side Coefficient of Friction–µs

0.08 0.07

7°

0.06

9°

0.05

2°

0.04 0.03 0.02

1°

0.01 0

0 10 20 30 40 50 60 70 80 90 100 110 120 Applied Normal Force (FN)–kN

Figure€4.53 Side coefficient of friction testing of bias-ply tires at five yaw angles on a wet, portland cement concrete runway. (From Yager, T.J, Stubbs, S.M., and Davis, P.M., Paper 901931, Emerging Technologies in Aircraft Landing Gear, SAE International, Warrendale, PA, 1997.)

incorporated into a unified theory of rubber friction formulated in Chapter 5. Figure€4.54 presents plots of three µS vs. applied normal load data sets at various yaw angles presented in the Yager et al. article for the radial-belted tire design. Data from three other yaw angle tests for this design are too inconsistent for present purposes and will not be discussed. The µS values seen in Figure€4.54 all decreased with increasing FN. Figure€4.55 presents plots of µS vs. FN for the H-type tire at three different yaw angles. As occurred with the radial-belted design, data from three other yaw tests for the H-type tire are too inconsistent for the present analysis and are not considered. Unlike all µS-vs.-increasing-FN test values previously discussed, the H-type tire rubber exhibits increasing coefficients of rubber friction with increasing normal loading.

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91

0.22 0.20 0.18

Yaw angle 5°

Side Coefficient of Friction–µs

0.16 0.14 0.12 0.10 0.08 2° 0.06 0.04

1°

0.02 0

0 10 20 30 40 50 60 70 80 90 100 110 120 Applied Normal Force (FN)–kN

Figure€4.54 Side coefficient of friction testing of radial-belted tires at three yaw angles on a wet, portland cement concrete runway. (From Yager, T.J., Stubbs, S.M., and Davis, P.M., Paper 901931, Emerging Technologies in Aircraft Landing Gear, SAE International, Warrendale, PA, 1997.)

4.5.4 Lubricated-Rubber Friction Testing with Smooth Spheres 4.5.4.1 Slow-Speed Testing with Lubricated Smooth Spheres As discussed in Section 3.10, Bowden and Tabor [9] discussed comparison friction tests involving sliding and rolling steel spheres of two sizes on rubber under well-lubricated conditions at a speed of a few millimeters per second. This was done to quantify bulk deformation hysteresis in the rubber. It was found that, up to a pressure of about 2.76 MPa (400 psi), FHb measurements were in close agreement between the two types of motion. At higher pressure, however, the FHb values diverged, apparently because of breakdown of the lubricating soap film, allowing an adhesion contribution (FA) to develop. The testing examined by Bowden and Tabor discussed in Section 3.10 was carried out by Greenwood and Tabor [19]. These Greenwood and Tabor data

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92 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Yaw angle 9°

0.20

7° 12°

0.18

Side Coefficient of Friction–µs

0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0

0 10 20 30 40 50 60 70 80 90 100 110 120 Applied Normal Force (FN)–kN

Figure€4.55 Side coefficient-of friction-testing of H-type tires at three yaw angles on a wet, portland cement concrete runway. (From Yager, T.J, Stubbs, S.M., and Davis, P.M., Paper 901931, Emerging Technologies in Aircraft Landing Gear, SAE International, Warrendale, PA, 1997.)

were utilized to calculate the coefficients of sliding friction that conformed to Bowden and Tabor’s FHb theory; that is, up to about 2.758 MPa (400 psi). These calculated results are presented in Figure€4.56. Two measurements with 0.635-cm (0.25 in.) diameter spheres and four measurements with 0.3175-cm (1/8-in.) diameter spheres conformed to the theory. In both cases, μ increased with increasing FN. The trends of these plots are consistent with the Bowden and Tabor parabolic equation for macrohysteresis, as qualified in Section 3.10:

μHb = c(FN)1/3.

(4.7)

Because only two data points are available for the 0.635 cm (0.25 in.) plot, the line is dashed. Figure€4.57 presents the three 0.38-cm (1/8-in.) diameter sphere measurements above 2.76 MPa (400 psi) by Greenwood and Tabor that did not

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Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber

93

0.11

¼ In sphere

Bulk Deformation Hysteresis–µHb

0.10

⅛ In sphere

0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

0

5 10 15 Applied Normal Force (FN)–lbs

20

Figure€4.56 Bulk deformation hysteresis testing of steel spheres sliding on rubber well lubricated with a soap solution. (From Bowden, F.P. and Tabor, D., The Friction and Lubrication of Solids, Part II, Clarendon Press, Oxford, 1964.) 0.09 0.08

⅛–In diameter steel sphere

Coefficient of Friction–µ

0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

0

1 2 3 4 5 6 7 8 9 10 Applied Normal Force (FN)–lbs

Figure€4.57 Coefficient-of-friction testing of a steel sphere sliding on rubber lubricated with a soap solution in which the film coating appeared to have broken down. (From Bowden, F.P. and Tabor, D., The Friction and Lubrication of Solids, Part II, Clarendon Press, Oxford, 1964.)

8136.indb 93

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94 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces conform to the Bowden and Tabor FHb theory. It is seen that μ increased as FN increased. 4.5.4.2 High-Speed Testing with Lubricated Smooth Spheres Sabey [20] carried out lubricated-rubber friction studies similar to the testing of Greenwood and Tabor [19] but focused specifically on the skid resistance of motor vehicle tires. Sabey idealized road-surface aggregate as spherical and derived an equation for the pressure distribution developed when a smooth, rigid sphere penetrates an elastic plane under load. Sabey applied the expression to analysis of coefficient-of-friction measurements of steel spheres sliding on tire-tread rubber when well lubricated with water. She utilized spheres of 0.48 cm (3/16 in.), 0.64 cm (0.25 in.), 0.95 cm (3/8 in.), 1.27 cm (0.5 in.), 1.91 cm (0.75 in.), and 2.22 cm (7/8 in.) diameter at a sliding speed of 1.83 m/sec (6 fpsec), up to a pressure of 5.86 MPa (850 psi). Figure€4.58 depicts Sabey’s results for the 0.48-cm (3/16-in.) and 0.64-cm (0.25 in.) diameter spheres. They were similar to those obtained by Greenwood and Tabor: a parabolic relationship between μ and FN appears to exist. The 0.9-cm (3/8-in.) sphere, whose measurements were insufficiently uniform for the current analysis and are not presented here, appears to be a size that falls in a transition range, after which μ varies hyperbolically with FN. Sabey’s hyperbolic data for the 1.27-cm (0.5 in.) sphere are also presented in Figure€4.58. 4.5.5 Lubricated-Rubber Friction Testing with Smooth Cones Sabey also investigated the friction forces developed when sharper road-surface aggregate, idealized as smooth rigid cones, penetrate tire-tread rubber at 1.83 m/sec (6 fpsec) when well lubricated with water. She also derived an equation for the pressure distribution under load in these conditions, basing it on the diameter of the cone at its deepest penetration and its interior apex angle. Figure€4.59 presents Sabey’s coefficient-of-friction results for this protocol. The plots are hyperbolic for interior apex angles of 70°, 90°, 100°, and 160°. For this study, pressures ranged up to 7.24 MPa (1,050 psi). For all four apex angles, μ decreased as FN increased.

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Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber 0.40

Sphere diameter

0.35

3/ 16

in. ¼ in.

0.30 Coefficient of Friction–µ

95

0.25

0.20

0.15 ½ in. 0.10

0.05

0

0 5 10 15 Applied Normal Force (FN)–lbs

Figure€4.58 Coefficient-of-friction testing of steel spheres sliding on tire-tread rubber lubricated with water. (Taken from Sabey, B.E., Proc. Roy. Soc. A, 71, 979, 1958.)

1.0

Interior apex angle

Coefficient of Friction–µ

0.9

70°

0.8 0.7 0.6 0.5

90°

0.4

100°

0.3 0.2 0.1 0

160° 0

5 10 15 Applied Normal Force (FN)–lbs

Figure€4.59 Coefficient-of-friction testing of a steel cones with various interior apex angles sliding on tire-tread rubber lubricated with water. (From Sabey, B.E., Proc. Roy. Soc. A, 71, 979, 1958.)

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96 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

4.6

Constant (Metallic) Coefficient-of- Friction Equation Not Applicable to Rubber

4.6.1

Review of the Analyzed Data

As mentioned in Chapter 3, Kummer [21] cautioned that relating friction forces to applied loads by division to obtain coefficients is not always meaningful and should be done only when it is completely justified. This chapter has presented a survey of rubber coefficient-of-friction test results in which the independent variable was applied normal force or pressure. A total of 132 data sets from the literature were utilized to assess whether the constant (metallic) coefficient-of-friction equation has been found applicable to rubber friction in practice. We have seen that it is not. The relationships of the µ values to applied loads for the 132 data sets are presented in Tables 4.2–4.5. Of the 132 data sets, 12 were of parabolic form in which µ increased with increasing PN or FN, while 114 were hyperbolic, Table€4.2 Characteristics of Test Results from Rubber Sliding on Dry, Smooth Surfaces Investigators

Tests Examined

Relationship between μ and PN or FN

Roth, Driscoll and Holt [1] (Automobile tire-tread rubber)

2

μ decreased as PN and FN increased

Thirion [2] (Gum rubber)

2

μ decreased as PN and FN increased

Schallamach [3] (Natural rubber)

3

μ decreased as PN and FN increased

Sigler, Geib and Boone [4] (Natural Rubber)

5

μ decreased as FN increased

Hurry and Prock [5] (Industrial belting)

4

μ increased as FN increased

Bartenev and Lavrentjev [6] (Natural rubber)

3

μ decreased as PN increased

Hample [7] (Aircraft tire rubber)

12

μ decreased as PN increased

Mori et al. [8] (Surface-modified rubber)

5 1

μ decreased as FN increased μ constant as FN increased

Redfern and Bidanda [11] (Shoe sole materials)

3

μ decreased as FN increased

Pfalzner [12] (Automobile tire-tread rubber)

3

μ increased then decreased as FN increased

5

μ decreased as FN increased

Total

47

μ = coefficient of rubber friction. PN = applied normal pressure. FN = applied normal force.

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Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber

97

Table€4.3 Characteristics of Test Results from Rubber Sliding on Dry, Textured Surfaces Investigators

Tests Examined

Relationship between μ and PN or FN

Sigler et al. [4] (Natural rubber)

1

μ decreased as FN increased

Hample [7] (Aircraft-tire rubber)

8

μ decreased as PN increased

Yager et al. [13] (Aircraft tires)

17

μ decreased as FN increased

Total

26

μ = coefficient of rubber friction. PN = applied normal pressure. FN = applied normal force.

Table€4.4 Characteristics of Test Results from Rubber Sliding on Wet, Smooth Surfaces Investigators

Tests Examined

Relationship between μ and PN or FN

Redfern and Bidanda [11] (Shoe sole materials)

9

μ decreased as FN increased

Denny [15] (Hycar, neoprene, reclaim, silicone, and natural rubber)

10

μ decreased as FN increased

Tisserand [16] (Shoe sole materials)

2

μ decreased as FN increased

Grönqvist [17] (Shoe sole materials)

7

μ decreased as PN increased

Total

28

μ = coefficient of rubber friction. PN = applied normal pressure. FN = applied normal force.

in that µ diminished with increasing PN or FN. Six data sets were consistent with the constant coefficient of friction expression, µ = FT/FN. One of these consistent sets involved sliding purposely reduced, low surface-freeenergy rubber on Teflon in dry conditions, an unusual set of circumstances. The other five consistent sets were obtained through side-force coefficient testing of bias-ply aircraft tires on a wet concrete runway. The six data sets evidence constant friction coefficients because of the rubber friction mechanisms developed during this testing. These mechanisms are physically and chemically different from those of metallic friction.

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98 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Table€4.5 Characteristics of Test Results from Rubber Sliding on Wet, Textured Surfaces Investigators

Tests Examined

Relationship between μ and PN or FN

Yager et al. [13] (Aircraft tires)

6

Denny [15] (Hycar rubber)

5

μ decreased as PN increased

Clayton [18] (Automobile tires)

4

μ decreased as PN increased

Greenwood and Tabor [19] (Natural rubber)

3

μ increased as FN increased

Sabey [20] (Tire-tread rubber)

5 2

μ decreased as FN increased μ increased as FN increased

Total

25

5

μ decreased as FN increased μ constant as FN increased

μ = coefficient of rubber friction. PN = applied normal pressure. FN = applied normal force.

4.6.2 Deformational and Constitutive Differences between Rigid Metals and Visco-Elastic Rubber As is common knowledge among scientists and engineers, and has been explained on a mechanistic basis in Chapter 2, the coefficient of friction for smooth metals (μm) is constant over a wide loading range. Under varying loads, however, we have seen that the coefficient of rubber friction as it is presently used is not generally constant. Over a wide loading range, the constant, smooth-metal coefficient of friction is independent of the nominal area of contact of the two surfaces involved. In Chapter 3, we saw from the testing of Roth et al. [1] (Figures€3.2a and 3.2b) and also from Thirion’s [2] study (Figure€3.3b), that μ is not always independent of the nominal contact area. Differences between the characteristics of metallic and rubber friction coefficients arise because of differences in their friction-force-producing mechanisms. These mechanisms are different because of dissimilarities between the physical and chemical properties of their constituents. In metallic friction, most contacting asperity tips on the two paired surfaces are in the plastic loading range. As discussed by Rabinowicz [22], contacting metallic asperities under compression bond by “cold welding.” Rubber asperity tips in contact with their paired surfaces remain elastomeric. Rubber adherence in this situation is by van der Waals’ adhesion, developed from surface free energy, a much weaker bonding mechanism than metallic cold welding. The analysis presented above involving the relationships between μ and FN and PN illustrated why the constant (metallic) coefficient-of-friction expression does not apply to rubber. Chapter 5, which develops a new, unified theory of rubber friction, further differentiates between the friction-forceproducing mechanisms of visco-elastic rubber and those of rigid metals.

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Metallic Coefficient-of-Friction Equation Does Not Apply to Rubber

4.7

99

Chapter Review

The laws of metallic friction have been inadvertently adopted by many engineers as their technical basis for all friction calculations, regardless of the materials involved. The metallic-friction equation is routinely utilized to quantify friction in rubber products, including tires and shoe heels and soles. This practice has resulted in an unnecessary, consensus approach to rubber friction analysis that lacks a foundation in physics. At present, engineering design of the friction characteristics of rubber products and their paired surfaces is seldom carried out scientifically. The chapter presented a survey of 132 rubber coefficient-of-friction (μ) test results. The testing included protocols involving rubber sliding on dry, smooth surfaces; on dry, textured surfaces; on wet, smooth surfaces; and on wet, textured surfaces. It was demonstrated that the metallic coefficient-of-friction equation does not apply to rubber. This is so because the laws of metallic friction do not apply to rubber friction. Differences between the characteristics of metallic and rubber friction arise because of differences in their friction-force-producing mechanisms. These mechanisms are different because of dissimilarities between the physical and chemical properties of metal and rubber. As discussed by Rabinowicz [22], frictional bonding between contacting metallic surfaces under compression is by “cold welding.” Rubber surfaces in contact with their paired materials under load remain elastic. Rubber adhesion in this situation arises from a much weaker bonding mechanism than metallic cold welding. Chapter 5, which develops a new, unified theory of rubber friction, further differentiates between the friction-force-producing mechanisms of elastic rubber and those of rigid metals.

References

8136.indb 99

1. Roth, F.L., Driscoll, R.L., and Holt, W.L., Frictional properties of rubber, J. Res. Nat. Bur. Stds., 28, 439, 1942. 2. Thirion, P., Les coefficients d’adhérence du caoutchouc, Rev. Gén. Caoutch., 23, 101, 1946. 3. Schallamach, A., The load dependence of rubber friction, Proc. Phys. Soc. London B, 65, 657, 1952. 4. Sigler, P.A., Geib, M.N., and Boone, T.H., Measurement of the slipperiness of walkway surfaces, J. Res. Nat. Bur. Stds., 40, 339, 1948. 5. Hurry, J.A. and Prock, J.D., Coefficients of friction of rubber samples, India Rubber World, 128, 619, 1953. 6. Bartenev, G.M. and Lavrentjev, V.V., The law of vulcanized rubber friction, Wear, 4, 154, 1961.

2/13/08 3:02:13 PM

100 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

8136.indb 100

7. Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955. 8. Mori, K., Kaneda, S., Kanae, K., Hirahara, H., Oishi, Y., and Iwabuchi, A., Influence on friction force of adhesion force between vulcanizates and sliders, Rubber Chem. Techn., 67, 797, 1994. 9. Bowden, F.P. and Tabor, D., The Friction and Lubrication of Solids, Part II, Clarendon Press, Oxford, U.K., 1964. 10. Johnson, K.L., Kendall, K., and Roberts, A.D., Surface energy and the contact of elastic solids, Proc. Roy. Soc. A, 324, 301, 1971. 11. Redfern, M.S. and Bidanda, B., Slip resistance of the shoe-floor interface under biomechanically relevant conditions, Ergonomics, 37, 511, 1994. 12. Pfalzner, P.M., On the friction of various synthetic and natural rubbers on ice, Can. J. Res. F, 28, 468, 1950. 13. Yager, T.J., Stubbs, S.M., and Davis, P.M., Aircraft radial-belted tire evaluation, Paper 901931, Emerging Technologies in Aircraft Landing Gear, Tanner, J.A. et al., Eds., SAE International, PT-66, Warrendale, PA, 1997. 14. Leland, T.J.W., Yager, T.J., and Joyner, U.T., Effects of Pavement Texture on WetRunway Braking Performance, NASA TN D-4323, 1968. 15. Denny, D.F., The influence of load and surface roughness on the friction of rubber-like materials, Proc. Phys. Soc. London 66, 9 – B, 721, 1953. 16. Tisserand, M., Progress in the prevention of falls by slipping, Ergonomics, 28, 1027, 1985. 17. Grönqvist, R., Mechanisms of friction and assessment of slip resistance of new and used footwear soles on contaminated floors, Ergonomics, 38, 224, 1995. 18. Clayton, J.H., An Investigation and Modification of a Pavement Skid-Test Trailer, M.S. thesis, The University of Tennessee, Knoxville, TN, 1962. 19. Greenwood, N.A. and Tabor, D., The friction of hard sliders on lubricated rubber: the importance of deformation losses, Proc. Phys. Soc., 71, 989, 1958. 20. Sabey, B.E., Pressure distributions beneath spherical and conical shapes pressed into a rubber plane, and their bearing on coefficients of friction under wet conditions, Proc. Roy. Soc. A, 71, 979, 1958. 21. Kummer, H.W., Unified Theory of Rubber and Tire Friction, Engineering Research Bulletin B-94, The Pennsylvania State University, State College, PA, 1966. 22. Rabinowicz, E., Friction and Wear of Materials, 2nd ed., J. Wiley & Sons, New York, 1995.

2/13/08 3:02:13 PM

5 A Unified Theory of Rubber Friction

5.1

Introduction

This chapter examines the hypothesis formulated by Savkoor [1] in 1965 that a surface-deformation-hysteresis friction mechanism can develop in rubber when it slides on a harder material. As discussed in Chapter 3, Savkoor accepted that macroscopically smooth surfaces, such as plate glass, can be microscopically rough. His hysteresis posit was based on the supposition that rubber surfaces in contact with microscopic asperities on harder solids can mechanically interlock with each other, providing deformational resistance to relative movement between the two materials. Further analyses of the rubber friction test data discussed in Chapters 3 and 4 of this book, as well as detailed examination of new material indicating the existence of such a microhysteretic mechanism, are presented here. This new analytical evidence for a surface-deformation-hysteresis mechanism in rubber suggests that this mechanism develops a constant friction force (FHs), independent of applied normal force or pressure. Incorporating an FHs force in the phenomenological approach to understanding the interplay of sliding rubber with its paired surfaces appears to provide a basis for more accurately differentiating and quantifying the friction mechanisms that can develop in such circumstances.

5.2

Rubber Microhysteresis Development on Macroscopically Smooth Surfaces

5.2.1

Roth, Driscoll, and Holt

Figure€3.2(a) presented the rubber coefficient-of-friction test results reported by Roth et al. [2] on two differently sized, rectangular specimens sliding on glass. Figure€3.2(b) depicted their data expressed as μ vs. FN. To analyze these data for the presence of microhysteresis, the coefficients and pressures seen in Figure€3.2(a) were utilized to back-calculate the unreported FT forces 101

8136.indb 101

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102 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Table€5.1 Back-Calculated Values of Forces and Adhesion Friction Ratios for the Small* Rubber Specimen Developed during the Dynamic, Variable Pressure Friction Testing of Roth et al. Pressure (psi)

FN (lb)

μ

FT (lb)

FHs (lb)

FA (lb)

FA/FN (μA)

7.5

2.64

3.35

8.84

3.0

5.84

2.2

10.0

3.52

3.25

11.48

3.0

8.48

2.4

15.0

5.28

3.10

16.37

3.0

13.37

2.5

20.0

7.04

2.95

20.77

3.0

17.77

2.5

30.0

10.56

2.78

29.36

3.0

26.36

2.5

40.0

14.08

2.73

38.44

3.0

35.44

2.5

FN = applied normal load. μ = coefficient of friction value on Roth et al. [2] plot. FT = total measured frictional resistance. FHs = indicated friction contribution from surface deformation hysteresis. FA = friction contribution from adhesion. μA = rubber adhesion friction ratio. * Small specimen area = 0.35 in.2 60

Friction Forces–lbs

50 40 30 20 10 0

0

5 10 15 20 Applied Normal Load (FN)–lbs

Figure€5.1 Back-calculated friction forces using the smallspecimen test data reported by Roth et al. (From Roth, F.L., Driscoll, R.L., and Holt, W.L., J. Res. Nat. Bur. Stds., 28, 439, 1942.)

8136.indb 102

indicated by the faired curve values associated with the experimental points on these plots. Table€5.1 presents back-calculated values for the small specimen, while Figure€5.1 is a plot of the determined friction forces and applied normal loads. The F T values for the small specimen plot to a straight line in Figure€5.1. The line does not pass through the origin but, when extrapolated, intercepts the y-axis at a value of about 1.4 kg (3 lb). Because there should be no significant cohesion losses or bulk deformation hysteresis resistance between the Roth et al. [2] rubber specimens and their plate glass test track, only adhesion and microhysteresis, if it is present, are likely to be represented in this line. In the physical sense, the presence of a y-intercept on rectangular coor-

2/13/08 3:02:14 PM

A Unified Theory of Rubber Friction

103

dinates can mean that each FT value on the intercepting line contains contributions from two sources, one numerically a constant at all x-axis values. A y-intercept value in Figure€5.1 is consistent with a 1.4 kg (3 lb) FHs contribution at all normal loads arising from a microhysteretic resistance on a macroscopically smooth surface that remains constant with increases in FN. As shown in Figure€5.1, subtraction of 1.4 kg (3 lb) from each calculated FT point yields a straight, parallel line passing through the origin when extrapolated. (The subtracted points are omitted for clarity.) Assuming that the y-intercept value can be regarded as a microhysteretic force, the line through the origin represents only a van der Waals’ adhesion contribution to friction, FA. Because the FA vs. FN line is straight, the adhesion force appears to be increasing in direct proportion to the applied normal load: FA divided by FN, or µA, is a constant; thus,

FA = µAFN.

(5.1)

In this testing range, the reported Roth et al. [2] results appear to be expressible as

FT = FHs + µAFN.

(5.2)

As seen in Table€5.1, the value of µA is about 2.5. The combined van der Waals’ adhesion forces from the two surfaces were of sufficient magnitude to develop an adhesion ratio above unity. As shown later in this chapter, µA for rubber is not always constant at higher loads. It will, therefore, be termed the rubber adhesion friction ratio, rather than the coefficient of friction, to emphasize this point and to avoid confusion with the metallic coefficient of friction. Figure€5.2 presents a plot of µA vs. FN for the small specimen. A constant relationship is depicted in much of the test loading range. At the lowest FN values, however, where the indicated magnitude of FHs exceeds FN or is close to it, two calculated adhesion friction ratios are below the others. Possible reasons for this are the numerical uncertainties associated with the back-calculation process. Further discussion of this issue is presented in Chapter 6. An identical approach to the one described above was used with the Roth et al. large-specimen data. Figure€5.3 is a plot of the back-calculated results. A straight line passing through the ordinate at about 0.7 kg (1.5 lb) was obtained, indicating an FHs contribution of that amount. Subtraction of 0.7 kg (1.5 lb) from the large specimen FT values again yields a straight, parallel line through the origin. Figure€5.4 depicts µA vs. FN with a generally constant ratio of about 2.8. At the lowest load applied in the test, one µA value is below the others. As depicted in Figure€5.4, once the indicated microhysteresis force is accounted for, the large rubber specimen exhibits a somewhat larger adhesion friction ratio (2.8) than does the smaller test sample’s ratio (2.5). As a

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104 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Adhesion Friction Ratios–µA

4.0

3.0

2.0

1.0

0

0

5

10

15

20

Applied Normal Load (FN)–lbs Figure€5.2 Back-calculated adhesion friction ratios using the small-specimen test data reported by Roth et al. (From Roth, F.L., Driscoll, R.L., and Holt, W.L., J. Res. Nat. Bur. Stds., 28, 439, 1942.) 60

Friction Forces–lbs

50 40 30 20 10 0

0

5 10 15 20 Applied Normal Load (FN)–lbs

25

Figure€5.3 Back-calculated friction forces using the large-specimen test data reported by Roth et al. (From Roth, F.L., Driscoll, R.L., and Holt, W.L., J. Res. Nat. Bur. Stds., 28, 439, 1942.)

result, the adhesive friction plot for the larger specimen is above that for the smaller sample, reversing their positions from Figure€3.2(a). To assist in understanding the theorized FHs mechanism, FT vs. PN plots for the small and large Roth et al. specimens are presented in Figure€5.5. It is

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105

A Unified Theory of Rubber Friction

Adhesion Friction Ratios–µA

3.0

2.0

1.0

0

0

5 10 15 Applied Normal Load (FN)–lbs

20

Figure€5.4 Back-calculated adhesion friction ratios using the large-specimen test data reported by Roth et al. (From Roth, F.L., Driscoll, R.L., and Holt, W.L., J. Res. Nat. Bur. Stds., 28, 439, 1942.) 50 45

Total Friction Forces–lbs

40

Large specimen

35 30 25

Small specimen

20 15 10 5 0

0

5

10 15 20 25 30 35 Applied Normal Pressure (PN)–psi

40

Figure€5.5 Back-calculated friction forces using the small- and large-specimen test data reported by Roth et al. plotted against applied normal pressure. (From Roth, F.L., Driscoll, R.L., and Holt, W.L., J. Res. Nat. Bur. Stds., 28, 439, 1942.)

seen that the same intercept values as in the FT vs. FN plots are produced: 1.36 kg (3 lb) and 0.68 kg (1.5 lb), respectively. This indicates that FHs is independent of both applied normal force and pressure.

8136.indb 105

2/13/08 3:02:16 PM

106 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Figure€5.5 indicates another point of interest: the small Roth et al. rubber specimen of the composition used in tire treads apparently exhibited directly proportional adhesive friction development up to 275.8 kPa (40 psi). This is in the pressure range employed in some motor vehicle tires. 5.2.2 Thirion A back-calculation friction force analysis similar to the one carried out on the Roth, Driscoll, and Holt [2] data was employed with Thirion’s [3] rubber test results from his two differently sized, rectangular specimens sliding on glass. Graphing the calculated forces yields two FT vs. FN plots evidencing extrapolated y-intercepts. Figure€5.6 presents the small-specimen data, indicating a FHs value of 3.5 kg (7.7 lb). Figure€5.7 illustrates the large-specimen data, suggesting an FHs value of 6 kg (13.2 lb). Subtracting these intercepts from the corresponding faired curve points produces parallel lines passing through the origin in the low-loading ranges. Thirion’s data are also consistent with the presence of separable rubber friction contributions from microhysteresis and van der Waals’ adhesion produced on macroscopically smooth surfaces. In contrast to the FHs values obtained from the back-calculation Roth et al. analysis, Thirion’s larger specimen data indicate a larger y-intercept, 6 kg (13.2 lb), than does his smaller sample’s 3.5 kg (7.7 lb). We revisit this issue later in the chapter. 25

Friction Forces–kg

20

15

10

5

0

0

5 10 15 20 Applied Normal Load (FN)–kg

25

Figure€5.6 Back-calculated friction forces using the small-specimen test data reported by Thirion. (From Thirion, P., Rev. Gén. Caoutch., 23, 101, 1946.)

8136.indb 106

2/13/08 3:02:17 PM

107

A Unified Theory of Rubber Friction 40 35

Friction Forces–kg

30 25 20 15 10 5 0

0

5

10 15 20 25 Applied Normal Load (FN)–kg

30

35

Figure€5.7 Back-calculated friction forces using the large-specimen test data reported by Thirion. (From Thirion, P., Rev. Gén. Caoutch., 23, 101, 1946.)

Also unlike the analysis of the Roth et al. data, the back-calculated friction forces from Thirion’s tests exhibited straight lines only in the lower FN range. At higher loadings, the plots curved parabolically in a way consistent with the increasing adhesion force, but at a slower rate than the applied normal load. Furthermore, as seen in Figures€5.6 and 5.7, subtraction of y-intercept values in the parabolic range produced parallel, curved lines. While this is expected graphically, we will see below that additional analysis suggests that the parallel, parabolic curves produced by subtraction represent a real rubber friction phenomenon. It is worth noting that while the Roth et al. pressure ranged up to 275.8 kPa (40 psi), Thirion’s maximum pressure was higher, about 1.52 MPa (220 psi). Both back-calculated µA values obtained from Thirion’s data are presented in Figure€5.8. In the lower loading range, the adhesion friction ratios for the two specimens are constant and appear to be approximately equal, with a ratio of about 1.2 to 1.3. At greater loads, Thirion’s FA/FN relationships are hyperbolic. As shown in Figures€5.9 and 5.10, graphing the back-calculation results from Thirion’s data on logarithmic coordinates is instructive. Figure€5.9 presents the FA vs. FN plots for both specimen sizes. The parabolic portions of the curves in Figures€5.6 and 5.7 have been rectified.

8136.indb 107

2/13/08 3:02:18 PM

Adhesion Friction Ratio–µA

108 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 13 kg

1.5

22 kg Large specimen

1.0 Small specimen

0.5 0

0

5

10 15 20 25 Applied Normal Load (FN)–kg

30

35

Figure€5.8 Back-calculated adhesion friction ratios using the small- and large-specimen test data reported by Thirion. (From Thirion, P., Rev. Gén. Caoutch., 23, 101, 1946.)

Adhesion Friction Force (FA)–kg

100

22 kg

50

Large specimen

20 10

13 kg

5

Small specimen

3 2 1

1

2

3 5 10 20 50 Applied Normal Load (FN)–kg

100

Figure€5.9 Back-calculated adhesion friction forces using the small- and large-specimen test data reported by Thirion plotted on logarithmic coordinates in terms of applied normal load showing the adhesion transition forces F Nt. (From Thirion, P., Rev. Gén. Caoutch., 23, 101, 1946.)

Both data sets yield straight, parallel lines at lower loadings with differently sloped, parallel straight lines in a higher FN range. The initial straight lines in each set on Cartesian coordinates are still parallel to each other on logarithmic coordinates but, as expected mathematically, they are now oriented at an angle of 45° with the x-axis. If we apply the generalized, hyperbolic Hertz expression for FA vs. FN relationships, FA = cA(FN)m, (Equation 3.8), the tangent of 45° (m) equals unity and FA = cA(FN)m reduces to μA = FA/FN. In addition, the higher-loading straight lines in each data set are also parallel to each other. The parallel orientation of these rectified parabolic segments tells us that their m values are equal, or at least approximately so.

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109

A Unified Theory of Rubber Friction 7 kg/cm2

Adhesion Friction Force (FA)–kg

50

Large specimen

10 Small specimen

5

1

1

5 10 20 50 Applied Normal Pressure (PN)–kg/cm2

Figure€5.10 Back-calculated adhesion friction forces using the small- and large-specimen test data reported by Thirion plotted on logarithmic coordinates in terms of applied normal pressure showing the adhesion transition pressure PNt. (From Thirion, P., Rev. Gén. Caoutch., 23, 101, 1946.)

Figure€5.9 may also be used to determine the approximate FN value at which µA for each specimen ceases to be constant and becomes hyperbolic. These values are 22 kg (48.4 lb) and 13 kg (28.6 lb) for the large and small specimens, respectively. The values correspond to the points at which the two straight lines for each specimen intersect. The FN values at which the small-specimen and large-specimen plots transition to hyperbolic, FNt, are also indicated in Figure€5.8. In this case, the transition value for the larger specimen is larger than the corresponding value for the smaller one. Figure€5.10, however, tells a different story. As seen in Figure€5.10, when Thirion’s data are expressed as FA vs. PN the pressure at which µA ceases to be constant — FA is no longer directly proportional — and becomes hyperbolic for both the small and large specimens, which we call the “adhesion transition pressure,” or PNt, is indicated to equal 7 kg/cm2 (100 psi). The adhesion transition pressure in sliding rubber appears to be a significant friction characteristic of this material, and it is the topic of Chapter 6. It was mentioned above that the parallel, parabolic curves produced by subtraction of y-intercept values from the parabolic portions of Thirion’s data appear to represent real rubber friction phenomena. The indicated equality of the adhesion transition pressures displayed by Thirion’s large and small specimens is consistent with this assertion. Only when the FHs values are subtracted from the total measured friction forces are the two adhesion transition pressures indicated by Thirion’s data equal.

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110 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 5.2.3 Schallamach Figure€3.4(a) presented the coefficient-of-friction test results reported by Schallamach [4] from his identically sized soft-, medium-, and hard-rubber specimens sliding on glass. The soft- and medium-rubber μ values yielded hyperbolic curves. Schallamach’s data points for the hard rubber, however, plotted to a straight line, part of which is dashed in the figure. As shown, he believed that a similar hyperbolic curve for the hard rubber coefficient-offriction measurements was to be expected, and he extrapolated the solid line for these data upward as a hyperbola. Figure€3.4(b) depicted the reported Schallamach results as μ vs. FN. Again we note two hyperbolae and a straight line corresponding to the specimens just discussed. By taking microhysteresis into account, however, the unexpected behavior of the hard-rubber friction results appears to be explained. Back-calculation friction force analyses carried out on the Schallamach results evidenced extrapolated y-intercepts for all three data sets. Subtraction of these apparent constants from the corresponding FT values also produced extrapolated plots that passed through the origin at lower loads. At higher loads, parallel parabolic curves were evident. The Schallamach data are also consistent with the presence of friction contributions from both surface deformation hysteresis and van der Waals’ adhesion produced on a macroscopically smooth surface. Figures€5.11, 5.12, and 5.13 present the back-calculated FT vs. FN plots for the soft-, medium-, and hard-rubber specimens, respectively. Like the Thirion data-analysis results, at higher loadings the Schallamach plots curve in a way consistent with the adhesion forces increasing at slower rates than do the FN values. The greatest pressure applied by Schallamach to his three samples was 2.25 kg/cm2 (32 psi). Figure€5.14 presents the FT vs. FN plots for the three different specimens on the same axes. We note in this figure that the back-calculated, extrapolated hard rubber plot crosses the other curves and “begins” at the lowest y-intercept value of the three specimens, about 0.4 kg (0.88 lb). The FHs values for the soft and medium samples are approximately 0.7 kg (1.54 lb) and 1.0 kg (2.2 lb), respectively. Figure€5.15 presents the back-calculated μA values for Schallamach’s soft-, medium-, and hard-rubber specimens. Like the Thirion data-analysis results seen in Figure€5.8, the Schallamach μA plots are constant in the lower loading ranges and hyperbolic at greater loads. One should note the difference, however, between the μ plots of Figure€3.4(a) and the μA plots of Figure€5.15. In Figure€5.15, the back-calculated μA values for the soft-, medium-, and hardrubber samples produce plots that have separated into rank order according to hardness. The hard-rubber plot does not cross the soft- and medium-rubber results as it did before microhysteresis was accounted for, but is now always above them. This implies that the van der Waals’ adhesion propensity increases with the hardness of these rubber specimens.

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111

A Unified Theory of Rubber Friction 12 11 10 9

Friction Forces–kg

8 7 6 5 4 3 2 1 0

0

1

2 3 4 5 6 Applied Normal Load (FN)–kg

7

8

Figure€5.11 Back-calculated friction forces using the soft-rubber specimen test data reported by Schallamach. (From Schallamach, A., Proc. Phys. Soc. London B, 65, 657, 1952.)

Exemplified by the back-calculation plots obtained from the Roth et al. [2], Thirion [3], and Schallamach [4] data, one can theorize that inadvertent inclusion of inherent FHs values in a so-called “adhesion” coefficient-of-friction curve can “anchor” that plot to a non-zero y-axis intercept. The microhysteresis value appears to determine the “starting point” of such curves, whatever the associated van der Waals’ adhesion forces may be. As is addressed later in this chapter, in connection with analysis of the Mori et al. [5] results, interplay between the surface free energy combined with the stiffness of rubber, and the microroughness of the harder, paired material, can be determinants of the elastomer’s FHs value. Apparently, while the subject hard rubber exhibited the highest adhesion, its hardness limited surface deformation hysteresis so that an FHs value of smaller magnitude was produced. Again, like Thirion’s data, graphing the back-calculated results from Schallamach’s measurements on logarithmic coordinates is instructive. Figure€5.16 presents the FA vs. FN plots for the three specimens. The hyperbolic portions of the curves in Figure€5.15 have been rectified. All data sets yield

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112 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 13 12 11 10

Friction Forces–kg

9 8 7 6 5 4 3 2 1 0

0

1

2 3 4 5 6 7 Applied Normal Load (FN)–kg

8

Figure€5.12 Back-calculated friction forces using the medium-rubber specimen test data reported by Schallamach. (From Schallamach, A., Proc. Phys. Soc. London B, 65, 657, 1952.)

straight, parallel lines at lower loadings with distinctly different, slightly nonparallel straight lines in a higher FN range. The nonparallel straight lines in Figure€5.16 begin where FA vs. FN first deviates from a straight line on rectangular coordinates. As shown in the rectified plots, this appears to occur at the same FN value for all three specimens, about 2.25 kg (5 lb). We are now able to formulate the constant adhesion-friction-ratio expressions for the Schallamach soft-, medium-, and hard-rubber specimens applicable to the lower loading ranges. The corresponding values of µA for these specimens are 2.04, 2.14, and 2.28, respectively. The expressions can be found in Table€5.2. Equation 3.8, FA = cA(FN)m, a generalized Hertz expression, can be applied to the rectified parabolic data in Figure€5.16 to quantify the van der Waals’ adhesion forces produced at higher loadings. The measured angles and their m values are 36° (0.726), 37° (0.753), and 38° (0.781), for the soft-, medium-, and hard-rubber samples, respectively. Because of the different rubber types, the slopes, and therefore the m values, are unequal.

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113

A Unified Theory of Rubber Friction 14 13 12 11 10

Friction Forces –kg

9 8 7 6 5 4 3 2 1 0

0

1

2 3 4 5 6 Applied Normal Load (FN)–kg

7

8

Figure€5.13 Back-calculated friction forces using the hard-rubber specimen test data reported by Schallamach. (From Schallamach, A., Proc. Phys. Soc. London B, 65, 657, 1952.)

By quantifying the values of cA as previously detailed, we can determine the equations expressing the hyperbolic portions of Schallamach’s FA vs. FN data. These relationships are presented in Table€5.3, along with the associated adhesion friction ratio equations, which are parabolic. It may be noted that the m values in Table€5.3 are unequal to the Hertzian value of 2/3. The deformation of the contacting asperities on Schallamach’s rubber samples does not conform to the Hertz model in the subject parabolic friction ranges. Although the µA values in Table€5.3 decrease with increasing FN, FA continues to increase as demonstrated by the positive exponent in the adhesive force expressions. A decrease in µA can be misleading unless the limitations of the friction ratios are kept in mind. It is of interest to compare the back-calculated µ A equations expressed in terms of pressure to the pressure-based µ relationships reported by

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114 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 15 Hard rubber

14

Medium rubber

13 12

Soft rubber

Total Measured Friction Force (FT)–kg

11 10 9 8 7 6 5 4 3 2 1 0

0

1

2 3 4 5 6 Applied Normal Load (FN)–kg

7

8

Figure€5.14 Back-calculated friction forces using the soft-, medium-, and hard-rubber specimen test data reported by Schallamach. (From Schallamach, A., Proc. Phys. Soc. London B, 65, 657, 1952.)

Schallamach. Pressure-based adhesion friction ratios in the hyperbolic range can be determined by employing Equation 3.10, µ A = c A(F N)-m, and converting to pressure. Dividing FN in Equation 3.10 by the specimen area (AS) to obtain pressure without changing the equality yields:

8136.indb 114



µA = cA(AS)–m[(FN)–m/(AS)–m], or



µA = cA(AS)–m[(PN)–m] = [cA/(AS)m][(PN)–m], and



µA = cP(PN)–m,

(5.3)

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115

Adhesion Friction Ratio–µA

A Unified Theory of Rubber Friction 2.25 kg

2.5 2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 0

Hard rubber

Medium rubber

Soft rubber 0

1

2 3 4 5 6 Applied Normal Load (FN)–kg

7

8

Figure€5.15 Back-calculated adhesion friction ratios using the soft-, medium-, and hard-rubber specimen test data reported by Schallamach. (From Schallamach, A., Proc. Phys. Soc. London B, 65, 657, 1952.)

Adhesion Friction Force (FA)–kg

15 10 2.25 kg

5

Medium rubber

Hard rubber

3 Soft rubber

1

0.9 1.0 1.5 2.0 2.5 3.0 4.0 5.0 6.0 Applied Normal Load (FN)–kg

8.0

Figure€5.16 Back-calculated adhesion friction forces using the soft-, medium-, and hard-rubber specimen test data reported by Schallamach plotted on logarithmic coordinates in terms of the applied normal load showing the adhesion transition force F Nt .(From Schallamach, A., Proc. Phys. Soc. London B, 65, 657, 1952.)

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116 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces where cP is the corresponding constant for pressure relationships. The three back-calculated, pressure-based adhesion friction ratios determined from the Schallamach data in the hyperbolic range are presented in Table€5.4. In accordance with Equation 5.3, the respective m values have not changed. For purposes of comparison, the μ relationships reported by Schallamach, which had apparently conformed to the Hertz model, are also included. Table€5.2 Back-Calculated Rubber Adhesion Forces and Adhesion Friction Ratios for Schallamach’s [A] Test Specimens in the Constant μA Range Soft rubber:

FA = 2.04FN

μA = 2.04

Medium rubber:

FA = 2.14FN

μA = 2.14

Hard rubber:

FA = 2.28FN

μA = 2.28

FA = adhesion friction force. µA = adhesion friction ratio. FN = applied normal force.

Table€5.3 Back-Calculated Rubber Adhesion Forces and Adhesion Friction Ratios for Schallamach’s Test Specimens in the Parabolic Range of Figure€5.14 Soft rubber: Medium rubber: Hard rubber:

FA = 2.49(FN)0.726

µA = 2.49(FN)–0.274

FA = 2.55(FN)

µA = 2.55(FN)–0.247

0.753

FA = 2.91(FN)0.781

µA = 2.91(v)–0.219

FA = adhesion friction force. µA = adhesion friction ratio. FN = applied normal force.

Table€5.4 Comparison of Back-Calculated Rubber Adhesion Friction Ratio Relationships in the Hyperbolic Range of Figure€5.14 to Schallamach’s Coefficient of Friction Equations Expressed in Terms of Applied Normal Pressure Back-Calculated

Schallamach

Soft rubber:

µA = 1.78(PN)–0.274

µ = 1.90(PN)–1/3

Medium rubber:

µA = 1.88(PN)–0.247

µ = 2.20(PN)–1/3

Hard rubber:

µA = 2.23(PN)–0.219

µ = 2.39(PN)–1/3

FA = adhesion friction force. μA = adhesion friction ratio. μ = rubber coefficient of friction. PN = applied normal pressure.

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117

A Unified Theory of Rubber Friction

Figure€5.17 presents the back-calculated FA vs. PN data plotted on logarithmic coordinates. Intersection of the straight lines in Figure€5.17 determines the PNt value where FA vs. PN first deviates from a straight line on Cartesian coordinates. As shown in the rectified plots, this appears to occur at the same PN value for all three specimens, about 0.66 kg/cm2 (64.7 kPa, 9.39 psi), the adhesion transition pressure, PNt. As a check of this analysis, we multiply the nominal specimen area, 3.4 cm2 (0.53 in.2), by the PN value of 0.66 kg/cm2 (64.7 kPa, 9.39 psi), to obtain 2.25 kg (4.95 psi), the adhesion transition force for the FA vs. FN plots. The FNt values for the three, constitutively different rubber samples are equivalent because their nominal areas are equal. 5.2.4 Bartenev and Lavrentjev Figure€4.3 presented the inverse coefficient-of-friction test results reported by Bartenev and Lavrentjev [6] from two vulcanized rubber specimens sliding on macroscopically smooth polished steel at 23°C (73.4°F). Because plot 2 in the figure apparently contains a variable inertial resistance force com15

Adhesion Friction Force (FA)–kg

10 0.66 kg/cm2

Medium rubber

Hard rubber

5

3 Soft rubber

1

0.25 0.3

0.5 0.8 1.0 1.5 2.0 Applied Normal Pressure (PN)–kg/cm2

2.5

Figure€5.17 Back-calculated adhesion friction forces using the soft-, medium-, and hard-rubber specimen test data reported by Schallamach plotted on logarithmic coordinates in terms of the applied normal pressure showing the adhesion transition pressure PNt. (From Schallamach, A., Proc. Phys. Soc. London B, 65, 657, 1952.)

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118 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces ponent, the plot 2 data were deemed unsuitable for the present analysis and were excluded from Table€4.2. The back-calculation technique was applied to the measurements reported in plot 1 of Figure€4.3. Figure€5.18 depicts the back-calculation results for this rubber-steel data set. An FHs value of about 8.5 kg (18.7 lb) is evidenced. Figure€5.19 presents the corresponding μA vs. FN ↜relationship. In the lower loading range, a constant adhesion friction ratio of approximately 0.23 is suggested. Figure€5.20 depicts the FA vs. FN data back-calculated from plot 1 in Figure€4.3 plotted on logarithmic coordinates to determine the FNt value. The adhesion transition force appears to be approximately 37 kg (81 lb). Figure€4.4 presented the inverse coefficient-of-friction test results reported by Bartenev and Lavrentjev [6] from their rubber specimens sliding on macroscopically smooth polished aluminum at 23°C (73.4°F) and 65°C (149°F). Figure€5.21 depicts the back-calculated FT vs. FN results for these two data sets. FHs values of 2.5 kg (5.5 lb) and 1.5 kg (3.3 lb) for the 23°C (73.4°F) and 65°C (149°F) tests, respectively, are indicated. Figure€5.22 portrays the μA vs. FN relationship for the 23°C (73.4°F) and 65°C (149°F) specimens from Figure€4.4. In the lower loading range of the 23°C (73.4°F) data, a constant μA value of approximately 0.39 is suggested. In 25

Friction Forces–kg

20

15

10

5

0

0

50 100 150 Applied Normal Load (FN)–kg

200

Figure€5.18 Back-calculated friction forces using the rubber-steel test data from plot 1 of Figure€4.3 reported by Bartenev and Lavrentjev. (From Bartenev, G.M. and Lavrentjev, V.V., Wear, 4, 154, 1961.)

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119

A Unified Theory of Rubber Friction 0.25

Adhesion Friction Ratio–µA

0.20

0.15

0.10

0.5

0

0

10

20

30

40 50 60 70 80 90 100 110 120 130 Applied Normal Load (FN)–kg

Figure€5.19 Back-calculated adhesion friction ratios using the rubber-steel test data from plot 1 of Figure€4.3 reported by Bartenev and Lavrentjev. (From Bartenev, G.M. and Lavrentjev, V.V., Wear, 4, 154, 1961.)

Adhesion Friction Force (FA)–kg

50

20

37 kg

10 5 3

1

5

10 20 30 50 100 Applied Normal Load (FN)–kg

200

Figure€5.20 Back-calculated adhesion friction forces using the rubber-steel test data from plot 1 of Figure€4.3 reported by Bartenev and Lavrentjev plotted on logarithmic coordinates in terms of applied normal load showing the adhesion transition force F Nt . (From Bartenev, G.M. and Lavrentjev, V.V., Wear, 4, 154, 1961.)

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120 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 23°C

40

35

Friction Forces–kg

30

25

20 65°C

15

10

5

0

0

50 100 150 200 Applied Normal Load (FN)–kg

250

Figure€5.21 Back-calculated friction forces using the rubber-aluminum test data from Figure€4.4 reported by Bartenev and Lavrentjev. (From Bartenev, G.M. and Lavrentjev, V.V., Wear, 4, 154, 1961.)

the lower loading range, the 65°C (149°F) specimen evidences a constant μA value of about 0.17. An attempt was made to determine the adhesion transition pressures for these two Bartenev and Lavrentjev [6] data sets. Unfortunately, the 65°C (149°F) data are too inconsistent to utilize this approach. As a consequence, dashed lines at the ends of the constant μA range and beginning of the hyperbolic segments of the adhesion friction ratio plot in Figure€5.22 is employed. Within the recognized limitations of the back-calculation technique, however, the different FHs values seen in Figure€5.21 suggest that surface deformation hysteresis is temperature dependent. These three Bartenev and Lavrentjev [6] data sets are consistent with the presence of friction contributions from both surface deformation hysteresis and van der Waals’ adhesion developed on macroscopically smooth surfaces. We now examine the possibility of microhysteresis development in a portable friction tester — a pendulum-impact device.

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121

A Unified Theory of Rubber Friction 0.40

0.35

23°C

Adhesion Friction Ratio–µA

0.30

0.25

0.20

0.15

0.10

65°C

0.05

0

0

50 100 150 200 Applied Normal Load (FN)–kg

250

Figure€5.22 Back-calculated adhesion friction ratios using the rubber-aluminum test data from Figure€4.4 reported by Bartenev and Lavrentjev. (From Bartenev, G.M. and Lavrentjev, V.V., Wear, 4, 154, 1961.)

5.2.5 Sigler, Geib, and Boone Figure€4.1 presented plots of antislip coefficients (μ) vs. FN from a portable pendulum-impact device used by Sigler et al. [7] to measure friction on five macroscopically smooth floors. Two of the plots were dashed because only two data points were obtained in those tests. The other three flooring materials had produced hyperbolic curves. The Tennessee marble and cellulose nitrate tile curves appeared to cross. These researchers utilized rubber for their test foot, conforming to the then-current (1948) U.S. Federal Specification ZZ-R-601a, Rubber Goods. The antislip coefficient values obtained by Sigler et al. were listed in Table€4.1. A back-calculation, friction force analysis was carried out on the data presented in Table€4.1. Extrapolated y-intercepts were evidenced for the rubber test foot on all five flooring materials. Subtraction of these values from their corresponding FT readings produced extrapolated plots that passed through the origin. These five pendulum-impact data sets are consistent with the presence

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122 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Total Measured Friction Force–lbs

of friction contributions from both surface deformation hysteresis and van der Waals’ adhesion developed on macroscopically smooth surfaces. Figure€5.23 presents the FT vs. FN plots for the standard rubber paired with the five flooring materials on the same axes. For clarity, the extrapolated portions of the FT vs. FN plots have been omitted, as have the plots obtained by subtracting y-intercept values from the corresponding FT measurements. As seen in Figure€5.23, the plotted points are consistent with straight lines in the loading ranges shown. In the figure, the plots for Tennessee marble and cellulose nitrate tile and the linoleum and rubber tile appear to cross. The extrapolated y-intercept values are 0.18 kg (0.4 lb), 0.23 kg (0.5 lb), 0.57 kg (1.25 lb), 0.68 kg (1.5 lb), and 0.68 kg (1.5 lb) for the asphalt tile, Tennessee marble, rubber tile, linoleum, and cellulose nitrate tile, respectively. Figure€5.24 illustrates the back-calculated antislip coefficient vs. FN relationships for these five smooth flooring materials paired with ZZ-R-601a Rubber tile

8 7

Linoleum

Asphalt tile

6

Cellulose nitrate tile

5 4 Tennessee marble

3 0

0

3

4 5 6 7 8 9 10 Applied Normal Load (FN)–lbs

11

12

Figure€5.23 Back-calculated friction forces using the standard rubber-in service flooring test data reported by Sigler et al. (From Sigler, P.A., Geib, M.N., and Boone, T.H., J. Res. Nat. Bur. Stds., 40, 339, 1948.) 0.9 Adhesion Friction Ratio–µA

Asphalt tile

0.8 0.7

Tennessee marble Rubber tile

0.6

Linoleum

0.5

Cellulose nitrate tile

0.4 0.3 0

0

3

4 5 6 7 8 9 10 Applied Normal Load (FN)–lbs

11

12

Figure€5.24 Back-calculated adhesion friction ratios using the standard rubber-in service flooring test data reported by Sigler et al. (From Sigler, P.A., Geib, M.N., and Boone, T.H., J. Res. Nat. Bur. Stds., 40, 339, 1948.)

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A Unified Theory of Rubber Friction

123

rubber. The antislip coefficients are 0.47, 0.54, 0.60, 0.67, and 0.88 for the cellulose nitrate tile, linoleum, rubber tile, Tennessee marble, and asphalt tile, respectively. It is immediately evident that the plots for Tennessee marble and cellulose nitrate tile do not cross, and neither do the linoleum and rubber tile plots. When the microhysteresis forces present are accounted for, and only adhesion is represented in the various plots, a clearer picture of the adhesive friction developed by these pairings is seen. Figure€5.24 also provides consistency to the impact device’s observed behavior during the subject testing. As indicated in Table€4.1 and depicted in Figure€5.24, the pendulum tester stalled on the asphalt tile and Tennessee marble at the highest load of 5.1 kg (11.2 lb), so that no friction measurements could be obtained. Stalling apparently occurred because the asphalt tile and Tennessee marble produced the highest adhesional friction resistance to movement under the highest loading. It should also be noted that the antislip-coefficient sequence for the five flooring materials is in precise reverse rank order of magnitude compared to the rubber FHs values obtained from these same surfaces. Recalling that Sigler et al. tested floors in actual service, this reverse rank order of the developed microhysteretic forces and adhesional antislip coefficients suggests an interesting implication: the subject in-service floors, all paired with the same rubber test foot, in part gave rise to the observed FHs values because the microroughness of these floors had experienced relative degrees of wear from prior pedestrian traffic corresponding to the observed antislip coefficient’s rank order. That is, the greater the adhesional propensity possessed by the subject five floors, the more smoothing of their microroughness occurred through adhesion-generated wear when contact with pedestrian shoe outsoles took place. 5.2.6 Mori et al. As discussed in Section 4.2.5, Mori et al. [5] conducted friction testing with acrylonitrile butadiene (NBR) and styrene butadiene (SBR) rubber in contact with macroscopically smooth aluminum and Teflon sliders at 20°C (68°F). The vulcanized specimens were formed in specially fabricated molds exhibiting different surface free energies. As a result, the NBR and SBR samples possessed “designed” surface free energies, while each retained its inherent bulk deformation properties. Use of low-surface-free-energy Teflon molds produced specimens with surfaces containing correspondingly low-surfacefree-energy butadiene groups. A mold with many polar groups, polyethylene terephthalate (a packaging film), yielded rubber surfaces with numerous high-surface-free-energy nitrile groups. Mori et al. employed a chrome-plated stainless steel mold to obtain intermediate surface-free-energy test samples. Figure€4.17 presented the Mori et al. test results for aluminum sliding on NBR. All three rubber specimens showed an initial decrease in the coefficient of friction followed by a constant, minimum segment. The rank order

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124 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces of the coefficient plots corresponded to the rank order of the combined surface free energies of the paired materials. Figure€4.19 presented the Mori et al. plots of their FT vs. FN measurements for NBR paired with aluminum. The researchers postulated that the slopes of the lines in Figure€4.19 represent the coefficients of adhesion friction for the three pairings. They extrapolated these lines to the FT axis, noting that intercept values were produced, and opined that the existence of measurable adhesive friction forces at zero load was therefore demonstrated. Mori et al. hypothesized that these no-load forces arose from the combinative effect of the surface free energies of the two materials involved. They cited the rubber adhesion pull-off test findings of Johnson et al. [8] to support this no-load, adhesion hypothesis, but Mori et al. did not carry out pull-off tests to determine if the resulting measurements matched the FT intercept values seen in Figure€4.19. Mori et al. intended to exclude all but the van der Waals’ adhesion mechanism in their testing. Although they cited Savkoor [1] and Moore [9], who discussed the potential existence of surface deformation hysteresis in sliding rubber, Mori et al. made no mention of the possible development of this mechanism in their article. The y-intercept values reported by Mori et al. in Figure€4.19 for the NBRaluminum, 0.3 N (0.7 lb), 1.6 N (0.35 lb), and 2.5 N (0.55 lb) for the low-, intermediate-, and high-adhesion rubber, respectively, are taken here to represent microhysteresis forces developed by the rubber in their tests. These FHs values were subtracted from the corresponding FT measurements and the resultants converted to adhesion friction ratios in the manner previously described. Figure€5.25 presents these ratios. Except for one low-adhesion-related data point High-adhesion

Adhesion Friction Ratios–µA

4

3

Rubber

Medium-adhesion Rubber

2

Low-adhesion

Rubber

1

0

0

1

2 3 4 5 Applied Normal Load (FN)–N

6

Figure€5.25 Back-calculated adhesion friction ratios using the NBR-aluminum test data reported by Mori et al. (From Mori, K., et al., Rubber Chem. Techn., 67, 797, 1994.)

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A Unified Theory of Rubber Friction

125

and two medium-adhesion-data points, the adhesion ratios appear generally constant. The apparently constant low-, intermediate-, and high-adhesion ratios were approximately 2.2, 3.0, and 3.85, respectively. We see that the FHs values associated with the NBR-aluminum pairing are in the same rank order of magnitude as the μA ratios produced by these pairings, from low adhesion to high adhesion. It should be noted that the FHs-μA rank-ordering behavior in the NBR-aluminum parings with one common tested surface exhibiting a constant microroughness and changing rubber composition is different from the Sigler et al. FHs-μA rank-ordering behavior with a constant, common rubber composition and changing tested surface presumably exhibiting different microroughness characteristics. In the Sigler et al. testing, the five differing floor surface microroughness configurations apparently accounted for the differing FHs values. In the Mori et al. data, the three differing surface free energies (adhesion propensities) appear to account for the differing FHs magnitudes. Nevertheless, these Mori et al. test results are consistent with the presence of friction contributions from both surface deformation hysteresis and van der Waals’ adhesion developed on macroscopically smooth surfaces. Figure€4.18 presented the Mori et al. test results for Teflon sliding on SBR. The two rubber specimens with the higher surface free energies showed an initial decrease in the coefficients of friction, followed by a constant minimum segment. The SBR-Teflon paring with the lowest combined surface free energies, however, told an apparently different story: μ is constant over the entire loading range. Mori et al. concluded that the relationship between the friction coefficients and FN for the SBR-Teflon results was essentially the same as for FN and the NBR-aluminum pairings. The five instances of coefficient decrease in the low loading ranges illustrated in Figures€4.17 and 4.18 were ascribed to an “enhancement” to the rubber adhesion forces involved produced by the higher surface free energies of these samples. Mori et al. postulated that the constant coefficient of friction at all loads in the lowest-adhesion SBR-Teflon plot seen in Figure€4.18 could be attributed to the combinative effect of the surface free energies of the Teflon and that SBR specimen. Their total energy was the lowest of the six mated surfaces tested. Mori et al. did not hypothesize a physical mechanism potentially explaining why the five pairings with the highest combined surface free energies exhibited decreasing coefficients, while the coefficient for the pairing with the lowest combined surface free energy failed to decrease in magnitude. The back-calculation friction force technique was applied to the three Mori et al. data sets from their SBR-Teflon testing depicted in Figure€4.18. The calculated FT vs. FN plots are presented in Figure€5.26. As depicted in this figure, the FT vs. FN plots for the highest and medium adhesion samples mimicked the NBR-aluminum pattern by showing extrapolated y-intercepts. In contrast, the extrapolated line representing the lowest adhesion SBR-Teflon specimen passed through the origin without the need to subtract a constant,

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Total Measured Friction Force (FT)–N

126 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

Highadhesion rubber

Intermediateadhesion rubber

Low-adhesion rubber 0

1

2 3 4 5 Applied Normal Load (FN)–N

6

Figure€5.26 Back-calculated friction forces using the SBR-Teflon® test data reported by Mori et al. (From Mori, K. et al., Rubber Chem. Techn., 67, 797, 1994.)

implying that no significant surface hysteresis force developed between the two materials in this pairing. Figure€5.27 presents the adhesion friction ratios for the SBR-Teflon pairings. All three adhesion plots appear constant. The apparently constant low-, intermediate-, and high-adhesion ratios were about 2.0, 2.0, and 2.2, respectively. The absence of a finite intercept value for the lowest adhesion SBR-Teflon pairing in Figure€5.26 is consistent with the difference in the shapes of the SBR coefficient-of-friction curves seen in Figure€4.18; that is, the shape of the calculated coefficient plot for the lowest adhesion sample was different from the other two. There was no measurable decrease in this coefficient over the loading range involved. This difference in shape suggests a causative link between the development of surface hysteresis forces in sliding elastomers and the hyperbolic coefficient-of-friction curves in the low loading range seen in most of the rubber friction data sets we have examined; that is, removing the indicated FHs forces from the total measured friction readings produced straight-line FA vs. FN plots passing through the origin and, at least initially, constant adhesion friction ratios. The initially decreasing segments of the Mori et al. coefficient curves are explained by these researchers’ unintentional inclusion of mechanistically different rubber surface hysteresis forces with the adhesive friction values. When the FHs/FN ratios become quantitatively negligible compared with the FA/FN ratios, the FT/FN plots become horizontal, at least until the adhesion transition loading range, if it is present. Mori et al. did not reach this range, their highest pressure being 14.5 kPa (2.1 psi).

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127

A Unified Theory of Rubber Friction 2.5

Adhesion Friction Ratio–µA

2.0

High-adhesion rubber

1.5

Intermediate-adhesion rubber Low-adhesion rubber

1.0

0.5

0

0

1

2 3 4 5 Applied Normal Load (FN)–N

6

Figure€5.27 Back-calculated adhesion friction ratios using the SBR-Teflon® test data reported by Mori et al. (From Mori, K., et al., Rubber Chem. Techn., 67, 797, 1994.)

This graphical phenomenon is depicted in Figure€5.28, a plot of FHs/FN vs. FN calculated from the Mori et al. highest adhesion NBR-aluminum FHs value reported in Figure€4.19. As shown in Figure€4.19, FHs equaled 2.5 N (0.55 lb). Graphing FHs/FN vs. FN yielded the hyperbolic curve in Figure€5.28, as expected when a constant is divided by an ever-increasing variable. At a FN value of 4 N (0.88 lb), the FHs/FN ratio equals 0.625. This may be compared to the µ value of about 4.2 for the subject specimen seen in Figure€4.17. The 2.5 N (0.55 lb) constant is tending toward insignificance at the 4-N (0.88-lb) applied load. The total measured ratio (FT/FN) is beginning to approach an asymptotically constant value in the figure because FA is increasing directly with FN, and FHs is becoming a smaller portion of FT. The results from the back-calculated analyses of the Mori et al. data also indicate that, while rubber microhysteresis appears to be mechanistically different from adhesion, the magnitudes of the FHs forces produced at least partially depend on the magnitude of the van der Waals’ forces present. Simply put, under a given set of conditions, the total adhesive strength (combined surface free energy from the paired materials) can be insufficient to produce surface deformation hysteresis in the pairing. Figure€4.18 presented the y-intercepts associated with the NBR-aluminum pairings. Their values decreased from about 2.5 N (0.55 lb) for the highest adhesion specimen to about 0.33 N (0.07 lb) for the lowest. As depicted in Figure€5.26, the back-calculated y-intercept values for the SBR-Teflon samples decreased from about 0.9 N (0.2 lb) to nil. In the Mori et al. protocols, the

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128 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Constant Microhysteresis Force/Applied Normal Load FHs/FN

2.0

1.0

0

0

1

2

3 4 5 6 Applied Normal Load (FN)–N

Figure€5.28 Plot of constant rubber microhysteresis force F Hs back-calculated using the NBR-aluminum test data reported by Mori et al., divided by applied normal load F N. (From Mori, K. et al., Rubber Chem. Techn., 67, 797, 1994.)

combined surface free energies of each pairing appear to determine whether microhysteresis develops. Apparently, the combined surface free energy of the lowest-adhesion SBR and the Teflon was insufficient to adhere the sliding rubber surface to the Teflon’s microroughness topography.

5.3

Rubber Microhysteresis Development on Macroscopically Rough Surfaces

5.3.1

Sigler, Geib, and Boone

Figure€4.35 presented a plot of the antislip coefficients vs. FN obtained by Sigler et al. when testing rubber tile containing Alundum grit. A hyperbolic curve is evident. Figure€5.29 presents the back-calculated FT vs. FN results from the Sigler et al. pendulum testing on the gritted tile. An FHs value of approximately 0.454 kg (1 lb) is evidenced. This data set is consistent with the presence of a friction contribution from surface deformation hysteresis on a macroscopically rough surface. Figure€5.30 illustrates the FT/FN ratio vs. FN relationship for the gritted tile. An apparently constant value of about 0.66 is observed. Because of contact with grit in the otherwise smooth, tested surface, both adhesion and

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Total Measured Friction Force (FT)–lbs

A Unified Theory of Rubber Friction

129

8 7 6 5 4 3 2 1 0

0

1

2

3 4 5 6 7 8 9 10 11 12 Applied Normal Load (FN)–lbs

Figure€5.29 Back-calculated friction forces using the standard rubber-in service flooring test data for the gritted rubber tile reported by Sigler et al. (From Sigler, P.A., Geib, M.N., and Boone, T.H., J. Res. Nat. Bur. Stds., 40, 339, 1948.) 0.7 Antislip Coefficient

0.6 0.5 0.4 0.3 0.2 0.1 0

0

1

2

3 4 5 6 7 8 9 10 11 12 Applied Normal Load (FN)–lbs

Figure€5.30 Back-calculated antislip coefficients with the microhysteresis force removed using the standard rubberin service flooring test data for the gritted rubber tile reported by Sigler et al. (From Sigler, P.A., Geib, M.N., and Boone, T.H., J. Res. Nat. Bur. Stds., 40, 339, 1948.)

bulk deformation hysteresis in the rubber test foot may have developed with increasing pendulum loading in this protocol. Nevertheless, the apparent microhysteresis force remained constant over the FN range involved. It is not known if the rubber in this tile was chemically identical to the rubber in the ungritted tile discussed in Section 5.2.5. 5.3.2 Chang Chang’s [10] dynamic friction testing, a pedestrian slip-resistance metrology investigation, focused on the roughness characteristics of walking surfaces.

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130 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces He reported and discussed correlation coefficients for 22 different surface texture parameters developed on the basis of his friction measurements. Chang did not address the possibility of an FHs force component in his test results. Of interest here are findings from a back-calculation analysis of Chang’s data that appear to cast additional light on the rubber microhysteresis mechanism. Chang’s study employed unglazed quarry tile, a Neolite® (Goodyear Tire and Rubber Company, Akron, Ohio) test liner pin-on-rotating-disk tester, and sandblasting. Neolite test liner is an elastomer commonly used in walking-surface slip-resistance metrology. The pins’ ends were configured into a hemispherical contacting surface. There were five tile test groups, each with its own preparation process. All tiles were first polished with an 80-grit aluminum oxide belt and then with 280-grit aluminum oxide paper, yielding uniformly smooth surfaces before sandblasting. Four tile groups were then roughened using the sandblasting technique, each with a different abrasive particle type, to obtain surfaces of different macroroughness. Various nozzle exit pressures and distances from the nozzle were employed. Process 1 produced the greatest macroroughness, which decreased through application of processes 2, 3, and 4. The fifth group of tiles was left smooth (process 5). The specimen preparation process parameters are summarized in Table€5.5. Three different normal loads were applied by the Neolite pin — 25 g (0.055 lb), 100 g (0.22 lb), and 250 g (0.55 lb) — at two different disk speeds — 15 cm/ sec (5.9 in./sec ) and 30 cm/sec (11.8 in./sec) — resulting in six testing conditions. These testing conditions, 1 through 6, are summarized in Table€5.6. Chang estimated the pin contact pressures to be 1.6 × 102 kPa (0.23 psi), 2.4 × 102 kPa (0.35 psi), 4.8 × 102 kPa (0.70 psi), respectively, for the three normal loads indicated. His estimated pressures were calculated on the basis of wear scars on the Neolite pins applied to the roughened tile specimens. We can expect, therefore, that cohesion losses (FC forces) constitute a component of Chang’s friction measurements on the sandblasted surfaces. The relative humidity during testing was kept between 30 and 40%, while the temperature was controlled at a constant 21°C (69.8°F). Table€5.5 Preparation Process Parameters Used by Chang for His Quarry Tile Specimens Exit Pressure Distance from Process Number Sand Particles (× 105 Pa) Nozzle (cm) 1 00 2.76 15.24 2 BB 2.07 7.62 3 0 2.07 7.62 4 1 2.07 12.70 5 — No sandblasting — BB = black beauty. Source: Reprinted from Safety Science, 29, Chang, W.-R., The effect of surface roughness on dynamic friction between Neolite and quarry tile, 89, copyright 1998, with permission from Elsevier.

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131

A Unified Theory of Rubber Friction Table€5.6 Testing Conditions Used by Chang for His Quarry Tile Specimens Test Condition 1 2 3 4 5 6 BB = black beauty.

Load (g) 25 25 100 100 250 250

Pin-on-Disk Tangent Speed (cm/sec) 15 30 15 30 15 30

Source: Reprinted from Safety Science, 29, Chang, W.-R., The effect of surface roughness on dynamic friction between Neolite and quarry tile, 89, copyright 1998, with permission from Elsevier.

Figure€5.31 presents the measured friction coefficients (μ) reported by Chang for the five different processes and six different testing conditions. It is seen that the three different loading conditions — 25 g (0.055 lb), 100 g (0.22 lb), and 250 g (0.55 lb) — and the five different specimen preparation processes plot as distinguishable groups. Process 5, which involved no sandblasting, produced the lowest coefficients at each applied normal load. The coefficients increase as the tile’s macroroughness increases. Figure€5.32 depicts plots of the back-calculated friction forces vs. applied normal loads for four of the processes. (The back-calculated process 4 friction values were found to be essentially identical to those of process 3 and were dropped from further consideration.) Because Chang found no significant difference in his measured friction values between the two speeds utilized, readings from the two speeds at each of the three applied normal loads were 1

Friction Coefficient

0.9 0.8

Condition 1 Condition 5

Condition 2 Condition 6

Condition 3 Condition 4

0.7

Loading

0.6

25 g

0.5 0.4 0.3

100 g

0.2

250 g

0.1 0

Process-1

Process-2

Process-3

Process-4

Process-5

Figure€5.31 Measured friction coefficients reported by Chang for his quarry tile specimens. (Reprinted from Safety Science, 29, Chang, W.-R., The effect of surface roughness on dynamic friction between Neolite and quarry tile, 89, copyright 1998, with permission from Elsevier.)

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132 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces averaged together for the present analysis. Thus, the back-calculated forces are the means from 16 samples. Perhaps not surprisingly, the extrapolated back-calculated plots seen in Figure€5.32 did not pass through the origin but intercepted the y-axis. In this case, all apparent FHs values are equal at about 7.5 gm (0.16 lb), suggesting equal surface deformation hysteresis development in the Neolite for all pairings. Subtraction of 7.5 gm (0.16 lb) from each data point yielded lines passing through the origin (not shown). The process 5 plot of friction results from the smooth tile is dashed from 100 to 250 gm (0.22 to 0.55 lb). Apparently, the adhesion transition point was reached between these loads, but the precise FN value at which this occurred could not be determined because of insufficient testing data. These back-calculated results are consistent with the presence of a constant friction force contribution from surface deformation hysteresis in sliding contact with four surfaces of different macroroughness. Figure€5.33 illustrates the back-calculated friction ratios with the microhysteresis forces removed. The values for process 5, obtained on the smooth tile surface, appear to be the adhesion friction ratios, μA, with constant and hyperbolic loading ranges. The plot is again dashed between the 100- and 250-gm (0.22- and 0.55-lb) points. The ratios for the remaining processes indicate constant values, although all likely contain adhesion, macrohysteresis, and cohesion (wear) components. The ratios for processes 1, 2, and 3 are 0.41, 0.35, and 0.25, respectively. Because the back-calculated results from Chang’s data were obtained from tile sets each possessing a different macroroughness, an interesting implica-

Total Measured Friction Force (FT)–g

120 Process 1

100 80

Process 2 60 Process 3

40 20

Process 5 0

25

100 Applied Normal Load (FN)–g

250

Figure€5.32 Back-calculated friction forces using test data reported by Chang for his quarry tile specimens. (From Chang, W.-R., Safety Science, 29, 89, 1998.)

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133

A Unified Theory of Rubber Friction 0.5 Process 1

0.4

Friction Ratios

Process 2 0.3

Process 3

0.2

Process 5

0.1

0

0

50 100 150 200 Applied Normal Load (FN)–g

250

Figure€5.33 Back-calculated friction ratios with the microhysteresis force removed using test data reported by Chang for his quarry tile specimens. (From Chang, W.-R., Safety Science, 29, 89, 1998.)

tion arises: the friction mechanism producing the constant y-intercept value appears to be independent of contacted surface macroroughness in these conditions. This implication also suggests that the smooth tiles exhibited the same microroughness as the roughened ones and that the polished, smooth-surface microroughness had not been changed on average by sandblasting. Putting this implication another way: when an elastomer slides on a roughened, previously smooth surface, the same microhysteresis force can develop as when the elastomer slid on that smooth surface. A further implication of the back-calculation analysis is that sandblasting with differently sized abrasive particles, each type possibly possessing a different microroughness, did not change the microroughness of those four tile groups; that is, neither the macro- nor microroughness of the abrasive particles affected the microroughness of the initially polished tile surfaces.

