Hydropneumatic Suspension Systems

Hydropneumatic Suspension Systems

Wolfgang Bauer

Hydropneumatic Suspension Systems

123

Dr. Wolfgang Bauer Peter-Nickel-Str. 6 69469 Weinheim Germany [email protected]

ISBN 978-3-642-15146-0 e-ISBN 978-3-642-15147-7 DOI 10.1007/978-3-642-15147-7 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010935667 © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of going to press, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

To Jingbo and Linda for their support and patience

Preface

Many people probably use daily life commodities with gas springs without even knowing or thinking about it. Like many other things in our life they’re simply there. Moreover there are quite a lot of things that are intrinsically tied to gas as an elastic medium. Maybe just in this moment you are actually sitting on a gas spring: your office chair, especially if it’s a swivel chair, is most likely equipped with such a system. In contrast to simple gas springs, like for example those used for the trunk lid of your car, the gas spring in your swivel chair is a rather sophisticated suspension system. Via a button or a lever you have the possibility to allow the transfer of gas between separate internal chambers. This feature provides the adjustment function for the seat level and you can easily adapt it to your body height – much easier than with older mechanical spindle systems like those from, for example, piano stools. If you use gas as an elastic, suspending medium, basically you always take advantage of the equation of state for the ideal gas. However, since usually the suspension motions are quick and allow little heat exchange, it is not possible to calculate with an isothermal change of state but rather with the polytropic approach. It is among others this special behavior of the gas which makes the respective spring characteristic disproportionately higher. Another advantage of gas springs is the just described possibility of easy adjustment of the suspension level. This is especially favorable in applications with different spring loads. Due to their undoubted positive characteristics, gas springs are used in many applications. However, when looking at the small hysteresis of the gas forces while cycling the spring between compression and rebound, it becomes directly obvious that a simple gas spring always needs the assistance of an additional damping element – usually a hydraulic damper. Like their mechanical counterparts (for example helical springs or torsion bars) the gas spring can dissipate only a little amount of energy during the suspension motion (except for the special so called air damping systems). The gas spring of the above mentioned swivel chair is rather special since it is only dampened by an (intentionally) high solid body friction of the setup. This is fully sufficient since this arrangement is mostly used as a shock absorber (when sitting down) and is not exposed to frequent excitation – well, except for the rather unpleasant case of an earthquake. Now is the time to take the step towards hydropneumatic suspensions. Here too, a gas volume acts as the elastic medium, so basically the same laws apply as for vii

viii

Preface

the pure gas spring. The only difference here is that the gas pressure is not directly in contact with the active surface of the spring element but is transferred by an additional component – the hydraulic fluid. It can be called a coupling medium since it acts just like a mechanical coupling rod. The fluid connection offers numerous advantages: on one hand fluids can be sealed better than gas which basically increases the possible working pressures and therefore reduces the space requirements for the suspension element. On the other hand the fluid offers the possibility to dissipate some of the motion energy into heat, just like in a regular hydraulic damper. This viscous friction inside the hydraulic fluid is more favorable for the damping of oscillations than for example the above mentioned solid body friction and it can quite easily be adapted to certain applications or even be made adjustable. So the bottom line is: a hydropneumatic suspension provides spring and damping function always in direct concurrence. Speaking for myself, I came in contact with hydropneumatic suspensions rather late, after graduation, through my employment at the John Deere Mannheim facilities (formerly Lanz tractor factory). My work on the wide field of hydraulics and, in particular, hydropneumatic suspension systems made me aware of the advantages of this technology. One important field for hydropneumatic suspensions is agricultural tractors. This is underlined by the fact that today almost every suspended tractor front axle is suspended with hydropneumatics. The reasons for this and much more is explained in the following chapters. This book is based on experience in design and testing which I gathered in the past decade. It is a translation of my initial German edition [BAU08] with some updates and additions. The intention of this book is to create a basic understanding of what is possible with a hydropneumatic suspension system and which particular advantages and peculiarities this system includes. In doing so, it is hoped that this technology will benefit many different applications in the future. I would like to express my gratitude to my parents and to all friends who encouraged me to write this book. Furthermore I am indebted to my professional colleagues, who supported me on my way from the raw version to the printable version and who created a fertile ground for new ideas in many inspiring discussions. Last but not least I thank Dr. Alastair McDonald who polished the linguistic roughness out of my English translation. Weinheim, Germany April 2010

Wolfgang Bauer

Contents

1 Suspension Systems Basics . . . . . . . . . . . . . . . . 1.1 Requirements for Suspension Systems . . . . . . . . 1.1.1 Minimize Accelerations on the Isolated Side 1.1.2 Equalize Variations of Vertical Wheel Forces 1.2 General Setup of a Suspension System . . . . . . . . 1.3 Hydropneumatic Suspensions Compared to Other Suspension Methods . . . . . . . . . . . . . . . . . 1.3.1 Comparison of Spring Characteristics . . . . 1.3.2 Comparison of Damping Characteristics . . 1.3.3 Level Control . . . . . . . . . . . . . . . . 1.3.4 Non-functional Requirements . . . . . . . . 1.4 Applications for Hydropneumatic Suspensions . . . .

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2 Spring and Damping Characteristics of Hydropneumatic Suspension Systems . . . . . . . . . . . . . . . . . . . . . 2.1 General Setup and Working Principle . . . . . . . . . . 2.2 Spring Characteristics . . . . . . . . . . . . . . . . . . 2.2.1 Thermodynamic Background . . . . . . . . . 2.2.2 Calculation Predeterminations . . . . . . . . . 2.2.3 Non-preloaded Hydropneumatic Suspensions . 2.2.4 Systems with Mechanical Preload . . . . . . . 2.2.5 Systems with Constant Hydraulic Preload . . . 2.2.6 Systems with Variable Hydraulic Preload . . . 2.3 Damping Characteristics . . . . . . . . . . . . . . . . 2.3.1 Boundary Friction Damping . . . . . . . . . . 2.3.2 Fluid Friction Damping . . . . . . . . . . . . 2.3.3 End-of-Stroke Damping . . . . . . . . . . . . 2.4 Combined Operation of Spring and Damper . . . . . .

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19 19 21 21 25 25 35 41 48 50 51 55 62 64

3 Dimensioning of the Hydropneumatic Suspension Hardware 3.1 Dimensioning of the Hydraulic Spring Components . . . . 3.1.1 Cylinder . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Accumulator Gas Precharge . . . . . . . . . . . . 3.1.3 Detailed Calculation of p0 and V0 . . . . . . . . .

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67 67 69 71 73 ix

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Contents

3.2

Dimensioning of the Hydraulic Damping Elements . . 3.2.1 Single-Acting Cylinder in a System Without Hydraulic Preload . . . . . . . . . . . . . . . 3.2.2 Double-Acting Cylinder in a System Without Hydraulic Preload . . . . . . . . . . . . . . . 3.2.3 Double-Acting Cylinder in a System with Hydraulic Preload . . . . . . . . . . . . . . . 3.2.4 End-of-Stroke Damping . . . . . . . . . . . .

4 Hydraulic Components Design . . . . . . . . . . . . . . 4.1 Cylinders . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Function and Requirements . . . . . . . . . 4.1.2 Types of Cylinders . . . . . . . . . . . . . . 4.1.3 Sealing Elements . . . . . . . . . . . . . . . 4.1.4 End-of-Stroke Damping . . . . . . . . . . . 4.1.5 Types of Support Elements . . . . . . . . . 4.2 Accumulators . . . . . . . . . . . . . . . . . . . . . 4.2.1 Function and Requirements . . . . . . . . . 4.2.2 Types of Accumulators . . . . . . . . . . . 4.2.3 Methods to Reduce Diffusion Pressure Loss 4.2.4 Integration into Available Design Space . . . 4.3 Flow Resistors . . . . . . . . . . . . . . . . . . . . . 4.3.1 Non adjustable Orifices and Throttles . . . . 4.3.2 Flow Direction Depending Resistors . . . . 4.3.3 Adjustable Flow Resistors . . . . . . . . . . 4.4 Hydraulic Lines and Fittings . . . . . . . . . . . . . 4.4.1 Function and Requirements . . . . . . . . . 4.4.2 Required Flow Cross Section . . . . . . . . 4.4.3 Tubes . . . . . . . . . . . . . . . . . . . . . 4.4.4 Hoses . . . . . . . . . . . . . . . . . . . . . 4.4.5 Fittings . . . . . . . . . . . . . . . . . . . .

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85

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91 91

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95 95 95 96 101 106 109 111 111 113 116 118 120 120 122 126 130 130 132 133 135 138

5 Level Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Self-Pumping Suspension Elements . . . . . . . . . . . . . . . . 5.2 Mechanical Level Control with External Hydraulic Power Supply . 5.3 Electronic Level Control with External Hydraulic Power Supply . 5.3.1 Function . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Hydraulic Circuits . . . . . . . . . . . . . . . . . . . . . 5.3.3 Control Algorithms . . . . . . . . . . . . . . . . . . . .

141 141 144 147 147 148 150

6 Special Functions of Hydropneumatic Suspension Systems 6.1 Suspension Lockout . . . . . . . . . . . . . . . . . . . . 6.1.1 Lockout by Blocking the Hydraulic Circuit . . . 6.1.2 Lockout at the Compression End Stop . . . . . . 6.1.3 “Quasi-Lockout” Through High Spring Stiffness

157 157 158 160 161

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Contents

6.2 6.3

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xi

Adjustment of the Zero Position . . . . . . . . . . . . . . . . Alteration of Roll and Pitch Behavior . . . . . . . . . . . . . 6.3.1 Coupling Cylinders on Corresponding Sides . . . . . 6.3.2 Decoupling Cylinders . . . . . . . . . . . . . . . . . 6.3.3 Coupling Double-Action Cylinders on Opposite Sides Spring Rate Adjustment by Selective Connection of Accumulators . . . . . . . . . . . . . . . . . . . . . . . . .

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162 163 163 164 166

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7 Design Examples . . . . . . . . . . . . . . . . . . . . . 7.1 Tractor Front Axle Suspension TLS by John Deere 7.2 Passenger Car Axle Suspension by Citroen . . . . . 7.2.1 Citroens First Hydropneumatic Suspension 7.2.2 Hydractiv Suspension . . . . . . . . . . . 7.2.3 Activa Suspension . . . . . . . . . . . . .

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173 173 180 181 183 188

8 Important Patents . . . . . . . . . . . . . . . . 8.1 Improvement of Suspension Characteristics 8.1.1 DE1755095 . . . . . . . . . . . . 8.1.2 DE19719076 . . . . . . . . . . . . 8.1.3 DE10107631 . . . . . . . . . . . . 8.1.4 DE10337600 . . . . . . . . . . . . 8.1.5 DE4221126 . . . . . . . . . . . . 8.1.6 DE4234217 . . . . . . . . . . . . 8.1.7 DE4223783 . . . . . . . . . . . . 8.1.8 US6167701 . . . . . . . . . . . . 8.1.9 DE19949152 . . . . . . . . . . . . 8.1.10 US6398227 . . . . . . . . . . . . 8.1.11 DE102008012704 . . . . . . . . . 8.2 Roll Stabilization and Slope Compensation 8.2.1 GB890089 . . . . . . . . . . . . . 8.2.2 DE3427508 . . . . . . . . . . . . 8.2.3 DE10112082 . . . . . . . . . . . . 8.2.4 US4411447 . . . . . . . . . . . . 8.2.5 US6923453 . . . . . . . . . . . . 8.3 Suspension Lockout . . . . . . . . . . . . . 8.3.1 US3953040 . . . . . . . . . . . . 8.3.2 DE4308460 . . . . . . . . . . . . 8.3.3 DE4032893 . . . . . . . . . . . .

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193 193 194 195 196 196 198 198 200 201 201 203 203 205 205 206 207 208 209 210 211 211 212

9 Looking into the Future . . . . . . . . . . . . . . . . . . . . . . . . .

215

Index of Symbols and Abbreviations . . . . . . . . . . . . . . . . . . . .

219

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

223

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 1

Suspension Systems Basics

1.1 Requirements for Suspension Systems As already mentioned in the preface, suspension systems have a broad range of applications in our daily lives. Usually people do not even know that they exist, yet they are doing a hard job in many cases. If they malfunction it is often the first time that one starts thinking about them. For example, anybody who has ridden a bicycle with too low tire pressure will probably remember how soft and wobbly the bike felt on smooth roads and how badly he felt the bumps when there was even the slightest unevenness. A ride behavior which is unsafe and uncomfortable. In this case the spring rate of the suspension system (i.e. the tire) was too low and the available suspension travel was too small. Therefore the suspension reached the limit of its stroke and ran heavily into the end stop – rim and road surface with the rubber of the tire in between. On the other hand, a too high tire pressure and an accordingly too high spring rate can also lead to discomfort on the bike. Without sufficient tire elasticity the roughness of the road is transferred directly into the bike frame and furthermore into the rider. This again has a negative effect on the comfort of the rider. It is clear that it is necessary to find a suitable level of tire pressure and thus spring rate which fits in particular to the weight of the rider. This brings us to the first basic objective of a suspension system: it has to protect the components of its isolated side (for example, chassis and driver) from the movements and accelerations of its input side (for example, road or wheel). This isolation of the vibration ensures comfort and health for the driver and prevents components on the isolated side from damage from inertial forces. If the suspension system fulfills these requirements for vehicles, another important advantage is achieved: compared to a vehicle without a suspension system it can be driven faster at equal or even lower vibration loads on the isolated side. Particularly for wheel suspension systems there is at least one more tremendously important objective: the time history of the vertical wheel forces on the road should be as smooth as possible in order to ensure that a high level of lateral and longitudinal wheel force can be transferred to the road surface at any time. Strong peaks in the vertical wheel force vs. time curve can lead to a situation where the

W. Bauer, Hydropneumatic Suspension Systems, DOI 10.1007/978-3-642-15147-7_1,  C Springer-Verlag Berlin Heidelberg 2011

1

2

1 Safety

Suspension Systems Basics

Easier operation of operators controls Better driver’s fitness Better road holding

Minimize accelerations on the isolated side

Comfort Health

Equalize variations of vertical wheel forces

Damage prevention

Increased productivity

Higher speeds possible Increased pulling force Increased efficiency

Fig. 1.1 Tasks and functional requirements for a wheel suspension system

normal force is lower than the necessary level to create a sufficient friction force for the transfer of lateral and longitudinal forces. This then causes a transition from static to sliding friction resulting in unexpected and unsafe ride behavior. But not only is road holding better with a smooth vertical wheel force transfer; a better transfer of pulling forces with lower wheel slip results in higher efficiency and productivity especially for pulling working machines like tractors or other off-road equipment. Further objectives especially for wheel suspension systems are, for example, the prevention of road damage (by high wheel forces) and an acceptable roll and pitch behavior of the chassis. For passenger cars it is also especially important to create a subjective ride behavior that fits to the type of vehicle – from supersports car to luxury sedan. Figure 1.1 explains the relationship between several tasks and the two deduced functional requirements “minimize accelerations on isolated side” and “equalize variations of vertical wheel forces” for a wheel suspension system. These two requirements will be explained in more detail on the following pages of this section.

1.1.1 Minimize Accelerations on the Isolated Side Mechanical components on the isolated side can often be designed to withstand the prevailing vibration level. Yet in many cases it is the human as the “living component” of the isolated side who is the limiting factor: he too must not be subjected to excessive vibrations. Vibrations are perceived by humans on different parts of the body and in different frequency ranges. From 1 to 100 Hz they are sensed to be accelerations and displacements, in the frequency range of 20 Hz–10 kHz they are perceived acoustically (noise). Reimpell points out that the range from 1 to 4 Hz

1.1

Requirements for Suspension Systems

3

determines the subjective estimation of the “suspension comfort” while the range from 4 to 80 Hz influences what is called “harshness” [REI05] – low amplitude and short term accelerations resulting for example from rides over cobblestone paving. In addition ISO2631-1 indicates that excitations in the frequency range from 0.1 to 0.5 Hz are responsible for motion sickness. From a certain level of amplitude, vibrations are rated uncomfortable by humans [DUB90]. Not only is this depending on frequency but also on subjective perception. In a mild form this only causes discomfort and faster operator fatigue. In severe cases a frequent subjection to high acceleration levels can cause damage especially to the human skeleton (for example, in the disks of the lower spine) [SEI04]. At certain predominating frequencies with high amplitudes certain parts of the body will be excited with their natural frequency. This can cause motion sickness as well as gastric or cardiac troubles. So the necessity to counteract these harmful factors is obvious. The legislative body has already issued detailed directives which regulate the allowed noise exposure, for example the European Council Directive 2003/10/EC. In addition in the past years another law became res judicata which regulates the allowed exposure to hand-arm and whole body vibrations (2002/44/EC). In particular employers in Europe will have to obey these regulations which basically also refer to all employees using mobile equipment, in particular in off-road use. The level of comfort provided by a suspension system can be determined by looking at the quality of isolation of the isolated side from the input side of the system. According to ISO 2631-1 the squared average values (for a time period T) of the frequency-weighted accelerations aW (t) are calculated for the isolated side. For a driver’s workplace all rotational and translational accelerations at the seat top are used for the calculation of the whole body vibration.

aW

  τ 1  = a2W (t)dt τ

(1.1)

0

These accelerations are then combined according to the Eqs. (1.2) and (1.3) and the results are the translational vibration RMS aV,t and the rotational vibration RMS aV,r . These values take into account the effect of the direction of the respective acceleration onto the subjective assessment of level of comfort by considering weighting factors for each direction.   2  2  2 (1.2) kaW,X + kaW,Y + kaW,Z aV,t =  aV,r =

 2  2  2 kX aW,RX + kY aW,RY + kZ aW,RZ

(1.3)

while k = 1, kX = 0.63, kY = 0.4 and kZ = 0.2. X is the longitudinal, Y is the lateral and Z the vertical axis for the comfort assessment of a sitting person according to

4

1

Suspension Systems Basics Extremely uncomfortable

Very uncomfortable Uncomfortable Fairly uncomfortable A little uncomfortable Not uncomfortable 0

0.5

1

1.5

2

2.5

aV [m/s2]

Fig. 1.2 Subjective assessment of comfort depending on the vibration total value

ISO2631-1. These values are then again combined and the result is the vibration total value aV which represents a measure for the comfort level. aV =

 a2V,t + a2V,r

(1.4)

The lower this value (at a given input side excitation) the better performs a suspension system in protecting the isolated side – in particular the driver – from the input side excitations and the better will be the subjective assessment of the comfort level. The relationship between the vibration total value and the subjective assessment of comfort by the driver is described in ISO2631-1 (Fig. 1.2).

1.1.2 Equalize Variations of Vertical Wheel Forces This is a very important issue for suspension systems that are used in mobile equipment for the suspension of axles and wheels. The vertical wheel force needs to be as constant as possible to provide maximum handling performance especially during longitudinal and lateral accelerations. This ensures that the vehicle is easily controllable and can be kept on the desired track. Reimpell describes a reduced but demonstrative example for a wheel going through a 60 mm deep ditch and shows impressively that a low spring rate is essential for constant vertical wheel forces [REI05]. The vertical wheel force is the normal force in the contact area of tire and road and therefore it affects directly the potential friction force and consequently also the longitudinal and lateral guiding forces. The dynamic tire load factor nR has been introduced as an assessment criterion for the steadiness of the vertical wheel forces. It is basically the standard deviation of the dynamic tire load compared to the static tire load [THO01]. The lower nR is, the smoother the time history of the vertical wheel force.

1.2

General Setup of a Suspension System

1 τ

nR =

τ

5

[F (t) − Fstat ]2 dt

0

Fstat

(1.5)

A tire load factor of up to 0.33 provides relatively good vehicle controllability, since from a statistical point of view the tire never loses contact with the road surface. The more the tire load factor exceeds this limit, the more difficult it becomes to keep control over the course of the vehicle – the vehicle’s deviations from the desired path and therefore the necessary corrective steering actions are increasing. In practical operation it was found that a tractor cannot be kept on a narrow farm track at dynamic tire load factors above 0.4 – the vehicle would leave the pavement [THO01]. In this context it needs to be mentioned that in real suspension systems only a limited displacement of the suspension elements is available. In case the entire stroke is used up, the suspension reaches the mechanical end stop of the component with the least possible stroke and therefore is blocked completely. No displacement means no equalization of vertical wheel forces and therefore the dynamic tire load factor is worsened dramatically if this happens – not to mention the unfavorable impact on comfort. Therefore it is crucial to choose the right combination of parameters for a suspension system (spring rate, damping, stroke, etc.). This will be further explained in Chap. 2. Up to this point only two essential functional requirements for a suspension system have been mentioned. Yet there are also the non-functional requirements, which basically arise from further boundary conditions. These requirements are in particular the system cost, the necessary/available design space for the components, reliability and safety, robustness and need for regular service. If the suspension system is externally visible as part of an overall system, in many cases it also needs to fit into the overall styling. Depending on the application and its boundary conditions, requirements are weighted in a different way and are considered differently when selecting the most suitable solution.

1.2 General Setup of a Suspension System A suspension system usually consists of a spring and a damper. The spring alone would already allow the decoupling of input side and isolated side just by its elastic properties and would compensate accelerations/displacements from the input side. Yet, due to the displacement, the spring would store energy and therefore the system would keep on oscillating permanently. Not only this, in case of further excitations with suitable frequency and phase, it would pick up further energy and the amplitude on the isolated side would increase even further (resonance). If this happens the

6

1

Suspension Systems Basics

result is the exact opposite of the original goal, instead of reducing the accelerations on the isolated side they are amplified above the level without a suspension system. This is why a spring is almost always used in combination with a damper. The energy that has been temporarily stored in the spring is converted into heat by the damper and the amplitude of the oscillation therefore decays. The higher the damping forces, the faster the amplitude will decay, yet the stronger is the direct (non-elastic) coupling of the input side to the isolated side and the input side excitations will be transferred with higher intensity. So to achieve the best possible result from the tuning of a suspension system, there is a lot of experience, intuition and effort (especially testing) necessary. Most commonly used dampers are hydraulic components which use the displacement of internal fluid and the respective viscosity to generate damping forces – the latter are therefore velocity dependent. Along with these viscous dampers comes usually a boundary friction which has a negative impact on the suspension behavior. In particular, the static friction is a direct link between input side and isolated side; all excitation forces that are below the static friction force level will directly be transmitted into the isolated side and cause an acceleration that reduces the comfort level. This acceleration amin also depends on the mass mF on the isolated side. amin =

Ffric,stat mF

(1.6)

However also the sliding friction has a worsening effect onto the dynamic system behavior. Both static and dynamic friction reduce the suspension quality in terms of harshness and noise transfer. That is why a lot of effort is taken to minimize the general interference factor “friction”. Figure 1.3 shows the general setup of a suspension system which isolates the excitations coming from the input side through a spring, a viscous damper and

Input side

Isolated side

Spring

m

Excitation Viscous damper

x

t

Friction

Fig. 1.3 General setup of a suspension system

Response x

t

1.3

Hydropneumatic Suspensions Compared to Other Suspension Methods

7

a friction element from being transferred into the mass on the isolated side. The amplitude of the reaction – the displacement and the acceleration of the mass – is reduced, compared to the amplitude of the excitation. An elegant and frequently used method to compensate for the amount of boundary friction is the integration of another spring-damper element in series to the hydraulic damper, for example a rubber bushing. This element has rather low damping and virtually no friction and is able to isolate the high frequency oscillations very well. A good example for this are the decoupled top mounts for shock absorbers in McPherson struts ([HAR04] and [ELL02]). In many cases suspension systems not only consist of one of the above shown oscillating systems but of multiple systems. For example, on a passenger car there are at least the tire, the wheel suspension and the seat which represent a suspension system as shown in Fig. 1.3 and all work together to isolate the driver from the excitations from the road surface.

1.3 Hydropneumatic Suspensions Compared to Other Suspension Methods Basically there are two other systems that compete with hydropneumatics in the area of suspension systems: the pneumatic and the mechanical suspension. In addition there are some exotic concepts like the suspension on an air cushion as used for a hovercraft or even the suspension on a magnetic field. Section 1.3.1 compares the (typical and most commonly used) mechanical, the pneumatic and the hydropneumatic suspension with regards to the requirements which have been explained in Sect. 1.1.

1.3.1 Comparison of Spring Characteristics For all further explanations in this section, the rule is established that all three suspension systems shall have the same spring rate at the chosen design point with its respective load so they have comparable suspension characteristics at this point. Furthermore the systems then are defined to be in the same position between both suspension end stops: the design position or normal position. The first essential difference between the systems becomes obvious when looking at the force vs. displacement curves in Fig. 1.4. While the spring rate of the mechanical spring is constant throughout the whole stroke (assuming that, for example, a linearly wound coil spring is used) both systems with gas suspension are (also depending on the layout) more or less progressive which is caused by the physical laws for a polytropic change of state of a gas. An exception is an air spring with a rolling piston with a non-cylindrical contour [MUR98]. When oscillating around the normal position with small amplitudes this has no significant impact, yet at greater amplitudes this is of importance, especially when getting close to the end stops. In particular the hydraulically preloaded hydropneumatic spring as well as the air

8

1

Suspension Systems Basics

Spring force

Design position

Displacement

Rebound (Suspension element is extended)

Compression (Suspension element is contracted)

Mechanical coil spring, linearly wound Mechanical coil spring, progressively wound, air spring with cylindrical rolling piston, non-preloaded hydropneumatic spring Hydraulically preloaded hydropneumatic spring, air spring with rolling piston with defined contour

Fig. 1.4 Force-displacement-curves for mechanical and gas-sprung systems

spring with a defined contour of the rolling piston can provide the advantage of increased spring rates near the mechanical end stops thus preventing the suspension from reaching these. An even more significant difference can be found with changing suspension load by varying the suspended mass. A suspension system without level control is compressed by increasing static load until the spring force is again equal to the static load. In Fig. 1.4 it becomes obvious that this causes an increasing spring rate for the air spring and the hydropneumatic spring (indicated by the progressively increasing inclination of these curves on the compression side of the figure), whilst the spring rate of a mechanical spring remains constant (constant inclination). This is a general problem for mechanical suspension systems with large load variations and with (as usual) no level control. The following example explains why: Assuming that a mechanically sprung passenger car is in a defined partially loaded condition (three passengers) and it therefore is in its design position (the desired position between the suspension travel limits, for example in the centre of both). If the load on the rear axle is increased by further passengers and luggage to the maximum allowed rear axle load, the suspension becomes compressed and the new neutral position is offset towards the compression end stop. Therefore the available residual suspension travel in compression direction is reduced compared to the design position. With high excitations from the input side (for example when riding over uneven ground) there is a risk that the suspension will run harshly into the end stops; even more so because the load has been increased without on the other hand increasing the spring rate and the suspension therefore becomes softer (lower natural frequency).

1.3

Hydropneumatic Suspensions Compared to Other Suspension Methods

9

So to make sure that the suspension is able to cope with these extreme conditions it must be tuned more stiffly and with higher damping overall. The problem is that this worsens the tuning for all other load cases (for example with only the driver inside). Hence it can be easily deduced that a linearly wound coil spring can only allow a compromise for most driving situations. In any case safety needs to be a major focus for the suspension tuning which means especially that the dynamic tire load factors should always be within the allowed range. It is possible to address this problem by using progressively wound coil springs but this only partially solves the root cause. Therefore in most cases a level control is the far better and the far more effective solution – after a load change it brings the suspension back to its design position and ensures constant residual suspension travel in both compression and rebound direction. On passenger cars a mechanical level control in conjunction with a coil spring can be found only rarely [ELL02]. Usually other/additional supporting elements are used for leveling: for example self pumping dampers or additional air springs are very common. Nevertheless a mechanical level adjustment – mostly manual – is for example often used on motorbikes. One reason for this is that the load ratio (maximum weight to curb weight), especially on the rear axle, is much higher than in other applications. Gas sprung suspension systems on the other hand are virtually always equipped with a level control, in most cases even automatic without need for driver input. Yet a major difference between an air spring and a hydropneumatic spring is how the desired design position is readjusted and how the spring rate is affected by this. In purely pneumatic springs the gas (usually air) is filled up or released. So the suspending gas volume of the pneumatic spring remains constant after the load change and subsequent level adjustment. The pressure of this gas volume changes linearly with the load. Therefore in purely pneumatic springs the gas mass and hence also the spring rate change in a linear correlation with the sprung mass. For a hydropneumatic suspension system it is the oil volume which is changed during the leveling process – so here it is the gas mass which remains constant at all times. Yet this gas mass changes its volume after a load change; a higher load means a smaller gas volume and therefore a higher spring rate. This is the reason why this system shows progressive behavior of the spring rate vs. the sprung mass. Figure 1.5 shows a comparison for all three systems, with the condition that they all have the same spring rate at the design load. In order to provide a constant natural frequency of the oscillating system it is basically preferable to have a spring rate increasing linearly with the spring load. Yet in some cases, depending on the reason for the load changes or the needs of the particular application, it can be favorable to change to a disproportionately higher spring rate. A spring rate that is constant at all loads, as with a linearly wound coil spring, is usually only a compromise and only recommended for suspension systems with small relative load changes. For good protection of the isolated side from the input side, the lowest possible natural frequency (obeying the motion sickness limit of 0.5 Hz) and therefore also the lowest possible spring rate needs to be aimed at, yet always considering the limited suspension stroke. A pneumatic suspension provides a constant low level of

10

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Suspension Systems Basics

Spring rate

Spring load

Design load Mechanical coil spring, linearly wound

Mechanical coil spring, progressively wound, air spring with cylindrical rolling piston, non-preloaded hydropneumatic spring Hydraulically preloaded hydropneumatic spring, air spring with rolling piston with defined contour

Fig. 1.5 Spring rate as a function of spring load for a mechanical, a pneumatic and a hydropneumatic suspension

natural frequency for all load conditions, while the natural frequency of a hydropneumatic system will more or less increase with increasing loads, depending on the system layout. On the other hand a mechanical spring will have a high natural frequency at low loads and a low natural frequency at high loads. Figure 1.6 illustrates this for the simple example of a single-mass oscillator.

m Natural frequency

Design load

Spring load

Mechanical coil spring, linearly wound Air spring with cylindrical rolling piston, hydraulically preloaded hydropneumatic spring close to the design point, both with level control Non preloaded hydropneumatic spring with level control

Fig. 1.6 Natural frequency as a function of spring load for a mechanical, a pneumatic and a hydropneumatic suspension

1.3

Hydropneumatic Suspensions Compared to Other Suspension Methods

11

In more advanced applications it is also necessary to have the ability to change suspension properties (such as the spring rate) depending on particular operating conditions. For a mechanical spring this is quite difficult. A pneumatic spring gives some possibility by switchable additional air volumes but a hydropneumatic spring gives great possibilities by either switchable accumulators or a variable precharge pressure (more detailed information in Sect. 2.2).

1.3.2 Comparison of Damping Characteristics In Sect. 1.2 it was already explained that the necessary damping for the decay of the oscillations is in most cases provided by viscous friction of a damping fluid – usually oil. The amount of viscous damping can be defined very well for all three types of suspension systems. Therefore this is not part of the comparison. Yet a negative side effect of the components of suspension systems is the additional damping by boundary friction, in particular in bushings, dynamic sealing systems and guiding elements. Friction in bushings of mechanical links and control arms has to be minimized, yet it is similar for all kinds of suspension systems and is therefore also not part of this comparison. The friction in sealing and guiding elements needs to be avoided as far as possible. There are different causes and therefore different friction levels for different suspension systems. This sub-section explains the reasons. The mechanical coil spring with a viscous fluid damper scores best when it comes to the friction level. The spring itself has no friction; all deformation is purely reversible, i.e. elastic. Therefore in this suspension element, boundary friction originates only from the friction in the sealing and guiding elements inside the viscous fluid damper. It is a general rule that friction forces from dynamic seals increase with the differential pressures at the seal and the length of the sealing edge. This explains why a monotube damper with its internal gas pressure and the rather large rod diameter has a much higher boundary friction than a dual-tube damper (with low or even without internal gas pressure) [MUR98]. On top of that for the monotube damper there is additional friction of the seals of the floating internal piston which separates gas and oil. As far as friction in guiding elements is concerned, it is essential to avoid lateral forces and bending moments onto the sliding components – this is actually valid for all types of suspension elements. More detailed explanations are given in Sect. 2.3.1. The above mentioned standard oil damper technology is used for pneumatic suspension systems as well, so it has on the damper side similar boundary friction as to that of a coil spring suspension. Yet for a pneumatic system there is additional friction coming from the rolling bellow which originates from its necessary deformation during the suspension movement. This friction causes an additional degradation in harshness behavior and is on a level of about 20 N for the most commonly known cross ply bellow for a passenger car air suspension. The newer technology of axial ply bellows enables a reduction of bellow friction forces down below 10 N [PEL04] and finds more and more applications especially in the field

12

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Suspension Systems Basics

of high comfort passenger car suspensions. A disadvantage of this technology is though, that the bellow needs additional guidance on the outer diameter to pick up the radial forces caused by the air pressure. The baseline is that the boundary friction in a pneumatic suspension system will always be slightly higher than in a coil spring suspension system. There is again another picture for the hydropneumatic suspension system. Although the suspension cylinder is the only component between input side and isolated side, it has to be taken into account that its seals need to cope with very high differential pressures. Therefore the level of friction would be much higher compared to the latter two suspension systems if no additional countermeasures are taken. The friction is caused on one hand by the rod seal (for single-acting cylinders) and additionally by the piston seal if a hydraulically preloaded system with a double-acting cylinder is used (see Sect. 1.3.3). The friction of the hydropneumatic suspension can be minimized by a suitable layout of the components (dimensions, pressures, see Sect. 2.3.1) as well as by the implementation of a high-grade, low friction sealing system [FIS06] (see also Sect. 4.1.3). Since spring and damper of a hydropneumatic suspension are integrated into one component it is difficult to use soft additional spring-damper-elements to decouple the direct transfer path of static damper friction as explained in Sect. 1.2. The reason behind it is that this additional element would have to carry the complete suspended mass and not only the damping forces as in the case of decoupled top mounts for passenger cars’ suspension elements. High loads and very soft rubber elements are goals that can hardly be achieved at the same time. The use of a rubber bushing is possible though and it can improve the noise transfer properties. It is obvious that boundary friction is a considerable and challenging issue when designing a hydropneumatic suspension.

1.3.3 Level Control For suspension systems with a coil spring/mechanical spring, level controls are rather seldom due to the high effort of automatic systems and their limited effect. Manual level adjustments are commonly used for example in motorbikes and for some passenger car sports suspensions. In the last years several new ideas have been developed for level control of mechanical springs. They have often been filed as patents ([US780], [JP945]) and some of them quite close to the hydropneumatic suspension technology ([US363] and with an exotic hydraulic power principle [JP103]). However, overall they currently play a minor roll in mechanical springs and therefore will not be explained any further in this book. For a hydropneumatic and a pneumatic suspension system a level adjustment is quite easily feasible by increasing/decreasing the amount of oil or gas in the system. Both systems have about the same leveling quality, maybe with slight advantages for the hydropneumatic system. Yet there is a major advantage for the hydropneumatic system in terms of leveling speed. Since it has a much higher energy density and an incompressible medium is used, the suspension can, after a load increase, be brought

1.3

Hydropneumatic Suspensions Compared to Other Suspension Methods

13

back to the normal position very quickly if the necessary power is available. If the same leveling speed had to be achieved with a pneumatic suspension system, a much higher volumetric flow rate and a higher power output would be necessary. This aspect is especially important for suspension systems that are often subjected to high load changes and if a fast readjustment of the desired normal position is necessary. In this case the hydropneumatic suspension is preferred.

1.3.4 Non-functional Requirements 1.3.4.1 Component Costs When it comes to costs the traditional mechanical spring suspension system is significantly ahead of the two gas suspended systems. One reason is that these components have been optimized over a long time of intensive development in particular concerning the costs. Another reason is that they lack the expensive cost for level control. In this context it needs to be mentioned that there are so called load sharing systems, a mechanical system in combination with a pneumatic or hydropneumatic spring. Yet they are not part of the explanations in this section; for more detailed information please refer to [EUL03]. Pneumatic and hydropneumatic suspension systems are more expensive especially due to the cost for the (mostly automatic) level control. Furthermore the pneumatic system has a slight advantage over hydropneumatics assuming that in both cases a fluid power supply needs to be provided. Yet if there already is a pneumatic or hydraulic system available in a certain application, the additional costs for both gas sprung systems will be reduced. In this case the selection between pneumatic and hydropneumatic system is often mainly based on what fluid power supply is already available. 1.3.4.2 Design Space Requirement Hydropneumatic systems have major advantages here. There are mainly two reasons for that: First is the high integration level of this suspension component, which fulfills the function of a spring and a damper at the same time. Secondly the cylinder diameters can be chosen very small due to the working principle and the high possible working pressures. Static pressures of up to 20 MPa in the design position are very common. They can be even higher if the components are selected accordingly. Therefore a suspension cylinder can be about as small as a regular oil damper. This offers advantages in particular if the available design space in the surrounding areas of the suspension system is very small. In addition to the cylinder(s), the accumulator(s) need to be accommodated. It is best to locate it close to or directly at the cylinder, yet it is not absolutely necessary. This option offers a lot of possible variations and makes the packaging of these components quite flexible. The design space for the level control system can be chosen in any position; all that has to be considered is a hydraulic line between the suspension components and the level

14

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Suspension Systems Basics

control system. In order to keep line lengths small (due to costs, space requirements and pressure drops over this line) it is favorable to keep the all components close together. For pneumatic suspension systems there are also lines necessary for the compressed air. Yet due to the much lower working pressures (normally up to 1 MPa of static pressure in normal position), the pneumatic suspension components need much more active area and therefore also more design space compared to hydropneumatics. As a rule of thumb, it can be stated that a pneumatic spring usually can be accommodated in the design space of the respective coil spring. Yet the latter normally has no level control system and that is why the overall design space requirement for it is somewhat smaller. 1.3.4.3 Reliability, Safety, Robustness and Service Requirements In general it can be stated that reliability and safety are granted and uncritical for all mechanical, pneumatic and hydropneumatic systems if the design work has been done properly and the systems are serviced regularly. For the mechanical suspension, service requirements are quite low; basically it is only the exchange or (rarely) reconditioning of the oil dampers. The mechanical spring is virtually service free. Only for metallic springs must corrosion be kept under surveillance since the protection coating can be damaged for example by stoning. On top of that comes the exchange of (especially rubber) bushings and mounts as and when required. A pneumatic suspension system needs a slightly higher maintenance effort compared to the mechanical system, yet additional design effort is necessary to protect the rather sensitive bellows of the air cushions. Especially in off-road vehicles the bellows need to be specially protected from dirt, stoning, sharp objects, etc. The bellow material (rubber with reinforcing plies) is subjected to aging in particular due to environmental influences like UV-radiation, chemical substances, ozone etc. That is why in some cases they need to be exchanged after a certain number of operating hours (on top of the exchange of the oil dampers). The hydropneumatic system requires maintenance as well, yet depending very much on the design of the components. Usually diaphragm accumulators are used to provide the gas which suspends the system. The diaphragm is made of flexible material – rubber – and this material does not completely seal off the gas from the oil. In fact there is diffusion of gas molecules resulting in a slow decay of gas pressure. Therefore this gas pressure has to be checked regularly and eventually be brought back to its original level. There are however special diaphragm materials and designs and also special kinds of gases which strongly reduce diffusion and therefore the need for regular checks (of course at higher costs). In addition, a change of the oil can be necessary since its properties, especially viscosity, are changing over time. Similarly to regular oil dampers, the oil in hydropneumatic systems can also degrade over time for example due to the cutting of the long-chain molecules by shearing in flow restrictors and valves or due to the intrusion of water. On a vehicle, hydropneumatic suspension systems are usually connected to the vehicle’s overall hydraulic system and therefore no special oil service is necessary for

1.4

Applications for Hydropneumatic Suspensions

15

Mechanical spring and damper

Pneumatic spring and damper

Hydropneumatic system

o

++

++

++

++

+

–

+

++

++

o

–

Design space requirement

o

–

+

Reliability + robustness

+

o

+

Service requirements

+

o

o

Spring characteristics Damping and friction characteristics Level control

Cost

Fig. 1.7 Fulfillment of the requirements by the different suspension systems

the suspension hydraulics. In general hydropneumatic systems have proven their robustness especially in dirty and harsh environment and under heavy suspension loads. Special sealing systems (in particular for the rod) and the heavy duty design of cylinder tubes grant this. Sections 4.1 and 4.2 give more detailed information about this. Figure 1.7 gives an overview of the fulfillment of the various requirements by the three different suspension systems.

1.4 Applications for Hydropneumatic Suspensions From Fig. 1.7 it can be deduced that hydropneumatic suspension systems are used especially in applications where: (a) a level control is needed in particular for level readjustments after major load changes, (b) a level control needs to work frequently and needs to react quickly, (c) a manual operator control for the suspension level is desired, (d) little space is available for suspension elements,

16

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Suspension Systems Basics

(e) possibly hydraulic cylinders are already available for control of the desired suspension degree of freedom, (f) robust components are required due to the harsh working environment, (g) a lockout of the suspension in the design position is required, (h) the spring rate needs to be adjustable, (i) a hydraulic energy supply is already available. Points a, b, f and i are the reasons why hydropneumatic suspension systems can be found in all kinds of off-road vehicles like for example construction machinery/trucks, mobile cranes, tanks, agricultural vehicles, mining and heavy load trucks as well as snow groomers. In these applications they usually provide the wheel or axle suspension and, depending on the special operation, other functions like the suspension of lift arms or implements. A further area of application is the wheel suspension in passenger cars. This has become popular since Citroen uses hydropneumatics for many of their cars’ suspension systems. In particular, the load independent constant level of the suspension (and therefore the possible low spring rate and legendary comfort) as well as the manual level adjustment (a and c) are major drivers for using hydropneumatics here. In former times the Citroens’ hydraulic power supply was not only used for the suspension but also for the brakes and the steering. Thus there was also a synergistic effect as mentioned in (i). But partly due to the high pressures that are needed for the suspension hydraulic system, Citroen introduced a separate suspension hydraulic system starting with their Hydractive III system. This way the (until then) expensive special components for steering and brakes could be replaced by much more cost effective standard components from the “regular” passenger cars (more information in Sect. 7.2). The hydropneumatic suspension is also used in rail applications. In low-platform city traffic tramcars hydropneumatics provide a major advantage in keeping the car always on the same level no matter how many people are on board (a). This way it is always perfectly aligned with the edges of the train station platforms. This allows easier entrance especially for disabled persons (wheelchairs) and families (prams). Due to the availability of hydraulic energy (i) as well as the possibility for level control (a) and therefore a soft tuning of the suspension system, John Deere – as well as many other manufacturers of agricultural equipment – has chosen a hydropneumatic system for their front axle and cabin suspensions throughout the whole range of tractors. The suspension elements are located in areas at the front and the rear axle which are exposed to heavy soiling, chemicals, high crops etc. and therefore need to fulfill highest requirements in terms of robustness (f). Furthermore there are for example boom suspensions of wheel loaders, telehandlers and front loaders on tractors as well as the suspension of the front hitches for front implement attachment on tractors. Here the cylinders that are already available for the lifting function of these devices are used as suspension cylinders by adding a hydraulic accumulator to the system (e). These heavy devices and the heavy loads that are carried by them are then suspended softly which is of great help, for example, during rides through rough terrain. For the same reason, a hydropneumatic

1.4

Applications for Hydropneumatic Suspensions

17

suspension is also available as aftermarket equipment for front ballast weights. The mass of these weights then acts as a vibration absorber mass to reduce accelerations in the tractor chassis and improve the dynamic tire load factor of the front wheels. A rather exotic area of application for hydropneumatic suspensions are the towbarless aircraft tractors. For easy ground handling on airports they lift the nose wheel of an aircraft and this way tow it to the parking or starting position. Lifted loads of up to 50 tons with curb weights of 30–40 tons make a level control inevitable. Last but not least, because of its high power density, the hydropneumatic system is perfectly suited for the axle suspension of such vehicles.

Chapter 2

Spring and Damping Characteristics of Hydropneumatic Suspension Systems

2.1 General Setup and Working Principle The simplest hydropneumatic suspension system consists of only three components: a hydraulic cylinder, a hydropneumatic accumulator, which is directly mounted on the cylinder and, of course, the hydraulic fluid. In case cylinder and accumulator need to be separated – for example due to design space reasons – additional oil lines and fittings are necessary to provide the hydraulic connection. After adjusting the hydraulic pressure to the required level (by adding or releasing hydraulic fluid) this system now already provides the suspension function. When displacing the piston rod, the fluid volume in the accumulator is changed and therewith the pressure (p1 → p2 ). This causes a change of the force at the piston rod which, in combination with the change of the position, defines the spring rate c. The external spring force FF which acts upon the piston rod is always in balance with the forces resulting from the pressures onto the piston, when neglecting inertial and friction forces (Fig. 2.1a). When the force FF is increased to FF ∗ (Fig. 2.1b) the position of the piston changes (s) and therefore some hydraulic fluid is displaced into the accumulator. This change proceeds until the pressure in the accumulator (and thus on the active surface of the piston) has reached a level which again provides a balance for the system. This balance of forces is the basis for the function and the understanding of the suspension system. It will be used in the following sections for further calculations. To allow for additional damping, a flow resistor is placed between cylinder and accumulator. It converts part of the kinetic energy of the hydraulic fluid into heat (viscous friction). This provides the desired damping in combination with the (undesirable) boundary friction caused by the cylinder sealing and guiding elements. This so called “suspension unit” consisting of cylinder, accumulator, flow resistor and hydraulic fluid already provides the suspension function and could replace the typical combination of mechanical spring and damper. Yet with this system the major advantage of hydropneumatic suspension systems is not yet used: level control. An additional level control unit provides a constant normal position of the suspension independent from the static spring load FF . The

W. Bauer, Hydropneumatic Suspension Systems, DOI 10.1007/978-3-642-15147-7_2,  C Springer-Verlag Berlin Heidelberg 2011

19

20

2

Hydropneumatic Suspension Systems p1

FF

(a)

AK

Δs

p2

FF*

(b)

AK FF = AK ⋅ p1

FF* = AK ⋅ p2

c=

FF − FF* Δs

Fig. 2.1 Balance of forces at the piston of a single-acting cylinder

level control unit consists of a position sensor which, directly or via an electronic control unit, sends signals to a hydraulic control valve, which then changes the amount of hydraulic fluid in the suspension unit in order to bring the suspension back to the design position if necessary. By increasing the amount of hydraulic fluid, the level of the system is increased; reducing the amount of hydraulic fluid

1 Cylinder

2

2 Accumulator 3 Flow resistor 3

7

4 Lines and fittings

8

5 Position sensor (+ electronic controls)

6 1

4

6 Hydraulic control valve 5

7 Hydraulic pressure supply 8 Reservoir

Suspension unit

Level control unit

Fig. 2.2 General setup of a hydropneumatic suspension system

2.2

Spring Characteristics

21

decreases the level of the system. Pressurized hydraulic fluid as well as the possibility to dispose of excessive fluid (to a hydraulic reservoir) need to be provided to enable that. By combining these two parts (suspension unit and level control unit) it is possible to draw a basic schematic of a hydropneumatic suspension system (Fig. 2.2). Section 2.2 describes two main functions of a hydropneumatic system: spring characteristics and damping characteristics regarding their basic principles and theoretical background, while Chap. 3 describes how predefined characteristics can be achieved with a certain component layout. The third main function, the level control, is described in more detail in Chap. 5.

2.2 Spring Characteristics The spring rate of a hydropneumatic suspension system can be determined from the pure spring force–displacement curve measured at the suspension cylinder when the hydraulic flow resistor, as shown in Fig. 2.2, is removed. An increase of force onto the cylinder leads to an increase in hydraulic pressure and therefore to a change in position of the piston rod. This is due to the following reasons: – compression of the gas in the accumulators – widening of the (elastic) fluid lines and fittings – compression of the hydraulic fluid Each of these three effects causes an individual spring rate. So what is measured at the suspension cylinder is the spring rate of a spring which is made up by a sequential combination of these three individual springs. Using general laws of physics, the following Eq. (2.1) is obtained: cges =

cG cL cF cG cL + cG cF + cL cF

(2.1)

The stiffness of the lines and fittings as well as the compression modulus of the hydraulic fluid are usually very high, so their impact on the overall spring rate cges is low. This means that the characteristic properties of a hydropneumatic spring are mainly influenced by the properties of the gas which is enclosed in the hydraulic accumulators. So before explaining the detailed function of the various types of hydropneumatic suspensions, the properties and the thermodynamic physics of gases and their effect on the suspension function is explained.

