FE contact and thermal simulation of an alumina-steel dry sliding friction pair

Transcription

1 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 35 FE contact and thermal simulation of an alumina-steel dry sliding friction pair Z. Lestyán 1, K. Váradi 1 & A. Albers 2 1 Budapest University Technology and Economics, Institute of Machine Design, Hungary 2 Universty of Karlsruhe, Institute of Product Development Karlsruhe, Germany Abstract In this study FE contact and thermal sliding analysis of an alumina-steel dry sliding friction pair was performed to investigate the real contact area, the contact pressure distribution and the temperature distribution considering the real worn topographies. A friction test was carried out to simulate the dry sliding friction of sliding pairs on the test rig designed for this purpose. The applied algorithm describes the real processes of the contact area formation, although local micro-level calculations will be necessary in the future. Keywords: dry sliding friction, real contact area, contact temperature. 1 Introduction Ceramics structural components provide novel opportunities for engineers due to their exceptional static and tribological characteristics. High purity alumina ceramics have some advantages such as good heat conduction, thermal stability, wear resistance, and high compression strength; they provide a promising friction material for clutches, CVTs, and brakes. Nevertheless, the properties of ceramic materials are unknown or only partially known in a number of areas. In the course of development, the special mechanical properties of ceramics require a new approach in terms of design and sizing. This requirement particularly applies to complex loads, such as sliding friction. Heat generation plays a dominant part in the behaviour of tribological systems of dry sliding friction. The investigation of heat generation requires contact phenomena to be studied. Characterization of the real tribological process requires the oint investigation of

2 36 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII the two phenomena, which have constituted the obective of many numerical and analytical research proects. Analytical approaches to determine the surface temperature of a sliding pair were developed in the first half of the 2th century. Blok [1] and Jaeger [2] assumed in their pioneering work that heat power evolved on a single discrete surface during a sufficiently long time. The definition of heat partition came from Blok, its condition was the existence of identical maximum contact temperatures. Archard [3] simplified the assumption mentioned above and applied it in the cases of slow and rapidly moving contacts. The refined calculation of temperature in the vicinity of the contact area was provided by Carslaw and Jaeger [4]. Allen [5] solved numerically the general problem of heat partition and than Kuhlmann-Wilsdorf [6] introduced an approximate solution of heat partition at intermediate velocities of an elliptical contact area. Tian and Kennedy [7] analysed the temperature state at macro stage and micro stage analytically. Bos and Moes [8], based on the results by Carslaw-Jaeger, yielded the identical contact temperature in the elliptical contact region by a developed algorithm. Váradi et al. [9] modelled the contact area distribution and contact temperature developed of rubbing surfaces by a surface substituting technique and finite element analysis. Muzychka and Yovanovich [1] studied surface temperature development in the case of rectangular and elliptical contacts in all cases of Peclet numbers by an evolved algorithm. Hou and Komanduri [11] investigated the surface temperature developed in fine grinding process which is a case of dry sliding friction of rough surfaces. In their calculation they took chip heat partition into consideration. The sliding components were high purity alumina ceramic and 1Cr6 steel. Hwang and Zum Gahr [12] had dominant activities in the tribology of these sliding pairs. The aim of this study is to determine the real contact area, the contact pressure distribution, and the real contact temperature in numerical and experimental ways. 2 Friction test A friction test was done to gain data on the physical and mechanical processes during dry sliding friction. The test rig and their components are shown in fig. 1. The friction test consists of a series of individual steps; the process of rubbing is dynamic. The ceramic palettes, fixed on the same pitch circle, were rotated at constant angular acceleration and pressed to a stationary steel disc according to the following steps: The ceramic palettes were pushed against the stationary steel disc, with a pressing force of 1N each. The revolver head holding the ceramics was rotated by constant 5 1/s 2 angular acceleration for 5 seconds. After 5 seconds the connection was broken between the ceramic palettes and the steel; the rotation of the ceramics was stopped and the sliding pairs were cooling down in the following 18 seconds. This step was repeated by 3 times; in the course of a single step, there were 62.5 revolutions in 5 seconds.

