Acoustic Emission in Friction, Volume 53 (Tribology and Interface Engineering) (Tribology and Interface Engineering)

ACOUSTIC EMISSION IN FRICTION

TRIBOLOGY AND INTERFACE ENGINEERING SERIES Editor B.J. Briscoe (U.K.) Advisory Board M.J. Adams (U.K.) J.H. Beynon (U.K.) D.V. Boger (Australia) P. Cann (U.K.) K. Friedrich (Germany) I.M. Hutchings (U.K.) Vol. 27 Vol. 28 Vol. 29 Vol. 30 Vol. 31 Vol. 32 Vol. Vol. Vol. Vol.

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Vol. 37 Vol. 38 Vol. 39 Vol. 40 Vol. 41 Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol.

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J. Israelachvili (U.S.A.) S. Jahanmir (U.S.A.) A.A. Lubrecht (France) I.L. Singer (U.S.A.) G.W. Stachowiak (Australia)

Dissipative Process in Tribology (Dowson et al., Editors) Coatings Tribology – Properties, Techniques and Applications in Surface Engineering (Holmberg and Matthews) Friction Surface Phenomena (Shpenkov) Lubricants and Lubrication (Dowson et al., Editors) The Third Body Concept: Interpretation of Tribological Phenomena (Dowson et al., Editors) Elastohydrodynamics – 96: Fundamentals and Applications in Lubrication and Traction (Dowson et al., Editors) Hydrodynamic Lubrication – Bearings and Thrust Bearings (Frêne et al.) Tribology for Energy Conservation (Dowson et al., Editors) Molybdenum Disulphide Lubrication (Lansdown) Lubrication at the Frontier – The Role of the Interface and Surface Layers in the Thin Film and Boundary Regime (Dowson et al., Editors) Multilevel Methods in Lubrication (Venner and Lubrecht) Thinning Films and Tribological Interfaces (Dowson et al., Editors) Tribological Research: From Model Experiment to Industrial Problem (Dalmaz et al., Editors) Boundary and Mixed Lubrication: Science and Applications (Dowson et al., Editors) Tribological Research and Design for Engineering Systems (Dowson et al., Editors) Lubricated Wear – Science and Technology (Sethuramiah) Transient Processes in Tribology (Lubrecht, Editor) Experimental Methods in Tribology (Stachowiak and Batchelor) Tribochemistry of Lubricating Oils (Pawlak) An Intelligent System For Tribological Design in Engines (Zhang and Gui) Tribology of Elastomers (Si-Wei Zhang) Life Cycle Tribology (Dowson et al., Editors) Tribology in Electrical Environments (Briscoe, Editor) Tribology & Biophysics of Artificial Joints (Pinchuk) Scratching of Materials and Applications (Sinha) Tribology of Metal Cutting (Astakhov)

Aims & Scope The Tribology Book Series is well established as a major and seminal archival source for definitive books on the subject of classical tribology. The scope of the Series has been widened to include other facets of the now-recognised and expanding topic of Interface Engineering. The expanded content will now include: • colloid and multiphase systems; • rheology; • colloids; • tribology and erosion; • processing systems; • machining; • interfaces and adhesion; as well as the classical tribology content which will continue to include • friction; contact damage; • lubrication; and • wear at all length scales.

TRIBOLOGY AND INTERFACE ENGINEERING SERIES, 53 EDITOR: B.J. BRISCOE

ACOUSTIC EMISSION IN FRICTION Victor Baranov Evgeny Kudryavtsev Gennady Sarychev and Vladimir Schavelin Moscow State Engineering Physics Institute Kashirskoe sh. 31, Moscow

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CONTENTS

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

1. Friction of Solids and Nature of Acoustic Emission . . . . . . . . . . . . . . . . 1.1. Friction Processes                                              1.2. Acoustic Emission and its Main Characteristics                   1.3. Sources of Acoustic Emission in Metals                         1.4. Sources of Acoustic Emission in Friction of Solids                1.5. Informative Content of Characteristics of Acoustic Emission at Friction                                                       References                                                   

1 1 10 15 18

2. Simulation of Characteristics of Acoustic Emission in Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Distribution of Pressure Over Microcontact Spots                 2.2. Evaluation of Changes in Friction Surface Statistical Characteristics and Size Distribution of Fatigue Wear Particles                                                 2.3. Amplitude Distribution and Count Rate of Acoustic Emission Pulses                                                         2.4. Spectral Density of Acoustic Emission                           2.5. Dynamic Model for Calculation of Characteristics of Acoustic Emission at Non-Stationary Friction Regimes                     References                                                   

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3. Instrumentation and Equipment for Studies of Acoustic Emission in Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.1. Sources of Noises in Registration of Acoustic Emission and Methods of Noise Control                                      97 3.2. Transducers for Registration of Acoustic Emission in Friction     100 3.3. Instrumentation for Registration of Acoustic Emission in Friction                                                     108 3.4. Equipment for Studies of Acoustic Emission in Friction           118 3.5. Set-Ups for Studies of Friction of Nuclear-Power Engineering Materials                                                      126 References                                                    132

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4. Basic Regularities of Acoustic Emission at Friction . . . . . . . . . . . . . . . . 135 4.1. Acoustic Emission in Running-in of Friction Surfaces             135 4.2. Dependence of Characteristics of Acoustic Emission on Sliding Velocity and Load                                             141 4.3. Acoustic Emission in Damage to Lubricating Films on Friction Surfaces                                                       153 4.4. Correlation between Characteristics of Acoustic Emission and Characteristics of Damage of Material Surface Layers in Friction                                                     164 4.5. Acoustic-Emission Methods for Condition Monitoring of Friction Units                                                  173 References                                                    181 5. Friction of Nuclear Power Engineering Materials . . . . . . . . . . . . . . . . . . 183 5.1. Effect of Ionizing Radiation on Triboengineering Behavior of Materials                                                      183 5.2. Friction of Materials of Fuel and Fuel Element Cladding of Nuclear Reactors                                               187 5.3. Acoustic Emission in Friction of Materials of Circulation Device Bearing Units of Ball Fuel Elements of Nuclear Power Plants with HTGCR                                                  197 5.4. Study of Friction of Sliding Bearing Materials of Nuclear Reactor Main Circulating Pump                                 206 References                                                    214 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

PREFACE

Acoustic techniques are widespread among the methods of engineering diagnosis used nowadays to assess the state of machines and mechanisms comprising rotating parts and movable joints. Noise and vibration diagnosis traditionally cover the majority of tests involving the acoustic methods and use of the registration and analysis of acoustic noises and vibrations of mechanisms in the low-frequency spectral band. The high-frequency component of acoustic emission is not usually analyzed in this case. A great part of this emission is acoustic emission (AE) which is induced by various processes running in the material and on the surfaces of parts making up movable joints, or friction pairs. Characteristics of AE are very sensitive to the state of the surfaces, the presence of a lubricant, changes in friction regimes and wear mode. For this reason AE has attracted the attention of tribologists during the last decade. In this book we have attempted to systematize theoretical and experimental results obtained till now in the application of the AE method in tribology. Great attention has been paid to the comparatively new and rapidly developed direction, namely the tribology of nuclear power engineering. Despite the fact that a substantial part of experimental data relates to this quite specific field of engineering we would like to emphasise the universality of the method and the possibility of its application wherever the field inspection of friction units is necessary. Therefore, we hope that this book will be of interest to a wide audience of engineers and experts involved in the development and maintenance of new equipment. We would like to thank Professor N. K. Myshkin and Dr. D. V. Tkachuk, Metal-Polymer Research Institute of Belarus National Academy of Sciences, for their assistance in preparing the English edition of the book. Victor Baranov, Evgeny Kudryavtsev, Gennady Sarychev, Vladimir Schavelin

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INTRODUCTION

The statistics of failures and malfunctions of machines and mechanisms has shown that their most part results from wear. To demonstrate the acuteness of the problem it is enough to note that losses of energy and materials due to friction and wear in the machine-building industries of developed countries have reached at least 5% of GNP in the mid 1980s. These losses inspired wide research in the field of tribology that is concentrated nowadays on the following six areas: Theoretical studies in the mechanics, physics and chemistry of surface and contact phenomena; Materials in tribosystems; Technologies controlling the tribological behavior of movable joints; Design of tribosystems; Condition monitoring of tribosystems; Information processing and analysis in tribology. Though such division of these directions is relative and they are closely interrelated, the given classification represents the frame of problems arising when studying friction as well as the relation of tribology with other fields of science and engineering. Despite the progress in tribology, many problems concerning the improvement of the wear resistance and the reduction of friction losses are still far from reaching a solution. This fact results from the complexity of phenomena simultaneously occurring in the friction contact. Therefore, the diagnosis and condition monitoring of friction units are of primary importance when providing the non-failure operation of machines and mechanisms. The diagnosis of friction units of equipment used at nuclear power stations (main circulation pumps, drives of control and protection systems, coolant circulators, turbines) being potentially dangerous engineering objects is of special significance. The non-failure operation of friction units of these mechanisms governs greatly the reliable operation of the whole energy system. As it follows from practical experience, the characteristics of tribosystem operation such as the friction coefficient, wear rate, and contact temperature are not adequate in controlling the tribosystem state in many cases. Hence, they do not allow one to predict the remained life of the system with a necessary accuracy. From the other hand, the diagnosis of friction units frequently requires them to be stopped and disassembled. Therefore, methods and means of the on-line monitoring of friction units are desired which implement functional diagnostics techniques. This forms a basis for monitoring friction units.

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The following basic requirements are put for these methods and means. First of all, the analysis of the state of tribosystem surfaces, wear measurement and the assessment of the efficiency of the system as a whole should exclude its disassembling and stopping. The time of collecting diagnostic data and selecting informative indicators and characteristics of signals should be minimal. The monitoring methods should be simple and the devices should be compact and include built-in algorithms of data processing and decision making. To minimize the subjective factor when interpreting diagnosis data automatic procedures are desired. Among the available monitoring methods the emission methods meet the above requirements best. They are based on registering radiation of different physical nature, which accompany structural transformations in solids including those occurring in friction. They are thermal electron emission, exoelectron emission, electromagnetic field, and acoustic emission. At present the acoustic emission (AE) method is one of the best developed ones and it is suitable for practical application in tribodiagnosis. It involves the registration and analysis of high-frequency acoustic emission generated in friction. Acoustic emission accompanies almost all known processes running in solids and provides important data on their current state. The advantages of the AE method are well known and it is used successfully to monitor the material state and diagnose the failure of power engineering objects. First attempts of the practical application of the AE method in tribosystem monitoring were made at the end of the seventies of the last century. Progress in nuclear power engineering posed some new problems in tribology. Among them are the study of friction between nuclear fuel pellets and the fuel element cladding in nuclear reactors, the development of materials and antifriction coatings for operation under extreme conditions, the development of methods and means of the monitoring and diagnosis of bearings used in nuclear power station equipment. Friction units of nuclear power objects operate under conditions far from common conditions – that is under heavy loads, at elevated temperatures, under the effect of ionizing radiation, in high-pure helium and liquid sodium, without or with few personnel. The solution of the above-mentioned problems requires the use of methods of the radiation physics of solids and nuclear materials science. Novel techniques and measuring instruments are necessary to perform experimental studies in this field. The AE method can be highly helpful when solving the problems. Specific features of the phenomena under study and the application of new experimental methods and means indicate the appearance of a new direction in tribology, i.e. radiation tribology or nuclear engineering tribology. Research centers are established worldwide to carry out studies in this field. Despite the fact that first studies dealing with the calculation of interrelation between AE characteristics and characteristics of friction surfaces were carried

INTRODUCTION

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out approximately fifty years ago generally accepted theoretical concepts on the relation between characteristics of acoustic emission and processes running in friction units have not been formed yet. For this reason the interpretation of the experimental data reported in publications is quite ambiguous that makes the analysis and comparison of results obtained by different researchers difficult. The lack of good theoretical results and monitoring methods based on them hampers the practical application of the AE method for the maintenance diagnostics of friction units. The authors of this book were involved for a long time in theoretical and experimental studies in the field of acoustic monitoring methods including the practical application of the methods. They hope to attract the attention of tribologists and designers of tribosystems and monitoring equipment to the potential of AE method. For this purpose we described the physical background of the AE phenomena, considered the methodical aspects of registering high-frequency acoustic emission accompanying friction unit operation, and outlined the design of the developed setups and instruments for studying AE in friction. In addition, the monograph contains a lot of experimental data illustrating the possibilities of the AE methods in studying the frictional behavior of materials and protective coatings and in diagnostics of friction unit state at different stages of operation including friction units of nuclear power station equipment. Chapter 1 presents the analysis of the main sources of AE signals in friction of solids, their informative content, and the possibilities of the AE method in the diagnosis and condition monitoring of friction units of machines and mechanisms. In Chapter 2 we disclose the theoretical basis of the tribological application of the AE method, the physical principles and mathematical models for calculating the main informative characteristics of AE resulted from solid friction. The effect of physical-mechanical characteristics of solids, statistical characteristics of solid surfaces and friction conditions and regimes on the amplitude, amplitude-time distribution and the spectral density of AE signals is considered. Chapter 3 contains the operation principles, design solutions and main technical characteristics of the experimental equipment and AE instruments for tribological studies of materials and antifriction coatings. The setups with wide possibilities for studying tribological characteristics of materials and protective coatings within a wide temperature range, in different environments and vacuum, particularly under the effect of reactor radiation, are described. We propose the circuit solutions of the developed measuring instruments for various applications including the condition monitoring of bearings used in machines and mechanisms operating under extreme conditions. Chapter 4 illustrates the experimental results showing main regularities of AE in friction of solids and protective antifriction coating failure when using the

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developed setups and instruments. Changes in the informative characteristics of AE signals resulted from varying friction conditions and regimes are interpreted on the basis of theoretical ideas on the nature of acoustic emission in friction. The acoustic emission techniques of friction pair monitoring are described. Chapter 5 deals with the study results of the friction of structural and fuel materials of fuel elements and bearing materials used in nuclear reactors. The data are reported on the resistance of protective barrier coatings covering the internal surfaces of fuel element claddings. The results of laboratory and bench tests of bearings are given which confirm the applicability of the proposed acoustic emission techniques of friction unit diagnostics. Some issues considered in the book might initiate discussion since friction is a complicated phenomenon accompanied by a variety of physical processes. The authors will thank everyone for remarks. Nevertheless, the presented material based mainly on the results of the authors’ studies will be helpful when analyzing the possibilities of the AE method. We hope that our data might be useful in evaluating advantages and disadvantages of AE method and advisability of its application for research work and the condition monitoring in tribology.

Chapter 1

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

1.1. FRICTION PROCESSES Friction (or external friction) is termed as a set of phenomena occurring within the zone of contact between relatively moving solids resulting in the appearance of contact forces. According to modern ideas, a variety of physical-chemical processes run simultaneously in friction. Among them, first of all, are mechanical and chemical interaction of surfaces in contact, structural and chemical changes in surface and subsurface layers of mating materials, the damage of surfaces and their strong interaction with the environment. As a rule, these processes are accompanied with corrosion, heat, electrical, magnetic and electromagnetic phenomena. The mentioned processes are interdependent that complicates their investigation. For example, results are reported proving that chemical phenomena and deformation in friction cannot be considered separately [1]. The interconnectivity of friction phenomena has resulted in an idea that friction is a self-organising process [2, 3] and tribosystems are dissipative systems, which obey the following self-organisation conditions [4]: • the system is thermodynamically open, i.e. it can interchange energy and matter with the environment; • the dynamic equations describing the system behaviour are nonlinear; • the deviation from the system equilibrium state exceeds a critical value; • microscopic processes proceed cooperatively in the system. Additionally to processes leading to surface damage, processes decreasing friction and wear may run in such systems. The latter phenomena really occur in friction units of animate nature and machinery. The lack of valid data on physical-mechanical properties of solid surface layers at high strain rates, significant temperature gradients, and heavy loads in various environments complicates the study of interrelated, dissimilar by nature phenomena occurring in friction. So far, there is no a common concept of the properties of these layers. The above list of the processes running in friction units, which is far from being full, shows that the development of adequate friction and wear models is an extremely arduous task. To solve it, coordinated efforts of researchers from various fields of science are required.

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Subsurface layers of contacting solids undergo significant changes due to friction. These changes govern the value of friction force. External friction results from overcoming both surface interaction forces and mechanical resistance related to surface deformation. The friction of solid surfaces occurs within discrete contact areas (contact spots) because of the heterogeneity and random shape of the surfaces. Three types of contact areas are distinguished, namely real, nominal, and contour areas. Real contact area is treated as a region over which atoms of one surface are within the range of repulsion forces of another surface. This is the only mechanism whereby atoms of the materials “bear” the load. The real contact area equals the sum of small regions where surface atoms interact. The nominal contact area is determined by the total dimensions of solids in contact while the contour contact area comprises zones of contact of deformed surface waviness. The size of real contact spots ranges from 0.1 to 10–40 m depending on surface roughness and contact load. Pressure on these spots may reach 10–20% of the theoretical strength of material. With increasing load the real contact area rises mainly due to the increase of the contact spot number while the spot dimensions grow insignificantly. The real contact area amounts to 10–4 –10–1 of the nominal contact area and does not exceed 40% even at heavy loads. In case of two metals differing in hardness the real contact area is governed by the characteristics of the softer metal and surface geometry of the harder one. Friction and wear have statistical nature because of discrete frictional contact of solids and random distribution of temperature and strain fields over real contact spots that result in the non-uniform damage of surface layers. For this reason stochastic models of friction are widely used to describe frictional interaction. Type and Strength of Bond. Dry friction and the friction of solid lubricant coatings (SLC) in vacuum or inert atmosphere at elevated temperatures are strongly governed by the type and strength of the bond between contacting surface spots. The formation of the bonds between dissimilar solids is referred to as adhesion while the interaction occurring when touching the surfaces of like solids is termed cohesion. When the materials are deformed plastically, molecular surface forces act within spots of real contact resulting in the appearance of adhesion junctions [5]. Forces of attraction between contacting solids are caused by practically all types of interaction which may act among molecules and atoms, namely metallic, covalent, ionic, and Van der Waals interactions. During the initial stage of the approaching of metallic bodies Van der Waals forces act which increase as the distance between the bodies decreases (in case of gold the interaction occurs at a distance ≈ 2 nm). When the approaching continues, ionic metallic bond appears and repulsion forces start to act which are effective at short distances and provide

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

3

ultimate equilibrium. The energy of metallic bond exceeds approximately by an order of magnitude that of Van der Waals interaction. Recently the electrostatic theory of adhesion has become popular. It takes into account the effect of the double electric layer appearing in molecular interaction of solids. D. Buckley has pointed that the strongest adhesion bond appears between donor and acceptor atoms [1]. As a result, the shear strength gradient rule has been formulated which has become a fundamental concept of tribology. According to the rule, the following processes running in the subsurface layers of interacting solids influence the value and sign of the gradient: • • • •

the appearance of excess vacancies resulting in a positive gradient; the generation of dislocations resulting in a negative gradient; the formation of protective films favouring a positive gradient; the elevation of contact temperature and the increase in material ductility providing a positive gradient.

It is thought that a positive shear strength gradient is the necessary condition for normal friction and wear. Deformation Mode and Residual Stresses. The following modes of surface asperity deformation occur in friction: elastic, elastoplastic without hardening, and elastoplastic with hardening. All these deformation modes take place simultaneously. However, any mode of asperity deformation may prevail depending on contact load, physical-mechanical properties of the mating materials and their surface roughness. During the initial interaction stage the asperity deformation of metallic surfaces having a standard engineering roughness is mainly plastic. Contact spots undergo repeated loading in friction that leads to the strain hardening of the surface layer and to changes in asperity shape. As a result, elastic deformation becomes predominant. The depth of the deformed zone can reach 3–25 m [6]. In the process of friction residual strains appear in real contact regions while residual compressive stresses occur in subsurface layers due to plastic deformation. Effect of Surface Films. Ultrathin films of gases, vapour of water, and other liquids containing in air, as well as of substances dissolved in liquids and contacting the solid surface are usually cover the surface. These films are classified as adsorbed and chemisorbed layers. As a rule, the films and even monomolecular layers weaken the surface bonds. It is known that metallic bond is completely ruptured if the interatomic distance exceeds 0.1 nm. Therefore, a layer of adsorbed gas ≈ 05 nm thick reduces interaction between the solids in contact to residual Van der Waals interaction that results in a noticeably weaker adhesion. The latter effect is most marked when the film thickness exceeds 2 nm. Oxide films with thickness 2–10 nm, which quickly appear on metallic

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surfaces under atmospheric conditions, also can be considered as such layers. They hamper the formation of metallic bond between the contacting solids and prevent underlying layers against direct contact. In the presence of liquid lubricants the monomolecular layers of fatty acids or soaps appear on the solid surfaces. Their molecules form a film about 2 nm thick which is quite elastic and adheres strongly to metals. In this case sliding occurs within the film reducing substantially the friction and wear of the surfaces. The presence of surfactants favours the effect of strength reduction through adsorption discovered by P.A. Rehbinder. This effect is governed by the influence of polar-active components of a liquid. When the surfactants are adsorbed on juvenile metallic surfaces being exposed in friction (for example, on internal surfaces of microcracks) the metal becomes loosed that leads to the softening of the surface layer and a lesser yield stress. Adsorbed surfactant molecules cover the fresh surface, penetrate into microscopic cracks and migrate over their walls with a velocity considerably exceeding the inlet velocity of the liquid in the gap. The crack can expand due to the propping effect of the surfactant molecules. It should be noted that refractory metals being in the liquid state (for example, sodium) are strong surfactants for refractory metals. Chemical Processes on Friction Surfaces. As a rule, friction is accompanied by chemical processes. During friction in air metallic surfaces very quickly get covered with oxide films, just as during machining. The rate of the film formation is very high at common conditions. For example, a layer 1.4 nm thick is formed during 0.05 s [7]. The elevation of the temperature promotes the acceleration of oxidation. In addition to oxidation other chemical reactions may run in friction including such reactions that do not occur without friction [1]. Friction intensifies chemical processes on the surfaces in contact. On the other hand, reaction products may substantially influence friction. For example, films of some oxides – Fe3 O4 and FeO – reduce friction and wear while Fe2 O3 films intensify them acting as an abrasive. The role of oxide films is mainly governed by the ratio between the parent metal and oxide hardnesses. Fast-Running and Emission Processes in Friction. When solid surfaces are in relative motion the life of single contact spots is short. For example, at a velocity of 1 m/s the life is 10–7 –10–5 s. During this period great energy is generated in the microcontact zone. Theoretical assessments and direct measurements show that the temperature of contact spots can reach 800–1000  C while the bulk temperature remains close to the ambient temperature and does not exceed 30–60  C [5]. The time of temperature flashes is about 10–3 s while the duration of transition regimes related to material heating and cooling at the appearance and disappearance of contact is 0.1–1.0 ms. Proceeding from these data, Tissen et al. made several hypotheses [5] on the state of the matter in the zone of temperature flashes some of which have been experimentally confirmed. For example, they supposed that in friction the valence electrons are detached

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5

from their atoms due to energy absorption within the real contact area and some share of the substance transforms into plasma. Thus, during some period the material exists in all four aggregative states within the area of contact spots, namely solid, liquid, gaseous, and plasma. Since spot dimensions are small and the spot lifetime is short the state of the material in the zone of temperature flashes is far from equilibrium and requires the application of nonequilibrium thermodynamics methods to be described. The presence of temperature flashes, heavy contact dynamic loads, and high energy absorption cause several emission processes accompanying friction. Among them are acoustic emission, electromagnetic radiation, luminescence, and other electrical, magnetic and electromagnetic phenomena [1, 5, 8]. S.N. Postnikov pointed out [9] that friction may be accompanied by almost all electrical effects known in the physics of solids: • thermal electron emission (TEE) being the liberation (“evaporation”) of highenergy (“hot”) electrons from the solid surface due to heating; • exoelectron emission (EEE) or the Kramer effect being the emission of electrons by a cold metallic surface owing to mechanical deformation or damage. Lubricants can reduce EEE while surfactants, as a rule, intensify it; • thermoelectronic phenomena such as the Seebeck effect being the appearance of electromotive force in a circuit with dissimilar conductors; the Peltier effect being heat liberation or absorption when passing electric current through a contact of two dissimilar conductors; the Thomson effect being heat liberation or absorption in a conductor with electric current along which a temperature gradient exists; • thermo- and galvanomagnetic effects resulted from the influence of magnetic fields on heat flows and electric currents in metals; • electrochemical effects related to the transition of charge from one phase into another, for example, through a metal–electrolyte interface and to the appearance of voltage jump (double electric layer) over the interface. As a rule, many of the above mentioned processes run simultaneously. For this reason, electromagnetic radiation results from their joint action and reflects the electron distribution variations in materials and electrochemical transformations in friction. Monograph [10] deals with triboengineering methods based on measuring characteristics of various emission phenomena. The analysis of emission processes opens up wide opportunities to monitor and diagnose friction units by studying their current state. Acoustic emission has been used for this purpose for enough long time while the engineering application of other emission processes is a prospective task.

CHAPTER 1

6

Stages of Wear. Materials of friction members pass three wear stages in operation. They are running-in, steady state, and catastrophic wear stage. Figure 1 presents schematically the time dependence of the wear rate. i

I

II

III

t

Figure 1.1. Time variation of wear rate Let us consider the first (I) stage, i.e. running-in. Running-in means the changes in the friction surface relief and physical-chemical characteristics of surface layers during the initial period of operation. At constant external parameters these changes consist in the decrease of the friction force, temperature of mating materials, and wear rate. During running-in the highest asperities become smaller and practically always new roughness appears in dry and boundary friction whose parameters depend on operation conditions of the friction pair, physical-mechanical characteristics of the mating materials and the environment conditions [12]. This roughness is optimal for a given friction regime and favours a minimal wear at these conditions. It is called the equilibrium roughness and is reproduced during all stage of the normal operation of the friction unit. In addition to changes in the surface geometry, the material structure varies during running-in when the material becomes textured along the sliding direction. In the course of running-in the tribosystem transits into an equilibrium state that is characterised by the minimal energy dissipation at given conditions. According to I.G. Goryacheva and M.N. Dobychin, geometrical characteristics of surfaces vary as long as the real pressure becomes equal over all contact spots [9]. For example, the well-known decrease in the friction coefficient of materials coated with molybdenum disulphide during running-in is explained by the changes in crystallite orientation. At the beginning of running-in, when the crystallites are randomly oriented on the substrate, the friction coefficient is rather high. After a lapse of time required for the original disoriented structure into the plane-parallel structure, the friction coefficient of molybdenum disulphide becomes minimal. During running-in recrystallization occurs on the surface of some polycrystalline materials including iron-containing alloys that is accompanied by grain ordering. The so-called white layer, or Beilby layer, appears which earlier was

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thought to be amorphous. In fact, this layer has a fine-grain structure formed during several recrystallization stages [1]. The second wear stage (II) is characterised by constant values on the average of practically all friction characteristics, namely the friction coefficient, wear rate, temperature, roughness, etc. Thus, at this stage the processes of friction and wear are stationary in the broad sense. The microgeometry of friction surfaces is continuously reproduced. The following features are typical for friction and wear at this stage: • physical-mechanical characteristics of surface layers of the materials in contact become stable; • the roughness of the friction surfaces is statistically reproducible; • the friction force and wear rate (as a rule) are constant. One important fact should be mentioned here. Friction characteristics including the friction force, wear, and temperature are constant only on average. This is proved by direct measurements of their instantaneous values [5] and can be explained by the statistical nature of surface roughness, non-uniformity of surface layer properties and fluctuations of environment condition characteristics and friction parameters (the velocity and load). The third wear stage (III) is characterised by sharp changes in friction characteristics. The friction coefficient, wear rate, and contact temperature increase. The tribosystem transits from normal to catastrophic wear. In real friction units such transition can result from the following reasons: • • • • • •

overload of the friction pair; contact temperature elevation; deterioration in lubrication conditions; reaching contact fatigue limit of the material; ingress of a lot of abrasive into the contact zone; lubricant degradation under the effect of external factors (heating, radiation, etc.); • damage of surface films and layers. As a rule, the third wear stage is characterised by the following processes: • • • • • •

damage of an oxide film and the deterioration of friction surface quality; changes in the properties of surface layers of mating materials; increase in the linear wear of parts and joint clearances; damage of an oil film or a solid-film lubricant separating the surfaces; increase in the friction coefficient; contact temperature elevation;

8

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• changes in the mode of interaction between asperities in contact; • changes in the energy state of surface layers leading to the intensive rupture of formed junctions by adhesive and cohesive mechanisms; • sharp increase in the volume of debris that results mainly from increasing dimensions of separated particles while their number grows insignificantly. Materials for friction units and lubricants should be selected having in mind the necessity to shorten the running-in stage and prolong the steady-state wear stage. To prevent the breakdown, methods and means of friction unit diagnostics should be used allowing one to reveal the beginning of the third (catastrophic) wear stage in due time and to exclude friction unit failure. Friction Surface Damage. Surface damage in friction can be divided into adhesive damage occurring within the zone of adhesive junctions and cohesive damage that takes place in surface layers of materials in contact. The abrasive, adhesive, fatigue, cavitation, corrosive, and erosive mechanisms of surface layer damage are distinguished. The damage of surface layers of solids in contact produces wear debris whose chemical composition, shape and dimensions depend on friction conditions and wear mode. As a rule, damage results from the joint effect of several elementary processes one of which may dominate. The combination and severity of the processes are governed by the mating materials, environment and friction conditions (load, velocity, temperature, the type of the relative motion of friction members – reciprocal or unidirectional, etc.). The following types of friction surface damage can be considered as elementary damage mechanisms: microcutting, plastic deformation, delamination, pitting, and bulk tearing. Microcutting usually occurs when wear debris or abrasive particles penetrate into the friction zone or lubricant causing surface cutting with chip formation. This process is inadmissible for normal wear since it can produce the emergency state of a friction unit. Plastic ploughing occurs when a counterface asperity or a wear (abrasive) particle deforms the material plastically and forms a track like a groove. Under repeated deformation of the surface layer the material exhausts its ability to be plastically deformed. Microcracks appear on the surface and more often beneath it. The propagation of the cracks leads to wear particle delamination. Delamination may occur when deformation does not produce noticeably pushing off the friction surface as well as when the surface is repeatedly deformed elastically. If stresses in surface layers exceed the material endurance the cracks appear in the layers inducing the delamination of the material. Wear particles resemble flakes whose thickness corresponds on average to the depth of microcrack origination. Since delamination results from material fatigue, its rate

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

9

is quite low especially in the presence of a liquid lubricant and it is considered as the most favourable mode of inevitable friction unit damage. Pitting is a frequently occurring mode of surface damage in rolling. Physical reasons causing pitting are similar to those described in the above wear modes (the exhaust of plasticity margin of the material and its fatigue). Wear particles are separated as a result of the gradual growth of microcracks which detach a small material volume from the bulk. Such cracks appear most probably over the boundaries of structure inhomogeneities, grains, inclusions, etc. Bulk tearing occurs at extreme friction conditions (elevated temperature, high pressure, inert atmosphere, vacuum, etc.) when adhesion junctions appear between the surface layers due to molecular interaction; their tensile strength exceeds the cohesive strength of one of the mating materials. Damage takes place inside this material. A particle of the torn material retains on the counterface and is involved in further friction. If the volume of such particle is large a score may appear later on this spot which can lead to the seizure or failure of the friction unit. Self-organization processes may run in a tribosystem for some materials at certain conditions. Wear particles migrate repeatedly from one friction surface onto another remaining always in the friction zone. The selective transfer mode occurs that is a wearless process by its nature [13]. For example, in the bronze – steel pair selective transfer manifests itself as the Kirkendal effect that involves the selective dissolving of alloying elements contained in alloys due to their different electrochemical potentials, chemical reduction of damaged fragments consisting of metal oxides, predominant precipitation of the particles including copper ions on the friction surfaces, heterogeneous catalysis running on the triboactivated surfaces, and the formation of polymerisation products (metalorganic monomers). The latter appear due to chemical interaction between the lubricant and the alloying elements. As a result, thin soft layers arise covering both surfaces and strongly adhering to them. These layers are formed from preliminary recovered damage particles which precipitate on active spots of the working surfaces and are renewed in friction [13]. In line with the elementary processes of damage and the friction conditions (contact geometry, environment, etc.) several wear modes are distinguished. Abrasive wear occurs when hard particles contained in a lubricant or operating environment affect the friction surface. Adhesive wear results from molecular interaction between solids and occurs when a junction formed within a contact spot is stronger than the underlying layer. This wear mode is typical for friction in vacuum and inert gases (helium, argon). It takes place when solid lubricants based on lamellar substances like graphite or molybdenum disulphide are used and also in friction of polymeric materials.

10

CHAPTER 1

Fatigue wear evolves from the repeated loading and heating of contact spots in friction. Irreversible changes in the surface layer structure appear in the vicinity of the spots. Inhomogeneities of the material structure are formed like stress concentrators, zones with a higher dislocation density, and slip bands originate. The migration of dislocations within the slip bands leads to the appearance of pores and loosening the surface layer. Then the pores agglomerate into microcracks under the effect of friction. The microcracks merge each other forming a macrocrack. As the latter propagates, a wear particle appears. Cavitation wear results from cavitation phenomena running in a lubricant close to a solid surface. It frequently occurs in sliding bearings lubricated with oils. In corrosive wear damage stems from oxidation activated by heating and mechanical loading. It is typical for friction units which operate in media containing corrosion-active substances like liquid sodium, water circulating in the primary coolant circuit of a nuclear reactor, etc. Adsorption-corrosive-fatigue wear is the predominant wear mode in friction units operating at boundary lubrication with solid lubricants. It is caused by material frictional fatigue occurring as a result of the repeated deformation of surface layers. Fatigue is governed by the Rehbinder effect and corrosive processes similar to those running in stress corrosion.

1.2. ACOUSTIC EMISSION AND ITS MAIN CHARACTERISTICS Acoustic emission is defined as radiation of mechanical elastic waves produced by a material due to the dynamic local rearrangement of its internal structure. In addition, recently high-frequency acoustic vibrations appearing when gases and liquids effuse from holes in vessels and pipelines are considered as acoustic emission as well as the acoustic signals accompanying the friction of solids. At present it is a generally recognised viewpoint that acoustic emission accompanies almost all physical phenomena in solids and their surfaces. The possibility to register the emission in various processes depends only on the sensitivity of measuring equipment. Acoustic emission occurs both in microprocesses caused by the movement of the smallest solid structure fragments and in macrophenomena related to the failure of assemblies and designs. For this reason, the registration of AE opens up wide opportunities to study solids, interaction between solids and between solids and liquids and gases as well as to diagnose materials used in power designs. The phenomenon of AE has been known from the middle of the 19th century as “tin cry” appearing when deforming tin and audible with the naked ear. Yet, during several decades it had been not applied in practice. Since the

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

11

fifties of the last century researchers had begun methodical studies of acoustic emission in structural materials. The phenomenon of AE and mechanisms causing it turned out to be more complicated than pathfinders of AE studies expected. The middle of the seventies is a period when the researchers realised the intricacy of problems arising when interpreting AE signals, developed highly sensitive measuring devices, gained some experimental data sufficient to solve both research and engineering problems. Acoustic emission had started to be used for friction unit diagnostics since the end of the seventies. Available monitoring methods are based on the analysis of characteristics of AE signals. Methods of processing signals and the determination of their informative characteristics strongly depend on the type of AE being registered. Acoustic emission is commonly divided into discrete AE and continuous AE. To understand how to select the informative characteristics when registering either type of AE let us consider basic conditions of AE appearing in solids. Since matter is of discrete nature, physical processes running in it are also discrete. The apparent continuity of the processes results from averaging lot of individual elementary events. An elementary event in a solid leads to its deformation yet so small that common measuring means are incapable to register the event. However, a huge number of the elementary events forming a sequence (flow) of events may cause macroscopic phenomena that change significantly the energy state of solid. When energy is released some its share is emitted as elastic waves. The appearance of such waves is acoustic emission. Acoustic emission can manifest itself in two ways. If the number of elementary events causing elastic waves is great and the energy being liberated in a single event is small AE signals are registered as quite continuous noise that is called continuous AE. Since the energy released in a single event is small the energy state of solid changes insignificantly. The probability of occurrence of the next event is almost independent of the previous event. As a result, continuous AE characteristics vary relatively slow with time and for this reason the process can be considered as a quasistationary process. If the state of the solid is far from equilibrium, avalanche processes may occur in which a great number of elementary events have become involved in the process during a short period. The energy of the elastic wave may exceed several orders of magnitude that of elastic waves in continuous emission. Such emission characterised by a great amplitude of acoustic pulsed registered is called discrete AE. It should be noted that the classification of AE into continuous and discrete is quite relative since the possibility of the separate recording of AE pulses depends only on characteristics of measuring devices. For example, an increased degree of signal discrimination makes it possible to record only high-amplitude surges of an acoustic signal that is to register discrete AE instead of continuous one. However, it is apparent that the nature of AE phenomenon does not change in this case.

12

CHAPTER 1

In reality, as a rule, both types of emission occur. For example, the undercritical crack growth in metals under the effect of external and internal factors runs step-wise. Long periods of the stable state of a crack accompanying by a possible increase of plastic strain in its tip alternate instants when the crack length changes with the near-sonic speed and the crack transits into a new equilibrium state. This transition is caused by variations in the material stress state (unloading) in the vicinity of the crack and accompanied by the emission of an elastic wave which is registered by a gage as a discrete AE signal. During intervals between steps when plastic strain is accumulated the continuous AE typical for plastic deformation occurs. A similar situation arises in the growth of fatigue cracks. The creep of the material at the first (stationary) and the second (nonstationary) stages is accompanied by continuous AE. At the third stage discrete AE occurs additionally resulted from origination and growth of microcracks. A similar process runs in stress corrosion whose final stage (corrosion cracking) produces intensive acoustic flashes of discrete AE. In all mentioned cases the average rate of crack growth does not exceed as a rule fractions of millimetre per hour during a sufficiently long period being the undercritical stage of growth. Though the crack is not yet dangerous for the structure, appearing AE proves defect growth, hence it is the precursor of the coming of catastrophic damage. The discrete AE component is usually used to predict damage since high-amplitude signals are easy to detect. Discrete AE is also used to monitor technological processes in which cracks may appear (welding; hardening; diffusion saturation, for example, hydrogen pickup, etc.) as well as to study and monitor corrosion cracking, strength, heat resistance, fatigue damage, and friction and wear. Continuous AE is related to plastic deformation, metal corrosion and other physical phenomena. We should note once again that both discrete and continuous AE components may occur in all the above processes. One should distinguish informative characteristics of single pulses of discrete AE, pulse flows, and characteristics of continuous AE. Pulses or signals of AE are characterised by amplitude, duration, shape, and occurrence time. The signal flow can be additionally characterised by the mean frequency of events, spectral density, amplitude, time and amplitude-time distributions, the correlation function, mean value, and variance. Each of these characteristics relates to some physical process causing AE and contains information on its running or on the state of the object under study. The following informative characteristics are used for discrete AE: 1. Total number of pulses N is the number of discrete AE pulses registered during the interval of observation. The definition of this characteristic means that it is suitable to describe only flows of non-overlapping pulses. The definition

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

2.

3.

4.

5.

13

characterises processes related to damage and points to the number of single acts of origination and propagation of defects in a material or design. AE activity is the total number of pulses per unit time. The information content of this characteristic is similar to those of the previous one, yet with better specification in time that allows one to observe damage in dynamics. Total AE is the number of overshoots of AE signals of a preset value registered during a certain time interval. For discrete AE this value characterizes the number of events with energy exceeding a threshold. When registering discrete AE some data are lost related to pulses whose amplitude is below the threshold value (discrimination level). Furthermore, the possibility to select this level arbitrary makes the characteristic ambiguous. If non-detected pulses being damped oscillating signals inputting from a piezotransducer are count that is frequently used, then additionally ambiguity of results arises caused by the repeated registration of one and the same pulse. In this case the multiplicity of its reproduction in the counter depends on the discrimination level, attenuation factor of oscillations in the object and transducer, and characteristics of receiving-amplifying channel. Count rate N˙ is the number of overshoots of AE signals of a preset value per unit time. This characteristic is the time derivative of the total AE and has the same disadvantages. Some authors call it AE intensity. Probability density of pulse amplitude wA characterises AE as a random process. This function determines the probability that AE pulse amplitude A0 is within the interval from A to A + dA: P A < A0 < A + dA = wAdA In practice another characteristic is used more often that is called the amplitude distribution of pulses nA. This function indicates the number of pulses whose amplitude is within a small interval from A to A + dA. If the total number of registered pulses is N , then the amplitude distribution is related to the probability density wA by the following formula: nA = NwA

where N =

 nAdA 0

The functions wA and nA can be found from experimental data by plotting the histogram of amplitude distribution of AE pulses. As is known, this histogram reflects the dependence of the number of pulses ni (or the share of such pulses ni /N ) whose amplitude is within a small interval from Ai to Ai + A on the value of the amplitude Ai . It is easy to find a correlation between these functions: NwAi  A = nAi  A = ni . Using these relations

CHAPTER 1

14

and experimental data the set of values of functions wAi  and nAi  can be found and then select analytical expressions to describe the functions wA or nA, for example, by means of the Pearson distributions (see part 1.5). 6. Distribution of time intervals w between single AE pulses contains important information on the physical nature of a phenomenon and how it evolves. If events are mutually independent and the probabilities of elementary events are equal then the sequence of the events (the flow of events) is described by Poisson’s law. If the flow is stationary then the distribution of time intervals between AE pulses obeys the exponential law: w = exp −  and the average time interval between the pulses equals 0 = 1/v. The reverse proposition is also true that if the distribution of intervals between single events is exponential, the events are distributed according to Poisson’s law. This conclusion proves no correlation among single events that is important information on how the process evolves. 7. Amplitude-time distribution of AE pulses nA t is the function representing the number of AE pulses dN registered within the time interval from t to t + dt whose amplitude varies within the interval from A to A + dA: dN = nA tdAdt If this function is integrated in time from 0 and T being the time of AE registration, the amplitude distribution of AE pulses is obtained. The next integration with respect to amplitude yields the total number of pulses during the registration time: nA =

T 0

nA tdt

N=

T 

nA tdtdA

0 0

In other words, the amplitude-time distribution represents time variation in the amplitude distribution of AE pulses. 8. Spectral density S of discrete AE has the same sense as that of a random process and equals the power of the process within a unit frequency band. The informative content of the spectral density is due to its correlation with the rate of the process inducing AE signals. In addition to the spectral density, the correlation function is sometimes more suitable for analysing acoustic emission. It has the same informative content as the spectral density since in stationary random processes they are correlated through the direct and inverse Fourier transform (the Wiener-Hinchin theorem) [14].

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

15

If we consider continuous AE some of the above characteristics acquire different content. Moreover, additional characteristics can be introduced to describe the process. Since the definition of the amplitude of a single pulse has no sense in this case the total AE and the AE rate are determined by the number of overshoots of the random process over the discrimination level, i.e. the number of excesses of the variable being registered (electric voltage, current) over a preset discrimination level during all time of registration or per unit time, respectively. Instead of the amplitude distribution the probability density of AE should be used representing the part of the observation period during which the variable being registered is within an interval close to a preset amplitude value. In addition, univariate and multivariate distribution functions of the above characteristics are introduced. The informative content of the mentioned characteristics in friction is analysed in detail in Part 1.5.

1.3. SOURCES OF ACOUSTIC EMISSION IN METALS At the current stage of AE studies the following AE sources acting in metals at different structure levels are distinguished [15–17]: 1. Mechanisms inducing plastic deformation: • processes related to the migration of dislocations (the conservative sliding and annihilation of dislocations, the generation of dislocations by the Frank-Read mechanism; the separation of dislocation loops from pinning points etc.); • grain–boundary slip; • twinning. 2. Mechanisms related to phase transformations and phase transitions of 1st and 2nd kind: • polymorphic transformations including martensite transformations; • formation of particles of the second phase in decomposition of oversaturated solid solutions; • phase transitions in magnetics and superconductors; • magnetomechanical phenomena due to boundary shift and reorientation of magnetic domains with varying external magnetising field. 3. Mechanisms relating to damage: • origination and accumulation of microdefects; • origination and growth of cracks; • corrosion damage including corrosion cracking.

CHAPTER 1

16

Table 1.1 lists data representing characteristics of some AE sources. Additionally, data are given on the value of acoustic noises resulted from the thermal motion of atoms. Table 1.1. Characteristics of AE Signals for Some Sources Type of AE source

Amplitude or energy of AE pulse, Pa or J

Duration of signal, s

Width of signal spectrum, MHz 1

Frank-Read dislocation source

(10−8 –10−7 )G

5−5 · 104

Annihilation of dislocation 10−8 –10−6 m long

4 · 10−18 –10−16 

5 · 10−5

102

Formation of microcrack

10−12 –10−10

10−3 –10−2

50

Disappearance of twin 10−9 m3 in size

10−3 –10−2

104

−

Plastic deformation of material volume with characteristic size 10−4 m

10−4

103

0.5

Energy of thermal noises in a unit frequency band

42 · 10−21 J/Hz

−

<10

Note: G is the shear modulus.

In polycrystalline materials the appearance of continuous AE is commonly attributed to the plastic deformation of single grains of a polycrystal. Due to the non-uniform stress distribution in the polycrystalline structure the plastic deformation of individual crystals occurs when total deformation is small and the metal is in the elastic region from the phenomenological viewpoint. For this reason, AE signals allow one to determine the appearance of inhomogeneities and microdefects during the initial stage of material deformation and damage. The practical application of AE phenomenon is based on the registration of elastic energy liberated in the material of an object under study. The origination, motion and growth of defects are accompanied by changes in the microstructure and stress-strain state. Given this, the elastic energy is redistributed that results in AE signal emission. Discrete AE appears when the defects grow. Therefore, it can be used to detect growing defects dangerous from the viewpoint of the

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

17

catastrophic structure damage. This is an advantage of AE method in comparison with common ultrasonic inspection methods. For this reason, most of experimental and theoretical AE studies deal with the investigation of a correlation between characteristics of AE signals and those of the stress state and damage of materials. Many researches made attempts to determine functional or correlation interdependencies between crack characteristics and AE signals registered. We do not consider in detail backgrounds allowing obtaining such dependencies (in some cases they are found by processing experimental data) and give some of them in Table 1.2. Table 1.2. Correlation between AE Characteristics and Characteristics of Material Failure Failure characteristics

Relations

Stress intensity factor K1

N = N0 KIm m ≈ 411

Total crack opening displacement 

  1 − vN/02  S  Ai i  n

l  Ai i  2

S  Ai E/KI2

Total area of opened crack S Crack length increment l Crack area increment S

i

Crack length L Critical of stress intensity factor Kc in corrosion cracking

L  cl T   dN/dtc  Kc5 − K05

Note: N is the total AE count; A0 is the AE amplitude;  is Poisson’s ratio; E is the Young’s modulus;  is the yield stress; cl is the velocity of longitudinal waves; T is the duration of the first half-wave; dN/dtc is the critical AE count rate; K0 is the threshold value of the stress intensity factor; n is a numerical coefficient.