2.2.1 Thermodynamic Background The gas in the accumulator(s) is the medium which is responsible for the elasticity of the complete setup. Because it fulfills the most important task (spring rate) its

22

2

Hydropneumatic Suspension Systems

properties are predominantly important for the behavior of the whole suspension system. In the initial state of an accumulator – with an unpressurized hydraulic system – a certain number of gas molecules and therefore a certain gas mass mG is trapped inside the accumulator. It is defined by the volume of the accumulator V0 (= gas volume if no hydraulic pressure is applied) and the accumulator precharge pressure p0 . The precharge pressure always refers to the room temperature 293.15 K (or 20◦ C) and is set during the production process of the accumulator. For this condition the equation of state for the ideal gas is: p0 V0 = mG RT

(2.2)

If the gas temperature changes during the production process (for example during paint-drying), during shipping or later during the operation of the suspension system, the gas pressure changes to a new precharge pressure according to the laws for the isochoric change of state. This temperature-dependent precharge pressure must be taken into account when laying out systems that are will be operated at various temperatures. p0,T = p0

T T0

(important: T, T0 in [K])

(2.3)

As soon as the accumulator is integrated into the hydraulic system and the system is pressurized, the gas volume in the accumulator does not change as long as the hydraulic pressure is less than or equal to the precharge pressure. As soon as the hydraulic pressure exceeds the precharge pressure, the gas volume is compressed until a balance of forces or, for equal active areas on gas and fluid side as in diaphragm accumulators, a balance of pressure is attained. The increase of hydraulic pressure can be caused for example by loading the suspension system with the suspended mass. The compression of the gas takes place rather slowly and the new pressure level is maintained over a longer period, so in this case an isothermal change of state according to Boyle-Mariotte can be assumed. The heat generated by compression dissipates into the environment and the temperature remains constant during the process. V1 = V0

p0 p1

(2.4)

This isothermal change of state can be used for the calculation of both the first time loading of the suspension system as well as all subsequent slow load changes: for example people getting on and off the suspended system, loading and unloading of payload, long term changes in external preloads and forces. The suspension movement itself, when absorbing the shocks during the regular operation of the suspension system, takes place quite rapidly. The excitation frequencies that the suspension system is able to absorb usually range from below 1 Hz to sometimes over 10 Hz. These high speed changes of state leave little time

2.2

Spring Characteristics

23

for the dissipation or adsorption of heat compared to an isothermal change of state as described above. The gas will therefore change its temperature. Assuming that no heat exchange is possible, an adiabatic change of state takes place which is described by the following equation: p1 V1κ = p2 V2κ

(2.5)

In this equation κ is the adiabatic exponent, which is the ratio of the specific heat capacity at constant pressure and the specific heat capacity at constant volume for a particular gas. In standard literature values are quoted that refer to the properties at low pressures and room temperature. These values are for example according to [DUB90]: κ ≈ 1.66 for monoatomic gases (e.g. He) κ ≈ 1.40 for biatomic gases (e.g. N2 , O2 and therefore also air) κ ≈ 1.30 for triatomic gases (e.g. CO2 ) Although it is rarely mentioned, for hydropneumatic suspension systems it is very important to consider that κ depends significantly upon temperature and gas pressure. Figure 2.3 gives an overview of the behavior for nitrogen. In real hydropneumatic suspensions there is always the possibility of a marginal heat exchange of the gas with its surrounding components and therefore there will never be the ideal adiabatic change of state. This means that hydropneumatic suspension processes are defined by a polytropic change of state characterized by 1 < n < κ. The more heat is exchanged during the change of state, the more the polytropic exponent n for this process will go from κ towards 1; the latter defines

Fig. 2.3 Adiabatic exponent κ of N2 as a function of T and p ([MUR01])

24

2

Hydropneumatic Suspension Systems

again the isothermal change of state with perfect heat exchange. The exact conditions for heat exchange are usually unknown and are very difficult to identify, which is the reason why it is extremely difficult to find out where exactly between 1 and κ the polytropic exponent needs to be chosen. Furthermore even the actual value for κ is difficult to determine due to the above mentioned effects of pressure and temperature onto κ; even more so because both parameters change constantly during the suspension processes. That is why it is only possible to estimate the polytropic exponent n for preliminary calculations. Figure 2.4 shows how much influence n has on the pressure–volume diagram. Starting from a pressure of one bar the gas is compressed. The resulting pressure can be read from the curve progression. It is clearly visible that the pressure and therefore also the force of the cylinder increases with increasing polytropic exponent. A strong impact on the spring rate can directly be deduced. Assuming a value of n = 1.3 usually works well for preliminary calculations. Only at higher pressures especially in combination with very low operating temperatures it is recommended to use n = 1.4 or higher (according to the behavior shown in Fig. 2.3). The most realistic average values for n can be deduced from measurements of force–displacement curves in experiments. Calculations need to be compared to the experiments and the polytropic exponent of the calculations needs to be readjusted to a level which provides best match of theoretical end experimental force–displacement curves. This empirically determined value for n can in the future be reused for the calculation/simulation of hydropneumatic systems with similar setups, especially concerning accumulators and their environment.

Fig. 2.4 p–V curves for different polytropic exponents

2.2

Spring Characteristics

25

2.2.2 Calculation Predeterminations All the calculations in this section are done under the following assumptions and conditions: (1) The influence of the ambient pressure is neglected. This is acceptable, since the usual working pressure levels in the cylinders as well as the precharge pressures of the accumulators (commonly specified as gauge pressure above the ambient pressure) are significantly higher than the ambient pressure – usually a factor of 50 and above for the working pressure and a factor of 25 and above for the precharge pressure. If this is not the case for special hydropneumatic suspension systems it is necessary to reconsider the question whether the influence of ambient pressure is really negligible. If not, it is necessary to multiply the ambient pressure with the externally effective active cylinder area (usually the piston rod cross-sectional area) and use this force value as a preload force without additional spring rate – please refer Sects. 2.2.3, 2.2.4, 2.2.5, and 2.2.6. Furthermore in this case the absolute accumulator precharge pressure (=specified precharge pressure + ambient pressure) needs to be used for the calculations. (2) For better comparison of the results and behaviors, all calculations are performed for a temperature of 293.15 K (or 20◦ C) – particularly important for the accumulator. Therefore the specified accumulator precharge pressure (referring to 293.15 K) can be directly used for the calculations. If the suspension behavior for other temperatures has to be calculated, it is necessary to first calculate the altered, temperature-dependent precharge pressure (see Sect. 2.2.1) and then use this value in the respective equations. (3) A polytropic exponent of 1.3 is used. (4) The suspended mass directly acts upon the suspension cylinder (i = 1). This means there is no mechanical linkage system that creates any kind of lever ratio of i = 1: cylinder force to gravitational force of the mass. This is often not the case for suspension systems but again for comparison of results this is assumed. Yet in Chap. 7 an example is given which explains the influence of a lever ratio i = 1. (5) The design position of the suspension is defined to be exactly in the center of the overall stroke between the compression and rebound end stop. (6) Damping (solid body and fluid friction) is not part of the calculations in Sect. 2.2. All hydraulic pressures do not include pressure losses (e.g. caused by flow restrictors). The focus here is purely on spring characteristics.

2.2.3 Non-preloaded Hydropneumatic Suspensions This is the simplest type of hydropneumatic suspension. This system consists of a single acting suspension cylinder and an accumulator. The suspension cylinder

26

2

Hydropneumatic Suspension Systems FF

FF

s=0

s=0 Fhydr.

(a) Plunger cylinder

s

Fhydr.

s

(b) Double-acting cylinder with interconnected cylinder sides

Fig. 2.5 Schematic illustration of non preloaded hydropneumatic suspensions

can be designed as a single-acting cylinder (for example, a plunger cylinder) or as a double-acting cylinder with interconnected pistonside and rodside of the cylinder. The latter system is able to provide higher amounts of rebound damping (more detailed information in Sect. 2.3). Both systems are depicted in Fig. 2.5. It is important to consider that the externally effective active area is only the cross-sectional area of the piston rod. It is due to the interconnection of piston chamber and rod chamber (the so-called regen(erative) system) that effectively only the fluid volume displaced by the piston rod flows into the accumulator while the other portion of the fluid displaced by the piston flows back into the rodside. The most important method to describe the behavior of a spring is the force– displacement curve for compression and rebound. It has been mentioned in Sect. 1.1 already that this curve is basically linear for a regular mechanical coil spring; other curves are possible by special winding techniques as well as parallel connection of multiple springs. The hydropneumatic spring however always has a disproportionately progressive shape of the force–displacement curve. This shape can be controlled by variation of several influencing factors. The important factors are deduced on the following pages. Before calculating the non preloaded hydropneumatic suspension it is necessary to define some of the various states that a suspension system can be in: State 0: Spring force FF0 = 0 . The pressure in the accumulator is the precharge pressure p0 , which is defined during the production process. The gas fills out the complete internal volume V0 of the accumulator. State 1: Now the static suspension force FF1 is loading the suspension system (while FF1 > FF0 ). The force is sufficient to compress the gas volume in the accumulator isothermally to the volume V1 and the pressure p1 . State 2: FF2 is the dynamic suspension force and oscillates around FF1 . Therefore the gas volume is compressed (compression) and expanded

2.2

Spring Characteristics

27

(rebound) by a polytropic change of state to the volume V2 and the pressure p2 . The starting point for the calculation is the correlation of the force acting onto the surface of the piston FK and the pressure in the piston chamber pK . FK (s) = pK (s)AK

(2.6)

Using the state equation for polytropic changes of state p1 V1n = p2 V2n

(2.7)

and the definition that an increase of the displacement s causes a compression of the gas V2 = V1 − AK s

(2.8)

p1 V1n p1 V1n = V2n (V1 − AK s)n

(2.9)

it can be deduced that: p2 =

On the basis of the isothermal change of state from 0 to 1 it is stated p1 V1 = p0 V0

(2.10)

and therefore V1 =

p0 V0 p1

(2.11)

As well as on the basis of the balance of forces at the piston FF1 = p1 AK

(2.12)

and thus p1 =

FF1 AK

(2.13)

For the following calculation it can be applied that pK (s) = p2

(2.14)

28

2

Hydropneumatic Suspension Systems

Combining all above equations brings us to ⎛ FF1 AK

·⎝

⎞n p0 V0 FF1

⎠

AK

FK (s) = ⎛

⎞n AK

(2.15)

⎝ p0 V0 − AK s⎠ F F1 AK

After canceling AK

p FK (s) = FF1  p

0 V0

n

FF1 0 V0

FF1

n −s

(2.16)

by the substitution p0 V0 = h0F FF1

(2.17)

the following simple relationship is obtained: FK (s) = FF1 ·

hn0F (h0F − s)n

(2.18)

The dimension h0F can be interpreted easily by a virtual image. It is equivalent to the height of a column of gas with the pressure p0 (the precharge pressure) and the volume V0 which has exactly the right base area so that it supports the force FF1 . Figure 2.6 depicts this for several different static spring loads FF1 . FF1 FF1 < FF1` < F F1``

h 0F

p0

FF1``

V0 FF1` p0 V0 h0F`

p0 V0 h 0F``

Fig. 2.6 h0F for various static spring loads FF1

2.2

Spring Characteristics

29

This illustration demonstrates one of the most important features of a hydropneumatic suspension: the higher the static springload, the smaller the height of the gas column h0F and therefore the more significant the change of the gas pressure forces on the piston at a given displacement s which then means a higher spring rate. The simple background to this is the relative change of the column height (h0F − s)/h0F ; it becomes more meaningful with smaller h0F and therefore the relative volume decrease and the relative pressure increase are more significant. This is the explanation of the increasing spring rate with increasing static springload for a hydropneumatic suspension. In case a hydropneumatic suspension is subjected to a wide range of static springloads, another important characteristic curve needs to be considered: the dependency of the spring rate on this very static springload. This is deduced by the following calculation. The general mathematical expression for the spring rate is: c=

dp d(pAK ) dF = = AK ds ds ds

(2.19)

After using Eq. (2.9) and differentiation with the chain rule: dp = p1 V1n (−n)(V1 − AK s)−n−1 (−AK ) ds

(2.20)

After applying the isothermal change of state from 0 to 1 and the balance of forces at the piston according to Eq. (2.13) and furthermore Eq. (2.11): dp FF1 c = AK = AK ds AK



p0 AK V0 FF1

n



p0 AK V0 (−n) − AK s FF1

−n−1 (−AK )

(2.21)

Dissolving and again using the dimension h0F Eq. (2.17) results in: c(s) = FF1 n

hn0F (h0F − s)n+1

(2.22)

It becomes obvious that h0F is also important for the spring rate. Yet we should remember that h0F is depending upon FF1 – it is not a constant value. For s=0 and dissolving h0F we obtain the spring rate in normal (design) position: c=n

FF12 p 0 V0

(2.23)

These are now the fundamental equations on which the function of every hydropneumatic suspension system is based upon. One extremely interesting consequence is that the geometry of the suspension cylinder(s) plays no role in these equations! Solely the gas fill in the accumulator as well as the suspended load determine the contour of the force–displacement curve and therefore also the spring rate.

30

2

Hydropneumatic Suspension Systems

On one hand the gas fill in the accumulator can be described by the product of accumulator precharge pressure p0 and the accumulator volume V0 . On the other hand it can, according to the equation of state for the ideal gas, be given as mG RT. This again points out clearly that, apart from the static spring load and the mass of the gas fill mG , the spring rate is also depending upon the temperature of the gas/the accumulator. So when laying out a hydropneumatic suspension system it has to be taken into account that the precharge pressure set during the production process refers to 20◦ C temperature. The actual operating temperature can vary due to influences from the environment but can also be increased due to heat in the hydraulic fluid that arises from the viscous damping. The general rule is: higher temperatures soften the spring, lower temperatures make it stiffer. Furthermore Eq. (2.23) makes it obvious that the static spring load affects the spring rate with its second power, a characteristic property of a hydropneumatic suspension. This means that the suspension behavior of the system spring-dampermass changes with changing suspended load. This is illustrated in the following calculation using the simple example of a single-mass oscillator. Using 

c mF

(2.24)

ω = 2π f

(2.25)

FF1 = mF g

(2.26)

ω= and

and

and additionally Eq. (2.23), it is possible to calculate the natural frequency f for the non preloaded hydropneumatic suspension: 1 f = 2π

nFF1 g p 0 V0

(2.27)

It becomes obvious that the natural frequency changes proportionally with the square root of the static springload. f ∼

 FF1

(2.28)

Generally spoken and from a theoretical point of view it is a goal to keep the suspension properties of a system constant throughout all loading conditions. For

2.2

Spring Characteristics

31

vehicle suspensions this is particularly important for ride behavior, comfort and road holding. Therefore it would be ideal to have a natural frequency independent of the static springload, especially for a single-mass oscillator. Yet in many applications not only the suspended mass/static spring load but also the moment of inertia with respect to various degrees of freedom have to be taken into account. In these cases the behavior described by Eq. (2.28) is often favorable since a disproportionate change of the spring rate often results in more constant overall suspension behavior than a spring rate changing proportionally with the static spring load. An explicit example of this is the hydropneumatic suspension for the front axle of an agricultural tractor. For lifting and moving heavy masses a so called front loader is optionally available, which consist of the hydraulically liftable boom in combination with a tiltable bucket or pallet fork attached to the end of it. When lifting a heavy mass, the center of gravity (COG) of this mass is very remote to the tractor’s center of gravity which increases significantly the moment of inertia for the pitch motion of the tractor (Fig. 2.7). The natural frequency for pitch motion needs to be kept above a certain level to prevent the tractor from becoming an uncontrollable rocking chair. Therefore it is beneficial to increase the spring rate more than it would be necessary for a constant bounce frequency. Hydropneumatic suspension systems fulfill this requirement and therefore contribute a lot to comfortable, stable and controllable ride behavior during front loader work. The force–displacement curve of a hydropneumatic spring as well as the curves of spring rate and natural frequency as a function of the suspended static load provide essential information about the suspension properties of a particular suspension system. On the following pages of this section these curves are shown and explained for the various hydropneumatic suspension systems. To ensure good comparability

COG plane for the unloaded tractor COG plane for a tractor with heavy front loader

COG plane for frontloader-bucket including payload

Fig. 2.7 Relocation of the tractor’s center of gravity during front loader work

32

2

Hydropneumatic Suspension Systems

between the different systems, all characteristic curves are calculated using the following basic setup for the suspension system: Single-mass oscillator Full suspension stroke (stop-to-stop) 100 mm Design position is the center between both end stops Static load for the suspension is 10 kN System tuned to a natural frequency of 2 Hz The following Figs. 2.8, 2.9 and 2.10 show the characteristic curves for the non preloaded hydropneumatic spring. For comparison the graphs also show the respective characteristic curves for a linear mechanical spring (thin line). The curves for spring rate and natural frequency are cut off below 2500 N static spring load. This range is not applicable for non preloaded hydropneumatic suspensions due to their low allowable load ratio (with the commonly used diaphragm accumulators, refer to Sect. 3.1.3) and therefore this is not relevant for real applications. In practice numerous examples can be found for applications of non preloaded hydropneumatic suspensions. For example most boom suspensions for tractors,

Spring force [kN]

40 Hydropn. spring Mech. spring

30 20

10 0 –50

–25

0 Displacement [mm]

25

50

Fig. 2.8 Force–displacement curve for the non preloaded hydropneumatic spring

Spring rate [N/mm]

800 Hydropn. spring Mech. spring

600 400 200 0 0

5

10 15 Static spring load [kN]

Fig. 2.9 Spring rate vs. static spring load for the non preloaded hydropn. spring

20

2.2

Spring Characteristics

33

Natural frequency [1/s]

4 3 2 1

Hydropn. spring Mech. spring

0 0

5

10 15 Static spring load [kN]

20

Fig. 2.10 Natural frequency vs. static spring load for the non preloaded hydropn. spring

telehandlers or wheel loaders (Fig. 2.11) – if they are suspended – are equipped with such a simple system: a cylinder whose pistonside is connected with an accumulator. This way the boom including the bucket/pallet fork etc. and the payload is suspended softly. In particular, the pitch oscillations of the usually completely unsuspended vehicle are reduced by this means. Comfort of the driver and in most cases ride stability are increased. Furthermore the reduced vibrations and accelerations at the bucket/pallet fork ensure safe transportation of the payload. In particular, bulk goods can be carried in a bucket more safely since the suspension prevents the payload from spilling and getting lost over the bucket’s edge. More detailed information about boom suspensions can be found in [LAT03] and for example the patents [DE205] and [US491].

Boom

Payload

Bucket Suspension cylinders

Fig. 2.11 Boom suspension of a wheel loader

The already mentioned next level of sophistication of non preloaded hydropneumatic suspensions is achieved by introducing a double-acting cylinder which is run in the regenerative mode (“regen”-mode) by connecting both cylinder sides (Fig. 2.5b). This type of system allows much higher rebound damping compared to the plunger cylinder. It can be found for example in the cab suspension of 6020series tractors produced by John Deere (HCS = hydraulic cab suspension). In the course

34

2

Hydropneumatic Suspension Systems

of improvements made since the start of serial production, the external line initially used for the connection of the two cylinder chambers (as shown in Fig. 2.5b) was eliminated. It was replaced by a passage in the piston with integrated flow resistor, thus providing identical damping characteristics at better cost. In this application an increased rebound damping level is necessary due to the kinematics of the suspension linkages to prevent the cab from strong pitching due to braking or even trailing throttle in the lower gears. The example of the HCS is shown in Fig. 2.12. It shows the integrated solution with cylinder (internal oil flow via piston cross drill) and accumulator being combined to the suspension unit. The connected hose is only used to provide oil for level control.

Fig. 2.12 Cab suspension cylinders of John Deere 6020series tractors

1 Piston rod

1 2

2 Protection cover 3 Hose to leveling valve 4 Cylinder tube

3

5 Accumulator 4 5

The currently highest level of development for non preloaded hydropneumatic suspensions is represented by the so called Hydractiv chassis suspension, which is used in several of Citroen’s latest passenger cars. In Fig. 2.13 it is shown that the center valve (7) allows two different operational modes for the suspension. If it is energized (and this is shown in the illustration) both suspension units of an axle are interconnected via a control valve (6) and are furthermore able to displace hydraulic fluid into a third accumulator (3). Its additional gas mass is the reason for a relatively low spring rate in this operational mode. Due to the interconnection of the suspension units, no roll stability (torsional spring rate relative to the longitudinal axis) is provided by the hydropneumatic springs, so it is only the mechanical anti-roll bars which are operative in this mode. In case the center valve is unenergized, both suspension units are separated from each other by the control valve and therefore act as individual springs. This causes additional roll stability compared to the interconnected operation. Furthermore in

2.2

Spring Characteristics 4

4

1

3

35

2

8

5

5

3 6

6

7 5

5

1 1 1

2

4

1 Accumulators front 2 Accumulators rear 3 Add. accumulator

4 Damping elements 5 Additional Damping elements 6 Control valve

4 7 Center valve 8 Controller

Fig. 2.13 Hydraulic schematic of the Citroen Hydractiv system (mod. from [HEN90])

the closed state, the third accumulator for each axle is decoupled from the suspension units, which causes a higher spring rate for the individual springs. So by closing the control valves, higher ride stability can be achieved especially during cornering and for “sporty” driving, while for opened control valves the soft suspension setup provides a high level of comfort which is typical for Citroen and their hydropneumatic suspensions. Detailed information about this can be found in Sect. 7.2.

2.2.4 Systems with Mechanical Preload It is clearly visible in Fig. 2.9 that there is a quadratic relationship between spring rate and spring load. Although this characteristic feature can have positive effects, as mentioned earlier in this section, it is in many cases favorable to attenuate it. This can be achieved by saddling an additional internal preload onto the hydropneumatic springs which is already active even when no external load is applied. In this case the preload acts as a basic load and all other external loads are added onto it. This has the effect that, for a given change of the external static load, the relative load change for the spring of the preloaded suspension system is smaller than for the non preloaded system.

36

2

Hydropneumatic Suspension Systems

The practical application of the preload is done in two different ways: (a) For the single-acting suspension cylinder the preload is applied by a mechanical spring for example by a helical coil spring or a torsional spring (mechanical preload). (b) By using a double-acting suspension cylinder it is possible to apply a hydraulic counter-pressure on the rod side by a second hydropneumatic spring (hydraulic preload). A third theoretical possibility is to load the isolated side with an additional mass to get the desired preload. Yet this is usually not accepted in mobile hydraulics since this would add significantly to the curb weight of the vehicle. This section now explains the systems with mechanical preload, Fig. 2.14 shows its schematic. Since the mechanical spring preloads the hydropneumatic spring with a compressive force, both springs are positioned figuratively opposite to each other although from a functional point of view it is a parallel connection of these springs. This is why the force application point of the overall, externally effective spring force is in the connection point of both springs, in the center. The illustration shows clearly that the mechanical spring causes, in addition to the preload, an additional spring rate for the system. This means that the system will have an effective spring rate resulting from the parallel connection of the hydropneumatic and the mechanical spring. c = chydr + cmech

F mech.

FF s=0 s

F hydr.

(also possible with doubleacting cylinder according to Fig. 2.5)

Fig. 2.14 Schematic illustration of a hydropneumatic spring with mechanical preload

(2.29)

2.2

Spring Characteristics

37

The spring rate for the hydropneumatic spring chydr can be calculated using Eq. (2.23). It is important to keep in mind though that the sum of the static spring load FF1 and the mechanical preload FV,mech (in the normal position of the suspension) need to be considered in the equation, replacing only FF1 . The spring rate for the mechanically preloaded hydropneumatic suspension therefore can be calculated by: c(s = 0) = n

(FF1 + FV )2 + cmech p0 V0

(2.30)

and the natural frequency for a single-mass oscillator with this system is:    n(F +F )2 V F1  + c mech g p0 V0 1  f = 2π FF1

(2.31)

The calculation for the force–displacement-curve can be deduced from Fig. 2.14: FF (s) = Fhydr (s) − Fmech (s)

(2.32)

The force of the mechanical spring is: Fmech (s) = FV − cmech s

(2.33)

In order to calculate FF (s) it is necessary to use Eq. (2.16) from Sect. 2.2.3 and then insert the sum of forces (FF1 + FV ) replacing FF1 in Eq. (2.16):  FF (s) = (FF1 + FV ) 

p0 V0 FF1 +FV

p0 V0 FF1 +FV

n

n − (FV − cmech s) −s

(2.34)

The following Figs. 2.15, 2.16 and 2.17 show the characteristic curves for the hydropneumatic suspension with mechanical preload. The preload force FV and the spring rate of the mechanical spring cmech are varied in the diagrams to show the influence of these parameters on the different curves. It is of major importance that a mechanical spring is, at a given design space, the more intricate (and therefore expensive) the higher the preload force and the higher spring rate. For this reason a preload force of 5 kN and a spring rate of 20 N/mm are chosen as a basis for the following diagrams and are varied from there. This means that for variations of the preload force, a spring rate of 20 N/mm is chosen and for the variation of spring rate in general a preload force of 5 kN is chosen. Both basis values are rather on the lower end of the optimum range, as we will see later on. Looking at the force–displacement curves one tends to assume that the properties vary only marginally in the near range around the design point at a displacement of

38

2

Hydropneumatic Suspension Systems

(a)

Spring force [kN]

40

30

FV = 0 kN FV = 5 kN FV = 10 kN FV = 15 kN

20

10

0 –50

–25

0 Displacement [mm]

25

50

25

50

(b)

Spring force [kN]

40

30

cmech = 0 N/mm cmech = 20 N/mm cmech = 40 N/mm cmech = 60 N/mm

20

10

0 –50

–25

0 Displacement [mm]

Fig. 2.15 Force–displacement curves for the hydropneumatic spring with mechanical preload. (a) Variable FV (cmech = 20 N/mm). (b) Variable cmech (FV = 5 kN)

0 mm, a static spring load of 10 kN and a natural frequency of 2 Hz. However, when looking at the areas remote from the design point and even more when looking at the curves for spring rate and natural frequency, significant differences become obvious. Increasing mechanical preload reduces the progression of the force–displacement curve as well as the progression of the spring rate over static spring load. This means a considerable reduction of some characteristic (and sometimes unfavorable) properties of a hydropneumatic suspension. The reason for this can be found in the reduced relative load change (per kN increase of static spring load) with increasing FV . The equation for the natural frequency indicates clearly, that an increased mechanical preload needs to be compensated by an increased gas mass p0 V0 if the natural frequency has to remain constant. Furthermore it can be deduced that the relative change of the characteristic curve (by changed mechanical preload) decreases, the higher FV is chosen. In Figs. 2.16a and 2.17a this can be seen from the larger distance of the curves 0–5 kN compared to the distance of the curves 10 and 15 kN.

2.2

Spring Characteristics

39

(a)

Spring rate [N/mm]

800 FV = 0 kN FV = 5 kN FV = 10 kN FV = 15 kN

600

400

200

0 0

5

10 15 Static spring load [kN]

20

(b)

Spring rate [N/mm]

800 cmech = 0 N/mm cmech = 20 N/mm

600

cmech = 40 N/mm cmech = 60 N/mm

400

200

0 0

5

10 15 Static spring load [kN]

20

Fig. 2.16 Spring rate vs. static spring load for the hydropneumatic spring with mechanical preload. (a) Variable FV (cmech = 20 N/mm). (b) Variable cmech (FV = 5 kN)

It is also clearly visible, that the trend of the curve of spring rate vs. static spring load shows a better linearity for the preloaded hydropneumatic suspension system compared to the non preloaded system. Resulting from this is a natural frequency which is very close to the design goal of 2 Hz over a broad range of static spring load. It is interesting that the minimum of the natural frequency is moved to higher static spring loads with increasing mechanical preload FV . In the example illustrated by Fig. 2.17a the natural frequency shows the best constancy in the range around the design point spring load (10 kN) when mechanical preloads between 5 and 10 kN are applied (reminder: cmech = 20 N/mm). An increase of the mechanical spring rate has a similar effect as an increase of mechanical preload. Here too, the progression of the force–displacement curve and the spring rate vs. static spring load curve decreases with increasing mechanical spring rate. This is due to the fact that more and more load is taken by the mechanical spring and off the hydropneumatic spring (same overall spring rate!) for

40

2

Hydropneumatic Suspension Systems

(a) Natural frequency [1/s]

4

3

2 FV = 0 kN FV = 5 kN FV = 10 kN FV = 15 kN

1

0 0

5

10 Static spring load [kN]

15

20

(b) Natural frequency [1/s]

4

3

2 cmech = 0 N/mm cmech = 20 N/mm cmech = 40 N/mm cmech = 60 N/mm

1

0 0

5

10 Static spring load [kN]

15

20

Fig. 2.17 Natural frequency vs. static spring load for the hydropneumatic spring with mechanical preload. (a) Variable FV (cmech = 20 N/mm). (b) Variable cmech (FV = 5 kN)

increasing mechanical spring rate. So the harder the mechanical spring the softer the hydropneumatic spring and therefore the lower its influence on the overall system behavior. However even an infinitely soft spring (cmech = 0 N/mm) cannot lower the minimum of the natural frequency as low as zero mechanical preload can. Furthermore the diagrams show that the change of the characteristic curves by increasing mechanical spring rate is independent from the original level of the mechanical spring rate. The difference between the curves for 0 and 20 N/mm is about the same as the difference between the curves for 40 and 60 N/mm. It can be easily deduced from the diagrams shown above that one drops back to the curves for a non preloaded system as of Sect. 2.2.3 if the preload FV and the mechanical spring rate cmech are both reduced to zero. A practical example for a hydropneumatic suspension system with mechanical preload is the front axle suspension system offered by the company Carraro for agricultural tractors. It is used for example in tractors built by Claas (formerly

2.2

Spring Characteristics

4

2

1 1 2 3 4 5 6

41

3

6

5

Hub Upper wishbone Lower wishbone Central axle body Inner pivot axis of lower wishbone (torsion bar invisibly behind) Suspension cylinder

Fig. 2.18 Tractor front axle suspension by Carraro

Renault), Case/Steyr, Massey Fergusson and Landini. Figure 2.18 is taken from the patent US5931486. It shows an independent wheel suspension by a double wishbone arrangement (2 and 3) which is mounted on a central axle body 4. On the inner side of each lower wishbone 3 a torsional spring is placed coaxially with the respective pivot axis 5. This torsion bar creates the mechanical preload for the hydraulic cylinders 6. An adaptation of the axle to different types of vehicles is (among other measures) enabled by changing the dimensions of the torsional spring.

2.2.5 Systems with Constant Hydraulic Preload In many cases it is difficult to integrate a mechanical preload into a hydropneumatic suspension. This is often due to the usually high demand for design space of an additional mechanical spring, which has to be able to cope with the whole stroke of the suspension. That is why it is more common to use double-acting cylinders instead and use the additional available rodside chamber to create an additional, preloading spring. This is done by pressurizing the rod chamber of the cylinder (between piston and rod end) thus applying a force which acts as the preload for the suspension. Since this active area is displaced when the piston is moved and with it the oil that is contained by the rod chamber, it too has to be connected to an accumulator, which can absorb and release the displaced hydraulic fluid of the rodside chamber. This arrangement then is basically a suspension system which consists of two individual single-acting hydropneumatic suspensions counteracting each other. The respective schematic is shown in Fig. 2.19. For a better illustration of the hydraulic

42

2

Fhydr,R

Hydropneumatic Suspension Systems

FF

FF

s=0

s=0 s

Fhydr

Fhydr,K

s

Fig. 2.19 Schematic illustration of a hydropneumatic spring with hydraulic preload

preload, pistonside and rodside are symbolically shown as separate single-acting cylinders. Again both systems are shown positioned figuratively opposite to each other although from a functional point of view it is a parallel connection of these springs. The spring rate for the overall system can be calculated as the sum of the spring rates of the pistonside spring chydr,K and the rodside spring chydr,R . c = chydr,K + chydr,R

(2.35)

The spring rates for hydropneumatic springs can simply be taken over from Sect. 2.2.3. However that preload force needs to be taken into account. It results from the preload pressure pV on the rodside and the respective hydraulically active area, the ring-shaped area of the piston. FV = pV AR

(2.36)

The result for the overall spring rate is c: c=

np2V A2R n(FF1 + pV AR )2 + p0,K V0,K p0,R V0,R

(2.37)

And therefore the natural frequency can be calculated as:    n(FF1 +pV AR )2  + p0,K V0,K 1  f = 2π FF1

np2V A2R p0,R V0,R

 g (2.38)

2.2

Spring Characteristics

43

Looking at Fig. 2.19 the balance of forces gives us: FF (s) = Fhydr,K (s) − Fhydr,R (s)

(2.39)

By considering the equations for the non preloaded spring, the individual forces for pistonside and rodside can be calculated:  Fhydr,K (s) = (FF1 + FV )   Fhydr,R (s) = FV 

 p0,K V0,K n FF1 +FV

n −s

p0,K V0,K FF1 +FV

 p0,R V0,R n FV

p0,R V0,R FV

+s

n

(2.40)

(2.41)

Here it is important to keep in mind that the displacement s has different preceding algebraic signs in both equations. The reason is that a positive displacement s results in a compression on the pistonside (force increases) while it leads to an expansion on the rodside (force decreases). Applying the equation for FV results in:  FF (s) = (FF1 + pV AR ) 

n p0,K V0,K FF1 +pV AR

p0,K V0,K FF1 +pV AR



 p0,R V0,R n pV AR

n − pV AR  n p0,R V0,R −s + s pV A R

(2.42)

While for the system with mechanical preload only two new parameters (FV and cmech ) were needed for the respective equation, the number of additional parameters for a system with hydraulic preload is much higher. These new parameters p0,R , V0,R , AR and pV are available to tune the suspension to the desired properties. Yet, in the equations, these parameters always show up in pairs as AR and pV , which represent (when multiplied) the hydraulic preload force, and p0,R and V0,R , which represent (when multiplied) the gas mass enclosed in the rodside accumulator. So the latter two parameters are (in combination with FV ) responsible for the spring rate of the rodside hydraulic system chydr,R . The bottom line is that here too are two additional determining factors just like for the system with mechanical preload. These two factors can be set to the desired level by changing the parameters influencing them. The following Figs. 2.20, 2.21 and 2.22 show the characteristic curves for the hydropneumatic spring with hydraulic preload. All figures are again split into two diagrams, one of them showing the influence of the preload force AR pV = FV and the other one showing the influence of the additional rodside spring rate chydr,R = (nFV2 )/(p0,R V0,R ). For a better comparison with the hydropneumatic spring with mechanical preload, a 10 kN static spring force and 2 Hz for the natural

44

2

Hydropneumatic Suspension Systems

(a)

Spring force [kN]

40

30

FV = 3 kN FV = 5 kN FV = 7 kN FV = 9 kN

20

10

0 –50

–25

0 Displacement [mm]

25

50

25

50

(b) 40

Spring force [kN]

c hydr,R = 7 N/mm c hydr,R = 14 N/mm 30

c hydr,R = 21 N/mm c hydr,R = 28 N/mm

20

10

0 –50

–25

0 Displacement [mm]

Fig. 2.20 Force–displacement curves for the hydropneumatic spring with hydraulic preload. (a) Variable FV (c = 21 N/mm). (b) Variable c (FV = 5 kN)

frequency are chosen as the basis for this design. The preload parameters have been chosen as: AR = 500 mm2 pV = 10 MPa p0,R = 5 MPa V0,R = 300, 000 mm3 This choice provides an effective preload force of 5 kN and a spring rate of the rodside hydropneumatic spring of 21 N/mm. These values are similar to those in Sect. 2.2.4, a comparison with the previous examples (Figs. 2.15, 2.16 and 2.17) is therefore easy. Please note: choosing identical values as in Sect. 2.2.4 would not show the full potential of a system with hydraulic preload, therefore this slight

2.2

Spring Characteristics

45

(a)

Spring rate [N/mm]

800 FV = 3 kN FV = 5 kN FV = 7 kN FV = 9 kN

600

400

200

0 0

5

10 15 Static spring load [kN]

20

(b)

Spring rate [N/mm]

800 c hydr,R = 7 N/mm c hydr,R = 14 N/mm c hydr,R = 21 N/mm c hydr,R = 28 N/mm

600

400

200

0 0

5

10 15 Static spring load [kN]

20

Fig. 2.21 Spring rate vs. static spring load for the hydropneumatic spring with hydraulic preload. (a) Variable FV (c = 21 N/mm). (b) Variable c (FV = 5 kN)

deviation was chosen. Furthermore this set of parameters provides an optimal ratio of pV and p0,R as will be shown in Sect. 3.1.3. For the hydropneumatic spring with hydraulic preload it can be stated that an increase of the rodside hydraulic spring rate chydr,R and an increase of the preload force FV have in general a very similar effect. This behavior can also be deduced from the Eq. (2.37) for the spring rate and Eq. (2.38) for the natural frequency. The precharge pressure and the rodside accumulator volume can be found in the denominator, while the preload force, represented by pV AR , is found in the numerator. It becomes obvious that it is basically possible to create similar curves with a hydropneumatic suspension system with hydraulic preload and with mechanical preload. One special feature is characteristic to both of them: at low static spring loads the natural frequency does not drop as drastically as for non preloaded systems. It stays on the desired level over a broad range of loads and even increases when the load gets close to zero. This can be ascribed to the preload force on one

46

2

Hydropneumatic Suspension Systems

(a) Natural frequency [1/s]

4

3

2 FV = 3 kN FV = 5 kN FV = 7 kN FV = 9 kN

1

0 0

Natural frequency [1/s]

(b)

5

10 Static spring load [N]

15

20

4

3

2 c hydr,R = 7 N/mm c hydr,R = 14 N/mm c hydr,R = 21 N/mm c hydr,R = 28 N/mm

1

0 0

5

10 15 Static spring load [kN]

20

Fig. 2.22 Natural frequency vs. static spring load for the hydropneumatic spring with hydraulic preload. (a) Variable FV (c = 21 N/mm). (b) Variable c (FV = 5 kN)

hand, which creates the effect that, even at FF1 = 0 N, there is still a significant force on the hydraulic spring and therefore spring rate available. On the other hand it is the spring rate of the mechanical spring or of the rod side system that is still effective at zero load. An increase in this preload force FV , by increasing the preload pressure, results in a weakening of the characteristic curve of the non preloaded system. The setting pV = 0 would represent the non preloaded system. Furthermore it is obvious that the spring rate depends less on the static spring load if the preload force is increased. In terms of the natural frequency an increase of FV results in a shift of the minimum of the natural frequency curve towards higher static spring loads. At high preload forces an additional characteristic effect can be seen to some extent: The progression of the force–displacement curve of the rodside hydropneumatic spring causes a strong reduction in the spring force when getting close to the rebound end stop. This effect is even more evident, if the gas mass in the rodside accumulator is changed. This is shown in the diagrams by the influence of the spring rate of the

2.2

Spring Characteristics

47

rodside chydr,R . At high chydr,R the compression of the rodside gas volume is very high at the end of the stroke close to the rebound end stop. This results in a strong force increase of the rodside hydraulic spring. One can make use of this for suspension systems. With a suitable choice of parameters, the spring rate in the range around the design position (center position) can be very low, so that the suspension is soft in its main working range. Due to the progression, the spring becomes the stiffer, the closer the piston gets to its end stops. This helps to prevent the suspension from bottoming out. The above mentioned effect can be emphasized if the preload force is reduced and a high rodside spring rate is chosen at the same time. The result is a progression of the force–displacement curve both in compression and rebound direction. The suspension can be tuned to provide this effect by the following setup of the rodside preload parameters: AR = 500 mm2 pV = 4 MPa p0,R = 1.4 MPa V0,R = 100, 000 mm3 Figure 2.23 shows the force–displacement curve for this configuration. For comparison reasons, that diagram also shows with a thin line the curve for a linear, mechanical spring. The end stop progression effect can be used without significant negative impact on the behavior of the natural frequency over static spring load. Furthermore this is also a cost effective solution since the smaller gas volume on the rodside requires only small rodside accumulators. However this can not always be used in practice since other effects and limits need to be considered – please refer to Sect. 3.1.3 for more information. Good examples of the hydropneumatic suspension with constant hydraulic preload are the front axle suspension systems on Fendt tractors as well as on John

Suspension force [kN]

40

30

Hydropn. spring Mech. spring

20

10

0 –50

–25

0 Displacement [mm]

25

50

Fig. 2.23 Force–displacement curve with distinct progression close to the end stops

48

2

Hydropneumatic Suspension Systems

Deere tractors with the so called TLS I system (Triple Link Suspension I) which can be found on their 6010 and 7010 series tractors. Yet both manufacturers go different ways when it comes to how the hydraulic preload is applied. Fendt applies the full pump pressure of about 20 MPa on a rather small rodside active area whereas John Deere applies a lower, regulated pressure as the preload pressure to a respectively larger rodside piston area. Their hydraulic control blocks contain a pressure regulating valve which enables this. The advantage of this is that the variable displacement pump used on these tractors does not have to go to full pressure during corrective action of the control system. Another advantage is cylinder friction, further explained in Sect. 2.3.1. The disadvantage is the need for a larger volume accumulator on the rodside since more oil is displaced due to the larger rodside active area. More information on the design and layout of John Deere TLS I system can be found in Sect. 7.1.

2.2.6 Systems with Variable Hydraulic Preload This is the next logical step forward from the suspension system with constant hydraulic preload. When looking at Eq. (2.37) it is easy to discover that it is possible to vary the preload and therefore the spring rate by changing a rather easily adjustable parameter: the preload pressure pV . This possibility to influence the spring characteristics allows the control of the suspension depending on other parameters such as the static spring load or other operation parameters in an open loop or even in a closed loop. A good example of the spring load dependent preload pressure control is the John Deere front axle suspension TLS II, which comprises a two-step adjustment of the spring rate level depending on the static spring load. This is enabled by using the pressure in the piston chamber as an input parameter for the control of the preload pressure in the rod chamber. Below a certain pistonside pressure limit pK,grenz , the rodside pressure is set to a high level pR,h . If the pistonside pressure is above pK,grenz , a low level of rodside pressure pR,n is set. The higher pressure level on the rodside for low pistonside pressures causes an increased spring rate at low front axle loads. The control of the rodside pressure is achieved purely by hydraulic components – one pressure switch valve and one special, switchable pressure regulating valve. Figure 2.24 illustrates schematically the relationship of spring rate and static spring load. In reality there is interaction between rodside pressure and pistonside pressure. This interaction causes a difficult to define transition area around the pressure switch point. In this area it also depends on other operational conditions whether the rodside pressure is on a high or a low level. Therefore in the schematic, the vertical part of the spring rate vs. load curve line is only idealized and does not represent the behavior in reality. There are several reasons to justify this additional effort: (1) The positive effect of the hydraulic preload on the characteristic of the curve of natural frequency vs. static spring load is further improved (constant over a wide range).

2.2

Spring Characteristics

49

Spring rate

Fig. 2.24 Spring rate vs. static spring load for the John Deere system TLS II

Rodside pressure high Rodside pressure low

Pressure switch point

Front axle load

(2) The system accounts for the fact that low front axle loads are caused by heavy implements and loads with a center of gravity far behind the tractor. These conditions increase the inertia relative to the lateral axis of the tractor which would cause a very low pitch natural frequency and therefore result in a spongy ride behavior of the tractor with frequently bottoming out suspension. The increased spring rate for these conditions compensates for this and therefore improves the suspension quality. (3) Since diaphragm accumulators are used in this suspension system, the mentioned setup helps to keep these accumulators within the allowed pressure range of operation (refer to Sect. 2.5 for more information). In a further step, a closed loop control of the rodside pressure provides the possibility to adapt the suspension to all kinds of different operating conditions. For this purpose, a parameter needs to be chosen as an input variable, which acts as a measure for the suspension quality. Therefore, if suspension quality worsens due to a change in operating conditions (for example an uneven road surface), the degradation in suspension quality can be detected and the spring stiffness can brought to a level which helps to re-improve the ride behavior and therefore the input variable. This is the step from a purely passive suspension system (yet with level control) towards an adaptive system. In this case it is usually necessary to use electronics as a support for the hydraulic system in order to set up a closed loop control for the rodside pressure. The electronic controller can monitor multiple input variables and can adjust the hydraulic system to the best possible setting by switching hydraulic valves and allowing oil to flow in and out of the hydraulic suspension units, especially their rodside portions. This system permits the use of the whole range of possible settings and spring rates allowed by the hardware components, in particular the accumulators. This means that there is no longer only the simple spring rate vs. static spring load curve of the constantly preloaded system and the more advanced curve for the two-step pressure adjusted system. For the system with fully variable rodside pressure, there is then a large area of possible operating points in the spring rate vs. spring load diagram. Figure 2.25 compares the three last-mentioned systems. A particular advantage of the continuously variable closed loop control system is the fact that it can be easily adapted to changes in vehicle dimensions/masses etc.

50

2

Hydropneumatic Suspension Systems

Spring rate

Constant rodside pressure 2-stage rodside pressure Continuously variable rodside pressure

Front axle load

Fig. 2.25 Comparison of the spring rates of the hydraulically preloaded systems with constant, 2-stage and continuously variable rodside pressure

as well as new operating conditions. It is therefore ideal for use in different vehicle platforms since it can be used universally only with specific software and without or only minor changes in hardware. The John Deere TLS Plus suspension system makes use of this advanced technology and therewith continues the consistent enhancement in hydropneumatic suspensions.

2.3 Damping Characteristics The energy that is transferred into the suspension by external excitations needs to be dissipated to achieve a decay of the resulting oscillation amplitude and to avoid increasing amplitudes due to resonance. Therefore additional elements in the suspension system are necessary to transform the kinetic and/or potential energy of the suspension. In most cases kinetic energy is transformed into heat by application of a retarding force during the motion of the suspension elements. This retarding damping force usually is based upon the principle of friction. In general two different fundamental principles create the damping in a suspension system: (1) Boundary friction, also called dry friction or solid body friction. Two solid bodies pressed onto each other with a normal force slide in their interface with a resistant force caused for example by catching of surface roughness and adhesion. The resistant force is called friction force and acts as a damping force. (2) Fluid friction, also called viscous friction or hydrodynamic friction. A flow resistor is placed in the flow path of a fluid and causes internal fluid friction which therefore causes a pressure increase upstream of the resistor. This additional pressure is acting upon the active areas of the cylinder thus creating a retarding force, a damping force.

2.3

Damping Characteristics

51

In addition to the above mentioned principles there are more rather exotic principles which are rarely used in suspension technology. For example there is the eddy-current principle, which is often used in vehicles as a wear-free retarder to reduce vehicle speed on downhill slopes. It is based upon the principle of induction of current in an electric conductor when it is moved through a magnetic field. Furthermore there are the so called gas-spring-damper-elements [GOL84], which provide the function of a spring as well as a damper only by their internal gas fill. In general one tends to keep the damping forces as low as possible to get the best possible decoupling of the suspended mass on the isolated side from the excitation on the input side. Yet if the level of damping is tuned to provide optimal results under normal operating conditions, the damping will most surely be too low under extreme operating conditions. This will result in high amplitude oscillations and, as a consequence, bottoming out of the suspension. To avoid heavy accelerations when the suspension hits the mechanical end stops, another type of damping is integrated into many suspension systems which is only active when the suspension reaches the end of its stroke: the so called end-of-stroke damping or end cushioning. Additional damping elements dissipate the excessive kinetic energy before the suspension reaches the end stop. Therefore this energy is prevented from being transferred into the isolated side by a short term but very high force peak. The following sections explain the boundary friction, the viscous friction and the special but very important area of end-of-stroke damping.

2.3.1 Boundary Friction Damping The boundary friction is a resistive force against sliding in the interface between two solid bodies which are pressed onto each other by the normal force FN . The direction of the normal force is perpendicular to the intended sliding direction, the resistive force, respectively the friction force, is acting opposed to the sliding direction (Fig. 2.26). There will be no movement in the interface as long as the tractive force FZ does not exceed a certain limit. This limit is the static friction force Fμ,H . In the case of static friction, the absolute value of the friction force Fμ is equal to the absolute

FN

v FZ

Fµ

Fig. 2.26 Forces involved in boundary friction

–FN

52

2

Hydropneumatic Suspension Systems

value of the tractive force FZ , the body is in a static balance of forces. The maximum static friction force depends upon the normal force FN and the coefficient of static friction μH . The latter depends on the properties of the two involved solid bodies, in particular the type of material and the nature of their surfaces. Fμ,H = μH · FN

(2.43)

The static friction force plays an important role in suspension systems. It is the parameter which determines the minimum level of excitation below which a suspension system cannot absorb and reduce acceleration. Up to this level of excitation, no movement between input side and isolated side is possible (hindered by the static friction, sometimes also called “stiction”). In this case the suspension components represent a fixed coupling between both sides. The level of static friction therefore very much affects what is called the response characteristic of the suspension. This describes whether it reacts sensitively on smallest excitations and irons these out or whether these excitations are passed non-elastically to the isolated side. Static friction forces are especially caused by elastomer seals in particular after long time intervals without operation and can even lead to partial damage of the seal [MUE]. It is important to notice that static friction does not contribute to the damping of the suspension system since it is only active at times without relative motion! As soon as the tractive force exceeds the static friction force, both solid bodies start to slide on each other. During sliding the so called sliding friction force Fμ,G is active, which is sometimes significantly lower than the static friction force. Just like μH , the coefficient of sliding friction μG depends mainly on the properties of the two sliding surfaces. Furthermore there can be an additional dependence for example on sliding velocity (not considered in the following equation). Fμ,G = μG FN

(2.44)

Due to the coincidence and counteraction of motion and sliding friction force, kinetic energy is transformed into heat and therefore drawn out of the suspension system. The higher the amount of energy stored in the suspension system, the larger the amplitude of the oscillation. Due to the increased displacement, the energy drawn out of the system by friction during each oscillation increases with the stored energy. This means that a damper, which works by the principle of boundary friction, is at least partially self adapting to the needs of the system. It will be shown in Sect. 2.3.2 that fluid friction is even more capable of providing this important feature. The first dampers which were used in suspension systems were based purely on the principle of boundary friction. Examples of these are the well known leaf springs, especially the laminated type, as well as the less well known torsional friction dampers which were even adjustable in friction by varying the normal force through the variation of the load of the (laminated) disk spring. Despite that, the pure friction dampers were not able to make it into modern suspension systems

2.3

Damping Characteristics

53

since they always had the negative side-effect of worsening the systems response characteristics. In all suspension systems boundary friction can be found in the kinematics’ bearings which are mandatory in providing the necessary suspension stroke. On top of that, there is the friction of suspension cylinders in hydropneumatic systems. Their friction originates from the guiding elements as well as the sealing elements of the cylinder. The friction in the guiding elements can be kept low if the lateral forces in the cylinders are kept as low as possible. Internal lateral forces arise on one hand from external lateral forces, which can originate for example from a clamped fixation of one cylinder end and on the other hand from bending moments superimposed on the cylinder. These lateral forces in the rod guiding element FSF and in the piston guiding element FKF act as normal forces which press the guiding elements onto their friction partners and therefore cause friction forces (Fig. 2.27). It becomes obvious that the supporting distance e between the rod guiding element and the piston guiding element becomes smaller, the further the rod moves in rebound direction. Apart from a potential risk of buckling or bending the piston rod, the normal forces in rod guide and piston guide increase and the respective friction forces with them – assuming constant external lateral forces and/or constant bending moment. On the other hand the friction in the elastomeric sealing elements of a suspension cylinder is inevitable, inherent to their functional principle. The sealing elements have to seal off a hydraulic pressure and therefore need a normal force which presses the sealing edge onto the respective opposite surface. An unfavorable by-product of this normal force is boundary friction. In hydropneumatic suspension systems very high pressures need to be sealed off, accordingly high friction forces can be expected. Therefore it is extremely important to put a high emphasis on the optimal design of these sealing elements ([TRA90], [GES97], [FIS06]). Among other MB

FQ

FSF

FSF FKF

e

Fig. 2.27 Lateral forces in the guiding elements of a suspension cylinder

FKF

54

2

Hydropneumatic Suspension Systems

influences it is the right choice of the seal geometry and the seal material as well as, in the very beginning of the system layout, the right choice of suspension system pressures and cylinder geometry. In particular the seal diameters have an easily illustratable influence: the larger the seal diameter, the longer the length of the sealing edge(s) and the higher the friction forces. In this context it is interesting to look at the following design task: a hydropneumatic suspension system with hydraulic preload has to be laid out. Mandatory input parameters are the piston diameter and the hydraulic preload force. For this preload force Eq. (2.36) states that FV = pV AR . This means that the same preload force can be created by a low preload pressure and a large active area on the rodside (and therefore small piston rod diameter) or with a high preload pressure and a small active area on the rodside (and therefore a large piston rod diameter). Looking at the previous explanations in this section, it becomes obvious that it makes sense to go for a small pV and a large AR for two important reasons: the sealed off pressure and the length of the sealing edge at the rod seal are lower and both effects result in lower friction forces of the rod seals. The comparison in Sect. 2.2.5 concerning the two hydropneumatic front axle suspensions with constant hydraulic preload, one with regulated low rodside pressure and one with constantly high rodside pressure (= max. vehicle system pressure) becomes even more interesting in the light of the previous explanations. A further important factor for friction is the mechanical layout of the suspension system, i.e. the kinematics. Assuming that the mechanical system is based on a simple rocker arm, there are various possibilities in terms of where to integrate the suspension cylinder. The further the cylinder is mounted away from the pivot point, the higher is the necessary stroke of the cylinder in order to provide a certain stroke of the suspension (at the wheels). Provided that the available hydraulic system pressure is obviously constant for all cylinder positions, the piston diameter of the suspension cylinder must increase, the closer the cylinder is positioned to the pivot point of the rocker arm – assuming, of course, the same suspended axle design load for all cylinder positions (Fig. 2.28). Under the assumption that a certain friction force is created per millimeter of sealing edge (type of seal and sealing pressure constant), it is possible to find a mathematical proof, that the ratio of external cylinder force to cylinder friction force improves, the closer the cylinder is positioned to the pivot point of the rocker arm. The background to this is that the hydraulically active surface increases to the power of two with the piston diameter, while the perimeter and therefore the necessary length of the seal increases only linearly. Yet in reality it has to be taken into account that the above mentioned assumption is not always true if the diameter jump is chosen to be too wide, even if the same type series of seals is used. Furthermore it is important to consider, that the forces in the cylinder bearings as well as in the rocker arm pivot bearing also increase, if the

2.3

Damping Characteristics

55

Rocker arm pivot point

Wheel-ground contact point

Fig. 2.28 Cylinder dimensions depending of its position relative to the pivot point

suspension cylinder is positioned close to the pivot axis. This also leads to an increase in friction. In the end it is the experiment which will give exact information about the quality of the layout of a suspension system, in particular concerning friction. Therefore friction test stands for hydropneumatic components as well as for complete systems are common in the industry. Interesting insight into latest investigations on friction by the technical university RWTH Aachen can be found in [VER08].