3 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 37 During the friction test the pressing force, the friction torque and the rotational speed was measured. The friction coefficient is reduced in a non-linear manner in the function of time. 3D Surface roughness measurements were performed on the worn surfaces of the sliding pair after 3 steps of the friction test by a Perthen stylus instrument. The sampling distance of the surface roughness measurement was 5 microns, which means information was gained in each 5 micron from the worn surfaces. Surface topographies are to determine the initial conditions of latter contact calculations. Snapshots were taken from the worn topographies of the sliding pairs by optical microscope in order to study worn topologies. Temperature measurement of the rubbing surface of a selected ceramic palette was done by a thermo-graphic camera (see fig. 1) after each revolution. The camera measured the maximum and the mean surface temperature when the ceramic piece was in front of the hole drilled into the steel disc. The measured data were the inputs of and references for latter numerical calculations. F N (t) M(t) v(t) g T(t) a b c d e f Figure 1: The assembly of the test rig: the power train (a), rotating gripping head (b), feeding unit (c), ceramic palettes (d), stationary steel disc (e), thermo-graphic camera (f) and computer (g). 3 Contact calculation Sliding contact simulation was performed considering the surface roughness to study the real contact area, the A R /A N ratio and the stress distribution during dry sliding friction assuming a two-body friction mechanism. Incremental sliding simulation consists of 1 consecutive steps where the incremental step is 5 microns. Therefore the simulation specifies the contact state of.5 mm of sliding in 1 steps. During the FE contact calculation the ceramic palette is pushed

4 38 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII against the steel surface. A surface roughness measurement was considered in order to specify the initial gap distribution of the contact calculation. The worn topographies are shown in fig. 2. The FE mesh represents the local environment of the contact area of the sliding pairs. The material properties assume linear elastic behaviour The load was surface pressure corresponding to the 1 N pressing force while the boundary conditions represents rigid supports. There are nodes, elements and 466 contact elements defined (fig. 3). Surface [µm] Surface [µm] 21.6 y x [µm] z [µm] 65 y Sliding z [µm] 55 direction x [µm] I) II) Figure 2: The surface roughness of the table like worn surface of a ceramic palette (I) and the worn groove of the steel disc (II) after 3 repetitions. The contact simulation of each step provided the contact forces. However, many individual point-like contacts occurred, which yielded inappropriate contact stress results. For that reason, according to the element size of the FE mesh, 5 micron by 5 micron square discrete contact areas were defined where contacts existed to define the real contact area. Furthermore, substitutive calculations were performed in each step to analyse the contact stress state based on the real contact area definition and the contact forces calculated. The model was loaded by normal and tangential pressure on the discrete surfaces of the real contact area at location i at step, as follows: * p N ( t ) F ci, (t)/a i, =, (1) p T ( t ) = µ ( t ) p N ( t ), (2) i, i, where F ci, is the actual contact force, p Ni, is the normal pressure, p Ti, is the tangential pressure, µ i is the coefficient of friction and A * is the constant discrete area. The A R /A N ratio was calculated by the actual real contact area divided by the estimated nominal contact area A W. The estimated nominal contact area was determined by the worn topography of the ceramic piece; it had an elliptical shape with a 6.5 mm semi maor axis and a 6. mm semi minor axis.

