Nonlinear parametric vibration and stability analysis of worm drive system with time-varying meshing stiffness and backlash

The worm drive system with time-varying meshing stiffness may produce parametric resonance, resulting in structural damage. However, few studies focus on the parametric vibration of the drive system. Under certain working conditions, parametric excitation from time-varying meshing stiffness could cause instability and severe vibration. Therefore, determining the working conditions that cause parameter instability is the key to the design of the drive system. A parametric vibration model of the drive system with time-varying meshing stiffness and backlash is developed to simulate actual working conditions. The instantaneous contact line between meshing teeth is obtained based on the geometric coordinate relationship. With the help of the tooth slice model, the static meshing stiffness is derived, which changes with the rotation angle of the worm shaft. The time-varying meshing stiffness model is established by Fourier series expansion. The influence of backlash on the system is integrated into the dynamic driving error, and the analytical function is obtained by polynomial fitting. The proposed meshing stiffness model was verified by static loading experiments, and experimental errors from different sources, such as base deflection and shaft key deformation, were explored. A dynamic response test rig with shaker excitation was developed to verify the proposed vibration model. The Floquet multiplier is applied to judge the stability. The dynamic snap-through phenomenon in the meshing drive and the influence of the damping ratio on the stability boundary are studied. The results show that it is valuable to use dynamic analysis to find measures to avoid parametric resonance.