Develop and Verify Energy-Based Statistical Linearization Technique to Analysis Nonlinear Stochastic Vibration of a Spur Gear Pair

In this article, an energy-based statistical linearization method (SL) is proposed to simulate a nonlinear dynamic model of spur gear pair. The gear pair operates under combined deterministic and random loads, and both backlash and time-varying mesh stiffness are considered in the dynamic model. The equivalent linear function approximates the teeth backlash nonlinearity in the gear model. The energy-based linearization, which minimizes the error in potential energy between the original and equivalent linear systems, is used. Simulations are conducted on a gear pair, and the effect of the input torque on the dynamic response of the gear pair is then examined. The results demonstrate that for high input torque, the system operates in the linear range. For low input torque, the results are not similar to the original because the system became strongly nonlinear. Monte Carlo simulations were carried out to verify the accuracy of the presented method.