Stiffness and deformation of asperities in a rough contact

Transcription

1 Stiffness and deformation of asperities in a rough contact A. Haiahem ^\ L. Flamand ^ Institut de mecanique universite de Annaba, BP 12 Annaba Algerie Laboratoire de mecanique des contacts INS A de Lyon Villeurbanne cedex France Abstract In rough contacts the load is transmitted through the micro-contacts generated the interactions between the asperities. These micro-contacts are submitted by pressures and important stresses appear in the superficial layers close to the surface which lead to plastic deformation of the asperities. In our experimental work, we study the contact between a rough surface and a flat supphire. The samples used are Nickel electroformaging with quasi-sinusoidal roughness. The elastic and plastic parts of the deformation process of the roughness are determined, the experimental apparatus is composed of the loading system and an interferometric microscope in order to measure deformations. The values of the elastic deformation are compared to the theoretical results and the plastic ones with those obtained by using a profilometer coupled with the computer. Finally we deduce the asperity stiffness which are compared to those of the bodies. The results show the primary loading. The interacting asperities are loaded as well as the bodies. Then the elastic deformation and the stiffness are the main functions of the roughness' slope ( ratio of the asperity height to the wavelength ( Rt /1)). The asperity stiffness is very high compared to those of the bodies. 1. Introduction In a rough contact, the load is transmitted through micro-contacts which appear with asperity interactions. The later come under very important pressures and stresses that exist in superficial layers, very close to the surface, and so, could lead to the plastic deformation of the asperities.

2 60 Computational Methods in Contact Mechanics Many authors studied the asperity deformation phenomena in a rough contact. All of them supposed that an asperity gets out of shape elastically [1-6], plastically [7-9] or plastically with a plastic index [10]. In real conditions, the roughness is deformed both plastically and elastically, but no evaluation has been made in order to separate and compare these two contributions. This will be the framework of our study, associated with the determination of the asperity stiffness. Moreover, values of plastic deformations obtained by optical interferometer will be compared with those measured by mechanical means and some theoretical results [11]. The elastic deformation values will be compared with theoretical results [12], and, in term of stiffness, with J.F. Cretegny's results [13]. 2. Experimental procedure A contact between a smooth transparent thin plate and a rough metallic surface is built up. It can be, therefore, possible to measure the asperity deformation by the interferometer technique Parameters measurement The total deformation of asperities ( 8 t) is the sum of two contributions, the one is elastic ( 8 ei) and the other, plastic ( 8 ^) 8 t = 8 el + 8 pi ( % ) If the depth of the initial roughness ( fig. l.a ) is known, the contact is photographed after each stage of loading and unloading ( fig. l.b); then, the deformations are measured after the contact is unloaded ( fig l.c). The elastic deformation is obtained by the difference between the depth of the loaded roughness (H?) and the roughness at no load (Hi): 8 ei = H - H, (2) Moreover, the plastic deformation is calculated by removing from the initial roughness depth ( H) before loading, the depth after ( H?) unloading. 5o, =H-H,

3 Computational Methods in Contact Mechanics 61 H f ^ H f \ 0 i L u initial A roughness B loaded roughness unloaded roughness W=0 Fig 1. Method for measuring the elastic and plastic deflections 2.2 Loading system: The device used is Imbued with the well known anvil pressure technique. The loading operation is made by two interdependent arm levers which are relatively loaded by a screw-nut system ( fig 2). Saphir Screw-nut Sample Dynamometer Fig. 2: Device of loading operation 2.3 Samples: The samples used are cutting tip of 2 mm in diameter, cutted on plates of nickel and realized by electroformaging process. They are used as standards for rough surface controls. Their roughness can be represented as parallel furrows. Sample EI E, Roughness ( R* ) ( LLm) ,89 Wavelength ( X ) ( M-m) Rt/Jt 0,027 0,037

4 62 Computational Methods in Contact Mechanics 3. Technique of roughness measurement Two techniques will be used : 3.1. Optical interferometer The optical device (fig 3 ) is based on the interferometer principle with a monochromatic light source. The generating black and white fringes. The ray emitted by the source goes through the transparent plate and is partly reflected by the semi-reflecting layer of the sample surface and partly absorbed by it. The two reflected waves interfere and form black and clear fringes which correspond to the isolevel curves of the sample surface. This technique enables us to measure the deformations roughness for both loaded and unloaded conditions. Photographic apparatus Microscope Light source Anti-reflective layer Transparent plate Semi-reflective layer Rough sample Base of the sample Fig 3 : Optical device Roughness by mechanical means This well-known technique permits to obtain treatment. the profile surface and its

5 Computational Methods in Contact Mechanics 63 Transactions on Engineering Sciences vol 24, 1999 WIT Press, ISSN Results and discussion 4.1. Comparison between experimental elastic deformation data and theoretical results The results are compared to the theoretical fundings which have been recently developed at the Contact Mechanics Laboratory [12]. In this model, the author has solved the normal contact problem of the Hertzian type, between two solids, by expending a variational formulation based on the virtual work principle. The model can be used for different surfaces: smooth, undulated and surfaces with roughness. He supposed that the roughness has a sinusoidal form, where (X) and (Rt / 2) are respectively the wave length and the amplitude, i, e, i: The corresponding results are presented in figures 5 and Comparison between plastic deformations measured by interferometer and by mechanical means After each loading operation, the plastic deformation values are measured by the interferometer technique and double-checked by mechanical means. The results are showed in fig 7, they are also in accordance with the theoretical work of X. Buob[ll] Parametric analysis of results The results are analyzed by using the following three normalized parameters: the deformation parameters which is the ratio of the deformation (5) to the sample radius Y= 5 / R. the load parameter which is the applied normal load (W) divided by equivalent Young's modulus of the two bodies and the square of the radius of the samples: W 1 l-v? 1-V? W - "" ' ER* E E, EI the roughness slope parameter which is the depth of roughness divided by the wave length X:

