The role of surface roughness in the friction of sliding contacts M. EI-Sherbiny* and F. Salem Results are presented of studies to assess the role of surface roughness in the friction of sliding contacts. A model of the surface roughness uses conical steel needles. A theoretical model based on the mechanics of interaction is included. Experimental and calculated results are discussed in relation to real engineering surfaces and the models compared Keywords: roughness (surface), friction, sliding, aspertties, mathematical models Early work on the friction of solids 1'2 attributed friction to molecular field force, plastic deformation, junction growth and interlocking of surface asperities. An early theory 1 , proposing the mechanism of adhesion between surfaces as the primary cause of friction, was developed further 2 to accommodate the presence of surface films of low shear strength and the deformation of surface asperities 3'4 . Although the results of a large number of studies on friction are available, it appears that most of them involve a number Department of Mechanical Design, Faculty of Engineering, Cairo University, Egypt MI ~ o" I \ M 2 , 0"2, a "/71, "q2, 01 0 2 , M, o-, 77, 0 superimposed b of the mechanisms mentioned and do not permit differen- tiation between the roles played by each mechanism. A number of authors 4-6 have attempted to decouple such mechanisms and isolate each one in a separate test or model. In this context Hailing 4 used a spherical asperity model to derive a friction theory for rough engineering surfaces of work hardening materials. Hisakada s used a conical asperity model to study the influence of surface roughness on abrasive wear. Myers 6 experimentally studied the effect of mean slope on friction using a slider with three pins. Here, an attempt is made to investigate the role of surface roughness in the friction of sliding contact. The surface asperities were simulated by steel needles with conical tips. A theoretical model based on the mechanics of inter- action is described. The results are compared with earlier experimental 6 and calculated 4 results. Theoretical model The theoretical model is based on the following assump- tions: • The shape of the hard asperities is conical. • The interfacial shear strength (r) and flow pressure (Y) are constant over the whole surface and during the entire period of the friction traverse. • The height of the conical asperities may be considered Gaussian, though the result is equally valid for any other distribution. • The distribution curve of the slope (0) is Gaussian and independent of the separation of the two mating surfaces. In the contact situation in Fig 1, the hard conical asperities move along a track, shearing metal along the contact inter- face and ploughing the metal in front of the track. The pressure produced by the resistance of the accumulated metal on the asperity is Y, while the flow of metal upwards and outwards produces two frictional forces G and T respectively (Fig 2). The normal force P acting on a side element ABC which lies on the ploughing surface is therefore given by 1 L~ Yd~- Y ai aid ~ (1) P=AY= 2 2 cos0 while Fig 1 Contact of a soft flat surface with a hard rough surface." (a) real engineering surfaces, (b ) idealized contact 1 a i G= ~ /a a Y aicos~ d~O (2) cos0 TRIBOLOGY international 0301-679X/84/040223-05 ;$03.00 © 1984 Butterworth & Co (Publishers) Ltd 223