Among the presented dependencies the power dependence between the total number of AE pulses and the stress intensity factor at the tip of a growing crack is the most valid and stable, according to most researchers. Many authors relate the value of the exponent m to the dimensions of the plastic deformation zone near the tip of the growing crack. Yet, if one follows this point of view, it should

18

CHAPTER 1

be taken that the value of m equals four. Experiments yield a broader range of m variation. We found that the exponent m is a function of the dimensionless grouping KIc2 /E comprising the critical stress intensity factor KIc , Young’s modulus E, and the surface energy  of the material. The value of m for various materials may range from 4 to 10.5 depending on the value of the above grouping that is in good agreement with experimentally obtained data. Paper [18] also should be noted which describes the results of thorough experimental studies proving that the sum of peak values of AE pulse amplitudes depends linearly on the area of a crack in fracture of steel 38XH3MA (0.33–0.40 C, 0.17–0.37 Si, 025–0.5 Mn, 1.2–1.5 Cr, 3.0–3.5 Ni, 0.35–0.45 Mo, 0.1–0.18 V).

1.4. SOURCES OF ACOUSTIC EMISSION IN FRICTION OF SOLIDS Various mechanical and physical-chemical processes occur on real contact spots in the friction of solids. Some of them are similar to processes occurring at deformation and damage of materials, other processes are specific for friction. For this reason, acoustic signals at friction result mainly from the same phenomena as at the mechanical loading and failure of materials with account for specific features of friction pair operation (Table 1.3). This is confirmed by the analysis of publications dealing with acoustic emission at friction. The main distinctive feature of acoustic emission at friction is the presence of additional sources in comparison with the deformation and failure. These sources result from fast-running processes occurring at friction. Among them are the elastic interaction of friction surface asperities (for example, collisions of asperities), chemical processes including corrosion which accompany friction in many cases, and the formation and rupture of adhesion junctions. In experiments it is difficult to provide conditions favouring one of the processes listed in Table 1.3. Therefore, it is impossible now to separate and study single sources. A small number of publications concerning these studies can be explained by this fact. Thus, at the end of the seventies of the last century only about ten papers dealt with this problem and intensive studies started at the beginning of the eighties. Researchers from the V.A. Belyi MetalPolymer Research Institute of the National Academy of Sciences of Belarus were successful in studying acoustic emission resulted from friction in metal-polymer contact [10]. Acoustic emission in friction is commonly attributed to changes in the stress-strain state of contact spots and to the appearance of wear debris, i.e. friction surface damage.

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

19

Table 1.3. Sources of AE Signals at Friction of Solids Sources of AE Elastic interaction, impacts Changes in stress-strain state of a local volume of solid surface layer Plastic deformation, damage Generation, motion and interaction of dislocations Energy liberation at repeated deformation or phase hardening-weakening and damage of surface layer Changes in friction surface structure Formation of microcracks, micropores and new surfaces because of wear Appearance of wear debris Surface spalling and formation of fatigue pit

Characteristics of AE are sensitive to the wear mode. Higher AE intensity values are typical for abrasive wear in comparison with adhesive and fatigue wear. When studying the shape of AE signals at steady-state friction it was found that materials damaged by adhesion and fatigue produce a continuous signal with a small amplitude while materials damaged by adhesion with seizure yield a signal of explosive type. When abrasive wear becomes to dominate the amplitude of signals increases approximately 2–3 times. Researchers make attempts to use AE method to monitor sliding and rolling bearings. The following processes are believed to cause AE: the plastic deformation of bearing members, friction surface spalling, the formation of fatigue flaws, the growth of surface and subsurface micro- and macrocracks. High sensitivity of AE method is mentioned in papers [19, 20]. In particular, it is shown that when monitoring rolling bearings, defects (scratches, pits) about 100 m in size were found that have not be detected by low-frequency (vibration) diagnostics techniques. Summarising the available data we can conventionally divide all sources of AE into three groups: – processes of impact of friction surface microrelief elements; – processes of surface damage including corrosion damage; – processes of the formation and rupture of friction junctions.

20

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Since energy being liberated in these processes is different they are accompanied by various types of AE. One can assume that the predominant AE type in damage of surface layers is discrete AE, continuous AE dominates in elastoplastic deformation while the formation and rupture of adhesion junctions on the friction surfaces may be accompanied by both continuous and discrete AE. In the latter case the size of the junctions is of great importance.

1.5. INFORMATIVE CONTENT OF CHARACTERISTICS OF ACOUSTIC EMISSION AT FRICTION AE signals in solids result from a variety of discrete random events, therefore the acoustic emission itself should be considered as a random (stochastic) process. Such processes should be described and analysed based on the random process theory and using mathematical statistics methods with account for the character of signal transformation in the measuring system. The great experience gained by statistical radio engineering, radiophysics, experimental nuclear physics, and other fields dealing with the study of random processes or filtering signals from noise turns to be useful. Like any signals, AE signals are characterised by some parameters (characteristics). Researchers strive to determine the most number of characteristics of AE signals. Each of them contains information on a physical phenomenon causing AE and can be used to assess the state of the object under study. It should be born in mind that when passing from a source to a detector and then through a measuring system, body of information contained in AE signals can only decrease. Therefore, when designing the hardware measures should be taken to minimise data losses. If for some reasons it is impossible, the distortion of the information on AE signals should be taken into account when interpreting the measurement results. For example, it is well known that the dispersion of some types of acoustic waves and the frequency dependence of their damping factor result in a substantial distortion of the shape of pulses of acoustic emission representing in a general case the superposition of types of waves that can transmit in the given object. Hence, the amplitude, duration and frequency spectrum of AE signals change. These changes can be allowed for if the response function (or the transfer function) of the acoustic channel is known. Yet, in some cases it is quit difficult to determine the functions when studying real objects. Experience gained in AE studies of material damage can be useful when analysing acoustic emission accompanying friction. In particular, experimental data are helpful on the informative content of AE signal characteristics (Table 1.4) [17].

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21

Table 1.4. Informative Content of Characteristics of AE Signals in Metals Informative content

Characteristics of AE Frequency spectrum

Nature of AE source

Amplitude

Energy of AE source

Amplitude distribution

Type of present defects; failure mode (ductile failure or brittle fracture)

Count rate

Rate of defect growth

Time distribution of pulses

Type of growing defects

Studies performed by a number of authors [10, 21] and our studies have shown that the analysis of discrete AE characteristics allows one to identify such processes in the friction zone as running-in, destruction of lubricating films and coatings, and wear. Based on these results, one can develop methods and AE instruments for the field inspection of friction units. When registering, processing and analysing AE signals it should be kept in mind that informative characteristics of continuous and discrete AE are different. Let us consider AE characteristics (see Part 1.2) from the viewpoint of their correlation with processes in the friction zone and requirements to hardware used to register the signals. The following statistical characteristics of electrical signals produced by an acoustic emission detector serve as basic characteristics of discrete AE: the total number of pulses, the number of pulses per unit time, the amplitude distribution of pulses and its statistical moments, the amplitude-time distribution of pulses, the spectral density (or the correlation function), and the probability densities of the signal characteristics. Number of Pulses and Rate of Pulse Flow. Discrete AE at friction is a random sequence (flow) of pulses whose amplitude Ak and time of occurrence tk are random variables: st =

N

Ak ut − tk 

(1.1)

k

The shape of pulses ut is determined by the frequency characteristic of the acoustic channel and detector; it can be roughly assumed to be the same for all pulses. Figure 1.2 presents schematically discrete AE pulses registered by a narrow-band detector. As a rule, these detectors have a higher sensitivity compared with broad-band detectors and make it possible to dejam noises which

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22

inevitably appear in tribotests. In this case the shape of a single signal presents the response of the detector to short pulse effect being a single act of acoustic emission; it can be written as follows: vt = A0 ut

ut = e−t/d sin d t

d >> 1/d t > 0

(1.2)

where vt is the output voltage; A0 is the amplitude of the pulse; d = 2fd ; d = Q/fd is the time constant characterizing signal attenuation; fd and Q are the resonance frequency and quality of the detector. 1 2

7

5

3 8

6 4

9

10

Figure 1.2. Schematic representation of AE signal: 1 – maximal amplitude of pulse; 2 – noise level; 3 – voltage; 4 – single oscillations; 5 – standard deviation of amplitude; 6 – interval between pulses; 7 – discrimination level; 8 – time; 9 – pulse duration; 10 – events If individual events inducing the emission of AE pulses are independent and equiprobable in time then the pulse flow in called the Poisson flow since the probability of registration of N pulses during time t is described by the Poisson distribution: PN t =

vtN exp −vt N!

(1.3)

where  is the average number of pulses per unit time or the flow rate. If the rate varies in time as t and AE events are independent then the pulse flow is called the Poisson flow with variable rate and the probability PN , t is calculated by the formula:

t  PN t =

N 

vt dt

0

N!



⎧ ⎫ ⎨ t ⎬   exp − vt dt  ⎩ ⎭ 0

(1.4)

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23

Pulse flows are divided into flows of non-overlapping AE pulses when the repetition rate of pulses is low and single pulses can be registered independently, and flows of overlapping pulses when pulses can partly superimposed. The average frequency of events (the rate of the pulse flow) is called the activity of AE (see Part 1.2) and characterises processes related to single acts of acoustic emission (the origination and propagation of defects in the material, impacts of microasperities, etc.). Since any equipment produces its intrinsic level of noises and has a finite threshold of sensitivity, the activity of AE can not be measured. Only those pulses can be registered whose amplitude exceeds the discrimination level of the equipment. Nevertheless, this characteristic is widely used in calculations. The authors of [22] assessed the activity of AE which is expectable in friction of steel 45 specimens with different sliding velocities. The calculations were performed having in mind that the number of AE events per unit time is proportional to the sliding velocity and the number of real contact spots for the spherical model of surface roughness. According to the calculations, for ground surfaces of the eighth roughness grade at normal loads from 1 to 100 N and the size of the nominal contact area up to 10 mm the expected average value of AE activity is about 105 pulses per second at a velocity of 1 m/s. It is apparent that these data present some assessment and can be used only to estimate the expectable rate of the random signal flow and formulate technical requirements to measuring devices. In particular, the obtained assessments show that the “dead time” of a device should be below 10 s. The number of pulses per unit time exceeding the device discrimination level is called the count rate of AE N˙ . This characteristic is most easy to be registered. That is why many researchers strove to relate it to the characteristics of the deformation and failure of materials and to the characteristics of processes in the friction zone. Postdetection and predetection pulse counts should be distinguished. In the former case (Fig. 1.2) a signal produced by a gage is amplified and detected then the number of overshoots of the waveform envelop over a preset discrimination level per unit time is found. In the latter case the signal is not detected and the number of overshoots of signal oscillations over the discrimination level is calculated (Fig. 1.2). It is apparently that in this case several pulses (oscillations) exceeding the discrimination level are counted instead of a single acoustic event. This characteristic presents to some extent the energy of the process. It is related to the amplitude of a single pulse, that is, the higher the amplitude, the greater number of oscillations is registered. Note that when registering continuous AE it is preferably to use predetection count. This yields the mean-square error of N˙ several times less compared with postdetection count. At the same time, the use of predetection count distorts such AE characteristics as the amplitude and amplitude-time distributions,

24

CHAPTER 1

the spectral density, the total count, etc. Therefore, the dependencies of these characteristics on friction conditions (load, sliding velocity, surface roughness) also change. Nevertheless, if characteristics of a narrow-band gage are known, the results of predetection count allow one to reconstruct some initial characteristics of acoustic emission, for example, the amplitude and amplitude-time distributions. Below we show how to implement this. Amplitude, Amplitude and Amplitude-Time Distributions. The amplitude is the most important characteristic of acoustic emission. The amplitude of AE pulses depends on the properties of mating materials, the load, friction conditions, surface roughness, temperature, and some other factors. Based on the analysis of data available in publications and results of our studies, these factors can be divided into two groups depending on how they affect the amplitude of AE pulses accompanying the friction of solids (see Table 1.5). This information is helpful when analysing and interpreting AE data and allows one to predict how the emission amplitude varies with varying friction regimes and conditions. The amplitude of pulses contains information on the energy of AE source while the amplitude distribution provides data on the energy distribution of sources. If the amplitude distribution is known it is easy to find the mean amplitude, mean-square amplitude and amplitude variance. The first two values characterise integrally the energy of the process while the latter characterises the scatter of the energy of AE sources. Variation of the amplitude distribution in time, or the amplitude-time distribution (see Part 1.2), presents the dynamics of friction processes. As has been noted above, the use of predetection count distorts the pattern of the amplitude and amplitude-time distributions of AE pulses. Let us consider how to reconstruct their original pattern if they were registered at predetection count. The superposition of pulses is neglected. Let the shape of a signal produced by a gage is described by relation (1.2) and the amplitude of the signal is A0 . Then in the case of predetection count NA additional pulses are registered instead of a single pulse with the amplitude A0 within the amplitude range from A– A to A ( A << A < A0 ):

NA = d fd ln

 f A  d d A A − A A

(1.5)

Note that the additional number of pulses does not depend on the amplitude A0 of the initial pulse provided that A < A0 .

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

25

Table 1.5. Factors Influencing Amplitude of AE Pulses Factors increasing amplitude

Factors decreasing amplitude

Rough relief

Smooth relief

High hardness

Low hardness

Surface anisotropy

Surface isotropy

Inhomogeneity of surface properties

Homogeneity of surface properties

Coarse grains

Fine grains

Absence of texture

Presence of texture

Low toughness

High toughness

Defects in surface layer

Absence of defects in surface layer

Low temperature

Elevated temperature

High sliding velocity

Slow sliding velocity

Heavy load

Light load

Non-stationary friction conditions

Stationary friction conditions

Abrasive wear

Adhesive wear

Failure due to microcutting

Failure due to plastic deformation

Dry friction

Presence of a lubricant

Boundary friction with a liquid lubricant

Boundary friction with solid lubricants

Presence of surfactants

Absence of surfactants

Presence of corrosive environment

Absence of corrosive environment

If n0 A is the initial distribution of AE pulse amplitude then the number of pulses with the amplitude exceeding A equals: NA0 ≥ A =

 A

n0 A dA 

CHAPTER 1

26

Since each of the pulses gives additionally NA pulses within the amplitude range from A– A to A then the amplitude distribution at predetection count is determined by the following relation:

NA Q  = n0 A + n0 A dA  nA = n0 A + A

A 

(1.6)

A

From formula (1.6) it follows that the distortion of the amplitude distribution depends on the parameter  = Q/. The reciprocal of 1 = /Q is called logarithmic decrement of oscillations. Figures 1.3, a, b illustrate examples of variations of normal and exponential distributions depending on the parameter . The initial distribution corresponds to  = 0. It follows from the figure that when analysing the amplitude distributions it should be specified how they are registered since at predetection count both the distribution parameters and the distribution pattern may vary. In particularly, it may transform from unimodal to J -type. n (A)/Nmax

n (A)/Nmax (b)

(a) 6.0

3.0

10.0 α = 10.0 6.0

α = 3.0

2.0

3.0 1.0 0.0

1.0

1.0 0.0 0

0.4

0.6

0.8

A /A0

0

1.0

2.0

A /A0

Figure 1.3. Normal (a) and exponential (b) distributions at various values of parameter  Relation (1.6) can be considered as an equation in n0 A. Multiplying both sides of (1.6) by A and differentiating with respect to amplitude we obtain the equation for determining n0 A: dnA nA dn0 A  − 1 +  − n0 A = dA A dA A

(1.7)

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

27

The solution of (1.7) is the function: n0 A = nA − A

−1



A − nA dA 

(1.8)

A

provided that lim n0 A = 0

A→

It follows from (1.8) that the lesser  (or the gage quality factor), the closer is the amplitude distribution at predetection count to the initial distribution. Thus, relation (1.8) serves to reconstruct the initial amplitude distribution of AE pulses based on the distribution registered at predetection count. It is apparent that the same reasoning is true for the amplitude-time distribution of AE pulses. In this case nA should be replaced with a function describing the amplitude-time distribution of pulses nA, t). The obtained relations allow one to determine a correlation between the total AE N and the count rate N˙ at predetection and postdetection count. If D is the signal discrimination level then integrating both sides of (1.8) from D to  we found that the total AE at postdetection count N0 is related to the same characteristic in case of predetection count by the following formula: ⎧ ⎫ ⎨ ⎬  −1  −     (1.9) N 0 = N − A A  nA dA dA ⎩ ⎭ D

A

If the amplitude distribution in formula (1.9) is replaced with the amplitudetime distribution then we obtain the expression relating the count rates at predetection N˙ and postdetection N˙ 0 counts of AE pulses: N˙ 0 t = N˙ t − 

 D

A−1

⎧ ⎨ ⎩

A

⎫ ⎬

A − nA tdA dA ⎭

(1.10)

A physically evident conclusion follows from formulas (1.9) and (1.10) that the lesser the quality factor of a gage, the closer are AE characteristics registered at predetection and postdetection counts. The analysis of the amplitude distribution of AE pulses is convenient to determine the mechanisms of metal deformation, for example, slip or twinning. In ductile failure and brittle fracture the probability densities of AE pulse amplitudes are greatly different. Brittle fracture is characterised by an almost

28

CHAPTER 1

symmetrical distribution with a mode at high amplitudes. A distinctly asymmetrical distribution with a great number of pulses of a high amplitude is typical for ductile failure. Most researchers dealing with practical applications of AE phenomenon recognise as necessary the analysis of the amplitude distribution. It is naturally since a certain distribution of the pulse amplitude corresponds to each deformation mechanism or physical process inducing AE. Publications contain data on different types of the experimentally obtained amplitude distribution, namely exponential, Rayleigh, -distribution, power-series, etc. As our studies have shown (see Chapter 4) the amplitude distribution of AE at friction may vary from J -type to unimodal. Based on sufficiently general assumptions on interaction between surfaces, we have developed a model (see Chapter 2) serving to explain a variety of amplitude distributions obtained in tribological experiments. Nevertheless, any model, even if it is perfect, can describe at best only some aspects of such complex process as friction. Therefore, one should not ignore direct methods that help to find a correlation between characteristics and regimes of friction, on the one hand, and the pattern of the amplitude distribution of AE and its characteristics, on the other hand. To calculate the latter it is necessary to approximate experimentally found distributions by some function. The method of moments or the system of Pearson distributions can be used for this purpose [23]. This system describes almost all known unimodal and J -type distributions and is widely used in various fields of science. If moments of distribution are known (they can always be found from experimental data) the Pearson system helps to select a suitable continuous function to describe the experimental distribution. The system of Pearson distributions is assigned by the differential equation for the probability density wx of a random variable x: 1 dwx x−a = wx dx b0 + b1 x + b2 x2 where a and bi (i = 0, 1, 2) are constant distribution parameters expressed through moments of the variable x. Pearson showed that the type of the distribution is governed by the value of the generalised coefficient : r32 r4 + 32   =  4 4r4 − 3r32 2r4 − 3r32 − 6

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

29

which, in its turn, depends by the values of two parameters r32 = 23 /32 and r4 = 4 /22 where n are nth central distribution moments: n =



x − x¯ n wxdx

and x¯ is the average of the random value x. Note that the parameters 1 = r3 and 2 = r4 − 3 are the coefficient of skewness and kurtosis, respectively. The system of Pearson distributions comprises a great part of the plane of parameters (r32 ; r4 ), that is, these distributions exist within a broad range of changing of the coefficient of skewness and kurtosis. V.I. Tikhonov [23] listed twelve types of Pearson distributions which are presented in Table 1.6 where c is a normalization constant and m, m1 and m2 are calculated parameters. When studying how the type of the amplitude distribution changes and determining its parameters one can judge the changes in physical processes Table 1.6. Types of Pearson Distributions [23] Type 1 2 3 4 5 6 7 8 9 10 11 12

Equation  m wx = cxm1 1 − ax 2   2 m wx = c 1 − ax2   wx = cxm exp − ax     2 −m wx = c 1 + ax2 × exp −barctg ax   wx = cx−m exp − ax  −m1 wx = cxm2 1 + ax  2 wx = c exp − 2x 2 m  wx = c 1 − ax m  wx = c 1 − ax    wx = c exp − 1 + ax  m wx = c ax − 1  m wx = c x+a 1−x

Variation interval 0≤x≤a −a ≤ x ≤ a 0≤x< − < x <  0≤x< 0≤x< − < x <  0≤x
CHAPTER 1

30

running into the friction zone and identify the processes if one has enough experience and necessary statistical data. Spectral Density. The spectral density characterises the random process energy which is liberated at unit load within a unit frequency band. In practice, the spectral density of AE signals is determined by implementing in series the following operations: • registration during time T of the random process realization st filtered by a narrow-band filter with a tuneable central frequency f and bandwidth f ( f << f ); this results in the function sf ; f ; t; • squaring sf ; f ; t; • averaging s2 f ; f ; t over T ; • dividing the obtained value by the filter bandwidth f . As a result, we have the assessment of the rate of change of the average square of filtered st values being the values of realisation of AE signal with varying frequency f that is the assessment of the so-called one-sided spectral density of AE signal: T 1  2 s f f tdt 0 < f <  Gt  T f 0

In calculations the two-sided spectral density is used: T 1 S = lim

FT  2 dt T → T 0

Here FT  2 = FT FT∗ ; FT∗  is a function, which is complex conjugate to FT , and FT  is the finite Fourier transform: + FT  = sT te−id dt −

sT t is a random process (AE signal) of a limited duration:  sT t =

st 0

0 ≤ t ≤ T t ≥ T

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

31

The two-sided spectral density is an even positive function; Gf and S are related as follows:  Gt =

f ≥ 0 f < 0

2S2f  0

The spectral density of AE like that of any random process can be characterised by several parameters. Among them the following parameters are the most common: the effective width of spectrum:  1 Gf df

fe = max Gf  

0

where max Gf is the maximal value of the spectral density; the mean frequency of the spectral density:   fGf df f¯ =

0



Gf df

0

the average square of the frequency of the spectral density:   f 2 Gf df f2 =

0



Gf df

0

the mean-square width of the spectral density:



 w2 =

f 2 − f¯ 2 =

⎧   ⎫1/2  ⎪ ¯ 2 Gf df ⎪ ⎪ ⎪ f − f  ⎨ ⎬ 0

⎪ ⎪ ⎩



Gf df

⎪ ⎪ ⎭



0

Similar parameters can be introduced for the two-sided spectral density S.

CHAPTER 1

32

To calculate the spectral density of a Poisson flow of AE pulses assigned by relation (1.1) one can use a Campbell formula: ⎛ S = vA2 F 2 + 2 ⎝vA¯



⎞2 utdt⎠ 

(1.11)

0

where v is the flow rate; A¯ , A2 are the mean amplitude and the average square of the amplitude of flow pulses; F is the Fourier transform of the function ut describing AE pulse shape;  is the Dirac delta function. If the mean of the function describing the pulse shape equals zero that is typical when registering AE with piezogauges then the spectral density is calculated by the following formula: S = vA2 F 2

(1.12)

which is called the Carson formula. In particular, the spectral density of the flow whose pulses has the shape assigned by formula (1.2) is S = 

vA2 2d d4   2  1 + 2d − 2 d2 + 4d2 2

(1.13)

The spectral density of registered AE depends significantly on the response function of the acoustic channel, the gage, and the amplifying and transforming channel. When using a broad-band amplifier whose response function can be assumed to be constant within the registered frequency band the following spectral density is found instead of the initial one: S1  = Hi 2 S where i is the imaginary unit; Hi 2 = H1 i 2 H2 i 2 ; H1 i and H2 i are the response functions of the acoustic channel and the gage. It follows from this fact that if it is necessary to reduce distortions of AE spectrum the broad-band gages with a uniform amplitude-frequency response should be used. However, while H2 i can be found when calibrating gages the measurement of the response function H1 i presents significant difficulties especially because the function depends on both the location of AE signal source and the coordinates of the gage, hence it varies when the latter is moved over the object under monitoring. For this reason it is quite difficult to restore completely the initial spectral density of acoustic emission from results of its measurements. Nevertheless, the spectral density is useful when interpreting AE data obtained

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

33

at varying conditions and regimes of friction. Some researchers propose to determine the nature of acoustic emission based on results of spectral density measurements. In Part 2.2 we describe our model for the calculation of AE in friction. In particular, it will be shown that the pattern of the spectral density is governed by correlation functions of the profiles of rubbing surfaces. Correlation Function. The time correlation function of the random process realization st is determined by the relation: Rxx  =



st + stdt

(1.14)

0

and it is an even function of the parameter . The correlation function presents the measure of statistical correlation of the random process at instants t and t + . To assess the time interval within which the statistical correlation between the values of the random process is substantial the correlation window c is used: 2  c = Rxx d Rxx 0 

0

When  > c the values of the process at instants t and t +  can be assumed uncorrelated and one may suppose Rxx   0. The correlation function of the Poisson flow of AE pulses (1.1) is calculated using the Campbell formula: Rxx = vA2

 0

⎛ 2 ut + utdt + v2 A¯ ⎝



⎞2 utdt⎠ 

(1.15)

0

Designations are the same as in formula (1.11). If the shape of pulses is described by relation (1.2) then  v2d d3 A2 −  /d sin d 

  Rxx  = e cos d  +  2 2 d d 4 1 + d d

(1.16)

The correlation function of random processes is determined by special devices called correlation meters or it can be calculated by a computer provided that the signal is digitised. Since the correlation function and spectral density of stationary random processes are related by the direct and inverse Fourier transforms (the Wiener–Hinchin theorem) the information content of the correlation

CHAPTER 1

34

function of AE signals is similar to that of the spectral density. For this reason in practice the correlation function is often calculated using the mentioned theorem and based on the experimentally obtained spectral density of acoustic emission. Time distribution of signals is the distribution of intervals between AE pulses during the observation time. The information content of this characteristic results from its relation to the kinetics of AE signal sources. To obtain the characteristic it is necessary to transform the time interval between pulses into the amplitude of standard signals; then the obtained amplitude distribution is analysed. This way is used when processing experimental data in nuclear physics. Energy of Acoustic Emission. Direct measurements of the energy of an acoustic signal are quite difficult. Many researchers propose to measure the energy of the electric signal of the gage. Thus, the authors of [24] proposed to assess AE energy by the parameter AN˙ where A is the signal amplitude. In our opinion, this is not quite correct because the energy is proportional to the square of the amplitude and to the signal duration (see Part 2.1). Moreover, the mentioned characteristic presents energy variation per unit time, that is, it is related to the signal power. From our viewpoint, to assess the energy of AE signal one should use the variable proportional to the product of the count rate and the root-mean-square amplitude, i.e. E = K T A2 N˙ where K is a proportionality coefficient; T is the duration of measurement. Hence, the power of an electric signal corresponding to AE signal is derived as W = KA2 N˙ . Above we have considered the so-called “absolute characteristics” of AE accompanying the friction of solids. Specific characteristics of AE can be helpful to describe friction processes; they present the emissivity of a unit area of the surfaces in contact. Specific count rate is determined by calculations as the number of AE pulses per unit friction path and presents the emissivity of unit friction area: Nsp =

N/ t N˙

N = = 

l

l/ t v

Here N is the number of pulses from the friction path l; t is the duration of AE registration; N˙ is the count rate; v is the sliding velocity. This characteristic allows one to compare friction processes at various velocities of relative motion of friction parts. Specific power of AE at friction is determined as the energy of acoustic emission per unit friction path: Esp =

E E/ t W = = 

l

l/ t v

FRICTION OF SOLIDS AND NATURE OF ACOUSTIC EMISSION

35

This characteristic is sensitive to changes in processes occurring at friction and the state of friction units.

REFERENCES 1. D.H. Buckley, Surface Effects in Adhesion, Friction, Wear and Lubrication, Amsterdam, 1981. 2. H. Haken, Advanced Synergetics. Instability Hierarchies of Self-Organizing Systems and Devices, Berlin, 1983. 3. Handbook of Triboengineering, ed. by M. Hebda and A.V. Chichinadze, vol. 1. Theoretical Foundations (in Russian), Moscow, 1989. 4. H. Haken (ed.), Springer Series in Synergetics, vol. 17, Berlin, Heidelberg, New York, 1982. 5. G. Polzer and F. Meissner, Fundamentals of Friction and Wear (Russian translation), Moscow, 1984. 6. I.V. Kragelskii and N.M. Mikhin, Handbook of Friction Units of Machines, New York, 1988. 7. C. Guerret-Piecourt, S. Bes, and D. Treheuz, Electrical charges and tribology of insulating materials, C. R. Acad. Sci. Ser. 4, 2001, vol. 2, no 5, p. 761–774. 8. A.L. Zharin, Method of Contact Potential Difference and Its Application in Tribology (in Russian), Minsk, 1996. 9. S.N. Postnikov, Electrophysical and Electrochemical Phenomena in Friction, Cutting, and Lubrication, New York, 1978. 10. A.I. Sviridenok, N.K. Myshkin, T.F. Kalmykova, and O.V. Kholodilov, Acoustic and Electrical Methods in Triboengineering, New York, 1988. 11. F.P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Oxford, 1986. 12. I.G. Goryacheva and M.N. Dobychin, Mechanism of roughness formation during running-in Soviet Journal of Friction and Wear, vol. 3, no 4, pp. 345–351, Allerton Press, NY, 1983. 13. D.N. Garkunov, Triboengineering (in Russian), Moscow, 1985. 14. J.S. Bendat, Random Data Analysis and Measurement Procedures, New York, 1986. 15. V.M. Baranov, A.M. Karasevich, E.M. Kudryavtsev, V.V. Remizov, et al., Acoustic Diagnostics and Monitoring at Fuel and Power Plants (in Russian), Moscow, 1998. 16. V.M. Baranov, A.M. Karasevich, E.M. Kudryavtsev, V.V. Remizov, et al., Diagnostics of Materials and Structures of Fuel and Power Plants (in Russian), Moscow, 1999. 17. R.A. Collacott, Structural Integrity Monitoring, New York, 1985. 18. I.G. Alekseev, A.V. Kudrya, and M.A. Shtremel, Acoustic emission characteristics describing single brittle crack, Defect Control (in Russian), 1994, no 12, pp. 29–34. 19. L.M. Rogers, The application of vibration signature analysis and acoustic emission source location to on-line condition monitoring of anti–friction bearing, Tribology International, 1979, vol. 12, no 2, pp. 51–59. 20. G.A. Sarychev and V.M. Schavelin, Acoustic emission method for research and control of friction pairs, Tribology International, 1991, vol. 24, no 1, pp. 11–16.

36

CHAPTER 1

21. V.A. Belyi, O.V. Kholodilov, and A.I. Sviridenok, Acoustic spectrometry as used for the evaluation of tribological systems, Wear, 1981, vol. 69, no 3, pp. 309–319. 22. V.M. Schavelin and G.A. Sarychev, Acoustic Monitoring of Friction Units of Nuclear Power Plants (in Russian), Moscow, 1988. 23. V.I. Tikhonov, Statistical Radioengineering (in Russian), Moscow, 1982. 24. R.M. Fisher and L.S. Lally, Microplasticity detected by an acoustic technique, Canad. J. Phys., 1967, vol. 63, no 1, pp. 63–81.

Chapter 2

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

2.1. DISTRIBUTION OF PRESSURE OVER MICROCONTACT SPOTS A great variety of interrelated sources of acoustic emission of different physical nature acting in solid friction complicates the development of the general theory of AE in friction. Besides, since the physical nature of friction has not been studied completely so far, no common concepts are available on the relation between characteristics of acoustic emission and processes occurring in friction units. At the same time, such concepts based on clear physical principles are necessary to clarify experimentally obtained regularities of AE in friction from united viewpoints. In particular, the interpretation of experimental data available in publications is quite ambiguous because of the lack of universally recognized theoretical models. This makes difficulties for the analysis and comparison of results reported by different researchers. For the same reason AE method is not widely used for the field inspection of friction units. Also undoubtedly that particular monitoring methods and performance specification of hardware should be based on theoretically grounded and experimentally confirmed regularities relating AE characteristics and changes in the state of friction units in their operation. As the analysis of publications has shown the elastic and plastic interactions between surface microasperities, the formation and rupture of adhesive junctions, the appearance of microcracks in surface and subsurface material layers contribute mostly to acoustic emission. The evolution of these processes in time governs the state and efficiency of friction units in most cases. The following characteristics of AE signals being analyzed in tribotests are considered as the basic characteristics: the total count, the count rate, the spectral, amplitude and energy distributions of AE pulses. These characteristics depend on the properties of surfaces in contact such as roughness parameters, the presence of microdamages and a lubricating film etc. Their variations are caused by changes in friction regimes, oil starvation, the wear of a material and other processes running in friction pairs. For this reason theoretical studies whose aim is to find a correlation between the mentioned characteristics and processes occurring in the friction zone, friction conditions and regimes are of great practical importance. Results of these studies are the basis for the development of methods and means to monitor friction units.

CHAPTER 2

38

Theoretical models dealing with characteristic of acoustic waves emitted in friction can be conventionally divided into two groups, namely static and dynamic models. In the former case parameters of a tribosystem such as the geometric characteristics of the surfaces in contact, friction regimes (the sliding velocity and load) and the condition of the environment are assumed to be constant. At these conditions characteristics of elastic waves are calculated based on available data or plausible assumptions. In contrast, dynamic models consider how the characteristics of waves change with varying regimes or external conditions of friction. Thus, the dynamic models serve to describe transient regimes in tribosystems while the static models take into account only that changes whose duration is longer than the duration of the transient processes in friction pairs. In this respect the latter models can be called quasidynamic models. This chapter deals with both types of models. In 1943 E.I. Adirovich and D.I. Blokhintsev published paper [1] considering the extreme case of the dry friction of two perfectly elastic bodies whose surfaces had similar periodically disposed asperities. The asperities interact by short pulses-impacts. This paper apparently represents one of the first theoretical static models dealing with the generation of elastic waves in solid friction. According to E.I. Adirovich and D.I. Blokhintsev, the friction force caused by energy dissipation due to the emission of waves is inversely proportional to the sliding velocity. The authors obtained a relation for the energy flux density q of the waves generated in sliding:  1 1  2 fa vtdt +  fp2 vtdt q= √ T  T  + 2 T

T

0

0

where v is the velocity of relative motion; T = 2l/v 2l is the asperity spacing;  is the material density;  and  are the Lame coefficients; fa vt is the shear stress resulting from interaction between the surface layers at the instant t fp vt is the pressure. The authors obtained a relation for the friction force per unit area which is induced by wave emission: f = q/v The authors’ assessment has shown that for the steel–steel pair these relations are applicable subject to the restriction that 10−2 m/s << v << ct ∼ cl  where ct and cl are the velocities of transverse and longitudinal elastic waves in steel, correspondingly.

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

39

Highly appreciating paper [1] and analyzing impact phenomena in friction A.S. Akhmatov arrived at a conclusion [2] that in most cases elastic wave radiant losses are relatively small. Yet, at certain conditions the losses can influence significantly the dependence of the friction force on the velocity. Unfortunately, these papers do not consider a possibility to use acoustic emission to study friction processes. Most researchers attribute acoustic emission in external friction mainly to the redistribution of elastic energy in surface and subsurface layers of solids. The energy depends on pressure variations on real contact spots in the process of the relative motion of the solid surfaces. Therefore, to assess characteristics of acoustic emission it is necessary to determine the distribution of stresses on the sites of contact between the surfaces. By now two approaches have been developed to solve the problem of determining the distribution of stresses on contact spots. The first approach is statistical, it is based on the use of the Hertz contact theory to describe elastic interaction between surfaces whose statistical characteristics obey the Gaussian distribution [3]. The second approach is numerical. The integral equations of the Hertz theory are solved by numerical methods using experimental data on the topography of real surfaces [4, 5]. Though the latter approach seems to be advantageous it demonstrates common drawbacks of numerical methods. The basic drawback is that it is difficult to find regularities if the number of initial parameters of a problem to be solved is great. Besides, the problem of reconstruction of the pressure distribution belongs to ill-defined problems because data on microasperity dimensions, the approach of the surfaces in contact and other characteristics that are rough are used in calculations. To solve such a problem special algorithms should be applied which are not involved, as a rule. For this reason, from our viewpoint the data obtained in such a way should be carefully relied on. The statistical approach is applied to a some extent in available models of friction and surface damage in friction developed by many researchers. Statistical models of discrete contact are well reviewed in monograph [6]. To calculate the pressure on the surfaces in contact we used the statistical approach [7, 8] developing the Greenwood–Williamson model [3, 6] and the theory of runs of random processes [9]. Let us consider contact between the surfaces whose profiles are described by a random continuous function zi r  i = 1 2 count off from the median plane of the corresponding surface. Let the median planes are parallel and the mean distance between them depending on the force pressing the bodies be d. On the median planes the Cartesian coordinates are oriented in such a way that points on the surfaces which are located vertically one under another have the same coordinates determined by the vector r = x y. The axes z1 and z2 are

CHAPTER 2

40

oppositely directed. Indices 1 and 2 designate values relating to the first and the second bodies, correspondingly (Fig. 2.1). Z2(x)

Z1

0

X

d

0

X Z1(x)

Z2

Figure 2.1. Profiles of surfaces in contact Because of the stochastic relief of the surfaces they contact only over single small regions or randomly located contact spots. Let elastic displacements of points of the surfaces in the directions opposite to those of the axes z1 and z2 caused by deformation be v1 r  and v2 r . If we introduce the function fr  = v1 r  + v2 r  − z1 r  − z2 r  + d then as is known [4, 10] within contact spots fr  = 0

(2.1)

and the pressure pr  ≥ 0 while within regions of no contact fr  > 0 and pr  ≥ 0. Substituting the known expressions describing the dependence of the elastic displacements vi r  on the contact pressure [10] into (2.1) and having in mind that the surfaces interact only within the contact spots we obtain the relation between the pressure distribution and the functions describing the surface profiles zi r  within the real contact area: M  Qr   rdx dy = z1 r  + z2 r  − d

j Sj

  Qr   r = pr  / r − r 

(2.2)

where r = x  y  M = 1 − v12 /E1 + 1 − v12 /E2 is the contact Hertz modulus;   Ei  i are the Young’s modulus and Poisson’s ratio of the materials; r = x2 + y2 1/2 . Summations is performed over all contact spots Sj .

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

41

If the characteristic size of the latter is less than the spacing between them then within a single spot we can neglect contributions of other spots to the surface deformation and assume the deformation to be determined only by the pressure distribution over the spot under consideration. Thus, for each spot with area Sj the following expression can be written: M Qr   rdx dy = z1 r  + z2 r  − d

(2.3)

Sj

Here the coordinates r = x y change within the spot and in its vicinity. Deformation within contact spots depends on the mean distance between the surfaces that is governed by the force pressing them together. Since the force is the sum of forces acting within microcontact regions the contact spots indirectly influence each other. As a result, we have a classical Hertz contact problem except that the parameter d depends on the sum of forces acting within all contact spots that is on the force pressing the surfaces together. It is naturally to assume that contact occurs over asperity summits. Suppose that the origin of local coordinates is situated at the summits of asperities in contact; then the equations of the surfaces in each asperity neighborhood can be written as [10] zi r  = i



i

  x x 

i = 1 2

(2.4)



Here i is the maximal value (height) of a local asperity of the ith surface i count off from its median plane;   = 1 2 x1 = x x2 = y   is a twoth dimensional symmetric curvature tensor of the i surface in the neighborhood of the asperity under consideration whose principal values are 1/2R1i and 1/2R2i , where R1i and R2i are the curvature radii of the asperities at the point of contact. Let pj is the average pressure over a contact spot Sj whose shape is approximated by a circle with a radius aj Sj = a2j . Since interaction between asperities is governed by the average pressure over the contact spot Fj = pj a2j and according to the Hertz solution Fj and aj are related as Fj = 4Ba3j /3M the radius of the contact spot is proportional to the average spot pressure: aj = 3 Mpj /4B

(2.5)

where B is the coefficient depending on components of the tensors of asperity curvature at the point of contact. If the asperities are assumed to be spheres with radii R1 and R2 then B = 1 + R1 /R2 /R1 . Later we shall omit the index j having in mind that all variables correspond to the contact spot under consideration.

CHAPTER 2

42

Introducing the parameters ui = i /i i = 1 2 where i is the standard deviation of the random functions zi r  from their median planes and assuming that x = y = 0 in (2.3) we obtain with account for (2.5) the relation between the average pressure and the maximal values (heights) of local asperities within a contact spot in dimensionless form: p2 /p02 = u1 + u2 − d 

(2.6)

where p0 = 2B1 /3 1/2 /M = 2 /1 and d = d/1 . If the asperities are approximated by spheres with radii R1 and R2 then   0 5   R1 1 − v22  E1 E1 2 1 1+ 1+ p0 = R2 1 − v12  3 R1 1 − v12  E2 It follows from (2.6) that the pressure distribution is determined by the distribution function of asperity heights. In general case this function is found from the following formula [9]:

0 w i  =

−

zi w i  0 zi dzi

0

−

 zi

w0

i = 1 2

zi dz

Here wzi  zi  zi  is the joint probability density of the function zi and its first zi and second zi derivatives; wzi  zi  is the joint probability density of the first and the second derivatives of the function zi : wzi  zi 

+ = wzi  zi  zi dz  −

where w i  0 zi  is the value of the function wzi  zi  zi  at zi = i and zi = 0. If z1 r  and z2 r  are statistically independent Gaussian uniform random fields then the probability densities of surface asperity summits are described by the following expression [9]:   2  2 1 2 2 wui  = √ i exp −ui /2i + 2 1 − i ui exp −ui /2 2

  2 ×  ui 1 − i /i  i = 1 2 (2.7)

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

 where x =

x

−

 2

exp−y /2dy

43

√ 2 is the error function; i is the

parameter depending on the surface roughness characteristics: i = 1 − i 2 /i i  where i and i are the standard deviations of the first and the second derivatives of the function zi r , correspondingly. It follows from (2.7) that the probability densities of the distribution of surface asperity summits are governed only by the parameters i varying between 0 and 1 [9]. The parameters depend on the width of wave spectra of the functions zi r . With widening wave band values of the parameters i tend to unity and the distribution of asperity summits approaches to the normal distribution according to (2.7)  √ wui  = exp −u2i /2 / 2 (2.8) This case corresponds to the absence of profile regularity and is apparently typical for polished surfaces. As the wave spectrum narrows i tend to zero and values of the asperity height obey the Rayleigh distribution with the following probability density  wui  = ui exp −u2i /2 (2.9) This case is typical for the surfaces having a regular relief which results from the machining of parts when a tool moves in one direction (for example, cutting). Let us consider both extreme cases. Their analysis will reveal what occurs in the general case if 0 < i < 1. If the distribution laws of u1 and u2 are known the probability density of the random value q = u1 + u2 is calculated using the standard procedure  wq = C wq − u2 wu2 du2 (2.10) The constant C is found from the normality condition of wq provided that q ≥ d . The latter condition results from the fact that only compressive stresses occur within microcontact regions and p ≥ 0. For i = 0 we can derive the following expression for wq:  √     1 + 2 2

2 q 2

q

2

wq = C q exp − + 3/2  √ 2 2    √     q2 d

2

q exp −  q ≥  (2.11) + 1 + 2 2  5/2 q 2  √   2 1

CHAPTER 2

44

where  = 1 + 2 . Numerical estimate shows that one may neglect the first item in (2.11). In this case the error of calculating wq at small q does not exceed a few percent and at great values of q it is negligible. Omitting the non-essential item we can represent wq as      q2

q 1 + 2 2 exp − q  √  wq = C 1 +   2 

(2.12)

where C is the normalization constant. For i = 1 we derive from formula (2.10)   C q2 wq = √  exp − 2 2 

q > d 

(2.13)

where C is the normalization constant. Then with account for (2.6) we find the probability density of the pressure distribution over contact spots. If the distribution of the parameter q is described by formula (2.12) then   2  d 1 + 2 2  p2 2p +  wq = C1 2 1 +  p0 p02 1     2    d d p2

p2 + exp − 2 + 2 × √  p02 1 p0 1

(2.14)

But if the distribution of q is assigned by expression (2.13) then the probability density of the pressure distribution is described by the following relation:   2   2p p2 d C exp − 2 + 2 wq = √ p0 1 2  1 p02

(2.15)

The pressure distribution depends strongly on the mean distance between the surfaces d that, in its turn, is governed by the force pressing the surfaces together. The force is the sum of forces acting over all contact spots F =

N  j

pj a2j 

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

45

where N is the total number of the contact spots. If we introduce the function describing the distribution of the spots over the pressure np such that N=

 npdp 0

then it is easy to see that np = Nwp. Then, having in mind (2.5) the pressing force can be written as  9 3 M 2 F= p3 wpdp = N 16B2 

(2.16)

0

Here we have made an assumption without loosing the generality of further results that all asperities in contact are characterized by the same value of the parameter B. In the general case averaging over this parameter is needed. The number of contact spots is determined by the number of intersections of the random functions z1 r  and z2 r  + d, hence it depends on the distance d that is N = Nd. Since wp is also the function of the parameter d then the expression (2.16) can be considered as an equation to calculate the dependence d = dN at a given pressing force. If the distance between the median planes of the surfaces is d then the number of contact spots contained within the apparent contact area L2 is [25, 153]  L2  2 d2 N= exp − 2  4 2 12  21 

(2.17)

where  2 = 12 + 22 . Substituting formula (2.17) into (2.16) and performing transformations with account for the distribution law (2.14) i = 0 for the dimensionless parameter √  = d/1  we obtain the equation whose solution describes the dependence of d on F : ⎫ ⎧ ⎬ ⎨ 3/2 2 2 2 y −  1 + 1 + 2 y  y exp−y /2dy ln ⎭ ⎩  ⎫ ⎧ ⎬ ⎨ 1 + 1 + 2 2 y2  y exp−y2 /2dy − 2 /2 + f = 0 (2.18) − ln ⎭ ⎩ 

where f = − lnF/F0  F0 = L2 E1 /D D is the dimensionless coefficient depending on both mechanical and geometrical characteristics of the surfaces

CHAPTER 2

46

in contact. If surface asperities are approximated by spheres with radii R1 and R2 then:  D = 16

1/4

 1/2    R1 1 − v22 E1 1 − v12 2 1 1+ 1+ 3R1 R2 2 1 − v12 E2

Performing similar calculations for i = 1 we derive the corresponding equation for determining the parameter : ⎧ ⎨ ln

⎩



⎫ ⎬

⎧ ⎨

y − 3/2 exp−y2 /2dy − ln ⎭ ⎩

exp−y2 /2dy



− 2 /2 + f = 0

⎫ ⎬ ⎭ (2.19)

The calculations have shown that if = 1    3 that is the roughnesses of the surfaces are essentially dissimilar the root of equation (2.19) hence d is almost √ √ independent on and we may suppose d/1  ≈ 2f with an error of a few percent. Figures 2.2 and 2.3 illustrate the dependencies of values of  on the pressing force calculated from equations (2.18) and (2.19). In fact, the dependencies represent the rigidity of contact between two bodies whose surface shapes are described by random functions. λ = d /σ1η1/2 1.0

0.8

λ = d /σ1η1/2

0.6

5

0.4

3

0.2

1 –5

α=3

–4

–3

–2

–1

0

α=1 α=2

Ig F/F0 0 1.5

1.6

1.7

1.8

1.9

2.0

F/F0

Figure 2.2. Dependence of parameter  determining mean distance between surfaces on force pressing them together i = 0

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

47

λ = d /σ1√η 1.0

0.8

λ = d /σ1√η 0.6

5 4

0.4

3 2

0.2

0.4

1

–6

–4 –2 Ig F/F0

0.5

0

0.6

0.7

0.8

F/F0

Figure 2.3. Dependence of parameter  determining mean distance between surfaces on force pressing them together i = 1 If we determine the dependence of the distance between the median planes on the pressing force we can calculate the probability density of the pressure distribution over contact spots using expressions (2.14) or (2.15). Figures 2.4 and 2.5 illustrate the dependencies of the function wp/p0  = p0 wp calculated by formula (2.14), the mean value and standard deviation of the pressure on the parameter = 1 /2 and the pressing force. It follows from the above data that the probability density of the pressure distribution and the mean value and standard deviation of the pressure on contact spots are substantially governed by variances of the random functions describing the shape of the surfaces. The more the difference in the roughnesses the higher is the average pressure on contact spots. It is known that during the running-in of a friction pair whose members are made of materials similar in their physico-mechanical properties roughness parameters become equilibrium and → 1. Also the mean value and variance of the real pressure decrease as it follows from calculations. The direct verification of theoretical expressions is difficult because of the lack of reliable data on the real pressure distribution and the complexity of direct measurements. However, results of the measurement of the wear debris

CHAPTER 2

48

ω (p /p0)

(b)

α=1

1.0

p /p0 1.1

α=2

0.8

0.9

σ (p /p0)

0.7 1.0

0.6

0.5

p /p0

2.0

0.4 0.3

3.0

α=3

0.4 (a) 0.2

F /F0 = 0.1 0

0.5

1.0

1.5

2.0

2.5 p /p0

Figure 2.4. Variation of probability density a, average pressure and its standard deviation b with parameter  ω (p /p0)

σ(p /p0)

p /p0

1.4

0.8

(b) p /p0

0.25

0.5

1.2

σ(p /p0) 0.2

1.0

0.30

0.20

–7 –5 –3 –1

Ig F /F0 10–7 10–3 F /F0 = 10–1

0.8 0.6 0.4

α=1 (a)

0.2 0

0.5

1.0

1.5 p /p0

Figure 2.5. Variation of probability density a, average pressure and its standard deviation b with force pressing surfaces together distribution may speak well of the validity of such approach. The fatigue failure of the surface layer under the effect of alternate stresses on contact spots is thought to be the main cause of wear [11, 12]. The characteristic size of a deformed material volume is proportional to the stress within contact spots.