5.4

Characteristics of the Rubber Microhysteresis Mechanism

5.4.1

Rubber Microhysteresis Mechanism

Rubber surface deformation hysteresis appears to be a distinct mechanism different from the adhesion friction mechanism. The adhesion rubber friction

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134 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces force arises from the combined surface free energies of the paired materials and increases with the applied normal load. Adhesion is an area phenomenon, not usually considered as generated by bulk deformation of the rubber surface. The greater the applied normal force, or pressure, the greater the real area of contact between the two surfaces and the larger the adhesion force developed. We have seen that, on macroscopically smooth solids, if what we have called the FHs forces are taken into account, adhesion seems to increase directly with FN or PN at first, and then less rapidly than the applied normal load when the adhesion transition force or pressure is exceeded. To all appearances, microhysteresis in sliding rubber is a point-related phenomenon, depending on the average topography of the contacted surface microroughness. We can postulate that if the microroughness of the harder material is comprised of sharp “peaks” with intervening “valleys,” surface deformation of the sliding rubber occurs at these peaks. If the microroughness of the harder solid is crater-like in shape, deformation of the elastomer’s surface apparently still takes place on points, tracing the crater’s circumference. If rubber microhysteresis is independent of applied force and pressure, as indicated by our earlier analyses in this chapter, FHs forces cannot arise as a result of the applied load’s “impaling” the elastomer’s surface onto the peaks or craters. Rather, it appears that adhesion performs this role. The extent of draping of the rubber surface over these peaks or points likely depends on the combined surface free energies of the two paired materials as the agents producing such contact. Microhysteretic friction seemingly arises when the adhering rubber surface is deformed by the peaks during sliding: the greater the combined surface free energies, the larger the FHs force generated. We can also theorize that because the microasperity depth of the harder surface is small, indeed microscopic in dimension, the magnitude of the rubber microhysteresis force does not measurably increase with increasing applied load due to additional draping. At the same time, the dependence of rubber adhesion on FN and PN must be accounted for in this theory. We know that smoothness of the paired, harder material promotes adhesion. On macroscopically smooth solids, microasperities impede the development of more intimate adhesive contact. As the applied normal loads increase, greater protrusion of rubber asperities into microscopic valleys and craters apparently occurs, fostering increased surface-to-surface contact and a larger adhesional friction force. Figure€5.34 presents an idealized depiction of the microhysteretic phenomena. 5.4.2 Independence of the Rubber Microhysteresis Force Table€5.7 summarizes the independence of the rubber microhysteresis force on harder, macroscopically smooth and rough surfaces as indicated from the back-calculation analyses presented in this chapter. The authors of the published friction test results, to which the back-calculation technique was applied, are included. We have seen that, on macroscopically smooth surfaces, FHs is apparently independent of applied normal forces and pressures.

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135

A Unified Theory of Rubber Friction PN Movement

Sliding rubber

Idealized Contacted Surface Figure€5.34 Idealized depiction of rubber sliding on a harder, macroscopically smooth, flat solid with a uniform average microroughness. If the paired materials possess sufficient combined surface free energy, adhesion between the microroughness peaks of the harder solid and rubber asperities will occur, generating surface deformation hysteresis in the rubber. Increasing applied normal pressure will produce more real areas of adhesive contact and a greater adhesional friction force, while microhysteresis does not sensibly increase.

Table€5.7 Indicated Independence of Rubber Microhysteresis Force on Macroscopically Smooth and Rough Surfaces Adduced by Back-Calculation of Previously Published Test Data Independence of Microhysteresis Force on Macroscopically Smooth Surfaces

Adduced from Data Obtained by:

Applied normal force and pressure

Roth et al. [2], Thirion [3], Schallamach [4], Mori et al. [5], Bartenev and Lavrentjev [6], Sigler et al. [7], and Chang [10]

Applied tangent force

Powers et al. [11] (Static testing)

Independence of Microhysteresis Force on Macroscopically Rough Surfaces

Adduced from Data Obtained by:

Applied normal force and pressure

Sigler et al. [7], Chang [10], Schallamach [12], and Yandell [13]

Macroroughness of contacted surface

Chang [10]

Concurrent wear of rubber

Chang [10], Schallamach [12]

In addition to applied normal forces and pressures, a back-calculation analysis of the work of Powers et al. [11] presented in Chapter 9 — “Rubber Microhysteresis in Static-Friction Testing” — suggests that FHs can be independent of the applied tangent force on macroscopically smooth surfaces under static testing conditions. Schallamach [12] carried out dynamic friction testing on various rubber compositions utilized in commercial products to investigate the stresses arising in such products when macrohysteresis forces are induced in them in dry conditions. His studies involved placing a stainless steel slider of cylindrical cross-section in contact with rubber test specimens and then applying normal forces to produce an ever-increasing “plowing” effect.

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136 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces during sliding. Because the plowing was done in dry conditions, both adhesion and bulk deformation hysteresis forces likely developed, along with the reported wear of the rubber surfaces. A back-calculation analysis (not plotted here) indicated that generation of microhysteresis forces arose in Schallamach’s [12] testing. These FHs forces appeared to be constant under increased macrohysteretic loading and concurrent rubber wear. Thus, surface deformation hysteresis appears independent of the applied normal force with concurrent rubber wear on macroscopically rough surfaces. This Schallamach work is, therefore, included in Table€5.7. We have further noted that, on macroscopically rough surfaces, FHs also appears to be independent of applied normal forces and pressures, as well as of the contacted surface macroroughness. Such independence seemingly extends to conditions in which wear of the microhysteretically and macrohysteretically deformed rubber concurrently occurs. Yandell [13] is also cited in Table€5.7. An analysis of his friction testing, which produced further indication that FHs is independent of macroroughness, is presented in Section 5.6.3. 5.4.3 Dependence of the Rubber Microhysteretic Force As discussed in Section 5.2.1, a back-calculation analysis of the Roth et al. [2] data indicated that rubber microhysteresis developed in their large and small specimens. The FHs value for the small specimen was about 1.4 kg (3 lb), while that for the large sample was approximately 0.7 kg (1.5 lb). These researchers reported that the two rubber specimens were identical except for size, and that they were tested under identical protocols, except for applied loads. As illustrated in Figure€3.2(a), Roth et al. [2] reported different μ measurements from their two tests in the loading range where the applied pressures were equal. Further, different back-calculated μA values were obtained over the entire loading range. Thirion [3], on the other hand, reported identical μ values for his two differently sized samples, and the back-calculated μA ratios from his rubber specimens of identical composition appeared equal. In addition, while the back-calculated FHs values were also different for Thirion’s two differently sized specimens, the large specimen’s value implied a larger microhysteresis force than did that for his small sample. Thirion’s data appear the more consistent of the two, and they will be considered more representative of the true frictional differences between two differently sized but otherwise identical rubber test specimens. Thirion’s data indicate that the rubber microhysteretic force depends on the nominal area of contact of the rubber product with the paired surface. Table€5.8 summarizes the dependence of the rubber microhysteresis force on harder, macroscopically smooth and rough surfaces as indicated from the back-calculation analyses presented in this chapter. The authors of the published rubber friction test results to which the back-calculation technique was applied are included.

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137

A Unified Theory of Rubber Friction Table€5.8

Indicated Dependence of Rubber Microhysteresis Force on Macroscopically Smooth Surfaces Adduced by Back-Calculation of Previously Published Test Data Dependence of Microhysteresis Force on Macroscopically Smooth Surfaces

Adduced from Data Obtained by:

Microroughness of contacted surface

Sigler et al. (suggestive) [7]

Nominal rubber contact area

Roth et al. [2], Thirion [3]

Rubber hardness (inversely)

Schallamach [4]

Temperature (inversely)

Bartenev and Lavrentjev [6],

Rubber surface free energy

Mori et al. [5]

Surface free energy of contacted surface

Mori et al. [5]

The Sigler et al. [7] data are listed as possible evidence indicating that rubber microhysteresis depends on the microroughness of the contacted surface. We have seen in Figure€5.23 that four different FHs values are indicated from five different macroscopically smooth flooring materials when friction tested with ZZ-R-601a rubber. While the differently constituted floors likely possessed different surface free energies, it is possible that they all exhibited identical average microroughness topographies. If this were so, the Sigler et al. data would not be consistent with FHs dependence on microroughness. There are no entries in Table€5.8 for the dependence of FHs on macroscopically rough surfaces. No testing data could be found in this category. 5.4.4 Relevance of the Intercept-Indicated Friction Force — Hurry and Prock Hurry and Prock [14] formulated the equation FT = μFN + b and considered the y-intercept value b to represent a constant friction force. On the basis of their findings, however, Hurry and Prock opined that, except for unworn rubber products, this force could be ignored in engineering applications of rubber friction. This opinion is not consistent with the findings of our present analysis. The intercept-indicated force appears as potentially important in many, and perhaps most, conditions in which the magnitude and nature of the developed rubber friction forces are of interest.

5.5

No-Load Adhesion Hypothesis

5.5.1

Use of the No-Load Adhesion Hypothesis in Rubber Friction Analysis

A number of investigators whose rubber friction test results we have discussed have plotted their data on rectangular coordinates and noticed that,

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138 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces when a straight portion of 1/μ vs. PN or FT vs. PN is extrapolated toward the y-axis, the extrapolated line does not pass through the origin. Instead, a yintercept is produced. Various explanations for these intercepts have been hypothesized, postulated, or theorized. As far as could be determined, no one has attributed such y-intercept values to a rubber microhysteresis force. Rather, variants of a no-load adhesion hypothesis have been proposed; that is, when the subject rubber being tested is placed in contact with the paired, harder material under no-load conditions, adhesion will develop between the two surfaces to the extent represented by the y-intercept value. Thirion [3] formulated the equation 1/μ = cPN + b and postulated that the extrapolated y-intercept value b equals 1/μ at zero pressure. He presented no confirmatory test data in support of his postulate. Adopting Thirion’s 1/μ approach, Bartenev and Lavrentjev [6] were interested in relating the adhesive friction force of rubber to its real area of contact with a paired material. Like Thirion, they hypothesized that as PN goes to zero, small, but finite, real areas of contact between the rubber specimens and the paired surfaces at zero load exist. Bartenev and Lavrentjev further hypothesized that the associated residual adhesion forces are constant, and the extent of the real areas of contact depend, at least in part, on the degree of rubber roughening and the time of contact with the test track (residence time) before commencement of sliding (3 minutes in their static friction testing protocol). They did not provide any laboratory test results in support of their hypothesis. Mori et al. [5] presented plots (Figure€4.19) of their FT vs. FN measurements for NBR sliding on aluminum. They theorized that the slopes of the lines in Figure€4.19 represent the coefficients of adhesive friction for the three pairings. Mori et al. [5] extrapolated these lines to the FT axis, noting that intercept values were produced, and postulated that the existence of measurable adhesive friction forces at zero load was therefore demonstrated. They further theorized that these no-load forces arose from the combinative effect of the surface free energies of the two materials involved. As discussed in Section 3.11, Johnson et al. [8] demonstrated through laboratory testing and rigorous analysis that when low-elastic-modulus rubber is formed into optically smooth spheres, and the two objects are placed in no-load contact, the surface free energies acting between the spheres flatten their asperities and adhesion develops. The magnitude of the resulting noload adhesion was significant enough to require modification of the Hertz equation for a loading range up to 5 gm (0.01 lb). While this combination of conditions investigated by Johnson et al. is not generally found in engineering practice, there can be little doubt that the no-load adhesion phenomenon in rubber exists. In the present context, the questions are whether the no-load adhesion phenomenon is significant in the test results we have examined, or do the y-intercepts represent the theorized microhysteresis force? We now discuss the potential relevance of no-load adhesion to rubber surface deformation hysteresis.

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A Unified Theory of Rubber Friction

139

5.5.2 Residence Time Considerations It is well known in friction metrology that when a testing surface remains in stationary contact with its paired, tested surface before sliding commences, the static friction of this pairing increases with residence time. According to Rabinowicz [15], the longer two surfaces remain in contact under loading, any adhesion bonding between them becomes stronger, even if the applied load is only a friction fit between the two objects. Braun and Roemer [16] showed this to be true between a mechanically lapped, chrome-plated, drag sled test-shoe and various floor wax formulations. Smith [17] also demonstrated this phenomenon in walking-surface slip-resistance metrology utilizing the elastomeric Neolite test liner as a test foot paired with polished marble floor tile. While adhesion-producing residence time is an important variable in static friction testing, examination of the literature has provided little indication that no-load adhesion is significant in dynamic rubber friction testing. 5.5.3 No-Load Adhesion in Sliding Rubber Bartenev and Lavrentjev [6] were, therefore, correct in attributing variation in the adhesion friction force that had to be overcome before sliding began in their static testing to variation in the residence times for particular protocols. Their next step, however, is in question. Bartenev and Lavrentjev, as well as Thirion [3] and Mori et al. [5], took a static friction phenomenon — residence time — and applied it to dynamic friction testing. From a phenomenological point of view, there appears little reason to believe that extrapolating a straight line segment on a dynamic friction plot to the y-axis quantifies forces or inverse coefficients that would develop under static, no-load circumstances. Even if significant no-load adhesion could develop between two paired surfaces under static conditions, how could dynamic friction test data quantify time-related, static friction test measurements? Johnson et al.’s [8] testing involved smooth spheres placed side-by-side in very slight contact, allowing their surface free energies to bond the two objects adhesively while their mutual deformation took place. After a period of time, equilibrium was reached and deformation ceased. Such conditions are not replicated in the Bartenev and Lavrentjev, Thirion, or Mori et al. dynamic testing we have examined. When a specimen is placed on a smooth, dry, horizontal track in preparation for static or dynamic friction testing, some residence time unavoidably occurs. In static testing, adhesion develops during this residence time, and inertial resistance to movement also becomes an issue. Both are measured when relative sliding between the paired surfaces is initiated. If movement is then continued at a constant horizontal velocity, the inertial resistance is eliminated and the static residence-time adhesive value becomes irrelevant. Adhesion friction now depends on the protocol for the dynamic segment of

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140 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces the test. In most of the dynamic tests of this type we have studied, extrapolated y-intercepts arose, and we theorized that the intercept values quantified rubber surface deformation hysteresis.

5.6

Rubber Surface Deformation Hysteresis Testing

Rubber friction researchers have discussed various issues connected with the possible existence of a surface deformation hysteresis mechanism. In his chapter on rubber friction models in a 2001 book, Savkoor [18] did not refer to any testing devoted to microhysteresis. As far as could be determined, no comprehensive testing program on the subject has been carried out; however, Kummer [19] and Yandell [13] have undertaken some limited, specifically focused research related to microhysteresis. 5.6.1

Kummer: Dry Testing

Kummer [19] focused his testing efforts on traction production between vehicle tires and roads. As part of this work, he reported laboratory research results involving dry and wet conditions thought to demonstrate the existence of rubber microhysteresis. On the basis of field observations by others, it had been previously hypothesized that roadway materials hostile to wetting (hydrophobic surfaces) provide low adhesion to tires because hydrophobic solids possess low surface free energies. Kummer investigated this hypothesis in the laboratory by sliding natural rubber (NR) on both hydrophobic calcium carbonate rock (CaCO3) and hydrophilic silica glass (SiO2). His results, expressed here as μT vs. sliding speed, are presented in Figure€5.35. For the purposes of these discussions, we define μT, the total friction ratio, as the ratio produced by dividing the total friction force developed in dry or wet rubber testing, including any viscous drag present, by the applied normal force or pressure. Contrary to the hypothesis, the dry NR-CaCO3 coefficients were higher than the dry NR-SiO2 coefficients. To explain the apparent error, Kummer pointed out that harder silicates are less prone to traffic polishing (surface smoothing) than is softer limestone, thereby producing the low tire skid resistance observed in the field on carbonate roadway materials. He further opined that the higher dry coefficients obtained in the laboratory with unpolished CaCO3 indicated that the CaCO3 specimen generated greater skid resistance than did the SiO2 sample, though greater microhysteretic force developed, arising because of the carbonate’s greater microroughness (2.25 × 10−5 cm RMS, 0.88 × 10−5 in. RMS) compared to that of the silica glass (7.5 × 10−6 cm RMS, 2.9 × 10−5 in. RMS). As discussed in Chapter 3, Kummer [19] hypothesized that microhysteresis is an ever-present component of rubber adhesion. He considered the dry

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141

A Unified Theory of Rubber Friction

Total Friction Ratio (µT)

3

Dry NR/

2

SiO2 CaCO3 T = 78F p = 17psi

Wet

1

Wet + agent 0

10

Wet 20 30 Sliding Speed, v, ipm

40

50

Figure€5.35 Friction test results obtained by Kummer thought to demonstrate the presence of microhysteresis in natural rubber when sliding on wet, smooth surfaces of silica glass and calcium carbonate. (From Kummer, H.W., Unified Theory of Rubber and Tire Friction, Engineering Research Bulletin B-94, The Pennsylvania State University, State College, PA, 1966.)

data points depicted in Figure€5.35 to be adhesion coefficients. Applying the microhysteresis analysis presented in Section 5.2, however, allows a somewhat expanded theoretical conclusion to be drawn from these data: the dry coefficient points in Figure€5.35 represent both adhesion and microhysteresis, but the microhysteresis mechanism present behaves differently than does van der Waals’ adhesion. As we have seen in this chapter with the data of Schallamach [4] depicted in Figure€5.15 and Sigler et al. [7] presented in Figure€5.24, removing the theorized microhysteresis component from what had been believed to be adhesion coefficients rearranges the rank order of the μA plots to reflect the surface free energy-adhesion propensities of the tested pairings in a rational scientific manner. 5.6.2 Kummer: Wet Testing Figure€5.35 also depicts Kummer’s [19] wet testing results. He found that when wet testing with water, the NR-SiO2 coefficient decreased to a low value and became speed independent. The NR-CaCO3 pairing, however, seemed to exhibit adhesion, as evidenced by the curved portion of its associated plot, suggesting that the carbonate had not been completely wetted by water, and some van der Waals’ attraction to the rubber developed. When Kummer included a wetting agent in the NR-CaCO3 test, the coefficient fell to a lower value and also became speed independent. He ascribed this further reduction in frictional resistance to increased wetting of the CaCO3 surface, so that adhesion-eliminating boundary layer lubrication conditions were thereby established in both carbonate and silica sliding regimes. Kummer theorized that both speed-independent coefficients, seen in Figure€5.35, represented only lubricant viscous losses and microhysteresis in the rubber as it passed over microasperities on the tested limestone and silica surfaces.

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142 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Figure€5.35 indicates that CaCO3 exhibited a slightly higher speed-independent wet coefficient than did silica. Kummer suggested this might be due to the limestone’s greater microroughness. It seems possible as well that the slightly higher value of the speed-independent, wetted-limestone coefficient arose, perhaps in part, from greater viscous losses in the water-wetting agent solution. Presumably, some wetting agent also attached itself to the sliding rubber. There was no wetting agent to increase viscous losses in the speedindependent NR-silica testing results. A requirement of Kummer’s theory is that some hysteretic surface deformation of the rubber specimens occurred in his testing under liquid boundary layer conditions that allowed no significant surface-to-surface contact of the rubber with the limestone or silica, thus negating van der Waals’ adhesion. Such a mechanism would be directly analogous to hysteretic bulk deformation in rubber when it slides over macroasperities on harder materials under lubricating liquid boundary layer conditions, as investigated by Greenwood and Tabor [20] and discussed in Section 4.5.4. Presumably, if Kummer’s microasperities were hemispherical, as in the Greenwood and Tabor testing, the quantifying friction expression for the two NR pairings in fully lubricated conditions when viscous losses are ignored might also be Equation 4.7, applicable to the Greenwood and Tabor data, μHs = c(FN)1/3, but with different c values. Kummer’s microhysteretic friction theory is inconsistent with the new analytical evidence presented in this chapter devoted to the mechanism of rubber surface deformation hysteresis. We have seen that FHs forces apparently develop in most dry conditions when rubber slides on a macroscopically smooth, harder material — for example, Roth et al. [2], Thirion [3], Schallamach [4], Bartenev and Lavrentjev [6], and Sigler et al. [7]. We have also seen, from the work of Mori et al. [5], that the values of FHs forces arising on such macroscopically smooth solids appear to decrease as the surface free energy (adhesion propensity) of the rubber decreases. Indeed, when Mori et al. slid low-adhesion rubber on Teflon, no indications of microhysteresis were evident. Two determinants of the development of microhysteretic friction in rubber appear to be microroughness topography of the contacted surface and the magnitude of the combined adhesive energies of the paired materials. If adhesion is too low, FHs forces will apparently not develop. Because development of van der Waals’ adhesion had presumably been prevented in Kummer’s speed-independent sliding regimes, we may postulate that a rubber microhysteresis mechanism analogous to bulk deformation hysteresis did not arise in his testing. 5.6.3 Yandell: Dry Testing Figure€3.12 depicted the phenomenological approach taken by Yandell [13] in his efforts to assist in understanding the possible contribution of roadway microroughness to tire traction in wet and dry conditions. He idealized the

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143

road surface texture and analyzed the macro- and microhysteretic contributions to friction by assuming that the macro- and microhysteretic coefficients are additive yielding the theoretical equation

μHt = μHb + μHs.

(5.4)

Yandell stated that this concept of texture analysis was based on the liquidlike flow of rubber, even up steep asperity surfaces, as demonstrated in the laboratory by Schallamach [12]. Yandell’s research involved a computer-based, two-dimensional, mechano-lattice analysis of sliding rubber utilizing 264 mathematical units in his model for simulating the plane stress behavior of rubber. As the rectangular units slid on rigid, model asperities, the units experienced cycles of load and deflection, generating hysteresis loops. Yandell defined the coefficient of hysteretic friction in his program as the vector sum of the horizontal forces acting on the lattice unit joints in contact with an asperity, divided by the vertical reactions acting on these joints. The idealized, lattice-model asperities were either isosceles triangular prisms or smooth cylinders. This latter shape was intended to emulate road chips whose fine texture had experienced smoothing from traffic polishing. The model also possessed the capability of inputting various rubber damping factors, ξ, to determine the resulting effect on the hysteretic coefficients. Yandell defined the damping factor as the energy dissipated in one loading cycle divided by the energy applied in this cycle. Because accounting for the sharpness of road surface asperities had been an issue in predictive quantification of tire friction, Yandell utilized average asperity slope as his independent variable. Figure€5.36 presents plots of Yandell’s findings for dry conditions expressed here as the total hysteretic friction ratio, μT, vs. average slope of the idealized triangular prisms and cylindrical asperities selected. (In the original figure, the y-axis was labeled μHt in accordance with Yandell’s terminology.) Five different sets of plots are depicted for rubber damping factors ranging from 0.1 to 0.5. We see that the triangular prisms produce higher μT values than do the cylinders. In addition, as the damping factor increases, so does the theoretical coefficient of hysteretic friction. To assess the accuracy of his lattice model, Yandell utilized small triangular prisms specially fashioned from brass and rigidly mounted in rows on a test bed. Friction measurements were carried out on this idealized asperity arrangement with a British Pendulum Tester. This pendulum device, designed to test at 130 load cycles per second at 70°F (21°C), was fitted with a rubber test foot exhibiting a damping factor of 0.45. Yandell considered that reasonably accurate hysteretic coefficients from these tests could be calculated by subtracting friction measurements taken parallel to asperity rows from those measured perpendicular to the rows, leaving the relevant hysteretic force from which ratios could be determined. In addition to placing his pendulum device perpendicular to the rows of brass asperities, Yandell

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144 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Normal load 5 lb. 3.1 lb. 1.5 lb.

0.3

Angle of swing to asperity ridges 90° 60°

Total Hysteretic Friction Ratio (µT)

Damping factor of friction test rubber, ξ = 0.45

Triangular ξ = 0.5 prisms

0.2

0.4 Cylinders ξ = 0.5

0.4

0.1

0.3 0.2 0

0.1 0

0.1 0.2 0.3 0.4 Average Slopes of Contacted Surfaces

0.3

0.2 0.1 0.5

Figure€5.36 Theoretical and actual dry test results obtained by Yandell to validate his phenomenological approach quantifying hysteretic rubber friction illustrated in Figure€3.12. Curves present total friction ratios μT vs. average slopes of contacted surfaces for five theoretical rubber damping factors ξ. (Reprinted from Wear, 17, Yandell, W.O., A new theory of hysteretic sliding friction, 229, copyright 1970, with permission from Elsevier.)

similarly obtained friction measurements by aligning the tester at an angle of 60° to them. In both alignments, he applied three normal loads: 0.68 kg (1.5 lb), 1.4 kg (3.1 lb), and 2.3 kg (5 lb). Figure€5.36 also depicts the measured coefficient values obtained by Yandell with the pendulum tester. We note that corresponding to the rubber test foot’s damping factor of 0.45, the measured friction ratio values are clustered about the theoretical rubber damping factor of 0.4 used in the model calculations. Yandell opined that the model’s predictions were close to the observed test results. It is seen, however, that of the six sets of friction coefficients measured on the brass asperities depicted in Figure€5.36, only one set is in rank order of applied normal load — the three ratios obtained at a 60° angle to the asperities, which possess an average surface slope of approximately 0.32. Because Yandell had theorized that what is often thought to be adhesion rubber friction is, in reality, a hysteretic phenomenon, the apparent areas of contact between the pendulum’s rubber test foot and the brass asperities

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145

A Unified Theory of Rubber Friction

were not involved in his calculations. Furthermore, the possible development of microhysteretic forces between the rubber test foot and the brass asperities by a different mechanism than that for the fine asperities depicted in Figure€3.12 was apparently not considered. A back-calculation analysis of Yandell’s data indicates that an adhesion-related FHs-friction mechanism of the type illustrated in Figure€5.34 developed in his testing. Figure€5.37 depicts total friction ratios calculated from Yandell’s data as measured at a tester swing angle of 90° vs. applied normal load. The plots for average asperity slopes of 0.37 and 0.50 peak at applied normal loads of 1.4 kg (3.1 lb), while at an average slope of 0.25, the two lowest normal loads yielded equal coefficient values, and the highest normal load coefficient was greater than both of them. One might expect that, with completely uniform data, these coefficients would either increase or decrease in rank order of magnitude of loading. Figure€5.38 presents the back-calculation analysis results expressed as total friction force vs. FN. It is seen that all three 90° data sets yield reasonably uniform plots, consistent with straight lines. Two of the plots, for average brass asperity surface slopes of 0.50 and 0.37, exhibit approximate y-intercepts of 50 gm (0.1 lb) and 20 gm (0.04 lb), respectively. These y-intercepts are consistent with the production of FHs forces in Yandell’s dry, 90° brass testing. 0.25 Average slope = 0.50

Total Friction Ratio–µT

0.2

0.15 Average slope = 0.37 0.1

0.05

0

Average slope = 0.25

0 1 2 3 4 5 Applied Normal Load (FN)–lbs

Figure€5.37 Back-calculated total friction ratios determined from dry testing data obtained by Yandell using a pendulum swinging at an angle of 90° over rows of triangular brass prisms with various slopes. (From Yandell, W.O., Wear, 17, 229, 1970.)

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146 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces The 0.25 average slope plot, however, appears to exhibit a negative y-intercept value. This suggests that, to represent the measured data more accurately and for the 0.25 slope values to be consistent in behavior with the other two 90° plots and the three 60° plots to be discussed below, all three straight lines in Figure€5.38 should be shifted vertically upward to some extent. Apparently, the subject practice of subtracting friction measurements taken parallel to asperity rows from those measured perpendicular to the rows, leaving the relevant hysteretic forces, may need adjustment. Figure€5.39 illustrates the back-calculated friction ratios for the 0.50 and 0.37 slopes after the apparent FHs forces have been removed. The corresponding ratios are approximately 0.15 and 0.10, respectively. Because these coefficients may contain both van der Waals’ adhesion and bulk deformation hysteresis components, the ordinate axis is labeled μA+Hb. Accounting for the apparent microhysteresis forces in Yandell’s 90° testing reduces these two ratios. When the higher-than-model 0.45 damping factor of the pendulum’s rubber test foot is also taken into account, the back-calculation hysteretic friction coefficients seem more consistent with Yandell’s theoretical 0.30 damping factor results. Figure€5.40 presents the hysteretic friction ratios as measured at 60° as defined by Yandell vs. applied normal load. The data points appear uniform. We see that the plots for average asperity slopes of 0.32 and 0.20 exhibit hyperbolic curves of the type often noted previously. The 0.44 slope plot is parabolic. 1.0 0.90

Average slope = 0.50

Total Friction Force–lb

0.80 0.70 0.60

Average slope = 0.37

0.50 0.40 0.30 0.20

Average slope = 0.25

0.10 0

0 1 2 3 4 5 Applied Normal Load (FN)–lbs

Figure€5.38 Back-calculated friction forces determined from dry testing data obtained by Yandell using a pendulum swinging at an angle of 90° over rows of triangular brass prisms with various slopes. (From Yandell, W.O., Wear, 17, 229, 1970.)

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147

A Unified Theory of Rubber Friction

Friction Ratios–µA+Hb

0.3

0.2

0.1

0

Average slope = 0.50

Average slope = 0.37

0 1 2 3 4 5 Applied Normal Load (FN)–lbs

Figure€5.39 Back-calculated friction ratios determined from dry testing data obtained by Yandell using a pendulum swinging at an angle of 90° over rows of triangular brass prisms with various slopes. Apparent microhysteresis forces have been removed. (From Yandell, W.O., Wear, 17, 229, 1970.)

Figure€5.41 depicts back-calculation analysis results for the 60° data expressed as total friction force vs. FN. All three data sets yield reasonably uniform plots, consistent with straight lines. The average brass asperity surface slopes of 0.44, 0.32, and 0.20 exhibit approximate y-intercepts of 20 gm (0.04 lb), 30 gm (0.07 lb), and 20 gm (0.04 lb), respectively. This is consistent with the production of FHs forces in Yandell’s dry, 60° brass testing. Figure€5.42 illustrates back-calculated friction ratios of 0.14, 0.07, and 0.05 for the 0.44, 0.32, and 0.20 slopes measured at 60°, respectively, after the apparent FHs forces have been removed. Again, because these coefficients may contain both van der Waals’ adhesion and bulk deformation hysteresis components, the y-axis is labeled μA+Hb. All three of the combined coefficients are constant. This is not consistent with the nonlinearity of Yandell’s theoretical, model-based curves presented in Figure€5.36. Further, when the 0.45 damping factor of the pendulum’s test foot is accounted for, the back-calculated hysteretic friction coefficients appear more consistent with Yandell’s 0.30 damping factor results than does his 0.40 theoretical curve. A requirement of Yandell’s theory, visually depicted in Figure€3.12, is that rubber surface deformation hysteresis is directly analogous to rubber bulk deformation hysteresis arising when rubber slides on macroasperities of harder material, except that the microdeformations in rubber sliding on microasperities are smaller. As seen in Figure€5.36, neither Yandell’s model-derived coefficients, nor his pendulum testing ratios are independent of applied normal load. The back-calculated FHs forces from the brass testing, however, are load independent. The subject hysteretic, textural analysis approach to rubber friction is not consistent with Yandell’s dry, brass microasperity test results.

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148 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 0.2

Total Coefficient of Friction–µT

Average slope = 0.44 0.15

0.1

0.05

Average slope = 0.32

Average slope = 0.20

0

0 1 2 3 4 5 Applied Normal Load (FN)–lbs

Figure€5.40 Back-calculated total friction ratios determined from dry testing data obtained by Yandell using a pendulum swinging at an angle of 60° over rows of triangular brass prisms with various slopes. (From Yandell, W.O., Wear, 17, 229, 1970.)

0.80

Total Friction Force–lb

0.70

Average slope = 0.44

0.60 0.50 0.40 0.30

Average slope = 0.32 Average slope = 0.20

0.20 0.10 0

0 1 2 3 4 5 Applied Normal Load (FN)–lbs

Figure€5.41 Back-calculated friction forces determined from dry testing data obtained by Yandell using a pendulum swinging at an angle of 60° over rows of triangular brass prisms with various slopes. (From Yandell, W.O., Wear, 17, 229, 1970.)

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149

A Unified Theory of Rubber Friction

Friction Ratios–µA+Hb

0.3

0.2 Average slope = 0.44 0.1

Average slope = 0.32 Average slope = 0.20

0

0 1 2 3 4 5 Applied Normal Load (FN)–lbs

Figure€5.42 Back-calculated friction ratios determined from dry testing data obtained by Yandell using a pendulum swinging at an angle of 60° over rows of triangular brass prisms with various slopes. Apparent microhysteresis forces have been removed. (From Yandell, W.O., Wear, 17, 229, 1970.)

Another requirement of Yandell’s theory is that asperity spacing and normal load are such that the effects of the asperities do not interact. Yandell ensured that this requirement was met in design of his theoretical, latticeanalysis approach. He did not have control of the microasperity spacing in his brass testing. Although the developed FHs forces appear to be independent of FN, the effects of the brass microasperities may interact. 5.6.4 Yandell: Wet Testing Yandell also applied his mechano-lattice program to the textural analysis of wet road chips, using Prospect dolerite, gneiss, volcanic breccia, and siliceous sandstone for both theoretical and accuracy-assessment testing purposes. Employing a stylus device developed by him to measure the surface roughness of naturally broken faces of these materials, he created computerplotted topographical representations of their surfaces and determined that the stylus device exhibited a lower-limit textural sensitivity of about 3.25 × 10−3 mm (130 μin.). By experimenting with various lubricants, Yandell found that applying glycerin at 21°C (70°F) completely masked the broken-face microroughness below the 3.25 × 10−3 mm (130 μin.) threshold, allowing consideration of only those textures capable of being measured by the stylus. The three-dimensional representations were then utilized to calculate the average slopes of the four different broken faces and thus their theoretical hysteretic friction ratios. Yandell employed the same British testing device for his wet-friction measurements by securing the broken chips to the pendulum individually, which then swung the chip along a 7.6-cm (3-in.) length of a fixed rubber pad, 0.64-

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150 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces cm (¼-in) thick. The pad exhibited a damping factor of 0.45. The four roadway materials all generated wet coefficients of hysteretic friction of approximately 0.4, as defined by Yandell, over an average asperity slope range of 0.4 to 0.6. Unlike the comparison test results presented in Figure€5.36, Yandell did not report accuracy-assessment data involving differences in applied normal load. It was, therefore, not possible to carry out a back-calculation analysis to determine whether microhysteretic forces from microasperities larger than 3.25 × 10−3 mm (130 μin.) were likely present. Yandell’s hysteretic friction theory, as it applies to rubber surface deformation hysteresis, is inconsistent with the new analytical evidence concerning the microhysteresis mechanism presented in this chapter. As discussed with regard to Kummer’s [19] data, two determinants of the development of microhysteretic friction in rubber appear to be (1) the microroughness topography of the contacted surface and (2) the magnitude of the combined adhesive energies of the paired materials. Although the microroughness texture is involved in Yandell’s approach, we found in this chapter that microhysteretic forces in rubber appear to be independent of applied normal loads. As illustrated in Figure€5.36, the friction coefficients computed in accordance with Yandell’s theory are not independent of FN.

5.7

A Unified Theory of Rubber Friction

Expanding on Kummer’s [19] relationship discussed in Section 3.9, we are now in position to formulate a unified theory of rubber friction for conditions by treating surface deformation hysteresis as a separate term. The unified theory can be simply expressed as

FT = FA + FHs + FHb + FC,

(5.5)

where: FT = total frictional resistance developed between sliding rubber and a paired surface, FA = frictional contribution from combined van der Waals’ adhesion of the two surfaces, FHs = frictional contribution from surface deformation hysteresis (microhysteresis), FHb = frictional contribution from bulk deformation hysteresis (macrohysteresis), and FC = cohesion loss contribution from rubber wear. Use of this expression appears to allow numerical friction calculations to be carried out that are within engineering accuracy. Examples of the use of Equation 5.4 applied to rubber are presented in later chapters.

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A Unified Theory of Rubber Friction

5.8

151

Chapter Review

This chapter continued our examination of the scientific research carried out to understand more fully the basic mechanisms of rubber friction. We employed the back-calculation technique to analyze rubber friction test results reported in the graphical form of the metallic coefficient of friction µ vs. the force or pressure applied to the rubber specimens during such testing. Back-calculation refers to the need to quantify friction forces from plots published in the technical articles reviewed in which the numerical frictionforce data itself was not provided. Obtaining these data was necessary to allow new plots to be drawn displaying the total friction forces measured vs. applied load. It was found that, in the lower loading range, all of the published data sets yielded straight lines when drawn in the total-friction-force form. Figure€5.5 provides examples of straight-line plots derived by back-calculation from two published data sets. Plots from some of the analyzed data sets exhibit curvature of the initially straight lines in the higher loading range. Figure€5.21, involving the effects of temperature on rubber friction, depicts such higher-load curvature in two of the examined data sets. The back-calculation analyses in this chapter encompassed seven diversified groups of published rubber friction studies producing 27 different sets of test results. Except for the back-calculated values from one of these 27 tests, extrapolating (extending) the straight-line portions of the corresponding plots to the y (vertical)-axis yielded intercept values. Figure€5.5 portrays the extrapolating dashed lines and their intersections with the y-axis. In this figure, the small- and large-specimen intercept values were 1.4 kg (3 lb) and 0.7 kg (1.5 lb), respectively. Such y-axis intercepts were found in data generated from rubber sliding on both smooth and rough surfaces. On the basis of plots from the 26 data sets exhibiting y-axis intercepts, we considered that these y-axis values quantify the constant surface deformation hysteresis force (FHs) in sliding rubber. Because FHs is indicated as a constant rubber friction force, independent of both the force and pressure applied to rubber sliding on smooth and rough surfaces, we considered that surface deformation hysteresis is a distinct rubber friction mechanism, different from the adhesion and bulk deformation hysteresis mechanisms previously discussed. In data sets obtained from tests of rubber sliding on smooth surfaces in conditions where no significant rubber wear is produced, subtraction of the FHs force from the total measured friction force is considered to quantify adhesion friction (FA) forces only. Division of these calculated adhesion friction forces by the force applied to the sliding rubber during testing yielded μA, termed the rubber adhesion friction ratio to differentiate it from the metallic coefficient of friction. When rubber adhesion friction ratios are calculated for the lower loading range and plotted against the force or pressure applied to specimens during testing, constant μA values are generally observed. Such constant μA values

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152 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces are depicted in Figure€5.4. In the higher loading range, however, μA values can decrease. As a result, plots of rubber adhesion friction ratios in this higher loading range show a downwardly curved shape. The point on the plot at which the rubber adhesion friction ratio vs. applied force or pressure ceases to be a straight line and begins to curve downward has been called the adhesion transition force or pressure. Examples of this downwardly curved shape after initially horizontal plots are presented in Figure€5.15. The adhesion transition force (FNt) and pressure (PNt) can be important when quantifying friction in the design of rubber products and their paired surfaces. Reports of this rubber adhesion transition phenomenon could not be found in the literature. The phenomenon is not considered in current rubber friction design practice. Indications are that surface deformation hysteresis is produced during sliding when rubber contacts the surface microtexture of the paired, harder material. For this reason, FHs has been termed the microhysteresis force. Microhysteresis in sliding rubber appears to be a point-deformation phenomenon depending, in part, on the microroughness of the contacted solid and the degree of adhesion between the two materials. Figure€5.34 presents an idealized depiction of this mechanism. Most rubber friction test results published in the graphical form of the coefficient of friction μ vs. the force or pressure applied to the rubber specimens while sliding yield downwardly curved lines showing a decrease in this coefficient with increasing loading. Examples of such curves are displayed in Figure€3.4(a). It was shown in this chapter that inadvertent inclusion of the microhysteresis forces present in the test data producing such plots can be responsible for this curvature. Such plots as those seen in Figure€3.4(a) can give a misleading picture of rubber friction: the developed friction force is increasing rather than diminishing, as might be implied by the plots’ downward trend. The presence of microhysteresis was indicated in 26 of the 27 data sets we analyzed in this chapter. In the single exception, the extrapolated plot of the total measured friction force vs. the force applied to the specimen did not evidence a y-axis intercept but instead passed through the origin, suggesting that no microhysteresis developed. This one exception is exhibited by the low-adhesion-rubber plot of Figure€5.26, depicting a specially prepared (artificially low friction) test specimen sliding on Teflon. The other two plots in the figure, also for rubber specimens sliding on Teflon, indicated development of microhysteretic forces. We can conclude that, in dry conditions, the rubber-microhysteresis-friction mechanism is usually generated and its associated force is produced. A new, unified theory of rubber friction was formulated by treating microhysteresis as a separate term, yielding Equation 5.5,

FT = FA + FHs + FHb + FC,

where:

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A Unified Theory of Rubber Friction

153

FT = total frictional resistance developed between sliding rubber and a harder paired surface, FA = frictional contribution from combined van der Waals’ adhesion of the two surfaces, FHs = frictional contribution from surface deformation hysteresis (microhysteresis), FHb = frictional contribution from bulk deformation hysteresis (macrohysteresis), and FC = cohesion loss contribution from rubber wear.

The remainder of the book is principally concerned with applications of the unified theory to calculation of friction in the design of rubber products and their paired surfaces.

References



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1. Savkoor, A.R., On the friction of rubber, Wear, 8, 222, 1965. 2. Roth, F.L., Driscoll, R.L., and Holt, W.L., Frictional properties of rubber, J. Res. Nat. Bur. Stds. 28, 439, 1942. 3. Thirion, P., Les coefficients d’adhérence du caoutchouc, Rev. Gén. Caoutch., 23, 101, 1946. 4. Schallamach, A., The load dependence of rubber friction, Proc. Phys. Soc. London B, 65, 657, 1952. 5. Mori, K., Kaneda, S., Kanae, K., Hirahara, H., Oishi, Y., and Iwabuchi, A., Influence on friction force of adhesion force between vulcanizates and sliders, Rubber Chem. Techn., 67, 797, 1994. 6. Bartenev, G.M. and Lavrentjev, V.V., The law of vulcanized rubber friction, Wear, 4, 154, 1961. 7. Sigler, P.A., Geib, M.N., and Boone, T.H., Measurement of the slipperiness of walkway surfaces, J. Res. Nat. Bur. Stds., 40, 339, 1948. 8. Johnson, K.L., Kendall, K., and Roberts, A.D., Surface energy and the contact of elastic solids, Proc. Roy. Soc. A, 324, 301, 1971. 9. Moore, D.F., The Friction and Lubrication of Elastomers, Pergamon Press, Oxford, 1972. 10. Chang, W.-R., The effect of surface roughness on dynamic friction between Neolite and quarry tile, Safety Science, 29, 89, 1998. 11. Powers, C.M., Kulig, K., Flynn, J., and Brault, J.R., Repeatability and bias of two walkway safety tribometers, J. Test. Eval., 27, 368, 1999. 12. Schallamach, A., Friction and frictional rise of wedge sliders on rubber, Wear, 13, 13, 1969. 13. Yandell, W.O., A new theory of hysteretic sliding friction, Wear, 17, 229, 1970. 14. Hurry, J.A. and Prock, J.D., Coefficients of friction of rubber samples, India Rubber World, 128, 619, 1953. 15. Rabinowicz, E., Stick and slip, Sci. Am., 194, 109, 1956.

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154 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 16. Braun, R. and Roemer, D., Influences of waxes on static and dynamic friction, Soap/Cosmetics/Chemical Specialties, 50, 60, 1974. 17. Smith, R.H., Test foot contact time effects in pedestrian slip-resistance metrology, J. Test. Eval., 33, 557, 2005. 18. Savkoor, A.R., Models of friction, in Handbook of Materials Behavior Models, Volume II Failure of Materials, Academic Press, San Diego, CA, 2001. 19. Kummer, H.W., Unified Theory of Rubber and Tire Friction, Engineering Research Bulletin B-94, The Pennsylvania State University, State College, PA, 1966. 20. Greenwood, N.A. and Tabor, D., The friction of hard sliders on lubricated rubber: the importance of deformation losses, Proc. Phys. Soc., 71, 989, 1958.

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6 The Rubber Adhesion Transition Phenomenon

6.1

Introduction

We saw in Section 5.2.2 concerning a back-calculation analysis of Thirion’s data [1] that, on Cartesian coordinates, the adhesive friction forces associated with the two differently sized rubber specimens sliding on a macroscopically smooth surface exhibited straight lines only in the lower FN range. At higher loadings (Figures€5.6 and 5.7), the plots curved parabolically in a way consistent with the adhesion force increasing, but at a slower rate than the applied normal load. Plotting Thirion’s adhesion data on logarithmic coordinates as FA vs. FN (Figure€5.9) produced two straight lines for each data set that intersected at different values of the applied normal force. Graphing Thirion’s data on logarithmic coordinates as FA vs. PN (Figure€5.10), however, yielded two straight lines for each data set that intersected at the same value of PN. We termed this value the adhesion transition pressure, or PNt. This chapter presents and discusses friction mechanisms associated with, or bearing on, the adhesion transition pressure evidenced when rubber slides on macroscopically smooth surfaces. It seems likely that rubber products and their paired surfaces can be designed to control the magnitude of PNt to some extent, making it larger or smaller in accordance with the desired friction development characteristics of specific engineering applications.

6.2

Further Aspects of the Rubber Adhesive Friction Mechanism

6.2.1 Arnold, Roberts, and Taylor In 1987, Arnold et al. [2] presented their investigations of the friction-related effects of Schallamach waves, which can be generated when smooth rubber slides on a flat, smooth harder surface. It had been previously found 155

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156 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces that when this wave regime develops, the observed friction magnitude only slightly depends on sliding speed, temperature, or rubber type (of similar hardness). Such findings contrast markedly with the results of Grosch’s [3] testing, from which Schallamach waves had been excluded. Both Schallamach waves and Grosch’s studies were addressed in Chapter 3. It also was previously shown that Schallamach waves act as a stress-relieving mechanism for rubber during sliding, and that the magnitude of the friction force developed is, therefore, determined by the elastic modulus of the elastomer involved. The existence of such waves limits true sliding — it will be remembered that Schallamach waves are likened to a caterpillar’s movement on a leaf — and reduces contact with the paired surface as depicted in Figure€3.11. Grosch, like most of the dynamic friction researchers discussed in Chapter 3, experienced difficulties during protocol optimization with chattering of smooth rubber and reproducibility of the friction measurements. Various steps were taken to surmount the problem, usually roughening the rubber and sometimes employing an undulating test track. After carrying out such refinements, there was broad accord between the test results within each protocol. Arnold et al. sought to explain these experiences on a scientific basis for use in engineering applications to rubber products. 6.2.1.1 Testing Protocols Arnold et al. [2] investigated the friction developed under varying pressures between smooth, natural rubber hemispheres sliding on six flat, smooth tracks, and compared those measurements with test results obtained after roughening the hemispheres with 180 grade emery paper and sliding them on the same surfaces. Most of the test tracks used were transparent. Schallamach waves could be observed in such cases, if they developed. Arnold et al. chose to quantify the pressure at each load applied during sliding using the static contact areas of the hemispheres under the same loads, which were determined before testing. (The contact areas of the hemispheres during sliding could not be accurately measured.) The static contact areas were found to agree well with values obtained by applying the Hertz equation:

FA = cA(FN)2/3.

(6.1)

The pressures shown in the two figures discussed below were calculated using these verified nominal Hertzian areas. The limits in applying this equation to rubber friction were discussed in Chapter 3. Also, unaccounted for FHs forces may have developed in this testing. The six smooth tracks, selected for their different surface free energies, were glass, nylon polyethylene (PE), polypropylene (PP), poly-(methyl methacrylate) (PMMA), and polytetrafluoroethylene (PTFE), or Teflon. Neither the surface free energies nor the microroughness of these materials were reported.

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157

The Rubber Adhesion Transition Phenomenon 6.2.1.2 Arnold et al.’s Interpretations of Their Test Data

Figure€6.1 presents Arnold et al.’s [2] smooth-hemisphere test results. The y-axis values are expressed in terms of a “shear strength” (τ), determined by dividing the measured friction force at each applied pressure by the corresponding static Hertzian area for that pressure. As observed in the figure, five of the test surfaces gave plots that approach coincidence. Schallamach waves were observed in all of these cases where the track was transparent. The lone exception was PTFE, for which the existence of two stable sliding regimes, with and without waves, was indicated. As seen in Figure€6.1, Arnold et al. observed Schallamach waves for rubber sliding on Teflon at the lowest pressure utilized in their testing, about 0.065 MPa (9.4 psi). Under the remainder of the applied pressures, starting at about 0.070 MPa (10 psi), no Schallamach waves could be detected on the PTFE. In these cases, a marked reduction in the calculated shear stress between the moving rubber and the Teflon was noted. When these greater pressures were applied, only true sliding (without waves) of the smooth rubber hemisphere on the PTFE without

Shear Strength, τ(MPa)

0.4

0.3

PTFE Nylon Glass PMMA PP PE PTFE Sliding speed = 0.2 mms–1 T = 23°C ± 1°C RH = 55%–60%

0.2

0.1

0

0

0.1

0.2

Contact Pressure, P(MPa) PMMA = poly-(methyl methacrylate) PP = polypropylene PE = polyethylene PTFE = polytetrafluoroethylene Figure€6.1 Plots of shear strength, determined by dividing the measured friction force at each applied pressure by the corresponding static Hertzian area for that pressure, versus applied pressure for smooth, natural rubber hemispheres sliding on various substrates. (From Arnold, S.P., Roberts, A.D., and Taylor, A.D., J. Nat. Rubb. Res., 2, 1, 1987. With permission.)

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158 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces chattering was evidenced. Barquins and Roberts [4] had previously confirmed that Schallamach wave generation is more likely to occur at lower pressures. The Arnold et al. PTFE findings were consistent with those of Barquins and Roberts. A lesson here is that high pressure, under the right conditions, can preclude the development of Schallamach waves in smooth rubber sliding on macroscopically smooth surfaces. Arnold et al. postulated that, at the higher pressures employed, insufficient adhesion existed in this PTFE pairing to generate the stress-relieving Schallamach-wave regime. Figure€6.2 presents the Arnold et al. rough-hemisphere τ plots. No Schallamach waves were observed in the testing that produced these data. Arnold et al. theorized that Schallamach waves do not appear to form on roughened rubber, and the six distinct plots seen in the figure correspond to the surface free energies of the tracks; that is, the lines were thought to be in rank order and separated in each case in agreement with the sum of the surface free energies of the sliding rubber specimen and the paired track. The absence of Schallamach waves was considered to indicate that “true” sliding had

Shear Strength, τ(MPa)

0.4

0.3

PMMA Nylon Glass PP PE PTFE Sliding speed = 0.2 mms–1 T = 23° ± 1°C RH = 55% – 60%

0.2

0.1

0

0

0.1

0.2

Contact Pressure, P(MPa) PMMA = poly-(methyl methacrylate) PP = polypropylene PE = polyethylene PTFE = polytetrafluoroethylene Figure€6.2 Plots of shear strength, determined by dividing the measured friction force at each applied pressure by the corresponding static Hertzian area for that pressure, versus applied pressure for roughened, natural rubber hemispheres sliding on various substrates. (From Arnold, S.P., Roberts, A.D., and Taylor, A.D., J. Nat. Rubb. Res., 2, 1, 1987. With permission.)

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The Rubber Adhesion Transition Phenomenon

159

occurred. Accordingly, Arnold et al. emphasized that, in dynamic friction investigations of elastomers, it is vital to report the protocol and the likely mechanisms involved. In furtherance of their focus on engineering applications, Arnold et al. commented on the use of referenced friction measurements, cautioning that minor distinctions among different rubber compositions and track surfaces will affect friction as measured both in the laboratory and in engineering practice. In applications such as motor vehicle tires and windshield wipers, these researchers advised that measurements obtained from testing of roughened rubber should be employed. On the other hand, when rubber seals are of interest, Arnold et al. referenced friction values should come from testing of smooth-surface pairings. In such uses, friction depends less on elastomeric hysteresis or surface free energy of the paired material, and is principally controlled by the bulk elastic modulus of the rubber component. 6.2.1.3 Additional Interpretations of the Arnold et al. Data An indication that can be drawn from the Arnold et al. [2] tests concerns the difference between the PTFE results from the smooth and roughened hemispheres. As seen in Figure€6.1, the mean τ value for smooth rubber, where no Schallamach waves were produced, equaled approximately 0.17 MPa (24.6 psi). Figure€6.2 depicts the τ values arising when roughened rubber was slid on the same PTFE surface and no waves were detected. The mean shear strength value appears to be about 0.07 MPa (10 psi), a noticeable decrease, arising only from roughening of the rubber. This decrease is consistent with the widely held belief that a smooth rubber surface slid on a macroscopically smooth paired surface allows greater van der Waals’ adhesion to develop than does a roughened specimen of the same rubber composition when slid on this same macroscopically smooth surface. We must express a caveat to this indication, however, in that the rubber microhysteresis mechanism may have developed in the two protocols involving PTFE. (This was seen to occur in the Mori et al. testing [11].) If so, the values of the FHs forces for roughened rubber on PTFE may have been different from its values for smooth rubber on this same Teflon surface. A greater rough-surface microhysteretic component of the total friction measured would, of course, lessen the apparent adhesional differences between the two rubber surface conditions. 6.2.1.4 Rubber Microhysteresis and Schallamach Waves A further question that arises is whether the rubber surface deformation hysteresis mechanism can develop when Schallamach waves are present. According to Arnold et al. [2], relative movement between a smooth rubber hemisphere and a smooth contacted surface when Schallamach waves have been induced may be due only to these detached, compressed-rubber

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160 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces segments moving above the test track from front to rear. Presumably, microhysteretic resistance in such moving rubber does not arise on the detached wave surfaces. Schallamach [5] had originally formulated this detachment theory, while also postulating that adhesion of the rubber to the contacted track between the waves was “complete.” Rubber contact between the waves is represented by the shaded area in Figure€3.11. We can be certain that Schallamach did not mean that the real area of contact between the rubber and track in these stationary regions always equaled the nominal area of contact, but rather that no detachment occurred. It is seen in Schallamach’s model in Figure€3.11 that rubber contacting the track experiences tangential stresses resisted by adhesion. We can hypothesize that these stresses induce concurrent microhysteretic forces in the rubber. The back-calculation analysis of the work of Powers et al. [6] presented in Chapter 9 — “Rubber Microhysteresis in Static Friction Testing” — indicates that the microhysteresis mechanism develops when tangent forces are applied by a rubber test foot to a macroscopically smooth surface in static testing. The correctness of this hypothesis for a Schallamach regime remains to be demonstrated.

6.3

Adhesive Friction of Metal and Non-Elastomeric Plastics in the Elastic Loading Range

The similar mechanisms of adhesive friction between pairings of metals and pairings of non-elastomeric plastics in the elastic loading range were investigated in the 1950s. Archard [7,8] carried out much of this work. When friction testing with these materials was conducted carefully, employing appropriately low loading, initial deformation of their contacting surface asperities could be kept elastic. It was found that adhesion in these pairings increases with increases in the real area of such elastic contact. With increased loading of the metals, however, their asperities quickly reach the plastic range, and their frictional characteristics were governed by the mechanisms discussed in Chapter 2. When investigating pairings of brass and pairings of poly-(methyl methacrylate), Archard [7,8] determined that, before the elastically deforming asperities of the metal and plastic reached the plastic loading range, two different adhesive friction mechanisms could arise. Archard [7,8] found that, depending on the asperity configurations of the materials, both the metal and plastic could evidence a directly proportional applied load-coefficient-offriction relationship in the elastic range; that is, both the metal and plastic could conform to the relationship

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The Rubber Adhesion Transition Phenomenon

FA = μA(FN).

161 (6.2)

With other asperity configurations, however, the friction developed in the elastic range by these two different materials was quantified by the generalized Hertz equation

FA = cA(FN)m.

(6.3)

That is, frictional pairings of metal and frictional pairings of non-elastomeric plastic can exhibit the elastic adhesion transition phenomenon. It is perhaps not surprising that rubber can also develop this mechanism. These findings [7,8] from adhesive friction research on pairings of metal and pairings of non-elastomeric plastic in the elastic loading range are consistent with the back-calculation analyses of rubber friction presented in this book. We have seen that, before PNt is reached, FA for rubber is expressed by Equation 6.2; while in the higher loading range, Equation 6.3 applies. In Archard’s [7,8] testing it was obvious that, as more load was applied in the elastic range, more real areas of contact in the pairings developed. During the elastic deformation of the asperities, new real areas of contact would be created, while existing areas of contact could be concurrently enlarged. A focus of Archard’s [7,8] studies was to decipher the interplay between these two mechanisms. Archard [7,8] postulated that if the primary result of greater loading is to establish new areas of contact, then the increased load and increased adhesive friction force will be directly proportional, conforming to Equation 6.2. If, on the other hand, the primary result of greater loading is to enlarge existing areas of contact, then the increased loading and adhesive friction force will not be directly proportional, but instead will conform to Equation 6.3. Archard’s [7,8] conclusions regarding areas of contact have been reexamined recently by Persson [9], who concurred with them. Archard’s [7,8] explanations for development of the adhesion transition phenomenon in metals and non-elastomeric plastics also appear applicable to rubber.

6.4

Determinants Controlling the Value of P Nt

6.4.1

Thirion’s Adhesion Data

As evidenced in Figure€5.10, presenting the Thirion [1] adhesion data from his two differently sized specimens — expressed as FA vs. PN — the pressure at which FA ceases to be directly proportional for both the small and large specimens, PNt, was indicated to equal 7 kg/cm 2 (100 psi). Thirion’s specimens were constitutively identical, molded in the same form materials and identically roughened, slid on the same macroscopically smooth glass

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162 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces surface at the same constant velocity, and tested under the same environmental conditions in the laboratory. With regard to the identical values of PNt in Figure€5.10, the two rubber specimens’ asperity configuration and the track’s glass asperity configuration are of special interest. We can adduce from the plots and equations pertaining to Thirion’s adhesion data that the as-tested asperity configurations of the different surfaces and the sliding behavior of the rubber asperities appear to play significant roles in friction development. Being mindful of Archard’s [7,8] findings, we can theorize that, under directly proportional loading, the rubber asperities compressed in a way that produced directly proportional increases in new real areas of contact with the paired glass. And further, after PNt was reached, the preponderant rubber asperity behavior was one in which greater loading enlarged existing areas of contact with the track. Thirion’s adhesion data are useful in formulating another theory: The asperity configurations of both paired surfaces are determinants of the value of PNt when involved rubber materials are constitutively identical and slip on a harder material. We will look at Schallamach’s [10] adhesion data involving rubber specimens that were not constitutively identical. 6.4.2 Schallamach’s Adhesion Data Figures€5.16 and 5.17 presented Schallamach’s [10] adhesion data from his three identically sized specimens, expressed as FA vs. FN and FA vs. PN, respectively. The applied normal force at which FA ceased to be directly proportional for all three specimens was indicated as about 2.25 kg (5 lb). The PNt value was seen as approximately 0.66 kg/cm2 (9.4 psi). Schallamach’s specimens were constitutively different but were molded in the same form materials and identically roughened, slid on the same macroscopically smooth glass surface at the same constant velocity, and tested under the same environmental conditions in the laboratory. We can theorize that the identical PNt values were evidenced because the three specimens were of identical size. In addition, it may be theorized that, the asperity configurations of both paired surfaces can be determinants of the value of PNt when involved rubber materials are constitutively different. It appears that, all else being equal, the value of PNt is independent of rubber composition.

6.5

Controlling Adhesion Transition Pressure to Optimize Friction Development

We have previously discussed the fact that applying the laws of metallic friction to rubber can be misleading. In the case of an elastomeric material, a

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163

The Rubber Adhesion Transition Phenomenon

decrease in the adhesion friction ratio does not mean that adhesion is diminishing; rather, when μA begins to decrease at the adhesion transition pressure, the adhesive force, FA, is still increasing, but at a slower rate than is FN. This transitioning behavior appears to offer practical opportunities for beneficially controlling the frictional characteristics of rubber products, at least to a degree. When the service conditions of a rubber product are such that it is subjected to changing loads and maximum friction development between the product and its paired surfaces is usually advantageous — such as in footwear heels and soles or motor vehicle tires — it may be desirable to make the value of PNt as high as reasonably possible. In this way, the pairing’s traction characteristics can be maximized through judicious design. On the other hand, causing the adhesion transition to occur as soon as possible during the loading cycle would assist in minimizing friction, if desired. Table€6.1 presents a list of product properties relevant to the control of PNt.

Table€6.1 Properties of Rubber and Its Paired Surfaces Relevant to the Control of the Adhesion Transition Pressure, PNt* Properties Apparently Controlling PNt

Figure Ref.

• Configuration of surface asperities Configuration of surface asperities on the two rubber specimens are identical. (Both rubber specimens molded on same mold surface.)

5.10

Configuration of surface asperities on the three rubber specimens are identical. (All rubber specimens molded on same mold surface.)

5.17

Configuration of asperities on the contacted surface are identical. (Both specimens slid on same glass surface.)

5.10

Configuration of asperities on the contacted surface are identical. (All specimens slid on same glass surface.)

5.17

Properties Apparently Not Controlling PNt

Figure Ref.

• Areas of nominal rubber contact patch with paired surface. The specimens are of different sizes.

5.10

• Rubber hardness. Testing involved specimens possessing different hardness values.

5.17

• Rubber adhesion propensity. Testing involved specimens possessing different surface free energies.

5.17

* Properties are considered in conditions in which all other involved variables are unchanged.

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164 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

6.6

“Low” μA Values in the Low-Loading Range

Figure€5.2 presented a plot of µA vs. FN for the back-calculated Roth et al. [12] small specimen data. A constant relationship was depicted in most of the test loading range. At the lowest FN values, however, where the indicated magnitude of FHs exceeded FN or was close to it, two calculated rubber adhesion friction ratios were below the others. A likely reason for these apparently anomalous values is now discussed. Archard [7,8] found that during the elastic deformation of metal and nonelastomeric plastic asperities in the low-loading range, new real areas of contact were created. He postulated that if the primary result of greater loading in this range is to establish new areas of contact, then the increased normal load and increased adhesive friction force will be directly proportional, conforming to Equation 6.2:

FA = μA(FN).

Rubber adhesion friction ratios in the low-loading range obtained from the back-calculation analyses presented in this book are generally consistent with Archard’s findings. We can expect, therefore, that all such back-calculated μA values for rubber should conform to Equation 6.2. As discussed in Section 5.4.2, an analysis of testing data from the work of Powers et al. [6] to be presented in Chapter 9 indicates that FHs can be independent of the applied tangent force on macroscopically smooth surfaces. Once the applied tangent force exceeds FHs in magnitude, as would be inherent in the dynamic friction testing we have been considering — where relative movement between rubber and its paired material always takes place — microhysteretic forces developed on macroscopically smooth surfaces appear constant. Thus, we can also expect the FHs force developed in the Roth et al. small-specimen testing to be constant. It seems likely that arithmetical uncertainties associated with the back-calculation process are responsible for apparently anomalous μA values determined from this process and presented in this book. In the low normal loading range, determination of rubber adhesion friction ratios involves division of small values of FA by small values of FN. This can produce large apparent differences in the results, thereby exaggerating apparent mechanistic effects. The data we have employed in back-calculation are necessarily obtained from “reading” published plots reporting friction test results. There are unavoidable numerical uncertainties in such read values.

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The Rubber Adhesion Transition Phenomenon

6.7

165

Chapter Review

The rubber adhesion transition phenomenon was introduced in Chapter 5. This chapter addresses more fully applications of the adhesion transition mechanism in the design of the friction characteristics of rubber products and their paired surfaces. In 1987, Arnold et al. [2] demonstrated that roughening a rubber surface decreases its adhesion-friction-force-development potential when sliding on smooth materials. Considering what had been learned previously, this was anticipated, but controlled laboratory testing was necessary to validate the expectation. The roughness of a rubber product’s surface is one of its physical properties that offers opportunities for controlling the value of the adhesion transition pressure (PNt) in specific engineering applications. Arnold et al. also showed that Schallamach waves, as discussed in Chapter 3, arise as a friction-stress-relieving mechanism for sliding rubber. Schallamach wave movement, likened to a caterpillar traveling on a leaf, involves waves of detachment of rubber from the paired surface. Generation of such waves can be precluded by roughening the rubber surface. In some circumstances, development of the wave mechanism can also be prevented by application of high pressure to the rubber product. Arnold et al. addressed the engineering applications of their research, commenting on the use of published friction measurements. They cautioned that minor distinctions among different rubber compositions and contacted surfaces will affect friction as it develops in practice. In applications such as motor vehicle tires, these researchers advised that friction measurements obtained from the testing of roughened rubber should be employed. When smooth rubber products, such as seals, are of interest, referenced friction values should come from testing of smooth-surface pairings. This chapter also considered relevant research on adhesive friction mechanisms in metals and plastics and their bearing on the behavior of rubber friction. In 1957, Archard [7,8] showed that when friction tests of metal-on-metal and plastic-on-plastic are carefully carried out under low loading, the points of surface contact deform elastically; that is, like rubber. Under low loading, adhesive friction force developed between metal surfaces and between plastic surfaces can be directly proportional to such loads. Archard determined that the directly proportional relationship arises when the primary result of increases in load applied to the metal or plastic pairings produces new areas of contact between their respective surfaces. With such metal or plastic pairings, however, a change in the adhesivefriction-force mechanism eventually occurs; that is, these materials can also experience an adhesion transition pressure, PNt. Archard further showed that when the predominant result of increasing the applied load is to expand existing areas of contact in the metal pairings and in the plastic pairings, the developed adhesive friction force ceased being directly proportional to the increasing load while the adhesion friction force is still growing.

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166 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Archard’s findings explain the workings of the elastic adhesion transition mechanism in metal and plastic. It is likely that Archard’s findings also explain this mechanism in rubber products. The existence of the elastic adhesion transition mechanism in metal and plastic is a confirmation of its existence in rubber and supports the use of the PNt phenomenon in design. Archard’s findings provide an understanding of the PNt mechanism useful in design so as to identify and address the correct variables needed to achieve the desired ends. As far as could be determined, the rubber adhesion transition mechanism has not been reported previously in the literature. This design aid is not generally included in current rubber friction design practice. Rubber products and their paired surfaces can be designed to control the magnitude of PNt to a degree, making it larger or smaller in accordance with the friction development characteristics desired for specific engineering applications. Table€6.1 presents a list of product properties relevant to PNt control.

References

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1. Thirion, P., Les coefficients d’adhérence du caoutchouc, Rev. Gén. Caoutch., 23, 101, 1946. 2. Arnold, S.P., Roberts, A.D., and Taylor, A.D., Rubber friction dependence on roughness and surface energy, J. Nat. Rubb. Res., 2, 1, 1987. 3. Grosch, K.A., The relation between the friction and visco-elastic properties of rubber, Proc. Roy. Soc. A, 274, 21, 1963. 4. Barquins, M. and Roberts, A.D., Rubber friction variation with rate and temperature: some new observations, J. Phys. D.: Appl. Phys., 19, 547, 1986. 5. Schallamach, A., How does rubber slide?, Wear, 17, 301, 1971. 6. Powers, C.M., Kulig, K., Flynn, J., and Brault, J.R., Repeatability and bias of two walkway safety tribometers, J. Test. Eval., 27, 368, 1999. 7. Archard, J.F., Elastic deformation and the contact of solids, Nature, 172, 918, 1953. 8. Archard, J.F., Elastic deformation and the laws of friction, Proc. Roy. Soc. A, 243, 190, 1957. 9. Persson, B.N.J., Sliding Friction, Physical Principles and Applications, Springer-Verlag, Berlin, 2000. 10. Schallamach, A., The load dependence of rubber friction, Proc. Phys. Soc. London B, 65, 657, 1952. 11. Mori, K., Kaneda, S., Kanae, K., Hirahara, H., Oishi, Y., and Iwabuchi, A., Influence on friction force of adhesion force between vulcanizates and sliders, Rubber Chem. Techn., 67, 797, 1994. 12. Roth, F.L., Driscoll, R.L., and Holt, W.L., Frictional properties of rubber, J. Res. Nat. Bur. Stds., 28, 439, 1942.

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7 Microhysteretic Friction in Dry Rubber Products

7.1

Introduction

Chapter 5 examined the hypothesis formulated by Savkoor [1] that a surface-deformation-hysteresis friction mechanism develops in rubber when it slides on a harder material. Savkoor accepted that macroscopically smooth surfaces, such as plate glass, can be microscopically rough. His hysteresis posit was based on the supposition that rubber surfaces in contact with microscopic asperities on harder solids can mechanically interlock with each other, providing deformational resistance to relative movement between the two materials. The back-calculation analyses of rubber friction test data presented in Chapter 5 indicated the existence of such a microhysteretic mechanism in concurrence with Savkoor’s hypothesis. The new analytical evidence for the existence of rubber microhysteresis suggests that this mechanism generates a constant friction force (FHs), independent of applied normal load, which depends on the presence of sufficient combined surface free energies resident in the paired materials to provide at least a minimum adhesive force. To all appearances, microhysteresis in sliding rubber seems to arise from deformation of the rubber surface while it adheres to microtopographic roughness points on the contacted material. Incorporating the FHs force in the phenomenological approach to understanding the interplay of sliding rubber with its paired surfaces provides a basis for more accurately differentiating and quantifying the other friction forces that can develop in such circumstances. The rubber friction data utilized in Chapter 5 to develop the microhysteretic findings presented there did not include all the wet and dry testing examined in Chapter 4. The present chapter addresses more of the friction research discussed in Chapter 4, focusing on rubber products in dry conditions.

167

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168 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

7.2

Microhysteresis in Automotive Tire Rubber in Dry Conditions

During the period following World War II, it was realized that the synthetic rubber tires of that time were more likely to slip on ice than were those with treads composed of natural rubber (NR). Pfalzner [2] carried out comparison coefficient-of-friction testing of these two general types of rubber to assist in improving the traction characteristics of synthetic tires. As discussed in Section 4.2.7, Pfalzner selected formulations of Hycar (acrylonitrile butadiene), GR-S (styrene butadiene), and Neoprene for this purpose. Pfalzner prepared 6.45 cm2 × 0.61 cm (1 in.2 × 0.25 in.) and 1.6 cm2 × 0.61 cm (0.25 in.2 by 0.25 in.) samples of the four rubber substances and affixed them to the underside of wood blocks that also served as loading platforms. A calibrated steel spring was attached to the blocks in the plane of the loaded block-rubber specimen’s center of mass to measure friction forces without inducing a vertical moment in the carriage. The specimens were loaded up to 89.6 kPa (42 psi) and 689.5 kPa (100 psi), respectively. The µ vs. FN testing was carried out at −4°C (+20°F) in a laboratory coldroom capable of controlling temperatures between 0°C (+32°F) and −29°C (−10°F). Pfalzner constructed a circular track on an electrically driven turntable into which water was poured and frozen. Freezing was done in such a manner that the surface of the ice was smooth. This dynamic testing, with the turntable rotating at a constant speed of 5.24 rad/sec (50 rpm), can be considered to have been conducted in dry conditions. Figure€4.22 presented plots of the back-calculated µ values vs. FN for Pfalzner’s 6.45 cm 2 (1 in.2) samples of the four different rubber compositions loaded up to 288 kPa (42 psi). It was observed that the µ values for natural rubber and GR-S decreased with increased loading; however, the Hycar and Neoprene samples, with the lowest indicated traction potential, exhibited a different behavior: their coefficients first increased and then decreased. Because the surface of the ice was smooth and macrohysteresis in the rubber samples was not expected, the Hycar and Neoprene specimens were apparently affected by temperature so as to produce this anomalous behavior. Figure€7.1 presents results from a back-calculation analysis of the 6.45 cm 2 × 0.61 cm (1 in.2 × 0.25 in.) natural rubber data in the lower loading range depicted in Figure€4.22. It is seen that an indicated microhysteresis force of approximately 0.23 kg (0.50 lb) arose in Pfalzner’s testing of this tire-compound specimen. Figure€7.1 also depicts the results from a backcalculation analysis of Pfalzner’s GR-S friction measurements. They, too, suggest the presence of a FHs force, in this case approximately 0.11 kg (0.25 lb). Because of the “humps” in the Hycar and Neoprene data shown in Figure€4.22, as opposed to the smooth hyperbolic curves expected in such µ

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Microhysteretic Friction in Dry Rubber Products

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Total Measured Friction Force (FT)–lbs

5

4

Natural rubber

3

GR-S 2

1

0

Hycar 0

10 20 30 Applied Normal Load (FN)–lbs

Figure€7.1 Back-calculated friction forces from coefficientof-friction testing involving 1-in.2 rubber specimens sliding on ice. (From Pfalzner, P.M., Can. J. Res. F, 28, 468, 1950.) 0.25 Natural rubber

Rubber Adhesion Friction Ratio–µA

vs. FN plots, it was concluded that these results were affected by the temperature of the ice track and are anomalous; nevertheless, the Hycar F T vs. F N plot in Figure€7.1 is of interest. The Hycar specimen evidences a constant microhysteresis force of about 0.36 N (0.08 lb). The Neoprene data did not indicate the presence of microhysteresis. This suggests that, at the low temperature — −4°C (20°F) — involved, the Neoprene rubber became too hard to be significantly deformed by the microtexture of the ice surface. Figure€7.2 depicts the adhesion friction ratios determined by back-calculation for the natural rubber, GR-S, and Hycar 6.45 cm 2 × 0.61 cm (1 in. 2 × 0.25 in.) testing in the low-loading range. The values are indicated to be 0.22, 0.15, and 0.17, respectively. The relative positions of the three rubber compounds in Figure€7.2 should be noted. The adhesion friction ratio for natural rubber is greatest, followed by those for Hycar and GR-S in that order. The relative ordering of the Hycar and GR-S plots in Figure€7.2 appears consistent with the Hycar curve depicted in Figure€4.22, most of which is above the GR-S curve. Figure€4.21 depicted the μ vs. FN data for Pfalzner’s [2] 1.6 cm2 × 0.61 cm (0.25 in.2 × 0.25 in.) samples. The natural rubber, GR-S, and Hycar specimens all evidenced hyperbolic curves, indicating that microhysteresis forces were also present in these tests.

0.20 Hycar 0.15

GR-S

0.10

0.05

0

0 2 4 6 8 10 12 Applied Normal Load (FN )–lbs

Figure€7.2 Back-calculated adhesion friction ratios from coefficient-of-friction testing involving 1-in.2 rubber specimens sliding on ice. (From Pfalzner, P.M., Can. J. Res. F, 28, 468, 1950.)

