An Improved Nonlinear Dynamic Model of Gear Transmission

This paper develops a new nonlinear dynamic model of gear transmission on the basis of combining friction, gear mesh stiffness and backlash. In calculating friction force, the dynamic distribution of the load along the actual line of action is taken into consideration. A new period-enlargement method is proposed to set up a friction force model and a gear meshing stiffness model. The non-linear dynamic model is a non-autonomous system. Compared with the former models, the damping coefficient and stiff coefficient in this model developed by the period enlargement method is a periodic function with the same period. Thus it is easier to apply EM (energy method) or other methods for finding the approximate analytical solution of the gear transmission dynamic equations combining with time-varying damping and stiffness. Frequency response function of the nonlinear dynamic model is obtained by using harmonic balance method. Compared the analytic and numerical results of the improved nonlinear model with that of the nonlinear models in the published papers, it is shown that: (a) the former numerical simulation techniques may not work or may result in misleading answers; (b) the coexistence of several different periodic solutions and various impacts are the same with the results in formerly published papers when gear parameters are the same. Finally, the accurate solutions of all three regimes are combined to obtain the overall frequency response of the gear pair.