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

49

Therefore, the wear debris distribution should also be proportional to the pressure distribution. Vast experimental data presented in [12] show that so it is. The pattern of the distribution functions of debris dimensions is similar to that of the probability density of the pressure distribution presented in Fig. 2.4 and 2.5 and formulas describing the distribution of debris dimensions are similar to expressions (2.14) and (2.15). The above considerations formed the basis of the model for assessing the fatigue wear of materials presented below [13, 14].

2.2. EVALUATION OF CHANGES IN FRICTION SURFACE STATISTICAL CHARACTERISTICS AND SIZE DISTRIBUTION OF FATIGUE WEAR PARTICLES The sliding friction of two bodies with different strengths is studied. Because of this, variations in the statistical characteristics of the stronger surface were ignored. The following basic assumptions were taken. 1. When the surfaces are mutually displaced they interact by individual asperities resulting in the formation of microcontact spots. 2. When the surfaces slide mutually their asperities are subjected to stochastic pulse loading due to the accidental formation and rupture of microcontacts. 3. The asperities fail due to fatigue. Given this, flake-like particles are formed whose characteristic sizes are in proportion to the contact spot size. The first two assumptions are traditional and widely used in both theoretical analysis and the interpretation of experimental data. The following should be noted with reference to the third assumption. The roughness varies during running-in due to the failure of the highest asperities. Therefore, wear occurs even at the running-in stage. When corrosive medium and abrasive particles are absent in light-loaded tribosystems fatigue wear dominates when failure results from the fatigue of microvolumes of the surface layer because of repeated contact stresses. Fatigue wear is discussed in many works (see, e.g. [15, 16]). The authors who studied the shape and sizes of wear particles note that the particles have the shape of plane leafs or flakes. The authors of paper [17] point out that the ratio of the maximal size of wear particles to their thickness is ≥ 5 while the authors of work [12] found a correlation between the sizes of wear particles and the distribution of contact spots. All these facts give reason to adopt the third assumption. Let us consider two surfaces whose profiles are described by the random functions z1 x and z2 x. The asperity of the height 1 measured from the mean line of the profile (hereafter it merely is asperity 1  is separated on weaker

50

CHAPTER 2

surface I and its interaction with asperities of surface II is studied. When the surfaces move with the relative velocity v surface II is displaced with respect to the asperity under examination by the distance L = vt. Given this, the asperity 1 is in contact only with the asperities 2 of surface II whose heights obey the expression [7]: u1 + u2 –d > 0

(2.20)

where u1 = 1 /1  u2 = 2 /2  = 2 /1  d = d/1  i2 are the variances of the functions zi x d is the distance between the mean lines of profiles I and II which depends on the compressing force F . If w 2  is the probability density of the asperity height distribution over surface II then dm2 asperities of surface II come in contact with the asperity 1 in a time dt: ⎫ ⎧ ⎬ ⎨  2 w 2 d 2 dt dm2 =  Nmax ⎭ ⎩ d− 1

If the asperity 2 of surface II is in contact with the asperity 1 then their contact spot is subjected to the average contact pressure p 1  2  (2.6): p 1  2  = p0 u1 + u2 –d 1/2 

(2.21)

where p0 = 2B1 /3 0 5 /M M = 1 − v1 2 /E1 + 1 − v2 2 /E2 is the Hertzian contact modulus; B is the constant depending on the shape of asperity peaks. For spherical peaks with the radii R1 and R2 the parameter B is defined by the relation: B = 1 + R1 /R2 /R1 . As a result of the interaction, the asperity 1 is deformed and a contact spot originates on which the shear load f p 1  2  acts, f is the friction coefficient. A definite stress distribution appears in the asperity. The disposition of the maximal stress max  1  2  depends on the asperity shape, so that we can write: max  1  2  = kfp 1  2 

(2.22)

where the coefficient k depends on the asperity shape. Because the heights 2 are random values the contact spot of the asperity 1 is subjected to random pulse load with the maximum kfp 1  2  when the surfaces move. At the point of the maximal stress a fatigue crack originates and its propagation is completed with the formation of a wear particle. In our estimation it is assumed that the cyclic strength of material I follows the Wöhler’s curve: N = −1 +

a  Nb

(2.23)

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

51

where N is the maximal stress generated by the cyclic load which is withstood by the material during N cycles of loading; a and b are the constants depending on the properties of the material; −1 is the stress which is withstood by the material during an infinitely large number of cycles. The presence of the safe stress implies that failure occurs only on contacts between the asperities where the stresses max  1  2  ≥ −1 are generated in the material. According to relation (2.21), such loads appear only in the contact of the asperities of surface II whose heights satisfy the condition:   2 −1 d 1 ∗ (2.24) + − 2 ≥ 2 = 1 kfp0 1 1 From (2.23) it follows that the material withstands the variable load with the amplitude  = max  1  2  during N cycles:  N =

a max  1  2  − −1

1/b

(2.25)

The number of the asperities of surface II with the height within the range  1  2 + d 2  which have already been in contact with the asperity 1 in a time dt is determined as 2 Nmax w 2 d 2 dt

 2 ≥ 2∗ 

Therefore, a part of the safety margin of the asperity 1 was consumed in a time dt: 2 w 2 d 2 dt Nmax  N max  1  2 

 2 ≥ 2∗ 

When interacting with asperities of different sizes the part is  N 2 w d dt 2 2 max N    max 1 2  ∗

2

Here N max  1  2  is the value of the function N at  = max  1  2  (see 2.25). Using the cumulative damage principle we find the time  =  1  in which the asperity 1 fails:  1    

0

2∗

2 Nmax w 2 d 2 dt = 1 N max  1  2 

(2.26)

CHAPTER 2

52

Since the statistical characteristics of both surfaces vary during wear then w 2  and N 2 max are time-dependent. If material II is stronger than material I variations in N 2 max and w 2  can be ignored. In this case the failure time for the asperity 1 is estimated as ⎫−1 ⎧ ⎪ ⎬ ⎨ N 2 w d dt ⎪ 2 2 max  1  = ⎪ ⎭ ⎩ ∗ Nmax  1  2  ⎪

(2.27)

2

As it has been shown in the previous item, the probability densities w i  i = 1 2 are determined by the parameter i . At i → 1 w i  follows 2 the normal distribution (2.8). Let us consider this case at which there are Nmax asperities per unit length of profile II: 2 Nmax =

i 2 i

(2.28)

Equation (2.25) can be presented in the following form:  N =

a kfp0

1/ b

1 u1 + u2 − d 1/ 2 − −1 /kfp0 1/ b



(2.29)

Substituting this expression in (2.27), in view of (2.24), and making manipulations for eliminating the statistical characteristics of the function z1 from the integrand, we obtain −1

  1  =

0−1



x1/ 2 − D1/ b e−x+q /2 dx 2

(2.30)

D2

where the following designations are introduced: 0−1

 2 = 2 3/ 2 2

D=

−1  kfp0



kfp0 a

 1/ b 

x = u2 − q

p0

q=

 = p0

2 1 = 1 M



2B2  3

d − 1 2

Numerical estimation shows that −1 << kfp0 , therefore, D entering (2.30) can be ignored and we obtain −1

  1  =

0−1

 0

x1/ 2b e−x+q /2 dx 2

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

53

The designation  = 1/b gives  1  = 0 F −1  q

(2.31)

where F q = e

−q 2 /2



x e−x /2 e−qx dx 2

(2.32)

0

The function F q occurs in the classical contact problems (see, e.g. [6]). Its main properties are presented in [14]. Figure 2.6 shows the dependence of the function F −1  q being the normalized time of the failure of the asperity on surface I on q at different  and Fig. 2.7 shows its dependence on  at different q. 3000

1.0

q=3

2000

q=0 0.8

1000

0.6

0

0.4

2.5 1

3

λ

5

–1

0.2

–2 –3

0.0 1

2

3

4

λ

5

Figure 2.6. Function F1  q at different  F –1 3000

4 1 5 λ=6 1.5

2

2.5

0.8

1000

λ=1

0 q

1.0

2000

3

0.6 2

0.4

3 4

0.2

5 q

–2.5

–2

–1.5

–1

Figure 2.7. Function F1  q at different q

–0.5

0

0.0

CHAPTER 2

54

The distribution of asperity heights varies during running-in. Due to fatigue failure particles are separated from asperities on weaker surface I. According to the adopted assumptions, their sizes are in proportion to the characteristic sizes of contact spots. The asperity spot area S1 on surface I which is subjected to failure varies stochastically because the size of counter-asperities on surface II varies accidentally. Therefore, in order to estimate the characteristic size of the wear particle I and its thickness h the average contact spot is used:

l = k1 S¯ 1 

h = k2 S¯ 1 

(2.33)

where k1  k2 are the non-dimensional coefficients. As was shown in [8], the contact area of two asperities with heights 1  2 is determined by the relation: S1 =

3 2  + 2 − d 8B 1

 2 > d − 1 

(2.34)

If w 2  is the probability density of asperity heights on surface II then  2  ¯S1 = 3

 1 + 2 − dw 2 d 2 8B d− 1

For the normal distribution w 2  (2.28) the sizes of wear particles produced at the failure of the asperity 1 are calculated by the equations: l = 2 1 f 1 

h = 2 2 f 1 

(2.35)

where 0 5 3 2 kj2 R2   j = 1 2 j = 81 + R2 R1  2     0 5  d − 1  d − 1 1 d − 1 2 f 1  = − 1− + √ exp −  (2.36) 2 2 222 2



and q is the error function. The function f 1  is plotted in Fig. 2.8. Let us find how the probability density of asperity heights on surface I varies during running-in. An asperity on this surface is examined. For simplicity, its height is denoted by x rather than 1 . The probability wx tdx that the height at the instant t is in the interval from x to x + dx is determined by the sum of the probabilities of two statistically independent events. The first term wx t − tdx is the probability that the height of the asperity at the instant

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

55

f(q) 1.5 1.0 0.5 0 –4

–2

0

2

q

Figure 2.8. Function f 1  t − t t << t was in the interval x x + x under the condition that the asperity did not fail in the time t. The second term is the probability that the asperity which had the height in the interval y y +dy y > x at the time t −t failed in the time t and its height falls into the interval x x + x. Treating the time defined by (2.31) as the average time of the failure of the asperity with height x the following equation is written for the probability wx t:   t wx t − tdx wx tdx = 1 − x  t w x ydx wy t − tdy (2.37) + y x

Here t/x is the probability that the asperity with the height x fails in the short time t wxydx is the conditional probability that the height of the asperity which had the height y falls in the interval x x + dx after its failure. The asperity height y y > x can fall in the interval x x + dx also after several failures. If a small time interval t is considered then the probability of several failures is negligibly small and it can be ignored. Failure lowers the asperity height y by h (2.35), therefore, the relation between y and x is as follows: x = y–h = y – 2 2 fy or x y = y – 2 2 fy – x = 0

(2.38)

Here fy is defined by (2.36). Given this, the conditional probability density is wxy = x y

(2.39)

CHAPTER 2

56

where  is the Dirac delta-function. If y0 = y0 x is a root of the equation x y0  = 0 then the relation is true:    x y0  −1  y − y0   x y =   y The parameters j (see (2.36)) depend on the ratio of the curvature radius of the asperity peak to the standard deviation of surface profile II, R2 /2 . Assuming that R2 << 2 these parameters can be considered as small ones. In this case, as the first approximation of 2 , the solution to (2.38) can be written as y0 x + 2 2 fx Then the following relation is true:      x y0  −1  x y0  x −1  =  = x = 1 + 2 2 f  x  x    y x y y Introducing the designations gx = x + 2 2 fx

gx = 1 + 2 2 fx x

(2.40)

we obtain the conditional probability density wxy: wxydx = gx xy–gx The substitution of wxy in (2.37), integration over y, and reduction by dx give the equation:   t t wx t − tdx + g  xwgx t − t (2.41) wx t = 1 − x gx x Using the direct integration of both the sides one can satisfy himself that the function wx t being the solution of this equation obeys the normalization condition at any t: + wx tdx = 1 −

Let us expand the right-hand side of (2.41) as the series in t → 0. Also, we take into account that gx and its derivatives (see (2.40)) differ from x and

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

57

unity by the value proportional to the small parameter 2 . Retaining the first order of 2 in the expansion of wgt t and gt we obtain the equation for the time-dependent probability density of asperity heights of the run-in surface: px wx ! wx t = wx ! + px ! x x

(2.42)

Here ! = t/0 is the non-dimensional time and the function px is as follows: px = 2 2 fxF d–x/2 

(2.43)

The initial condition is wx 0 = wx where wx is the probability density of asperity heights on surface I. Let us solve equation (2.42) with the boundary condition: wx 0 = wx. The changes of the variables: y = yx ! T = ! are made. In new variables (2.42) becomes wy T  wy T  = px xwy T  + pxyx − y!   T y

(2.44)

Given this, x and ! in the right-hand side should be replaced with y and T . The function y = yx T is selected so that the expression in braces vanishes. To do this, yx ! must meet the equation: px

y y − = 0 x !

Its solution is as follows: yx ! = Cexp y! + x

x =

 x dx px 

(2.45)

d

From two parameters C and y, the former is selected arbitrarily taking t = 1. In the variables y = Cexp ! + x T = ! equation (2.44) takes the simple form: wy T  = px xy T wy T  T

(2.46)

CHAPTER 2

58

Its solution can be written as wy T  = C1 y exp



pxy T  dT x



(2.47)

Let us consider the integral entering the exponent. Here y can be treated as a parameter. Introducing the change x = xy T we write dx = xT dT . According to conditions (2.46), the relation in the variables y T is obtained: xy T  = lny/C – T The differentiation of both the sides of this relation with respect to T gives xT d/dx = −1. Since d/dx = 1/px xT = −pxy T and dT = −dx/px. As the final result, the integral entering (2.47) develops into the form: 

 1 px pxy T  dT = − dx = − ln pxy T x px x

Substituting this expression in the exponent and returning to the variables x ! in terms of the relation xyx ! ! ≡ x we obtain wx ! =

C1 C expx + ! px

(2.48)

The form of the function C1 is found from the initial conditions. Putting ! = 0 one can write C1 Cexp x = pxwx 0 Here wx 0 = wx is the initial value of the probability density of asperity heights on surface I. The function  inverse of x is introduced. The function meets the condition: if x is not constant then the function  should satisfy the equality x ≡ x for  = x. For example, x = expx and  = ln  are such functions. The introduction of the variable z = C expx gives x = lnz/C and C1 z = plnz/Cwlnz/C. Now we obtain C1 Cexpx + ! = px + !wx + ! for the argument z = Cexpx + !. After the substitution of this expression in (2.48) the time-dependent probability density of asperity heights on surface I is obtained: wx ! = wx + !

px + ! px

(2.49)

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

59

Let us demonstrate that the probability density wx ! meets the normalization condition for any !. Now we calculate the integral: I=



wx + !

−

px + ! dx px

According to solution (A2.2), dx = pxdx then one can write: I= =

 

wx + !px + !dx wx + !px + !dx + !

Hereafter the infinite limits of integration are dropped. Let x˜ depending on x and ! be the value of the variable x which satisfies the condition: ˜x = x + !

(2.50)

Figure 2.9 shows how x˜ is related to the variables x and !. μ

μ (x) + τ μ (x ) τ

μ (x) x

x

Figure 2.9. Relation of x˜ and variables x and ! Therefore, l = Since



w˜xp˜xd˜x.

˜x = x + ! = x˜  then I =



w˜xp˜xd˜x.

(2.51)

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60

On the other hand, since p˜xd˜x = d˜x (see (2.45)), I = which proves the statement. Therefore, wx ! = w˜xx !

p˜xx ! px



w˜xd˜x = 1,

(2.52)

Here x˜ = x˜ x ! is the function defined by relation (2.51) and being the solution of (2.50) which in terms of (2.45) can be represented as 

d−x/2

dq + 2 ! = 0 fqF q

(2.53)

d−x/2

Given this, to the first approximation of 2  x˜ x + 2 !2 fd − x/2  F d − x/2 . The function x˜ x ! can be expressed through the inverse functions of  and . To do this we take into account that, according to formula (2.36), fx depends on x through the parameter d − x/2 . Therefore, px in (2.44) can be written as px = 2 2 fqF q

q = d–x/2

Thus, the function x in (2.45) depends on x also through the parameter q and it is represented in the following form: 1 x = 1 q 2

1 q = −

q 0

dq  fq  F q  

If 1  is the function inverse of 1 q, i.e. 1 q = q, then the function  inverse of  can be expressed through 1 "  = d – 2 1 2 . Really, after substitution we are able to verify that x = d – 2 1 × 2 1/2 1 q = d – 2 q = x. Thus, the solution of Eq. (2.50) x˜ = x˜ x ! can be presented in the following form: x˜ x ! = d − 2 1 1 d − x/2  + 2 !

(2.54)

The relations derived allow us to analyze how the surface roughness varies during running-in. As an example, Fig. 2.10 shows the variation of the probability density of the asperity height on surface I in time. The distributions are given for different values of the non-dimensional time 2 ! = 2 t/0 d/1 = 2 5.

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

61

w (x, τ) 4

4

3

2

3

1 2

1 –2

–1

0

1

x /σ1

Figure 2.10. Variation in probability density of asperity heights during run-in: 1 – 2 = 0 (normal distribution); 2 – 102  3 – 103  4 – 104 ; initial ratio d/ 1 = 2 5 The probability density in the original state follows the normal distribution (Fig. 2.10, 1). The asperity heights x are normalized with the initial standard deviation 1 of the run-in surface on the abscissa axis. As the time increases, the plot wx ! takes the asymmetric shape. The probability density decreases sharply in the region of great x/1 proving that the run-in surface is smoothed. The less effective width of the distribution indicates that the asperity height variance decreases during running-in. In addition, as it follows from the calculations, the probability density at the initial stage of running-in 2 ! < 10 has the bimodal shape (it is not shown in Fig. 2.10). The asymmetric shape of the probability density and its abrupt drop at great x indicates that run-in surface I is smoothed due to the failure of the highest asperities that occurs in practice (see, e.g., [17]). Moreover, the calculations have shown that with increasing pressing force (the ratio d/1 decreases) the running-in rate rises. This agrees with the available results demonstrating that heavier loads accelerate surface smoothing. Let us estimate a variation in the pressure distribution on the real contact spots during running-in. To do this we use relation (2.15) and consider 1 as the time-dependent function. It is calculated by formula (2.52). Figure 2.11 presents the calculated variation of the pressure distribution on the real contact spots in time, i.e., as the variance of asperity heights of the run-in surface 12 t is decreasing. The initial ratio of the standard deviations of asperity heights is 2 /1 = 2. With decreasing variance 12 t both mean value and variance p2 t of the pressure on contact spots decrease. The time-dependent variance is given in Fig. 2.12 (the non-dimensional parameter ! = t/0 is on the abscissa axis). Therefore, during running-in the pressure is leveled off and

CHAPTER 2

62

w(p/p0) 3

3 2

2 1

1

0

0.4

0.8

p/p0

Figure 2.11. Variation in probability density of pressure distribution when variance of peak heights of run-in surface decreases: 1 – 1 t/ = 1 0 2 – 0 6 3 – 0 2

σ 2p(t )/σ 2p(0)

0.8

0.6

0.4

0

2000

4000

6000

ετ

Figure 2.12. Relative change in variance of pressure distribution over contact spots during run-in

its mean value decreases. The rate of these processes is high at the initial stage while it approaches zero after a time. It seems likely that this time should be taken as the running-in time. It should be noted that the conclusion followed from our calculations provides support for Kragelskii’s assumption that running-in is completed when the pressure is leveled off on real contact spots. The fatigue failure of asperities resulting in the appearance of wear particles is the reason why the probability density of the peak height distribution varies in time. Therefore, knowing the time-dependent distribution of asperity heights 1 we can determine the size distribution of wear particles. If Nmax is the number of surface asperities per unit length and L is the friction path then the function nl ! defining the number of the particles at the instant ! (the non-dimensional

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

63

time) whose sizes are in the interval from l to l + dl is calculated by the equation: ⎧ ⎫  ⎨ x¯x! ⎬    wx dx dx nl !dl = ⎭  2 fx ⎩ 1 L Nmax

x



(2.55)

x=xl

In the right-hand side x should be replaced with l in order to turn to the variable l. These values are related by the equation: l = 2 fx which is the mathematical consequence of the assumption that the characteristic size of wear particles is in proportion to the size of contact spots. Integrating the right-hand side from 0 to  we find the total number of particles N! by the time !. Then the probability density of the particle sizes is wl ! = nl !/N!. The time-dependent function wl ! is presented in Fig. 2.13 where the relative size of particles is on the abscissa axis. First, attention is drawn to the fact that the distribution depends on the running-in duration. At the initial stage when the share of large particles is great the most probable size of the particles is maximal (distribution 1, Fig. 2.13). As the highest asperities fail and the surface is smoothed out, the share of small particles increases. The variance of the particle sizes decreases, the distribution becomes narrower, and the most probable particle size increases. w (l, τ) 10

3

8 6

2

4 1

2

0

0.1

0.2

0.3

0.4

0.5

l /εσ2

Figure 2.13. Variation in probability density of wear particle sizes during run-in: 1 –  = 10 2 – 102  3 – 103 The calculation results were compared with the well-known data on the wear particle size. We have analyzed the results of some authors who studied the size distribution of wear particles of different materials from metals

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64

to polymers. The data were obtained on different setups and presented as histograms. The reported data were recalculated by the standard procedure in order to compare the size distributions of the particles which were formed due to the wear of the materials with properties varying in the wide range. The aim of the recalculation was to determine the probability density of the size distribution as a function of the ratio l/lp lp is most probable particle size found from the histograms). The probability densities of the distribution of particle sizes l and the parameter l/lp are related by the equation: wl/lp  = lp wl. Clearly all the presented distributions have the maximum at the point = 1. It should be noted that a change to the relative units obviates the necessity for knowing the variance of surface asperity heights which, as a rule, is not given in the original works. Moreover, the use of relative units allows us to eliminate the model parameter  from the theoretical estimates because the calculated value lp is expressed through the parameter. The results of such processing with the calculated plot are shown in Fig. 2.14. w(l/lp; τ) 0.8

1 2

0.6

3 4

0.4

5

0.2 0 0.0

1.0

2.0

3.0

4.0

5.0

l/lp

Figure 2.14. Comparison of theoretical distribution of wear particle sizes (solid line) with data of different authors Points 1 correspond to the wear data of the brass †63–steel 45 pair with the addition of inactive paraffin oil [12]. The roughness of steel specimens was Ra = 0 5 #m. The tests were conducted on a block-on-ring friction machine at a sliding velocity of 0.65 m/s and under different pressures. The particle distribution was determined using a special technique [19]. Sediments of wear products were examined with a scanning electron microscope JSM-50A after their washing on a paper filter and the deposition of a thin gold layer to eliminate electric charges. The analysis of the micrographs indicated that the majority of particles are of the flat and petal-like shape with some microns in size. It is pointed out that an increase in the normal load applied to the friction pair affects slightly the most probable size of wear particles and the distribution pattern.

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

65

Points 2 present data on antimony wear study borrowed from monograph [12]. The descriptions of the test technique and setup are also given here. The author points out that “the similar results were obtained for zinc, tin, copper, and lead”. It should be noted that the author uses the lognormal law or the Rayleigh distribution. Data 3, 4 relate to the results of tests of epoxy specimens as plates of the rectangular cross-section rubbing against a steel cylindrical indenter under a load of 25.4 N [20]. The highest velocity of the indenter was 0.125 m/s. The elastic modulus of the specimen was varied by heat treatment. Fatigue wear was predominant. When the polymer treated at 60  C and having the elastic modulus of 680 MPa is worn out the particles whose average size is in the range 14–28 #m are most often formed (points 3). The similar distribution is observed at the wear of polymers with a higher modulus of elasticity (1250 MPa) (points 4). Given this, the peak of the distribution shifts to the range of smaller sizes. Based on the study, the authors conclude that at the friction of thermosetting polymers their failure begins from the surface while the mechanism of subsurface failure is not practically realized. It is interesting to note that the calculated distribution describes satisfactorily also the abrasive wear data. Thus, points 5 correspond to the variance analysis of wear particles of glass ƒ…C-24. The particles were generated by grinding with free abrasive particles in water [12]. The tests were carried out at the room temperature. The similar pattern of the distribution was observed at the grinding of other glasses. A good agreement of the calculated and experimental data points to the fact that, in all likelihood, the proposed technique for calculating the variation of the surface roughness can be used also in this case if the abrasion failure time is properly defined. The above model involves the coefficients k1 and k2 . The former relates the maximum value of stresses in the asperity to the pressure on the contact spot. The latter depends on the asperity shape and it governs the size of a particle formed due to asperity failure. Principally it can be found from the solution of the contact problem for asperities having a real geometric shape. Such problem is independent and not simple. We made estimations of the coefficient for spherical asperity peaks and the conical shape of the lateral surface of asperities. It was assumed that the deformation of asperities is associated with the shear stresses on the contact spot which are proportional to the average contact pressure and friction coefficient. The location of the point with the maximum internal stresses was determined. We believe that it is just the point where a fatigue crack appears. The following estimates were obtained: k1 = 16/27 tan  √ k2 = 1/2 tan  where is the angle between the normal to the contact area and the generatrix of the asperity conical surface. Given this, the lengthto-thickness ratio for the wear particle is l/h ∼6 tan in order of magnitude. According to Garkunov’s data [21], the angle between the asperity base and the

CHAPTER 2

66

tangent to the lateral surface of the asperity is in the range $ ≈ 1    20 depending of the type of machining. Since ≈ 90 – $ we obtain the estimate l/h > 5. This is in agreement with the experimental data (see, e.g. work [21]).

2.3. AMPLITUDE DISTRIBUTION AND COUNT RATE OF ACOUSTIC EMISSION PULSES When solid surfaces are in relative motion asperities entering contact are deformed and areas in contact are unloaded. Some share of this energy is registered as AE signals. Before calculating the amplitude distribution we shall show that taking into account the time ! of the emission of AE pulse with the energy  the amplitude of the pulse should be considered to be proportional to /!1/2 . Indeed, if the time dependence of the signal registered by a gage is described by the function st = Aut where A is the signal amplitude and ut is a dimensionless function describing the signal shape then the energy of the signal is ≈



s tdt = A 2

0

2



u2 tdt ≈ A2 !

0

Here ! is the effective pulse duration. It follows from this that A ≈ /!1/2 . This expression can be easily validated for signals of different shapes. The energy of the compressive elastic deformation of the contacting asperities depends on the approach h [103]: =

8 √ h5/2 15M B

In its turn, the approach is related to the average pressure p and the radius of a contact spot a as follows [103]: 

9 2 2 2 4 h= M Bp a 16

1/3

From two these formulas we obtain with account for (2.5): =

81 5 M 4 5 p 640B3

(2.56)

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

67

If the velocity of the relative motion of the surfaces is v then the time interval during which the asperities contacting over the spot with the radius a are deformed and unloaded is determined as !≈

a 3 M p = v 4B v

(2.57)

If AE is registered by a piezoelectric gage with the electromechanical force factor Kem then an acoustic pulse with the energy  generates an electric signal with the energy e = Kem . If the absolute value of the input impedance of the gage is Z the amplitude of the electric signal is A = KZKem /! where K is the dimensionless coefficient taking into account the attenuation and transformation of AE signal when it is transmitted from a source to the gage and the amplification factor of the measuring instrument. Substituting (2.56) and (2.57) into this expression we obtain  1/2 2 p v A = A0  (2.58) v0 p02 where p0 is the coefficient from formula (2.6); v0 = 1 m/s is the constant introduced to use dimensionless parameters; A0 is the coefficient having the dimension of the electric voltage (V) and determined from the relation 

3 2 Kem z12 v0 A0 = K 80M

1/2

(2.59)

It follows from formula (2.58) that the amplitude distribution of AE is similar to the distribution of the squared real pressure. Using the rule of the transformation of the positive random values A and p to expressions (2.14) and (2.15) we obtain the probability density of the amplitude distribution of AE signals at i = 0:

  2  1 + 2 2  A  v0 1/2 d 1  v0 1/2 wA = C1 1+ + A0 v  A0 v 1    1/2    1/2 2    A v0 d A v0 d

+ exp − + 2 × √  A0 v 1 A0 v 1 (2.60) at i = 1:

  2   C A  v0 1/2 d 1  v0 1/2 wA = √ exp − + 2  A0 v 1 2  A0 v

(2.61)

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68

where C is the normalization constant. If to determine wA it is easy to calculate the basic parameters of the amplitude distribution. In particular, the mean amplitude and average square amplitude of pulses are calculated as follows: A¯ = A0

√



v  v0

1/2 A2 = A20 

J1 

v J  v0 2

Gk  G0 

Jk  =

(2.62)

Here the functions Gk  are determined by the following expressions: at i = 0: Gk  =



y − k 1 + 1 + 2 2 y2   y exp−y2 /2dy

k = 0 1 2



at i = 1: Gk  =



y − k exp−y2 /2dy

k = 0 1 2



and the parameter  depending on the ratio F/F0 is the root of corresponding equation (2.18) or (2.19). Figures 2.15 and 2.16 illustrate the dependencies of the functions Jk  on the ratio F/F0 ; the functions are almost independent of the parameter as it J2

J1

3.0

3

1.5 1.4

b

2

2.7

1.0 a

0.6

1.3 –5

–4

–3

–2

–1

2.4

0

1

α=3 α=2

1.1 a

α=1 1.8

b 1.8

2.1

1.9

2.0

2.1 F/F0

Figure 2.15. Dependence of functions Jk  on force pressing surfaces together i = 0" a – J1  b – J2

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

69

J2

J1 J1

0.8

J2 0.7

1.0

0.7 2

0.5

0.5 0.3

0.7

0.8

1

0.3

0.1 0.1

–6

–4

0.6

0

–2

0.6

lgF/F0

0.5

0.4 0.4

0.5

0.6

0.7

0.8

F/F0

Figure 2.16. Dependence of functions Jk  on force pressing surfaces together i = 1" a – J1  b – J2 follows from the calculations. Within a small range of the pressing force they can be approximated by linearly ascending functions. Therefore, the parameters A¯ and A¯2 = A20 change in the same manner. The pattern of the amplitude distribution at various sliding velocities and pressing forces is shown in Figs. 2.17 and 2.18. It is seen from the figures that the pattern of the distribution of acoustic signals is practically governed by the velocity v and parameter F/F0 which A0w (A) 0.5 V = 0.6 m/s

1.4 0.3 1.5

2.5

0.1

0

1.0

2.0

3.0

4.0

5.0

A /A0

Figure 2.17. Variation in amplitude distribution of AE signals with sliding velocity;  = 1 0 F/F0 = 0 6

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70

A0w (A)

F/F0 = 0.4

0.5 0.6

0.8 0.3

1.2 0.1

0

1.0

2.0

3.0

4.0

5.0

A /A0

Figure 2.18. Variation in amplitude distribution of AE signals with force pressing surfaces together;  = 1 0 v = 0 5 m/s depends on the material elastic constants and surface roughness parameters in addition to the pressing force. To determine the count rate of AE pulses let us reason as follows. By analogy with other models we shall suppose that the count rate of AE in sliding friction is proportional to the time variation of the number of contact spots. In the relative motion of the bodies, for example, along the x axis their apparent contact area changes by Lv per unit time (L is the characteristic size of the nominal contact area along the y axis). Then, according to (2.14), the rate of change in the contact spot number is  dN L 2 v d2 = exp − dt 4 2 12  212 

(2.63)

√ √ Since in the first approximation one can suppose  = d/1  ≈ 2f then the following expression for the count rate of AE pulses can be written: N˙ AE = N0

L 2 F v 8 2 12  F0

(2.64)

Here N0 is the empirical coefficient indicating how many AE pulses are emitted when one contact spot disappears. Formulas (2.60)–(2.64) serve to calculate the basic characteristics of acoustic emission in sliding friction and determine dependencies of the characteristics

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

71

on the physical-mechanical properties of the materials and the statistical characteristics of the friction surfaces. It follows from the expressions that the amplitude distribution, its characteristics and the count rate of AE pulses are practically governed by three parameters; they are the sliding velocity, the ratio of the standard deviations of the functions describing the surface shapes, and the parameter F/F0 which can be called “the relative force pressing the surfaces together”. The latter parameter comprises the complex of the elastic constants of the mated materials and the statistical characteristics of the surfaces such as the standard deviations of the functions describing the surface shapes and their derivatives in addition to the pressing force. The values of the mentioned characteristics and their variations in friction govern the count rate of AE pulses, the pattern of the amplitude distribution and their changes in operation of a friction pair. Results of the calculations and the experimental data we obtained in acoustic-emission tribotests and reported in publications are compared in Chapter 4. It is shown in this Chapter how, based on the proposed model, one can explain an experimentally observed change in the pattern of the amplitude distribution of AE pulses from the unimodal to J -type one in the running-in of a friction unit.

2.4. SPECTRAL DENSITY OF ACOUSTIC EMISSION E.I. Adirovich and D.I. Blokhintsev were first who studied how the generation of acoustic vibrations penetrating inward rubbing bodies influences the friction force; they reported their results in already mentioned paper [1]. They have shown that the component of the friction force caused by the generation of acoustic vibrations is inversely proportional to the velocity of the relative motion of the bodies. Paper [13] deals with interaction between the surfaces having real profiles that do not demonstrate strict periodicity in general case. This yields a different dependence of the contribution of acoustic emission to the friction force on the sliding velocity compared with [1]. Let us consider the friction of two surfaces whose shapes are described by the random continuous functions zi r  i = 1 2 which are count off from the median plane of the corresponding surface (Fig. 2.1). Just as in the previous Part let these planes be parallel and let the mean distance between them depending on the force of attraction between the bodies be d. Like previously, the indices 1 and 2 correspond to the variables relating to the first and the second half-spaces (Fig. 1.2). The surfaces move one relatively to another with a velocity v in the direction of the x axis. The normal zz and tangential xz stresses occurring on the surface due to interaction depend on the coordinate x, time t and relative velocity v: zz x t = z x x − vt

xz x t = x x x − vt

(2.65)

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72

where the dependence on the first argument is due to the non-uniformity of the surface z1 and the dependence on the second argument is caused by the non-uniformity of the surface z2 . The surfaces are assumed to be uniform along the y axis so that all the variables are independent on the coordinate y. Below the dimension of the bodies in contact along the y axis is assumed to be equal to the unity without loss of generality. Let us implement the integral transformation of the components of the stress tensor (2.65) L T 1  jz  p = dx jz x x − vteix eipt dt LT 0

j = x z

0

Here L is the dimension of the surfaces along the direction of motion. If the consecutive substitutions u = x – vt q =  + p/v and k = p/v are made and the equality L = vT is taken into account this expression is reduced to the following form jz q k = L

−2

L

L dx

0

jz x ueiqx−k! d!

(2.66)

0

It is easy to see that at L →  expression (2.66) is the Fourier transform of the components of the stress tensor per unit area of interaction. The components of the stress tensor are calculated by the following formula:  jz x ! = L−2 fj ! − x  d + z2 x − z1 xdx Here fj is the j th component of the force with which a unit area of the surface z2 with the coordinate x acts on a unit area with the coordinate x of the surface z1 at the instant t = x – !/v. It is apparently that the Fourier component jz q k determined by expression (2.66) does not depend on the velocity v. This statement arising from (2.65) is correct at small deformations when one may neglect variations in the profiles of the mated surfaces. Stresses (2.65) cause elastic vibrations in material I. The time and space dependencies of x, a, and zth -components of the displacement vector are described by common equations of the elasticity theory   2 2  + 2 −  ¨ = − +    2 x z x  2  2   (2.67) + 2  − ¨ = − +   2 x z x

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

  + 



2

2

x

z2

+ 2

73

 − ¨ = 0

where  = a/ x + / z   are the Lame constants which determine the velocities of the transversal and longitudinal elastic waves, correspondingly: cl = /1/2 , ct =  + 2/1/2   is the density of the material within which the elastic waves propagate. On the surface z = 0 the following boundary conditions are assigned:  

   + = x   + 2 = z (2.68) z x  z The substitution of the Fourier-series expansions of the functions ax x − vt z and x x − vt z over the variables x and ! = x − vt in (2.67) and (2.68) yields the following expressions for the Fourier components ak q z and k q z: ak q z = a1 exp−ipz + a2 exp−irz k q z = 1 exp−ipz + 2 exp−irz

(2.69)

k q z = 2 exp−irz where p = signkvkv/ct 2 − k + q2 1/2  a1 = ip

r = signkvkv/cl 2 − k + q2 1/2 

x p2 − k + p2  + 2rz k + q  p2 − k + q2 2 + 4rpk + q2

2px k + q − z p2 − k + q  p2 − k + q2 2 + 4rpk + q2 k+q r a1  2 = − a 1 = p k+q 2 a2 = ik + q

=

p2 − k + p2 z − 2px k + q  + p2 − k + q2 2 + 4rpk + q2

The sign in the expressions for p and r is chosen in such a way that the solution of (2.69) describes the elastic waves travelling from the surface z1 and propagating in material I. The time average energy flux density removed from the rubbing surfaces by sound is determined by the following expression: −1

Q = LT

T

L dt

0

0

      2  a + + ˙  +  dx a˙ z x  z

(2.70)

CHAPTER 2

74

where T is the time interval over which the variable is averaged. Here we should assume z = − so that contribution related to Rayleigh waves and all items oscillating with z vanish. Substituting the Fourier-series expansions (2.70) into (2.69) we obtain in the limit at T →   L2 v  kp2 + k + q2 px k q2 + rz k q2  Q= dk dq · (2.71) 2 2  p2 + k + q2 2 + 4rpk + q2 Expression (2.71) determines the emission power for any surface profile. Note that the multiplier L2 appearing in (2.71) is cancelled by the multiplier in the Fourier components of the stresses. The range of integration in (2.71) is restricted by the condition Imr p = 0. If we make substitutions % = kv and k + q = K in (2.71) then the integral over K gives the spectral density of acoustic emission: G% =

dQ% d%

(2.72)

In elastic interaction the components of the stress tensor depend on the approach of the surfaces d + z2 − z1 . If we assume that the mean distance between the surfaces is much greater than the asperity height d >> Z1  Z2  then the components of the tensor jz x ! can be expanded into a series in the parameter z2 − z1 /d keeping only terms of the second order. Transforming this expansion according to (2.66) we obtain jz q k = −L−2

2

jz d Z1 qZ2 −k d2

where Z1 q and Z2 −k are the integral transforms of the functions z1 x and z2 x. The remaining items do not contribute to the flux density and the spectral density of acoustic emission since they correspond to the waves which quickly attenuate as the distance from the surfaces increases. Let us consider the quantities appearing in expression (2.71): 2 jz q k2 = −L−4 bjz Z1 q2 Z2 −k2 

where bjz =

2

jz d/ d2 . The functions S1 q = L−1 Z1 q2 

S2 k = L−1 Z2 k2

have the physical sence of wave spectra being analogous of the spectral densities of the random functions z1 x and z2 x9. To calculate S1 q and S2 k one can

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

75

use the Wiener–Hinchin theorem according to which the spectral density and correlation function of a random value are related by direct and inverse Fourier transforms. The correlation functions of the surface profiles can be obtained when analyzing profile traces. Let we designate q k = S1 qS2 k then 2 q k jz q k2 = L−2 bjz

(2.73)

The analysis of expressions (2.69) has shown that p and r being wave numbers should be real and positive quantities because only in this case waves propagating into the materials correspond to the wavenumbers. This condition and expressions (2.69) produce the following restriction for the parameters k and q: k + q2 /k2 ≤ v2 /cl2 Let we introduce the variable  = k + q/k  = v/cl  varying within the interval −1 ≤  ≤ 1 then q k = k − 1 k. Since  ≤ 1 and in reality the velocities of the relative motion of the surfaces are much slower than the velocity of longitudinal waves in the materials  ≤ 1 we can assume that k − 1 k = −k k with a high accuracy. Substituting expression (2.73) into formula (2.71) and taking into account the latter remarks we obtain the expression for the energy flux of AE in friction: Q=

 v&2 C& b  b  k−k kdk xz zz 2 2 

(2.74)

2 2 where & = cl /ct  C& bxz  bzz  = bxz I1 & + bzz I2 & and Ii & i = 1 2 are the functions of the parameter &:

Ii & =

+1 −1

a2i − x2 1/2 dx  &2 − 2x2 2 + 4x2 &2 − 2x2 1 − x2 1/2

 & ai = 1

i = 1 i = 2

If we set k = %/v (% is the circular frequency) in (2.74) then the integrand produces an expression for the spectral density of AE in friction: G% =

&2 %  % %  C& b  −   b  xz zz 2 2  v v v

(2.75)

The analysis of numerous profile traces has shown that in general case functions describing surface profiles of machine parts can be presented in the following form [24] zi x = fi x + ni x

i = 1 2

(2.76)

CHAPTER 2

76

where fi x are the periodical functions with the period li  ni x are the random functions. The functions ni x depend on the macroinhomogeneity of the part materials, the polycrystalline structure of the metals and other random factors. One can state without loss of generality that fi x and ni x are statistically independent and that the average values of the functions fi x and ni x equal to zero. In this case the correlation functions Ri   i = 1 2 and the spectral densities S1 q and S2 k of the profiles can be represented in the following form: Ri   = Fi   + Ni    q i = 1 (i = k i = 2 '

'

'

Si  = F i (i  + N i (i 

i = 1 2 (2.77)

'

and F i (i  and N i (i  are Fourier transforms of the correlation functions Fi   and Ni  . Since fi x are the periodical functions with the period li then  

2 n  li n=1        ' 2 n 2 n 2 2 F i (i  = A0i (i  + Ani   (i − +  (i +  li li n=1 Fi   = A20i + 2

Ani 2 cos

(2.78)

where Ani are Fourier coefficients in the expansions of the functions fi x  is the Dirac delta function. Taking into account expressions (2.77) and (2.78) for the functions q k we obtain the following formula:      2 n 2 n q k = Cn Bm  q − + q+ l1 l2 n=1 m=1      2 m 2 m ×  k− + k+ l1 l2        ' 2 m 2 m Bm  k − + k+ + N 1 q l2 l2 m=1        ' 2 n 2 n + N 2 k Cn  q − + q+ l1 l1 m=1  

'

'

+ N 1 qN 2 k

(2.79)

Let we analyze expressions (2.74) and (2.75) and compare the obtained results with the available data of theoretical and experimental studies.

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

77

1. Let the functions zi x i = 1 2 do not contain periodical components fi x ≡ 0 and the random functions ni x have the correlation functions of the following form: Ni   = ai e− /i 

(2.80)

where ai are constants; i are the correlation distances of the surface profiles. Performing the Fourier transform of the functions Ni ( and having in mind expression (2.79) we obtain that in this case the spectral density of AE in friction is described by the following expression: G% =

% a1 a2 1 2 &2 C& bxz  bzz  2

 v 1 + %1 /v2 1 + %2 /v2 

(2.81)

Within the low-frequency band at % << v/1  v/2 : G% =

&2 % C& bxz  bzz a1 a2 1 2 2

 v

Within the high-frequency band %  v/1  v/2 and G% =

a1 a2 v3 &2  b  C& b xz zz 1 2 %3

2

According to (2.81), the maximal spectral density of AE corresponds to the frequency %m =

 !1/2 v  1 +  2 2 + 12 2 − 1 +  2  6 2   1

where  = √ 2 /1 . In particular, if both surfaces identical 1 = 2 =  and %m = v/ 3. Figure 2.19 illustrates the dependence of AE spectral density on the frequency plotted in relative units for the friction of the like surfaces  = 1. The energy flux density of acoustic emission is determined by integrating expression (2.81) for G%: Q=

2&2 v a1 a2 1 2 ln1 /2 

2  21 − 22 

Since Q ∼ v the component of the friction force related to the emission of elastic waves does not depend on the velocity in this case: f = Q/v ∼ const.