2.3.2 Fluid Friction Damping The hydraulic fluid in a hydropneumatic suspension system is used as a medium to transfer the pressure on the active areas of the piston to the accumulator(s). Due to the suspension movement and therefore the displacement of the piston, the hydraulic fluid steadily flows between cylinder and accumulator with regularly changing flow direction. If a flow resistor is placed in the fluid flow, the kinetic energy of the hydraulic fluid is transformed into heat due to shear flows inside the fluid. The flow resistor creates a pressure loss, which causes, via the active areas of the piston, a force which counteracts the motion of the piston. This force is therefore taking energy out of the oscillation and hence is a damping force (Fig. 2.29). FD,hyd = pAK

(2.45) ·

PD,hyd = FD,hyd v = p V

(2.46)

It is typical for fluid friction that the pressure loss depends very much on the amount of volume flow through the flow resistor. This is the reason, why the fluid friction damping force depends, as opposed to the boundary friction, significantly on

56

2

Hydropneumatic Suspension Systems Δp

FD,hyd

v Flow resistor AK . Volume flow V

Fig. 2.29 Active principle of fluid friction damping

the speed of the suspension motion. This means that a fluid friction damper adapts even twice to the amount of energy stored in an oscillation: firstly by the amplitude of the oscillation and therefore indirectly secondly (for the same oscillation frequency) also by the velocity of the oscillation. Simple flow resistors can be divided into two basically different types, which show a different characteristic in the dependency of pressure loss and volume flow. (a) Throttle: The flow is decelerated by a slow transition of the flow cross-section from wide to narrow and back to wide. The cross-section of a dedicated throttle for defined additional damping usually has a circular shape and is provided by an intentionally small bore in a component in the fluid path between cylinder and accumulator. The small cross-section causes high flow velocities of the hydraulic fluid. Due to the high gradient of flow velocity from the flow center to the inner wall of the bore, high shear forces and therefore high pressure losses are generated. The latter therefore is theoretically/ideally proportional to the volume flow. Another important characteristic of the throttle therefore also is the direct dependency of pressure losses on the viscosity of the hydraulic fluid. This aspect becomes especially important since most of the common hydraulic fluids have a strongly temperature dependent viscosity (Fig. 2.30) which also makes the damping effect of a throttle temperature dependent – this is most cases very unfavorable. Another remarkable fact is the change in viscosity due to the pressure level inside the fluid. The diagram in Fig. 2.30 shows that the kinematic viscosity ν at the ISO reference temperature of 40◦ C increases by about 50% when the pressure is increased from 0 to 200 bar. This means another advantageous adaptation effect of fluid friction damping in throttles depending on operating conditions: higher loads mean higher hydraulic fluid pressures and therefore a higher fluid viscosity causing higher damping. The pressure loss across a throttle bore with laminar flow can be calculated by: ·

p = V νρKD

(2.47)

2.3

Damping Characteristics

57

Fig. 2.30 Relationship of kinematic viscosity, temperature and pressure for a typical hydraulic fluid according to [FIN06]

Let KD be a constant that is related to the geometry and dimensions of the throttle bore while ρ is the density of the hydraulic fluid. KD can be calculated for the throttle geometry below:

D D D

(2.48) Typical hydraulic components with the character of a throttle are for example tubes, hoses and hose fittings without tight bends, bores with constant diameter in control blocks or also straight pipe fittings with constant inner diameter. (b) Orifice: The fluid flow is subjected to one or more sudden transitions from a wide to a narrow or a narrow to a wide flow path. This causes strong turbulence in the hydraulic fluid which is the reason for internal fluid friction and hence a transformation of fluid flow energy into heat and therefore, in the end, damping. Ideally this type of flow resistor is characterized by a quadratic dependency of the pressure loss on volume flow. Opposed to the throttle only a minor amount of additional surface is in contact with the fluid flow in regions with

58

2

Hydropneumatic Suspension Systems

high flow velocities. Therefore this type of resistor is ideally not depending on fluid viscosity and therefore temperature. ·2

p = V KB

(2.49)

Let KB be a constant that is related to the geometry and dimension of the throttle as well as the density of the hydraulic fluid. KB can be calculated for an orifice:

B D

B

(2.50) The parameter α D is called the flow coefficient and depends mainly upon the geometry of the inlet edge and the Reynolds number. Typical hydraulic components with the character of an orifice are for example components with changes in flow direction especially with a low turning radius (for example elbow fittings or crossdrills in control blocks), furthermore components with sudden changes in cross-section for example the bore in the cylinder wall for the hydraulic connection of pistonside/rodside or often also fittings with a wide jump in sizes on their connectors. Figure 2.31 compares the behavior of the (ideal) throttle and orifice and also shows the influence of fluid viscosity. More information about the throttle and orifice flow resistors can be found in the respective literature for hydraulics basics (for example [MUR01], [FIN06] and [EBE74]) and is therefore not further explained here. In these books further details can be found about flow resistance of various line routing elements. These apply to hydropneumatic suspension systems, just like they apply to all other hydraulic systems.

Pressure loss Δp

ν4

Fig. 2.31 Pressure loss p as a function of volume flow and viscosity

ν3 ν2

Throttle (ν1 < ν2 < ν3 < ν4)

ν1

Orifice

.

Volume flow V

2.3

Damping Characteristics

59

In reality you almost never have a flow resistor of purely one type but mostly a mixture of the basic throttle and orifice resistors. Therefore it is often better to assign the attribute “throttle character” or “orifice character” to a flow resistor, depending on which character prevails. In general a damping is preferred which is not depending upon fluid temperature (viscosity). Therefore, at first sight a flow resistor with a strong orifice character seems to be the best choice. But caution is necessary here. Owing to its very nature this flow resistor dampens out oscillations with low amplitudes only very weakly and therefore causes a long reverberation time. Furthermore, especially in axle wheel suspensions, this also can cause a sensation of a “loose connection” between input side and isolated side, making the driver think that he is not fully in control of the vehicle. On the other hand the orifice reacts very strongly to heavy excitations for example when driving through a pothole. Due to the quadratic relationship of pressure drop and volume flow, the p will be very high, causing a high damping force and therefore high accelerations on the isolated side. A damping system of this type therefore often is only partly satisfactory. This is the reason why special flow resistors have been contrived which often provide a rather strong basic damping already at low piston velocities by using one of the above mentioned flow resistors combined with a pressure reducing valve to avoid extreme damping forces. The high basic damping is favorable especially in axle/wheel suspensions since this provides a good feedback from the suspension system to the driver. Furthermore the higher damping forces provide better driving safety during for example evasive maneuvers, fast lane changes or “sporty” driving in general due to the reduction of the roll motion of the vehicle body. Yet to ensure that this higher basic damping does not reach extreme values for high piston velocities, the basic flow resistor is bypassed by a special kind of pressure relief valve. It opens at high differential pressures and therefore keeps the pressure loss of the overall damping valve arrangement (and with it the damping forces) on an acceptable level from a comfort perspective (Fig. 2.32, further information can be found in Sect. 4.3.2). The start of the bypassing through the pressure relief valve can be identified as the sharp bend in the damper’s characteristic curve. It is a further advantage of this valve that the opening point of the pressure relief

Damping force FD relief valve opens

Piston velocity v

Fig. 2.32 Damping force as f(v) for an automotive shock absorber

Compression

Rebound

60

2 fA=50/min

Hydropneumatic Suspension Systems F

F

s

−0.26

0.26

v [m/s]

100 mm

Fig. 2.33 Force–displacement curve and force–velocity curve derived from it

valve is mostly independent from fluid temperature, so the limiting of the damping forces always starts in about the same range which results in a fairly constant suspension behavior at different temperatures. Please consider that only in Figs. 2.32 and 2.33, opposed to the regular definition in this book, the force and the displacement during the compression stroke are negative and during the rebound stroke are positive, since this is a frequently found definition in shock absorber technology. The force-velocity curve for a damper is typically derived from force– displacements curves recorded for an amplitude of 100 mm at different excitation frequencies fA . The excitation frequency then determines the maximum piston velocity of the damper during the crossing of the center position between both ends of the stroke. Therefore experiments of this kind provide information about the damping force as a function of piston velocity. By extracting the maximum force (rebound) and minimum force (compression) at the center position for various excitation frequencies and transferring them into a diagram of force vs. piston velocity, the characteristic curve for the damper is obtained. Figure 2.33 shows the step from the force–displacement to the force-velocity curve for an excitation frequency of 50/min. The above diagrams show that the damping forces for compression are lower than for rebound. This is at first sight an unsteady distribution of damping forces. Yet it takes into account that compression motions (for example when riding over an obstacle) often cause higher piston velocities than rebound motions. Furthermore it is obvious that the increasing spring force during compression adds to the damping forces and helps to decelerate the piston velocity, while during rebound motion, the spring forces decrease and therefore damping needs to take over more of the decelerating effect. The shown ratio for rebound damping force to compression damping force of about 2:1 provides a more effective and more comfortable reduction of the accelerations on the isolated side as would be possible by equal damping forces in compression and rebound.

2.3

Damping Characteristics

61

Due to the path of the hydraulic fluid from the active area of the cylinder all the way to the accumulator diaphragm, a certain inevitable basic fluid damping of the hydropneumatic suspension system is caused by the hydraulic lines and fittings between both ends. It basically depends upon the sizing of these components. In many suspension systems on the market the fluid friction damping is purely defined by these line elements. In this case ideally they have been tested and readjusted/selected for correct layout in specific tests. However some systems show indications that this has not been or insufficiently carried out. Especially systems with long distances between suspension cylinder and accumulator show only partly the potential effect which would be achievable with shorter and/or larger diameter lines. This is why it is necessary to ensure from the very start of a design of a suspension system that suspension cylinder and accumulator are positioned close to each other. The lower the basic damping, the better the possibilities for influencing the damping characteristic of a system by targeted integration of additional damping elements. This possibility to integrate specific damping components can be used to further adapt the damping, depending on the spring rate. This is a major advantage in particular in hydropneumatic suspension systems with their wide range of spring rates depending on spring load and preload. If the operating conditions are changed, for example by a change in static spring load, it is good to adjust the spring rate in order to get (back) to the desired natural frequency, but it is better to adjust the damping characteristics on top of that, so the dissipation of oscillation energy is also adapted to the new demands. Such load adaptive damping systems are already available for example for trucks with air suspended axles. The damping elements are adjusted by the average pressure in the air bags and therefore adapted to the static spring load (ZF Sachs PDC – Pneumatic Damping Control [MUR98], [CAU01]). For a hydropneumatic suspension this could be done for example by an adjustable flow resistor which is either operated hydraulically directly by the pressure on the pistonside or operated electrically by an electronic controller which reads the pistonside pressure by a pressure sensor. The electrical adjustment offers the possibility to include further information in the algorithm for the right selection of the necessary damping forces. Significant, meaningful parameters are for example the temperature of the hydraulic fluid (and therefore viscosity), certain operating conditions or driver settings. A sufficiently fast adjustable system can even provide a semi-active damping, for example via the Skyhook-algorithm, or an end-of-stroke damping (see Sect. 2.3.3). The adjustment of the flow resistor does not necessarily have to be continuous, like for example in the ZF Sachs CDC system (Continuous Damping Control, [REI05], [EUL03], [CAU01]). An adjustable damper with a stepped characteristic might also provide good results, for example like the Bilstein ADS (Adaptive Damping System) which allows for an individual two step adjustment for both compression and rebound damping [SCM00].

62

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Hydropneumatic Suspension Systems

2.3.3 End-of-Stroke Damping “A passive suspension system, which never gets close to its end stops during all operating conditions, is probably not tuned to be soft enough or wastes suspension travel.”

This kind of provocative sentence contains important information. Every suspension system only has a limited stroke available to isolate the excitations coming from the input side. Basically the softer a suspension system is tuned (keeping the correct relation of spring rate and damping in mind), the more it will reduce accelerations on the isolated side, yet the longer will be the displacement between input side and isolated side for certain excitations. If these excitations exceed a certain limit, the necessary displacement becomes greater than the available suspension stroke and therefore the suspension bottoms out. This causes short term high forces and accelerations which reduce subjective comfort and furthermore can overload components of the suspension system as well as components on the input side or isolated side. One way to avoid this problem would be to tune spring and damper to a harder level, so that even under the worst conditions and most extreme excitations the available suspension stroke is always sufficient. Yet, in doing so, the result is a reduced comfort level in all other operating conditions. Therefore it is important to also consider the expected frequency and amplitude distribution of the various excitations to find an optimum level for spring rate and damping. When taking this into account it becomes obvious that it can be quite acceptable to have the suspension bottoming out slightly sometimes, if in the same turn the overall comfort level in all other operating conditions is improved by a softer setting. A suspension system can be even tuned to be softer than that if an additional end-of-stroke damping is used and the (rare) cases of bottoming out are softened by an additional damper or an additional spring. All in all this results in a remarkable gain in comfort. To reduce the harshness of a bottoming out event at the end of the stroke it is necessary to reduce the velocity of the piston relative to the cylinder. So if the piston gets close to the end positions (for example the last 10% of the stroke in each direction) an additional decelerating force (damping or spring) needs to be activated. Most suitably this additional force creates a constant or slightly progressive gradient of velocity over displacement, meaning the deceleration is constant or increases slightly as the piston gets closer to the cylinder bottom. Ideally the end-of-stroke damping system recognizes the excessive kinetic energy which needs to be dissipated until the end of the stroke and then adapts its properties in a way such that a constant and lowest possible force level decelerates the piston until shortly before the end stop. Many suspension systems use elastomer elements for end-of-stroke damping. Just before hitting the end stops, the suspension motion is decelerated by an additional elastomer spring with a minor amount of damping. So strictly speaking this is more of an end-of-stroke spring than an end-of-stroke damping. The spring force and therefore also the deceleration of the piston velocity increases from the first contact to the elastomer up to the mechanical end stop. The characteristic curve of

2.3

Damping Characteristics

63

deceleration force vs. displacement is at least a linear increase but in most cases even a disproportionately higher increase, and can be shaped for example by the outer contour of the elastomer element, by internal bores or even by collars supporting the circumference of the elastomer. This layout allows soft cushioning of minor impacts with small spring forces and, on the other hand, taking even the most extreme bumps without the bottoming out of steel parts. In passenger cars this type of end-of-stroke damping is then clearly noticeable for passengers, yet it fulfills the requirement to protect the components from overload. During the rebound motion out of the end stop, the elastomer extends back to its original shape and reintroduces most of the absorbed energy back in to the suspension system. Due to a slight damping effect, a minor amount of energy remains as heat inside the elastomer, this behavior is characterized by the loss angle of the elastomeric material. A major disadvantage of the elastomer elements is the fact that the material is subjected to strong aging and settlement depending on the extent of use and the stresses induced therewith as well as the environmental conditions (UV-radiation, ozone, chemicals, etc.). This makes an exchange of the elements necessary in some applications. In order to prevent overloading of the elastomer elements, in some cases an additional mechanical end stop is designed into the system which limits the stroke and therefore reduces the maximum deformation of the elastomer to a level which is acceptable for the material in long term. In hydropneumatic suspension systems another type of end-of-stroke damping is popular since it can be designed into the suspension cylinder. Theoretically a use of elastomer elements is possible here as well, but mostly it is the hydraulic end-ofstroke damping that is used for these cylinders. Opposed to the elastomer elements, here it is not an additional spring force with minor damping but purely an additional damping force that decelerates the piston velocity. The effect of the hydraulic end-of-stroke damping is achieved by reducing the cross-section of the oil path out of the cylinder when the piston reaches a freely selectable distance to the end stop. So during a compression stroke the pistonside chamber is active while during a rebound stroke the rodside chamber is active for end-of-stroke damping. A pressure drop across the flow resistor is generated which then causes a pressure increase inside the respective cylinder chamber. The active area of the respective cylinder chamber is subjected to this additional pressure and therefore causes the damping force. If the cross-section area of the additional flow resistor is designed to be variable with cylinder stroke, a possibility is created to define the effect of the flow resistor depending on piston position. This way a more constant end-of-stroke damping force level and a lower maximum force can be achieved compared to a flow resistor with constant cross-section area. The lower force peak also reduces the maximum accelerations due to end-of-stroke damping Eq. (2.34). Please consider: It is always the same amount of energy that has to be dissipated throughout the displacement of the end-of-stroke damping. Therefore the damping force – displacement integral of both curves must be identical. More information about a suitable layout of the end-of-stroke flow resistor can be found in Sect. 3.2.4.

64

2

Hydropneumatic Suspension Systems

Force

Constant flow resistor Displacement-depending flow resistor

Start of end-ofstroke damping

Mechanical end stop

Displacement

Fig. 2.34 Damping force–displacement curve for end-of-stroke damping with a constant and a displacement-depending flow resistor

2.4 Combined Operation of Spring and Damper In Sects. 2.1, 2.2, and 2.3 the individual force components of a hydropneumatic suspension system have been described. In this section they are combined and considered as a whole system. The basis for the following explanations is a sinusoidal excitation of the input side while the isolated side is fixed. Therefore the suspension element’s displacement is a sinusoidal oscillation. These conditions are chosen similar to the method for the determination of characteristic curves for regular automotive shock absorbers, described at the end of Sect. 2.3.2 (Fig. 2.33). However the main focus will be on the force–displacement curve. The force–displacement curve can be synthesized from the individual theoretical curves for the gas spring, for boundary friction and for fluid friction – and furthermore, if applicable, the curve for end-of-stroke damping. The here mentioned example is a hydropneumatic suspension system without preload which is subjected to boundary friction and which has a simple throttle to provide fluid friction damping. The theoretical considerations of Sects. 2.1, 2.2, and 2.3 result in the individual curves shown in the Fig. 2.35. The effect of the gas spring is idealized and therefore the same for compression and rebound which make the characteristic curve only one line. In reality this is almost true; the dissipation of spring energy due to heat rejection of the accumulators is very small so virtually no hysteresis can be detected in this curve (a). On the other hand the characteristic curves (b) and (c) show a significant hysteresis. The curve for boundary friction is exaggerated for better illustration; these friction forces should be lower in practice. In the end points (left and right) at v = 0 m/s there is a transition from sliding friction to static friction to sliding friction, this explains the slight force peaks there due to the higher coefficient of sliding friction. Furthermore it is visible, that the friction forces are higher, the more the suspension is compressed. This is due to the dependency of seal friction forces on hydraulic pressure. The viscous damping forces reach their extreme values when

2.4

Combined Operation of Spring and Damper

65

FF Compression

a) Gas spring

FF1

Rebound

s

b) Boundary friction

Fµ Compression s Rebound

c) Fluid friction

FD

Compression

s Rebound

Fig. 2.35 Force–displacement curves for gas spring, boundary friction and fluid friction

the center position is crossed. Minimum and maximum have the same absolute values which indicates that the flow resistor has the same effect in both flow directions. By adding up the individual characteristic curves to one curve, the following characteristic force–displacement diagram for the hydropneumatic suspension is composed (Fig. 2.36). FF

Compression

FF1 Rebound

s

Fig. 2.36 Characteristic force–displacement diagram for hydropneumatic suspensions

66

2

Hydropneumatic Suspension Systems

This type of diagram will be found in a more or less similar shape in every experiment with a hydropneumatic suspension system when recording the force– displacement history. Such measurements provide information about the detailed character of the individual contributions spring rate, boundary friction and fluid friction. This information can be derived from the main curve by splitting it up into its individual components as shown above. Even more information can be derived when the measurements are taken at different amplitudes, static spring loads, oil viscosities (or temperatures) or with different excitation frequencies. Then conclusions can be drawn such as: (a) which adiabatic exponent has to be chosen for a calculation under the respective conditions (derived from the shape of the pure characteristic curve of the spring and matching it with the calculation); (b) whether the fluid friction damping is more like an orifice or more like a throttle (derived from relationship of damping forces to viscosity and dependency of damping forces on oscillation amplitude and frequency); (c) the magnitude of static and sliding friction and the influence of cylinder pressures on friction (derived from comparisons of measurements at different amplitudes and static spring forces). Figure 2.37 shows an actual measured force–displacement diagram of a hydropneumatic suspension. It is possible that the actual magnitude of the static friction forces has not been completely recorded due to an insufficient sample rate. However for the detailed measurement of friction forces dedicated experiments with very low frequencies (for example 0.01 Hz or 0.1 Hz) are recommended. This fully eliminates the influence of fluid friction. Simulation results like in [HYV01] show the same shape of their force–displacement curves as shown in Fig. 2.37.

Suspension force [%]

70 60

50 40 30 –30

–15

0

15

Suspension displacement [%] Fig. 2.37 Force–displacement diagram taken from actual measurements

30

Chapter 3

Dimensioning of the Hydropneumatic Suspension Hardware

At the beginning of this chapter it is important to mention that there will be no deduction of the optimum properties of the suspension system, what spring rate and which damping should be set for best performance – these topics are covered extensively in the literature for conventional suspension systems (for example [REI89], [REI05], [CAU01], [KOC]). Instead it is explained, how already known necessary system properties, such as the spring rate, can be provided by the correct layout and dimensioning of the components of a hydropneumatic suspension system.

3.1 Dimensioning of the Hydraulic Spring Components The very basis of the dimensioning process is to determine the hydraulic pressure in the suspension system. Depending on the pressure level, the elements need to have the correct dimensions to provide the right amount of active area (rodside and pistonside) and to provide enough mechanical stability to withstand inner pressure loads. A lot of factors influence this hydraulic pressure which is to some extent necessary and can to some extent be chosen appropriately. Certain factors are predefined due to external circumstances, others can be chosen freely. Figure 3.1 shows an overview of possible influencing factors which determine the static hydraulic pressure on the pistonside when the suspension is in design position. The parameters which are usually predefined by external circumstances are listed on the left side of the diagram: – Since the suspension is designed for a certain purpose/application, this automatically predetermines the necessary range for the static spring load that needs to be supported by the suspension. – The geometry of the suspension, in particular the position of the suspension cylinder as part of the suspension, is often predetermined by its packaging inside the installation space. This also predetermines the lever ratio i of the suspension kinematics.

W. Bauer, Hydropneumatic Suspension Systems, DOI 10.1007/978-3-642-15147-7_3,  C Springer-Verlag Berlin Heidelberg 2011

67

68

3 Dimensioning of the Hydropneumatic Suspension Hardware Mostly predefined:

Mostly selectable:

Load range FF1,min … FF1,max Suspension geometry/ lever ratio Max. available supply pressure

Piston diameter

Pistonside pressure

If preload: type and intensity Pressure rating of hydraulic components

Fig. 3.1 Influencing factors for the static pistonside pressure in design position

– In many cases a hydraulic supply already exists, for example in construction equipment. If it is necessary to use this supply also for the suspension hydraulics (and this is usually the case) this already defines the maximum available supply pressure. On the right hand side of the diagram, various parameters are listed which in most cases can be chosen by the system developer: – Within the given design space the piston diameter can be chosen according to the (especially load-) requirements of the system. – The type and the intensity of the preload affect especially the changes of the suspension properties when changing the static spring load. Since the preload adds to the external spring load, the piston diameter needs to be chosen to be larger, the higher the preload is – of course assuming a given, constant supply pressure. – The standard portfolio of hydraulic components is usually available in certain pressure ratings for different ranges of operating pressure. There are significant cost differences between these rating levels. If a certain pressure rating is preferred for the suspension system (for example, because this is used for all other parts of the overall system), the piston diameter can be adjusted to exploit the full pressure potential out of these components and therefore get the highest possible power density and best cost-benefit ratio. For the correct dimension of the components it is essential to consider that dynamic pressure variations (due to the suspension motion) add to the pressure in static state of the suspension (in design position). Depending on the amount of oil that is exchanged between cylinder and accumulator, and depending on the kind of operation of the accumulator (gas volume at static pressure), these additional dynamic pressure spikes are quite distinct. Therefore the suspension hydraulic system needs to be protected from them, for example by a pressure relief valve.

3.1

Dimensioning of the Hydraulic Spring Components

69

This means that the dynamic portion of the pistonside pressure mostly depends upon the suspension motion and the size and the amount of gas in the pistonside accumulator. Increasing suspension motion leads to increasing pressure variations. On the other hand, an increasing amount of gas lowers the pressure variations. The same is of course the case for the pressure in the rodside hydraulic circuit.

3.1.1 Cylinder Usually the dimensioning of the components starts with the piston diameter of the suspension cylinder, especially if a hydraulic system is already available and predetermines further development steps – and this is actually true in most cases. The piston diameter is determined by trying to make the maximum use of the available system pressure. For non preloaded systems with double-acting cylinders the rod diameter is determined instead. The following information is needed to start with the calculations: – Available maximum supply pressure psys – Maximum static spring load FF1,max , which still allows the system to readjust the level to the design position – Preload force FV which acts upon the cylinder in design position (in variable systems: maximum preload force) The basis for the calculation of the necessary piston diameter is once again the balance of forces acting upon the piston: FK = FF1,max + FV

(3.1)

Expressing FK via the active pistonside area and the system pressure acting upon it π dK2 psys = FF1,max + FV 4

(3.2)

and solving the equation for dK yields   4 FF1,max + FV dK = π psys

(3.3)

If the actually necessary preload force FV is unknown in the beginning of the dimensioning calculations, this value can be assumed to be something between one third and one quarter of the maximum static spring load. This experience-based value can be used as a basis for hydropneumatic suspension systems with diaphragm accumulators. However it can happen that in the end a significant deviation from this value is necessary to achieve the desired suspension properties.

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3 Dimensioning of the Hydropneumatic Suspension Hardware

For FV = 0.25 · FF1,max the piston diameter can be calculated as dK =

5FF1,max π psys

(3.4)

Please note: 1) During a leveling process the system has to get back to the design position within a limited amount of time. Therefore the parameter psys in Eq. (3.4) should not be set to the maximum system pressure, but to a pressure somewhat below this value. This is due to the fact that the pressure of the hydraulic fluid which actually reaches the cylinder is lower compared to what has been send out by the hydraulic system. The reason for this is pressure losses on the way from the pump to the cylinder. An intended and for a controlled leveling process inevitable pressure loss is created by the valve system inside the leveling control block. It is necessary to limit the volume flow to the cylinder and therefore the speed of the leveling process. The amount of additional pressure margin needs to be chosen depending on the type of the flow restriction such as throttle/orifice, flow control valve, proportional solenoid valve (please also refer to Chap. 5) and depending on drains of other volume flows (for example, for the transmission of a loadsense signal). For a system with orifices used to control the leveling flow a difference of 1 MPa has proven to be sufficient. This means that for a system with a maximum pump pressure of 20 MPa it is necessary to set psys to 19 MPa in Eq. (3.4). 2) The lever ratio i of the suspension kinematics is chosen to be 1 for the following examples to enable a clearer comparability. This means that the cylinder is in line with the sprung mass. Yet in many real applications this is often not the case and the i = 1 must be taken into account in the calculations respectively. Section 7.1 shows an example how to do that. In case a hydropneumatic suspension system with hydraulic preload is dimensioned, the next step is to choose the rod diameter. The first thing is to determine which hydraulic preload force should be created by the rodside hydraulic system. The higher the preload pressure on the rodside, the lower is the necessary active ring-shaped area on the rodside in order to generate a given preload force and therefore the larger is the rod diameter. A small active area on the rodside means on one hand that less oil is displaced during the suspension motion and therefore a smaller rodside accumulator can be chosen. On the other hand this smaller accumulator must be designed for higher operating pressures and also the friction increases according to the mechanism described in Sect. 2.3.1. In the end the decision on the right size of the rod will depend on multiple boundary conditions. The general approach is: FV = pV (dK2 − dS2 )

π 4

(3.5)

3.1

Dimensioning of the Hydraulic Spring Components

71

And therefore: dS =

dK2 −

4FV π pV

(3.6)

If the lever ratio i is different from 1, the stroke of the cylinder needs to be calculated as well from the required overall suspension stroke at the suspension reference point sB (basically the point of action of the suspended mass). The necessary stroke h of the cylinder can be calculated by h = sB i

(3.7)

Piston diameter, rod diameter and cylinder stroke are the defining parameters for a cylinder. Now it is possible to start the selection of suitable accumulators by taking into account the pressure levels on both the pistonside and the rodside. The process of dimensioning the accumulators is divided into two steps. The first step is to calculate the necessary gas fills in the accumulators by using the equations in Sect. 2.2. The second step is to find the ideal combination of p0 and V0 which works best under the given operating conditions. This will be described in the next section.

3.1.2 Accumulator Gas Precharge The equations in Chap. 2 for the calculation of the natural frequencies of the different hydropneumatic suspension systems help to calculate the necessary gas fills p0 V0 . 3.1.2.1 Non preloaded Systems and Systems with Mechanical Preload The calculation of the accumulator parameters for the non preloaded hydropneumatic suspension as well as for its alternative with mechanical preload is relatively simple since only one gas mass needs to be calculated, i.e. the gas fill of the pistonside. For the non preloaded system, Eq. (2.27) is solved for p0 V0 :  p0 V0 =

1 2π f

2 nFF1 g

(3.8)

The respective result is achieved for the system with mechanical preload by solving Eq. (2.31): p0 V0 =

n(FF1 + FV )2 FF1 (2π f )2 g

− cmech

(3.9)

The respective gas fill can be obtained by inserting the desired natural frequency for a certain static spring load FF1 into the above equations. If, like in most cases,

72

3 Dimensioning of the Hydropneumatic Suspension Hardware

the spring load varies, a typical spring load (which, for example, is effective most of the time) should be used when calculating the necessary gas fill. Another method is the determination of an average spring load from a minimum and maximum spring load and then using this average to calculate the gas fill. In the case of a system with mechanical preload, the preload force and the spring rate of the mechanical spring have to be chosen in a way so the shape of the characteristic curves corresponds to the requirements of the application. Please refer to Chap. 2 for the force vs. displacement diagram, spring rate vs. spring load diagram and natural frequency vs. spring load diagram. For this purpose it is useful to create the diagrams and to watch how their shape changes as the preload force and the spring rate of the mechanical spring are changed. A kind of iterative approach towards the right setting needs to be accepted since a certain p0 V0 has to be assumed when creating the initial diagrams. 3.1.2.2 Systems with Hydraulic Preload The tricky thing about the following calculations is that two gas fills have to be determined at once, the gas mass for the piston side and the gas mass for the rodside. Yet there is only one equation available for their determination – Eq. (2.38). This means, that first one gas fill needs to be determined by another way before calculating the other one. Furthermore, like for the system with mechanical preload, a suitable setting for the rodside parameters needs to be found – rodside hydraulic spring rate and preload – which fits best to the requirements of the characteristic curves. The suspension effect is mostly dominated by the effect of the pistonside hydraulic spring; it is the latter which carries the suspended mass. Therefore the first step is to roughly determine the gas fill for the rodside, since it has less effect onto the overall spring rate. In a second step the gas fill for the pistonside is calculated. The volume of the rodside accumulator must be sufficient to accommodate all the oil which is displaced from the rodside of the suspension cylinder(s). If this was not the case, it would not be possible to reach the ends of the stroke without either destroying the accumulator (cylinder fully extended and therefore rodside completely empty) or running into cavitation (cylinder fully compressed, rodside filled with maximum amount of hydraulic fluid, accumulator empty). The volume of the accumulator therefore must at least be equal to the maximum rod chamber volume in the fully compressed cylinder, assuming of course that the accumulator is half filled when the cylinder is at the center of its stroke. Of course this is not sufficient at all; there is at least some margin necessary, especially in case diaphragm accumulators are used as shown later on. It has been proven to be a good basis for development if the volume of the rodside accumulator V0,R is predefined to be three times the rod chamber volume of the suspension cylinder(s). This has to be eventually increased for systems with variable rodside preload pressure. π  V0,R = 3h dK2 − dS2 4

(3.10)

3.1

Dimensioning of the Hydraulic Spring Components

73

The calculation of the rodside accumulator precharge pressure is based upon the assumption that the gas volume inside the accumulator is compressed to half of its original volume when the preload pressure pV is applied to the rodside system – under the assumption that the design position of the piston is exactly in the center of both end stops. This ensures that there is enough and equal margin of oil for the piston motion to both sides of the cylinder. In case the piston design position is chosen off center, the position of the rodside accumulator diaphragm when subjected to preload pressure has to be chosen accordingly. With a center design position, the accumulator precharge pressure p0,R should therefore be about half of the preload pressure pV . p0,R = 0.5pV

(3.11)

Since the parameters for the rodside accumulator are now determined, Eq. (2.38) can be solved for the pistonside gas mass p0,K V0,K =

n(FF1 + pV AR )2 FF1 2 g (2π f )

−

np2V A2R p0,R V0,R

·

(3.12)

Since p0,R and V0,R have not been chosen with regards to spring rate but for another goal, it is now necessary, just like before for the system with mechanical preload, to check with the help of the characteristic curves, whether this set of accumulator parameters provides the desired suspension properties. If this is not the case, here too an iterative approach needs to be used to determine the parameters p0,R and V0,R which provide the desired shape of the characteristic curves and therefore the desired suspension behavior. It can happen that for further optimization, also p0,K und V0,K have to be changed.

3.1.3 Detailed Calculation of p0 and V0 The accumulator gas fill is represented by the product p0 V0 which has been calculated in Sect. 3.1.2. It basically represents the mass of the gas or in other words the number of gas molecules inside the accumulator. The next step is to find suitable values for the most important accumulator parameters: p0 and V0 . For the following calculations in this section, it is predefined that the suspension level is exactly in the center between compression and rebound end stop. For hydropneumatic suspension systems usually welded diaphragm accumulators are used – you can find more information in Chap. 5. Yet it is a characteristic of this type of accumulator that it may only be operated in a certain pressure range. This pressure range is defined by two basic criteria: 1. Maximum pressure criterion: the design, in particular the material and the dimensioning of the outer shell, defines the permissible maximum pressure

74

3 Dimensioning of the Hydropneumatic Suspension Hardware

for an accumulator. It must not be exceeded in any operating condition if the accumulator has to be fatigue resistant throughout the lifetime of the suspension. 2. Diaphragm deformation criterion: the diaphragm has a permissible maximum deformation for its deflection inside the accumulator. This deformation must not be exceeded during the oscillation of the diaphragm position throughout the entire operating time of the suspension system. A simple guideline for the use of diaphragm accumulators in hydropneumatic suspensions is the 10% rule. It states that at any time during operation, the inner accumulator volume should be filled with either at least 10% hydraulic fluid or with 10% gas to ensure that the maximum deformation is not exceeded (Fig. 3.2). This rule therefore sets another upper pressure limit as well as a lower pressure limit. These limits need to be accepted to ensure fatigue resistance of the diaphragm throughout the lifetime of the suspension. The 10% rule for the application in suspension systems is actually somewhat more permissive than is usual in other applications ([MAT03], [FIN06]). This is due to the fact that the amplitude of the suspension oscillation is usually significantly lower than the full suspension stroke, which means that these extreme values are usually rarely reached. In any case it is important to discuss with the manufacturer of the accumulator whether the accumulator and in particular its diaphragm material is designed for the needs of the application. It is possible that certain materials and special suspension setups ask for other deformation limits than stated with the 10% rule. It can be deduced from the diaphragm deformation criterion that the pressure limits arising from it also depend on the precharge pressure of the accumulator. In the following, isothermal changes of state are used for the calculations since this represents the more critical condition concerning the inner volume portion of oil and gas and their minimum values. An accumulator with a precharge pressure p0 and a volume V0 must be operated (according to the diaphragm deformation criterion) between V = 0.1 · V0 and V = 0.9 · V0 . For the isothermal change of state, the minimum and maximum pressure can be calculated: pmin =

p0 V0 = 1.11p0 0.9V0

(3.13)

10% gas

90% gas 90% oil 10% oil

Fig. 3.2 Limits for diaphragm deformation for the application in a suspension system

3.1

Dimensioning of the Hydraulic Spring Components

pmax =

p0 V0 = 10p0 0.1V0

75

(3.14)

The permissible pressure ratio pmax /pmin is therefore 9. Yet this calculated ratio applies only if all changes of state take place at room temperature. If the suspension system and therefore the hydraulic fluid and the gas are (as usual) subjected to a wide range of temperatures it is essential to consider that the specified precharge pressure relates to room temperature. Yet at other temperature levels, the actual temperature-dependent precharge pressure p0,T will be different and with it changes the permissible pressure range according to the second criterion. High temperatures therefore increase the minimum pressure and low temperatures decrease the maximum pressure. For a temperature range from −20 to +60◦ C the pressure range is narrowed according to Eq. (2.3) in Sect. 3.1.2: 333.15 K = 1.26p0 293.15 K 253.15 K = 10p0 = 8.64p0 293.15 K

pmin = 1.11p0 pmax

(3.15) (3.16)

This looks like a minor change but actually the permissible pressure ratio has been reduced from 9 to the value of 6.85, which means significant functional losses for the use of the suspension system. In practice it is therefore extremely important to assess the temperature range as realistically as possible, also asking the question if in these cases of very high or low temperatures the full suspension displacement will be used up and therefore the diaphragm will be fully deflected. If the calculation is too conservative, there will be losses in performance of the system which need to be compensated by (expensive) countervailing measures – if at all possible. If the calculation is too generous, this will be penalized by a premature failure of the accumulator diaphragm, gas pressure losses and a deterioration of the suspension behavior. There is another parameter influencing the pressure ratio: the production process always contains small errors, also with regards to the gas precharge pressure. Therefore the precharge pressure will not always have the exact value but will have a slight production tolerance. For later calculations a tolerance of ±5% is assumed and the pressure limits will be even more constricted. A positive deviation of the precharge pressure will increase the minimum pressure; a negative deviation decreases the maximum pressure. pmin = 1.26 p0 × 1.05 = 1.32 p0

(3.17)

pmax = 8.64 p0 × 0.95 = 8.21 p0

(3.18)

This additionally lowers the pressure ratio to 6.2. Another peculiarity of diaphragm accumulators must be considered for the correct choice of parameters. The gas diffuses through the diaphragm into the hydraulic

76

3 Dimensioning of the Hydropneumatic Suspension Hardware

fluid and therefore is partially lost – and the suspension characteristics with it. So the accumulator is subjected to a diffusion pressure loss (Chap. 5). Although this is not a problem for the minimum pressure, it has to be considered when calculating the maximum pressure. Assuming a permissible pressure loss of 10% of the precharge pressure between service (and refill) intervals, the maximum pressure is reduced to: pmax = 8.21 p0 × 0.9 = 7.39 p0

(3.19)

The permissible pressure ratio then is 5.6. So the formerly good pressure ratio of 9 has shrunk to a value of 5.6. As a by-product the previous calculation shows why a non-preloaded hydropneumatic suspension with diaphragm accumulators is not suitable for suspension systems subjected to wide ranges of static spring loads: the accumulators would frequently be operated at or beyond their pressure limits. It is very important to mention in this context that the permissible pressure ratio of the accumulator is not the same as the permissible load ratio FF1,max to FF1,min ! The latter is even smaller since not only the variable suspended load but also the suspension movement causes pressure variations – more information can be found in Sect. 3.1.3.1. There is one further point to notice: the determination of the parameters p0 and V0 is easier to perform for a piston accumulator since the piston may be displaced throughout its complete possible stroke. There is no 10% rule like there is for the diaphragm accumulator. Therefore the minimum operating pressure of a piston accumulator would be the precharge pressure corrected by the respective temperature change and the production tolerance for the precharge. If the actual operating pressure would fall below this minimum value, cavitation in the respective part of the system would result. On the other hand, the maximum operating pressure is the maximum pressure permitted by the design of the outer shell. This pressure needs to be protected by a pressure relief valve – just like for the diaphragm accumulator. Despite these advantages, piston accumulators are rather rarely used in suspension applications due to their higher cost and their inner friction. The further explanations for a hydropneumatic suspension system with hydraulic preload therefore only deal with diaphragm accumulators as in all previous examples.

3.1.3.1 Rodside Accumulator The selection of the right parameters for the rodside accumulator is relatively simple, if it is done for a system which is always subjected to a constant rodside preload pressure. According to the diaphragm deformation criterion, the diaphragm should be in middle position if the suspension respectively the piston of the cylinder is in its center position. This ensures maximum possible margin to both sides for the deformation of the diaphragm. Middle position of the diaphragm means: V = 0.5V0

(3.20)

3.1

Dimensioning of the Hydraulic Spring Components

77

Therefore the optimum rodside accumulator precharge pressure p0 depends on the selected rodside preload pressure pV : p0 =

pV 0.5V0 = 0.5pV V0

(3.21)

If the desired gas mass for best suspension performance is already calculated (as deduced in Sect. 3.1.2), the optimal V0 for the rodside accumulator can be calculated accordingly. However in reality, accumulator manufacturers only have certain accumulator sizes in their portfolio. Although there are tricks which help to vary the V0 within the accumulator size (for example, by a partial oil fill or a solid insert on the gas side) it becomes necessary to accept a compromise for the parameters p0 and V0 . This compromise can also influence the selection of the rodside preload pressure and therefore the necessary size of the rodside active area. The next step is to check whether the filling with or the draining of hydraulic fluid during a suspension motion with full stroke leads to the deformation limits of the diaphragm being exceeded. Again the diaphragm deformation criterion is applied: 1. When the suspension cylinder is in compression stroke and the rodside system hydraulic fluid flows out of the accumulator into the cylinder’s rod chamber the volume filled by the gas inside the accumulator increases and must not exceed a portion of 90% of the total volume. The worst case for the accumulator is the maximum operating temperature, a gas fill at the upper tolerance limit during the production process and no diffusion pressure loss. All these conditions contribute to a maximum precharge pressure p0,T,korr and therefore to a diaphragm which is already bent somewhat towards the oil side of the accumulator when subjected to the regular preload pressure. Therefore the “90% gas volume” limit is reached earlier than under the normal conditions. V0 ·

h p0,T,korr + AR ≤ 0.9V0 pV 2

(3.22)

2. During the rebound motion of the cylinder and therefore when hydraulic fluid is flowing into the accumulator, the gas volume must not drop below 10% of the accumulator volume. In this case, the worst boundary conditions are the minimum operating temperature, the lower limit of the production tolerance for the precharge pressure and maximum pressure loss due to diffusion up to the limit when servicing is necessary. Again these aforementioned conditions are then accounted for in the pressure p0,T,korr , which is now down at its minimum level. V0

p0,T,korr h − AR ≥ 0.1V0 pV 2

(3.23)

At this point it is important to keep in mind that the hydraulic fluid volume AR h/2 flowing in and out of the accumulator is independent of the position of the cylinder in the kinematics of the mechanical suspension setup. Just like for the non-preloaded system, the stroke of the cylinder is changed due to the lever ratio i, but the amount

78

3 Dimensioning of the Hydropneumatic Suspension Hardware

of the displaced hydraulic fluid volume does not change since also the rodside active area changes/needs to be changed with i – assuming of course that the preload force in the suspension reference plane is the same for all configurations. Usually the above mentioned limits can be easily met for systems with constant rodside preload pressure. Yet for systems with variable rodside preload pressure another approach for the selection of p0 and V0 is necessary. Here not only does the position of the diaphragm vary with the position of the piston (and therefore the displaced hydraulic fluid) but it also varies with the selected rodside preload pressure. Like already explained for the above mentioned temperature and precharge pressure tolerance effects, this too leads to an offset of the diaphragm position towards one end of the accumulator interior (fluid side or gas side). If these offset positions are too close to the 10% limits for diaphragm deformation the suspension motion can lead to unacceptable high diaphragm deflection. In general it would be possible, according to the logic in Eq. (3.21), to assume the average of the intended minimum and maximum rodside preload pressure, to calculate a first combination of p0 and V0 . However this is quite imprecise since pressure and volume do not have a linear relationship and in the end it is the right average volume what counts for the correct layout of the system. Therefore the first step is to calculate the gas volumes at p = pV,min and p = pV,max . V(pV,min ) = V0 V(pV,max ) = V0

p0 pV,min p0 pV,max

(3.24) (3.25)

The average value of these volumes must then be equated with 0.5 · V0 , since at this point the diaphragm needs to be in its center position. p0 p0 + V0 pV,max V0 pV,min

2

=

V0 2

(3.26)

and by resolving for p0 p0 =

1 1 pV,min

+

1 pV,max

(3.27)

the optimum accumulator precharge pressure can be calculated: p0 =

pV,min pV,max pV,min + pV,max

(3.28)

The already calculated necessary gas fill allows the necessary V0 to be calculated. Again it is consequently necessary to check this set of parameters to see whether it fulfills the diaphragm deformation criterion. The Eqs. (3.22) and (3.23) need to be slightly modified by taking the lower and upper limit pV,min and pV,max of the rodside preload pressure into account.

3.1

Dimensioning of the Hydraulic Spring Components

V0 · V0

79

h p0,T,korr + AR ≤ 0.9V0 pV,min 2

(3.29)

p0,T,korr h − AR ≥ 0.1V0 pV,max 2

(3.30)

By resolving the equations above for pV,min and pV,max it is possible to calculate the actually permissible range of rodside preload pressure variation for this particular chosen combination of p0 and V0 . pV,min = pV, max =

V0 p0,T,korr

(max. T, upper gas fill tolerance, no diffusion) (3.31)

0.9V0 − AR h2 V0 p0,T,korr 0.1V0 + AR h2

(min. T, lower gas fill tolerance, max. diffusion) (3.32)

If this calculation shows that the permissible range for the variation of pV does not extend far enough to the lower preload pressures, a slight increase of V0 (and respective decrease of p0 ) can help. If this turns out to be insufficient, an overall increase of the gas fill needs to be taken into consideration, even though the rodside hydraulic spring rate would be lowered this way. Figure 3.3 illustrates the interactions of the different parameters influencing the diaphragm position. It becomes clear that the rodside preload pressure (dark hatched area) may only vary up to the point so that at full compression and rebound of the cylinder 0% gas volume

0.1·V0 V0·(p0,t,korr/pV,max) AR·h V0·(p0,t,korr/pV,min)

0.9·V0 V0

AR·h

Diaphragm position

0.1·V0

Impermissible range for diaphragm position

Diaphragm position change due to suspension movement

100% gas volume

Diaphragm position change due to preload pressure variation

Fig. 3.3 Optimum utilization of the rodside accumulator limits according to the diaphragm deformation criterion

80

3 Dimensioning of the Hydropneumatic Suspension Hardware

(light hatched area) the diaphragm does not get deflected beyond its limits into the forbidden zone (cross hatched area). Furthermore it has to be proven, that suspension movements which compress the gas down to 10% of the accumulator volume do not cause rodside pressures which exceed the maximum operating pressure defined by the strength of the accumulator’s outer shell (maximum pressure criterion). With  pV,max

V0 p0,T,korr pV,max

n

 = pmax

h V0 p0,T,korr − AR pV,max 2

n (3.33)

The maximum pressure pmax can be calculated:  pmax = pV,max 

 V0 p0,T,korr n pV,max

V0 p0,T,korr pV,max

− AR h2

n

(3.34)

In this equation, p0,T,korr is related to the state of the suspension, when the gas volume is at its minimum while the suspension cylinder is in its center position. This means it describes the state of minimum operating temperature, lowest possible precharge pressure within production tolerance and maximum diffusion pressure loss within service intervals. In case it turns out that pmax is above pzul , pV,max has to be reduced to reduce pmax and therefore ensure the fatigue endurance of the outer shells. It was already mentioned that protection of the maximum pressure by a relief valve can help, too. This is especially true if the system is layed out very aggressively and therefore with little fault-tolerance. 3.1.3.2 Pistonside Accumulator Again it is useful to recall the balance of forces at the piston as described in Sect. 2.1: FK = FF1 + FV

or

(3.35)

p1 AK = FF1 + pV AR

(3.36)

This equation helps to understand that two different cases need to be distinguished: 1) The non preloaded system and the systems with constant preload (mechanical or hydraulic). In this case there is only one variable which has an effect on p1 : the static spring load FF1 in the design position of the suspension.

