Abstract: A multistage gear transmission dynamic model was developed， where the nonlinearity factors such as timevarying stiffness， transmission error， and backlash were considered. This model took the relevant physical， geometrical and load parameters as random variables. When the random section of the variables was much smaller than the determining section， the kinetic equations were expanded to the first order at the mean value of the random parameter vector by Taylor series expansion theorem using the stochastic perturbation theory. Then the finishing equations were solved numerically， with the first fourthorder moment of the system response obtained based on the Kronecker product algebra and matrix differential theory. To assess the stability of the system， the first secondorder moment of the dynamic transmission error of a gear pair was solved and compared with the Monte Carlo method. At the same time，the dimensionless mean sensitivity of dynamic transmission error to the random parameters was analyzed. The results provide a basis for improving the system stability.

Key words: multistage gear, stochastic perturbation, Kronecker product, dynamic transmission error, sensitivity of parameter