Three-Dimensional Viscoelastic Bodies in Steady State Frictional Rolling Contact with Generalisation to Knothe Rolling

摘要

The title problem is solved by largely reducing it to methods of solving contact problems in the theory of elasticity. As in that work, the rolling bodies are approximated by half-spaces, but for the purpose of calculating the viscoelastic field only. The only thing then left to do is to calculate the surface displacement due to certain simple loadings that move, unchanging, over the viscoelastic half-space with rolling velocity. The surface displacement is finally found as the convolution of the elastic solution with the relaxation function. This relaxation function is a decreasing exponential; this renders the convolution a Laplace integral, which can be evaluated numerically. Rolling contact is controlled by several parameters, of which the author mentions the mutual approach of the rolling bodies, and the creepages. The viscoelastic theory which was first derived is applied to find the response of the rolling bodies to harmonic variations of the controlling parameters (Knothe rolling). (Copyright (c) 1989 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)