Velocity-dependent mesh stiffness calculation and dynamic analysis of a helical gear system

The evaluation of mesh stiffness for helical gear pairs is traditionally confined to statics. Additionally, the influence of driving speed fluctuations on gear meshing impact state has not been thoroughly studied. Based on this, an original computational algorithm (OCA), which integrates the analytical-FEM framework with the slicing principle, is proposed to calculate the velocity-dependent mesh stiffness (VMS) of helical gear pairs by considering driving speed effects, and whose validity is thoroughly validated through comparisons with several literature studies and ANSYS commercial simulations. Meanwhile, a 7-degree-of-freedom (DOF) dynamic model considering driving speed fluctuation is developed to analyze its influences on multi-stage of meshing impact, and its rationality is verified through experimental comparisons. Numerical results demonstrate the effect of driving speed, helix angles and normal modules on VMS and their influence on the dynamic behavior of the gear system, along with the mechanism by which driving speed fluctuations affect the meshing impact state. The results analysis indicates that VMS fluctuates with driving speed, stabilizes with increased helix angle, and exhibits an opposite trend with normal modulus. Moreover, VMS leads to more complex dynamic behavior than static mesh stiffness (SMS). In addition, the meshing impact state becomes more sensitive as speed fluctuation amplitude increases, with higher speeds amplifying this sensitivity. This findings provides a theoretical foundation for further analyzing the influence of driving speed on helical gear dynamics.