Optimization of bias modification and dynamic behavior analysis of helical gear system

A generalized finite element dynamic model of helical gear system considering time-varying mesh stiffness and loaded composite mesh error is developed. Bias modification is introduced into this model, and the corresponding time-varying mesh stiffness and loaded composite mesh error are determined based on improved loaded tooth contact analysis model. By introducing vibration exciting force, the time-variant differential equations of the system are transformed into time-invariant differential equations which can be solved faster by Fourier series method. Meanwhile, the internal excitation of the system can be captured clearly. Aiming to reduce vibration of the system, optimization method of bias modification is proposed with the objective of minimizing fluctuation of the vibration exciting force. The global optimal modification parameters are obtained using brute force optimization method. The sensitivity of dynamic response of the modified helical gear system to gear misalignment is then investigated. Simulation results suggest that bias modification has little effect on time-varying mesh stiffness but reduces system vibration significantly. Increasing gear misalignment will decrease time-varying mesh stiffness and increase the system vibration. Bias modification shows a well robustness in reducing vibration of helical gear system when gear misalignment is not too large.