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International Journal of Rotating Machinery
Volume 2017, Article ID 1264904, 8 pages
Research Article

Dynamic Model of Spur Gear Pair with Modulation Internal Excitation

1School of Mechanical Engineering, Liaoning Institute of Science and Technology, Benxi, Liaoning, China
2School of Mechanical Engineering, Shenyang University of Technology, Shenyang, Liaoning, China

Correspondence should be addressed to Lei Zhang; moc.anis@9684lgnahz

Received 28 November 2016; Revised 27 February 2017; Accepted 15 March 2017; Published 18 April 2017

Academic Editor: Hyeong Joon Ahn

Copyright © 2017 Zhong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the actual measurements, vibration and noise spectrum of gear pair often exhibits sidebands around the gear mesh harmonic orders. In this study, a nonlinear time-varying dynamic model of spur gear pair was established to predict the modulation sidebands caused by the AM-FM modulation internal excitation. Here, backlash, modulation time-varying mesh stiffness, and modulation transmission error are considered. Then the undamped natural mode was studied. Numerical simulation was made to reveal the dynamic characteristic of a spur gear under modulation condition. The internal excitation was shown to exhibit obvious modulation sideband because of the modulation time-varying mesh stiffness and modulation transmission error. The Runge-Kutta method was used to solve the equations for analyzing the dynamic characteristics with the effect of modulation internal excitation. The result revealed that the response under modulation excitation exhibited obvious modulation sideband. The response under nonmodulation condition was also calculated for comparison. In addition, an experiment was done to verify the prediction of the modulation sidebands. The calculated result was consistent with the experimental result.