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170 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

7.3

Microhysteresis in Dry Aircraft Tires

7.3.1

B-29 Tire Rubber on Dry Concrete

7.3.1.1 Testing on Smooth Concrete Hample [3] carried out coefficient-of-friction tests on segments of a rubber B-29 tire. Circular tread samples were cut from the thickest portion of a worn, ten-ply, nose-wheel tire in storage for at least 18 months after use in flight. Figure€4.5 indicated the area on the tire from which the specimens were taken. Figures€4.6 and 4.7 illustrated the high-pressure and low-pressure configurations employed by Hample for his testing. Three test runs were typically made for each set of conditions and averaged to obtain mean reported values. Hample stated that, prior to his study, there had been doubt as to the validity of previously utilized static friction data obtained from testing without taking temperature effects into account. It was realized that rapid changes in pressure and temperature during aircraft wheel spin-up occurred while landing. The purpose of his investigations was to gain insight into these effects, which can produce nearly molten tire rubber when landing on portland cement concrete runways. As evidence of this effect, the landing area portions of such runways are often coated with aircraft tire material. 7.3.1.1.1

High-pressure testing on smooth concrete

Three different types of portland cement concrete finishes were selected for testing. These were a purposely smooth surface obtained by conventional troweling, a broom-swept rough surface, and a semi-smooth surface produced by finishing the placed concrete with a 2 × 4. The smooth-surface testing is addressed in this section. 7.3.1.1.1.1 Ambient-temperature testing on smooth concrete: 24°C (75°F) A back-calculation analysis was carried out on Hample’s high-pressure, smooth-surface, ambient-temperature, coefficient-of-friction plot depicted in Figure€4.8. The nominal sample area of 15.5 cm2 (2.40 in.2) was utilized to calculate FN values. Figure€7.3 presents the results of this analysis. The rubber coefficient-of-friction data obtained on this smooth surface exhibited a hyperbolic curve when plotted as μ vs. FN, and the back-calculated FT vs. FN values indicated an extrapolated y-intercept value — in this case equaling approximately 18.6 kg (40 lb). As shown in Figure€7.4, subtraction of 18.6 kg (40 lb) from each FT value for the smooth concrete in Figure€7.3 to obtain the FA forces for the subject protocol yielded a plot passing through the origin when extended. The FA plot is initially straight, but becomes parabolic above an applied load — the FNt value — of about 227 kg (500 lb). In these calculations and those to follow involving Hample’s data, any contributions to the total measured friction force from wear of the test samples, or cohesion losses (FC), are ignored.

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Microhysteretic Friction in Dry Rubber Products 1300

Smooth concrete surface

1200 Rough concrete surface

1100

Total Measured Friction Force (FT)–lbs

1000 900 800 700 Semi-smooth concrete surface

600 500 400 300 200 100 0

0

500

1000 1500 2000 2500 Applied Normal Load (FN)–lbs

3000

Figure€7.3 Back-calculated tangent forces from coefficient-of-friction testing involving B-29 tire segments sliding on smooth, semi-smooth, and rough portland cement concrete. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

Figure€7.5 depicts the calculated adhesion friction ratio-FN plot for the smooth concrete. Before the μA relationship becomes hyperbolic at the adhesion transition point, the apparently constant adhesion friction ratio equals approximately 0.86. 7.3.1.1.1.2 High-temperature testing on smooth concrete: 149°C (300°F) Figure€7.6 presents high-temperature friction measurements reported by Hample from his high-pressure testing. The data are for the smooth, semismooth, and broom-swept concrete surfaces at 149°C (300°F). It is instructive to refer to Figure€4.8 where three distinct curves can be seen for these three surfaces and compare the corresponding coefficient plots to the μ values in

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172 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 1300 1200 Rough concrete surface

1100

Smooth concrete surface

1000

Friction Forces–lbs

900 800 700

Semi-smooth concrete surface

600 500 400 300 200 100 0

0

500

1000 1500 2000 2500 Applied Normal Load (FN)–lbs

3000

Figure€7.4 Back-calculated friction forces from coefficient-of-friction testing involving B-29 tire segments sliding on smooth, semi-smooth, and rough portland cement concrete with y-axis-intercept values removed. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

Figure€7.6. It is observed that the plots for all three concrete surfaces in Figure€7.6 have become nearly coincident at 149°C (300°F). In addition to changes in the properties of Hample’s tire-tread specimens as a result of subjecting them to a higher temperature, it seems likely that heating the concrete to a temperature above the boiling point of water physically altered the concrete’s surface, the cementitious constituents of which are hydrates that shrink as a result of water loss. Such alteration of the concrete’s surface may have changed its microstructure. Figure€7.7 displays the results of a back-calculation analysis of Figure€7.6’s data for the smooth concrete. A rubber surface deformation hysteresis value

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173

Rubber Friction Ratios

Microhysteretic Friction in Dry Rubber Products 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Rough concrete surface (µA+Hb)

Smooth concrete surface (µA)

Semi-smooth concrete surface (µA+Hb)

0

500

1000 1500 2000 2500 Applied Normal Load (FN)–lbs

3000

Figure€7.5 Back-calculated rubber friction ratios from coefficient-of-friction testing involving B-29 tire segments sliding on smooth, semi-smooth, and rough portland cement concrete. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.) 1.40

Coefficient of Friction–µ

1.20 1.00 .80 .60 .40 .20 0

Rough surf. Smooth surf. Semi-smooth surf. Arithmetical average (b) 200

400 600 800 Normal Pressure, psi

1000

1200

Figure€7.6 High-temperature — 300°F (149°C) — coefficient-of-friction testing involving B-29 tire segments sliding on smooth, semi-smooth, and rough portland cement concrete. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

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174 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Total Measured Friction Force (FT)–lbs

600

500

400

300

200

100

0

0

500 1000 1500 2000 Applied Normal Load (FN)–lbs

2500

Figure€7.7 Back-calculated friction forces from high-temperature — 149°C (300°F) — coefficient-of-friction testing involving B-29 tire segments sliding on smooth, semi-smooth, and rough portland cement concrete using data shown in Figure€7.6. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

of approximately 40.9 kg (90 lb) is indicated for the three concrete surfaces. At ambient temperature, the smooth-concrete microhysteretic force was indicated as 18.6 kg (40 lb). The increase in FHs as a result of heating the concrete is consistent with microcracking of its smooth surface resulting from shrinkage in the cementitious matrix. Figure€7.8 portrays the corresponding rubber friction ratio vs. FN plot for the smooth concrete, as well as the plots for the semi-smooth and rough surfaces. Before the μA relationship becomes hyperbolic at the adhesion transition point, the apparent adhesion ratio for the tire-smooth concrete pairing equals approximately 0.41. The corresponding μA value at ambient temperature for the smooth concrete was 0.86. This reduction in the rubber adhesion friction ratio is consistent with our findings from the examination of the Bartenev and Lavrentjev [4] temperature-related data depicted in Figure€5.22. The indicated adhesion friction ratio values for the Bartenev and Lavrentjev vulcanized rubber specimen sliding on polished steel also decreased with increasing temperature.

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175

Microhysteretic Friction in Dry Rubber Products

Rubber Friction Ratio – µA+Hb

0.5 0.4 0.3 0.2 0.1 0

0

500 1000 1500 2000 Applied Normal Load (FN)–lbs

2500

Figure€7.8 Back-calculated rubber friction ratios from high-temperature — 300°F (149°C) — coefficient-of-friction testing involving B-29 tire segments sliding on smooth, semi-smooth, and rough portland cement concrete using data shown in Figure€7.6. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

7.3.1.1.2

Low-pressure testing on smooth concrete at ambient temperature: 24°C (75°F)

A back-calculation analysis of Hample’s [3] low-pressure testing results from the smooth concrete at ambient temperature was also carried out, the results of which are presented in Figure€7.9. The original data, depicted in Figure€4.10, were quite scattered. The smooth-surface microhysteresis force from the low-pressure analysis is also indicated as about 18.6 kg (40 lb). The adhesion friction ratio from the low-pressure, smooth-surface test (not plotted) was slightly lower, however, (approximately 0.75) compared to the μA value of 0.86 at high pressures. The difference in the two μA values may have arisen from differences in the two test configurations, perhaps associated with failure to take into account inertial resistance to movement, as discussed in Section 4.2.4. Hample considered that his high-pressure testing configuration was not accurate in the low-pressure range. 7.3.1.2 High-Pressure Testing on Textured Concrete 7.3.1.2.1 Ambient-temperature tests on textured concrete: 24°C (75°F) Hample’s [3] high-pressure, coefficient-of-friction test measurements for the semi-smooth and broom-swept concrete at ambient temperature were presented in Figure€4.8. Back-calculation results for these two surfaces are depicted in Figure€7.3. The indicated constant microhysteretic forces for the semismooth and rough surfaces are 23.6 kg (52 lb) and 34 kg (75 lb), respectively.

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176 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Total Measured Friction Force (FT)–lbs

600

500

400

300

200

100

0

0

50 100 150 200 250 300 350 400 450 500 550 600 650 Applied Normal (FN)–lbs

Figure€7.9 Back-calculated friction forces from low-pressure coefficient-of-friction testing involving B-29 tire segments sliding on smooth portland cement concrete. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.) 1.4

Coefficient of Friction–µ

1.2 1.0 Room temperature

.8 .6

300°F 400°F

.4 .2

500°F

600°F

700°F 40

80

120 160 200 240 Normal Pressure, psi

280

320

Figure€7.10 High-temperature, low-pressure coefficient-of-friction testing involving B-29 tire segments sliding on smooth, semi-smooth, and rough portland cement concrete. The plots represent test results from the three surfaces averaged together. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

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Microhysteretic Friction in Dry Rubber Products

177

As shown in Figure€7.4, subtraction of the indicated FHs forces from the respective FT values yields plots passing through the origin when extended. We are now in a position to divide the semi-smooth and broom-swept FT↜渀屮↜渀屮minus-FHs forces by FN to obtain friction ratios; however, care must be taken in naming the resultant. The two textured concrete surfaces were purposely roughened to simulate superior runway tire traction compared to smooth concrete. Such superior traction should arise by generating bulk-deformation-hysteresis forces in the rubber. In the dry conditions of Hample’s testing, however, adhesion forces would also develop. In this situation with the two textured surfaces, it is not possible to separate the FA forces from the FHb forces. When a ratio is calculated, the numerator will represent these two forces. To differentiate this ratio from the rubber adhesion friction ratio μA, and to assist in keeping the different mechanisms in mind so as to avoid confusion with the metallic friction equation, we will call the multiple-force division values the rubber friction ratios, μA+Hb. The back-calculated μA+Hb values for the semi-smooth and broom-swept surfaces before the plots became hyperbolic were 0.73 and 1.1, respectively. As Figure€7.5 clearly shows, a transition between different friction-producing mechanisms can also take place when rubber slides on macroscopically rough surfaces. This issue is addressed more fully in Section 7.6. It is seen that the rank order of increasing friction ratios for the three surfaces in Figure€7.5 is semi-smooth, smooth, and rough (broom-swept). This same rank order of friction development for the three surfaces is portrayed in Figures€4.8, 7.3, and 7.4. Referring to Figure€4.8, Hample [3] remarked that this rank order appeared anomalous but reported that his results had been checked, and no suitable explanation for the possible anomaly could be found. We can theorize an explanation for the plots’ positioning by considering the mechanisms involved. The broom-swept concrete evidenced the highest friction forces, likely because of macrohysteresis in the rubber along with concurrent development of roughness-diminished adhesion in a lower amount than the smooth finish provided. The net result was to produce more FHb-plus-FA friction than the adhesion generated in the tire rubber-smooth concrete pairing. The lower roughness of the semi-smooth concrete also reduced adhesion, but the rubber macrohysteresis that developed was insufficient to make up for this loss, leaving the smooth concrete in second place. 7.3.1.2.2 High-temperature tests on textured concrete: 149°C (300°F) Figure€7.6 presents high-pressure friction measurements reported by Hample [3] from his high-temperature testing. The data are for the smooth, semismooth, and broom-swept concrete surfaces at 149°C (300°F). The plots for all three surfaces are nearly coincident. Figure€7.7 illustrates back-calculation results obtained from Figure€7.6’s data. A tire-rubber microhysteresis force of approximately 40.9 kg (90 lb) for all three surfaces is indicated. The high-pressure microhysteretic forces for the smooth, semi-smooth, and broom-swept surfaces at ambient temperature were indicated to be 18.6 kg (40 lb), 23.6 kg (52 lb), and 34 kg (75 lb), respectively. We theorized that heating

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178 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces the smooth concrete to a temperature above the boiling point of water physically altered its microstructure. It appears likely that the microstructures of the semi-smooth and broom-swept concrete were also affected by the high temperature. Equal FHs values in Figure€7.7 imply that microcracking resulting from exposure to a temperature of 149°C (300°F) produced a uniform average microroughness on the three differently finished but constitutively identical concrete surfaces. In another consideration, it is reasonable to believe that the higher temperature of the concrete surfaces in these tests diminished the deformational resistance of the rubber, at least topically. At the same time, however, Hample’s high-temperature data suggest that the concrete’s microstructure was sufficiently roughened to overcome the reduction in deformational resistance and still yield the indicated higher microhysteretic forces on each surface. 7.3.1.3 Additional Hample Test Results This chapter has examined only a few of Hample’s [3] test results that were discussed in Sections 4.2.4 and 4.3.1. In total, Hample published 19 different graphs depicting his μ vs. PN test measurements. These graphs contained 26 different μ-vs.-PN plots. In every case, the curves were of the hyperbolic form, evidencing the presence of microhysteresis in all B-29 tire-rubber data. Hample’s graphs included Figure€7.10, illustrating his low-pressure results for the three concrete surfaces averaged together at temperatures up to 371°C (700°F). Even at this degree of temperature elevation, the presence of microhysteresis in the tire rubber was indicated. 7.3.2

Commercial Aircraft Tires on Dry, Textured Concrete

In 1990, Yager et al. [5] presented an overview of test results developed in the Surface Traction and Radial Tire (START) Program being carried out as a joint effort by the National Aeronautics and Space Administration (NASA), the Federal Aviation Administration (FAA), and the aircraft industry. The program focused on evaluating the rolling resistance, braking, and cornering performance of three different 40 × 14 tire types: (1) bias-ply, (2) radialbelted, and (3) H-type. The three types of tires were tested for cornering performance on a dry runway surface employing a 5.44 × 104-kg (60-ton) carriage operating at a speed of 185.3 km/h (100 knots). The three tire types were of equal Shore hardness (69) but had different tread patterns. Their possible differences in rubber compounding, and thus adhesion propensity, were not reported. Five values of FN were applied to each of the three tire types in the dry testing: 22.2 kN (5,000 lb), 44.5 kN (10,000 lb), 66.7 kN (15,000 lb), 89.0 kN (20,000 lb), and 111.2 kN (25,000 lb). Figure€4.32 presented plots of µS values vs. applied normal loads at six different yaw angles for the bias-ply design, calculated from the data presented in the Yager et al. article. Figure€4.33 depicted plots of µS values vs. applied

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179

Microhysteretic Friction in Dry Rubber Products

normal load at six different yaw angles for the radial-belted tires, calculated in the same manner. Figure€4.34 illustrated plots of µS values vs. the applied normal load at five different yaw angles for the H-type tires, also calculated from the subject article. It is seen in the figures that at each yaw angle for all tire types in dry conditions, µS decreased as FN increased, implying the presence of microhysteresis in the tested tires. Figures€7.11, 7.12, and 7.13 present results from back-calculation analyses of the bias-ply, radial-belted, and H-type tires in the form of FST vs. FN, where FST is the total side friction force measured in these tests. In every case, yintercept values are evidenced, indicating the development of FHs forces in these tires. Also in every case for the three tire types — except for testing of the H-type tire at a 9° yaw angle shown in Figure 7.13 — the plots eventually become parabolic. Some of the yaw-angle plots display an absolute reduction in FST at the highest applied loads. The mechanisms producing this phenomenon remain to be determined. The production of Schallamach waves is suggested. 80 76 72

Total Measured Side Friction Force (FST) – kN

68 64 60 56 52 48 44

Yaw angles 12°

9° 7°

40 36 32

5°

28 24 20 16 12 8 4 0

2°

1° 0 10 20 30 40 50 60 70 80 90 100 110 120 Applied Normal Force (FN)–kN

Figure€7.11 Back-calculated friction forces from side coefficient-of-friction testing of bias-ply tires on a portland cement concrete runway at various yaw angles. (From Yager, T.J., Stubbs, S.M., and Davis, P.M., Paper 901931, Emerging Technologies in Aircraft Landing Gear, Tanner, Ulrich, Medzorian, and Morris, Eds., SAE International, PT-66, Warrendale, PA, 1997.)

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180 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 40

9° 7°

Total Measured Side Friction Force (FST)–kN

35

Yaw angles

30 5° 25

20 3°

15

2°

10

5

0

1°

0 10 20 30 40 50 60 70 80 90 100 110 120 Applied Normal Force (FN)–kN

Figure€7.12 Back-calculated friction forces from side coefficient-of-friction testing of radial-belted tires on a portland cement concrete runway at various yaw angles. (From Yager, T.J., Stubbs, S.M., and Davis, P.M., Paper 901931, Emerging Technologies in Aircraft Landing Gear, Tanner, Ulrich, Medzorian, and Morris, Eds., SAE International, PT-66, Warrendale, PA, 1997.)

7.4

Rubber Microhysteresis in Dry Footwear Materials

7.4.1

Shoe Heels on Dry, Smooth Floors

Redfern and Bidanda [6] developed the Programmable Slip Resistance Tester (PSRT), a device that measures the dynamic coefficient of friction (µ) arising between a sliding shoe and a flooring surface of interest. The coefficient is defined in the usual manner:

µ = FT/FN.

(7.1)

Redfern and Bidanda selected seven independent variables for testing thought to be of principal interest in walking-surface slip-resistance metrol-

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Microhysteretic Friction in Dry Rubber Products

60

Yaw angles 9°

Total Measured Side Friction Force (FST)–kN

7° 50 5° 40

30

20

2° 1°

10

0

0 10 20 30 40 50 60 70 80 90 100 110 120 Applied Normal Force (FN)–kN

Figure€7.13 Back-calculated friction forces from side coefficient-of-friction testing of H-type tires on a portland cement concrete runway at various yaw angles. (From Yager, T.J., Stubbs, S.M., and Davis, P.M., Paper 901931, Emerging Technologies in Aircraft Landing Gear, Tanner, Ulrich, Medzorian, and Morris, Eds., SAE International, PT-66, Warrendale, PA, 1997.)

ogy: the shoe outsoles, the flooring, the shoe angle to the floor at heel strike, any contaminants present, the shoe’s likely sliding velocity that must be stopped, and the applied normal load. Redfern and Bidanda chose a number of different test samples and protocols representing these independent variables so that an analysis of variance (ANOVA) could be carried out to determine their effects on µ. Four smooth flooring surfaces were utilized: (1) untreated vinyl tile, (2) vinyl tile waxed and buffed, (3) stainless steel, and (4) sealed portland cement concrete. There were three types of elastomeric shoe outsoles: (1) hard PVC, durometer 83, no tread pattern; (2) soft urethane, durometer 34, no tread pattern; and (3) rubber, durometer 60, with a typical workboot tread pattern. These were tested dry and in three wet conditions on the four flooring surfaces, utilizing two vertical loads at three different sliding velocities. Our focus here is the effect of changes in FN on µ for the three outsole materials under dry conditions. In this case, Redfern and Bidanda averaged over floor type, heel strike angle, and sliding velocity. While the effects of these three independent variables on µ arising from changes in FN could not be differentiated using the presented data, the ANOVA results are of interest.

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182 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Figure€4.20 presented the calculated Redfern and Bidanda results for their dry coefficient-of-friction testing. The rubber, urethane, and PVC heels all experienced decreases in µ with increasing normal force in the manner indicating the presence of rubber microhysteresis. The curved lines are dashed because only two data points were available. Figure€7.14 illustrates results from back-calculation analyses of the rubber, urethane, and PVC outsoles in the form of FT vs. FN. In every case, y-intercept values are evidenced, indicating the development of FHs forces in these dry shoe outsole materials. 7.4.2

A Rubber Test Foot on in-Service Floors

Total Measured Friction Force (FT)–kg

Sections 5.2.5 and 5.3.1 discussed the anti-slip coefficients measured by Sigler et al. [7] to assess pedestrian footwear traction on five dry, smooth floors in service. The floors were Tennessee marble, cellulose nitrate tile, linoleum, rubber tile, and asphalt tile. These researchers also measured antislip coefficients on rubber tile in service containing Alundum grit. Sigler et al. [7] utilized a pendulum device fitted with a rubber test foot conforming to then-current (1948) U.S. Federal Specification ZZ-R-601a, Rubber Goods. Figure€5.23 presented back-calculated FT vs. FN plots for these five floors. Figure€5.29 depicted the FT vs. FN plot for the gritted tile. In this case, a yintercept value is evidenced, indicating the development of FHs forces in the pendulum’s rubber test foot. 7 Rubber

6 5 4

Urethane

3

PVC

2 1 0

0

1

2

3

4

5

6

7

8

Applied Normal Load (FN)–kg Figure€7.14 Back-calculated friction forces from ANOVA coefficient-of-friction testing of three shoe outsole compositions. (From Redfern, M.S. and Bidanda, B., Ergonomics, 37, 511, 1994.)

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Microhysteretic Friction in Dry Rubber Products

7.5

Microhysteresis in Dry Rubber Belting

Hurry and Prock [8] carried out rubber friction testing of three representative types of industrial belting that had experienced four different degrees of wear, produced under controlled conditions in the laboratory. Figure€4.2 presented the mean-value test data for the set of different belt types that were unworn. Hurry and Prock took the least-squares approach and utilized the straight-line equation y = cx + b, where c represented the coefficient of rubber friction, x represented FN, and b was the y-axis intercept value. They considered that the y-intercept values obtained in their testing represented constant friction forces, but, except for the value from the unworn belting set that was twice as high as the next highest set, Hurry and Prock concluded that these intercepts could be ignored. The unified theory of rubber friction discussed in Section 5.7 incorporates the y-axis intercept values as rubber microhysteresis forces. If we utilize the data reported by Hurry and Prock in accordance with the unified theory, their c term represents μA. Figure€7.15 presents plots of μA vs. FN for the Hurry and Prock results. As would be expected in the initial loading range in these conditions, the rubber adhesion friction ratios are constant. It is worth noting that all the worn-belt coefficients were lower than the unworn-belt μA values. Apparently, the laboratory wearing process roughened the belt surfaces and thus reduced their adhesion propensities with the polished steel test track. Wearing time None

Adhesion Friction Ratio–µA

0.5

0.4 Five minutes 96 Hours One hour

0.3

0.2

0.1

0

0

50 Applied Normal Load (FN)–lbs

100

Figure€7.15 Back-calculated rubber friction ratios from coefficient-of-friction testing of previously worn industrial belting sliding on polished steel. Periods of wear before testing are indicated. (From Hurry, J.A. and Prock, J.D., India Rubber World, 128, 619, 1953.)

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184 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

7.6

Rubber Adhesion-Transition-Pressure Phenomenon on Macroscopically Rough Surfaces

7.6.1

Development of the Adhesion-Transition-Pressure Phenomenon in Hample’s Testing of Rough Portland Cement Concrete

Chapter 5 introduced the rubber adhesion-transition phenomenon. An explanation of when the mechanism develops between rubber and macroscopically smooth paired surfaces, what is occurring in such circumstances, and how the adhesion transition pressure value PNt can be determined was included in Section 5.2. Further discussion of the PNt phenomenon was presented in Chapter 6. As is illustrated in Figure€7.5 of this chapter depicting a portion of Hample’s [3] test results, a transition between different frictionproducing mechanisms can also take place when rubber slides on macroscopically rough surfaces. Development of the rubber PNt mechanism on rough surfaces is now addressed more fully. 7.6.1.1 Accounting for Inertial Bias in Hample’s Testing Part of Hample’s [3] investigations using segments of a B-29 tire involved high-pressure testing of smooth, semi-smooth, and rough concrete. His coefficient-of-friction results were displayed in Figure€4.8. The findings of our back-calculation analysis of these data are presented in Figure€7.3: y-intercepts were evidenced in the plots for all three concrete surfaces. Because Hample’s protocols constituted static-friction testing, however, the y-intercept values seen in Figure€7.3 include an inertial-force bias, FI. While a method for calculating the inertial bias in Hample’s investigations utilizing assumed measurements is presented below, insufficient data are available to allow actual quantification of this bias. The true magnitudes of FHs for the smooth, semi-smooth, and rough concrete tests, obtained by subtracting FI from the y-intercept values, cannot be determined; nevertheless, subtracting the three y-intercept values indicated by Hample’s testing from their respective FT forces allows a design-relevant adhesion-transition analysis to be performed. 7.6.1.2 Adhesion-Development Issues in Hample’s Testing For the adhesion-transition-pressure phenomenon to develop when a rubber product is paired with a macroscopically rough surface, FA forces must be present over a range of applied normal loads. In the case of Hample’s [3] high-pressure testing on the semi-smooth and rough concrete, there seems little doubt that this adhesion requirement is met as a range of FA forces arose in his smooth-concrete testing. Figure€7.4 presents a plot of the developed FA forces vs. FN from these tests. In addition, physical contact between the rubber tire specimen’s asperities and the macrotexture of the two concrete

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Microhysteretic Friction in Dry Rubber Products

185

surfaces took place in the semi-smooth and rough testing. When physical contact between rubber and a paired surface arises in these circumstances, generation of adhesive friction forces can usually be expected. Another relevant point concerns the physical and chemical compositions of the three concrete test mixes: they were one and the same. The semi-smooth and rough concrete were constitutively identical to the smooth concrete, the only difference being in the physical configuration their surface finishes. On average, the surface free energies of all three concrete surfaces were likely substantially identical. Furthermore, Hample’s high-pressure testing on the semi-smooth and rough concrete was carried out with rubber test samples from the same B29 tire employed in the smooth-surface protocol. On average, we can expect that the surface free energies of the rubber-tire segments were also substantially identical. Thus, the surface-free-energy-related adhesion propensities for the three pairings appear to have been identical. 7.6.1.3 Transition Pressure Mechanisms in Hample’s Testing Figure€7.16 presents a log-log plot of FA vs. PN for Hample’s [3] high-pressure testing on smooth concrete. An adhesion transition pressure of about 2.76 MPa (400 psi) is indicated. Plots of (FA + FHb) vs. PN for the semi-smooth 2000

Rough concrete

1000

Friction Forces – lbs

500 Semi-smooth concrete 200 100 Smooth concrete

50

0

0

50 100 200 500 1000 2000 Applied Normal Pressure (PN)–psi

Figure€7.16 Back-calculated adhesion-transition-pressure plots from high-pressure testing of B-29 tire segments sliding on smooth, semi-smooth, and rough portland cement concrete. (From Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

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186 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces and rough concrete are also presented. Transition pressures for these two concrete surfaces of approximately 2.48 MPa (360 psi) and 1.79 MPa (230 psi), respectively, are evidenced; thus, Figure€7.16 illustrates that the magnitudes of the PNt values for the three surfaces decrease with increases in macroroughness of the concrete. The question arises: What adhesion transition-pressure mechanisms can develop on such macroscopically rough surfaces? Before addressing this issue, however, a consistency check for Figure€7.16’s plots should be performed. As a consistency check for the arrangement of the three data sets in Figure€7.16, it should be noted that the rank order of the plots in the figure is the same as the rank order of the plots in Figure€7.5, depicting the corresponding rubber friction ratios. As a further consistency check, it is seen that, prior to reaching their Figure€7.16 transition points, all three plots exhibit angles of approximately 45° with the x-axis. This is expected because the FA forces developed on the smooth concrete and the (FA + FHb) forces generated on the semi-smooth and rough concrete were all directly proportional to PN prior to reaching their respective transition points. The initial horizontal orientation of the rubber friction ratio plots in Figure€7.5 also demonstrates this direct proportionality. Because it is perhaps somewhat surprising, the direct proportionality between the (FA + FHb) forces and PN on Hample’s semi-smooth and rough concrete testing should be emphasized. We can further note that the back-calculation analysis of Chang’s [9] data portrayed in Figure€5.33 also indicated that rubber sliding on macroscopically rough surfaces generates combined FA and FHb forces that are directly proportional to the applied normal load. This phenomenon is evidenced in the process 1, process 2, and process 3 plots of that figure. Figure€7.16 illustrates that the semi-smooth and rough concrete plots above the transition pressures in Figure€7.16 are straight, demonstrating rectification. We can now theorize that the development of the PNt phenomenon in Hample’s semi-smooth and rough concrete was due to the presence of the adhesion transition mechanism explained in Chapter 6. This is consistent with our earlier finding that the magnitudes of the PNt values for the smooth, semi-smooth, and rough surfaces decrease with increases in macroroughness of the concrete; that is, as the contacted surface became rougher, the sooner increases in applied load failed to produce directly proportional increases in the real area of rubber asperity contact with their corresponding concrete surface. 7.6.2

Quantifying Inertial Bias in Hample’s Testing

Hample’s [3] investigations utilized segments of a B-29 tire sliding on smooth, semi-smooth, and rough concrete under high pressure. The findings of the back-calculation analysis of data from this testing are presented in Figure€7.3. The y-intercepts were evidenced in the plots for all three concrete surfaces. Because Hample’s protocols constituted static-friction testing, the y-intercept values seen in Figure€7.3 include an inertial-force bias, FI. The true magni-

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187

Microhysteretic Friction in Dry Rubber Products

tudes of FHs for the smooth, semi-smooth, and rough concrete tests, obtained by subtracting FI from the y-intercept values, cannot be determined; nevertheless, by assuming texture roughness measurements for the three surfaces, a method of approximating the FI force can be exemplified. This is so because Hample’s high-pressure test setup generated an essentially constant maximum inertial force during each test run. Table€7.1 presents the y-intercept values for the three concrete surfaces seen in Figure€7.3 and assumed corresponding texture roughness measurements. These assumed measurements are expressed as the mean of the concrete surfaces’ asperity heights, also known as the center line average of surface heights (CLA). We can note that the relative magnitudes of the y-intercepts are consistent with the objects used to produce the different concrete surfaces. The steel-trowel-smoothed concrete evidenced the smallest y-intercept, while the broom-swept surface yielded the largest intercept value. The smooth concrete’s microtexture should, in some measure, reflect the microtexture of the metal trowel used for finishing. The broom-swept concrete’s microtexture should reflect the nature of the bristles making up the broom. The semi-smooth concrete, obtained by utilizing a wood board as the finishing device, exhibited an intercept value between the other two surfaces. Figure€7.17 presents a plot of the y-intercepts from Figure€7.3, versus the assumed CLA measurements. Extrapolating the assumed straight line to the y-axis yields an intercept of approximately 89 N (20 lb), the FI force. CLA values were chosen to produce a straight line. Had plotted points from actual measurements indicated a curved relationship, extrapolation would still have provided an indicated FI value. In this method of approximating the constant maximum inertial force developed in Hample’s high-pressure testing, the zero point on the x-axis is taken to represent molecular smoothness. Johnson et al. [10] were able to approach this smoothness in their testing, discussed in Section 3.11.

Table€7.1 Assumed Microtexture Height Measurements for Hample’s Concrete Specimens Expressed as the Center Line Average of Surface Heights (CLA) Compared to the y-Intercept Values Seen in Figure€7.3

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y-Intercept Values

Assumed Microtexture Measurements

Smooth concrete

40 lb

3.9 × 10–4 in.

Semi-smooth concrete

52 lb

5.9 × 10–4 in.

Rough concrete

75 lb

9.8 × 10–4 in.

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188 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 100

Y-Intercept Values–lbs

90 Broom-swept concrete

80 70 60

Wood-boardsmoothed concrete

50 40

Steel-trowel smoothed concrete

30 20 10 0

0

5.0 × 10–4 10.0 × 10–4 Assumed Center-Line-Average Texture Roughness (CLA)–In

Figure€7.17 Plot of back-calculated y-intercept values from high-pressure testing of B-29 tire segments sliding on smooth, semi-smooth, and rough portland cement concrete vs. assumed center-line-average (CLA) texture measurements from these surfaces. (y-intercept values from Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955.)

7.7

Chapter Review

A principal purpose of this book is to present a newly developed, scientifically based, unified theory of rubber friction incorporating a fourth basic rubber friction force: surface deformation hysteresis, or microhysteresis. Chapter 5 examined 27 data sets from rubber-friction tests evidencing the existence of this force. None of these data sets were obtained, however, from friction testing of rubber products. The present chapter focused on microhysteresis development in rubber products from the automotive, aviation, footwear, and industrial fields. Rubber microhysteresis was indicated as being present in dry conditions in:



8136.indb 188

1. Automobile tire rubber sliding on ice; 2. Segments from a B-29 tire sliding on concrete at ambient and higher temperatures; 3. Bias-ply, radial-belted, and H-type commercial aircraft tires sliding on a concrete runway; 4. Natural rubber, PVC, and urethane shoe outsole materials sliding on untreated vinyl tile, waxed and buffed vinyl tile, stainless steel, and sealed portland cement concrete; and 5. Industrial rubber belting that had undergone four different degrees of pre-test wear sliding on polished steel.

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Microhysteretic Friction in Dry Rubber Products

189

Chapter 6 explained how the adhesion-transition-pressure phenomenon develops in rubber sliding on smooth surfaces in dry conditions. This chapter set forth evidence indicating that the adhesion-transition phenomenon can also develop when rubber slides on rough surfaces in dry conditions.

References

8136.indb 189

1. Savkoor, A.R., On the friction of rubber, Wear, 8, 222, 1965. 2. Pfalzner, P.M., On the friction of various synthetic and natural rubbers on ice, Can. J. Res. F, 28, 468, 1950. 3. Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955. 4. Bartenev, G.M. and Lavrentjev, V.V., The law of vulcanized rubber friction, Wear, 4, 154, 1961. 5. Yager, T.J., Stubbs, S.M., and Davis, P.M., Aircraft radial-belted tire evaluation, paper 901931, Emerging Technologies in Aircraft Landing Gear, Tanner, Ulrich, Medzorian, and Morris, Eds., SAE International, PT-66, Warrendale, PA, 1997. 6. Redfern, M.S. and Bidanda, B., Slip resistance of the shoe-floor interface under biomechanically relevant conditions, Ergonomics, 37, 511, 1994. 7. Sigler, P.A., Geib, M.N., and Boone, T.H., Measurement of the slipperiness of walkway surfaces, J. Res. Nat. Bur. Stds., 40, 339, 1948. 8. Hurry, J.A. and Prock, J.D., Coefficients of friction of rubber samples, India Rubber World, 128, 619, 1953. 9. Chang, W.-R., The effect of surface roughness on dynamic friction between Neolite and quarry tile, Safety Science, 29, 89, 1998. 10. Johnson, K.L., Kendall, K., and Roberts, A.D., Surface energy and the contact of elastic solids, Proc. Roy. Soc. A, 324, 301, 1971.

2/13/08 3:03:02 PM

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8 Microhysteresis in Wet Rubber Products

8.1

Introduction

Chapter 7 continued our examination of the hypothesis formulated by Savkoor [1] that a surface-deformation-hysteresis friction mechanism develops in rubber when it slides on a harder material. The back-calculation analyses of rubber friction test data presented in Chapter 5 indicated the existence of such a microhysteretic mechanism in concurrence with Savkoor’s hypothesis. The rubber friction data utilized in Chapter 5 to develop the microhysteretic findings presented there did not include all the friction testing examined in Chapter 4. Chapter 7 addressed more of the research discussed in Chapter 4, focusing on rubber products from the automotive, aviation, footwear, and industrial fields in dry conditions. The present chapter addresses more of the research discussed in Chapter 4, focusing on rubber products in wet conditions.

8.2

Effects of Wet Lubricants on the Rubber Adhesion Mechanism

8.2.1 Wet-Lubricant Investigations in Friction Testing To gain a mechanistic sense of the importance of water and other liquids on the adhesion components of rubber friction, it is useful to examine relevant metallic friction studies. Bowden and Tabor [2,3] described the effects of liquid lubricants on the adhesive friction force developed between two smooth contacting metals. The term lubricant is defined here to mean any liquid adsorbed onto — rather than absorbed into — the surface of metal, rubber, or its paired material, whether or not such adsorption is desired. According to Rabinowicz [4], in ambient conditions the surfaces of metals are usually covered by thin films of water vapor, 191

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192 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces oxide, and other contaminants adsorbed from the atmosphere, which can remain even after cleaning. Bowden and Tabor [3] reported that such cleaning may include lapping, polishing, or scraping with a degreased diamond tool, yet contaminants will remain. Heating of the metal surfaces in a vacuum chamber is the only effective method of removing all adsorbed vapor contaminants from metals so their effects on friction can be readily studied. When this was done with iron specimens that were allowed to cool to room temperature in a vacuum device, seizure of the contacting metal surfaces took place, resulting in metallic coefficient-of-friction values greater than 3. When this same experiment was carried out with nickel, large-scale seizure of the paired surfaces produced a coefficient of friction of approximately 100. Very small quantities of adsorbed water vapor admitted to the vacuum chamber after cooling decreased the real area of metal contact in the iron experiment and reduced the adhesive friction force by separating the metal surfaces by a thin water film, even after formation of the “cold welded” metallic junctions of the type discussed in Chapter 2 had developed. Bowden and Tabor [3] further reported that formation of the water film was partly due to chemisorption and partly due to van der Waals’ attraction of the vapor molecules to the metal. The forces associated with these adsorption mechanisms were strong enough to reduce the real area of iron contact through surface separation, such that the coefficient of friction fell to about 2.2 after 10 seconds of exposure, and to approximately 1.4 after 10 minutes of adsorption. This friction-force-reduction effect is not limited to solid-surface separation by liquids; adsorption of gas molecules onto metal can produce the same result. Bowden and Tabor [3] reported that gasses demonstrated to possess this ability include carbon dioxide, nitrogen, chlorine, hydrogen, helium, and hydrogen sulfide. Liquids, vapors, and gasses have all been shown to be lubricants fostering slippage through reduction in the real area of adhesional contact between solids. Bowden and Tabor [3] reported that this phenomenon occurs in metals, plastics, and rubber.

8.2.2 Rubber Friction in “Dry” and Wet Conditions In most practical engineering applications, frictional contact of rubber with its paired surface will take place with adsorbed water vapor interposed between them. As the relative humidity increases, more adsorbed water vapor will accumulate. Unknown amounts of water vapor were likely present between the rubber specimens and their paired surfaces in all the “dry” testing conditions discussed in Chapters 4, 5, 6, and 7. The question arises: “When do we consider that wet conditions predominate?” For the tests to be discussed in this chapter, wet conditions will be defined as those in which a liquid has been purposely applied to rubber or its contacted surface.

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Microhysteresis in Wet Rubber Products

8.3

Microhysteresis in Automotive Tire Rubber under Wet Conditions

8.3.1

Dependence of Wet-Tire Traction on Rubber Microhysteresis

193

Chapter 4 discussed the state of Tennessee’s design for a two-wheeled trailer, utilized in evaluating tire friction forces developed on roadways possessing various texture characteristics [5]. Figure€4.50 depicted the trailer’s basic configuration. As seen in the figure, the left wheel was equipped with an air brake so it could be locked during skid testing. The skid-test trailer accommodated removable weights for applying a normal load. The towing vehicle was usually a 1814-kg (2-ton) truck. Because pavements are usually much more skid-resistant when dry than when wet, roadway surfaces are often traction tested in the wet condition. In the Tennessee design, the towing vehicle carried a 1892-L (500-gal) tank with a quick-opening valve controlling water flow from a sprinkler bar located at the rear of the truck. The skid-test trailer results reported by Clayton [5] were obtained on asphaltic concrete roads wetted in this manner. The towing vehicle was driven so that the test wheel tracked in the usual path of the left wheels of typically sized automobiles. Clayton chose to examine a worst-case skidding scenario by employing smooth tires (670-15) in his investigation. Figure€4.52 depicted the results of Clayton’s studies to determine the effect on μ from increases in tire inflation pressure at four different test speeds. In all cases, μ decreased with increasing tire pressure. Clayton’s skid-trailer studies involved a weight W applied to the single trailer wheel as depicted in Figure€4.51. Because only one weight was employed — 414.5 kg (913 lb) — throughout these wet-asphalt investigations [5], it was not possible to carry out a back-calculation analysis to obtain plots of FT vs. FN for this data. Nevertheless, by utilizing the pavement-tire friction forces reported by Clayton, we are able to assess the possible presence of rubber microhysteresis forces in his locked-wheel measurements with a constant wheel load. Figure€8.1 presents a plot of Clayton’s measured friction forces (FT) vs. tire inflation pressure for a constant trailer speed of 33.9 km/h (20 mph). As would be expected from the coefficient plots in Figure€4.52, the friction forces decreased with increasing tire pressure. While tire inflation pressure was apparently the only independent variable at the subject speed, a number of unmeasured dependent variables were present. These included the decrease in the tire contact patch area with increasing pressure. Indeed, it seems likely that Clayton’s constant-W coefficients are not themselves constant because of the changing footprint area. It was demonstrated in Section 5.2.2 when analyzing Thirion’s [6] data that FHs forces for differently sized but otherwise identical rubber test specimens can be different. Thirion’s data indicate that the greater the nominal area of contact, the larger the microhysteretic force. The hyperbolic shape of Clay-

8136.indb 193

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194 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces ton’s curve in Figure€8.1 is consistent with a decrease in surface deformation hysteresis with increasing tire inflation pressure as the contact patch area diminished. Furthermore, while the average local pressure in a tire increases slightly with inflation pressure, FHs is independent of PN. On the basis of Thirion’s data and the back-calculation analyses presented thus far, we can theorize that had Clayton’s locked-wheel tire been sliding on dry, highly traffic-polished asphalt where no significant macrohysteresis or cohesion losses were present, and potential frictional heating effects could be ignored, FA and FHs forces would predominate. In such a situation, tire traction would depend, in part, on microhysteresis. If we now add water to this mix, where rubber surface deformation hysteresis develops in wet conditions, tire traction would again depend, in part, on FHs forces. 8.3.2 Rubber Microhysteresis in Tire-Tread Test Specimens in Wet Conditions Sabey carried out lubricated-rubber friction studies focusing on the skid resistance of motor vehicle tires. She idealized road-surface aggregate as spherical and carried out coefficient-of-friction measurements of steel spheres sliding on tire-tread rubber when well lubricated with water. Her sliders included a sphere of 1.27-cm (0.5 in.) diameter moving at a speed of 1.83 m/sec (6 fpsec).

Total Measured Friction Force–lbs

600 500 400 300 200 100 0

0

10 20 30 40 Tire Inflation Pressure–psi

45

Figure€8.1 Back-calculated friction forces (F T) vs. tire inflation pressure from Clayton’s skid-trailer testing at a constant speed of 33.9 km/h (20 mph) on a wet asphaltic concrete roadway. (From Clayton, J.H., An Investigation and Modification of a Pavement Skid-Test Trailer, M.S. thesis, The University of Tennessee, Knoxville, 1962.)

8136.indb 194

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195

Microhysteresis in Wet Rubber Products

Total Measured Friction Forces (FT)–lbs

Figure€4.58 depicted Sabey’s results for the 1.27-cm (½-in.) diameter sphere. It is seen that a hyperbolic relationship between μ and FN is displayed. The results of a back-calculation analysis of these data are illustrated in Figure€8.2. Extrapolation of the straight-line plot indicates that a constant microhysteretic force of approximately 28.3 gm (0.25 lb) developed in Sabey’s 1.83-m/s (6-fps) testing. Sabey also investigated the friction forces developed when sharper roadsurface aggregate — idealized as smooth, rigid cones — penetrate tire-tread rubber at 1.83 m/sec (6 fpsec) when well lubricated with water. Figure€4.59 presented Sabey’s coefficient-of-friction results for this protocol. The plots are hyperbolic for interior apex angles of 70°, 90°, 100°, and 160°. As in her 1.27-cm (0.5 in.) diameter sphere testing [7], μ decreased as FN increased. The results of a back-calculation analysis of these data are portrayed in Figure€8.3. Extrapolation of the straight-line plots indicates that microhysteretic forces arose in all four cases involving wet conditions. As previously observed, the FHs forces appear to be independent of the applied normal load. The conical slider with the sharpest peak, exhibiting a 70° interior apex angle, produced the largest indicated microhysteresis value, approximately 0.91 kg (2 lb). The effects of the presence of water on the development of rubber microhysteresis in tires in actual service merits detailed consideration. While no suitable friction test results could be found for a microhysteretic analysis of motor vehicle tires in wet-driving conditions, the back-calculation technique applied to the Yager et al. [8] data, to be discussed in Section 8.4, indicates the existence of FHs forces in commercial aircraft tires on wet runways. Sphere diameter ³∕₁₆ in.

6 5

¼ in.

4 3 ½ in.

2 1 0

0

5

10

15

Applied Normal Load (FN)–lbs Figure€8.2 Back-calculated friction forces (F T) from Sabey’s wet testing of idealized (spherical) road-surface aggregate with indicated diameters using tire-tread rubber. (From Sabey, B.E., Proc. Roy. Soc. A, 71, 979, 1958.)

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196 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 10 Interior apex angle

Total Measured Friction Forces (FT)–lbs

9

70°

90°

8 7

100°

6 5 4 3 2

160°

1 0

0

5 10 Applied Normal Load (FN)–lbs

15

Figure€8.3 Back-calculated friction forces (F T) from Sabey’s wet testing of idealized (conical) road-surface aggregate with indicated interior apex angles using tire-tread rubber. (From Sabey, B.E., Proc. Roy. Soc. A, 71, 979, 1958.)

8.4

Microhysteresis in Wet Aircraft Tires

We have examined the possibility of microhysteresis arising in the dry-tire testing of Yager et al. [8] in Section 7.3.2. Their program focused on evaluation of the rolling resistance, braking, and cornering performance of three different tire types encompassing the ground operational speed range for commercial aircraft. Bias-ply, radial-belted, and H-type 40 × 14 size tires were tested at various yaw angles. Figure€4.53 portrayed the back-calculated side coefficient-of-friction (μS) values obtained from the Yager et al. [8] bias-ply tire traction measurements in wet conditions. The coefficients were all directly proportional to the applied normal load. Figure€4.32 depicted the back-calculated side coefficient-of-friction results obtained from the Yager et al. [8] bias-ply tire traction measurements in dry conditions. These dry coefficients were not directly proportional to the applied normal load, but diminished with increasing FN. It was shown in Chapter 5 that decreasing μ values with increasing FN can be attributed to the presence of a constant microhysteresis force in rubber friction measurements. Indeed, Figure€7.11 indicated the presence of constant FHs forces in the Yager et al. [8] dry bias-ply tires at all six yaw angles. We can theorize,

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197

Microhysteresis in Wet Rubber Products

therefore, that the Yager et al. [8] bias-ply tire traction measurements in wet conditions contained no rubber microhysteresis components. Figure€4.54 illustrated the back-calculated side coefficient-of-friction values obtained from the Yager et al. [8] radial-belted tire traction measurements in wet conditions. The coefficients were not directly proportional to the applied normal load, but decreased with increasing FN. Figure€4.33 depicted the back-calculated side coefficient-of-friction values obtained from the Yager et al. [8] radial-belted tire traction measurements in dry conditions. These dry coefficients also diminished with increasing FN. Figure€7.12 indicated the presence of constant FHs forces in the Yager et al. [8] dry radial-belted tires at all six yaw angles. We can theorize, therefore, that Yager et al. [8] radialbelted tire traction measurements in wet conditions also contained rubber microhysteresis components. These FHs forces are evidenced in Figure€8.4 for yaw angles of 5°, 2°, and 1°. Data for the other radial-belted, yaw-angle tests were not sufficiently consistent to include in the present analysis. It is of interest to ask: “Why did the Yager et al. [8] radial-belted tires seemingly generate beneficial microhysteretic forces in wet conditions while 17

Yaw angles 5°

16 15 14

Total Friction Force (FT)–kN

13 12 11 10 9 8

2°

7 6 5

1°

4 3 2 1 0

0 10 20 30 40 50 60 70 80 90 100 110 120 Applied Normal Load (FN)–kN

Figure€8.4 Back-calculated friction forces (F T) vs. applied normal load from wet testing of radial-belted aircraft tires at indicated yaw angles. (From Yager, T.J., Stubbs, S.M., and Davis, P.M., Paper 901931, Emerging Technologies in Aircraft Landing Gear, SAE International, PT-66, Warrendale, PA, 1997.)

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198 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Side Friction Ratios–µS(A+Hb)

the bias-ply tires tested on the same wet runway apparently did not?” One answer may concern the relative surface free energies of the radial-belted and bias-ply tread compositions. We had seen from our back-calculation analyses of the Mori et al. [9] data in Section 5.2.6 that the greater the surface free energy of a rubber specimen paired with the given material, the higher the FHs forces are in magnitude. If the rubber adhesion propensity is too low, however, development of rubber microhysteresis can be precluded. Figure€8.5 presents the side μS(A+Hb) friction ratios — side coefficients of friction in the Yager et al. [8] terminology — for the radial-belted tires in wet conditions but with the apparent microhysteresis components removed. It is seen that μS(A+Hb) friction ratios for the radial-belted tires at yaw angles of 5°, 2°, and 1° are 0.13, 0.06, and 0.04, respectively. While Yager et al. [8] did not report the chemical compositions of their various tire-tread types, the higher radial-belted tire friction ratios are consistent with its tread composition exhibiting a greater surface free energy than does the tread compound of the bias-ply tire. Another possible explanation of the superior traction-development performance of the radial-belted tires may have been the ability of their tread design to remove water from the tire’s footprint area during testing. A thinner water film would have provided a higher likelihood of greater tire-runway microtexture contact [10]. The viscous contribution to friction from shearing the water present has been ignored in this analysis. The possible contribution to skid resistance of moving bulk water in front of the tires in a bow-wave-like mechanism has also been ignored. Wet testing of the Yager et al. [8] H-type tires has not been addressed. Their data from this protocol was not amenable to a back-calculation analysis. 0.15

0.10

0.05

0

Yaw angles 5°

2° 1°

0 10 20 30 40 50 60 70 80 90 100 110 120 Applied Normal Load (FN)–kN

Figure€8.5 Back-calculated side friction ratios (μ S(A+Hb)) vs. applied normal load from wet testing of radial-belted aircraft tires at indicated yaw angles. (From Yager, T.J., Stubbs, S.M., and Davis, P.M., Paper 901931, Emerging Technologies in Aircraft Landing Gear, SAE International, PT-66, Warrendale, PA, 1997.)

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Microhysteresis in Wet Rubber Products

8.5

Rubber Microhysteresis in Wet Footwear Outsoles

8.5.1

Rubber Microhysteresis in Wet Work Shoe Outsoles

199

Tisserand [11] realized that few pedestrian slip-and-fall incidents occur on dry floors; and because liquid contaminants can reduce the adhesion friction component between a shoe outsole and the walking surface, he concluded that footwear slip-resistance testing should be carried out on wet surfaces. Tisserand conducted traction investigations utilizing the dynamic INRS (Institut National de Recherche et de Sécurité) whole-shoe testing device. He selected a sliding velocity of 20 cm/sec (7.87 in./sec). Figure€4.41 presented a generalized depiction of his µ-vs.-FN results for two unidentified work shoes sliding on stainless steel coated with ordinary engine oil. In both cases, the coefficient of rubber friction decreased with increasing applied normal load. The back-calculation technique was applied to Tisserand’s wet-testing data. Figure€8.6 depicts the results of these calculations. The plot for work shoe A evidences a wet microhysteresis force of about 4 kg (8.8 lb), while that for work shoe B indicates a constant FHs value of approximately 0.9 kg (2 lb). Inasmuch as the physical and chemical characteristics of the two shoe outsoles were not reported by Tisserand, we are unable to hypothesize an explanation for the frictional differences between the subject shoes. 8.5.2 Rubber Microhysteresis in Wet Safety Shoe Outsoles In 1995, Grönqvist [12] reported findings from a walking-surface slip-resistance study of three types of new and used safety shoes with dissimilar tread patterns. The study encompassed various testing parameters and environmental conditions. Its protocol employed an artificial foot device of Grönqvist design, an apparatus that operates dynamically and is capable of Total Friction Forces (FT)–kg

20 16 12

Work shoe A

8 Work shoe B

4 0

0

4

8 12 16 20 24 28 32 36 40 44 48 52 56 60 Applied Normal Load (FN)–kg

Figure€8.6 Back-calculated friction forces (F T) vs. applied normal load from wet testing of two work shoes. (From Tisserand, M., Ergonomics, 28, 1027, 1985.)

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200 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces controlled variation of shoe (heel) contact angle, sliding speed, and applied normal load. As part of this investigation, Grönqvist examined the variation of μ vs. PN obtained from new samples of five different molded shoe sole materials: thermoplastic rubber (TR), nitrile rubber (NR), styrene rubber (SR), polyurethane (PU), and polyvinylchloride (PVC). Three tread patterns were involved: rectangular, waveform, and triangular. The rectangular pattern was formed with asperities possessing an arithmetic average roughness (Ra) of 9 × 10−4 cm (3.54 × 10−4 in.). Both the waveform and triangular tread patterns were molded to exhibit a smooth surface with Ra equal to 2 × 10−4 cm (7.87 × 10−5 in.). All of the μ-vs.-PN testing was carried out at room temperature on a smooth stainless steel floor lubricated with glycerol having a viscosity of 200 cP (89% by weight). Grönqvist considered this combination to represent “very slippery” walking conditions. The sample contact angle with the steel flooring was 0° (flat), with a horizontal sliding speed of 0.4 m/sec (1.31 ft/sec). Grönqvist utilized differently sized samples for testing. Only one size (1000 mm2, 155 in.2) was tested at more than one PN value. This discussion is limited to Grönqvist’s data obtained from the 1000-mm2 (155-in.2) specimens. Figure€4.42 presented Grönqvist’s μ-vs.-PN results for the nitrile rubber with waveform (NRw) and triangular (NRt) tread patterns and the styrene specimens with the same patterns (SRw and SRt). Figure€4.43 illustrated the variation of μ with PN for the thermoplastic rubber (TRr), polyvinylchloride (PVCr) and polyurethane (PUr), all with rectangular tread patterns. All pairings exhibited reductions in μ with increasing PN. The back-calculation technique was applied to Grönqvist’s wet-testing measurements. Figure€8.7 depicts the results of these calculations for the nitrile rubber triangular and waveform tread patterns. The development of microhysteresis forces in Grönqvist’s protocols is indicated: approximately 2.7 kg (6 lb) in triangular pattern and 1.4 kg (3 lb) in the waveform tread. Figure€8.8 illustrates the wet adhesion friction ratios for the two materials. The waveform adhesion friction ratio appears constant in the low loading range with a value of about 0.17 and then exhibits a hyperbolic trend. The triangular tread evidences an approximately constant wet adhesion friction ratio of 0.15, which then also becomes hyperbolic. Figure€8.9 presents back-calculation results for the styrene rubber triangular and waveform patterns. The development of microhysteresis forces in these Grönqvist protocols is evidenced: approximately 1.4 kg (3 lb) in the triangular pattern and 1.4 kg (3 lb) in the waveform tread. Figure€8.10 displays the wet adhesion friction ratios for the two styrene patterns. The waveform adhesion friction ratio appears constant in the low loading range with a value of about 0.20 and then exhibits a hyperbolic trend. The triangular tread evidences an approximately constant wet adhesion friction ratio of 0.15. Figure€8.11 portrays back-calculation results for Grönqvist’s PVC, polyurethane, and thermoplastic rubber data obtained with rectangular tread patterns in wet conditions. The generation of microhysteresis forces in these

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201

Microhysteresis in Wet Rubber Products 45 40 Triangular pattern

Total Friction Forces (FT)–lbs

35 30 25

Waveform pattern

20 15 10 5 0

0

50

100 150 200 250 300 Applied Normal Load (FN)–lbs

350

Figure€8.7 Back-calculated friction forces (F T) vs. applied normal load from wet testing of nitrile rubber triangular and waveform shoe tread patterns. (From Grönqvist, R., Ergonomics, 38, 224, 1995.)

Adhesion Friction Ratios–µA

0.20

0.15

Triangular pattern

0.10 Waveform pattern

0.05

0

0

100 200 300 Applied Normal Load (FN)–lbs

400

Figure€8.8 Back-calculated adhesion friction ratios (μA) vs. applied normal load from wet testing of nitrile rubber triangular and waveform shoe tread patterns. (From Grönqvist, R., Ergonomics, 38, 224, 1995.)

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202 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 50 45

Total Friction Forces (FT)–lbs

40 Waveform pattern

35 30

Triangular pattern

25 20 15 10 5 0

0

50

100 150 200 250 300 Applied Normal Load (FN)–lbs

350

Figure€8.9 Back-calculated friction forces (F T) vs. applied normal load from wet testing of styrene rubber triangular and waveform shoe tread patterns. (From Grönqvist, R., Ergonomics, 38, 224, 1995.)

protocols is indicated: approximately 0.57 kg (1.25 lb), 0.8 kg (1.75 lb), and 0.3 kg (0.6 lb) in the PVC, polyurethane, and thermoplastic rubber plots, respectively. Figure€8.12 depicts the wet adhesion friction ratios for the rectangular tread patterns. These patterns evidence approximately constant adhesion friction ratios of 0.044, 0.055, and 0.038, respectively. 8.5.3 Microhysteresis in Wet ANOVA Testing of Elastomeric Shoe Outsoles In addition to carrying out analysis-of-variance slip-resistance testing of dry, elastomeric shoe heels, Redfern and Bidanda [13] also conducted an ANOVA investigation assessing the effects on μ of three floor lubricants: water, SAE 10 oil, and SAE 30 oil. As in their dry studies, they averaged the slip-resistance results over floor type, heel strike angle, and sliding velocity. Figures€4.44, 4.45, and 4.46 presented the Redfern and Bidanda measurements obtained with water, SAE 10 oil, and SAE 30 oil lubricants, respectively, paired with rubber, urethane, and PVC heels on smooth untreated and waxed vinyl tile, stainless steel, and sealed concrete. For all nine wet-data sets, μ

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203

Microhysteresis in Wet Rubber Products Waveform pattern

Adhesion Friction Ratios–µA

0.20

0.15 Triangular pattern 0.10

0.05

0

0

100 200 300 Applied Normal Load (FN)–lbs

400

Total Friction Forces (FT)–lbs

Figure€8.10 Back-calculated adhesion friction ratios (μ A) vs. applied normal load from wet testing of styrene rubber triangular and waveform shoe tread patterns. (From Grönqvist, R., Ergonomics, 38, 224, 1995.)

17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

PVC Polyurethane

Thermoplastic rubber

0

50

100 150 200 250 300 Applied Normal Load (FN)–lbs

350

Figure€8.11 Back-calculated friction forces (F T) vs. applied normal load from wet testing of polyurethane, PVC, and thermoplastic rubber rectangular shoe tread patterns. (From Grönqvist, R., Ergonomics, 38, 224, 1995.)

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204 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 0.060

Polyurethane

Adhesion Friction Ratios–µA

0.050 Polyvinylchloride

0.040

Thermoplastic rubber 0.030

0.020

0.010

0

0

100 200 300 Applied Normal Load (FN)–lbs

400

Figure€8.12 Back-calculated adhesion friction ratios (μ A) vs. applied normal load from wet testing of polyurethane, polyvinylchloride, and thermoplastic rubber rectangular shoe tread patterns. (From Grönqvist, R., Ergonomics, 38, 224, 1995.)

diminishes with increasing FN. Because of the analysis detailed in Chapter 5, we can expect that hyperbolic curves for these test results would be evidenced if three or more values of FN had been applied. For this reason, the curved lines between the corresponding data points in the figures are dashed. Figures€8.13, 8.14, and 8.15 illustrate results from back-calculation analyses of the rubber, urethane, and PVC heels in the form of FT vs. FN for the three lubricants — water, SAE 10 oil, and SAE 30 oil. In every case, the development of FHs forces in the wet shoe heels is indicated.

8.6

Ramifications of the Presence of Microhysteresis in Wet Rubber Products

A principal purpose of this book is to present a newly developed, scientifically based, unified theory of rubber friction incorporating a fourth basic rubber friction force: surface deformation hysteresis, or microhysteresis. As we have seen in Chapters 5 and 7, a microhysteretic force FHs usually develops when rubber slides on a dry harder material, even if that contacted surface

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205

Microhysteresis in Wet Rubber Products

Total Friction Forces (FT)–kg

6 5 4

Rubber

3 Urethane

2

PVC

1 0

0

1

2 3 4 5 6 Applied Normal Load (FN)–kg

7

8

Total Friction Forces (FT)–kg

Figure€8.13 Back-calculated friction forces (F T) vs. applied normal load from wet testing of rubber, urethane, and PVC shoe heels with water. (From Redfern, M.S., and Bidanda, B., Ergonomics, 37, 511, 1994.)

5 4 3 Rubber

2

ane Ureth

1 0

PVC 0

1

2 3 4 5 6 Applied Normal Load (FN)–kg

7

8

Figure€8.14 Back-calculated friction forces (F T) vs. applied normal load from wet testing of rubber, urethane, and PVC shoe heels with SAE 10 oil. (From Redfern, M.S. and Bidanda, B., Ergonomics, 37, 511, 1994.)

is very smooth or macroscopically rough. The magnitude of this microhysteretic resistance to movement is seemingly independent of applied normal force and pressure. The presence of microhysteresis in elastomers prevents the general application of a constant coefficient-of-friction equation to rubber products. When rubber microhysteresis develops in dry conditions, the generated friction forces are not directly proportional to the applied normal load. This inequality is properly expressed as

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206 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Total Friction Forces (FT)–kg

2.0

1.5 Urethane Rubber 1.0 PVC 0.5

0

0

1

2 3 4 5 6 Applied Normal Load (FN)–kg

7

8

Figure€8.15 Back-calculated friction forces (F T) vs. applied normal load from wet testing of rubber, urethane, and PVC shoe heels with SAE 30 oil. (From Redfern, M.S., and Bidanda, B., Ergonomics, 37, 511, 1994.)



μ ≠ FT/FN.

(8.1)

In this chapter we have shown that FHs forces are also frequently generated when rubber is paired with very smooth or macroscopically rough surfaces in wet conditions. Thus, the presence of microhysteresis in elastomers also prevents the general application of a constant coefficient-of-friction equation to wet rubber products.

8.7

Rubber Adhesion-Transition Phenomenon on Wet Surfaces

8.7.1

Automobile Tire-Tread Rubber

Sabey [7] conducted lubricated-rubber friction testing focusing on the skid resistance of motor vehicle tires. She idealized road-surface aggregate as spherical and conical elements and obtained coefficient-of-friction measurements of smooth steel spheres and cones sliding on tire-tread rubber well lubricated with water. We now investigate the possible development of the adhesion-transition phenomenon in Sabey’s studies.

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207

Microhysteresis in Wet Rubber Products

Adhesion Plus Macrohysteresis Forces (FA + FHb)–lbs

Figure€4.59 presented Sabey’s coefficient-of-friction results for the idealized conical aggregate. The plots are hyperbolic for interior apex angles of 70°, 90°, 100°, and 160°. The results of a back-calculation analysis of the data in Figure€4.59 are illustrated in Figure€8.3. Extrapolation of the straight-line plots to the y-axis indicates that microhysteretic forces arose in the tire-tread rubber in all four cases. As we have seen in the portions of Chapter 5 dealing with rubber sliding on smooth paired materials, development of the surface deformation hysteresis force requires physical contact between rubber asperities and the microtexture of the harder surface. In addition, sufficient combined surface free energies from the two materials must be present to produce adhesion between the rubber asperities and contacted microtexture. As a result of this physical contact, FA forces also developed. Generation of the FHs forces evidenced in Figure€8.3 indicates that adhesion between the tire-tread rubber and conical metal aggregate was present in Sabey’s testing. Figure€8.16 presents a logarithmic plot of (FA + FHb) vs. FN for Sabey’s conical aggregates possessing interior apex angles of 70°, 90°, and 100°. Because the reported theoretical pressures were not uniform [7], applied normal force was chosen for the x-axis scale in the present analysis. Adhesion transition points are evidenced in the three plots at applied normal loads of 16 N (3.5 lb), 29.5 N (6.5 lb), and 27 N (6 lb) for the 70°, 90°, and 100° cones, respectively. The lowest normal load applied to each cone in Sabey’s testing was 22.2 N (5 lb). To provide a comprehensive picture of the potential for development of the adhesion-transition phenomenon in general, Figure€8.16 includes data points obtained by extrapolating the plots in the figure to an FN value of 4.4 N (1 lb). It was observed that the adhesion transition points for the 90° and 100° cones were above the smallest load actually applied, 22.2 N (5 lb), while 20 90°

10 5 100° 2 1

70° 1 3 5 10 Applied Normal Load (FN)–lbs

20

Figure€8.16 Back-calculated adhesion plus macrohysteresis friction forces (FA + F Hb) vs. applied normal force from Sabey’s wet testing of idealized (conical) road-surface aggregate with indicated interior apex angles using tire-tread rubber. Intersections of the two lines in each plot evidence development of the adhesiontransition mechanism. (From Sabey, B.E., Proc. Roy. Soc. A, 71, 979, 1958.)

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208 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces that for the 70° cone was below it. This difference illustrates the need to conduct rubber-friction testing on a comprehensive basis if determination of the mechanisms developed in such studies is important. 8.7.2

Aircraft Tires

Side Friction Forces [FS(A + Hb)]–kN

Figure€4.54 illustrated the back-calculated side coefficient-of-friction values obtained from the Yager et al. [8] radial-belted-tire-runway traction measurements in wet conditions. Figure€8.4 presents evidence for the production of FHs forces in this testing. Utilizing the y-intercepts depicted in Figure€8.4 allowed for calculating the values of the side friction force (FS(A + Hb)) for the different plots. Figure€8.17 presents a logarithmic plot of FS(A + Hb) vs. FN for the 5° yawangle data. As seen, an FNt value of about 88 kN (19,775 lb) is indicated. While development of the adhesion-transition phenomenon in the subject radial-belted tires is evidenced, this result is best employed as an indicator of the potential for the phenomenon’s presence in all commercial aircraft tires in wet-runway conditions. As observed, the adhesion-transition phenomenon can be produced when FA forces arise between rubber and a contacted harder material. In the Yager et al. [8] testing, generation of FA forces depended, in part, on the efficacy of water removal in the tire contact patch and the combined surface free energies of the tire and runway. These independent variables were not controlled in this testing. Consequently, the indicated presence of the adhesion-transition phenomenon in the radial-belted tires should not be taken as restricting the development of this mechanism only to that tire type. 20 10 5

1

10 50 100 Applied Normal Load (FN)–kN

200

Figure€8.17 Back-calculated side friction forces (FS(A+Hb)) vs. applied normal load from wet testing of radial-belted aircraft tires at a five-degree yaw angle. Intersection of the two lines in the plot evidences development of the adhesion-transition mechanism. (From Yager, T.J., Stubbs, S.M., and Davis, P.M., Paper 901931, Emerging Technologies in Aircraft Landing Gear, SAE International, PT-66, Warrendale, PA, 1997.)

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209

Microhysteresis in Wet Rubber Products 8.7.3

Footwear Outsoles

8.7.3.1 Work Shoes Tisserand [11] conducted traction investigations utilizing the dynamic INRS whole-shoe testing device. Figure€4.41 presented a generalized depiction of his µ-vs.-FN results for two unidentified work shoes sliding on smooth stainless steel coated with ordinary engine oil. In both cases, the coefficient of rubber friction decreased with increasing applied normal load. The back-calculation technique was applied to Tisserand’s wet-testing data. Figure€8.6 depicts the results of these calculations. The plot for work shoe A evidences a wet microhysteresis force of about 40 N (8.8 lb). Figure€8.18 presents a logarithmic plot of FA vs. FN for work shoe A. As seen, an FNt value of about 125 N (27.5 lb) is indicated. 8.7.3.2 Safety Shoes Figure€4.42 presented back-calculated coefficient-of-friction test results from Grönqvist’s [12] walking-surface slip-resistance study examining three types of safety shoes with rubber outsoles possessing dissimilar tread patterns. The pairings, comprising nitrile outsoles with waveform (NRw) and 20

Adhesion Friction Forces (FA)–kg

10 5

1

0.1

5 10 20 50 Applied Normal Load (FN)–kg

100

Figure€8.18 Back-calculated adhesive friction forces (FA) vs. applied normal load from wet testing of Tisserand’s work shoe A. Intersection of the two lines in the plot evidences development of the adhesion-transition mechanism. (From Tisserand, M., Ergonomics, 28, 1027, 1985.)

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210 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces triangular (NRt) tread patterns and styrene outsoles with the same patterns, SRw and SRt, all exhibited reductions in μ with increasing PN. Figures€8.7 and 8.9 depict findings from a microhysteretic analysis of Grönqvist’s data from these tests. The nitrile and styrene rubber evidenced production of constant surface deformation hysteresis forces for both tread patterns. Figure€8.19 presents a logarithmic plot of FA vs. PN for Grönqvist’s nitrile outsoles. As illustrated, PNt values of about 579 kPa (84 psi) and 634 kPa (92 psi) are indicated for the waveform and triangular patterns, respectively. Figure€8.20 presents a logarithmic plot of FA vs. PN for Grönqvist’s styrene outsole with a waveform tread pattern. A PNt value of approximately 800 kPa (116 psi) is indicated. In this case, the styrene triangular tread pattern did not develop the adhesion transition phenomenon. Figure€4.43 presented back-calculated coefficient-of-friction test results from Grönqvist’s study of safety shoes with outsoles composed of thermoplastic rubber, polyurethane, and polyvinylchloride. These pairings, all possessing a rectangular tread pattern, exhibited reductions in μ with increasing applied normal pressure. Figure€8.11 depicts findings from a microhysteretic analysis of Grönqvist’s data from these tests. All three outsoles evidenced production of a constant surface deformation hysteresis force. Figure€8.21 presents logarithmic plots of FA vs. PN for Grönqvist’s thermoplastic rubber, polyurethane, and polyvinylchloride outsoles. As shown, PNt values of about 1,172 kPa (170 psi), 724 kPa (105 psi), and 1,241 kPa (180 psi) are indicated for the thermoplastic rubber, polyurethane, and polyvinylchloride, respectively.

Adhesion Friction Forces (FA)–lbs

50

Triangular

Waveform

10 5

1

10

20

50

100

200

500

Applied Normal Load (PN)–psi Figure€8.19 Back-calculated adhesion friction forces (FA) vs. applied normal pressure from wet testing of nitrile rubber triangular and waveform shoe tread patterns. Intersections of the two lines in each plot evidence development of the adhesion-transition mechanism. (From Grönqvist, R., Ergonomics, 38, 224, 1995.)

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211

Microhysteresis in Wet Rubber Products

Adhesion Friction Forces (FA)–lbs

20 Waveform tread pattern

10

5

1

10

20

50

100

200

500

Applied Normal Load (PN)–psi

Adhesion Friction Forces (FA)–lbs

Figure€8.20 Back-calculated adhesion friction forces (FA) vs. applied normal pressure from wet testing of styrene rubber waveform shoe tread pattern. Intersection of the two lines in the plot evidences development of the adhesion-transition mechanism. (From Grönqvist, R., Ergonomics, 38, 224, 1995.)

20 10 5

1

10

20 50 100 200 Applied Normal Load (PN)–psi

500

Figure€8.21 Back-calculated adhesion friction forces (FA) vs. applied normal pressure from wet testing of thermoplastic rubber, polyurethane, and polyvinylchloride shoe outsoles with a rectangular tread pattern. Intersection of the two lines in each plot evidences development of the adhesion-transition mechanism. (From Grönqvist, R., Ergonomics, 38, 224, 1995.)

8.7.4

Ramifications of the Presence of the Adhesion- Transition Phenomenon in Wet Rubber Products

The rubber adhesion transition phenomenon was introduced in Chapter 5. It was shown in Chapter 6 that the adhesion friction force between rubber and

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212 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces harder materials can increase with growth in the real area of mutual contact developed in such pairings. Under certain circumstances, FA in rubber can be expressed by FA = μA(FN).



(8.2)

Equation 8.2 applies when the primary result of increases in FN or PN is to produce new areas of contact between rubber and its paired surfaces. This occurs only in the lower loading range. With such pairings, a change in the adhesive friction-force-producing mechanism can eventually take place — that is, when the adhesion transition pressure PNt is reached. At that point, Equation 8.2 is no longer valid. We have also seen that when the predominant result of increasing FN or PN is to expand existing areas of contact between rubber and its paired surfaces, the generalized Hertz equation applies. This relationship, valid for use in rubber friction analysis and design at PNt and above, can be expressed as FA = cA(FN)m.



(8.3)

In practical engineering applications in wet conditions where FA develops, it seems likely that if the applied normal load on a rubber product is sufficiently increased, the adhesion transition force or pressure will be attained. Equation 8.2, the relationship expressing direct proportionality, cannot account for the rubber adhesion-transition phenomenon. Consequently, the constant coefficient-of-friction expression does not comprehensively apply to rubber friction in such wet conditions, even if the microhysteretic force FHs does not arise or has been accounted for.

8.8

Chapter Review

This chapter focused on the development of the microhysteretic friction force FHs in rubber products paired with wet surfaces. Development of the rubber microhysteresis friction mechanism can depend on the degree to which two such contacting surfaces are covered with water or other liquids. In most practical engineering applications, frictional contact of rubber with its paired surface takes place with adsorbed water from the surrounding atmosphere in the interface between them. Because of high attraction forces resident in the two surfaces, it is impossible to exclude such adsorption. Furthermore, if the surrounding relative humidity increases, more such adsorbed water will accumulate. Nevertheless, testing has shown that these circumstances can usually be considered as representing a “dry” condition. For the friction testing in which we are interested, wet conditions were defined as those in which a liquid is purposely applied to the contacting interface. This

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Microhysteresis in Wet Rubber Products

213

is common when testing walking surfaces, roadways, and runways in order to assess the friction-reducing effects of such contaminants. This chapter examined testing in which rubber microhysteresis forces were indicated to develop in wet conditions in the following:

1. Smooth automobile tires sliding on asphalt roadways wetted with water;



2. Automobile tire-tread rubber tested on idealized roadway surface aggregate wetted with water;



3. Radial-belted commercial aircraft tires sliding on a concrete runway wetted with water;



4. Work shoe outsoles sliding on a smooth, stainless steel plate contaminated with engine oil;



5. Safety shoe outsoles comprised of polyvinylchloride, polyurethane, thermoplastic rubber, nitrile rubber, and styrene rubber sliding on smooth, stainless steel flooring contaminated with glycerol; and



6. Rubber, urethane, and polyvinylchloride shoe heels sliding on untreated and waxed vinyl tile, stainless steel, and sealed portland cement concrete contaminated with water, SAE 10 oil, and SAE 30 oil.

Development of microhysteresis forces in pairings involving sliding wet rubber appears to be commonplace; thus, analysis and design of the friction characteristics of these pairings must include consideration of microhysteretic forces, if such efforts are to be scientifically based. This chapter also examined the development of the rubber friction adhesion-transition mechanism in wet conditions. Evidence was presented indicating that this phenomenon can arise when wet rubber slides on both smooth and rough surfaces.

