Dynamic Analysis of Gear Systems with Dynamic Mesh Stiffness and Time- Varying Bearing Stiffness

In this study, a novel analytical model for dynamic mesh stiffness of spur gears is developed using variable cross-section beam theory, explicitly accounting for driving speed effects. The dynamic mesh stiffness is determined by applying the modal superposition method to analytical model equations, and subsequently validated using both finite element method and potential energy method. A displacement-dependent time-varying bearing stiffness model is developed, along with a 6-DOF gear system nonlinear dynamic model that integrates dynamic mesh stiffness, tooth friction, and time-varying bearing stiffness. The influence of dynamic mesh stiffness and time-varying bearing stiffness on the dynamic characteristics of gear systems is investigated through numerical simulation. The results indicate that the dynamic mesh stiffness demonstrates more pronounced fluctuations compared to the static mesh stiffness as driving speed increases, resulting in larger vibration amplitudes. The introduction of dynamic meshing stiffness and time-varying bearing stiffness significantly influences the dynamic characteristics of gear systems, thereby enhancing the accuracy of the dynamic model. This research provides a theoretical foundation for improving the performance of gear transmission.