On Statistical Analysis of Gear Dynamic Loads

Statistical analysis of the gear dynamic load is carried out using piecewise constant mesh stiffness approximation. The dynamics of the spur gear system is modeled as a nonlinear, nonstationary process, and the gear transmission error which acts as a random input to the gear system is generated by passing a Gaussian white noise process through a time invariant shaping filter. The equivalent discrete time state equation and the mean and covariance propagation equations are then written for the augmented system. Then starting from known initial conditions these propagation equations are used to compute the statistics of the steady state response and hence those of the dynamic load. A procedure is presented for the selection of proper initial conditions so as to reach the steady state condition faster, thereby reducing the computational time required. The variations in the statistics of the dynamic load with respect to changes in contact position, random error magnitude, and operating speed are also investigated with the help of a numerical example. The results show that the approach presented in this study provides truer results than the statistical linearization approach used by Tobe et al. [13]. Moreover, the proposed procedure has the advantage that it can be applied to higher-order systems with complex mesh stiffness and torque fluctuations and to systems with symmetrical or nonsymmetrical nonlinearities.