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The homotopy analysis for the nonlinear dynamics of a multi-mesh gear train |
XUN Chao,WU Haixuan,WANG Yunlong |
School of Mechanical Engineering, Nanjing Institute of Technology, Nanjing 211167, China |
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Abstract The nonlinearity in the multi-mesh gear train due to the periodically time-varying mesh stiffness, contact loss, and the couplings between the multi-mesh stiffnesses are considered. The nonlinear oscillation is investigated by the homotopy analysis method (HAM). And closed-form approximations for the primary resonance, sub-harmonic resonance, and super-harmonic resonance are obtained. In contrast to the method of multi-scale (MMS), the HAM is independent of the contact loss ratio. Results indicate that with large contact loss ratios over 30%, the amplitude-frequency curves obtained by HAM agree better with the numerical integration (NI) results than those obtained by the MMS. This study lays a higher accurate foundation for more complex nonlinear dynamic analysis of gear sets.
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Received: 26 July 2023
Published: 28 April 2024
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