5 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 39 Rigid support Detailed view a Normal pressure b Figure 3: The contact FE model, mesh, load, boundary conditions, detailed view of the steel side mesh and material discretization: (a) ceramic, (b) steel. 4 Thermal simulation Heat generation and temperature distribution was determined by FE transient simulation in the course of sliding friction. Thermal calculations took into consideration the contact area and the contact stress state during sliding. The total length of the thermal sliding simulation was 88.5 mm which was about the first 1/6 revolution, while the contact calculations simulated only.5 mm long sliding friction. Thus the block of 1 consecutive steps of the contact simulation was repeated 177 times consequently to form a basis for thermal calculations. The thermal simulation applied an incremental technique with the same step size which was applied in the case of contact calculations, therefore it had 177 steps to study heating up during dry friction. The thermal simulation of the two sliding pairs had to be performed parallel. In the case of the thermal model of the rubbing surface of the ceramic palette, the thermal load does not move in the direction of sliding, while its spatial distribution changes continuously by the actual real contact area at each step of the simulation. In the thermal model of the steel rubbing surface, the location of the thermal loads is changing by the actual real contact area at each step, while it moves in the direction of sliding by incremental steps. The thermal load of the models was heat flux at location i and step, that is qi, (t) = q i, (t) = p Ni, p (t)µ (t)v (t)β (t) Ni, (t)µ (t)v (t)(1 β (t)) in the case of steel side, (3) in the case of ceramic side, (4) where p Ni, is the normal pressure, q i,, is the heat flux, v is the sliding velocity, and ß is the heat partition of the steel side. Heat partition is the rate of distribution of the heat generated between the sliding pairs. It is essential to define it and describe its change in time for a reliable thermal sliding simulation.

6 4 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII Time-dependent heat partition was determined by an iterative algorithm based on FE calculations, which checks compliance with Blok s postulate at each step and determines the changes of heat partition accordingly in an iterative manner. 5 Results Severe wear can be observed on the worn surface of the ceramic palette by optical microscope, as shown in fig. 4. Comparisons of the estimated nominal and the real contact areas with the optical microscope images of the worn sliding pairs are shown in fig. 5/I and fig. 5/II, respectively. fig. 6/I shows the pressure distribution of a step, characterized by large contact stress peaks. The coincidence of the contact areas with the worn topographies verifies the correctness of contact calculations. The calculated contact area falls within the severe wear area on both the ceramic and the steel side. Many constant and many temporary contacts evolve in the course of simulation. The A R /A N ratio is in the range of 1.2 to 1.5% during the 1-step simulation (fig. 6/II). Sliding direction severe wear 1 mm Figure 4: Severe wear region on the worn surface of a ceramic (top view). The maximum surface temperature changes periodically due to the repeated contact areas and contact stresses. In order to illustrate the temperature change, fig. 7/I. shows the maximum temperature results at each 4 mm, which define the top boundary curve of maximum temperature change. The deviation between the maximum temperatures of the two sliding pairs is less than 7%. The approximative temperature difference above could be achieved only by nonlinear time dependent heat partition as shown in fig. 7/II. The maximum temperature results of the ceramic surface were compared with the thermographic measurement results in fig. 8. The comparison shows that the calculated and the measured data are in good agreement, which verifies thermal simulation results. A characteristic geometrical point (point A in fig. 5/I) was selected on the worn groove of the steel disc in order to analyze the impact of the contact area. There are intensive mechanical and thermal processes along the surface; their impact on failure and wear processes are intended to be analyzed in the future. It

7 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 41 results from the examination of contact stress and temperature distribution below point A that the bearing force on the top 12.5 microns is the highest, where both the Mises stress and the temperature show maximum values (fig. 9). The results suggest that surface failure is most probable in the topmost 12.5 micron range. The results of surface roughness measurement show that surface failure occurs in the top 7-1 micron layer. Sliding direction Sliding direction Point A 1 mm I) II) 1 mm Figure 5: (I) The top view of the worn groove of the steel surface (the dashed white bold line indicates the estimated normal area while the real contact area of a step is marked by black spots, the black arrows indicate the margins of the groove). (II) The top view of the worn ceramic (the dashed white bold line indicates the estimated nominal contact area while the real contact area of a step is marked by black spots). σ normal [MPa] 1 Z [µm] 55 5 Sliding direction A R /A w [%] X [µm] Figure 6:.5 s [mm] I) II) (I) The normal pressure distribution, based on the real contact area definition on the steel surface of a contact solution of ten-step simulation. (II) The A R /A W ratio in function of the sliding distance (in the course of ten step sliding simulation).