3.1

Dimensioning of the Hydraulic Spring Components

81

2) The system with variable hydraulic preload. In addition to the spring load, the variable preload force FV , respectively the variable preload pressure pV also has an effect on the pistonside pressure p1 . For the first case, the calculation of the suitable parameters for the pistonside accumulator is similar to the calculation for the rodside accumulator in a system with variable rodside preload pressure. However, while the variable rodside preload pressure is actively influenced (for example, by an electronic controller), the pressure in the pistonside accumulator (with the cylinder piston in design position) is given by an external boundary condition, the static spring load. Therefore the logical steps towards the right set of pistonside accumulator parameters start with the calculation of the pressures at minimum and maximum static spring load. p1,min AK = FF1,min + FV

(3.37)

p1,max AK = FF1,max + FV

(3.38)

and therefore FF1,min + FV AK FF1,max + FV = AK

p1,min =

(3.39)

p1,max

(3.40)

According to Eq. (3.28) (for the rodside accumulator) the same kind of derivation can be performed for the optimum precharge pressure of the pistonside accumulator. The result is: FF1,min + FV FF1,max + FV AK AK p0 = FF1,max + FV FF1,min + FV + AK AK

(3.41)

and further resolved: p0 =

(FF1,min + FV ) · (FF1,max + FV ) AK (FF1,min + FF1,max + 2FV )

(3.42)

With p0 and the already calculated value for the gas fill in the accumulator, V0 can be calculated. The actually permissible minimum and maximum pistonside pressure at static spring load in suspension design position can then be calculated according to the diaphragm deformation criterion:

82

p1,min = p1,max =

3 Dimensioning of the Hydropneumatic Suspension Hardware

V0 p0,T,korr 0.9V0 − AK 2h V0 p0,T,korr 0.1V0 + AK h2

(max. T, upper gas fill tolerance, no diffusion) (3.43) (min. T, lower gas fill tolerance, max. diffusion) (3.44)

By resolving Eq. (3.35) for FF1 and applying the minimum and the maximum allowed pistonside pressure, the actually permissible range for the static spring load is obtained. FF1,min = FF1,max =

V0 p0,T,korr 0.9V0 − AK h2 V0 p0,T,korr 0.1V0 + AK 2h

AK − p V AR

(3.45)

AK − pV AR

(3.46)

If the initially required load range is not within the load range calculated above, the latter can be slightly widened at the lower end if V0 is increased – similar to the tuning possibility described for the rodside accumulator. In many cases it is the lower end of the load range which is more critical for the accumulator. An increase of the gas mass in the pistonside accumulator by increasing the volume V0 at constant precharge pressure p0 is also possible, if the decrease of the natural frequency (and therefore softening of the suspension) connected to this parameter is tolerable. Furthermore it is possible to increase the preload force pV AR . Since this internal cylinder force is acting in the same direction as the external spring load force, the latter can be further lowered without compromising the diaphragm deformation criterion. However a higher preload causes a higher spring rate. This can be compensated by increasing the gas mass in the accumulators which lowers the spring rate back to the desired level and therefore keeps the natural frequency at its design point. However it is very important to consider that, assuming a limited supply pressure, an increase of the preload force will always result in a decrease of the maximum permissible static spring load! If this load is exceeded, the system is not capable of lifting the suspension back into its design position. This leads us to the second case, the variable preload force. It is obvious that it provides the advantage that it can be changed depending, for example, on the static spring load. Therefore, if it is increased at low static spring loads, the minimum permissible static spring load FF1,min is reduced. On the other hand, the preload force can be reduced at high axle loads to allow for a FF1,max , which is as high as possible. This means that a variable preload can not only improve the ride quality by an adjustable spring rate but can also widen the permissible range for the spring load. Following the logic of Fig. 3.3 it can be shown in another diagram, how the parameters influencing the pistonside pressure (and therefore the pistonside accumulator diaphragm position) interact. These parameters are the suspension

3.1

Dimensioning of the Hydraulic Spring Components

83

Minimum preload pressure at FF1,max and maximum preload pressure at FF1,min

All preload pressures allowed at any static spring load

0% gas volume pV,max pV,min

V0

pV,min

pV,max

Diaphragm position pV,min

pV,max

AK·h

100% gas volume

Impermissible range for diaphragm position

Diaphragm position change due to suspension movement

Diaphragm position change due to preload pressure variation

Permissible range for the diaphragm position change due to the static spring load

Fig. 3.4 Optimum utilization of the pistonside accumulator limits according to the diaphragm deformation criterion

movement, the rodside preload pressure and the static spring load. It also shows how the right selection of the rodside preload pressure at the right time can lead to a wider range of permissible static spring loads (Fig. 3.4). It is clearly visible that the limits for the permissible static spring load can be extended by making ideal use of the variable rodside preload pressure. This is indicated by the length of the grey area. This allows the extension into ranges which would be impossible with constant preload force systems. The permissible load ratio can be increased significantly. As for all accumulators, here too the permissible inner pressure pzul needs to be considered to ensure a fatigue endurable outer shell. Following the logic of Eq. (3.34), the pressure on the pistonside can be calculated.  pmax = p1,max 

V 0 p0 p1,max

V0 p0 p1,max

n

− AK 2h

n

(3.47)

84

3 Dimensioning of the Hydropneumatic Suspension Hardware

After applying p1,max according to Eq. (3.40) and reducing AK , pmax is  pmax

FF1,max + FV  = AK

V0 p0 FF1,max +FV

V 0 p0 FF1,max +FV

n

−

h 2

n

If pmax exceeds pzul either the maximum static spring load FF1,max or FV need to be reduced accordingly to meet the maximum pressure criterion. A pressure relief valve in the load carrying pistonside hydraulic circuit is highly recommended. In practice there are many possible circumstances which can lead to excessive pistonside pressures: high gas precharge pressure losses, improper use in certain applications or intentional (but wrong) system changes by system users are only some examples. In the long run, the outer shell would not be able to withstand this overload. In the worst case, the result would be a burst of the accumulator. The arising damage to the suspension components and furthermore the consequential damage due to a sudden loss of the suspension function cannot be overseen and should in any case be avoided! Yet this is only the worst case; in most of these cases the accumulator failure is slow, a crack in the outer shell develops and shows the damage by increasing leakage (which is nevertheless also very problematic and needs to be avoided). With the help of the pressure in the accumulator and the gas volume, Fig. 3.5 illustrates in a p–V-diagram how the changes of state take place for a change in static spring load (isothermal) and for the suspension movement itself (polytropic). The operational limits for the gas volume and the inner pressure of the accumulator can be clearly seen.

p pmax

polytropic

isothermal

A·h

polytropic

A·h

p0 0.1·V0

0.9·V0

V0

V

Fig. 3.5 Illustration of the operational limits of an accumulator in a p–V-diagram

3.2

Dimensioning of the Hydraulic Damping Elements

85

3.2 Dimensioning of the Hydraulic Damping Elements As already mentioned in Chap. 2, the hydraulic damping is generated by flow resistors which cause pressure losses. These pressure losses act upon the respective active areas inside the cylinder and ensure the necessary damping forces. The damping forces depend on the velocity of the compression and rebound motion since the pressure losses depend on the flow velocities inside the flow resistors. The damping forces are always oriented opposed to the direction of piston motion. If only a non-variable damping system is available, a compromise needs to be found for the level of damping forces. This is especially difficult for suspension systems which need to cover a wide range of static suspension loads. The damping forces must be sufficiently high to provide enough damping for the high load levels and on the other hand they must not cause a decreasing comfort at low suspension load levels due to a too stiff coupling of the suspension system’s input side to the isolated side. It is important for the determination of the necessary flow resistors that cavitation due to the pressure loss at a flow resistor must be avoided at all times. Apart from the noise and possible destruction of the internal cylinder components and the flow resistor, it is also the limitation of the damping forces due to cavitation which needs to be avoided. Depending on the type of hydropneumatic suspension the damping elements need to be dimensioned differently to ensure that no cavitation will occur.

3.2.1 Single-Acting Cylinder in a System Without Hydraulic Preload The damping force is a result of the pressure loss p at the flow resistor which acts upon the hydraulically active area, in this case the head area of the plunger AS . So the next step is to find the right size and type of the flow resistor which best fulfills the requirement for the damping forces. Please remember that, as mentioned in the introduction to this section, the determination of these requirements is not part of the explanation here. The basic equation for the calculation of the damping force is: FD,hyd = pAS

(3.48)

However, as mentioned above, there are limitations in the dimensioning which originate from the danger of excessively high pressure losses and cavitation caused thereby. The situation is illustrated in Fig. 3.6. During the compression phases, when the hydraulic fluid flows out of the cylinder, cavitation is not an issue, since the pressure, which is needed to push the fluid through the flow resistor, is directly generated by the cylinder itself. It is therefore: p = pZ − pSp pZ > pSp

(3.49)

86

3 Dimensioning of the Hydropneumatic Suspension Hardware

Rebound

Compression

pSp

p Sp Δp

AS

Δp

pz

pz

pZ > pSp

pZ < pSp

Fig. 3.6 Behavior of a single-acting cylinder during compression and rebound

and since pSp >> pKav

it is also ensured that

pZ >> pKav On the other hand during the rebound phases, when hydraulic fluid flows into the cylinder, the possible pressure loss is limited. This is due to the fact that the pressure, which forces the fluid through the flow resistor, is generated by the hydraulic accumulator. However its internal pressure pSp has a certain level (depending especially on its precharge pressure and the current fluid level inside) and therefore the possible flow rate through the flow resistor into the cylinder is limited. It is therefore obvious that the possible rebound velocity (without creating cavitation) is limited. This is shown in the following calculation. p = pSp − pZ

(3.50)

Furthermore the requirement to avoid cavitation is: pZ > pKav So it can be deduced that: p < pSp − pKav

(3.51)

According to Sect. 2.3.2 the pressure loss in a throttle is defined by: ·

p = V νρKD

(3.52)

3.2

Dimensioning of the Hydraulic Damping Elements

87

The flow rate can be replaced by the product of plunger head area AS and rebound velocity. By resolving the equation for the rebound velocity, the velocity limit vkav is obtained, which represents the point when the pressure drop p over the flow resistor gets close to the pressure in the hydraulic accumulator pSp and therefore pressure in the cylinder pZ becomes equal to the cavitation pressure limit pKav . vKav =

pSp − pKav νρKD AS

(3.53)

A correct dimensioning of the flow resistor (or rather the sum of all flow resistors in the path of the hydraulic fluid from the accumulator to the cylinder) helps to provide sufficient distance between cylinder pressure and the cavitation pressure limit. Figure 3.7 shows impressively how the cavitation affects the force–displacementdiagram in an experiment. It is clearly visible that the force-displacement curve loses its typical hydraulic-damping-specific curvature and shows a flattening around the middle of the oscillation amplitude. In this area, the damping force is at its maximum possible level of AZ (pSp − pKav ), although the rebound velocity keeps increasing up to the maximum at the center of the overall displacement (s = 0%). In the course of the further oscillation motion, the regular shape of the force–displacement curve is again adopted, when the motion velocity drops back below the critical velocity vKav . Now this limitation in the possible damping forces is, at all times, necessary for the rebound phase. This is quite unfortunate, since this phase should be dampened more strongly than the compression phase to achieve the best vibration isolation. If the maximum available damping force of a single-acting cylinder according to the above explanations is not sufficient for all operating conditions, a double-acting cylinder must be used as described in Sect. 3.2.2.

Suspension force FF [%]

140 120

compression

100 cavitation area

80

rebound

60 –30

15 0 –15 Displacement s [%]

Fig. 3.7 Shape of a force–displacement-curve with temporary cavitation

30

88

3 Dimensioning of the Hydropneumatic Suspension Hardware

3.2.2 Double-Acting Cylinder in a System Without Hydraulic Preload A double-acting cylinder is operated with two separate flow resistors, one of them being installed in the rodside hydraulic circuit, the other one in the pistonside hydraulic circuit. By correct arrangement and sizing of the flow resistors, a significantly higher rebound damping is enabled. Figure 3.8 illustrates in an exemplary manner the most obvious possibility for a hydraulic circuit of this type. Yet this system can be designed even more simply by removing the additional external fluid line, including the additional flow resistor, and instead integrating the latter into the piston, so a direct cylinder-internal connection between pistonside and rodside is created. This system too provides the advantage of high possible rebound damping, however the additional effort compared to a single-acting cylinder is relatively low (Fig. 3.9). This system is further explained in the following calculations. The calculation of the damping forces via pressure losses and the respective active areas on the piston is rather laborious and cumbersome. An easier and more elegant way is the calculation of the heat output generated inside the flow resistors from the kinetic energy of the hydraulic fluid. This heat output is equal to the damping power PD,hyd . ·

·

PD,hyd = pK VS +pR VR

(3.54)

It is important to consider that, due to the regenerative type of circuit for the suspension cylinder, in the above example the pistonside flow resistor is not subjected to the full volume flow coming from the piston chamber, but only to the volume flow ·

VS caused by the displacement of the rod with its active area AS ! By calculating: ·

VS = A S v

(3.55)

s Δ pR pR AR pSp AK

Fig. 3.8 Use of a double-acting cylinder for more rebound damping

pK

Δ pK

3.2

Dimensioning of the Hydraulic Damping Elements

89

s Alternative illustration of the hydraulic circuit:

pR AS AR

s

ΔpR

pSp Δ pK

AK pK

Fig. 3.9 Flow resistor in the piston provides a simplified setup

and ·

VR = A R v

(3.56)

as well as FD,hyd =

PD,hyd v

(3.57)

Resolving for FD,hyd leads us to: FD,hyd = pK AS + pR AR

(3.58)

This equation can be used for the dimensioning of the flow resistors. However it is very important to coordinate and to harmonize both flow resistors. If this is not performed, cavitation can be caused. If the rodside flow resistor is chosen to be significantly over-restrictive compared to the pistonside flow resistor, cavitation in the rod chamber of the cylinder during the compression phase will be the result. On the other hand, if the pistonside flow resistor is too restrictive, cavitation in the piston chamber of the cylinder will be caused during the rebound phase. The respective pressures and the limit for the cavitation will be further explained in the following, assuming that both pistonside and rodside flow resistor are throttles (as explained in Sect. 2.3.2). Compression: pR = pSp + pK − pR

(3.59)

pR = pSp + AS vνρKD.K − AR vνρKD,R

(3.60)

90

3 Dimensioning of the Hydropneumatic Suspension Hardware

Rebound: pK = pSp − pK

(3.61)

pK = pSp − AS vνρKD,K

(3.62)

The last equation can be used to calculate the limit for the pistonside flow resistor KD,K,grenz by setting pK = pKav and resolving for KD,K KD,K,grenz =

pSp − pKav AS vνρ

(3.63)

By setting pR = pKav in Eq. (3.60) and resolving for KD,R , the limit for the rodside flow resistor KD,R,grenz is obtained: KD,R,grenz =

pSp − pKav + AS vηKD,K AR vνρ

(3.64)

By setting KD,K,grenz for KD,K in Eq. (3.64), the result is: KD,R,grenz =

2(pSp − pKav ) AR vνρ

(3.65)

By calculating the ratio of both limit values, the ideal ratio of the maximum restricting flow resistors is obtained, therefore aiming for the maximum possible damping. If this high damping level is not required, this ratio can also be used as a basis for the selection of any other kind of throttle combination KD,R 2AS = KD,K AR

(3.66)

Both values KD,K,grenz and KD,R,grenz are of course limit values for the maximum flow restriction of the flow resistors. Please be aware that they depend in particular on the accumulator pressure, which varies throughout the suspension stroke (!), and furthermore on the piston velocity. Be also aware that the latter is moreover a variable which, at a given external excitation of the suspension, depends on the strength of the damping and therefore the size of the flow resistor. So there is mutual influence of flow resistor size/fluid damping on one hand and piston velocity on the other hand. The above is therefore only a simplified, but, as practice shows, useful calculation. Experiments are essential, especially when it comes to the fine tuning of damping of this kind. In case the restrictions due to the previously described system impede the required tuning of the damping, it is also possible to assign a check valve to each flow resistor. This needs to be done in a way so that, during the rebound phase, only the rodside flow resistor is active while the pistonside resistor is bypassed by

3.2

Dimensioning of the Hydraulic Damping Elements

91

the check valve and during the compression phase only the pistonside flow resistor is active and the rodside flow resistor is bypassed. This completely removes the problem of cavitation and allows the free choice of dedicated damping levels for compression and rebound direction. Most modern automotive suspension dampers are set up in this manner (please also refer to Sect. 4.3.2).

3.2.3 Double-Acting Cylinder in a System with Hydraulic Preload In this case the rodside and pistonside are completely separated from each other. Therefore the respective flow rates and the pressure losses resulting from them can be calculated separately which simplifies the calculation. It can therefore basically be calculated as the combination of two single-acting systems as in Sect. 3.2.1. The overall hydraulic damping force is therefore: FD,hyd = pK AK + pR AR

(3.67)

When calculating the piston velocity limits for cavitation it is important to distinguish between the pressure levels in the accumulators for the rodside and for the pistonside. vKav,Ein =

pSp,R νρKD,R AR

(3.68)

vKav,Aus =

pSp,K νρKD,K AK

(3.69)

Here too, suitable sizing of the flow restrictors, similar to the calculation in Sect. 3.2.2, helps to avoid cavitation. Again, the danger of cavitation can be eliminated completely by placing an additional check valve parallel to each flow resistor.

3.2.4 End-of-Stroke Damping It was already stated in Sect. 2.3.3 that the end-of-stroke damping should be as smooth as possible by avoiding deceleration force peaks and keeping the force level as low as possible. This can be achieved by a layout which ensures a possibly constant force level extending over the entire end-of-stroke damping range. The closer the piston gets to the end stop the lower the velocity and, for a constant force level, the more restrictive the flow resistor needs to be. This sizing of the flow resistor over the end-of-stroke damping range can be calculated as the following explanation shows. The change of the spring force throughout the end-of-stroke damping displacement as well as the general damping of the suspension system are not considered for this calculation. The influence of both is relatively small and has in

92

3 Dimensioning of the Hydropneumatic Suspension Hardware AED

v0

ΔpED

Flow resistor

m

.

xM

V

x

Fig. 3.10 Deceleration of a Mass by a Cylinder and a Flow Resistor

addition a favorable (decelerating) effect. The schematic in Fig. 3.10 shows the basic setup for the calculation. The above considerations allow the following approach: FED = ma = const.

(3.70)

FED is created from the pressure loss pED at the flow resistor multiplied with the active area during the end-of-stroke damping AED . Therefore the pressure loss is: pED =

FED ma = = const. AED AED

(3.71)

Assuming that the flow resistor has the character of an orifice, it is possible to also express the pressure loss according to Sect. 2.3.2: ·

pED = V 2 (x)KB (x)

(3.72)

and using ·

V (x) = v(x)AED

(3.73)

it is possible to calculate KB (X) KB (x) =

pED v2 (x)A2ED

(3.74)

Furthermore the velocity can be calculated according to the general laws of kinematics (for example in [KUC87]): v (x) =

 v20 + 2ax

(3.75)

where v0 is the initial velocity when reaching the starting point of the end-of-stroke damping and a is the deceleration of the mass and therefore is negative. Applying Eqs. (3.71) and (3.75) to Eq. (3.74) results in the equation defining the displacement-depending orifice:

3.2

Dimensioning of the Hydraulic Damping Elements

93



v2 only defined for 0 < x < − 0 2a

ma KB (x) = 3 AED (v20 + 2ax)

 (3.76)

And for a throttle accordingly: ma  KD (x) = A2ED νρ v20 + 2ax



v2 only defined for 0 < x < − 0 2a

 (3.77)

For the initial velocity v0 the realistically expected maximum value v0,max must be inserted into the equations as well as the maximum decelerated mass mmax . This mass must then be decelerated by the end-of-stroke damping to v = 0 m/s within the available end-of-stroke displacement xM . amax = −

v20,max

(3.78)

2xM

Furthermore it can be proven by calculation that in case of the application of Eq. (3.76) (orifice) no matter what the initial velocity is, the piston will always be decelerated to zero throughout the whole end-of-stroke displacement, thus granting the softest possible damping independent of the initial velocity. This way a soft impulse and a rather slow motion towards the end stop is more softly cushioned than a heavy impact. So the system dissipates energy only as much and as quickly as necessary to ensure the softest possible cushioning; it automatically adapts to the needs of the operating conditions just by its physical principle (Fig. 3.11). In practice at the beginning of the end-of-stroke damping, the flow resistance will be increased slowly to the calculated nominal value in order to ensure that there is a smooth transition into the constant deceleration process.

Force v0 = v0,max F = Fmax

F = ¼·Fmax F = 1/9 ·Fmax

v0 = ½·v0,max v0 =1/3 ·v0,max

Start of end-ofstroke damping

Mechanical end stop

Displacement

Fig. 3.11 End-of-stroke damping force vs. displacement for an ideally designed displacementdepending orifice at different v0

94

3 Dimensioning of the Hydropneumatic Suspension Hardware

Due to this advantage and the fact that the flow resistance of an orifice is mostly independent of fluid viscosity (and therefore temperature), an orifice type flow resistor is recommended over a throttle type for the displacement-depending end-ofstroke damping. Furthermore it is important to consider for hydraulic end-of-stroke damping that it should let the piston move freely without additional damping when its direction of motion changes and it is on its way back out of the end-of-stroke damping range, away from the end stop. This ensures that the piston returns quickly to its normal operating range with normal levels of damping and comfort. The hydraulic end-of-stroke damping is virtually wear free. There is only an additional stress factor for the hydraulic fluid due to the flow conditions with higher shear stresses in additional sealing gaps or the orifice itself. Yet this can be covered by the normal oil servicing. All in all, for hydropneumatic suspension systems the hydraulic end-of-stroke damping provides functional advantages over the solution with elastomer elements.

Chapter 4

Hydraulic Components Design

The schematic setup of a simple hydropneumatic suspension system has been illustrated already in Sect. 2.1. Section 4.1 describes the design of the basic components for the suspension unit: cylinder, accumulator, flow resistors and lines/fittings.

4.1 Cylinders

4.1.1 Function and Requirements The cylinders are the load-carrying elements in the suspension system; they transfer the forces between input side and isolated side which keep the suspended mass in the intended design position. At the same time, the cylinder also provides the travel of the suspension, which enables the reduction of oscillations and respectively accelerations on the isolated side. Forces and the coincident displacements therefore lead to energy exchange between the mechanical setup (chassis, wheels, control arms etc.) and the hydraulic suspension system. Usually the geometry and the kinematics of the suspension system are designed in a way that the cylinders are subjected to a compressive force. This means that the complete surface of the piston is acting as the active area and carries the suspended mass. This way the design maximizes the use of the available cylinder diameter and therefore available space. Only very rarely has the cylinder the additional function of contributing to the kinematics in a way the regular guiding elements do (like, for example, control arms). The system is usually designed so the cylinder only transfers forces along its longitudinal axis. One reason for this is that an additional load coming from transverse forces or torsional moments can lead to an overload of the cylinder and W. Bauer, Hydropneumatic Suspension Systems, DOI 10.1007/978-3-642-15147-7_4,  C Springer-Verlag Berlin Heidelberg 2011

95

96

4

Hydraulic Components Design

therefore to its destruction. But the far more important reason is the friction caused by these types of load. This would result in a deterioration of the suspension properties especially the comfort quality as already explained in Chap. 2. If transverse forces and/or torsional moments cannot be avoided due to the chosen kinematics setup/design space limitations, they can sometimes be at least partly compensated by other design tricks. A good example of this is to have an offset angle between the line of action of the spring force and the damper longitudinal axis on McPherson struts, reducing the unfavorable loads on the damper to a minimum. In addition to the definition by a drawing or a 3-dimensional model, the following short checklist summarizes several important specification features for suspension cylinders (additional to common cylinder specifications): • Permissible operating pressures: can be above system pressure due to suspension motion! • Temperature ranges (short term, long term): can be above system and above ambient temperature due to the additional heat rejection of damping elements! • External forces or torsional moments during operation, particularly compression and rebound end stop: should the cylinder provide this function or are there external end stops? • Static and dynamic friction under different operating conditions (pressures, temperatures, piston velocities) • If applicable: hydraulic damping forces, end-of-stroke damping (at specified hydraulic fluid viscosity and piston velocity) • Maximum piston velocity • Qualification testing in particular in terms of fatigue endurance: at a certain load spectrum defined for the suspension (as far as possible, should consider short and long stroke displacements and different oscillation frequencies) • General operating and environmental conditions: especially important if the cylinder is located in a harsh environment and exposed positions such as in the wheel house or at an axle.

4.1.2 Types of Cylinders The general layout of a suspension cylinder is illustrated by a schematic partial cross section in Fig. 4.1. The key element of the cylinder is the cylinder tube. It adjoins all other elements except for the piston rod. The cylinder tube is closed at one end by the cylinder bottom, which usually also has the function of transferring the force at this end of the cylinder. The supporting element can be designed in different ways; in Fig. 4.1 for example a simple slide bearing is sketched. At the other end the cylinder tube is closed by the rod guide, which, as indicated by its name, guides the piston rod and the components attached to it along the longitudinal axis of the cylinder. At one end of the piston rod a support element is

4.1

Cylinders

97

Rodside support element Piston rod Rod guide with sealing and guiding elements Hydraulic connectors Air bleeding elements Cylinder tube Piston with sealing and guiding elements Cylinder bottom with bottomside support element

Fig. 4.1 Partial cross section of a suspension cylinder

attached, which transfers the cylinder forces at this end of the cylinder. At the other end of the rod, the piston is attached. In case of a double-acting cylinder (as shown in Fig. 4.1) the piston separates the volume inside the cylinder tube into two individual chambers: the piston chamber and the rod chamber. For a tight separation of these chambers, a seal is installed in the circumferential surface of the piston. The seal slides on the inner surface of the cylinder tube. Additionally there are guiding elements, which are supposed to transfer lateral forces between piston and inner cylinder surface with the lowest possible friction and lowest possible lateral play. The guiding elements prevent a metal-to-metal contact of piston and cylinder tube and furthermore provide a defined gap between them both to enable the best possible function of the sealing element(s). More sealing elements are located between the rod surface and the inner surface of the rod guide. Their function is to separate the rod chamber from the environment. The guiding of the piston rod is either by metallic contact of rod and rod guide surfaces or by additional guiding elements similar to the piston. In case no piston is integrated into single-acting cylinders the rod sealing elements are the only dynamic seals (example: Fig. 4.2 plunger cylinder). Furthermore hydraulic connectors are provided which enable the flow of hydraulic fluid in and out of the cylinder chambers. In the above example, the connectors are connected to the cylinder tube, yet they might as well be part of, for example, the rod guide and/or the cylinder bottom. Special air bleeding elements are provided in particular for suspension cylinders. They ensure that the suspension function, especially the damping, is not spoiled by any residual air in the hydraulic fluid. These elements are located at the very ends of the respective chambers to ensure best bleeding results. The location of the bleeding elements also needs to be selected considering the position of the installed suspension cylinder in the overall system. Not only must they be in the highest position of each cylinder chamber, but they also must be able to be reached by service personnel.

98

4 Single-acting cylinders with plunger

with piston

Hydraulic Components Design

Double-acting cylinders differential cylinder

synchronous cylinder

Fig. 4.2 Functional principle of the most common types of cylinders

Other elements (not shown in Fig. 4.1) are integrated in the cylinder depending on its function and type. Such elements include an end-of-stroke damping, sensors or special connection flanges, for example, to directly mount accumulators at the cylinder. There are basically two possibilities to categorize cylinders: their functional principle and their design principle. The functional principle can be distinguished between the single-acting cylinder designed either with a plunger or with piston and rod, and furthermore the double-acting cylinder designed as a differential cylinder or a synchronous (i.e. double-rod) cylinder. The design principle is subdivided into different basic types which differ especially with respect to the type of connection between the three main cylinder components rod guide, cylinder tube and cylinder bottom. Well known and frequently used connection types are especially welding connections for the connection cylinder bottom to cylinder tube and the screw-intype or the drop-in-type connection for the connection of cylinder tube and rod guide. Furthermore the tie rod design and the crimped design are used for the overall cylinder in special cases. These short explanations will be further explained in Sects. 4.1.2.1 and 4.1.2.2. 4.1.2.1 Functional Principle Figure 4.2 categorizes cylinders according to their different functional principles. Suspension systems with only low static spring load variations or with external mechanical preload can be run with single-acting cylinders. If the requirements in terms of rebound damping are not too high, a simple plunger cylinder can be used. Its particular advantages are low production cost, a high safety factor for buckling

4.1

Cylinders

99

and a robust connection of the rodside support element. On the other hand there is, when built from solid material, a relatively high component weight with the additional disadvantage of the increase of unsprung mass. If this is a critical design criterion, the rod of the plunger cylinder can be designed hollow. Another possibility is to use the more complex single-acting cylinder with piston and rod, while the rod chamber is ventilated or connected to the hydraulic fluid reservoir and only the piston chamber is subjected to hydraulic pressure. The double-acting cylinder with piston and rod should be used, when higher rebound damping is required. As described in Sect. 3.2.2 this cylinder is equipped with a bore in the piston which connects piston and rod chamber. The flow through this bore is limited by a flow resistor (for example, an orifice) and thus an increased rebound damping is possible. If normal flow resistors are used, providing the same restriction in both flow directions, a suitable sizing is necessary to avoid cavitation. Compared to regularly used double-acting cylinders the cylinder here can be operated without a piston seal. The gap between the circumferential surface of the piston and inner cylinder wall and the guiding element are then the only sealing design features between pistonside and rodside. In particular, if the guiding element has a special shape to provide minimum leakage, this is usually sufficient for these types of cylinders. Furthermore it has no rodside oil connectors like a regular double-acting differential cylinder. However it is still more expensive than a simple plunger type single-acting cylinder. If a suspension system is subjected to wide load variations, it is common to implement a hydropneumatic suspension system with hydraulic preload and therefore with a double-acting cylinder. The differential cylinder is the best choice in this case; the necessary preload pressure is set in its rod chamber and then the pressure in the piston chamber is brought to a level which enables it to support the static spring load and the preload forces and therefore can keep the suspension level in the desired position. This directly implies that the piston chamber and the rod chamber must be separated from each other by a sealing element at the piston. This logically means that this cylinder also needs a separate hydraulic connector for the rod chamber. This sealed separation of piston chamber and rod chamber also helps to provide an effective damping of the suspension motion by integrating flow resistors between the cylinder chambers and their respective accumulators. Just by the nature of the preload, the general level of suspension hydraulics pressures is higher than in the single-acting systems. Accordingly the risk of cavitation during fast suspension motions is smaller. The synchronous cylinder with a rod and a rod guide at each end of the cylinder tube is also very well known in standard hydraulics – for example, for steering systems. The diameter of both rods is the same, therefore the cylinder has equal active areas on both sides of the piston. For hydropneumatic suspensions this is only interesting for some exotic applications, for example, if separate roll stabilization is required (please also refer to Sects. 6.3 and 8.2). Therefore this type of cylinder is not described in detail here.

100

4

Hydraulic Components Design

There are of course other types of cylinders, usually for special applications with other functional principles, such as cylinders with three different active chambers. However they are only rarely used and are also not included here. 4.1.2.2 Design Principle Figure 4.3 shows three different design principles which can be used universally for the aforementioned types of cylinders. The welded design is a very common concept and is particularly characterized by its high degree of robustness. In this case the cylinder bottom is welded to the cylinder tube and the rod guide (if installed) is screwed into the cylinder tube; sometimes it is also only dropped in and mechanically interlocked, for example, with a steel ring. The sealing between rod guide and cylinder tube is provided by standard sealing components, usually by o-rings. Such cylinders can withstand high forces in longitudinal and also lateral direction. Due to the compact design, their space requirements are relatively low. The tie rod design abstains completely from welding by tying the components rod guide, cylinder tube and cylinder bottom together with the help of outboard located threaded rods. The sealing among the different components and towards the environment is provided by standard elastomeric sealing elements. This way all the problems arising from a weld are completely ruled out (welding distortion, changes to the material structure, residual stresses, etc.). A further advantage is that

screwed or dropped in welded

with tie rod

Fig. 4.3 Examples for design principles of suspension cylinders

crimped

4.1

Cylinders

101

the leakage test for porous welds, often performed on 100% of the welded production cylinders, can be omitted for the tie rod design. The machining of the cylinder tubes is relatively simple; in best case, it is sufficient to cut to length, deburr and chamfer (this helps the assembly of the seals). The hydraulic connectors are then usually integrated in the cylinder bottom and the rod guide (not shown in Fig. 4.3). For the tie rod design it is essential to keep a close eye on the exact positioning of the components especially with regards to the longitudinal axis of the cylinder. This means additional effort for machining of the respective mating surfaces as well as for the final assembly. Due to their very nature, tie rod cylinders may not be subjected to high lateral forces or high longitudinal overload. This means in particular that in many cases the cylinder cannot provide the end stop function and it is therefore necessary to plan on external mechanical end stops, for example, as part of the suspension kinematics. A further disadvantage is the additional space requirement for the external tie rods and the lateral tie rod supports at both the rod guide and the cylinder bottom. The crimped design is quite common for mass production shock absorbers in the automotive industry as well as for small damping elements. Here too the problems of a welded design are avoided. Serviceability of the cylinders is sacrificed for the benefit of lower production cost. The cylinder bottom and the rod guide are crimp-connected to the cylinder tube. The sealing of these connections is usually an elastomeric element like in the tie rod design, yet in some cases connections can be found where one of the two mating components is designed similarly to a cutting ring of a hydraulic connection. When crimped, this cutting ring is pressed into the surface of the mating surface and this way seals the connections. However, the manufacturing of the crimped design gets increasingly difficult with increasing cylinder tube wall thickness. That is the reason why crimping has only a limited applicability for hydraulic cylinders with their rather large wall thickness, unless a suitable manufacturing process can be developed.

4.1.3 Sealing Elements Sealing technology is of especially high importance for suspension cylinders. Seals are distinguished into the group of static seals and the group of dynamic seals, which are again distinguished into rotary and translational dynamic seals. The latter seals are responsible for the level of friction in a suspension cylinder and therefore have a major influence on the ride quality that can be provided by a suspension cylinder and therefore by the whole suspension system. In particular the sealing element between rod and rod guide as the separating element between hydraulic fluid and the environment is of major importance. On one hand it is subjected to a high pressure difference and therefore causes the major amount of the overall friction. On the other hand it has the important task of avoiding oil leaks out of the cylinder into the environment and at the same time of keeping dirt particles from the environment out of the hydraulic system.

102

4

Hydraulic Components Design

Due to its very nature, the functional principle of a dynamic seal should rather be called a controlled minimum leakage. The reason is that an extremely thin lubricating film on the sliding surface of the seal is necessary to ensure smooth sliding. This lubricating film usually is thinner than 1 μm, which is about the order of magnitude of the surface roughness of the sliding partner [MUE]. The lubricating film helps to keep the friction forces low and this also keeps the friction induced heat rejection low. The remaining heat rejection is partially absorbed by the lubricating film and therefore dissipated into the hydraulic fluid in the cylinder chambers. Low friction forces and low temperatures provide the additional benefit of low wear of the sealing edge(s). During the relative motion of both sliding partners of the sealing system, the lubricating film takes along hydraulic fluid through the sealing gap. To make sure that this does not cause leakage, this amount of hydraulic fluid has to be brought back to its original side during the motion in the opposite direction. The amount of hydraulic fluid drawn through the sealing gap is in particular depending on the gradient of the contact pressure at the sealing edge along the path from one side of the seal to the other. In particular the maximum contact pressure gradient for both motion directions individually is responsible for the transportation of the hydraulic fluid through the gap. The higher the gradient’s maximum, the lower the amount of hydraulic fluid escaping through the gap. Mueller has illustrated this relationship very colorfully by a truck that carries hydraulic fluid on its open, bowl-shaped cargo area over a hill. The hill is the shape of the pressure-position curve along the path of the oil from the high-pressure side to the low-pressure side. Now, the steeper the inclination of the hill on the high-pressure side, the more hydraulic fluid will get spilled out of the transportation bowl on the truck and therefore the less oil he will bring to the low-pressure side [MUE]. Figure 4.4 exemplifies how the contour of the sealing element (b) pressed onto the sliding surface (c) by the normal force (a) affects the formation of this pressure gradient. The lower the gradient of the contact pressure curve (d), the higher is the leakage (e) in the respective direction (indicated by the size of the arrow). It is important to realize that the pressure curve is also affected in particular by the pressure difference from oil to air side (in many cases this changes the normal force) and by the fluid forces of the hydraulic film between sealing edge and sliding surface. The radius of the sealing edge has a major influence as well: The larger the radius, the easier the hydraulic fluid can get between sealing element and sliding surface and the lower will be the friction, however the higher will be the leakage.

a b c

Fig. 4.4 Schematic relationship of seal contour, pressure gradient and leakage

d e

4.1

Cylinders

103

Since it is very important for a rod sealing element that it is virtually leakage-free, the seal contour needs to have a rather high angle on the hydraulic fluid side (low leakage during cylinder extension) and a lower angle on the air side (good transportation of hydraulic fluid back into the rod chamber during cylinder compression). This ensures that during the frequent cylinder position oscillations more hydraulic fluid can be transported back than is leaking out of the cylinder. For sealing elements between piston and inner wall of the cylinder tube it is necessary that the seal’s fluid transportation behavior is as symmetric as possible to avoid pumping hydraulic fluid from one chamber into the other during the piston movement. Therefore piston seals favorably have a similar contour on both sides of the seal, but also depending on the (average) pressure difference between both sides. It is obvious that the properties of the sliding surface play an important role as well. In case the roughness is too high, the result is a thicker lubricating film yet also stronger wear at the sealing edges due to a scratching effect of the surface roughness peaks. In case the roughness is too low, a lack of indentations which can accommodate hydraulic fluid leads to reduced lubrication and hence an increase of the friction forces. Special surface coatings can help improving the situation. For example, high quality shock absorbers and front forks for motorbikes are equipped with rods coated with the gold-colored titanium nitride, providing a substantial and durable reduction of friction. An important issue is that the dynamic seals should have a reliable sealing function also in a static state. Especially important is the transition from the static to the dynamic state. Static friction is an important factor here. Since in the static state no friction-reducing lubricating film is available, the level of static friction is usually higher than the sliding friction. Moreover for a suspension system, the static friction determines the minimum level of excitation for the proper function of the suspension. The higher the static friction, the higher are these accelerations. When selecting the sealing elements, it is also important to avoid the stick-slip effect which arises on one hand from a high difference in static and sliding friction coefficient, on the other hand from the elastic behavior of the sealing elements and other components. The following factors are of major importance for the selection of suitable dynamic sealing elements for suspension cylinders: – – – –

Low friction No leakage (especially for rod seals) Maximum sliding velocity (compression and rebound) Pressure level (maximum pressure can be above hydraulic system pump pressure!) – Robustness and permissible operating temperatures (in particular for seals in exposed suspension cylinders in off-road equipment) To achieve proper dynamic sealing, it is common to combine several sealing elements in a complete sealing system. This way the positive characteristics of each type of sealing element can be specifically used for an overall improved sealing

104

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Hydraulic Components Design

function. The following explanations describe the sealing locations rod to rod guide and piston to cylinder tube in more detail.

4.1.3.1 Rod Seal System As mentioned above, one requirement for the rod seal system is to be leakagefree in static and dynamic sealing condition. To be able to ensure this, especially considering the low friction requirements, it is common to arrange two sealing elements in series to keep the hydraulic fluid inside the cylinder. Additionally, on the low pressure-side (air side) a wiper is installed to keep dirt particles, water etc. away from the delicate sealing edges of the fluid seals and out of the hydraulic system in general (Fig. 4.5). It is state of the art to design the first seal (primary seal, counted from the fluid side) as a very low friction seal with a therefore thicker lubricating film. This is often a PTFE sealing ring (polytetrafluorethylene, a low friction thermoplastic) with a step-shaped contour which is preloaded and therefore pressed onto the rod by an O-ring. Normally this sealing element catches most of the pressure difference between fluid side and air side. To enable this, it must be designed in a way so it has a pump effect towards the fluid chamber, this way keeping the chamber between primary and secondary seal free of excessive hydraulic fluid and therefore free of pressure. The secondary seal is then designed more conservatively to further reduce the film thickness during the extension stroke and hence to prevent leakage. It is usually a lip seal ring in particular a u-ring. Since the latter must only catch a small portion of the overall pressure difference, its friction is relatively low. The friction level of a suspension cylinder with this type of rod sealing system therefore is a good indication of the proper functioning of the primary seal. If it loses its sealing function, the pressure in the chamber between primary and secondary seal increases and the u-ring is loaded with higher pressure thus causing higher friction. If it has to catch the whole pressure difference between fluid and air side this will cause a drastic increase of friction (factor 2 and more).

primary seal rod guide

high pressure side (hydraulic fluid)

Fig. 4.5 Rod sealing system

secondary seal

wiper piston rod

low pressure side (air)

4.1

Cylinders

105

For an even lower friction it is possible to use special rod sealing systems, known from servo-hydraulic test benches, although a higher leakage comes along with it, since in many cases this is basically a very tight sealing gap. Now instead of sealing the leakage with another sealing element, which would build up a pressure difference and therefore cause friction, the leakage can also be routed back to the hydraulic reservoir via a leakage oil return line. Therefore the secondary seal can be designed with almost no friction since it is basically only an oil wiper. This element and its low additional friction can even be omitted if a gaiter is used to protect the complete piston rod from dirt and keep the hydraulic fluid away from the environment. This type of design is used in the hydropneumatic suspensions for Citroen passenger cars to reach the lowest possible level of friction. The non leakage free rod sealing system is probably one of the reasons why vehicles with these hydropneumatic suspensions very slowly drop down onto the compression end stops during longer standstill periods. 4.1.3.2 Piston Seal Since the piston seal only seals internally, it is not so important to have an absolutely leakage free seal. Indeed during standstill (no excitations on the input side) and therefore in case of static sealing, it is desired to have possibly low leakage to keep the suspension level in its design position. But when excitations arise and the suspension is in operation, it is not a problem to have a slight leakage at the piston seal due to the sliding over the inner cylinder tube wall. For the sake of lower friction and therefore better ride comfort it will be usually accepted that the leveling system needs to be activated from time to time to bring the suspension back to the design position. In a suspension cylinder the piston seal usually consists of a PTFE slide ring which is preloaded by an o-ring. This type of arrangement makes use of the positive properties of both types of material just like the primary seal mentioned for the rod seal system. At the dynamic sealing location low-friction and low-wear PTFE provides the sealing. To ensure that this function is given in long term, a preload must be applied which does not decrease throughout the life of the suspension system. This function is provided by an elastomeric O-ring. It has the additional advantage that, due to its elastic deformation under pressure, it provides the more radial preload for the slide ring, the higher the differential pressure between both cylinder chambers. On top of that, the O-ring has the function to seal the possible leakage path between slide ring and piston through the groove (Fig. 4.6). The companies Merkel Freudenberg Fluidtechnik and Weber-Hydraulik were able to further improve the sealing properties (especially the friction) by a special rounded shape of the contact surface of the slide ring. This reduces the pressure gradient and therefore the transition from mixed friction to hydrodynamic friction at the sealing element can be reached more easily. This seal reduced the friction by more than 30% compared to standard slide rings (average value for the different main operation pressure ranges of the suspension cylinder). It was further possible to prove that the leakage during the dynamic sealing function is on the same level as

106

4

Hydraulic Components Design cylinder tube guiding element PTFE slide ring O-ring for preload piston longitudinal axis of cylinder

Fig. 4.6 Slide ring and O-ring for piston seal

for standard slide rings. The seal enables the compensation of the higher fluid film thickness by providing the same thickness for both sliding directions [FIS06].

4.1.4 End-of-Stroke Damping It is the basic principle of a hydraulic end-of-stroke damping to reduce the opening for the hydraulic fluid flow out of the respective chamber from a certain point of suspension displacement/piston position. This creates a differential pressure which retroacts into the respective cylinder chamber and therefore onto its hydraulically active area. This leads to an additional decelerating force in the cylinder. A widely used design solution is to cut off the cylinder chamber from the outlet port starting from a certain piston position towards the end of the stroke. In addition to that, a predefined (sometimes also displacement-dependent) opening area is created, which then is the only path for the outflowing hydraulic fluid to the outlet port. Here the simplest solution is to create a bypass-bore which contains a (eventually externally adjustable) flow resistor. Figure 4.7 shows the example of a rodside endof-stroke damping which becomes effective during rebound phases. An additional check valve can be found in the arrangement. It is responsible for enabling an unhindered motion back towards the design position of the suspension once the rebound motion has come to an end. However a disadvantage of this whole setup is that the constant flow resistor does not allow an even and low level of deceleration. Due to the flow rate dependency of the flow resistance, it has a high deceleration peak at the beginning of the end-of-stroke damping (high piston velocity → high flow) with a subsequently decreasing damping force. Sizing the constant flow resistor therefore is always a compromise: if its opening area is chosen to be too large, the deceleration might not be sufficient and the suspension will bottom out harshly. On the other hand if it is chosen to be too small, the flow resistance and therefore the deceleration is too high. In both cases a noticeably high level of acceleration will reduce the comfort.

4.1

Cylinders

107 piston

flow resistor

rodside port

check valve

effective displacement

pistonside port

Fig. 4.7 Bypass-bore with fixed flow resistor

To avoid this disadvantage, a displacement-depending end-of-stroke damping flow resistor is necessary. This way, the high initial velocity can be evenly reduced to a very low velocity level when reaching the mechanical end stop. This requires a constant level of decelerating force and therefore a constant pressure loss at the flow resistor. At the beginning of the end-of-stroke damping the opening area therefore must be high and then gradually be reduced – please refer to Sect. 2.3.3. There are different possibilities to provide such a characteristic of the opening area vs. displacement. It is very common to machine grooves into the part of the piston which shuts off the cylinder chamber from the outlet port. These grooves flatten out until the end of the cylinder stroke and therefore fulfill the requirement of a reducing opening area. The grooves can be arranged axially as well as helically (Fig. 4.8) [KON07]. It was already mentioned above that it is important for the end-of-stroke damping to be only active during the motion towards the end stop but should let the piston move freely on the way back to the design position. The check valve function of the setup presented in Fig. 4.7 can, for example, be provided by a ball valve, which has to be sized correctly for high flow (unfavorably large ball diameter), or by a spring loaded washer. In the setup shown in Fig. 4.9 the damping element itself has been modified to provide this function. The ring contains on its outer circumference the axial grooves which define the opening area of the end-of-stroke damping and additionally is designed to be axially

Fig. 4.8 End-of-stroke damping grooves

axially

helically

108

4

a) Motion towards end of the stroke

Hydraulic Components Design

b) Motion back towards design position

Fig. 4.9 Floating ring provides check valve function

slidable on the rod. During the motion of the piston towards the end of the stroke the ring slides towards its own end stop which is located, due to the pressure difference, in the motion direction of the piston. Here the ring seals at its front surface and the hydraulic fluid can only pass the path through the axial grooves. The motion is therefore decelerated according to the depth of the grooves. During the motion back towards the design position, the ring again slides on the rod in the direction of the piston motion and now hits the end stop at the piston. Yet this side of the front surface is additionally machined with radial grooves which open up an additional path for the hydraulic fluid through the annular gap between ring and rod into the rod chamber. If the opening area of this flow path is chosen to be sufficiently large, the motion back to design position can be unrestricted, only subjected to the regular fluid damping. Another possibility to create the function of an end-of-stroke damping is given, when a rapidly adjustable damping system and a position sensor are available. If the electronic controller discovers with the help of the sensor signal, that the piston is close to one of its end stops – or will get there soon due to the energetic conditions of the suspension system – the damping element can be adjusted to prevent the system from bottoming out. Since the rapidly and electronically adjustable dampers are usually only used for semi-active suspension systems, the end-of-stroke damping algorithm can be expected to be part of the overall damping logic. Usually end-of-stroke damping has the disadvantage that it adds to the overall length of the cylinder, which is unfavorable especially in tight packaging conditions. That is why cylinder manufactures try to find solutions to avoid additional length. One possible solution is to make use of extendable elements, which, during end-ofstroke damping are reduced in length. Some examples are described in the patents [DE960] and [EP721]. One further possibility to provide an end-of-stroke damping shall be mentioned although it is not commonly used in hydropneumatic suspensions: an axial groove in the inner wall of the cylinder. Here it can only be used for regeneratively operated non hydraulically preloaded systems with a double acting cylinder (see Sect. 3.2.2). The axial groove extends over the portion of the stroke for which the regular damping is desired. Fluid can then flow through the groove from one cylinder chamber to the other. The size and therefore the flow resistance of the groove has a main

4.1

Cylinders

109

influence on the damping behavior in this range. If the piston position exceeds this range, the flow path through the grooves is closed and the fluid must take an alternative path from one cylinder chamber to the other, for example, through the piston. The flow resistance of this path determines the strength of the end-of-stroke damping. This principle is known especially from automotive shock absorbers and is used there especially to create a soft damping around the design position and an increased damping when getting outside of this range [CAU01].

4.1.5 Types of Support Elements It was already mentioned that cylinders usually are not used as guiding elements in suspension systems. Yet a suspension system usually has a 2-dimensional often also 3-dimensional suspension kinematic setup. Therefore the cylinders must be hinged at both ends to avoid unfavorable tension resulting from bending moments or lateral forces. In the simplest case, a pivot bearing is sufficient and it can be designed, for example, as a slide bearing. If a 3-dimensional movement requires a cardanic bearing, for example, a spherical slide bearing or a rubber-metal bushing can be integrated (Fig. 4.10). Independently of the selection of the support element, it is important that the bending moments transferred through the support element are as low as possible since they cause lateral forces in the cylinder’s guiding elements and therefore cause friction. This means especially that the center of the support elements needs to be on the cylinder longitudinal axis as precisely as possible since the slightest eccentricity causes bending moments in the cylinder. In particular, if a sliding bearing is used, the radius of the sliding surface (and therefore the effective radius for its sliding friction) should be chosen as small as possible. From the range of sliding bearings fulfilling the specified durability goals, the type with the smallest possible sliding interface radius should be chosen for lowest cylinder friction. Spherical slide bearing

rubber-metal bushing cylinder bottom boss outer ring rubber inner ring pin

Fig. 4.10 Spherical slide bearing and rubber-metal bushing

110

4

Hydraulic Components Design

Furthermore the selection of sliding bearings should also be focusing on a possibly low coefficient of friction inside the bearing. This means for a steel slide bearing that a regular and sufficient injection of lubricant needs to be ensured. Unfortunately in practice this is not always the case. In particular in suspension systems with many greasing locations (including the mechanical setup) the lubrication intervals are prone to be stretched due to the high effort for greasing. A possible but costly solution for this is a centralized lubrication system, possibly with automatic control. On the other hand there are maintenance free sliding bearings with sliding surfaces made from or covered with synthetic low-friction material with lifetime self-lubricating properties, for example, combinations of PTFE, bronze, graphite etc. For them the best possible protection against external contaminations like dirt, water or chemicals is very important. When the cylinders are used in dirt-exposed areas the use of maintenance-free bearings is only recommended, if a special protection comes with it. Despite this, a certain amount of wear of sliding bearings and therefore the formation of internal play during their lifetime is usually inevitable. Up to a certain amount of wear/play, this is usually not a problem especially if the bearing is permanently loaded in one direction. Since the bearing then always has the same contact surface, the play will not be noticeable. However, if the load direction changes, especially if it changes by 180◦ to the opposite direction (for example, during fast transitions between compression and rebound) the contact surface will also change to the opposite side of the bearing. In this transition of contact surfaces the play of the bearing causes a short period without force. As soon as the inner and outer ring come in contact again, a short force peak is the result. This force peak spreads out into the overall system and can cause damage and/or discomfort if the play is too large and the peak is too high. The play can be completely avoided by the use of rubber-metal bushings. However, since they provide the desired degrees of freedom by the deformation of the rubber, the disadvantage arises that the elasticity of the rubber causes a relative displacement between inner and outer ring of the bushing. This is the main load direction for the use in cylinders and therefore it has to be ensured that the rubber’s deformation limit is not exceeded even at maximum axial load of the cylinder. This can either be achieved by a sufficiently large surface and/or high stiffness of the rubber, or an internal metallic end stop can be designed in to limit the deformation. However if this end stop is active, it will cause friction in the bearing and therefore also bending moments in the cylinder. Due to the elastic properties of the rubber, it is part of the very nature of rubbermetal bushings to create a returning torque when twisted. This can have a negative impact on the cylinder friction, too. Therefore when considering the fatigue endurability and its vibration properties the softest possible bushing should be selected to ensure lowest cylinder friction. Variables are, for example, the shore hardness of the elastomer as well as the dimensions of the bushing and the internal preload of the rubber element. As mentioned in Chap. 1 already, rubber-metal bushings have the positive characteristic to isolate excitations (to a limited extent) which would be otherwise transferred directly into the isolated side. These are especially high frequency, low

4.2

Accumulators

111

amplitude excitations with low accelerations which do not create sufficient forces to overcome the friction forces inside the suspension cylinder. So the rubber-metal element can help to reduce noise transfer on the path through the suspension elements. Another positive thing about rubber-metal bushings is their freedom from maintenance. Since the rubber is only deformed elastically but no relative motion between surfaces takes place, there are no dynamic sealing locations and therefore no possibility for the intrusion of contamination. It has proven to be a major advantage to make use of these positive properties of the rubber-metal bushing in combination with the high load capacity of a maintenance-free slide bearing. This way the rubber-metal element can be laid out very softly (and adds only low bushing torques) and provides the best sealing of the arrangement while the main load is carried by the maintenance free bushing.