References



8136.indb 213

1. Savkoor, A.R., On the friction of rubber, Wear, 8, 222, 1965. 2. Bowden, F.P. and Tabor, D., The adhesion of solids, in Structure and Properties of Solid Surfaces, Gomer, R. and Smith, C.S., Eds., The University of Chicago Press, Chicago, IL, 1952, chap. 6. 3. Bowden, F.P. and Tabor, D., The Friction and Lubrication of Solids, Part II, Clarendon Press, Oxford, U.K., 1964. 4. Rabinowicz, E., Friction and Wear of Materials, 2nd ed., J. Wiley & Sons, New York, 1995. 5. Clayton, J.H., An Investigation and Modification of a Pavement Skid-Test Trailer, M.S. thesis, The University of Tennessee, Knoxville, 1962.

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214 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

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6. Thirion, P., Les coefficients d’adhérence du caoutchouc, Rev. Gén. Caoutch., 23, 101, 1946. 7. Sabey, B.E., Pressure distributions beneath spherical and conical shapes pressed into a rubber plane, and their bearing on coefficients of friction under wet conditions, Proc. Roy. Soc. A, 71, 979, 1958. 8. Yager, T.J., Stubbs, S.M., and Davis, P.M., Aircraft radial-belted tire evaluation, Paper 901931, Emerging Technologies in Aircraft Landing Gear, Tanner, Ulrich, Medzorian, and Morris, Eds., SAE International, PT-66, Warrendale, PA, 1997. 9. Mori, K., Kaneda, S., Kanae, K., Hirahara, H., Oishi, Y., and Iwabuchi, A., Influence on friction force of adhesion force between vulcanizates and sliders, Rubber Chem. Techn., 67, 797, 1994. 10. Yager, T.J., Tire/runway friction interface, Aircraft Paper 901912, Emerging Technologies in Aircraft Landing Gear, Tanner, Ulrich, Medzorian, and Morris, Eds., SAE International, PT-66, Warrendale, PA, 1997. 11. Tisserand, M., Progress in the prevention of falls by slipping, Ergonomics, 28, 1027, 1985. 12. Grönqvist, R., Mechanisms of friction and assessment of slip resistance of new and used footwear soles on contaminated floors, Ergonomics, 38, 224, 1995. 13. Redfern, M.S. and Bidanda, B., Slip resistance of the shoe-floor interface under biomechanically relevant conditions, Ergonomics, 37, 511, 1994.

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9 Rubber Microhysteresis in Static-Friction Testing

9.1

Introduction

Since at least the 1950s, there has been a lack of agreement among both scientific researchers and engineering practitioners involved in friction testing as to whether a distinct static coefficient of rubber friction exists. This chapter addresses the static-coefficient-existence issue. As one might expect, the existence of “static” resistance to pending movement can be a matter of definition. As static friction is defined in this chapter, it does exist and it has direct relevance to rubber friction metrology. This being so, the rubber friction mechanisms developed under static-testing conditions are examined. An understanding of these mechanisms can provide a more complete picture of rubber friction generally and also assist in the design of rubber products and their paired surfaces. Evidence is presented indicating that rubber microhysteresis develops in static-friction testing and that this FHs force can be independent of the applied static tangential load.

9.2

Does Static Friction in Rubber Exist?

9.2.1

Hurry and Prock’s Position

In addition to the test results reported by Hurry and Prock [1] involving industrial belting already discussed, they investigated the “start-of-slip” issue. Utilizing the test setup and basic protocol detailed in Section 4.2.2, Hurry and Prock also measured the values of FT and the belting sample’s displacement at given time intervals. Changes in the coefficient of friction with velocity from the start of sliding were then calculated using Equation 9.1:

μ = FT/FN.

(9.1)

215

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216 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Figure€9.1 depicts the Hurry and Prock start-of-slip test results from an unworn belt segment. The rubber sample began sliding slowly, eventually reaching a constant velocity determined by the rate of towing cable wind-up. Unfortunately, Hurry and Prock did not measure inertial resistance to movement and their FT values in the pre-constant-velocity time intervals included both static friction and inertial-resistance-force components. Nevertheless, it is useful to present their conclusions because they represent one view of the static-coefficient-existence issue. Furthermore, had Hurry and Prock quantified inertial resistance and subtracted these values from FT, the general shape of the plot in Figure€9.1 would have remained unchanged. Hurry and Prock stated that: This study appears to indicate that the samples start to slide in such a way that there is no distinct coefficient of static friction. More boldly stated, we can say that the coefficient of static friction has no meaning for the samples used under the conditions of testing described. (p. 622)

9.2.2 Kummer’s Position

Coefficient of Friction–µ

Kummer [2] also carried out rubber-friction experiments concerned with the static-coefficient-existence issue. On the basis of these studies, Kummer stated: “Under ordinary conditions and at room temperature a rubber slider resists a finite shear force without movement, and it therefore has a static coefficient” (p. 7). Utilizing a practical, every-day event as a further example, Kummer points out that an automobile parked on a hill can remain there indefinitely, and therefore a static coefficient of rubber friction must exist. 0.4 0.3 0.2 0.1 0

1 2 Velocity–10–3 ft/min

3

Figure€9.1 Results of start-of-slip investigation carried out by Hurry and Prock to determine the variation of the rubber coefficient of friction (μ) with velocity of the sliding specimen. The coefficients inadvertently contain varying inertial force components. (From Hurry, J.A. and Prock, J.D., India Rubber World, 128, 619, 1953. With permission.)

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Rubber Microhysteresis in Static-Friction Testing

9.3

217

Two Portable Static-Friction Testing Devices

Slippery walking surfaces are known to be a common cause of pedestrian slips and falls. The cost of injuries sustained from falls is projected to reach $85 billion annually by 2020 [3]. A considerable number of portable testing devices [4], often called tribometers, have been developed to allow assessment of walking-surface slip resistance in the field. Two of the more popular proprietary testers had been the subject of operational ASTM standards, which were recently withdrawn by that organization. Withdrawal was principally occasioned because ASTM does not wish to grant standards to proprietary devices; nevertheless, it is likely that these more popular tribometers will continue in common use. We now examine test results from two of these testers to illustrate the concurrent development of rubber microhysteresis and adhesion in static-friction testing. For a testing instrument to be the subject of an ASTM operational standard, it is desirable for that device to have undergone bias testing so that conventional calibration adjustment can be made during use, if necessary. Before the decision to withdraw standards on proprietary tribometers was announced by the ASTM, Powers et al. [5] carried out dry bias testing on two of these devices in dry conditions: (1) the PIAST, formerly described in ASTM F 1677, Standard Test Method for Using a Portable Inclineable Articulated Strut Tester (PIAST); and (2) the VIT, formerly described in ASTM F 1679, Standard Test Method for Using a Variable Incidence Tribometer (VIT). The PIAST is depicted in Figure€9.2, while the VIT is displayed in Figure€9.3. Figure€9.4 presents a close-up of the VIT’s operational setting scale. Powers et al. bias-tested the PIAST and the VIT on a force plate covered with smooth vinyl composition tile to which its recommended wax had been applied. The tribometers were mounted separately on specially designed, rigid metal frames to ensure that, upon their activation, only their test feet could come in contact with the force plate. The protocols for operation of the two devices, as stated in their former ASTM standards, were followed during the bias testing. Both tribometers were fitted with Neolite test liner test feet possessing a Shore A hardness of 93-96 as determined by the ASTM D 2240 test method. Neolite test liner is an elastomer manufactured in a controlled manner so that reasonably constant properties are provided from all production runs. Both tribometers tested by Powers et al. [5] are designed to quantify the measured walking-surface slip resistance by impact loading applied at preselected angles of incidence to the floor in the manner described below. When these tribometers are set at a selected angle of incidence to the walking surface and activated, both horizontal and vertical forces are applied to that surface by the test feet. The test feet will slip when the applied horizontal force exceeds the maximum friction available in the test foot–walking surface pairing and the inertial resistance to movement of the test foot’s components is overcome. The test foot’s angle of incidence to the walking

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218 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Figure€9.2 The Portable Inclineable Articulated Strut Tester (PIAST).

Figure€9.3 The Variable Incidence Tribometer (VIT).

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Rubber Microhysteresis in Static-Friction Testing

219

Figure€9.4 Close-up of the Variable Incidence Tribometer (VIT) setting scale.

surface from the vertical is increased by the operator until slip occurs. In the Powers et al. study, however, measurements were limited to incident angles at which no slip took place. Clearly, in the Powers et al. testing, static friction measurements were being made.

9.4

Definition of Static Friction

In this book, static friction is defined as friction developed at the contacting interface of an elastomeric material and a paired solid, one element of which is applying a tangent force to the other, but no sustained relative movement between them occurs. While some deformation of the contacting surface asperities must take place in response to the applied tangent force, such deformation must be insufficient to produce sustained acceleration of the moveable element. This definition applies in wet or dry conditions. As an example of static friction, we can cite the slip-resisting forces recorded in the Powers et al. [5] investigation. This type of static slip resistance is akin to the friction developed in the contact patch of a free-rolling tire on pavement — that is, where no tire slip takes place. Static friction also develops in the footprint of a shoe-rubber outsole during normal pedestrian walking — that is, when no slipping occurs. This is significant because many engineering practitioners in the slip-resistancetesting community utilize static-friction testing as a basis for determining the traction between outsoles and walking surfaces.

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220 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

9.5

Rubber Microhysteresis in Static-Friction Testing

9.5.1

Findings of the Powers et al. Testing

While the Powers et al. [5] study measured friction forces, the possible friction-force mechanisms that may have developed in the testing were not examined. The investigation was statistical, focusing on differences between the force-plate readings and the test settings selected on the tribometer by the operator. Both the VIT and the PIAST employ Equation 9.1 to quantify measured slipresistance values. The design of both tribometers assumes that FT divided by FN will yield applied friction-force ratios representative of a single force-producing mechanism at any angle of incidence. Each device is furnished with a scale from which slip-resistance values can be read directly. In the case of the VIT, the slip-resistance reading is sometimes called the “slip index.” As seen in Figure€9.4, presenting a close-up of the VIT setting scale, the scale on each device utilizes ratios from 0.0 to 1.0, or 0° to 45°, representing the tangent of the angle at which the test foot strikes the walking surface relative to the vertical. For example, if the VIT or PIAST were activated at a setting of 0.4, and the test foot did not slip, the static slip resistance would be taken as 0.4, quantifying μ in Equation 9.1. The setting angle at this ratio is 21.8°. Powers et al. compared the ratios selected on the tribometer setting scales with ratios of the corresponding FT and FN values measured by the force plate. The peak forces recorded by the force plate at each setting angle were utilized in these calculations. Data were obtained from five readings at each scale setting in the non-slip positions. Interclass correlation coefficients (ICCs) were taken to represent the extent of agreement between the mean FT/FN ratios from the five force plate trials and the tribometer setting ratios involved. Powers et al. concluded that both tribometers demonstrated “remarkably low bias” under the dry conditions of testing, evidencing ICC values of 0.89 to 0.90, where a value of 1.00 represents the strongest agreement. This testing was statistically focused. Not addressed were the mechanistic causes of the biases that were indicated to exist in the testers. Furthermore, the assumption inherent in the design of the two tribometers that FT forces arise from a single force-producing mechanism is not consistent with the indicated presence of two different friction-force mechanisms in the Powers et al. testing. We will see that both adhesion and microhysteresis forces appear to have developed in the tribometers’ Neolite test liner test feet. 9.5.2 Adhesion and Rubber Microhysteresis in PIAST Testing The PIAST device, depicted in Figure€9.2, employs gravity to accelerate a 4.5-kg (10-lb) weight sliding downward on stainless steel rods to impact the walking surface with the device’s test foot. The area of the square, Neolite-

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221

Rubber Microhysteresis in Static-Friction Testing

covered test foot is 7.6 cm2 (9 in.2). Powers et al. [5] determined that the PIAST’s effective contact time with the force plate during testing was approximately 0.0075 sec. ASTM standard E 456 defines bias as “[t]he difference between the population mean of the test results and an accepted reference value.” In the case of the subject tribometer testing, the accepted reference value is the FT/FN ratio setting selected by the operator. Bias is considered a potentially controllable systematic error — in contrast to random errors, which are uncontrollable. If the causes of systematic bias in a testing instrument can be identified, accounting for such bias by routine engineering calibration is sometimes possible. Powers et al. showed that the PIAST did not strictly conform to Equation 9.1 under the normal loads applied. The ICC value representing agreement between the measured force-plate ratios and the tribometer’s ratio settings was 0.90. Smith [6] analyzed the Powers et al. test results, focusing on potential mechanistic causes for the systematic bias present in the two tribometers. In his analysis of the Powers et al. test results, Smith determined that, instead of Equation 9.1, an expression of the generalized Hertz type

μ = c(FN)-m

(9.2)

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807.5 N

807.2 N–FN

can be used to quantify numerically the PIAST’s test results. Because Equation 9.2 is hyperbolic with a negative exponent, development of the rubber microhysteresis mechanism in the PIAST’s elastomeric test foot during the Powers et al. testing was evidenced. Moreover, the present analysis indicates that another bias-introducing mechanism appears to be at work: misalignment of the PIAST’s setting scale at the zero-ratio setting. Figure€9.5 depicts the PIAST’s misaligned condition. Powers et al. initiated testing by employing the zero-ratio setting. This was intended to produce a perpendicular loading between the PIAST’s test foot and the force plate, yielding only an FN force; instead, a small FT force, 22.1 N (4.9 lb), was also generated. The measured FN and FT forces are presented in the figure, as is the calculated 22.1 N–FT resultant, 807.5 N (178 lb). Application of simple trigonometry yields a Figure€9.5 misalignment angle, θM, of 1.5°. Representation showing misalignment of It should be noted that, due to the PIAST’s setting scale when its test foot is perPIAST’s design, the applied tan- pendicular to tested surface. (Calculated from gent force FT increases as the applied data reported by Powers et al., J. Test. Eval., 27, normal force FN decreases. This is 368, 1999.)

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222 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces illustrated in Figure€9.6. The figure presents a plot of the developed PIAST friction forces as measured by the force plate vs. the setting ratios utilized. The ratios and corresponding angles depicted are 0 at 0°, 0.1 at 5.7°, 0.2 at 11.3°, 0.3 at 16.7°, and 0.4 at 21.8°. Figure€9.6 reveals a discontinuity between the zero-ratio setting, FN = 807.2 N (177.6 lb), FT = 22.1 N (4.9 lb), and the 0.1-ratio setting, FN = 776.3 N (170.8 lb), FT = 89.1 N (19.6 lb). The source of this discontinuity appears to be the misalignment just mentioned. Examination of the Powers et al. test data reveals that, except for the zeroratio setting to the 0.1-ratio setting range, the difference between the FT forces at the various settings was 50 N (11 lb). The difference in the FT forces between the zero-ratio setting and the 0.1-ratio setting was about 70 N (15.4 lb). Subtracting the 50-N (11-lb) value from the 70-N (15.4-lb) measurement yields 20 N (4.4 lb), an amount closely approximating the misaligned FT mea800

FN

Forces Generated by PIAST’s Test Foot–N

700

600

500 FN = Applied normal force FT = Measured tangent friction force

400

FA = Calculated adhesion friction force FHs = Surface deformation hysteresis force

300

FT

200

100

0

FA FHs 0

0.10

0.20 0.30 PIAST Setting Ratios

0.40

0.50

Figure€9.6 Plot of forces generated by the PIAST’s test foot vs. that device’s setting ratios as measured by a force plate covered with vinyl composition tile; y-intercept of FT plot indicates presence of FHs force. (Calculated from data reported by Powers, M. et al. J. Test. Eval., 27, 368, 1999.)

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Rubber Microhysteresis in Static-Friction Testing

223

surement of 22.1 N (4.9 lb). These FT relationships are illustrated in Figure€9.6, in which a straight line representing the measured tangent forces for 0.1, 0.2, 0.3, and 0.4 setting ratios is evidenced. We see that if the FT plot in Figure€9.6 is extrapolated to the y-axis, the presence of a constant surface-deformation-hysteresis force of approximately 40 N (8.8 lb) is indicated. Subtracting this amount from the FT measurements at the 0.1, 0.2, 0.3, and 0.4 ratios yields a straight line representing adhesion forces FA passing through the origin when extrapolated. Figure€9.6 portrays the development of two different rubber friction forces, one of which (FA) varied under applied normal load. The other( FHs) appears to be constant. The figure indicates that rubber friction forces can arise through static tangential loading with consequent generation of two different slip-resisting-force mechanisms on a macroscopically smooth surface.

9.6

Independence of the Rubber Microhysteresis Force in Static-Friction Testing

In the dynamic friction tests analyzed in previous chapters, only one tangent force was ususally applied to the rubber test specimen. In contrast to this single-tangent-force regime, Figure€9.6 evidences a constant FHs force of about 40 N (8.8 lb), generated when five different tangent forces were applied: 22.1 N (4.9 lb), 89.1 N (19.6 lb), 140.0 N (30.8 lb), 190 N (41.8 lb), and 238.1 N (52.4 lb). It has been shown previously that the rubber microhysteresis force is indicated as being independent of the applied normal load in dynamicfriction testing. We can now theorize that, in static-friction testing, FHs can be independent of both the normal and tangent forces applied to the rubber test specimen. This double independence of FHs is relevant to Figure€9.6. The x-axis scale of PIAST setting ratios in the figure is uniform, while the FT and FN forces generated by the device are not. They vary in accordance with the sine and cosine of the setting angles, respectively. The independence of rubber microhysteresis from the FN and applied tangent forces, however, allows one to draw conclusions concerning FHs from the relationships portrayed in the figure.

9.7

Adhesion and Rubber Microhysteresis in VIT Testing

The VIT device, portrayed in Figure€9.3, is powered by compressed CO2 gas, which, upon release, applies a constant force to a piston rod with the 3.2-cm (1.25-in.)-diameter test foot mounted at the other end. The design includes a pressure regulator, normally set by the operator to 172 kPa (25 psi). Powers et al. [5] determined that the VIT’s effective contact time with the force plate

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224 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces during that testing was approximately 0.5 sec in that testing. Figure€9.4 presents a close-up of the VIT’s setting scale. Smith’s [6] analysis of the Powers et al. VIT test results focused on indicated bias in the VIT’s measured tangent force FT. Powers et al. had determined that the ICC value representing agreement between the VIT’s measured force-plate ratios and the tribometer’s ratio settings was 0.89. Because the VIT’s piston and test foot assemblies are initially at rest before application of gas pressure, and they are then accelerated by this pressure, Smith concluded that inertial resistance to movement of these mechanical components was at least one source of the bias demonstrated by the ICC value of less than 1.0. Inertial bias in VIT testing will be examined in Chapter 10. Bias associated with development of microhysteresis in the VIT’s test foot is addressed here. Figure€9.7 presents a plot of the measured FT forces vs. the VIT’s ratio settings from the Powers et al. testing. In contrast to the corresponding FT plot for the PIAST presented in Figure€9.6, the VIT friction values do not plot to a straight line but describe a gentle parabolic curve to the largest tribometer 20 19

FHs = Surface deformation hysteresis force FT = Measured tangent friction force FA = Calculated adhesion friction force

18 17 Forces Generated by VIT’s Test Foot–N

16 15 14 13

FT

12 11 10 9 8

FA

7 6 5 4 3 2

FHs 1 0

0

0.1

0.2

0.3 0.4 0.5 VIT Setting Ratios

0.6

0.7

Figure€9.7 Plot of forces generated by the VIT’s test foot vs. that device’s setting ratios as measured by a force plate covered with vinyl composition tile; y-intercept of FT plot indicates presence of FHs force. (Calculated from data reported by Powers, M et al. J. Test. Eval., 27, 368, 1999.)

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Rubber Microhysteresis in Static-Friction Testing

225

setting, 0.7. Like the PIAST, the VIT displays a discontinuity at the zero-ratio setting; in this case, 0.8 N (0.2 lb) at a force-plate-ratio value of 0.03. When a line between the plotted FT points for the 0.1 and 0.2 ratio settings is extrapolated to the y-axis, an FHs value of approximately 0.5 N (0.10 lb) is evidenced. Subtracting 0.5 N (0.10 lb) from the FT measurements yields a line representing the adhesion forces FA. The adhesion plot passes through the origin, when extrapolated. Like the PIAST, the VIT evidences rubber microhysteresis in its test results. The indicated microhysteresis value of approximately 0.5 N (0.10 lb) appears to be an unaccounted-for bias in the VIT’s measurements.

9.8

Chapter Review

Since at least the 1950s, there has been a lack of agreement among both researchers and engineering practitioners involved in friction testing as to whether a distinct static friction force develops when a rubber product begins to slide on a paired surface. Static friction was defined in this chapter as friction developed at the contacting interface of a rubber product and its paired surface, one element of which is applying a pushing or pulling force to the other, but no sustained relative movement between them occurs. The contacting interface between the two materials may be wet or dry. Examples of static-friction testing of a rubber-like material were provided. The existence of static friction in rubber products is significant because many engineering practitioners in the walking-surface-safety community utilize static-friction testing as a basis for determining the traction provided by the footwear-walking surface pairing. This chapter analyzed static-friction testing of a floor tile carried out by Powers et al. [5]. The examination provided evidence of the generation of rubber microhysteresis forces — FHs forces — in the test feet of both walking-surface slip-resistance testers employed in the Powers et al. study; the Portable Inclineable Articulated Strut Tester (PIAST), and the Variable Incidence Tribometer (VIT). The walking-surface-safety community has neither generally recognized the existence of this force, nor considered it when interpreting results from slip-resistance testing. Analysis of the PIAST test results from the Powers et al. investigation produced evidence that the FHs forces generated in static-friction testing can be independent of the pushing or pulling forces applied to the rubber product in which this microhysteretic-friction mechanism arises. In this context, “independent” means that as long as the magnitude of the applied pushing or pulling force on the rubber product equals, or is greater than, the maximum attainable rubber microhysteresis force FHs, the measured value of FHs will be constant. Ramifications of these findings bearing on the scientific validity of testing utilizing the PIAST and VIT are discussed in Chapter 10.

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226 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

References

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1. Hurry, J.A. and Prock, J.D., Coefficients of friction of rubber samples, India Rubber World, 128, 619, 1953. 2. Kummer, H.W., Unified Theory of Rubber and Tire Friction, Engineering Research Bulletin B-94, The Pennsylvania State University, State College, 1966. 3. Englander, F., Hodson, T.J, and Terregrossa, R.A., Economic dimensions of slip and fall injuries, J. Foren. Sci., 41, 733, 1996. 4. Chang, W.-R. and Courtney, T.K., Eds., Measuring Slipperiness-Human Locomotion and Surface Factors, Taylor & Francis, London, 2003, chap. 7. 5. Powers, M., Kulig, K., Flynn, J., and Brault, J.R., Repeatability and bias of two walkway safety tribometers, J. Test. Eval., 27, 368, 1999. 6. Smith, R.H., Assessing testing bias in two walkway-safety tribometers, J. Test. Eval., 31, 169, 2003.

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10 Inertial, Residence-Time, AdhesionTransition, and Contact-Time Bias in Portable Walking-Surface Slip-Resistance Testers

10.1

Introduction

This chapter concerns the scientific validity of slip-resistance measurements obtained by portable testers that develop bias during their operation. It is desirable that portable slip-resistance testers undergo scientifically based bias testing so that calibration adjustment for bias can be made during use, if necessary. The chapter focuses on four bias-producing mechanisms sometimes overlooked when portable slip-resistance testers are employed to assess traction provided by footwear–walking surface pairings: (1) inertial bias, or unaccounted-for resistance to movement of a tester or its mechanical components; (2) residence-time bias, the increase in friction that occurs during the period between placement of a tester on its paired surface and the start of the test run; (3) bias associated with development of the adhesion transition mechanism; and (4) contact-time bias for tribometer comparability. Chapter 9 analyzed the bias testing carried out by Powers et al. [1] utilizing two portable, proprietary slip-resistance testers: (1) the PIAST, formerly described in ASTM F 1677, Standard Test Method for Using a Portable Inclineable Articulated Strut Tester (PIAST); and (2) the VIT, formerly described in ASTM F 1679, Standard Test Method for Using a Variable Incidence Tribometer (VIT). The PIAST was depicted in Figure€9.2 while the VIT was displayed in Figure€9.3. These operational standards have been withdrawn recently, in part because the ASTM does not wish to grant standards to proprietary devices; nevertheless, it is likely that these testers, which employ rubber-like test feet, will continue in common use. As such, their operational biases are of interest. In this chapter we carry out bias analyses on two portable slip-resistance testers possessing active ASTM standards: (1) the Horizontal Pull Slipme227

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228 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces ter, described in ASTM F 609, Standard Test Method for Using a Horizontal Pull Slipmeter (HPS); and (2) another device, to be known herein as the HPM, described in ASTM C 1028, Standard Test Method for Determining the Static Coefficient of Friction of Ceramic Tile and Other Like Surfaces by the Horizontal Dynamometer Pull-Meter Method. Figure€10.1 depicts the HPS while Figure€10.2 presents the HP-M. Neither the HPS nor the HP-M is sufficiently proprietary to occasion withdrawal of these ASTM standards.

A B C A–Chatillon DPP-5.gage B–Steel block C–Test sample Figure€10.1 The Horizontal Pull Slipmeter (HPS), described in ASTM F 609, Standard Test Method for Using a Horizontal Pull Slipmeter. (Copyright ASTM INTERNATIONAL. Reprinted with permission.)

Figure€10.2 The Horizontal Dynamometer Pull-Meter (HP-M), described in ASTM C 1028, Standard Test Method for Determining the Static Coefficient of Friction of Ceramic Tile and Other Like Surfaces by the Horizontal Dynamometer Pull-Meter Method.

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Bias in Portable Walking-Surface Slip-Resistance Testers

10.2

229

Remediable Inertial Bias in Portable Walking-Surface Slip-Resistance Testers

Before inertial bias in portable walking-surface slip-resistance testers can be properly addressed, an introduction to friction testing that scientifically accounts for this issue is appropriate. Such testing has been accomplished using the Hoechst device. 10.2.1 Quantifying Inertial Forces in Static- Friction Testing Using the Hoechst Device In 1974, Braun and Roemer [2] reported definitive friction studies utilizing the accelerometer-equipped Hoechst drag sled in conjunction with a sophisticated laboratory setup capable of quantifying the sled’s inertial resistance to movement when it first begins to slide on a test surface. The circular sled (or as it is sometimes called, sensor shoe) employed three equally spaced, mechanically lapped, chromium test feet for sliding on various floor-treatment materials, such as wax and polish, applied to conventional floor tiles. The Hoechst device is pulled by an axially stiff but flexible strap attached to a variable-speed motor having a large-diameter drive wheel. The investigators’ purpose was to quantify the effects of such treatment materials on floor slip resistance. It was shown that, with proper formulation, wax and polish improved the floor’s frictional resistance to slipping in dry conditions. The Braun and Roemer conclusions were reached by comparing static-friction test measurements from which inertial resistance to movement of the test shoe was properly excluded. Braun and Brungraber [3] subsequently commented on the use of the Hoechst device in static-friction testing and presented an idealized depiction of its typical results, seen in Figure€10.3. As shown in the figure, both the total pulling force F, along with the acceleration of the sled a, are measured and plotted against time t. Figure€10.3 clearly illustrates that the static friction force Fs between the Hoechst device’s test shoe and its paired surface is first overcome, at which point movement and acceleration of the tester then begins. A maximum force Fmax is ultimately attained, after which diminishing amplitude oscillations in F and a occur until complete damping of these variations takes place. At that time, acceleration has been eliminated, and constant-velocity sliding under the action of a constant dynamic friction force Fd occurs. It should be noted that Fd is only slightly lower than Fs. Braun and Brungraber [3] characterized oscillations in the pulling force F as the stick-slip phenomenon. It is worth repeating the emphasis Braun and Brungraber placed on accounting for acceleration and inertial resistance in static testing. Braun and Brungraber stated that:

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230 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces F

Fmax.

a

F

Fs

Fd a t a = acceleration F = measured force Fmax = maximum slip-resistance force developed (inertial + static friction) Fs = maximum static friction force developed Fd = dynamic friction force t = time

Figure€10.3 Idealized depiction of static-friction test results utilizing the Hoechst pull-meter device illustrating the possibility of inertial bias in such testing when Fmax is incorrectly taken as the staticfriction force. (From Braun and Brungraber, A comparison of two slip-resistance testers, in Walking Surfaces: Measurement of Slip Resistance, ASTM STP 649, Anderson, C. and Senne, J., Eds., American Society for Testing and Materials, West Conshohocken, PA, 1977, pp. 49–59. Copyright ASTM INTERNATIONAL. Reprinted with permission.)

The acceleration indicates the start of movement, and in this way it allows the determination of the static friction. It must be pointed up, however, that one does not use the maximum force, as is done in other devices. The maximum force occurs only after motion has already started, and it consists of dynamic friction and mass forces (during acceleration of the sensor shoe). It can be as much as three or four times the actual static friction and results in artificially high values. (p. 51)

10.2.2 Inertial Bias in VIT Testing 10.2.2.1 Static-Friction Testing Utilizing the VIT Device The VIT device, shown in Figure€9.3, is powered by compressed CO2 gas, which, upon release, applies a selected constant force to a piston rod with the 3.2-cm (1.25-in.)-diameter test foot mounted at the bottom end. In the Powers et al. [1] testing, the VIT’s test foot was covered with Neolite, a rubber-like material. The design includes a pressure regulator, normally set by the operator to 172 kPa (25 psi). A close-up of the VIT’s setting scale was presented in Figure€9.4. Smith’s [4] analysis of the Powers et al. VIT test results focused on bias in the VIT’s measured tangent force FT. Powers et al. had determined that the ICC value representing agreement between the measured force-plate ratios and the VIT’s ratio settings was 0.89. Because the VIT’s piston and test-foot

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231

Bias in Portable Walking-Surface Slip-Resistance Testers

Forces–N

assemblies are initially at rest before application of gas pressure, and they are then accelerated by this pressure, Smith [4] concluded that inertial resistance to movement of these mechanical components was at least one source of the bias indicated by the ICC value of less than 1.0. Figure€10.4 presents a plot of the measured FT values vs. the VIT’s ratio settings from the Powers et al. testing in the dry condition. The FT values describe a gentle parabolic curve to the largest tribometer setting, 0.7. When a straight line between the plotted FT points for the 0.1 and 0.2 ratio settings is extrapolated to the y-axis, an intercept value of approximately 0.5 N (0.10 lb) is indicated. As discussed in Chapter 9, the VIT evidences rubber microhysteresis in its test results. The indicated FHs value of approximately 0.5 N (0.10 lb) is an unaccounted-for bias in the VIT’s measurements. This bias is addressed more fully in Chapter 11. Subtracting 0.5 N (0.10 lb) from the FT measurements yields a line representing adhesion forces (FA). The measured-adhesion plot passes through the origin, when extrapolated. This was illustrated in Figure€9.7. Because the VIT’s design assumes that only one friction-force-producing mechanism develops when this device is employed on macroscopically smooth surfaces and the magnitude of that friction force will be zero when the tribometer’s test foot is oriented perpendicular to the force plate, the 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

FAE + FHs Expected measured friction values Actual measured friction values FT = FA + FHs

FHs = FIT

FAE

0

0.1

0.2

FT = Total measured friction force FA = Adhesive friction force FHs = Constant microhysteresis friction force FIT = Tangent inertial resistance force FAE = Expected adhesive friction force

0.3 0.4 0.5 VIT Setting Ratios

0.6

0.7

Figure€10.4 Plot of forces arising in VIT testing vs. the device’s setting ratios. (Calculated from Powers, C.M. et al., J. Test. Eval., 27, 368, 1999.)

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232 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces expected adhesion-force (FAE) plot represents the expected friction-force line. Values for points on this line were determined by calculating the expected friction forces at the ratio settings indicated in Figure€10.4. The expected adhesion force at any ratio setting is that required to obtain the FAE/FN ratio set by the VIT’s operator. Although generation of a rubber microhysteresis force was not expected in the Powers et al. testing, if it had been foreseen and could have been correctly calculated on a scientific basis, its value would likely have been approximately 0.5 N (0.10 lb). This is so because FHs is independent of both FT and FN in static-friction testing. Whether the FT and FN forces actually measured in the Powers et al. study were equal to their expected values, the measured FHs force would have equaled its expected magnitude. So as to reference the constant FHs force in Figure€10.4, a plot including this force is shown in the figure. The values representing FHs at the various setting ratios were calculated by adding 0.5 N (0.10 lb) to the expected adhesion friction forces FAE. A plot fairing the FT forces measured by the force plate is also presented in Figure€10.4. These points constitute the sum of FHs and the FA values at the ratio settings utilized. The various plots presented in Figure€10.4 are labeled accordingly. Figure€10.4 illustrates that measured FT values begin a trend between the 0.2- and 0.3-ratio settings that takes them below the expected FAE line. The differences between the measured FT forces and the expected FAE values increase as the setting ratio increases. Smith [4] concluded that these differences likely demonstrate a systematic static-friction-testing bias that is accounted for by inertial resistance to movement in the accelerated VIT components discussed above. Inasmuch as this indicated inertial static-friction-testing bias is systematic, routine engineering calibration can be utilized to eliminate its significance in VIT static-friction testing of dry walking surfaces in the field. Numerical values for such calibration can be found in the Powers et al. [1] and Smith [4] articles. An example is given below. 10.2.2.2 Correcting for Inertial Bias in Dry VIT Static-Friction Testing Because the Powers et al. [1] static-friction testing involved operation of the VIT on a force plate, the reported readings for inertial bias can be corrected by applying the above findings. Figure€10.4 illustrates that, as a result of inertial bias, the VIT “reads high” on the ratio setting scale over the entire range presented in the figure. Depending on the ratio selected, a variable portion of the force applied to the VIT’s piston rod by the compressed CO2 gas is utilized to overcome inertia and is therefore not applied to the tested surface. We must subtract the appropriate correction factor from the ratios measured by the force plate to account for this inertial effect through calibration. When the VIT’s activation button is pressed, the released CO2 gas begins to accelerate the at-rest but moveable components associated with application

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Bias in Portable Walking-Surface Slip-Resistance Testers

233

of the test foot’s forces to the tested walking surface. An inertial resistance force FI begins to develop. This resistance, of course, arises at whatever setting angle has been chosen by the operator. If the test foot is oriented precisely perpendicular to the walking surface, the inertial resistance force will be completely in this normal direction. As the setting angle begins to increase from 0° toward 45° as depicted in Figure€9.4, an inertial-force component, tangent to the tested surface, arises. The inertial-force component (FIT) is indicated by the shading in Figure€10.4. As depicted by the shaded area in the figure, FIT increases as the VIT’s piston rod’s orientation rotates toward the horizontal from the vertical as the setting ratios increase. The dotted line in Figure€10.4 is employed to assist in differentiating the highlighted growth of the tangential inertial resistance from the friction forces developed in the lower ratio range as the VIT’s settings increase. It is of interest to note that the measured tangent force FT can be represented by the expression

FT = FAE + FHs − FIT.

(10.1)

Therefore, when the variable tangential-inertial-force component equals the constant microhysteretic force, the faired measured-tangent-force equals FAE. This point is depicted in Figure€10.4. Utilizing the 0.5 ratio setting as an example for inertial-bias correction, the force plate measured a corresponding ratio of 0.48; thus, a ratio equivalent to 0.02 was “utilized” to overcome tangential inertia. Referring to Figure€10.4, we see that the corrected FT value is about 17 N (3.7 lb) when the FHs force is included. This calibrated FT value has two components: (1) an FHs force of about 0.5 N (0.10 lb) and (2) an FA value of 16.5 N (3.6 lb). The calibrated FT values can be used in the calibration process after accounting for the normal inertial bias. Figure€10.5 presents a plot of the VIT’s applied normal forces measured by the force plate vs. the setting ratios utilized in the Powers et al. static-friction testing. The calculated expected FN values are also depicted. While the applied normal forces were undoubtedly reduced by the normal inertial-resistance components, the cosine of the angle from the vertical does not change a great deal at the setting angles involved. No clear pattern of normal-force inertial bias is evident; instead, uncontrollable random errors appear to predominate. As such, the calculated expected FN values shown in Figure€10.5 can be used in calibration. Again using the 0.5 ratio setting as an example, the calculated corrected normal force indicated in Figure€10.5 is approximately 33.2 N (7.3 lb). The calibrated FT value of 17.0 N (3.6 lb), including the FHs force, is divided by 33.2 N (7.3 lb) to obtain a calibrated VIT reading of 0.51. Naturally, the calibration corrections have a greater influence as the setting ratio increases. In this regard, one should note that, in practice, the use of VIT at setting ratios of 0.8 and 0.9 is not unusual. One should further note that, for a fully scientific

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234 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 40 35

Normal Forces (FN)–N

30

Expected FN forces Actual FN forces

25 20 15 10 5 0

0

0.1

0.2

0.3 0.4 0.5 VIT Setting Ratios

0.6

0.7

Figure€10.5 Plot of actual and expected applied normal forces (F N) in VIT testing vs. the device’s setting ratios. (Calculated from Powers, C.M. et al., J. Test. Eval. 27, 368, 1999.)

assessment of the VIT’s indicated inertial bias, accelerometer testing should be performed. There seems little doubt, however, that the inertial resistance is a culprit. Remedial static-friction bias corrections as detailed above could be routinely applied for calibration purposes in general use of the VIT when it is employed on macroscopically smooth surfaces. The VIT’s inertia forces, quantified by the analysis of the Powers et al. testing, should always develop to the same extent when the device is kept in proper repair and utilized for static-friction testing in the manner detailed above. Use of the VIT without such inertial calibration constitutes operation of the device without quantifying a dependent variable (FIT) that changes in response to changes in setting ratios. If such inertial bias is not accounted for in static-friction testing, the VIT is being operated in a less-than-fullyscientific manner. 10.2.2.3 Inertial Bias in the VIT When Used as a Dynamic-Friction Tester As a further example of bias calibration of portable walking-surface-slipresistance testers, we now address dynamic use of the VIT. The VIT is used as a dynamic-friction tester when setting-ratio readings are taken after its

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235

Orientation varies with setting ratio

Cylindrical housing

Test foot Setting–ratio scale

Walking Surface Figure€10.6 Depiction of VIT’s swing-out mechanism. (From U.S. Patent 5,259,236; 1993.)

hinged test foot slips by rotating upward and “swinging out.” Figure€10.6 depicts the VIT’s swing-out mechanism. The quarter-circle outline of the setting-ratio scale is also shown. Dynamic measurements at specific ratio settings are quantified by application of the supposedly constant coefficientof-friction equation

μ = FT/FN.

(10.2)

The largest setting ratio employed in the Powers et al. [1] VIT testing was 0.8. Because test-foot slip occurred at this ratio, the corresponding FT measurement was not reported or utilized in the ICC calculations discussed in Chapter 9. Slip of the test foot upon its application to the force plate apparently occurred so rapidly that meaningful force-plate readings could not be obtained. Before contact of the VIT’s test foot with the force plate at the 0.8 setting took place, linear acceleration of the VIT piston-test-foot assembly contributed to FIT inertial bias, as described above. In addition to this bias, two other contributions to inertial bias in the 0.8 ratio measurement at the slipping point also arose: (1) resistance to rotational acceleration of various VIT components and (2) resistance to bending deformation during such rotation of the plastic CO2-feed and -vent hoses employed in the piston pressurization system. Portions of these hoses were pictured in Figure€9.3. The VIT’s piston-rod assembly is partially enclosed in a metallic cylinder that rotates upward in a mounting bracket at the piston’s upper end. The.

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236 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Figure€10.7 Depiction of VIT’s cylindrical housing showing piston rod and return spring. (From U.S. Patent 5,259,236; 1993.)

piston-rod assembly, including its return spring within the cylinder, is depicted in Figure€10.7. Inertial resistance to rotational acceleration of the involved VIT components must arise before swing-out of the test foot can occur. The involved components are the piston-test foot assembly, the cylindrical housing with its contents, and the CO2 feed and vent hoses. The combined weight of these rotating components is approximately 0.7 N (0.15 lb). The mean FT force applied to the force plate at the 0.7 ratio was 19.9 N (4.4 lb). It is not uncommon, when using the VIT in the field to assess the dynamic slip-resistance of walking surfaces, for the operator to witness a stick-slip incident experienced by the device’s test foot. As the test-foot’s swing-out point is approached, the test foot will sometimes slip forward a small amount on the walking surface and then stop. Increasing the setting ratio one increment will then usually result in a conventional test-foot slip. It is likely that such stick-slip incidents are sometimes associated with resistance to rotational acceleration of the involved VIT components. Mere visual watchfulness of the VIT’s operation cannot, of course, tell the operator when the frictional resistance of the walking surface has been exceeded by the applied tangent force, and further increases in the setting ratio are required to overcome rotational inertia. Accelerometer testing of the VIT’s involved rotating components is necessary to quantify inertial resistance to rotation. This should be done at each setting ratio to ensure that static-friction measurements are not inadvertently biased in the increasing direction by FIR forces. Use of the VIT without calibration for inertial resistance to rotational acceleration constitutes operation of the device without quantifying a dependent variable (FIR) that changes in response to changes in setting ratios. If such inertial bias is not accounted for in dynamic-friction testing, the VIT is being operated in a less-than-fully-scientific manner. 10.2.3 Inertial Bias in the PIAST When Used as a Dynamic-Friction Tester The PIAST, discussed in detail in Chapter 9, is also employed as a dynamicfriction tester when readings are taken after its test foot slips and the readings are utilized in Equation 10.2. In this case, inertial bias associated with linear acceleration of its test foot on the tested surface would arise. Because of lack of relevant data, such dynamic bias cannot be depicted or quantified

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237

Bias in Portable Walking-Surface Slip-Resistance Testers

at present. Nevertheless, with suitable testing, remedial inertial-bias calibration corrections for the PIAST could also be calculated. Use of the PIAST, without inertial calibration for resistance to acceleration of its slipping test foot, constitutes operation of the device without quantifying a dependent variable. If such inertial bias is not accounted for in dynamic-friction testing, the PIAST is being operated in a less-than-fullyscientific manner. 10.2.4 Inertial Bias in the HPS When Used as a Static-Friction Tester The HPS can also develop inertial bias during static-friction testing. Like the VIT and the PIAST, inertial bias in the HPS is also remediable. The HPS, depicted in Figure€10.1, is comprised of a dynamometer gage mounted on a steel block. Three identical test specimens of 1.27-cm (0.5-in.) diameter each are fixed within appropriately sized recesses in the underside of the block. These test specimens can be footwear sole, heel, or related materials. In this configuration, the HPS can be pulled on a reference surface. The HPS can also be used in the reverse manner with, for example, three Neolite test feet to assess the slip resistance of walking surfaces of interest. The tester is pulled by a portable, battery-operated power unit, which winds a cord attached to the HPS. The power unit (not depicted) can be selected by the operator. The HPS is accelerated from an at-rest condition on the walking surface as the dynamometer measures the total resistance force generated with time during the test. The maximum measured force developed is recorded by the device and is utilized as FT in Equation 10.2. When used in accordance with ASTM F 609, the total weight of the HPS is 2,700 ± 34 g (5.9 ± 0.1 lb). The HPS is employed in a manner similar to the Hoechst drag sled, except that the HPS is not equipped with an accelerometer. Referencing the symbols provided in Figure€10.3 for the Hoechst tester, one can see that the HPS utilizes Fmax. as its measured FT force. The static slip resistance, or Fs, the objective in using the HPS, is not determined; thus, the inertial resistance force can be overlooked during operation of this device. Remedial static-friction-bias corrections applicable to the HPS can be quantified by operating the device with an accelerometer attachment in the manner carried out by Braun and Roemer [2]. Calibration testing should be done for each different power unit employed because such units may develop different rates of acceleration. By application of Equation 10.3 during such testing, the calibration factor (HPSCF) can be determined:

HPSCF = Fmax. − Fs.

(10.3)

The HPSCF value can then be subtracted from measured FT values to determine Fs in subsequent usage of the HPS when assessing footwear materials or quantifying the slip resistance of a walking surface.

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238 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces An indication of the importance of calibrating the HPS for inertia can be gained by estimating the static-friction force likely generated by the HPS had it been fitted with Neolite test feet and been used to test the vinyl composition tile employed in the Powers et al. VIT study. This VIT testing, utilizing a Neolite test foot, determined that the maximum static friction force measured — arising at the 0.7 ratio setting — was 22 N (4.8 lb) when inertia in that device is taken into account. The combined area of the three 1.27-cm (0.5-in.) diameter HPS test feet is 49% of the VIT’s test foot area. While there are significant differences in the protocols of these two portable testers that must be considered for a rigorous comparison between them to be possible, the difference in test-foot area indicates that the static-friction force developed in vinyl-composition-tile testing by the HPS would have been approximately 11 N (2.4 lb). The weight of the HPS is about 27 N (5.9 lb), exerting a mass force more than double the magnitude of the probable friction force developed. This rough calculation suggests that the inertial bias in the HPS is likely significant. Use of the HPS without inertial calibration for resistance to acceleration of the tester from its initial at-rest condition constitutes operation of the device without measuring and incorporating a controlled variable, Fmax. − Fs, in the friction-determination process. If such inertial bias is not accounted for, the HPS is being operated in a less-than-fully scientific manner. Table€10.1 presents a list of the portable walking-surface slip-resistance testers examined in this chapter that develop remediable inertial bias during operation. Unfortunately, engineering calibration for such bias in these devices is not always performed.

10.3

Irremediable Inertial Bias in Portable Walking-Surface Slip-Resistance Testers

As we have seen, inertial bias can be avoided in the PIAST by utilizing that device as a static-friction tester. Inertial bias in the VIT and HPS cannot be avoided, but it can be remediated through engineering calibration. In certain portable walking-surface slip-resistance testers, however, inertial bias is neither avoidable nor remediable. Table€10.1 Selected Portable Walking-Surface Slip-Resistance Testers That Develop Remediable Inertial Bias during Operation Horizontal Pull Slipmeter (HPS) Portable Inclineable Articulated Strut Tester (PIAST) Variable Incidence Tribometer (VIT)

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Bias in Portable Walking-Surface Slip-Resistance Testers

239

Calibration of the VIT for inertial bias in static-friction testing can be accomplished because this bias arises due to acceleration of the device’s certain mechanical components. Each time the device is activated at a given ratio setting, when operated as detailed in the Powers et al. [1] testing, the same acceleration force arises; that is, the bias is internal, mechanically produced, and quantitatively constant in nature. In the HPS, inertial bias is also internal, mechanically produced, and quantitatively constant in nature. After the friction developed between the HPSwalking surface pairing has been overcome by the power unit, only inertial resistance to movement of the HPS remains. This inertial force is mechanically produced and of a constant magnitude each time the tester is employed on dry, macroscopically smooth surfaces. 10.3.1 Irremediable Inertial Bias in the HP-M The manually operated HP-M is also a portable walking-surface slip-resistance tester in which inertial bias arises during operation; unfortunately, however, in its case the inertial bias is irremediable. The three-component device is depicted in Figure€10.2. A principal component of the HP-M is its dynamometer, specified as to capacity (22 N, 100 lbf) and accuracy (0.45 N, 0.1 lbf) by ASTM C 1028, but no requirement as to weight is stipulated. The weight (accelerated mass) of the force-measuring component, which includes a pull-rod attachment, is left to operator selection. The second principal component of the HP-M is the Neolite sled assembly. The sled’s construction is specified by ASTM C 1028 as to size: 20.3 × 20.3 × 1.9 cm (8 × 8 × ¾ in.); and as to configuration, a 6061-T6 aluminum plate or similar material with a 7.6 × 7.6 × 0.3 cm (3 × 3 × 1/8 in.) Neolite test foot centrally attached underneath. But because of the “similar material” provision for the plate, a specific mass for the sled assembly is not required. The third principal component of the HP-M is the 22-kg (50-lb) weight to be placed on the sled. This weight may be cylindrical or rectangular in shape and must be stable when the sled is manually accelerated by the operator. ASTM C 1028 permits two of the three HP-M components to vary in weight. This allows different masses to be accelerated from an at-rest condition during “standard” HP-M operation. Thus, a bias-producing, uncontrolled, dependent inertial variable related to mass, which changes in response to variation in the weights of the dynamometer and sled assemblies, can be present in HP-M testing. This variable can be controlled, of course, by modifications to ASTM C 1028 so that all weights are specified. While this bias is remediable, a second inertial bias inherent in HP-M operation—the development of variable inertial forces in accordance with subjective judgments of its human operators as to rate of acceleration—is irremediable.

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240 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces This second inertial bias in the HP-M varies in accordance with the rate at which the tester is pulled on the walking surface by its operator. The bias associated with this tester is not mechanically produced or quantitatively constant in nature. Constancy of inertial-force development depends on the subjective, non-quantified rate of acceleration the tester experiences. Use of the HP-M without inertial calibration for this bias constitutes operation of the device with an uncontrolled variable in the friction-determination process. Because this inertial bias is irremediable, the HP-M operates in a less-than-fully scientific manner.

10.3.2 Irremediable Inertial Bias in Other Manually Operated Pull-Meter Testers In 1991, ASTM Committee F 13 on Pedestrian/Walkway Safety and Footwear conducted a workshop at Bucknell University devoted to the evaluation of walking-surface slip-resistance testers, including portable, manually operated pull-meters [5]. Another manually operated pull-meter, the Technical Products Corporation Model 80, to be known herein as the TPCM 80, was assessed at the Bucknell workshop [5]. Relevant findings of the F 13 workshop are discussed in Chapter 11. Manually operated pull-meters have been popular for decades, and devices of their type form a class within the portable slip-resistance-tester group. Like the HP-M, use of the TPCM 80 and other manual pull-meters without inertial calibration for bias constitutes operation of these devices without measuring and incorporating a supposedly “controlled” variable in the friction-determination process. Because such bias is irremediable, the entire class of manual-pull meters is operated in a less-than-fully scientific manner. Table€10.2 lists slip-resistance-testing devices analyzed in this chapter that display irremediable inertial bias. As they are presently designed, employment of these devices on a fully scientific bias is not possible. Table€10.2 Selected Portable Walking-Surface Slip-Resistance Testers That Develop Irremediable Inertial Bias during Operation Horizontal Dynamometer Pull-Meter (HP-M) Technical Products Corporation Model 80 (TPCM 80) Other manually operated pull-meters

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241

Bias in Portable Walking-Surface Slip-Resistance Testers

10.4

Remediable Residence-Time Bias in Static-Friction Testing

10.4.1 Quantifying Residence-Time Bias Using the Hoechst Device In addition to investigating inertial effects arising in static-friction testing, Braun and Roemer [2] utilized the Hoechst device to quantify the influence of residence time on the friction forces developed between the test shoe and the waxed floor tiles. Figure€10.8 presents a back-calculated plot of static FT vs. test-shoe residence time (±) ranging from 1 sec to 30 sec, calculated from the Braun and Roemer test results. Figure€10.8 illustrates the considerable influence of residence time when inertial effects are accounted for by use of the accelerometer-equipped Hoechst device. The FT values increased from 44.3 N (9.95 lb) at 1 sec to 79.7 N (17.9 lb) at 30 sec. The emphasis placed on their residence-time findings by Braun and Roemer [2] merits repeating: One factor that is decisive for the static friction is the standing time (±) between putting down the test shoe on the…[tile] and the start of the test run. At first…[friction] shows a remarkable increase with…[±] and reaches a limiting value only after a prolonged time. (p. 66)

On the basis of their findings, Braun and Roemer decided to use a residence time of 1 sec for the Hoechst test shoe in their static-friction study. 80

Static-Friction Force (FT)–N

70 60 50 40 30 20 10 0

10 20 Residence Time (t)–s

30

Figure€10.8 Back-calculated plot of measured static-friction force vs. residence time using Hoechst test shoe. (Calculated from Braun, R. and Roemer, D., Soap/Cosmetics/Chemical Specialties, 50, 60, 1974.)

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242 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 10.4.2 Demonstrating the Residence-Time Effect Using the VIT Using a two-protocol approach, Smith [6] demonstrated the residence-time effect with a dry Neolite test foot by employing the VIT and two operators in a manner that permitted prolonged contact time with the test surface — in this case, a polished marble floor tile. While other biases associated with VIT operation also developed during the testing, their presence did not prevent illustration of the residence-time effect. The first protocol determined [6] the dynamic slip resistance of the VITmarble tile pairing by the conventional means discussed in Section 10.2.2.3, utilizing a test-foot contact time of 0.5 sec. A slip resistance of 0.72 was indicated. The second testing scheme involved selecting an initial setting ratio below 0.72 and releasing the VIT’s CO2 pressure. Instead of a contact time of 0.5 sec, however, the CO2 pressure was continually applied to the piston rod-test foot assembly. Concurrently, the second operator increased the VIT’s ratio setting until slip occurred. A mean contact time of 17 sec was observed, producing a slip-resistance reading of 0.84, an increase of 17%. 10.4.3 Remedying Residence-Time Bias in Portable Slip-Resistance Testers As exemplified by Braun and Roemer [2], remedying residence-time bias in pull-meter slip-resistance testers is a simple matter. Braun and Roemer selected a residence time of 1 sec for the Hoechst device, and utilized this value in subsequent testing. For the pull-meter type of walking-surface slipresistance testers we have discussed, listed in Table€10.3, a specified residence time should be selected by the appropriate entity associated with each device and used thereafter.

10.5

Irremediable Adhesion-Transition Bias in Portable Walking-Surface Slip-Resistance Testers

10.5.1 Irremediable Adhesion-Transition Bias in VIT Testing The possibility that the adhesion transition pressure PNt is reached during testing with the VIT must be considered. The VIT’s design cannot account Table€10.3 Selected Portable Walking-Surface Slip-Resistance Testers that Develop Remediable Residence-Time Bias during Operation Horizontal Dynamometer Pull-Meter (HP-M) Horizontal Pull Slipmeter (HPS) Technical Products Corporation Model 80 (TPCM 80) Other manually operated pull-meters

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Bias in Portable Walking-Surface Slip-Resistance Testers

243

for the development of the PNt phenomenon. Equation 10.2 does not apply when the VIT generates PN values above the adhesion transition pressure for a given pairing. In this higher range, the increase in pressure does not produce a directly proportional increase in the real area of contact or a directly proportional increase in the adhesive friction force. To investigate the possible development of the adhesion transition pressure phenomenon in the Powers et al. [1] testing, the faired FN forces depicted in Figure€10.5 (corrected for the existence of an FHs force and random bias) were converted to pressure and plotted against the FA forces exhibited in Figure€10.4. Figure€10.9 presents this plot. It is seen that a PNt value of approximately 43.4 kPa (6.3 psi) is indicated. As such, PNt falls at approximately the 0.35 VIT setting ratio. Because of the VIT’s design, its generated FA forces increase as FN and PN decrease; thus, the largest test-foot pressure applied in the Powers et al. VIT testing occurred at the 0.1 setting ratio. The applied pressure at this setting had already exceeded PNt in magnitude. It is in the 0.1 to 0.35 setting-ratio range — a to b in Figure€10.9 — that PNt was exceeded and FA is not directly proportional to FN or PN. Equation 10.2 does not apply in this lower setting5.0

c

4.0 Adhesion Friction Forces (FA)–lbs

3.0 b

2.0 1.5

1 0.9 0.8

a

0.7 2.0

3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 Applied Normal Pressure (PN)–psi

Figure€10.9 Plot of adhesion friction forces (FA) vs. applied normal pressure (PN) illustrating development of the adhesion-transition-pressure phenomenon in VIT testing. (Calculated from data reported by Powers, C.M. et al., J. Test. Eval. 27, 368, 1999.)

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244 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces ratio range. Above the 0.35 setting ratio — b to c in the figure — FA is directly proportional to FN and PN. Determining the existence of the PNt phenomenon in the Powers et al. testing is possible because the actual forces developed by the VIT were measured by a force plate and were available for analysis. During conventional use of the VIT in the field, which involves contacted-surface microtextures different from the one present in the Powers et al. testing, determination of the possible presence of the adhesion transition phenomenon is not possible. Adhesion-transition bias in the VIT can be irremediable. 10.5.2 Irremediable Adhesion-Transition Bias in PIAST Testing An investigation of the possible presence of the adhesion-transition-pressure bias in the Powers et al. [1] PIAST testing was also performed. The results are presented in Figure€10.10. The largest test-foot pressure was applied at the 0.1 setting ratio (point a in the figure). A PNt value of approximately 110 kPa (16 psi) was indicated, falling at about the 0.15 PIAST setting ratio. In the 0.1 to 0.15 setting-ratio range (a to b in Figure€10.10) PNt was exceeded and FA is not directly proportional to FN or PN. Equation 10.2 does not apply in this lower setting-ratio range. Above the 0.15 setting ratio (b to c in the figure) FA is directly proportional to FN and PN.

Adhesion Friction Forces (FA)–lbs

50

c

40

30

20

b

15

a 10

10

15 20 30 Applied Normal Pressure (PN)–psi

40

Figure€10.10 Plot of adhesion friction forces (FA) vs. applied normal pressure (PN) illustrating development of the adhesion-transition-pressure phenomenon in PIAST testing. (Calculated from data reported by Powers, C.M. et al., J. Test. Eval. 27, 368, 1999.)

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245

Bias in Portable Walking-Surface Slip-Resistance Testers

During conventional use of the PIAST in the field, which involves contacted-surface microtextures different from the one present in the Powers et al. testing, determination of the possible presence of the adhesion transition phenomenon is not possible. The adhesion-transition bias in the PIAST can be irremediable. Table€10.4 lists the slip-resistance testers we have analyzed and shown to possess irremediable adhesion-transition bias.

10.6

Contact-Time Bias for Tribometer Comparability

Another bias can be exhibited by walking-surface slip-resistance tribometers — that of contact-time bias for comparability. In accordance with the designs of the various tribometers, their test foot/feet may be in contact with the walking surface for a different and variable time period during each test. During these different, and sometimes variable, contact-time periods, the friction force being measured increases. This was shown by Braun and Roemer [3] and Smith [6]. The longer the testing contact time, the greater the total friction force (FT) that will be measured. In some cases, quantifying the contact time is problematic; furthermore, FT will increase at different rates for different paired surfaces. Unless the testing contact times for any two tribometers are identical, their results are not comparable. An example of this bias is seen in the test results reported by Powers et al. The VIT exhibited a controlled contact time of 0.5 sec, while the PIAST’s friction force contact time was approximately 0.075 sec. Table€10.5 lists the static-friction tribometers we have examined, along with their respective contact times. Table€10.4 Selected Portable Walking-Surface Slip-Resistance Testers That Develop Irremediable Adhesion-Transition Bias during Operation Portable Inclineable Articulated Strut Tester (PIAST) Variable Incidence Tribometer (VIT)

Table€10.5 Portable Walking-Surface Slip-Resistance Testers Examined in This Chapter That Can Develop Test-Foot Contact-Time Bias for Comparability during Operation Testing Device Horizontal Dynamometer Pull-Meter (HP-M)

Varies

Horizontal Pull Slipmeter (HPS)

Varies

Portable Inclineable Articulated Strut Tester (PIAST)

0.075

Technical Products Corporation Model 80 (TPCM 80)

Varies

Variable Incidence Tribometer (VIT)

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Test Foot/Feet Contact Time (sec)

Controllable, (0.5 in [1])

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246 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

10.7

Chapter Review

This chapter discussed important concerns that arise when measuring walking-surface slip resistance. These concerns bear on the scientific validity of such efforts: the development of remediable and irremediable bias in portable friction testers utilized for these measurements. When a remediable bias is present, engineering calibration of the testing device must be carried out for it to be operated in a fully scientific manner. When an irremediable bias develops in a particular tester, employment of the device on a fully scientific basis is not possible. Examples of both these situations were presented, utilizing five of the more common portable slip-resistance testers currently in use and four types of bias found in these devices. The five portable testers are listed in Table€10.6. 10.7.1 Inertial Bias Inertial bias arises from the generation of forces resisting movement of an initially at-rest slip-resistance tester or its mechanical components. Occupants of a stopped automobile can sense this inertial effect, for example, when the accelerator pedal is “floored” by the driver and the vehicle begins to accelerate forward at a high rate. As a result of such acceleration, the vehicle occupants can feel as if they are forcibly “thrown backward” in their seats. When friction testers or their components begin to move forward from an at-rest state during operation, these devices or components experience this same inertial-force resistance. Table€10.1 presents a list of the portable slip-resistance testers examined in this chapter that develop remediable inertial bias during operation. Unfortunately, calibration for this remediable bias in these devices is not often performed. Table€10.2 lists slip-resistance-testing devices analyzed in this chapter that display irremediable inertial bias. Employment of these devices in a completely scientific manner is not possible. Table€10.6 Portable Walking-Surface Slip-Resistance Testers Examined in This Chapter That Develop Bias during Operation Horizontal Dynamometer Pull-Meter (HP-M) Horizontal Pull Slipmeter (HPS) Portable Inclineable Articulated Strut Tester (PIAST) Technical Products Corporation Model 80 (TPCM 80) Variable Incidence Tribometer (VIT)

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10.7.2 Residence-Time Bias Residence-time bias is associated with an increase in the friction force that occurs during the period between placement of a slip-resistance tester — or its test feet — on the walking surface of interest and the beginning of the tester’s operation. This interval is often called the residence time. Residencetime bias is particularly relevant because many professional members of the walking-surface-safety community utilize static testers to quantify the slip resistance developed between types of footwear and their paired surfaces. Table€10.3 provides a list of the portable slip-resistance measuring devices considered in this chapter that can develop residence-time bias. At least theoretically, this bias is remediable. A specified residence time must be selected by the controlling entity associated with each device and disseminated to the community of users. If test results from these devices are to be comparable, however, the selected residence times must be identical. 10.7.3 Adhesion-Transition Bias Adhesion-transition bias can develop in portable slip-resistance testers that apply a range of pressures to the walking surface whose traction characteristics will be measured. This range may encompass pressures in which two different adhesive friction mechanisms arise. When this is so, two different equations must be employed to quantify the adhesive slip-resistance forces produced. At present, there are no portable walking-surface slip-resistance testers that are designed to accomplish this task. The adhesion-transition bias can be irremediable in these devices. Table€10.4 presents a list of the slip-resistance testers we have analyzed that can exhibit irremediable adhesion-transition bias. As presently designed, these devices cannot always be operated in a fully scientific manner. 10.7.4 Test Foot Contact-Time Bias for Tribometer Comparability Another bias can be exhibited by walking-surface slip-resistance tribometers: contact-time bias for comparability. In accordance with the designs of the various tribometers, their test foot/feet may be in contact with the walking surface for a different and variable time during each test. During these different, and sometimes variable, contact-time periods, the friction force being measured increases. The longer the testing contact time, the greater the total friction force (FT) that will be measured. In some cases, quantifying the contact time is problematic; furthermore, FT will increase at different rates for different paired surfaces. Unless the testing contact times for any two tribometers are identical, their results are not comparable. Table€10.5 lists slip-resistance-testing devices we have examined, along with their respective contact times.

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248 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

References



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1. Powers, C.M., Kulig, K., Flynn, J., and Brault, J.R., Repeatability and bias of two walkway safety tribometers, J. Test. Eval., 27, 368, 1999. 2. Braun, R. and Roemer, D., Influences of waxes on static and dynamic friction, Soap/Cosmetics/Chemical Specialties, 50, 60, 1974. 3. Braun, R. and Brungraber, R.J., A comparison of two slip-resistance testers, in Walking Surfaces: Measurement of Slip Resistance, ASTM STP 649, Anderson, C. and Senne, J., Eds., American Society for Testing and Materials, Philadelphia, 1977, pp. 49–59. 4. Smith, R.H., Assessing testing bias in two walkway-safety tribometers, J. Test. Eval., 31, 169, 2003. 5. Anon., Bucknell University F-13 workshop to evaluate various slip resistance measuring devices, Stand. News, 20, 21, 1992. 6. Smith, R.H., Test foot contact time effects in pedestrian slip-resistance metrology, J. Test. Eval., 33, 557, 2005.

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11 Nonscientific Application of the Laws of Metallic Friction to Rubber Tires Operated on Pavements

11.1

Introduction

It is common engineering practice for the laws of metallic friction to be inadvertently misapplied to rubber products. A principal purpose of this book is to demonstrate that the constant (metallic) coefficient-of-friction equation does not apply to rubber. A second purpose is to introduce a unified theory of rubber friction incorporating the fourth basic elastomeric friction force — surface deformation hysteresis, or microhysteresis — and to exemplify the theory’s use in engineering applications. Few individuals would dispute the proposition that further progress toward developing maximum understanding and control of the traction characteristics of tire-pavement pairings is desirable. This chapter provides a philosophical and technical blueprint to assist in accomplishing that goal by replacing use of the laws of metallic friction in tire-pavement testing, analysis, and design with a scientifically based, mechanistically focused, unified theory of rubber friction. In 1973, at the request of ASTM Committee E-17 on Skid Resistance, Ludema and Gujrati [1] published an extensive literature survey and analysis of tireroad traction testing. As part of their assessment they addressed then-current attempts to correlate different road-friction measurements. Ludema and Gujrati [1] stated: The vast amount of data in the literature has aided in a better understanding of the complex problem of tire-road interaction; however, the data have been primarily derived from different sources employing different methods. There is no comprehensible means of analyzing and comparing all the available data due to incompatibility of test conditions, measuring techniques, and the presence of numerous unspecified variables influencing the relative values of data obtained from different test programs. (p. 47)

249

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250 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces While subsequent efforts at standardization have reduced the difficulties in comparing tire-roadway friction test results, most ASTM standards discussed in this chapter contain comparability-related disclaimer language that may be able to be eliminated to some extent and thereby increase the usefulness of these protocols. The most reliable means of fostering comparability of tire test results is to utilize a scientifically based approach to the design and analysis of tiretraction research. This chapter focuses on elements of tire-pavement friction testing that appear amenable to improvement through the use of the unified theory. Furthermore, the need to employ improved means of quantifying such data also exists. The unified theory of rubber friction presented in this book was formulated for that purpose. To set the stage for a discussion of the inadvertent misapplication of the laws of metallic friction to tires and pavements, this chapter first reviews the comparison of the characteristics of rubber friction to metallic friction. A synopsis of the effects of development of microhysteretic forces in rubber will then be presented. This is followed by an examination of factors relevant to tireroadway testing data comparability. Next, ASTM testing standards that inadvertently utilize the constant (metallic) coefficient-of-friction equation when quantifying tire traction are addressed. This chapter also highlights examples of traditional application of the laws of metallic friction to rubber tires in motor vehicle accident reconstruction and the geometric design of roadways.

11.2

Comparing the Characteristics of Rubber Friction to Metallic Friction

In Chapter 4 we questioned whether the constant (metallic) coefficient of friction µ is applicable to rubber and showed that it is not. The expression

µ = FT/FN,

(11.1)

when applied to rubber, is not scientifically based. The following are relevant points in this regard:

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1. Because of the deformational and constitutive differences between rigid metals and visco-elastic rubber, the friction-force-producing mechanisms of these two materials are physically and chemically different.



2. Application of the laws of metallic friction to rubber can misstate the meaning of decreases in the magnitude of rubber coefficients. A diminishing metallic coefficient demonstrates that frictional resistance to movement between metals is also decreasing. Decreases in the magni-

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tude of rubber coefficients calculated by Equation 11.1 often mean that the rate of increasing frictional resistance to motion is diminishing.

3. Expressions for µ involving concurrently acting rubber friction mechanisms can be non-additive and require a different approach to quantify true sliding resistance, one in which coefficients are not involved and only forces are considered.



4. Chapter 2 demonstrated that the constant coefficient of friction equation is a material property of metals. In Chapter 6 it was shown that rubber friction ratios, when properly constituted, represent mechanistic behavior indicators.

The inapplicability of the laws of metallic friction to rubber is particularly relevant when comparing one set of tire friction test data to another. This finding is not new: Kummer and Meyer [2] reached the same conclusion in 1962 and urged care in utilizing coefficients when quantifying tire-pavement traction. Speaking of the rubber coefficient of friction µ, they stated that: The coefficient, regardless of how it is measured, has the character of a performance value and is not a material property. A coefficient is valid for a specific set of conditions only; that is, for the combination of tester and pavement at which it was measured under the prevailing environmental and operating conditions. (p. 5)

Unfortunately, the Kummer and Meyer cautionary recommendation has not been generally followed. The rubber coefficient μ is often treated as a material property that applies to nonequivalent combinations of tires and pavements under different vehicle operating conditions.

11.3

Effects of the Development of Microhysteretic Forces on Tire-Friction Analysis

11.3.1 Development of the Constant Microhysteretic Friction Force in Rubber Tires Chapter 5 continued our examination of the scientific research carried out to understand more fully the basic mechanisms of rubber friction. The backcalculation technique was employed to analyze rubber friction test results published in the graphical form of μ vs. the force or pressure applied to rubber specimens during such testing. We found in our graphs that, in the lower loading range, all of the published data sets we reviewed yielded straight lines when plotted as the total measured friction force vs. applied normal force or pressure.

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252 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Extrapolation of the straight-line portions of the plots depicting FT vs. FN or PN to the y-axis yielded y-axis intercept values. These intercepts were found in data generated from rubber sliding on both smooth and rough surfaces. It was considered that such y-axis intercepts quantify a surface deformation hysteresis force (FHs) in rubber. Because FHs is indicated as constant and independent of both the force and pressure applied to rubber sliding on smooth and rough surfaces, it was considered that surface deformation hysteresis is a distinct rubber friction mechanism, different from the adhesion and bulk deformation hysteresis mechanisms previously discussed. Most rubber friction test results published in the graphical form of the coefficient of friction μ vs. the force or pressure applied to rubber specimens while sliding yield downwardly curved lines evidencing a decrease in this coefficient with increasing loading, at least initially. It was shown that inadvertent inclusion of the microhysteresis forces present in test data producing such plots can be responsible for this curvature. Accounting for FHs by subtracting its constant value from the total friction force generated allows the adhesion and macrohysteresis forces to be more easily quantified. 11.3.2 Development of the Adhesion-Transition Phenomenon in Rubber Tires Chapter 6 showed that the adhesion friction force between rubber and harder materials increases with growth in the real area of mutual contact developed in such pairings. When tires are operated on smooth roadways, the adhesion friction force in rubber (FA) can sometimes be expressed by the following equation:

FA = μA(FN),

(11.2)

where μA is the constant adhesion friction ratio. Equation 11.2 applies when the primary result of increases in FN or PN is to produce new areas of contact between rubber and its paired surfaces. This occurs in the lower loading range. With such pairings, however, a change in the adhesion-friction-force-producing mechanism eventually takes place; that is, when the adhesion transition pressure PNt is reached. At that point, Equation 11.2 is no longer valid. We have also seen that when the predominant result of increasing FN or PN is to expand existing areas of contact between rubber and its paired surfaces, the generalized Hertz equation applies. This relationship, applicable in rubber friction analysis and design at PNt and above, can be expressed as

FA = cA(FN)m.

(11.3)

Chapters 7 and 8 examined the development of the rubber adhesion-transition mechanism in dry and wet conditions, presenting evidence indicating

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that this phenomenon can arise when wet and dry rubber slides on smooth or rough surfaces. In practical engineering applications in wet and dry conditions where FA is generated, we can expect that if the wheel load on a rubber tire is sufficiently high, the adhesion-transition pressure might be surpassed. Figure€8.17 evidenced development of the adhesion-transition phenomenon in wet testing of radial-belted aircraft tires. And in the field, of course, attainment of the PNt value is not readily discernible; that is, one would not know whether Equation 11.2 or Equation 11.3 applies. As such, prior testing is required. 11.3.3 Development of the Macrohysteresis Friction Force in Rubber Tires Bowden and Tabor [3] formulated a rubber coefficient-of-friction expression by equating friction produced in lubricated sliding of harder objects on rubber to rolling friction on the same material. They hypothesized that if lubricated sliding conditions are such that adhesion is reduced to negligible proportions — physical contact of the two solids being effectively prevented — and the lubricant’s viscous resistance is also negligible, then the only significant friction present would arise from macrohysteresis in the rubber. If this were so, macrohysteretic resistance in a given lubricated rubber specimen would be essentially equal when generated either by sliding or rolling spheres of identical size on it. Bowden and Tabor discussed testing involving rolling and sliding steel spheres on soap-lubricated rubber at a constant velocity on the order of a few millimeters per second and derived an equation for the macrohysteretic rubber friction ratio under these conditions, μHb: μHb = c(FN)1/3.

(11.4)

While Equation 11.4 does not apply to all situations in which macrohysteresis develops in rubber, the form of the equation exemplifies a situation wherein μHb is not directly proportional to the applied load when no microhysteretic friction forces are generated. 11.3.4 Application of a Unified Theory of Rubber Friction to Analysis of Tire-Roadway Traction-Testing Results In Chapter 5 we formulated a unified, mechanistic theory of rubber friction by treating rubber microhysteresis as a separate term. The theory is quantified by

FT = FA + FHs + FHb + FC, (11.5)

where:

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254 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

FT = total frictional resistance developed between sliding rubber and a harder material; FA = frictional contribution from combined van der Waals’ adhesion of the two surfaces; FHs = frictional contribution from surface deformation hysteresis (microhysteresis); FHb = frictional contribution from bulk deformation hysteresis (macrohysteresis); and FC = cohesion loss contribution from rubber wear.

When water-drag on a moving tire is included, two additional liquid-related force-producing mechanisms should at least be considered: (1) bulk displacement of water by the tire when thick films are present, represented by FWb, and (2) viscous losses due to liquid boundary-layer friction when thin surface films exist (FWs). Varying water film thickness under a tire can be envisaged such that these forces act concurrently. Equation 11.5 then becomes

FT = FA + FHs + FHb + FC + FWb + FWs.

(11.6)

Inasmuch as water-drag should not be counted on as a reliable vehiclestopping friction force from a safety point of view, the two liquid-related force terms can be removed from Equation 11.6. When utilized in the analysis of tire-roadway traction testing results, the cohesion-loss contribution from rubber wear in Equation 11.6 appears to be small, or even insignificant. In any case, the contribution should at least be considered; thus, Equation 11.6 reduces to

11.4

FT = FA + FHs + FHb + FC.

(11.7)

Comparability of Rubber-Friction Testing Data

As part of their discussion of the limited usefulness of the rubber coefficient of friction μ, Kummer and Meyer [2] enumerated factors that must be identical for roadway-friction-testing apparatus to produce numerically equal results. Table€11.1 presents a partial list of these factors. The other items in their list concerned quantification of tester bias. When two different tire testers of the same type are utilized on the same pavement, their results are comparable only if their test values are equal within the accepted statistical confidence limits for random error and a scientifically based approach to design and analysis of such testing involving the factors in Table€11.1 is taken.

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Table€11.1 Factors Involved in Tire-Road Skid-Resistance Testing That Must Be Included in Analysis of Results To Allow Scientifically Based Comparability of Friction Measurements Type of testing apparatus:

Constant braking Straight-ahead driving or cornering Tire slipping or locked

Tire properties:

Geometry Carcass stiffness Rubber composition Tread design State of wear

Operational conditions:

Speed Tire inflation pressure Wheel load

Conditions in the contact zone:

Pavement surface characteristics Degree of wetness Temperature

Source: Based on Kummer, H.W. and Meyer, W.E., in Symposium on Skid Resistance, American Society for Testing and Materials, STP 326, Philadelphia, 1962.

