Dynamic modeling and analysis of the internal gear transmission with tooth crack subjected to the heavy torque

This work addresses the free and nonlinear vibrations of the internal gear transmission. A rigid-elastic coupled model is established using Hamilton's principle and the nonlinear in-extensional assumption, where the cracked time-varying mesh stiffnesses regarding torque-dependent and geometric nonlinearity caused by the heavy torque on the elastic ring gear are considered. Based on the coupled model, the natural frequencies and vibration mode shapes are given, and the distinctive modal properties associated with the torque are investigated by comparing with a rigid model. The differences of the nonlinear behaviors between the two models are presented through bifurcation diagrams, the largest Lyapunov exponent (LLE) diagrams, phase diagrams, Poincare maps, time histories, and FFT spectra. The effects of parameters such as excitation frequency, torque, and crack depth on the dynamic responses are examined. The results show that the nonlinear behaviors are rich, and quasi-periodic motion replaces periodic-1 motion when the elasticity of the ring gear is considered. The dynamic responses indicate that the larger crack depth becomes, the more obvious the sidebands can be found in the frequency domain. As for lower excitation frequency, the main frequencies also include the mesh, elastic vibration, modulation, and natural frequencies.

Automated summary

This study investigates the free and nonlinear vibrations of the internal gear transmission and establishes a rigid-elastic coupled model. The research reveals that considering the elasticity of the ring gear leads to richer nonlinear behaviors, and the larger the crack depth, the more prominent the sidebands in the frequency domain.