4.2 Accumulators

4.2.1 Function and Requirements Accumulators are the element in the hydropneumatic suspension system which provide the elastic medium for the spring function. For these systems almost exclusively gas-filled accumulators are used. Mechanically loaded accumulators (helical spring or mass loaded) are usually not used in suspension systems and are therefore not further explained. In particular, accumulators preloaded by an external mass (basically upright hydraulic cylinders with a mass pushing down the rod) don’t make any sense for a suspension system since they provide a constant pressure independent from the absorbed amount of hydraulic fluid. Therefore the force displacement curve of a cylinder connected to such an accumulator is a flat line. This means no restoring forces are available and no spring rate can be generated. The gas fulfills these requirements for restoring forces: it is compressible and provides increasing pressure with increasing compression according to the laws of gas physics. The characteristic force–displacement curve results from these laws (see Chap. 2). Usually nitrogen (N2 ) is used as the filling gas, in some cases other gases like tetrafluormethane CF4 (R14) are used. Since the enclosed pressurized gas represents a potential hazard, accumulators are subjected to certain regulations such as the German pressure vessel directive and the European pressure equipment directive 97/23/EC. These directives determine, for example, how to lay out and dimension an accumulator for the respective

112

4

Hydraulic Components Design

pressure ranges, what needs to be considered for their production, what the qualification tests should cover and which regular and recurring examinations of the accumulators have to be performed. Since in practice sometimes hair-raising examples of misuse of accumulators can be found and service intervals are sometimes completely ignored, it is very wise that accumulators need to satisfy stringent safety regulations. All maintenance and repair activities performed on a hydropneumatic suspension system require highest caution. A very important basic rule before starting any kind of work, especially when opening the suspension hydraulic circuit, is to release all pressure enclosed in these circuits. This also means that the design has to include the possibility to drain the system. If the system is not drained before opening, major damage can be caused to both people and equipment, for example, by: • • • •

High pressure fluid jet Hot hydraulic fluid Parts, especially accumulator(s), rapidly shooting around Sudden and rapid movement of the suspension and parts connected to it due to sudden pressure changes in the connected cylinder(s)

It was mentioned in Chap. 3 already that all different kinds of accumulators have certain limits with regards to the operating pressure, which depend in particular on the type of accumulator. If these limits are disrespected, in the long run a premature aging and possibly destruction of the accumulator can be the result. Furthermore most accumulators have in common the slow loss of gas precharge pressure due to diffusion of the gas into the hydraulic fluid (see Sect. 4.2.3). This pressure loss can further constrict the operating limits of the accumulator. As part of the regular maintenance this precharge pressure loss must be compensated by refilling gas to the specified pressure level in order to keep the performance of the suspension system. For the refill it is crucial to use the right kind of filling gas specified on the accumulator or in the manual. Carbon dioxide, oxygen or acetylene as commonly found in workshops must not be used! From a designer’s point of view it is a further possibility to permanently connect the accumulator’s gas side connector to an additional gas pressure vessel. This way the amount of gas suspending the system can be further increased which is another possibility and degree of freedom in finding the optimum setup of the suspension. In addition to the geometrical definition by a drawing or a 3-dimensional model, the following short checklist summarizes several important specification features for accumulators used in hydropneumatic suspensions: • Nominal precharge pressure at 20◦ C including tolerance and type of gas • Inner volume of the accumulator, possibly also the deformation limits of the diaphragm • Maximum flow rate (in and out) • Permissible operating pressures can be above system pressure due to suspension motion!

4.2

Accumulators

113

• Temperature ranges (short term, long term) can be above system and above ambient temperature due to the additional heat rejection of damping elements! • Permissible diffusion gas pressure loss at a given pressure and temperature range with a certain number of operating hours (usually the time between service intervals) • If applicable hydraulic pressure losses (for example, if a flow restrictor is integrated into the hydraulic port of the accumulator) • Qualification testing in particular in terms of fatigue endurance: at a certain load spectrum defined for the suspension (as far as possible, should consider high and low flow rate amplitudes and different oscillation frequencies) • General operating and environmental conditions and if applicable the respective protective countermeasures.

4.2.2 Types of Accumulators Basically a gas pressure accumulator is made up of the elements: fluid-side connector, outer shell, fluid/gas-separating element, gas, gas-side connector with cover. Depending on the type of the accumulator these elements are designed differently. The most common types of gas pressure accumulators are illustrated in sketches in Fig. 4.11. It is differentiated between the diaphragm accumulator (a), bladder accumulator (b), the rarely mentioned flexible sleeve accumulator (c) (for example, in [EBE74]) and the piston accumulator (d). The metallic gaiter accumulator (not shown in Fig. 4.11) works similar to the piston accumulator, however without a piston seal, only using the sealing function of the gaiter. In general, the naming of the accumulator already gives information about which element is used to separate the fluid from the gas. Figure 4.11 shows each accumulator with the fluidside connector in the lower portion and the gasside connector in the upper portion of the shell. Furthermore diaphragm accumulators are distinguished into welded and screwed versions. The latter offer more possibilities for the design of the inner contour of the

a Fig. 4.11 Types of accumulators

b

c

d

114

4

Hydraulic Components Design

shell and therefore can provide a better permissible pressure ratio. Additionally, a worn out diaphragm can be exchanged. A detailed description of these accumulators is skipped here since a lot of information can be found in the respective literature (for example, [GAU04] and [FIN06]). Flexible sleeve accumulators are used only in special cases in suspension systems such as the “Nivomat”-suspension of the ZF Sachs corporation (more explanations in Sect. 5.1). Compared to the other types of accumulators, the cylindrical shape of the sleeve fits best into the contour of the strut and therefore allows perfect use of the given design space. Due to their exceptional, rather exotic position, no further information is given for the flexible sleeve accumulators. For hydropneumatic suspension systems, the most important specification accumulator features are, apart from the basic data precharge pressure and inner volume, the permissible pressure ratio and the maximum flow rate. The latter is especially important since the motion of the suspension is often characterized by rapid, shock-type events causing high flow rates. A rough calculation will further illuminate this: A chassis suspension system is given with a suspension cylinder which displaces 0.5 l of hydraulic fluid during a full stroke (rebound end stop to compression end stop). Assuming a frequency of 2 Hz, a full stroke is performed four times per second. This therefore causes an average flow of 2 l/s or 120 l/min. However during a ride over major ground irregularities and over heavy single event excitations the flow rates can be much higher than this if the cylinder is compressed. For a short term, a factor of 2 or more is possible. The accumulators need to be designed accordingly. For diaphragm and bladder accumulators the deformation velocities and therefore strain rates for the elastic material need to be considered, especially at low temperatures where rubber shows brittle behavior. For piston accumulators on the other hand, the permissible relative velocity for the dynamic seal is an important limiting factor. Furthermore accumulators have to be designed in a way so the jets created by high flow fluid intrusion into the accumulator cannot damage any sensitive internal parts such as the rubber diaphragm. Figure 4.12 shows an overview of the characteristic features of diaphragm, bladder and piston accumulators (table created from basic data [GAU04] modified with information from [FIN06], [MAT03] and others). It can be deduced from the diagram data that the bladder accumulators are no option for wide-load-range hydropneumatic suspensions due to their low pressure ratio. Furthermore, the accumulator size required for usual suspension systems is rather at the low end of the bladder accumulator range which makes these accumulators relatively expensive. This is why bladder accumulators are only rarely used in hydropneumatic suspensions. Piston accumulators, too, are rather high in cost and have the additional disadvantage of friction in the piston sealing system. This friction results in a hysteresis of the pressure that is necessary to move the piston of the accumulator. In particular for low-leakage gas-tight sealing systems this pressure hysteresis can be up to 2 MPa [FIN06]. This friction is added onto the friction in the cylinders and worsens the response characteristic of the suspension. Therefore piston accumulators are only sometimes used in suspensions. The piston seal of the

4.2

Accumulators

115

Diaphragm accu. welded

Diaphragm accu. screwed

Bladder accumulator

Piston accumulator

Size [l]

0.2−4

0.1−10

0.2−450

0.5−2500

Max. pressure [bar]

250 (350)

750

1000

1000

Flow rate [l/s]

<150

<150

<140

<400

Max. pressure ratio [ ]

1:(6…8)

1:10

1:4

1:∞

Cost per volume [€/l]

very low

low to average

low to high (depending on accumulator size)

average to high

Response characteristic

Very good

Very good

Very good

Good to reasonable

Small accumulators produced in high numbers for medium pressures, for example, suspension systems, pulsation damping

Small and mid size accumulators with high operating pressure

Large withdrawal volumes, for example, to compensate for power peaks but also pulsation damping in large volume systems

Especially suitable for

High pressure ratios and flow rates, for example, for crash test equipment

Fig. 4.12 Characteristic features for different accumulator types

accumulator must then be optimized for low friction which in consequence usually also improves the permissible piston velocity. This is why usually the diaphragm accumulator is favored for use in hydropneumatic suspensions. It provides a good pressure ratio in combination with the best cost/volume-ratio, especially when the welded version is used. The range of available sizes is sufficient for most suspension applications. Only when the suspended load reaches extreme values, for example, in very heavy off-road vehicles (mining dump trucks) the usual maximum accumulator size of 4 l is a slight disadvantage and several accumulators need to be clustered. Most other applications usually get along with a maximum of two accumulators per cylinder chamber. According to Fig. 4.13 in some cases it can offer a cost advantage to use two small accumulators instead of one large one since the cost/volume-ratio reaches a minimum in the range of the most commonly used 0.75–1 l accumulators. The fluidside connector of an accumulator to the suspension hydraulics can be designed in different ways. A common and widely spread type of connectors are O-ring-ports and stud ends according to, for example, ISO6149 or ISO11926 with male and female thread. Depending on the preferences of a customer the accumulator manufacturers can provide virtually all established types of connectors. The gasside connector on welded diaphragm accumulators is not standardized, however several large accumulator manufacturers agreed upon a certain design and therefore a certain way to connect, check pressure and refill gas. Some other gas

Fig. 4.13 Cost/volume-ratio for welded diaphragm accumulators

4

Hydraulic Components Design

Cost/ volume-ratio [€/l]

116

0

1

2 3 Volume [l]

4

filling systems still exist and sometimes adaptors are needed. It is normal to protect the gasside connector with a screwed on protection cap. In mobile hydraulics, especially in mounting positions with high exposure to dirt/water/obstacles etc. caps made from metal have proven to give better protection than plastic caps since the latter can be damaged or removed easily by environmental influence.

4.2.3 Methods to Reduce Diffusion Pressure Loss A diaphragm accumulator is generally subjected to a loss of gas pressure which results from diffusion (permeation) of the filling gas through the diaphragm into the hydraulic fluid. The rate of diffusion is especially influenced by the type of diaphragm material, the type of filling gas and the size of the diaphragm surface. Furthermore the operating conditions rule the intensity of gas diffusion especially by the temperature and the pressure conditions inside the accumulator. A general rule: The relative pressure loss will be the higher, the smaller the accumulator, the lower the precharge pressure, the higher the temperature and the higher the operating pressure. Findeisen [FIN06] and Korkmaz [KOR82] claim that the relative pressure loss for bladder and diaphragm accumulators is about 1–3% per year at 20◦ C and 6–10% per year at 60◦ C. They mentioned that the pressure loss in piston accumulators is higher, since no hermetic sealing is given and a widening of the accumulator cylinder (steel tube) causes additional gas loss in the dynamic seal. However there are applications where significantly higher pressure losses need to be considered. For example, 30% per year is not unusual when the suspension system is operated frequently (for example, daily 12 h) and in adverse operating conditions. In practice with mobile working equipment, gas pressure losses are related to the operating hours of the system. In lab tests for actual pressure loss or when calculating the theoretical loss, it is necessary to use a load spectrum of pressure and temperature which gets closest to the normal operating conditions. On top of that, for piston accumulators, the movement of the piston is important, too. This way the pressure loss per operating hour can be determined for a particular accumulator in

4.2

Accumulators

117

a particular suspension system. By taking the maximum permissible pressure loss into account, it is possible to calculate the necessary service intervals for the refill of the accumulator. A usual number could be, for example, 1000 operating hours. So the first method to account for diffusion pressure loss is the establishment of service intervals and the refill of gas. When checking the accumulator precharge pressure it is important to drain the complete hydraulic fluid pressure out of the suspension hydraulic system! If this is not done, the gauge will read the system pressure instead of the precharge pressure. If no gasside connector is available, the precharge pressure can be determined quite accurately by reading the pressure decay on the fluidside. This is done by unloading the suspension system and releasing the hydraulic pressure through a flow resistor with constant opening. The change of the pressure over time is monitored. There will be a point when the slow decay (due to the flow resistor) will suddenly increase rapidly and pressure will drop instantly to zero. This last pressure before the fast drop represents the precharge pressure of the accumulator (Fig. 4.14). Of course the same can be done by slowly filling the empty accumulator with oil. Reducing the diffusion pressure loss by further activities can be necessary, for example, due to the following reasons: – The calculated service intervals are too short and do not fit into the maintenance schedule of the overall system. – Bad accessibility of the accumulator makes it difficult to check and refill gas. – It is likely that a short maintenance schedule is not respected, for example, because necessary tools are not always available or due to bad accessibility (see above). This could cause damage to the accumulator or even the rest of the suspension hydraulic system.

pressure

Further methods to reduce precharge pressure loss are related to the design of the accumulator. In particular, the type of diaphragm material as well as the type of gas have a major impact on diffusion. Therefore a suitable change in these design parameters will also lead to a lower diffusion by hindering the passage of the gas molecules through the diaphragm.

initial hydraulic pressure accumulator precharge pressure

start of pressure release

time

Fig. 4.14 Determination of precharge pressure by evaluating fluid pressure decay

118

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Hydraulic Components Design

• On one hand this hindrance can be achieved by confronting the gas molecules with a highly consolidated, close meshed diaphragm material. This is provided, for example, by special types of elastomers as well as multilayer-diaphragms with an interlayer of a diffusion-inhibiting material. • On the other hand a special gas can be used which causes slower diffusion by the very nature of its molecules. Formerly, one reasoning was that gas molecules of larger size just don’t sneak though the gaps in the diaphragm material as quickly as smaller ones do. Today this explanation has been expanded referring to chemical and intermolecular interactions of gas molecules and diaphragm molecules. Anyway it is a fact that, for example, tetrafluormethane CF4 permeates significantly slower compared to nitrogen N2 . However CF4 has been found to be harmful for the atmospheric ozone layer and is therefore not recommended. If one or both of the above design features are implemented, the accumulator becomes a low-maintenance component. Depending on the application, the resulting service interval for refill can get close to the regular lifetime of the accumulator (for example, due to diaphragm wear). Then it makes no sense to refill the accumulator; rather it is better to exchange it directly as part of the regular (long term) service. Since no refill is required, the gasside connector can be omitted and this way cost and design space can be saved. If the diaphragm is not made from elastomer but from a special material respectively a composite material with some metal content, diffusion and therefore pressure loss can be completely avoided. These types of accumulators are then completely maintenance free. One example is the use of a plastic-coated thin metal diaphragm in special shaped accumulators. Furthermore the already mentioned metallic gaiter accumulators are fully diffusion-resistant and have already proven their fatigue endurability in suspension systems.

4.2.4 Integration into Available Design Space Accumulators are comparatively large components of a hydropneumatic suspension. This makes their integration into a cramped system environment quite challenging, especially for example, in mobile applications. However on top of the available design space, other requirements for the right placement need to be considered: • Accumulators should possibly be located in a protected position • The gasside connectors must be accessible for maintenance. • Depending on the requirements for damping, the accumulators need to be located close to the suspension cylinders for low flow resistance of the connecting lines. • If the accumulators are visible as part of the overall system, in some cases it is required that they fit in harmoniously. • Due to the rather high mass of the accumulators, solid and inelastic mounting is necessary to avoid deformation or vibration.

4.2

Accumulators

119

There are two basic types of mountings which are most commonly used: 1. clamping the accumulator on its circumferential surface, for example, by a suitable, round shaped bracket or 2. using the fluidside connector and bolting it to a bracket, control block, cylinder etc. with the help of the thread of the stud end or the port respectively. Solution number one often requires rather complex brackets due to the round contour of the accumulator. In most cases a fastener strap is used which is bent along the accumulator’s contour and fixed in two positions so it presses the accumulator into a bracket on the opposite side. Using the John Deere 6000 tractor’s front axle suspension TLS as an example, Fig. 4.15 illustrates firstly a solution with a fastener strap and a suitable contour integrated into the front end of the tractor’s framework (left) and secondly another solution with a fastener strap and an accordingly bent bracket (right). When the fluidside connector of the accumulator is being used for its mounting, the most popular solutions are: • Screwing the accumulator into a special adapter piece, which is then firmly connected to the main structure of the system. This solution is especially beneficial in case several accumulators need to be connected to a cluster. • Screwing the accumulator into a hydraulic control block. If packaging allows it, this is a very cost-effective solution. The hydraulic control block is equipped with hydraulic connections and ports anyway so additional ports for the accumulators cause little additional effort (Fig. 4.16a). • Screwing the accumulator into a special port directly at the cylinder. Here too, the necessary design space has to be given in this location. This kind of mounting offers the major advantage that the pressure losses are minimized due to the minimized length of the oil path between accumulator and cylinder. This way a setup can be created which offers very low basic damping and/or offers a wide range of possible damping for the tuning of the system (Fig. 4.16b).

Fig. 4.15 Clamping of the circumferential surface

120

a)

4

Hydraulic Components Design

b)

Fig. 4.16 Direct mounting via fluidside connector. (a) On a hydraulic control block. (b) On a cylinder

• Dropping the accumulator’s fluidside connector through a hole in a mounting plate and locking it with a special nut from the opposite side in the style of a bulkhead fitting. The accumulator needs to have a suitable connector to enable this. In particular, sufficient thread length must be available. This solution too can be very cost-effective.

4.3 Flow Resistors As already mentioned the necessary lines and fittings between cylinder and accumulator contribute to the damping of a hydropneumatic suspension. Their share can be called non-adjustable damping or basic damping. It is recommended that for a high flexibility of the suspension tuning, their share is below 100% so the rest of the damping can be created by one or more additional flow resistors, which can allow a selectable restriction and therefore selectable damping. This section explains the possibilities for the provision of selectable damping to complement the basic damping of the system.

4.3.1 Non adjustable Orifices and Throttles

4.3

Flow Resistors

121

The different characteristics and properties of those two basic types of flow resistors have been extensively illustrated in Chap. 2. They are the simplest possibilities for generating a pressure loss and in this way increase damping forces. Both components can be integrated into the system in different ways. If the amount of damping and therefore the size of the necessary flow resistor is already predefined, one of the most simple and cost effective solutions is to make the flow resistor part of one of the already existing components. All components on the path between cylinder and accumulator can be used for this: for example, the cylinder itself, the accumulator itself, the fittings in between and (if also in the path) the leveling control block. The integration into tubes and hoses would be possible as well, but is rarely done, since expensive special components would have to be used instead of the low cost standard components (the same is sometimes true for the fittings). Figure 4.17 shows examples of how the flow resistor can be made part of the already existing components. In other cases it is favorable to keep the possibility to change the flow resistor as needed. One reason could be because the system is still in the test and evaluation phase, another reason could be that the same hydropneumatic system is used for different variants (and masses) of the system and needs to be tunable to each of those variants. For this case it is recommended to use exchangeable flow resistors. They can be screwed in some other component or maybe only dropped in and secured with a snap ring. Favorable locations for exchangeable flow resistors are especially fittings and ports/studs. Figure 4.18 shows different possibilities for integration into a straight hydraulic coupling. When designing a flow resistor, it is essential to keep in mind that these can be subjected to very high hydraulic flow forces during the operation of the suspension. They arise from the high pressure losses generated by these components. Therefore they have to be designed and sized accordingly to avoid distortions or displacements which can have a negative influence on the flow behavior. Thread lengths and snap rings need to be sized sufficiently; supporting and guiding surfaces need to be large enough to withstand the arising forces.

Fig. 4.17 Flow resistors as part of other components

accumulator

fitting

122

4

a) Screwed in

b) Dropped in and secured

Hydraulic Components Design

c) Inserted

Fig. 4.18 Integration of exchangeable flow resistors

When trying to find the optimum setup of the suspension damping, it is essential to place the exchangeable flow resistors possibly in the same location as planned for the final product. Furthermore, the basic design of the resistors, too, should be as close as possible to the planned final design. In many cases the flow conditions are quite complex and the behavior of a flow resistor would be quite different if it is positioned differently in the flow path. It is also due to this complex flow condition and on top of that due to the two different flow directions that the use of laws and values given for ideal flow conditions, such as the flow coefficient αD and the pressure loss coefficient ζ, is severely limited. Lab tests and/or experiments with the complete system under real operating conditions are therefore indispensable. A good way to define a flow resistor (for example, to a supplier) is by the required pressure loss vs. flow curve. If this is not possible it needs to be defined by its geometry. Some of the most important specification features are: • dimensions of the cross-sectional constriction and of the cross-section before and after the constriction • Tolerances: need to be very low for low variation of restriction • Edges in the flow path: free of burrs, possibly detailed definition of edges • Maximum flow rate: accounts for flow forces onto the resistor and correct structural design (sizing of the wall thicknesses etc.). Especially important if flow resistor is made from low strength material.

4.3.2 Flow Direction Depending Resistors This type of flow resistor is necessary if the damping during the compression and rebound phase needs to be on different levels. As already mentioned, the rebound damping is usually chosen to be higher than compression damping, often with a ratio of about 2:1–3:1. This is achieved by different flow paths for the respective flow directions. When utilizing standard hydraulic components this can be done by arranging two flow resistors parallel to each other, both connected to the

4.3

Flow Resistors

123 WZ

WD,zus rebound (higher resistance)

compression (lower resistance)

Fig. 4.19 Simple hydraulic circuit for a direction depending resistor

flow path between cylinder and accumulator. A check valve assigned to one of the flow resistors then creates different flow situations for the different flow directions (Fig. 4.19). For the rebound phase, the hydraulic fluid can take only the path through the first flow resistor WZ since the fluid flow through the alternative, parallel path with flow resistor WD,zus is blocked by the check valve. For the reverse direction, the compression phase, the check valve gives way to the hydraulic fluid so it can flow through both flow resistors and therefore can pass the hydraulic damping circuit with a lower pressure drop compared to the rebound phase. This kind of hydraulic circuit is, for example, used in the damping control block of a hydropneumatic suspension for the front ballast weight of a tractor. In this special case the second flow resistor is even made adjustable to make the system adaptable for different sizes of weights. It is essential that the check valve is designed for this type of permanent operation. Since the suspension is working permanently and, for example, assuming a natural frequency of about 2 Hz, the flow direction changes four times per second, it is easy to see that the number of load cycles for the check valve is extremely high. It is also possible to assign another check valve to the first flow resistor WZ thus separating flow paths for the different flow directions completely. However, on first sight, no real benefit can be found in this since another component only adds cost and complexity while both setups can fulfill the same requirements. When taking a closer look, having a second check valve can be beneficial if flow rates are generally low and the flow resistors needed to be sized very small and therefore would be difficult (and expensive) to produce. Another elegant way of implementing direction depending flow restriction is by setting up a hydraulic damping circuit similar to the damping pistons in standard vehicle suspension damping units (Fig. 4.20). On top of direction-dependent damping, they allow variation in the characteristic behavior of pressure drop vs. flow rate. Damping pistons are well known and a lot of literature is available to get more insight ([CAU01], [KOC], [MUR98] and [REI89]). Looking at design details, damping pistons can be laid out in many different ways. However the characteristic feature, which is typical for most of them, is a general separation of the flow paths for compression and rebound direction in combination with a pressure relief valve function. From a hydraulics point of view, a damping piston system can be illustrated as shown in Fig. 4.21. Depending on the

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shims inlet bores piston shim seating surface outlet bores

Fig. 4.20 Damping piston [KOC]

piston chamber piston

cylinder wall piston rod rod chamber valve arrangement rebound (left)

valve arrangement compression (right)

Fig. 4.21 Example for a hydraulic schematic of a damping piston

application and the setup of the piston, the arrangement of the check valves, the throttles/orifices and the pressure relief valves can differ from the illustration. The function of the pressure relief valve is provided by so called “shims”. These are flexible, thin, round pieces of metal and are available in many different diameters and thicknesses. They are stacked onto the piston covering certain passage bores in the piston, eventually by additional use of spacers. By covering these bores they shut off the oil flow in a certain direction, however, due to their flexibility, letting it pass with the function of a pressure relief valve in the other direction. The characteristic of this pressure relief valve function can be fine tuned by a suitable choice of shims and spacers. For a vehicle suspension it is often a goal to generate a relatively high p already at low flow rates in order to provide a good feedback for the driver about what is going on in the interface between road and vehicle. On the other hand the p should not rise too high at higher flow rates (caused by major road irregularities) to maintain a good level of comfort for the passengers. This cutting off

4.3

Flow Resistors

125

in the characteristic curve is provided by the pressure relief valve function (please refer to Sect. 2.3.2 in particular Fig. 2.32). Instead of simple disks, for example, star-shaped preload elements, or, if rather high preload is required, spring discs are commonly used. The sealing function and the flexibility of the shims can also be provided by a rigid, thicker shim which is pressed onto its seating surface by a helical coil spring, if enough space is available. This arrangement too acts like a pressure relief valve. The technology of the damping piston for the hydropneumatic suspension can be adapted relatively easily. Basically it is necessary to take the hydraulic function of the damping piston and place it in the flow path between cylinder and accumulator. Accommodating it in a dedicated, new component is possible, but, from a packaging point of view, also the integration of such a system, for example, into the accumulator or the cylinder, can be beneficial. By sizing the above described components (shims/spacers/springs, throttles/ orifices, bores/gaps etc.) the characteristic of the pressure drop vs. flow curve can be shaped (see also Fig. 2.32). The initial rise of the pressure-flow curve, when starting from zero flow, is mostly defined by the possibility for the hydraulic fluid to bypass the pressure relief valve, thus flowing directly through other available crosssectional area. The latter is indicated in Fig. 4.21 by the throttles in the piston. This behavior at low flow rates (low-speed behavior) can therefore be altered by changing the size of the directly connecting throttles/orifices. The gradient of this part of the pressure-flow-curve gets lower, as the respective flow restrictor widens. With increasing flow rate the curve flattens out at a certain point. This is caused by the opening of the pressure relief valve. If the pressure drop across the throttle/orifice reaches a certain value, the pressure on the first shim reaches the cracking point and the shim starts to lift from its seating surface and lets hydraulic fluid pass through the gap. This cracking point is especially defined by the preload on the shim. The higher the preload, the higher the cracking pressure will be. If the flow keeps increasing, the gap between the shim and the seating surface will open up more however depending especially upon the shims’ flexibility and on whether other shims have been arranged (possibly with the help of spacers) which hinder the free flexing of the first shim. It is especially these two parameters which influence the further course of the curve and determine the high-speed behavior. It has proven in practice that different flow restrictions for the different flow directions can also be generated by only one throttle/orifice which is subjected to different inflowing conditions for both directions. For example, a flow resistor could be subjected to a straightforward, linear flow of hydraulic fluid from one direction but is assembled just after a 90◦ flow deflection when passed from the other direction. This will result, at the same flow rate, in different pressure drops for the different flow directions. Experiments will show what needs to be done to create the required ratio of both pressure drops. However this is a very sensitive system with little forgiveness for dimension tolerance. Slightly different diameters, edge properties, resistor positions can result in a major change in flow conditions and therefore also pressure drop.

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Hydraulic Components Design

4.3.3 Adjustable Flow Resistors Hydropneumatic suspension systems have particular advantages for applications with a wide range of suspended load. The reason is the possibility to quickly readjust the level and furthermore the spring rate, which automatically adapts to the suspended load. Due to the variation of the oscillating mass, the energy stored in this oscillation also varies. So especially for wide variation it is recommended to also adjust the means for dissipation of oscillation energy. An adjustable damping therefore offers advantages in the oscillation behavior in all loading conditions. With regards to especially speed of adjustment, there are basically three different types of damping adjustment: 1. Manual damping selection: a person, usually the driver, selects the desired level of damping by adjusting some kind of control (for example, mechanical knob or electronic switch) which then changes the damping by changing the properties of the flow resistor(s). 2. Automatic, slow adjustment (adaptive): the suspension system automatically chooses the suitable damping. This can be done mechanically, for example, by using the load-dependent pistonside pressure as the control signal for the damping element or electronically by evaluation of sensor signals and electric adjustment of the damping element (stepper motor, solenoid etc.). The system reacts slowly and chooses a damping suitable for the general operating condition, for example, with a damping level decision based upon the average value of the last 60 s of the sensors inputs. 3. Automatic, fast adjustment (semi-active): the damping adjustment reacts in realtime to the requirements of the external excitations and operating conditions with the help of fast sensors, electronic controllers and rapidly adjustable damping elements. This type of system allows amplitude and frequency selective damping. For example, it can absorb a short but very fast bump by a short-term opening of the damping valve thus providing lower accelerations on the isolated side compared to the above mentioned simple suspension systems. The challenge with these systems is to find the right control algorithms to get the most out of this new technology. An older, but interesting summary of adjustable dampers can be found in [HEY88]. It is interesting and encouraging to see that some of the systems claimed to be in development at that time are today in serial production ([ATZ08], [HAR04], [MIL07]). 4.3.3.1 Types of Adjustable Resistors For adjustable flow resistors it is an essential requirement that it has only a low pressure loss in fully opened state, even when subjected to the high peak flow rates arising in suspension systems. This ensures a wide operating range of the component. On the other hand, the flow resistor should not be chosen to be too large

4.3

Flow Resistors

127

because resolution in adjustability would be lost. The right sizing therefore is very important. Depending on the way the adjustment is applied to the flow resistor, they can be distinguished in the translational and the rotary type. For flow resistors used as damping elements for suspension systems, it is usually of minor importance to be completely leak-free. Therefore the general setup could be a spool design as well as a poppet design. For flow resistors with translational restriction variation elements, probably the simplest and most common design is the needle valve which is adjustable by a threaded spindle. Moreover there are, for example, flow resistors with a longitudinal notch in a spool or with a slot throttle. Figure 4.22 shows these different designs [according to [FIN06] and [EBE74]). The ball valve is probably the best known design of the flow resistors with rotary restriction variation elements. Furthermore there is, for example, the throttle with adjustable circumferential gap on the outer shape of a cylinder (Fig. 4.23). There are variations and combinations of these two types available which are not explained here. The different types of designs differ mainly with regards to the viscosity- and temperature-effects, the fine adjustment, the applicability for low flow rates and the necessary adjustment forces ([EBE74], [FIN06]). The already mentioned hydropneumatic suspension of a front ballast weight uses a manually adjustable needle valve. A small taper angle and a low thread pitch enable a relatively fine adjustment of the flow restriction. This way the damping can be adjusted to the mass of the suspended weight(s). Needle valves are often used for the adjustment of pre-opening and therefore low-speed damping. An example is the suspension struts for motorcycle’s rear wheel suspensions. If different flow paths exist for compression and rebound oil flow, two needle valves can be integrated for separate low-speed adjustment in both directions [KOC]. If, as often the case, the high-speed damping is also made adjustable, this is

needle

longitudinal notch

slot throttle

Fig. 4.22 Variable flow resistors with translational restriction variation elements

Fig. 4.23 Variable flow resistors with rotary restriction variation elements

ball

circumferential gap

128

4 1

Hydraulic Components Design

1

hose from strut to reservoir

2

high-speed valve housing with spring loaded valve

3

adjustment screw high-speed

4

adjustment screw low-speed

4

5

low-speed valve housing with needle valve

5

6

floating piston with seal between hydraulic fluid and gas cushion

7

12bar nitrogen gas cushion

2 3

6

7

Fig. 4.24 Combined low-speed and high-speed adjustment [KOC]

achieved by the adjustment of the preload of the spring for the pressure relief valve: the higher the preload, the higher the high-speed damping. In many cases it is sufficient to make only the compression direction adjustable in high-speed damping since, during rebound, the damping is mostly in the low-speed or intermediatespeed range. Figure 4.24 shows a combined low-speed and high-speed damping adjustment for the compression phase, integrated into the expansion reservoir of a motorcycle strut. It is important to consider that a change in low-speed damping will also affect the high-speed damping since the low-speed throttle is still open in the high-speed range. 4.3.3.2 Activation of the Adjustment A manual, mechanical adjustment is usually performed by turning an adjustmentscrew in the damping element (see Fig. 4.24). Remote mechanical adjustment is possible, for example, by attaching a lever to the screw and actuating it with the help of a Bowden cable. If the damping element is adjusted electrically, two possible drives are the solenoid and the electric motor, typically a stepper motor. The latter is suitable, in particular with the right electronic controls, for a continuous, stepless and rather slow adjustment. On the other hand the solenoid is better suited for fast adjustment, but with steps in damping (if it is not a proportional solenoid).

4.3

Flow Resistors

129

It is essential that the flow forces do not influence the setting of the flow restriction variation element (increase or decrease cross-sectional area). Therefore it is beneficial to design these elements in a way so they are possibly force-free in the direction of adjustment. Since this is not always possible, it is necessary to connect a large enough actuator with enough retention force. But also the fluid flow forces acting on the restriction variation element in directions other than the direction of adjustment are important; they can cause significant friction forces which then require a strong actuator for the change of the elements position. Yet in this context suspension systems have the major advantage that there are regular moments of zero flow (in the reversal point of the piston motion) and therefore also moments of minimal, sometimes zero fluid forces. Due to its limited speed of actuation the electric motor is rather used for adaptive damping adjustment while a solenoid actuation, if proper components are chosen, is also suitable for a semi-active damping adjustment (Fig. 4.25). It is important for any kind of adjustable damping system, in particular for vehicle suspension systems, that incorrect operation or malfunction (for example, of the controller) automatically brings the system into a fail-safe mode. In this mode the damping must be high enough to provide sufficient damping for any possible condition and therefore ensure safe operation. The increase of accelerations on the isolated side needs to be accepted in this case. In vehicle suspensions this has the positive effect that it indicates to the driver that something is not working properly and needs to be checked. This is the background for the common requirement that the restriction variation elements need to be in a high-damping position when unenergized.

two-stage

stepless

Fig. 4.25 Semi-active damping adjustment by solenoid forces (according to [MUR98])

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Hydraulic Components Design

4.4 Hydraulic Lines and Fittings 4.4.1 Function and Requirements The different components of a hydropneumatic suspension system are usually not located directly side by side but are often separated due to, for example, local design space restrictions or due to the setup of the system (e.g. one leveling valve or one accumulator assigned to two suspension cylinders). The hydraulic lines and fittings enable the connections of the components according to the hydraulic schematic. Lines for hydropneumatic suspension can be distinguished into three general functional areas: 1. Suspension circuit lines between suspension cylinders, accumulators, damping elements: these lines need to handle the high flow rates of the hydraulic fluid which is moved back and forth during the oscillation of the suspension. 2. Control circuit lines between the suspension circuit and the hydraulic control block for level control and, if applicable, also the preload pressure control: these lines only conduct the hydraulic fluid which is necessary for the readjustment of the suspension’s design position or the readjustment of the preload pressure respectively. The flow rate here is significantly smaller than the flow rate in the suspension circuit (factor of 20 and more). 3. Supply lines between the control circuit and the fluid power supply system: these lines provide or dispose of the hydraulic fluid which is requested or released by the hydraulic control block during a control event. The suspension circuit lines are of highest importance since the hydraulic fluid in these lines is in permanent motion and their flow restriction effect has a direct influence on the behavior of the suspension. Due to the high flow rates and because the basic flow restriction by lines should be kept low, the diameter of these lines should be chosen to be as large as possible. Since the fluid guiding elements, in particular the tubes and hoses, have a mainly throttle-type flow resistance, their influence on damping is very strongly dependent on fluid viscosity and (usually) therefore fluid temperature. So it is especially important for suspension systems in applications with low operating temperatures to pay special attention to low flow resistance of the lines. Otherwise improper suspension function would be the result. Since suspension cylinders are often mounted to be moveable relative to the other components of the suspension system and the main structure, their hydraulic connection needs to be flexible. Therefore usually hoses are necessary. During the operation of the system, these hoses are subjected to permanent alternating bending moments. This cyclic loading needs special consideration when selecting the right types of hoses. It is an everlasting clash in goals that the maximum operating pressure of a hose increases with the number of steel layers in the hose wall, however flexibility decreases and higher flexing strain will result. It is also important for the selection of the necessary component dimensions that a sudden rupture of a line in the suspension circuit leads to sudden high loss of

4.4

Hydraulic Lines and Fittings

131

hydraulic fluid and therefore hydraulic pressure. Apart from the hazards caused by hot oil or a high-pressure fluid jet, such a failure leads to a more or less instant malfunction of the suspension system. In particular, for a vehicle axle suspension system this will have negative impact on ride comfort and driving safety. The use of the commonly known hydraulic burst pipe protection circuits is difficult for most suspension circuits, therefore it is recommended to use a higher safety factor for the calculations and apply aggravated test conditions for laboratory and field tests. For the same reason, the suspension circuit lines need to be designed in a way so the hazard of an excessive load due to external conditions can be minimized. These are, for example, adverse environmental conditions (an example are off-road rides through rough terrain) as well as the misuse by the operator – this could be, for example, the use of a horizontally routed steel line as a foot step or the use of a tube as a supporting point for a lever. Although gross misuse can never be fully excluded, it is better to try to avoid these kinds of hazards already in the planning phase for a system. The control circuit lines are often quite short or sometimes don’t even exist if it is possible to locate the hydraulic control block directly next to or as part of the suspension circuit. The control circuit lines can be connected generally to any position and component of the suspension circuit; the effect of the adjustment of level and/or preload pressure will in most cases be the same. Only if rather small or special flow restrictors for damping purposes are located between suspension cylinder and accumulator is it necessary to consider their effect onto the control system. In this case it is often better to place the connection point between the damping flow resistor and the cylinder to get a more direct response from the suspension circuit to the fluid flow from the control circuit. If the control circuit lines are rather long, a sufficient flow cross-section needs to be chosen due to the high pressure drop in small diameter lines at high fluid viscosities/low temperatures. A reduced leveling speed at low temperatures is often not acceptable. The latter is also true for supply lines. These are often quite long since hydraulic pump and hydraulic reservoir are in many applications located remotely from the suspension system. In particular, on large equipment line lengths of several meters are not unusual. Anybody who has ever tried to stir regular hydraulic fluid in a cup at a temperature of –20◦ C can imagine how difficult it is to force this highly viscous fluid through long lines with a small cross section. In particular when the hydraulic power is supplied by a load sensing system, it is important to consider that a load sense line with a too small cross section can not only slow down the leveling process but can completely suppress it. Depending on the setup of the loadsense hydraulic system, a certain flow is always present in the loadsense line. This causes a certain pressure loss in the line which needs to be subtracted from the original loadsense signal sent out by the suspension control block. If this pressure loss in the loadsense line exceeds the pressure margin, the hydraulic power supply does not generate enough pressure to pump hydraulic fluid into the suspension circuit. In addition to the definition by a drawing or a 3-dimensional model, the following short checklist summarizes several important specification features for lines in

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Hydraulic Components Design

suspension systems, in particular, in the suspension circuit (additional to common hydraulic lines specifications): • Permissible minimum bending radius for hoses: due to the relative motion of some suspension components (cylinders) the actual bending radius has to be checked in every position of the suspension, design position only is not sufficient. • Temperature ranges (short term, long term): can be above system and above ambient temperature due to the additional heat rejection of damping elements. • Qualification testing, especially endurance test according to a special load spectrum, if applicable also with superimposed cyclic mechanical loading (bending, torsion, etc.).

4.4.2 Required Flow Cross Section A first sizing of the required cross section of the flow path can be done with the help of the recommended maximum flow velocity. This recommendation is based upon a possibly laminar and therefore low-loss fluid flow and is furthermore related to the pressure range for the particular system (Fig. 4.26). For hydropneumatic suspension systems this rule for the layout applies especially to the control circuit lines as well as the supply lines. The equation for the sizing of the inner line diameter is then in general: di =

(4.1)

return line

inner line diameter

suction line

4Qmax π vzul

pressure line

flow rate

Fig. 4.26 Sizing of the cross section of tubes and hoses (according to [FIN06])

4.4

Hydraulic Lines and Fittings

133

For suspension circuit lines very high flow rates are generated at high excitations on the input side, for example, when a vehicle rolls over a high bump in the road surface. If the line size was chosen according to this maximum flow rate, its diameter would become very large. Apart from the problem of accommodating lines of this size (also keep the bending radii in mind!) this would add drastically to the cost, too. Therefore a significantly lower flow rate is usually used for the calculations. It represents the regular use piston velocities of the suspension system. It is then accepted that the lines are somewhat undersized for the above mentioned rather seldom maximum flow rates. An example: Assuming a suspension system which generates a flow rate of 120 l/min at its maximum compression piston velocity. Assuming furthermore that the system works in the pressure range of 10–20 MPa, the necessary inner line diameter would be 21 mm according to the diagram in Fig. 4.26. However if the same calculation is done at 40% of the maximum flow rate (48 l/min) which represents a regular, very high piston velocity, the required inner diameter drops down to 13 mm. Cost effectiveness and design space issues are then often preferred over getting the last few percent of improvement in suspension performance.

4.4.3 Tubes When it comes to the decision for the type of fluid link, in particular for a system with exactly specified geometry, the general rule is: tube beats hose! Tubes have numerous advantages: – High strength material offers small dimensions, in combination with relatively small bending radii this offers the optimum use of the available design space – Exactly defined, clear routing, brackets hold the tubes in place – High reliability, rarely any leakage – Very good fatigue endurance compared to hoses – Better cost-effectiveness compared to hoses, especially for high annual volumes. However there are some disadvantages: – Low flexibility: especially rather short tubes with high wall thickness and diameter offer little forgiveness to production tolerances and therefore require a smaller tolerance band. – A change in design space and packaging results in a higher effort for the design changes (a hose could possibly still be used just with a slightly different routing). – Difficult handling of long tubes, especially transport, storage, assembly and service parts shipping. Tubes are available in different diameter levels. Important: the specification of the tube dimensions contains always the outer diameter and the wall thickness. This means that the hydraulic engineer needs to first calculate the more important

134

4

Hydraulic Components Design

inner diameter from these values. In general a hydraulic tube is made from steel. It must have good deformation properties to enable bending also for tight radii. The dimensions of the tube in combination with the material properties allow the calculation of the nominal working pressure (pressure rating) for a specific tube. The table shown in Fig. 4.27 (according to ISO 10763) summarizes the nominal working pressures for different tube dimensions. Similar tables are also available for inchsized tubing according to, for example, SAE J524, SAE J525, SAE J526 and SAE J536. Usually the nominal working pressure is calculated to be 25% of the burst pressure. Usually, tubes are not used in their originally produced straight form but need to be bent to fit in the design space. The wall thickness of the tube decreases at the outside of a bend, while it increases at the inside. This is the more distinct, the smaller the bending radius. In practice, certain minimum bending radii have been established for certain tube sizes. Although the wall thickness decreases at the outside of a bend, the high strain is on the other hand advantageous since it increases the yield strength of the material by strain hardening in this area. This again helps to improve fatigue endurance. If unclear, a test with dynamic alternating pressure load must provide the information whether a selected tube in combination with a certain bending radius is suitable for an application. In particular, the specific pressure levels caused by permanent motion of the suspension need to be considered for the load spectrum. Please remember again that, due to the nature of the hydropneumatic suspension, these pressures can be higher than the system pressure supplied by the pump! For the optimum use of the available design space one would tend to choose the bending radius to be as small as possible. But from the fluid flow point of view it is always the largest bending radius which provides lowest addition flow resistance. As is often the case, here too it is necessary to find the best possible compromise.

wall thickness

Tube outer diameter [mm] 6

8

[mm]

10

12

15

16

18

20

Nominal working pressure [MPa]

0.8

27.9

20.1

15.7

12.9

10.2

9.5

----

----

1

36.5

25.9

20.1

16.4

12.9

12

10.6

9.5

1.5

62.4

42.3

32.1

25.9

20.1

18.7

16.4

14.6

2

98.9

62.4

46

36.5

27.9

25.9

22.6

20.1

2.5

----

88.3

62.4

48.5

36.5

33.7

29.3

25.9

3

----

----

----

62.4

46

42.3

36.5

32.1

Fig. 4.27 Table for the selection of tube dimensions [ISO 10763]

4.4

Hydraulic Lines and Fittings

135

The tube manufacturer often provides tubes for hydraulic applications with zinc plating as corrosion protection. A high-quality zinc layer will withstand the bending process. Connectors at the ends of the tubes can be hard-soldered or welded. In these cases the original zinc plating is damaged and therefore the assembly has to be re-plated in these areas to provide full corrosion protection. Since these processes are rather elaborate, in the last decade it became more and more popular to use tube end connections which do not damage the original zinc plating. Please read more in Sect. 4.4.5. The mounting of tubes is often done with the help of plastic clamps made from, for example, PA66 GF30, in other cases with steel clamps with a thin rubberlike plastic layer (applied by dipping the steel part into the liquid plastic). In particular, tubes which are prone to oscillations, for example, coming from the hydraulic system, should be clamped with elastic elements. This reduces the transfer of structure-borne vibrations into other, maybe larger components and therefore reduces noise. Speaking of vibration loads on the tube, there is one more important thing to know: it is essential to avoid that a steel tube touches another component, especially when made from rubber or plastic. Although the steel is the stronger one of the two interfering parts, it will be worn in the long run. The reason is that abrasive dirt particles will settle into the plastic surface and wear off the metal slowly but steadily. Therefore a protective sheathing for the steel tube might be necessary if contact cannot be avoided.

4.4.4 Hoses Compared to tubes, hoses have some particular advantages, which are the reason why they are preferred in special cases: • Connection of hydraulic components with motion relative to each other • Flexible line routing can quite simply be adapted to new circumstances and does not require narrow tolerances for the dimensions of the connected components • One hydraulic component on one side can be connected alternately and selectively to several other components on the other side with one and the same hose • Reduced transfer of hydraulic pressure peaks and mechanical vibrations However the disadvantages are more than obvious: • Suboptimal usage of the available design space due to high bending radii and large wall thickness • Flexibility is also a disadvantage since no predefined routing is possible, hoses tend to take their own route and need to be clamped frequently otherwise they tend to contact other components especially in a tight packaging. Slight exception: preformed hoses for low pressure applications • Lower reliability due to many possible points of failure (especially leakage)

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4

Hydraulic Components Design

• Limited fatigue endurability of partly organic hose material especially in harsh environment (ozone, UV-radiation, chemicals etc.) • Higher cost compared to tubing especially at high annual volumes Hoses are available in various nominal sizes, for example, in metric sizes of 5, 6, 8, 10, 12, 16 mm etc. in inner diameter. Therefore they offer less variability compared to tubes which have on top of the nominal size the wall thickness which can be varied. This brings us to the major difference in the specification of a hose compared to a tube: the nominal size of a hose refers to the inner diameter whereas the nominal size of a tube refers to the outer diameter. A hydraulic hose usually consists of at least three different layers: the inner lining, the reinforcement layer(s) and the external layer. The inner lining consists of an elastomer or a thermoplastic elastomer, which needs to have the necessary resistance against hydraulic fluids. Furthermore it needs to withstand flow forces and fully seal the hydraulic fluid from the reinforcement layer(s). This reinforcement provides the necessary mechanical resistance to the pressure inside the hose and usually consists of one or more layers of textile or metallic braid or helically wound wire, depending on the pressure rating of the hose. The external layer usually consists of a special rubber blend and acts as protection especially for the reinforcement layers from external loads such as mechanical stresses or aggressive substances/UV-radiation. It is easy to understand that the different types of reinforcement layers have a major influence on the flexibility of the hose. The characteristic parameter describing the degree of flexibility is the minimum permissible bend radius of the hose. The more reinforcement layers and the stiffer the reinforcement material the less flexible is the hose. Furthermore the nominal diameter of the hose also has a major influence. It is especially important for hoses with large diameters and low inner pressure that they do not buckle when routed according to the intended design. On one hand, buckling leads to damage in this particular area; on the other hand it reduces the inner cross section and therefore increases the flow resistance of the hose. However, a hose assembly does not only consist of the (bulk stock) hose itself but also of the connection parts at both ends of the hose: the hose fittings. For high-pressure hoses usually crimped fittings are used. In this technology the actual connection piece, the nipple, is pushed into the hose end. Then a socket is slid over the overlap area of nipple and hose and is then deformed plastically so its diameter decreases and is clamped onto the hose. During this crimping process the hose, too, is compressed onto the nipple. The high contact pressure in combination with the saw tooth-like outer shape of the nipple provides a positive locking of nipple and hose. A similar saw tooth shape on the inner surface of the socket positively locks onto the outer surface of the hose. Socket and nipple are furthermore positively locked and all these connections ensure that the hose assembly can withstand the axial forces between nipple and hose generated by the internal hydraulic pressure (Fig. 4.28). Similar fittings are available with a screw-on style socket which offers the advantage of being reusable and the hose can be exchanged when damaged.