6 64 Computational Methods in Contact Mechanics To make an approximation in the sense of the least squares, we have used the average values of the elastic and plastic deformations of each bearing and sought a law of the form: The results obtained are : Elastic deformation with a correlation coefficient of: 0,99 Plastic deformation R With a correlation coefficient of: 0.99 The parametric analysis shows that the load parameter influences greatly the plastic and elastic asperity deformations. On the other hand, the ratio R/A, considerably influences elastic deformations whereas is contribution to plastic deflection is far less pronounced. 5. Conclusion 5.1. The roughness elastic and plastic deformations The results show that the plastic and elastic deformations appear under the first loads and from their increase. These observations, illustrated in fig 5 and 6 show that the elastic deformation of roughness is large where its slope, R, A,, is important and this has lead to a satisfactory agreement with the theoretical results. We observe an elastic deformation comparable to the plastic deformation although the plasticity index Y is larger than 1. In our work, the asperities interact and share the load with the bulk whereas in the case of Greenwood model, the load is only supported by the asperities which act separately as individual Hertzien contacts. The plasticity index of the authors do not take into account the roughness interdependence and the bulk elastic deformation. In our case, the two aspects are considered.

7 Computational Methods in Contact Mechanics 65 Transactions on Engineering Sciences vol 24, 1999 WIT Press, ISSN The stiffness of asperities Figure 7 shows the variation of the stiffness as a function of the load. The stiffness increases with this one. The stiffest sample is the one that has the smallest roughness slope. So, an increase of the roughness slope leads to an increase of the elastic deformation and therefore to a decrease of their stiffness. This is in agreement with results of J. F. Cretegny. Also, we notice that the bulk stiffness has an order of magnitude of l(f N/m in general and that of the roughness is of 10^, approximately 10* bigger. 1,4-3 0,6 c<l) 0,4 -o o Rt/^0,035 RtA=0, Charge (N) Fig. 4. a : Experimental elastic deformation variation as a function of the load \_y O <D (J -S 0.5 o -e ojsh ' Rt/l=0,027 Rt/^0.035 Fig. 4. b : Theoretical elastic deformation as a function of the load for EI and E? samples

8 66 Computational Methods in Contact Mechanics Load UN) 3000 Fig. 5. a : Theoretical and experimental elastic deformations as versus load for EI sample 1.5 -Exp. Els.Def. ofe2 c: o Theo. Els. Def. ofe? % 0.5 o c8 ^ Load (N) Fig. 5. b : Theoretical and experimental elastic deformations as versus load for 2 sample

9 Computational Methods in Contact Mechanics 67 o- mecha. Plas. Def -* Inter. Plas Load (N) 3000 Fig. 6 : Experimental plastic deformation measured by mechanical means and interferometer I OJ I Rt/X=0,027 Rt/l=0,037.-a 1000 to Vi < Load (N) Fig. 7 : Asperity stiffness for both sample EI and E?

10 68 Computational Methods in Contact Mechanics References [1] Hertz, H., On the contact of the elastic bodies, Journal fur die reine and angewandte mathematics, vol. 92, 1881, p [2] Archard, J. F., Elastic deformation and the laws of friction, Proc. Roy. Soc., London England, Vol. 243, A 1957, p [3] Greenwood, J. A., Tripp, J. H, The elastic contact of rough spheres, J. Appl. Mech. 1967, serie E, 34, p [4] Vergne, P., Villechaise, b., Berthe, d., Etude elastique de contacts multiples, interaction des asperites, J. Mec. The et Ap., 1983, vol. 2, N 6,p [5] Michau, B., Effets du champ de contraintes sur la fatigue des surfaces dans les contacts Hertziens rugueux, These de doct. Ing., Universite Claude Bernard de Lyon, 1987, p , N 169, 262 p. [6] Seabra, J. O., Berthe, D., Influence of surface waviness and roughness of the normal pressure distribution in the Hertzien contact, J. Trib., vol , p [7] Pullen, J., Williamson, J.B.P., On the plastic contact of rough surfaces, Proc. Roy. Soc., London, A327, 1972, p [8] Yip, F. C., Venard, J. E. S., An plastic analysis of the rough spheres and rough cylinder in contact Jour. Phys. D. Applied Phys., 1971 p [9] Hisakado, T., Tsukisoe, T., Effects of distribution surfaces slopes and flow pressures of the contact asperities on contact between solids surfaces, Wear, 30, 1974, p [10] Greenwood, J. A., Willianson, J. B. P., Contact of nominally flat surfaces, Proc. Roy. Soc., 1966, London, A 295, 1972, p [11] Buob, X., Moderation de la deformation plastique dans un contact Hertzien, D.E.A., I.N.S.A. de Lyon, 1990, 46 p. [12] Seabra, J. O., Influence de 1'ondulation des surfaces sur le comportement des contacts Hertziens sees ou lubrifies, These de doctorat, I.N.S.A. de Lyon, 1988, 209 p. [13] Cretegny, J. F., Etude theorique et experimentale des raideurs de contacts, These de doct. Ing., I.N.S.A. de Lyon, 1985, 226 p.