# FINITE ELEMENT SIMULATIONS OF THE EFFECT OF FRICTION COEFFICIENT IN FRETTING WEAR

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1 Proceedings of the 5 th International Conference on Fracture Fatigue and Wear, pp , 216 FINITE ELEMENT SIMULATIONS OF THE EFFECT OF FRICTION COEFFICIENT IN FRETTING WEAR T. Yue and M. Abdel Wahab Soete Laboratory, Faculty of Engineering and Architecture, Ghent University, Belgium Abstract: Assuming a constant coefficient of friction () is a simplification in the finite element (FE) modelling of fretting wear. is an essential factor of energy model for predicting fretting wear. Therefore, taking the variation of into account during fretting wear cycles is necessary. In this research, based on the cylinder/flat fretting wear model, the effects of are studied. At the end of fretting wear cycles, only slightly lower wear depth and wear width for the case of variable model compared to the case of constant model is observed. At the end of the initial running-in stage, the wear depth obtained from the variable model is significantly different from that obtained from the constant model. Keywords: Fretting wear, FEM, Friction coefficient 1 INTRODUCTION Finite element method (FEM) is widely used in the simulation of fretting wear. However, to balance efficiency and accuracy, FE model of fretting wear is usually simplified in some aspects, such as assuming constant coefficient of friction () during the wear process. is a system-dependent parameter rather than an intrinsic property of a material or combination of materials. It is sensitive to the sliding distance and environment parameters, such as contact pressure and surface quality [1]. Blau [2] grouped the factor impacting the friction behavior as: contact geometry, fluid properties and flow, lubricant chemistry, relative motion, applied forces, third-bodies, temperature and stiffness, and vibrations. During fretting wear, both applied normal load and displacement have significant influence on. Zhang et al. [3] shows that the of the steady stage decreases with increasing the normal load for a given displacement condition. Similar tendency could also be found in the fretting coupling of high strength alloy steel [4] and steel wire [5]. This tendency may be explained as when the normal load is small, elastic deformation causes asperities of contact surfaces interlock with each other, inducing high. When increasing normal load to activate plastic deformation of asperities, the becomes lower due to less interlocking [3]. In addition, the displacement does affect the under both dry and lubricated contact in a given normal load condition. Besides the continuous changing of contact pressure induced by evolution of contact geometry, debris also plays a significant role. Due to composition of the debris, a critical contact pressure exists at which a transition to a higher occurs [6]. For a given fretting couple, evolution of with number of fretting wear cycles usually could be divided into 3 stages. In the initial running-in stage, is low since the contact surfaces are covered by the oxide and nature pollution film weakening the adhesion between contact surfaces. Later on in the second stage, increases gradually because of the removing of this film, and due to the increase of adhesion and abrasion in the substrate interfaces. Then, the balance between generation and ejection of debris are reached. Therefore, keeps stable at this last stage [3]. The motivation of this work is to improve FE modelling of fretting wear in order to increase the accuracy compared to the experimental results. In this study, the effects of variation of during the first few thousands cycles on fretting wear are studied. This paper is divided into 4 parts. After the introduction section, the FE model is described. Then, the effect of are presented. Finally, a conclusion is presented. 2 FE MODEL 2.1 Geometry information Fig. 1 shows the geometry of the FE model. The dimensions are the same as used in the literature [4], since the simulation results could be validated by the experimental results. The 4-node plane strain element (CPE4) 58

2 is chosen and the mesh size is refined to 5 µm in the contact surfaces for both pad and sample. The masterslave, surface to surface and finite sliding are defined as the contact interaction. The bottom surface of cylinder is defined as master surface and the slave surface is the top surface of the sample. R = 6 mm Y 6 mm X 12 mm Fig. 1 Geometry and dimensions of basic model 2.2 definition of the first 25 cycles In most FE simulations of fretting wear, the is defined as a constant in which case both Archard model and energy model produce the same results. While as Fig. 2 from reference [4] indicated, at the beginning of fretting wear process, it is in the running-in stage and increases significantly during the first three thousands cycles in both normal load cases, i.e. 185 N and 5 N. Therefore, the influence of variable should be considered in the fretting wear FE model, especially in the study of the running in stage. 1,9,8,7 185N 5N,6,5,4,3,2, Number of cycles Fig. 2 Evolution of during process of fretting wear for displacement amplitude 25 µm [4] In order to obtain the relation between and number of cycles, the of 185 N and 5 N were extracted and the best fit is made, as illustrated in Fig. 3 and Fig. 3, respectively. Since the purpose of best fit is to gain the most accurate formulation describing this relation, the value of is the only factor considered. Thus, it is polynomial relation in which cases is closed to 1. When normal load is 185 N, the best fit function which.989 is: ( 1 ) When normal load is 5 N, the best fit function which.985 is: ( 2 ) 59

3 1,9,8,7,6,5,4,3,2,1 fitting curve data points Number of wear cycles,9,8,7,6 fitting curve,5,4 data points,3,2, Number of wear cycles Fig. 3 points and fitting curves, normal load=185 N, normal load=5 N 2.3 Wear model Due to explicitly including, the energy wear model is utilized here to simulate the process of fretting wear. This model is proposed by Paulin et al. [7] and also described in our previous research [8]. For completeness and conciseness, the flow chart of wear calculation is presented in Fig. 4. The wear depth is calculated at the end of each time increment after achieving convergence of FE results, by the subroutine UMESHMOTION in ABAQUS. Inc =1 Umeshmotion for calculating wear depth "#\$% &#\$% '(' Inc=Inc+1 Yes No Output Fig. 4 Flow chart for fretting wear simulation: details of fretting wear module 2.4 Simulation parameters The material property is the same as that used in reference [4]. Young s modulus is 2 GPa and Poisson ratio is.3. For capturing the influence of variation at the beginning stage, the jump cycle is 1 in both loading conditions until 25 cycles. The after 25 cycles of basic model and the coefficient of wear employed in this study are listed in Table 1. Parameters Table 1 Normal load and wear properties used in basic model Normal load(n) in steady state MPa ! ! Displacement amplitude (µm), S Total number of cycles, N T Running-in cycles, N R Jump cycle in running-in cycles, N JC1 1 1 Jump cycle in transition 5 5 Jump cycle in remaining cycles, N JC