8 42 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII Figure 7: T max [ C] s [mm] a b β [-] s [mm] I) II) (I) The maximum temperatures calculated of steel side (a) and ceramic side (b) in function of the sliding distance. (II) The heat partitions of steel side (a) and ceramic side (b) in sliding distance. a b T [ C] a b c s [mm] Figure 8: The temperature results of calculation and measurement: the measured maximum (a) and mean (b) temperatures; calculated maximum temperature of ceramic side (c) σ HMH 1 1 [MPa] T [ C] Depth [µm] Depth [µm] I) II) Figure 9: (I) Mises stress distribution in the function of the depth below point A. (II) The temperature distribution ust below point A.

9 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 43 6 Conclusion An algorithm with an incremental technique based on FE calculations was developed to study dry sliding friction. The algorithms applied can describe the real contact area and real heat generation in the course of dry sliding friction, by taking into consideration the surface roughness of real worn surfaces. The A R /A N ratio changes in the % range during sliding friction. The heat generated can be transferred through the real contact area to the sliding pairs. Therefore, during the sliding distance of 88.5 mm covered in.246 s, temperature reaches 21 C. The Mises stress and temperature distribution below surface is concentrated in the upper 12.5 micron region. The contact area going through the worn surface of the steel generates highly intensive stress and temperature fluctuations. Large fluctuations may play a considerable role in surface failure. Heat partition changes in a non-linear manner in time due to accelerated sliding motion. A local micro model is needed to be studied in the near future to analyse the elastic-plastic contact and thermal behaviour of the asperities. Acknowledgement The authors would like to express their thanks to the Hungarian-German Partnership Proect (MÖB-DAAD) for the financial support of mobility. References [1] Blok, H., Theoretical study of temperature rise at surfaces of actual contact under oiliness conditions. Proc. Inst. Mech. Eng. General Discussion on Lubrication, Inst. Mech. Eng., London, pp , [2] Jaeger, J.C., Moving sources of heat and the temperatures of sliding contacts. Proc. Roy. Soc. N.S.W., pp , [3] Archard, J.F., The temperatures of rubbing surfaces. Wear, (2), pp , [4] Carslaw, H.S. & Jaeger, J.C., Conduction heat in solids, Oxford University Press: Oxford, [5] Allen, D.N. de G., A suggested approach to finite-difference representation of differential equations with an application to determine temperature-distribution near a sliding contact. Journal Mech. and Applied Math., (15), pp , [6] Kuhlmann-Wilsdorf, D., Temperatures at Interfacial Contact Spots: dependence on velocity and on role reversal of two materials in sliding contact. Journal of Tribology Transactions of ASME, (19), pp , 1987.

10 44 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII [7] Tian, X. & Kennedy, F.E., Contact surface temperature models for finite bodies in dry and boundary lubricated sliding. Journal of Triblogy Transactions of ASME, (115), pp , [8] Bos, J. & Moes, H., Frictional Heating of Tribological Contacts. Journal of Triblogy Transactions of ASME, (117), pp , [9] Váradi, K., Bercsey, T. & Néder, Z., Modelling sliding friction between engineering components, Proceedings of the International Tribology Conference, Nagasaki, pp , 2. [1] Muzychka, Y.S. & Yovanovich, M.M., Thermal resistance models for non-circular moving heat sources on a half space. Journal of Heat transfer Transactions of ASME, (123), pp , 21. [11] Hou, Z. B. & Komanduri, R., On the mechanics of the grinding process, Part II-thermal analysis of fine grinding. Int. Journal of Machine Tools & Manufacture, (44), pp , 24. [12] Hwang, D.H. & Zum Gahr, K.-H., Transition from static to kinetic friction of unlubricated or oil lubricated steel/steel, steel/ceramic and ceramic/ceramic pairs. Wear, (255), pp , 23.