Kummer and Meyer addressed the basic conditions that must be present to correlate test results from different apparatus of the same type. They stated that: In general, the results obtained with testers that give different answers on the same pavement can be correlated if (1) there is a physical relationship between the different modes of [apparatus] operation and (2) the testers have system errors [biases] that are predictable both as to magnitude and direction. (p. 6)

The requirements for scientifically based comparability between results from different roadway-friction-testing apparatus can be summarized as follows:

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1. The apparatus should be of the same type (e.g., locked-wheel skid tester).



2. There can be a physical relationship between modes of different roadway-friction testers of the same type if the mechanistic approach to quantifying rubber tire traction is utilized. As we have seen by following this path in prior chapters, the various rubber-friction mechanisms can be differentiated to a considerable degree and the corresponding forces produced by them can be quantified.



3. Any electromechanical biases inherent in the different apparatus must be known so that appropriate calibration corrections to instrument readings can be made. At the same time, the existence

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256 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces of random error must be accepted, but statistical techniques can be used to calculate confidence limits as desired.

4. The same factor selected from Table€11.1 must be utilized as the independent variable for both testers, while all other variables are not only controlled, but also kept constant and identical during the different tester runs.



5. All apparatus of interest must be capable of measuring the same dependent variable (e.g., the skid-resistance force) in a manner isolating the different friction-producing mechanisms to an acceptable degree. In this way, possible development of the adhesion transition mechanism can be determined and the proper expressions for quantifying the friction-force components present can be employed.



6. The apparatus must possess the capability to apply differing wheel loads to the pavement involved. In this way, plots as seen in Figure€8.4 can be constructed and y-axis intercepts determined. Their values will quantify the constant tire microhysteresis force.



7. Analysis of tire test results should include application of the unified theory of rubber friction discussed in Section 11.3.4 to quantify the traction forces developed. This is a straightforward process. We have seen how the microhysteretic side friction force in radial-belted aircraft tires operating in wet conditions is obtained graphically as exemplified in Figure€8.4. Subtraction of this value from the total measured friction force isolates the combined adhesion and macrohysteretic side forces if wear and water-drag are ignored. Adhesion and macrohysteretic forces were used in Figure€8.17 to determine whether the adhesion transition mechanism arose. Once the rubber friction mechanisms involved are determined, other factors in Table€11.1 can be taken as the independent variable when appropriate.

The additional effort needed to meet the conditions for comparability summarized in this list may be manageable at times, while in other circumstances a challenge will exist. These efforts can be viewed against the studies carried out previously. For example, in 1962 the correlation study [4] conducted during the summer of that year at Tappahannock, Virginia, went a long way toward satisfying the above requirements. Table€11.2 presents factors kept constant or measured in the Tappahannock, VA, testing. Taking the additional steps necessary to achieve scientifically based comparability should be attempted. The rubber microhysteresis-related factors are also listed in Table€11.2. As we have seen from analysis of Pfalzner’s work [5], microhysteretic tire traction can be important even on ice-covered roadways.

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Table€11.2 Test Factors Measured or Kept Constant in the 1962 Road-Slipperiness Correlation Study at Tappahannock, VA, and Microhysteresis-Related Factors That Must Be Included in Analysis of Test Results To Allow Scientifically Based Comparability of Tire Friction Measurements Test Factors Measured or Kept Constant at Tappahannock Tire properties:

Geometry (one type of tire utilized) Carcass stiffness (one type of tire utilized) Rubber composition (one type of tire utilized) Tread design (one type of tire utilized)

Operational conditions:

Speed (kept constant) Tire inflation pressure (kept constant) Wheel load (kept constant for speed tests) Treadprint area — specimen size (one type of tire utilized)

Conditions in the contact zone:

Pavement surface characteristics (kept constant) Degree of wetness (depth of water controlled) Temperature (pavement surface temperature measured)

Required Microhysteresis-Related Test Factors Differing wheel load tests:

Required to determine microhysteresis force

Nominal tire contact area:

Rubber microhysteresis force increases with increasing nominal contact area

Tire asperity roughness profile:

Adhesive and microhysteresis forces decrease with increasing tread roughness

Source: Tappahannock issues based on: Dillard, J.H. and Mahone, D.C. in Measuring Road Surface Slipperiness, American Society for Testing and Materials, STP 366, Philadelphia, 1963.

11.5

Inadvertent Misapplication of the Laws of Metallic Friction to Rubber Tires in ASTM Test Standards

ASTM standards are continually reviewed to determine if they should be updated or withdrawn. Progress has been made in harmonizing these protocols to reduce difficulties in comparing different tire-pavement friction test results. Unfortunately, many ASTM standard tests inadvertently misapply the laws of metallic friction to rubber-tire-traction studies. In these instances, test values are reported or utilized as coefficients in the form of Equation 11.1:

µ = FT/FN.

Application of a unified theory of rubber friction to replace Equation 11.1 in such cases not only will foster comparability of test results, but also will promote scientific accuracy. The unified theory integrates the microhysteresis-produced FHs force into an expression quantifying the forces generated by the other basic rubber friction mechanisms, yielding the total tire friction

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258 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces force that can arise on pavement (FT). To apply the unified theory, it is necessary that the ASTM standards to be discussed take into account certain issues or characteristics associated with microhysteretic force development. By way of example, some of these issues will be mentioned when each standard is addressed. Table€11.3 summarizes the various characteristics that can be of concern. 11.5.1 ASTM Test Standards with an “E” Designation ASTM standard tests having an “E” designation that inadvertently misapply the laws of metallic friction to rubber tires operated on pavements are listed in Table€11.4. 11.5.1.1 ASTM E 274 – 06, Standard Test Method for Skid Resistance of Paved Surfaces Using a Full-Scale Tire This method employs a skid number (SN) to represent the steady-state friction force generated between a tire on a locked wheel dragged on wetted pavement at constant speed under a constant normal load. The SN value is intended to be used for evaluation of the skid resistance of a pavement relative to that of other pavements. SN is defined as where:

SN = (F/W) × 100,

(11.8)

Table€11.3 Characteristics of the Rubber Microhysteresis Friction Force That Should Be Taken into Account if the Unified Theory of Rubber Friction Presented in This Book Is To Be Fully Integrated into the ASTM Test Standards Discussed in This Chapter Indicated independence of microhysteresis force on macroscopically smooth pavements: Applied normal force and pressure Applied tangent force Indicated independence of microhysteresis force on macroscopically rough pavements: Applied normal force and pressure macroroughness of pavement Indicated dependence of microhysteresis force on macroscopically smooth pavements: Microroughness of pavement Nominal tire tread contact area Rubber hardness (inversely) Temperature (inversely) Tire tread surface free energy Pavement surface free energy Tire tread roughness (asperity configuration)

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Table€11.4 ASTM Standards Having an “E” Designation That Inadvertently Misapply the Laws of Metallic Friction to Rubber Tires ASTM E 274 – 06, Standard Test Method for Skid Resistance of Paved Surfaces Using a FullScale Tire ASTM E 445/E 445M – 88 (Reapproved 2001), Standard Test Method for Stopping Distance on Paved Surfaces Using a Passenger Vehicle Equipped with Full-Scale Tires ASTM E 503/E 503M – 88 (Reapproved 2004), Standard Test Methods for Measurement of Skid Resistance on Paved Surfaces Using a Passenger Vehicle Diagonal Braking Technique ASTM E 670 – 94 (Reapproved 2000), Standard Test Method for Side Friction Force on Paved Surfaces Using the Mu-Meter ASTM E 1337 – 90 (Reapproved 2002), Standard Test Method for Determining Longitudinal Peak Braking Coefficient of Paved Surfaces Using a Standard Reference Tire ASTM E 1859 – 97 (Reapproved 2006), Standard Test Method for Friction Coefficient Measurements between Tire and Pavement Using a Variable Slip Technique ASTM E 1890 – 01 (Reapproved 2006), Standard Guide for Validating New Area Reference Skid Measurement Systems and Equipment ASTM E 1911 – 98 (Reapproved 2002), Standard Test Method for Measuring Paved Surface Frictional Properties Using the Dynamic Friction Tester ASTM E 1960 – 03, Standard Practice for Calculating International Friction Index of a Pavement Surface ASTM E 2100 – 04, Standard Practice for Calculating the International Runway Friction Index



F = horizontal force applied to the test tire in the contact patch, and W = dynamic vertical load on the test tire.

The resulting fraction is multiplied by 100 to obtain a whole number. Inasmuch as the different pavements tested may have differing microtextures, macrotextures, and surface free energies, varying FA, FHs, and FHb forces produced by different mechanisms are likely to arise. We see that Equation 11.8 is another form of Equation 11.1. Equation 11.8 is incapable of differentiating these three rubber friction forces. 11.5.1.2

ASTM E 445/E 445M – 88 (Reapproved 2001), Standard Test Method for Stopping Distance on Paved Surfaces Using a Passenger Vehicle Equipped with Full-Scale Tires

This test method pertains to measurements of the stopping distance of a passenger vehicle on wetted pavement utilizing specified full-scale test tires on four locked wheels. The testing vehicle is brought to a stop in a skid from a given speed, and the covered distance is measured. Vehicle stopping distance values are intended for use in characterizing pavement slip resistance in regard to suitability and adequacy of surface materials and finishing techniques.

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260 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces The test results are used to compute the stopping distance number (SDN) as determined from Equation 11.9:

SDN = (V2/255 SD) × 100,

(11.9)

where: V = speed of test vehicle at moment of brake application in km/h, and SD = stopping distance in meters. The resulting fraction is multiplied by 100 to ensure a whole number. Inasmuch as different pavements can have differing microtextures, macrotextures, and surface free energies, varying FA, FHs, and FHb forces produced by different mechanisms are likely to arise. Equation 11.9 is another form of the geometric roadway design relationship for braking distance d:

d = V2/255μ.

(11.10)

As seen, the constant (metallic) coefficient of friction μ appears in this expression. 11.5.1.3

ASTM E 503/E 503M – 88 (Reapproved 2004), Standard Test Methods for Measurement of Skid Resistance on Paved Surfaces Using a Passenger Vehicle Diagonal Braking Technique

This protocol employs specified full-scale vehicle tires to measure skid resistance utilizing the diagonal braking mode. In this approach, two diagonal wheels are locked as the vehicle decelerates to a full stop over a wetted pavement starting from a desired speed under specific limits of static wheel load. The skid resistance is reported as SDN when calculated in metric units in accordance with Equation 11.9:

SDN = (V2/127.5 SD) × 100. Equation 11.9 can also be expressed as



μ = V2/127.5d.

(11.11)

11.5.1.4 ASTM E 670 – 94 (Reapproved 2000), Standard Test Method for Side Friction Force on Paved Surfaces Using the Mu-Meter The Mu-Meter is a proprietary side-friction-force measuring trailer operated on dry or wet aircraft runways. Its two measuring wheels are angled to the

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direction of towing to produce side friction forces under a constant static wheel load. Results are reported as a Mu Number (MuN), or coefficient of friction (μ) on a strip chart included in the instrumentation provided by the manufacturer. 11.5.1.5

ASTM E 1337 – 90 (Reapproved 2002), Standard Test Method for Determining Longitudinal Peak Braking Coefficient of Paved Surfaces Using a Standard Reference Tire

A focus of this standard is on the traction produced by current-technology passenger car radial tires on different pavement surfaces. This traction is expressed as the peak braking force coefficient, calculated in accordance with Equation 11.1:

µ = FT/FN.

The test protocol requires use of a specified ASTM Radial Standard Reference Test Tire mounted on a trailer. This apparatus is usually brought to a speed of 64 km/h (40 mph) and the brake is then applied progressively until the maximum braking torque is reached prior to wheel lockup. The longitudinal force and vertical load are recorded and employed in Equation 11.1. The test standard recognizes that pavements exhibit different traction characteristics depending, in part, on surface texture, binder content, traffic volume, and environmental exposure. 11.5.1.6 ASTM E 1859 – 97 (Reapproved 2006), Standard Test Method for Friction Coefficient Measurements between Tire and Pavement Using a Variable Slip Technique This standard involves longitudinal friction testing with a measuring device that can create braking-slip between a tire and the contacted pavement. The maximum friction developed at a given speed (s) is expressed as the peak slip friction number, SFNpeak (s), where

SFN = FT/FN × 100.

(11.12)

In this case, FT and FN represent the friction force and applied vertical wheel load at any instance in time and location, respectively. Thus, under the specified conditions, Equation 11.12 can be expressed as Equation 11.1:

µ = FT/FN.

The method requires that a series of incremental measurements be taken of friction forces developed on the test tire as it is pulled over a contaminated

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262 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces pavement. During the test, the rotational velocity of the braked wheel is controlled to produce a predetermined variable slip ratio. Test results are used in assessments of braking friction forces on pavements in relation to other pavements, evaluation of changes in such traction forces developed on a particular driving surface over a period of time, investigations of the effects of polishing pavement macrotexture caused by traffic, and the effects of the presence of different roadway contaminants on a given pavement. These contaminants can include ice, snow, pollen, vehicle oil spills, and condensates from vehicle engine exhaust. 11.5.1.7 ASTM E 1890 – 01 (Reapproved 2006), Standard Guide for Validating New Area Reference Skid Measurement Systems and Equipment This guide focuses on validation of area reference skid measurement systems (ARSMS) and associated equipment. These systems have been employed since 1976 for evaluation and correlation of ASTM Test Method E 274 skid-tester results. The guide constitutes a process helping to identify and quantify variables involved in such roadway-friction testing. The primary application of the ARSMS approach is as a pavement management tool by state departments of transportation through monitoring the changing friction characteristics of driving surfaces. One segment of the ARSMS validation process addresses determination of the SN quantified by Equation 11.8. Inasmuch as the different pavements tested may have differing microtextures, macrotextures, and surface free energies, varying FA, FHs, and FHb forces produced by different mechanisms are likely to arise. 11.5.1.8 ASTM E 1911 – 98 (Reapproved 2002), Standard Test Method for Measuring Paved Surface Frictional Properties Using the Dynamic Friction Tester The Dynamic Friction Tester (or DF Tester) is a portable device intended for use in the field or the laboratory and designed to measure wet frictional properties of pavement as a function of speed — in this case, the speed of a horizontal spinning disk fitted with three uniformly spaced spring-loaded rubber sliders on a radius of 14.2 cm (5.6 in.). Torque developed during operation is continually measured and automatically converted to a force as the disc’s rotational speed is reduced (spun-down) due to friction between the sliders and the contacted surface. Testing is usually carried out at 20, 40, 60, and 80 km/h (12, 24, 36, and 48 mph), and a friction-speed relationship is plotted. The DF Tester is primarily intended for use in assessing the relative effects of different polishing mechanisms on pavements. Friction values are reported as coefficients, quantified by dividing the measured force by the weight of the disc and its motor assembly; that is, by application of Equation 11.1:

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Nonscientific Application of the Laws of Metallic Friction

263

µ = FT/FN.

These coefficients are reported as DFT Numbers for the speeds involved. 11.5.1.9 ASTM E 1960 – 03, Standard Practice for Calculating International Friction Index of a Pavement Surface This practice prescribes a method by which the International Friction Index (IFI) is calculated on the basis of measurements of pavement friction and macrotexture. The practice provides a uniform approach for reporting the friction characteristics of roadway testers that utilize smooth-tread tires. The IFI concept was developed by PIARC, the Permanent International Association of Road Congresses [6]. Although the practice is intended to be applied to roadway-testing devices equipped with tires, ASTM E 1960 – 03 also involves utilization of DFT Numbers obtained from the DF Tester operated in accordance with ASTM E 1911. The intended benefit of the IFI approach is to allow friction measurements obtained by roadway testers at other than 60 km/h (36 mph) to be reported at the standard IFI speed of 60 km/h. While certain of the factors listed in Table€11.2 that are necessary for scientifically based comparability of friction measurements are included in the ASTM E 1960 – 03 calibration protocols, other such factors are omitted from the standard. Both the roadway testers utilized in computing the IFI and the DF Tester calculate measured friction values by application of Equation 11.1:

µ = FT/FN.

11.5.1.10 ASTM E 2100 – 04, Standard Practice for Calculating the International Runway Friction Index The purpose of applying this practice is to allow harmonization of friction test results obtained on different runways and other aircraft movement areas by different testers through calculation of the International Runway Friction Index (IRFI). As stated in ASTM E 2100 – 04, the index results from “the adjustment of the outputs of different devices used for measurement of a specific phenomenon so that all devices report the same value.” The practice prescribes the method by which the index is calculated. It is intended for use as an airport maintenance tool to monitor changes in pavement friction characteristics during winter. The index is considered applicable under four conditions: (1) bare dry pavement, (2) bare wet pavement, (3) compacted snow, and (4) bare ice. ASTM E 2100 – 04 provides details of the IRFI reference tester, a threewheeled trailer pulled by a motor vehicle. One of these wheels is used for measuring, and it can be fitted with various tire types of interest. The normal load on the measuring wheel is specified as 1800 N (404 lb). This trailer must

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264 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces be used as a benchmark for calibration of other pavement testers so that friction measurements obtained by them can be converted to IRFI values. For a candidate tester to be calibrated, it must take part in a program of joint pavement friction measurements with the reference tester or another device that has been calibrated by the reference tester. The harmonized aircraft movement area friction value IRFI, is calculated, in part, using Equation 11.1. This standard practice involves both different tires and different pavements. Inasmuch as the different tires may have differing surface free energies, and the different pavements tested may have differing microtextures, macrotextures, and surface free energies, varying FA, FHs, and FHb forces produced by different mechanisms are likely to arise. 11.5.2 ASTM Test Standards with an “F” Designation We now examine ASTM test standards with an “F” designation that inadvertently misapply the laws of metallic friction to rubber tires operated on pavements. Table€11.5 lists these standards. 11.5.2.1 ASTM F 403 – 98, Standard Test Method for Tires for Wet Traction in Straight-Ahead Braking, Using Highway Vehicles ASTM F 403 – 98 utilizes an accelerometer-based approach to measurement of braking traction of automobiles and light trucks that are not equipped with antilock braking systems (ABS). This method is intended for use on dry and wet pavements, as well as on ice and snow. The testing is carried out utilizing either two front tires or one front and one rear tire positioned in a diagonal relationship. The two selected wheels are locked for at least 1 sec in the speed range 32 to 96 km/h (20 mph to 60 mph). During this period, the other wheels are free rolling. The method is considered suitable for use Table€11.5 ASTM Standards Having an “F” Designation that Inadvertently Misapply the Laws of Metallic Friction to Rubber Tires ASTM F 403 – 98, Standard Test Method for Tires for Wet Traction in Straight-Ahead Braking, Using Highway Vehicles ASTM F 408 – 99, Standard Test Method for Tires for Wet Traction in Straight-Ahead Braking, Using a Towed Trailer ASTM F 538 – 03, Standard Terminology Relating to the Characteristics and Performance of Tires ASTM F 1649 – 96 (Reapproved 2003), Standard Test Methods for Evaluating Wet Braking Traction Performance of Passenger Car Tires on Vehicles Equipped with Anti-Lock Braking Systems ASTM F 1805 – 00, Standard Test Method for Single-Wheel-Driving Traction in a Straight Line on Snow- and Ice-Covered Surfaces

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Nonscientific Application of the Laws of Metallic Friction

in research and development programs in which tires are compared during a single test series. This test method permits determination of either the peak braking force coefficient μp, defined as “the maximum value of tire braking force coefficient that occurs prior to wheel lockup as the braking torque is progressively increased,” or the slid braking force coefficient μs, defined as “the value of braking force coefficient obtained on a locked wheel.” The standard employs a number of equations to quantify braking coefficient values. For example, the peak braking force coefficient is calculated as:

μp = 2(a − ad),

(11.13)

where: a = measured peak vehicle deceleration, and ad = drag deceleration measured when vehicle is free rolling on a horizontal pavement. Although this method is intended for research and development comparison of tires during a single test series, different tires are being investigated. As a result, different tread surface free energies are involved. These different energies will influence both the adhesion and microhysteresis forces that arise. 11.5.2.2 ASTM F 408 – 99, Standard Test Method for Tires for Wet Traction in Straight-Ahead Braking, Using a Towed Trailer This test method also specifies a protocol for measuring braking traction developed by automobiles and light trucks. In this case, however, a towed trailer is utilized as the testing device, fitted with tires of interest in a research and development program. The trailer’s required capabilities are specified in the standard. ASTM F 408 – 99 is intended for use on both wet and dry pavements. The method incorporates the braking force coefficient, defined as “the ratio of braking force to normal force” as a function of time t, in accordance with Equation 11.14:

μ(t) = f h(t)/fv(t),

(11.14)

where: μ(t) = dynamic tire braking force coefficient in real time, f h(t) = dynamic braking force in real time, and fv(t) = dynamic vertical load in real time. Because this method is utilized for testing of different tires, differing tread surface free energies can be involved. These different adhesion-producing energies will influence both the adhesion and microhysteresis forces.

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266 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 11.5.2.3 ASTM F 538 – 03, Standard Terminology Relating to the Characteristics and Performance of Tires ASTM F 538 – 03 enumerates definitions for certain technical terms found in standards under the jurisdiction of Committee F-9 on Tires. The list comprises eight coefficients calculated in accordance with Equation 11.1, which is derived on the basis of inadvertent misapplication of the laws of metallic friction to rubber tires on pavements. These terms are presented in Table€11.6. 11.5.2.4

ASTM F 1649 – 96 (Reapproved 2003), Standard Test Methods for Evaluating Wet Braking Traction Performance of Passenger Car Tires on Vehicles Equipped with Anti-Lock Braking Systems

The tire-traction-measuring test methods specified in this standard concern two types of behavior exhibited by vehicles possessing anti-lock braking systems (ABS): (1) stopping distance in wet conditions from the speed at which the brakes are applied and (2) adequacy of trajectory control during such brake application. The protocol requires that tests be carried out on two specially constructed pavements providing a “split-μ” driving surface; that is, traction developed between the test tires and the two pavements must be markedly different. In these methods, the traction value μ is defined as the friction coefficient. ASTM F 1649 – 96 allows two standard vehicle braking tests to be utilized: (1) ASTM method E 274 for the slide coefficient or (2) ASTM method E 1337 for the peak coefficient. As we have seen, these standards employ Equation 11.1:

µ = FT/FN. Table€11.6 Coefficient Terms Defined in ASTM Standard F 538 – 99 Calculated in Accordance with Equation 11.1, Which Is Derived on the Basis of Inadvertent Misapplication of the Laws of Metallic Friction to Rubber Tires Braking coefficient Braking force coefficient Breaking force coefficient, peak Braking force coefficient, slide Driving coefficient Peak braking coefficient Skid number Sliding braking coefficient

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Nonscientific Application of the Laws of Metallic Friction

11.5.2.5 ASTM F 1805 – 00, Standard Test Method for Single-Wheel- Driving Traction in a Straight Line on Snow- and Ice-Covered Surfaces ASTM F 1805 – 00 should be used for measuring driving traction of passenger automobile and light truck tires. It requires employment of a specially designed four-wheeled vehicle with an instrumented, rear-wheel-drive axle equipped to measure the vertical and longitudinal forces acting on one of the driven test tires. The method assesses the performance of tires on snow and ice in a research and development setting. Test results are presented as values of the driving coefficient μ, defined as

μ = F/W,

(11.15)

another form of Equation 11.1, where: F = average longitudinal force, and W = average vertical wheel load.

11.6

Inadvertent Misapplication of the Laws of Metallic Friction to Rubber Tires in Motor Vehicle Accident Reconstruction

11.6.1 Background As discussed in Chapter 1, many physics textbooks do not emphasize to the reader that the laws of metallic friction are accepted for application to relative movement between contacting smooth metals, but have no applicability in the scientific sense to elastic materials such as rubber. Although the laws of metallic friction do not apply to rubber tires operated on pavement, it is common in engineering theory and practice to apply them nevertheless. One such area of practice is in motor vehicle accident reconstruction. In this usage, the total friction force developed between a tire and its contacted pavement, divided by the wheel load, or axle load, as expressed in Equation 11.1,

µ = FT/FN,

is taken as a constant rubber friction coefficient. Such coefficients are considered to be key tire-road properties in analysis of how and why motor vehicle accidents occurred. Limpert [7] has stated that, “Since the tire-road friction coefficient is an important parameter in accident reconstruction, all necessary steps should be taken to measure the value existing at the time of the accident or at a similar condition.”

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268 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Because the equation relating force and mass — often referred to as Newton’s second law of motion — can be utilized to calculate other motion parameters, such as velocity, distance, and time, advantageous employment of this relationship in motor vehicle accident reconstruction is possible. Unfortunately, application of Newton’s second law to this subject is often predicated on direct proportionality between tire or axle load and the total tire friction force developed, a condition that usually does not exist. 11.6.2 Traditional Use of Newton’s Second Law of Motion in Accident Reconstruction It is conventional practice in motor vehicle accident reconstruction to designate f, instead of µ, to represent the rubber tire-road friction coefficient, the total friction force produced divided by the applied normal load. To emphasize the inapplicability of the laws of metallic friction to rubber, however, we will employ µ in this regard. Reconstruction of a motor vehicle accident often requires determination of the time taken for a vehicle to move from point A to point B while braking; for example, from the location of its brake application to impact with another object. This involves deceleration a. The relationship between the force slowing a vehicle in opposition to its inertia and its deceleration can be expressed by Newton’s second law, FS = ma, where: FS = applied slowing force, and m = mass of the subject vehicle.

(11.16)

Because the mass and static weight of a vehicle (W), or any object, are related to the acceleration of gravity g, Equation 11.16 can be expressed as

a = FS/(W/g).

Convenient rearrangement yields

a = (FS/W)g.

(11.17)

If we take FS as the tire-road friction force developed by brake application in straight-ahead driving on horizontal pavements, Equation 11.17, expressed in g units, apparently becomes

a = μg, (?) [for rubber tires]

(11.18)

where μ is a constant rubber tire-road friction coefficient for any value of W. In Equation 11.18, W is equivalent to the weight-force, which is replaced by the applied normal load FN. The question mark asks the question: Is this relationship correct?

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Nonscientific Application of the Laws of Metallic Friction

That is, it has been considered in the accident-reconstruction community that there is a corresponding value of vehicle deceleration a for every value of the tire-pavement coefficient of friction, μ, regardless of the value of W or FN. Values of a have been used to calculate other motion-related parameters; that is, time, distance, and velocity. It is seen, however, that Equation 11.18 is not scientifically correct for rubber — μ for tires is not generally constant under different W or FN loading, and

a ≠ μg. [for rubber tires]

(11.19)

11.6.2.1 Use of Newton’s Second Law of Motion When Only the Rubber Adhesion and Microhysteresis Mechanisms are Present Chapter 3 discussed results from studies involving the simplest form of rubber friction testing: rubber specimens sliding on macroscopically smooth surfaces at constant velocity and temperature in dry conditions. In these rubber specimens, unlike tires on rough roadways, no significant macrohysteresis or cohesion-loss friction forces could arise. Roth et al. [8], Thirion [9], and Schallamach [10] reported seven sets of test data presented as μ vs. FN in Figures€3.2(b), 3.3(b), and 3.4(b). All seven of these data sets plot as hyperbolic curves quantified by a relationship of the form,

μ = c(FN)-m.

(11.20)

Indeed, Equation 11.20 represents the relationship applicable to nearly all rubber friction data sets we have examined in which no macrohysteresis or cohesion-loss friction forces arose; that is, the equation generally fits the measured values from the simplest type of rubber friction test. Substituting this expression for μ in Equation 11.18 yields

a ≠ [c(FN)-m]g.

(11.21)

Clearly, even with the simplest combination of rubber friction mechanisms — adhesion and microhysteresis — Equation 11.18 does not apply to slipping or sliding rubber tires on smooth pavements. The value of μ is not always constant at every value of W or FN in these conditions. 11.6.2.2 Use of Newton’s Second Law of Motion When the Rubber Macrohysteresis Mechanism is Present Bowden and Tabor [3] formulated a rubber coefficient-of-friction expression by equating friction produced in lubricated sliding of harder objects on rubber to rolling friction on the same material. They discussed testing involving rolling and sliding steel spheres on soap-lubricated rubber at a constant velocity on the order of a few millimeters per second. For this well-lubricated

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270 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces condition, somewhat comparable to braked rubber tires slipping or sliding on an equivalently lubricated rough surface with spherical protuberances of the stated size, the coefficient of friction for pure macrohysteresis in rubber could be expressed as Equation 11.4:

μHb = c(FN)1/3.

Substituting the Equation 11.4 relationship for μHb into Equation 11.18 yields

a ≠ [c(FN)1/3]g.

(11.22)

For this situation in which pure macrohysteretic friction could develop in rubber tires, traditional use of Newton’s second law of motion is not appropriate. 11.6.2.3 Use of Newton’s Second Law of Motion When the Rubber Cohesion-Loss Friction Mechanism is Present While Kummer [11] has postulated that rubber cohesion loss (wear) can be ignored as a significant mechanism that produces the tire friction force FC in ordinary driving, this may not be true in accident-involved tires experiencing locked-wheel skidding on dry pavement. Cohesion losses in such circumstances can range from rubber “dust” worn off contacting tire surfaces when wear of the tread is imperceptible, through noticeable abrasion in the form of torn, separated pieces of rubber, to a complete wearing-through of the tire. The unified theory of rubber friction presented in this book includes FC losses as an individual term. It has not been possible, however, to quantify this force alone as a separate contribution to rubber friction. We do not know if FC itself is directly proportional to W. Frictional resistance from cohesion losses in tires is not always considered in accident reconstruction. As far as could be determined, no scientific basis presently exists for application of Newton’s second law of motion to accident reconstruction involving the frictional characteristics of rubber when cohesion losses arise in vehicle tires. It is nevertheless common engineering practice to apply this law in these circumstances. 11.6.2.4 Use of Newton’s Second Law of Motion When Tread Temperatures Change Accident reconstruction experience has shown that skid marks can be more common and prominent on bituminous roadway surfaces than on portland cement concrete. In the former instance, tar or asphalt binders may soften from frictional heating generated by sliding locked-wheel tires. Such softening may produce a smearing of the tar or asphalt in the direction of motion. On concrete, heating of the tire tread during locked-wheel sliding can soften the rubber, which may allow abrasion and a tacky condition to develop. The

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271

Nonscientific Application of the Laws of Metallic Friction

tacky rubber may then adhere to the concrete surface and produce a skid mark. In either type of roadway surface, heating of the tire tread can occur during skidding. As discussed in Chapter 7, Hample [12] has shown that B-29 tire tread rubber in contact with heated concrete exhibits lowered frictional resistance. Such reductions are seen in Figure€7.10, which depicts combined friction test results from tire segments sliding on smooth, semi-smooth, and rough concrete surfaces. Figure€7.3 indicates that microhysteresis developed in all three testing protocols — three y-intercepts are suggested. The Figure€7.5 plots evidence adhesion on all three surfaces and are consistent with the development of macrohysteresis on the semi-smooth and rough concrete surfaces. While possible changes in the concrete microtexture as a result of heating above the boiling point of water complicates interpretation of Hample’s [12] high-temperature results, as do the unquantified tread cohesion losses he reported, Hample’s findings are consistent with a reduction in the magnitudes of the microhysteretic, macrohysteretic, and adhesion friction components with increasing temperature. It has not been possible to quantify the precise effects of such temperature changes on the different friction forces present. We do not know if tread temperature changes alter the relationship between FS and W in a nonlinear manner. Frictional resistance change arising from temperature increases in tire treads is not always considered in accident reconstruction. As far as could be determined, no scientific basis presently exists for application of Newton’s second law of motion to accident reconstruction involving the frictional characteristics of rubber when temperature increases occur in vehicle tire treads. It is nevertheless common engineering practice to apply this law in these circumstances. 11.6.2.5 Traditional Use of Newton’s Second Law of Motion When Dynamic Load Transfer Occurs Nonscientific use of Equation 11.18 in accident reconstruction is further exemplified by a common acceleration-related analysis. The approach involves wheel loads and equates a to the dynamic front tire-road friction coefficient μFD and the dynamic rear tire-road friction coefficient (μRD). When a vehicle is stationary or traveling at constant speed on a horizontal roadway, the front-to-rear weight apportionment may produce significantly different static axle load distribution values Ψ [7]. The static rear axle load FRS can be defined as

Ψ = FRS /W.

(11.23)

The related static front axle load is then given by

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1 − Ψ = FFS /W.

(11.24)

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272 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Thus, when a two-axle vehicle decelerates from a given velocity, dynamic load transfer off the rear axle and onto the front axle can take place. Not surprisingly, the amount of load redistribution depends, in part, on the magnitude of a, usually expressed as a percentage of g. Ignoring aerodynamic effects, optimum straight-ahead braking has been inadvertently defined as [7]

a = μFD = μRD. (?)

(11.25)

We have seen, however, that, in general,

a ≠ μFD ≠ μRD. [for rubber tires]

(11.26)

Newton’s second law of motion has not been shown generally applicable to accident reconstruction involving rubber friction when the a term is replaced by a μ term. Inadvertent misapplication of the laws of metallic friction to rubber tires has caused many such analyses to be performed. A new analytical approach involving the effects of rubber-tire friction on vehicle motion must be devised before accident reconstruction involving this parameter can be conducted on a rigorous basis.

11.6.2.6 Equations of Motion Utilized in Accident Reconstruction in Which a μ Term May Not be Substituted for an a Term There are a number of equations presently employed in accident reconstruction that utilized Newton’s second law of motion and that involve a. These same expressions are also used to characterize movement of a free body in space. While such equations are correct, of course, when a free body in space is acted upon only by Earth’s gravitational field, we have seen that one cannot generally substitute the μ term for the a term in these expressions and calculate tire traction-related values on a scientific basis. Unfortunately, nonscientific use of these motion equations in accident reconstruction is common. Such use is exemplified in the simple situation of a vehicle decelerating to a complete stop from an initial velocity, V, while covering a distance, S, without contacting another object. Table€11.7 presents the relevant expressions quantifying distance, velocity, time, and deceleration under these conditions. Each equation listed in Table€11.7 contains the a term. Table€11.8 lists various accident reconstruction determinations in which care must be taken to avoid improper replacement of an a term by the μ term and so avoid nonscientific application of Newton’s second law of motion.

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273

Table€11.7 Deceleration-Related Equations of Motion Inadvertently Used in Motor Vehicle Accident Reconstruction for a Vehicle Decelerating to a Complete Stop from an Initial Velocity, V, while Covering a Distance, S, in Time, t, without Hitting Another Object, Expressed in I-P Units Distance:

S = V2/2a S = at2/2 Velocity: V = at V = (2aS)½ Time: t = V/a t = (2S/a)½ Deceleration: a = V/t a = V2/2S a = 2S/t2 Note: ↜The constant deceleration term in these relationships, a, cannot be replaced by a tireroad coefficient of friction, μ. Such use of μ constitutes inadvertent misapplication of the laws of metallic friction to rubber. Source: Derived from Limpert, R., Motor Vehicle Accident Reconstruction and Cause Analysis, 5th ed., Michie, Charlottesville, VA, 2005.

Table€11.8 Types of Accident Reconstruction Determinations Involving Application of Newton’s Second Law of Motion in which Care Must Be Taken To Avoid Traditional Replacement of an a Term by a μ Term Car-trailer braking Influence of view obstructions as determined from rolling and sliding tire marks Lines of constant deceleration plotted on figures Lines of constant roadway friction coefficients plotted on figures Low-speed collisions Mechanical subsystem operation determined from rolling and sliding tire marks Motorcycle accident reconstruction from rolling and sliding tire marks Optimum straight-line braking forces Right-side and left-side tires on different surfaces Road friction measurements Time and distance to slide to a stop Truck accident reconstruction from rolling and sliding tire marks Speed calculations from skid marks Speed calculations from spin marks Speed calculations from yaw marks

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274 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 11.6.3 Drag Factors 11.6.3.1 Use of Drag Factors in Tire-Traction-Related Motor Vehicle Accident Reconstruction The definition of “drag factor,” when used in accident reconstruction in connection with tire traction, is based on Newton’s first law of motion: an object at rest or in motion at a given velocity will remain in that condition unless a force — in this case a tire-roadway friction force — is applied to it. A form of Equation 11.1,

μ = FT/FN,

in which W is substituted for FN, is employed to calculate the drag factor μ. In the field, drag sleds are sometimes utilized to measure FT, while the value of μ is considered constant for any value of W. Unfortunately, this is another example of inadvertent misapplication of the laws of metallic friction to rubber tires. As such,

μ ≠ FT/W.

(11.27)

For the reasons discussed in this book, use of μ as a tire-traction-related drag factor cannot be scientifically justified. A new analytical approach involving tire-roadway friction must be devised before application of Newton’s first law of motion to accident reconstruction in this way can be carried out on a rigorous basis. 11.6.3.2 Use of Drag Factors in Motorcycle Accident Reconstruction Motorcycle accidents can involve loss of control by the cyclist, allowing the motorcycle to tip onto its side and slide on pavement. This situation is common enough that four different research organizations have carried out motorcycle side-sliding tests [7]. When utilizing the thought-to-be constant coefficient-of-friction Equation 11.27, measured drag factors from these studies clustered around 0.56. As discussed in Chapter 2, this equation applies to two smooth metal surfaces in contact. It does not apply when one or both metal surfaces are rough. When a motorcycle slides on its side on asphalt or concrete pavement, at least one of the paired surfaces is nonmetallic. While a motorcycle’s tire may contact the roadway during side-sliding, paint on metal surfaces, as well as the metal structure of the bike, may also contact the pavement. The friction mechanisms of metal-pavement and paint-pavement pairings have not been thoroughly investigated in the motorcycle side-sliding context. A new analytical approach to side-sliding-motorcycle friction needs to be devised for application to investigative study of such motion if it is to be carried out on a rigorous basis in these incidents.

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275

11.6.4 Definition of the Maximum Braking Force in Motor Vehicle Accident Reconstruction Studying driver behavior in an emergency-stop situation, Limpert [7] considered that, “when maximum [brake] pedal force rates are involved, the maximum braking force between the tire and the ground existing at optimum tire slip, and hence, vehicle deceleration can be computed from vehicle parameters” (p. 587). He utilized the following equation — in inch-pound units — to calculate the deceleration buildup time tb, in seconds:

tb = (STIWV)/12μFNR2 + (12μFNR)/k,

(11.28)

where: ST = tire slip, IW = mass moment inertia of wheel, V = speed of vehicle, R = tire radius, and k = brake torque rate. After buildup time has elapsed, a state of constant vehicle deceleration is considered to exist. Here again, the laws of metallic friction have been inadvertently misapplied to rubber tires. In its present form, Equation 11.28 cannot be utilized in accident reconstruction on a rigorous basis. 11.6.5 Traditional Use of Energy Methods in Motor Vehicle Accident Reconstruction A basic law of physics mandates that energy must be conserved in a physical process. This allows energy-balance equations to be written and applied to accident reconstruction. Limpert [7] utilizes the following relationship in this regard:

Ee = Eb + Ea − E0,

(11.29)

where: Ee = energy at the end of the process, Eb = energy at the beginning of the process, Ea = energy added during the process, and E0 = energy removed during the process. During slipping or sliding of a braked tire in contact with pavement, the kinetic energy of the vehicle can change into thermal and acoustical energy in the tire contact patch. The frictional work expended in this process (Ef) can be quantified as the product of the rubber friction force Ff and the distance over which the force acts, or

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276 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Ef = Ff S,



(11.30)

Application of Equation 11.30 to accident reconstruction can be correct, of course, but only if the Ff force is properly expressed, taking into account its variation with W or FN. In Chapter 3 we discussed derivation of the generalized Hertz equation,

FA = cA(FN)m,

(11.31)

quantifying the adhesion friction force FA developed between rubber and macroscopically smooth surfaces. Equation 11.31 applies within loading ranges in which the adhesion transition pressure is reached. Applying Equation 11.5, quantifying the unified theory of rubber friction to tires in dry conditions, and substituting Ff for FT and the relationship for FA in Equation 11.31 into Equation 11.30 yields Ef = [cA(FN)m + FHs + FC]S



(11.32)

for macroscopically smooth roads. On rough pavements, Equation 11.32 becomes Ef = (FA + FHs + FHb + FC)S,



where, unfortunately, it is difficult to separate the FA and FHb terms so that they may be quantified individually. In such cases, determination of how FA and FHb vary with W and FN is problematic. It is common in accident reconstruction to misapply the laws of metallic friction to rubber tires inadvertently and substitute W and the nonequivalent μ term for the rubber friction force Ff in Equation 11.30, yielding Ef ≠ WμS.



A new analytical approach for the use of energy methods in accident reconstruction involving tire friction is necessary if this technique is to be applied on a rigorous basis.

11.7

Inadvertent Misapplication of the Laws of Metallic Friction to Rubber Tires in the Geometric Design of Roadways

11.7.1 Background Perhaps not surprisingly, some parameters involved in the formulas needed to design the geometric aspects of roadways are the same as those found

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in the analysis of motor vehicle accidents. This is so because tire traction is a key issue in both fields. For example, it is also conventional practice in roadway design to designate f as the coefficient of friction between tires and pavement. Similarly, and unfortunately, both fields have inadvertently misapplied the laws of metallic friction to rubber tires. In this section we discuss formulas made use of in roadway design, and, to emphasize the inapplicability of the constant (metallic) coefficient of friction to rubber, we again employ μ instead of f to represent the total rubber friction force generated, divided by the applied normal load. Various elements of roadway design employing μ in a nonscientific manner are addressed. These are listed in Table€11.9. 11.7.2 Braking Distance on Horizontal Pavement 11.7.2.1 Macroscopically Smooth Pavements A standard formula [13] used in roadway design to calculate the distance, d, required for a vehicle to decelerate while braking to a stop on horizontal pavement in I-P (inch-pound) units is d = V2/30μ, (?) where: V = initial speed of the vehicle.

(11.33)

Table€11.9 Standard Formulas Expressed in Terms of the Constant (Metallic) Coefficient of Friction μ Utilized in the Geometric Design of Roadways That Inadvertently Misapply the Laws of Metallic Friction to Rubber Tires, Expressed in I-P Units Braking distance of vehicle to stop on level road (d):

d = V2/30μ

Braking distance of vehicle to stop on grades (d):

d = V2/30(μ ± G)

Maximum degree of road curvature (Dmax):

Dmax = 85,660(e + μS)/V2

Minimum safe radius of curve (Rmin):

Rmin = V2/15(e + μS)

Side friction factor (μS):

μS = (V2/15R) – e

Superelevation (e):

(e + μS)/1–eμS = 0.067 V2/R = V2/15R

Superelevation runoff length (L):

L = 47.2μSVD/C

Note: New analytical approaches to these design parameters are necessary if they are to be quantified on a rigorous basis. V = initial speed of vehicle, G = grade/100, R = radius of curve, VD = design speed, and C = rate of change of μS↜渀屮↜, I–P = inch–pound. Source: Derived from formulas presented in AASHTO, A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D.C., 1984.

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278 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces If the Equation 11.20 relationship is substituted for μ in the simplest case of braked tires slipping or sliding on macroscopically smooth, horizontal pavement in dry conditions, Equation 11.33 becomes

d ≠ V2/30c(FN)–m.

(11.34)

Even in the simplest case, the value of μ in Equation 11.34 is not always constant at every value of FN. The standard formula utilized to calculate d in the geometric design of roadways — Equation 11.33 — inadvertently misapplies the laws of metallic friction to rubber. A new analytical approach involving the effects of rubber-tire friction on vehicle stopping distance needs to be devised before roadway design involving this parameter can be carried out on a rigorous basis. 11.7.2.2 Macroscopically Rough Pavements Use of the situation in which rubber tires slide on a macroscopically smooth pavement so that only adhesion and microhysteretic forces are generated to exemplify the inadvertent misapplication of the laws of metallic friction to elements of geometric roadway design will be repeated for the other elements we discuss. It should be kept in mind, however, that the Equation 11.20 relationship for μ is a simple case in which only the FA and FHs forces arise. When other basic rubber friction mechanisms develop, producing other basic rubber friction forces, derivation of formulas quantifying the roadway design elements listed in Table€11.9 becomes more problematic. While, as Kummer [2] postulates, it may be safe to assume that FC friction forces are negligible in ordinary driving, the FHb force is not. As yet, we have not determined how to separate concurrently arising FA and FHb forces in tires. Individual expressions for each of these forces, derived from their production mechanisms, are desirable if the geometric design of roadways is to be carried out on a rigorous basis. When a braked tire skids on macroscopically rough pavement and skid marks are produced, FHb, together with FC friction forces, could become significant in slowing the vehicle. Their development would affect the skid mark length. As yet, we have not determined how to quantify these two forces separately when they are generated concurrently in dry conditions. Similarly, we have yet to quantify the FA, FHs, FHb, or FC forces individually when the temperature is continuously increasing in the tire contact patch. It is probably safe to surmise that temperature increases decrease a tire’s frictional resistance and thereby lengthen the stopping distance. Separate mechanistically based expressions for each friction force under varying temperature conditions are also needed to achieve scientific rigor in these circumstances. We should further note that Equation 11.33 is not identical to the corresponding expression presented in accident reconstruction-related Table€11.7 when μ replaces a:

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Nonscientific Application of the Laws of Metallic Friction

S ≠ V2/2μ,

279 (11.35)

although both relationships are based on Newton’s second law of motion. This is because Equation 11.33 is employed in roadway design as an overall expression recognized as attempting to be representative of μ while encompassing the entire speed range involved. It is also known that μ varies with V, as well as with other parameters such as tire inflation pressure, chemical composition of tire treads, tire tread pattern, roadway wetness, and pavement texture [13]. Application of the mechanistic, unified theory of rubber friction may assist in allowing more accurate determination of braking distances and other parameters utilized in the geometric design of roadways. 11.7.3 Braking Distance on Up- or Down-Grades When selecting the grade of a roadway during design, engineers utilize another standard formula, in I-P units [13]:

d = V2/30(μ ± G), (?)

(11.36)

where: G = percent of an up- or down-grade divided by 100. If we again substitute the Equation 11.20 relationship for μ in the simplest case of tires slipping or sliding on macroscopically smooth, horizontal pavement in dry conditions, Equation 11.36 becomes

d ≠ V2/30[c(FN)–m ± G].

(11.37)

Even in the simplest case, the value of μ in Equation 11.37 is not always constant at every value of FN. A new analytical approach involving the effects of rubber-tire friction on vehicle stopping distance on grade needs to be devised before roadway design involving this parameter can be carried out on a rigorous basis. 11.7.4 Side Friction Factor Because of the considerable variation of vehicle speeds on roadway curves, a potentially unbalanced outward force can develop on the vehicle, whether or not the pavement is banked against sideslip. This force must be counteracted by tire traction so outward sideslip does not occur. A standard formula — in I-P units — employed to calculate the side coefficient of friction developed in the tire contact patch in these conditions, also termed the side friction factor μS, is [13]:

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μS = (V2/15R) − e, (?)

(11.38)

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280 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces where: R = radius of the curve, and e = rate of roadway superelevation. The side friction factor is defined in the same way as μ — that is, the quotient of the total side friction force generated divided by the applied normal load. As such, Equation 11.20 for side tire traction becomes

μS = cS(FN)−m.

(11.39)

In turn, Equation 11.38 becomes cS(FN)−m ≠ (V2/15R) − e.



(11.40)

Even in the simplest case, the value of μS in Equation 11.39 is not always constant at every value of FN. A new analytical approach relating tire friction, curve radii, and superelevation should be formulated before roadwaycurve design can be carried out on a rigorous basis. 11.7.5 Superelevation A basic focus of geometric roadway design is to assist in making the driving environment as safe as reasonably possible, while also providing for vehicle occupant comfort. As part of this effort, roadway curves are often banked against outward sideslip so the weight of the vehicle itself assists in keeping it in the proper operating lanes; that is, by tilting the pavement inward, a portion of the vehicle’s weight is directed inward by gravity. This slope is called “superelevation, e.” A standard formula [13] for e in I-P units can be written as

(e + μS)/1−eμS) = 0.067V2/R = V2/15R. (?)

(11.41)

Like other formulas discussed in this section, Equation 11.41 assumes that μS is directly proportional to FN for all values of normal load, when such is not the case. Equation 11.41 is properly written as

(e + μS)/1−eμS) ≠ 0.067V2/R ≠ V2/15R.

(11.42)

Equation 11.41 inadvertently misapplies the inapplicable laws of metallic friction to rubber tires. 11.7.6 Superelevation Runoff Length A geometric design element related to superelevation is its runoff length, L. This is the length of roadway after maximum curvature that remains sloping inward to prevent outward vehicle sideslip, but this slope decreases as

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a straightaway is approached. This element also involves driving safety and comfort. A standard formula [13] for L in I-P units may be written as:

L = 47.2μSVD/C, (?)

(11.43)

where: VD = design speed of the roadway, and C = the rate of change of μS. Substituting the Equation 11.39 relationship for μS into Equation 11.42 yields

L ≠ 47.2μScS(FN)−mVD/C.

(11.44)

The inapplicable laws of metallic friction have again been inadvertently misapplied to a relationship involving tire traction and superelevation. 11.7.7 Maximum Degree of Curvature The degree of curvature D of a circular roadway curve is defined as the angle subtended at the center by an arc 30.48 m (100 ft) in length. The maximum allowable degree of curvature Dmax depends on design speed, maximum rate of superelevation, and maximum allowable side friction factor [13]. Sharper curves are presently considered unsafe. A standard formula in I-P units for calculating Dmax can be written as [13]:

Dmax = 85,000(e + μS)/V2. (?)

(11.45)

Substituting the Equation 11.39 relationship for μS in Equation 11.45 yields

Dmax ≠ 85,000{e + cS(FN)−m}/V2.

(11.46)

Equation 11.45 inadvertently misapplies the inapplicable laws of metallic friction to rubber tires. 11.7.8 Minimum Radius of Curvature The radius R of curvature of a roadway segment can be defined as the radius of the circle whose curvature matches that of the roadway when the segment is designed to follow a circular curve. If the radius of curvature is too small, the curve is too sharp for the given conditions and is considered unsafe. It is conventional practice in geometric roadway design to calculate the minimum safe radius Rmin in accordance with the formula [13]

R min = V2/15(e + μS). (?)

(11.47)

Again substituting the Equation 11.20 relationship for μS yields,

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282 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

R min ≠ V2/15{e +c(FN)–m}.

(11.48)

Equation 11.47 inadvertently misapplies the laws of metallic friction to rubber tires.

11.8

Chapter Review

It is common engineering practice to misapply inadvertently the laws of metallic friction to rubber tires and their paired surfaces, whether these surfaces are concrete pavement, bituminous asphalt, or the tire-rubber-coated landing areas of aircraft runways. A principal purpose of this book is to demonstrate that the laws of metallic friction, which often take the form of the constant coefficient-of-friction equation, do not apply to rubber. A second purpose is to introduce a unified theory of rubber friction incorporating the fourth basic rubber friction force: surface deformation hysteresis or microhysteresis. By utilizing a mechanistic approach to illustrate rubber friction theory in prior chapters, an intuitively based explanation for generation of the different rubber friction forces was presented. Through examination of these forces, we have been able to differentiate them quantitatively to a considerable degree and thereby assist in interpreting their contributions to tire traction. This chapter outlined a blueprint for developing more efficacious methods to analyze and design the friction-related characteristics of tirepavement pairings. Few individuals would dispute the proposition that, in the interest of automotive safety, further progress toward acquiring maximum practical understanding and control of the traction characteristics of tires and roads is desirable. This chapter addressed the problematic topic of comparing roadway-traction test results obtained from different test apparatus. It was followed by a discussion of the ASTM test standards in which the laws of metallic friction are misapplied inadvertently to rubber tires. Motor vehicle accident reconstruction and the geometric design of roadways were then considered. 11.8.1 Comparing Rubber Friction to Metallic Friction In preparation for a discussion of tire-traction-test-result comparability, we first reviewed a comparison of the characteristics of rubber friction to metallic friction. It was shown in previous chapters that:

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1. Because of the deformational and constitutive differences between rigid metals and elastic rubber, the friction-force-producing mechanisms of these two materials are physically and chemically different. The constant friction coefficient is a material property of metals. Ratios of rubber friction forces, when properly utilized, are mechanistic behavior indicators; that is, the values of such ratios point to what

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rubber friction mechanisms have developed and indicate the equations to be used to quantify traction-test results. In current practice, tire-traction coefficients are often considered to represent material properties of the tread and pavement surfaces in contact.

2. Application of the laws of metallic friction to rubber can misstate the meaning of decreases in the magnitude of rubber friction coefficients. A diminishing metallic coefficient demonstrates that frictional resistance to movement between contacting metals is also decreasing. Decreases in the quotient of the total rubber friction force produced, divided by an increasing applied load, means that the rate of increasing frictional resistance to motion is diminishing.



3. The metallic coefficient-of-friction equation applies only to smooth metals. When one or both metal surfaces in contact are rough, measured coefficients are not necessarily constant. Nevertheless, it is common engineering practice to misapply the laws of metallic friction for smooth surfaces to rubber tires operated on rough roadways. On rough pavements, different mathematical expressions must be used for the forces generated by the different rubber friction mechanisms to quantify true tire braking or skidding resistance.

11.8.2 Aspects of Microhysteretic Friction Force Development in Rubber The chapter presented a synopsis of the effects of microhysteresis force (FHs) development in tire rubber. Because FHs is indicated as constant and independent of vehicle wheel load on both smooth and rough roadways, it is considered that microhysteresis is a distinct tire friction mechanism, different from the adhesion and macrohysteresis mechanisms we also examined. Adhesion signifies temporary bonding between a skidding tire and pavement arising from attractive forces residing in their surfaces. Macrohysteresis involves bulk deformation of the tread rubber by the pavement’s macrotexture. Differentiating these three forces assists in comparing tiretraction-test results. The effects of the presence of microhysteresis forces in tires can be summarized as follows:

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1. Accounting for the FHs force by subtracting its constant value from the total tire friction force generated allows one to differentiate and quantify the tread adhesion and macrohysteresis forces. Indeed, development of the FHs mechanism demonstrates that adhesion is present. Proper inclusion of the microhysteresis force in the analysis and design of rubber tires and their paired surfaces is necessary if a

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284 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces scientifically based theory providing maximum control of road surface slipperiness is to be utilized in engineering practice.

2. Depending on the characteristics of the pavement surface — smooth or rough — subtracting the measured constant FHs force from the total tire friction force developed allows one to determine the magnitude of either the tire adhesion force FA or the combined adhesion force plus the macrohysteresis force, FA + FHb. With smooth pavements, no significant macrohysteresis forces arise. Rough roads contribute FHb forces.



3. Chapter 6 showed that the adhesion friction force between rubber and smooth, harder materials increases with growth in the real area of mutual contact between them. When the primary result of increasing tread-pavement pressure in sliding tires is to produce new areas of contact between the tread and roadway, the tire’s adhesion force increases in direct proportion to the increase in this pressure. When the primary result of increasing tire-pavement pressure is to expand existing areas of contact between a sliding tire and a road, the adhesion-transition pressure (PNt) has been reached. After that point, the adhesion force is no longer directly proportional to increases in tire-pavement pressure. Testing is needed to determine the PNt value in any given set of conditions. The rubber adhesion transition phenomenon also develops in tires sliding on rough pavements. Testing is similarly needed to quantify the adhesion transition pressure in these situations.



4. A further effect of the presence of microhysteresis in tires concerns comprehensive application of the unified theory of rubber friction to the analysis of roadway-traction test results. In such efforts, the FHs force should be included to quantify friction by using the following equation:



FT = FA + FHs + FHb.

This expression assumes that frictional resistance from automotive tiretread wear is negligible. When applying the unified theory to automotive tires when wear is appreciable, or to aircraft tires during landing, tread wear may be a significant friction force. In such cases, the tread-wear term (FC) must be included in the above equation, which becomes

FT = FA + FHs + FHb + FC.

11.8.3 Comparability of Tire-Friction Test Results The chapter then discussed comparability between tire-traction-test results obtained by different testing apparatus. The most reliable means of fostering

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comparability of traction-test data is to utilize a scientifically based approach to the design of the testing program to identify physical and chemical causeand-effect relationships in the tire-pavement contact patch. This is done by selecting factors that may influence such relationships and carrying out experiments in which these factors are employed as physical or chemical variables. There are three kinds of such variables: (1) independent, (2) dependent, and (3) controlled. The engineer chooses a single independent variable for testing — say, the tire wheel load — and changes its value to observe what happens to the magnitude of the dependent variable — for example, the friction force produced. During such testing, all other variables must be controlled by keeping their values unchanged. One physical variable in tire traction investigations is often the type of testing apparatus utilized — for example, a locked-wheel device for skid studies. Kummer and Meyer [2] divided the relevant factors into categories that must be included in the analysis of results in order for different tire-traction testers of the same type to produce comparable values. Their list is presented in Table€11.1. If all aspects of a scientifically based test are carried out properly, results obtained from different testers of the same type will usually be comparable if they produce numerically equal results. If they do not produce such equality at an acceptable statistical confidence level, test results from the different devices should not be considered comparable. While Table€11.1 is comprehensive in regard to categories of the physical and chemical factors to considered, one requirement for traction-test comparability is inadvertently missing: specification of a unified theory of rubber friction incorporating tire microhysteresis for use in quantification of test results. As far as could be determined, the rubber microhysteresis force generated by the mechanism theorized in this book has never been taken into account in tire-traction testing in a quantitative manner. Instead, the inapplicable laws of metallic friction in the form of the constant coefficientof-metallic-friction equation have been employed. As a consequence, traditional tire-traction testing is not generally carried out on a scientific basis. 11.8.4 Related ASTM Test Standards The chapter also addressed ASTM test standards in which the laws of metallic friction in the form of the constant coefficient-of-metallic-friction equation have been inadvertently misapplied to rubber tires. Application of a unified theory of rubber friction in such standards will not only facilitate comparability of test results, but will also promote scientific accuracy. These standards are presented in Tables€11.4, 11.5, and 11.6. ASTM tire-traction-testing standards do not require such testing to be carried out on a demonstrably scientific basis. Incorporation of this requirement in the relevant standards would also further scientific accuracy.

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286 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 11.8.5 Motor Vehicle Accident Reconstruction Another area of traditional engineering practice involving tire friction in which scientific accuracy needs to be promoted is motor vehicle accident reconstruction. In this specialty, the total friction force developed between a tire and its contacted pavement, divided by the wheel load, or axle load, is thought to yield the supposedly constant coefficient-of-rubber friction µ. Such supposedly constant μ-coefficients are considered key tire-roadway properties in the analysis of how and why motor vehicle accidents occurred. Limpert [7] has stated that, “Since the tire-road friction coefficient is an important parameter in accident reconstruction, all necessary steps should be taken to measure the value existing at the time of the accident or at a similar condition” (p. 587). We have shown, however, that µ is not generally constant for different values of applied wheel load. Use of μ in these situations is another example of the inadvertent misapplication of the laws of metallic friction to tires. Unfortunately, in an another inadvertent misapplication of the laws of metallic friction to rubber tires, Newton’s second law of motion — inappropriately modified by incorporating μ — is routinely utilized in accident reconstruction to measure tire-roadway traction. This approach is based on a vehicle’s weight, W. When W is employed to compute µ, the friction coefficient is often called a “drag factor.” If properly utilized, Newton’s second law of motion correctly relates the weight of a moving object, such as a motor vehicle, to its deceleration when braking forces are applied to it. A problem arises, however, when the laws of metallic friction become involved. Because µ is not generally constant for all values of W, the approach is invalid. Nevertheless, it is considered in the accident-reconstruction community that there is a corresponding value of vehicle deceleration for every value of the tire-pavement coefficient of friction μ, regardless of vehicle weight or tire load. As a result, incorrect values of acceleration have been traditionally used to quantify other vehicle motionrelated parameters — for example, time, distance, and velocity. Table€11.7 presents a list of deceleration-related equations in which a μ term may not be substituted for an acceleration term. Table€11.8 lists types of accident reconstruction determinations in which care must be taken to avoid traditional replacement of an acceleration term for a μ term. Another situation in which care must be taken in accident reconstruction involves the energy-analysis approach to the subject. A basic law of physics mandates that energy must be conserved in a physical process. This allows energy-balance equations to be written and applied. During sliding of a braked tire in contact with pavement, kinetic energy of the vehicle is changed into thermal (heating) and acoustical (tire screech) energy. The frictional work expended can be quantified as the product of the rubber friction force and the distance over which the force acts. If this traditional approach is to be applied, the friction force must be properly expressed, taking into account its variation with vehicle weight or tire load.

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11.8.6 Geometric Design of Roadways Perhaps not surprisingly, some tire-friction-related formulas used to design the geometric aspects of roadways are the same as those found in the analysis of motor vehicle accidents. Unfortunately, traditional geometric design practice has also inadvertently misapplied the laws of metallic friction to rubber tires and their paired surfaces through use of the supposedly constant coefficient of rubber friction μ. Formulas used to quantify elements of roadway design employing µ in the traditional manner are listed in Table€11.9. These driving-safety-related elements include vehicle braking distance under different conditions, determination of tire-roadway friction values, required pavement banking to prevent vehicle sideslip on curves, and the sharpest allowable roadway curvature reasonably manageable by a driver. New approaches involving tire traction as it relates to the formulas presented in Table€11.9 need to be devised before the design of these elements can be carried out on a scientific basis.

References

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1. Ludema, K.C. and Gujrati, B.D., An Analysis of the Literature on Tire-Road Skid Resistance, American Society for Testing and Materials, STP 541, Philadelphia, 1973. 2. Kummer, H.W. and Meyer, W.E., Measurement of skid resistance, in Symposium on Skid Resistance, American Society for Testing and Materials, STP 326, Philadelphia, 1962. 3. Bowden, F.P. and Tabor, D., The Friction and Lubrication of Solids, Part II, Clarendon Press, Oxford, 1964. 4. Dillard, J.H. and Mahone, D.C., Measuring Road Surface Slipperiness, American Society for Testing and Materials, STP 366, Philadelphia, 1963. 5. Pfalzner, P.M., On the friction of various synthetic and natural rubbers on ice, Can. J. Res. F, 28, 468, 1950. 6. Wambold, J.C., Antle, C.E., Henry, J.J., and Rado, Z., International PIARC Experiment to Compare and Harmonize Texture and Skid Resistance Measurements, Final Report, Permanent International Association of Road Congresses, Paris, 1995. 7. Limpert, R., Motor Vehicle Accident Reconstruction and Cause Analysis, 5th ed., Michie, Charlottesville, VA, 2005. 8. Roth, F.L., Driscoll, R.L., and Holt, W.L., Frictional properties of rubber, J. Res. Nat. Bur. Stds. 28, 439, 1942. 9. Thirion, P., Les coefficients d’adhérence du caoutchouc, Rev. Gén. Caoutch., 23, 101, 1946. 10. Schallamach, A., The load dependence of rubber friction, in Proc. Phys. Soc. Sec. London B, 65, 657, 1952. 11. Kummer, H.W., Unified Theory of Rubber and Tire Friction, Engineering Research Bulletin B-94, The Pennsylvania State University, State College, 1966.

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288 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 12. Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955. 13. AASHTO, A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D.C., 1984.

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12 Friction Analysis in the Design of Rubber Tires and Their Contacted Pavements

12.1

Introduction

This chapter focuses on application of the unified theory of rubber friction detailed in previous chapters to tire-pavement systems. One intent of this book is to improve the analysis of friction in tire-pavement systems as they are presently designed and constituted. Suggestions for potentially desirable changes in tires and pavements stemming from application of the unified theory will not be made; such possibilities are beyond the scope of this book. Nevertheless, improving our understanding of the traction forces generated in the tire contact patch through scientifically based analysis of the friction mechanisms developed therein can be useful in reexamining existing roadways and perhaps serve as a starting point in improving present design practice. The chapter first addresses the importance of rubber microhysteretic forces in tires slipping or skidding on wet roadways. A discussion of the need to reformulate the traditional friction force vs. tire slip relationship is presented. We then consider measurement of tire microhysteresis on wet pavements, followed by a suggested process through which the unified theory can be applied to assist in the analysis of friction in the design of tire-pavement systems.

12.2

Importance of Tire Microhysteresis on Wet Pavements

It has long been recognized in the study of tire traction that numerous interacting phenomena develop in the tire contact patch, often defined as the nominal area of contact between tread rubber and the road surface. Meyer and Schrock [1] recommended that this region be studied as a volume rather than an area. They considered that this volume should include interacting tread rubber and tire grooves and sipes, related roadway asperities and channels, and any contaminants between them. Examination of this volume is appropriate because deformation of the tire rubber is a volumetric mechanism. 289

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290 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces We consider the displacement of water by a tire when a vehicle is moving on pavement, such as asphalt or portland cement concrete, and on how microhysteresis can make a contribution to traction in wet conditions. Wettire traction is a complex subject. This discussion is limited to the apparent microhysteretic contributions to wet traction arising from characteristics of the FHs force indicated by our back-calculation analyses of the rubber friction tests previously reviewed. 12.2.1 Three-Lubrication-Zones Concept Gough [2] was the first to formalize the frequently utilized Three-Lubrication-Zones concept of water displacement by a rolling or sliding tire at velocity V on wet pavement. Figure€12.1 illustrates this concept. Gough considered that while some encountered water is displaced to the front of the moving tire upon contact, the tire rides on an unbroken water film in the front lubrication Zone 1, as some of this water is gradually squeezed out the sides. The middle Zone 2 is one of transition in which initial physical contact between the tire and the roadway develops, while in Zone 3 only a thin water film at most remains, and the tire makes contact with the pavement through this film. The relative size of these zones varies with speed. If speed becomes excessive for the given conditions, hydroplaning can occur. While this concept provides a useGough 3-zone concept ful picture for visualizing friction V mechanisms that might arise under such circumstances, comprehensive testing was necessary to assist in the formulation of relationships quantifying wet-tire traction in terms of the significant variables involved. The macro- and microroughness of the pavement are two such variables. Gough postulated that roadway microtexture breaks through Zone Zone Zone the water film in the transition zone 1 2 3 and that Zone 3 is substantially dry, Bulk Thin Dry apparently including possible macwater film contact rohysteretic forces generated in this zone as a traction contributor. Moore [3] also utilized the ThreeFigure€12.1 Lubrication-Zones concept and Gough’s Three-Lubrication-Zones concept of water displacement by a rolling or sliding tire with developed it in greater mathemativelocity V. (From Horne, W.B., Status of Runway cal detail than did Gough. Moore Slipperiness Research, National Aeronautics and postulated that the function of Space Administration, N77-18092, Washington, roadway microroughness was to D.C., 1976.) provide adhesional-friction (FA force) contact between the tire and

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pavement under wet conditions, such as might arise after a light rain. Moore considered that the tire floats on the thin water film of Zone 1 in Figure€12.1. He further considered that the tire begins to drape dynamically on the pavement macrotexture in Zone 2, along with some roadway aggregate microroughness penetration of the water film in this segment. Moore additionally postulated that nearly all wet-traction skid resistance is developed in Zone 3. 12.2.2 Traditional Wet Roadway Microtexture Analysis Bond et al. [4] carried out investigations concerning the importance of roadway micro- and macroroughness on tire performance. They found that wetroadway skid resistance is governed by pavement macroroughness facilitating removal of bulk water and pavement microroughness in the role of creating real areas of tire contact. Apparently, it was not considered that macrohysteretic deformation of the tire on rough roadways could supply significant traction in wet conditions. Bond et al. reported on a study examining the seasonal variation of wetroadway skid resistance, as measured by the British Pendulum Tester. Such testing indicated that wet traction rose to a maximum in the winter and fell to a minimum in the summer months. Photomicrographs of in-service pavements revealed that surface microroughness also increased to a maximum in winter due to frost and other natural weathering action on the road aggregate during this period. On the other hand, traffic-polishing of the roadway’s aggregate was dominant during the summer, removing the aggregate’s microroughness to a considerable degree. The trends correlate well with the number of wet-skidding incidents in Britain — fewer in winter and a greater number in summer. The trends are also consistent with increased oil on pavements in summer from tire wear when less rain falls to wash away such residues. Bond et al. also found that wet traction thought to be provided by the microroughness remained low unless the aggregates’ surface topography attained a depth greater than the thin films of water covering them, allowing real areas of contact with the tire. They reported that the minimum microroughness depth for such penetration is on the order of 5 × 10−4 cm (1.95 × 10−4 in.), above which wet-roadway skid resistance increases rapidly. This study covered a microroughness range from an unquantified “smooth” up to 0.1 cm (0.039 in.). Bond et al. did not specifically address the rubber friction mechanism(s) involved when real areas of tire contact with the wet roadway microroughness were attained. In addition to the discussed seasonal variations in skid resistance of in-service roadways associated with surface aggregate microroughness in Britain, the same climatologically related phenomenon has been observed under controlled conditions at a highway pavement research facility in North America. Beginning in 1974, the Transportation Research Center of Ohio became involved in a U.S. Federal Highway Administration program designed to

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292 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces develop test centers where skid-trailers could be calibrated on skid pads and modified to improve their compliance with the American Society for Testing and Materials’ Test Method for Skid Resistance of Paved Surfaces Using a Full-Scale Tire (E 274). Whitehurst and Neuhardt [5] reported on this skidpad program. The program’s intention was to provide primary reference surfaces (PRSs) on which the skid-trailers could be tested. Two of the subject PRS skid pads are of interest in the present context. These pads employed finely graded silica sand aggregate as the testing surface. This sand was bonded to a concrete base using an epoxy adhesive. The skid pads measured 159 m (520 ft) long and 5 m (15 ft) wide. At the time of construction, an epoxy seal coat overspray was applied to one pad, while the other did not receive this seal-coat treatment. The purpose of the overspray was to try to inhibit traffic polishing and to prevent surface aggregate loss. In this way, it was intended that the wet and dry skid resistance of the sealed reference pad would exhibit as little change as possible throughout the years of use. Whitehurst and Neuhardt reported findings from a 9-year period involving approximately 12,000 individual skid tests. Test results were quantified using the skid number (SN), an artifice commonly employed in pavement testing and discussed in Chapter 11. During the skid-test run, instruments record the horizontal and vertical forces acting on the trailer’s locked wheel, usually in wet conditions. The average horizontal force is divided by the average vertical force to obtain the coefficient of total friction μT. This value is then multiplied by 100 to obtain a whole number. Thus, a μT of 0.5 for a skid test equals an SN of 50. While this is an inadvertent misapplication of the laws of metallic friction to tires, the test results are of interest. The test pad to which the seal-coat overspray had been applied maintained a nearly constant SN during the reported 9-year period, and its surface was visually unaffected. The unsealed pad, however, exhibited a gradual average annual SN decrease for these 9 years, falling from an original 63 to about 46 over that period. This was partly due to an observed loss of the silica sand aggregate from the unsealed pad’s surface. The untreated pad evidenced a seasonal variation in skid resistance, generating maximum average monthly SN values in the winter, which fell to a minimum in the summer months. While no microroughness measurements were carried out, Whitehurst and Neuhardt theorized that significant traffic polishing of the untreated pad’s surface aggregate had occurred during the summer. The winter increases in the untreated surface’s SN values are consistent with an increased contribution from microhysteresis to skid resistance measurements made during that season, when harsher weather apparently produced degradation-roughening of the sand surfaces. In 1992, Williams [6] reviewed the then state-of-the-art of roadway tire traction in relation to tread pattern, tread compounding, and road surface conditions, particularly in regard to a tire’s roadholding ability on wet pavement. In addition to the need for adequate tread depth, the road’s surface charac-

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Friction Analysis in the Design of Rubber Tires

293

teristics had been accepted as especially important. One of these — road surface macrotexture — had been studied for some time, leading to proposals for a road macrotexture geometry that minimizes bulk water drainage time. Williams stated that, “The road surface macrotexture, assisted by the [tire] tread pattern, is responsible for the removal of the bulk water from the tire contact patch” (p. 132). Williams also summarized the recognized requirement for availability of an adequate microtexture on the road surface aggregate to provide a reasonably safe wet-driving environment, stating that: There is no substitute for the appropriate level of microtexture for aggregates in the new and traveled condition. The most desirable level of microtexture relates to its ability to remove the remaining thin film of water in order to create real areas of contact with the tread compound. Levels of microtexture below this minimum fail to generate high levels of wet friction. (p. 132)

Williams considered that suitable roadway-surface-aggregate microtexture should be on the micron (1 × 10−5 cm, 3.94 × 10−5 in) scale. He did not, however, specifically address the rubber friction mechanism(s) involved when real areas of tire contact with the wet roadway microroughness were attained. 12.2.3 Importance of Aircraft Tire Microhysteresis on Wet Pavement Just as the importance of a roadway’s microtexture regarding a tire’s roadholding ability in wet conditions was accepted by highway design engineers [6], the importance of aircraft runway and taxiway microtexture to pilots during landing and taxiing in wet conditions has been accepted by the aviation community. Yager [7] discussed this issue in his 1990 article concerning the tire-runway friction interface. Yager [7] stated that, “…the magnitude of the friction at a given speed is related to the surface microtexture (fine, smallscale, surface features such as found on individual stone particles)” (p. 296). However, Yager [7] did not specifically address the tire-pavement friction mechanisms involved in this interaction. 12.2.4 Quantifying Tire Microhysteresis on Wet Pavement Using the Unified Theory of Rubber Friction Our analysis of the Yager et al. research [8], involving wet testing of radialbelted aircraft tires at various yaw angles and applied normal loads, is consistent with Yager’s opinion [7] concerning the importance of pavement surface microtexture in wet conditions. Figure€8.4 presented results from our back-calculation analysis of the Yager et al. [8] wet testing at three yaw angles. Extrapolation of the total measured friction force vs. applied normal

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294 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces load plots to the y-axis evidenced intercepts indicating development of a different rubber-tire microhysteresis force in each of the three test protocols. While a literature search was unable to locate reports of friction testing of automobile or truck tires on wet pavements in which the applied normal load was purposely varied and all other variables were held constant, a number of the wet-tire-tread studies we examined also produced results consistent with development of a constant microhysteresis force in such circumstances. It was shown in Section 5.2.2 when analyzing Thirion’s [9] data that FHs forces for differently sized but otherwise identical rubber test specimens can be different. Thirion’s data indicate that the greater the nominal area of contact, the larger the microhysteretic force generated. Consistent with this finding, the hyperbolic shape of our back-calculated plots in Figure€8.1 derived from Clayton’s [10] data for automobile tires on wet pavement is consistent with decreasing surface deformation hysteresis with increasing tire inflation pressure as the contact patch area diminished. Furthermore, while the average local pressure in a tire increases slightly with inflation pressure, FHs is independent of PN. Sabey [11] investigated the friction forces developed when sharp road-surface aggregate — idealized as smooth, rigid cones — penetrate tire-tread rubber at 1.83 m/sec (6 fpsec) when well lubricated with water. The results of a back-calculation analysis of Sabey’s data [11] were portrayed in Figure€8.3. Extrapolation of the straight-line plots indicates that microhysteretic forces arose in all four cases. The FHs forces appear independent of the applied normal load. The conical slider with the sharpest peak, exhibiting a 70° interior apex angle, produced the largest indicated microhysteresis value, approximately 0.91 kg (2 lb). The back-calculation findings from the Yager et al. [8], Clayton [10], and Sabey [11] data are all consistent with the microroughness-related investigation results reported by Bond et al. [4] and Whitehurst and Neuhardt [5]. The research reported by Bond et al. quantified pavement microtexture depth but not the microhysteresis forces. While the back-calculation findings from the Sabey data were not derived from full-scale tire testing, her protocol did employ tire treads. As such, determinations of the magnitude of microhysteresis forces through back-calculated analysis of the Yager et al. [8] and Sabey data indicate that quantification of microhysteretic forces generated in the tire-pavement contact patch in wet conditions can be routinely carried out using the unified theory of rubber friction. 12.2.5 Corroboration for the Three-Lubrication-Zones Concept Our back-calculation findings from the Yager et al. [8], Clayton [10], and Sabey [11] data are also consistent with Gough’s [2] Three-Lubrication-Zones concept of water displacement by a rolling or sliding tire. Zone 3 in Figure€12.1, at the rear of the tire, is considered dry — or nearly so — unless hydroplaning takes place. According to the unified theory of rubber friction presented in this book, physical contact between rubber tire asperities

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295

Friction Analysis in the Design of Rubber Tires

and pavement surface asperities — allowing van der Waals’ adhesion (FA) forces to develop between them — is required if microhysteretic forces are to arise. The indicated production of such microhysteresis forces in these three wet-traction studies implies that dry, asperity-to-asperity contact occurred in this testing and most likely in Zone 3 of the tires utilized in the Yager et al. [8] and Clayton research. Because Sabey employed rigid cones sliding horizontally on flat, well-lubricated tread rubber to simulate tire operation in a wet environment, a circular sliding or rolling surface was not involved, and the three zones would not have developed. In her testing, highly localized dry areas of adhesional contact between the cone’s microtexture and the tread-rubber asperities likely arose.

