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.
Nonlinear Dynamics of a Spur Gear Pair with Time-Varying Stiffness and Backlash