Steady Sliding of a Circular Cylinder over a Dissimilar Thermally Conducting Half-plane

-The problem of a thermally conducting cylinder sliding steadily over the surface of an elastic half-plane with different thermal properties was analyzed. Appropriate Green's functions are used to reduce the problem to an integral equation which is solved numerically. Thermoelastic distortion due to frictional heating causes the contact patch to be smaller than that predicted for isothermal (Hertzian) contact although solutions assuming a single, perfectly conducting contact patch are not found for all values of parameters. I N T R O D U C T I O N Rubbing contact between convex bodies occurs frequently in engineering, in particular in certain types of brakes, in sliding electrical contacts and in wear tests. It has been conventional in analyzing these configurations to ignore the effect of thermal distortion produced by the heat generated, and to utilize Hertzian contact theory. However recent work by Barber and others (see Johnson [1] ) has shown that because of thermoelastic coupling between the distorted profile and heat generation at the interface, very pronounced differences from isothermal contact are found, with much higher contact pressures. In particular, Barber [2] has shown that steady sliding of a conducting cylinder over an insulating half-plane (such that the contact is stationary in the conducting body) always results in a contact width which is narrower than that obtained in the isothermal problem. As the contact load is increased whilst the sliding speed is kept constant, the contact width asymptotically approaches a constant value which it cannot exceed. This is in contrast to the isothermal problem, where the contact size increases indefinitely with the applied load, within the other limits prescribed for Hertzian contact. It is the principal object of this paper to relax the assumption that the cylindrical contacting body is non-conductive, and investigate the effects of this generalization on the contact behaviour. The more general case of two surfaces sliding together such that the contact patch is moving with respect to each body may be formulated by a similar technique. However, this serves to introduce further parameters into the argument, and hence for the present the particular case of one body being stationary is considered. This has the added advantage that comparison with an exact solution may be made. F O R M U L A T I O N The geometry of the contacting pair is shown in Fig. 1. It is assumed that the cylinder is rotating with a peripheral velocity v, and that the region of contact is spatially fixed with . . . . . . a " l . . . . "b . . . . . . x I Bocly 2 FIG. I. Geometry of contact.