THEORY AND NUMERICAL METHOD OF ELASTIC BODIES IN ROLLING CONTACT WITH CURVE CONTACT AREA

Based on Kalker’s Non-Hertz theoretical model of three-dimensional elastic bodies in rolling contact, this paper develops a new model for solving three-dimensional elastic bodies on rolling contact with the contact patch of curved surface, in which the influence exerted by the boundary conditions and arbitrary geometry of the bodies in rolling contact is taken into account. Finite element method (FEM) was used to discrete the elastic bodies in contact and calculate the flexibility coefficients between outside forces and displacements of the bodies. The theoretical model was transformed into a nonlinear programming problem which was solved by Lagrange multipliers method. The detailed numerical simulations of two-dimensional elastic bodies in static contact and with rotation around a fixed axis were carried out by using the present model. The results obtained were very reasonable. For the two-dimensional elastic bodies in static contact, the results obtained by the present model were compared with those by commercial finite element software. There was a good agreement between the results by the two methods. After the further improvement on the present theoretical model and numerical method, they can be used to analyze the complicated phenomena of rolling contact.