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7.1 Sliding of Non-Conforming Elastic Bodies

In our preliminary discussion in Chapter 1 of the relative motion and forces which can arise at the point of contact of non-conforming bodies we distinguished between the motion described as sliding and that described as rolling. Sliding consists of a relative peripheral velocity of the surfaces at their point of contact, whilst rolling involves a relative angular velocity of the two bodies about axes parallel to their tangent plane. Clearly rolling and sliding can take place simultaneously, but in this chapter we shall exclude rolling and restrict our discussion to the contact stresses in simple rectilinear sliding. The system is shown in Fig. 7.1. A slider, having a curved profile, moves from right to left over a flat surface. Following the approach given in Chapter 1, we regard the point of initial contact as a fixed origin and imagine the material of the lower surface flowing through the contact region from left to right with a steady velocity V. For convenience we choose the x-axis parallel to the direction of sliding.

Fig. 7.1: Sliding contact.

A normal force P pressing the bodies together gives rise to an area of contact which, in the absence of friction forces, would have dimensions given by the Hertz theory. Thus in a frictionless contact the contact stresses would be unaffected by the sliding motion. However a sliding motion, or any tendency to slide, of real surfaces introduces a tangential force of friction

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