12.3

Reformulation of the Traditional Friction Force vs. Tire Slip Relationship

Figure€12.2 presents a traditional depiction of the developed friction coefficient (μ) vs. tire slip relationship during braking of a rolling tire to slow its rotation, with corresponding deceleration of the moving vehicle. In this case, by inadvertently misapplying the laws of metallic friction to a tire-pavement system, the coefficient of friction for tire slip is plotted against the tire slip ratio sR.

Friction Coefficient, µ

Free roll 1.0

Locked wheel µMAX

0.8

µAV 0.6 µSKID

0.4 0.2 µr (rolling resistance) 0

0

0.2

0.4 0.6 Slip Ratio, sR

0.8

1.0

Figure€12.2 Traditional depiction of the developed rubber friction coefficient (μ) vs. tire slip relationship (sR). (From Horne, W.B., Yager, T.J., and Taylor, G.R., Review of Causes and Alleviation of Low Tire Traction on Wet Runways, NASA Technical Note TN D-4406, Washington, D.C., 1968.)

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296 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces A free-rolling tire is considered to possess a slip ratio of 0. As the vehicle brakes are applied, tire rotation slows and the tread begins to slip on the pavement surface. In this situation, the difference between the peripheral velocity of the wheel and the horizontal velocity of the wheel axle is defined as the relative slipping velocity VR. The ratio of this relative slipping velocity to the horizontal velocity of the axle VH is defined as sR, yielding:

sR = VR/VH.

(12.1)

When sR equals 1.0, the wheel has stopped rolling and, if the vehicle has not stopped, a locked-wheel skid develops. As seen in Figure€12.2, the coefficient of friction is then considered to be μSKID. Before application of the brakes, a free-rolling condition exists and a coefficient μr is employed to quantify rolling resistance. Horne et al. [12] opined that μr is determined by the resistance of the rolling tire, wheel bearings, and unloaded brakes. With regard to the free rolling resistance of a tire, Limpert [13] states that the reasons for rolling resistance are connected to the bending and straightening of the tread and carcass when the rubber meets and leaves the road surface. A second reason is the nonuniform pressure distribution between tire and road, resulting in a forward shifting of the resultant ground force. The free-rolling resistance of a tire is comprised of mechanisms that do not generate rubber friction forces; nevertheless, it is traditional to begin the μTS vs. sR plot at the μr (rolling-resistance coefficient) value. Clearly, inadvertent combined application of the laws of metallic friction to such things as wheel bearing resistance and tire carcass flexing is not consistent with the primary intention of the Figure€12.2 plot: illustrating the developed tire friction coefficient vs. tire slip relationship. Figure€12.2 illustrates another traditional inadvertent misapplication of the laws of metallic friction to vehicle tires: utilization of a coefficient μAV to represent an average tire-pavement friction value in the slip-ratio range of 0.1 to 0.5. As the figure reveals, this range is thought to encompass the maximum frictional resistance generated, μMAX. While 0.1 to 0.5 slip ratios might be representative of typical non-emergency braking situations and are therefore sR values frequently employed in pavement testing, measured μAV coefficients for different pavements and tires from such testing are compared. The indicated tire-pavement traction characteristics apparently revealed by these tests are relied on, and seemingly reasonable safety-related, action-producing conclusions are drawn from these implied characteristics. As has been shown, however, the laws of metallic friction do not apply to rubber, and the coefficient of rubber friction μ is not generally constant under all applied normal loads. The traditional approach to quantifying sR-related relationships is not founded on the physical mechanisms producing the friction forces being generated during tire slip. A scientifically based approach to determination of the friction forces and their magnitudes produced in tire

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slip must be employed if maximum reliability is to be attached to our understanding of tire slip effects. Reformulation of the tire friction vs. sR relationship utilizing a unified theory of rubber friction encompassing all the friction forces arising in these circumstances is needed. Such reformulation must be based on appropriate testing, testing in which the possible presence of tire microhysteresis is ascertained.

12.4

Measuring Tire Microhysteresis on Wet Pavements in the Design Process

To determine the possible presence of tire microhysteresis in given wet-pavement conditions, access to readily available, conveniently used testing apparatus capable of measuring this rubber friction force in the field is desirable. Proceeding on the indicated basis that rubber microhysteresis FHs is independent of both applied normal force and pressure, such a testing device could be portable and simple to operate. The apparatus need only be capable of applying a reasonable range of dynamic normal loads to pavements at constant velocity through a tire-tread material exhibiting appropriate properties and configured with sufficient mating planer surface area to ensure that the representative microhysteresis mechanisms are generated during testing. Although adhesion (FA), microhysteresis, and macrohysteresis (FHb) friction components could develop on typical pavements, plotting the total friction force measured vs. the normal loads employed would allow extrapolation of this curve to the y-axis and quantification of the FHs force. While a search for existing friction testers intended to be used on pavements, and also capable of applying multiple normal loads, failed to identify such apparatus, there is one device that could likely be modified to meet these requirements and a second potentially practicable tester that is not now used but which could be resurrected if sufficient demand arose. These are the British Pendulum Tester (BPT) and the North Carolina State University Variable-Speed Friction Tester. Among the design alterations to these devices necessary to allow them to measure microhysteretic forces is to eliminate their misapplication of the laws of metallic friction to rubber. The British pendulum device is addressed first. 12.4.1 Using the British Pendulum Tester for Microhysteresis Measurements 12.4.1.1 Background The 10-year developmental history of the BPT was reviewed by Giles et al. [14] in a 1962 ASTM publication; thus, the device has been utilized in a practical manner for many years. It is employed to measure the skid resistance

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298 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces of wet pavements, as an instrument to determine the frictional properties of experimental rubber tread compounds paired with different road surface textures, and to assess the degree of roadway aggregate traffic polishing. The degree of such polishing — that is, the extent to which the exposed aggregate’s original microtexture has been smoothed — is sometimes termed the pavement’s “harshness.” The BPT is presently the subject of active ASTM standard, E 303 – 93 (Reapproved 2003), Standard Test Method for Measuring Surface Frictional Properties Using the British Pendulum Tester. A feature of the BPT is that it is designed to produce a nominal average pressure on the pavement of the same order as that between a tire and the road, approximately 207 kPa (30 psi). A second feature is that the BPT’s test foot is wide enough and long enough to sample a representative road surface for exposed aggregate sizes up to 2.54 cm (1 in.). The BPT’s nominal applied load is 2.3 kg (5 lb). This is controlled by an adjustable tension spring in the pendulum arm. As we will address presently, Yandell [15] apparently reduced the BPT’s spring tension to obtain the lower applied loads employed in his testing, examined in Chapter 5. The BPT operates on the same basis as the Sigler [16] pendulum device (discussed in Chapter 4). The measured residual energy (as determined from the maximum height of the BPT pendulum’s center of mass during upswing after pavement contact) is subtracted from the known potential energy of the pendulum before release. This energy loss value is equated to the work WBPT done in overcoming friction between the device’s test foot and the pavement, yielding the relationship WBPT = μFNavgDBPT, (?) (12.2) where: FNavg = average normal force between the test foot and pavement, and DBPT = the BPT’s contacted sliding distance. We see, however, that Equation 12.2 involves inadvertent misapplication of the laws of metallic friction to rubber. Equation 12.2 should be written as

WBPT ≠ μFNavgDBPT.

Redesign of the BPT’s readout scale to provide direct reading of forces is necessary if it is to be suitable for measuring rubber microhysteresis. A potentially significant difference between the Sigler and BPT devices is that the latter utilizes a block of tread rubber inclined at approximately 20° to the tested surface, such that only the trailing edge of the tread material makes contact with the pavement. Lack of substantially mating planer surfaces may not allow representative microhysteresis mechanisms to develop during testing. A design alteration to the BPT to account for this concern, perhaps including a beveled forward edge on the horizontal tread block, may be appropriate.

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Friction Analysis in the Design of Rubber Tires

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12.4.1.2 Back-Calculation Analysis of Yandell’s BPT Test Results Figure€3.12 depicted the phenomenological approach taken by Yandell [15] in his efforts to assist in understanding the contribution of roadway microroughness to tire traction in wet and dry conditions. He idealized the road surface texture and analyzed the macro- and microhysteretic contributions to friction by assuming that the macro- and microhysteretic coefficients are additive, yielding the following theoretical equation:

μHt = μHb + μHs. (?)

(12.3)

Because Equation 12.3 involves inadvertent misapplication of the laws of metallic friction to rubber, the expression should be written as

μHt ≠ μHb + μHs;

nevertheless, Yandell’s test data are of interest in regard to the use of the BPT to measure tire-tread microhysteresis. Yandell’s research involved a computer-based, two-dimensional, mechano-lattice analysis of sliding rubber utilizing 264 mathematical units in his model for simulating the plane stress behavior of rubber. As the rectangular units slid on rigid, model asperities, the units experienced cycles of load and deflection, generating hysteresis loops. Yandell defined the coefficient of hysteretic friction in his program as the vector sum of the horizontal forces acting on the lattice unit joints in contact with an asperity, divided by the vertical reactions acting on these joints. The idealized, lattice-model asperities were either isosceles triangular prisms or smooth cylinders. This latter shape was intended to emulate road chips whose fine texture had experienced smoothing from traffic polishing. Figure€5.36 presented plots of Yandell’s findings for dry conditions expressed here as the total hysteretic friction ratio μT vs. average slope of the idealized triangular prisms and cylindrical asperities selected. Five different sets of plots are depicted for rubber damping factors ξ ranging from 0.1 to 0.5. It is seen that the triangular prisms produce higher μT values than do the cylinders. In addition, as the damping factor increases, so does the theoretical coefficient of hysteretic friction. To assess the accuracy of his lattice model, Yandell utilized small triangular prisms specially fashioned from brass and rigidly mounted in rows on a test bed. Friction measurements were carried out on this idealized asperity arrangement with a BPT. The device was fitted with a rubber test foot exhibiting a damping factor of 0.45. Yandell considered that reasonably accurate hysteretic coefficients from these tests could be calculated by subtracting friction measurements taken parallel to asperity rows from those measured perpendicular to the rows, leaving the relevant hysteretic force from which ratios could be determined.

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300 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces In addition to placing his pendulum device perpendicular to the rows of brass asperities, Yandell obtained friction measurements by aligning the tester at an angle of 60° to them. In both alignments, he applied three normal loads — 0.68 kg, (1.5 lb), 1.4 kg (3.1 lb), and 2.3 kg (5 lb). Although not specifically stated by Yandell, he was apparently able to obtain the 0.68-kg (1.5-lb) and 1.4-kg (3.1-lb) normal loads by reducing the BPT’s spring tension below the commonly used value that generated an applied load of 2.3 kg (5 lb). Because Yandell had theorized that what is often thought to be adhesive rubber friction is, in reality, a hysteretic phenomenon, the apparent areas of contact between the pendulum’s rubber test foot and the brass asperities were not involved in his calculations. Furthermore, the possible development of microhysteretic forces between the rubber test foot and the brass asperities by a different mechanism than that for the fine asperities depicted in Figure€3.12 was apparently not considered. A back-calculation analysis of Yandell’s data indicates that an adhesion-related rubber friction mechanism of the type illustrated in Figure€5.34 developed in his testing. Figure€5.38 presented back-calculation analysis results of the 90° data expressed as total friction force vs. FN. It is seen that all three 90° data sets yield reasonably uniform plots, consistent with straight lines. Two of the plots, for average brass asperity surface slopes of 0.5 and 0.37, exhibit approximate y-intercepts of 50 g (0.1 lb) and 20 g (0.04 lb), respectively. These yintercepts are consistent with the production of FHs forces in Yandell’s dry, 90° brass testing. Figure€5.41 depicted back-calculation analysis results for the 60° BPT data expressed as the total friction force vs. FN. All three data sets yield reasonably uniform plots, consistent with straight lines. The average brass asperity surface slopes of 0.44, 0.32, and 0.20 exhibit approximate y-intercepts of 20 g (0.04 lb), 30 g (0.07 lb), and 20 g (0.04) lb, respectively. This is consistent with the production of FHs forces in Yandell’s dry, 60° brass testing; thus, it appears that, when fitted with tire-tread material, the BPT can be used to measure roadway pavement microhysteresis. 12.4.2 Using the North Carolina State University Variable- Speed Friction Tester for Microhysteresis Measurements An implementation program for use of the North Carolina State University Variable-Speed Friction Tester (VST) was outlined in a 1977 report by Mullen et al. [17]. An ASTM standard for application of the tester in the field and laboratory, ASTM E 707–90 (Reapproved 2002), Standard Test Method for Skid Resistance Measurements Using the North Carolina State University Variable-Speed Friction Tester — was first approved in 1979. Due to lack of industrial usage and support, this ASTM standard was withdrawn without replacement in 2006. The VST is also a pendulum device. It utilizes the loss of energy experienced during the pendulum’s contact with a pavement as the basis for a trigonometric calculation that yields a variable-speed number (VSN). This VSN

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Friction Analysis in the Design of Rubber Tires

301

value is read directly from a scale on the device by means of a pointer. The VSN is equivalent to 100 multiplied by sin θ, where θ is the angle between the maximum upward limit of the pointer after pendulum contact with a pavement or other test specimen and the maximum limit of the pointer when the pendulum is made to swing without specimen contact. The VST can be used in both wet and dry conditions and under different simulated vehicle speeds. The device is equipped with an adjustable nozzle that provides a thin sheet of water on the pendulum’s tire-pavement contact patch. The velocity of the impinging water stream is meant to represent, or account for, the tire-over-pavement vehicle speeds of interest. An appealing feature of the VST is that it utilizes a rubber tire at the lower end of the pendulum with which to contact the pavement. The tire is specified as 4.10/3.50-5, 90-mm (3.5-in.) tread width. It is mounted on a 25 × 75mm (5 × 3-in.) rim. A further appealing feature of the VST is its ability to generate different normal loads. The vertical positioning of its pendulum is adjusted before each test for this purpose. An operator could readily apply different values of FN so that plotting the total friction forces measured vs. the loads employed would allow extrapolation of this curve to the y-axis and thereby quantify surface deformation hysteresis. There appears to be only modest design changes required to utilize the VST for quantification of the FHs force. Among the design alterations to the VST device needed to allow it to measure microhysteretic forces is to eliminate its inadvertent misapplication of the laws of metallic friction to rubber. Allied with this change, redesign of the pointer scale is necessary to provide direct readout in units of friction force.

12.5

Application of the Unified Theory to Analysis of Friction in the Design of Tire-Pavement Systems

12.5.1 Potential Benefits from Application of the Unified Theory to Friction Analysis The laws of metallic friction do not apply to rubber. The traditional approach to quantifying tire-traction relationships is not founded on the physical mechanisms producing the friction forces being generated in the tire-pavement contact patch. A scientifically based approach to the determination of friction forces developed during tire operation and the magnitudes of these forces must be employed if maximum reliability is to be attached to our understanding of tire-roadway traction properties. Application of the unified theory of rubber friction promotes accuracy by helping eliminate the all-too-common error made by some engineers who believe that a decreasing coefficient of rubber friction (μ) under increasing

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302 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces loading means that tire traction is decreasing. This belief is incorrect. Friction is still increasing, but at a decreasing rate. Unlike the coefficient of metallic friction — which is a material property — the rubber friction ratio is an artifice. Care must be taken when using rubber friction ratios to ensure that they are meaningful. Application of the unified theory can provide the means to maximize the adhesion, microhysteresis, and macrohysteresis friction components of rubber tires on an optimal, comprehensive, and scientific basis. Use of the unified theory affords the opportunity to utilize a systems approach to friction analysis in the design of rubber tires and pavements in both dry and wet conditions. Detecting the presence of microhysteresis in a test tire in wet conditions — which can only arise from solid-to-solid contact — tells us that the roadway microtexture has penetrated the liquid. Because microhysteresis depends on adhesion, the desirable presence of the adhesion friction component is also indicated. Designing to increase the readily detectable and quantifiable microhysteresis force can increase adhesion. 12.5.2 Rubber Macrohysteresis Mechanisms It has been traditionally considered that a principal benefit of pavement macrotexture is to allow rapid water drainage from the surface. Yager [7] stated that: During aircraft ground operations in wet weather, a water removal or drainage problem is created at [the] tire/pavement interface. Runway surface water encountered by moving aircraft tires must be expelled rapidly from the tire-pavement contact area or viscous and dynamic water pressures that build up with increasing ground speed will significantly reduce the friction performance. Research studies have shown that the slope of the tire friction-speed gradient curve is primarily a function of surface macrotexture. (p. 296)

Yager attributed the magnitude of the tire friction force generated in wet conditions to pavement microtexture; however, analysis of the data and figures presented in these pages leads to the conclusion that macrohysteresis is also a significant traction-production mechanism. At least two different rubber macrohysteretic friction mechanisms appear to exist: the adhesionassisted form in wet and dry conditions and the non-adhesion-assisted type in wet conditions. The adhesion-assisted means of generating the FHb force is addressed first. 12.5.2.1 Adhesion-Assisted Macrohysteresis on Dry Surfaces An illustration of both adhesive and macrohysteretic friction in rubber tires as envisaged by Kummer [18] was portrayed in Figure€3.8. The resultant adhesion forces are depicted operating parallel to the surface of the road chip,

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Friction Analysis in the Design of Rubber Tires

303

while the macrohysteresis forces are shown perpendicular to the chip, indicating bulk compression of the tire tread on both sides of the protuberance. As discussed by Persson [19], however, adhesion between rubber and a hard surface can be considered a pull-off phenomenon in which tensile forces are attempting to hold together the two paired materials. This visualization is illustrated in Figure€12.3. That is, the extent of draping of a tire tread over a dry pavement’s macrotexture is likely augmented by adhesion between the two surfaces, such that the area of physical contact between them is greater than that which would be produced by the applied normal load acting alone. Evidence is presented in support of a new theory: that the mechanism of adhesion-assisted macrohysteresis in tires can be physically linked to the adhesion friction mechanism in both dry and wet conditions. It appears that, when the adhesion friction force (FA) is directly proportional to the applied normal load (FN) on macroscopically rough pavements, so too is the macrohysteresis (FHb) friction force. This allows the two forces to be represented by the following equations:

FA = FNμA

(12.5)

FHb= FNμHb,

(12.6)

and

where: μHb = rubber bulk deformation hysteresis friction ratio. Moreover, when the tire’s adhesion transition pressure on macroscopically rough pavements is reached, the adhesion-assisted macrohysteresis friction

Tire tread Chip

Figure€12.3 Visualization of adhesion-assisted macrohysteresis in which the extent of draping of a tire tread over a roadway chip is augmented by adhesion between the two surfaces, such that the area of physical contact is greater than that which would be produced by the applied load acting alone.

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304 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces mechanism transitions accordingly, and both the adhesion friction force and the macrohysteresis friction force can be represented by the following equations:

FA = c(FN)m

(12.7)

FHb = c(FN)m.

(12.8)

and

It should be noted, however, that the values of c and m in these expressions are not necessarily equal for the two mechanisms. Also, separation of FA from FHb is problematic 12.5.2.1.1 Hample’s testing Chapter 7 examined Hample’s [20] coefficient-of-friction tests on segments of a rubber B-29 tire. Figure€7.9 presented a plot of the results from backcalculation analysis of Hample’s low-pressure testing on smooth portland cement concrete, in which no significant macrohysteresis could be expected. A straight line is indicated, evidencing a constant FHs force of about 22.7 kg (50 lb). This low-pressure testing ranged up to an applied normal load of approximately 295 kg (650 lb). The straight-line character of the plot indicates that the adhesion transition pressure had not been reached in this testing. Plots of results from our back-calculation analysis of Hample’s high-pressure tire-segment testing on smooth, semi-smooth, and rough (broom-swept) concrete from which the FHs forces had been subtracted were presented in Figure€7.4. The smooth-concrete plot was straight up to approximately 295 kg (650 lb), but began to curve shortly thereafter. This curvature indicates that the adhesion transition point had been reached; thus, the low- and highpressure plots are consistent, as far as the magnitude of the adhesion transition pressure is concerned. Figure€7.16 illustrated that the adhesion transition pressure on smooth concrete, found in the high-pressure plot, was approximately 2.76 MPa (400 psi). Figure€7.4 revealed that friction-force values for the broom-swept concrete plot were greater than corresponding values for the smooth concrete. Figure€7.16 illustrated that the adhesion transition pressure for the rough concrete was approximately 1.79 MPa (260 psi), lower than the PNt value for the smooth-concrete testing. Figure€7.5 presented plots of back-calculated rubber friction ratios from Hample’s high-pressure testing of the smooth and broom-swept surfaces. Both test results exhibited horizontal — that is, directly proportional — friction ratios initially, transforming to hyperbolic curves after the adhesion transition pressures are reached. Chapter 6 showed that, on macroscopically smooth surfaces, the adhesion transition phenomenon arises at the point where, on average, equal increases in applied normal load produce diminishing increases in the real area of contact between rubber asperities and their paired surfaces. This behavior accounts

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305

for decreases in the rate of adhesion friction force increase. It will be theorized that this same adhesion mechanism operates on macroscopically rough surfaces: the rate of FA force increase diminishes when equal increases in FN produce expansion of existing areas of contact between the paired materials. If the adhesion component of the initial portion of the broom-swept concrete plot in Figure€7.5 was directly proportional to FN, so also must have been the macrohysteresis friction force component. The plot’s initial portion is horizontal, indicating direct proportionality throughout this segment. It can be theorized, therefore, that both FA and FHb forces were directly proportional to the applied normal load in the horizontal portion of the roughsurface plot presented in Figure€7.5. Application of this theory permits the FA and FHb forces developed in the broom-swept concrete testing to be represented by Equations 12.5 and 12.6, respectively. Similarly, it can be theorized that the FA and FHb forces generated in the semi-smooth-concrete testing are represented by Equations 12.5 and 12.6, respectively. We can apply the same theory to the hyperbolic portions of the rough- and semi-smooth-concrete plots seen in Figure€7.5, quantifying the combined FA and FHb forces produced under loading above PNt in Hample’s testing: the adhesion and macrohysteretic friction mechanisms are related, and their generated forces are represented by Equations 12.7 and 12.8, respectively. 12.5.2.1.2 Dry testing by Yager, Stubbs, and Davis Figures€7.11, 7.12, and 7.13 presented the side friction forces back-calculated from the Yager et al. [8] bias-ply, radial-belted, and H-type tire tests in dry conditions. These tests were conducted on a portland cement concrete test track runway that had a surface appearing to be moderately broom-swept. Because of this macrotexture, generation of both FA and FHb friction-force components can be expected. Identification of the tire friction mechanisms developed in this testing can be carried out by inspection of Figures€7.11, 7.12, and 7.13. Extrapolation of all 17 yaw-angle plots depicted in the figures evidences y-intercepts, indicating the production of FHs forces. The presence of microhysteresis in the test tires and the dry conditions of the protocol suggest that FA forces, as well as FHb forces, were produced. Except for the 9° yaw-angle plot in Figure€7.13, all plots appear initially straight — implying direct proportionality — followed by a curved portion indicating that the adhesion transition pressure had been exceeded. The 9° yaw-angle plot appears straight throughout its length. The friction-mechanism-related characteristics portrayed in Figures€7.11, 7.12, and 7.13 are consistent with the presence of FA and FHb friction-force components in all 17 data sets. We can apply the adhesion-assisted macrohysteresis theory to our findings from examination of Hample’s testing: the adhesion and macrohysteretic friction mechanisms are physically linked, and their generated forces are represented by Equations 12.7 and 12.8, respectively.

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306 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 12.5.2.1.3 Yandell’s testing Figures€5.38 and 5.41 presented forces back-calculated from Yandell’s [15] hysteretic friction testing in dry conditions utilizing a British Pendulum Tester fitted with a rubber test foot. These tests were conducted on rows of triangular brass asperities at angles of 90° and 60° to the rows. The brass asperities exhibited slopes specified in the figures. Because of the macrotexture involved, generation of both FA and FHb friction-force components likely occurred. Identification of the rubber friction mechanisms developed in this testing can be carried out by inspection of Figures€5.38 and 5.41. Extrapolation of five of the plots in the figures evidences y-intercepts, indicating the production of FHs forces in those tests. The presence of microhysteresis in the rubber test foot and the dry conditions of the protocol imply that FA forces, as well as FHb forces, were generated in all six tests. All plots appear straight — implying direct proportionality — without subsequent curvature, suggesting that the adhesion transition pressure had not been exceeded. The friction-mechanism-related characteristics portrayed in the figures are consistent with the presence of FA and FHb friction-force components in all six data sets. We can apply the adhesion-assisted macrohysteresis theory to these results of our back-calculated findings from Yandell’s [15] testing: the adhesion and macrohysteretic friction mechanisms are physically linked, and their generated forces FA and FHb are represented by Equations 12.5 and 12.6, respectively. FN

Tire tread

V Chip

Figure€12.4 Suggested mechanism for dry, adhesion-assisted macrohysteresis in a tire tread on one road chip with a microtexture as indicated. The adhesional area of contact between the tread and pavement occurs where the rubber asperities are compressed onto the chip’s surface at sliding velocity V. As the applied force (F N) increases, the adhesion and macrohysteretic friction forces increase.

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12.5.2.1.4 The adhesion assisted macrohysteresis mechanism in dry conditions Figure€12.4 portrays a suggested mechanism for dry, adhesionassisted macrohysteresis in a tire tread on one road chip with a microtexture as indicated. The adhesional area of contact between the tread and pavement occurs where the rubber asperities are compressed onto the chip’s surface at sliding velocity V. As FN increases, more compression of the rubber asperities takes place and FA increases. Assuming the increase in adhesion occurs in direct proportion to FN, the real area of contact will be growing in a constant, directly proportional manner. In addition to deformation of the rubber asperities, bulk deformation of the tire tread is also taking place.

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Compressing forces pass through the compressed rubber asperities, and the tread volumetrically assumes the chip’s configuration in a localized region. As we have seen, FHb appears to increase in constant, direct proportion to the applied normal load when FA exhibits this behavior. Apparently, the tread volume experiencing bulk deformation as a result of tire sliding increases in constant amounts when the real area of adhesional contact is also growing in equal increments. After the adhesion transition pressure has been reached, FA grows at a diminishing rate with increases in FN, as does the deformed bulk volume and rubber macrohysteresis friction force. 12.5.2.2 Adhesion-Assisted Macrohysteresis in Wet Conditions 12.5.2.2.1 Yager, Stubbs, and Davis testing of radial-belted tires Figure€8.4 presented the side friction forces back-calculated from the Yager et al. [8] radial-belted tire tests in wet conditions. These tests were also conducted on a portland cement concrete test track runway that had a surface that appeared moderately broom-swept; and because of this macrotexture, generation of both FA and FHb friction-force components can be expected. Inspection of Figure€8.4 reveals that the three yaw-angle plots depicted in the figure evidence y-intercepts, implying the production of FHs forces. Development of microhysteresis in these test tires suggests that FA forces, as well as FHb forces, were generated. The 5° yaw-angle plot is initially straight, followed by a curved segment indicating that the adhesion transition pressure had been reached in this test. The plot in Figure€8.17 also supports this conclusion. The 1° and 2° yaw-angle plots in Figure€8.4 are straight throughout their length, indicating direct proportionality. The mechanistic behavior evidenced in Figures€8.4 and 8.17 is consistent with the presence of FA and FHb friction forces in the three data sets. The indication of FA forces is consistent with the development of a nearly dry Zone 3 in accordance with the model discussed in Section 12.2.1. The adhesionassisted macrohysteresis theory can, therefore, be applied to this analysis of the Yager et al. [8] radial-belted tire tests, and their generated forces are represented by Equations 12.5 and 12.6 in the case of the 1° and 2° yaw-angle plots and Equations 12.5, 12.6, 12.7, and 12.8 in the case of the 5° plot. 12.5.2.2.2 Sabey’s testing in which Zone-3 conditions developed Sabey [11] carried out lubricated-rubber coefficient-of-friction studies focusing on the skid resistance of motor vehicle tires, idealizing road-surface aggregate as spherical. Her steel spheres were slid on tire-tread rubber when lubricated with water. Such penetrated sliding produced bulk deformation in the tire-tread rubber, resulting in the development of FHb friction forces. Figure€4.58 depicted Sabey’s results for a 1.27-cm (0.5 in.) diameter sphere. A hyperbolic relationship between μ and FN was displayed. The results of a back-calculation analysis of these data were illustrated in Figure€8.2. The straight-line plot evidences a constant microhysteretic force of approximately

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308 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 28.3 gm (0.25 lb). Generation of this FHs force indicates that dry conditions — and FA forces — developed in this test as a result of breakdown of the lubricating water film. The friction-mechanism-related characteristics portrayed in Figures€4.58 and 8.2 for the 1.27-cm (0.5 in.) diameter sphere are consistent with the presence of FA and FHb friction-force components. The indication of FA forces is also consistent with the development of a nearly dry Zone-3-type condition for this sphere. We can, therefore, apply the adhesion-assisted macrohysteresis theory to these results of our back-calculated findings from this Sabey test: the adhesion and macrohysteretic friction mechanisms are physically linked, and their generated forces are also represented by Equations 12.5 and 12.6. Sabey also investigated the macrohysteretic friction forces developed when sharper road-surface aggregate — idealized as smooth, rigid cones — penetrate tire-tread rubber well lubricated with water. Figure€4.59 presented her coefficient-of-friction results for this protocol. The plots are hyperbolic for interior apex angles of 70°, 90°, 100°, and 160°. The results of a back-calculation analysis of these data were portrayed in Figure€8.3. Extrapolation of the straight-line plots indicates that microhysteretic forces arose in all four cases, suggesting that FHs, FA, and FHb forces developed in a nearly dry Zone-3-type condition on these cones. Figure€8.16 presented log-log plots of our back-calculated findings from Sabey’s cone testing. These plots include points from the extrapolated segments of the lines. We see that evidence of development of the adhesion transition phenomenon is present in each of the three data sets. In these cases, however, the slopes of the plots above the apparent adhesion transition point are 45°, demonstrating that the represented friction forces from single asperities are directly proportional to the applied normal load. Apparently, direct proportionality develops after the PNt pressure has been reached. The friction-mechanism-related characteristics portrayed in Figures€4.59, 8.3, and 8.16 are consistent with the presence of FA and FHb friction-force components. The indication of FHs and FA forces is also consistent with development of nearly dry Zone-3-type conditions on these cones. We can, therefore, apply the adhesion-assisted macrohysteresis theory to the results of our back-calculated findings from these Sabey tests: the adhesion and macrohysteretic friction mechanisms are physically linked. Their generated FA forces appear to be represented by Equations 12.5 and 12.7, while the FHb forces can be represented by Equations 12.6 and 12.8. 12.5.2.2.3 The adhesion-assisted macrohysteresis mechanism in wet conditions Figure€12.5 illustrates a proposed mechanism for wet, adhesion-assisted macrohysteresis in a tire tread on one road chip with a microtexture as indicated. The adhesional area of contact between the tread and pavement occurs where the rubber asperities are compressed by FN onto the chip at sliding velocity V. This model is similar to the one depicted in Figure€12.4, except that liquid is present. Nevertheless, the applied normal load, road-

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309

Friction Analysis in the Design of Rubber Tires way macrotexture drainage characteristics, and tire tread design have combined to produce a nearly dry Zone-3-like area of contact with the chip’s microtexture. In addition to deformation of the rubber asperities, bulk deformation of the tire tread is also taking place. As postulated in regard to Figure€12.4, FHb increases in constant, direct proportion to the applied normal load when FA exhibits this behavior. When FA grows at a diminishing rate with increases in FN, so do the deformed bulk volume and the rubber macrohysteresis friction force. 12.5.2.3 Nonadhesion-Assisted Macrohysteresis on Fully Wetted Surfaces

FN

Tire tread

V Chip

Water

Figure€12.5 Suggested mechanism for wet, adhesion-assisted macrohysteresis in a tire tread on one road chip with a microtexture as indicated. The adhesional area of contact between the tread and pavement occurs where the rubber asperities are compressed onto the chip’s surface at sliding velocity V. The applied force (F N), roadway macrotexture drainage characteristics, and tread design combine to produce a nearly dry Zone-3 area of contact. As the applied force increases, the adhesion and macrohysteretic friction forces increase.

In contrast to conditions in which adhesion-assisted macrohysteresis is generated in a tire tread-pavement system by producing a nearly dry Zone-3-like area of contact with the roadway surface, it appears that non-adhesion-assisted macrohysteresis arises only in fully wetted conditions. Under these specified circumstances, lubricated sliding is such that adhesion is reduced to negligible proportions — physical contact of the two materials is effectively prevented — and the only significant friction present arises from bulk deformation macrohysteresis in the tread. Tire sliding resistance from movement of, or adhesion of, the liquid is considered negligible. When these conditions are met, macrohysteresis in the tire tread is sometimes represented by Equation 12.6:

FHb = FNμHb.

Three previously discussed rubber-friction investigations appear to have developed the fully wetted condition. 12.5.2.3.1 Yager, Stubbs, and Davis testing of bias-ply tires in fully wetted conditions Figure€4.53 presented back-calculated side coefficient-of-friction (μS) values obtained from the Yager et al. [8] bias-ply tire traction measurements in wet

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310 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces conditions. The coefficients were all directly proportional to the applied normal load. It was shown in Chapter 5 that decreasing μ values with increasing FN can be attributed to the presence of a constant microhysteresis force in rubber friction measurements. It can be theorized, therefore, that the Yager et al. [8] bias-ply tire traction measurements contained no rubber microhysteresis components and that no significant adhesion developed when testing these tires in wet conditions. The only significant friction present apparently arose from bulk deformation macrohysteresis in the rubber, represented by Equation 12.6. 12.5.2.3.2 Sabey’s testing with fully wetted surfaces Figure€4.58 depicted Sabey’s [11] results for the 0.48-cm (3/16-in.) and 0.64cm (0.25 in.) diameter spheres. The corresponding plots for these data sets are parabolic. By inspection, one can expect that no rubber microhysteresis or adhesion friction forces developed in these tests. Figure€8.2, presenting findings from a back-calculation analysis of the two spheres’ friction data, provides corroboration for this belief: the plots for the 0.48-cm (3/16-in.) and 0.64-cm (0.25 in.) diameter spheres are straight — evidencing direct proportionality — but do not intersect the y-axis at a positive value when extrapolated. There is no indication that either FHs or FA forces were generated in these protocols, allowing us to theorize that the only significant friction present arose from bulk deformation macrohysteresis in the rubber, represented by Equation 12.6. It must be emphasized, however, that Equation 12.6 should be considered applicable only to tire-pavement systems in which pavement macrotexture is of the broom-swept type, or at least approximates this roughness. Equation 12.6 does not apply to the macrohysteretic conditions discussed by Bowden and Taber [21]. 12.5.2.3.3 Greenwood and Tabor’s testing with fully wetted surfaces Bowden and Tabor [21] discussed Greenwood and Tabor’s [22] testing involving sliding steel spheres on soap-lubricated rubber. These considerations were presented in detail in Section 3.10. The rubber-friction-force relationship that successfully quantified the test data took the following form:

FHb = c(FN)4/3.

(12.9)

While Greenwood and Tabor also tested with fully wetted surfaces, it is clear that Equations 12.6 and 12.9 are not equivalent. Apparently, the Greenwood and Tabor macrotexture — that is, the sliding spheres — generated bulk deformation of the rubber in which the volume experiencing such deformation did not increase in direct proportion to the applied normal load. The deformational differences accounting for the two types of macrohysteresis-force generation may be associated with testing velocity. While Greenwood and Tabor’s sliding velocity was a few millimeters per second,

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311

Sabey [11] employed a “high speed” of 6.6 km/h (6 fpsec), and Yager et al. [8] utilized a velocity of 185.3 km/h (100 knots) in their testing. As implied in the traditional tire-slip plot depicted in Figure€12.2, at lower sliding speeds, the frictional resistance increases with velocity. This arises because, in a given time interval, more slip-resisting pavement surface must be traversed. At a certain speed, however, the curve reaches a maximum and begins to decline. Kummer [18] attributed this phenomenon in dry conditions to stick-slip and temperature; that is, the bulk volume of deforming tread begins to diminish with increasing speed, while at the same time, frictional heating softens the tire rubber. Inasmuch as we are considering fully wetted conditions, it appears reasonable to expect that frictional-heating effects would become less important, leaving changes in the bulk-deformation-hysteresis mechanism as a principal reason for the different FHb relationships. At low velocities, FHb can sometimes be represented by Equation 12.9; but at higher speeds, Equation 12.6 could apply. This leads to another theory: the rubber bulk-deformationhysteresis mechanism can be different at different sliding velocities. 12.5.2.3.4 The non-adhesion-assisted macrohysteresis mechanism in fully wetted conditions Figure€12.6 presents a proposed mechanism for non-adhesion-assisted macrohysteresis in a tire tread sliding at velocity V and compressed by FN onto one road chip with a microtexture as indicated. Because of the fully wetFN ted conditions, no adhesion between the tread and pavement develops. A partially dry Zone-3-like area of contact with the chip’s microtexture Tire tread is not produced. The liquid present prohibits physical contact of the tire and pavement surface. Bulk deformation of the tread is the only sigV nificant tire-friction mechanism to Chip develop. Water 12.5.2.3.5 Velocity dependence of the macrohysteresis friction mechanism The above analysis suggests that, in wet-roadway conditions, the mechanism of FHb-force development changes with increases in testing velocity. It has long been known from testing that rubber-tire coefficients of friction μ evidence general declines with increasing velocity. If

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Figure€12.6 Suggested mechanism for wet, non-adhesionassisted macrohysteresis in a tire tread on one road chip with a microtexture as indicated at sliding velocity V. Because of the fully wetted conditions, the liquid present prohibits physical contact between the tread and pavement. As the applied force (F N) increases, so does the macrohysteretic friction force.

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312 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces friction analysis in the design of tire-pavement systems is to be carried out on a scientific basis, changes in the expression representing macrohysteretic traction in wet conditions must be taken into account. It appears likely that such mechanism changes can develop on both portland cement concrete and asphalt surfaces. Figure€12.7 presents coefficient-of-friction results from a correlation study [23] to determine if ground-vehicle pavement testers can be substituted for specially instrumented aircraft to assess wet-runway slipperiness. It has been considered too expensive and impractical to utilize such aircraft for this purpose [23]. The data in Figure€12.7 were obtained on smooth portland cement concrete that was either wetted or flooded with water. Five different ground-vehicle (roadway-pavement) testers were employed, along with two specially instrumented aircraft. Although the results, reported as μ vs. ground speed, exemplify inadvertent misapplication of the laws of metallic friction to rubber tires, the data trends are instructive. In all cases, μ decreases with speed. Figure€12.8 displays the reported μ vs. ground speed values for grooved asphalt. As in the concrete testing, a general decline in μ vs. speed is seen. 12.5.3 The Load Dependence of Tire-Tread Rubber Friction In 1942, as one conclusion of their study on the frictional properties of rubber, Roth et al. [24] stated that, “The coefficients [of rubber friction] decrease slightly with pressure” (p. 455). Since that time, the perception that the load dependence of the coefficient of rubber friction (μ) on FN and PN is small has persisted. While this can sometimes be true in the mathematical sense,

Coefficient of Friction–µ

1.0

Test vehicle 1 GM skid trailer

4 1

0.8

3

0.6

5

0.4

6 2

0.2 0

8 0

50

2 GM skid trailer 3 Swedish skiddometer

µB,skid

4 NASA DBV 5 MU-meter

µB,skid µS

6 Miles trailer

7

100

Ground Speed, Knots

150

Tire test mode µB,max

7 CV-990 aircraft 8 F-4D aircraft

µB,max (13% slip)

µB,skid µeff µeff

Figure€12.7 Coefficient-of-friction results from a correlation study to determine if ground-vehicle pavement testers can be substituted for specially instrumented aircraft to assess smooth-concrete runway slipperiness in wet and flooded conditions. (From Horne, W.B., Status of Runway Slipperiness Research, National Aeronautics and Space Administration, N77-18092, Washington, D.C., 1976.)

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313

Friction Analysis in the Design of Rubber Tires 4

Coefficient of Friction–µ

1.0

3

0.8

5

6

0.4

4 NASA DBV 5 MU-meter

7

0.2

8

0

50

Tire test mode µB,max

2 GM skid µB,skid trailer 3 Swedish µB,max (13% slip) skiddometer

2

0.6

0

Test vehicle 1 GM skid trailer

1

100

Ground Speed, Knots

6 Miles trailer 7 CV-990 aircraft 8 F-4D 150 aircraft

µB,skid µS µB,skid µeff µeff

b

Antiskid

Figure€12.8 Coefficient-of-friction results from a correlation study to determine if ground-vehicle pavement testers can be substituted for specially instrumented aircraft to assess grooved-asphalt runway slipperiness in wet and flooded conditions. (From Horne, W.B., Status of Runway Slipperiness Research, National Aeronautics and Space Administration, N77-18092, Washington, D.C., 1976.)

the conclusion has been drawn by inadvertent misapplication of the laws of metallic friction to rubber and the use of μ values as material properties of tire-tread compounds and other rubber products. In nearly all the rough-surface testing analyzed in this book, once the microhysteretic friction force (FHs) is subtracted from the total friction force developed (FT), the adhesion (FA) and macrohysteretic (FHb) friction forces are seen to be directly proportional to the applied load at least initially. Equal increases in FN and PN produce equal increases in FA and FHb. In such cases, the load dependence of rubber friction is not necessarily small. 12.5.4 Use of the Unified Theory for Friction Analysis in Design of Tire-Pavement Systems The microhysteresis contribution to rubber friction can be quantitatively separated from the adhesion, macrohysteresis, and wear components when the only independent variable in controlled testing is FN or PN. Because of this characteristic of rubber, utilization of the unified theory for friction analysis in the design of tire-pavement systems would allow a scientifically based approach to be taken that is founded on the physical mechanisms producing the traction forces developed in the tire contact patch. A fundamental outline of a process involving the steps necessary to allow utilization of the unified theory in the design of tire-pavement systems can now be presented. This approach will require assembling an extensive library of design data, some of which is not currently available. It will

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314 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces also necessitate heightened interdisciplinary cooperation between the tiredesign and pavement-design communities. The individual steps in the proposed process mimic those often found in the initial aspects of engineering design. 12.5.4.1 Process Brief The process brief is a statement of intent. Our intent is to outline a means by which the unified theory can be utilized for friction analysis in the design of tire-pavement systems. 12.5.4.2 Process Specifications The process specifications are a list of action-item requirements necessary to allow application of the unified theory to friction analysis in the design of tire-pavement systems. A suggested preliminary list of specifications is presented in Table€12.1. 12.5.4.2.1 Theoretical basis for application of the unified theory Application of the unified theory requires that the steps taken to allow its use be focused on the friction-producing mechanisms generating the traction forces developed in the tire contact patch and on the quantification of these forces. This, in turn, necessitates that the appropriate relationships expressing the traction forces be employed. The relationship expressing the unified theory of rubber friction can be stated as

FT = FHs + FA + FHb + FC,

(12.10)

where: FT = total frictional resistance developed between sliding rubber and a harder material; FA = frictional contribution from the combined adhesive forces of the two surfaces; Table€12.1 Specifications for Suggested Process To Allow Use of the Unified Theory for Rubber Friction Analysis in the Design of Tire-Pavement Systems Theoretical Basis for Application of the Unified Theory Action items for the tire-design community Action items for the pavement-design community Action-item concept design Action-item detail design

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FHs = frictional contribution from surface deformation hysteresis (microhysteresis); FHb = frictional contribution from bulk deformation hysteresis (macrohysteresis); and FC = cohesion loss contribution from rubber wear.

When tire cohesion losses due to wear are negligible in the short term, Equation 12.10 reduces to

FT = FHs + FA + FHb.

(12.11)

It is suggested that Equation 12.11 should be employed as the general relationship quantifying the unified theory. 12.5.4.2.2 Action items for the tire-design community Two action items for the tire-design community are suggested, both of which would be undertakings of considerable magnitude:

1. Review presently used expressions for assessing the adequacy of tire traction that misemploy the coefficient of rubber friction μ. Reformulate the technical approaches to these assessments and replace them with one or more based on FT, the total friction force generated.



2. Review current tire-testing practices, identify those tests that purport to quantify friction in the contact patch, and redesign such protocols and associated equipment to measure the friction terms in Equation 12.11.

12.5.4.2.3 Action items for the pavement-design community Two action items for the pavement-design community are proposed, which also would be undertakings of considerable magnitude.

1. Review the presently used technical approaches and associated equations for assessing the adequacy of pavement traction utilizing the coefficient of rubber friction μ. Reformulate these approaches to base them on FT, the total friction force generated.



2. Review current pavement-testing practices, identify those tests that purport to quantify friction in the tire contact patch, and redesign such protocols and associated equipment to measure the friction components in Equation 12.11.

12.5.4.3 Action Item Concept Design Identify and outline the key steps in their proper order necessary to carry out the action items suggested above as efficiently as possible.

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316 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces While the exact details involved in these steps need not be determined at this stage, it is beneficial to consider the process specifications as well as the downstream activities needed to carry out the above-mentioned action items. Depending on the circumstances involved, it may be advantageous to design a number of different viable concepts for accomplishing the desired action items and to evaluate them to determine the most suitable approach to be developed further. Concept design is often a two-stage process of generation and evaluation. Preliminary discussions between the tire-design and roadway-design communities may be appropriate at this stage. 12.5.4.4 Action Item Detail Design Develop the chosen action item concept design in detail. The steps necessary to accomplish the action items are now designed in detail. This may well include organizational and/or personnel assignments, task allocation, location, equipment involved, field testing, cost projections, and timelines. Interdisciplinary partnerships between the tire-design and roadway-design communities are called for at the stage to accomplish the desired tasks in a manner producing technical results with the maximum reasonable degree of scientific certainty.

12.6

Chapter Review

This chapter focused on application of the unified theory of rubber friction detailed in previous pages to tire-pavement systems. One intent of the book is to improve the analysis of friction in tire-pavement systems as they are presently designed and constituted; however, suggestions for potentially desirable changes in tires and pavements stemming from application of the unified theory will not be made, such possibilities being beyond the scope of this book. Nevertheless, improving our understanding of the traction forces generated in the tire contact patch through scientifically based analysis of the friction mechanisms developed therein can be useful in reexamining existing roadways and perhaps serve as a starting point in improving present design practice. The chapter first addressed the importance of rubber microhysteretic forces in tires operated on wet roadways. This topic was followed by a discussion of the need to reformulate the traditional rubber friction coefficient vs. tireslip relationship. We then considered measurement of tire microhysteresis on wet pavements, followed by a suggested process through which the unified theory can be applied to assist in the analysis of friction in the design of tire-roadway systems.

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12.6.1 Importance of Tire Microhysteresis on Wet Pavements 12.6.1.1 Three-Lubrication-Zones Concept The Three-Lubrication-Zones Concept is a frequently used model of water displacement by a rolling or sliding tire on wet pavement. Figure€12.1 illustrates this concept. It is considered that while some encountered water is displaced to the front of the moving tire, the tire rides on an unbroken water film in lubrication Zone 1, as some of this water is gradually squeezed out the sides. The middle Zone 2 is one of transition in which initial physical contact between the tire and the pavement develops, while in Zone 3 only a thin water film at most remains, and the tire makes contact with the roadway microtexture through this film. It has been traditionally thought that much of the wet-traction skid resistance develops in Zone 3. The relative size of these zones varies with speed. If speed becomes excessive for given conditions, hydroplaning can occur. 12.6.1.2 Traditional Wet-Roadway Texture Analysis Studies have traditionally concluded that wet-roadway skid resistance is governed by pavement macroroughness regarding removal of bulk water and pavement microroughness in the role of creating real areas of tire contact and adhesive traction. A British study [4] examining the seasonal variation of wet-roadway skid resistance indicated that wet traction rose to a maximum in the winter and fell to a minimum in the summer months. Photomicrographs of in-service pavements revealed that surface microroughness also increased to a maximum in winter due to frost and other natural weathering action on the road aggregate during this period. On the other hand, traffic-polishing of the roadway’s aggregate was dominant during the summer, removing the aggregate’s microroughness to a considerable degree. These trends correlate well with the number of wet-skidding incidents in Britain — fewer in winter and a greater number in summer. The same climatologically related phenomenon has been observed under controlled conditions at a highway pavement research facility in the United States. Beginning in 1974, the Transportation Research Center of Ohio became involved in a U.S. Federal Highway Administration program designed to develop test centers where skid-trailers could be calibrated on skid pads and modified to improve their compliance with the American Society for Testing and Materials’ Test Method for Skid Resistance of Paved Surfaces Using a Full-Scale Tire (E 274) [5]. The program’s intention was to provide primary reference surfaces (PRSs) on which the skid-trailers could be tested. The skid pads were operated over a 9-year period. They also evidenced a seasonal variation in skid resistance, generating maximum average monthly traction values in the winter, which fell to a minimum in the summer months. The winter increases are consistent with an increased contribution from microhysteresis to skid resistance measurements made during that season, when harsher weather apparently produced degradation-roughening of

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318 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces the pad surfaces. It has been generally recognized [6] by the roadwaydesign community that availability of an adequate microtexture on the road surface aggregate is required to provide a reasonably safe wet-driving environment. 12.6.1.3 Importance of Aircraft Tire Microhysteresis on Wet Pavement Just as the importance of a pavement’s microtexture regarding tire roadholding ability in wet conditions was accepted by roadway design engineers [6], the importance of aircraft runway and taxiway microtexture to pilots during landing and taxiing in wet conditions has been accepted by the aviation community. Yager [7] spoke to this issue in his 1990 article concerning the tire-runway friction interface. Neither of these communities, however, had developed a means by which the microhysteretic contribution to tire traction could be quantified. Such quantification is possible through application of the unified theory of rubber friction. 12.6.1.4 Quantifying Tire Microhysteresis on Wet Pavement Using the Unified Theory of Rubber Friction Figure€8.4 presented results from our back-calculation analysis of the Yager et al. [8] wet testing of aircraft tires at three yaw angles. The measured friction force vs. applied load plots in the figure evidenced development of a rubbertire microhysteresis force in each of the three tests. While a literature search was unable to locate any reports of friction testing of automobile or truck tires on wet pavements suitable for a complete microhysteretic analysis, a number of laboratory wet-tire-tread studies examined in this book produced results indicating development of a constant microhysteresis force in such circumstances. 12.6.1.5 Corroboration for the Three-Lubrication-Zones Concept Our findings from analysis of the laboratory studies involving wet testing provide corroboration for Gough’s [2] Three-Lubrication-Zones concept of water displacement by a rolling or sliding tire. Zone 3 in Figure€12.1, at the rear of the tire, is considered dry or nearly so. According to the unified theory of rubber friction presented in this book, physical contact between tire and pavement surface — allowing adhesion (FA) forces to develop between them — is required if microhysteretic forces are to arise. The production of microhysteresis forces in these three wet-traction studies implies that such dry contact occurred. 12.6.2 Reformulation of the Friction Force vs. Tire-Slip Relationship Figure€12.2 presents a traditional depiction of the developed friction coefficient vs. tire-slip relationship during braking of a rolling tire to slow its

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rotation, with corresponding deceleration of the moving vehicle. In this case, by inadvertently misapplying the laws of metallic friction to a vehicle-tirepavement system, the coefficient of friction for tire slip μ is plotted against the tire slip ratio sR. Figure€12.2 involves utilization of a coefficient μAV to represent an average tire-pavement friction value in the slip-ratio range of 0.1 to 0.5. As seen in the figure, this range is thought to encompass the maximum frictional resistance generated, μMAX. In this plot, measured μAV coefficients for different pavements and tires from such testing are utilized. The indicated tire-pavement traction characteristics thought to be revealed by these tests are relied on, and seemingly reasonable safety-related, action-producing conclusions are drawn from these implied characteristics. As we have shown, however, the μ relationship is not scientifically based. The traditional approach to quantifying tire-slip relationships is not founded on the physical mechanisms producing the friction forces being generated during tire slip. Reformulation of the tire-slip relationship utilizing the unified theory of rubber friction encompassing all the friction forces arising in these circumstances is needed. Such reformulation must be based on appropriate testing, testing in which the possible presence of tire microhysteresis is determined. 12.6.3 Measuring Tire Microhysteresis on Wet Pavements in the Design Process To determine the possible presence of tire microhysteresis in given wetpavement conditions, access to readily available, conveniently used testing apparatus capable of measuring this rubber friction force in the field is desirable. Proceeding on the basis that the rubber microhysteresis force FHs is independent of both applied normal force and pressure, such a testing device could be portable and simple to operate. While a search for existing suitable friction testers failed to identify such apparatus, there is one device that could likely be modified to meet these requirements and a second potentially practicable tester that is not now used, but which could be resurrected if sufficient demand arose. These are the British Pendulum Tester and the North Carolina State University Variable-Speed Friction Tester, respectively. 12.6.4 Application of the Unified Theory to Analysis of Friction in the Design of Tire-Pavement Systems 12.6.4.1 Potential Benefits from Application of the Unified Theory to Friction Analysis Application of the unified theory of rubber friction promotes accuracy in design calculations by helping eliminate the all-too-common error made by some engineers who believe that a decreasing coefficient-of-rubber.

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320 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces friction (μ) under increasing loading means that tire traction is decreasing. This belief is incorrect. Friction is still increasing, but at a decreasing rate. Employment of the unified theory can provide the means to maximize the adhesion, microhysteresis, and macrohysteresis friction components of rubber tires on an optimal, comprehensive, and scientific basis. Use of the unified theory affords the opportunity to utilize a systems approach to friction analysis in the design of rubber tires and pavements in both dry and wet conditions. In this case, “systems approach” means that properties of the tread and pavement are selected to complement each other for optimum traction. Detection of the presence of microhysteresis in a test tire in wet conditions, which can only arise from solid-to-solid contact, tells us that the roadway microtexture has likely penetrated the liquid. Because microhysteresis depends on adhesion, the desirable presence of the adhesion friction component is also indicated. 12.6.4.2 Rubber Macrohysteresis Mechanisms It is traditionally considered that a principal benefit of pavement macrotexture is to allow rapid water drainage from the surface; however, analysis of the data presented in these pages leads to the conclusion that the macrohysteresis force, developed on rough pavement, is also a significant traction component. At least two different rubber macrohysteretic friction mechanisms appear to exist: (1) the adhesion-assisted form in wet and dry conditions and (2) the non-adhesion-assisted type in wet conditions. 12.6.4.2.1 Adhesion-assisted macrohysteresis on dry surfaces Adhesion between rubber and a pavement can be considered as a pull-off phenomenon in which adhesive forces attempt to hold together the two paired materials. Figure€12.3 illustrates a visualization of this model. In this concept, the extent of draping of a tire tread over a dry pavement’s macrotexture is augmented by adhesion between the two surfaces, such that physical contact between them is greater than that which would be produced by the applied load acting alone. This chapter presented evidence in support of a new theory — that the mechanism of adhesion-assisted macrohysteresis in tires can be physically linked to the adhesion friction mechanism in both dry and wet conditions. It appears that, when the adhesion friction force (FA) is directly proportional to the applied load (FN) on rough pavements, so is the macrohysteresis (FHb) friction force. When the tire’s adhesion transition pressure on rough pavement is reached, however, the adhesion-assisted macrohysteretic friction transitions accordingly, and neither the adhesion friction force nor the macrohysteresis friction force is directly proportional at greater loads. Figure€12.4 presents a suggested mechanism for adhesion-assisted macrohysteresis in a tire tread on a dry road chip. The adhesional area of contact between the tread and pavement occurs where the rubber contacts the chip’s

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surface at sliding velocity V. As the load (FN) increases, more compression of the rubber takes place and the adhesion force increases. In addition to adhesional draping of the tread over the road chip, bulk deformation of the rubber is also taking place. Compressing forces pass through the rubber, and some of the tread’s bulk volumetrically assumes the chip’s configuration in a localized region. Apparently, the tread volume experiencing bulk deformation as a result of tire sliding increases in constant amounts when the real area of adhesional contact is also growing in equal increments. After the adhesion transition pressure has been reached, the adhesive force grows at a diminishing rate with increases in load, as does the deformed bulk volume and rubber macrohysteresis friction force. 12.6.4.2.2 Adhesion-assisted macrohysteresis in wet conditions Figure€12.5 illustrates an envisaged mechanism for wet adhesion-assisted macrohysteresis in a tire tread on one road chip. The adhesional area of contact between the tread and pavement occurs where the rubber is compressed by FN onto the chip at sliding velocity V. This model is similar to the one depicted in Figure€12.4, except that liquid is present. Nevertheless, the applied load, pavement macrotexture drainage characteristics, and tire tread design have combined to produce a nearly dry Zone-3 area of contact with the chip, as bulk deformation of the rubber takes place. The Zone-3 area of contact allows adhesive friction forces to develop. 12.6.4.2.3 Non-adhesion-assisted macrohysteresis on fully wetted surfaces In contrast to conditions in which adhesion-assisted macrohysteresis is generated in a tire tread-pavement system by producing a nearly dry Zone-3 area of contact with the roadway surface, non-adhesion-assisted macrohysteresis arises only in fully wetted conditions. Under these specified circumstances, lubricated tire slipping or sliding is such that adhesion is reduced to negligible proportions — physical contact of the two materials is effectively prevented — and the only significant friction present arises from bulk deformation macrohysteresis in the tread. Tire slipping or sliding resistance associated with the contaminating liquid is considered negligible. Figure€12.6 presents a proposed mechanism for non-adhesion-assisted macrohysteresis in a tire tread sliding at velocity V and compressed by FN onto a road chip. Because of the fully wetted conditions, the liquid present prohibits physical contact of the tire and pavement surface. 12.6.5 The Load Dependence of Rubber Tire-Tread Friction In 1942, as one conclusion of their study on the frictional properties of rubber, Roth et al. [24] stated that, “The coefficients [of rubber friction] decrease slightly with pressure” (p. 455). Since that time, the perception that the load dependence of the coefficient of rubber friction (μ) is small has persisted. Put another way, the friction produced by a set of tires supporting a motor vehicle has little to do with the weight of that vehicle. This conclusion has

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322 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces been drawn by inadvertent misapplication of the laws of metallic friction to rubber and the incorrect use of μ values as material properties of tire-tread compounds. In most of the testing analyzed in this book, once the microhysteretic friction force (FHs) is subtracted from the total friction force developed (FT), the adhesion (FA) and macrohysteretic (FHb) friction forces are seen, at least initially, to be directly proportional to the applied load. Equal increases in loading produce equal increases in FA and FHb. In such cases, the load dependence of rubber friction is not necessarily small, e.g., twice the load generates twice the friction. 12.6.6 Use of the Unified Theory for Friction Analysis in Design of Tire-Pavement Systems The microhysteresis contribution to rubber friction can be quantitatively separated from the adhesion, macrohysteresis, and wear components when the only independent variable in controlled testing is applied force or pressure. Because of this characteristic of rubber, utilization of the unified theory for friction analysis in the design of tire-pavement systems would allow a scientifically based approach to be taken that is founded on the physical mechanisms producing the traction forces developed in the tire contact patch. A fundamental outline of a process involving the steps necessary to allow utilization of the unified theory in the design of tire-pavement systems was presented. This approach requires assembling an extensive library of design data, some of which is not currently available. It will also necessitate heightened interdisciplinary cooperation between the tire-design and pavementdesign communities. The individual steps in the proposed process mimic those often found in the initial aspects of engineering design. 12.6.6.1 Process Brief The process brief is a statement of intent. The intent is to outline a means by which the unified theory can be utilized for friction analysis in the design of tire-pavement systems. 12.6.6.2 Process Specifications The process specifications are a list of action-item requirements necessary to allow application of the unified theory to friction analysis in the design of tire-pavement systems. A suggested preliminary list of process specifications is presented in Table€12.1.

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323

References





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1. Meyer, W.E. and Schrock, M.O., Tire Friction, A State-of-the-Art Review, Autom. Saf. Res. Progr., Rept. S34, Pennsylvania State University, DOT Hs-800 485, 1969. 2. Gough, V.E., A tyre engineer looks critically at current traction physics, in The Physics of Tire Traction-Theory and Practice, Hays, D.F. and Browne, A.L., Eds., Plenum Press, New York, 1974, chap. III. 3. Moore, D.F., The Friction of Pneumatic Tyres, Elsevier, New York, 1975, 111. 4. Bond, R., Lees, G., and Williams, A.R., An approach towards the understanding and design of the pavement’s textural characteristics required for optimum performance of the tyre, in The Physics of Tire Traction-Theory and Practice, Hays, D.F. and Browne, A.L., Eds., Plenum Press, New York, 1974, chap. IV. 5. Whitehurst, E.A. and Neuhardt, J.B., Time-history performance of reference surfaces, in The Tire Pavement Interface, ASTM STP 929, Pottinger, M.G. and Yager, T.J., Eds., American Society for Testing and Materials, West Conshohocken, PA, 1986, 61. 6. Williams, A.R., A review of tire traction, in Vehicle, Tire, Pavement Interface, Henry, J.J. and Wambold, J.C., Eds., American Society for Testing and Materials, West Conshohocken, PA, 1992, 125. 7. Yager, T.J., Tire/runway friction interface, Paper 901912, Emerging Technologies in Aircraft Landing Gear, Tanner, Ulrich, Medzorian, and Morris, Eds., SAE International, PT-66, Warrendale, PA, 1997. 8. Yager, T.J., Stubbs, S.M., and Davis, P.M., Aircraft radial-belted tire evaluation, Paper 901931, Emerging Technologies in Aircraft Landing Gear, Tanner, Ulrich, Medzorian, and Morris, Eds., SAE International, PT-66, Warrendale, PA, 1997. 9. Thirion, P., Les coefficients d’adhérence du caoutchouc, Rev. Gén. Caoutch., 23, 101, 1946. 10. Clayton, J.H., An Investigation and Modification of a Pavement Skid-Test Trailer, M.S. thesis, The University of Tennessee, Knoxville, 1962. 11. Sabey, B.E., Pressure distributions beneath spherical and conical shapes pressed into a rubber plane, and their bearing on coefficients of friction under wet conditions, Proc. Roy. Soc. A, 71, 979, 1958. 12. Horne, W.B., Yager, T.J., and Taylor, G.R., Review of Causes and Alleviation of Low Tire Traction on Wet Runways, NASA Technical Note TN D-4406, Washington, D.C., 1968. 13. Limpert, R., Motor Vehicle Accident Reconstruction and Cause Analysis, 5th ed., Michie, Charlottesville, VA, 2005. 14. Giles, C.G., Sabey, B.E., and Cardew, K.H.F., Development and performance of the portable skid-resistance tester, in Symposium on Skid Resistance, American Society for Testing and Materials, Philadelphia, 1962, 50. 15. Yandell, W.O., A new theory of hysteretic sliding friction, Wear, 17, 229, 1970. 16. Sigler, P.A., Geib, M.N., and Boone, T.H., Measurement of the slipperiness of walkway surfaces, J. Res. Nat. Bur. Stds., 40, 339, 1948. 17. Mullen, W.G., Whitfield, J.K., and Matlock, T.L., Implementation for Use of Variable Speed Friction Tester and Small Wheel Circular Track Wear and Polishing Machine for Pavement Skid Resistance, Report ERSD 110-76-2, Highway Research Program, North Carolina State University, Raleigh, NC, 1977.

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324 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 18. Kummer, H.W., Unified Theory of Rubber and Tire Friction, Engineering Research Bulletin B-94, The Pennsylvania State University, University College, PA, 1966. 19. Persson, B.N.J., Sliding Friction, Physical Principals and Applications, Springer-Verlag, Berlin, 2000. 20. Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955. 21. Bowden, F.P. and Tabor, D., The Friction and Lubrication of Solids, Part II, Clarendon Press, Oxford, 1964. 22. Greenwood, N.A. and Tabor, D., The friction of hard sliders on lubricated rubber: the importance of deformation losses, Proc. Phys. Soc., 71, 989, 1958. 23. Horne, W.B., Status of Runway Slipperiness Research, National Aeronautics and Space Administration, N77-18092, Washington, D.C., 1976. 24. Roth, F.L., Driscoll, R.L., and Holt, W.L., Frictional properties of rubber, J. Res. Nat. Bur. Stds. 28, 439, 1942.

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13 Nonscientific Application of the Laws of Metallic Friction to Footwear Outsole-Walking Surface Pairings

13.1

Introduction

It is common engineering practice for the laws of metallic friction to be applied to rubber products. A principal purpose of this book is to demonstrate that this inadvertent misapplication is not scientifically correct. A second purpose is to introduce a unified theory of rubber friction incorporating the fourth basic elastomeric friction force: surface deformation hysteresis, or microhysteresis, and to exemplify the theory’s use in engineering applications. Few individuals would dispute the proposition that, in the interest of walking safety, further progress toward developing maximum understanding and control of the slip-resisting characteristics of footwear-walking surface pairings is desirable. This chapter is intended to assist in accomplishing that goal by suggesting areas in which use of the laws of metallic friction in slip-resistance testing, analysis, and design can be replaced with a scientifically based, mechanistically focused, unified theory of rubber friction. (This chapter and the next will be confined to discussions of footwear with elastomeric outsoles, that is, bottoms that are rubber-like in nature.) In the preface to a 1992 article reporting findings of the ASTM Committee F-13 workshop held at Bucknell University in 1990, the F-13 Task Force on Slip Testers stated [1]: There are as many methods for measuring walkway and footwear friction as there are ASTM committees, not to mention the procedures developed outside ASTM. Unfortunately, as the debate goes on about which test method is best, many people are hurt or killed as a result of falling accidents. The National Safety Council publication, Accident Facts, 1990 edition, stated that 12,400 died as a result of falls. (p. 21)

More than 15 years later, this debate is still going on, and little progress has been made toward identifying the best testers and testing methods for accurately quantifying walking-surface slip resistance. 325

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326 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces The most reliable means of fostering comparability of friction measurements for use in identifying the best slip-resistance test methods and devices is to utilize a scientifically based approach that focuses on the friction mechanisms that develop when an outsole contacts a walking surface. This chapter focuses on elements of walking-surface slip-resistance testing that appear amenable to improvement through application of the unified theory of rubber friction. As background for a discussion of the traditional misapplication of the laws of metallic friction to walking-surface slip-resistance testing, we review our comparison of the characteristics of rubber friction to those of metallic friction. A synopsis of the effects of microhysteretic friction forces in rubber is then presented, followed by an examination of factors relevant to slipresisting-testing data comparability. Next, we address slip-resistance-testing devices and ASTM testing methods that inadvertently misapply the laws of metallic friction to rubber.

13.2

Comparing the Characteristics of Rubber Friction to Metallic Friction

Chapter 4 showed that the laws of metallic friction, exemplified by the constant coefficient of friction,

µ = FT/FN,

(13.1)

do not scientifically apply to rubber. Because of the deformational and constitutive differences between rigid metals and viscoelastic rubber, the friction-force-producing mechanisms of these two materials are physically and chemically different. Chapter 2 demonstrated that the constant coefficientof-friction equation is a material property of metals. Chapter 6 showed that rubber friction ratios, when properly constituted, represent mechanistic behavior indicators. Use of the constant (metallic) coefficient-of-friction equation for friction analysis in the design of footwear outsoles and walking surfaces can produce the following undesirable consequences:

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1. Application of the laws of metallic friction to rubber can misstate the meaning of decreases in the magnitude of rubber coefficients. A diminishing metallic coefficient demonstrates that frictional resistance to movement between metals is also decreasing. Decreases in the magnitude of rubber coefficients calculated by Equation 13.1 often mean that the rate of increasing frictional resistance to motion is diminishing.



2. Expressions for µ involving concurrently acting rubber friction mechanisms can be non-additive and require a different approach to quantify true sliding resistance, one in which coefficients are not involved and only forces are considered.

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Nonscientific Application of the Laws of Metallic Friction

13.3

327

Effects of the Development of Microhysteretic Slip-Resistance Forces on Rubber-Friction Analysis

13.3.1 Development of the Microhysteretic Slip- Resistance Force in Pedestrian Ambulation Chapter 5 continued our examination of the scientific research carried out to understand more fully the basic mechanisms of rubber friction. We employed the back-calculation technique to analyze rubber coefficient-of-friction (μ) test results published in the graphical form of μ vs. the force or pressure applied to rubber specimens during such testing. We found in our graphs that, in the lower loading range, all the published data sets we reviewed yielded straight lines when plotted as the total measured friction force vs. applied normal force or pressure. Extrapolation of the straight-line portions of the plots depicting FT vs. FN or PN to the y-axis yielded y-axes intercept values. These intercepts were found in data generated from rubber sliding on both smooth and rough surfaces. We considered that such y-axis intercepts quantify a surface-deformationhysteresis friction force (FHs) in rubber. Because FHs is indicated to be constant and independent of both the force and pressure applied to rubber sliding on smooth and rough surfaces, we considered that surface deformation hysteresis is a distinct rubber friction mechanism, different from the adhesion and bulk deformation hysteresis mechanisms we have previously discussed. Most rubber-friction test results published in the graphical form of the coefficient of friction vs. the force or pressure applied to rubber specimens while sliding yield downwardly curved lines showing a decrease in this coefficient with increasing loading, at least initially. It was shown that inadvertent inclusion of the microhysteresis forces present in test data producing such plots can be responsible for this curvature. Accounting for FHs by subtracting its constant value from the total friction force generated allowed the adhesion and macrohysteresis forces to be more easily differentiated and quantified. 13.3.2 Development of the Adhesion Transition Phenomenon in Pedestrian Ambulation Chapter 6 showed that the adhesion friction force between rubber and harder materials increases with growth in the real area of mutual contact developed in such pairings. When footwear outsoles contact smooth walking surfaces, the adhesion friction force in rubber (FA) can be expressed by

FA = μA(FN),

(13.2)

where μA is the constant adhesion friction ratio.

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328 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Equation 13.2 applies when the primary result of increases in FN or PN is to produce new areas of contact between rubber and its paired surfaces. This occurs in the lower loading range. With such pairings, however, a change in the adhesion friction-force-producing mechanism usually takes place — that is, when the adhesion transition pressure PNt is reached. At that point, Equation 13.2 is no longer valid. We have also seen that when the predominant result of increasing FN or PN is to expand existing areas of contact between rubber and its paired surfaces, the generalized Hertz equation applies. This relationship, applicable in rubber friction analysis and design at PNt and above, can be expressed as,

FA = cA(FN)m.

(13.3)

Chapters 7 and 8 examined the development of the rubber adhesiontransition mechanism in dry and wet conditions. Evidence was discussed indicating that this phenomenon can arise in outsole materials sliding on glycerol-contaminated smooth floors. Figure€8.8 presented our back-calculation results from Grönqvist’s [2] data in the form of plots of μA vs. applied normal load from wet testing of nitrile rubber triangular and waveform shoe tread patterns on stainless steel. Figure€8.10 depicted plots of our back-calculation results from Grönqvist’s [2] data in the form of adhesion friction ratios vs. applied normal load from testing of glycerol-contaminated styrene rubber triangular and waveform shoe tread patterns on stainless steel flooring. The waveform pattern evidenced development of the adhesion transition phenomenon in both figures, while the triangular pattern exhibited a hyperbolic segment at higher loads only in Figure€8.8. Testing is necessary to determine when the adhesion transition phenomenon develops in ordinary pedestrian ambulation; nevertheless, it is clear that Equation 13.2 is not equivalent to Equation 13.3. The constant-coefficient relationship expressing the direct proportionality feature of metallic friction cannot account for the rubber adhesion transition phenomenon. And in the field, of course, attainment of the PNt value is not readily discernible; that is, we would not know whether Equation 13.2 or Equation 13.3 applies. 13.3.3 Development of the Macrohysteresis Slip-Resistance Force in Pedestrian Ambulation Development of the macrohysteresis slip-resistance force (FHb) between footwear outsoles and walking surfaces in pedestrian ambulation is a common occurrence, although not much discussed. Many portland cement concrete walkways and asphalt pavements traversed by pedestrians are macroscopically rough. Comprehensive friction analysis in the design of footwear outsole-walking surface systems is particularly important for pedestrians walking down-slope on ramps in wet conditions. Figure€13.1 presents a commonly encountered metal “diamond plate” utility box cover in a sloped concrete walking surface. Figure€13.2 depicts a

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Figure€13.1 Typical metal “diamond plate” utility box cover often found on concrete walking surfaces in urban areas.