CHAPTER 2

78

G (ω)~x /(1 + x 2)2

0.3 ∼1/ω 3

0.2 0.1

∼ω 1/√3 1.0

2.0

3.0

x = ωk/v

Figure 2.19. Spectral density of AE in friction of like surfaces  = 1 2. If the functions zi x do not contain periodical components fi x ≡ 0 and the correlation functions of the random functions ni x have the following form Ni   = ai e− /i cos)i 

(2.82)

then calculations by the above formulas give AE spectral density: 2  " % 1/1 − )i i  &2 G% = 2 C& bxz  bzz  a1 a2 1 2 2 v

 i=1 1 + %i /v1 − )i i   1/1 + )i i  + (2.83) 1 + %i /v1 + )i i 2

At low frequencies % << v1 − )i i /i : G% =

&2 % a1 a2 1 2 C& bxz  bzz  2 2 2

 1 − )1 1  1 − )1 1   v

At high frequencies % << v1 + )i i /i : G% =

&2 a1 a2 v3  b  C& b xz zz

2 1 2 %3

Asymptotic expressions (2.80) and (2.82) for the spectral density of acoustic emission within the low-frequency and high-frequency bands for the correlation functions of the surface profiles coincide up to constant multipliers. Performing the direct integration of (2.83) one can show that AE flux density is proportional to the velocity of the surface motion. For this reason, just

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

79

as in the above case the friction force resulting from the emission of elastic waves does not depend on the velocity: f = Q/v ∼ const. 3. Let us consider the case of periodical profiles ni x ≡ 0. This case is interesting because it is considered in a number of papers dealing with the simulation of acoustic emission in friction and results of calculations can be compared with the data obtained by other researchers. To simplify our calculations we shall assume in the first approximation that cl ct = c. Since random components of the functions describing the surface profiles are absent only the first item remains in (2.79). Substituting the function q k into (2.71) and integrating over the parameter q then making the substitution k = %/v and extracting the integrand we obtain the spectral density of acoustic emission for the periodic functions of the profiles of the mated surfaces in the following form:  1/2    2 2 + bzz   bxz l2 n c2 c Cm Bn 1 − 1 − G% = 4 2  l1 m v 2 nm=1      2 v 2 v ×  %− m + %+ m l2 l2

(2.84)

This expression contains only those items which have corresponding acoustic waves propagating into the bodies. Only those values of n and m should be kept in sum (2.84) for which the radicand is non-negative. In reality c/v  1, therefore the items that obey the equality l1 m = l2 n make the most contribution to the sum. Hence, AE frequency spectrum comprises the following spectral components %nm = 2 vm/l2 = 2 vn/l1  n m = 1 2    . In the particular “resonance” case l1 = l2 = l AE spectrum comprises the frequencies %n = 2 vn/l. Integrating (2.84) over the frequency we obtain the energy flux density of waves which does not depend on the velocity v. Therefore, the component of the friction force caused by acoustic emission is inversely proportional to the velocity: f = Q/v ∼ 1/v that agrees with the result obtained by the authors of [1]. 4. Let the functions zi x i = 1 2 contain both periodical and random components and the correlation functions of the profiles are the same and described by the following expression 

 2

R  = A cos + ae− / l

(2.85)

Such case is typical for a friction pair whose members are made of similar materials with the working surfaces machined in the same way. Combining the results obtained in Parts 1 and 3, taking into account formulas (2.75)

CHAPTER 2

80

and (2.79) and assuming that cl ct = c & = 1 we derive the following expression for the spectral density of acoustic emission:     2 2 + bzz  A2 bxz c 4 2 n va × 1+ G% = 4 2   n=1 c l A 1 + 2 n/l2      2 v 2 v n + %+ n ×  %− l l  %/v a2 (2.86) + 2 2 A 1 + %/v2 2 According to (2.86) one should expect √ that the maxima of AE spectral density occur at the frequencies fm = v/2 3 and fn = vn/l n = 1 2     in friction. The pattern of the spectral density is presented in Fig. 2.20 with account for damping taking place in real tribosystems.

G(f )

fm

f1

f2

f3

f, kHz

Figure 2.20. Spectral density of AE in friction of surfaces whose correlation functions are described by expression (2.85)

In the dry friction of materials one should expect a similar pattern of the spectral density (it is really observed) (see Part 4.2). Such a pattern of the spectral density of acoustic emission is also possible when a lubricating film separating the rubbing surfaces and damping elastic waves is damaged. Since the statistical characteristics of the surface profiles change during the running-in and wear of the surfaces then, according to the above calculations, ratios between the the maxima of spectral components of AE signals should also change.

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

81

The mentioned fact can be used to develop methods of friction unit monitoring based on the comparison and registration of time variations of components of the acoustic emission spectrum within narrow frequency bands. It is essential because broad-band gages are necessary to register acoustic signals within a broad frequency band. The widening of the band results in increased noises which do not relate to the operation of a friction unit. When comparing the intensity of AE signals obtained in optimally selected frequency bands by several, for example, two narrow-band gages the signal-to-noise merit can be improved, on the one hand. On the other hand, this reduces the effect of the hardly measurable frequency response of the acoustic channel of the measuring instrument. Also the effect of errors resulted from the mounting of the gages and differences in their characteristics narrows down. In conclusion we note that the proposed approach to the calculation of the spectral density and energy flux of AE does not cover all variety of physical processes running in the zone of friction contact. However, using this approach we have obtained the results describing the most typical features of the frequency spectrum of acoustic emission in friction. They are the presence of a characteristic frequency at which emission is maximal; the linear rise of the intensity with increasing frequency ∼ % in the low-frequency band of the spectrum and its decrease ∼%−3  in the high-frequency band; the decrease of the low-frequency component with increasing sliding velocity. These features are really observed in acoustic emission tribotests. In particular, the drop of the intensity proportionally to the frequency cubed in the high-frequency band 2    3 MHz is proven well to be true. The analysis of AE correlation functions convinces us of the existence of a characteristic frequency of emission within the band from hundreds hertz to a few kilohertz. Low-frequency components rises as the rotational velocity in sliding bearings decreases.

2.5. DYNAMIC MODEL FOR CALCULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION AT NON-STATIONARY FRICTION REGIMES In this part we propose a model to describe non-stationary and transient regimes in tribosystems based on the theory of Markov random processes [25]. In this model friction is considered as a two-stage random process involving the formation and rupture of friction junctions on rubbing surfaces. It is supposed that with varying number of the junctions energy is liberated and absorbed and some share of the energy is registered as acoustic emission. A friction junction is a single contact spot appearing under the joint action of the normal and tangential loads and disappearing when the normal load becomes zero.

82

CHAPTER 2

The following quite general assumptions are used in the model: – the number of friction junctions nt is a random function of time; – AE appears as a random sequence of acoustic pulses, each of them is the response of the material to the pressure pulse arising on the material surface in the formation or rupture of a friction junction; – the discrete random process nt does not depend on its previous history that is the number of friction junctions nf at some future instant tf is only determined by the value of n at the present instant t and does not depend on the number of junctions in the past; – the force of friction between the surfaces is proportional to the number of appeared friction junctions. With this assumptions the random process nt can be considered as a simple Markov process [26] for which the conditional probabilities of transition are represented as follows: ⎧ ⎪ ot ⎪ ⎪ ⎪ ⎪ ⎪n ttot ⎨ pnf  tf n t = 1 − n t + n tt + ot ⎪ ⎪ ⎪ n tt + ot ⎪ ⎪ ⎪ ⎩ot

nf nf nf nf nf

< n − 1 = n − 1 = n = n + 1 > n + 1

(2.87)

Here ot are terms of the first orders of vanishing relative to ot t = tf − t nf  n = 0 1 2     n t and n t are the rates of the formation and rupture of friction junctions, respectively. In this case the number of AE pulses N appearing during the period t is N = n t + n tt The functions n t and n t are governed by the nature of friction thus they are implicitly dependent on external conditions (the temperature, load, sliding velocity) as well as on physical properties (the density of defects, yield stress of the materials etc.) and geometric characteristics (the roughness, the number and shape of contact spots etc.) of the surfaces. Further we shall consider only the case when the rate of friction junction formation does not explicitly depend on n that is n t = t and the linear approximation is used for n t: n t ≈ tnt

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

83

where t = n tnt is the relative rate of friction junction rupture. Then the activity of acoustic emission N˙ t is N˙ t = t + tnt

MN˙ t = t + Mnt

DN˙ t = t2 Dnt

(2.88)

Here Mxt and Dxt are the expectation and variance of the random function xt, respectively. The above assumptions on the pattern of the functions n t and n t are valid for friction with the overlapping factor (the ratio of the areas of the part friction surfaces) close to zero Kover → 0 that occurs in tribotests using the pinon-disc geometry. In this case friction junctions within the contact area appear with a rate t which does not depend on the number of current junctions and disappear with a rate t proportional to the number of junctions in contact [27]. For friction with Kover → 0 one can consider that physical characteristics of the surface contacting the pin vary slightly. This means that the disc surface enters contact whose properties almost have not changed after one pass of the pin; in other words, the surface entering contact is always “new”. For this reason friction resulting from the formation and rupture of friction junctions can be presented as a simple Markov process. To describe a discrete random process nt one should determine conditional probabilities Pn t = pn tn0  t0  where n0 = nt0  is the number of friction junctions at the initial instant t0 . Let us use the Kolmogorov–Chapman equation for Markov processes: Pn t =



pn tn  t pn  t 

n =nt 

where t ≥ t ≥ t0 . Substituting conditional probabilities of transition (2.87) into this equation at t = t + t and proceeding to the limit t → 0 we obtain the following difference-differential recurrence equation Pn t = tPn − 1 t + tn + 1Pn + 1 t t − t + tnPn t Initial condition are as follows Pn t0  = nn0 

(2.89)

CHAPTER 2

84

where nn0 is the Kronecker delta:  1 nn0 = 0

n = n0  n = n0

Multiplying both sides of the equation by sn and summing over n we obtain the following partial differential equation Fs t Fs t = t1 − s − t1 − sFs t t s

(2.90)

Here Fs t =

 

Pn tsn

n=0

is the generating function for the probabilities Pn t. The initial condition for Fs t is as follows: Fs t0  = sn0

(2.91)

The characteristic equation for (2.90) is written as ds dF = dt = 1 − st 1 − stF

(2.92)

The solution of the left equation yields 1 − s = C1 u˜ t where u˜ t = u˜ t t0  = exp

⎧ ⎨ t ⎩

t0

(2.93) ⎫ ⎬

t dt ⎭

Substituting expression (2.93) into the right side of equation (2.92) we obtain  ! F = C2 exp C1 u˜   d According to boundary conditions (2.91) sn0 = C2 

1 – s = C1

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

85

Then C2 = 1 − C1 n0 and it follows from (2.93) that C1 = 1 − sut where ut = ut t0  = exp

⎧ ⎨ t ⎩

t0

⎫ ⎬

t dt ⎭

Performing simple transformations we can present the solution of differential equation (2.90) with initial condition (2.91) in the following form Fs t = 1 + s − 1utn0 exps − 1vt where vt = exp

⎧ ⎨ t ⎩

t0

⎫ ⎬

t ut t dt ⎭

(2.94)

Using the expression for Fs t we derive  1 n F  Pn t = n! sn s=0  e−vt minnn0 k k!Cnk Cn0 1 − utn0−k uk tvn−k t n! k=0   2   2  F F F 2 Dnt = + Pn t nt − Mnt = + 2 s s s n=0 =

(2.95)

s=1

= n0 ut1 − ut + vt Here Cnk =

n! k!n − k!

is the number of combinations of n things k at a time. If at t →  the rate of junction formation t and the relative rate of junction rupture t tend to some stationary values  and  which are constant in time then using expression (2.94) we derive lim ut = 0

t→

lim vt =  /

t→

CHAPTER 2

86

Hence, in this case Pn = lim Pn t = t→

e− / n!

MN˙  = lim MN˙ t = 2  t→



n

 



Mn = lim Mnt = t→

Dn = lim Dnt = t→

  

  

DN˙  = lim DN˙ t =  

(2.96)

t→

The obtained expressions coincide with the solution of the corresponding stationary problem. It follows from (2.87), (2.94) and (2.95) that the discrete random processes nt and N˙ t are determined by the functions t and t. Therefore, to perform further analysis we should find a possible pattern of the dependencies t and t and their correlation with mechanisms and physical characteristics of friction. Such a problem is highly complicated. For this reason we shall restrict ourselves by an indirect method of analysis when a desired dependence chosen from general considerations contain a number of parameters whose values can be found by comparing the obtained analytical expressions with experimental data. Let us suppose that  and  can be considered as internal parameters of the system; to describe them we should use the common thermodynamical approach when the dependencies t and t can be presented in the following form if one of external parameters of the system (the load, temperature, sliding velocity) changes stepwise:

t = 0 +  − 0 

$

$ !1 − e−t/! d!

0

t = 0 +  − 0 

$

$ !1 − e−t/! d!

0

Here 0 = t0  and 0 = t0  are the equilibrium values of  and  at the initial instant t0  $ ! and $ ! are functions representing the correlation between the parameters  and  and other internal parameters of the system and obeying the following condition $ 0

$ !d! =

$ 0

$ !d! = 1

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

87

Let  and  are independent internal parameters of the system. In this case $ ! = ! − ! 

$ ! = ! − ! 

where ! and ! are the relaxation time of the parameters  and , correspondingly; x is the Dirac delta function. Then we obtain t = 0 + 1 − e−t/! 

t = 0 + 1 − e−t/! 

(2.97)

where  =  − 0   =  − 0  t = t − t0 . Substituting these dependencies into expression (2.94) we derive ut = exp− t + ! 1 − e−a    −a vt = exp−! e   F − !  − ! + 1 ! e−a   1 1 ! − t −e 1 F1 − !  − ! + 1 !  −  ! − 1  ! ! × e−t/! 1 F1 − ! +  − ! + + 1 ! e−a  ! !  ! ! − t  − ! + + 1 !  (2.98) −e 1 F1 − ! + ! ! Here a = t/! and 1 F1 x y z =

  xk zk k=0

yk k!

is the degenerate hypergeometric Kummer function; xk = xx + 1    x + k is the Pohgammer symbol. Expressions (2.98) are quite cumbersome and difficult to analyze. Let us consider the case when ! → 0. Then the relative rate of friction junction rupture t either constant  → 0 or varies stepwise ! → 0 that is t = 0 + ht where

 1 x > 0 hx = 0 x ≤ 0

CHAPTER 2

88

is the Heavyside function. Proceeding to the limit ! → 0 in (2.98) and using (2.95) and (2.98) we obtain:    ! ! −  e− t − e  + n0 − + Mnt =    ! − 1  ! − 1   ! e− t MN˙ t = 2 + n0 − 0 + ht −  +  ! − 1 2 ! − 1 − (2.99) e   ! − 1    ! ! −  − t + − n0 e e  + n0 − − Dnt =    ! − 1  ! − 1   ! − t 2 − n0 e  + DN˙ t =   +  n0 −   ! − 1 −

−

! 2 − e  ! − 1

(2.100)

Similarly, for the case when t! → 0 we can derive Mnt = n0 exp− t + ! 1 − e−a  exp−! e−a    # + F − !  − ! + 1 ! e−a z  1 1 $ − t  −e 1 F1 − !  − ! + 1 ! 

(2.101)

MN˙ t =  +  − e−a n0 exp− t + ! 1 − e−a  +  − e−a  exp−! e−a    # × F − !  − ! + 1 ! e−a   1 1 $ − t  −e 1 F1 − !  − ! + 1 ! 

(2.102)

Dnt = n0 exp− t + ! 1 − e−a  × 1 − exp− t − ! 1 − e−a  + exp−! e−a    # + F − !  − ! + 1 ! e−a   1 1 $ − t  (2.103) −e 1 F1 − !  − ! + 1 ! 

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

89

DN˙ t = 2 n0 exp− t + ! 1 − e−a  + 1 − exp− t + ! 1 − e−a  + 2 exp−! e−a    # × F − !  − ! + 1 ! 1 − e−a  − e− t   1 1 $ (2.104) − 1 F1 − !  − ! + 1 !  Note that at ! = 0 expression (2.99) and at ! = 0 expression (2.101) coincides with the dependence of the average number of friction junctions on time obtained in [27] for stepwise variation in the rate of junction formation and the relative rate of junction rupture. Some calculation results of the dependencies of the average number of friction junctions and AE activity on time are presented in Fig. 2.21, a–d. If the rate of junction formation varies stepwise the functions Mnt and MN˙ t have the maximum while when the relative rate of junction rupture changes in the same manner the functions have the minimum. It is significant that the average values of the number of friction junctions and AE activity reach their extreme points at different instants. In case when the junction formation rate and relative junction rupture rate can be presented in the form (2.97) the period during which the average value of AE activity reaches its maximum is longer as compared with the average number of friction junctions. This time difference increases with increasing values of the parameters  ! and  ! and decreasing ratio  / n0 . Different instants of the occurrence of the extreme points on the dependencies result in the diversity of entering AE activity and the number of friction junctions into a stationary region. In other words, the period of reaching the stationary state for AE activity is longer in comparison with the number of friction junctions. Let us consider the behavior of the function MN˙ t in the neighborhood of the point t0 . This case is useful to assess the behavior of AE characteristics when external factors such as the sliding velocity and load vary stepwise and to interpret AE appearing when a lubricating film or a coating is failed. Let us assume that till the instant t0 the stationary friction process run with an average steady-state AE activity MN˙ t < t0  = 2 . At the instant t0 some changes occurred in the system “the friction pair – the environment” which resulted in variations in the junction formation rate and relative junction rupture rate according to expressions (2.97). Then  = 0 and  = 0 . Such a change may stem, for example, from gradual temperature elevation, gradual variation in the environment composition or changes in the lubrication mode (the addition or partial removal of a lubricant). In this case a gradual shift from values of MN˙ t Mnt corresponding to the parameters  = 0   = 0 to new steady-state values MN˙  = 2 and Mnt =  / occurs on the time dependencies MN˙  and Mnt in the neighborhood of the point t0 .

CHAPTER 2

90

2.0

·

M [N(t )] μ∞n0

2.0

M [n(t )] n0

λ∞

= 0.5

μ∞n0 τμ = 0; λ0 = 0; μ0 = 0

1.0

0.5 μ∞(t – t0) 1.0 1.5 2.0 2.5 2.0 4.0 6.0 8.0 10.012.014.0

2.0 4.0 6.0 8.0 10.0 12.0 14.0

3.0

(a)

μ∞τλ

μ∞τλ

· M [N(t )] μ ∞n0

M [n(t )] n0 3.0

3.0

λ∞ = 1.5 μ∞n0 τμ = 0; λ 0 = 0; μ 0 = 0

2.0

1.0

0.5

μ∞(t – t0)

1.0 1.5 2.0 2.5 2.0 4.0

μ ∞τλ

3.0 6.0 8.010.012.014.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

μ ∞τλ

(b)

Figure 2.21. Dependencies of average values of number of friction junctions and AE activity on time and parameters governing formation rate and relative rupture rate of friction junctions

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

2.0

· M [N(t )] μ ∞n0

2.0

M [n(t )] n0

λ∞ = 0.5 μ ∞n0 τμ = 0; λ 0 = 0; μ 0 = 0

1.0

0.5

μ ∞(t – t0)

1.0 1.5 2.0 2.5 2.0 4.0 6.0 8.0 10.012.014.0

μ ∞τλ

(c)

3.0 2.0 4.0 6.0 8.0 10.0 12.014.0 μ ∞τλ

· M [N(t )] μ ∞n0

3.0

M [n(t )] n0

λ∞ = 1.5 μ ∞n0 τμ = 0; λ 0 = 0; μ 0 = 0

2.0

0.5

μ ∞(t – t 0)

1.0 1.5 2.0 2.5 3.0 2.04.0 6.0 8.0 10.012.0 14.0

μ ∞τλ

Figure 2.21. (Continued)

2.04.0 6.0 8.010.0 12.0 14.0

μ ∞τλ

(d)

91

92

CHAPTER 2

If the junction formation rate and relative junction rupture rate vary stepwise, for example, when a lubricating film is damaged then expressions (2.97) can be presented in the following form: t =  + 0 −  ht +  − 0 1 − et/!  t =  + 0 −  ht +  − 0 1 − et/! 

(2.105)

The time dependencies MN˙ t and Mnt show a jump. Let us consider a simple case when  =  = 

! = ! = 0

that is at the instant t0 the junction formation rate jumps from  to 0 =  while the relative junction rupture rate does not change. The jump of the average AE activity is N˙ =  +  n0 − 2 and the average number of friction junctions changes by n = n0   −  / . Here    are the initial junction formation rate and relative junction rupture rate, respectively; n0 is the number of friction junctions in the system at instant t0+ , i.e. just after the change in friction conditions;  is the steady-state value of the junction formation rate under new conditions. It is easy to show that the variations of the average AE activity and the average number of friction junctions are related as follows MN˙ t0  =  −  +  Mnt0  that is the jump of the time dependence of MN˙ t0  is at least Mnt0  times greater than that of the time dependence of  . Let us analyze the dependence of the average AE activity on external factors of friction under stationary conditions at t → . We shall consider only the component of friction resulted from the mechanical interaction of the surfaces in contact. In this case a friction junction is a single contact spot which appears under the simultaneous effect of the normal and tangential loads and disappears when the normal load becomes zero [28]. Let us determine the average number of friction junctions that is the number of real contact spots n assuming that surface asperities are simulated by spherical segments: n = 1 2

d1 + d2 2 S 4

where 1  2  d1  d2 are the densities and average dimensions of surface asperities in the section plane at the level of contact; S is the contact area.

SIMULATION OF CHARACTERISTICS OF ACOUSTIC EMISSION IN FRICTION

93

Let us determine steady-state values of the junction formation rate and relative junction rupture rate:  = 1 2 d1 + d2 2 Sv =  =

n

 n

4v

d1 + d2 



4v n 

d1 + d2   =

n=0

4v

d1 + d2 

(2.106)

Here d1 + d2 vt is the area swept by an asperity with the effective size d1 + d2  for a period t at a sliding velocity v; d1 + d2 vt 4d1 + d2 2 is the share of friction junctions which have exited contact for the period t. Substituting expressions (2.106) into formulas (2.96) we obtain

d1 + d2 2 S = n  4 8v Mn MN˙  = 21 2 d1 + d2 Sv =

d1 + d2  Mn = 1 2

(2.107)

Let us use now the known dependencies relating the average number of contact spots and their average size with the applied load, geometric characteristics and physico-mechanical properties of the surfaces in contact [29]. In the case of elastic contact of two surfaces with small roughness and negligible waviness we can write according to [29] 0 66 pc  pr  −0 33 pc 0 5  Sr = K2 rRa  pr   Ra pc0 14  pr = K 3 2 rM A n r = K1 c rRa



where Ki  i = 1 2 3 are numerical coefficients; pc and pr are the contour and real pressure, respectively; Ac is the contour contact area; r is the curvature radius of asperity summits; Ra is the arithmetic average roughness; M is the Hertz modulus; nr is the number of real contact spots; Sr is the average area of a real contact spot.

CHAPTER 2

94

It follows from (2.107) that n MN˙  ∼  r v Sr and using the above expressions we obtain the following formula: MN˙  = K

0 71 0 71 A0 29  c F v r 0 9 R1 6 a

(2.108)

Here K is a numerical coefficient and F is the normal load. As it has been shown in Part 1.5, AE count rate is sensitive to the pattern of the amplitude distribution of AE pulses which, in its turn, is governed by both external parameters of friction and physical and geometrical characteristics of the surfaces in contact. For this reason interrelations between variations in AE count rate and changes in friction conditions can be more intricate than those described by expressions (2.100) and (2.108). Though the proposed way of describing AE in friction does not consider all variety of processes running in the zone of friction contact it allows one to describe the most typical manifestations of AE in friction. The obtained expressions describe in general the dynamics of the friction coefficient and AE activity under non-stationary regimes like running-in, the failure and deposition of a lubricating film or coating, stepwise variations in the load or velocity. In the particular case when the rates of the formation and rupture of friction junctions change stepwise the obtained results agree with the known expressions reported in [27]. The performed calculations prove a higher sensitivity of acoustic emission characteristics to changes in friction conditions in comparison with the friction coefficient that is confirmed by data of acoustic emission tribotests.

REFERENCES 1. Adirovich E. and Blokhinzev D. On the forces of dry friction // J. of Physics. 1943, vol. VII, no. 1, pp. 29–36. 2. Akhmatov A.S. Molecular Physics of Boundary Lubrication, Israel Program for Scientific Translation, 1966. 3. Greenwood J.A. and Tripp J.H. The Contact of Two nominally Flat Rough Surfaces // Proc. Inst. Mech. Engrs., 1970–71, vol. 185, pp. 625–633. 4. Palasantras G. Contact area calculation between elastic bodies bordered by mound rough surface. Solid State Commun., 2003, 125, nos 11–12, pp. 611–615. 5. Xian L. and Zheng L.Q. A numerical Model for Elastic Contact of Three– Dimensional Real Rough Surfaces // Wear, 1991, vol. 148, pp. 91–100.

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6. Sviridenok A.I., Chizhik S.A., and Petrokovets M.I. Mechanics of Discrete Friction Contact (in Russian), Minsk, 1990. 7. Baranov V.M., Kudryavtsev E.M., and Sarychev G.A. Application of the theory of random processes to estimate probability density of pressure distribution on surface microcontact spots // Journal of Friction and Wear, vol. 16, no. 4, pp. 9–16, 1995. 8. Baranov V.M., Kudryavtsev E.M., and Sarychev G.A. Modelling of the parameters of acoustic emission under sliding friction of solids // Wear. 1997, vol. 202, pp. 125–133. 9. Akhmanov V.A., Dyakov Yu.E., and Chirkin A.S. Introduction to Statistical Radiophysics and Optics (in Russian), Moscow, 1981. 10. Landau L.D. and Lifshits E.M. Theory of Elasticity, Pergamon Press, London, 1959. 11. Ireman P., Klarbring A., and Stromberg N. A model of damage complied to wear. Int. J Solids and Struct., 2003, vol. 40, no.12, pp. 2957–2974. 12. Tsesnek L.S., Mechanics and Microphysics of Surface Wear (in Russian), Moscow, 1979. 13. Baranov V.M., Kudryavtsev E.M., Sarychev G.A., and Stopyra A.Z. Variation in Statistical Characteristics of Friction Surfaces During Run-In // Journal of Friction and Wear, 2002, vol. 23, no. 1, pp. 43–55. 14. V.M. Baranov, E.M. Kudryavtsev, G.A. Sarychev, and A.Z. Stopyra. Technique for Estimating Variation in Roughness Parameters and Wear Particle Size Distribution During Run-In of Tribosystems // Journal of Friction and Wear, 2002, vol. 23, no. 2, pp. 24–30. 15. D.H. Buckley, Surface Effects in Adhesion, Friction, Wear and Lubrication, Amsterdam, 1981. 16. Ireman P., Klarbring A., and Stromberg N. A model of damage complied to wear. Int. J Solids and Struct., 2003, vol. 40, no. 12, pp. 2957–2974. 17. Myshkin N.K., Chung K.K., and Petrokovets M.I. Introduction to Tribology. Seol: Cheong Moon Gak, 1997, 292 p. 18. Kragelskii I.V., Dobychin M.N., and Kombalov V.S. Friction and Wear Calculations Methods, Oxford, 1982. 19. A.V. Belyi and N.K. Myshkin. On size of wear particles // Proceedings of Belarus Academy of Sciences, 1981, vol. 25, no. 1, pp. 35–38. 20. P.V. Sysoev, P.N. Bogdanovich, and A.D. Lizarev. Deformation and Wear of Polymers in Friction (in Russian), Minsk, 1985. 21. D.N. Garkunov. Triboengineering (in Russian), Moscow, 2001. 22. Yu.A. Fadin and Yu.P. Kozyrev. Fractal features of wear particles // Letters to Journal of Technical Physics, 2000, vol. 26, no.13, pp. 46–50. 23. Aleksandrov A.S., Elesin V.F., and Schavelin V.M. Acoustical Emission at Friction of Rough Surfaces // Surface. Physics, Chemistry, Mechanics (in Russian), no. 8, pp. 127–132, 1985. 24. Khusu A.P., Vitenberg Yu.R., and Palmov V.A. Surface Roughness (in Russian), Moscow, 1975. 25. Sarychev G.A., Schavelin V.M., Baranov V.M., and Gryazev A.P. Analysis of acoustic emission in solid friction // Journal of Friction and Wear, 1985, vol. 6, no. 1, pp. 28–34. 26. Tikhonov V.I. and Mironov M.A. Markov Processes (in Russian), Moscow, 1977.

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27. Saibel E. A statistical approach to run–in and the dependence of the coefficient of friction on velocity // Wear. 1975, vol. 35, no. 3, pp. 383–385. 28. Kragelskii I.V. Friction and Wear, Pergamon Press, Elmsford, 1982. 29. I.V. Kragelskii and V.V. Alisin. Tribology – Lubrication, Friction, and Wear, Moscow, 2001.

Chapter 3

INSTRUMENTATION AND EQUIPMENT FOR STUDIES OF ACOUSTIC EMISSION IN FRICTION

3.1. SOURCES OF NOISES IN REGISTRATION OF ACOUSTIC EMISSION AND METHODS OF NOISE CONTROL The registration of acoustic emission in friction is characterized by the simultaneous occurrence of continuous and discrete AE, a broad dynamic range of variation of the signal amplitude, the effect of acoustic, electrical and electromagnetic noise. The validity of conclusions on the condition of friction units based on AE measurement data depends on many factors including the reliable selecting of signal from unwanted noises accompanying the signal. Therefore, when developing the instrumentation and equipment for studies of AE in friction it is necessary to take measures to dejam noises and ghost signals attending tribotests and to provide a high signal-to-noise merit. Let us consider the nature of interference and sources of noise in AE tribotests. Some of the sources are conventional for AE measurements and methods of controlling them are described, for example, in [1], other are specific and resulted from friction. First of all, AE instrumentation like any electronic measuring instruments experience the effect of external noise and intrinsic electrical noise resulting in masking and distortion of data being registered. Sources of intrinsic noise are fluctuation phenomena occurring in the instrumentation including thermal noise, fluctuations of the number of charge carriers in semiconductors, the instability of leakage currents etc. External noise is caused by the influence of electromagnetic fields on components of electronic devices and electromechanical sensing devices. Acoustic and mechanical effects on the object under study and AE gages also produce external noise. The process of friction itself is a source of noise. It is known that friction is accompanied both acoustic emission and electric, magnetic and electromagnetic phenomena. Such noise is difficult to eliminate since its nature and mode are similar to those of acoustic signals under study. Two main sources of acoustic noise in registration of AE accompanying friction are distinguished. They are acoustic emission resulted from the operation of other friction pairs which available in the set-up or mechanism (they are not under study) and the vibration of movable parts and units of the testing device itself. One can eliminate such noise by using acoustic insulation of the friction

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pair under study and (or) by selecting an optimal frequency band of signal registration within which the signal-to-noise merit is enough high to determine surely characteristics of the signals. Frequency filtering and amplitude discrimination of signals are the simplest, hence the most common methods of noise control. For this reason all AE instruments are equipped with a device to control the discrimination level. In addition to acoustic insulation of a friction pair under study a difference in the amplitude distributions of AE signals can be used to eliminate or minimize acoustic interference resulted from the operation of other friction units. Because the distance between the noise source and the gage is longer than the distance between the pair under study and the gage acoustic waves attenuate faster in the former case. For this reason the amplitude of noise produced by the noise source is smaller than that of signals generated by the pair being tested. Also design measures reducing the severity of loading of friction units which provide the operation of a testing system are effective as well as the use of suitable lubricants. To eliminate such interference it is enough as a rule to choose a proper discrimination level. In practice the discrimination level is varied so that the measuring instrument does not perceive unwanted noise before the beginning of tests. For example, if it is necessary to register the instant when a lubricating film is damaged the discrimination level should be selected in such a way that at least single AE pulses are registered in friction with the lubricant. The amplitude of AE pulses increases by 1–3 orders of magnitude depending on the sliding velocity, load and mated materials when the lubricating film is damaged and sites of “dry” friction appear. The count rate also increases considerably. Such variations in AE characteristics are reliably registered by measuring instruments and prove the damage of the lubricating film. The method of amplitude discrimination is suitable in monitoring of processes whose change results in a significant variation in the amplitude of AE pulses, for example, the determination of the instant when a lubricating film or a solid-film lubricant on the friction surface is failed, transition from one wear mode to another, particularly, from adhesive to abrasive wear etc. When carrying out studies this method of noise control is not always justified since only those signals are registered which exceed noticeably the noise level; this leads to significant data losses. In this case it is possible that some effects accompanying friction are not registered. When selecting the frequency band of the registration of AE in friction one should keep in mind the following. AE is known to have a quite broad frequency spectrum ranging from tens of hertz to tens of megahertz. At the same time, the analysis of data on the acoustic diagnostics of machines and mechanisms has shown that acoustic noise resulting from the vibration and impacts of machine

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parts due to the unbalance of rotating shafts has a spectrum with the upper boundary 20–40 kHz. When selecting the upper boundary of the frequency pass band of AE measuring instruments one should take into account the significant attenuation of ultrasonic waves in the high-frequency band of spectrum. For example, at 2–5 MHz the reach of available AE instruments is below a few tens of centimeters for steel objects being tested. A noticeable attenuation of signals from friction pairs not under testing occurs also in joints between parts operating as good dampers and reflectors of elastic waves. Therefore, in most cases the suitable frequency band for AE registration ranges from 20–100 kHz to 2–3 MHz. When choosing the frequency band natural resonance frequencies of gages should be taken into account. If the frequencies are within the registration band the spectral density, correlation function and other characteristics of acoustic emission can be substantially distorted. If these characteristics serve as informative characteristics in AE monitoring it is necessary to smooth the frequency response of the gages. This is achieved by damping the gages, by the mechanical and electrical matching of them with the object being monitored and with the amplifying channel of the measuring device and by some additional techniques [2] some of which are described in the next part. Electromagnetic interference has a broad frequency spectrum, therefore methods of frequency filtering are unsuitable to eliminate it. For this reason it is necessary to shield thoroughly components of instrumentation (gages, amplifiers) and to use circuit design solutions reducing noise level, for example, to apply photon-coupled decouplings. The use of differential AE transducers and preamplifiers with bipolar circuits at input is an effective method to control noise. The transducers are recommended to be installed into a case made of magnetically soft steel. Pulse electromagnetic interference like hum noises, meteors etc are effectively controlled by locking the signal amplification channel during a period when the interference acts. For this purpose measuring devices are equipped with special electronic units. To eliminate electromagnetic interference various circuits of signal timing are widely used. The authors of paper [3] report that the application of such circuits excludes almost completely electromagnetic interference. Yet, we should note that when registering acoustic emission in friction signal timing is not effective without special techniques. Electromagnetic radiation caused by friction is a random sequence of short pulses affecting a transducer which transforms them into electric signals similar to signals of acoustic emission being registered. The main method to control such noise is to shield the receiving channel and the transducer. The transducer should be insulated from the friction pair under testing especially thoroughly

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while reliable acoustic contact should be provided which can be realized, for example, by connecting the transducer with the pair by an acoustic line made of electric insulating material.

3.2. TRANSDUCERS FOR REGISTRATION OF ACOUSTIC EMISSION IN FRICTION Transducers are the most important component of measuring devices. Transducers used to register AE in friction should satisfy a number of requirements depending on operating conditions and specific features of the object being monitored. Among them are: • possibility to perform measurements under operation conditions of the object being monitored (the stability of characteristics under the effect of the environment, heat and radiation resistance etc.); • the uniformity of the frequency response when registering AE within a broad frequency range; • the maximal sensitivity within a selected frequency band; • the simplicity and manufacturability of the design; • protectability from atmospheric electromagnetic interference, vibroacoustic noises, and electromagnetic signals generated by the friction pair under testing; • mechanical strength. A typical transducer serving to register elastic waves and transform them into electric signals for further analysis comprises the following basic members: a converter transforming elastic oscillations into electric signals (a piezoelectric cell), a case, electric contacts and a socket and other members if necessary (a damper, an acoustic line, a protector etc.). If the transducer is remote from the measuring device due to operation conditions it can be combined with a preamplifier of electric signals. Converters of various types can be used in transducers to transform the energy of elastic oscillations into electric signals. Converters involving the direct and reverse piezoelectric effect are most widespread for AE studies. The direct piezoelectric effect or the Curie effect is the appearance of unlike electric charges hence voltage on certain surfaces of a piezoelectric cell covered with metallic electrodes when the cell is mechanically deformed. The reverse piezoelectric effect is the deformation of the cell under the effect of electric voltage applied to the electrodes. The direct piezoelectric effect is used to register elastic waves while the reverse effect serves to induce such waves. About one and a half thousand of natural anisotropic crystalline dielectrics like piezoelectric quartz, tourmaline, Rochelle salt etc. show piezoelectric behavior.

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Yet, since the piezoelectric effect of natural materials except crystalline quartz is weak artificial piezoceramic materials are mainly used in engineering along with quartz. Converters made of ceramics on the basis of lead zirconate-titanate (LZT) with a relatively high Curie point 410  C are mostly used. This ceramics retains its efficiency under normal temperature conditions of water-moderated reactors. Numerous scientific and engineering papers deal with the calculation and design of piezoelectric converters. Therefore we dwell only on some specific properties of piezoceramics important from the viewpoint of measurements under extreme conditions such as elevated temperatures and the effect of ionizing radiation. Characteristics of widespread piezoelectric materials are listed in Table 3.1. Table 3.1. Characteristics of Piezoelectric Materials Type

g 103 kg/m3 E 1011 Pa

Tc   C



Kem

d33  10−11 m/V

LZT-19

70

0.55–0.85

290

1250–1850

0.5

200

LZT-21

70

0.85–0.95

410

400–700

0.16

67

LZT-22

70

0.85–1.00

330

600–1000

0.16

100

LZT-23

74

0.65–0.85

285

1100

0.2

150

LZT-29

70

—

350

500–900

Silica (11)

26

—

576

Lithium niobate

464

—

1210

—

—

4.5

0.095

2.3

29

0.3

7.1

Note:  is the density; E is the Young’s modulus; TC is the Curie point;  is the relative permittivity; Kem is the electromechanical coupling factor; d33 is the piezomodulus. Crystallographic orientation is 33 for piezoceramics, 11 for quartz, 33 for lithium niobate. The values of the characteristics are given at 16–20  C.

LZT ceramics is resistant to neutron and gamma radiation. The study of the radiation resistance of this ceramics has shown that it almost does not change its characteristics at a neutron fluence of 1018 –1022 neutrons/m2 and temperatures up to 200  C. The exposure of the material to radiation with a dose rate of 19 · 105 r.h.m. and an accumulated dose of 135 · 107 r. also did not deteriorate significantly its piezoelectric characteristics. Piezoelectric properties of lithium niobate are poorer than those of LZT ceramics, yet this material has a higher Curie point. Lithium niobate is also

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quite resistant to radiation. Unfortunately, the operation of converters based on lithium niobate at elevated temperatures requires the use of a special inert gas therefore they are not widely applied in practice. Transducers with piezoelectric converters represent the class of generating transducers. Since their output power is small they are connected to the input of an amplifier with a high output resistance and small input capacity. Lower resonance frequencies fr of converters of simple shapes (a thin disc, a rod, a cylinder) are derived from the condition of the generation of a stationary wave in the converters and can be found from the following formula: fr  c/2h where c is the sound speed in the piezoelectric material; h is the characteristic dimension of the converter (the disc thickness for thickness resonance or the disc diameter for radial resonance, the length of a rod or a cylinder for longitudinal resonance). Corresponding resonance frequencies of oscillations of LZT ceramics converters can be calculated as fr = 19h−1 MHz where h is the characteristic dimension in millimeters. An important characteristic of a transducer is the operating frequency range. Depending on the width of the range transducers are divided into resonance and broad-band transducers. When carrying out studies broad-band transducers are preferable. They distort characteristics of registered AE to a lesser extent that is important if to investigate features of acoustic signals accompanying the phenomenon under study. The following three groups of methods are used to widen the frequency range of piezoelectric converters: • methods based on the mechanical and electrical damping of half-wave converters, optimal electric and acoustic matching of the converters and the object being monitored and the measuring instrument, the use of multi-layer converters with active and passive layers etc.; • methods based on the use of special electronic circuits to connect piezoelectric cells; • methods involving the use of piezoelectric cells of special shapes, for example, spherically concave, cells with uneven electric field or specially treated cells. As a rule these methods are used in various combinations. The damping of piezoelectric converters with compounds whose acoustic characteristics are similar to those of piezoceramics is the most widespread technique. The basis of such compounds is a fine tungsten powder or fine piezoceramics, epoxy resin is used as a binder. A broad-band transducer can be easily fabricated from thin piezoceramics discs whose thickness is selected so that the frequency of the first thickness

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resonance exceeds the upper boundary of the frequency range of registered signals. The diameter of the discs is found from the condition that lower radial resonance frequencies of the discs overstep the lower boundary of the transducer frequency pass band. Other radial resonances are rejected by damping, for example, by special fixing of the disc in the transducer case. The sensitivity of resonance converters several times and sometimes a few tens of times better than that of damped broad-band converters. Dimensions of piezoelectric cells are selected so that their resonance frequencies are within the frequency range where conditions for signal reception are optimal, particularly, the signal-to-noise merit is maximal. Since resonance transducers have a relatively narrow pass band they distort significantly the registered signal. When a short AE pulse affects such transducer the latter generates an electric signal with pulled leading and trailing edges in the form of an attenuating sinusoid whose frequency is determined by the basic resonance frequency of the piezoelectric cell. Characteristics of a signal being registered are governed by the technique of bonding of the transducer to the object under testing and the design of the friction unit where the acoustic signal is transmitted. The latter is due to the fact that the object responses to pulse effect mainly at frequencies of its free oscillations whose values depend on material properties and the configuration and dimensions of the friction unit. As a result the transducer receives elastic waves having a frequency spectrum with dominating components close to resonance (definitely speaking, free) frequencies of oscillations of the design being monitored. Besides, when AE signals propagate being a superposition of various types of elastic waves able to transmit into the object the pulse shape is distorted due to wave dispersion. Since the attenuation coefficient depends on the frequency the amplitude of single spectral components of acoustic emission decreases to different extent. For this reason one should warily consider quantitative assessments of signal spectral characteristics. First of all, this concerns friction pairs made of polymeric materials. At the same time, if transducers are fixed stationary to the friction unit variations in the spectrum pattern prove changes in conditions or regimes of friction, this fact can be used in friction unit monitoring. Because the registration of AE signal within a broad frequency band is labor consuming and requires special measures of noise control and the use of narrow-band transducers distorts the signal shape we have propose a compromise alternative of the measuring technique involving the registration and comparison of intensities of AE spectrum components in different frequency bands [4]. For this purpose we used an undamped converter shaped, for example, as a thin disc and having significantly different frequencies of the first thickness and radial resonances. AE signals are registered within frequency bands of these resonances. This technique allows us to use only one transducer when retaining

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a high sensitivity in various frequency bands. Errors resulted from the installation and rearrangement of transducers and their not-identical characteristics are eliminated. Also the effect of the acoustic line of the measuring system on monitoring results is reduced. Frequency bands assigned to register AE are governed by the selection of the converter size. In testing AE transducers are fixed to one of the friction members under monitoring. In order to provide good acoustic contact it is necessary to use a contact liquid, for example, oil. When using oil the transducer sensitivity is almost independent on the pressing force. If it is impossible to place the transducer directly on one of the friction members for some reasons (an elevated temperature of the object under testing, the effect of radiation, straitened space, the presence of a corrosive agent or the necessity to retain high-pure gas atmosphere etc.) acoustic lines can be used to provide acoustic contact with the object. The experience of their application to register acoustic emission under the effect of radiation is described in monograph [5]. The main recommendations are as follows. Long thin rods or wire are best suitable to make the acoustic line. The dimensions of the line are governed by the condition that the band of signal registration frequencies should be as higher as possible than the lower resonance frequency of the line. Lower proper frequencies of oscillations of rods making up the acoustic line are found from the following formulas: the longitudinal frequency – fl = c/2lline ; the flexural frequency – ff = d/8l√ line c. Here d and lline are the diameter and length of the acoustic line; c = E/ is the acoustic speed in the rod; E and  are the Young’s modulus and density of the line material, respectively. The line diameter is found from the condition d ≤ 04c/f , where f is the upper cutoff frequency of AE signal registration. In this case only one longitudinal wave transmits in the acoustic line and the distribution of the oscillation amplitude is quite uniform (at d ≤ 01 c/f the distribution is constant). Usually acoustic lines <10 mm in diameter are used, if it is possible they are made of the same material as that of the member to which they are fixed. The choice of the fixing technique is governed by design and technological conditions, test duration and some other factors. Welding, soldering, calking, pressing through a lubricating film or without it are the most widely used techniques. It is necessary to provide the minimal acoustic resistance of the contact between the object and the acoustic line, contact stability and to eliminate spurious signals generated in the contact zone, for example, due to the slip of the line relatively to the specimen caused by unit vibrations. Members making up the set-up, namely measuring or loading beams, levers, parts of loading devices directly contacting the friction pair under study can be used as acoustic lines. First, these elements should not touch sources of

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acoustic emission not under monitoring, second, they should be protected against oxidation since severe oxidation processes are itself sources of AE signals. The calibration of transducers is an important procedure. It includes the measurement of constants and the determination of dependencies governing the efficiency of the transformation of the mechanical energy of an elastic wave into electric energy and back. The measurement of the transducer amplitudefrequency response and phase response is one of calibration methods. Two types of calibration are distinguished, namely relative and absolute. Relative calibration means the determination of the relative variation of the electric signal amplitude with varying the acoustic wave frequency being registered by the transducer. The determination of absolute values of the conversion factor within a broad frequency band is rather complex. Some compromise is also possible. Relative calibration is performed within a frequency band while absolute calibration is made at a selected frequency. Further, the transducer sensitivity at other frequencies is calculated using the data of absolute calibration [5]. A source of acoustic signals having a broad frequency spectrum is necessary to calibrate transducers. Elastic waves resulted from impact interaction, for example, from the impact of a hard ball against a massive base have such spectrum. An auxiliary drive converter installed on a massive metallic base at some distance from the transducer being calibrated can be used as a signal source. If the dimensions of the drive converter are less than the wavelength of the respective upper frequency limit of the calibration band the frequency dependence of the amplitude of the signal from the transducer under calibration corresponds to its amplitude-frequency response. Acoustic noises generated by a jet of sand or fine shot being strewed on the transducer surface have a broad acoustic spectrum. The transducer with the attached acoustic line can be performed as follows. The acoustic line is immersed into electrolyte solution, for example, the solution of sodium chloride, into which an auxiliary electrode is also immersed. When electric current passes between the line and the electrode gas bubbles appear on the line surface due to electrochemical interaction between the electrolyte and the line metal, they are sources of broad-band acoustic noise. The advantage of the method is that it is very simple. Characteristics of acoustic noises produced by the above mentioned sources can be calculated and used to determine parameters describing the sensitivity of transducers. Calibration methods involving acoustic noises are disclosed in detail in monograph [5]. The National Bureau of Standards of the USA recommends the method of transducer absolute calibration based on the registration of an acoustic pulse appearing when crushing a glass capillary on the surface of a massive aluminum block [6]. At the initial stage oscillations of the massive base are registered by a capacitive transducer having known metrological characteristics. Further, it is replaced by the transducer being calibrated and when breaking a new capillary characteristics of the signal registered by the transducer are compared with

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indications of the capacitive transducer. Characteristics of the transducer under calibration are found from the comparison results. The drawback of the method is the inevitable scatter of characteristics of the elastic wave generated when capillaries are broken. This results from the statistic nature of the strength of such brittle material as glass. Therefore, a random error of measuring characteristics of the transducer appears. This remark relates also the modified technique involving the crushing of a thin graphite rod instead of the glass capillary. The absolute calibration of AE transducers using laser interferometry is apparently the most accurate method at present. Yet, it is quite labor consuming and requires the application of special instrumentation. Since characteristics of registered signals depend on both the amplitudefrequency response of the transducer and the transfer function of the whole acoustic channel as well as the method of fixing the transducer to the object to improve AE data reliability transducers installed directly on the object being monitored should be calibrated. In many cases such calibration is complex and labor consuming. For this reason no data are generally reported on resulting amplitude-frequency responses of measuring systems and absolute values of the sensitivity of transducers installed on the objects under study. Certification of Transducer M 01-91 Working frequency band, MHz 02 20 Sensitivity, V · m2 /N 10−5 Gain flatness within working frequency band, db +6 Output resistance, O 230 Output capacitance, PF 700 Operating temperature range,  C −40 + 85 Maximal humidity, % 90 2 103 Impacts (max), m/s Weight (without cable), g 10 Characteristics of Preamplifier Input resistance, M 2.0 Amplification factor, db 60 Intrinsic noise reduced to input, V 7 The experience of AE tribotests and the recommendations stated above are embodied in transducers which we developed to register AE signals in friction. Figure 3.1 presents some designs of such transducers. They have a piezoelectric cell made of LZT ceramics TC-19 and shaped as a disc which is polarized in depth and leans along its perimeter on a circular recess in the case covered with an insulating glue. The signal output electrode of the cell is soldered to a

INSTRUMENTATION & EQUIPMENT FOR AE IN FRICTION

(a)

107

(b)

8 7 6 5

2 1

4

3

3 37

2 5 1

4

φ7

φ 12

(c)

2

1

3

4

45 No. 1

No. 1

5

(d ) No. 3

Figure 3.1. AE transducers: a – fixing to acoustic line: 1 – case with collet for acoustic line; 2 – piezoelectric cell; 3 – cover; 4 – contact; 5 – spring; 6, 7, 8 – insulators; b – fixing with clamp: 1 – shielded cable; 2 – case; 3 – piezoelectric cell; 4 – insulator; 5 – conductive coating connected to case; c – flange fixing: 1 – high-frequency socket; 2 – high-frequency cable; 3 – conductor; 4 – case with flange; 5 – piezoelectric cell. high-frequency cable cord whose screen is soldered to the transducer case. The second electrode of the cell is tined and connected to the ground transducer case. To improve interference immunity against electromagnetic fields appearing in friction the case is made of magnetically soft steel and covered with a thin layer of the insulating material, namely epoxy resin. The transducers were calibrated using a device developed by Scientific and Production Amalgamation “Dalstandart” (Khabarovsk, Russia). By way of example, we list the ratings of a broad-band transducer used to register acoustic emission in friction.

