A study of the contact stress analysis of cylindrical gears using the hybrid finite element method

Abstract

In this study, the hybrid finite element method combined with the tooth contact analysis was applied to solve the static contact stress problem of meshing a cylindrical gear set. The hybrid finite element method has two special features. First, the dimension of the stiffness matrix was reduced to a small condensed compliance matrix with degrees of freedom in the possible contact region. The contact force was iteratively solved based on the condensed compliance matrix by the normal gap distance at the contact point. Second, the contact force at the meshing positions was solved using the same condensed compliance matrix with a different normal gap distance calculated by the tooth contact analysis. Using the examples in this study, the contact stress of the meshing gears was calculated and compared to the data obtained by ANSYS in order to validate the proposed hybrid finite element method. The hybrid finite element method with tooth contact analysis proposed in this study can be used to determine the amount of tooth surface modification.