Analytical Algorithm for Time Varying Mesh Stiffness of Gear Pairs Considering Impact and Loading

Due to the inability of the current theory to accurately calculate the changes in the stiffness of the gear during loading and impact，the Hertz nonlinear contact theory is employed to construct an analytical model of length-limited line contact elasticity theory. The normal contact stiffness of the gear under different loads is obtained from the changes in the three-dimensional contact spot size and the principal curvature radius in the meshing process. Later，using the Weber energy method，a time-varying meshing stiffness correction algorithm considering the load condition is proposed to clarify the mapping relationship between load deformation and stiffness hardening. At the same time，the mathematical model of off-line meshing impact is established，and the change law of the meshing stiffness caused by the meshing impact is investigated according to the dynamic contact relationship of the gear pair at the impact time. The research findings demonstrate that the contact stiffness curve is consistent with the change law of the principal curvature radius. When the meshing impact is considered，the meshing stiffness of the gear pair changes abruptly from the large to the small. As the load increases，the contact and comprehensive meshing stiffness increase non-linearly，the single tooth meshing region gradually decreases，and the impact on the stiffness is more markedly. © 2024 Hunan University. All rights reserved.