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3.3. INSTRUMENTATION FOR REGISTRATION OF ACOUSTIC EMISSION IN FRICTION Nowadays vast experience has been gained in the development of AE instrumentation of various purposes from laboratory equipment for studying physical processes being accompanied with AE to commercial instruments intended to monitor structures and processing equipment. Regardless of its purpose and level of complexity any AE measuring system comprises the following basic design units: a unit of electric signal amplification, units of signal characteristic transformation, indication or data presentation. The above units can be embodied in different ways which depend on the purpose of the instruments and their operating conditions. However, many developers of instrumentation intended to test high-pressure vessels, pipelines and other energy-loaded objects and structures obtained quite close results concerning the main characteristics of units of data reduction, namely a similar frequency band of signal registration; a noise level reduced to the preamplifier input; a dynamic range of registered signals as well as control levels of the amplification factor and the discrimination level. Devices differ mainly in the number of signal registration channels, the set of AE informative characteristics being determined and the mode of data presentation. Since the time when portable computers like “Notebook” have become available they are an organic part of the instrumentation. Such information-measuring systems provide wide functionality and are equipped with software and hardware corresponding to their purposes. Depending on purposes the following types of instruments are distinguished: • multifunctional instruments intended for complex studies in laboratory and plant conditions; • special-purpose instruments intended to solve particular research problems or to perform process monitoring. Instruments belonging to the first group have wide possibilities and allow one to register a great number of informative characteristics of acoustic signals. As a rule, such instruments are connected to a computer. They are characterized by polyvalent data presentation involving the output of a great number of intermediate data, for example, various distribution functions of characteristics of AE signals as well as by many adjustments. Special-purpose instruments are developed based on the results of preliminary theoretical and experimental studies of AE accompanying the process being monitored. Characteristics of these instruments are optimized and selected so that to solve best a specific problem, for example, the monitoring of gas or

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liquid leakage etc. Therefore, such instruments are more compact, have a few adjustments and suitable to perform monitoring in operating or field conditions. Information may be presented in an integrated digital, sound or color indicator or in an operator console in any acceptable form. When developing multi-purposed instrumentation the modular approach became the most reasonable. It allows one to widen the functionality of instrumentation, its improvement and the development of new modifications of instruments without radical changes in their structure, for example, by replacing or introducing additional units. Both multifunctional and special-purpose instruments are used to study AE in friction and to monitor friction units. Let us consider two groups of known devices, namely instruments intended for registration within a broad and a narrow frequency bands. Figure 3.2 shows a typical block diagram of a device belonging to the first group. Converter 2 of elastic waves into electric signals made of piezoceramics TC-19 is fixed to stationary member 1 of the friction pair through an oil film. The converter is connected to preamplifier 3 with a coaxial cable. Then the signal is filtered by high-pass filter 4 and amplified by main amplifier 5. Further the signal is transmitted to devices of registration and visualization of data, namely oscillograph 6, frequency meter 7, ratemeter 8, integrator 9 and chart-recorder 10. Pulse former 11 and comparator circuit 12 can also be used. The frequency pass band of electric signals ranges from 0.2 to 1.5 MHz or from 0.4 to 1.2 MHz. P

3

2 5

10 6

1 4

A

7

9

· N

11 8

Figure 3.2. Block diagram of set-up for AE signal registration The block diagram of a device belonging to the second group of instruments used to study AE in friction is shown in Fig. 3.3. An electric signal is transmitted from piezoelectric cell 4 to selective voltmeter 5 acting as an amplifier. As for the rest, the diagram of signal processing is similar to that of devices of the first group. The width of the pass band of the amplifying channel is 1 kHz with the average value of 40 kHz.

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110

6

2

3

4

7

5

8 10

1

11

9

12

Figure 3.3. Block diagram of set-up for AE signal registration: 1 – holder; 2 – specimen; 3 – ball counterbody; 4 – piezoelectric cell; 5 – selective voltmeter; 6 – amplitude meter; 7 – former; 8 – counter; 9 – ratemeter; 10 – recorder; 11 – integrator We emphasize once again that one should warily treat data obtained when using a narrow-band registration system, particularly, a selective voltmeter. AE signals have a broad frequency spectrum (wider than 2 MHz) while conclusions on processes running in a friction unit are made on the basis of the registration of acoustic emission within a narrow frequency band. The use of a narrow band of signal registration is reasonable only in special-purpose instruments when the research stage is completed and characteristics of AE signal containing information on the process being monitored are obtained. In this case the optimal choice of the frequency band improves the interference immunity of instruments. Unfortunately, the performance specifications of the used instruments are not reported in the most papers. Probably, it is caused by the lack of available means to calibrate the whole system of registration and analysis of acoustic emission. However, these data are necessary to analyze correctly the obtained information. Regardless of the functionality area of instrumentation one should take into account the specificity of AE tribological measurements when designing the instrumentation. The specificity is that, first, friction is accompanied by quite strong acoustic emission and, second, as has been mentioned above, noises produced by mechanisms of the testing device or other operating units appear along with AE signals. These specific features govern approaches or principles of processing and transformation of signals being implied when designing measuring devices. At present two such principles are realized. The first principle involves the registration of a total AE signal and one can determine processes running in the friction zone based on variations in signal characteristics, for example, the count rate or energy characteristics. According to the second principle, only those pulses are registered and analyzed whose amplitude exceeds the noise level produced by a normally operating friction unit. If diagnostic characteristics of such signals reach a preset threshold a

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decision on the malfunction of the mechanism under monitoring is taken and its operation becomes inadmissible. The decision-making behavior can be inputted into programmable units of the instrument that provides the full automation of the monitoring process. Depending on the principle being realized one can consider instruments of the first or the second types. The specificity of tribological measurements influences also the choice of basic performance characteristics of AE instrumentation such as the amplification factor and the band of its adjustment, the pass band and the gain slope of filters. Let us briefly consider which reasons should be taken into account when assigning the values of the listed characteristics. Amplification Factor. The amplitude of the signal incoming from the piezoelectric cell depends on the design of the cell, method and place of its fixing, the length of the connecting cable, the dimensions of the acoustic line if any and the friction unit design. For example, in case of rolling friction units the signal amplitude varies from 50 V to 1 mV. Supposing the maximal output voltage of the instrument signal to be equal about 1 V we obtain the variation range of the amplification factor being 103 2 · 104 . For indicator instruments octave discreteness of amplification adjustment is enough. Therefore, one can choose the amplification factor within 1000 16000 with discreteness of adjustment of 6 db. Pass Band. It is known that the upper boundary of the frequency band of vibronoise is 50 80 kHz according to different assessments [7]. Therefore the lower boundary of the instrument pass band should be at least equal to this value. The upper frequency of the pass band is restricted by the highfrequency attenuation of AE signals in the material of the object under testing. For metals the attenuation is substantial only at frequencies of 10 MHz. Taking in mind modern ideas on sources of AE in friction one may not register acoustic emission at so high frequencies. Therefore, the value of the upper boundary of the pass band is not very important and depends on the circuit design of the instrument. As experience has shown it is enough to select this value equal 1–2 MHz. The frequency response falloff slope from the side of low frequencies is an important characteristic. The studies have shown that the frequency spectrum of vibronoise drops with a slope of 25 10 db/octave with increasing frequency. To suppress vibrations well it is necessary that the instrument gain slope exceed the corresponding value of the vibronoise frequency spectrum. If well-known and widespread active fourth-order filters are used for signal filtering then the frequency response falloff slope from the side of low frequencies is approximately 24 db/octave. Taking into account experience gained when studying AE and results of studies of acoustic emission in friction of solids one can formulate the basic engineering requirements to AE instrumentation.

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Instrumentation should • have a high input resistance for matching with the electromechanical transducer of acoustic waves; • have a discretely or continuously variable signal amplification factor; • have adjustable lower (LL) and upper (UL) signal discrimination levels; • contain a unit of continuous or tunable filters; • be equipped with matched external recorder outputs to record and analyze signals in analog and (or) digital formats; • measure assigned characteristics of AE signals and indicate measurement results. We developed several instruments to register and analyze AE in friction [8, 9]. The base device in this series is ‹ƒ−l‡ƒ−ƒ instrument. According to our classification it belongs to the first type of instruments and carries out the following functions: the reception of acoustic signals being a composition of a pulse useful signal and a noise which can be both continuous and pulse; preamplification, filtering and final amplification; the determination of the pulse amplitude, the discrimination of pulses with an adjustable threshold; the formation and standardization of pulses; the indication of the count rate. The block diagram of the instrument is shown in Fig. 3.4. An acoustic signal registered by the transducer comes to the preamplifier having the highpass filter at 100 kHz and then to the discrete filtering unit comprising the high-pass filters with frequencies 100 (the end-to-end channel), 300, 500 and 700 kHz. In the end-to-end channel the signal is amplified, detected and further divided into two channels. One of them serves to integrate the signal and to output it to secondary recorders in analog format. In the second channel the signal comes to the peak detector and then to the pulse analyzer or integrator or it can be outputted to external recorders (a chart recorder, an oscillograph, an

11

1

3

2

4

6

7

t n f

~ ~

5

10 PV

9 G

f

u

8 0000

Figure 3.4. Functional diagram of ‹ƒ−l‡ƒ−ƒ instrument: 1 – high-pass filter; 2 – adjustable main amplifier; 3 – detector; 4 – discriminator; 5 – pulse duration former; 6 – frequency divider; 7 – ratemeter; 8 – visual indication unit; 9 – second pulse generator; 10 – power unit

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indicator etc.) in analog format. Also the signal can be outputted to the recorders from other three discrete filters. The time chart of the basic unit is shown in Fig. 3.5. The signal coming to the preamplifier input is generally an additive composition of the useful signal, the pulse electronic interference, the signal generated by other friction pairs and the low-frequency vibration signal. The experience has shown that vibrations are the strongest source of interference. For this reason we restrict ourselves by the case when only the vibration and acoustic emission signals come to the (a)

U

1 2 t

2 (b)

1

U

3

t 2 (c)

4

5

U

t

6 (d )

U

(e)

U

7

t

t

Figure 3.5. Time diagram of main unit operation: a – output from transducer; b – output from preamplifier; c – output from main amplifier; d – output from detector; e – output from pulse former; 1 – vibration noise; 2 – useful noise; 3 – preamplifier noise; 4 – discrimination level; 5 – amplifier noise; 6 – detected signal; 7 – normalized signal

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preamplifier input (Fig. 3.5, a). The preamplifier produces a combination of the amplified acoustic emission and attenuated vibration signals and the preamplifier intrinsic noise (Fig. 3.5, b). The main amplifier yields the amplified AE signal, the intrinsic noise of the preamplifier-amplifier system and the vibration signal attenuated by the high-pass filter (Fig. 3.5, c). The attenuation factor of the vibration signal equals 80 db. After detection (Fig. 3.5, d) and discrimination the number of events whose amplitude exceeds the preset threshold is determined. When using the pulse former (Fig. 3.5, e) amplitude analysis can be performed by standard pulse analyzers. The instrument provides the light indication of the overload of the preamplifier and main amplifier. The following characteristics of acoustic emission can be registered: the count rate, the spectral density and the amplitude distribution. Based on these data one can determine almost all informative characteristics of AE using known calculation methods. The instrument has shown to advantage when studying the efficiency of sliding bearings. The intrinsic stationary noise of such bearings is low therefore the total AE signal characterizes the process of friction to a good extent. The characteristics of the instrument (without the preamplifier) are listed in Table 3.2. The structural diagram of the measuring system based on ‹ƒ− instrument is presented in Fig. 3.6 and its appearance is shown in Fig. 3.7. At present several modifications of ‹ƒ− instrument have been developed with different ranges of the amplification factor, operating frequency bands, overall dimensions and weight, line supply or supply by an internal DC source. Figure 3.8 represents the functional diagram of the compact autonomous instrument ‹ƒ−l‡ƒ−ƒlŠ‹ intended for the on-line monitoring of friction units. The second principle of AE instrumentation design has been realized in this device, i.e. an electric signal generated by the piezoelectric cell comes to the input of former 1 which forms the operating frequency band and performs signal preamplification. The amplified signal comes to the input of envelope detector 4 selecting the process envelope Uc . When integrating the envelope with a time constant of about 1 s unit 5 forms the lower discrimination level Udl . The envelope and the voltage Udl come to inputs of amplitude discriminator 7 selecting the discrete AE component. The appearance of the signal Uk at the output of the amplitude discriminator indicates the presence of an AE pulse. To reduce the effect of reverberation and noises timer 9 is used which is triggered in the absence of Uk and after 100 s produces the chain of short pulses T1 and T2 . The expectation of the discrete AE component is determined as follows. The signal envelope comes to the input of peak detector 6 which stores its peak value. In 100 s after AE signal transmission timer 9 produces the pulse T1 serving to rewrite the peak detector voltage into choice and storage device 8. The next pulse T2 dumps the voltage on the peak detector.

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Table 3.2. Characteristics of ‹ƒ−l‡ƒ−ƒ Instrument Amplification factor of main amplifier (is varied stepwise), db Pass band, kHz

40, 46, 52, 56, 58, 60 100–2000

Slope of filter edge, db/dec

60

Maximal amplitude of output signal within pass band, V

8

Gain compression, %

3

Input resistance of preamplifiers, M

2,4

Input capacitance, pF

8

Average square of intrinsic noise reduced to input within pass band, V

5

Amplification factors of preamplifiers, db

1.4; 20; 40; 100

Dynamic band of amplifier, db

40

Time constant of detector, s

20

Overall dimensions, mm Weight, kg

300 × 200 × 80 5

The signal from the output of 8 is averaged by low-pass filter 10. It is easy to see that the signal of 8 averaged over a quite long period does not depend on the AE pulse repetition rate and is equivalent to the expectation of the acoustic emission pulse amplitude. The instrument contains voltage stabilizer 2 and separate indicators of overload and battery discharge 3. The characteristic being measured is the amplitude of the discrete AE component. The output characteristic is the expectation of the amplitude of the discrete AE component. This characteristic is indicated by the pointer indicator graduated in relative units. The position of the amplification factor switch determines the scale factor. The main characteristics of ‹ƒ−l‡ƒ−ƒlŠ‹ instrument are listed in Table 3.3. The procedure of bearing monitoring involves the comparison of current values of AE diagnostic characteristics with their threshold values. The frequency band of signal registration, the certain diagnostic characteristic or the set of characteristic and their threshold values should be selected with account for conditions of equipment operation, load, power etc. Tests are performed periodically and the frequency of monitoring increases with prolonging time of unit operation.

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16 1

2

3

4

To recoder

5

14

15

18 11

12

13

6 7 10 8

9

19

20 24

17

21

22

25

23

To recoder To recoder

Figure 3.6. Block diagram of registration, selection and analysis of AE signals: 1 – disc specimen; 2 – pin specimen; 3 – specimen holder; 4 – AE transducer; 5 – piezoelectric cell; 6 – strain-measuring beam; 7 – strain gage; 8 – thermocouple; 9 – DC amplifier; 10 – strain-measuring amplifier; 11 – preamplifier; 12 – high-pass filter; 13 – main amplifier; 14 – spectrum analyzer; 15 – storage oscillograph; 16 – camera; 17 – oscillograph; 18 – frequency meter; 19 – transcription system; 20, 23 – operating console; 21 – detector; 22 – pulse analyzer; 24 – ratemeter; 25 – recorder. Units 11, 12, 13, 21, 24 are ‹ƒ−l‡ƒ−ƒ instrument

Based on ‹ƒ− device we have developed special-purpose instruments for friction pair monitoring [8, 10]. Let us consider briefly their operation principle. Figure 3.9 represents the block diagram of the instrument intended for the automatic determination of the instant when a friction pair stops to run-in using two characteristics, namely the count rate and the pulse amplitude variance [8]. Adjusting the initial level of signal registration (“zero”) in unit 8 and the duration of data storage in unit 7 one can determine the measure of approximation to the run-in state and assign the measurement accuracy of the running-in completion. The method and device with improved interference immunity hence providing high diagnostic validity have been developed to monitor the efficiency of sliding bearings [10]. The operation principle of the device is explained in Fig. 3.10. It is known that the loaded bearing has two regions of the minimal and maximal loading disposed approximately at an angle of 30 relative to the vertical axis in the rotation direction. In these regions the probability of the damage of a lubricating film and friction surfaces is minimal and maximal, respectively.

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(a)

117

(b)

(c)

Figure 3.7. AE instruments for friction and wear studies and condition monitoring of bearings: a – instrument for condition monitoring of bearings equipped with built-in transducer; b – instrument for studying tribological and strength characteristics of coatings; c – compact version of instrument b Proceeding from the analysis of the maximum possible signal amplitude only those signals are registered which appear in the zone of maximal loading. Transducers are located on the bearing surface over points of extreme loading. The signals registered by the transducers are shifted in time and have different amplitudes. The amplitude of the signal of the transducer located within the maximal loaded region is the highest. As damages accumulate the difference in signal amplitudes rises. The difference in amplitudes and the registration time of signals depends on the bearing overall dimensions and the lubricant composition and can be experimentally determined for every certain type of the bearing. Results of the comparison of AE signal characteristics registered by the transducers allow estimating the condition of the bearing.

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1

Uc

4

Ud

T1

Uk 7

9

T2

5

U

2 +10 V

6

10

8

3

Figure 3.8. Functional diagram of compact autonomous instrument ‹ƒ−l‡ƒ−ƒlŠ‹

Table 3.3. Characteristics of ‹ƒ−l‡ƒ−ƒlŠ‹ Instrument Amplification factor Variation step of amplification factor, db Pass band at level of 3 db, kHz

103 16 · 104 6 100 500

Input resistance, M

1

Intrinsic noise, V

10

Consumption current, mA

≤30

With scale illumination, mA

≤75

Overall dimensions, mm Weight, kg

245 × 85 × 200 3

3.4. EQUIPMENT FOR STUDIES OF ACOUSTIC EMISSION IN FRICTION The study of AE in friction of materials requires the use of set-ups allowing one to realize various modes of relative motion and geometries of friction contact between members. They should provide measurements within broad load and velocity ranges in different environments including vacuum. The selection of the contact geometry is important when designing AE friction machines. In our opinion, the “pin-on-disc” geometry is the most advantageous among all variety of designs. A doubtless merit of the geometry is its

INSTRUMENTATION & EQUIPMENT FOR AE IN FRICTION

1 0

3

2

5

7

6

7

5

7

6

7

119

8

4

9

10

8

Figure 3.9. Block diagram of instrument for automatic determination of running-in end using two AE characteristics (count rate and pulse amplitude variance): 1 – AE transducer; 2 – preamplifier; 3 – main amplifier; 4 – electronic switch; 5 – pulse counter; 6 – unit of amplitude variance determination; 7 – internal storage; 8 – comparator circuit; 9 – control unit; 10 – recorder

30° 5 4

1

6 &

2 7

3

F

Figure 3.10. Block diagram of device for bearing efficiency monitoring: 1, 2 – bearing (shaft, insert); 3, 4 – AE transducers; 5 – unit of preliminary processing of AE signals (amplification, filtering, detection, discrimination); 6 – comparator circuit; 7 – delay circuit simplicity. The members are a disc with the flat working surface and a counterbody being a spherical or cylindrical indentor. In this geometry the overlapping factor is close to zero that provides a great effect of the environment on the friction and wear processes and reduces the influence of thermal processes on measurement results. When using the spherical indentor one can install the members less accurate and the design of the indentor attachment unit can be substantially simplified. We used the “pin-on-disc” geometry in set-ups −‹ƒ…ƒ‰. These setups served to study acoustic emission in friction and adhesion of materials, the results of the studies are discussed in the next chapter. Unlike commercial

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machines ‡Š4l and ‡ our set-ups have some specific features improving the reliability of test data. First, to reduce interference when registering AE we took special measures to improve the sound insulation of auxiliary systems of the set-ups. Particularly, low-noise motors are applied installed on separate bases through dampers. Elastic members are used to transmit motion from the motor to the set-up. Second, the attachment unit of the spherical indentor is made as a rocker to improve metrological characteristics. One or both arms of the rocker serve as sensors of the dynamometering system. The advantage of such attachment is that one can examine the working surfaces without dismounting specimens. Third, all set-ups of −‹ƒ…ƒ‰ type comprise specially chosen AE transducers with almost the same amplitude-frequency response that allows one to compare results of tests performed under various conditions. Also similar specimens-indentors can be used in all set-ups. Table 3.4 lists the characteristics of set-ups of −‹ƒ…ƒ‰ type. Table 3.4. Characteristics of −‹ƒ…ƒ‰ Set-Ups Characteristics Type of main motion Velocity range, mm/s

−‹ƒ…ƒ‰-1

Designation of set-up −‹ƒ…ƒ‰-B

Rotational unit-directional Rotational unit-directional

−‹ƒ…ƒ‰lŠ Reciprocal

20–20000

20–1000

0.2–1.0

Normal load range, N

0.5–50

0.1–4

0.5–10

Environment, T = 300 K

Air

Controlled, vacuum

Air

Error of velocity setting, %

10

10

4

Error of load setting, %

1

1

2

Error of friction force measurement, %

4

4

4

Error of temperature measurement,  C

±1

±1

±1

Maximal face motion variation of disc specimen,

m

±5

±3

–

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It is seen from data of the Table that these set-ups are suitable to carry out tests of materials within quite broad velocity and load ranges, in various gas environments and in vacuum and when introducing radiation, for example, laser radiation into the working zone. Such possibility allows solving some new problems in tribology, surface physics and solid physics. The overlapping factor ranges from 0 to 0.8 in these set-ups. Their design features are considered below. 1

2

3

4 5

9 10 6 7

12

8

11 14 15 16

13

Figure 3.11. Set-up −‹ƒ…ƒ‰l The set-up −‹ƒ…ƒ‰l (Fig. 3.11) is intended to perform tests at atmospheric conditions and involves the geometry “the rotating disc – the stationary pin”. Direct-current motor 1 with variable speed serves as a drive. Belt drive 2 transmits motion from the motor to the spindle pulley equipped with device 3 for continuous measuring the rotation speed comprising the stroboscopic disc, the photocell and the tachometer. To reduce the face motion variation of the disc specimen a commercial high-speed internal wheelhead with liquid lubrication served as spindle 4. The motion variation of the wheelhead working cone to which face plate 5 is fixed amounts to 4–6 m. The working surface of the

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plate was finally ground together with the spindle. As a result, the face motion variation decreased to 0.5–1 m. Movable disc specimen 6 is mounted on the plate working surface. Stationary specimen 7 with transducer 8 is fixed into the holder installed on strain-measuring cantilever 9. The cantilever has strain gages glued on it and serving to measure the friction force. Another strain-measuring cantilever 10 is used to measure the normal load. These cantilevers act as both carrying and measuring cantilevers and are additionally the arms of rocker 11 used to attach the indentor. The friction pair is loaded by weights 13 hanged on the rope sliding over pulley 12. The radius of the friction track is varied by changing the relative position of the specimens. The position is set by moving the whole attachment unit mounted on slide rest 14 with the help of screws 15 of longitudinal and transverse motion relative to base 16. Since the sliding velocity can reach 20 m/s the measurement of the contact temperature is provided. The temperature is measured by a chromel-alumel thermocouple touching the working face of the indentor. Figure 3.12 explains the technique of fixing AE transducers to the indentor.

1

2

3

4

7

5

6

5 (a) 4 3 2

1

(b)

Figure 3.12. Fixing of AE transducers to specimens (indentors) in −‹ƒ…ƒ‰l (a) and −‹ƒ…ƒ‰lŠ (b) set-ups: a – 1 – nut; 2 – specimen holder; 3 – PTFE washer; 4 – AE transducer; 5 – specimen; b – 1 – specimen; 2 – specimen holder; 3 – AE transducer; 4 – case; 5 – nut; 6 – cover; 7 – cable

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The set-up −‹ƒ…ƒ‰l" (Fig. 3.13) is intended to perform tests in special gas environments and in vacuum 13 · 10−3 Pa. Shaft 1 transmits rotational motion from the drive (is not shown in the Figure) to specimen stage 4 through hermetic feedthrough 2 arranged in the bottom of vacuum chamber 3. Rotating disc specimen 5 is placed on the stage and fixed by nut 6. A depression appearing above the specimen working surface can be filled with a liquid if necessary. Stationary specimen 7 is fixed into specimen holder 8 which is mounted on strain-measuring cantilever 9 intended to measure the friction force. The cantilever is one arm of the rocker serving to attach the indentor and rocking on axis 10. Another rocker arm is made as screw 11. Counterweight 12 can be moved along the screw to set the normal load. The relative position of the specimens is changed by moving the whole attachment unit along the dovetail guideways installed on base 3.

13 12 11

10 9 8 7 6 5 4 3 2 1

14

Figure 3.13. Set-up −‹ƒ…ƒ‰l" The whole set-up is covered with glass cap 13 and connected to the vacuum system or the system filling the cap with gas (these systems are not shown in the Figure). In order to improve metrological characteristics AE preamplifier 14 is placed close to the transducer. The set-up −‹ƒ…ƒ‰lŠ (Fig. 3.14) is intended to perform tests in air at slow velocities of reciprocal motion. This makes it possible to register AE signals from both specimens simultaneously.

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1

18

2

14

3

13

4 10 9

5

8

7 5 6 17 16

15

12 11

Figure 3.14. Set-up −‹ƒ…ƒ‰lŠ

Compact low-speed low-power electric motor 1 with high transmission ratio is used as a drive. Rotation is transmitted to the feed screw through the rubber coupling and worm gearing 2, 3. The feed screw drives slider 5 moved in guides 6 by screw 4. The velocity of slider motion can be changed by replacing the motor or the worm gearing. Rest 7 is installed into the slot of the slider, it can be moved by cross-feed screw 8 to adjust the specimens. Flat movable specimen 9 and AE transducer 10 are fixed to the rest. The transducer registers acoustic signals from the movable specimen through indentor 11. Stationary specimen 12 is fastened into another head 13 installed on strain-measuring cantilever 14 serving to measure the friction force. The cantilever is one arm of the rocker which is used to attach the indentor and rotates on axis 15. Counterweight 16 is placed on another rocker arm. The normal load is varied by moving the counterweight along screw 17. Cables 18 are connected to the device of the registration and processing of acoustic signals. A specific feature of the set-up is the possibility of the simultaneous registration of AE appearing in both specimens. The transducer is fixed to the flat specimen by the flanges (Fig. 3.12, b). To test rolling bearings we have developed the set-up −‹ƒ…ƒ‰l… whose schematic is presented in Fig. 3.15. The set-up is intended to study acoustic emission when defects in rolling bearing members such as rolling elements, cages etc. develop and are simulated. It comprises a housing to insert the

INSTRUMENTATION & EQUIPMENT FOR AE IN FRICTION

6

125

7

8

5 4

9 10

3 2 1

11 12

15

14

13

Figure 3.15. Set-up −‹ƒ…ƒ‰l… bearing under testing, a joint box, a direct-current motor with variable speed, amortization bases and measuring devices including AE instruments. Shaft 1 with bearings 3 is fixed in supports 14 and driven with the motor by belt drive 8. This reduces noises caused by the vibration of the motor. Rolling bearings under testing 15 are installed on the cantilever journals of shaft 1 from both sides. The bearings are fastened with nuts 11. The outer rings of bearings 15 are fixed into special clamps 9 transmitting the load. Also transducers 12 are placed on the clamps. The bearings are loaded by rotating screw 6. The load is transmitted to clamps 9 through strain-measuring ring 7 and beam 4. The outer rings of the bearings and the clamps are fixed by screws 5. The use of removable adapter sleeves 2 allows one to test bearings of various dimensions and types. In addition to some obvious design advantages the two-cantilever loading device makes it possible to perform comparative tests of bearings of the same type one of which is reference part. Since both bearings operate under same conditions the effect of different interference on the test results is reduced to zero. These set-ups were used to obtain regularities of AE in friction of metals which are discussed in Chapter 4. The data and their analysis have formed a basis to developed engineering methods of AE diagnostics of the condition and efficiency of friction units of machines and mechanisms which are described in Part 4.5.

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3.5. SET-UPS FOR STUDIES OF FRICTION OF NUCLEAR-POWER ENGINEERING MATERIALS Experience gained when developing −‹ƒ…ƒ‰ set-ups and in their operation has been used to design in-channel experimental devices for tribotests of nuclearpower engineering materials under the effect of ionizing radiation in the active zone of a research reactor. Progress in nuclear engineering tribology is governed by problems arising when selecting materials for parts of the active zone of various nuclear reactors and when developing means and devices for the monitoring of friction units used in process equipment of nuclear power plants [11, 12]. The method of AE is highly useful in intrareactor (in the reactor active zone) studies of the friction of fuel materials against the fuel element jacket. Theses studies are the part of the investigation of mechanical interaction of fuel with reactor jackets. Fuel elements of the most widespread water-moderated and reactors are a thin cylindrical jacket made of zirconium alloy within which fuel pellets of uranium dioxide are inserted. Temperature conditions in the reactor change when it is heated or stopped or when its power is varied. Since thermal expansion coefficients of the fuel and the jacket material are different these parts shift with varying temperature. In this case the seizure of the fuel pellets causing the deformation and failure of the jacket should be avoided. To reduce negative effects of interaction between the fuel and the jacket various barrier (protective) inner coatings of the jackets are used having a lesser friction coefficient against the fuel material. The determination of the efficiency and resistance of such coatings forms the subject of tribological studies. The next problem is to study the friction of materials of sliding bearings used in process devices of the primary-coolant system of high-temperature gascooled nuclear reactors. The reliability of these devices governs the operating safety of the whole nuclear power plant. Intrareactor studies are expensive, labor consuming and specific. Many experimental devices are necessary to carry out such investigations from laboratory devices serving to perfect methods and engineering solutions and to select materials to in-channel apparatuses intended for direct measurements within the reactor active zone. Let us note the specific features of intrareactor studies and give the recommendations necessary when developing methods and designing in-channel devices: • a long length and a small diameter of study channels of the reactor; for example, the distance between the cover of a research reactor of ƒ‹4 type and its active zone amounts to 7 m while the diameter of a channel within which the device should be installed is only 20–52 mm;

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• significant restrictions when selecting materials. Materials should not be activated by reactor radiation and should not distort substantially the neutron flux distribution; • journals of the system transmitting main motion should not be placed in the active zone; • simple and fast replacement of single units of devices located immediately close to the active zone should be provided; • a required number of channels for filling and exhausting the working zone of the devices with inert gas and for laying wiring without destroying the biological shielding of the reactor channel plug should be made.

1

2

3

4 3

5 6

8

7

2

14

9 15 10 16 11

17

12 13

Figure 3.16. Schematic of 4‹%…l set-up Figure 3.16 illustrates the schematic of 4‹%…l device intended for laboratory tribotests of the “fuel pellets — jacket material” pair. The loading device with adjusting screws 2 is installed on baseplate 14 of vacuum chamber 1. The loading device loads fuel pellets 3 with a necessary force by bellows 7. Flat movable metallic specimen 4 is fixed to rod 8 which is introduced into the chamber through bellows 9 and is set in reciprocal motion by the drive arranged outside the chamber. Heater 5 surrounds the zone of contact. The temperature of

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the metallic specimen is measured by thermocouple 6 embedded into a drilled channel going from the specimen lateral surface to the center of the working zone. Also thermocouples are installed in every fuel specimen (through the central hole). Nipple 15 serves to exhaust and fill the chamber with helium to atmospheric pressure. The force of friction between the specimens is measured by strainmeasuring ring 10 built into rod 8. The driving device comprises reversible electric motor 16, belt drive 17, screw pair 13 and bearing guides 11 of rod 12 which include rolling bearings. Bearings with dampers and the belt drive are used to eliminate the vibration of the motor. The stroke and speed of the movable specimen are varied from 8 to 50 mm and from 0.1 to 20 mm/s, respectively. The bellows device provides load up to 1300 N. Figure 3.17 represents the geometry of the friction unit. AE signals are registered by transducer 4 made as a screw and providing good acoustic contact between the transducer case working surface and the flat specimen. The further processing of signals is performed by ‹ƒ−l‡ƒ−ƒ instrument. This geometry of friction contact is advantageous as to the possibility of testing standard pellets of uranium dioxide shaped as cylindrical inserts with the outer diameter 7.5 mm and the inner diameter 1.5 mm and about 10 mm tall. Pellets were selected for experiments whose end working surface roughness was Ra = 09 18 m and having no noticeable cracks and chips. To find

1 2 P

P

v 3 4 5

Figure 3.17. Design of friction unit of 4‹%…l set-up: 1 – flat specimen; 2 – pellet specimen; 3 – specimen holder; 4 – AE transducer; 5 – rod

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internal defects in the pellets such as cracks, blisters, large pores they were examined by ultrasonic spectroscopy. The flat specimen made of zirconium alloy Zr + 1% Nb is shaped as a slab with dimensions 80 × 12 mm and 2 mm thick. Such thickness provides a required longitudinal rigidity in order to “pull” the loaded specimen and to “push” it when the motion direction changes. It is important if to have in mind that the specimen is fixed to the rod like a cantilever (Fig. 3.17). The Vickers hardness of the metallic specimens is HV = 1300 2300 MPa and their working surface roughness ranges within Ra = 02 03 m. The specimen surfaces were treated in the same way as the surfaces of common fuel element jackets. Similar specimens and friction geometries were used in intrareactor devices developed to carry out tests in vertical channels of ƒ‹4l‡ƒ−ƒ reactor at neutron flux densities from 1 · 1016 to 2 · 1017 neutrons/m2 · s. The results of the registration of AE in friction of the fuel and the jacket materials obtained in laboratory conditions are described in Chapter 5. yPT-4 device equipped with the “Pincers” loading system is intended for operation in the vertical research channel 52 mm in diameter at neutron flux densities up to 2 · 1017 neutrons/m2 · s. The maximal friction force amounts to 2500 N. The schematic of the device is shown in Fig. 3.18, a. The flat specimen placed into removable capsule 4 is set in motion with drive 1 through feedthrough 2 and biological shielding 3. The removable capsule (Fig. 3.18, b) has system 5 to connect to electric sockets and gas joints allowing fast mantling and dismantling of the capsule, compensating system 6 serving to supply communications to movable parts of the device, complex measuring system 7 and loading system 8 with the specimen under testing installed in the reactor active zone. The connecting system allows one to remove the capsule quick and simply and facilitates the installation of the device into the reactor. The “Pincers” loading system operates as follows (Fig. 3.19). Bellows mechanism 1 produces force up to 1500 N under the pressure of gas being supplied through pipe 2. The force is transmitted to levers 5 by rod 3 and bars 4, the levers counterrotate around axes 6. Cylindrical specimens 7 are fixed to the levers. The transmission ratio of the lever system is so that the force applied to the specimens can reach 250 N. The general view of the system is presented in Fig. 3.20, a; one of the levers is dismantled from journals and turned (Fig. 3.20, b). The structure of the complex measuring system of yPT devices is shown in Fig. 3.21. Friction forces resulted from interaction between specimens 1 and 2 are transmitted to measuring ring 4 arranged close to the reactor active zone through cantilever 3. The measuring rings are connected to drive rod 10 by bar 8 with spherical journals 7 and 9 to compensate tilt distortions which may appear

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130

1

2

0

3

φ 54 4 3260

3260 5

4000

6 4760

7

8 6600 6850 (a)

(b)

6510 6600 6850

Figure 3.18. Design of in-reactor devices for study of solid friction: a – ®‹4-4 set-up; b – removable capsule of ®‹4-4 set-up when assembling the system. The planes of the measuring rings are rotated at 90 relative to the movable specimen plane that reduces the specimen alignment error. The general view of the measuring system is shown in Fig. 3.21. In the center of the figure one can see the measuring ring arranged close to the reactor active zone and the gas joint of the loading system. The main drawback of this measuring system is that its sensitive elements (strain gages, as a rule) are located in the irradiated zone. For this reason their sensitivity can vary in time. To arrange them outside the irradiated zone it is necessary to use intermediate journals on the rod. Yet, friction in these journals produces errors when measuring the force of friction between the specimens. At the same time, as the studies have shown the sensitivity of the gages connected into differential circuit changes insignificantly at neutron fluxes typical for

INSTRUMENTATION & EQUIPMENT FOR AE IN FRICTION

6

131

6 5 7

5

4

4 3

2 1

Figure 3.19. Loading system of in-reactor device

Figure 3.20. General view of “Pincers” loading system

ƒ‹4l‡ƒ−ƒ reactor and test duration required to reveal basic regularities of the radiation effect on tribological behavior of the materials under study. The developed devices served to carry out laboratory and intrareactor investigations on determining the tribological behavior of the jacket and the fuel materials and assessing the wear resistance of different barrier coatings of fuel element jackets of nuclear reactors. Main results of these studies are discussed in Part 5.2.

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4010 10

4760 9 4890 8 5275

5385

7

6

5510 5 6260 6385

4

3 6600

2 1

Figure 3.21. Design of measuring system of Y‹4 set-ups

REFERENCES 1. A.A. Pollock. Acoustic emission–2. Acoustic emission amplitudes, Non–Destructive Testing, 1973, vol. 6, no. 10, pp. 264–269. 2. K.V. Williams. Acoustic Emission, Bristol, Hilger, 1980. 3. V.V. Klyuev, F.R. Sosnin, V.N. Filinov et al. Non-Destructive Monitoring and Diagnostics. Handbook. Ed. by V.V. Klyuev (in Russian), Moscow, 1995. 4. V.M. Baranov, E.M. Kudriavtsev, and G.A. Sarychev. The analysis of acoustic emission frequency spectrum at friction, Journal of Friction and Wear, vol. 15, no. 6, 1994, pp. 40–46. 5. V.M. Baranov. Acoustic Measurements in Nuclear Engineering (in Russian), Moscow, 1990.

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6. N.N. Hsu and F.R. Breckenridge. Characterization and calibration of acoustic emission sensors, Material Evaluation, 1991, vol. 39, no. 1, pp. 60–68. 7. I. Balogh. The formation of spherical particles under abrasive conditions, Period. Polytechn. Mech. Eng., 2002, vol. 46, no. 1, pp. 29–35. 8. USSR Patent no. 1128136. Device for monitoring of efficiency of bearing. V.M. Revenko, G.A. Sarychev, and V.M. Schavelin, Bulletin of Inventions (in Russian), 1984, no. 45. 9. USSR Patent no. 1158903. Method of determining moment of completion of friction pair running-in. V.M. Schavelin, G.A. Sarychev, M.I. Shakhnovskii, V.M. Revenko, I.G. Goryacheva, M.N. Dobychin, and O.V. Kholodilov, Bulletin of Inventions (in Russian), 1985, no. 20. 10. USSR Patent no. 1244565. Device for determining moment of completion of friction pair running-in. G.A. Sarychev, V.M. Schavelin, and V.M. Revenko, Bulletin of Inventions (in Russian), 1985, no. 20. 11. E.J. Robbins. Tribology for the atomic and space industries, Industries Atomiques Spatiales, 1974, no. 2, pp. 1–11. 12. W.H. Roberts. Tribology in nuclear power generation, Tribology International, 1981, no. 2, pp. 17–27.

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Chapter 4

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

4.1. ACOUSTIC EMISSION IN RUNNING-IN OF FRICTION SURFACES When designing friction units of machines and mechanisms one should solve, as a rule, the following common problems: • selection of friction materials and assessment of their wear resistance; • selection and determination of the resistance of solid-film lubricants; • study of the efficiency of friction units in non-stationary regimes (running-in, transient regimes) and when varying friction conditions such as the velocity, load, composition and state of the environment. As experience has shown, the application of AE method facilitates to solve these problems. The results obtained in the studies can form the methodical basis for the development of methods and equipment to monitor friction units in operation. This chapter describes the study results of dependencies of AE characteristics on friction regimes and conditions. Experiments were carried out on set-ups described in Chapter 3 (F1, FP, FV). AE was registered and analyzed by the measuring system based on RIF instrument. As it is known [1], running-in results in the appearance of surface roughness optimal under given conditions which is spontaneously reproduced during some period and does not depend on the initial roughness. Surface microasperities shape in such a way that friction and wear losses are minimal under the given conditions and the stability of a lubricating film is maximal. The stress-strain state of surface layers also changes, i.e. microasperities pass into elastic contact. The non-uniformity of stress distribution over real contact spots decreases with increasing friction path and stresses become uniform at the end of running-in [2]. Thin-film structures are formed on friction surfaces resistant to physical and chemical effects. Repeated loading changes the dislocation structure in surface layers [3] and depending of external factors and material properties the materials either soften or become harder and more brittle; also they can transit to the quasi-liquid state. These processes result in a decreased wear rate. From statistical viewpoint both friction and wear during running-in are nonstationary random processes. If external parameters are constant the tribosystem including the friction surfaces, the third body and the environment evolves to

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a non-equilibrium stationary state in which exchange and dissipation of energy occur. Characteristics of the system and parameters of its state become singlevalued functions of external factors. At the end of running-in friction and wear proceed in the steady-state mode and this state retains until the third wear stage, namely friction pair failure occurs. It is apparent that AE characteristics representing the dynamics of changes of the surface stress-strain state should follow all mentioned stages of tribosystem evolution during running-in, that is, indeed observed in experiments. Table 4.1 lists typical dependencies of AE characteristics on time during running-in under dry friction conditions. A common tendency is seen when the count rate, mean amplitude, variance, and AE energy decrease to some values and then become stable. Dependencies of the mentioned characteristics can be both monotonous and extreme. Table 4.1. Variation of AE parameters in friction time N˙ · 10−3  s−1

A¯ , rel. units

 2 , rel. units

E, rel. units

672

604

915

306

6 · 103

1718

556

768

664

12 · 103

290

498

657

91

346

364

21

Time, s 8

192 · 103

1372

Note: Disc (steel 45) – pin († 20) friction pair; F = 5 N v = 13 m/s, without lubricant.

The influence of the friction path on AE characteristics under boundary friction conditions with liquid lubricants and greases was studied on F1 set-up. The following friction pair was selected: the brass †62 disc – the steel 45 pin. Initially, degreased and dry surfaces were tested at a velocity of v = 045 m/s  = 24 s−1  and a load of F = 3 N. These conditions were retained until the steady-state friction occurred, the occurrence of the steady-state mode was determined by the friction coefficient and AE count rate (Fig. 4.1). Then a drop of oil MC-20 was added into the contact zone. In tests the count rate, the amplitude distribution, and the spectral density of AE pulses were continuously registered. The observation time when determining the mentioned characteristics was 20 s. Figure 4.2, a presents the probability density of AE pulse amplitude at the end of running-in and at different instants after adding the oil. The time variation of the mean pulse amplitude after adding the oil is shown in Fig. 4.2, b. Figures 4.3, a and 4.3, b illustrate similar dependencies for the distributions of

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

137

· N · 10–3, pulse/s 3 2

*

1

Δ

0 f 0.3

Δ

* 0.2 0.1 0

100

200

300

1000

t, s

Figure 4.1. Time dependencies of AE count rate and friction coefficient: ∗ – dry friction;  – lubrication with oil MC-20 w (A)

A, rel. units 60 40

0.06

20 0

0.04

250 500 750 t, s (b)

0.02

0

50

100

150 (a)

200

A, rel. units

Figure 4.2. Probability density of amplitude and average amplitude of AE pulses: lubrication with oil MC-20: ♦ – after 5 s; • – after 180 s;  – after 680 s; × – dry friction the acoustic emission energy and AE signal power. It is seen from these data that when approaching the steady-state mode the distributions shift to lower amplitudes and the pattern of the amplitude distribution changes, that is, the unimodal distribution is replaced with the J -type one. Decrease in the mean

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138

w (A)

W · 10–3, rel. units 4

0.04

3 2

0.03 1

0.02

0

250

500 (b)

750 t, s

0.01

0

50

100

150

200

A, rel. units

(a)

Figure 4.3. Probability density of energy and average amplitude of AE pulses: lubrication with oil MC-20: ♦ – after 5 s; • – after 180 s;  – after 680 s; × – dry friction amplitude and the power of signals proves the transition of the system “the rubbing specimens – the lubricant – the environment” to a stable state with minimal energy dissipation. The deformation and damage of surface layers of the friction members also become less severe that is confirmed by a decrease in AE count rate. Similar results have been obtained for the running-in of friction members covered with solid-film lubricants on the basis of molybdenum disulphide. Particularly, in rubbing of the hemi-spherical indenter with radius 8 mm made of hardened steel 45 against the steel 45 disc with a coating at a velocity of 0.6 m/s and a load of 17.5 N running-in came to end after 1300–1600 s. Figure 4.4 shows typical dependencies of AE count rate and the friction coefficient on time during running-in [4]. Let us consider how one can explain variation in the pattern of the amplitude distribution during running-in proceeding from the theoretical ideas given in Part 2.1. It follows from formulas (2.24) and (2.25) that in addition to the force pressing the surfaces together and the sliding velocity the amplitude distribution depends on material properties and surface relief. The material properties and the surface microgeometry are included in the coefficient D whose value depends to a great extent on the sum of variances of derivatives of the surface profiles  2 (see (2.17)) √ d/1 ≈ − lnF/F0 1/2  Numerical assessments have shown that at loads used in the experiments the inequality F/F0 << 1 is true. If  2 0 is the value of  2 at the beginning of

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

139

· N · 10–3, pulses/ s f N 30

f

20

0.3 0.2

10 0.1

0

1

2

3

4

5

6

t, 10–3, s

Figure 4.4. Time dependencies of AE count rate and friction coefficient: specimens – steel 45, coating – on the basis of MoS2 F = 175 N v = 06 m/s running-in and  2 t is the dependence of  2 on time during running-in then the latter expression can be presented as follows: √ d/1 ≈ − lnF/F0  + ln 2 t/ 2 01/2  where the value of F0 is calculated at  2 =  2 0. As it is known, microasperities become smoother during running-in that is the ratio  2 t/ 2 0 < 1 decreases. If the pressing force is constant the mean distance between the surfaces and the √ parameter d/1 also decrease. As calculation show (see Fig. 2.7), this leads to the shift of the amplitude distribution maximum towards low amplitudes. Since acoustic emission is registered at a preset discrimination level being sometimes quite high the shift of the amplitude distribution maximum to the band corresponding to signal discrimination appears as change in the distribution pattern from unimodal to J -type. The causes of such change when adding the oil are discussed in Part 4.2. AE was used to monitor the running-in of the specimens whose surfaces were treated by laser beam. Experiments were carried out on FP set-up using steel 45 specimens of three types. Specimens of the fist type had the hardness HRC  18, specimens of the second type were hardened to HRC  47, and the surface layer of specimens of the third type was hardened by laser radiation to HRC  47–50. The “815 steel ball 4 mm in diameter served as a counterbody. The sliding velocity was 0.8 m/s, the normal load was 17.5 N and the length of half-cycle was 48 mm. One cycle comprised two passes of the ball over the specimen surface in the direct and reverse directions.

