Nonlinear mesh stiffness model using slice coupling for straight bevel gear considering axial mesh force component and extended tooth contact

As one of the most important dynamic excitation sources of the gear system, time-varying mesh stiffness (TVMS) is a key parameter of the gear system dynamics model. To calculate the mesh stiffness of straight bevel gears, a semi-analytical model for calculating the single mesh stiffness (SMS) was proposed based on the infinitesimal method and energy equivalence theory, considering the real transition surface of the tooth root, elastic coupling effects between tooth segments, and nonlinear contact between tooth pairs. Based on the principle of deformation compatibility and force balance and considering the extended tooth contact, which is the phenomenon of the incoming tooth pair coming in contact ahead of the theoretical start of contact and the outgoing tooth pair coming out of contact later than the theoretical end of contact, a semi-analytical calculation model of TVMS was established. Based on the analytical model, the TVMS with different torques and gear parameters was compared with that obtained from the finite element method (FEM). The causes of errors were then analyzed to verify the validity of the semi-analytical method. The results show that the mesh stiffness calculated by the semi-analytical model is in good agreement with that calculated by the FEM, and the calculation efficiency is considerably higher than that of the FEM. Finally, the influence of the gear parameters on the mesh stiffness is analyzed. This study is expected to be helpful in further enriching and developing the calculation theory of gear stiffness and providing a theoretical tool for gear dynamics research.