Calculation of gear mesh stiffness and loaded tooth contact analysis based on ease-off surface topology

Abstract

Based on the theory of rack-gear common-tangential conjugate generating, the constructing of ease-off surface has been done by means of the topology modification of polynomial surface. By analyzing topological structure characteristics of ease-off surface, the meshing characteristics such as the contact area, the contact line, and transmission error are determined. By using the geometric analysis of ease-off surface and the potential energy method, the calculation methods of gear tooth stiffness and loaded transmission error are given, and a series of results for the tooth meshing stiffness, loaded transmission error, and load distribution map under varied loads are obtained. In order to solve the stress problem of tooth surface edge contact, the calculation method of quasi-Hertz contact is proposed by subdividing finite contact elements. Taking the second-order parabolic topological modification as an example, the time-varying history characteristics of tooth surface meshing are analyzed. The simulation results of the maximum contact stress and contact area are in good agreement with those calculated by MASTA software. Based on the integration of the geometric analysis of ease-off surface, the tooth stiffness calculation of potential energy method and the quasi-Hertz contact, it provides a convenient method for loaded tooth contact analysis.