Three-dimensional Contact of a Rigid Roller Traversing a Viscoelastic Half Space

In this paper, the authors consider a nontrivial three-dimensional viscoelastic contact problem which has some physical significance. (Although the subject of the analysis is an elliptical roller, it is only a small step onward to the consideration of a crowned cylindrical roller.) Generally, it is the intractability of the mathematics which hinders analytic solution of true three-dimensional problems in (visco)elasti city. The traditional method of surmounting this difficulty is to reduce the problem to two dimensions, either by choosing a suitable geometry, or by using an appropriate co-ordinate system. The elastic line integral theory represents another approach; certain approximations are used to simplify the governing equations, thus allowing the solution of the problem. After the development of a viscoelastic analogue of the Boussinesq equation valid for the solution of quasi-steady state viscoelastic contact problems, analysis proceeds making use of near field and extended line integral approximations. Results are generated showing the velocity dependence of several physical parameters, including the size and shape of the contact zone. One additional point of interest is uncovered, namely the presence of a pressure peak near the leading edge of the contact zone.