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140

N, pulses 600

f

500

0.7

fav

f

400

0.6

300

0.5

200

0.4

100

0.3 N

0

10

5

15

20

25

N, cycles

(a) N, pulses f

f 100

0.5

80

0.4

60

0.3 fav

40

0.2 N

20 0

0.1 10

5

15

20

25

N, cycles

(b) N, pulses f 60

0.4

50 40

0.3

fav

f 30 20 0

5

10

15

20 (c)

N

0.2

25

N, cycles

Figure 4.5. Dependence of friction coefficient f and number of AE pulses per cycle N on number of cycles: specimens – steel 45: a – initial state; b – heat treatment; c – laser surface treatment; load – 17.5 N; sliding velocity – 0.8 m/s; half-cycle length – 48 mm Figure 4.5, a–c illustrates the dependencies of the number of AE pulses in each cycle, the friction coefficient and its scatter on the number of cycles. The measurements have shown that the running-in of the specimens with the hardened surface layer proceeds very slowly while with specimens of the first and

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

141

the second types it lasts 15 and 25 cycles, respectively. The mode of running-in is different. This is confirmed by noticeable maxima on the dependencies of the friction coefficient and the number of AE pulses for the specimens of the first type. For the specimens made of hardened steel only the maximum of the number of pulses is registered while for the laser-treated specimens no maxima are found on both dependencies. Summarizing the obtained data we can state that under constant friction conditions (sliding velocity, load, environment state, mating materials) the AE characteristics such as the pulse count rate, specific count rate, parameters of the amplitude distribution (variance, mean amplitude, specific power) become stable at the end of the running-in of the friction pair. Some of them tend to a minimal value that indicates the transition of the tribosystem to a stable state. The decrease of the variance of AE amplitude distribution confirms the hypothesis that on completion of running-in the stresses on single real contact spots become even [1, 2] and the decrease of the mean amplitude indicates the fact that stress values become minimal possible under the given friction conditions. This agrees with an assumption that the end of running-in corresponds to the transition of asperities to elastic contact [2]. The decrease of AE energy characteristics proves a lesser energy dissipation and the wear of materials. Note that the authors of [5] studied friction in metal-polymer pairs also found that AE characteristics became stable when running-in completed.

4.2. DEPENDENCE OF CHARACTERISTICS OF ACOUSTIC EMISSION ON SLIDING VELOCITY AND LOAD Changes in friction conditions, for example the sliding velocity or load are accompanied by variations in AE characteristics. If AE method is used for the field inspection of friction units such variations in AE characteristics can be interpreted as their malfunction resulting from, for example, the damage to a lubricating film. Therefore, when developing methods of friction unit monitoring one should know how these AE characteristics depend on these factors. Additionally, it should be kept in mind that variation in the sliding velocity and load can result in other mode of the friction and wear of mating parts that influences acoustic emission. This part comprises the study results of the effect of the load and velocity on main informative characteristics of AE. To study how AE characteristics depend on the sliding velocity under dry friction experiments were carried out at different loads [4]. The following friction pair was tested: “the steel 45 disc – the brass † 20 pin”. The sliding velocity was varied from 0.8 to 3.5 m/s. Initially the pair was run-in, then AE count rate was measured at a given sliding velocity. The measurement results

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are presented in Fig. 4.6. Solid lines are plotted by processing the data by the least-squares method. The count rate rises with increasing sliding velocity and the data scatter grows with increasing both the velocity and load. Note that the selected settings of measuring instruments affect significantly the pattern of the dependence. Particularly, the data presented were obtained at the discrimination level reduced to input of 10 V that is equal to the intrinsic noise of the recorder.

· N · 10−4, pulses/s

3

2

1

0

1.2

2.4

v, m/s

Figure 4.6. Dependence of AE count rate on sliding velocity: specimens: disc – steel 45; pin – brass † 20; load:  – 2.0 N;  – 9.0; noise level un = 10 V

Figure 4.7 shows AE count rate as a function of the sliding velocity for the same materials under a load of 5 N. The discrimination level was 3 mV. A higher sliding velocity as compared with the experiments above described was selected for the reason that at constant instrument settings such as the amplification factor and the discrimination level AE signal amplitude at a velocity <35 m/s was so small that it did not exceed the discrimination level, hence signals were not registered. After the processing of data by the least-squares method we found

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

143

· N · 10−3, pulses/s

2

1

0

2

4

6

8

v, m/s

Figure 4.7. Dependence of AE count rate on sliding velocity: specimens: disc – steel 45; pin – brass † 20; load F = 50 N; discrimination level ud = 3 V that they can be described by the regression relationship for the count rate with the correlation coefficient 0.99: N˙ = −15 · 103 + 5 · 102 v The fact that this dependence plotted in Fig. 4.7 with the solid line does not pass the coordinate origin is explained, first, by the finite value of the signal discrimination level and, second, by the large data scatter at slow sliding velocities. The large scatter of the count rate can be explained as follows. It is known that the reproducibility of friction test results is poor. Particularly, under common atmospheric conditions the scatter of the friction coefficient is substantial. The scatter is caused by the effect of a great number of factors (the composition and temperature of the environment, the microgeometry and physico-chemical properties of the surfaces in contact) varying even at constant loads and velocities on the tribological behavior of the surfaces. These factors influence more noticeable AE characteristics being more sensitive to processes running in the contact zone as compared with the friction coefficient. In addition, AE in friction is a continuous random process whose overshoots exceeding the discrimination level are registered in tests. However, it is known that the variance of the number of overshoots increases with increasing the discrimination level. The results presented in Figs. 4.6 and 4.7 are obtained using the measurement system based on a device for nuclear-spectrometric data processing which is lacking the detection of registered signals. So, the figures illustrate the results of the predetection count of AE pulses. These data are useful since

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144

they reflect the effect of the conditions of registration on AE informative characteristics (see Part 1.5). Particularly, the nonlinear dependence of N˙ on the sliding velocity at a low signal discrimination level (Fig. 4.6) results exactly from the use of predetection count when several oscillations of a signal caused by the response of the transducer to pulse effect are registered instead of a single acoustic pulse. A noticeable increase in the discrimination level in predetection count reduces considerably this effect. Only pulses with high amplitude are count which exceeds the preset discrimination level. In this case AE characteristics become less distorted (see formulas (1.9) and (1.10)). Thus, a linear dependence of N˙ on the sliding velocity can be seen in Fig. 4.7. Such pattern of the dependence is also predicted by the theory presented in Part 2.1 (see formula (2.28)). σ2, rel. units W, rel. units 8

· N · 10−3 pulses A, W

6

23 19

W

σ

2

N

5

7

4.0 4 6

15 3 11

3.2

+

A

2

5

7 1 3

2.4

4.0

5.0

6.0

7.0 v, m/s

4

Figure 4.8. Dependence of parameters of AE amplitude distribution (total ¯ variance  2 and power W ) on numbers of pulses N, average amplitude A, sliding velocity: specimens: disc – steel 45, pin – brass † 20; load F = 10 N Figure 4.8 shows the dependencies of the total number of pulses, the mean amplitude, the variance, and power of AE on the sliding velocity under a load of 1 N at a discrimination level of 300 V. These results and the results described below are obtained using RIF instruments (see Chapter 3) involving the detection of registered signals. The above characteristics increase with increasing sliding velocity within the tested range and the dependencies of some characteristics on the velocity are close to linear. Such pattern of the dependencies of AE characteristics on the velocity is predicted by the theoretical model described in Part 2.1. Particularly, according to (2.28) one should expect that the dependence of N˙ on the sliding velocity is

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

145

linear that is just so in measurements (see Figs. 4.7 and 4.8). As it follows from (2.26) the mean amplitude of AE pulses is proportional to the square root of the sliding velocity and the average square amplitude (AE power) is proportional to the velocity. In this case the variance of AE amplitude also linearly depends on the velocity. Such patterns of the dependencies of the above characteristics are confirmed experimentally. Figure 4.9 presents typical amplitude distributions of acoustic signals for the steel 45 – brass † 20 pair under different loads at a velocity of 4.6 m/s. If the load varies within the small range the pattern of the amplitude distribution

N · 10–2, pulses/s (Σ N ) · 10–4, pulses/s

25

A, mV 40

W, rel. units

σ2

8

8.5

7

8

6

7.5

1.5 3.2

20

1 2.4

2

1

5 3 P, N

7

15 1H 2H 10 3H

5

0

30

60

90

120

140

A, rel. units

Figure 4.9. Parameters and amplitude distributions of AE signals under various loads: specimens: disc – steel 45; pin – brass † 20; v = 46 m/s; ¯  – W  –  2  – N + – A

146

CHAPTER 4

remains unchanged. Only the maximum of the distribution, hence the mean amplitude and the amplitude variance slightly increase. The sliding velocity influences the energy characteristics of AE signals (mean amplitude and power) to a greater extent than the load. For example, the increase of the velocity 1.8 times leads to the increase of the mean amplitude and power of acoustic emission 1.4 and 1.8 times, respectively. The triplication of the load yields the increase of AE power only 1.5 times and the mean amplitude of AE pulses rises insignificantly. These results agree well with the theoretical model presented in Part 2.1. In fact, according to (2.26) the mean amplitude is proportional to the square root of the velocity and the average square amplitude is proportional to the velocity. Therefore, the increase of the velocity 1.8 times leads to the same increase of the emission power proportional to the average square amplitude while the mean √ amplitude increases 18  134 times. According to calculations performed in Part 2.1 the dependencies of the above characteristics on the load are determined by the functions J1   and J2   (see (2.26)). It follows from 2.6 and 2.7 that the characteristics slightly depend on the load that can indirectly confirm the concordance of the experimental data with the theoretical model. To study how the velocity and load influence AE characteristics at boundary lubrication we carried out experiments using −‹ƒ…ƒ‰-1 set-up. The specimens were made of steel 45 (disc) and brass † 62 (pin). The friction surface of the pin was flat. The surface relief corresponded to the eighth roughness class. Greases †ƒ4‰†, graphite solution and AC-8 were deposited onto the disc surface. AE was registered by ‹ƒ− instrument with the discrimination level 40 V and the amplification factor 1000. Tests were performed under loads 2.2 and 9.0 N. The sliding velocity was varied from 0.8 to 8.5 m/s. AE count rate, friction force and temperature were continuously being registered in the tests. The temperature was measured by a chromel-alumel thermocouple disposed at a depth of 0.5 mm under the pin friction surface. These characteristics are presented for the steady-state friction mode occurred at a corresponding sliding velocity. AE count rate rises sharply with increasing sliding velocity at friction with †ƒ4‰† at 1–3 m/s. When the velocity reaches 8 m/s N˙ almost remains constant (Fig. 4.10). The dependencies N˙ = fv under various loads differ slightly. At velocities 1–8 m/s and load 9 N the pin temperature increased by 7  C and at 22 N by 9  C. Under a load of 22 N the friction coefficient rises linearly with increasing velocity from 1.0 to 4.5 m/s while at higher velocities it decreases to 0.1. Under a load of 9 N the friction coefficient remains almost unchanged. Only it slightly tends to decrease from 0.15 to 0.14. Note that the friction coefficient under 9 N is higher than that under 22 N. The dependence of the count rate on the sliding velocity when using AC-8 grease is similar to the dependence N˙ = fv obtained with †ƒ4‰†. The pin

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

147

· N · 10–3, pulses/s 3

2

1

0

1

2

3

4

5

6

7

8

v, m/s

Figure 4.10. Dependence of AE count rate on sliding velocity: specimens: disc – steel 45; pin – brass † 62; lubricant: , • – graphite solution;   – AC-8;    – †ƒ4‰†; load – 22 N and 9 N, respectively temperature increases linearly with increasing velocity by 10 and 15  C under loads 9 and 22 N, respectively. The friction coefficient slightly decreases with the velocity and a lesser friction coefficient corresponds to the lower load. When using the graphite solution a considerable effect of the force pressing the friction members on all characteristics being registered was found. A high (more than by an order) increase in AE count rate is observed at sliding velocities 1–6 m/s under a load of 22 N and at 1–3 m/s under a load of 9 N. The specimen temperature varies in the same manner as with other greases, that is, it grows linearly with increasing sliding velocity. Yet, the temperature rise is higher as compared with other experiments, it amounts to 15 and 39  C under 9 and 22 N, respectively. The friction coefficient slightly decreases with the velocity. Just as with †ƒ4‰† it is higher under 9 N (0.15) than at 22 N (0.1). Figure 4.11 shows the changes in the amplitude distribution of AE signals in friction with AC-8 grease. As the velocity rises the distribution shifts from J - to unimodal type. With increasing velocity the share of signals having small amplitudes decreases while the number of pulses with high amplitudes grows. For different greases the dependencies of N˙ on v clearly differ under various loads. In case of †ƒ4‰† the count rate is almost independent on the pressing force and its maximal value is 25 · 104 pulses/s. For AC-8 the effect of the load is noticeable and N˙ max  2 · 104 pulses/s. The effect of the pressing force is the most pronounced when using the graphite solution. The maximal count rate is N˙ max  3 · 104 pulses/s under 22 N and N˙ max  15 · 104 pulses/s under 9 N. This difference in the count rate can be explained by the fact that in addition to common AE sources (the formation and merging of microcracks, the

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148

n(A) · 10–3, pulses

(b) 40 –3 n(A) · 10 , pulses

50

(a) 30

40

30

20

20 10 10

0

50

100

150

200 A , rel. units

0

50

100

150

200

A , rel. units

Figure 4.11. Amplitude distributions of AE signals at various sliding velocities: specimens: disc – steel 45; pin – brass † 62; lubricant – AC-8; a: load – 9 N; sliding velocity:  – 0.72 m/s;  – 2.3 m/s; • – 3.8 m/s; – – 6.4 m/s; b: load – 22 N; sliding velocity:  – 0.75 m/s;  – 1.92 m/s; • – 3.8 m/s; - - - - – 7.2 m/s separation of wear particles, elastic impacts of microasperities) the damage of the surface layer due to microcutting contributes acoustic emission when using the graphite solution. The solution contains fine graphite particles which are strong and can charge the surface. The maximal value of the friction coefficient (0.16) under the given conditions and the maximal specimen temperature (600 K instead of 300 K) also prove that the surfaces operate under more severe conditions if they are lubricated with the graphite solution. Similar results were obtained for the “steel 45 pin – brass † 62 disc” pair under a load of 5 N at velocities 0.4–2.5 m/s with MC-20 oil. Figure 4.12 presents the dependencies of the count rate, the specific AE count rate, and the friction coefficient on the sliding velocity. Experimental points correspond to the data obtained under steady-state friction. Both characteristics increase monotonously to some values as the velocity rises, that is, the pattern of the dependency N˙ = fv is similar to that presented in Fig. 4.10. If one assumes that AE pulse results from the impact of surface microasperities then the time interval between single pulses is equal to  ∼ l/v, where l is the asperity spacing and v is the sliding velocity. The interval  decreases as v grows. At a certain velocity value  becomes equal to the resolution time constant of the measuring instrument at which signals can be still registered separately. The effect of saturation occurs with further velocity increase. The measuring system is incapable of counting all AE pulses. This explains the fact that the dependence of the count rate becomes constant and the specific

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

149

· N · 10–4, pulses/s f

·

N/v · 10–3, pulses/s 21

5

14

0.4

7 0

4

0.3

0.5 1.0 1.5 2.0 v, m/s

3 0.2 2 · N

f

1

0

0.5

1.0

0.1

1.5

2.0

v, m/s

Figure 4.12. Dependence of count rate, specific count rate of AE and friction coefficient on sliding velocity: specimens: disc – steel 45; pin – brass † 62; lubricant – MC-20; load – 5 N count rate decreases at high sliding velocities. This factor requires the proper choice of the amplification coefficient and the signal discrimination level and the selection of informative characteristics when performing AE diagnostics of friction units. Figures 4.13 and 4.14 illustrate the probability densities of the amplitude and the squared amplitude of AE pulses and variations of their mean values as w (A) A , rel. units 0.03 80 40

0.02 0

0.5

1.0

1.5 2.0 v, m/s

0.01

0 50

100

150

200 A , rel. units

Figure 4.13. Amplitude distributions of AE signals at different sliding velocities: specimens: disc – steel 45; pin – brass † 62; lubricant – MC-20; load – 5 N; sliding velocity:  – 0.6 m/s; × – 0.8 m/s;  – 1.4 m/s; • – 1.6 m/s;  – 2.2 m/s

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150

W · 10−3, rel. units

w(A2)

20 15

0.03

10 5

0.02

0

0.5 1.0 1.5 2.0 v, m/s

0.01

0

100

50

150

200 A, rel. units

Figure 4.14. Energy distributions of AE signals at different sliding velocities: specimens: disc – steel 45; pin – brass † 62; lubricant – MC-20; load – 5 N; sliding velocity:  – 0.6 m/s; × – 0.8 m/s;  – 1.4 m/s; • – 1.6 m/s;  – 2.3 m/s

a function of the sliding velocity. The amplitude distributions become broader with increasing velocity and their maxima become less pronounced and shift to higher amplitudes. The pattern of the energy distribution is similar, but in the latter case the above changes are more noticeable. The dependence of the count rate of AE pulses on the sliding velocity at friction of specimens made of steel “815 is shown in Fig. 4.15. The conditions of acoustic emission registration were as follows: the signal discrimination level was 30 V and the amplification factor was 1000. The presented data

· N · 10−3, pulses/s

50

25

0

0.2

0.4

0.6

0.8

v, m/s

Figure 4.15. Dependence of AE count rate on sliding velocity: specimens: disc an pin – steel “815; lubricant – MC-20; load – 22.5 N

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

151

can be described by the following regression dependence with the confidence probability 0.95 N˙ = 86v − 52 · 103  where N˙ has the dimension pulses/s and v – m/s. In friction of hard materials including steel “815 the elastic interaction and impacts of surface microasperities can be thought to be the primary AE source. This is also proven by the fact that no signs of wear were found when examining the friction surfaces after the tests visually and using a profilometer. The processes of plastic deformation and changes in the dislocation structure of the surface and subsurface layers also induce acoustic signals but their contribution to AE in friction of hard materials is apparently insignificant. Proceeding from the above stated, one should expect the linear dependence of N˙ on the sliding velocity. This is found in experiments and confirms well the results of calculations (see (2.28)) obtained with an assumption on elastic interaction between the surface microasperities. Experiments intended to determine dependencies of AE characteristics on the load applied to the mating members were carried out at a constant sliding velocity. Figure 4.16 shows changes in the friction coefficient and AE count rate for the “steel 45 disc – brass † 62 pin” pair at a sliding velocity of 0.44 m/s. The proportional dependence of the count rate on the load corresponds to the conclusions made in Part 2.1 (see (2.28)). Variations in the probability densities of the amplitude and the squared amplitude of AE signals and the mean values of these characteristics with the load are presented in Figs. 4.17 and 4.18. As it is seen from the data the dependence of the probability densities on the load is not so pronounced as the dependence on f

· N · 10−J, pulses/s 8

· N 0.15

f

6 0.10 4 0.05 2

10

20

P, N

Figure 4.16. Dependence of AE count rate and friction coefficient on load: specimens: disc – steel 45; pin – brass † 62; lubricant – MC-20; sliding velocity – 0.44 m/s

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152

A, rel. units

w (A)

30

0.03

20 10

0.02

0

5

10

15

20 P, N

0.01

0

20

40

60

80

100

A, rel. units

Figure 4.17. Amplitude distributions of AE signals under different loads: specimens: disc – steel 45; pin – brass † 62; lubricant – MC-20; sliding velocity – 0.44 m/s; load: • – 5 N; × – 10 N;  – 20 N w (A2) 0.03 W · 10−2, rel. units 10

0.02 5

0

5

10

15 P, N

0.01

0

50

100

150

200

A, rel. units

Figure 4.18. Energy distributions of AE signals under different loads: specimens: disc – steel 45; pin – brass † 62; lubricant – MC-20; sliding velocity – 0.44 m/s; load: • – 5 N; × – 10 N;  – 20 N the velocity. This fact has been already discussed when analyzing the results presented in Fig. 4.9. Here we only note that the distribution maxima shift to higher amplitudes and the distributions become broader as the load grows. When using a solid-film lubricant based on molybdenum disulphide similar dependencies of AE characteristics on the load and sliding velocity were obtained.

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

153

Resuming the analysis of the experimental data we note that almost all AE parameters being registered increase with increasing load and sliding velocity both at dry friction and under boundary lubrication. It should be remembered that the friction coefficient either remained constant or varied slightly in the experiments, that is, the friction force increased linearly as the load rose. The basic experimentally obtained dependencies of AE characteristics such as the count rate of AE pulses, the characteristics of the amplitude distribution (the mean amplitude, the average square amplitude and the variance of AE pulse amplitude) on the sliding velocity and load are well described by theoretical relations derived in Part 2.1. The type of the amplitude distribution and the pattern of its variation with varying friction regimes also agree well with the results of mathematical modeling (compare Figs. 2.8 and 2.9 with Figs. 4.13 and 4.17). The obtained results can be interpreted qualitatively as follows. With increasing the sliding velocity the time of interaction between contacting microasperities decreases. Hence, the power of emission increases even if the energy dissipated from a single contact spot is constant. On the other hand, this increases the amplitude of acoustic emission pulses (see the dependence of the amplitude of AE pulse on its energy and duration in Part 2.1). Besides, since the stress-strain state of real contact spots changes and the tangential force pulse lasts longer the amplitude of AE pulses grows. New sources of acoustic emission can appear such as the origination of microcracks, hence variation in the number of pulses generated by a single contact spot. If we assume that the number of AE pulses is proportional to the number of real contact spots then AE activity should rise with increasing sliding velocity. Also the mean amplitude, the variance of the pulse amplitude, and the power of acoustic emission should rise that is really observed in the experiments. The analysis of the experimental data has confirmed the fact that the postdetection count of AE pulses should be used at a minimal possible discrimination level in order to obtain valid information on how AE characteristics depend on friction regimes. This requires the development of AE measuring instruments with low intrinsic noises.

4.3. ACOUSTIC EMISSION IN DAMAGE TO LUBRICATING FILMS ON FRICTION SURFACES The majority of friction units are lubricated by liquid lubricants or solid-film lubricants. Time to the failure of lubricating films on friction surfaces is an important characteristic governing the efficiency of friction pairs. In the present part we report the results of the experimental studies which prove the suitability of AE method to determine the instant of the failure of lubricating films in friction units. The studies were carried out on −‹ƒ…ƒ‰-1

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154

set-up using solid-film lubricants based on molybdenum disulphide and greases such as †ƒ4‰†, AC-8, and the graphite solution. Figures 4.19 and 4.20 illustrate the study results of the friction of a hemispherical steel 45 pin with curvature radius 6 mm against |P!'9-4 bronze disc f

N · 10−2, pulses/s

f

15

0.3

0.2

10

0.2 11.5

0.1

12

5

0.1

0

3

6

9

12 t, hour

Figure 4.19. Time dependencies of AE count rate and friction coefficient: specimens: disc – bronze |P!'9-4; pin – steel 45 (hemispherical); coating – MoS2 · N · 10−3, pulses

N, pulses 70

18

60 50

12

40 30

6

20 10

0

10

20

30

40

50

60

70 80 90 100 A, rel. units

Figure 4.20. Amplitude distributions of AE signals: specimens: disc – bronze |P!'9-4; pin – steel 45 (hemispherical); coating – MoS2 ; load – 5 N; sliding velocity – 0.8 m/s; duration of friction:  – 4 h 40 min; × – 12 h 14 min;  – 12 h 17 min

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

155

covered with a coating on the basis of molybdenum disulphide 10 m thick at a sliding velocity of 0.8 m/s under a load of 5 N [4]. It is seen from the data in Fig. 4.19 that in friction with the lubricating coating AE count rate gradually monotonously rises at an almost constant friction force. After 11.5 hours of operation the coating starts to fail and oscillations of the friction force and the count rate are registered. Further the frequency of the oscillations increases and their duration and amplitude also rise. Such behavior of the friction force and AE count rate retains until they reach values corresponding to the dry friction of the materials. If the coating is locally damaged the share of pulses with a high amplitude in the amplitude and amplitude-time distributions increases. It is also proven by variations in the moments of the amplitude distributions given in Table 4.2. Table 4.2. Variation of Characteristics of Amplitude Distribution in Damage of Coating on the Basis of MoS2 Time

m1 , rel. units m2 , rel. units m3 , rel. units m4 , rel. units



4 h 40 min

132

226

50

6

19

12 h 14 min

151

350

122

20

−3

12 h 17 min

164

424

155

28

−1.4

Similar results were obtained when the MoS2 coating deposited on the disc surface became worn out. Just as in the previous case a hemispherical steel 45 pin served as a counterbody [4]. The tests were carried out in the following sequence. Initially the dry surfaces were tested. Then a layer of MoS2 was deposited onto the disc surface by rubbing. The friction coefficient and the count rate of AE pulses decreased almost instantly (Fig. 4.21). The count rate dropped approximately 500 times. During the next 8 times of operation the steady-state friction mode run then AE count rate was increasing monotonously during one hour at an almost constant friction coefficient. In approximately 30,000 s both characteristics had become to rise sharply and they reached the values typical for dry friction during a few seconds. At the same time the friction coefficient changed with oscillations. The repeated rubbing with MoS2 reduced the registered characteristics. The damaged lubricating film was recovered. The change in the characteristics of acoustic signals in the repeated deposition of the coating indicates that AE method is suitable to monitor lubrication conditions. Characteristics of the amplitude and amplitude-time distributions vary when the solid lubricant film is damaged (Fig. 4.22 and Table 4.3). First of all an

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156

· N · 10–3, pulses/s

f

1.5

0.2 f 1.0 *

*

*

0.5

N=3

0.1

N=2

0

·

N N=1

*

* 20

30

25

t · 10–3, s

Figure 4.21. Time dependencies of AE count rate and friction coefficient: specimens: disc – bronze |P!'9-4; pin – steel 45 (hemispherical); coating – MoS2 ; load – 5 N; sliding velocity – 0.4 m/s; ∗ – beginning of spreading MoS2 from briquette; time since beginning of experiment: spectrum 1 – 30·103 s; spectrum 2 – 308·103 s; spectrum 3 – 314 · 103 s . N · 10–3, pulses

N, pulses

30

60

N2

50 N1 20

N2

40

N1

30 N3

10

20 10

N3 0

20

40

60

80

A, rel. units

Figure 4.22. Amplitude distributions of AE signals for Fig. 4.21 increase in the amplitude variance and the mean energy of AE pulses should be mentioned. Note that characteristics of acoustic emission are well reproducible in the experiments with the MoS2 coating during running-in and in damage to the

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

157

Table 4.3. Variation of Characteristics of Amplitude Distribution in Damage of Molybdenum Disulphide Coating N

m1 , rel. units

m2 , rel. units

1

114

137

2

127

206

3

1512

330

 2 , rel. units

W , rel. units



63

11

−002

434

48

101

17

−42 −6

coating. Therefore the friction of materials with such lubricant can be considered as AE source with assigned characteristics. This AE is suitable to adjust and compare the characteristics of available and developed measuring instruments. To find a correlation between AE characteristics and the state of the surface at different instants such as running-in, steady-state friction, the beginning of the coating failure the measurements were carried out with one and the same disc specimen at a constant velocity and load but at different friction path along each track. The dependencies of the friction coefficient f , the count rate N˙ , the ampli¯ the power W , and the tude and energy distributions, the mean amplitude A, 2 variance of the amplitude distribution  on time in friction of steel specimens with a MoS2 coating at 0.6 m/s and 17.5 N (hemispherical pin with curvature radius 6 mm) are presented in Fig. 4.23. When approaching the steady-state mode the count rate of AE pulses decreases noticeably along with the friction coefficient. The amplitude and energy distributions change, they shift to small amplitudes. This is confirmed by ¯  2 and W . On the contrary, a decrease in the distribution parameters such as A these parameters increase sharply when the lubricating film is failed. The data given in Table 4.4 present the values of the parameters at different stages of friction unit operation. The analysis of profilograms obtained from the friction tracks has shown that at the initial stage of friction the indenter penetrates into the coating to the whole coating thickness. A thin lubricating film is formed on the specimen surface under the indenter which is retained for a long time and governs the coating efficiency. Tests lasting until the coating becomes worn out prove that it fails gradually. Sites of damage appear in the local surface regions, probably on single contact spots. The authors of papers [8] have found that the failure of the MoS2 film deposited onto the metallic surface by rubbing begins with the formation of microbulges 400 Å in size which further expand to 1–4 mm. The film above the bulge becomes brittle and delaminates. It is supposed in publications that

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158

· N · 10–3, pulse/sec

(a)

60

· –3 N · 10 , pulse

f

· N f

Ni , pulse

(b)

t = 2–8 sec t = 5.65 ksec

0.3 12

12

t = 29 ksec

40

0.2 8

8

20

0.1 4

4

0

5

10

Wi · 10–6

15

t = 2–8 sec

(c)

t = 5.65 ksec

20 σ2

Wi · 10–4

160

180

200

A

A

16 20 –20

2

8

A W · 10–8

(d)

σ W

24 30 –30

4

0

40

2

t = 29 ksec

6

0

t · 10–3, sec

20

10 –10 0

20

40

160

180

200

A

5

10

15

20

–3 t · 10 , sec

˙ friction coefficient f – (a), Figure 4.23. Dependence of AE count rate N, amplitude – (b) and energy – (c) distributions; power W and variance of amplitude distribution – (d ) on duration of friction; specimens: disc and pin – steel 45; coating – on basis of MoS2 ; sliding velocity – 0.6 m/s; load – 17.5 N

Table 4.4. Variation of AE Characteristics and Friction Coefficient in Time Friction mode

Characteristics nonstationary

steady-state

k1

coating damage

k2

N˙ , pulses/s

1400

A, rel. units

9.5

W , rel. units

18 · 10

 2 , rel. units

13.1

11

12.1

12

11

f

0.47

015

0.42

3

3

5

5200

2 6

16·10

6.1 2

42 · 10

6

25 · 102

103

5

3

11 · 10

4

26 · 104

Note: k1 is the ratio of parameters of the non-stationary mode to those of the steady-state mode; k2 is the ratio of parameters of the coating damage mode to those of the steady-state mode. Specimens – steel 45, coating – on the basis of MoS2 v = 06 m/s P = 175 N.

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

159

such bulges appear at sites of stress concentration. Stresses initiate fatigue in the surface layers of molybdenum disulphide and its chemical activity increases that appears as its reactions with moisture and air oxygen. In opinion of the researchers, the combination of these processes results in the fatigue damage of the film. In some cases local damages of the protective film can be healed by the friction transfer of MoS2 . Yet, the number of damaged spots rises in time and they expand; friction transfer is no longer capable of recovering the protective film. Note that changes in the state of the lubricating film, for example, its damage on a single real contact spot will scarcely produce a noticeable increase in the friction force. Damage should occur over at least 10–20% of the real contact area [9]. AE characteristics are more sensitive to the state of single spots. Therefore variations in AE characteristics can indicate the occurrence of coating damage at earlier stages in comparison with the use of the friction coefficient for this purpose. Considerable increase in AE characteristics was found when the lubricating film failed in all experiments under boundary lubrication [4]. Figure 4.24 illustrates the dependence of the friction coefficient and AE count rate on time in the process of the failure of †ƒ4‰† film for the “steel disc – cylindrical pin 3.3 mm in diameter” pair at a velocity of 1 m/s and a load of 5 N. As it is seen from the plot, the count rate increases approximately 90 times in transition to dry friction. The maximum of the amplitude distribution shifts to higher amplitudes that is · N · 10–3, pulses/s

k

80 0.3 70 60 50

0.2

40 30 0.1

· N

20 10 0 85

86

87

88

89

t · 10–3, s

Figure 4.24. Dependencies of AE count rate and friction coefficient on duration of friction: specimens: disc and pin – steel 45; lubricant – †ƒ4‰†; sliding velocity – 1 m/s; load – 5 N

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160

the mean amplitude of AE pulses rises (Fig. 4.25). Table 4.5 serves for comparison and contains data on the characteristics being registered in friction of the specimens both without the lubricant and with it in the steady-state friction mode. It is seen that the count rate of AE pulses changes to the most extent. n(A) · 10–2, pulses

3

90000 s

2 1

82500 s

50

100

150

A, rel. units

Figure 4.25. Amplitude distributions of AE signals: specimens: disc and pin – steel 45; lubricant – †ƒ4‰†; sliding velocity – 1 m/s; load – 5 N

Table 4.5. Variation of AE Characteristics and Friction Coefficient Depending on Presence of Lubricant Friction mode

Characteristics

Ratio

dry friction

lubrication

N˙ , pulses/s

1    15 · 103

20–40

50

A, rel. units

24

14

1/7

W , rel. units

1800

300

6

f

0.35

0.05

7

To verify indirectly the fact that AE count rate is governed by the damage to the lubricating film on single contact spots we carried out the experiments with a hemispherical pin with radius 6 mm instead of the cylindrical one, that is, almost point contact was used. Since †ƒ4‰† is thicker than molybdenum disulphide it demonstrates better drag behavior. For this reason the failure of †ƒ4‰† film lasts longer and one can expect an earlier change in AE count rate as compared with the use of the molybdenum disulphide film. This is indeed observed in the experiments, the results of one of the experiments are presented

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

161

in Fig. 4.26. Single peaks of the count rate of AE pulses are registered long before the film is failed. The friction coefficient also increases sharply at these instants. This proves the failure of †ƒ4‰† film on the point contact spot and the sensitivity of AE characteristics to this effect. · N, pulses/s

f 0.3 0.2

104 0.1 0.05

103

0 102

10

1

2

3

4

5

6

t, hours

Figure 4.26. Time dependencies of AE count rate and friction coefficient: specimens: disc and pin (hemispherical) – steel 45; lubricant – †ƒ4‰†; sliding velocity – 1 m/s; load – 5 N When the lubricant is introduced into the contact zone or the state of the lubricating film changes AE frequency spectrum varies. In dry friction (Fig. 4.27) the spectrum contains periodic components whose values decrease with increasing frequency. The decrease in the maxima of the spectral components can be explained by the ascending frequency dependence of the attenuation factor of elastic waves in the material. Note that the pattern of the registered spectrum is similar to that of the spectrum calculated from the mathematical model presented in Part 2.2 (see Fig. 2.10). According to theoretical results of Part 2.2 such AE spectrum is typical for the friction of the surfaces whose profile correlation functions contain periodic components. As it follows from formulas (2.48) and (2.50) the asperity spacing can be assessed. Indeed, since maxima of the spectral density alternate with an interval of about 100 kHz and the velocity of the relative motion of the surfaces is 1 m/s then the average spacing between asperities is about 10 m that agrees well with the data obtained from surface profilograms. The pattern of AE spectral density changes when a lubricant is added. If we do not consider the low-frequency band which presents in all spectra to the same extent (see Fig. 4.27) and results apparently from the low-frequency vibration of the set-up then when adding the lubricant the spectral density becomes close to

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162

A/A0

(a)

A/A0

0.75

0.75

0.50

0.50

0.25

0.25

0

0

A/A0

(c)

A/A0

0.75

0.75

0.50

0.50

0.25

0.25

0

(b)

(d )

0 200 400

600

800 f, kHz

200

400

600

800

f, kHz

Figure 4.27. Averaged spectral densities of AE signals: a – dry friction; b – lubrication with oil MC-20, after running-in; c – beginning of failure of lubricating film; d – failure of lubricating film the unimodal distribution (Fig. 4.27, b). According to the calculations performed in Part 2.2 this pattern of the spectral density is typical for the friction of the surfaces whose profiles have an exponentially descending correlation function. As it has been mentioned above, ground and polished surfaces have such functions. Hence, the pattern of the spectral density indicates that the introduction of the lubricant produces the same effect as the smoothing of the surfaces. This phenomenon indeed takes place. Particularly, A.S. Akhmatov mentioned in his fundamental monograph [6] dealing with the physics of boundary friction that “the substance of a lubricant conceals the microgeomertric profile of a surface which acquires the properties of a mirror highly elastic plane”. Since lubricants damp effectively elastic waves the maximum of the spectral density is quite small (Fig. 4.27, b). When the lubricating film begins to fail the surface partially loses its “mirror state”. In this case its profile differs from the initial profile of the dry surface. Therefore the pattern of AE spectral density differs from both the frequency spectrum for dry friction and the spectrum for friction with the lubricant (Fig. 4.27, c). The share of high-frequency components in the spectrum increases and their values rise. When the lubricating film is damaged spectral peaks typical for dry friction are again clearly seen in AE spectrum (Fig. 4.27, d). They are comparatively small since the remaining lubricant damps effectively AE high-frequency components. Let us analyze processes which can occur in the local damage of the lubricating film. According to Yu.N. Drozdov et al [9], four types of surface

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

163

microasperity contact can be distinguished under boundary lubrication: contact through the lubricating film; contact between dry summits; contact between summits with elevated temperature over which the material can melt; contact between summits over which adhesion junctions can occur. AE activity under boundary lubrication can be written as N˙  = N˙ l + N˙ d + N˙ pl + N˙ adg + N˙ disl  where N˙ l is the number of pulses per unit time resulted from friction junctions realized through the lubricating film; N˙ d  N˙ pl and N˙ adg are contributions to AE activity of pulses resulted from impacts of dry asperities, junctions at melt asperities, and the formation of adhesion junctions, respectively; N˙ disl is AE component caused by changes in the dislocation structure of the surface layer and the appearance of defects including microcracks. In our experiments the contribution of N˙ pl and N˙ adg to the total AE activity is negligible at friction with oils and greases. First, the tests were performed under relatively light loads (contact pressure did not exceed 0.1–1.0 MPa) and at slow sliding velocities. Therefore, the contact spot temperature rise was small. Second, the environment was air; hence adsorbed layers of moisture and gas molecules covered the surfaces and hindered the formation of adhesion junctions between them. Thereupon it seems that under boundary lubrication AE results mainly from interaction between asperities through the lubricating film. Because the lubricant damps elastic waves the amplitude of acoustic pulses appearing in this case is less than that of AE signals induced by the “dry” impacts of surface asperities (see Table 4.5). If the lubricating film fails even on single contact spot, AE amplitude increases. In addition, owing to variations in the stress-strain state of asperities in contact an additional AE source appears caused by changes in the dislocation structure of the surface layer, the growth of microcracks, and the formation of wear particles. We note once again that the increase of AE amplitude at different registration techniques (predetection or postdetection count) can cause the number of registered AE pulses to rise. The main conclusion following from the experimental results is that the failure of the lubricating film leads to the increase of all AE characteristics somehow or other related to AE energy. The analysis of variation in AE count rate in the process of the failure of the lubricating film (Fig. 4.21, 4.23, 4.26) proves that the film becomes to fail locally, possible on single real contact spots. Further on depending on friction conditions the damage site can either be healed or expand leading to the catastrophic damage of the film followed by the seizure of the friction members. These data corroborate the hypothesis on the local character of lubrication film damage and the possibility of the healing of individual regions where the film fails [9].

164

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In lubrication with lamellar solid lubricants like molybdenum disulphide AE is apparently caused mainly by the formation and rupture of adhesion junctions and the origination of microcracks in the film due to fatigue failure, that is, the terms N˙ adg and N˙ disl prevail in the above expression. Impact processes play a less significant role in this case because of good damping properties of molybdenum disulphide. In addition, since the visual examination of friction tracks and the study of their profilograms shows that after a few first cycles (disc revolutions) the coating surface is smoothed to 9–11 roughness classes the impacts of microasperities seem unlikely to occur. The failure of the solid lubricant film just as the failure of the liquid lubricant film is accompanied by the appearance of AE pulses induced by impacts of surface asperities. The intensity of such AE is higher than that of emission caused by the formation of microcracks in the surface layer of the substrate in case of the coated surface. The presented results show that almost all AE characteristics can be used as diagnostic parameters to assess the state of lubricating films in friction units. The count rate of AE pulses is the simplest characteristic from viewpoint of the registration and automation of the measurement process [1, 3]. However, to improve monitoring validity and to analyze the state of bearings in more detail the amplitude and frequency analysis of AE signals is advisable. This is due to the fact that under some friction conditions AE pulses can be redistributed over various amplitude ranges while the total number of pulses remains constant. The results of theoretical studies presented in Parts 2.1 and 2.2 can be helpful when interpreting AE data.

4.4. CORRELATION BETWEEN CHARACTERISTICS OF ACOUSTIC EMISSION AND CHARACTERISTICS OF DAMAGE OF MATERIAL SURFACE LAYERS IN FRICTION Some papers dealing with studies of AE in friction describe efforts made to relate the wear of material surface layers to characteristics of acoustic emission. For example, the authors of paper [10] studied the abrasive wear of specimens made of bronzes |P808, |P|2, |P‰−10–1, |P!'9-4 and steel 07X16H6 against corundum clothes glued on a disc and obtained the following dependence of the specific number of AE pulses on the dispersity of wear particles: N S = C = C V V In this expression N is the total number of AE pulses registered when the volume V of the specimen fails;  = S/V is the dispersity of wear particles;

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S is the total surface area of wear particles appeared when the volume V of the specimen fails; C is a proportionality constant depending on material properties. It follows from the expression that the total number of AE pulses emitted in failure of a material volume is proportional to the surface area of the appeared wear particles irrespective of their dispersity. Note that this is true if postdetection pulse count is used and the signal discrimination level is selected properly in registration. AE studies of the failure of metals prove these statements [12]. The authors of paper [11] suppose that acoustic emission appears only in formation of wear particles therefore the energy distribution of AE signals reflects the process of friction surface damage. Besides, they suppose that the energy of acoustic emission induced by the formation of a wear particle is proportional to the energy that is released when the particle is separated from the bulk material. Proceedings from these suppositions and using the experimental data the authors found the relation between the distribution of linear dimensions of wear particles and spectral characteristics of AE signals. The obtained data are apparently valid only provided that distortions of AE spectral density by the acoustic line along which acoustic waves transmit, the transducer and the measuring device are taken into account. Unfortunately, the authors left out these aspects. The analysis of scanty papers dealing with relation between wear and AE characteristics has shown that the dependence of AE total count and either mass wear or the surface area of the formed wear particles is linear. To determine how characteristics of the failure of surface layers of solids in friction are related to AE signal characteristics we carried out the experiments involving various materials and set-ups. −‹ƒ…‰-1 set-up was used to determine the wear of specimens made of the following materials: the disc – steel 45, the pins – brasses † 62 and † 59, tough-pitch copper, duralumin ¨16 and steel 45. Mass wear was measured by periodical weighing and linear wear was determined by a micrometer. AE was registered by a device based on ‹ƒ− instrument. The count rate, the average count rate over test duration, the average amplitude, the power and the product of the count rate and the average amplitude of AE pulses were registered and analyzed in the experiments. It was found that all the above characteristics correlate with the value of wear or the wear rate to some extent. The best correlation was found between the wear rate i and the sum of amplitudes of registered AE pulses (Fig. 4.28). The corresponding dependence can be presented in the following form with the correlation coefficient 0.9 i=

B ¯ N A = BN˙ A T j j j

(4.1)

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166

Mass wear U · 10–3, g

5

0

1 2 Parameter ΣNAi · 10–7 i

Figure 4.28. Dependence of mass wear on total AE amplitude: friction pair: steel 45 – brass †# 62; sliding velocity – 1.0 m/s; load – 1.7 MPa where B is a dimension coefficient depending on properties of the specimen materials; T is the test duration; Nj is the number of pulses with the amplitude Aj registered during the test; A is the average pulse amplitude; N˙ = N /T is the average count rate over the test duration; N is the total number of AE pulses. The next set of experiments was performed in the Institute of Machines Science of the Russian Academy of Sciences using a four-ball friction machine whose friction unit and acoustic signal measuring unit are shown schematically in Fig. 4.29. The friction force was continuously registered in tests and ‹ƒ−‡ƒ−ƒ instrument served to register AE count rate. The area of the worn surfaces of the stationary specimens was determined by an optical microscope in certain time intervals then using the known formula the depth of the worn layer averaged over three balls h was calculated. It was found that the pattern of the dependence of AE pulse count rate on time at the maximal discrimination level at input (400 mV) and minimal coefficient of signal amplification (250) is similar to that of the time dependence of the wear rate i = h/t t is the observation time (Fig. 4.30, a). The appearance of peaks of AE count rate and the wear rate is caused by a short-term transition from one wear mode (predominantly, adhesive wear) to another (mainly, abrasive wear). The occurrence of abrasive wear during a short period in the experiments can be explained as follows. When abrasive particles accumulate in oil the wear rate increases. As a result, the real contact area grows. Since the tests were carried out under a constant normal load the contact

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

P

(a)

167

(b)

1 1

ω

2 2 3

3 4

4

Figure 4.29. Design of friction unit of four-ball friction machine (a) and AE transducer (b): a: 1 – rotating specimen; 2 – balls; 3 – AE transducer; 4 – case; b: 1 – socket; 2 – case; 3 – damper; 4 – piezoelectric cell · N · 10–4, pulses/s l · 105 mm/s 4 3

n(A) · 10–4, pulses (b)

(a) 8

l · N

2 – t = 8200 s 6

2

4

1

2

0

5

1 – t = 500 s

10

t · 10–3, s

1

100

200

2

300

A, mV

Figure 4.30. Time dependencies of AE count rate, wear rate (a) and amplitude distribution of AE signals (b) pressure hence the wear rate decreased with increasing real contact area. This leads to change in the wear mode. The transition from one wear mode to another occurred almost instantly during about 1 s that was proven by a sharp increase in AE count rate (Fig. 4.30, a). If the wear rate is measured to determine the wear mode change then the transition time can be found with an error of at least 15 min being the time interval between measurements of wear spots. Figure 4.30, b illustrates histograms of the distributions of AE pulse amplitude. It is seen that abrasive wear is accompanied by AE with considerably higher amplitude compared to adhesive wear. So, the number of pulses with amplitudes exceeding 400 V increases from 2400 to 54000 that is approximately 20 times while the number of pulses with amplitudes below 400 V decreases from 45000 to 23600 that is approximately twice.

