Internal Contact of Cylindrical Geometries: A New Approach

Abstract

Most of the models available in the literature describing the contact between cylindrical geometries express the contact force as an implicit function of the indentation. As a result, a numerical iterative technique is required to evaluate the contact force at each integration time step, during the solution of the dynamics of a system, which represents a numerical difficulty when implementing it in a computational program [1]. An analytical model that explicitly defines the indentation as a function of the contact force is more efficient for implementation in a computational code for impact simulation of dynamical systems. A new analytical model for cylindrical contact that in which the force is an explicit function of the indentation, still providing a force-indentation curve similar to that of the Johnson model [2], is proposed and discussed here. The new force contact law expresses the contact force as a function of the indentation and of geometric and material parameters for the contacting cylinders. The new analytical force model parameter identification is based on a sensitivity analysis of the response of the model against the response of the Johnson model [2] for specific contact geometries of the cylinders and Young modulus and Poisson coefficients of the materials of these elements. A comparative study is established to evaluate the performance of the new model with respect to the model presented by Johnson. Considering moderate load values, the force-indentation results show that the new model has always differences lower than 10% from the Johnson model for all geometries and materials, i.e., for a wide range of cylinder diameters and metallic materials properties. Nevertheless, the new model inherits some of the foundations of the Johnson model, which in turn is based on the Hertz non linear contact theory. The Hertz elastic contact theory includes several assumptions that limit its application is restricted to non-conformal contact situations [2]. Therefore, the applicability of the Hertz theory to describe the contact of internal cylinders, in particular for very low clearances, is questionable, to say the least. To show the performance of the new proposed model for internal contact of cylinders with low clearance numerical and experimental studies are performed. The comparative evaluation of results of the experimental studies with those resulting from the analytical model proposed by Johnson and from the new model is presented. The experimental and numerical results using the new model, for cylindrical contact with similar clearance values, show differences smaller than 3%. The experimental results difference with respect to the Johnson model reaches values of 15%. Finally, it can be concluded that not only for a wide range of large clearance values but also for very small clearance/external radii ratios, both the Johnson model and the new model are perfectly suitable to describe the contact between cylindrical bodies.