4.4

Hydraulic Lines and Fittings

137 socket hose

connector side

nipple

hose side

Fig. 4.28 Crimp-connection of a fitting for high-pressure applications

However they are more expensive and the assembly is more time consuming which is why they are usually not used in high volume applications. The details and rules for correct routing of hoses are not explained here; this is already extensively described in the available literature (for example, [FIN06], [EBE74], and [MUR01]). More information about selection, storage, use and maintenance can be found in ISO8331. However some additional hints from practical experience are given with special regards to hydropneumatic suspension systems: 1. During operation the hose is stretched and settles back with the amount of internal hydraulic pressure. This deformation does not only relate to the increase of the hose diameter but also to the change of curve shaped by the hose axis, especially for 3-dimensionally routed hoses. In particular, the hoses of the suspension circuit are permanently subjected to pressure variations and are therefore permanently more or less in motion. The hose deformations can result in interference of the hose with other components that seem to have sufficient clearance in the non pressurized state. 2. The contact of the hose to edges of other parts has to be absolutely avoided. This is the more critical, the sharper the edge and the more the hose is in motion (see above). This dynamic contact to sharp edges can sooner or later lead to a completely worn external layer of the hose which means that the reinforcement layers are exposed to the environmental conditions without protection. Wear and/or chemical decomposition (corrosion) of the reinforcement wires/fibers can lead to a weakening and consequent failure, usually a leakage, of the complete hose. If such conditions cannot be avoided, an additional protection is necessary for the external hose layer. For example, other hoses with larger diameter can be used which are slipped over the actual hydraulic hose. There are also special fabric hoses available made from, for example, aramid fibers. In certain cases even heat shrinkable tubing can be used, but keeping the stress concentrations at its ends in consideration. Furthermore there are helical metallic coils available which are clamped onto the socket of the crimped fitting. Although the readily available simple plastic spirals have the advantage of allowing installation even after crimping the hose, they cannot be recommended for protection against sharp edges.

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4

Hydraulic Components Design

3. In order to keep the hoses on the design-intended path, they need to be guided by other dedicated elements. A direct clamping of the rubber hose’s external layer, for example, with plastic clamps is not recommended. If such a rigid guidance is necessary, a metal sleeve could be crimped onto the hose and the plastic clamp then grabs the metal surface. Very often hydraulic hoses are guided rather loosely, which leaves a certain amount of axial degree of freedom. It is especially important that these guiding elements have no sharp edges. This then allows the hose to follow its natural deformation during pressure variations, however with the guidance on the desired routing path. 4. In particular, hoses with metallic reinforcement layers are delivered slightly prebent to the customer due to the hose production process with subsequent coiling up and storage as a roll. For example, if a hose with two steel reinforcement layers is cut to length from the roll and then put on the workbench, it will not remain straight but remember its curvature during storage on the roll and try to return to this position. This effect must be considered or can even be used for better and easier routing and assembly. It needs to be specified in the drawing particularly when the hose has elbow fittings and therefore is fixed in a certain position once crimped (hoses with straight fittings at both ends can still be rotated relative to their axis). The routing of hoses with their more or less defined routing path and position needs a lot of experience. Long-standing experts have definite advantages here. Especially in crammed design spaces, trial fits are necessary to ensure a proper design (hose lengths, fitting’s angular position etc.). Purely virtual routing with the help of CAE tools is often insufficient due to the above mentioned peculiarities.

4.4.5 Fittings Fittings are used as short connection pieces between tubes, hoses and other hydraulic components (for example, pumps, cylinders, control blocks etc.). They provide the function of an adapter between the connection (port) on the hydraulic component on one side and the connector of the hose or tube on the other side. One of the most popular connection types on hydraulic components is a (female) threaded port which can accommodate a male thread of another connector. There are several explanations why it is usually done this way. One of them is that it is easier to machine a female thread into a rather bulky component than it is to provide a male thread on it. The hydraulic sealing of the connector in the port can be done in different ways. Three basically different methods are mentioned here. The first one is the sealing with a metallic sealing edge, which is pressed into the opposed component’s surface when the thread is tightened. Secondly there is the sealing with a metallic sealing element which is pressed tightly by the axial forces created by the thread – so the sealing quality very much depends on the correct torque. And furthermore there is the sealing with an elastomer sealing material which is

4.4

Hydraulic Lines and Fittings

with sealing edge

139

with metallic seal

with elastomer seal

Fig. 4.29 Examples for the connection of straight connectors

compressed into a defined volume and therefore to predefined preload force during the tightening of the thread (Fig. 4.29). The major advantage when using an elastomer seal is the complete separation of the functions “mechanical connection” and “sealing”. Even if the mechanical connection looses its torque/preload, a tight sealing function is still ensured as long as the seal is still trapped inside its volume. The sealing loses function only if the mechanical connection loosens further and a gap opens up into which the seal can extrude. This is a design with high forgiveness which is one reason why elastomersealed connections are nowadays very widespread – especially for the sealing of connections with permanent and highly dynamic pressure variations. The connections for tubes and hoses have also developed over time. In former times the pure metallic seal by a cutting ring was predominant; today more and more elastomer seals are used here as well. This can still be done in combination with a cutting ring, which then is mainly responsible for the mechanical connection while the elastomer takes over the main sealing function. On the other hand there are new systems like the sealing cone with o-ring or the o-ring-face-seal (ORFS) connection – both defined in ISO 8434. The path towards elastomer seals was followed here, too, because of more forgiveness for assembly errors and dynamic loading, hydraulically as well as mechanically. Many of these elastomer sealing systems require only a simple deformation process (for example, flanging) for the tube end and the tube is ready to assemble. Depending on the type of system, additional parts are needed on the tube such as a swivel nut or a support sleeve [FIN06]. The above described connectors are available in different sizes so the designer can choose the right one which fits to the cross section of the tubes and hoses to which they connect. Many different adapters can be created from the combinations of all the different connector types on the component side and on the hose/tube side. Furthermore they need to be available in different sizes. Moreover, the connections for tubes and hoses are usually available as the male (external thread) and female version (internal thread). And on top of that fittings are not only, as described so

140

4

Hydraulic Components Design

far, available in straight form, but also as angled fittings (30◦ . . . 90◦ ) or as tees and crosses. Many of them are even position adjustable relative to the screw-in axis. Most of these combinations are actually available. What is not yet available can be made available for special applications. In particular for hydropneumatic suspension systems two more things need to be kept in mind. On one hand the fittings should always be chosen in a way so the flow resistance is minimized (use of straight fittings rather than angled ones) and, for the same reason, the number of fittings should be kept as low as possible. Both of these considerations have another positive side effect: the design is often more cost-effective this way. In particular the adjustable angled fittings are, due to their elaborate production, much more expensive than their straight counterparts (often by a factor of 4 or more).

Chapter 5

Level Control

One of the major advantages of hydropneumatic suspension systems is the capability to readjust the suspension position after a change of the suspended load, simply by adding or removing hydraulic fluid. This is one of the reasons why a hydropneumatic suspension is virtually always used in combination with a level control. One way to distinguish level control systems is, for example, by the source of energy for the upward leveling (extension of the cylinder). Although most level control systems are connected to an external hydraulic power supply, some systems gain the power from the input side excitations of the suspension itself. All necessary components, namely pump and fluid reservoir, are in this case part of the suspension cylinder. These so called self-pumping systems are particularly used in passenger cars and mostly only partially carry the suspended load in collaboration with a regular mechanical spring. Systems with an external hydraulic power supply and mechanical level control can also be found in passenger cars while electronically controlled systems with external hydraulic power supply dominate the wide field of working machines especially off-road equipment such as agricultural and construction machinery.

5.1 Self-Pumping Suspension Elements The function of this system is based on the effect that the cylinder uses the energy from the relative movement between input side and isolated side to pump (when necessary) hydraulic fluid from a reservoir to the high pressure side. This enables the suspension to be pumped back into its design position after it has sunk down due to a load increase. For this purpose three different functional systems are integrated into the cylinder: the load carrying system, the level control system and the pump+fluidrelease system (Fig. 5.1). If the suspended load is increased, the suspension sinks down and therefore the cylinders are compressed (Fig. 5.1, left hand side). This brings the piston of the level control system to a position which prevents fluid from flowing from the load carrying system to the fluid reservoir. If the suspension is now excited on the input side, the piston rod oscillates longitudinally to the cylinder axis which activates the W. Bauer, Hydropneumatic Suspension Systems, DOI 10.1007/978-3-642-15147-7_5,  C Springer-Verlag Berlin Heidelberg 2011

141

142

5 Level Control after leveling

after load change

high pressure accumulator

fluid reservoir

high pressure accumulator

level sensor

level sensor load carrying system

level control system

pump

fluid reservoir

fluid release

load carrying system

piston rod

level control system

fluid release pump

piston rod

Fig. 5.1 Working principle of the ZF Sachs Nivomat [EUL03]

pump. It draws hydraulic fluid through a check valve from the reservoir and pumps it through another check valve to the load carrying system. This steadily brings the suspension back into its design position. At this point the piston of the level control system returns to a position which connects the pump directly with the load carrying system. On the other hand the fluid release is opened from time to time (due to the oscillation) and the fluid, eventually moved into the load carrying system, can be released back into the fluid reservoir. When working in the range of the design position, the system steadily works alternating pump and fluid release and in this way keeps the design position (Fig. 5.1 right hand side). This can be considered as a permanent flow of hydraulic fluid through different kinds of flow resistors, which therefore also contributes to the necessary fluid damping of the suspension system. If on the other hand the suspended load is reduced, the fluid release, in cooperation with the level control system, releases oil into the reservoir and this way the suspension keeps the design position. Opposed to the pumping effect, the release of fluid works even without the oscillation motion of the suspension. The working principle is clear and understandable; however the design of such a system is rather complex and elaborate. Figure 5.2 shows a Nivomat element of the compact length type. The function is explained in detail in [EUL03]. The above described Nivomat system is only partially carrying the suspended load, while an additional mechanical spring carries most of the curb weigh (= minimum load). The Nivomat damper takes over the rest of the curb weight and all of the additional weight loaded onto the suspension. It is important to mention that in this system the spring properties of the mechanical spring and the hydropneumatic spring add up in a positive manner. The natural frequency of the chassis can

5.1

Self-Pumping Suspension Elements

143

1 1 2 3 4 5 6

Suction bore Pump plunger Fluid reservoir Damping piston Fluid release path Elastic diaphragm separates fluid and gas 7 Bypass which defines the design position (level sensor) 8 High pressure accumulator 9 Pump inlet valve 10 Pump chamber 11 Control sleeve, creating the pump in combination with plunger, in- and outlet valve 12 Pump outlet valve

2 3

4 5 6 7 8 9 10 11 12

Fig. 5.2 Compact length Nivomat [EUL03]

be quite consistent even with varying load since the increasing characteristic of the hydropneumatic spring and the decreasing characteristic of the mechanical spring (please refer to Fig. 1.6) combine to a rather constant characteristic. The damping, too, is positively influenced since the pumping action of the Nivomat provides a load-depending additional damping. This self-pumping suspension element is also offered in a slightly different type as the Hydromat-strut which then is usually carrying the full suspension load. One major design difference from the Nivomat system is that the full diameter of the piston carries the load. This large load carrying surface ensures a relatively small overall diameter of the Hydromat element at reasonable hydraulic pressures – in the Nivomat, only the rod diameter carries the load [REI89]. The great congeniality of self-pumping systems is the fact that aside from the suspension cylinder (eventually with some directly mounted auxiliary parts), no other components are needed. This greatly improves space and service requirements and can also improve cost, reliability, etc. Furthermore the system does not need external energy which would have to be created and would add to a vehicle’s fuel consumption. Instead, kinetic energy, which would be dissipated into heat by the damper anyway, is used to bring the suspension level back to its design position – a very charming solution.

144

5 Level Control

5.2 Mechanical Level Control with External Hydraulic Power Supply This system represents the simpler variant of level control systems with external hydraulic power supply. In addition to the components of the suspension hydraulic circuit, a leveling valve and a hydraulic power supply is necessary. Figure 5.3 shows a simplified representation of the setup using a level controlled axle suspension as an example. It is the task of a level control valve to react to a deviation from the suspension design position with a supply/release of hydraulic fluid to/from the suspension circuit, to bring the suspension back to the desired position. For this purpose, for example, a 3/3-way spool valve can be used with the spool actuated by a connection rod. The connection rod, for its part, is connected to the axle and therefore is moved with every relative movement between input side and isolated side. Hence if the axle is moved towards the chassis (compression) the connection rod is pushed upward and the spool of the leveling valve with it. This opens a path in the valve from the pump to the suspension units, hydraulic fluid flows into the units and the suspension level is increased. On the other hand if the axle is moved away from the chassis, the spool is moved downwards and therefore connects the suspension units with the fluid reservoir – the suspension level is lowered. In the center position of the spool all three ports of the valve are separated from each other and the level is kept constant. Figure 5.4 shows the level control mechanism of a Citroen according to [US585]. However a major disadvantage of such a valve is that it has a small but permanent leakage. Therefore pressurized hydraulic fluid from the suspension circuit will flow back into the reservoir or, when the pump is switched off, even back into the pump circuit (if no additional check valve is provided). Since the leakage is rather low, this will not be an issue while the vehicle is in operation since it will be compensated

SV

P

S

P

pump

R

fluid reservoir

SV 3/3 spool valve R

S

spool

C

connection rod

U

suspension unit

A

axle

U

U C

A

Fig. 5.3 Basic setup of a mechanically controlled leveling

5.2

Mechanical Level Control with External Hydraulic Power Supply

145

20

1 housing 2 port to cylinder 3 port to pump 4 port to fluid reservoir 9 spool 11+12 rubber diaphragms 13 +14 fluid chambers 15 connection bore 20 Attachment point for connection rod

Fig. 5.4 Level control valve of a Citroen [US585]

by the level control. But if the vehicle is standing un-operated for a longer time, without activated pump, the chassis will gradually sink down and, in the end, sit on its compression end stops. This is one of the reasons why older Citroen models usually sink all the way down over night. To improve this, Citroen has integrated so called “anti-drop” valves in their later models. This valve is basically a leakage-free poppet valve with hydraulic release. When the engine is stopped (and therefore the pump is deactivated) the anti-drop valve separates the suspension circuit from the level control valve and therefore prevents leakage. More detailed information about the Citroen suspension system can be found in Sect. 7.2. Back to the level control setup shown in Fig. 5.3: There is a direct connection between the spool of the level control valve and the axle. So every little suspension movement in the input side would lead to a movement of the spool and therefore a leveling action. This however is not practical and wastes energy by permanently pumping up and lowering the chassis. This is the reason why in many cases a deadband is integrated into the control elements. The deadband allows some suspension movement around the design position without activation of the control. The deadband can be provided, for example, by a suitable design of the control valve with a

146

5 Level Control

higher overlap of the control edges or a defined slackness in the connection between spool and axle. In his doctoral thesis Naumann has made interesting observations about the influence of such elements onto the control characteristics [NAU71]. It is also possible to set up a low pass filter with mechanical elements, which only transfers low-frequency portions of the input side excitations to the spool of the level control valve. This ensures that only long-term, quasi-static load changes are considered for level control while middle- and high-frequency portions are filtered out (dynamic load changes). Such mechanical low pass filters are, for example, known from level control systems for pneumatic suspension systems as used for truck axle suspensions [MUR98]. Figure 5.5 shows the schematic setup of a mechanical low pass filter by a suitable arrangement of springs and dampers. The axle movement is transferred by the connection rod to the input side of the low pass filter (left hand side in Fig. 5.5). The right interaction of spring 1 and damper 2 ensures that only low frequency oscillations pass through to the output side (right hand side in Fig. 5.5). The higher the damping of damper 2 and the softer the spring 1, the lower will be the cutoff frequency of the low pass. The springs 3 take care of a centering of the position of the output side. This ensures that the oscillations on the output side have a defined center position. This position is also the center position of the spool in the level control valve. An additional mass can be integrated between spring 1 and damper 2 to influence the transfer function but it is often not necessary. The simple design is the major advantage of such a system. For this reason it is/was used on axle suspension systems on Citroen passenger cars (parts of the low pass filter are visible in Fig. 5.4). If furthermore a mechanical length adjustment of the connection rod is provided, the additional possibility is created to manually adjust the design position of the suspension. This is also done by Citroen: the driver has a corresponding height control lever next to the gearshift lever. The disadvantage of a mechanically controlled system is the lack of possibilities for further external influence on the control – well, at least influence is very complicated. For example the integration of safety algorithms (fail-safe mode) is difficult. The proper tuning of the control circuit is also rather complicated since it can be only done by mechanical means, for example, the inner design of the control valve or the kind of coupling to the axle. The right tuning requires that the level control may not

axle movement transferred by the connection rod

filtered signal to the level control valve 1 2

Fig. 5.5 Schematic setup of a mechanical low pass filter

3

3

5.3

Electronic Level Control with External Hydraulic Power Supply

147

overshoot (which would cause a subsequent control action in the opposite direction), nor may it switch off the control action too early since, within a short time, a further control action in the same direction would be necessary. On top of that, the level control for hydropneumatic suspension systems with hydraulic preload would be very complicated, since a further mechanically operated control valve would be necessary for the rodside pressure control. Both the level control and the pressure control would interact and possibly mess up the intended setup. This is why in many cases an electronic/hydraulic control is preferred over the mechanical/hydraulic control.

5.3 Electronic Level Control with External Hydraulic Power Supply 5.3.1 Function This level control system is based on the principle, that the information about the relative position of isolated side vs. input side is not only sensed and transferred mechanically but transformed to an electric signal by a level sensor. This signal is reported to an electronic controller, which evaluates the signal and decides according to its control algorithms, whether a readjustment of the level is necessary, in what direction the adjustment needs to go and, if applicable, also how fast the readjustment needs to be. Figure 5.6 shows the basic setup of such a system. The major advantage of such a system is the possibility to use other signals as additional parameters for the control algorithm, for example, the vehicle velocity v, accelerations a, temperature T of the hydraulic fluid etc. Furthermore this system offers high flexibility, the control algorithm can be changed quite easily by a change of the software. This also allows the use of the same hardware (not only electronic

P V

C

v a

P

pump

T

R

fluid reservoir

V

hydraulic control valve block

C

controller

S

position sensor

U

suspension unit

A

axle

R U

S

U

A

Fig. 5.6 Basic setup of an electronically controlled leveling

148

5 Level Control

hardware but also mechanical and hydraulic hardware) for different products while the necessary adaptation is performed by different programming of the controller.

5.3.2 Hydraulic Circuits Like on Citroen’s mechanically controlled system, here too a 3/3-way spool valve can be used. However this now must be operated by an electric actuator. For safety reasons it is favorable to have the unenergized valve in the fully closed position and therefore the spool usually in the middle position. In this case, like on the Citroen cars, the leakage problem arises which needs to be cured by another poppet valve with external release. This could be, for example, a hydraulic release (pilot-operated check valve) which only releases as long as the hydraulic power supply HY provides enough pressure for the leveling system (Fig. 5.7a). If this hydraulic power supply was dedicated only to the suspension system, the pump needed to be activated in case of leveling down, too. This allows the check valve to be opened to enable release of fluid through the 3/3-way spool valve to the fluid reservoir. An alternative is an electric opening of the check valve which is then basically a 2/2-way poppet style solenoid valve (unenergized = closed). It is energized by the controller C if the level needs to be lowered (Fig. 5.7b). The above circuits are especially useful if the 3/3-way spool valve is used as a proportional valve, which then allows sensitive as well as fast readjustment of the level. If it is sufficient to use an on/off control of the hydraulic valve, a modified circuit can be utilized, which consists of a 3/2-way spool valve (unenergized = connection of the suspension circuit with the fluid reservoir) in combination with an electrically releasable poppet valve (unenergized = closed) – see Fig. 5.8. If both

C

C HY

HY

(a)

(b)

Fig. 5.7 3/3 spool valve with releasable check valve. (a) Check valve with hydraulic release. (b) Check valve with electric release

5.3

Electronic Level Control with External Hydraulic Power Supply

Fig. 5.8 3/2-way spool valve with electrically releasable check valve

149

C HY

LS

valves are unenergized, the poppet valve isolates the suspension circuit leakage-free from the hydraulic power supply. By energizing the 3/2-way spool valve, the suspension circuit is connected to the hydraulic pump, hydraulic fluid is transported into the cylinders and the system is leveling upwards. If the poppet valve is energized, a connection to the fluid reservoir is opened, hydraulic fluid is released from the cylinders and the system is leveling downwards. A further approach for a leveling hydraulic circuit is to completely separate the paths for the ingoing (leveling up) and outgoing (leveling down) hydraulic fluid. This can be done by two electrically releasable check valves (both valves closed when unenergized) and a simple check valve in the fluid path for the inflowing fluid (Fig. 5.9a). An alternative is the use of one electrically releasable check valve in combination with a 2/2-way blocking valve as shown in Fig. 5.9b.

C

C

HY

HY

LS

(a)

(b)

Fig. 5.9 Separate paths for inflowing and outflowing fluid. (a) Two electrically releaseable check valves and one simple check valve. (b) One electrically releasable check valve and 2/2-way blocking solenoid valve

150

5 Level Control

Figure 5.9a offers, just like the solution in Fig. 5.8, the possibility to create an LS-signal, which is necessary to operate the leveling system with a hydraulic power supply with loadsense-control. Solution b requires slightly lower design space. In both cases the solenoid valve on the pump side is energized for leveling up, and the solenoid valve on the fluid reservoir side is energized for leveling down. When using Figs. 5.8 or 5.9a pressure is only requested from the pump if it is required for leveling up. In all other previously shown solutions this is either infeasible or only feasible with increased design effort. The electrically releasable check valves can be used in a proportionally controllable version as well. If this is not the case (like for all other aforementioned circuits), it is necessary to integrate flow control means into the paths for inflowing and outflowing fluid in order to set a certain leveling speed. The flow control means could be simple orifices or throttles but also, for example, more sophisticated valves, in particular flow regulators, to ensure constant leveling speed in all operating conditions. Additionally it is worthwhile to mention that the above Fig. 5.9a is not only suitable to provide the leveling function but, in hydropneumatic suspensions with hydraulic preload, also suitable for the regulation of the rodside preload pressure. Instead of the signal of a level sensor, here the respective pressure sensor signal is the input parameter for the pressure control circuit. John Deere uses this hydraulic circuit in their latest front axle suspensions both for the level- and the pressurecontrol [DE600] – read more about this system in Sect. 8.1.

5.3.3 Control Algorithms The way the electronic sensor signals are processed plays a leading role in the function of a hydropneumatic suspension system. The best level control fulfills its leveling function sufficiently but does not even show that it is there. This means it should readjust the position as rarely as possible but as often as necessary. The quality of the control algorithm is of major importance and therefore the algorithm often is one of the best-kept secrets of the supplier or the user of a suspension system. The interaction of the controller with the controlled system can be illustrated for suspension leveling basically as shown in Fig. 5.10. When starting from scratch with a leveling control algorithm, one useful way is to analyze the logic of an existing (and well functioning) mechanical leveling system (see Sect. 5.2) and then transform it into an electronic control algorithm. A simple P-controller is one of the easiest ways to implement a level control. The more the (actual) position deviates from the position target, the more electric current is sent to the hydraulic control valve and the more this valve opens the connection between hydraulic power supply and suspension circuit to bring the system back to the position target (Fig. 5.11). A major disadvantage of such a control algorithm becomes directly obvious; due to the nature of the suspension the fulfillment of its most basic task requires permanent (oscillating) displacements and

5.3

Electronic Level Control with External Hydraulic Power Supply

151

reference variable: position target

control variable: position

correcting variable: electric current

controller position sensor

electronic controller

controlled system suspension cylinder accumulator and suspended mass

hydraulic lines

disturbances: for example load changes, roadway irregularities, acceleration/deceleration, uphill/downhill slopes

hydraulic control valve

disturbances: for example pressure level of the hydraulic power supply, valve reaction time

Fig. 5.10 Interaction of controller and controlled system for axle suspension leveling position target controller – position

+

xe

xa = Kp ⋅ xe

xa

electric current to control valve

xa

xe

Fig. 5.11 Logic and control behavior of a P-controller

therefore position changes. These are deviations from the position target and hence the level control would be permanently trying to readjust position, although unnecessary. This would not only mean higher energy consumption but, for example, also a higher noise level by activated hydraulics and a higher wear of the activated components.

152

5 Level Control

It is important to mention that the control tends to become instable since many components of the controller and the controlled system show delay times, especially the hydraulic and mechanical components but in particular also the overall behavior of the hydropneumatic suspension system. Furthermore the proportional behavior of most components will always be subjected to tolerances. If on top of that (temperature caused) variations in the viscosity of the hydraulic fluid, variations in suspended masses, inertial forces (for example, during braking/acceleration) come into play, it is instantly clear that a pure P-controller will have difficulties in handling the level control. In this case an additional deadband will help to calm down the control algorithm in the range around the design position – comparable to the already described mechanical control with a high overlap of the control edges of spool and housing. As long as the suspension movement takes place inside the deadband, the level control will not try to readjust the position. Only if high load changes cause major suspension movement, which causes xe to move out of the deadband, then the hydraulic valve(s) for position readjustment are activated (Fig. 5.12). However in using this trick, the problem arises that, also depending on the spring rate, the deadband must be chosen quite wide to really allow for all kinds of ground irregularities without activation of readjustment. Also, a wide deadband means that the leveling quality is low since the deadband is so to say the tolerance band for the design position. This can cause insufficient remaining suspension travel in either compression or rebound direction and the suspension can bottom out on heavy bumps. So the bottom line is that the deadband is a suitable means to improve the control algorithm, however the width should be chosen wisely so as not to compromise the quality of control and subsequently comfort. Both systems described so far work frequency-independent, since the step response of the P-controller is a step as well, only modified by the proportionality factor KP . Since the excitations of the suspension system are highly dynamic and periodical, it makes sense to include a time/frequency dependency in the control algorithm. This will help to distinguish excitations by ground irregularities from excitations and displacements by long-term load changes. A simple possibility to create such a frequency-dependent control algorithm is the introduction of waiting periods before action is taken to readjust position. This means the position signal must be out of the tolerance range for a certain period in order to initiate the readjustment [GUG02]. This can be done, for example, by

xa

xe

Fig. 5.12 xa as a function of xe for a P-controller with deadband

deadband

5.3

Electronic Level Control with External Hydraulic Power Supply

153

a timer which is started whenever the position signal exceeds the upper or lower tolerance limit. The timer continues to run as long as the position is out of tolerance range. If the timer reaches a predefined value, the waiting period ton , the level readjustment is activated and brings the position back into the desired range. On the other hand, if the timer does not reach ton before the position gets back into the tolerance band (with no readjustment action, just by effect of ground excitation), no readjustment action is taken and the timer is reset to zero. Yet if the readjustment has been started and a control valve has been energized, the valve remains energized until the end of the waiting time toff after reentry of the position into the tolerance band (Fig. 5.13). This toff is introduced to bring the position back as close to the position target as possible. Therefore toff needs to be chosen the shorter the faster the hardware components readjust the position (for example, the more hydraulic fluid flows). It is therefore useful to distinguish between ton and toff . Furthermore it can be helpful to also treat leveling up and leveling down differently (not shown in the example). Further improvement can be found in the implementation of a low pass filter into the control algorithm. This type of filter was already mentioned for Citroens hydropneumatic suspension, in this case provided by an arrangement of mechanical components. It is used to process the feedback signal of the control variable before it is fed into the P-controller (Fig. 5.14). This way the excitations resulting from ground irregularities (and therefore with higher frequency) are filtered out of the control variable. Hence the P-controller is only informed about long term position changes, for example, as caused by changes in suspended load, and only these will then lead to an activation of the hydraulic control valves. The right choice of the filter’s cutoff frequency is an important criterion for the proper function of the control system. If the cutoff frequency is chosen to be too high, suspension motion due to ground irregularities will lead to an activation of the hydraulic control valves. If the cutoff frequency is too low – and that is the more critical case – the leveling reacts too slowly, the hydraulic valves are activated very

position

readjustment command “level down” starts readjustment command “level down” stops

ton

upper tolerance

toff

position target load changes lower tolerance

toff ton

time

Fig. 5.13 Control algorithm with waiting periods

154

5 Level Control position target controller – position

low pass

transfer element

xe

+

xa

electric current to control valve

Fig. 5.14 Controller with low pass filter

late and it can happen that the suspension bottoms out in these situations due to the lack of sufficient suspension travel in one direction. Additionally a very low cutoff frequency has the effect that, after a strong deviation from the design position, the filtered position signal returns very late back into the tolerance band and therefore the respective control valves are switched off very late. Under adverse circumstances this can lead to an overshoot of the actual position and subsequently a position readjustment in the opposite direction is necessary. This is undesirable behavior, which can, depending on the amount of overshoot, even lead to a complete instability of the control. Therefore a compromise between stable control and low sensitivity to ground irregularities needs to be found. It is probably also due to the above described behavior that, for example, in some passenger car’s pneumatic suspension systems even a double low pass filter is used to condition the position signal. Both filters have significantly different cutoff frequencies. The filters are arranged in parallel and both perform an individual processing of the position signal, hence two separate signals are fed back into the transfer element (Fig. 5.15). This allows better tuning of the software parameters to the properties of the suspension hardware such as control valves, cylinder sizes, available fluid flow for level readjustment etc. In particular, their delay times, the leveling speed and the gain of the different components play a major role in the overall system. Good coordination of the control algorithm with the suspension hardware ensures a stable control along with the optimum compromise of fast reaction time after load changes and low sensitivity to ground irregularities. position target controller – position

low pass 1 low pass 2

xe1

+

+

–

Fig. 5.15 Controller with double low pass filter

xe2

transfer element

xa

electric current to control valve

5.3

Electronic Level Control with External Hydraulic Power Supply

155

The well known manufacturer of off-road equipment, John Deere, describes in the patent application [US859] a level control algorithm for their hydropneumatic front axle suspension system TLS. The algorithm works similarly to the above mentioned control logic with double low pass filter. The patent application proposes to continuously calculate two average values of the position signal: one over a longer time period of about 6 s and one over a short time period of 0.8 s. It is generally recommended that the long average value should be calculated at least for the duration of five full oscillations while the averaging time for the short time mean value should be chosen in a way such that an overshoot of the axle position during leveling is avoided. The readjustment of the level is not activated until the long average value leaves the tolerance band range of ± 7.5% around the design position relative to the overall suspension travel. Then the respective valve(s) is energized to bring the level back into the tolerance band. To avoid a too long activation of the valves and therefore an overshoot of the level control, the valves are de-energized as soon as the short average value reenters the tolerance band. Another type of controller which also can be used for suspension systems is the three-state controller with switching hysteresis. For the leveling system it provides three switching states: “no action”, “level up” and “level down”. If the actual position is within the wide tolerance bandwidth, which means between the values of the high switching hysteresis (−xeSo to +xeSo ) the state “no action” is active. If the high switching hysteresis +xeSo is exceeded, for example, by too high an actual position, the switching state “level down” is activated. It remains active until xe drops below the value of the low switching hysteresis +xeSu . Then the controller returns to the state “no action” (Fig. 5.16). This type of controller seems to be similar to the control algorithm with waiting periods (Fig. 5.13), where the hysteresis is based on time delay, the effect of the waiting time. The right tuning of the parameters xeSo and xeSu , especially their difference (the width of the hysteresis) is essential for the proper function of the leveling system. In accordance with the previous examples, the difference xeSo –xeSu should be the smaller, the faster the leveling speed, meaning the higher the flow of hydraulic fluid which brings the level back to the design position. On the other hand the delay time of the components is important; the slower the hydraulic and mechanical components react upon the command, the smaller should be the hysteresis. Systems with high flow rates and at the same time high delay time are in general difficult

xa xeSo

command “level down”

xeSu xeSu command “level up”

xeSo

Fig. 5.16 Three-state controller with switching hysteresis

xe

156

5 Level Control

to handle. If this cannot be avoided, the three-state controller might not be suitable. Then preferably the above mentioned controller with double low pass filter should be taken into consideration. It makes sense to also low pass filter the feedback position signal for the threestate controller. Again, like for the P-controller, the cutoff frequency of the filter must not be chosen too low with regards to the already mentioned stability problems. Even more complicated is the development of a leveling algorithm if two (or more) controllers can be active simultaneously and can interfere and mutually exchange disturbing effects. This is the case when (as on the John Deere TLS Plus system [DE600]) one control algorithm acts, for level control, upon the pistonside of the suspension cylinders while the other control algorithm acts for preload pressure control upon the rodside. If a control valve is energized for a readjustment of the level, the fluid volume in the rod chamber is directly affected as well. This fluid volume is transferred in or out of the respective accumulator and therefore causes a change in rodside pressure. This however can result in a corrective action of the control algorithm for the rodside preload pressure control. It is easy to see that positive cooperation of both control algorithms is necessary to avoid mutual adverse influence and therefore unfavorable increasing amplitudes of the control variables. A suitable setup for the control parameters of both algorithms as well as eventually an additional supervising logic are needed to get a grip of possibly arising problems. Once again it needs to be emphasized here that the designed leveling system needs to provide a stable function under all possible circumstances: components tolerances, temperatures, different suspended loads, ground excitations etc.

Chapter 6

Special Functions of Hydropneumatic Suspension Systems

6.1 Suspension Lockout Undoubtedly a suspension system provides many benefits. In most applications the most important benefit is the reduction of accelerations on the isolated side, where, in case of a vehicle suspension system, the driver is usually located. However, in some situations, especially on working machines, it is an advantage to have as little suspension movement as possible. This is a frequent requirement, for example, for the axle suspensions of working machines. It is due to the fact that, in some cases, uncontrollable motion of the chassis is unfavorable – it should be more “tied to the ground”. A good example is the common situation when loads are lifted or put down. Due to the change in suspended load, the axle suspension will react with a change in position and this complicates an exact positioning of the load (for example inside a compartment of a storage rack). In many cases, the above mentioned desired inelastic behavior is such a critical factor for the working machine, that the possibility of suspension lockout is one of the key selection criteria for customers when buying a new machine. Often the customer chooses a non-suspended vehicle in preference to a suspended one if it does not offer suspension lockout. Since suspension lockout for an axle suspension implies major disadvantages in terms of comfort and driving safety, the lockout should only be activated during the appropriate operating conditions (for example the above mentioned situation). The strategy, as to when and how to activate is open to debate. One very controversial issue concerns driver control/automatic control on one hand and safety issues on the other. Automatic activation of the lockout is recommended only when the criteria for lockout activation can be clearly defined and detected (for example by sensors) and no other than the appropriate operating conditions can trigger the same sensor signals. If this cannot be clearly defined, it is better to leave it to the driver to decide when to activate the lockout. On the other hand, automatic deactivation of the lockout (and therefore re-activation of the suspension) can also be useful in matters of driving safety; one example is automatic suspension re-activation when a certain vehicle speed is exceeded. For the same reason it can make sense to have the suspension system always in suspended mode when the working machine is powered up.

W. Bauer, Hydropneumatic Suspension Systems, DOI 10.1007/978-3-642-15147-7_6,  C Springer-Verlag Berlin Heidelberg 2011

157

158

6 Special Functions of Hydropneumatic Suspension Systems

6.1.1 Lockout by Blocking the Hydraulic Circuit It is one of the major advantages of hydropneumatic suspension systems that a lockout can be implemented relatively easily (compared to mechanical and purely pneumatic suspension). It is just necessary to shut off the fluid flow between the cylinders piston chamber and the respective accumulator(s). Figure 6.1 shows this principle with the example of flow blocking by an electrically actuated 2/2-way blocking valve (poppet design). A 2/2-way spool valve can provide this function as well if leakage can be accepted. The later is a lower cost valve and offers better fluid flow conditions and therefore lower pressure losses (comparing valves with the same nominal size). When blocking the fluid flow, some small sources of elasticity are still present (see Sect. 2.2), however the resulting elasticity is usually very small and the suspension can well be called “locked out”. The lockout of the suspension however means that excitations on the input side are now no longer cushioned but transferred almost rigidly into the isolated side. This causes high accelerations and forces, especially as a result of heavy impacts, and all components subjected to these high forces must be laid out accordingly. For the suspension system these forces additionally mean high pressure peaks in the hydraulic circuit between the piston chamber and the blocking valve. To prevent damage to the components, they either need to be designed for these high pressures or a fast reacting pressure relief valve must be integrated in this part of the hydraulic circuit. For the latter case it must be mentioned that, when the relief valve opens, the suspension is no longer rigid but deflects more or less depending on the extent of the load peak. If the hydropneumatic suspension is locked out in its design position, it can be an advantage to keep the level control system active during this operational mode. This way slight position changes due to small leakage (of the blocking valve and/or the level control circuit) or fluid losses after the cracking of the relief valve can be compensated. It is easy to see that this requires the leveling control hydraulics to be connected to the suspension hydraulics between cylinder and blocking valve. Since in the locked out state all the fluid from the level control block goes to the cylinder

often possible as well

Fig. 6.1 Blocking of the pistonside hydraulic circuit

6.1

Suspension Lockout

159

(the accumulator is shut off), it can be useful to reduce the leveling fluid flow during the locked out state to avoid leveling overshoots. If an axle suspension needs to be locked out in a position other than the rebound end stop, in certain cases this can only be done with preloaded suspension systems. The reason for this are the unsprung masses (wheels and axle) which would pull out the cylinder rod(s) when the wheel is fully unloaded (lifted off the ground). This negative external force would lead to cavitation in the suspension cylinder and to (undesired) extension of the cylinder. If a preloaded system is designed for this case, the preload (no matter whether hydraulic or mechanical preload) must be at least equal to the unsprung masses. The lever ratio of the mechanical linkage needs to be considered as well (see Sects. 2.2.2 and 7.1 with Fig. 7.4). However, to additionally account for dynamic load variations here, the preload force is, as a rule of thumb, recommended to be at least 50% higher than the gravitational force of the unsprung masses. When blocking the fluid flow from/to the accumulator it is an important aspect that after shutting off, a certain hydraulic pressure is enclosed in the accumulator, which is related to the static spring load in the moment before shutoff. If the static spring load changes during the lockout, the pressure inside the piston chamber changes as well. In this situation, if the suspension is reactivated and the blocking valve is opened, the pressure in the now reconnected circuit will balance out between the pressures in the cylinder and the accumulator. If the static spring load has decreased during the lockout phase, the cylinder pressure is lower than the pressure inside the accumulator. Therefore the cylinder will extend when the suspension is re-activated since the higher pressure fluid in the accumulator will partly flow into the piston chamber. If the static spring load has increased during the lockout phase, accordingly the cylinder will be compressed after suspension re-activation. Depending on the extent of the load change and the system-inherent fluid damping, the reaction can be very intense and the suspension can instantly drop or jump into its end stops – provided no flow restriction is installed which dampens the process of pressure equalization. Such sudden and uncontrolled movements need to be avoided since they imply numerous risks. This reaction can be slowed down if, during the re-activation, only a small cross section is opened between accumulator and cylinder and the pressure can only balance out slowly. If the respective cross section is suitably chosen, the level control can compensate for the level changes caused by the pressure equalization and the suspension movement will be much slower and with lower amplitude. Subsequently the full cross section can be opened which is designed for the high flow rates during normal suspension operation. Even more elegant, but also more expensive, is the method to match the pressure in the accumulator to the current pressure in the cylinder before opening the blocking valve. One approach is, for example, to utilize the well known accumulator charging valves which can then be modified for the needs of this special application. Another possibility is to permanently connect the accumulator to the cylinder by a small flow resistor which helps to automatically adjust accumulator pressure. Level control can then take over the task to keep the position in the desired range.

160

6 Special Functions of Hydropneumatic Suspension Systems

6.1.2 Lockout at the Compression End Stop An axle suspension can also be locked by running the suspension cylinder to one of its end stops and locking it there with a preload force from pressurized hydraulic fluid on the opposite side of the piston. For example the cylinder could be fully retracted and the piston runs to the compression end stop, the piston chamber being fully depressurized. With a preload pressure in the rod chamber, the piston is clamped to the end stop and all excitation forces from the input side are now directly transferred to the isolated side through the end stop. As opposed to the hydraulic lockout, no pistonside pressure peaks will be caused by high forces due to the direct mechanical force transfer. However a sufficient preload force must be ensured here as well to keep the system securely fixed between end stop and preload. Many front axle suspension systems of the manufacturer of agricultural equipment AGCO-Fendt implement a lockout function with this principle. Their hydropneumatic tractor front axle suspension system with hydraulic preload is depressurized on the pistonside and simultaneously the rodside is subjected to maximum pressure of the hydraulic power supply system. The cylinder therefore is completely compressed to the mechanical end stop (by the axle load as well as by the rodside pressure force) and then fixed in this position by the rodside preload pressure. Figure 6.2 shows the suspension in this locked-out state. It is important to mention that the vertical suspension of the axle is completely separated from the rotation of the axle relative to the longitudinal axis of the tractor. Therefore the axle can still oscillate with locked out suspension and hence equalize differences in surface structure of left and right. The hydropneumatic suspension with mechanical preload, for example, produced by the drivetrain components and tractor manufacturer Carraro, offers a suspension lockout function based on the same principle. These axles can be found in particular on tractors of the OEMs Claas and Case/Steyr. They are designed as oscillation

1 Chassis front frame 1

2 pivot axle of trailing arm

3 2

4

3 elastomer end-of-stroke damping element 5

6

4 solid mechanical compression end stop 5 lh suspension cylinder 7

6 longitudinal trailing arm 7 front axle

Fig. 6.2 AGCO-Fendt front axle suspension with lockout at compression end stop

6.1

Suspension Lockout

161

axles with wheels individually suspended by the double wishbone principle. If the single acting cylinders are depressurized, the suspension is fully compressed into the respective end stop and then kept in this position by the mechanical preload of the torsional springs. Here too, an oscillation of the axle is still possible while the suspension is locked out.

6.1.3 “Quasi-Lockout” Through High Spring Stiffness For hydropneumatic suspension systems with variable preload it is possible to bring the preload force to a maximum value and this way increase the spring rate to a high level. If the achieved stiffness is high enough, the difference between the maximum stiffness state and a fully (mechanically) locked out state can barely be distinguished. This is especially true for applications where other suspension systems (for example soft tires) add onto the effect of the hydropneumatic suspension and therefore provide a “basic softness” anyway. When applying maximum preload, it is important that the leveling system is still able to level up even when maximum preload and maximum permissible axle load occur at the same time – please keep in mind the limited pressure from the hydraulic power supply! This is actually in many cases the most important criterion for the determination of the maximum level of the preload. An adjustment of the preload is especially easy with a hydraulic preload of the rodside. In this case it is furthermore important to ensure that the rodside hydraulic circuit is not overloaded and pressures are kept within the permissible range. According to Eq. (2.37) in Sect. 2.2 the spring rate for a hydropneumatic suspension with hydraulic preload can be calculated: c=

np2V A2R n(FF1 + pV AR )2 + p0,K V0,K p0,R V0,R

(6.1)

It becomes obvious that the preload pressure pV has an influence on the spring rate in two terms of the equation. This can be illustrated quite well by the fact that the increase in preload pressure not only compresses the gas volume in the rodside accumulator but also reduces the gas volume in the pistonside accumulator due to the higher pistonside pressure resulting from the increased preload force. It is easy to understand that both these reduced gas volumes lead to less elasticity and therefore to a higher spring rate. The desired effect of reduced suspension motion can be reached by increasing the spring rate to at least two to three times the original value – the higher the spring rate, the more easily is the effect perceived. An additional effect of the high rodside pressure is the increased pressure difference on the rod seal and therefore significantly increased friction there. This friction, too, contributes to the reduction of the suspension motion when the suspension is set to the “quasi-lockout”-state. On one hand the higher static friction increases the minimum forces which are necessary to initiate a suspension motion. One the other hand the increased sliding friction dampens the suspension motion which also favors

162

6 Special Functions of Hydropneumatic Suspension Systems

the system tuning; with increasing spring rate the damping forces, too, need to be increased since less suspension travel is available to draw the motion energy out of the oscillating system. John Deere uses this principle for the front axle suspension TLS Plus on their tractors in the 6000 series and partly also in the 7000 series range. For many applications this is a good compromise between limited suspension motion on one hand and comfort and driving safety on the other. Since during “quasi-lockout” the suspension is still in its intended design position, the attitude of the chassis for work with tractor mounted implements is better compared to systems which provide a lockout at the mechanical compression end stop, thus lowering the tractors front end.

6.2 Adjustment of the Zero Position Adjusting the zero position (the average level around which the suspension oscillates) provides several advantages. First thing is that on axle suspension systems the ground clearance can be varied. Higher ground clearance is useful for off-road operation; lower ground clearance can be favorable, for example, on passenger cars to improve the aerodynamic drag and the position of the center of gravity (an example are the latest Citroen models). For large machines this can also simply provide the possibility to reduce the overall height and allow them, for example, to pass under low bridges. In some cases the accessibility to service components is improved when the zero position is increased or lowered (consider securing elements for safe work). In some applications it is even possible to exchange tires without a lifting jack. On working machines like tractors, axle height adjustment can allow additional vertical travel of front or rear implements. This can improve their handling, efficiency, etc. The zero position of a hydropneumatic suspension can be varied by changing the amount of hydraulic fluid in the pistonside hydraulic circuit. At least two general strategies are known in setting up the controls for the operator. One is that the operator directly activates the respective hydraulic valves, for example, by pushing a button. He will keep the button pressed and therefore the valve open until the desired suspension position is reached. The other possibility is that the operator preselects the desired height and the system automatically adjusts the height to this new position. This however has the safety-related disadvantage that after selecting the position and starting the process, the system can only be stopped by another reaction of the operator. This is usually slower than if he just had to raise his finger from a button. For safety critical applications such as working machines often surrounded by bystanders, it therefore seems to be better if the operator keeps the valves actively open. In case of an emergency he will then instantly release the button and the system comes to a stop. However it has to be clear that any change in suspension position leads to a change in the remaining travel in both rebound and compression direction. Comfort and driving safety could therefore be reduced. If the newly set suspension position is close to one of the end stops, the suspension is likely to bottom out when subjected to impacts above a certain level. This is neither beneficial for the components’

6.3

Alteration of Roll and Pitch Behavior

163

lifetimes nor for comfort and ride behavior. Therefore it is recommended to limit the operators’ possibilities for manual adjustment. This could mean, for example, that it is only allowed up to a certain velocity, that the permitted adjustment range is smaller than the actual overall suspension displacement or that it is only allowed in combination with a hydraulic lockout of the suspension. Depending on the application, such limitations are possible without giving the driver the impression of being disempowered.

6.3 Alteration of Roll and Pitch Behavior Roll and pitch are related in particular to a vehicle’s suspension with a suspended mass with not only the vertical degree of freedom but also a rotational degree of freedom relative to the longitudinal axis (roll) and the transverse axis (pitch). Such systems need to have more than one suspension element. The suspension elements provide through their spring rate and their position relative to the center of gravity of the suspended mass a torsional moment which counteracts the roll and pitch motions induced by excitations from the input side. For example for a vehicle chassis suspension it is (of course depending on the application) favorable to have an increased roll stiffness and pitch stiffness to reduce the angular motion of the chassis during cornering and acceleration/braking. An increase of the roll stiffness is achieved by changing the suspension setup of an axle. A good example of a component increasing the roll stiffness by mechanical means is the well known torsion bar, which is basically a flexible connection of left and right suspension elements. An increase in pitch stiffness is achieved by changing the setup of the front and rear suspension elements of a vehicle side. This is at least on passenger cars rather seldom since the wheelbase is usually larger than the track width which basically helps pitch stiffness. In the following, only the possibilities for alteration of the roll stiffness are explained. However these principles can also easily be applied to the pitch behavior. As the roll and pitch stiffness are altered, it is important to consider that damping of the respective motions is also necessary. In hydropneumatic suspensions this damping can be provided just like the damping for vertical motion by means of flow resistors in the fluid path between cylinders and accumulators. In fact damping of roll/pitch motion and damping of vertical motion are usually closely related. The calculation of the flow resistors is described in Sect. 2.3.2, therefore no further explanation of roll and pitch damping is given here.

6.3.1 Coupling Cylinders on Corresponding Sides When looking at the two cylinders of, for example, a hydropneumatic axle suspension (left and right), the lowest possible roll stiffness is obtained if the cylinders are connected directly on corresponding sides, meaning, the piston chambers of both cylinders are interconnected and (if existing) the rod chambers are interconnected.

164

6 Special Functions of Hydropneumatic Suspension Systems

Fig. 6.3 Connection of two hydropneumatic suspension cylinders without roll stiffness

Figure 6.3 shows an example of two single-acting cylinders coupled accordingly. In this case it is possible to use only one accumulator for both suspension cylinders. The roll stiffness provided by this arrangement is nil since the hydraulic fluid can move freely between the respective cylinder chambers. Therefore the effect of both cylinders, no matter the distance in between, is the same as if both cylinders were arranged exactly in the middle and the upper structure in the arrangement shown in Fig. 6.3 can therefore rotate freely.

6.3.2 Decoupling Cylinders A first step towards roll stiffness now is to hydraulically separate both cylinders from each other and assign a dedicated accumulator to each cylinder (Fig. 6.4). Both then act as individual hydropneumatic suspension elements and both counteract a torsion

L FF

MD

P

s FF

Fig. 6.4 Separate hydropneumatic springs for improved roll stiffness

6.3

Alteration of Roll and Pitch Behavior

165

of the upper structure about point P with their suspension force FF acting on the lever length L/2. The balance of torsional moments relative to the rotation center P can be calculated for the torsional moment MD , the given geometry and the spring forces FF :   L 2 MD = FF 2 Setting FF = cs and s =

L 2

(6.2)

sin α results in:

L L L2 MD = c sin α 2 = c sin α 2 2 2

(6.3)

sin α ≈ α is true for small α [rad] and therefore MD = c

L2 α 2

(6.4)

Therefore the roll stiffness w is: w=

MD L2 =c α 2

in [Nm/rad]

(6.5)

This equation already shows the dominating influence of the support distance L between both cylinders. The spring rate c is often already determined by the requirements for the vertical natural frequency of the suspended mass, so it is in this case only the support distance L which is a variable parameter influencing the roll stiffness. In the case of a vehicle’s axle suspension, the support distance is determined by the track width. Since the range of variation of the roll stiffness is quite narrow in this case, the above mentioned mechanical torsion bars are often used for roll stabilization in addition to the roll stiffness provided by the wheel springs. In the above calculation it is important to consider that the suspension elements spring rate c is, due to the very nature of hydropneumatic suspensions, furthermore depending on the velocity of the roll excitation. This means that for a short term lateral acceleration, coming, for example, from a quick collision avoidance maneuver, the respective spring rate c is higher than during a long term constant lateral acceleration resulting, for example, from a steady-state skidpad circle drive or a ride along the side of a hill. This is due to the fact that, in the first case, a polytropic change of state takes place, while in the second case, the gas in the accumulator changes its state nearly isothermally (see Sect. 2.2.1). With their Hydractiv-suspension, Citroen offers a suspension system, which can be switched from the hydraulically unstabilized mode (cylinders coupled according to Fig. 6.3) to the hydraulically stabilized mode (cylinders decoupled according to Fig. 6.4). More detailed information can be found in Sect. 7.2.