4 3 NUMERICAL RESULTS 3.1 Validation After 18 cycles, comparison between the results using variable, constant and experiments results of wear depth and wear width is shown in Fig. 5. For both normal load cases, the wear width and wear depth of variable model are slightly lower than the basic model with constant. However, considering experimental results, significant differences exist. When the normal load is 185 N, the wear width is underestimated by 2% and the wear depth is larger by 16%. When it increases to 5 N, FE model results are 2% more in wear width and 35% less in wear depth. The reasons for these differences between FE results and experimental ones could be because: a) the wear coefficient used in FE models is global wear coefficient instead of local wear coefficient and b) the influence of debris is not considered in FE models. From this comparison, it is found that variable in full cycles of fretting wear simulation has little impact on the final result of FE fretting wear simulation. 5N Difference of Scar width Variable COF Constant COF Experiment 5N Difference of Scar depth Variable COF Constant COF Experiment 185N 185N (%) (%) Fig. 5 Comparison of scar width and depth between cylinder/flat FE model and experiments, N=185 N and 5 N, respectively. R=6 mm, applied displacement 25 mm scar width, scar depth 3.2 Fretting wear in the first 25 cycles Fig. 6 shows the wear scar after 25 cycles in both models. It is reasonable that the prediction of variable model attains smaller wear scar. This is because that, at the running-in stage, the is changing with time, but still less than the constant used. Due to this lower, less dissipated energy from frictional work is used for wear. From this point of view, energy wear model brings more realistic explanation for wear simulation than Archard model. 185 N,E+ -,15 -,1 -,5,5,1,15 5 N,E+ -,25 -,15 -,5,5,15,25 wear depth(mm) -3,E-4-6,E-4 Variable wear depth(mm) -1,E-3-2,E-3 Variable Constant Constant -9,E-4 contact line (mm) -3,E-3 contact line (mm) Fig. 6 Wear scar comparison between variable and constant cylinder/flat models in first 3 cycles, normal load=185 N, and normal load=5 N The specific changes in percentage differences between the two models with number of cycles are shown in Fig. 7. For both normal load conditions, differences in wear depth, wear scar and peak contact pressure exhibit similar tendency; i.e. by increasing number of cycles, the differences between variable and constant models decreased. Especially, the differences of wear depth decreased smoothly from 61

5 approximately 55% after 2 cycles to approximately 1% after 25 cycles. These changes could be described by a polynomial formula as: when normal load is 185 N, )*++,-,\$%, ,.9993 ( 3 ) When it is 5 N, )*++,-,\$%, ,.9978 ( 4 ) Thus, the wear depth after 25 cycles could be calculated by the best fitting curve instead of fretting wear simulation. However, the other three variables are oscillated with number of cycles. The reasons for this oscillation would be further studied in future work N 6 5 N 5 Wear depth 5 Wear depth difference(%) Peak contact pressure Wear width Fitting curve difference(%) Peak contact pressure Wear width Fitting curve Number of cycles Number of cycles Fig. 7 Influence of variable in wear depth, peak contact pressure and wear width in the first 25 cycles. normal load=185 N, and normal load=5 N 4 CONCLUSIONS Two FE models are generated to study the fretting wear process. The effect of variable on fretting wear are analysed based on a basic model having a constant. After 18 cycles, there are very limited differences in wear width and wear depth between constant and variable fretting wear models. However, after the first 25 cycles, where increases significantly, the differences in wear width, wear depth and peak contact pressure are clear. All the differences of these variables decreased with time. Particularly, the differences of wear depth reduced smoothly from 55% to 1%. 5 ACKNOWLEDGEMENTS The first author would like to acknowledge the research funding from China Scholarship Council and CWO - Mobility fund of Ghent University. 6 REFERENCES [1] N. P. Suh and H.-C. Sin, The genesis of friction, Wear, 69 (1), , [2] P. J. Blau, The significance and use of the friction coefficient, Tribology International, 34 (9), , 21. [3] D. K. Zhang, S. R. Ge and Y. H. Qiang, Research on the fatigue and fracture behavior due to the fretting wear of steel wire in hoisting rope, Wear, 255 (7 12), , 23. [4] I. R. McColl, J. Ding and S. B. Leen, Finite element simulation and experimental validation of fretting wear, Wear, 256 (11-12), , 24. [5] Y. Shen, D. Zhang, J. Duan and D. Wang, Fretting wear behaviors of steel wires under frictionincreasing grease conditions, Tribology International, 44 (11), ,

6 [6] N. Diomidis and S. Mischler, Third body effects on friction and wear during fretting of steel contacts, Tribology International, 44 (11), , 211. [7] C. Paulin, S. Fouvry and C. Meunier, Finite element modelling of fretting wear surface evolution: Application to a Ti 6A1 4V contact, Wear, 264 (1-2), 26-36, 28. [8] T. Yue and M. Abdel Wahab, Finite element analysis of stress singularity in partial slip and gross sliding regimes in fretting wear, Wear, 321 (), 53-63,

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