Dynamic statistical responses of gear drive based on improved stochastic iteration method

Mechanical equipment is always influenced by environmental factors or random excitations, such as random collision, rock fall, sea wave and wind force. It is significant to analyze the statistical information of the system performance for the operation security and kinematic accuracy. Considering time-varying stiffness and nonlinearity, a stochastic iteration method is proposed for dynamic responses in the gear drive subjected to deterministic and stochastic excitations. Also, the convergence analysis is investigated. Considering the parametric correlation, the improved iterative schemes are analyzed for the mathematical expectation and standard deviation of any multi-stage gear drive with the backlash and mesh stiffness, respectively. Also, covariance and correlation coefficient are investigated to represent the dynamic relationship between each gear pair. The crude Monte Carlo simulation is performed to provide benchmark results, and the data of simulation have good coincidence with the iteration results. It is shown that auxiliary hole of gear drive can reduce the fluctuation of stochastic response in operation. The reasonable modification gear can decrease the dispersion of system response at the transient and stable stage.