166

6 Special Functions of Hydropneumatic Suspension Systems

6.3.3 Coupling Double-Action Cylinders on Opposite Sides Opposed to systems with mechanical springs, hydropneumatic suspension systems offer another quite effective alternative to further increases in roll stiffness. For this purpose, double-acting cylinders must be coupled in a way so the piston chamber of one cylinder is connected with the rod chamber of the other cylinder and vice versa. These two completely separated hydraulic suspension circuits then are equipped with at least one accumulator each, which provides the suspension function. The pressure inside both hydraulic circuits is, in a static condition, regulated to the same value. The leveling is done by adding or removing hydraulic fluid from both circuits simultaneously. It is easy to see that in this special arrangement (with the so called cross-connection of cylinders) the suspended load is carried only by the cross sectional area of the rod just like in the examples described in Sects. 2.2.3 and 3.2.2 (Fig. 6.5). As opposed to the individually operating cylinders mentioned above, the roll stiffness of such a system can be set to a certain value (at a certain spring load) just by the right choice of the cylinder dimensions. In the following, the respective roll stiffness w is calculated from the following example: During the torsion of the upper structure about point P for an angle α, the pistons of both cylinders are displaced for a distance s. This displacement also causes a displacement of hydraulic fluid into or out of the accumulators and therefore causes a pressure change inside circuits a and b. Through the active areas of the pistons, this results in a change of cylinder forces and therefore via lever arm L in a torsional moment MD which counteracts the torsional motion. Please note that, for a simplification of the calculation, all pressure differences are defined to be positive when

L FLi

MD P

s FRe

circuit a

circuit b

Fig. 6.5 Cross-connection of cylinders for high roll stiffness

6.3

Alteration of Roll and Pitch Behavior

167

the displacement s is positive. To start the derivation, the differences in force are calculated for the left hand and right hand side cylinder (FLi , FRe ). FLi = pa AR + pb AK

(6.6)

FRe = pa AK + pb AR

(6.7)

The torsional moment MD can be calculated with the help of the force differences: MD = FLi

L L L + FRe = (pa + pb ) (AR + AK ) 2 2 2

(6.8)

With α ≈ sin α for small α, the roll stiffness w can be calculated as follows: w=

MD L MD MD MD ≈ = s = α sin α 2s L

(6.9)

2

and after inserting MD : w=

(pa + pb ) (AR + AK ) L2 4s

(6.10)

For the calculation of the pressure differences pa and pb , the change in cylinder volume of both circuits must be calculated. This is done by taking the displacement s as well as the respective active areas of the cylinder into account. Va = sAR + sAK = s(AR + AK )

(6.11)

Vb = −sAR − sAK = −s(AR + AK )

(6.12)

The pressures in these circuits can then be calculated: n V1 pa = p1 V1 + s (AR + AK )  n V1 pb = p1 V1 − s (AR + AK ) 

(6.13) (6.14)

And due to the above mentioned assumption of positive pressure differences: n V1 V1 + s (AR + AK )  n V1 − p1 pb = p1 V1 − s (AR + AK ) 

pa = p1 − p1

(6.15) (6.16)

168

6 Special Functions of Hydropneumatic Suspension Systems

After inserting theses pressure differences into Eq. (6.10), the rather bulky equation for the roll stiffness w for a set of cross-connected cylinders is the result.  w=

V1 V1 −s(AR +AK )

n

−



V1 V1 +s(AR +AK )

n 

4s

(AR + AK ) p1 L2 (6.17)

where p1 =

mF g 2 (AK − AR )

(6.18)

and V1 = V0

p0 p1

(6.19)

The above equation shows that the roll stiffness w basically only depends upon the pistonside active area AK and the rodside active area AR as well as on the support distance L. The values for p1 and V1 are already predefined by the requirements for the vertical natural frequency and the suspended load. Furthermore the (virtual) displacement s is only an auxiliary parameter in the calculation and does not have much influence if the roll stiffness w is calculated for a position s ≈ 0; this is usually the reference position anyway. Equation (6.17) also shows that the roll stiffness w increases with increasing suspended mass and increasing displacement s. Both of these correlations have a positive effect on suspension behavior. The active area of the suspension cylinders which carries the load is the cross sectional area of the rod. Therefore, at constant rod diameters and therefore constant vertical spring rate, it is possible to create virtually any required level of roll stiffness. Equation (6.17) shows that the larger the piston diameter (while the rod diameter is constant), the larger is the term (AR + AK ) and the higher is the roll stiffness w. Figure 6.6 shows this characteristic behavior for a system of two crossconnected cylinders with 20 mm rod diameter, about 1m of support distance and tuned to a vertical natural frequency of 1.2 Hz. The lowest possible value for the piston diameter of course is 20 mm. When taking a close look at this point, it becomes clear that the roll stiffness is not zero there! If the piston diameter is equal to the rod diameter, the ring-shaped active area on the rodside is AR = 0. This therefore causes a roll stiffness which is equal to the value caused by two decoupled hydropneumatic springs with single-acting cylinders with a plunger diameter of 20 mm. This once again shows impressively how much more roll stiffness the cross-connection of differential cylinder provides compared to two decoupled cylinders according to Sect. 6.3.2. Rakeiha et al. have investigated this special kind of hydraulic suspension arrangement by computer simulation. After setting up the necessary model, they investigated the impact of various excitations known from real operation [RAK93]. The baseline is that improvements of the suspension behavior could be found almost

6.4

Spring Rate Adjustment by Selective Connection of Accumulators

169

Roll stiffness [Nm/rad]

500000

400000 300000

200000 100000

ca. 3000 Nm/rad 0 0

10

20 30 40 Piston diameter [mm]

50

60

Fig. 6.6 Roll stiffness as a function of the piston diameter for a constant rod diameter

in every aspect, such as the roll angle and also the decay of roll oscillations after a special excitation in roll direction. The principle can be developed even further by the creation of a “double crossconnection” of four cylinders, one at each corner of a vehicle suspension. This system even enables the creation of roll and pitch stiffness at the same time. This is achieved on a two-axle vehicle by establishing the mentioned cross-connection between the front left and the rear right cylinders as well as between the front right and the rear left cylinders. Applications of this principle can be found, for example, in mobile cranes and off-road trucks. Just one more thought: If synchronous cylinders would be used and crossconnected, additional roll stiffness would be the result here as well. However, since AR and AK are equal, there would be no active load carrying area and therefore also no vertical spring rate. The use of this arrangement is therefore limited to very special applications.

6.4 Spring Rate Adjustment by Selective Connection of Accumulators An adjustment of the spring rate makes special sense in applications where the suspension is subjected to very different operating conditions. For the best possible function, an adaptation of the suspension properties is very useful. The hydropneumatic suspension with hydraulic preload offers the possibility to vary the rodside preload pressure and therefore vary the spring rate. For non-preloaded and also for mechanically preloaded suspension systems, another method of adjustment needs to be found.

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6 Special Functions of Hydropneumatic Suspension Systems

Equation (2.30) for the calculation of the spring rate of a hydropneumatic suspension system with mechanical preload can also be used for the non-preloaded system by setting FV = 0 and cmech = 0. From this equation it is clearly visible that only the variables p0 and V0 as well as the parameter n can be used to change the spring rate. An adjustment of FV and cmech is possible, however only with a (usually) unjustified effort. c=n

(FF1 + FV )2 + cmech p0 V0

(6.20)

Active adjustment of the polytropic exponent for the gas inside the accumulators is hard to imagine. New principles would have to be found to allow this. So what remains is the possibility of changing p0 and V0 . A change of the precharge pressure p0 by a specific increase or decrease of the gas fill inside an accumulator with the volume V0 seems to be complicated. However it has already been described in patents – see Sect. 8.1. Although this principle offers the advantage of an infinitely variable precharge pressure and therefore an also infinitely variable spring rate, it is not known if this has ever been used in a practical application. Therefore no further explanations are given here. More promising is the adjustment of V0 . It can be done by assigning two or more accumulators to the suspension system and switching them on and off depending on how much gas volume is needed (Fig. 6.7). The respective accumulators could then all have the same precharge pressure p0 or could be charged to different pressure levels. In any case, the selective connection of (a limited number of) accumulators provides a stepwise alteration of the suspending gas mass. The spring rate then changes according to the change in gas mass (“number of gas molecules”). In particular for the non-preloaded hydropneumatic suspension, this can be illustrated as follows: when cutting down the gas mass to half of the

Fig. 6.7 Hydropneumatic suspension with switchable accumulator

6.4

Spring Rate Adjustment by Selective Connection of Accumulators

171

original value, the spring rate will double; for a third of the gas mass the spring rate will triple and so on. It is therefore easy to see that the selective connection of accumulators is an effective way of achieving noticeable changes in suspension characteristics. However, the criteria mentioned in Sect. 3.1.3 for the selection of accumulator parameters still need to be considered (maximum pressure criterion, diaphragm deformation criterion). In particular, this means that, even in the condition with minimum accumulator volume and utilization of the full suspension stroke, enough gas volume must be available to meet these criteria. Otherwise there would be risk of damaging the accumulators. As mentioned in Sect. 6.1.1, here too the pressure equalization processes during the reactivation of accumulators must be kept in mind, along with their effect of a suddenly changing piston position and therefore also suspension level. Due to the permanently connected accumulator this sudden level change will be somewhat less severe, also depending on its size. Nevertheless the counteractions described in Sect. 6.1.1 need to be considered here as well to prevent possible safety issues. Citroen utilizes the principle of de- and reactivation of accumulators in their Hydractiv suspension system. In this case, one accumulator is directly assigned to each of the two suspension cylinders of an axle, while a third accumulator is placed centrally and is connected to both struts when a comfortable ride is desired. At the same time this circuit connects the two struts with regards to reduced roll stiffness – read more in Sect. 7.2. It is also possible to use multiple accumulators to influence suspension properties depending on the suspended load. In this case the accumulators are not actively selected on/off by an external signal but the precharge pressures of the accumulators themselves determine when they are active and when not. So at low suspended loads which result in a low hydraulic pressure in the cylinders, one accumulator with a low precharge pressure can be active and suspending, while another accumulator is still not filled with hydraulic fluid since its precharge pressure is above the cylinder pressure. If the suspended load is increased to a high level, the pressure in the cylinders increases and the other accumulator too is filled with hydraulic fluid and takes an active part in the spring characteristics. However such systems are difficult to handle especially with regards to the diagram deflection criterion (Sect. 3.1.3). If the load cases are very well known and clearly determined and reproducible this system is definitely an option. In this case the accumulator sizes and precharge pressures can be predetermined in a way such that the diagram deflection criterion is not infringed.

Chapter 7

Design Examples

In this chapter the content of the previous chapters will be explained in more detail using two actual design examples. Both are located in the wide area of vehicle chassis suspensions since most hydropneumatic suspensions can be found in these applications.

7.1 Tractor Front Axle Suspension TLS by John Deere In 1997 John Deere introduced the first generation of their Triple Link Suspension (TLS I) and it was available for tractors of the 6010 series. The special concept with the long longitudinal trailing arm and the rather short lateral link (panhard rod) has a special function with regards to the suspension behavior during braking. The components are arranged in a way so the front wheel brake forces create a torsional moment on the trailing arm which helps to avoid the usual forward pitch motion (nose dive). A characteristic feature of the TLS I on 6000 series tractors is the limitation of the axle oscillation angle (relative to the longitudinal vehicle axis) by special chains. However this is not necessarily required as one of the earlier developments of the TLS axle shows on the John Deere tractors of the 7020 and 7030 series. The function of the original setup and working principle is very well described in the respective patent applications [EP512] and [US859]; the following illustrations in Figs. 7.1, 7.2 and 7.3 have been taken from there. The illustrations show clearly the longitudinal trailing arm 24, the panhard rod 60, the chains 88 and 90 as well as the suspension cylinders 68 and 70. The latter are connected to the accumulators 82 and the hydraulic control block 80 via hydraulic lines. Figure 7.3 shows the schematic of the hydraulic circuit. The setup is a hydropneumatic suspension with hydraulic preload applied by a constant hydraulic pressure in the rod chamber, regulated by the pressure control valve 52. This valve is only active, if solenoid valve 44 is energized and hydraulic fluid can flow from the pump P to the rod chambers 28 and 29 of the cylinders (if necessary). Moreover, with energized valve 44 the check valves 48 and 54 are hydraulically released and this free connection of the rod chambers with the pressure control valve allows full control of the preload pressure (increase and decrease). W. Bauer, Hydropneumatic Suspension Systems, DOI 10.1007/978-3-642-15147-7_7,  C Springer-Verlag Berlin Heidelberg 2011

173

174 Fig. 7.1 Partially exploded view of the TLS front axle suspension

Fig. 7.2 Detailed front view

7

Design Examples

7.1

Tractor Front Axle Suspension TLS by John Deere

175

Fig. 7.3 Hydraulic schematic of the front axle suspension TLS I

The mentioned check valves ensure a leakage-free separation of the suspension circuits from the leveling control circuits for the periods without control actions. Solenoid valve 42 in cooperation with the flow resistor 46 allows the change of the suspension level. The electronic controller 40 decides on the need for level changes based on various input signals such as the level signal from the position sensor 58 and the vehicle velocity signal. For leveling up, both solenoid valves 42 and 44 are energized; for leveling down only solenoid valve 44 is energized. The patent [US859] also gives information about the basic data of this suspension system for a 96 kW agricultural tractor, which corresponds to the 6910, the largest model of the 6010 series in 1997. In column 9 of the patent the following information can be found: Piston diameter: 50 mm Rod diameter: 38 mm Lever ratio of the mechanical setup (wheel position, cylinder position): 0.868 Accumulator volume, pistonside, per axle: 2800 cm3 Accumulator pressure, pistonside: 3.2 MPa Accumulator volume, rodside, per axle: 1000 cm3 Accumulator pressure, rodside: 3.3 MPa Polytropic exponent: 1.3 Preload pressure rodside, constant: 9.2 MPa Maximum rebound displacement from design position: –52 mm Maximum compression displacement from design position: 52 mm

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Design Examples

The patent text furthermore explains that the axle loads for such a tractor range from about 10,000 to 70,000 N. The equation of the spring rate of hydropneumatic suspensions with constant hydraulic preload deduced in Sect. 2.2.5 c=

np2V A2R n(FF1 + pV AR )2 + p0,K V0,K p0,R V0,R

(7.1)

would now directly allows to calculate the spring rate as a function of the axle load. However, one more important thing has to be considered: the mentioned equation is only valid for a suspension system with a lever ratio of i = 1, which means that the suspension cylinders are directly connected to the wheel without any leverage. Now this is not the case in this example (i = 0.868) and therefore further calculations need to be performed to take the respective leverage into consideration. The following examination of the geometry and forces at the longitudinal trailing arm will help with this. In Fig. 7.4 D is the pivot point of the trailing arm, while A is the force application point of the suspension cylinder and B is the force application point of the suspended axle load FF1 . Both forces are defined to be perpendicular to the lever in this example. The lever ratio i is i=

xB lB = xA lA

(7.2)

The balance of torsional moments relative to point D brings us to: FB lB = FA lA

(7.3)

Introducing the spring stiffness to express the respective forces with FA = cA xA and FB = cB xB results in: cB xB = cA xA

1 i

and converted

cB = cA

xA 1 xB i

lA lB

FA A

B xB

D FB = FF1

Fig. 7.4 Influence of the lever ratio of the mechanical setup

xA

(7.4)

7.1

Tractor Front Axle Suspension TLS by John Deere

177

and therefore: cB = cA

1 i2

(7.5)

Before combining Eqs. (7.1) and (7.5), please consider that the spring rate cA is calculated for another spring load, i.e. the spring load actually acting onto the suspension cylinder. So, in order to calculate the axle spring rate cB as a function of the suspended axle load FB = FF1 , the load on the suspension cylinder FA = FF1 · i needs to be calculated to achieve to the correct result. With these relationships, the equation for the axle spring rate cB as a function of the suspended axle load FF1 for hydropneumatic suspensions with hydraulic preload and a lever ratio i can be expressed as:  cB =

np2V A2R n(FF1 i + pV AR )2 + p0,K V0,K p0,R V0,R

 ·

1 i2

(7.6)

1400

3,5

1200

3,0

1000

2,5

800

2,0

600

1,5

400

1,0 Spring rate

200

0,5

Vertical natural frequency 0 0

20000

40000 60000 Suspended axle load [kN]

Fig. 7.5 Axle spring rate and vertical natural frequency of TLS I

0,0 80000

Vertical natural frequency [1/s]

Axle spring rate [N/mm]

Considering the above mentioned basic data of the setup, the characteristic curve for the axle spring rate vs. the suspended axle load can be calculated and is shown in Fig. 7.5. It is easy to recognize that a vertical natural frequency of about 2 Hz is achieved for most of the range of the suspended axle load. This enables constant suspension properties and therefore a relatively constant ride behavior, of course also depending on which load distribution causes the front axle load. An additional positive aspect of this spring characteristic is the suspension behavior during the work with a heavy

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Design Examples

rear implement (such as a plough). The center of gravity of the mass of the plough is far behind the tractor causing on one hand a reduction in front axle load and on the other hand a high moment of inertia for pitch motion. With a non-preloaded hydropneumatic suspension this would lead to a very low pitch natural frequency and therefore spongy and difficult to control ride behavior. The preloaded system provides a relatively high spring rate in the lower load range which results in a higher vertical natural frequency and therefore an acceptable pitch natural frequency and better ride behavior. The TLS I system uses diaphragm accumulators. Therefore the following calculations will clarify whether the system meets the diaphragm deformation criterion. Rodside accumulator: The rodside preload pressure is set to 9.2 MPa and the 1 l accumulator is precharged to 3.3 MPa. This means that, when preloaded, the diaphragm of this accumulator is not in the center between the 10 and 90% oil fill limit but already somewhat closer to the high pressure side – the gas is compressed to about one third of its original volume. From this point of view, a 0.75 l accumulator with a 4.4 MPa precharge (and therefore the same “number of gas molecules”) would possibly have been a bit more suitable, since its diaphragm would have been in its center position at 9.2 MPa preload pressure. However it has been proven by years of experience that the 1 l accumulator works well and without problems. The following calculation of the permissible range of precharge pressures (according to Sect. 3.1.3) for this 1 l accumulator reconfirms this. pV,min = pV,max =

V0 p0,T,korr 0.9V0 − AR 2h V0 p0,T,korr 0.1V0 + AR 2h

(max. T, upper gas fill tolerance, no diffusion)

(7.7)

(min. T, lower gas fill tolerance, max. diffusion) (7.8)

It is important that for the calculation of the full cylinder stroke the lever ratio i is also considered. This makes: h = 2 × 52 mm

1 ≈ 120 mm 0.868

(7.9)

Assuming a relevant temperature range of −20 to +60◦ C, a gas fill tolerance of ±0.15 MPa and a permissible maximum diffusion pressure loss of 0.5 MPa that preload pressure limits can be calculated according to the equations in Sect. 3.1.3: pV,min ≈ 4.9 MPa and pV,max ≈ 11.5 Mpa The specified preload pressure of 9.2 MPa is well within these limits and is therefore permissible. The next step is to calculate the maximum pressure in the rodside circuit according to Sect. 3.1.3:

7.1

Tractor Front Axle Suspension TLS by John Deere

 pmax = pV 

 V0 p0,T,korr n pV

V0 p0,T,korr pV

− AR h2

n

179

(7.10)

(minimum temperature T, lower gas fill tolerance, maximum diffusion) Applying the respective values results in a maximum rodside pressure of 17.9 MPa. Normal pressure ratings for accumulators usually are 20, 25 and 35 MPa. Therefore this value seems to be acceptable even without the knowledge of the maximum permissible pressures in this particular suspension system. Pistonside accumulator: This accumulator is exposed to the pressure which results from the equilibrium of forces between, on one hand, the force on the pistonside area and, on the other hand, the sum of the forces on the ring-shaped rodside area and the suspended load. Based on this equilibrium and the relevant diaphragm deformation criterion, equations for the determination of the limits of the static spring load have been established in Sect. 3.1.3 – remember the assumption, that the lever ratio i there was predefined to be 1. FF1,min =

V0 p0,T,korr 0.9V0 − AK h2

AK − pV AR

(7.11)

(maximum temperature T, upper gas fill tolerance, no diffusion)

FF1,max =

V0 p0,T,korr 0.1V0 + AK h2

AK − p V AR

(7.12)

(minimum temperature T, lower gas fill tolerance, maximum diffusion) Once again the lever ratio i of the mechanical setup needs to be considered and therefore a value of 120 mm has to be applied for the cylinder stroke h. Including the above mentioned values for the temperature range, the gas fill tolerance and the diffusion, results in a range for the permissible static spring load at the suspension cylinders of minimum 3100 N and maximum 31,700 N. Considering the lever ratio this means a permissible range for the static axle spring load from Fmin = 3570 N to Fmax = 36, 520 N. It becomes obvious that the initially mentioned range for the suspended axle load of 10,000–70,000 N is not completely fulfilled in the upper region. However it is possible without severe restrictions to reduce the requirements. For example, the cylinder stroke applied in the calculation can be cut down to half of its overall value, since at −20◦ C suspension motions all the way to the mechanical end stop are almost impossible considering the extremely high damping of a highly viscous hydraulic fluid at these low temperatures. Furthermore the permissible diffusion pressure loss can also be cut down to 0.3 MPa which is about 10% of the original precharge pressure. When recalculating the maximum suspended static axle load with these two assumptions, one ends up at about 58,000 N. This is still not at the upper limit of 70,000 N however it is a reasonable value for a 96 kW

180

7

Design Examples

agricultural tractor with a curb weight of 5400 kg. Please remember that this is the suspended axle load. So the actual ground force of the wheels is higher by the weight of the wheels and the axle itself. Assuming that this wheel+axle-weight is about 900 kg, the ground force at maximum static suspended axle load is about 67,000 N. The calculated maximum value is a limit which should not be exceeded permanently. This means that under certain circumstances it can be permitted to exceed the value sometimes, for example, in extreme situations. In particular, for a tractor, which is usually a multi-purpose machine, this is usually not an issue, since not all applications cause extreme pressures in the suspension hydraulic system. The ultimate answer to this question will be provided by a long term test of the overall system in practical applications. From a theoretical point of view, the highest axle load that can be lifted by the system pressure is:  1 FF1,max,theo = pSys AK − pV AR i

(7.13)

Assuming pSys = 20 MPa for the available maximum system pressure, the result is FF1,max,theo ≈ 72, 500 N Not much can be said about the damping of the TLS I suspension since it is provided by many individual flow resistors on the fluid path from the cylinder to the accumulator, both in the pistonside circuit and in the rodside circuit. Examples for these flow resistors are the outlet port at the cylinder, the fittings, hoses and tubes as well as the hydraulic level control block (which is, in this design, also passed by the fluid). Again it is the testing which will provide real numbers about the actual overall flow resistance and therefore the damping behavior.

7.2 Passenger Car Axle Suspension by Citroen The story of Citroen’s hydropneumatic suspension begins in the early 1950s. At first it was presented at exhibitions before it was brought into serial production for the first time on the rear axle suspension of the Citroen 15CV in 1954 (part of the well known model range of the “Traction Avant”). However the start of the hydropneumatic system will be forever related to the, at that time, newly developed Citroen DS ([de’εs], the goddess), which, for the first time ever, offered this new suspension system for front and rear wheels. This car was introduced in 1955. The comfort and the special driving sensation accomplished by its soft suspension behavior is legendary today. Over the years, as part of the further development and advancement of Citroen’s hydropneumatic technology, the suspension became somewhat stiffer. This is partly due to the new design of suspension components, but, on the

7.2

Passenger Car Axle Suspension by Citroen

181

other hand, was probably also intentional in some cases since the market today wants more sporty and agile cars. Amongst other things, this and the higher cost of the hydropneumatic suspension are assumed to be two reasons why, in the fifties as well as today, especially smaller Citroen cars are equipped with conventional coil spring and damper elements. However in the larger models, hydropneumatic suspension is still standard or at least available as an option. The technology has been on one hand upgraded and extended with more features, on the other hand refined in the design details. One of the main goals of all developments was obviously an improvement of the driving behavior and safety, without compromising comfort. Two major milestones in the advancement of Citroen’s hydropneumatic suspension are worthwhile to be mentioned: 1. The “Hydractiv”-Technology, which has been introduced in 1989 with the new model XM and which has been improved over the years in basically three stages. 2. The “Activa”-suspension, offered from 1995 for the model Xantia. It provides an active stabilization of the vehicle body with regards to roll motion. A more detailed description is given on the following pages.

7.2.1 Citroens First Hydropneumatic Suspension This is the basis for all future models and it had a relatively (!) simple setup when it was introduced in the 1950s. It is a non-preloaded, hydropneumatic suspension system with single-acting cylinders and accumulators directly mounted to them. In the fluid path between cylinder and accumulator a damping unit is located, which acts similarly to a damping unit of a monotube-damper. Both suspension cylinders are hydraulically connected so the entire roll stability is provided by the mechanical stabilizer bars at the front and the rear axle. The system is equipped with two level control units (see also Sect. 5.2) which are assigned to the front and rear axle. They are connected to a central vehicle hydraulic supply system which, for example, also feeds the brakes, the steering and gearbox and clutch. Figure 7.6 illustrates the schematic setup of the system. An important issue, which Citroen has solved in a superior manner, is the friction of the hydropneumatic suspension cylinder. Due to the higher operating pressures, it is higher than on a regular shock absorber. A high level of friction would lead to worsened response of the suspension with regards to many small, short-term accelerations from uneven surfaces such as cobblestone (harshness). Citroen solved the friction problem with two particular design features: 1. A sealing system with very low friction is used. The disadvantage of some leakage has been consciously accepted and therefore the leaking fluid is returned to the reservoir by separate lines.

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7

Design Examples

level controller

reservoir

pump

pressure regulator

accumulator

priority valve

to brakes, steering and gearbox/clutch

level controller

Fig. 7.6 Schematic setup of the basic Citroen suspension system

2. The lever ratio i for the connection of the suspension cylinder in the mechanical linkage has been chosen to be very high. This helps to reduce the ratio of friction forces and spring forces as explained in Sect. 2.3.1. The design implementation from the DS until the model CX was to guide the front wheels by (costly) double-wishbones and connecting the suspension cylinder to the upper wishbone [REI89]. The principle of the slightly leaking sealing system is still part of the latest Citroen suspensions while the double-wishbone arrangement was replaced by a McPherson-type strut at the front axle in the late eighties, probably due to design space requirements and cost reasons. This system reduced the lever ratio to about i = 1 with a negative impact on friction. Furthermore with this design, forces coming from the wheel have to be partially supported by the strut, which results in lateral forces and torsional moments in the sliding components and therefore also to an increase in friction. Some “life-long” Citroen owners claim that with this setup the suspension comfort is no longer able to reach the high levels of the earlier years. However it is unclear whether this subjective assessment is true, in particular, when considering the technological advancements over the past 50 years. Anyway, the soft, low-frequency setup of the suspension is still typical for Citroen and a characteristic of Citroen cars with this suspension principle. The natural frequency of the pure spring-mass combination is tuned to significantly below

7.2

Passenger Car Axle Suspension by Citroen

183

1 Hz, while other cars are usually above this value, sometimes even up to 1.4 Hz or more for sports cars. The low natural frequency is only possible in combination with a level control system. If not, even small variations of the chassis weight would lead to bottoming out suspension struts.

7.2.2 Hydractiv Suspension The above mentioned soft spring setup would lead to a high roll angle during cornering if no countermeasures were taken. The original suspension system therefore had very strong roll stabilizer bars. However these strong mechanical stabilizers have the disadvantage, especially when driving in a straight line, that excitations coming only from one side of the vehicle are cushioned less comfortably compared to a soft stabilizer bar. This is where the Hydractiv-principle shows its advantages: For most of the time while driving, a soft roll stabilization, provided by relatively soft stabilizer bars, is effective and provides good comfort. Then, in driving situations with lateral acceleration, the suspension hydraulics are changed in a way so it creates additional roll stiffness. Moreover the spring rate at each vehicle corner is increased which results in a further stabilization –also during longitudinal acceleration, resulting in reduced pitch motion. An electronic controller decides, based upon a number of input signals, when to set which suspension setup. Citroen claims as a rule of thumb, that for about 85% of the operation time of such a vehicle, the suspension remains in the soft and comfortable setup, while for the remaining 15% of the time the harder mode with increased vehicle stability is activated [HEN90]. Figure 7.7 shows the hydraulic schematic which provides the ability to switch spring stiffness and roll stabilization (please refer also to Fig. 2.13). The soft setting can be chosen by energizing a solenoid valve which acts as a pilot valve for one 4/2-spool valve per axle. Only one axle is shown in the illustration. When energized, this solenoid valve directs pressurized hydraulic fluid to one end face of the valve spool, bringing it into a position which connects all ports at once. This way the suspension struts of an axle are interconnected by a fluid path through damping elements. Additionally a connection is established to a third accumulator; the oil from and to it must also pass through the mentioned damping elements. The effective amount of suspending gas per wheel is therefore provided by one accumulator directly at the cylinder plus the half of the center accumulator. The spring rate is then very low and the hydraulic suspension does not provide any roll stiffness. When de-energizing the solenoid of the pilot valve, the respective end face of the valve spool is unpressurized. Now the pressure on the opposite spool end face (created by the center accumulator) will move the spool to the other position, which separates all ports from each other. The effect is that both struts of an axle work individually and on top of that with a lower amount of gas. So the struts then have a higher spring rate and therefore provide a higher vertical natural frequency. On top of that, hydraulic roll stiffness is created by the individual springs. This state of the suspension creates a safer ride behavior which is most probably the reason why it was chosen as the fail-safe state (unenergized). However leveling must be

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Design Examples

D

D D

D

level control valve

pilot valve

pump

D

= Damping element

reservoir

4/2-spool valve shown in "hard” setting

Fig. 7.7 Hydraulic schematic of Citroens Hydractiv-suspension

possible also in this state of separate struts. For this purpose a special hydraulic circuit was created with two check valves with hydraulic release arranged according to the illustration. These check valves allow only an interconnection oil flow during leveling actions, at all other times they keep the struts separate. It is not an evident, but nevertheless important detail that in the transition between the two suspension settings, all four ports of the 4/2-spool valve (12a, 12b, 13 and the invisible port 14 for the level control valve) must be connected and disconnected at once or at least within a very short time. This helps to avoid different suspension settings left and right during the transition phase. Figure 7.8 is taken from [US672] and shows how this function is implemented in the 4/2-spool valve. It seems to make even more sense for the transition from the soft to the hard setting that initially the center accumulator is separated from the other ports and then shortly after that both struts are disconnected. This ensures that the disconnected center accumulator is loaded exactly with the average pressure which was active at the struts shortly before the disconnection. In the opposite direction, the transition to the soft setting then would start with at first a connection of both struts and subsequently a connection of them with the center accumulator. It is unclear whether or how Citroen accounted for the fact that the disconnected center accumulators could be loaded with pressures which differ from the pressures in the respective struts – please also refer to Sects. 6.1.1 and 8.3. There are however some indications that this problem is only a minor issue for the application in the Hydractiv system:

7.2

Passenger Car Axle Suspension by Citroen

185

10 valve spool

16 a+b damping elements

12a bore to left cylinder

17a connection to left cylinder

12b bore to right cylinder

17b connection to right cylinder

13 bore to accumulator

25 connection to level control valve

Fig. 7.8 Hydractiv setting control valve

1. The hard setting is only activated when the vehicle is in motion; load changes by passengers getting in and out are therefore no problem. 2. During the hard setting (disconnected state of the center accumulators) there are only minor load changes with respect to the average load of an axle. 3. If load changes occur, the reconnection of the center accumulators could be slightly delayed. 4. Since each strut incorporates its own accumulator, a pressure impulse from the center accumulator would be reduced by the strut accumulator and therefore barely noticeable. 5. It is possible that the leakage between the bores 12a, 12b and 13 allows an equalization of respective pressure differences. Maybe even a defined slightly increased leakage is built in for this purpose. The equation for the spring rate of non-preloaded hydropneumatic suspension systems allows us to calculate the stiffness for both suspension settings. It is particularly convenient that neither the cylinder dimensions nor the lever ratio i need to be considered for this calculation (all these parameters are not available anyway). The spring rate at the wheel only depends upon the amount of gas (the gas mass expressed by the accumulator volume and the precharge pressure), the properties of

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Design Examples

the gas (expressed by the polytropic exponent n) and the load on the spring. This is shown in the following short calculation. cB = cA

2 2 nFA nFF1 1 n (FF1 i)2 = = = i2 p 0 V0 i 2 p 0 V0 i 2 p 0 V0

(7.14)

This means that also the vertical natural frequency only depends on the above mentioned parameters and additionally the gravitational acceleration. It can therefore be calculated according to the equation in Sect. 2.2.3: 1 f = 2π

nFF1 g p 0 V0

(7.15)

A rough calculation of the chassis vertical natural frequency is subsequently shown for the example of the Citroen model XM. Curb weight (including fuel and driver) is 1700 kg at an assumed weight distribution of 65% front and 35% rear, while the maximum permissible gross laden weight is 2150 kg at a weight distribution of 55% front and 45% rear. Unsprung masses are not considered. The following data are used for the accumulator parameters: Accumulator at the strut, front: 5 MPa/400 cm3 Center accumulator, front: 7 MPa/500 cm3 Accumulator at the strut, rear: 3 MPa/400 cm3 Center accumulator rear: 5 MPa/400 cm3 The calculated wheel loads are: Empty (incl. driver): front 552.5 kg rear 297.5 kg Maximum loaded: front 591.25 kg rear 483.75 kg With these data the vertical natural frequencies can be calculated. The hard setting for the empty vehicle including driver at the front axle results in: fFA,empty,hard

1 = 2π

1.3 · 552.5 kg · (9.81 N/kg)2 5 × 106 N/m2 · 4 × 10−4 m3

= 0.94 Hz

The corresponding value for the rear axle is: fRA,empty,hard = 0.89 Hz At maximum load these values increase to 0.97 Hz for the front axle and 1.13 Hz for the rear axle. For the soft setting the additional gas mass provided by the center accumulator needs to be considered. The calculation for the front axle for the empty vehicle results in:

7.2

Passenger Car Axle Suspension by Citroen

1 fFA,empty,soft = 2π

187

1.3 · 552.5 kg · (9.81 N/kg)2 5 × 106 N/m2 · 4 × 10−4 m3 + 7 × 106 N/m2 · 0.5 · 5 × 10−4 m3

= 0.68 Hz

The corresponding value for the rear axle is: fRA,empty,soft = 0.66 Hz. At maximum load these values increase to 0.70 Hz for the front axle and 0.84 Hz for the rear axle. The calculated values are very low compared to conventionally sprung passenger cars (with coil springs). However they fit to the natural frequency of 44 min−1 (which is about 0.73 Hz) which Reimpell and Stoll mention for the Citroen model GSA [REI89]. Such a low vertical natural frequency can only be provided in conjunction with a level control system. Additionally the fast adjustment of the suspension setting, too, allows tuning such a low frequency in the basic setup, since excessive chassis movements during cornering or acceleration/deceleration can be avoided by switching to the hard setting. It is moreover important to mention that the damping elements between cylinders and center accumulator have not been taken into consideration for the above calculation of the spring rates during the soft setting. On one hand these damping elements act as dampers for the fluid flow from one side to the other and therefore take the oscillation energy out of the roll motion. On the other hand they additionally restrict the fluid flow between the cylinder and the center accumulator. So if these damping elements create a strong restriction, the fluid will be directed the more to the cylinder mounted accumulators (and not to the center accumulator), the faster the motion of the piston and therefore the higher the flow rate from the cylinder. This means that, depending on the piston speed, different spring rates will result from the hydropneumatic setup – the higher the speed, the higher the spring rate. The roll stiffness of only the hydropneumatic setup is zero in case the soft setting is active. Since both cylinders are connected to each other, roll damping is created according to the above description. So for the soft setting the required roll stiffness is purely provided by the mechanical stabilizers, the anti-roll bars. The bar diameter is for the Citroen XM 24 mm at the front axle and 22 mm at the rear axle. When switching to the hard setting, the hydropneumatic springs are decoupled from each other and create additional roll stiffness as described in Sect. 6.3.2: w=

L2 MD =c α 2

in [Nm/rad]

(7.16)

where c is the wheel spring rate and L the track width. For the front axle of the Citroen XM the wheel spring rate of the empty vehicle (including fuel and driver) can be calculated: cW = n

2 FF1,W

p0 V0

= 1.3

(552.5 · 9.81 N)2 N ≈ 19, 100 6 2 −4 3 m 5 × 10 N/m · 4 × 10 m

188

7

Design Examples

Using L ≈ 1.5 m allows to calculate the roll stiffness: w = 19, 100

N (1.5 m)2 ≈ 21, 500 Nm/rad m 2

This value is in the expected range of for the mechanical front stabilizer bar with the above mentioned geometry. This means that the hard setting of the hydropneumatic suspension adds significantly to the roll stiffness and therefore significantly reduces the roll angle during cornering compared to the effect of only the mechanical anti-roll bar. The electronic control system of the Hydractiv suspension system is not explained here; however detailed information can be found in [CAR90].

7.2.3 Activa Suspension For a further reduction of the chassis roll angle, Citroen developed an active roll stabilization system called the Activa suspension. While the Hydractiv suspension within its different development stages was basically improved in the details of the hydropneumatic suspension elements and controls, the Activa suspension offered a completely new solution to the problem of excessive roll motion of softly sprung cars. The basic principle was to make use of the already available anti-roll bar setup and use it to actively control the roll angle. This is achieved by a hydraulic cylinder coupled on one side of the vehicle between the strut and the anti-roll bar (Fig. 7.9). This cylinder can: 1. act as an additional (hydropneumatic) spring softening the roll stiffness if it is connected to an accumulator (state 1). 2. act as a rigid coupling rod if fluid flow from and to the cylinder is fully blocked (state 2).

struts coupling rod

wishbones hydraulic cylinder

anti-roll bar

Fig. 7.9 Interaction of Activa-cylinder, anti-roll bar and strut

7.2

Passenger Car Axle Suspension by Citroen

189

3. be used as an active actuator for a targeted torsion of the anti-roll bar by filling/draining the cylinder chambers with a specific amount of hydraulic fluid (state 3). In order to allow these different additional functions of the Activa suspension with as few new components as possible, Citroen developed the necessary hydraulic circuit based on the components of the Hydractiv suspension. Figure 7.10 is derived from information in [CIT95]. It shows a setup which seems, on first glance, to be quite similar to the Hydractiv system. The 4/2-position spool valve acts as a 3/2-position valve and the level control valve is replaced by the roll angle control valve (the same basic component). The latter now controls the position of the wheels in a way so both struts of an axle are possibly extended by the same amount, opposed to the level control valve which ensures that the average position of both struts is kept in the desired range. Since now one double-acting cylinder per axle needs to be controlled, a trick is necessary to be able to utilize the available components originally designed for the (single-acting) level control system. The trick is to constantly preload the rodside of the Activa cylinders by applying the full pump pressure there. Additionally, to ensure elasticity of the rodside circuit, an accumulator is included for both axles. So the Activa cylinders are retracted by connecting the piston chambers to the reservoir

Activa cylinder front

D

D

Activa cylinder rear

roll angle control valve pilot valve position difference of front wheels

pressure source

reservoir

Fig. 7.10 Functional schematic of the roll angle control in the Citroen Activa suspension

190

7

Design Examples

which lets the high rodside preload drive the fluid out of the piston chambers and therefore retract the cylinders. If the spool of the roll angle control valve is in its middle position, the pistons of the Activa cylinders are clamped between the rodside preload force and the blocked fluid volume in the piston chambers. The cylinders are then rigid, of course only if the pistonside accumulator is disconnected by the 3/2-position valve. When driving straight, the system is in state 1. The pilot valve is energized and therefore the 3/2-position valve connects the accumulator to the piston chambers of the cylinders. The roll stabilization is then very soft since the mechanical torsion spring and the hydropneumatic springs are connected in series. Therefore different wheel positions on one axle are counteracted by the system with only a low restoring force. In combination with the Hydractiv suspension system in the soft setting, a maximum level of comfort is achieved during rides with low longitudinal and lateral acceleration. When straight driving ends and cornering is initiated, at first the Hydractiv portion of the suspension is switched to the hard setting (as described above) and state 2 of the Activa system is activated – the cylinder turns into a rigid coupling rod. The rigidity is achieved by de-energizing the pilot valve which brings the 3/2-position spool valve into the position which decouples the accumulator from the cylinders’ piston chambers. This setup provides the maximum roll stiffness of the selected components. It is particularly high due to the large diameters of the mechanical stabilizer bars. The Xantia Activa has a 28 mm diameter anti-roll bar in the front and a 25 mm anti-roll bar in the rear [GOR95]. The roll angle is correspondingly low. If, in the course of the cornering, the lateral acceleration increases, the roll angle will increase as well. If it exceeds a certain value, state 3 of the Activa system is activated. The difference in piston displacement of both struts at the front axle leads to an activation of the roll angle control valve and hydraulic fluid is pressed into or released from the piston chambers of the front and rear axle Activa cylinder. This brings the chassis back into a position which is supposed to be as parallel as possible to the road surface. Citroen claims that their system keeps the roll angle below 0.3◦ at lateral accelerations up to 0.6 g and even at 0.8 g the roll angle does not exceed 1◦ . They furthermore state that the maximum value for lateral acceleration is 1.2 g – this for sure also depends on the tires. The correction time to bring the roll angle back to (possibly) 0◦ after a change in lateral acceleration is claimed to be about 1 s. The control algorithm of the suspension system with Hydractiv and Activa technology takes (among others) the following signals into account: – steering angle (also speed of actuation) – velocity – throttle position (also speed of actuation)

7.2

– – – –

Passenger Car Axle Suspension by Citroen

191

brake pressure (or brake pressure switch signal) chassis motion sensor Drivers ride selector “Sport”/“Comfort” Door and trunk lid contact switch

More information about the Citroen Activa suspension can be found in [CIT95] and [GOR95].

Chapter 8

Important Patents

A wide variety of patent applications has been submitted in the technical area of hydropneumatic suspensions. Some of the most representative and future oriented patents are briefly explained in this chapter. Since the design of the Citroen suspension systems has been illustrated in detail in Chap. 7 (representing important developments in passenger car hydropneumatic suspensions), the main focus of this chapter is put on patents in the area of commercial vehicles. Most patent applications in hydropneumatic suspensions specialize in certain areas of this technology, typically enhancing already advantageous features of the hydropneumatic principle, or compensating for its weaknesses. In this chapter three areas: improvement of the suspension characteristics, roll stabilization/slope compensation and suspension lockout are selected and respective important patents are explained. The main content of these patents is briefly summarized and the most important figures are shown. The years mentioned refer to the point in time when the patent application was submitted to the patent office (filing date). The descriptions of the technical innovation of the patents are boiled down to their very basics; therefore please recall that no liability is assumed for the content of this book in general and in particular of this chapter. For a clarification of details, the respective patent text (including all figures) needs to be consulted, preferably with additional help from a patent attorney.

8.1 Improvement of Suspension Characteristics The relevant patents for hydropneumatic suspension systems with non-changeable suspension characteristics are not explained, since this technology is well known and state of the art for a long time already. Two patent applications representing this level of technology are, for example, the DE4308460 submitted in 1993 by Fendt (Marktoberdorf, Germany) and the DE19748224 submitted in 1997 by Deere&Co. (Moline, USA). Both documents describe suspensions with constant hydraulic preload applied to an axle suspension of an agricultural tractor. Now in the

W. Bauer, Hydropneumatic Suspension Systems, DOI 10.1007/978-3-642-15147-7_8,  C Springer-Verlag Berlin Heidelberg 2011

193

194

8 Important Patents

following, patents are described with a technology which purposefully influences variable parameters, for example, the rodside preload pressure, active accumulator volume and active gas mass.

8.1.1 DE1755095 It was back in the year 1968 when the company Industrial Development Co. (Vaduz, Liechtenstein) submitted a patent application for a suspension concept with an interesting background. The basis for this system was a hydropneumatic suspension with hydraulic preload and level control. Contrary to the common and obvious method, the level was not only adjusted by an increase or decrease of the amount of hydraulic fluid on the pistonside (11 in Fig. 8.1) but also by variation of the hydraulic preload on the rodside (30). Therefore, when the load on the system was increased, parallel to the oil flow into the piston chamber, the hydraulic preload on the rodside was reduced to bring the suspension back to its design position. So it was a mixed level control system with level adjustment actions both from the pistonside and the rodside system. The rodside pressure is controlled with regards to the pressure in the piston chamber, which is kept constant according to the invention. The intention was to improve the disproportionately high increase of the spring rate depending on the load, which in some cases is a disadvantage of the hydropneumatic technology. So the intention and the approach are interesting, however, particularly due to the complicated interactions of the piston and rodside system, it is not fully clear if the mechanism really worked and whether it got into production. It seems that the system, especially when not designed properly, is likely to overshoot the mark and create a disproportionately lower or maybe even inverse spring rate vs. load curve. Furthermore, for large load ratios, a large hydraulically active rodside area is necessary which causes an increased cylinder diameter and/or a low rod diameter (including respective stability problems).

Fig. 8.1 System with constant piston chamber pressure

8.1

Improvement of Suspension Characteristics

195

8.1.2 DE19719076 A similar goal had Integral Hydraulik (Meerbusch, Germany – today part of the Carl Freudenberg KG Weinheim, Germany) with their patent application submitted in 1997. However their approach was to set a pressure in the rod chambers (7 and 8 in Fig. 8.2) which is in inverse proportion to the pressure in the piston chambers (3

Fig. 8.2 System with rodside pressure as a function of pistonside pressure

196

8 Important Patents

and 4) in order to flatten out the spring rate vs. load curve. This is achieved by a variable spring preload of the pressure regulating valve (20) on the rodside. The spring preload is changed by the arrangement of the components (41–46 and 51–53). Via a control line (50) the pistonside pressure acts upon the ring-shaped piston surface (47) and displaces the piston (45). With increasing pistonside pressure, the rod (42) is moved further to the left, thus reducing the spring preload of the pressure regulating valve and therefore causing a lower pressure in the rod chambers. This principle enables the setting of an overall spring rate which is almost proportional to the suspended load. When running the system with diaphragm accumulators, it helps to keep the diaphragm deflections within the allowed range and still provide the required load range. The mutual influence of level control on one hand and rodside pressure control on the other hand is certainly a challenge in transforming theory into hardware.

8.1.3 DE10107631 With this patent filed in 2001, Integral stepped back slightly from the inversely proportional rodside pressure (depending on piston chamber pressure) mentioned in the patent above, making it a two step rodside pressure adjustment, implemented via a pressure switch (54 and 56 in Fig. 8.3) controlled by the pistonside pressure. For low pistonside pressures (low axle loads) a defined high rodside pressure is set by having valve (56) in the shown position, this way putting pressure on plunger (55) of the pressure switch mechanism (54) and moving the plunger into its position at the right end position (not clearly shown in the figure). This causes a high preload of the spring (41) of the pressure regulating valve and therefore a high rodside preload pressure. On the other hand during high pistonside pressures, valve (56) flips to its other position depressurizing the chamber of valve (54) to the tank line (26). Therefore the piston (55) is moved to its left end position and therefore a low rodside pressure is set. Both rodside pressure levels (high and low) as well as the switching point can be set to the desired values by hardware changes, especially by the active areas and the springs of valves (54) and (56). This way the hardware can be adapted to the respective system requirements.

8.1.4 DE10337600 This patent submitted by Deere&Co. (Moline, USA) in 2004 further extends the possibility of rodside pressure control. Not only do the solenoid valves allow for any desired level setting via oil flow from and to the piston chamber (14 and 16 in Fig. 8.4) but they also allow variable adjustment of the preload pressure in the rod chambers (18 and 20). The respective pressure is picked up by an electronic pressure sensor (84) and its signal is fed into the control electronics (82). This way a closed loop control of the rodside pressure is possible and the pressure can be adjusted to

8.1

Improvement of Suspension Characteristics

197

Fig. 8.3 Two step rodside pressure adjustment

the actual requirements by an increase or reduction of the hydraulic fluid volume in the rodside system via solenoid valves (60 and 62). The former characteristic curve of spring rate vs. spring load is therefore extended to a “characteristic area” (see Sect. 2.2.6, in particular Fig. 2.25), allowing a high variability of the suspension system; for a given spring load, not only one spring rate but a whole range of spring rates is possible. In contrast to the previously mentioned systems, the control

198

8 Important Patents

Fig. 8.4 Steplessly variable rodside pressure

mechanisms here are purely electronic, while the hydraulic control block is reduced to an actuation and measuring component. A simple and therefore reliable hydraulic system is the result. Moreover, various patents have been filed for hydropneumatic suspensions with mechanical preload. Many patent applications were submitted by the company Herrmann Hemscheidt Maschinenfabrik (Wuppertal, Germany).

8.1.5 DE4221126 This patent from the year 1992 describes a hydropneumatic suspension with cylinder (2 in Fig. 8.5), accumulator (20) and leveling solenoid valves (46), preloaded by a mechanical spring (30). Furthermore, the description says that the spring can be designed as a tension spring, that it can be made from steel or plastic, and that it can have different characteristic curves and preloads. The latter allows the suspension characteristics to be tuned to the specified needs.

