Abstract
This paper investigates the dynamics of a spur gear system with time-varying and square nonlinearities, by both analytical method and numerical simulation. First, the equations of motion of a 2 degree-of-freedom system are established and the harmonic balance method is used to analyze the stability and the steady-state response of the system under the main resonant condition. Then the perturbation method is used to analyze the parameter instability under the main, subharmonic and nonresonance conditions. Finally, the interactions between the main and subharmonic resonant amplitudes and the nonlinearity and the contact ratio are analyzed. The results reveal that the system response contains various frequency components, such as meshing frequency and its higher harmonic terms due to the nonlinearity and the time-varying stiffness. The existence of the time-varying meshing stiffness can also result in the subharmonic resonance, and even chaos through period-doubling bifurcations as the input torque increases.
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