%0 Journal Article
%T Dynamic analysis of nonlinear time
%A Mengjuan Xu
%A Pan Zhao
%A Yang Du
%A Yi Yang
%A Yiping Dai
%J Journal of Vibration and Control
%@ 1741-2986
%D 2019
%R 10.1177/1077546318814951
%X Due to the complex working environment, gear systems always suffer from multiple excitations in actual engineering. This paper concerns the frequency response characteristics of a nonlinear time-varying spur gear system subjected to multi-frequency excitation. Firstly, a single degree-of-freedom gear pair model is established with consideration of the gear backlash, time-varying mesh stiffness and multiple harmonic excitations. Then, using the multiple time scales method, a comprehensive theoretical study is conducted to analyze various resonant cases including primary, parametric and combination resonances. Besides, parametric studies are accomplished to reveal the effects of the multi-frequency excitation on gear dynamics and to provide some useful references for reducing the vibration level. With the help of the fifth-order Runge¨CKutta method, the numerical results are obtained to verify the validity of the analytical solutions and to emphasize the significances of the multi-frequency excitation. In addition, a comparison is performed between the numerical results and the published experimental results to validate the proposed gear model. Results show that the presence of the multi-frequency excitation will introduce the interaction between different harmonic excitations, which significantly affects the nonlinear vibration characteristics of a spur gear system. The proposed gear model with multi-frequency excitation could be more reliable and universal than that with single-frequency excitation. In addition, the results of parametric study could provide some suggestions to designers and researchers attempting to obtain desirable dynamic behaviors of a gear system subjected to multi-frequency excitation
%K Spur gear system
%K multi-frequency excitation
%K gear backlash
%K time-varying mesh stiffness
%K multiple time scales method
%U https://journals.sagepub.com/doi/full/10.1177/1077546318814951