Theory And Numerical Method Of Elastic Bodies In Rolling Contact With Curve Contact Area

The paper gives the state of art of the existing contact and rolling contact theories, and the review of the detailed derivation of rolling contact model with contact patch of curved area. It derives the2D model for static contact, contact with fixed slip and steady rolling contact, based on the existing the model for three-dimensional elastic bodies in rolling contact with curved contact patch. In the model the influence exerted by the boundary conditions and arbitrary geometry of the bodies in rolling contact is taken into account. Using finite element method (FEM) makes the discretization of the elastic bodies in contact and calculates the flexibility coefficients between outside unit forces and displacements of the bodies. The theoretical model is transformed into a nonlinear programming problem which is solved by Lagrange multipliers method. The present model considers the effect of the curvatures of the contact patch, and the real geometry sizes and boundary conditions of the bodies on rolling contact behavior. The results calculated with the present model are more close to the reality.The detailed numerical simulation regarding a few of two-dimensional elastic bodies in static contact and with rotation around a fixed axis is carried out by using the present model. For the two-dimensional elastic bodies in static contact, the results obtained by the present model are compared with those by commercial finite element software. There is a good agreement between the results by the two methods. From the results it found that, for much conformal contact of two bodies in static contact, the material of the body with positive curvature in the contact patch approaches to the contact patch center, around the two boundaries of the curved contact patch. The so called "positive curvature of a body" means that the curvature center is in the body. If the curvature center is out of the body, the curvature is called "negative curvature". For the contact with fixed slip the slip between the two bodies occurs from the leading and trailing boundaries of the contact patch, and approaches to the contact area center with the slip increasing. For the steady rolling contact, the slip between the two bodies occurs from the leading boundary of the contact patch, and approaches to the trailing boundary with the continue slip increasing. The obtained results are very reasonable.According to the above statements, the present model is beneficial for solving the rolling contact problems with conformal contact patches. It breaks the assumption based on an elastic half-space and the flat contact patch, which were adopted in the Kalker3D non-Hertz rolling contact theory.