Figure€13.2 Curb ramp equipped with protuberances intended to provide additional slip resistance and to alert pedestrians with visual impairments to a change in walking-surface slope.

representative curb ramp surfaced with protuberances intended to provide additional slip resistance and to alert pedestrians with visual impairments to a change in walking-surface slope. Contact between footwear outsoles and the protuberances seen in the figures can generate macrohysteretic friction forces. Figure€13.3 portrays a typical grooved surface in a concrete curb ramp. Interaction between such grooves and footwear outsoles can also produce macrohysteretic friction. As discussed in Chapter 12 concerning rubber tire-roadway interactions, there are at least two mechanisms by which FHb-friction forces can be generated in dry and wet conditions: adhesion-assisted and non-adhesion-assisted macrohysteresis. Development of the macrohysteresis friction mechanism in pedestrian ambulation is addressed in Chapter 14.

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330 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

Figure€13.3 Typical grooved surface in a concrete curb ramp.

13.3.4 Application of the Unified Theory of Rubber Friction to Analysis of Footwear Outsole-Walking Surface Slip-Resistance Testing Chapter 5 formulated a unified, mechanistic theory of rubber friction by treating rubber microhysteresis as a separate term. The theory is quantified by

FT = FA + FHs + FHb + FC,

(13.4)

where: FT = total frictional resistance developed between sliding rubber and a harder material, FA = frictional contribution from combined van der Waals’ adhesion of the two surfaces, FHs = frictional contribution from surface deformation hysteresis (microhysteresis), FHb = frictional contribution from bulk deformation hysteresis (macrohysteresis), and FC = cohesion loss contribution from rubber wear. In wet conditions, a liquid-related force-producing mechanism should be considered: viscous drag due to liquid boundary-layer friction when thin surface films exist, FV. Equation 13.4 then becomes

FT = FA + FHs + FHb + FC + FV.

(13.5)

Inasmuch as water-drag should not be counted on as a reliable slip-resistance force from a safety point of view, the liquid-related force can be removed

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from Equation 13.5. When the FC term is not significant in pedestrian ambulation, it too may be eliminated, reducing Equation 13.5 to,

FT = FA + FHs + FHb.

(13.6)

While testing is required, it appears likely that Equation 13.6 can be used for most friction analyses in the design of footwear outsole-walking surface pairing.

13.4

Comparability of Slip-Resistance Testing Data

Unfortunately, the walking-surface-safety community has been inadvertently misapplying the laws of metallic friction to rubber and other elastomeric footwear outsoles for a considerable period of time. One of the earliest slip-resistance testers, reported by Hunter [3] in 1931, employed the oblique thrust principle in an effort to mimic a shoe during normal walking. The Hunter machine incorporated a 34-kg (75-lb) weight sliding between two vertical guide bars. A pivoting thrust arm was attached to the weight near its center of mass, while a pivoting test foot was attached to the arm’s other end, thus constituting an articulated-strut mechanism. The loaded test foot was drawn forward on the tested surface in small increments to increase the applied horizontal-force component until slipping occurred. The coefficient of friction μ was calculated trigonometrically as the tangent of the angle made by the thrust arm with the vertical at the point of slip. New slip-resistance-testing apparatus need to be developed if scientifically based assessments of footwear-floor traction are to be possible. It is desirable that a number of such devices be constructed, utilized, and compared so that the maximum reasonable level of certainty as to walking-surface slip resistance is attained. The requirements for scientifically based comparability between results from different slip-resistance-testing apparatus can be summarized as follows:

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1. The apparatus should be of the same type (i.e., static or dynamic).



2. There can be a scientific relationship between different slip-resistance testers of the same type if the mechanistic approach to quantifying footwear-floor traction is utilized.



3. Any electromechanical biases inherent in the different apparatus must be known so that appropriate calibration corrections to instrument readings can be made. While we must accept the existence of random error, statistical techniques can be used to calculate confidence limits as desired.

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332 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

4. The same independent variable to be compared (e.g., FN) must be utilized while all other variables are not only controlled, but also kept constant and identical during the different tester runs.



5. All apparatus of interest must be capable of measuring the same dependent variable (e.g., FT) in a manner isolating the various friction-producing mechanisms to an acceptable degree. Ascertaining if rubber microhysteresis arises should be part of such testing. In this way, possible development of the adhesion transition mechanism can be determined, and the proper expressions for quantifying the developed slip-resistance-force components can be used.



6. Analysis of test results should include application of the unified theory of rubber friction discussed in Section 13.3.4 to quantify the slip-resistance forces developed. This is a straightforward process that must consider the effects of microhysteretic forces on footwearwalking surface traction analysis. These rubber microhysteresisrelated factors are listed in Table€13.1.

We now look at relevant ASTM testing methods that inadvertently misapply the laws of metallic friction to rubber. Replacing use of the laws of metallic friction in traditional slip-resistance testing with a unified theory Table€13.1 Characteristics of the Rubber Microhysteresis Friction Force That Should Be Taken into Account if the Unified Theory of Rubber Friction Presented in This Book Is To Be Fully Integrated into Walking-Surface Slip-Resistance Analysis Indicated Independence of Microhysteresis Force on Macroscopically Smooth Walking Surfaces Applied normal force and pressure Applied tangent force Indicated Independence of Microhysteresis Force on Macroscopically Rough Walking Surfaces Applied normal force and pressure Macroroughness of the walking surface Indicated Dependence of Microhysteresis Force on Macroscopically Smooth Walking Surfaces Microroughness of walking surface Nominal footwear outsole contact area Rubber hardness (inversely) Temperature (inversely) Outsole surface free energy Surface free energy of the walking surface Outsole roughness (rubber asperity configuration)

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333

of rubber friction would be beneficial in the analysis of footwear-walking surface traction during the design process and will also aid in pedestrian slip-and-fall investigations.

13.5

Inadvertent Misapplication of the Laws of Metallic Friction in ASTM Slip-Resistance Testing Methods

ASTM standards and test methods are continually reviewed to determine if they should be updated or withdrawn. While updating of walking-surfaceslip-resistance standards has occurred, a number of ASTM test methods inadvertently misapply the laws of metallic friction to footwear outsole-walking surface traction measurements. In these instances, values are reported and utilized as coefficients in the form of Equation 13.1: µ = FT/FN.



Application of the unified theory of rubber friction in such instances will not only foster comparability of test results, but will also promote scientific accuracy. The unified theory integrates the microhysteresis-produced FHs force in an expression quantifying the forces generated by the other basic rubber friction mechanisms, yielding the total slip-resistance force (FT) that can arise on a walking surface for a given footwear outsole and set of environmental conditions. 13.5.1 Irremediable Bias in Slip-Resistance Testers with Active ASTM Test Standards A list of ASTM test methods that inadvertently misapply the laws of metallic friction to walking-surface slip-resistance testing is presented in Table€13.2. Table€13.2 ASTM Test Methods That Inadvertently Misapply the Laws of Metallic Friction to Walking-Surface Slip-Resistance Testing. Such Misapplication Produces Irremediable Bias in the Subject Testers. ASTM C 1028 – 06, Standard Test Method for Determining the Static Coefficient of Friction of Ceramic Tile and Other Like Surfaces by the Horizontal Dynamometer Pull-Meter Method ASTM D 2047 – 04, Standard Test Method for Static Coefficient of Friction of Polish-Coated Flooring Surfaces as Measured by the James Machine ASTM E 303 – 93(2003), Standard Test Method for Measuring Surface Frictional Properties Using the British Pendulum Tester (BPT) ASTM F 609 – 05, Standard Test Method for Using a Horizontal Pull Slipmeter (HPS)

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334 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Such application results in irremediable bias in all four of these testers. Three of the listed test methods were discussed in previous chapters — (1) ASTM C 1028 – 06, Standard Test Method for Determining the Static Coefficient of Friction of Ceramic Tile and Other Like Surfaces by the Horizontal Dynamometer Pull-Meter Method; (2) ASTM E 303 – 93(2003), Standard Test Method for Measuring Surface Frictional Properties Using the British Pendulum Tester (BPT); and (3) ASTM F 609 – 05, Standard Test Method for Using a Horizontal Pull Slipmeter (HPS). 13.5.1.1 ASTM D 2047 – 04, Standard Test Method for Static Coefficient of Friction of Polish-Coated Flooring Surfaces as Measured by the James Machine The ASTM D 2047 – 04 test method concerns the James Machine [4], illustrated in Figure€13.4, an apparatus very much like the Hunter device [3] described in Section 13.4. The James Machine incorporates three weights totaling 34 kg (75 lb) that are applied to an articulated strut with a test foot on its opposite end that can slide on the walking surface of interest. As portrayed in Figure€13.4, the walking surface being tested is placed on the James Machine’s table in contact with a retaining bar, with the test foot resting on this tested surface. The smaller hand wheel seen in the figure raises the weights and strut until the strut is vertical, while the table is moved to the right. The table is then moved to the left at a uniform rate until the test foot slips. The chart depicted in the figure records the point at which slipping occurred by the sudden drop in the trace. The µ value is read from the chart. The use of µ produces irremediable bias in the machine. 13.5.1.2 Irremediable Inertial and Residence-Time Bias in the James Machine As evidenced in Figure€13.4, when the James Machine test foot slips on the walking surface of interest, the total friction force developed must first be counteracted by the applied horizontal force component, after which the inertial resistance to movement of the strut and test foot must also be overcome. The James Machine’s design does not account for this inertial force resistance; consequently, the device reads high. As presently designed, the James Machine exhibits an irremediable inertial bias. The James Machine also exhibits a residence-time bias. Braun and Roemer [5] utilized the Hoechst device to quantify the influence of residence time on the friction forces developed between the test shoe and the waxed floor tiles. Figure€10.8 presented a back-calculated plot of static FT vs. test-shoe residence time ±â†œæ¸€å±®â†œæ¸€å±®, ranging from 1 to 30 sec, calculated from the Braun and Roemer test results. Figure€10.8 illustrated the considerable influence of residence time when inertial effects are accounted for by use of the accelerometer-equipped Hoechst device. The back-calculated FT values increased from 44.3 N (9.95 lb)

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335

Nonscientific Application of the Laws of Metallic Friction

b

a

c d e

n

f g h i j k l

m

a–Weights b–Cushion c–Chart d–Chart board e–Spring clip f–Recording pencil g–Set screw

h–Strut i–Specimen j–Shoe k–Test table l–Retaining bar m–Back plate n–Ball Bearing rollers

Figure€13.4 The James Machine. (From ASTM D 2047 – 04, Standard Test Method for Static Coefficient of Friction of Polish-Coated Flooring Surfaces as Measured by the James Machine, Annual Book of ASTM Standards, Vol. 15.04, American Society for Testing and Materials, Philadelphia, 2002. Copyright ASTM INTERNATIONAL. Reprinted with permission.)

at 1 sec to 79.7 N (17.9 lb) at 30 sec. The emphasis placed on their residencetime findings by Braun and Roemer [5] merits repeating: One factor that is decisive for the static friction is the standing time ± between putting down the test shoe on the…[tile] and the start of the test run. At first…[friction] shows a remarkable increase with…[±] and reaches a limiting value only after a prolonged time. (p. 66)

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336 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces On the basis of their findings, Braun and Roemer decided to use a prestartup residence time of 1 sec for the Hoechst device in the subject staticfriction study. Using a two-protocol approach, Smith [6] demonstrated the residence-time effect with a dry Neolite test foot by employing the VIT and two operators in a manner that permitted prolonged contact time with the test surface — in this case, a polished marble floor tile. The first protocol determined [6] the dynamic slip resistance of the VIT-marble tile pairing operated in the conventional manner in dry conditions, utilizing a test-foot contact time of 0.5 sec. A slip resistance of 0.72 was indicated. The second testing scheme involved selecting an initial ratio setting below 0.72 and releasing the VIT’s CO2 pressure. Instead of a contact time of 0.5 sec, however, the CO2 pressure was continually applied to the piston rod-test foot assembly. Concurrently, the second operator increased the VIT’s ratio setting until slip occurred. A mean contact time of 17 sec was observed, producing a slip-resistance reading of 0.84, an increase of 17%. Because the James Machine test foot contacts the tested flooring surface for a variable time in a given test, and FT increases during that stationary period, the contact-time effect cannot be accurately quantified. The James Machine exhibits an irremediable residence-time bias as it is presently designed. 13.5.2 ASTM F 1646 – 05, Standard Terminology Relating to Safety and Traction for Footwear As its title indicates, the terminology defined in this ASTM standard relates to walking-surface safety and footwear traction. Unfortunately, definitions for “coefficient of friction” and “static slip resistance” are fashioned in accordance with misapplication of the laws of metallic friction to rubber friction. Use of these definitions fosters bias when interpreting the slip-resistance-test results to which they are applied.

13.6

Inadvertent Misapplication of the Laws of Metallic Friction by Slip-Resistance Testing Devices That are Not the Subject of Active ASTM Standards

13.6.1 Irremediable Bias in Slip-Resistance Testers That are Not the Subject of Active ASTM Test Standards A partial list of slip-resistance testing devices that inadvertently misapply the laws of metallic friction to rubber friction by use of Equation 13.1 and are not the subject of ASTM standards is presented in Table€13.3. Such misapplication results in irremediable bias in these tribometers. Two of the listed

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Table€13.3 Partial List of Slip-Resistance Tribometers That Are Not the Subject of ASTM Standards That Inadvertently Misapply the Laws of Metallic Friction to WalkingSurface Slip-Resistance Testing. Such Misapplication Produces Irremediable Bias in These Testers. ASM 825 Digital Slip Meter Portable Articulated Strut Slip Tester (PAST) Portable Inclineable Articulated Strut Tester (PIAST) Technical Products Corporation Model 80 tester Variable Incidence Tribometer (VIT) All manually operated pull-meters not listed above

testers — the PIAST and VIT — have been discussed in previous chapters. The other devices in the list will be described shortly. 13.6.2 Misapplication of the Laws of Metallic Friction in the PIAST and VIT When Used as Static-Friction Testers Our mechanistic analysis of the Powers et al. [7] static-friction testing in Chapter 9 showed that rubber microhysteresis can develop in the Portable Inclineable Articulated Strut Tester (PIAST) and Variable Incidence Tribometer (VIT) test feet. These forces were indicated in Figures€9.6 and 9.7, respectively. Unfortunately, the systematic bias demonstrated in these devices arising from generation of FHs forces in their test feet cannot be corrected by routine engineering calibration. This microhysteretic-force bias will vary with the walking surface being tested, remaining an unquantified, uncontrolled, independent variable in the operation of these devices. Both the PIAST and VIT use Equation 13.1 to quantify their slip-resistance measurements. As we have seen, Equation 13.1 cannot account for rubber microhysteresis. Use of Equation 13.1 produces irremediable bias during operation of these two devices for static testing as they are presently designed. 13.6.3 Misapplication of the Laws of Metallic Friction in the PIAST and VIT When Used as Dynamic-Friction Testers The PIAST and VIT are employed as dynamic-friction testers when readings are taken after their test feet slip and such measurements are quantified by application of Equation 13.1. Up to the slip-point, static-friction testing prevails. A constant microhysteresis force developed during such static-friction testing will still be present when these devices are utilized as dynamic testers. Employing Equation 13.1 produces irremediable bias during operation of these two devices for dynamic testing as they are presently designed.

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338 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 13.6.4 ASM 825 Digital Slip Meter The ASM 825 Digital Slip Meter is a drag-sled similar in design to the Horizontal Pull Slipmeter (ASTM F 609) and is intended to measure the static coefficient of friction. The ASM 825 is equipped with Neolite and leather testfoot materials and a gage that records the pulling force required to initiate motion of the tester on the flooring surface of interest. The device employs Equation 13.1 for calculation of μ. 13.6.5 Portable Articulated Strut Slip Tester (PAST) The Portable Articulated Strut Slip Tester (PAST) had previously been the subject of an ASTM standard that was withdrawn because of proprietary concerns. The PAST is intended to measure the static coefficient-of-friction by use of the articulated-strut mechanism. The device has been utilized on ordinary flooring, but has perhaps found its greatest application in assessing the slipperiness of bathtub and shower surfaces in conjunction with ASTM F 462-79(1999), Consumer Safety Specification for Slip-Resistant Bathing Facilities. The PAST also employs Equation 13.1 for calculation of μ. 13.6.6 Technical Products Corporation Model 80 Tester The Technical Products Corporation Model 80 Tester, herein known as the TPCM-80, is also a drag-sled. It utilizes the same design concept as the Horizontal Pull Slipmeter (ASTM F 609) and is intended to measure the static coefficient-of-friction. Like the ASM 825 Digital Slip Meter and the PAST, the TPCM-80 makes use of Equation 13.1 for calculation of μ.

13.7

Irremediable Inertial and Residence-Time Bias in Slip-Resistance-Testing Devices That are Not the Subject of ASTM Standards

As seen in Chapter 10, inertial bias can be avoided in the PIAST by utilizing the device as a static-friction tester. Inertial bias in the VIT cannot be avoided, but it can be remediated through routine calibration by application of the Powers et al. [7] testing results. Calibration of the VIT for inertial bias can be carried out because this bias arises due to acceleration of certain of the device’s mechanical components. Each time the device is activated at a given incidence angle, when operated as detailed in the Powers et al. testing, the same acceleration force occurs; that is, the bias is internal, mechanically produced, and quantitatively constant in nature. Consequently, remediation by calibration is possible. In certain walking-surface slip-resistance tribom-

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eters, however, inertial bias is neither avoidable nor remediable. Two of these testers are discussed. 13.7.1 Irremediable Inertial and Residence-Time Bias in the ASM 825 Digital Slip Meter The ASM 825 Digital Slip Meter is a pull-meter similar to the HPS, but it does not utilize a motor to provide the pulling force necessary to initiate movement of the device on the floor being tested; thus, this pulling force and its rate of application are subject to differences in manual operation. Because rate-of-force application is a determinant of the inertial resistance arising during testing, the developed inertial force will likely vary from operator to operator and cannot be accounted for by routine engineering calibration. This aspect of the ASM 825 Digital Slip Meter’s operation produces an irremediable inertial bias in the device. The variation in use of the device among operators is also a concern in regard to residence time. Differences in unrecorded pulling-force magnitude and rate of application will cause differences in the time that the ASM 825 Digital Slip Meter rests on the floor surface before movement begins. As shown by Braun and Roemer [5], the friction force arising between a drag sled and paired flooring increases as the device rests motionless on the tested surface. This aspect of the ASM 825 Digital Slip Meter’s operation produces an irremediable residence-time bias in the device. 13.7.2 Irremediable Inertial and Residence-Time Bias in the Technical Products Corporation Model 80 Tester The Technical Products Corporation Model 80 Tester is also a manually operated pull-meter. Consequently, it as well develops irremediable inertial and residence-time biases during operation. Table€13.4 presents a partial list of pull-meters that develop irremediable inertial and residence-time bias during their operation.

13.8

Chapter Review

This chapter provided a philosophical and technical blueprint to assist in furthering progress toward developing maximum understanding and control of the slip-resistance characteristics of footwear-walking surface pairings. The approach taken is to replace the present inadvertent misapplication of the laws of metallic friction in walking-surface slip-resistance testing, analysis, and design with a scientifically based, mechanistically focused, unified theory of rubber friction.

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340 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Table€13.4 Partial List of Walking-Surface Slip-Resistance Testers That Are Not the Subjects of ASTM Standards That Develop Irremediable Inertial and Residence-Time Bias during Their Operation ASM 825 Digital Slip Meter Technical Products Corporation Model 80 Tester All manually operated pull-meters not listed above

Unfortunately, insufficient progress has been made toward identifying the best testers and testing methods for accurately quantifying walking-surface slip resistance. Better comparability of measured friction values is required. The most reliable means of fostering comparability of results for use in identifying the best slip-resistance test methods and devices is to utilize a scientifically based approach that focuses on the friction mechanisms that develop when a footwear outsole contacts a walking surface. The chapter focused on elements of walking-surface slip-resistance testing that are amenable to improvement through application of the unified theory of rubber friction. The chapter compared the characteristics of rubber friction to those of metallic friction. A synopsis of the effects of microhysteretic friction force development in rubber was presented. This was followed by examination of factors relevant to slip-resistance-testing data comparability. Slip-resistancetesting devices and ASTM testing methods that inadvertently misapply the laws of metallic friction to rubber were addressed. The biases arising during operation of various testers were also considered. 13.8.1 Comparing the Characteristics of Rubber Friction to Metallic Friction It is common engineering practice for the laws of metallic friction to be misapplied to rubber and rubber-like footwear outsoles. This is done through the use of the metallic coefficient-of-friction (μ) equation. Such inadvertent misapplication can produce the following undesirable consequences:

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1. Application of the laws of metallic friction to rubber can lead to incorrect interpretations of outsole slip-resistance measurements. A diminishing metallic coefficient demonstrates that frictional resistance to movement between metals is also decreasing. Decreases in the magnitude of rubber coefficients can mean that the rate of increasing outsole slip-resistance is diminishing.



2. Equations for the coefficient µ when concurrently acting rubber friction mechanisms arise require a different approach to quantify true slip resistance, one in which coefficients are not involved and only forces are considered.

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13.8.2 Effects of the Development of Microhysteretic Slip-Resistance Forces on Rubber-Friction Analysis 13.8.2.1 Development of the Microhysteretic Slip-Resistance Force in Pedestrian Ambulation In the analysis of friction tests involving constant-velocity sliding of rubber on rough, harder surfaces, we found that the developed rubber microhysteresis friction force FHs is constant, and its magnitude is independent of both the force and pressure applied to the rubber specimens in these studies. Accounting for FHs by subtracting its constant value from the total friction force generated in the tests (FT) allowed the adhesion (FA) and macrohysteresis (FHb) forces to be more easily differentiated and quantified. 13.8.2.2 Development of the Adhesion-Transition Phenomenon in Pedestrian Ambulation When a rubber footwear heel first touches a walking surface, the adhesive friction force FA can be generated between the two materials. As the perpendicular force FN applied by the pedestrian’s leg and foot through the heel to the floor increases as more weight is placed on the leading leg, FA usually increases. If the FN force becomes large enough, however, a change in the manner in which the adhesive slip-resistance force is generated takes place; that is, the adhesion-transition phenomenon arises. The adhesion transition phenomenon develops at the adhesion transition pressure PNt. It was shown in Chapter 6 that the equations quantifying the adhesive slip-resistance force above and below the PNt value are different. Development of the adhesion-transition phenomenon makes things complicated for engineers trying to determine the slip-resistance of an outsole-walkway pairing — the scientifically based relationship quantifying the rubber adhesion friction force can change during the foot’s landing and stationary phases in normal walking. The chapter presented evidence indicating that the adhesion-transition phenomenon can arise even in wet conditions. Grönqvist [2] slid samples of rubber shoe-tread materials — with triangular and waveform tread patterns — on smooth, stainless-steel flooring. In this slip-resistance testing, the flooring was lubricated with glycerol, a clear, colorless, odorless, and syrupy liquid. Figures€8.8 and 8.10 presented our back-calculation-analysis results from Grönqvist’s data. The shapes of the Figure€8.8 plots tell us that the adhesion-transition phenomenon developed in both the triangular and waveform nitrile treads. The shape of the waveform plot in Figure€8.10 reveals that the adhesion-transition phenomenon arose in the styrene waveform tread material. Laboratory and field testings are necessary to determine when the adhesion-transition phenomenon develops in footwear outsoles during ordinary walking. The slip-resistance characteristics of footwear outsole-walking surface pairings are not currently designed to account for this phenomenon.

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342 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 13.8.2.3 Development of the Macrohysteresis Slip-Resistance Force in Pedestrian Ambulation on Rough Walking Surfaces Development of the rubber macrohysteresis slip-resistance force (FHb) between footwear outsoles and walking surfaces in pedestrian ambulation is a common occurrence, although not much discussed. Many concrete walkways and asphalt pavements traversed by pedestrians are rough. Comprehensive slip-resistance analysis in the design of footwear outsole-walking surface pairings is particularly important for pedestrians walking downslope on ramps in wet conditions. Such wet conditions can eliminate all traction forces except FHb. Figure€13.1 presents a commonly encountered metal “diamond plate” utility box cover in a sloped concrete walking surface. Figure€13.2 depicts a representative curb-ramp covering designed with protuberances intended to provide additional slip resistance and to alert pedestrians with visual impairments to the change in walking-surface slope. Contact between footwear outsoles and the protuberances seen in the figures can generate macrohysteretic traction forces. Figure€13.3 portrays a typical grooved surface in a concrete curb ramp. Interaction between such grooves and footwear outsoles can also produce macrohysteretic slip-resistance forces. There are at least two mechanisms by which FHb-slip-resistance forces can be generated: (1) adhesion-assisted and (2) non-adhesion-assisted macrohysteresis. Development of the macrohysteresis slip-resistance mechanisms in pedestrian ambulation is addressed in Chapter 14. 13.8.3 Application of the Unified Theory of Rubber Friction to Analysis of Footwear Outsole-Walking Surface Slip-Resistance Testing Chapter 5 formulated a unified, mechanistic theory of rubber friction by treating rubber microhysteresis as a separate term. The theory is quantified by Equation 13.4:

FT = FA + FHs + FHb + FC,

where: FT = total frictional resistance developed between sliding rubber and a harder material, FA = frictional contribution from the combined adhesive forces of the two surfaces, FHs = frictional contribution from surface deformation hysteresis (microhysteresis), FHb = frictional contribution from bulk deformation hysteresis (macrohysteresis), and FC = cohesion loss contribution from rubber wear.

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Inasmuch as outsole wear is not normally significant in pedestrian ambulation in the short term, FC can usually be eliminated from Equation 13.4, reducing it to Equation 13.5:

FT = FA + FHs + FHb.

A form of this equation can usually be employed for analyses of slip resistance in the design of footwear outsole-walking surface pairings. 13.8.4 Comparability of Slip-Resistance Testing Data Unfortunately, the walking-surface-safety community has been inadvertently misapplying the laws of metallic friction to rubber and other elastomeric footwear outsoles for a considerable period of time. New slip-resistance-testing apparatus need to be developed if scientifically based determinations of footwear-walking surface traction are to be possible. It is desirable that a number of such devices be constructed, utilized, and compared so that the maximum reasonable level of certainty as to walking-surface slip resistance is attained. The requirements for scientifically based comparability between results from different slip-resistance-testing apparatus can be summarized as follows:

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1. The apparatus should be of the same type (i.e., static or dynamic).



2. There can be a scientific relationship between different slip-resistance testers if the mechanistic approach to quantifying walking-surface slip resistance is utilized.



3. Any biases inherent in the different apparatus must be known so that appropriate calibration corrections to instrument readings can be made.



4. The same variable to be compared (e.g., applied foot force) must be utilized while all other variables are not only controlled, but also kept constant and identical during the different tester runs.



5. All apparatus of interest must be capable of measuring the same variable (e.g., FT, the total slip-resistance forced produced) in a manner isolating the various friction-producing mechanisms to an acceptable degree. Ascertaining if rubber microhysteretic forces arise should be part of such testing.



6. Analysis of test results should include application of the unified theory of rubber friction to quantify the slip-resistance forces developed. This is a straightforward process that must consider the effects of microhysteretic slip resistance on footwear-walking surface traction analysis. These rubber microhysteresis-related factors are listed in Table€13.1.

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344 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 13.8.5 Inadvertent Misapplication of the Laws of Metallic Friction in ASTM Slip-Resistance Testing Methods ASTM test standards and methods are continually reviewed to determine if they should be updated or withdrawn. While updating of walking-surface slip-resistance standards has occurred, a number of ASTM test methods traditionally apply the laws of metallic friction to walking-surface slip-resistance testing. A list of ASTM test methods that inadvertently misapply the laws of metallic friction to walking-surface slip-resistance testing is presented in Table€13.2. ASTM F 1646 – 05, Standard Terminology Relating to Safety and Traction for Footwear, relates to walking-surface safety and footwear slip resistance. Unfortunately, definitions for “coefficient of friction” and “static slip resistance” are fashioned in accordance with the traditional application of the laws of metallic friction to rubber friction. Use of these definitions fosters misinterpretation of the slip-resistance-test results to which they are applied. 13.8.6 Inadvertent Misapplication of the Laws of Metallic Friction by Slip-Resistance Testing Devices That are Not the Subject of Active ASTM Standards A partial list of slip-resistance testing devices that are not the subject of ASTM standards and that inadvertently misapply the laws of metallic friction to rubber footwear outsole-walking surface pairings is presented in Table€13.3. Such traditional application produces irremediable bias in these testers as they are presently designed.

References

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1. Bucknell University F-13 workshop to evaluate various slip resistance measuring devices, ASTM Standardization News, 20, 21, 1992. 2. Grönqvist, R., Mechanisms of friction and assessment of slip resistance of new and used footwear soles on contaminated floors, Ergonomics, 38, 224, 1995. 3. Hunter, R.B., A method of measuring frictional coefficients of walkway materials, J. Nat., Bur. Stds., 5, 329, 1931. 4. Annual Book of ASTM Standards, Vol. 15.04, American Society for Testing and Materials, Philadelphia, 2002. 5. Braun, R., and Roemer, D., Influences of waxes on static and dynamic friction, Soap/Cosmetics/Chemical Specialties, 50, 60, 1974. 6. Smith, R.H., Test foot contact time effects in pedestrian slip-resistance metrology, J. Test. Eval., 33, 557, 2005. 7. Powers, C.M., Kulig, K., Flynn, J., and Brault, J.R., Repeatability and bias of two walkway safety tribometers, J. Test. Eval., 27, 368, 1999.

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14 Slip-Resistance Analysis in the Design of Footwear Outsoles and Their Paired Walking Surfaces

14.1

Introduction

This chapter focuses on application of the unified theory of rubber friction detailed in previous chapters to slip-resistance analysis in the design of footwear outsoles and their paired walking surfaces. An intent of this book is to improve such analysis for application to outsoles and walking surfaces as they are presently designed and constituted. Suggestions will not be made for potentially desirable changes in them stemming from application of the unified theory. Such possibilities are beyond the scope of this book. Nevertheless, improving our understanding of the traction forces generated between elastomeric outsoles and harder contacted surfaces through scientifically based analysis of the friction mechanisms developed between them can be useful in reexamining existing designs and can perhaps serve as a starting point in improving present-day design practice. The chapter first addresses the importance of rubber outsole microhysteretic forces in wet conditions, followed by a discussion of the need to reformulate the traditional approach to walking-surface slip-resistance testing. It then considers measurement of outsole microhysteresis in wet conditions and suggests a process through which the unified theory can be applied to assist in the analysis of slip resistance in design.

14.2

Importance of Footwear Outsole Microhysteresis in Wet Conditions

It has long been recognized in the study of rubber-tire traction that pavement microroughness plays an important role in allowing drivers to control their vehicles on wet roadways. Recognition of the importance of walking345

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346 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces surface microroughness in wet conditions is not so widespread in the pedestrian ambulation safety community. This unfortunate situation exists even though most foot slips are thought to occur on liquid-contaminated surfaces. Potential benefit could accrue if the pedestrian ambulation safety community would integrate the motor vehicle world’s understanding of microhysteretic wet-traction into analysis and testing of slip resistance in liquid-lubricated conditions. A synopsis of the motor vehicle world’s research findings in this regard will be presented. 14.2.1 Three-Lubrication-Zones Concept Gough [1] was the first to formalize the frequently utilized Three-Lubrication-Zones Concept of water displacement by a rolling or sliding tire at velocity V on wet pavement. Figure€12.1 illustrates this concept. Gough [1] considered that while some encountered water is displaced to the front of the moving tire upon contact, the tire rides on an unbroken water film in the front lubrication Zone 1, as some of this water is gradually squeezed out the sides. The middle Zone 2 is one of transition in which initial physical contact between the tire and the roadway develops, while in Zone 3 only a thin water film at most remains, and the tire makes contact with the pavement through this film. The relative size of these zones varies with speed. If speed becomes excessive for given conditions, however, hydroplaning can occur. 14.2.2 Traditional Wet Roadway Microtexture Analysis Bond et al. [2] conducted investigations concerning roadway micro- and macroroughness and tire performance, as measured by the British Pendulum Tester. They found that wet-roadway skid resistance is governed by pavement macroroughness regarding removal of bulk water and by pavement microroughness in the role of creating real areas of tire contact. While this testing inadvertently misapplied the laws of metallic friction to rubber through use of Equation 14.1,

μ = FT/FN,

(14.1)

the results are instructive. This testing indicated that wet traction rose to a maximum in winter and fell to a minimum in summer [2]. Photomicrographs of in-service pavements revealed that surface microroughness also increased to a maximum in winter due to natural weathering of the road aggregate during this period. On the other hand, more traffic-polishing of this aggregate occurred during the summer, removing much of the aggregate’s microroughness. Also, more oil from tire wear was likely present on the pavement in summer. These trends correlate well with the number of wet-skidding incidents in Britain: fewer in winter and a greater number in summer.

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347

In addition to the discussed seasonal variations in skid resistance of inservice roadways associated with surface aggregate microroughness in Britain, the same climatologically related phenomenon has been observed under controlled conditions at a highway pavement research facility in the United States. Beginning in 1974, the Transportation Research Center of Ohio became involved in a U.S. Federal Highway Administration program designed to develop test centers where skid trailers could be calibrated on skid pads and modified to improve their compliance with the American Society for Testing and Materials’ Test Method for Skid Resistance of Paved Surfaces Using a Full-Scale Tire (E 274). Whitehurst and Neuhardt [3] reported on this test-pad program from a 9-year period involving approximately 12,000 individual skid tests. The test pads evidenced a seasonal variation in skid resistance, generating maximum average monthly skid-resistance measurements in the winter, which fell to a minimum in the summer months. Whitehurst and Neuhardt theorized that significant traffic polishing of surface aggregate had occurred during the summer. The winter increases in skid resistance are consistent with an increased contribution from microhysteresis to skid resistance measurements made during that season, when harsher weather apparently produced degradation-roughening of the pad surfaces. In 1992, Williams [4] reviewed the then state-of-the-art of roadway tire traction in relation to tread pattern, tread compounding, and road surface conditions, particularly with regard to a tire’s roadholding ability on wet pavement. In addition to the need for adequate tread depth, the road’s surface characteristics had been accepted as especially important. Williams stated that, “The road surface macrotexture, assisted by the tread pattern, is responsible for the removal of the bulk water from the tire contact patch.” Williams also summarized the requirement for availability of an adequate microtexture on the road surface aggregate to provide a reasonably safe wetdriving environment: There is no substitute for the appropriate level of microtexture for aggregates in the new and traveled condition. The most desirable level of microtexture relates to its ability to remove the remaining thin film of water in order to create real areas of contact with the tread compound. Levels of microtexture below this minimum fail to generate high levels of wet friction. (p. 132)

14.2.3 Importance of Aircraft Tire Microhysteresis on Wet Pavement Just as the importance of a roadway’s microtexture regarding a tire’s roadholding ability in wet conditions was accepted by highway design engineers, the importance of aircraft runway and taxiway microtexture to pilots during landing and taxiing in wet conditions has been accepted by the aviation community. Yager [5] discussed this issue in his 1990 article concerning the tirerunway friction interface: “…the magnitude of the friction at a given speed is

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348 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces related to the surface microtexture (fine, small-scale, surface features such as found on individual stone particles)” (p. 296).

14.2.4 Corroboration for the Three-Lubrication-Zones Concept as Applied to Walking-Surface Slip Resistance In 1985, Strandberg [6] theorized that the friction mechanisms that develop between a rolling tire on wet pavements also appear to determine footwear-wet-walking-surface slip resistance; that is, the conditions depicted in Figure€12.1 also arise when an outsole exhibiting a tread pattern contacts a macroscopically rough walking surface. While a literature search revealed no walking-surface slip-resistance studies involving macroscopically rough surfaces suitable for the microhysteretic back-calculation technique to be applied, we have analyzed slip-resistance data from testing protocols utilizing macroscopically smooth walking surfaces. The indicated production of microhysteresis forces in these studies implies that a Zone-3-like area can develop in wet slip-resistance testing and therefore likely also arise on footwear outsoles during pedestrian ambulation on smooth surfaces in wet conditions. 14.2.4.1 Tisserand’s Testing Tisserand [7] conducted traction investigations utilizing the dynamic INRS (Institut National de Recherche et de Sécurité) whole-shoe testing device that allows application of a normal load to be made inside a shoe at the heel and toe positions by employing an artificial foot. He selected a sliding velocity of 20 cm/sec (7.87 in./sec). Figure€4.41 presented a generalized depiction of his µ vs. FN results for two unidentified work shoes sliding on stainless steel coated with ordinary engine oil. Tisserand did not report whether the tested shoes possessed a tread pattern. In both cases, the coefficient of rubber friction decreased with increasing applied normal load. The back-calculation technique was applied to Tisserand’s wet-testing data. Figure€8.6 depicted the results of these calculations. The plot for work shoe A evidences a wet microhysteresis force (y-axis intercept) of about 4 kg (8.8 lb), while that for work shoe B indicates a constant FHs value of approximately 0.9 kg (2 lb). We can theorize that generation of microhysteretic forces in this testing indicates the development of a localized area — that is, a Zone-3 region — where the combined adhesive forces from the two surfaces in contact were sufficient to produce microhysteresis. 14.2.4.2 Grönqvist’s Testing Figure€4.42 presented back-calculated coefficient-of-friction test results from Grönqvist’s [8] walking-surface slip-resistance study examining three types of new safety shoes with rubber outsoles possessing dissimilar tread

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patterns. The pairings, comprising nitrile outsoles with waveform (NRw) and triangular (NRt) tread patterns and styrene outsoles with the same patterns, SRw and SRt, all exhibited reductions in μ with increasing PN. Figures€8.7 and 8.9 depicted findings from our microhysteretic analysis of Grönqvist’s data. The nitrile and styrene rubber evidenced production of yaxis intercepts and constant surface deformation hysteresis forces for both tread patterns. Figure€4.43 presented back-calculated coefficient-of-friction test results from Grönqvist’s study of outsoles composed of thermoplastic rubber, polyurethane, and polyvinylchloride. These pairings, all possessing a rectangular tread pattern, exhibited reductions in μ with increasing applied normal pressure. Figure€8.11 depicted findings from a microhysteretic analysis of data from these tests. All three outsoles evidenced production of a constant surface deformation hysteresis force. All seven of Grönqvist’s data sets evidenced microhysteretic force production. This is consistent with the development of localized areas — that is, Zone-3 regions — where the combined adhesive forces from the two surfaces in contact were sufficient to produce microhysteresis. 14.2.4.3 Redfern and Bidanda’s Testing Redfern and Bidanda [9] conducted an analysis-of-variance (ANOVA) slipresistance investigation assessing the effects on μ of three floor lubricants (water, SAE 10 oil, and SAE 30 oil), averaging the measured friction values over floor type, heel strike angle, and sliding velocity. Figures€4.44, 4.45, and 4.46 presented the Redfern and Bidanda measurements obtained with water, SAE 10 oil, and SAE 30 oil lubricants, respectively, paired with rubber, urethane, and PVC heels on smooth untreated and waxed vinyl tile, stainless steel, and sealed concrete. For all nine wet-data sets, μ diminished with increasing FN. Because of the analysis detailed in Chapter 5, one can expect that hyperbolic curves for these test results would be evidenced if three or more values of FN had been applied. For this reason, the curved lines between the corresponding data points in the figures are dashed. Figures€8.13, 8.14, and 8.15 illustrated results from a back-calculation analyses of the Redfern and Bidanda rubber, urethane, and PVC heels in the form of FT vs. FN for the three lubricants (water, SAE 10 oil, and SAE 30 oil). In every case, y-axis intercepts and generation of FHs forces in the wet shoe heels are indicated. This is consistent with the development of localized areas — that is, Zone-3 regions — where the combined adhesive forces from the two surfaces in contact were sufficient to produce microhysteresis. The Tisserand [7], Grönqvist [8], and Redfern and Bidanda [9] test results provide corroboration for the Three-Lubrication-Zones Concept as applied to walking-surface slip resistance.

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350 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces

14.3

Reformulating the Traditional Approach to Walking-Surface Slip-Resistance Testing

Regrettably, much of the pedestrian ambulation safety community has been inadvertently misapplying the laws of metallic friction to rubber friction for a considerable period of time. Because of this situation, reformulation of the traditional approach to walking-surface slip-resistance testing, in both dry and wet conditions, is necessary if scientifically reliable footwear traction information is to be developed. Because most pedestrian slips occur when the walking surfaces are wet, we focus mostly on this condition. The findings and recommendations presented in this chapter are, however, also applicable to dry walking surfaces. In the present context, it is useful to exemplify consequences that can arise when slip-resistance measurements obtained by testers unknowingly exhibiting various forms of bias are used to draw erroneous conclusions and incorrect findings. We do this utilizing wet and dry test results obtained at the ASTM Committee F-13 Bucknell University workshop [10]. The incorrect findings in this case are particularly important because they contribute to widespread misinterpretation of wet-slip-resistance-testing results. It is vital, of course, to interpret wet-testing results in a fully scientific manner to reduce the frequency of pedestrian slips and falls on wet walking surfaces as much as reasonably possible. 14.3.1 Test Results from the ASTM F-13 Bucknell University Workshop The purpose of the 1991 workshop conducted by ASTM Committee F-13 at Bucknell University [10] was to: • Evaluate the performance of slip testers in dry and wet conditions. • Compare each tester’s readings to measurements from a force plate. • Determine which testers provide reliable, consistent results. The evaluation involved testing a glazed, smooth tile mounted on a force plate. Nine devices were investigated, but this analysis will be restricted to the five testers we have previously examined. These five devices are listed in Table€14.1. In the workshop [10] test series of interest, all five devices were fitted with Neolite test feet and were operated on a force plate in the 23.9 to 25°C (75 to 77°F) temperature range. All Neolite test feet were prepared for use by sanding them in an identical manner. The laboratory’s relative humidity ranged between 66 and 69%. The testers were employed in accordance with their respective ASTM standards, if such existed. Six trials were carried out with each device. Mean coefficients, involving the total forces measured (FM) by the workshop testers — including inertial resistance to be discussed — were reported as μW values, calculated by applying the relationship:

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351

Slip-Resistance Analysis in the Design of Footwear Outsoles Table€14.1 Selected Walking-Surface Slip-Resistance Testers Involved in the 1991 ASTM Committee F-13 Bucknell University Workshop Tester

Type

Sigler Pendulum Tester

Dynamic

Portable Inclineable Articulated Strut Tester (PIAST)

Static/dynamic

Horizontal Pull Slipmeter (HPS)

Static

Horizontal Dynamometer Pull-Meter (HP-M)

Static

Technical Products Corporation Model 80 (TPCM 80)

Static

Source: Bucknell University F-13 workshop to evaluate various slip resistance measuring devices, ASTM Standardization News, 20, 21, 1992.



μW = FM/FN.

(14.2)

14.3.1.1 Effect from Inadvertent Misapplication of the Laws of Metallic Friction to Rubber Friction Figure€14.1 presents reported wet and dry μW values from the workshop [10] test series of interest — calculated by inadvertent misapplication of Equation 14.1 — displayed in a manner to facilitate clarity. Because the relationship quantifying slip-resistance measurements did not account for the frictionforce-producing mechanisms developed during the testing, neither an evaluation of tester performance nor a determination of measurement reliability or consistency could be made on a scientific basis. 14.3.1.2 Effect from the Presence of Test-Foot-Area Bias on Test Measurements Analysis of the Roth et al. [11] and Thirion [12] data in Chapter 5 revealed that the total friction force produced can depend on nominal specimen area. The devices listed in Table€14.1 possess different test foot areas. Because of the test-foot-area bias present in the workshop investigations, neither an evaluation of tester performance nor a determination of measurement reliability or consistency could be made on a scientific basis. 14.3.1.3 Effect from the Presence of Inertial Forces in Test Measurements Figure€14.2 depicts the results of a back-calculation analysis of Figure€14.1’s data — utilizing the nominal test-foot areas of the slip-resistance devices being examined — in which the problematic μW values are replaced by FM. While this is intended to allow data-set comparison on the basis of the slip-resistance forces developed, we must still consider the unquantified

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352 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 0.8

HPS

0.7 HP-M

Coefficient Values (µw)

0.6 0.5

TPCM 80

0.4

Sigler device

0.3

PIAST

0.2 0.1

0

Dry

Wet

HPS = Horizontal pull slipmeter HP-M = Horizontal dynamometer pull-meter TPCM 80 = Technical products corporation model 80 PIAST = Portable inclineable articulated strut tester Sigler device = Sigler pendulum tester Figure€14.1 Reported wet and dry coefficient (μW) values — calculated by inadvertent misapplication of the laws of metallic friction to rubber — obtained from various slip-resistance testers involved in the ASTM Committee F-13 workshop at Bucknell University held to evaluate slip-resistancemeasuring devices.

inertial-force components generated in all devices except the Sigler [13] pendulum tester. Because of these unquantified inertial-force components, neither an evaluation of tester performance nor a determination of measurement reliability or consistency could be made on a scientific basis. 14.3.1.4 Effect from the Presence of Contact-Time Bias on Test Measurements As might be expected, there was a noticeable difference between the Sigler [13] pendulum tester’s dynamic slip-resistance results and those of the other devices, all of which can be considered to measure static slip resistance (although some classify the PIAST as a dynamic tester). The wet and dry Sigler [13] results were the lowest of the group of five in both conditions. These lower values can be ascribed, at least in part, to a shorter contact time

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353

Slip-Resistance Analysis in the Design of Footwear Outsoles 350

Measured Longitudinal Forces (FM) N

300 PIAST

250 200

HP-M 150 100 50 0

TPCM 80

Dry

Sigler device

HPS Wet

HPS = Horizontal pull slipmeter HP-M = Horizontal dynamometer pull-meter TPCM 80 = Technical products corporation model 80 PIAST = Portable inclineable articulated strut tester Sigler device = Sigler pendulum tester Figure€14.2 Back-calculated, measured longitudinal forces (FM) using the nominal test-foot areas of slipresistance devices involved in the ASTM Committee F-13 workshop at Bucknell University. Except for the Sigler tester, all FM values contain unquantified inertial-force components.

for the pendulum’s test foot compared to the magnitudes of s experienced by the other devices; that is, FT increases with increased contact time. The magnitude of such an FT increase depends on the design of the particular tester. The measured slip-resistance values in the ASTM F-13 workshop [10] were not comparable because different contact times for each device were involved. Because of the contact-time bias present in the workshop investigations, neither an evaluation of tester performance nor a determination of measurement reliability or consistency could be made on a scientific basis. 14.3.2 Conclusions from the ASTM F-13 Bucknell Workshop: Sticktion Unfortunately, a preconceived notion concerning friction measurements of smooth, wet walking surfaces obtained from portable slip-resistance testers was (and still is) in wide circulation in the walking-surface-safety community before the ASTM F-13 workshop [10]. This notion concerns “sticktion,” or the development of surface tension adhesion in a thin liquid layer between a

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354 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces test foot and the floor. Such surface tension is believed to develop significant adhesion between the test foot and floor during testing, biasing obtained slip-resistance measurements to falsely high values. On the basis of the test results presented in Figure€14.1, the ASTM F-13 Task Force organizing the workshop [10] concluded that sticktion developed during use of the three pull-meters cited in the figure — the HPS, HP-M, and TPCM 80. This conclusion as to tester reliability and consistency was stated as follows: When both the walkway surface and shoe sole or heel surface are smooth, liquid contaminants may develop adhesion between two surfaces, thus exhibiting a falsely high coefficient of friction or slip resistance. This arises from the fact that even a short time delay between application of the normal or contact force and application of the tangential force can permit the squeezing out of any liquid present, resulting in a thin layer of liquid that can cause adhesion and a high resistance to slip…it was observed that many of the testers had this problem when tested under wet conditions. (p. 23)

It has been shown, however, that neither an evaluation of tester performance nor a determination of measurement reliability or consistency could be made on a scientific basis because of inadvertent misapplication of the laws of metallic friction to rubber, the presence of unquantified inertial forces in the test measurements, test-foot-area bias, and the contact-time bias when test results from these devices are compared. The “observation” by the participants that many testers evaluated in the ASTM F-13 workshop at Bucknell University [10] exhibited sticktion was not scientifically based. This is unfortunate because the findings developed on the basis of this testing have had wide consequences. Before addressing these consequences, however, a detailed discussion of the basis for the conclusions is presented. Smith [14] has examined the issue of sticktion development when utilizing portable walking-surface slip-resistance testers equipped with Neolite test feet. He found that the magnitude of surface tension adhesion forces that can arise between water and a Neolite test foot paired with a smooth surface is not significant. Any previous slip-resistance studies misapplying the laws of metallic friction to elastomeric materials and purporting to demonstrate the development of sticktion using a Neolite test foot are invalid. No significant sticktion developed between the workshop [10] testers fitted with a Neolite test foot and the tile surface. The higher slip-resistance measurements observed in wet testing with the HPS, HP-M, and TPCM 80 devices came, in part, from the presence of the unaccounted-for inertial forces.

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14.3.3 Exemplifying Inertial and Residence-Time Bias in an ASTM F-13 Workshop Pull-Meter Force-plate traces from an unspecified pull-meter tested during the ASTM F-13 workshop [10] are presented in Figure€14.3. The testing conditions — wet or dry — were not reported. Examination of the figure suggests that the traces were produced by a Horizontal Pull Slipmeter (HPS); for example, the normal force value of 2.7 kg (6 lb) equals the HPS weight. In addition, the nearly uniformly increasing longitudinal pulling force — mislabeled as “lateral” force in the figure — implies that the device was motor operated. Point (a) represents commencement of the test, at which time the HPS was placed on the force plate. Application of the pulling force after 2 sec is seen. Segment (b), of about 4.5 sec, portrays the nearly uniformly increasing longitudinal force. The horizontal orientation of the longitudinal force after the breakaway point (c) evidences movement of the device. Segment (d) depicts removal of the longitudinal force. The spike seen in the normal-force plot of Figure€14.3 at point (a) illustrates a temporary disturbance in the force plate’s equilibrium after placement of the HPS. The bottom plot in the figure depicts inadvertent misapplication of the laws of metallic friction to the elastomer Neolite and is intended to quantify instantaneous coefficient values (μI) during testing. A static-coefficient-of-friction (μ) value of approximately 0.7 is alleged.

14.3.3.1 Inertial Bias The longitudinal-force plot in Figure€14.3 reveals that a maximum value of 1.8 kg (4 lb) was generated at breakaway. The increasing longitudinal force in this plot first overcame the total friction force (FT) developing and then counteracted the inertial resistance to movement (FI) exhibited by the HPS device. At breakaway, this may be expressed as

FT + FI = 1.8 kg (4 lb).

(14.3)

Point (e) in the longitudinal-force plot of Figure€14.3, evidencing a change in slope, appears to indicate the time at which inertial forces first arose, although testing with an accelerometer would have been required to verify this supposition. In any case, it is seen that not all of the longitudinal force applied to the HPS constitutes the static slip-resistance force developed between the device and the force plate: the HPS read high in these circumstances. The 1.8-kg (4-lb) force used to quantify the workshop’s [10] findings and develop its conclusions was erroneously high.

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Lateral Force (lb)

356 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 6

(e)

4 2 0 –2

(b) (a)

Normal Force (lb)

Lateral force inception Time

8 4

(a)

(d) (c)

(b)

2

1 Second

0

Lateral Force Normal Force

(d)

Breakaway

10 6

Static coefficient of friction 0.8

Time

(c) (d)

0.4 0.0

(c)

(b) (a)

Figure€14.3 Force-plate traces from an unspecified pull-meter. The testing conditions — wet or dry — were not reported. Point (a) represents commencement of the test, at which time the device was placed on the force plate. Application of the pulling force after 2 sec is seen. Segment (b), of about 4.5 sec, portrays a nearly uniformly increasing applied longitudinal force. Segment (c) evidences movement of the tester after breakaway. Segment (d) indicates removal of the longitudinal force. Point (e) suggests a change in slope of the longitudinal force trace. (From Bucknell University F-13 workshop to evaluate various slip resistance measuring devices, ASTM Standardization News, 20, 21, 1992. Copyright ASTM INTERNATIONAL. Reprinted with permission.)

14.3.3.2 Contact-Time Bias Figure€14.3 reveals that the HPS experienced a contact time of approximately 4.5 sec. As demonstrated by Braun and Roemer [15] and depicted in Figure€10.8, FT increases during a pull-meter’s contact time. Clearly, the HPS contact time of 4.5 sec in the workshop [10] and that of the dynamic Sigler [13] pendulum device, for instance, were unequal. The pendulum’s linear velocity is approximately 76 cm/sec (2.5 ft/sec) at contact with the floor, while the floor contact distance is 9.6 cm (3.76 in.). We see, therefore, that the slip-resistance values obtained from the different testers assessed in the ASTM F-13 workshop [10] were not comparable because of the different times of testfoot contact with the force-plate surface inherent in the design of the devices

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involved. Unfortunately, these differences in test-foot contact time were not accounted for in quantifying the workshop’s [10] results and developing its conclusions. 14.3.4 Developments Arising from the ASTM F-13 Workshop Conclusions The ASTM F-13 Task Force’s conclusions regarding sticktion appeared to validate the hypothesis that significant surface tension adhesion can develop in thin liquid layers between Neolite test feet and their smooth, paired surfaces. ASTM Committee F-13 contains many members active in the walking-surface-safety community who are users of Neolite test feet. As a result of the incorrect belief regarding the importance of sticktion, held by a large majority of the walking-surface-safety community, needed progress toward acquiring a better understanding of slip-resistance measurements from wet walking surfaces has been limited.

14.4

Measuring Footwear Outsole Microhysteresis on Wet Walking Surfaces in the Design Process

If the possible presence of footwear outsole microhysteresis in given wet conditions is to be determined, access to readily available, conveniently used testing apparatus capable of measuring this rubber friction force in the field is desirable. Proceeding on the basis that rubber microhysteresis force (FHs) is independent of both applied normal force and pressure, such a testing device could be portable and simple to operate. The apparatus need only be capable of applying a reasonable range of dynamic normal loads to walking surfaces at constant velocity through a selected material exhibiting appropriate properties and configured with sufficient mating planer surface area to ensure the representative microhysteresis forces are generated during testing. Although adhesion (FA) and macrohysteresis (FHb) slip-resistance components could also develop on macroscopically rough walking surfaces, plotting the total friction force measured vs. the normal loads employed would allow extrapolation of this curve to the y-axis and quantification of the FHs force. While a search for existing portable friction testers designed for use on macroscopically rough walking surfaces and also intended to apply multiple normal loads failed to identify such apparatus, there is one device that could likely be modified to meet these requirements for slip-resistance testing — the British Pendulum Tester. Among the design alterations to this device, necessary to allow it to measure microhysteretic forces, is the elimination of its inadvertent misapplication of the laws of metallic friction to rubber.

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358 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 14.4.1 Using the British Pendulum Tester for Microhysteresis Measurements on Rough Walking Surfaces 14.4.1.1 Background The 10-year developmental history of the British Pendulum Tester (BPT) was reviewed by Giles et al. [16] in a 1962 ASTM publication; thus, the device has been utilized in a practical manner for many years. It is employed to measure the skid-resistance of wet roadway pavements with different surface textures and to assess the degree of roadway aggregate traffic-polishing. The degree of traffic polishing is the extent to which the exposed aggregate’s original microtexture has been smoothed. The BPT is presently the subject of active ASTM Standard E 303 – 93 (Reapproved 2003), Standard Test Method for Measuring Surface Frictional Properties Using the British Pendulum Tester. The BPT test foot is wide enough and long enough to sample a representative road surface for exposed aggregate sizes up to 2.54 cm (1 in.). The British Pendulum Tester’s nominal applied load is 2.3 kg (5 lb). This is controlled by an adjustable tension spring in the pendulum arm. As will be addressed presently, Yandell [17] apparently reduced the BPT’s spring tension to obtain the lower applied loads employed in his testing, discussed in Chapter 5. The BPT operates on the same basis as the Sigler et al. [13] pendulum device (discussed in Chapter 4). The measured residual energy (as determined from the maximum height of the BPT pendulum’s center of mass during upswing after pavement contact) is subtracted from the known potential energy of the pendulum before release. This energy loss value is equated to the work WBPT done in overcoming friction between the device’s test foot and the pavement, yielding the following relationship,

WBPT = μFNavgDBPT, (?)

(14.4)

where: FNavg = average normal force between the test foot and pavement, and DBPT = the BPT’s contacted sliding distance. One can see, however, that Equation 14.4 involves application of the laws of metallic friction to rubber. Equation 14.4 should be written as follows:

WBPT ≠ μFNavgDBPT.

(14.5)

Redesign of the BPT’s readout scale to provide direct reading of forces is necessary if it is to be suitable for measuring rubber microhysteresis. Similar to the Sigler et al. [13] tester, the BPT device utilizes an inclined test foot. In the case of the BPT, a block of tire tread rubber inclined at approximately 20° to the tested surface, such that only the trailing edge of the tread material makes contact with the pavement. Lack of substantially mating planer surfaces may not allow representative microhysteresis mechanisms

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to develop during testing. A design alteration to the BPT to account for this concern, perhaps including a beveled forward edge on a horizontal tread block, does not appear impossible. 14.4.1.2 Back-Calculation Analysis of Yandell’s BPT Test Results Figure€3.12 depicted the phenomenological approach taken by Yandell [17] in his efforts to assist in understanding the contribution of roadway microroughness to tire traction in wet and dry conditions. He idealized the road surface texture and analyzed the macro- and microhysteretic contributions to friction by assuming that the macro- and microhysteretic coefficients are additive, yielding the theoretical equation

μHt = μHb + μHs. (?)

(14.6)

Because Equation 14.6 involves inadvertent misapplication of the laws of metallic friction to rubber, the expression should be written as

μHt ≠ μHb + μHs;

(14.7)

nevertheless, Yandell’s test data are of interest with regard to the use of the BPT to measure footwear outsole microhysteresis. Yandell’s research involved a computer-based, two-dimensional, mechano-lattice analysis of sliding rubber utilizing 264 mathematical units in his model for simulating the plane stress behavior of rubber. As the rectangular units slid on rigid model asperities, the units experienced cycles of load and deflection, generating hysteresis loops. The idealized, lattice-model asperities were either isosceles triangular prisms or smooth cylinders. This latter shape was intended to emulate road chips whose fine texture had experienced smoothing from traffic polishing. Figure€5.36 presented plots of Yandell’s findings for dry conditions, expressed here as the total theoretical hysteretic friction ratio μT vs. average slope of the idealized triangular prisms and cylindrical asperities selected. Five different sets of plots are depicted for rubber damping factors ξ, ranging from 0.1 to 0.5. It is seen that the triangular prisms produce higher μT values than do the cylinders. In addition, as the damping factor increases, so does the theoretical coefficient of hysteretic friction. To assess the accuracy of his lattice model, Yandell utilized small triangular prisms specially fashioned from brass and rigidly mounted in rows on a test bed. Friction measurements were carried out on this idealized asperity arrangement with a British Pendulum Tester. The device was fitted with a rubber test foot exhibiting a damping factor of 0.45. Yandell considered that reasonably accurate hysteretic coefficients from these tests could be calculated by subtracting friction measurements taken parallel to asperity rows from those measured perpendicular to the rows, leaving the relevant hysteretic force from which ratios could be determined.

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360 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces In addition to placing his pendulum device perpendicular to the rows of brass asperities, Yandell similarly obtained friction measurements by aligning the tester at an angle of 60° to them. In both alignments, he applied three normal loads — 0.68 kg (1.5 lb), 1.4 kg (3.1 lb), and 2.3 kg (5 lb). Although not specifically stated by Yandell, he was apparently able to obtain the 0.68 kg (1.5 lb) and 1.4 kg (3.1 lb) normal loads by reducing the BPT’s spring tension below the commonly used value that generated an applied load of 2.3 kg (5 lb). Because Yandell had theorized that what is often thought to be adhesion rubber friction is, in reality, a hysteretic phenomenon, the apparent areas of contact between the pendulum’s rubber test foot and the brass asperities were not involved in his calculations. Furthermore, the possible development of microhysteretic forces between the rubber test foot and the brass asperities by a different mechanism than that for the fine asperities depicted in Figure€3.12 was apparently not considered. A back-calculation analysis of Yandell’s data indicated that the adhesion-related rubber friction mechanism suggested in Figure€5.34 developed in his testing. Figure€5.38 presented our back-calculation analysis results of the 90° data expressed as total friction force vs. FN. It is seen that all three 90° data sets yield reasonably uniform plots, consistent with straight lines. Two of the plots, for average brass asperity surface slopes of 0.5 and 0.37, exhibit approximate y-intercepts of 50 g (0.1 lb) and 20 g (0.04 lb), respectively. These y-intercepts indicate the production of FHs forces in Yandell’s dry, 90° brass asperity testing. Figure€5.41 depicted back-calculation analysis results for the 60° BPT data expressed as the total friction force vs. FN. All three data sets yield reasonably uniform plots, consistent with straight lines. The average brass asperity surface slopes of 0.44, 0.32, and 0.20 exhibit approximate y-intercepts of 20 g (0.04 lb), 30 g (0.07 lb), and 20 g (0.04 lb), respectively. This is consistent with the production of FHs forces in Yandell’s dry, 60° brass asperity testing. It appears that, when fitted with suitable footwear outsole material, the British Pendulum Tester can be modified to measure microhysteretic walkingsurface-slip-resistance forces. Testing is needed to assess this possibility. 14.4.2 Using the Sigler Pendulum Tester for Microhysteresis Measurements on Smooth Walking Surfaces In 1948, Sigler et al. [13] described the development and use of a portable floor slip-resistance tester of the pendulum impact type that became known as the National Bureau of Standards (NBS), or Sigler, device. The measured residual energy (as determined from the maximum height of the pendulum’s center of mass during upswing after floor contact) is subtracted from the known potential energy of the pendulum before release. The result is considered to equal the work done during sliding of a 3.8-cm2 (1.5-in.2) testing foot over the floor surface. The work is considered equal to the average friction force developed during sliding, multiplied by the observed contact distance. An “antislip coefficient” is determined by dividing this calculated average slip-resistance force

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by a preset, average vertical force applied by the pendulum’s mechanical heel. Sigler et al. [13] employed a rubber test foot conforming to U.S. federal specification ZZ-R-601a. Their rubber test foot was abraded using No. 3/0 abrasive paper and brushed clean before each use to maintain a uniform roughness condition. Sigler et al. carried out calibration testing to determine the optimum, preset average vertical force to be applied through the mechanical heel by use of a spring. A variation in antislip coefficient values at different contact pressures was observed. Table€4.1 presented these results for the rubber test foot sliding on five macroscopically smooth floors in actual service. The three springs used in the calibration testing exerted the average forces presented in the table. These forces represent an approximate applied pressure during contact of 274 kPa (40 psi), 496 kPa (72 psi), and 827 kPa (120 psi). The pendulum stalled under the highest applied normal load on the Tennessee marble and asphalt tiles. As a consequence, no reading was obtained. A back-calculation, friction force analysis was carried out on the data presented in Table€4.1. Extrapolated y-intercepts were evidenced for the rubber test foot on all five flooring materials. Subtraction of these values from their corresponding FT readings produced extrapolated plots that passed through the origin. These five pendulum-impact data sets evidenced the presence of friction contributions from both surface deformation hysteresis and van der Waals’ adhesion developed on macroscopically smooth surfaces. Figure€5.23 presented the FT vs. FN plots for the standard rubber paired with the five flooring materials on the same axes. For clarity, the extrapolated portions of the FT vs. FN plots were omitted. The extrapolated y-intercept values were 0.18 kg (0.4 lb), 0.23 kg (0.5 lb), 0.57 kg (1.25 lb), 0.68 kg (1.5 lb), and 0.68 kg (1.5 lb) for the asphalt tile, Tennessee marble, rubber tile, linoleum, and cellulose nitrate tile, respectively. It appears that the Sigler pendulum device [13] can be used to measure microhysteretic walking-surface slip-resistance forces if interchangeable test-foot springs, possessing different spring constants, are supplied with the apparatus. A design alteration to this device necessary to allow it to measure microhysteresis is to eliminate its inadvertent misapplication of the laws of metallic friction to rubber.

14.5

Application of the Unified Theory to Analysis of Slip Resistance in the Design of Footwear Outsole-Walking Surface Pairings

14.5.1 Potential Benefits from Application of the Unified Theory to Friction Analysis As has been shown, the laws of metallic friction do not apply to rubber. The traditional approach to quantifying slip-resistance relationships is not

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362 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces founded on the physical mechanisms producing the friction forces generated during contact of footwear outsoles with walking surfaces. A scientifically based approach to determination of the magnitudes of these forces must be employed if maximum reliability is to be attached to our understanding of footwear traction properties. Application of the unified theory of rubber friction promotes accuracy by helping to eliminate the all-too-common error made by some engineers who believe that a decreasing coefficient of rubber friction (μ) under increasing loading means that walking-surface slip resistance is decreasing. This belief is incorrect. Slip resistance is still increasing, but at a decreasing rate. Unlike the coefficient of metallic friction — which is a material property — the rubber friction ratio is an artifice. Care must be taken when using rubber friction ratios to ensure they are meaningful. Application of the unified theory can provide the means to maximize the adhesion, microhysteresis, and macrohysteresis friction components of slip resistance on an optimal, comprehensive, and scientific basis. Use of the unified theory affords the opportunity to utilize a systems approach to analysis of slip resistance in the design of rubber footwear outsole-walking surface pairings in both dry and wet conditions. Detecting the presence of microhysteresis in an outsole in wet conditions — which can only arise from solid-to-solid contact — indicates that the walking surface microtexture has penetrated the liquid. Because microhysteresis depends on adhesion, the desirable presence of the adhesive slip-resistance component is also indicated. Designing to increase the readily detectable and quantifiable microhysteresis force can help to increase adhesion, which is not so readily quantifiable when macrohysteresis concurrently develops on rough, wet walking surfaces. 14.5.2 Rubber Outsole Macrohysteresis Mechanisms Rubber macrohysteresis is not often considered by walking surface safety specialists, although its development in footwear outsoles in contact with exterior, macroscopically rough walking surfaces is common as indicated by the walkways in Figures€13.1, 13.2, and 13.3. Analysis of data presented in these pages leads to the conclusion that macrohysteresis is a significant slipresistance-production mechanism. At least two different rubber FHs-force mechanisms appear to exist: (1) the adhesion-assisted form in wet and dry conditions and (2) the non-adhesion-assisted type in wet conditions. 14.5.2.1 Adhesion-Assisted Macrohysteresis on Dry Surfaces An illustration of both adhesive and macrohysteretic friction in rubber tires on roadway pavements, as envisaged by Kummer [18], was portrayed in Figure€3.8. The resultant adhesion forces are depicted operating parallel to the surface of the road chip, while the macrohysteresis forces are shown per-

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pendicular to the chip, indicating bulk compression of the tire tread on both sides of the protuberance. As discussed by Persson [19], however, adhesion between rubber and a hard surface can be considered as a pull-off phenomenon in which tensile forces are attempting to hold the two paired materials together. This visualization is illustrated in Figure€12.3. That is, the extent of draping of a tire tread over a dry pavement’s macrotexture is likely augmented by adhesion between the two surfaces, such that the area of physical contact between them is greater than that which would be produced by the applied normal load acting alone. We can expect that such assisted draping can also occur in footwear outsoles contacting protuberances present on macroscopically rough walking surfaces. Evidence will be presented in support of a new theory — that the mechanism of adhesion-assisted macrohysteresis in footwear outsoles can be physically linked to the adhesion friction mechanism in both dry and wet conditions. It appears that when the adhesion friction force (FA) is directly proportional to the applied normal load (FN) on macroscopically rough walking surfaces, so too is the macrohysteresis (FHb) friction force. This allows the two forces to be represented by the following equations:

FA = FNμA

(14.8)

FHb= FNμHb,

(14.9)

and

where: μA = rubber adhesion friction ratio, and μHb = rubber bulk deformation hysteresis friction ratio. Moreover, when the outsole’s adhesion transition pressure on macroscopically rough walking surfaces is reached, the adhesion-assisted macrohysteresis friction mechanism transitions accordingly, and the adhesion friction force and the macrohysteresis friction force can be represented by the following equations:

FA = c(FN)m

(14.10)

FHb = c(FN)m.

(14.11)

and

It should be noted, however, that the values of c and m in these expressions are not necessarily equal for the two mechanisms. Also, separation of FAfrom FHb is problematic.

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364 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 14.5.2.1.1 Hample’s testing Because of the lack of reported macrohysteretic friction testing of walking surfaces in the slip-resistance literature, it will be necessary to rely on such friction testing utilizing rubber tires on pavements and adapt the results to walking-surface safety. Chapter 7 examined Hample’s coefficient-of-friction tests on segments of a rubber B-29 tire. Figure€7.9 presented a plot of the results from a back-calculation analysis of Hample’s low-pressure testing on smooth portland cement concrete, in which no significant macrohysteresis could be expected. A straight line is indicated, which, upon extrapolation to the y-axis, evidences a constant FHs force of about 22.7 kg (50 lb). This lowpressure testing ranged up to an applied normal load of approximately 295 kg (650 lb). The straight-line character of the plot indicates that the adhesion transition pressure had not been reached in this testing. Plots of results from our back-calculation analysis of Hample’s high-pressure tire-segment testing on smooth, semi-smooth, and rough (broom-swept) concrete from which the FHs forces had been subtracted were presented in Figure€7.4. As shown in the figure, the smooth-concrete plot is straight up to approximately 295 kg (650 lb), but begins to curve shortly thereafter. This curvature indicates that the adhesion transition point had been reached; thus, the low- and high-pressure plots are consistent, insofar as the magnitude of the adhesion transition pressure is concerned. Figure€7.16 illustrated that the adhesion transition pressure on smooth concrete, found in the high-pressure plot, was approximately 2.76 MPa (400 psi). Examination of Figure€7.4 also reveals that friction-force values for the broom-swept concrete plot are greater than corresponding values for the smooth concrete. Figure€7.16 illustrates that the adhesion transition pressure for this rough concrete was approximately 1.79 MPa (260 psi), lower than the PNt value for the smooth-concrete testing. Figure€7.5 presents plots of our back-calculated rubber friction ratios from Hample’s high-pressure testing of the smooth and broom-swept surfaces. As shown, both test results exhibit horizontal — that is, directly proportional — friction ratios initially, transforming to hyperbolic curves after the adhesion transition pressures are reached. It was shown in Chapter 6 that on macroscopically smooth surfaces, the adhesion transition phenomenon arises at the point where, on average, equal increases in applied normal load produce diminishing increases in the real area of contact between rubber asperities and their paired surfaces. This behavior accounts for the corresponding decreases in the generated adhesion friction force. We will theorize that this same adhesion mechanism operates on macroscopically rough surfaces: the FA forces decrease when equal increases in FN produce reduced real areas of contact between the paired materials. If the adhesion component of the initial portion of the broom-swept concrete plot in Figure€7.5 was directly proportional to FN, so also must have been the macrohysteresis friction force component. The plot’s initial portion is horizontal, indicating direct proportionality throughout this segment. It

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will be theorized, therefore, that both FA and FHb forces were directly proportional to the applied normal load in the horizontal portion of the roughsurface plot presented in Figure€7.5. Application of this theory permits the FA and FHb forces developed in the broom-swept-concrete testing to be represented by Equations 14.8 and 14.9, respectively. Similarly, we can theorize that the FA and FHb forces generated in the semi-smooth concrete testing are represented by Equations 14.8 and 14.9, respectively. We can apply the same theory to the hyperbolic portions of the rough and semi-smooth concrete plots seen in Figure€7.5, quantifying the combined FA and FHb forces produced under loading above PNt in Hample’s testing: the adhesion and macrohysteretic friction mechanisms are physically linked, and their generated forces are represented by Equations 14.10 and 14.11, respectively. 14.5.2.1.2 Yandell’s testing Figures€5.38 and 5.41 presented forces back-calculated from Yandell’s [17] hysteretic friction testing in dry conditions utilizing a British Pendulum Tester fitted with a rubber test foot. These tests were conducted on rows of triangular brass asperities at angles of 90° and 60° to the rows. The brass asperities exhibited slopes specified in the figures. Because of the macrotexture involved, generation of both FA and FHb friction-force components likely occurred. Identification of the rubber friction mechanisms developed in this testing can be carried out by inspection of Figures€5.38 and 5.41. As seen in these figures, extrapolation of five of the plots evidences y-intercepts, indicating the production of FHs forces in those tests. The presence of microhysteresis in the rubber test foot in the dry conditions of the protocol implies that FA forces, as well as FHb forces, were generated in all six tests. All plots appear straight — evidencing direct proportionality — without subsequent curvature, suggesting that the adhesion transition pressure had not been exceeded. The friction-mechanism-related characteristics portrayed in the figures are consistent with the presence of FA and FHb friction-force components in all six data sets. We can apply the adhesion-assisted macrohysteresis theory to these results of the back-calculated findings from Yandell’s testing: the adhesion and macrohysteretic friction mechanisms are physically linked, and their generated forces FA and FHb are represented by Equations 14.8 and 14.9, respectively. 14.5.2.1.3 The adhesion-assisted macrohysteresis mechanism in dry conditions Figure€14.4 portrays a suggested mechanism for dry, adhesion-assisted macrohysteresis in a footwear outsole sliding on a walking-surface protuberance with a microtexture, as indicated. The adhesional area of contact between the sliding outsole and walking surface occurs where the outsole’s rubber asperities are compressed onto the protuberance at sliding velocity V. As FN increases, more compression of the rubber asperities takes place and FA increases. Assuming the increase in adhesion occurs in direct proportion to

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366 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces FN

Outsole

V

Figure€14.4 Suggested mechanism for dry, adhesionassisted macrohysteresis in a footwear outsole sliding on a walking-surface protuberance with a microtexture as indicated. The adhesional area of contact between the sliding outsole and walking surface occurs where the outsole’s rubber asperities are compressed onto the protuberance at sliding velocity V. As the applied force (F N) increases, the adhesion and macrohysteretic slip-resistance forces increase.