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When determining the transition from one wear mode to another at a low signal discrimination level no pronounced change in AE count rate was found in contrast with the above case. This can be explained by the fact that a great number of AE pulses with a low amplitude is registered which result from impacts of surface asperities rather than from the damage of surface layers. Thus, it has been established that change in the wear mode is accompanied by variations in AE amplitude distribution. In addition, the amplitude of acoustic pulses emitted in failure of surface layers exceeds considerably that of signals induced by the impact interaction of surface microrelief elements and the rupture of adhesion junctions. This should be taken into account when developing AE methods of the wear assessment of surface layers of friction member materials and when designing measuring devices to implement these methods. The gained experience was used to study the wear resistance of surface layers of Ni–Cr–B–Si system produced by different techniques and steel 45 specimens heat treated in different ways including normalizing, hardening with high tempering, furnace hardening at 870  C and laser treatment. Self-fluxing powder alloys were faced onto specimen surfaces by RF current using “frosting” technique, sprayed by plasma followed by fusing with gas flame and deposited by gas-powder laser facing. The obtained alloys acquired specific structure features depending on the deposition technique. Experiments to study the wear resistance of the above coatings were carried out in −‹ƒ…‰-1 set-up. The end surfaces of the disc specimens were coated with alloy by one of the mentioned technique either over the whole surface area or as single concentric bulges. Then the specimens were ground to provide the coating surfaces to be parallel to the base plane. A pin made of "…-8 hard alloy served as a counterbody. Tests were performed under dry friction, the surfaces of the disc specimens and the counterbody were degreased with acetone before the tests. Test regimes were the same for all the coatings: the normal load – 19.6 N, the sliding velocity – 0.65 m/s, the total friction path – 1250 m. The average area of the wear scar S was determined after a hour of tests by averaging three profilograms obtained by the profilometer at an angle of 120 relative to the disc center. Then the volume of the removed material V was calculated. The test results given in Table 4.6 show that the tribological characteristics of the surface layers deposited by various techniques differ significantly. For the coatings obtained by RF current facing pronounced changes appear in the time dependencies of AE count rate N˙ and the friction force F which can be related to running-in lasting about 30 s. Besides, great oscillations of the friction force, high values of N˙ and N˙ (Table 4.6) and a large scatter of the friction coefficient prove the possibility of the formation of seizure spots followed by the tearing of the faced material. The spalling of the hardest and the most brittle particles of the hardening phase contained in the faced layer

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Table 4.6. Results of Wear Resistance Tests of Ni–Cr–B–Si Coatings on Steel Specimen Surfaces Deposition method Characteristics

RF current

plasma deposition

gas-powder laser facing

AE count rate N˙ , pulses/s

250

150

5

Amplitude of AE count rate N˙ , pulses/s

25

25

0

Running-in time t, s

30

30

5

Friction coefficient f

0.5

0.4

0.56

Amplitude of friction coefficient f  ¯ , Parameter I = Nj Aj = N˙ AT

0.2

0.05

0.05

(820)21

(200)5

(38)1

Area of wear track S · 10−2  m2

190

46

9.9

Volume of wear track V · 10−8  m3

27

6.1

2.3

Relative wear resistance by S

19.3

4.7

1.0

Relative wear resistance by V

11.5

2.6

1.0

j

rel. units

is also like to occur. This is confirmed by signs of tearing and spalling on the specimen worn surfaces. The duration of running-in of the layers deposited by plasma and fused by gas flame is almost the same as that of the coatings faced by RF current. Yet, considerably less values of AE count rate and a smaller scatter of the friction coefficient are registered in this case (see Table 4.6). This is apparently related to the refining of structure components and the increase of the alloy homogeneity. The coatings obtained by the gas-powder deposition are remarkable for a short duration of running-in. The wear rate and the character of processes running in friction retain unchanged as the friction surface moves deep into the deposited layer. Time dependencies of the friction force and the count rate

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are almost direct lines parallel to the time axis. Values of N˙ and N˙ for these coatings are considerably less than for other coatings. This fact is explained by no signs of the spalling and failure of brittle particles on the specimen surfaces. The surface of the wear scar is smooth without visible signs of the tearing or spalling of the deposited material. The scatter of the friction coefficient is small that proves the homogeneity of the material structure. Owing to features of wear caused by the deposited material structure, the wear resistance of layers obtained by this technique exceeds more than ten times that of layers deposited by RF current and 3–5 times that of plasma coatings fused by gas flame. It should be noted that mean values of the friction coefficient of all the coatings differ slightly. Therefore, this characteristic is mainly governed by the type of the material matrix being the same for all deposited coatings (solid solution with Ni3 B inclusions). In this case AE characteristic i correlates well to the data of the measurement of the wear resistance over the area and volume of the removed material (see Table 4.6). Also a relation is found between the wear value and AE characteristics such as the count rate and the average amplitude of pulses. When testing steel 45 specimens treated in different ways including laser treatment the similar results were obtained on the relation of AE characteristics and the metal wear resistance. A continuous CO2 laser was used to irradiate specimens. An absorbing coating based on zinc oxide was deposited on the specimen surfaces before irradiation. The surfaces were scanned by a laser beam perpendicular to them with the spot diameter 3 mm. The scanning speed was 25 mm/s, the scanning amplitude was 10 mm and the radiation power was 1 kW. Under these conditions the metal surface did not melt. As a result, the surface material hardness increased to HRC = 47–54 and the depth of the hardened layer was about 1 mm. Before the tests the treated specimens were hand-ground to the 8-th roughness class. The roughness was measured by a profilometer. The tests were carried out on −‹ƒ…‰-Š set-up. A hemispherical pin made of steel “815 with the curvature radius 4 mm served as a counterbody. The normal load was 17.5 N, the sliding velocity was 0.8 mm/s and the sliding distance was 48 mm. The friction force and the count rate of AE pulses were measured in the steady-state mode. After 100–300 cycles since running-in continued the experiments were stopped, the completion of running-in was determined by AE characteristics. Wear was found by measuring the cross profile of the friction track at least in eight different track regions using the profilometer. The relative wear rate was calculated by the formula I = S/Ln mm2 /m where S is the cross-section area of the track in mm; L is the sliding distance in m; n is the number of test cycles. Table 4.7 presents the friction coefficients and wear characteristics for the tested specimens. It is seen from the table that the laser treated specimens have

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171

Table 4.7. Results of Wear Tests of Steel 45 Specimens Material – steel 45

n

f

S mm2

I mm2 /m

N˙ , pulses/s

After hardening with high tempering

150

042

468

65

150

After normalization

160

044

387

54

150

After furnace hardening

180

068

720

84

–

After laser treatment

310

039

143

10

40

Note: n is the total number of cycles; f is the friction coefficient in the steady-state mode; S is the area of the wear track; I is the relative wear resistance; N˙ is the count rate in the steady-state mode.

the maximal wear resistance. The count rate of AE pulses equal 40 pulses/s was also minimal. The analysis of AE sources acting when using such geometry and regimes of tests allows one to think that acoustic signals are mainly caused by crack formation in the material surface layers. The growth and origination of microcracks result in material wear and are accompanied with AE. When studying time dependencies of the number of AE pulses registered in one cycle it was found that this characteristic varies periodically with increasing number of cycles. This proves periodical changes in the structure of the material surface layer and the periodical character of wear particle separation. Therefore, a conclusion can be derived that under given friction conditions wear is caused by fatigue processes running in the material surface layer. The minimal wear rate of the laser treated specimens can be explained probably by the occurrence of compressive stresses in the metal surface layers in laser treatment without fusion (at the fusion limit) which hamper the development of fatigue cracks. AE tests of specimens made of different materials obtained or treated using one of the above mentioned methods have shown that their wear is proportional  to the parameter j Nj Aj (see expression (4.1)). O.V. Gusev called it AE generalized parameter [12] and found that it characterizes the degree of the brittle fracture of the material and is an integral (additive) parameter when describing the processes of the accumulation and growth of microcracks in brittle solids. Let us show that in the fatigue wear of friction surfaces caused by crack formation this parameter can be related to the wear value being the volume or mass of the removed material.

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Fatigue wear is the result of the accumulation of defects (microcracks) in the surface layer followed by the separation of material particles. The value of such wear can be assessed by a parameter related to the size of a critical surface microcrack which finally governs the volume of a wear particle. Critical microcracks result from several stages of the propagation of initial cracks (socalled stepwise crack propagation), each stage is accompanied by AE. In many papers dealing with AE studies of metal fracture a relation between crack dimensions and AE characteristics is mentioned (see Table 1.2). For example, it is shown in paper [12] that the amplitude of AE pulses is proportional to the length of the crack propagation step. Recently correlation between the amplitude of AE pulses and dimensions of uniformity brakes in materials has been experimentally proven. If we suppose that the growing-up of a crack induces AE pulse whose amplitude n0 Ak is proportional to the length of the propagation step lk then the sum k=1 Ak (n0 is the number of crack propagation steps) hence the number of AE pulses are proportional to the total length of appearing microcracks. The following equalities are apparent: n0  k=1

Ak =

 j

Nj Aj n0 =



Nj 

j

 where Nj is the number of pulses with amplitude Aj . So, the parameter j Nj Aj can serve as a measure of the total length of cracks in the material surface layer. Assuming that the wear rate i is proportional to the total length of cracks appearing per unit time we obtain expression (4.1). Therefore, one can assess the wear rate by the value of the product of the count rate and the average amplitude of AE pulses that is confirmed by the study results described above. It is known that the proportionality between the wear and the total AE count retains for the steady-state friction mode when AE characteristics including the amplitude distribution of pulses became stable. Different patterns of the time dependencies of the “average” count rate and the wear at the initial friction stage (running-in) can be explained by the variation of the amplitude distribution of AE pulses in time (see, for example, Figs. 4.1 and 4.25). It follows from the model considered in [5] that AE count rate allows one to assess the wear rate of materials during steady-state friction. It should be noted that proposed dependence (4.1) is of a more general pattern; it agrees well with the experimental results (Fig. 4.28) and makes it possible to assess the wear rate at any stage of friction. To apply formula (4.1) in practice one should determine the range of acoustic pulse amplitudes corresponding to the processes of crack formation in surface layers of the materials under testing (it is best to do this experimentally). Note that in some cases it is an arduous task. Nevertheless, the dependence

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173

can be used to assess qualitatively the wear resistance of surface layers. If roughness parameters of the surfaces and physical-mechanical characteristics of the specimen materials are the same this expression is promising for the expressmonitoring of the wear resistance of materials treated by different physicalmechanical and physical-chemical methods. It is enough to obtain one or two datum points to determine the coefficient B in formula (4.1) and then measure only the mentioned combined parameter of AE.

4.5. ACOUSTIC-EMISSION METHODS FOR CONDITION MONITORING OF FRICTION UNITS When carrying out the theoretical and experimental studies whose main results are described in the above parts the basic regularities of AE at friction both with and without lubricants were established. The obtained data formed the basis for the development of methods of the condition monitoring and diagnostics of friction units.

4.5.1. Monitoring of Running-In in Friction Pairs As it was noted above running-in is the process of change in the microrelief of friction surfaces and physical-mechanical properties of the surface layers during the initial period of friction under constant external conditions. As a result, the friction work, temperature, and wear rate decrease and become stable in time. For this reason all methods of determining the completion of running-in involving AE characteristics are based on the registration of an instant when some characteristic of acoustic emission stops to vary in time. Almost any informative characteristic of AE mentioned in Parts 1.2 and 1.5 is suitable for this purpose. Values of the selected characteristic are measured in equal time intervals. The obtained data set is a sampling of random values which can be analyzed by common methods of mathematical statistics. For example, in order to determine if AE characteristics vary in time the obtained sampling can be analyzed for the availability of trend being the slow monotonous or low-frequency periodical change of the measured characteristic in time. The presence of the trend indicates that running-in continues. Trend verification is a well-developed statistical procedure and we do not consider it in detail. We only note that since values in the sampling (AE characteristics) can obey different distribution laws, as a rule unknown a priori, at different stages of friction pair operation non-parametric tests are advisable to be used which do not requires the knowledge of distribution laws. Run test and inversion test are the examples of such tests [13].

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174

Practical experience shows that the count rate, the variance of amplitudes of AE pulses, and the correlation coefficient are the most suitable AE characteristics for running-in monitoring from the registration and processing viewpoint. For this reason we describe below the methods of determining the completion of running-in involving exactly these characteristics despite the above mentioned fact that similar methods can be developed using other AE characteristics [14, 16, 17, 18, 19]. The analysis of AE count rate. The essence of the method is as follows [15]. Values of the count rate of AE pulses are measured in equal time intervals, for example, in 1 min. As a result, a sampling with amount n random values being the values of AE count rate {N˙ i } is obtained. The mean and the standard deviation of the sampling are found from known formulas:

N˙ =

1 n

n 

N˙ i

  n   =  N˙ − N˙ i 2 nn − 1

i=1

i=1

Then confidence limits of the mean value N˙ are determined N˙ = tn−1 

(4.2)

where tn−1 is the Student’s test;  is the confidence probability. Then the relative variation of the count rate at the beginning and end of the measurements is found: N˙ =

N˙ N˙

· 100%

which characterizes the degree of running-in. Running-in is considered to stop if the parameter N˙ is within a preset range from 1 to 2 . The limits are usually 1 = 5% and 2 = 10%. The sampling should contain at least 8–10 measurements at a certain interval of measurement time to obtain statistically significant results. The instant starting with which the parameter N˙ is within the above range is considered as the completion of running-in. The analysis of the variance of AE pulse amplitude. The variance of the pulse amplitude is calculated from the results of the registration of AE amplitude distribution. The latter is determined by connecting a pulse analyzer to the recorder, for example, ‹ƒ−-‡ƒ−ƒ instrument or is calculated by processing AE signals provided that a computer is contained in the measuring system used to register signals.

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175

The algorithm of the processing of the measurement results is as follows. The average value of the pulse amplitude or the number of the analyzer channel corresponding to the average amplitude are calculated: I¯ =

n 

Ni i

 n 

i=1

Ni

i=1

where Ni is the number of pulses in the i-th channel of the analyzer; n is the number of filled channels of the analyzer. Then the variance of the pulse amplitude is found: D=

n 

 Ni I¯ − i2

n 

Ni 

i=1

i=1

Then confidence limits for the parameter I are determined by formula (4.2) and operations are performed described in the previous item. The instant starting with which the parameter I¯ is within the above limits is the time when runningin stops. The analysis of the correlation coefficient. A sampling of values of the count rate of AE pulses N˙ measured in equal time intervals is obtained. The duration of the intervals is selected in accordance with the probable duration of running-in (from a few seconds to a few minutes). The sampling should contain at least fifty values of the measured characteristic. The correlation coefficient is calculated for the instant T1 = n1 t: n1 

R1  T1  =

N˙ itN˙ it + 

i=1

n1  

2 N˙ it



i=1

Here t is the time interval between instants of registering AE count rate;  = kt k = 1 2     is the phase shift. Then the correlation coefficient is calculated by the same formula for the instant T2 = n2 t. The difference R = R2 – R1 and the ratio R =

R · 100% R2

are determined. If R <10% then running-in is considered to continue at the instant of the determination of the count rate N˙ .

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The measurement error of the instant of running-in completion depends on the duration of the time interval T = T2 –T1 , the phase shift  and the amount of the sampling. It decreases with increasing amount of the sampling, parameter  and decreasing interval T .

4.5.2. Condition Monitoring of Lubricating Film in Friction Pairs The failure of a lubricating film on friction surfaces is usually determined by changes in the friction force, temperature, wear rate or the state of the friction track. In the latter case it is necessary to stop the machine, dismantle the friction unit and examine the surfaces of the rubbing parts. These methods are apparently labor-consuming and expensive if the matter concerns the field inspection of massive units and machines. Moreover, they are inapplicable in some cases. In such cases AE methods are evidently advantageous. Below we describe the methods which allow one to determine an instant when the damage of friction surfaces begins, the severity of damage and the relative area of the damaged films [20, 22]. The determination of the instant of the damage to films on the friction surfaces. The count rate of AE pulses is registered in certain time intervals under constant conditions influencing the friction mode including the sliding velocity, load, temperature etc. As it was mentioned above, when the friction pair is run-in this characteristic varies in a random way from one reading to another within a small range relative to its mean value. A sharp (by 20% or more) increase of the count rate at some instant indicates the beginning of film or coating damage. The non-stationary variation of AE count rate with great oscillations relative to the mean value corresponds to further friction. The instant when the lubricating film begins to fail can be determined more precisely if one checks the sampling of values of the registered count rate for trend. The determination of the damage degree of a lubricating film on friction surfaces. The average value of AE count rate N˙ r is previously determined for the steady-state friction of the pair with a coating or a lubricating film under study. Then the average value of the count rate N˙ d is determined for the friction of the same materials with dry surfaces. In both cases tests are performed under the same conditions including the sliding velocity, load, temperature, etc. Also settings of the measuring instruments used such as the discrimination level, amplification factor, frequency pass band and others should be the same. All the listed factors should correspond to conditions under which the state of the lubricating film or protective coating are monitored in operation of the friction unit.

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177

The damage degree of the film or coating is assessed by the parameter  =

N˙ f − N˙ r  N˙ d − N˙ r

Here N˙ f is the value of AE count rate in the process of coating damage. The time history of the parameter  allows one to determine the kinetics of the damage of the coating or film. The determination of the relative damaged area of a protective coating on friction surfaces. To determine this characteristic it is necessary to know the values of AE count rate for dry friction of the materials N˙ d and for the steady-state friction N˙ r . AE count rate is being continuously registered in the process of test. If signs of damage appear (see above) the instant T1 is noted when N˙ f ≥ 12N˙ r . In further measurements the instant T2 is noted when the count rate N˙ is again equal to the value corresponding to friction with the undamaged coating. The time interval T = T2 – T1 is determined during which the coating has been damaged. The relative value of the damaged area S of the coating is calculated by the following formula S=

vbT  Sa

where v is the sliding velocity; b is the width of the friction track; Sa is the apparent contact area. To give an example of the application of the method let us consider the data obtained in monitoring of the materials coated with MoS2 which are presented in Fig. 4.31. The tests were carried out in a set-up involving the “pin-on-disc” geometry. The disc was made of steel 45 and was covered with a protective coating and the pin was made of brass †62. Test conditions were as follows: the sliding velocity – 0.01 m/s, the load – 5 N, the friction track radius – 50 mm. The average AE count rate after running-in was 160 pulses/s. The count rate in friction of the same materials without the coating was N˙ d = 180 pulses/s. In 120 s after running-in the count rate increased to N˙ f = 310 pulses/s and in 123 s it became equal to its initial value (see Fig. 4.31), that is, T = 3 s. In accordance with the mentioned formula we can determine the relative value of the coating damaged area S = 3 · 001 · 0006/0006 · 314 · 005 · 2 = 01

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178

N - 10 -2, pulses/s 8

6

4

2

NP Nn T2

T1 0

115

120

125

1000

1005

t,s

Figure 4.31. Time dependence of count rate of AE pulses: friction pair: steel 45 – brass † 62; coating – on basis of MoS2 ; sliding velocity – 0.01 m/s; load – 5 N

4.5.3. Optimization of Friction Surface Microrelief The microrelief of rubbing surfaces plays an important role in dry friction and boundary lubrication, it governs frictional characteristics of a friction unit to a great extent. Proceeding from the molecular-mechanical theory of friction the possibility of microrelief optimization has been shown using the criteria of maximal wear and scuffing resistance and minimal friction coefficient [6]. Such optimization can be provided by depositing regularly disposed grooves perpendicular to the sliding direction on the friction surface. In this case a problem arises how to select optimally their parameters, namely the ratio of the spacing between the grooves a to their width b. If the ratio a/b is great the molecular component of friction increases otherwise the mechanical component rises. It has been found that AE phenomena can be used for the purposes of surface microrelief optimization. Let us describe the method of such optimization using the following example [23]. The experiments were carried out on −‹ƒ…‰-Š set-up described in Part 3.4. The geometry of friction between the moving and stationary specimens was implemented in the set-up using a specially designed additional unit. AE characteristics were registered by ‹ƒ− instrument. A parallel-sided plate made of steel 45 and polished to Ra = 02 m was used as a moving specimen. A thin film of the lubricant under study was deposited onto the adsorption refined plate surface and spread by the counterbody under a load of 15 N before each test. Two lubricants were tested which differed significantly in their properties, namely ƒ!4ƒ‡-201 grease and ƒ-20A oil.

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179

During the first set of experiments we assessed the fit of the registered results of AE signal characteristics to the data obtained when measuring the electric conductivity of the specimen contact. For this purpose the stationary specimen was made multipiece, that is, as a set of thin steel plates with thickness l = 001–01 mm placed vertically and separated with insulating spacers with thickness s = 01–02 mm. Specimens with different ratios a/b and s/l were tested. The critical parameter s/lc was determined by an increase in AE count rate. During the second, main set of experiments, we determined the optimal ratio a/b and used steel 45 bars polished to Ra = 02 m having grooves on their working surfaces with a certain ratio a/b for each bar. In addition, specimens without grooves were tested. The specimen, which produced the minimal AE count rate, was determined in the tests. The friction coefficient and the total number of AE pulses Np in one pass of the moving specimen averaged over ten cycles were measured. The amplitude distribution of detected pulses, the average values of the amplitude, and the number of AE pulses Na were registered. The results of the first set of experiments are presented in Table 4.8.

Table 4.8. Results of Measuring Parameter (s/l)c Lubricant

Parameter obtained when measuring electric conductivity

acoustic emission

ƒ-20A

15

14

ƒ!4ƒ‡-201

27

27

As it is seen from the table the values of the measured characteristic corresponding to the beginning of film starvation and to increase in the molecular component of friction are almost the same when assessing the friction mode by electric conductivity measurements and AE characteristic measurements. The results of the second set of experiments are listed in relative units in Table 4.9. It is seen from the data in the table that the use of grooves in case of oil ƒ-20A little apt to oil starvation increases AE count rate hence the antifriction effect reduces due to the increase of the mechanical component of friction. The greater the portion of the apparent contact area occupied by the grooves the more severe is friction. When using grease ƒ!4ƒ‡-201 apt to oil starvation the use

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180

Table 4.9. Values of AE Characteristics at Various Ratio a/b Lubricant a/b

ƒ-20A

ƒ!4ƒ‡-201

Na

Np

¯ A

Na

Np

¯ A

5.0

19

52

11

13

09

12

3.5

25

59

11

12

10

10

2.5

28

77

12

09

07

09

1.0

33

86

20

14

16

15

of the grooves with certain parameters reduces oil starvation and improves the antifriction characteristics of the contact as it follows from the data in the table. The optimal value of the parameter a/b = 25 that corresponds to the results obtained by other researchers used more complex methods.

4.5.4. Determination of Number of Juvenile Contact Spots The analysis of data on the friction of specimens with different surface relief in the normal friction and oil starvation modes has shown that AE characteristics allows one both to identify the friction mode and to determine the number of juvenile contact spots and their size distribution. For this purpose the amplitude distribution of AE pulses is registered in friction at a given distance between the plate specimens, for example 0.2 mm, with a lubricant. In this case the normal mode of boundary lubrication occurs. Then the distance between the specimens is reduced to 0.05 mm and AE amplitude distribution is again registered under the same conditions. In the latter case oil starvation takes place. AE characteristics change significantly that indicates the beginning of the lubricating film damage. Spots of juvenile contact between the rubbing materials appear. Subtracting one amplitude distribution from another we obtain a function which is proportional to the size distribution of juvenile contact spots. The analysis of this distribution has shown that with confidence probability 90% it coincides with the normal law. This is proven by the data of measuring the electric conductivity of contact by the arbitration method. The number of AE pulses in the distribution obtained by subtracting the initial amplitude distributions is proportional to the number of juvenile contact spots which can be calculated using an experimentally determined scaling factor [23].

BASIC REGULARITIES OF ACOUSTIC EMISSION AT FRICTION

181

The presented data show that AE characteristics contain information on friction conditions for real contact spots and that AE method can be used to optimize the surface microrelief in order to realize completely the lubricity of oils and additives.

REFERENCES 1. Kragelskii I.V., Friction and Wear, Pergamon Press, Elmsford, 1982. 2. Goryacheva I.G. and Dobychin M.N., Mechanism of formation of roughness during running-in, Soviet Journal of Friction and Wear, vol. 3, No. 4, pp. 16–22, 1982. 3. Poltzer G. and Maissner F. Foundation of friction and wear (Russian translation) Moscow, 1984. 4. Possibilities of sliding pair diagnostics and control due to acoustic emission signals generated by friction contact zone processes/Szchavelin V.M., Sarychev G.A., Schachnovskyi M.I., and Revenko V.M. // Proceedings of the III Symposium of the IMEKO Technical Committee on Technical Diagnostic (th 10). Moscow. Oct. 1983. Budapest. IMEKO. 1984, pp. 501–512. 5. Belyi V.A., Kholodilov O.V., Sviridenok A.I. Acoustic spectrometry as used for the evaluation of tribological systems. // Wear. 1981, vol. 69, no 3, pp. 309–319. 6. Akhmatov A.S., Molecular Physics of Boundary Lubrication, Israel Program for Scientific Translation, 1966. 7. Baranov V.M., Kudryavtsev E.M., Sarychev G.A., On Interrelation Between the Amplitude Distribution of Acoustic Emission Signals and the Statistical Parameters of Rubbing Surfaces. // J. of Friction and Wear, 1999, v. 20, n. 2, pp. 70–73. 8. De Ge A.V.D., Salomon G., and Zaat D.Kh., Mechanism of failure molybdenum disulfide film in sliding friction (Russian translation), New to lubricants, pp. 242–254, Moscow, 1967. 9. Drozdov Yu.N., Archgov V.G., and Smirnov V.G., Anti-scuffing stability of rubbing bodies. Moscow, 1981. 10. Filatov S.V., Acoustic emission at abrasive wear of metals, Soviet Journal of Friction and Wear, vol. 3, no. 3, pp. 24–29, 1982. 11. Sviridenok A.I., Kalmykova T.F., and Kholodilov O.V., Study of real area of friction polymer-metal contact using acoustic emission, Soviet journal of friction and wear, vol. 3, No 5, pp. 808–812, 1982. 12. Gusev O.V., Acoustic emission at deformation of monocrystals of refractory metals (in Russian) Moscow, 1982. 13. Bendat J.S. Random Data Analysis and Measurement Procedures. John Wiley & Sons. New York, 1986, – 540 p. 14. USSR Patent 849046. Method for determination of instant of coating failure, Szchavelin V.M., Baranov V.M., Sarychev G.A., Molodtsov K.I. 15. USSR Patent 1073614. Method for determination of instant of friction pair runningin completion, Szchavelin V.M., Sarychev G.A., Revenko V.M.

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16. USSR Patent 1158903. Method for determination of instant of friction pair runningin completion, Szchavelin V.M., Sarychev G.A., Shakhnovskii M.I., Revenko V.M., B.M., Goryacheva I.G., Dobychin M.N., Kholodilov O.V. 17. USSR Patent 1244565. Device for determination of instant of friction pair runningin completion, Sarychev G.A., Szchavelin V.M., Revenko V.M. 18. USSR Patent 1582068. Method for determination of instant of friction pair running-in completion, Gerasimov G.A., Sarychev G.A., Shakhnovskii M.I., Szchavelin V.M. 19. USSR Patent 1656401. Method for determination of friction regime, Kuznetsov A.A., Sarychev G.A., Szchavelin V.M. 20. USSR Patent 938095. Device for determination of friction coefficient of solids, Kostochka A.V., Kuznetsov A.A., Sarychev G.A., Shakhnovskii M.I., Szchavelin V.M. 21. USSR Patent CP 938133. Method for control of coating material, Szchavelin V.M., Sarychev G.A., Shakhnovskii M.I. 22. USSR Patent 1330516. Method for determination of instant of friction pair coating failure, Bykov A.N., Sarychev G.A., Szchavelin V.M. 23. USSR Patent 1352317. Method for determination of friction process, Kragelskii I.V., Sarychev G.A., Gitis N.V., Szchavelin V.M., Shakhnovskii M.I.

Chapter 5

FRICTION OF NUCLEAR POWER ENGINEERING MATERIALS

5.1. EFFECT OF IONIZING RADIATION ON TRIBOENGINEERING BEHAVIOR OF MATERIALS Materials and process equipment of nuclear power plants (NPP) are intended for operation in various gaseous and liquid media under extreme conditions including the effect of ionizing radiation and elevated temperature up to 1000  C. Inert gases, carbon dioxide, distilled water, water-steam mixture at high state parameters, and liquid sodium can be used as an operating fluid depending on a reactor type and the destination of parts and mechanisms. Both the operating fluid and operation conditions of materials influence triboengineering characteristics of the materials. It should be noted that the mentioned factors affect jointly the materials or units of mechanisms and their effect is not a simple sum of individual effects of the factors. One also encounters radiation effects when using different types of ionizing radiation for processing purposes if it is necessary to obtain certain properties of materials, particularly to improve the wear resistance of surface layers of parts. Radiation tribology deals with the study of the effect of specific operation conditions of nuclear power systems on triboengineering behavior of materials and how this behavior changes when using ionizing radiation as a technique of part processing. This is a relatively new direction of tribology which rests first of all upon progress in radiation physics of solids and radiation materials science. Undoubtedly, the use of the acoustic emission method can be helpful when obtaining experimental data on the behavior of materials in so unusual conditions. One of the aims in this direction is to select materials of friction members and lubricants for operation under reactor conditions. Most of oils, greases, and polymers loss their antifriction properties under extreme conditions. It is mentioned in review [1] that corrosion-resistant materials, hard alloys, hard coatings such as graphite-containing composites, molybdenum and tungsten disulphides, chrome steels, chrome and tungsten carbides are best suitable for operation under the effect of radiation. Reviews [2, 3] and hand-book [4] contain only brief information on the effect of extreme conditions on the triboengineering behavior of materials. The effect of temperature. The elevation of temperature in oxygencontaining environment results usually in the activation of oxidation, diffusion and sintering which in their turn increase adhesion and vary physico-mechanical

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characteristics and the structure of material surface layers [4–6]. Since the mentioned processes are interrelated and governed by interaction between surface layers and the environment their effect on the friction and wear of materials requires profound analysis. First of all, the elevation of temperature leads to the oxidation of metal surfaces. As a rule, oxide films reduce friction and prevent seizure and catastrophic wear. Yet, in friction of molybdenum disulphide in heated helium impurities of water vapor and oxygen cause a considerable increase of the friction force and wear rate. The presence of moisture in carbon dioxide results in similar effects. As experimental studies have shown [1], a low moisture content can reduce significantly the service life of ball bearings in carbon dioxide. Similar data on the effect of oxygen were obtained in friction of chromium steels at 500–600  C. Friction in gas, water and sodium coolants is characterized by considerable variations in the wear rate at elevated temperatures. The severe damage of material surface layers occurs in inert media. This can be explained by the fact that a protective oxide film covering material surfaces is very thin and easily fails in friction and no new film is formed. Intensive mass transfer runs and, as a rule, the total material wear is low. Note that no satisfactory explanation of many effects related to the influence of temperature is available so far. The influence of ionizing radiation. Till recently the effect of ionizing radiation on the frictional behavior of materials has been studied by testing irradiated specimens of the materials in shielded chambers. Such tests were called post-radiation tests. The development of intrareactor friction devices makes it possible to carry out studies directly inside the reactor active zone. It has been found that in some cases data of post-radiation tests differs from those of intrareactor studies. This is of great importance for materials and mechanisms intended for operation directly in the irradiated zone. Variations in physico-mechanical properties of materials due to the effect of radiation result mainly from the action of neutrons and gamma-quantums. The influence of the latter appears basically as the radiation heating of materials and can be neglected in the first approximation. Irradiation with neutrons increases the yield point and reduces the ductility, causes the expansion of materials and accelerates corrosion processes. All these processes can change material frictional behavior. Little data are available on the friction of irradiated materials. Paper [7] contains data on the post-reactor tests of iron and copper alloys. Armcoiron, annealed and hardened steel 45, malleable cast iron, commercial copper, brass, and lead bronze were tested. Specimens were irradiated with fluences 1020  1021  1022  1023 , and 1024 neutrons/m2 at a temperature of 220  C. The face contact geometry was used. Three cylindrical specimens 3 mm in diameter slid over a steel 45 plate with hardness HRC 42 under boundary lubrication. Diesel oil ¨Š-14 was used as a lubricant. Ferrous metal specimens were tested under

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185

a pressure of 6 MPa while non-ferrous metal specimens – under 14 MPa. The sliding velocity was 4.1 m/s in the former case and 6.6 m/s in the latter case. Test duration was 10 hours. The wear, friction coefficient and lubricant temperature were measured. Antifrictional properties of annealed steels and malleable cast iron have been found to deteriorate at a low exposure dose and to improve at doses 1023 neutrons/m2 and more. The materials became somewhat weaker after irradiation with 1020 –1022 and harder at 1023 neutrons/m2 . The wear resistance of hardened steel changed similarly to its hardness. Therefore a conclusion was derived that results of hardness measurements can be used to assess the wear resistance of irradiated materials. The friction coefficient of the irradiated ferrous metals was almost constant. It only tended to rise with increasing exposure dose. It was found that the friction coefficient of irradiated materials changed similarly to the ratio of the yield stress to the hardness of the materials. Tests of austenite stainless steel X18H9T are of great practical importance. This steel is known to have poor antifrictional properties due to its susceptibility to seizure and scoring. Different coatings were selected and tested which might harden the steel surface and had good antifrictional properties. Specimens of the materials were irradiated with a fast neutron fluence of 27 · 1024 neutrons/m2 at a temperature of 650  C. Coatings were obtained by the plasma deposition of molybdenum, thermodiffusion chromizing with nitridizing and the thermodiffusion penetration of chrome boride and carbide, their hardness and wear resistance were studied. In the initial state at room temperature the Vickers hardness of steel was 2300 MPa. It decreased monotonously in heating and halved at a temperature of 600  C. A Vickers hardness tester served to measure the coating hardness under a load of 100 N. The indent depth was less than 0.05 mm. Such conditions were selected to exclude the effect of the ductility of bulk metal on the results of measuring the hardness of the surface layer. It is found that the hardness of the coatings changes under the effect of radiation. Thus, the hardness of the chrome boride coating decreased in comparison with the initial and thermostated states after irradiation at 600–650  C. The hardness of the molybdenum coating decreases especially noticeably (almost twice) after irradiation. Based on the obtained data a conclusion has been derived that irradiation at elevated temperatures is a weakening factor. The neutron irradiation of steels, chrome nitride, boride coatings and (l` alloy coatings causes changes in their structure and hardness and intensifies diffusion. As a result, the frictional behavior of the materials varies. Stainless steel and hardening coatings were tested at elevated temperatures in argon, liquid sodium and argon mixed with sodium vapor. The tests were carried out using the end contact of two bushings. The friction torque, wear and temperature of the environment in the operating chamber were registered. Test conditions were as follows: the sliding velocity – 5 m/s; the pressure – 2.5 MPa;

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the temperature – 350  C. The excessive pressure in the chamber was 2–3 kPa. The test duration was 5 h that corresponded to 1.5 km long friction path. Specimens were gradually loaded during 40 min. Non-irradiated, thermostated and irradiated specimens were tested. The specimens were irradiated with fast and thermal neutrons with fluences 11 · 1024 and 37 · 1024 neutrons/m2 , respectively at 500  C during 410 hours. The following results were obtained. Irradiated specimens tested in argon purified from moisture and oxygen had the highest wear and friction coefficient. Steel X18H9T had the minimal wear resistance. Yet, its friction coefficient was high. The elevation of the temperature to 350  C in dry friction resulted in the severe plastic deformation and seizure of austenite steel due to its low hardness, high toughness and ductility. Under these conditions the molybdenum coating on the steel surface reduced the friction coefficient to 0.4–0.5 yet the steel wear resistance did not increase. Chrome boride and carbide coatings showed the best antifrictional properties. Their wear rate was 4–5 times less than that of steel X18H9T and the friction coefficient was 0.3–0.5. After neutron irradiation the wear of all materials in argon decreased and their friction coefficient increased. The latter fact can be attributed to material weakening due to the radiation damage of irradiated specimens. Indeed, the deformation of friction surfaces increases with decreasing hardness and elasticity modulus, hence the real contact area grows. This causes the friction coefficient to rise. The measurement of the hot hardness of specimens has shown that in most cases it is less than the hardness of non-irradiated material at temperatures 20–600  C. In friction of irradiated stainless steel against cermet material Fe15 Mo6 CaF2 in argon mixed with sodium vapor the strain hardening of steel and the transfer of cermet material on the steel surface occur. The cermet alloy acts as a protective layer preventing the steel part against wear. The wear of the steel part is by two orders of magnitude less than that of the cermet insert. Paper [7] presents the study results of the strength and efficiency of friction member materials used in mechanisms of nuclear reactors with sodium coolant. The diffusion chrome nitride coating on steel X18H10T, cobaltless faced alloys (-6 and (-12M, faced stellite (-12 and high-speed steel P18 were tested. Steels X18E9, X18H10T and precipitation-hardening steel Š˘ı(8¯´¯‡|4™‹) with improved high-temperature strength served as substrate materials. Test conditions were as follows: the test geometry – “pinon-disc”; the load – 2 MPa; the sliding velocity – 3.1 m/min; the friction path – 3600 m. Specimens were irradiated in |‹-5 reactor with fluences up to 27 · 1025 neutrons/m2 at temperatures 350–500  C. The hardness of steel P18 and alloy -6 remained almost unchanged after irradiation in comparison with that of reference specimens exposed at 500  C while the hardness of alloys -12 and -12M increased slightly. The wear

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187

resistance of the materials in argon mixed with sodium vapor and in pure sodium increased with increasing hardness of the mated surfaces. This dependence was more pronounced in the former case. It should be kept in mind that sodium acts as a lubricant and coolant thus improving antifrictional properties of the materials being tested. It is found that under conditions corresponding to the operating conditions of intrareactor devices steels faced with the wear-resistant chrome nitride layer and steel P18 are preferable. The wear of these materials is within the permissible range. The irradiation with fluence 27 · 1025 neutrons/m2 causes the embrittlement of the wear-resistant faced alloys and steel P18 which appears mainly as a decrease in the ductility or as a sharp drop of the strength if the ductility has been exhausted. The hardness and antifrictional characteristics of the studied materials related to it did not become worse when irradiating specimens at 500  C. The irradiation of steel P18 at 640  C reduces its hardness additionally to the effect of the temperature. Data on the influence of the irradiation of materials by charged particles with a small penetration depth, namely electrons, alpha-particles and ions, on friction are of interest. In this case the effect of extremely low friction occurs. For example, if specimens of molybdenum disulphide, tungsten disulphide, polyethylene, polypropylene and some other materials rub against a ball made of steel “815 and are irradiated by alpha-particles with energy 32 · 10−16 j (2 keV) at current density 75 A/cm2 in vacuum 10−4 –10−3 Pa the friction coefficient decreases and reaches 10−3 –10−2 that is typical for hydrodynamic or rolling friction. This effect occurs only provided that the surface of one of the rubbing bodies is irradiated. The effect does not appear if irradiation is stopped. The friction coefficient grows gradually to its initial value corresponding to the friction of non-irradiated materials. The effect of extremely low friction is explained by the fact that highly intensive radiation causes the cleaning of surface layers of some materials from contaminations, first of all, water molecules, being the source of strong adhesion junctions.

5.2. FRICTION OF MATERIALS OF FUEL AND FUEL ELEMENT CLADDING OF NUCLEAR REACTORS The friction of nuclear fuel pellets against structural alloy Zr + 1% Nb in fuel elements of energy reactors and the efficiency of some kinds of barrier coatings deposited onto the inner surface of claddings made of the same alloy have been investigated in the framework of studies intended to solve the problem of interaction between the fuel and the cladding. Some aspects of the problem were discussed above and they are described in detail in papers [8–10].

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188

Intrareactor studies of friction in the “uranium dioxide – zirconium alloy” pair were carried out in yPT-4 set-up (see Part 3.5) in the vertical channel of ƒ‹4 ‡ƒ−ƒ research reactor at flux densities of thermal neutrons 15    3·1017 and fast neutrons with energies more than 0.1 MeV – 3    5·1016 neutrons/m2 ·s. To retain the necessary test temperature the capsule device of the set-up were equipped with a resistive heater which provided temperature in the contact zone 800 K with account for heat generation in fuel pellets. The dynamic friction force, the static friction force and the temperature in the contact zone were registered. The nominal pressure was varied from 5 to 30 MPa. The sliding velocity was 11 · 10−6 and 13 · 10−3 m/s. The measurements were performed under the following conditions: at the rise of the reactor power in stepwise and continuous regimes, in the stationary regime when the reactor operated with a preset power, at the decrease of the reactor power with different rate, and in stopping the reactor at the same temperature as the irradiation temperature. The basic results of the intrareactor tests are as follows. With increasing reactor power the sliding friction coefficient somewhat increased that can be explained by the heating of uranium dioxide due to the effect of radiation. Measurements performed at stepwise and sharp power decrease (when modeling the emergency operation mode) at a constant temperature has shown that the sliding friction coefficient remained unchanged at a velocity of 13 · 10−3 m/s. Figure 5.1 illustrates the dependence of the sliding friction coefficient fsl for the UO2 – Zr + 1% Nb alloy pair on the fluence of thermal neutrons at a nominal pressure of 5 MPa. Data on the influence of irradiation on the static friction coefficient fst are of great practical importance. It is seen from Fig. 5.2 and 5.3 that fst rises with prolonging duration of exposure of specimens under load. In this case the static friction coefficient depends on both the neutron flux density and the absorbed fluence. fsl 0.5 0.4 0.3 0

1017

1018

1019

F, neutrons/cm2

% Nb alloy pairs as a Figure 5.1. Sliding friction coefficient of UO2 – Zr +1% function of neutron fluence E < 01 eV When interpreting the results of measurements of the static friction coefficient one should have in mind that the shear resistance depends on both mechanical properties of mated materials and the real contact area. The latter, in its turn, is determined by the surface microgeometry and the material creep.

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189

fst 1.0 1

0.9 0.8

2 0.7 0.6 0.5 1022

1023

1024 F, m–2

Figure 5.2. Effect of neutron flux density E < 01 eV on static friction coefficient at T= 573 K: 1, 2 – preliminary exposure under load during 20 and 0.5 h, respectively fst 1.0 0.9 1 0.8 2

0.7 0.6 0.5 0.4 1015

1016

Φ, m–2 · s–1

Figure 5.3. Effect of neutron fluence E < 01 eV on static friction coefficient at T = 573 K (designations see in Fig. 5.2) Depending on the creep rate and the duration of the preliminary loading of specimens the real contact area can change significantly that influences the value of fst . In the absence of radiation microasperities of the surface of a fuel pellet penetrate into the alloy surface layer because the hardness of uranium dioxide is 3–3.5 times higher than that of the alloy and they deform its surface microasperities. With prolonging duration of loading the approach of the mated specimens increases due to the creep of the zirconium alloy. The real contact area grows, hence the static friction coefficient rises. As the alloy becomes harder in the

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190

contact zone the rate of fst rise decreases with prolonged duration of loading (see Fig. 5.4, curves 3 and 4). Such behavior of the static friction coefficient agrees well with known ideas about the effect of the creep of the softer pair’s material on the value of the real contact area. fst 1 0.8

2

0.7

0.6 3

4

0.5 0.4 0

5

10

15

t, h

Figure 5.4. Dependence of static friction coefficient on duration of preliminary exposure under load at T= 573 K: 1, 2 – irradiation with neutron fluence 1024 neutrons/m2 E < 01 eV and 1022 neutrons/m2 ; 3, 4 – in laboratory conditions (without irradiation) for zirconium alloy specimen with hardness HV 1500 and 1700 MPa As it is known, irradiation varies many physico-mechanical properties of materials such as the hardness, creep rate, yield stress, ductility etc. The rise of the creep rate of uranium dioxide under the effect of radiation plays the most significant role for friction in the pair under study. This rise can be thought to be proportional to the flux density of thermal neutrons. At the same time the creep rate of the zirconium alloy is almost independent of the flux density. For example, the creep rate of uranium dioxide is approximately ten times higher than that of the alloy Zr + 1% Nb at a temperature of 573 K, stress of 160 MPa and irradiation conditions corresponding to the conditions of the described experiments. Therefore, one can suppose that the rise of the approach of the surfaces in contact, the contact area, hence the increase of fst in irradiation is mainly due to the creep of uranium dioxide (Fig. 5.4, curves 1 and 2). It was found in the experiments that the static friction coefficient rose with increasing neutron fluence (Fig. 5.3). One of the reasons is the hardening of the zirconium alloy in the process of irradiation. At a temperature of 573 K and fuence of fast neutrons of 2    4 · 1023 neutrons/m2 the alloy yield stress

FRICTION OF NUCLEAR POWER ENGINEERING MATERIALS

191

increases noticeably in comparison with the initial state. As a result, the material shear strength and fst grow. Besides, solid-phase chemical reactions on real contact spots are activated by radiation. This accelerates the seizure of the surfaces in contact that contributes somewhat to the rise of the static friction coefficient. After the intrareactor tests the specimens of Zr + 1% Nb alloy were placed into a heated chamber. They were examined visually and used to prepare metallographic sections to measure the microhardness. The microhardness was determined in the region of the friction track and outside it over the section using Š‡4-3 hardness tester under loads 0.5 and 2.0 N. The measurement results are listed in Table 5.1. Figure 5.5 represents data on the measurement of the microhardness in depth of the cross section of the friction track under a load of 0.5 N. It is seen that the depth of the softer zone characterized by the microhardness decrease is approximately the same for irradiated and non-irradiated specimens and amounts to 25–30 m. Table 5.1. % Nb Alloy Specimens Results of Microhardness Measurement of Zr + 1% Specimen number

Microhardness, MPa initial state

outside friction track

over friction track

, T, K neutrons/ m2

H1

H2

H1

H2

H1

H2

1

1710

1680

1830

1820

1870

1840

5 · 1023

586

2

1740

1660

1840

1770

2000

1920

86 · 1023

592

3

1730

1610

1920

1900

2100

1980

4

1680

1600

–

–

–

–

10

24

–

602 573

Note: H1 is the microhardness measured under a load of 0.5 N; H2 is the microhardness measured under a load of 2 N;  is the thermal neutron fluence; T is the test temperature. 4 – the specimen was tested under laboratory conditions.