8.1.6 DE4234217 It was also in 1992 when Hemscheidt submitted a further patent application in this area. Its basic idea is to apply the preload not onto the suspension cylinder but onto the piston (22 in Fig. 8.6) of a piston accumulator (6). The preload force can be cre-

8.1

Improvement of Suspension Characteristics

Fig. 8.5 Hydropneumatic suspension with mechanical preload

Fig. 8.6 System with mechanical preload on the accumulator piston

199

200

8 Important Patents

ated internally by a spring (28) on the fluid side of the accumulator as well as by an external spring while its spring force is transferred into the accumulator by a piston rod (30). The external spring is an interesting aspect which creates new possibilities: large springs, adjustable preload and therefore adjustability of the suspension characteristics. However, in many cases it is better to have the preload forces act upon the cylinder or the mechanical components of the suspension. This is because the preload then directly counteracts tensile forces acting onto the cylinder, while in the system with a spring inside the accumulator (as shown in Fig. 8.6), tensile forces on the cylinder could cause cavitation due to a lower hydraulic pressure. The following patents deal mainly with changes to the accumulators and their use respectively, which aim to improve the suspension characteristics especially at different suspended loads or in different operating conditions.

8.1.7 DE4223783 This development by Hemscheidt was also filed in 1992 and refers to a hydropneumatic suspension system with at least two hydraulic accumulators (20 and 22 in Fig. 8.7) connected to the suspension cylinder (2) and precharged with different gas pressures. The result is that these accumulators are active in different loading conditions. At low suspended loads, the smaller accumulator (20, precharged with a lower gas pressure) is active, while the larger accumulator (22, with a higher precharge pressure) is inactive and its piston rests at its fluidside end stop – this state is shown in Fig. 8.7. At higher pressures in the suspension cylinder, the piston of the smaller

Fig. 8.7 Several accumulators with different precharge pressures

8.1

Improvement of Suspension Characteristics

201

accumulator (20) is clamped to its gasside end stop by the high hydraulic pressure while the larger accumulator (22) is now active. However for medium pressures in the suspension cylinder there will be a transition load range where both accumulators are active. The problem here is that under these conditions the pistons of the accumulators (26) will frequently run into their end stops due to the oscillation of the cylinder piston (6). The corresponding accumulator components must therefore be designed to be very robust. This makes it obvious that only piston accumulators can do this job. On top of that, unsteadiness in the force vs. displacement curve as well as the spring rate vs. load curve can be expected from such a system. Overall this setup can provide an improvement in the spring rate at different suspended loads (similar to the method of the two-step rodside pressure adjustment). It is especially favorable for applications where medium load levels do not or only rarely occur. One example is large mining dump trucks or articulated haulers which virtually always run either empty or fully loaded.

8.1.8 US6167701 Something similar to the aforementioned Hemscheidt patent has been filed by Caterpillar (Peoria, USA) in 1998. However Caterpillar does not mention that the accumulators alternate in their function depending on the load but only state that the accumulators need to be precharged with different gas pressures. Furthermore, Caterpillar enables with a valve (38 in Fig. 8.8) the connection and disconnection of the accumulator cluster to/from the suspension cylinders and therefore makes it possible to lock out the suspension. Moreover, the text of the patent mentions the possibility that the accumulators can be selectively connected and disconnected by valves which are directly assigned to each accumulator. This gives further possibilities for the adjustment of the suspension properties.

8.1.9 DE19949152 Another approach in improving accumulator behavior was pursued by the company MOWAG (Kreuzlingen, Switzerland) with their patent application in 1999. In contrast to the aforementioned systems and developments, the MOWAG system does not (only) act upon the fluidside of the suspension system but also on the gasside by a targeted increase or reduction of the gas mass inside the accumulator(s). For this purpose, the so called metering cylinder (3 in Fig. 8.9) can be connected to the hydropneumatic springs (1a and 1b), which allows the gas mass in the system and therefore the spring rate to be changed. Moreover the two hydropneumatic springs can be selectively connected or separated on their gas side by the controlling valve system (2). If both springs are used, for example, on the suspension of a vehicle’s axle, this enables switching between soft and stabilized roll behavior.

202 Fig. 8.8 Accumulators with different precharge pressures, suspension lockout

Fig. 8.9 MOWAG suspension system with variable suspending gas mass

8 Important Patents

8.1

Improvement of Suspension Characteristics

203

8.1.10 US6398227 The Case Corporation (Racine, USA) submitted a similar patent application in 2000 which mentions a gas reservoir (20 in Fig. 8.10) which can, if necessary, be connected to the accumulator(s) (22) via valve (36) for the purpose of changing the suspending gas mass in the system. The gas can be transferred by actuating valves (16) and (36) which can increase or reduce the volume for the gas mass in the gas reservoir (20). Position sensors track the position of the pistons in the accumulators which provides the precharge pressure controller (70) with information for proper change of the gas mass. The load holding circuit (14), as Case calls it, could consist, for example, of a suspension cylinder and a level control arrangement and could be mounted to various types of vehicles. Case explicitly refers to wheel loaders and forklift trucks.

Fig. 8.10 Case suspension system with variable suspending gas mass

8.1.11 DE102008012704 One of the most recently published patent documents concerning the improvement of suspension characteristics is DE102008012704 submitted by Deere & Co. in 2008 - the respective US Publication Document No. is US020090230637. The goal of the concept is to allow fast adjustment of the suspension characteristics in order to quickly react to excitations of the system. The approach is a double acting cylinder (20 in Fig. 8.11) with an accumulator (26) connected to the piston chamber (12) and

204

8 Important Patents

Fig. 8.11 John Deere suspension with variable spring and damping characteristic

an accumulator (30) connected to the rod chamber (14) while both cylinder chambers can be connected through a variable flow resistor (34). With this arrangement the spring rate as well as the damping of the hydropneumatic suspension can be varied within the range between the hardest setting (when flow resistor 34 is fully closed) and the softest setting (when flow resistor 34 is fully opened). Figure 8.11 explains the active principle of the concept for a compression stroke. It is important to pay special attention to the thickness of the arrows along the oil lines, which indicate the magnitude and the direction of flow. The upper part of Fig. 8.11 shows the fully closed state. It is clearly visible that all the hydraulic fluid from the piston chamber (12) is displaced into the pistonside accumulator (26) and all the hydraulic fluid streaming into the rod chamber 14 is provided by the rodside accumulator (30). These high fluid volume changes in the accumulators cause large changes in gas pressure and therefore a very high spring rate. Additionally the high flow rates through flow resistors (24) and (32) cause high pressure drops and therefore a high damping of the suspension motion. On the other hand, when the flow resistor (34) is fully open (shown in the lower part of Fig. 8.11) it is obvious that the flow schematic has drastically changed. Now most of the hydraulic flow which leaves the piston chamber is fed back (through flow resistor 34) into the rod chamber while the remaining flow (represented by the displacement of the rod 18) is divided and flowing into the accumulators (26) and (30). This means that only a comparatively small amount of fluid is displaced into the accumulators and therefore the spring rate is quite low. Since the flow rates through resistors (24) and (32) are low as well, the hydraulic damping is also significantly reduced compared to the state with closed

8.2

Roll Stabilization and Slope Compensation

205

flow resistor (34). Intermediate positions of the flow resistor valve (34) create spring rate and damping characteristics in between the above mentioned extreme values.

8.2 Roll Stabilization and Slope Compensation 8.2.1 GB890089 One of the first patents on this topic is the GB890089 submitted by Volvo AB (Goteborg, Sweden) in 1960, one year after the patent application in Sweden. The document describes the coupling of differential cylinders on opposite sides (“crossconnection”) for the purpose of roll stabilization. The figures in this patent give a very good illustration of the working principle of this type of system in general. Furthermore, they do not only mention the cross-connection of the suspension cylinders (5 and 7 in Fig. 8.12) of one vehicle axle but also a cross-connection of the suspension cylinders longitudinally (cross-connection of cylinders on one vehicle side) or diagonally (cross-connection left rear with right front and right rear with left front) on vehicles with at least two axles. The longitudinal cross-connection provides additional pitch stabilization (with no additional roll stabilization) while the diagonal cross-connection provides both an additional roll and pitch stabilization. Figure 8.12 shows that each of the separated suspension circuits is equipped with its own level control valve (26). It is not described how the separate level control valves cooperate and if they are somehow matched or interconnected to each other. Especially in the case of the diagonal cross-connection, a mutual influence of the separate circuits is very likely and could lead to instabilities of the level control system.

Fig. 8.12 Roll-stabilization by cross-connected cylinders

206

8 Important Patents

In the course of development, numerous other patent applications have been submitted, for example, by companies like Caterpillar, Hemscheidt Fahrwerktechnik and Carl Freudenberg/Integral Accumulator.

8.2.2 DE3427508 A patent application submitted by Hemscheidt Fahrwerktechnik in 1984 describes the possibility to connect the suspension cylinders (1 and 2 in Fig. 8.13) of two opposite vehicle sides by a 4/3-position valve (9) in a way, such that the cylinders can either act as individual springs (valve position A) or they can be cross-connected (valve position B). Valve position C even allows the flow out of the piston chamber to be blocked, thus providing a lockout for the suspension movement. The position of the accumulators (10) is chosen intentionally on the rodside (6) of the cylinder since in this case the compression of the cylinder is completely blocked by an inelastic pistonside hydraulic system while a rebound movement is prevented by the pressure in the accumulator acting onto the rodside active area. The three different suspension settings provide the possibility for the operator to adapt the level of roll stabilization to the respective operating conditions. Figure 8.13 shows how the 4/3-valve is integrated into the overall suspension components arrangement. In the patent document it is explicitly mentioned that the described system is arranged

Fig. 8.13 Variable interconnection of the suspension cylinders (Hemscheidt)

8.2

Roll Stabilization and Slope Compensation

207

in addition to an existing vehicle suspension. In case the latter is designed with mechanical springs, the positive effects according to Sect. 2.2.4 will be an additional benefit.

8.2.3 DE10112082 Carl Freudenberg/Integral Accumulator submitted another patent application in 2002 which also aimed at an adjustment of the suspension via a different interconnection of the suspension cylinders and, in addition to the aforementioned patent, the accumulators. Here two different suspension settings are possible: one is the crossconnection of the suspension cylinders, the other is the arrangement in form of the coupling of cylinders on corresponding sides according to Sect. 6.3.1. On top of that, during the coupling of corresponding sides (valves 22 and 23 in Fig. 8.14 are then both in their energized position), the system is operated with a rodside hydraulic preload (accumulator 18 connected to the rod chambers 6 and 7). Moreover, in this setting, an additional accumulator is connected to the pistonside system which

Fig. 8.14 Variable interconnection of suspension cylinders (Freudenberg)

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8 Important Patents

will soften the suspension effect. All in all, this shows similarities to the possibilities of the Hydractiv-suspension by Citroen. However the latter only works with single-acting cylinders, which is the reason why the hydraulic roll stabilization effect can be expected to be lower.

8.2.4 US4411447 Caterpillar found another interesting way to create a roll stabilization effect. In this case it is roll stabilization which can even be designed with only single-acting suspension cylinders (19 and 20 in Fig. 8.15). The function of this system is based on the principle that, additionally to both suspension cylinders, a special piston accumulator (32) is used with two active hydraulic areas (instead of the regular one). The gas pressure then acts upon the full piston area (45) while the first hydraulic pressure acts upon the rod cross-sectional area and the second hydraulic pressure acts upon the differential area of piston area and rod area. The (ring-shaped) differential area and the rod cross-sectional area need to be of the same size. Each of them is connected to one suspension cylinder (with same piston diameter). This way the movement of one cylinder is directly coupled to the movement of the other cylinder just like in a regular synchronization circuit for two lift cylinders. If this kind of suspension was designed only with accumulator 32, it would only create a vertical degree of freedom with a fully rigid roll degree of freedom. However such a vehicle would be uncomfortable since every roll excitation from the road surface would be directly transferred to the operator. This is why the patent includes one additional accumulator for each suspension cylinder (30 and 35) which provides elasticity also for the roll degree of freedom. Depending on the layout and dimensioning of these accumulators, the roll stiffness can be varied. However the influence of their gas fill

Fig. 8.15 Roll stabilization by a special accumulator

8.2

Roll Stabilization and Slope Compensation

209

onto the pure vertical spring rate needs to be considered for the layout of the main accumulator (32). Despite the requirement for the special main accumulator (32) – including the additional frictional forces – this system offers a valuable advantage over the cross-connected cylinder: only one active area in the cylinder is necessary to realize it. This means that the second active area of a double-acting cylinder can be used for a hydraulic preload which makes the setup suitable for applications with wide load ranges. Therefore this patent from 1981 can be highlighted as a very important development. Furthermore, in addition to these technologies for passive stabilization of the roll motion, there were developments which aimed at an active reduction of the lateral tilt during vehicle cornering. “Active” in this case means that external energy is used to keep the vehicle body in a position parallel to the street surface. The ideas were based on the principle that, during cornering, the suspension cylinder of the outside wheel is filled with additional pressurized hydraulic fluid, which extends the cylinder, while on the other hand fluid is released from the inside cylinder, which retracts this cylinder. Only two exemplary patents are mentioned here: one is the DE2048323 submitted in 1970 by Daimler Benz (Stuttgart, Germany), who at that time were quite active on the field of hydropneumatic suspensions. The other one is the US3572746 submitted by Caterpillar (Peoria, USA) which combines the crossconnected cylinders’ roll stiffness with active roll reduction. The principles patented at that time have probably been one of the starting points for the development of the Citroen Activa suspension (find more in Sect. 7.2) and the ABC-suspension (active body control) introduced by Daimler-Chrysler for models like the CL- the SL- and the S-class. On top of roll stabilization, the ABC-suspension also provides a reduction in pitch motion during longitudinal acceleration and a compensation for the aerodynamic forces of cross winds.

8.2.5 US6923453 Caterpillar submitted another patent application in 2001 which describes a technology similar to the working principle of the both aforementioned suspensions. However their goal is mainly to compensate the inclination of a vehicle driving alongside a hill with a steep slope. In the patent this is described for a timber forwarder, the load of which should maintain a substantially horizontal position to keep the machine from tipping. The compensation is provided by hydraulic cylinders between wheels and chassis. The cylinders facing uphill are retracted while the cylinders facing downhill are extended according to the steepness of the slope. The system is governed by a controller (201 in Fig. 8.16) with the help of the inclination sensor signal (205) at the chassis and position sensors signals (202) which basically provide information about the current length of the cylinders (133) and therefore the position of the wheel relative to the chassis. Additionally signals (218) from pressure sensors (215) on each cylinder are mentioned. A similar patent on slope compensation by New Holland (Coex, France) has been filed in 1995 for the wheel suspension, for example, of a grape or berry

210

8 Important Patents

Fig. 8.16 Lateral slope compensation for a timber forwarder

harvester (EP0692183) and by Same-Deutz-Fahr (Treviglio, Italy) in 1998 for the operator’s cab of an agricultural vehicle (EP0994009). The so called “Galileo”-cab was an option for the Same-model “Rubin”. However, like the US6923453, these patents do not include a hydropneumatic suspension. The cylinders therefore are not connected to accumulators. Such a slope compensation could be used with a hydropneumatic suspension as well; however the necessary additional travel for the suspension function needs to be provided.

8.3 Suspension Lockout It is quite obvious that the lockout of a hydropneumatic suspension can be achieved by blocking the flow of hydraulic fluid between the accumulator and the suspension cylinder. Since in this case no fluid can be displaced out of the cylinder, the movement of the piston and therefore the movement of the suspension is stopped.

8.3

Suspension Lockout

211

8.3.1 US3953040 This patent by Caterpillar filed in 1975 is only an example of the numerous patents in this area. It describes a level control system with the additional possibility to lock out the suspension movement of a vehicle’s axle. The lockout is enabled by a 4/2position valve (62 in Fig. 8.17) and allows, when blocked, free oscillation of the axle and a pressure equalization of the accumulators (72 and 74). Interestingly the patent also mentions a mechanical low pass filter (46 and 48) which is installed between the coupling rod (axle mounted) and the leveling valve (34, chassis mounted). It is meant to slow down the control actions so only the long term level changes are compensated.

Fig. 8.17 Suspension lockout by Caterpillar

8.3.2 DE4308460 The company Fendt (Marktoberdorf, Germany) created a similar system in 1993 in this case for a hydropneumatic suspension system with hydraulic preload. The accumulator (16 in Fig. 8.18) for the piston chamber and the accumulator (25) for the rod chamber are decoupled via the valves (28) and (29) from their respective cylinder portions. The suspension can be locked out in any desired, previously adjusted position. Fendt also explicitly mentions the possibility for automatic control of the

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Fig. 8.18 Suspension lockout by Fendt

locking function, for example, a speed-dependent switching between locked and unlocked which is meant to be used for front loader work. Both aforementioned patents do not mention the issue that, after a load change during the locked out state, different pressure levels prevail in the cylinders and in the accumulators. The latter can, as already mentioned in Sect. 6.1, lead to rapid suspension movements due to pressure equalization effects when the lockout is disengaged. This effect is accounted for by the previously mentioned Caterpillar patent US6167701 (see Sect. 8.1). A special hydraulic circuit keeps the pressure level in the decoupled pistonside accumulators always on the level of the piston chamber pressure of the suspension cylinders. Valve (48) in US6167701 ensures that the pressure level in the accumulators is raised if necessary and valve (54) reduces the pressure in the accumulators if it is above the pressure in the cylinder.

8.3.3 DE4032893 Besides the lockout function by a blocking of the fluid flow between cylinder and accumulator, Fendt described in 1990 another method of blocking the suspension. It is also achieved hydraulically but in this case interacts with the mechanical portion of the suspension. In the described example, this is an oscillating axle (10 in

8.3

Suspension Lockout

213

Fig. 8.19 Hydromechanical suspension lockout by Fendt

Fig. 8.19) which is mounted to a transverse pivoting arm (6) rotating in the bearing (3) and this way providing the suspension function. For the lockout, the plunger cylinders (14 and 16) are hydraulically driven into their end stops and thus force the transverse pivoting arm into its middle position. This stops the vertical suspension motion. The oscillation however is still possible since the axle can still rotate in the bearing (8).

Chapter 9

Looking into the Future

After many decades of development, the hydropneumatic suspension today can be called a mature technology, which is proven by its successful application in many different areas. However the technical possibilities are far from being exhausted, many improvements are still possible and imaginable. Improvements on the component level as well as on the system level which provide – and this is extremely important – not only functional advancement but also a reasonable cost-benefit-ratio, making them favorable also from an economic point of view. On the component level, solid body friction is still an important issue. Further reductions are necessary to achieve even more sensitive response behavior. Particularly the brainpower and creativity of engineers and researchers in the field of sealing technology are important in finding further possibilities to reduce friction. Advances in the recent past suggest that we have not yet nearly reached the end of the road. And these advances are necessary since, particularly in high level applications, static friction can be crucial for success or failure of a suspension system. Another objective is the technology of accumulators. Topics such as servicing, packaging into available space and, in particular for modern passenger cars and airplanes, weight are still outstanding challenges. The accumulators, as the actual elastic element of a suspension system, offer many possibilities to improve spring characteristics (for example, variable or self-adapting). Not only are the volume and the precharge pressure relevant parameters but also the properties of the filling gas. Its adiabatic exponent as a function of temperature and pressure also has a major impact on the suspension properties. One approach would therefore be to make the adiabatic exponent somehow variable and adjustable. This would allow the suspension properties to be varied by tackling the hydropneumatic suspension at its very roots, namely, the gas. In our times of fast increasing functional density, the design space claim of a component is, in particular in vehicles, an important issue as well. Although hydropneumatic suspensions already have advantages in this area, a further size reduction in combination with even higher design flexibility could create unbeatable pros for the use of this technology in some applications. One possible path to achieve this is a further increase of working pressures. This reduces the necessary sizes for the

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active areas inside the cylinder as well as the oil flow which therefore also reduces the required line size and accumulator size. And of course there are the component costs that are hanging like the sword of Damocles over all new developments. It can be expected that through new materials and production technologies further cost reductions are possible. A good example are the widely used shock absorbers for passenger cars’ wheel suspensions. Over many years they have been functionally improved and yet reduced in cost. This development can be seen as a role model for hydropneumatic suspensions if they want to make their way into widespread applications. Comparing automotive dampers with a regular hydraulic cylinder, the enormous potential for further cost reductions becomes obvious. Without any doubt, production numbers play a major role and hopefully this opens new possibilities also for suspension cylinders. This is equally true for hydraulic accumulators which, too, are responsible for a major portion of the overall cost of a hydropneumatic suspension. On the system level the requirement is very clear but to the same extent difficult to achieve: the suspension should fulfill its functions “minimize accelerations on the isolated side” and “equalize variation of vertical wheel forces” even better than today. The conventional mechanical suspension has shown already that a better tuning of the suspension parameters, like separate damping for compression and rebound, high-speed and low-speed, can lead to improvements. However the finding is that we are getting closer and closer to the functional limits of passive suspension systems and that we therefore need to buy further improvements of standard (mechanical) suspensions with high cost increases. The possibilities of passive hydropneumatic suspensions are not yet this far exhausted, but here, too, we will soon reach the point where it becomes questionable whether the additional benefit justifies the extra spending. This is the reason why the possibility of semi-active and active suspension technology is also investigated for hydropneumatic suspensions. The basic principles are known for quite a while already. For example, there are Karnopp’s considerations about the Skyhook-principle [KAR74] and several investigations on a theoretical basis, for example [DEP02], [ELD96] and [SCU02]. Experiments have been carried out as well (examples: [CAS96], [GIL98]), however it was not until roughly the change of the millennium when the semi-active suspension with mechanical and pneumatic springs found a wider use in the automotive industry. Based on damping systems like CDC by ZF Sachs and ADS by ThyssenKrupp Bilstein, as well as the technology of magnetorheologic fluids by Lord, the semi-active systems first found their way into luxury cars and sports cars and today are also available as an option in compact and mid size cars. This technology can also be applied to hydropneumatic suspension systems. However, the often higher flow rates can make it difficult to use standard components from the automotive industry. Further development of these automotive components and/or similar components from other hydraulic applications is then necessary. Basic control algorithms can be adopted from existing automotive applications. In contrast, the active suspension technology had difficulties finding its way into vehicle suspension technology. The main reasons for that are the elaborate and

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costly components and the high energy consumption of such systems. The power eaten by such systems can be several percent of the maximum engine power of a vehicle [BRE96], depending, for example, on the suspended mass, the stroke of the suspension and the required frequency range for isolation, as well as on travel speed and condition of the road surface. In times of rising energy cost and call for CO2 reduction it is difficult to find enough pros to compensate for that. Anyway energy consumption should not immediately be the general argument used to condemn active suspensions. Please keep in mind that the peak power is only required in extreme situations so the average power consumption is significantly lower. Furthermore be aware that passive suspension systems also dissipate energy into heat and this energy originally comes from vehicle motion and therefore, indirectly, from the engine. In fact the only example where active suspension technology is widely used in the automotive industry is the Daimler Active Body Control suspension system, which particularly compensates roll and pitch motions and is assisted by a regular spring/damper system for higher frequency excitations. In commercial vehicles, particularly agricultural tractors there is the active damping for oscillations of implements mounted to the rear three-point-hitch and the active suspension of the drivers seat on larger John Deere tractors. In all these cases the power demand for the active suspension is relatively low since on one hand the isolation is only provided for rather low frequencies and especially for the drivers seat the suspended mass is quite low. But once again here we should remember that all these systems are not hydropneumatic suspensions since the cylinders are only fast reacting linear motors with only minor elasticity (no accumulators). However there are interesting approaches that allow the use of hydropneumatic suspensions directly as a new type of active suspension. It was already back in 1972 when C. Mueller submitted a patent application [DE348] for a concept which is elsewhere called “Schaltspeicherfeder”, literally translated as switchable accumulator spring. In this design the gas mass is divided into two separate volumes which can be connected or disconnected by a controlling spool valve, which is controlled particularly with respect to the pressures in the accumulators. This system takes out energy in certain states of the suspension, namely when the oscillation reaches its top dead center and releases it back into the system particularly when the oscillation reaches the bottom dead center. The system was especially meant for off-road vehicles; however it is unknown whether this suspension system has been actually used in an application. In the end of the 1990’s this principle was again mentioned in a similar concept by de las Heras [HER99] who calls it “variable stiffness control”. Glasner et al. [GLA96] mention in 1996 a similar principle for air suspension systems and call it semi-active air spring. The switching in this case is controlled by an electronic control unit. In a further refined design a similar air suspension principle has been brought into serial production by Grammer as the EAC (electronic active control suspension) a few years ago [HIM06]. The EAC seat uses two air volumes which can be connected/disconnected by a fast switching valve. This technology allows a transfer function which shows virtually no resonance amplification in the whole frequency range and therefore results in very good isolation.

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If we succeed in adopting the previously mentioned technology or finding similar energy re-using principles for hydropneumatic suspensions, this could be a first promising step towards a further improvement of the suspension qualities similar to the functional gain for air springs. In general it seems to be a very valuable approach to store the undesired energy from relative motions and make use of it advantageously at a later state. Giliomee has made a first step by using this energy for an adjustment of the ride height [GIL98] similar to what the Nivomat systems already do. The next step could now be to actively use this energy to improve the isolation effect. In several applications a trend is noticeable that systems with a simple hydraulic setup and, where required, complex electronic controls are preferred over complex hydraulics. Lower cost and higher design (change) flexibility are often the driving advantages. This is the trend from hydraulics to electrohydraulics, from the brain in the valve to the brain in the electronics. And this is only one example of new developments that offer new tools and allow new approaches for us engineers. All in all creative and smart ideas are needed to further improve the function and the characteristics of hydropneumatic suspension systems. All the possibilities in this area of technology are far from being used up. Many effective and yet simple solutions are still waiting to be discovered. Explore with enthusiasm, break new ground!

Index of Symbols and Abbreviations

Dimensions and Dimension Related Parameters AK

AR

AS s

sB

h L α h0F

dK dS e v

Pistonside active area: Active piston area that displaces fluid out of the cylinder during compression. For the single acting cylinder this is the full area of the planar piston surface facing towards the cylinder bottom. For the double-acting cylinder operated in regenerative mode, this is the cross-sectional area of the rod. Rodside active area: Active piston area that displaces fluid out of the cylinder during rebound. This area is only available on double-acting cylinders and is defined by the ring shaped planar surface of the piston between cylinder tube inner diameter and rod outer diameter. This area faces towards the rod end of the cylinder. Cross-sectional area of the rod Displacement/position of the piston. s=0 means the piston is in its design position. In all the examples in this book, this is defined as the exact center between the compression end stop and the rebound end stop. A further definition is that s>0 means a compression and s<0 means a rebound/retraction of the cylinder. Full suspension travel relating to the respective reference point/plane (for example the position of the suspended component (e.g. front axle) or the COG of the suspended mass) Full cylinder stroke Distance between the two suspension cylinders of an axle General angular dimension Relative gas column height, a virtual dimension. The height of a gas column with the pressure p0 (accumulator precharge pressure) which has – at a volume V0 , the accumulator inner volume – exactly the right base area to carry the load FF1 (see Fig. 2.6). Outer diameter of the piston = inner diameter of the cylinder tube Outer diameter of the rod Distance between the guiding elements of piston and rod Velocity of the compression/rebound motion of a cylinder

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Index of Symbols and Abbreviations

a

acceleration in general

V i

(Volume) flow rate Lever ratio of the mechanical linkage of the suspension

•

Forces and Force Related Parameters FF FF1 FF2 FK FR FV Fhydr Fmech FD,hyd PD,hyd MD

Suspension force acting onto cylinder Static spring load in design position s=0 Dynamic spring load during suspension motion Force caused by the pressure pK onto the pistonside active area AK Force caused by the pressure pR onto the rodside active area AR Preload force in design position Force of the hydraulic system Force of the mechanical system Damping force caused by fluid friction (hydraulic damping force) Power withdrawal from the suspension motion caused by fluid damping Torque

Accumulator Related Parameters and Pressures V V0 V1 V2 p p0 p0,T p0,T,korr

p1 p2 pV pzul psys pZ pSp mG

Volume Internal accumulator volume = gas volume when no external hydraulic pressure is applied Gas volume inside the accumulator after the suspension system has been loaded with the static spring load FF1 Gas volume inside the accumulator during dynamic suspension motion Pressure Accumulator precharge (gas) pressure at room temperature (293.15 K) Temperature depending accumulator precharge pressure Temperature depending accumulator precharge pressure, additionally considering the production tolerance of the precharge pressure and the diffusion pressure loss between service intervals Hydraulic pressure on the load carrying side of the suspension system after it has been loaded with the static spring load Hydraulic pressure on the load carrying side of the suspension system during the suspension motion Hydraulic preload pressure on the rodside active area AR Maximum permissible operating pressure of the accumulator Maximum available system pressure of the hydraulic power supply Pressure in a cylinder in general Pressure in an accumulator in general Mass of the gas inside the accumulator

Index of Symbols and Abbreviations

R κ n

Gas constant (J/kg K) Adiabatic exponent Polytropic exponent

Parameters Defining the Dynamic Suspension Behavior mF ω f g c cG cL cF chydr cmech w nR

Suspended mass Natural angular frequency Natural frequency Gravitational acceleration Spring rate Spring rate provided by the compression of the gas Spring rate provided by the elasticity of the fluid lines Spring rate provided by the compression of the hydraulic fluid Spring rate of the hydraulic system Spring rate of the mechanical system Roll stiffness, resistance of the system against roll motions Dynamic tire load factor

Miscellaneous Parameters K ν ρ T t

Parameter representing the behavior of a fluid flow resistor Dynamic viscosity of the hydraulic fluid Density of the hydraulic fluid Temperature Time

General Use of Indices XXmin XXmax XXgrenz XXges XXK XXR XXS XXLI XXRE XXa XXb

Minimum value for parameter XX Maximum value for parameter XX Limit for parameter XX Overall behavior of parameter XX Parameter referring to the pistonside system Parameter referring to the rodside system Parameter referring to the rod Parameter referring to the left side Parameter referring to the right side Parameter referring to the hydraulic circuit a Parameter referring to the hydraulic circuit b

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Index

A Accelerations minimization during end-of-stroke damping, 62–64, 91–94 on isolated side, 2–4 See also Vibrations Accumulators costs, 115 diaphragm, operational limits, 73–74 diffusion pressure loss reduction methods, 116–118 dimensioning aspects accumulator gas precharge, 71–73 non preloaded systems, 71 p0 and V0 calculation, 73–84 system with hydraulic preload, 72–73 system with mechanical preload, 71–72 function and requirements (gas-filled accumulators), 111–113 future research aspects, 215 gas precharge, 21–23, 74–76 integration into available design space, 118 fluidside connectors, 119–120 mountings types, 119 spring rate adjustment by selective connection of, 169–171 types bladder, 113–115 diaphragm, 113–116 piston, 113–115 Activa suspension passenger car axle suspension (Citroen), 188–191 principle, 188 See also Hydractiv suspension Active suspension technology future research aspects, 216–217 See also Activa suspension; Hydractiv suspension

Adjustable flow resistors activation of adjustment, 128–129 damping adjustment automatic, fast adjustment (semi-active), 126 automatic, slow adjustment (adaptive), 126 manual damping selection, 126 types, 126 ball valve, 127 needle valve, 127 See also Non adjustable flow resistors Air spring SEE Pneumatic suspension systems Axle suspension passenger car axle suspension (Citroen), 180–191 Activa suspension, 188–191 Hydractiv suspension, 183–188 tasks and functional requirements, 2 TLS (John Deere), 173–180 See also Tractor front axle suspension B Ball valve flow resistor design, 127 See also Needle valve Bearings (cylinder support elements), 110 pivot bearing, 109 sliding bearings, 109 Bladder accumulators, 113–115 Blocking Valves, 149, 158 Boundary friction damping, 51–55 defined, 50 See also Fluid friction C Cab suspensions, 16, 33–34, 202–204 Cavitation, 76, 85–91 See also Hydraulic damping

229

230 Check valve with hydraulic release, 148, 173, 184 with electric release, 148–149 Citroen, see Passenger car axle suspension (Citroen) Comfort, see Suspension comfort Compression end stop lockout at, 160–161 Compression phases, 8, 27, 85–86 See also Rebound phases Connections for tubes and hoses, 139 spring rate adjustment by selective connection of accumulators, 169–171 types on hydraulic components, 138 Control algorithms, 151 double low pass filter, 154 frequency-dependent, 152 frequency-independent, 152 long/short average value, 155 low pass filter, 153 three-state controller with switching hysteresis, 155–156 waiting periods, 152 See also Level control Control circuit lines, 130–131 See also Suspension circuit lines Costs component costs, 13 hydropneumatic suspension systems future aspects, 215 Coupling cylinders on opposite sides, 166–169 on corresponding sides, 164 See also Decoupling cylinders; Roll and pitch behavior alteration Crimped design cylinders, 101 See also Tie rod design; Welded design Cross section required flow, 132–133 See also Hydraulic lines/fittings Cylinders double-acting cylinder in system with hydraulic preload, 26, 42, 91 without hydraulic preload, 85–91 end-of-stroke damping design, 106–109 function and requirements, 95–96 hydraulic spring components dimensioning, 69–71 lateral forces, 53, 97, 109

Index sealing elements, 101–106 piston seal system, 105–106 rod seal system, 104–105 single-acting cylinder, 15, 85–87 support elements types, 109–111 types, 96–97 crimped design, 101 design principle, 100–101 double-acting cylinder, 99 functional principle, 98, 99 single-acting cylinder, 99 tie rod design, 101 welded design, 100 D Damper suspension systems setup, 5–7 Damping adjustment, manual, adaptive, semi-active, 126 boundary friction, 51–55 dimensioning of hydraulic damping elements double-acting cylinder in system with/without hydraulic preload, 88–91 end-of-stroke damping, 91–94 single-acting cylinder in system without hydraulic preload, 85–87 end-of-stroke, 62–64 cylinder design aspects, 106–108 fluid friction, 55–61 forces, 6 hydropneumatic suspension systems characteristics, 50 boundary friction damping, 51–55 combined operation of spring and damper, 64–66 end-of-stroke damping, 62–63 fluid friction damping, 55–61 hydropneumatic suspensions comparison to pneumatic and mechanical suspension methods, 11–12 See also Flow resistors; Spring DE10107631 patent, 196 DE10112082 patent, 207 DE102008012704 patent, 203–205 DE10337600 patent, 196–198 DE1755095 patent, 194 DE19719076 patent, 195–196 DE19949152 patent, 201–202 DE3427508 patent, 206–207 DE4032893 patent, 212

Index DE4221126 patent, 198 DE4223783 patent, 200 DE4234217 patent, 198–199 DE4308460 patent, 211–212 Deadband, 145, 152 Decoupling cylinders, 164–165 See also Coupling cylinders Deformation, see Diaphragm deformation criterion Design axle suspension design examples passenger car axle (Citroen), 180–191 tractor front axle (John Deere), 173–180 hydraulic components, see Hydraulic components design space requirement, 13, 118–120, 133 Diaphragm accumulators, 73–76, 113–118 diffusion pressure loss reduction methods, 116–118 screwed, 115 welded, 115–116 Diaphragm deformation criterion, 74 See also Maximum pressure criterion Diffusion pressure loss dimensioning aspects and, 76 reduction methods in accumulators design aspects, 117–118 general rule, 116 service aspects and refill of gas, 117 special gas, use of, 118 Dimensioning hydraulic damping components double-acting cylinder in system with hydraulic preload, 91 double-acting cylinder in system without hydraulic preload, 88–91 end-of-stroke damping, 91–94 single-acting cylinder in system without hydraulic preload, 85–87 hydraulic spring components, 67 accumulator gas precharge, 71–73 cylinder, 69–71 non preloaded systems, 71 p0 and V0 calculation, 73–84 pistonside accumulator, 80–84 pressure variations aspects, 68, 69 rodside accumulator, 76–80 system with hydraulic preload, 72–73 system with mechanical preload, 71–72 See also Hydraulic components design Double-acting cylinders functional principle based aspects, 99 in system with hydraulic preload, 91

231 in system without hydraulic preload, 88–91 See also Single-acting cylinder Dry friction, see Solid body friction Dynamic friction, 6 Dynamic seals, 101, 103 E Elastomer elements and end-of-stroke damping, 62–63 sealing, 138 Electrohydraulics future research aspects, 218 Electronic active control (EAC) suspension, 217 Electronic level control with external hydraulic power supply control algorithms, 150–156 function, 147 hydraulic circuits, 148–150 See also Mechanical level control; Self-pumping systems End-of-stroke damping cylinder design aspects, 106–108 dimensioning of components, 91–94 elastomer elements for, 62–63 See also Boundary friction; Fluid friction European Council Directive 2002/44/EC, 3 European Council Directive 2003/10/EC, 3 F Fittings, 138–140 connection types on hydraulic components, 138 connections for tubes and hoses, 139 integration of flow resistors, 122 See also Hydraulic lines/fittings Flow coefficient, 58 Flow crossection sizing, 132–133 Flow resistors adjustable, 126–129 flow direction depending resistors, 122–125 integration, 121–122 non adjustable, 120–122 pressure loss, 55–59 Fluid friction damping, 55–61 defined, 50 orifice, 57–59 throttle, 56–59 See also Boundary friction Frequency-dependent control algorithm, 152 Frequency-independent control algorithms, 152

232 Friction, 7 boundary, 50 dynamic, 6 fluid, 50 sliding, 52 static, 6, 51–52 Friction dampers, 52 Front axle suspension, see Tractor front axle suspension Front loader suspension, 16, 31–33 G Gas, ideal changes of state adiabatic, 23, 66 isochoric,22 isothermal, 22–26, 74, 84, 165 polytropic, 23–27, 84, 165 Gas precharge accumulator, 71–73 See also Dimensioning Gas-filled accumulators, 111–113 GB890089 patent, 205–206 H Harshness, 3, 11, 181 See also Suspension comfort Hoses, 135–139 advantages, 135–136 connections for, 139 routing, 137 See also Tubes Hydractiv suspension passenger car axle suspension (Citroen) advantages, 183 hard setting, 184–186, 188 roll stiffness, 187 soft setting, 183, 187 See also Activa suspension Hydraulic circuit suspension lockout by blocking, 158–159 Hydraulic components design see Accumulators Cylinders Design; Dimensioning; Flow resistors; Hydraulic lines/fittings Hydraulic damping dimensioning of components double-acting cylinder in system with hydraulic preload, 91 double-acting cylinder in system without hydraulic preload, 88–91

Index end-of-stroke damping, 91–94 fluid friction damping, 55–61 single-acting cylinder in system without hydraulic preload, 85–87 See also Hydraulic spring Hydraulic fluid viscosity, 57 Hydraulic lines/fittings fittings, 138–140 function and requirements control circuit lines, 130–131 supply lines, 130–131 suspension circuit lines, 130–132 hoses, 135–138 required flow cross section, 132–133 tubes, 133–135 Hydraulic preload systems with constant hydraulic preload, 41–48 double-acting cylinder, 91 hydraulic spring components dimensioning (accumulator), 72–73 variable hydraulic preload, 48–50 systems without double-acting cylinder in system, 87–91 single-acting cylinder, 85–87 See also Mechanical preload; Non-preloaded systems Hydraulic spring dimensioning of components, 67–69 accumulator gas precharge, 71–73 cylinder, 69–71 non preloaded systems, 71 p0 and V0 calculation, 73–84 pistonside accumulator, 80–84 rodside accumulator, 76–80 system with hydraulic preload, 72–73 system with mechanical preload, 71–72 See also Hydraulic damping Hydrodynamic friction, see Fluid friction Hydropneumatic suspension systems applications, 15–17 comparison to pneumatic/mechanical suspension methods damping characteristics, 11–12 level control, 12–13 non-functional requirements (component costs), 13 non-functional requirements (design space requirement), 13–14 non-functional requirements (reliability, safety, robustness and service requirements), 14–15 spring characteristics, 7–11

Index damping characteristics, 50 boundary friction, 51–55 combined operation of spring and damper, 64–66 end-of-stroke, 62–63 fluid friction, 55–61 design examples passenger car axle suspension (Citroen), 180–191 TLS by John Deere, 173–180 dimensioning of components, 67 hydraulic damping elements, 85–94 hydraulic spring components, 67–84 future aspects, 215–218 costs, 216 design space, 215 electrohydraulics, 218 semi-active and active suspension technology, 216 solid body friction, 215 hydraulic components design accumulators, 111–119 cylinders, 95–111 flow resistors, 120–129 hydraulic lines/fittings, 130–140 patents, see Patents (hydropneumatic suspensions) setup and working principle level control unit, 19–21 suspension unit, 19, 21 special functions, 157 roll and pitch behavior alteration, 163–169 spring rate adjustment by selective connection of accumulators, 169–171 suspension lockout, 157–162 zero position adjustment, 162–163 spring characteristics, 21 calculation predeterminations, 25 non-preloaded hydropneumatic suspensions, 25–35 systems with constant hydraulic preload, 41–48 systems with mechanical preload, 35–41 systems with variable hydraulic preload, 48–50 thermodynamic background, 21–24 See also Mechanical suspension systems; Pneumatic suspension systems Hysteresis, see Three-state controller with switching hysteresis

233 I ISO 2631–1, 3 Isolated side, accelerations minimization, 2–4 L Level control hydropneumatic suspensions comparison to pneumatic/mechanical suspension methods, 12–13 manual, 162 self-pumping suspension elements, 141–143 unit in hydropneumatic suspension systems, 19–21 with external hydraulic power supply electronic level control, 147–156 mechanical level control, 144–147 Lever ratio of mechanical linkage, 176 Loadsense hydraulic system, 70, 131, 150 Lines/fittings, see Hydraulic lines/fittings Lockout, 157 at compression end stop, 160–161 by hydraulic circuit blocking, 158–159 quasi-lockout through high spring stiffness, 161–162 Low pass filter, 153 double low pass filter, 154 mechanical low pass filter, 146 See also Level control M Maximum pressure criterion, 73 See also Diaphragm deformation criterion Mechanical level control with external hydraulic power supply, 144–147 See also Electronic level control; Self-pumping systems Mechanical preload system with, 35–41 hydraulic spring components dimensioning (accumulator), 71–72 See also Hydraulic preload; Non-preloaded systems Mechanical suspension systems damping characteristics, 11 level control, 12 non-functional requirements component costs, 13 reliability, safety, robustness and service requirements, 14 spring characteristics, 7–10

234 See also Hydropneumatic suspension systems; Pneumatic suspension systems Multilayer-diaphragms, 118 N Natural frequency, 10, 30, 36, 42, 142, 177, 186 in pitch motion, 31, 49, 178 Needle valve flow resistor design, 127 See also Ball valve Nivomat, 114, 141–143 Non adjustable flow resistors, 121–122 See also Adjustable flow resistors Non-functional requirements component costs, 13 design space requirement, 13, 14 reliability, safety, robustness and service requirements, 14–15 Non-preloaded systems, 25–35 hydraulic spring components dimensioning (accumulator), 71 states 0, 1, 2, 26 See also Hydraulic preload; Mechanical preload O Orifices, 57–59 character, 59 design aspects of non adjustable, 120–121 See also Fluid friction; Throttle P Passenger car axle suspension (Citroen), 180 Activa suspension, 188–191 first hydropneumatic suspension, 181–183 Hydractiv suspension, 183–188 See also Triple Link Suspension (TLS) Patents (hydropneumatic suspensions), 193 roll stabilization and slope compensation DE10112082, 207 DE3427508, 206 DE4032893, 212 DE4308460, 211–212 GB890089, 205–206 US3953040, 211 US4411447, 208–209 US6923453, 209–210 suspension characteristics improvement, 193 DE10107631, 196 DE102008012704, 203–205 DE10337600, 196–198

Index DE1755095, 194 DE19719076, 195–196 DE19949152, 201–202 DE4221126, 198 DE4223783, 200 DE4234217, 198–200 US6167701, 201 US6398227, 203 Triple Link Suspension by John Deere, 175–176 P-controller, 150 See also Level control Piston accumulators, 76, 113–116, see also Pistonside accumulators diffusion pressure loss reduction methods, 116 balance of forces, 19–29, 42, 69 seal systems, 105–106 See also Cylinders; Rod Pistonside accumulators p0 and V0 calculation, 84 constant pistonside preload pressure, 80–83 non preloaded system, 80 variable pistonside preload pressure, 81–84 TLS by John Deere, 179 See also Double-acting cylinders; Rodside accumulators Pitch stiffness, 163 See also Roll Pivot bearings cylinder support element, 109 Pneumatic suspension systems damping characteristics, 11, 61 level control, 12–13 non-functional requirements component costs, 13 design space requirement, 14 reliability, safety, robustness and service requirements, 14 spring characteristics, 9, 11 See also Hydropneumatic suspension systems; Mechanical suspension systems Precharge accumulator gas, 71–73 See also Dimensioning Preload double-acting cylinder in system with hydraulic preload, 91 without hydraulic preload, 88–91

Index hydraulic spring components dimensioning (accumulator) non preloaded systems, 71 system with hydraulic preload, 72–73 system with mechanical preload, 71–72 pistonside accumulator, 84 constant pistonside preload pressure, 80–83 non preloaded system, 80 variable pistonside preload pressure, 81–83 rodside accumulator constant rodside preload pressure, 76–77 variable rodside preload pressure, 78–80 single-acting cylinder in system without hydraulic preload, 85–87 systems with constant hydraulic preload, 41–48 mechanical preload, 35–41 variable hydraulic preload, 48–50 See also Damping; Spring Pressure diaphragm deformation criterion, 74 diffusion pressure loss, 76 reduction methods in accumulators, 116–118 loss, gas accumulator see diffusion loss, flow resistor see flow resistor maximum pressure criterion, 73–74 p0 and V0 calculation, 73–76 pistonside accumulator, 80–84 rodside accumulator, 76–80 production tolerance and precharge pressure, 75 ratio, 74–76, 115 reducing/relief valve, 59, 68, 124, 128 tubes, 134 variations (hydraulic spring components dimensioning) dynamic state of suspension, 68–69 static state of suspension, 68 Q Quasi-lockout through high spring stiffness, 161–162 R Rebound phases, 8, 86 See also Compression phases; Hydraulic damping Reliability requirements, 14 Robustness requirements, 14

235 Rod guide, 53, 96–98 seal system, 104–105 See also Cylinders; Piston Rodside accumulators p0 and V0 calculation, 76–77 constant rodside preload pressure, 76–77 variable rodside preload pressure, 78–80 TLS by John Deere, 178–179 See also Double-acting cylinders; Pistonside accumulators Roll Hydractiv suspension (passenger car axle suspension by Citroen), 187 stabilization and slope compensation (hydropneumatic suspensions patents), 205–210 stiffness, 163–169 Roll and pitch behavior alteration coupling cylinders double-acting cylinders on opposite sides, 166–169 on corresponding sides, 163–164 decoupling cylinders, 164–165 Rubber-metal bushings, 110–111 See also Cylinders S Safety requirements, 14 Schaltspeicherfeder concept, 217 Screwed diaphragm accumulators, 115 Sealing elements cylinders, 101–106 dynamic, 101, 103 functional principle, 102 piston seal system, 105–106 rod seal system, 104–105 static, 101, 103 Self-pumping systems, 141–143 See also Electronic level control; Mechanical level control Semi-active suspension technology characterization, 126 future research aspects, 216 speed of actuation, 129 See also Activa suspension; Hydractiv suspension Service requirements, 14, 76, 116–118 Single-acting cylinders functional principle based aspects, 98–99 in system without hydraulic preload, 85–87

236 See also Boundary friction; Double-acting cylinders Sliding bearings, 109 Sliding friction, 52 See also Static friction Slope compensation roll stabilization and slope compensation (hydropneumatic suspensions patents), 205–210 Solid body friction, 50 future research aspects, 215 See also Boundary friction Specification features accumulators, 112 cylinders, 96 flow resistors, 122 lines, 132 Spool valves, 144–149, 183–190 Spring combined operation of spring and damper, 64–66 dimensioning of hydraulic spring components, 67–69 accumulator gas precharge, 71–73 cylinder, 69–71 non preloaded systems, 71 p0 and V0 calculation, 73–84 system with hydraulic preload, 72–73 system with mechanical preload, 71–72 hydropneumatic system spring characteristics calculation predeterminations, 25 non-preloaded hydropneumatic suspensions, 25–35 systems with constant hydraulic preload, 41–48 systems with mechanical preload, 35–41 systems with variable hydraulic preload, 48–50 thermodynamic background, 21–24 hydropneumatic systems comparison to pneumatic/mechanical suspension methods, 7–11 suspension systems setup, 5–7 Spring load, 10, 26 Spring rate, 19, 21 adjustment by variable hydraulic preload, 48–50 adjustment by selective connection of accumulators, 169–171 spring rate vs. load curve, 32–45 TLS by John Deere, 176–177

Index Static friction, 6, 51–52 See also Damping; Sliding friction Static seals, 101, 104 Stiction, see Static friction Stiffness pitch, 163 quasi-lockout through high spring, 161–162 roll, 163 passenger car axle suspension (Citroen), 187 Supply lines, 130–131 Suspension circuit lines, 130–132 See also Control circuit lines Suspension lockout see Lockout Suspension comfort, 3–4 Suspension systems, 1 requirements, 1–5 accelerations minimization on isolated side, 2–4 non-functional requirements, 5 vertical wheel forces variations equalization, 4–5 setup, 5–7 See also Hydropneumatic suspension systems; Mechanical suspension systems; Pneumatic suspension systems Suspension travel, 8, 62 Suspension unit hydropneumatic suspension systems, 19–21 See also Hydraulic components design T Temperature influence on diffusion, 116 gas, 21–24, 30, 75 hydraulic fluid, 56–59, 131 rubber, 114 Tetrafluormethane (CF4 ), 118 Thermodynamic background spring characteristics, 21–24 Three-state controller with switching hysteresis, 156 Throttle, 56–57 character, 59 design aspects of non adjustable, 120–121 See also Fluid friction; Orifices Tie rod design cylinders, 101 See also Crimped design; Welded design Tire load factor, 5

Index Tractor front axle suspension AGCO-Fendt, 47, 160, 212 Carraro, 39–41, 160 John Deere see Triple Link Triple Link Suspension (TLS) by John Deere TLS I, 47, 173–180 TLS II, 48 TLS Plus, 50, 156, 162 Tubes advantages, 133 connections for, 139 mounting, 135 pressures for, 134 See also Hoses U US3953040 patent, 211 US4411447 patent, 208–209 US6167701 patent, 201 US6398227 patent, 203 US6923453 patent, 209–210 V Variable stiffness control, 217 Vertical wheel forces

237 defined, 4 variations equalization, 4–5 Vibrations accelerations minimization requirements of suspension systems, 2–4 value and comfort level, 3–4 Viscous friction, see Fluid friction Volume p0 and V0 calculation pistonside accumulator, 80–84 rodside accumulator, 76–80 See also Dimensioning; Pressure W Welded design cylinders, 100 See also Crimped design; Tie rod design Welded diaphragm accumulators, 115–116 Wheel suspension systems requirements, 1–2 See also Vertical wheel forces Working pressure, 13, 25, 134, 215 Z Zero position adjustment, 162–163