Protuberance

FN, the real area of contact will be growing in a constant, directly proportional manner. In addition to deformation of the outsole’s asperities, bulk deformation of the outsole is also taking place. Compressing forces pass through the deformed rubber asperities, and the outsole volumetrically assumes the protuberance’s configuration in a localized region. As we have seen, FHb appears to increase in constant, direct proportion to the applied normal load when FA exhibits this behavior. Apparently, the rubber volume experiencing bulk deformation as a result of outsole sliding increases in constant amounts when the real area of adhesional contact is also growing in equal increments. After reaching the adhesion transition pressure, FA grows at a diminishing rate with increases in FN, as do the deformed outsole bulk volume and rubber macrohysteresis slip-resistance force. 14.5.2.2 Adhesion-Assisted Macrohysteresis in Wet Conditions 14.5.2.2.1 Yager, Stubbs, and Davis testing of radial-belted tires Figure€8.4 presented the side friction forces back-calculated from the Yager et al. [21] radial-belted tire tests in wet conditions. These tests were also conducted at NASA Langley’s Aircraft Landing Dynamics Facility on a concrete test track runway that had a surface appearing to be moderately broomswept. Because of this macrotexture, generation of both FA and FHb frictionforce components can be expected. Identification of the tire friction mechanisms developed in this testing can be carried out by inspecting Figure€8.4. Extrapolation of the three yaw-angle plots depicted in the figure produces y-intercepts, indicating the generation of FHs forces. The presence of this microhysteresis in the test tires implies that FA forces, as well as FHb forces, developed. The 5° yaw-angle plot is initially straight — evidencing direct proportionality — followed by a curved portion indicating that the adhesion transition pressure had been exceeded. The plot in Figure€8.17 is also consistent with this conclusion. The 1° and 2° yaw-

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angle plots in Figure€8.4 appear straight throughout their length, suggesting direct proportionality in these tests. The friction-mechanism-related characteristics portrayed in Figures€8.4 and 8.17 are consistent with the presence of FA and FHb friction-force components in all three data sets. The indication of FA forces is also consistent with development of a nearly dry Zone 3 of the Three-Lubrication-Zones Concept discussed in Section 12.2.1. We can, therefore, apply the adhesion-assisted macrohysteresis theory to these results of our back-calculated findings from the Yager et al. [21] radial-belted tire tests: the adhesion and macrohysteretic friction mechanisms are physically linked, and their generated forces are represented by Equations 14.8 and 14.9 in the case of the 1° and 2° yaw-angle plots and by Equations 14.8, 14.9, 14.10, and 14.11 in the case of the 5° plot. 14.5.2.2.2 Sabey’s testing in which Zone-3 conditions developed Sabey [22] carried out lubricated-rubber coefficient-of-friction studies focusing on the skid resistance of motor vehicle tires. She slid steel spheres on tiretread rubber at a speed of 1.83 m/sec (6 fpsec) when lubricated with water. Such penetrated sliding produced bulk deformation in the tire-tread rubber, resulting in the development of FHb friction forces. Figure€4.58 depicted Sabey’s results for a 1.27-cm (0.5 in.) diameter sphere. It is seen that a hyperbolic relationship between μ and FN is displayed. The results of a back-calculation analysis of these data were illustrated in Figure€8.2. Extrapolation of the straight-line plot evidences a constant microhysteretic force of approximately 28.3 gm (0.25 lb). Generation of this FHs force indicates that dry conditions — and FA forces — developed in this test as a result of breakdown of the lubricating water film. The friction-mechanism-related characteristics portrayed in Figure€4.58 and Figure€8.2 for the 1.27-cm (0.5 in.) diameter sphere are consistent with the presence of FA and FHb friction-force components. The indication of FA forces is also consistent with development of a nearly dry Zone-3-type condition for this sphere. We can, therefore, apply the adhesion-assisted macrohysteresis theory to these results of our back-calculated findings from this Sabey test: the adhesion and macrohysteretic friction mechanisms are physically linked, and their generated forces are also represented by Equations 14.8 and 14.9. Sabey also investigated the macrohysteretic friction forces developed when sharper road-surface aggregate — idealized as smooth, rigid cones — penetrate tire-tread rubber at a sliding speed of 1.83 m/sec (6 fpsec) when well lubricated with water. Figure€4.59 presented Sabey’s coefficient-of-friction results for this protocol. The plots are hyperbolic for interior apex angles of 70°, 90°, 100°, and 160°. The results of a back-calculation analysis of these data were portrayed in Figure€8.3. Extrapolation of the straight-line plots to the y-axis indicates that microhysteretic forces arose in all four cases, suggesting that FHs, FA, and FHb forces developed in a nearly dry Zone-3-type condition on these cones.

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368 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Figure€8.16 presented log-log plots of our back-calculated findings from Sabey’s cone testing. These plots include points from the extrapolated segments of the lines. We see evidence of the adhesion transition phenomenon in each of the three data sets. In these cases, however, the slopes of the plots above the apparent adhesion transition point are 45°, demonstrating that the represented friction forces from single asperities are directly proportional to the applied normal load. Apparently, direct proportionality developed after the PNt pressure has been reached in these tests. The friction-mechanism-related characteristics portrayed in Figures€4.59, 8.3, and 8.16 are consistent with the presence of FA and FHb friction-force components. The indication of FHs and FA forces is also consistent with development of nearly dry Zone-3-type conditions on these cones. Thus, we can apply the adhesion-assisted macrohysteresis theory to the results of the backcalculated findings from these Sabey tests: the adhesion and macrohysteretic friction mechanisms are physically linked. Their generated FA forces appear to be represented by Equations 14.8 and 14.10, while the FHb forces can be represented by Equations 14.9 and 14.11. 14.5.2.2.3 The adhesion-assisted macrohysteresis mechanism in wet conditions Figure€14.5 illustrates a proposed mechanism for wet, adhesion-assisted macrohysteresis in a rubber outsole on a protuberance in a walking surface with a microtexture as indicated. The adhesional area of contact between the outsole and walking surface occurs where the rubber asperities are compressed by FN onto the protuberance at sliding velocity V. This model is similar to the one depicted in Figure€14.4, except that liquid is present. Nevertheless, the applied normal load, walking surface macrotexture drainage characteristics, and the outsole’s tread design have combined to produce a nearly dry Zone3-like area of contact with the chip’s microtexture. In addition to compression of the rubber asperities, bulk deformation of the outsole tread is also taking place. As postulated in regard to Figure€14.4, FHb increases in constant, direct proportion to the applied normal load when FA FN

Outsole

V

Protuberance

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Water

Figure€14.5 Suggested mechanism for wet, adhesionassisted macrohysteresis in a rubber outsole on a protuberance in a walking surface with a microtexture as indicated. The adhesional area of contact between the outsole and walking surface occurs where the rubber asperities are compressed by FN onto the protuberance at sliding velocity V. The applied normal load, walking surface macrotexture drainage characteristics, and the outsole’s tread design have combined to produce a nearly dry Zone3-like area of contact with the protuberance’s microtexture.

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exhibits this behavior. When FA grows at a diminishing rate with increases in FN, so do the deformed outsole bulk volume and the rubber macrohysteresis slip-resistance force. 14.5.2.3 Nonadhesion-Assisted Macrohysteresis on Fully Wetted Surfaces In contrast to conditions in which adhesion-assisted macrohysteresis is generated in an outsole-walking-surface system by producing a nearly dry Zone-3-like area between the contacting surfaces, we will consider that nonadhesion-assisted macrohysteresis arises only in fully wetted conditions. Under these specified circumstances, lubricated sliding is such that adhesion is reduced to negligible proportions — physical contact of the two solid materials is effectively prevented — and the only significant slip-resistance force present arises from bulk deformation macrohysteresis in the outsole. Sliding resistance from movement of, or adhesion of, the liquid is considered negligible. When these conditions are met, directly proportional macrohysteresis in the outsole is represented by Equation 14.9:

FHb = FNμHb.

Furthermore, we will theorize that a number of previously discussed rubber-friction investigations developed the fully wetted condition. It must be emphasized, however, that Equation 14.9 should be considered applicable only to outsole-walking-surface systems in which the walkingsurface macrotexture is of the broom-swept type, or at least approximates this roughness. As we have seen, and which is addressed briefly below, Equation 14.9 does not apply to the macrohysteretic conditions discussed by Bowden and Taber [23]. 14.5.2.3.1 Yager, Stubbs, and Davis testing of bias-ply tires in fully wetted conditions Figure€4.53 presented our back-calculated side coefficient-of-friction (μS) values obtained from the Yager et al. [21] bias-ply tire traction measurements in wet conditions. The coefficients were all directly proportional to the applied normal load. It was shown in Chapter 5 that decreasing μ values with increasing FN can be attributed to the presence of a constant microhysteresis force in rubber friction measurements. It will be theorized, therefore, that the Yager et al. bias-ply tire traction measurements in wet conditions contained no FHs components. Because Figure€7.11 indicated the presence of constant FHs forces in the Yager et al. dry bias-ply tires at all six yaw angles, along with generation of FA forces, we will theorize that no significant adhesion developed when testing these tires in wet conditions, and the only significant friction present arose from bulk deformation macrohysteresis in the rubber, represented by Equation 14.9.

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370 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 14.5.2.3.2 Sabey’s testing with fully wetted surfaces Figure€4.58 also depicted Sabey’s [22] results for the 0.48-cm (3/16-in.) and 0.64-cm (0.25 in.) diameter spheres. The corresponding plots for these data sets are parabolic. By inspection, we can expect that no rubber microhysteresis or adhesion friction forces developed in these tests. Figure€8.2, presenting findings from a back-calculation analysis of the two spheres’ friction data, provides corroboration for this belief: the plots for the 0.48-cm (3/16in.) and 0.64-cm (0.25 in.) diameter spheres are straight — evidencing direct proportionality — but do not intersect the y-axis at a positive value when extrapolated. There is no indication that either FHs or FA forces were generated in these protocols, allowing us to theorize that the only significant friction present arose from bulk deformation macrohysteresis in the rubber, represented by Equation 14.9. 14.5.2.3.3 Greenwood and Tabor’s testing with fully wetted surfaces Bowden and Tabor [23] discussed Greenwood and Tabor’s [24] testing involving sliding steel spheres on soap-lubricated rubber at speeds on the order of a few millimeters per second and deriving an equation for the macrohysteretic friction force developed in such circumstances. These considerations were presented in detail in Section 3.10. The rubber-friction-force relationship that successfully quantified the test data took the following form:

FHb = c(FN)4/3.

(14.12)

While Greenwood and Tabor also tested with fully wetted surfaces, it is clear that Equations 14.12 and 14.9 are not equivalent. Apparently, the Greenwood and Tabor macrotexture (i.e., the sliding spheres), generated bulk deformation of the rubber in which the volume experiencing such deformation did not increase in direct proportion to the applied normal load. The deformational differences accounting for the two types of macrohysteresis-force generation are likely associated, at least in part, with testing velocity. While Greenwood and Tabor’s sliding velocity was a few millimeters per second, Sabey employed a “high speed” of 6.6 km/h (6 fpsec), and Yager et al. utilized a velocity of 185.3 km/h (100 knots) in their testing. As implied in the traditional tire-slip plot depicted in Figure€12.2, at lower sliding speeds, frictional resistance increases with velocity. This arises because, in a given time interval, more slip-resisting pavement surface must be traversed. At a certain speed, however, the curve reaches a maximum and begins to decline. Kummer [18] attributed this phenomenon in dry conditions to stick-slip and temperature; that is, the bulk volume of deforming tread begins to diminish while, at the same time, frictional heating softens the tire rubber. Inasmuch as we are considering fully wetted conditions, it appears reasonable to expect that frictional-heating effects would become less important, leaving changes in the bulk-deformation-hysteresis mechanism as a principal reason for the different FHb relationships.

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371

Slip-Resistance Analysis in the Design of Footwear Outsoles Figure€14.6 Suggested mechanism for non-adhesionassisted macrohysteresis when an outsole slides at velocity V while being compressed by the applied load FN onto a walking surface protuberance with a microtexture as indicated. Because of the fully wetted conditions, no adhesion between the outsole and walking surface develops. The liquid present prohibits physical contact of the two materials. Bulk deformation of the outsole is the only significant slip-resistance mechanism to arise.

FN

Outsole

V

Protuberance

Water

14.5.2.3.4 The non-adhesion-assisted macrohysteresis mechanism in fully wetted conditions Figure€14.6 presents a proposed mechanism for non-adhesion-assisted macrohysteresis when an outsole slides at velocity V while being compressed by FN onto a walking surface protuberance with a microtexture as indicated. Because of the fully wetted conditions, no adhesion between the outsole and walking surface develops. A partially dry Zone-3-like area of contact with the protuberance’s microtexture is not produced. The liquid present prohibits physical contact of the outsole and walking surface. Bulk deformation of the outsole is the only significant slip-resistance mechanism to arise. 14.5.2.3.5 Velocity dependence of the macrohysteresis slip-resistance mechanism In a study of the dynamics of pedestrian slipping incidents under dry and wet conditions utilizing a force plate, Strandberg and Lanshammer [25] recorded the movement of 124 subjects’ shoe heels with a motion picture camera. It was revealed that heel slips often occurred upon contact with the force plate without a subsequent fall (arrested by a safety harness if one took place) or even a loss of balance. Strandberg and Lanshammer [25] stated: In most of the recorded experiments the heel was sliding upon heel strike. The sliding motions were often unnoticed [in a slip-stick situation] by the subject and occurred even without lubricant. Thus, dynamic properties seem to be more important than the static ones for avoiding slips and falls. The slip-stick data…indicate that sliding terminated if the so-called “friction use” (forward force divided by the downward force) increased after skid start. (p. 159)

While the “friction use” approach constitutes an inadvertent misapplication of the laws of metallic friction to rubber footwear outsoles, Strandberg and Lanshammer’s [25] findings are of note. The walking-surface-safety community has yet to reach consensus as to whether a static or dynamic

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372 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces basis should be utilized for quantifying a reasonably safe, slip-resistant walking surface. In any case, Strandberg and Lanshammer’s [25] finding that slipping can arise upon heel contact, without incident or notice by the pedestrian, demonstrates that dynamic slip-resistance mechanisms should be more fully investigated and integrated in the design of footwear outsoles and their paired walking surfaces. As such, we examine the velocity dependence of the macrohysteretic traction mechanism in rubber tires. The above analysis of the deformational differences accounting for the two types of macrohysteretic force generation mechanisms we have examined from roadway-traction testing indicates that, in wet-roadway conditions, the mechanism of FHb force development can change with increases in testing velocity. It has long been known from testing that rubber-tire coefficients of friction μ evidence general declines with increasing velocity. Figure€12.7 presented coefficient-of-friction results from a correlation study [26] to determine if ground-vehicle pavement testers can be substituted for specially instrumented aircraft to assess wet-runway slipperiness. The data in Figure€12.7 were obtained on smooth portland cement concrete that was either wetted or flooded with water. Five different ground-vehicle (roadwaypavement) testers were employed, along with two specially instrumented aircraft. Although the results, reported as μ vs. ground speed, exemplify inadvertent misapplication of the laws of metallic friction to rubber tires, the data trends are instructive. In all cases, μ decreases with speed. Figure€12.8 displayed reported μ vs. ground speed values for grooved asphalt. As in the concrete testing, a general decline in μ vs. speed is observed. The possible velocity dependence of macrohysteretic slip-resistance forces in footwear outsoles merits investigation. 14.5.3 Use of the Unified Theory for Slip-Resistance Analysis in Design of Footwear Outsoles and Their Paired Walking Surfaces The microhysteresis contribution to walking-surface slip resistance can be quantitatively separated from the adhesion and macrohysteresis components when the only independent variable in controlled testing is applied normal force or pressure. Because of this characteristic of rubber and other elastomers, utilization of the unified theory for slip-resistance analysis in the design of footwear outsoles and their paired walking surfaces would allow a scientifically based approach to be taken that is founded on the physical mechanisms producing the friction forces developed between the two surfaces. A skeletal outline of a process involving the steps necessary to allow utilization of the unified theory in the design of outsole-walking surface systems is now presented. This approach requires assembling an extensive library of design data, much of which is not currently available. It will also necessitate heightened interdisciplinary cooperation between the footwear-design and walking-surface design communities. The individual steps in the proposed process mimic those often found in the initial aspects of current engineering design practice.

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373

Slip-Resistance Analysis in the Design of Footwear Outsoles 14.5.3.1 Process Brief

The process brief is a statement of intent. Our intent is to outline a means by which the unified theory can be utilized for friction analysis in the design of footwear outsole-walking surface systems. 14.5.3.2 Process Specifications The process specifications are a list of action-item requirements necessary to allow application of the unified theory to friction analysis in the design of footwear outsole-walking surface systems. Table€14.2 presents a suggested preliminary list of specifications. 14.5.3.2.1 Theoretical basis for application of the unified theory Application of the unified theory requires that the steps taken to allow its use be focused on the friction-producing mechanisms generating the slipresistance forces developed between outsoles and walking surfaces. This, in turn, necessitates that the appropriate relationships expressing the slip-resistance forces be employed. The relationship expressing the unified theory of rubber friction can be stated as

FT = FHs + FA + FHb + FC.

(14.13)

where: FT = total frictional resistance developed between sliding rubber and a harder material, FA = frictional contribution from combined van der Waals’ adhesion of the two surfaces, FHs = frictional contribution from surface deformation hysteresis (microhysteresis), FHb = frictional contribution from bulk deformation hysteresis (macrohysteresis), and FC = cohesion loss contribution from rubber wear. Table€14.2 Specifications for Suggested Process To Allow Use of the Unified Theory for Rubber Friction Analysis in the Design of Footwear-Outsole-Walking Surface Systems Theoretical basis for application of the unified theory Action items for the footwear-outsole-design community Action items for the walking-surface-design community Action item concept design Action item detail design

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374 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Because cohesion losses due to outsole wear are usually negligible in the short term, Equation 14.13 reduces to

FT = FHs + FA + FHb.

(14.14)

It is suggested that Equation 14.14 be employed as the general relationship quantifying the unified theory. On macroscopically smooth walking surfaces, however, the macrohysteresis slip-resistance term can be ignored, and Equation 14.14 reduces to

FT = FHs + FA.

(14.15)

14.5.3.2.2 Action items for the footwear-outsole-design community Two action items for the footwear-outsole-design community are suggested:

1. Review presently used expressions for assessing the adequacy of footwear traction that inadvertently misapply the coefficient of rubber friction μ. Reformulate the technical approaches to these assessments and replace them with one or more based on FT, the total slip-resistance force generated.



2. Review current footwear wear outsole testing practices; identify those tests that purport to quantify slip resistance, and redesign such protocols and associated equipment to measure the slip-resistance terms in Equations 14.13 or 14.14.

14.5.3.2.3 Action items for the walking-surface-design community Two action items for the walking-surface-design community are proposed:

1. Review the presently used technical approaches and associated equations for assessing the adequacy of walking-surface slip resistance that inadvertently misapply the coefficient of rubber friction μ. Reformulate these approaches to base them on FT, the total slipresistance force generated.



2. Review current walking-surface-testing practices; identify those tests that purport to quantify slip resistance, and redesign such protocols and associated equipment to measure the slip-resistance components in Equations 14.13 and 14.14.

14.5.3.3 Action Item Concept Design Identify and outline the key steps in their proper order necessary to carry out the action items suggested above as efficiently as possible.

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While the exact details involved in these steps need not be determined at this stage, it is beneficial to consider the process specifications as well as the downstream activities needed to carry out the above-mentioned action items. Depending on the circumstances involved, it may be advantageous to design a number of different viable concepts for accomplishing the desired action items and to evaluate them to determine the most suitable approach to be developed further. Concept design is often a two-stage process of generation and evaluation. Preliminary discussions between the tire-design and roadway-design communities may be appropriate at this stage. 14.5.3.4 Action Item Detail Design Develop the chosen action item concept design in detail. The steps necessary to accomplish the action items are now designed in detail. This may well include organizational and/or personnel assignments, task allocation, location, equipment involved, field testing, cost projections, and timelines. Interdisciplinary partnerships between the footwear-design and walking-surface-design communities are called for at the stage to accomplish the desired tasks in a manner producing technical results with the maximum reasonable degree of scientific certainty.

14.6

Chapter Review

This chapter focused on the application of the unified theory of rubber friction detailed in previous chapters to footwear-outsole-walking surface pairings. One intent of this book was to improve the analysis of slip resistance as it is developed between outsoles and walking surfaces as they are presently designed and constituted. Improving our understanding of the traction forces generated between outsoles and walking surfaces through scientifically based analysis of the slip-resistance mechanisms they develop can be useful in reexamining existing outsoles and walking surfaces and perhaps serve as a starting point in improving present design practice. The chapter first addressed the importance of rubber microhysteretic forces in wet conditions. This was followed by a discussion of the need to reformulate the traditional approach to walking-surface slip-resistance testing. We then considered measurement of outsole microhysteresis on wet walking surfaces and suggested a process through which the unified theory can be applied to assist in the analysis of slip resistance in the design of outsoles and their paired surfaces.

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376 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 14.6.1 Importance of Rubber Microhysteresis in Wet Conditions It has long been recognized in the study of rubber-tire traction that pavement microroughness plays an important role in allowing drivers to control their vehicles on wet roadways. Recognition of the importance of walkingsurface microroughness in wet conditions is not so widespread in the pedestrian ambulation safety community. This unfortunate situation exists even though most foot slips resulting in serious falls occur on liquid-contaminated surfaces. It is thought by some [6] that considerable potential benefit exists if the pedestrian ambulation safety community would integrate the motor vehicle world’s understanding of microhysteretic wet-traction into analysis and testing of walking-surface slip resistance in liquid-lubricated conditions. A synopsis of the motor vehicle world’s research findings in this regard was presented. 14.6.1.1 Three-Lubrication-Zones Concept The Three-Lubrication-Zones Concept is a frequently used model of water displacement by a rolling or sliding tire on wet pavement. Figure€12.1 illustrated this concept. It is considered that while some encountered water is displaced to the front of the moving tire, the tire rides on an unbroken water film in lubrication Zone 1, as some of this water is gradually squeezed out the sides. The middle Zone 2 is one of transition in which initial physical contact between the tire and the roadway develops, while in Zone 3 only a thin water film at most remains and the tire makes contact with the pavement microtexture through this film. It has been traditionally thought that nearly all wet-traction skid resistance is developed in Zone 3. 14.6.1.2 Traditional Wet-Roadway Texture Analysis A number of studies [2] have concluded that wet-roadway skid resistance is governed by pavement macroroughness regarding removal of bulk water and pavement microroughness in the role of creating real areas of tire contact and adhesive traction. A British study examining the seasonal variation of wet-roadway skid resistance found that wet traction rose to a maximum in the winter and fell to a minimum in summer. Photomicrographs of inservice pavements revealed that surface microroughness also increased to a maximum in winter due to frost and other natural weathering action on the road aggregate during this period. On the other hand, traffic-polishing of the roadway’s aggregate was dominant during the summer, removing the aggregate’s microroughness to a considerable degree. These trends correlate well with the number of wet-skidding incidents in Britain — fewer in winter and a greater number in summer. The same climatologically related phenomenon has been observed under controlled conditions at a highway pavement research facility in the United States. Beginning in 1974, the Transportation Research Center

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of Ohio became involved in a U.S. Federal Highway Administration program designed to develop test centers where skid trailers could be calibrated on skid pads [3]. The skid pads operated over a 9-year period and evidenced a seasonal variation in skid resistance, generating maximum average monthly traction values in the winter, which fell to a minimum in the summer months. The winter increases are consistent with an increased contribution from microhysteresis to skid resistance measurements made during that season, when harsher weather apparently produced degradation-roughening of the pad surfaces. These microhysteretic roadway-related findings correlate well with the unpublished experience of the author when making walking-surface-slipresistance measurements on flooring in both dry and wet conditions. The older and more worn smooth flooring surface was found to be, the lower were the slip-resistance measurements obtained from it, compared to readings taken on unworn but otherwise identical material. (Such flooring can often be found in a little-used corner of the subject room.) 14.6.1.3 Importance of Aircraft Tire Microhysteresis on Wet Pavement Just as the importance of a pavement’s microtexture regarding tire roadholding ability in wet conditions was accepted by roadway design engineers [4], the importance of aircraft runway and taxiway microtexture to pilots during landing and taxiing in wet conditions has also been accepted by the aviation community. Yager [5] reported this acceptance in his 1990 article concerning tire-runway friction. 14.6.1.4 Corroboration for the Three-Lubrication-Zones Concept as Applied to Walking-Surface Slip Resistance The chapter presented an analysis of slip-resistance data from testing carried out by Tisserand [7], Grönqvist [8], and Redfern and Bidanda [9] utilizing smooth walking surfaces. The evidenced production of microhysteresis forces in these studies indicates that a Zone-3-like area can develop in wetslip-resistance testing and therefore likely also to arise on footwear outsoles during pedestrian ambulation on smooth surfaces in wet conditions. 14.6.2 Reformulating the Traditional Approach to Walking-Surface Slip-Resistance Testing Regrettably, much of the pedestrian ambulation safety community has been inadvertently misapplying the laws of metallic friction to rubber friction for a considerable period of time. Because of this situation, reformulation of the traditional approach to walking-surface slip-resistance testing, in both dry and wet conditions, is necessary if scientifically reliable footwear traction information is to be developed.

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378 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Because most pedestrian slips occur when walking surfaces are wet, the chapter focused mostly on this condition. The findings and recommendations presented are, however, also applicable to dry walking surfaces. It is instructive to exemplify consequences from use of slip-resistance measurements obtained by testers unknowingly exhibiting various forms of bias employed to draw erroneous conclusions and incorrect findings. This was done utilizing wet and dry test results obtained at the ASTM Committee F13 Bucknell University workshop [10]. The incorrect findings in this case are particularly important because they contribute to widespread misinterpretation of wet-slip-resistance-testing results.

14.6.2.1 Test Results from the ASTM F-13 Bucknell University Workshop The purpose of the 1991 workshop conducted by ASTM Committee F-13 at Bucknell University [10] was to: • Evaluate the performance of slip testers in dry and wet conditions. • Compare each tester’s readings to measurements from a force plate. • Determine which testers provide reliable, consistent results. This evaluation involved testing a glazed, smooth tile mounted on a force plate. Nine devices were investigated but the present analysis was restricted to the five testers previously examined. These five devices are listed in Table€14.1. In the workshop [10] test series of interest, all five devices were fitted with Neolite test feet. All Neolite test feet were prepared for use by sanding them in an identical manner. The testers were employed in accordance with their respective ASTM standards, if such existed.

14.6.2.2 Effect from Inadvertent Misapplication of the Laws of Metallic Friction to Rubber Friction Figure€14.1 displays the reported wet and dry μ values from the workshop [10] test series of interest, calculated by inadvertent misapplication of the laws of metallic friction to rubber. Because the equation used to quantify the measurements did not account for the rubber friction-force-producing mechanisms developed during testing, neither an evaluation of participant tester performance nor a determination of measurement reliability or consistency could be made on a scientific basis.

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14.6.2.3 Effect from the Presence of Unquantified Inertial Forces in Workshop Test Measurements Figure€14.2 depicts the results of an analysis of Figure€14.1’s data in which the problematic μ values are replaced by the total force measured in each case. As seen in Figure€14.2, a different picture is revealed. The testers are in different relationships to each other. Furthermore, while Figure€14.2 is intended to allow comparison on the basis of the slip-resistance forces developed, such is not possible. The unquantified inertial-force components — which are not slip-resistance forces — present in all devices except the Sigler pendulum tester, make up a portion of the total force measured. Because of these unquantified inertial-force components, neither an evaluation of tester performance nor a determination of measurement reliability or consistency could be made on a scientific basis. 14.6.2.4 Effect from the Presence of Contact-Time Bias in Workshop Test Measurements As depicted in Figure€14.2, there is a noticeable difference between the Sigler pendulum tester’s dynamic slip-resistance results and those of the other devices, all of which measure static slip resistance (although the PIAST can be considered to be a dynamic tester). The wet and dry Sigler results were the lowest of the group of five in both conditions. These lower values are due, at least in part, to a shorter contact time for the Sigler pendulum’s test foot compared to the contact times experienced by the other devices. Contact time is important because the slip-resistance force generated increases with increased contact time. The magnitude of the slip-resistance force time-dependent increase varies with the design of the particular tester. The slip-resistance forces generated in the ASTM F-13 workshop [10] were not comparable because different contact times for each device were involved. Because of this contact-time bias present in the workshop investigations, neither an evaluation of tester performance nor a determination of measurement reliability or consistency could be made on a scientific basis. 14.6.2.5 Effect from the Presence of Test-Foot-Area Bias in Test Measurements Analysis of the Roth et al. [11] and Thirion [12] data in Chapter 5 revealed that the total friction force produced can depend on rubber specimen size. The devices listed in Table€14.1 possess different test-foot areas. Because of the test-foot-area bias present in the workshop investigations, neither an evaluation of tester performance nor a determination of measurement reliability or consistency could be made on a scientific basis.

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380 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces 14.6.3 Conclusions from the ASTM F-13 Bucknell Workshop: Sticktion Unfortunately, a preconceived notion concerning friction measurements of smooth, wet walking surfaces obtained from portable slip-resistance testers was (and still is) in wide circulation in the walking-surface-safety community before the ASTM F-13 workshop [10]. This notion concerns “sticktion,” or the development of surface tension adhesion in a thin liquid layer between a test foot and the floor. Such surface tension is believed to develop significant adhesion between the test foot and floor during testing, biasing obtained slip-resistance measurements to falsely high values. On the basis of the test results presented in Figure€14.1, the ASTM F-13 Task Force organizing the workshop [10] concluded that sticktion developed during use of the three pull-meters cited in the figure — the HPS, HP-M, and TPCM 80. This conclusion as to tester reliability and consistency was stated as follows: When both the walkway surface and shoe sole or heel surface are smooth, liquid contaminants may develop adhesion between two surfaces, thus exhibiting a falsely high coefficient of friction or slip resistance. This arises from the fact that even a short time delay between application of the normal or contact force and application of the tangential force can permit the squeezing out of any liquid present, resulting in a thin layer of liquid that can cause adhesion and a high resistance to slip…it was observed that many of the testers had this problem when tested under wet conditions. (p. 23)

It was shown in this chapter, however, that neither an evaluation of tester performance nor a determination of measurement reliability or consistency could be made on a scientific basis because of inadvertent misapplication of the laws of metallic friction to rubber, the presence of unquantified inertial forces in the test measurements, the existence of test-foot-area bias, and the contact-time bias exhibited by all testers but the Sigler [13] device. The “observation” by the participants that “many” testers evaluated in the ASTM F-13 workshop [10] exhibited sticktion was not scientifically based. This is unfortunate because the findings developed on the bases of this testing have had wide and detrimental consequences. The ASTM F-13 Task Force’s conclusions regarding sticktion appeared to validate the preconceived notion that significant surface tension adhesion can develop in thin liquid layers between Neolite test feet and their smooth, paired surfaces. ASTM Committee F-13 contains many members active in the walking-surface-safety community who are users of Neolite test feet. As a result of the incorrect belief regarding the importance of sticktion, held by a majority in the walking-surface-safety community, needed progress toward acquiring a better understanding of slip-resistance measurements from wet walking surfaces has been limited. No significant sticktion developed between the workshop [10] testers fitted with a Neolite test foot and the tile surface. The higher measurements

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observed in wet testing with the HPS, HP-M, and TPCM 80 devices observed in Figure€14.1 came, in part, from the presence of the unaccounted-for inertial forces. Smith [14] provided corroboration for the absence of sticktion in the workshop [10] test-foot measurements. He examined the issue of sticktion development when utilizing walking-surface slip-resistance testers equipped with Neolite test feet. It was found that the magnitude of surface tension adhesion forces that can arise between water and a Neolite test foot paired with a smooth surface is not significant. Any previous slip-resistance studies misapplying the laws of metallic friction to rubber materials and purporting to demonstrate the development of sticktion in Neolite are invalid. 14.6.4 Measuring Footwear Outsole Microhysteresis on Wet Walking Surfaces in the Design Process To determine footwear outsole microhysteresis in given wet conditions, access to readily available, conveniently used testing apparatus capable of measuring this rubber slip-resistance force in the field is desirable. The apparatus must be capable of applying a reasonable range of dynamic loads to walking surfaces through a selected test-foot material exhibiting appropriate properties to ensure that representative microhysteresis forces are generated during testing. While a search for existing slip-resistance testers designed for use on rough walking surfaces and also intended to apply multiple normal loads failed to identify such apparatus, there is one device that could likely be modified to meet these requirements for slip-resistance testing: the British Pendulum Tester (BPT). This chapter reviewed its design. 14.6.4.1 Using the British Pendulum Tester for Outsole Microhysteresis Measurements on Rough Walking Surfaces The 10-year developmental history of the British Pendulum Tester (BPT) was summarized by Giles et al. [16] in a 1962 ASTM publication; thus, the device has been utilized in a practical manner for many years. It is usually employed to measure the skid resistance of wet roadway pavements with different surface textures and to assess the degree of roadway aggregate traffic polishing. The degree of traffic polishing is the extent to which the exposed aggregate’s original microtexture has been smoothed. At present, the BPT inadvertently misapplies the laws of metallic friction to rubber. The BPT’s test foot is wide enough and long enough to test walking surfaces containing exposed aggregate sizes up to 2.54 cm (1 in.). The BPT’s applied load is controlled by an adjustable tension spring in the pendulum arm. The tester operates on the same basis as the Sigler et al. [13] pendulum device (discussed in Chapter 4). Redesign of the BPT’s readout scale

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382 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces to provide direct reading of forces is necessary if it is to be suitable for measuring microhysteretic slip resistance on walking surfaces. 14.6.4.2 Using the Sigler Pendulum Tester for Microhysteresis Measurements on Smooth Walking Surfaces In 1948, Sigler et al. [13] described the development and use of a portable floor slip-resistance tester of the pendulum impact type that came to be known as the National Bureau of Standards (NBS), or Sigler, device. As part of their investigations, Sigler et al. [13] conducted calibration testing to determine the optimum force to be applied to the tested surface through the device’s mechanical heel by use of three different springs. A variation in antislip coefficient values μ at different spring loads for each material was observed. Although the Sigler et al. [13] tester inadvertently misapplies the laws of metallic friction to rubber, a slip-resistance force analysis detailed in Chapter 5 revealed that microhysteretic forces were measured on five floors. It appears that the Sigler device can be used to measure microhysteretic walking-surface slip-resistance forces if interchangeable test-foot springs of different strengths are supplied with the apparatus. 14.6.5 Application of the Unified Theory to Analysis of Slip Resistance in the Design of Footwear Outsole-Walking Surface Pairings 14.6.5.1 Potential Benefits from Application of the Unified Theory to Slip-Resistance Analysis Previous chapters have shown that the laws of metallic friction do not apply to rubber. The traditional approach to quantifying slip-resistance is not founded on the physical mechanisms producing the friction forces generated during contact of footwear outsoles with walking surfaces. A scientifically based approach to determination of the magnitudes of these forces must be employed if maximum reliability is to be attached to our understanding of footwear traction properties. Application of the unified theory of rubber friction to slip-resistance analysis promotes accuracy by helping to eliminate the all-too-common error made by some engineers, who believe that a decreasing coefficient of rubber friction (μ) under increasing loading means that walking-surface slip resistance is decreasing. This belief is incorrect. Slip resistance is still increasing, but at a decreasing rate. Application of the unified theory can provide the means to maximize the adhesion, microhysteresis, and macrohysteresis friction components of slip resistance on an optimal, comprehensive, and scientific basis. Use of the unified theory affords the opportunity to utilize a systems approach to analysis of slip resistance in the design of rubber footwear-outsole-walking-surface pairings in both dry and wet conditions. Detecting the presence of microhysteresis in an outsole in wet conditions — which can only arise from solid-to-

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solid contact — tells us that the walking surface microtexture has penetrated the liquid. Because microhysteresis depends on adhesion, the desirable presence of the adhesive slip-resistance component is also indicated. 14.6.5.2 Rubber Outsole Macrohysteresis Mechanisms in Wet and Dry Conditions Rubber outsole macrohysteresis is not often considered by walking surface safety specialists; nevertheless, its development in footwear outsoles in contact with rough exterior walking surfaces is common. Such surfaces are depicted in Figures€13.1, 13.2, and 13.3. Analysis of data and figures presented in these pages leads to the conclusion that macrohysteresis is a significant slip-resistance-production mechanism for pedestrians. At least two different rubber macrohysteretic slip-resistance mechanisms appear to exist: (1) the adhesion-assisted form in wet and dry conditions and (2) the nonadhesion-assisted form in wet conditions. 14.6.5.2.1 Adhesion-assisted outsole macrohysteresis on dry walking surfaces An illustration of both adhesive and macrohysteretic friction in rubber tires on roadway pavements, as envisaged by Kummer [18], was portrayed in Figure€3.8. The resultant adhesion forces are depicted operating parallel to the surface of the road chip, while the macrohysteresis forces are shown perpendicular to the chip, indicating bulk compression of the tire tread on both sides of the protuberance. As discussed by Persson [19], however, adhesion between rubber and a hard surface can be considered as a pull-off phenomenon in which tensile forces are attempting to hold the two paired materials together. This visualization is illustrated in Figure€12.3. That is, the extent of draping a tire tread over a dry pavement’s macrotexture is likely augmented by adhesion between the two surfaces, such that the area of physical contact between them is greater than that which would be produced by the applied load acting alone. We can expect that such adhesion-assisted draping can also occur in footwear outsoles contacting protuberances present on rough walking surfaces. This chapter presented evidence in support of a new theory: that the mechanism of adhesion-assisted macrohysteresis in footwear outsoles can be physically linked to the adhesion friction mechanism in both dry and wet conditions. It appears that when the adhesion slip-resistance force (FA) is directly proportional to the applied load (FN) on rough walking surfaces, so too is the macrohysteresis (FHb) slip-resistance force. Moreover, when the outsole’s adhesion transition pressure on rough walking surfaces is reached, the adhesion-assisted macrohysteresis friction mechanism transitions accordingly, and the adhesion slip-resistance force and the macrohysteresis slip-resistance force are not directly proportional. Figure€14.4 illustrates a suggested mechanism for dry, adhesion-assisted macrohysteresis in a footwear outsole initially sliding at velocity V on a rough walking-surface protuberance with a microtexture, as indicated. If

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384 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces the total slip-resistance force developed (FT) is great enough, the foot will stop sliding. The adhesional area of contact between the sliding outsole and walking surface occurs where the outsole is compressed onto the protuberance. When FN increases as more of the pedestrian’s weight is applied to the protuberance, additional compression of the outsole takes place, and FA increases. Assuming the increase in adhesion occurs in direct proportion to FN, FA will be growing in a directly proportional manner. In addition to deformation of the outsole’s surface, bulk deformation of the rubber is also taking place. Compressing forces from the pedestrian’s weight pass through the compressed rubber, and the outsole volumetrically assumes the protuberance’s configuration in a localized region. The FHb force appears to increase in direct proportion to the applied load when FA exhibits this behavior. If the adhesion transition pressure is reached, FA then grows at a diminishing rate with increases in FN, as does the rubber macrohysteretic slip-resistance force. 14.6.5.2.2 Adhesion-assisted outsole macrohysteresis on wet walking surfaces Figure€14.5 suggests a proposed mechanism for wet, adhesion-assisted macrohysteresis in a rubber outsole on a protuberance in a rough walking surface with a microtexture, as indicated. The adhesional area of contact between the outsole and walking surface occurs where the rubber is compressed by FN, as more of the pedestrian’s weight is applied to the protuberance at sliding velocity V. This model is similar to the one depicted in Figure€14.4, except that liquid is present. Nevertheless, the applied load, walking surface macrotexture drainage characteristics, and the outsole’s tread design have combined to produce a nearly dry Zone-3-like area of contact with the protuberance’s microtexture. As postulated in regard to Figure€14.4, FHb increases in direct proportion to the applied normal load when FA exhibits this behavior. When FA grows at a diminishing rate with increases in FN, so does the rubber macrohysteresis slip-resistance force. 14.6.5.2.3 Non-adhesion-assisted macrohysteresis in fully wetted conditions In contrast to wet conditions, in which adhesion-assisted macrohysteresis is generated in an outsole-walking surface pairing by producing a nearly dry Zone-3-like area between the contacting surfaces, at least two non-adhesion-assisted macrohysteresis mechanisms appear to develop in fully wetted conditions. Under these circumstances, lubricated sliding of footwear on a contaminated walking surface is such that adhesion is reduced to negligible proportions — physical contact of the outsole and walkway is effectively prevented — and the only significant slip-resistance force present, FHb, arises from bulk deformation hysteresis in the outsole. The equations used to calculate FHb for the different macrohysteresis mechanisms are different. Figure€14.6 presents a proposed mechanism for non-adhesion-assisted macrohysteresis when an outsole slides at velocity V while being compressed by FN onto a rough walking surface protuberance with a microtexture, as

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indicated. Because of the fully wetted conditions, a partially dry Zone-3-like area of contact with the protuberance’s microtexture is not produced. The liquid film present prohibits physical contact between the outsole and walking surface. 14.6.5.3 Use of the Unified Theory for Slip-Resistance Analysis in Design of Footwear Outsoles and Their Paired Walking Surfaces The rubber microhysteretic force contribution to walking-surface slip resistance can be quantitatively separated from the adhesion and macrohysteresis force components when properly controlled testing is performed. Because of this characteristic of rubber, utilization of the unified theory detailed in these pages for slip-resistance analysis in the design of footwear outsoles and their paired walking surfaces would allow a scientifically based approach to be taken that is founded on the physical mechanisms producing the friction forces developed between the two surfaces. A process involving the steps necessary to allow utilization of the unified theory in the design of outsole-walking surface systems will require assembling an extensive library of design data, much of which is not currently available. It will also necessitate heightened interdisciplinary cooperation between the footwear-design and walking-surface-design communities. The individual steps in such a design process would mimic those often found in the initial aspects of current engineering design practice.

References





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1. Gough, V.E., A tyre engineer looks critically at current traction physics, in The Physics of Tire Traction—Theory and Practice, Hays, D.F. and Browne, A.L., Eds., Plenum Press, New York, 1974, chap. III. 2. Bond, R., Lees, G., and Williams, A.R., An approach towards the understanding and design of the pavement’s textural characteristics required for optimum performance of the tyre, in The Physics of Tire Traction—Theory and Practice, Hays, D.F. and Browne, A.L., Eds., Plenum Press, New York, 1974, chap. IV. 3. Whitehurst, E.A. and Neuhardt, J.B., Time-history performance of reference surfaces, in The Tire Pavement Interface, ASTM STP 929, Pottinger, M.G. and Yager, T.J., Eds., American Society for Testing and Materials, West Conshohocken, PA, 1986, 61. 4. Williams, A.R., A review of tire traction, in Vehicle, Tire, Pavement Interface, Henry, J.J. and Wambold, J.C., Eds., American Society for Testing and Materials, West Conshohocken, PA, 1992, 125. 5. Yager, T.J., Tire/runway friction interface, Paper 901912, Emerging Technologies in Aircraft Landing Gear, Tanner, Ulrich, Medzorian, and Morris, Eds., SAE International, PT-66, Warrendale, PA, 1997.

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6. Strandberg, L., The effect of conditions underfoot on falling and overextension accidents, Ergonomics, 28, 131, 1985. 7. Tisserand, M., Progress in the prevention of falls by slipping, Ergonomics, 28, 1027, 1985. 8. Grönqvist, R., Mechanisms of friction and assessment of slip resistance of new and used footwear soles on contaminated floors, Ergonomics, 38, 224, 1995. 9. Redfern, M.S. and Bidanda, B., Slip resistance of the shoe-floor interface under biomechanically relevant conditions, Ergonomics, 37, 511, 1994. 10. Bucknell University F-13 workshop to evaluate various slip resistance measuring devices, ASTM Standardization News, 20, 21, 1992. 11. Roth, F.L., Driscoll, R.L. and Holt, W.L., Frictional properties of rubber, J. Res. Nat. Bur. Stds. 28, 439, 1942. 12. Thirion, P., Les coefficients d’adhérence du caoutchouc, Rev. Gén. Caoutch., 23, 101, 1946. 13. Sigler, P.A., Geib, M.N., and Boone, T.H., Measurement of the slipperiness of walkway surfaces, J. Res. Nat. Bur. Stds., 40, 339, 1948. 14. Smith, R.H., Examination of sticktion in wet-walkway slip-resistance testing, in Metrology of Pedestrian Locomotion and Slip Resistance, ASTM STP 1424, M.I. Marpet and M.A. Sapienza, Eds., ASTM International, West Conshohocken, PA, 73, 2002. 15. Braun, R. and Roemer, D., Influences of waxes on static and dynamic friction, Soap/Cosmetics/Chemical Specialties, 50, 60, 1974. 16. Giles, C.G., Sabey, B.E., and Cardew, K.H.F., Development and performance of the portable skid-resistance tester, in Symposium on Skid Resistance, American Society for Testing and Materials, Philadelphia, PA, 1962, 50. 17. Yandell, W.O., A new theory of hysteretic sliding friction, Wear, 17, 229, 1970. 18. Kummer, H.W., Unified Theory of Rubber and Tire Friction, Engineering Research Bulletin B-94, The Pennsylvania State University, University College, PA, 1966. 19. Persson, B.N.J., Sliding Friction, Physical Principles and Applications, Springer-Verlag, Berlin, 2000. 20. Hample, W.G., Friction Study of Aircraft Tire Material on Concrete, National Advisory Committee for Aeronautics, Washington, D.C., 1955. 21. Yager, T.J., Stubbs, S.M., and Davis, P.M., Aircraft radial-belted tire evaluation, paper 901931, Emerging Technologies in Aircraft Landing Gear, Tanner, Ulrich, Medzorian, and Morris, Eds., SAE International, PT-66, Warrendale, PA, 1997. 22. Sabey, B.E., Pressure distributions beneath spherical and conical shapes pressed into a rubber plane, and their bearing on coefficients of friction under wet conditions, Proc. Roy. Soc. A, 71, 979, 1958. 23. Bowden, F.P. and Tabor, D., The Friction and Lubrication of Solids, Part II, Clarendon Press, Oxford, 1964. 24. Greenwood, N.A. and Tabor, D., The friction of hard sliders on lubricated rubber: the importance of deformation losses, Proc. Phys. Soc., 71, 989, 1958. 25. Strandberg, L. and Lanshammer, H., The dynamics of slipping accidents, J. Occupational Accidents, 3, 153, 1981. 26. Horne, W.B., Status of Runway Slipperiness Research, National Aeronautics and Space Administration, N77-18092, Washington, D.C., 1976.

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Index A Acrylonitrile butadiene rubber, 56, 63, 64, 65, 123, 168 coefficient of friction testing of aluminum sliding on, 60 coefficient of friction testing of Teflon® sliding on, 61 measure friction vs. applied normal for aluminum sliding on, 61 Adhesion bulk deformation hysteresis and, 27 mechanism, 305, 364 effects of wet lubricants on, 191–192 van der Waal’s, 60, 124 metallic coefficient, 11–12 as rubber friction mechanism, 18, 39 sliding rubber and, 28–30, 43 on smooth solids, surface free energy and, 56, 59–61 van der Waals’, 28 Adhesion-transition, 162–163 bias, 247 irremediable, 242–245 in pedestrian ambulation, 327–328, 341 in rubber tires, 208, 252–253 in wet rubber products, 206–212 aircraft tires, 208 automobile tire-tread rubber, 206–208 footwear outsoles, 209–211 ramifications of, 211–212 safety shoes, 209–211 work shoes, 209 on wet surfaces, 206–212 Aircraft tire(s), 208 dry microhysteresis in, 170–180 B-29 rubber, 170–178 commercial, 178–180 testing on smooth concrete, 170–175

testing on textured concrete, 175–180 friction bias-ply and radial-belted, 89–91 on textured surfaces, 67, 71–73 on cement concrete finishes, 51–56, 65–67 ambient-temperature testing, 53 high-normal-load testing, 52 high-pressure testing, 54, 55, 56, 57, 58 high-temperature testing, 54, 56 low-normal-load testing, 53 low-pressure testing, 55, 57, 58, 59 on Portland cement concrete finishes, 65–67 wet, ungrooved, 89–91 on textured surfaces, 65–67 ambient-temperature testing, 65, 68 microhysteresis under dry conditions, 170–180 B-29 rubber, 170–178 commercial, 178–180 testing on smooth concrete, 170–175 testing on textured concrete, 175–180 on wet pavements, 293, 347–348, 377 importance of, 318 Aluminum surfaces, 50 Ambient-temperature testing, 53 aircraft tire friction on textured surfaces, 65, 68 American Society for Testing and Materials, 217. See also ASTM Committee E-17, 249, 266 Committee F-13, 240, 325 test standards, 257–267, 285

387

8136.indb 387

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388 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces with E designation, 258–264, 298, 300, 333, 334, 358 with F designation, 217, 227, 264–267, 336 ANOVA, 349 slip-resistance testing, elastomeric shoe heels, 62 wet, 81, 83, 84 Arnold’s tests interpretation of data, 157–159 protocol’s, 156 Schallamach waves in, 159–160 ASTM C 1028, 228, 230, 334 ASTM D 2047, 333, 334, 335 ASTM D 2240, 217 ASTM E 303, 333, 334 ASTM E 456, 221 ASTM F 609, 228, 237, 333, 334 ASTM F 1677, 217, 227 ASTM F 1679, 217, 227 ASTM F-13 Bucknell University Workshop, 350–357 conclusions, 353–354, 380–381 developments arising from, 357 pull-meter, 355–357 contact-time bias, 356–357 inertial bias, 355–356 test results, 350–357 contact-time bias and, 352–353 inadvertent misapplication of laws of metallic friction to rubber friction and, 351 inertial forces and, 351–352 from test-foot-area bias, 351 ASTM STP 649, 230

aircraft tire friction on, 51–56, 65–67 ambient-temperature testing, 53 high-normal-load testing, 52 high-pressure testing, 54, 55, 56, 57, 58 high-temperature testing, 54, 56 low-normal-load testing, 53 low-pressure testing, 55, 57, 58, 59 Hample’s testing of rough, 184–186 Portland aircraft tire friction on, 65–67 wet, ungrooved, 89–91 Coefficient of friction rubber, 3, 15–44 applied normal force vs., 17, 64, 65 applied pressure vs., 17, 21 Denny’s, 76, 85 determining, 16 on dry, smooth surfaces, 45–65 on dry, textured surfaces, 65–73, 97 load and, 15–18, 38–39 metallic friction coefficient vs., 98–99 Thirion’s inverse, 19 Tisserand’s, 81 on wet smooth surfaces, 74–83 on wet textured surfaces, 84–95 testing back-calculated adhesion friction ratios from, 169 back-calculated friction forces from, 169 Cold welding, 98

B

D

Bias-ply and radial-belted aircraft tire friction, 89–91 Boots, walking surface slip-resistance of wet work, 80 BPT. See British pendulum tester (BPT) British pendulum tester (BPT), 297–300, 358–360, 381–382 back-calculation analysis of Yandell’s result in, 359–360

Denny’s coefficient of rubber friction, 76 on roughened , oil coated surfaces, 85 Digital Slip Meter, 338 irremediable inertial and residencetime bias in devices not subject to ASTM standards, 339 Dry rubber belting, microhysteresis in, 183 Dry surfaces adhesion-assisted macrohysteresis on, 302–307, 320–321, 362–366, 383–384

C Cement concrete

8136.indb 388

2/13/08 3:04:21 PM

Index Hample’s testing, 304–305, 364–365 mechanism in, 306–307, 365–366 Sabell’s testing, 367–368 testing by Yager et al., 305, 366–367 Yandell’s testing, 306, 365 aircraft tires microhysteresis on, 170–180 B-29 rubber, 170–178 commercial, 178–180 testing on smooth concrete, 170–175 testing on textured concrete, 175–180 automotive tire rubber microhysteresis on, 168–169 footwear microhysteresis on, 180–182 rough aircraft tires microhysteresis testing on, 175–180 smooth aircraft tires microhysteresis on testing on, 170–175 coefficient of rubber friction on, 45–65 natural rubber tire friction, 96 textured, 65–73, 97

E Elastic loading range, 160 Elastomeric friction, 36 Elastomeric shoe heels, slip-resistance testing, 62

F Footwear microhysteresis in dry conditions, 180–182 in wet conditions, 199–204, 345–346, 357–361 outsoles adhesion-transition in, 209–211 design of, slip-resistance analysis in, 330–331, 342, 372–375, 382–385 macrohysteresis mechanisms, 362–372, 383–385 microhysteresis, 381–382

8136.indb 389

389 in wet conditions, 199–204, 345–346, 357–361 standard terminology relating to safety and traction for, 336 Friction aircraft tire bias-ply and radial-belted, 89–91 on textured surfaces, 67, 71–73 on cement concrete finishes, 51–56, 65–67 ambient-temperature testing, 53 high-normal-load testing, 52 high-pressure testing, 54, 55, 56, 57, 58 high-temperature testing, 54, 56 low-normal-load testing, 53 low-pressure testing, 55, 57, 58, 59 on Portland cement concrete finishes, 65–67 wet, ungrooved, 89–91 on textured surfaces, 65–67 ambient-temperature testing, 65, 68 high-temperature testing, 65, 68 coefficient of rubber, 3, 15–44 applied normal force vs., 17, 64, 65 applied pressure vs., 17, 21 Denny’s, 76, 85 determining, 16 on dry, smooth surfaces, 45–65 on dry, textured surfaces, 65–73, 97 load and, 15–18, 38–39 metallic friction coefficient vs., 98–99 Thirion’s inverse, 19 Tisserand’s, 81 on wet smooth surfaces, 74–83 on wet textured surfaces, 84–95 elastomeric, 36 metallic, 7–9 adhesion theory, 9–10, 160–161 evidence for, 11 coefficient, 96 rubber friction coefficient vs., 98–99

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390 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces equation for constant for, 9 laws, 12, 249–288 application to rubber tires, 249–288 inadvertent misapplication of, 257–282, 337 real surface-to-surface contact, 8 rubber friction vs., 2, 250–251, 282–283, 326, 340 theory, 10 natural and synthetic tire-tread rubber on ice, 63–65 rough-metal, 12 rubber, 63–65 adhesional ratio, 24 adhesive mechanism, 155–160 Arnold’s test, 155–160 aluminum surfaces, 50 analysis traditional metallic-friction approach to, 3 area of contact and, 19–22, 40 coefficient, 3, 15–44 applied normal force vs., 17, 64, 65 applied pressure vs., 17, 21 Denny’s, 76 determining, 16 on dry, smooth surfaces, 45–65 on dry, textured surfaces, 65–73, 97 load and, 15–18, 38–39 metallic friction coefficient vs., 98–99 Thirion’s inverse, 19 Tisserand’s, 81 on wet smooth surfaces, 74–83 on wet textured surfaces, 84–95 comparability of testing data, 254–257 in dry and wet conditions, 192 on gritted floor, 73 industrial rubber belting, 47–49 mechanism, 3, 15–44 adhesion as, 18, 39 concurrently acting, 26–27, 41–42

8136.indb 390

metallic friction vs., 2, 250–251, 282–283, 340 natural, 63–65 on dry, textured surfaces, 97 on ice, 63–65 on smooth , dry surfaces, 96 on wet, smooth surfaces, 97 on wet, textured surfaces, 98 on oil-coated surfaces, 74–79 testing with roughened rubber specimens, 76, 78 testing with smooth rubber specimens, 75–76 steel surfaces, 49–50 testing, 74–79 with roughened rubber specimens, 76, 78 with smooth cones, 94–95 with smooth rubber specimens, 75–76 with smooth spheres, 91–94 unified theory, 2, 150 in analyzing friction in design of tire-pavement systems, 301–316 in analyzing tire-roadway traction-testing results, 253–254 in quantifying tire microhysteresis on wet pavements, 293–294 smooth-metal, 7–9 adhesion theory of, 9–10 theory, 10 synthetic rubber tire, on ice, 63–65 testing, 191–192 lubricated-rubber with smooth cones, 94–95 with smooth spheres, 91–94 tire comparability of results, 284–285 effects of development of microhysteretic forces on, 251–254 with skid-test trailer, in wet conditions, 86–89

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391

Index wet-lubricant investigation, 191–192 wet-rubber microhysteretic contributions to, 37–38 on smooth surfaces, 74–83 on textured surfaces, 84–95

G Geometric design of roadways, 276–282 Glass, 156, 157, 158 GR-S. See Styrene butadiene rubber Grönqvist’s testing, 348–349 Grosch’s test, 26–27, 42

H Hample’s high-pressure testing, 54, 55, 56 Hample’s low-pressure testing, 55 Hample’s testing, 178 accounting for initial bias, 184 adhesion-development issues, 184–185 quantifying inertial bias, 186–187 of rough cement concrete, 184–186 transition pressure mechanisms, 185–186 Hertz equation, 22–24 derivation for deformation of elastic planes and planes in contact, 22 generalized, 24 modified, 32–33 High-temperature testing, 54, 56 aircraft tire friction on textured surfaces, 66–67, 68, 69 Hoechst device, quantifying residencetime bias using, 241 Horizontal Dynamometer Pull-Meter, 228 irremediable bias in, 239–240 Horizontal Pull Slipmeter (HPS), 228 inertial bias in, 237–238 HP-M. See Horizontal Dynamometer Pull-Meter HPS. See Horizontal Pull Slipmeter (HPS) Hurry and Prock’s equation, 137

8136.indb 391

Hycar®, 63. See also Acrylonitrile butadiene rubber coefficient of friction testing, backcalculated adhesion friction ratios from, 169 coefficient of friction testing, backcalculated friction forces from, 169 Hysteresis. See also Macrohystereis; Microhysteresis bulk deformation, 25, 40–41 adhesion and, 27, 28–30 expressions for, 31 van der Waals’ adhesion and, 29 surface deformation, 2–3, 42 van der Waals’ adhesion and, 28

I Ice, friction of natural and synthetic tire-tread rubber on, 63–65 Industrial rubber belting, 47–49, 96, 188, 215 Inertial bias, 246 in Hample’s testing, 186–187 in HPS testing, 237–238 in PIAST testing, 236–237 remediable in portable walking-surface slipresistance testers, 229–238 in VIT testing, 230–236

J James Machine, irremediable inertial and residence-time bias in, 334–336

L Laws of metallic friction, 249–288 inadvertent misapplication of, 257–282, 337 in ASTM test standards, 257–267 in geometric design of roadways, 276–282 in motor vehicle accident reconstruction, 267–276 Low-loading range, 164 Low-temperature testing, for rough concrete, 70, 71

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392 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Lubricated-rubber friction testing with smooth cones, 94–95 with smooth spheres, 91–94 high-speed, 94 slow-speed, 91–94

M Macrohysteresis adhesion-assisted, 302–309 on dry surfaces, 302–307, 320–321, 362–366, 383–384 Hample’s testing, 304–305, 364–365 mechanism in, 306–307, 365–366 Sabell’s testing, 367–368 testing by Yager et al., 305, 366–367 Yandell’s testing, 306, 365 in wet conditions, 307–309, 321, 366–369, 384 mechanism in, 308–309, 368–369 Saber’s testing, 307–308 testing of Yager et al., 307 mechanisms, 302–312, 320–321 rubber outsole, 362–372, 383–385 non-adhesion-assisted on fully wetted surfaces, 309–312, 321, 369–372, 384–385 Greenwood and Tabor’s testing, 310–311, 370 mechanism of, 311 Sabey’s testing, 310, 370 Yager et al. testing, 309–310, 369 velocity dependence of, 311–312 slip-resistance force in pedestrian ambulation, 328–329, 342 Material property, 9 Mechanistic performance indicators, 9 Metallic coefficient, adhesion, 11–12 Metallic friction adhesion theory, 160–161 evidence for, 11 coefficient, 96 rubber friction coefficient vs., 98–99 equation for constant for, 9 laws, 12

8136.indb 392

application to rubber tires, 249–288 inadvertent misapplication of, 257–282, 337 real surface-to-surface contact, 8 rubber friction vs., 2, 250–251, 282–283, 326, 340 Microhysteresis, 283–284 aircraft tire, on wet pavements, 293, 318, 347–348, 377 automotive tire rubber, 168–169, 251–252 in dry conditions, 168–169 in wet conditions, 193–196 in dry aircraft tires, 170–180 B-29 rubber, 170–178 commercial, 178–180 testing on smooth concrete, 170–175 testing on textured concrete, 175–180 in dry rubber belting, 183 footwear outsole, 381–382 on rough walking surfaces, 358–360 rubber in dry footwear materials, 180–182 finding of Powers et al. testing, 220 force of, 21–252, 134–137 on macroscopically rough surfaces, 128–133 Boone’s test, 128–129 Chang’s test, 129–133 Geib’s test, 128–129 Sigler’s test, 128–129 on macroscopically smooth surfaces, 101–128 Bartenev’s test, 118–121 Boone’s test, 121–123 Driscoll’s test, 101–106 Geib’s test, 121–123 Holt’s test, 101–106 Lavrentjev’s test, 118–121 Mori’s test, 123–128 Roth’s test, 101–106 Schallamach’s test, 110–116 Sigler’s test, 121–123 Thirion’s test, 106–109 mechanism of, 133–134 in PIAST testing, 220–223

2/13/08 3:04:23 PM

393

Index in static friction testing, 220–223 independence of, 223 in tire-tread test specimens in wet conditions, 194–196 in VIT testing, 223–225 in wet conditions, 376–377 in wet safety shoe outsoles, 199–202 wet-tire traction and, 193–194 in wet work shoe outsoles, 199 slip-resistance force in pedestrian ambulation, 327, 341 on smooth walking surfaces Sigler’s pendulum device for, 360–361 tire, on wet pavements, 289–295 importance of, 317 in wet ANOVA testing of elastomeric shoe outsoles, 202–204 in wet rubber products, 191–212 aircraft tires, 196–199 footwear outsoles, 199–204 ramifications of, 204–206 Microroughness, 345 Motor vehicle accident reconstruction, 267–276, 286

N Natural rubber, 34, 64, 140, 188 coefficient of friction testing, backcalculated adhesion friction ratios from, 169 coefficient of friction testing, backcalculated friction forces from, 169 industrial belting, 47 roughened hemispheres on glass, 158 on nylon, 158 on PE, 158 on PMMA, 158 on PP, 158 on PTFE, 158 smooth hemispheres on glass, 157 on nylon, 157 on PE, 157 on PMMA, 157 on PP, 157

8136.indb 393

on PTFE, 157 tires, 63 friction on dry, textured surfaces, 97 on ice, 63 on smooth , dry surfaces, 96 on wet, smooth surfaces, 97 on wet, textured surfaces, 98 synthetic rubber tires vs., 168 Neoprene, 63, 64, 65, 76 Nitrile rubber, 80, 82 No-load adhesion hypothesis, 137–140 residence time considerations, 139 in sliding rubber, 139–140 use, 137–138 Nylon, 157, 158

O Oil-coated surfaces, rubber friction on, 74–79

P PAST. See Portable Articulated Strut Slip Tester (PAST) PE. See Polyethylene (PE) Pedestrian ambulation adhesion transition phenomenon in, 327–328 macrohysteretic slip-resistance force in, 328–329, 342 microhysteretic slip-resistance force in, 327, 341 Pedestrian foot traction, on dry smooth floors, 182 Pendulum device, for walking surface slip-resistance testing, 45–46, 47 PIAST. See Portable Inclineable Articulated Strut Tester (PIAST) Poly-(methylmethacrylate), 156, 157, 158 track, 78, 79 Polyethylene (PE), 156, 157, 158 Polyisoprene, 34 Polypropylene (PP), 156, 157, 158 Polytetrafluoroethylene (PTFE), 156, 157, 158 Polyurethane, 80 Polyvinylchloride (PVC), 80, 182

2/13/08 3:04:23 PM

394 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces Portable Articulated Strut Slip Tester (PAST), 338 Portable Inclineable Articulated Strut Tester (PIAST), 220–223 as dynamic friction tester, 337 inertial bias in, 236–237 irremediable adhesion-transition bias in, 244–245 misapplication of laws of metallic friction in, 337 as static friction tester, 337 Portable slip-resistance testers, remedying residence-time bias in, 242 Portable walking-surface slip-resistance testers irremediable adhesion-transition bias in, 242–245 irremediable inertial bias in, 238–240 remediable inertial bias in, 229–236 Portland cement concrete finishes, 65–67, 89–91 Powers et al. testing, 220 PP. See Polypropylene (PP) Programmable Slip Resistance Tester (PSRT), 180 PTFE. See Polytetrafluoroethylene (PTFE) PVC. See Polyvinylchloride (PVC)

R Radial-belted tires, 67, 71–73 Redfern and Bidanda’s testing, 349 Remediable inertial bias, in portable walking-surface slip-resistance testers, 229–238 Remediable residence-time bias, 241 Residence-time bias, 247 quantifying, 241 remediable, 241 in static-friction testing, 241–242 using portable slip-resistance testers, 242 Roberts’s test. See Arnold’s tests Rough-metal friction, 12 Rubber acrylonitrile butadiene, 56, 60, 61 (See also Acrylonitrile butadiene) adhesion, 56, 59–61

8136.indb 394

mechanism, effects of wet lubricants on, 191–192 in PIAST testing, 220–223 in VIT testing, 223–225 hysteresis in bulk deformation, 25, 28–30, 40–41, 43 surface deformation, 2–3, 28 lubricated friction testing with smooth cones, 94–95 with smooth spheres, 91–94 microhysteresis in dry footwear materials, 180–182 finding of Powers et al. testing, 220 force of, 21–252, 134–137 on macroscopically rough surfaces, 128–133 Boone’s test, 128–129 Chang’s test, 129–133 Geib’s test, 128–129 Sigler’s test, 128–129 on macroscopically smooth surfaces, 101–128 Bartenev’s test, 118–121 Boone’s test, 121–123 Driscoll’s test, 101–106 Geib’s test, 121–123 Holt’s test, 101–106 Lavrentjev’s test, 118–121 Mori’s test, 123–128 Roth’s test, 101–106 Schallamach’s test, 110–116 Sigler’s test, 121–123 Thirion’s test, 106–109 mechanism of, 133–134 in PIAST testing, 220–223 in static friction testing, 220–223 independence of, 223 in tire-tread test specimens in wet conditions, 194–196 in VIT testing, 223–225 in wet safety shoe outsoles, 199–202 wet-tire traction and, 193–194 in wet work shoe outsoles, 199 nitrile, 80, 82 sliding, 28–30, 43 styrene, 80, 82

2/13/08 3:04:23 PM

395

Index styrene butadiene, 56, 61 Rubber adhesion-transition on wet surfaces, 206–212 aircraft tires, 208 automobile tire-tread rubber, 206–208 footwear outsoles, 209–211 safety shoes, 209–211 work shoes, 209 Rubber belting industrial, 47–49, 96, 188, 215 microhysteresis in dry, 183 Rubber friction, 63–65 adhesional ratio, 24 adhesive mechanism, 155–160 Arnold’s test, 155–160 aluminum surfaces, 50 analysis traditional metallic-friction approach to, 3 area of contact and, 19–22, 40 coefficient, 3, 15–44 applied normal force vs., 17, 64, 65 applied pressure vs., 17, 21 Denny’s, 76 determining, 16 on dry, smooth surfaces, 45–65 on dry, textured surfaces, 65–73, 97 load and, 15–18, 38–39 metallic friction coefficient vs., 98–99 Thirion’s inverse, 19 Tisserand’s, 81 on wet smooth surfaces, 74–83 on wet textured surfaces, 84–95 comparability of testing data, 254–257 in dry and wet conditions, 192 on gritted floor, 73 industrial rubber belting, 47–49 mechanism, 3, 15–44 adhesion as, 18, 39 concurrently acting, 26–27, 41–42 metallic friction vs., 2, 250–251, 282–283, 340 natural and synthetic tire-tread, 63–65 on oil-coated surfaces, 74–79

8136.indb 395

testing with roughened rubber specimens, 76, 78 testing with smooth rubber specimens, 75–76 steel surfaces, 49–50 testing, 74–79 with roughened rubber specimens, 76, 78 with smooth cones, 94–95 with smooth rubber specimens, 75–76 with smooth spheres, 91–94 unified theory, 2, 150 in analyzing friction in design of tire-pavement systems, 301–316 in analyzing tire-roadway traction-testing results, 253–254 in quantifying tire microhysteresis on wet pavements, 293–294 Rubber surface deformation hysteresis testing, 140–150 Kummer’s, 140–142 Yandell’s, 142–150 Rubber test foot, on in-service floors, 182 Rubber tires adhesion-transition in, 208, 252–253 application of metallic friction laws to, 249–288 natural vs. synthetic rubber, 168

S Schallamach waves, 34–36, 42 model, 34 tangential displacement model, 35 Schallamach’s test, adhesion data, 162 Shoe outsole coefficient-of-friction testing, backcalculated friction forces from ANOVA, 182 PVC, 182 rubber, 182 urethane, 182 Shoes elastomeric heels, 62 heels, 62, 180–182 molded sole materials, 80

2/13/08 3:04:24 PM

396 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces nitrile rubber, 80, 82 polyurethane, 80 polyvinylchloride, 80 styrene rubber, 80, 82 thermoplastic, 80 walking surface slip-resistance of wet safety, 80–81 Sigler’s pendulum device for microhysteresis on smooth walking surfaces, 360–361, 382 for walking surface slip-resistance testing, 45–46, 47 Slip-resistance testing comparability of data, 331–333, 343 devices irremediable inertial and residence-time bias in devices not subject to ASTM standards, 338–339 inadvertent misapplication of laws of metallic friction in ASTM methods of, 333–336, 344 inadvertent misapplication of laws of metallic friction in devices not subject to ASTM standards, 336–338, 344 Smooth-hemisphere test, 157 Smooth-metal friction, 7–9 adhesion theory of, 9–10 theory, 10 Smooth-metal surfaces friction force between, 7–8 origin of, 10–11 friction mechanism between, 7–8 Smooth-rubber-friction, on roughened, oil-coated surfaces, 84–86 Static friction defined, 219 existence of, 215–216 Hurry and Prock’s position, 215–216 Kummer’s position, 216 testing portable devices, 217–218 quantifying inertial forces using Hoest device, 229–230 remediable residence-time bias in, 241–242 in rubber microhysteresis, 220–223

8136.indb 396

Steel surfaces, 49–50, 76, 77 Steel track, polished, 76, 77 Styrene butadiene rubber, 56, 61, 63, 64, 65, 123, 168 coefficient of friction testing, backcalculated adhesion friction ratios from, 169 coefficient of friction testing, backcalculated friction forces from, 169 Styrene rubber, 80, 82 Surface free energy, 56, 59–61 Surface slip-resistance testing, with pendulum device, 45–46 Surface Traction and Radial Tire (START), 178–179

T Taylor’s test. See Arnold’s tests Technical Products Corporation Model 80 Tester, 338 irremediable inertial and residencetime bias in devices not subject to ASTM standards, 339 Teflon® sliders, 56, 61, 89, 97, 123, 152 Thermoplastic rubber, 80 Thirion’s inverse rubber coefficient of friction, 19 Thirion’s test, adhesion data, 161–162 Three-lubrication-zones concept, 290–291, 294–295, 307–308, 317, 346, 376 corroboration for, 318, 348–349, 377 Tire(s) aircraft (See also Aircraft tire(s)) dry microhysteresis in, 170–180 friction bias-ply and radial-belted, 89–91 on cement concrete finishes, 51–56, 65–67 on Portland cement concrete finishes, 65–67 on textured surfaces, 65–67 microhysteresis under dry conditions, 170–180 on wet pavements, 293, 347– 348, 377

2/13/08 3:04:24 PM

397

Index friction testing comparability of results, 284–285 effects of development of microhysteretic forces on, 251–254 with skid-test trailer, in wet conditions, 86–89 II-type, 74 microhysteresis on wet pavements, 289–295, 300–301 in design process, 297–301, 319 measuring, 297–301 quantifying, 293–294 natural rubber, 63 friction on dry, textured surfaces, 97 on ice, 63 on smooth , dry surfaces, 96 on wet, smooth surfaces, 97 on wet, textured surfaces, 98 synthetic rubber tires vs., 168 Tire-roadway traction-testing results application of unified theory to analysis of, 253–254 Tire-slip relationship vs. friction force, 318–319 Tire-tread rubber friction, load dependence of, 312–313, 321–322 Tisserand’s coefficient of rubber friction, 81 Tisserand’s testing, 348 Traditional friction force vs. tire slip relationship, 295–297 Tribometer comparability, contact-time bias for, 245, 247

U Unified theory of rubber friction, 2, 150 in analyzing friction in design of tire-pavement systems, 313–316, 319–322 action item concept design, 315–316 action item detail design, 316 potential benefits of, 301–302, 319–320 process brief, 314, 322

8136.indb 397

process specifications, 314–315, 322 in analyzing tire-roadway tractiontesting results, 253–254 benefits, 361–362 in quantifying tire microhysteresis on wet pavements, 293–294, 318 for slip-resistance analysis in design of footwear outsoles, 330–331, 342, 372–375, 382–385 action item concept design, 374–375 action item detail design, 375 process brief, 373 process specifications, 373–374

V van der Waals’ adhesion bulk deformation hysteresis and, 29 surface deformation hysteresis and, 28 Variable Incidence Tribometer (VIT), 223–225 adhesion-transition bias in, 242–244 demonstrating residence-time effect using, 242 inertial bias in, 230–238 VIT. See Variable Incidence Tribometer (VIT) as dynamic friction tester, 337 misapplication of laws of metallic friction in, 337 as static-friction tester, 337

W Walking surface slip-resistance, 45–46 testing, 377 from ASTM F-13 Bucknell University Workshop, 378 from inadvertent misapplication of laws of metallic friction to rubber friction, 378 in presence of contact-time bias in workshop test measurements, 379 in presence of test-foot-area bias in test measurements, 379

2/13/08 3:04:24 PM

398 Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces in presence of unquantified inertial forces in workshop test measurements, 379 reformulating traditional approach, 350–357 of wet safety shoes, 80–81 of wet work boots, 80 Wet pavements, 289–295 aircraft tire microhysteresis on, 293 tire microhysteresis on, 289–295 quantifying, 293–294 Wet roadway microtexture analysis, 291–293 traditional, 346–347 Wet roadway texture analysis, traditional, 317–318, 376–377 Wet-rubber friction microhysteretic contributions to, 37–38 on smooth surfaces, 74–83 on textured surfaces, 84–95 Wet surfaces, 289–295 adhesion-assisted macrohysteresis on, 307–309, 321, 366–369, 384 mechanism in, 308–309, 368–369 Saber’s testing, 307–308 testing of Yager et al., 307 aircraft tire friction on, 89–91 aircraft tire microhysteresis on, 293

8136.indb 398

ANOVA slip-resistance testing on, elastomeric shoe heels, 81, 83, 84 footwear microhysteresis on, 199–204, 345–346, 357–361 microtexture analysis, 291–293, 346–347 non-adhesion-assisted macrohysteresis, 309–312, 321, 369–372, 384–385 Greenwood and Tabor’s testing, 310–311, 370 mechanism of, 311 Sabey’s testing, 310, 370 Yager et al. testing, 309–310, 369 smooth, coefficient of friction rubber on, 74–83 texture analysis, 317–318, 376–377 textured, coefficient of rubber friction on, 84–95 tire microhysteresis on, 289–295 quantifying, 293–294 walking surface slip-resistance of safety shoes on, 80–81 Wet work boots, 80

Y Yandell model, 37

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