The difference in the sliding and static friction coefficients of the “uranium dioxide – zirconium alloy” pair causes relaxation oscillations of the friction force. In laboratory conditions these oscillations are small while they are quite noticeable in intrareactor tests. Relaxation oscillations appear at sliding velocities below 02 · 10−8 m/s under the effect of radiation. In laboratory conditions at the same temperature and sliding velocity relaxation oscillations transform into quasi-monotonous just during the first sliding cycle. With increasing neutron flux density the amplitude of relaxation oscillations rises and their frequency decreases, and the static friction coefficient reaches values exceeding unity. The

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192

Hμ · 103, MPa

2

1

0

10

20

30

40

h, μm

Figure 5.5. Variation of microhardness in depth of Zr + 1% Nb alloy specimens: • – specimen in initial state;  – specimen after tests in laboratory conditions at T = 293 K – the same at T = 573 K × – specimen irradiated with thermal neutron fluence about 1024 neutrons/m2 at T = 573 K; nominal pressure 5 MPa

rise of the load results in a higher amplitude and period of friction force oscillations. The obtained data prove that reactor radiation influences significantly the frictional behavior of parts of nuclear reactor fuel elements. AE studies of friction between uranium dioxide and the structural alloy Zr + 1% Nb were carried out in 4‹%…-1 set-up. The set-up design and specimens under testing are described in Part 3.5. Figure 5.6 represents the dependencies of the total number of AE pulses N and the friction coefficient f on the number of the test cycle. These characteristics gradually decrease and become stable that indicates the completion of the running-in of the pair. It is seen from the dependencies of the count rate of AE pulses and the friction force on the number of cycles (Fig. 5.7) that in the beginning of tests (portion I) when running-in starts the value of the count rate is approximately two times higher than after running-in (portion II). The friction force and friction coefficient differ significantly less over these portions. If the load increases twice from 0.15 to 0.3 MPa running-in is more pronounced. This is indicated by variations in the count rate values registered during different cycles: N˙ decreases from 250–400 pulses/s in the third cycle to 50–100 pulses/s in the sixth and seventh cycles under a load of 0.3 MPa while under a load of 0.15 MPa it decreases from 100–150 to 50 pulses/s, respectively. The scatter of the friction force during each cycle decreases with prolonging friction duration. At the same time the friction force itself decreases slightly in tests.

FRICTION OF NUCLEAR POWER ENGINEERING MATERIALS

193

f

N · 10–3, pulses

–1 –2

0.6

–3 10 0.4 ΦOH

5

0.2

0

5

10

15

20

25

n

Figure 5.6. Dependencies of number of registered AE pulses N(1, 2) and friction coefficient f (3) on number of friction cycles: 1, 2 – up and down motion of plate, respectively; sliding velocity – 0.1 m/s; F – 130 N; Q – 0.3 MPa N, pulses/s 500

I

II

250

0

3

4

6

7

6

7

8

n

a

F, N 40 0 –40

3

4

8

n

b · N, pulses/s 500

I

III

II

250 0 F, N 0 –25

1 1

2

3

9

2

3

9

10 10

11 11

27

n

27

n

b

Figure 5.7. Dependencies of AE count rate N˙ and friction force f on number of friction cycles: sliding velocity – 0.1 m/s; a – F = 130 N; Q = 03 MPa; b – F = 70 N; Q = 015 MPa

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The friction of the materials under study is accompanied by sharp jumps of AE count rate which result from the formation of wear particles due to the microcutting of the zirconium alloy. This is proven by a special experiment. To determine how the failure mode of the friction surface influences AE characteristics the experiment was carried out which simulated the friction of materials under plastic contact conditions. Balls made of steel “815 6 mm in diameter were used as stationary specimens. The sliding velocity was 0.1 mm/s, the load was 1 N that provided the contact pressure approximately 1 MPa. Under these conditions the failure of the plate surface occurred as a result of plastic deformation. No pulses with amplitudes exceeding the acoustic noise of the set-up were registered in friction at the maximal amplification factor of the AE instruments equal ≈80 db and the discrimination level 40 mV. The value of the acoustic noise was determined when starting the set-up with unloaded specimens. Therefore, in the given friction conditions and at the selected regimes of signal registration acoustic emission induced by the plastic deformation of the zirconium alloy does not exceed the set-up intrinsic noise. In friction of the “the zirconium alloy – UO2 pellets” pair the amplitude of AE pulses exceeds the set-up noise level especially in the beginning of tests (Fig. 5.6. and 5.7). The visual and optical microscope examination of the alloy specimen has revealed scratches on the alloy surface resulted from microcutting and signs of fuel spalling were found on the pellet surface. Therefore, at the initial stage of friction that is during running-in the shape of the surfaces changes strongly and microcutting is the predominant failure mode. This process is accompanied by intensive acoustic emission; the ratio of the average amplitudes and powers of AE signals corresponding to the initial state and the stationary state (after running-in) is 10–100. In this case the friction coefficient varies by 20–40%. It should be mentioned that the plots represent the values of the friction coefficient averaged over the half-cycle and the scatter between its maximal and minimal values. Low-amplitude AE in the stationary state of the friction pair indicates that the microcutting of the zirconium alloy almost does not occur in this regime and no signs of spalling are found on pellet surfaces. Maximal jumps of AE count rate occur when the specimens stop to change the direction of motion, i.e. in the reversing zone. This is clearly seen in the plot presented in Fig. 5.7. It is known from the study of the friction of such specimens in 4‹%… set-ups that pellets are severely spalled just in reversing regions. The next set of experiments was carried out to test plates made of Zr + 1% Nb alloy covered with antifrictional coatings based on Cu–C and Ni–C. Fuel pellets were 7.5 mm in diameter and had flat working surfaces. Tests lasted until the protective coating failed. In friction with coatings running-in completes already after 2–4 cycles (Fig. 5.8). The count rate and maximal amplitude of AE pulses after running-in

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195

f

N · 10–3, pulses 1.5

0.20 0.15

1.0 0.10 0.5

0.05

0

1

2

3

n

Figure 5.8. Dependencies of number of AE pulses and friction coefficient on number of cycles: friction pair: plate – pellets; coating – on basis of Cu–C; sliding velocity – 0.2 mm/s; F = 350 N; Q = 08 MPa do not exceed corresponding noise values. Acoustic emission is apparently caused by the plastic deformation of a thin coating layer. Figures 5.9 and 5.10 illustrate the kinetics of the friction coefficient and AE characteristics in the beginning of coating failure and in the process of failure. When plotting the dependence N = Nn acoustic noise equal approximately 5000 pulses was subtracted. It is seen from the presented plots that when the coating is close to full failure AE characteristics change non-monotonously. Cycles are clearly visible during which all AE characteristics increase sharply. Thus, the number of pulses per one test cycle rises from almost zero (the noise level) to 1    2 · 103 pulses, the average amplitude and the variance of the amplitude distribution increase several times while AE power grows by several orders of magnitude. Fig. 5.8. Dependencies of number of AE pulses and friction

N · 10–3, pulses 2.0

f

Failure 1 2

0.20

1.5

0.15

1.0

0.10

0.5

0.05

0

100

150

110

115

n

Figure 5.9. Dependencies of number of registered AE pulses N (1) and friction coefficient f (2) for Ni–C-based coating on number of friction cycles: sliding velocity – 0.2 mm/s; F = 350 N; Q = 08 MPa

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196

σ 2 · 10–1, rel. units

W · 10–5, rel. units –

A, rel. units 100 6

Failure

–1 –2 –3

10

10 4

5

5 2

0

100

105

110

115

n

¯ (1), energy W (2) and Figure 5.10. Dependencies of average amplitude A 2 variance of amplitude distribution  (3) of registered AE pulses in tests of Ni–C-based coating on number of friction cycles: sliding velocity – 0.2 mm/s; F = 350 N; Q = 08 MPa coefficient on number of cycles: friction pair: plate – pellets; coating – on basis of Cu–C; sliding velocity – 0.2 mm/s; F = 350 N; Q = 08 MPa The fact that the number of AE pulses per cycle N in the process of failure and close to the instant of the full failure of the protective coatings increases to several thousands agrees well with the results of tests of the zirconium alloy without coatings under the same conditions. Particularly, the number of AE pulses per cycle exceeds the noise level during running-in (Fig. 5.6) by the value of the same order, namely 1    5 · 103 pulses. Comparing the obtained data with the results of studies of acoustic emission in degradation of protective lubricating films (see Part 4.3) the following conclusions can be derived about processes occurring in failure of barrier coatings on the zirconium alloy. The pattern of AE characteristic variation proves that local zones of coating failure appear which can be temporarily healed due to a quite good ductility of the coating material. No similar changes in the pattern of the friction coefficient were found. This can be explained by either its poor sensitivity or small dimensions of a damaged coating region which does not vary significantly the real contact area, hence the friction force. The monotonous rise of the friction coefficient indicates that the antifrictional coating becomes thinner and the substrate surface layers (the zirconium alloy) are involved in friction. When the coating is damaged that is when it loses its antifrictional properties running-in begins again but for the “uranium dioxide – zirconium alloy” pair. As it has been shown above the latter process

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197

is accompanied by the microcutting of the alloy and the spalling and chipping of fuel pellets that increases AE level. It can be concluded that basic regularities of AE in running-in and failure of antifrictional coatings established for some structural materials are also true for such materials non-traditional for tribology as uranium dioxide and zirconium alloy.

5.3. ACOUSTIC EMISSION IN FRICTION OF MATERIALS OF CIRCULATION DEVICE BEARING UNITS OF BALL FUEL ELEMENTS OF NUCLEAR POWER PLANTS WITH HTGCR The reliability of bearing units of processing equipment such as main circulation pumps, gas blowers, devices of shield control, turbines and other mechanisms is known to provide the safe operation of nuclear power plants (NPP). When developing and upgrading friction units of such devices tribological characteristics of bearing materials should be studied. These studies are carried out during experimental tests of the unit design. If AE method is used in addition to common monitoring methods one can obtain more information on the behavior of friction unit materials. On the other hand, the experience gained in tests allows one to assess reliably the possibilities of AE method application for the field inspection of friction units of NPP processing equipment. The current and next parts describe the result of these studies. We used AE method to study the triboengineering behavior of the materials of circulation device bearing units of ball fuel elements of nuclear power plants based on high-temperature gas-cooled reactors (HTGCR). A specific feature of the operation of most of HTGCR mechanisms is that oils and greases are almost not used in friction units. Bearings should operate in high-pure helium for a long time (up to 12000 h) at temperatures about 300  C and under gamma-radiation with a dose of about 108 r. For this reason either friction units are not lubricated or solid-film lubricants based on dichalconides of transition metals of V–VI groups of the periodical system are used. Below basic results are presented of the study of processes running in the friction zone of materials with the antifrictional solid-film lubricant “Dymolyt” based on molybdenum disulphide at temperature and environment similar to those used in operation of circulating device sliding bearings of ball fuel elements of a nuclear power plant on the basis of "˜-50 reactor. The friction and wear of the coating “Dymolyt-4” were studied using ‡4˜ set-up developed in the Russian Research and Design Institute of Nuclear Machine Building. Friction tests were performed involving the end geometry “ring – ring (disc)” with varying overlapping factor in controlled gas environments under pressures

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198

4

ω p

1

2

p 3

Figure 5.11. Diagram of friction unit 0.1–10 MPa at peripheral velocities 0.5–2.0 m/s and temperatures 20–400  C. The solid-film lubricant “Dymolyt-4” on the basis of molybdenum disulphide was deposited onto the working surfaces of both specimens made of steel 20X13. Figure 5.11 illustrates the schematic of the friction unit of MT˜ set-up. Acoustic signals appearing in specimens 3 and 4 transmitted to AE transducer 1 through acoustic line 2. The use of the acoustic line is necessary to remove the transducer from the heating zone. The temperature in the region of transducer location did not exceed 100  C. Helium with purity 99.985% served as an operating environment, its composition and humidity were monitored by an automatic chromatograph and humidity meter. The concentrations of impurities being monitored were as follows: hydrogen 2    4 · 10−4 %, nitrogen 04    2 · 10−4 %, oxygen 02    1 · 10−4 %, carbon dioxide below 10−6 %, methane 02    05 · 10−4 %, water vapor 6    15 · 10−4 %. AE signals were processes and analyzed by ‹ƒ− instrument. AE count rate N˙ , the power W of emission and parameters of the amplitude distribution ¯ the variance  2 and statistical characteristics such as the average amplitude A, determining the pattern of the amplitude distribution curves ( 1 and 2  were used as informative characteristics. The friction force was continuously being measured in addition to AE count rate. Figures 5.12 and 5.13 represent typical time dependencies of AE characteristics and the friction coefficient at a sliding velocity of 1.2 m/s under a load of 2.0 MPa. The temperature on the specimen surfaces reached 100  C due to frictional heating. Column a) of Table 5.2 contains the values of AE characteristics in the beginning of running-in and in the steady-state friction mode as well as the ratio of the values. The instant when running-in completed was determined by the stabilization of AE characteristics [11, 12]. The steady-state friction is characterized by considerably less values of AE characteristics compared with the beginning of running-in. The average amplitude of pulses decreases several times, the amplitude variance – tens times while the count rate and power – by

FRICTION OF NUCLEAR POWER ENGINEERING MATERIALS

· In N ; In σ 2

A, rel. units

· In N In σ 2 A f

10

5

0

5

10

199

f

30

0.10

15

0.05

t · 10–2, s

15

Figure 5.12. Time dependencies of AE characteristics and friction coefficient: sliding velocity – 1.2 m/s; Q = 20 MPa (a)

N · 10–3, pulses/s D = 90 mV 20 D = 130 mV D = 20 mV 15

2 A, mV σ

200

4

150

3

100

2

50

1

W · 108, rel. units 6

A

σ2 W

10 5

4 2 (b)

0

0.5

1.0

1.5

v, m/s

0

0

0.5

1.0

1.5

2.0

v, m/s

Figure 5.13. Dependencies of AE count rate N˙ (a) and parameters of ampli¯  2  W (b) on sliding velocity (Q = 20 MPa) tude distribution A 1–3 orders. The pattern of amplitude distributions of AE pulses does not change  = −12    − 11 and corresponds to the first type of Pearson distributions. Therefore, the features of processes inducing AE remain unchanged under the given conditions. As it has been noted in Part 4.1 the occurrence of the steady-state mode in the friction pair being determined by the stabilization of AE characteristics is registered later than the friction force becomes stable. The interval between these instants reached 1000 s (800 s in Fig. 5.12). This is due to a higher sensitivity of AE characteristics to processes running in the contact zone and due to broad dynamic ranges of their variation. Running-in occurred under constant friction conditions in every repeated start of the set-up with one and the same specimens and when varying the

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Table 5.2. Values of AE Characteristics and Friction Coefficient as Functions of Test Duration Characteristic

a Ratio of characteristics

Time, s 20

N˙ , pulses/s ¯ rel. units A, 2

b

stationary nonnon3 stationary stationary 1 2

1800

1180

6

37.6

9.1 22

State of pair

200

505

1600

2840

4

18.7

13.8

15.5

45

370

127

 , rel. units

1020

W , rel. units

3 · 10

1

2.2

2.2

–

6.1

4.7

2.0

2

5.6

5.0

–

10.9

12.6

5.3

−13

−134

–

0.3

1.8

−10

f

0.07

0.07

0.09

0.08

0.07

8

6 · 10

4

5000

1

36 · 10

125 6

5 · 10

6

10 · 106

load. In repeated starts registered time dependencies of AE characteristics were monotonously descending. The friction force also decreased, as a rule. Yet, this decrease (by 10–20%) is insignificant compared with variations in AE characteristics. Figure 5.13 illustrates the dependencies of AE count rate on the sliding velocity obtained at different lower discrimination levels. AE count rate was registered in the steady-state friction mode. With decreasing discrimination level the dependence of AE count rate on the sliding velocity approaches to linear one. As it has been noted in Part 4.2 detected signals should be registered at the minimal discrimination level in order to exclude measuring device distortions when determining the dependence N˙ = fv. As it follows from the theoretical assessments given in Part 2.1 one should expect a linear dependence of the count rate on the sliding velocity that is indeed found in experiments. Values of characteristics of acoustic signals and the friction coefficient measured in the steady-state mode at different sliding velocities are listed in Table 5.3. It is seen that the friction coefficient remains unchanged within the studied range of the sliding velocity. Parameters governing the pattern of amplitude distributions ( 1 and 2  vary slightly with increasing velocity. Therefore, a conclusion can be derived that the pattern of the amplitude distribution does

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Table 5.3. AE Characteristics and Friction Coefficient as Functions of Sliding Velocity Characteristics

Velocity, m/s ¯ rel. N˙ , pulses/s A, units

 , rel. units

65

22

0.67

86

2

W , rel. units

1

2

62 · 104

40

75

062 007

7

23

54

0.92

1100

128

73

03 · 10

1.07

3200

155

152

10 · 107

19

50

210

14 · 10

7

09

36

−06

007

270

28 · 10

7

10

40

−09

007

414

68 · 10

7

13

45

−09

007

592

100 · 10

13

45

−09

007

1.09 1.21 1.37 1.57

3500 5200 7650 10700

139 165 210 264

7

−15

f

007

092 007

not change and relates to the first distribution type, namely -distribution. The amplitude distributions whose parameters are listed in column (a) of Table 5.2 also belong to this type. Hence, if the sliding velocity increases during repeated running-in the nature of physico-chemical processes occurring in the friction zone under the given conditions does not vary. Only quantitative characteristics of the processes change. This is also confirmed by no inflexions of the dependencies of the count rate and average amplitude of AE pulses on the sliding velocity (Fig. 5.13). Since physico-mechanical processes in friction remain the same within a broad range of the sliding velocity it is possible to carry out accelerated life tests of bearing materials setting the maximal permissible velocity. The concentration of oxygen in helium was measured in tests. An automatic device was used for the dosed supply of oxygen, the device allowed one to produce gas mixtures with the volume concentration of oxygen from 0.001 to 1%. When adding oxygen the pattern of AE changed. Similar results were obtained when adding air into the testing chamber (Fig. 5.14). The state of the specimen surfaces also changed. To understand the causes of such changes let us consider the factors influencing the friction and wear of molybdenum disulphide coatings when oxygen or air are added into the environment. First, layers of water vapor are adsorbed on the friction surfaces which increase the adhesion component of the friction force. Second, air oxygen intensifies oxidation processes in the friction zone accompanied by the formation of corrosion products which act as abrasive. When testing the “Dymolyt-4 – Dymolyt-4” pair considerable changes in friction were

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202

· N · 10–2, pulses/s 4

2

0 0.16 f 0.08

0

4

5

6 t · 10–3, s

Figure 5.14. Time dependencies of count rate of AE pulses and friction coefficient: pair with overlapping factor 0.3; coating – “Dymolyt-4”; sliding velocity – 1.1 m/s; Q = 80 MPa; instants of air ∗  and helium   supply

found if the concentration of oxygen in the environment reached 0.5–0.6%. The friction coefficient becomes unstable, jumps of the friction force occur and the wear rises strongly (10–20 times). The metallographic examination of specimens coated with “Dymolyt-4” performed using a scanning electron microscope has shown that at the concentration of oxygen in helium more than 0.5% microcracks and signs of microcutting oriented along the sliding direction appear on the friction surfaces. It is found that the microcracks result from the acceleration of oxidation processes in the friction zone and the grooves are caused by the abrasive effect of corrosion products. In our studies AE count rate increased significantly with increasing oxygen concentration and pulses appeared whose amplitude exceeded by an order that of signals typical for steady-state friction in the environment with the oxygen concentration below 10−4 %. The predominant friction mode of molybdenum disulphide layers after running-in in helium is adhesion and their wear is caused by material fatigue. For this reason the processes of the rupture and formation of adhesion junctions and the fatigue wear of the coatings should be considered as the most probable sources of AE. Since the relative wear of “Dymolyt” coatings is negligible (about 10−12 ) in our conditions the formation and rupture of adhesion junctions is the main cause of AE in steady-state friction in helium. Therefore, sharp changes in AE characteristics with increasing oxygen concentration are due to the appearance of two new powerful sources of acoustic emission, namely microcracks resulted from intensive oxidation on the

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203

friction surfaces and scratches resulted from the abrasive action of oxidation products. The addition of air into the testing chamber leads to similar variations in AE characteristics. Pulses with high amplitudes appear and the amplitude variance and AE power increase significantly (see Fig. 5.14 and Table 5.4). Table 5.4. Time Variation of AE Characteristics Characteristics

Time, s

¯ pulses/s A,

 , rel. units

3550

48

165

4250

80

4650

66

4700

2

1

2

0074

288

−012

21500

420

936

62

508

13500

342

991

1.37

71

659

22100

136

531

2.62

5100

71

49

2180

041

321

−042

5450

65

73

8890

1056

5500

72

74

26500

302

967

0.96

5500

84

123

55200

187

584

8.89

5700

77

138

17200

467

801

−197

186

W , rel. units 697

190

97

If the testing chamber is flushed with helium the friction coefficient decreases almost reaching its initial value. The acoustic activity of friction also decreases. This means that damaged regions of the friction surfaces are gradually healed after eliminating oxygen and air and abrasive particles are removed from the friction zone. Judging from the pattern of changes in AE characteristics the tribosystem returns into the state in which the same physico-mechanical processes occur as in the steady-state friction mode. The difference is in numerical values of characteristics of the processes (see, for example, the time interval in the vicinity of 510 s in Fig. 5.14 and corresponding data in Table 5.4). Note once again that changes in the failure mode of coating surface layers can be detected at much less oxygen concentrations if one use AE characteristics rather than such common characteristic as the friction force. In other words, AE method is more sensitive than the methods based on measurements of the friction force or coefficient. In real conditions noticeable variations in these characteristics are mostly related to the following occurrence of the catastrophic wear of the friction pair.

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The elevation of the temperature of specimens under testing leads to a considerable decrease of AE count rate while lower temperatures result in the rise of the count rate. Since the elevation of the temperature up to 400  C almost does not influence physico-mechanical properties of “Dymolyt” grease the behavior of this AE characteristic is explained by the change of the concentration of water vapors adsorbed by the friction surfaces with varying temperature. Water molecules form strong adhesion bonds increasing the adhesion component of the friction force. The heating of the specimens results in water evaporation from the friction surfaces, decreasing the number of adhesion bonds hence reducing acoustic activity. When cooling the testing chamber moisture is condensed on the friction surfaces therefore the number of adhesion bonds rises that is accompanied by the increase of AE activity. Such behavior of AE when varying testing temperature confirms the fact that the formation and rupture of adhesion junctions is the main source of acoustic emission in friction of molybdenum disulphide. High sensitivity of AE characteristics to changes in processes running in the friction zone is also confirmed by the fact that when AE count rate varies sharply (Fig. 5.15 and data from column (b) of Table 5.2) the parameters 1 and 2 of the system of Pearson distributions change in such a way that one might say that the law of the amplitude distribution of AE pulses varies. This proves the change of processes running in the friction zone, for example, the appearance of fatigue wear particles acting as abrasive.

In n(a)

· N

3

2

10 1 t 5 1

0

2

25

3

50

75

100 A, rel. units

Figure 5.15. Time dependence of amplitude distribution of AE pulses: sliding velocity – 1.2 m/s; Q = 20 MPa Figure 5.16 illustrates typical time dependencies of the count rate of AE pulses and the friction coefficient in failure of molybdenum disulphide coatings. It is seen that these characteristics vary stepwise and that jumps of the count rate occur much earlier than those of the friction force. The latter fact is explained

FRICTION OF NUCLEAR POWER ENGINEERING MATERIALS

· N · 10–3, pulses/s

205

f 0.06

2

f 0.04 · W

1

0

98

99

100

0.02

101 t · 10–3, s

Figure 5.16. Time dependencies of count rate of AE pulses N˙ and friction coefficient f: sliding velocity – 1.0 m/s; Q = 40 MPa by the local pattern of the failure of surface layer and by the healing of damaged regions due to the ductility of the coating material. The lateness of friction force jumps results from the fact that this characteristic varies only when changes occur over about 20% of the real contact area. These data prove a higher sensitivity of AE characteristics to the change of processes running in the contact zone as compared to the friction force or coefficient. Note that the most common regularities of AE characteristic variations when changing conditions and regimes of the friction of molybdenum disulphide coatings can be considered from the viewpoint of the dynamic model for the calculation of AE characteristics in non-stationary friction conditions described in Part 2.5. Indeed, the model is based on the idea that friction is a simple Markov process consisting in the change of the number of friction junctions. Like AE, friction results from the formation and rupture of the junctions. One of the basic conclusions of the model is that when the friction pair shifts to the stationary state AE characteristics, for example, the count rate become stable later than the friction coefficient. This regularity was typical for all our experiments. Besides, if one assigns the law describing change in the number of adhesion junctions as a function of environment parameters and friction regimes it is possible to determine the dynamics of AE characteristics in transient states of the tribosystem. To find these regularities physico-chemical processes occurring on friction surfaces should be thoroughly investigated. So, the performed studies yielded main factors influencing the efficiency of lubricants like “Dymolyt”. It is shown that in failure of coatings AE characteristics change by two or three orders of magnitude that provides the high sensitivity of AE method of the condition monitoring of solid-film lubricants used in circulation device bearing units of ball fuel elements of nuclear power plants.

206

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5.4. STUDY OF FRICTION OF SLIDING BEARING MATERIALS OF NUCLEAR REACTOR MAIN CIRCULATING PUMP The safety operation of nuclear power plants in normal, transient and emergency regimes depend on the non-failure operation of pumps providing the circulation of the coolant in the active zone, steam generators and auxiliary circuits of a reactor. First circuit pumps, i.e. main circulating pumps (MCP) operate in the most severe regimes since they pump the irradiated coolant under high pressure and elevated temperature. Direct service access to the pumps is hampered because of high radiation fluxes. For this reason MCP should meet strict requirements on reliability and efficiency. The problem is how to provide the optimal service of the pumps by their real state rather than by schedule and operating time. This requires the availability of methods and means of technical diagnostics allowing one to perform continuous and, that is especially important, remote monitoring of the efficiency of both main pump units and the pump as a whole. Seals and sliding bearings are presently the most vulnerable parts of MCP. The experience of operation during 250 reactor-years and the implementation of 128 overloads have shown that failures of MCP due to the malfunction of seals are among the main causes of annual stoppages of nuclear power plants equipped with reactors of PWR type [15] and that the service reliability of MCP is governed to a great extent by the efficiency of bearing units. The available methods of vibrodiagnostics are capable of identifying a large number of faults and normal operation variations of MCP. For example, when analyzing amplitude-frequency spectra, mutual correlation functions and probability densities of a vibroacoustic signal in bench tests of a non-immersed pump the damage of sliding bearings was found caused by the wear of bearing shells and the shaft [16]. Such failures occur when the rotating shaft contacts the bearing shell due to the lack of the lubricant or does not raise in acceleration. Unfortunately, the common drawback of the vibroacoustic methods is that they are incapable of detecting the initial stage of defect origination. In our opinion, AE method is promising in the field inspection of bearings and sealing devices of MCP. First of all, the method provides the continuous monitoring of pumps. Second, it is easy from the design viewpoint to arrange registration instruments at a distance of up to 100 m from the object under monitoring that is to locate them outside the zone of high radiation. It is also important that AE is a passive method, i.e. acoustic emission is analyzed which is generated by a friction unit itself in its operation. Therefore, no need to use an external signal source in contrast with common ultrasonic inspection, more simple technical means of monitoring can be applied, hence they are more reliable. The latter fact is important having in mind extreme conditions of pumping device operation.

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207

We have no information on the application of AE method fore the diagnostics of friction units of MCP despite the fact that it is used in Russia and abroad [17] for the condition monitoring of metals of nuclear reactor cases and pipelines. In our opinion, this is due to the lack of information about features of acoustic emission in friction of metals applied in MCP. In addition, the operation of pumps is accompanied with great noises that makes it difficult to select a useful signal. To check the applicability of AE method for the efficiency monitoring of MCP bearings AE accompanying the friction of pump bearing materials was studied. The studies were carried out in set-ups simulating operating conditions of sliding bearings and seals of MCP of water-moderated reactors and in a real main circulating pump in its bench tests. The schematic of a set-up simulating friction conditions of MCP sliding bearings is shown in Fig. 5.17. The set-up contains a chamber filled with distilled water under pressure in which stationary and rotating specimens are placed. Two contact geometries are used, namely the “flat – ring” and “flat – three pins”. The specimens are loaded by a lever device passing a bellows in the chamber wall.

1 2

ω

3

4

5 8

6

7

9

p

Figure 5.17. Schematic diagram of friction machine for testing sliding bearings of MCP: 1 – electric motor; 2 – shaft; 3 – sealed case; 4 – distilled water; 5 – rotating specimen; 6 – transducer 2; 7 – loading lever; 8 – stationary specimen; 9 – transducer 1

208

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AE signals were registered by two same transducers. Transducer 1 was fixed to the stationary specimen. It generated an electric signal which was transmitted outside the chamber through a tight high-frequency socket. Transducer 2 is arranged outside the chamber on the loading lever of the friction machine. This was used to check the possibility to register AE signals on the case outer surface of the operating set-up using its parts as acoustic lines. Two sets of experiments were carried out. In the first set of experiments the first friction pair comprised the upper rotating disc made of steel `˘8˚`|-“ and the lower stationary specimen made of PTFE-graphite composite 7B-2A. In the second set of experiment the second pair was tested including #˜-Š 0,5 silicated graphite disc (the upper rotating specimen) and three cubes made of the same material symmetrically disposed over the circumference with the mean radius 52 mm (lower specimens). The specimen working surfaces were ground before tests to Ra ≈ 06 m. When the transducers had been fixed and checked the chamber was filled with distilled water and sealed. Tests were performed at water temperature of about 200  C. To exclude the boiling of water nitrogen was supplied into the chamber under a pressure of 5 atm. The consumed power of the electric motor and the temperature of water in the chamber were measured in the experiments (the thermocouple was located below the friction zone). The friction coefficient was found from the consumed power during idling and with the loaded friction contact. The roughness of the working surfaces was measured before and after the tests and the specimen wear was obtained from profilograms. The rotational speed of the specimens was 3000 r.p.m., therefore their sliding velocity was 16.5 m/s at the mean radius of 52 mm. Normal operation tests of the bearing materials of pumps had been carried out under pressures 0.2, 0.4, 0.6, 0.8, and 1.0 MPa during 100 hours and a noticeable wear of the material was found only under 1.0 MPa. The count rate, parameters of the amplitude distribution and the spectral density of AE were registered in the tests. Emergency, i.e. transition to dry friction, was simulated by the gradual removal of water from the set-up chamber in the process of experiments. The tests were performed in the following sequence. The set-up was startedup and their intrinsic noises had been registered during a few minutes without loading the specimens. The adjustment parameters of the measuring devices were selected to provide the count rate of the registered acoustic signals below 1–15 pulses/s. Further these values were assigned as the noise level and subtracted in data processing. The signals of the first transducer were registered using the following adjustment parameters: the amplification factor – 250 and 625, the lower signal discrimination level reduced to the main amplifier output – 40 mV. The amplification factor of the second transducer signals was 104 with the same lower discrimination level. The load was increased stepwise starting from 0.4 to 1.0 MPa with a step of 0.2 MPa. At each load friction lasted till values of

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209

AE count rate became stable then the following load regime began. The power consumed to rotate the specimen was measured in the beginning and end of each stage. When testing the second part transducer 1 was pressed to the surface opposite to the friction surface of one of the cubes. The load was increased stepwise – 0.2, 0.4, 0.6 and 1.0 MPa. The test results confirmed in general common regularities of AE in the friction of solids described in Chapter 4. For example, the decrease and stabilization of AE characteristics with prolonging friction were found at a constant load. At the same time stepwise load increase from 0.2 to 1.0 MPa not always resulted in the adequate rise of stationary values of AE count rate. When varying load 5 times the count rate increased only by 10–100%. This can be apparently explained, on the one hand, by a quite high discrimination level of registered signals (see Part 4.2) and, on the other hand, by the fact that when varying load within the above range the friction mode remained almost unchanged therefore no noticeable wear of the material was found. Results of tests of the first set of specimens. Table 5.5 lists measurement data obtained in transition of the first friction pair to dry friction under a nominal load of 0.6 MPa. The instant when the friction mode changed was determined by both a sharp increase of the consumed motor power and a considerable change in AE count rate. Table 5.5. Variation in AE Count Rate When Changing Friction Mode of 7B-2A – `˘8˚|-“ Pair Amplification factor Friction mode Normal Dry

Transducer 1

Transducer 2 104

250

625

0

0

100

500

5000

5000

It is seen from the table that in transition to dry friction the count rate increased more than one hundred times when registering signals from the specimen and about fifty times when taking signals from the loading lever. The visual examination of the stationary specimen friction surface has shown marked signs of wear. The friction track 1 mm deep had been formed on the surface during 75 s of dry friction and the friction coefficient increased from about 0.01 to 0.12. In some cases other results were obtained for the materials of this pair in changing the friction mode. Two of them are presented in Fig. 5.18 and 5.19. In the first case (Fig. 5.18) AE characteristics sharply dropped to zero after about

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210

· N · 10–3, pulses/s

M, kWt 1.8

6

· N 1.6

4 M

2

0

1.4

4

12 t · 10–2, s

8

1.0

Figure 5.18. Time dependencies of count rate of AE pulses N˙ and electric motor power M: friction pair: `˘8˚`|-III – 7B-2A; Q = 20 MPa; ∗ – beginning of water discharge · N · 10–3, pulses/s

M, kWt 2.2

12 M

I

1.9 1.6 1.3

0

1

150

100

· N

6

/, μm

2

3

t · 10–3, s

1.0

50

0

˙ electric motor Figure 5.19. Time dependencies of count rate of AE pulses N, power M and linear wear of specimens I: friction pair: `˘8˚`|-III – 7B-2A; Q = 20 MPa; water discharge: start – (∗ ), stop –  500 s since the beginning of discharging water. AE signals were not registered even at the maximal amplification factor equal to 2400. The friction unit was disassembled. The examination of the specimens by a microscope with 50× magnification has shown no signs of wear and well run-in surfaces. The experiment with changing friction mode was repeated for this friction pair. It was stopped after about 400 s since the beginning of discharging water and continued only after the expiration of 300 s (Fig. 5.19). When water discharge was interrupted the count rate and power consumed by the electric motor increased significantly and AE characteristics dropped sharply to zero only after about 750 s since water discharge continued. Then single jumps of the count rate of AE pulses occurred after approximately 400 s, their frequency increased and the

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211

dependence N˙ = ft gradually had become linear. The linear wear of the specimens simultaneously grew. It was determined from the variation of the position of the loading lever measured by a micrometer. The amplitude of AE signals changed in transition to dry friction. At instant 1500 s the maximal amplitude of electric pulses corresponding to AE pulses did not exceed 1.0 V and under dry friction at instant 3500 s the maximal amplitude of electric pulses was 0.4 V. Note that in these experiments AE signals were registered by transducer 2. The sharp drop of all AE characteristics almost to zero when water was completely discharged in tests of the first pair materials can be explained as follows. At a certain combination of friction conditions such as the rate of water discharge, the load, the state and temperature of the friction surfaces etc. the soft component of PTFE-graphite composite is extruded into the contact zone and acts as a lubricant. It should be noted that such “wear-free” friction mode was typical only for the materials of the first pair. As wear grew the count rate, count rate variance, pulse amplitude and other AE characteristics increased and non-periodical jumps of the count rate were registered in the beginning of the process corresponding to the coming of AE pulse bursts to the transducer. The latter result apparently from single local acts of the wear and scoring of the friction surfaces. This is also confirmed by the results of all other experiments lasting till the lubricating film worn out. Therefore, the conclusion can be derived that in the normal friction mode acoustic emission is induced by noises appearing from the friction of liquid against the specimen surfaces and chamber walls and possibly by cavitation phenomena. So, it has been found in the experiments that in transition to dry friction the count rate and amplitude of AE pulses change significantly. A broad dynamic range of variations of these characteristics (for example, the count rate changes by more than 40 db) provides the reliable registration of the variations. It is not important either the transducer fixed directly to one of the specimens is used or signals are registered by the transducer arranged on the lever mechanism despite the fact that in the latter case signals undergo substantial changes in some design joints when passing from the source to the transducer. Results of tests of the second set of specimens. Let us illustrate main data obtained when studying the second pair materials using the example of testing specimens under 0.4 and 4 MPa. In one of the experiments AE signals were registered by transducer 1 at an amplification factor of 250. In this case the count rate increased from about 300–400 to 16000 pulses/s that is 40–50 times during 15 s in transition to dry friction. At the fifteenth second since changing the friction mode the motor was stopped by the emergency protection. Yet, the visual examination of the friction surfaces had shown almost no any signs of the damage of the cube specimen surfaces.

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In the second experiment AE was registered by transducer 2. The amplification factor was selected to be 104 . The count rate of AE pulses equal to 200–300 pulses/s had been registered before the beginning of transition to dry friction. After 27 s its value exceeded 20000 pulses/s at the amplification factor equal to 1250. It should be noted that at such amplification factor the acoustic emission of the friction pair under normal operation was not registered by transducer 2. The amplitude of single electric pulses corresponding to AE signals exceeded a few millivolts in dry friction that was proven by the overload of the preamplifier and the main amplifier with the amplification factors of 200 and 500, respectively. The visual examination of the specimen surfaces had shown marked signs of material wear. In transition to dry friction the power consumed by the electric motor changed from 1.19 to 8.5–10 kW. The results of tests of the specimens under a pressure of 4 MPa when registering signals by transducer 2 at an amplification factor of 1200 are presented in Table 5.6. Table 5.6. Variation in AE Characteristics When Changing Friction Mode of ˜-Š 0,5 – ˜-Š 0,5 Pair Friction mode Normal Dry

AE characteristics N˙ , pulses/s 100 10000

¯ V A,

 2 , rel. units

W , rel. units

1

2

04

13

12 · 105

002

201 −001

586

11 · 10

09

8

164

265

−27

As it is seen from the table all AE characteristic varied substantially when changing friction mode. The count rate, emission power and pulse amplitude variance increased 100, 1000 and 45 times, correspondingly. Changes in the coefficients 1 , 2 and indicate the variation of the pattern of the amplitude distribution of AE pulses. Figure 5.20 illustrates the profile traces of the specimen surfaces in the initial state and after tests under dry friction. The average wear of the stationary cube specimens was 0.2 mm. Results of bench tests. In bench tests of a real MCP of BBP-100 reactor AE spectral density was analyzed. Acoustic signals were registered by transducers arranged in different sites of the pump surface. The following features of the acoustic emission of the operating pump were found. All spectra contain peaks at frequencies less than 1 MHz caused by resonance properties of transducers (see Part 1.5). The amplitude of spectral components of AE within 1–4 MHz decreases by almost linear law and the total decrease of the amplitude is about 10 db.

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a

213

b

c

Figure 5.20. Profile traces of specimen surfaces of ˜-Š 0,5 – ˜-Š 0,5 pair: a – original surface of stationary specimen; b – stationary specimen surface after dry friction during 100 s; c – the same, rotating specimen surface normally to friction track. Vertical magnification 1000, horizontal magnification 8 The comparison of the obtained spectra has allowed us to conclude that the source of the most intensive high-frequency (3–4 MHz) AE is located in the region of the main thrust bearing of the pump. Further a transducer was fixed here to study how AE characteristics change in response to variations in operation conditions of MCP. AE signals were registered within the 1    4 MHz frequency band. The limiting sensitivity of the measuring device was increased by 5–10 db by selecting optimal adjustment parameters. The following features of AE were found when testing the pump. If air presented or appeared in the coolant (water) circuit and air-water mixture was formed the count rate of AE pulses grew significantly when the coolant pressure increased sharply and it decreased gradually when the pressure was monotonously reduced (Fig. 5.21). A similar dependence of N˙ on the pressure was not found when no air presented in the circuit. This characteristic changed slightly (within the error). Single AE pulse bursts were registered only in the presence of air-water mixture at stopways of the pump, the count rate for the bursts was several hundred pulses per second. The maximal value of the count rate equal to 1000 pulses/s was registered when the shaft stopped fully. The count rate and average amplitude of AE pulses rise significantly with increasing the rotational speed of the pump shaft. For example, the increase of the rotational speed from 800 to 1500 r.p.m. leads to the rise of the average amplitude of pulses by several orders of magnitude. The obtained results and experience gained when carrying out tribological studies prove the necessity of the improvement of AE method and its applicability for nuclear power engineering. Owing to its broad possibilities it can be used both in the research stage including the selection and tests of materials for friction units of mechanisms and devices of nuclear power plants,

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· N · 10–3, pulses/s 4

Q, MPa 4

3

3

Q

2

2

0

1

· N

1

100

200

300

400

t, s

0

Figure 5.21. Time dependencies of count rate of AE pulses N˙ and pressure in MCP circuit Q (rotating speed of shaft  = 750 r.p.m.) checking and bench tests of real units etc. and in the field inspection and diagnostics of friction units of processing equipment of the plants. ∗∗∗∗∗∗∗∗∗

In conclusion, we can say that in addition to the monitoring and state assessment of structural materials of powerful engineering objects AE method can be successfully used in the diagnostics of friction units of machines and mechanisms and in tribology studies. Numerous experimental data presented in this book prove the effectiveness and some advantages of AE method in comparison with common methods of the monitoring and diagnostics of friction units. Along with this, the lack of normative documents and metrological provision hampers the wide application of AE method for friction unit diagnostics. Evidently, such documentation can be developed in the near future.

References 1. W.H. Roberts, Tribology in nuclear power generation, Tribology International, 1981, no 2, pp. 17–27. 2. T.C. Chivers, Gas–cooled civil power reactors: twenty one years experience in the field of tribology, Proc. Conf. Bristol 20–24 Sept. 1982, vol. 1, London, 1982, pp. 197–204. 3. E.J. Robbins, Tribology for the atomic and space industries, Industries Atomiques Spatiales, 1974, no 2, pp. 1–11. 4. Yu.N. Drozdov, V.G. Pavlov, and V.G. Puchkov, Friction and Wear Under Extreme Conditions. Handbook (in Russian), Moscow, 1986. 5. F.P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Oxford, 1986.

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6. D.H. Buckley, Surface Effects in Adhesion, Friction, Wear and Lubrication, Amsterdam, 1981. 7. E.A. Markovskii, M.M. Krasnoschekov, and D.D. Pereverzev, Antifriction Behavior of Irradiated Alloys (in Russian), Moscow, 1978. 8. V.A. Belyi, O.V. Kholodilov, and A.I. Sviridenok, Acoustic spectrometry as used for the evaluation of tribological systems, Wear, 1981, vol. 69, no 3, pp. 309–319. 9. J.O. Barner, R.J. Quenter, and M.D. Freshley, Fuel–cladding mechanical interaction in PC 1 resistant LWR fuel designs during normal operation and power ramping, Nucl. Technology, 1983, vol. 63, no 1, pp. 63–81. 10. T. Tachibana, Tokai Works Semi–Annual Progress Report, Power Reactor and Nuclear Fuel Development Corporation, Japan, July 1978, pp. 4–51. 11. Method of determining moment of end of friction pair run-in, USSR Patent no 1073614, V.M. Schavelin, G.A. Sarychev, and V.M. Revenko, Bull. of Inv., 1984, no 6. 12. Method of determining moment of end of friction pair run-in, USSR Patent no 1158903, V.M. Schavelin, G.A. Sarychev, M.I. Shakhnovskii, V.M. Revenko, I.G. Goryacheva, M.N. Dobychin, and O.V. Kholodilov, Bull. of Inv., 1985, no 20. 13. A.B. Anapolskii, R.G. Bogoyavlenskii, V.P. Glebov et al., Selection and study of dry friction pair for sliding bearings operating in helium, Friction and Wear, 1983, vol. 4, no 5, pp. 34–38. 14. Yu.N. Drozdov, V.G. Archegov, and V.I. Smirnov, Scuffing Resistance of Solids (in Russian), Moscow, 1981. 15. V.A. Ostreikovskii, Physical-Statistical Models of Reliability of NPP Components (in Russian), Moscow, 1986. 16. G.P. Gaev, N. Hippman, H.A. Sturm, Beitrag zur Diagnose von Mischreibungvorgangen an den Lager einer Hauptumwalzpurmpe, Kernenerge, 1984, Bd. 27, no 10, S. 434–438. 17. P.G. Bentley, A review of acoustic emission for pressurized water reactor application, NDT International, 1984, vol. 14, no 6, pp. 329–335.

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SUBJECT INDEX

Acoustic emission (AE): — continuous, 11, 12, 15, 23 — discrete, 11, 12, 13, 14, 20, 21, 114 Adhesion, 2, 19, 163, 168, 202 AE method, 17, 19, 135, 197, 207, 213, 214 Campbell formula, 32, 33 Carson formula, 32 Cohesion, 2 Contact zone: — real, 2, 61, 93, 153, 159 — nominal, 2, 23, 70 — contour, 2, 93 Creep, 12, 188, 189, 190 Discrete acoustic emission’s (AE) characteristics: — AE activity; amplitude distribution: exponential, 14, 28 Rayleigh, 28, 65 -distribution, 28 power-series, 28 Pearson distributions, 14, 28, 29 — amplitude-time distribution, 14, 21, 23, 24, 27 — average frequency of events, 23 — correlation function, 33, 75, 162 — count rate, 13, 21, 66–71 — distribution of time intervals, 14 — energy of AE, 16, 24 — probability density of pulse amplitude, 13, 18, 27, 153, 174–5 — shape of pulse, 21, 33 — specific count rate, 34 — specific power, 34 — spectral density: average square of the frequency of, 31 spectrum, 31, 32, 103, 161 effective width of spectrum, 31 mean frequency of spectrum, 31 mean-square width of spectrum, 31 one-sided, 30 two-sided, 30

218

SUBJECT INDEX

Discrete acoustic emission’s (AE) characteristics (Continued) — total AE, 13, 166 — total number of pulses AE, 12–13 Dissipative systems, 1 Elementary damage mechanisms: — microcutting, 8, 194 — plastic deformation, 3, 12, 16, 19, 194 — delamination, 8 — pitting, 9 — bulk tearing, 9 Emission: — electrical emission, 5, 97 — electrochemical effects, 5 — galvanomagnetic effects, 5 — Kramer effect, 5 — Seebeck effect, 5 — thermoelectron emission, 5 — thermomagnetic effects, 5 — Thomson effect, 5 Fourier transform, 14, 30, 72, 76 Kirkendal effect, 9 Logarithmic decrement of oscillations, 26 Mechanisms of surface layer damage: — abrasive, 8 — adhesive fatigue, 8 — adsorption-corrosive-fatigue, 10 — cavitation, 8 — corrosive, 10 — erosive, 8 Poisson flow, 22, 33 Postdetection pulse counts AE, 23, 27 Predetection pulse counts AE, 23, 27, 163 Rehbinder effect, 10 Sources of AE in friction of solids, 19 Sources of AE in metals: — plastic deformation, 15 — phase transformations, 15 — origination and accumulation of microdefects, 15 — growth of cracks, 15 Wear stages, 6 Wiener–Hinchin theorem, 14, 33, 75