Purpose

The vibration characteristics of gear transmission systems with a fault can be influenced by nonlinear factors. To obtain accurate fault vibration signals and analyze vibration characteristics, a nonlinear dynamic model of a fault gear transmission system considering these factors is required.

Methods

A nonlinear dynamics model of a spur gear transmission system with a root crack is proposed, and the time-varying friction and dynamic backlash are considered in the model. First, the time-varying meshing stiffness (TVMS) is calculated by the potential energy method, and the effect of time-varying friction is fully considered. The dynamic backlash is obtained by the fractal theory. Then, the tooth surface roughness is seen as a link between friction and backlash, and they are calculated at the different tooth surface roughness. The vibration differential equations of the model can be deduced by the Lagrange equation. Finally, the equations are solved by the Runge–Kutta method to investigate the vibration characteristics.

Results

The theoretical simulation results show that the change in tooth surface roughness can directly affect the friction coefficient and backlash of the tooth. Time-varying friction excites sidebands near the meshing frequency. The system adds new frequency components due to dynamic backlash, and these frequencies are only related to the microscopic changes in the tooth surface. Moreover, an early crack (1 mm) is not apparent in the time-domain waveforms, but amplitudes can surge in the high-frequency region in the time-frequency domain. The extent of fluctuation in the high-frequency region can be used to diagnose the damage degree of the crack. The same phenomenon is also obtained by experimental analysis.

Conclusions

The influence of tooth surface roughness on the gear system is revealed by the model proposed in this paper. Precise fault characteristics of cracked gears are obtained. The experimental and simulation results can provide some references for the diagnosis of the crack defect extent.