A new effective mesh stiffness calculation method with accurate contact deformation model for spur and helical gear pairs

Abstract

This paper proposes a new effective mesh stiffness calculation method for spur and helical gear pairs, which is explicitly formulated by an original FE-analytical slice model for tooth local contact deformation, efficient FE model for gear global deformation and mathematical programming approach for gear contact. The original FE-analytical slice model comprehensively integrates the advantages of FE method, Hertz contact theory and slice approach, which can address the displacement datum and elastic interaction of tooth slices effectively, so that tooth contact deformation is determined accurately. The geometry modeling of tooth slices is established and the pressure configuration in the contact region of each slice is prescribed by Hertz distribution. A specified FE programming is developed to derive the tooth contact flexibility matrix accurately. Thus, the mesh stiffness can be effectively calculated by using the proposed method with the FE-analytical slice model. The local contact deformation of gear tooth and mesh stiffness of gear pairs under ideal and error conditions are simulated. The accuracy and efficiency of the proposed method are validated against the ANSYS benchmark and common existing methods.