Normal Force-Displacement Relationship of Spherical Joints With Clearances

Abstract

The spherical joint with clearances can be modeled as an axi-symmetric quasi-static contact of a sphere in a cavity. The Hertz theory based on the assumption of nonconformal contact is often used to represent the normal force-displacement relationship for the spherical joint with clearances. This assumption limits the application of the theory, especially in the case of occurring large deformation in contact area. The Steuermann theory is effective to solve the conformal contact problem in some cases, but it is strictly dependent on the selecting index n of the polynomial, which is used to represent the contact profiles. In this paper, an approximate contact model of the spherical joints with clearances is developed that is based on using the distributed elastic forces to model the compliant of the surfaces in contact. The new formulation is simple and straightforward, and its validity has been tested by comparison to the finite element results.