Statistical Linearization of Nonlinear Stiffness Matrix of Planetary Gear Train

Stochastic dynamic analysis of the planetary gear train is complicated and it becomes more challenging when the nonlinear term is considered in the equation. A backlash between gears’ teeth is one of the nonlinearity sources in the gearbox which changes the equation of random vibration to nonlinear. In this paper, the linearization of the random vibration of multi-degrees of freedom (MDOF) with nonlinear stiffness is examined for planetary gear trains. The method used to treat nonlinearity is the statistical linearization method (SL). At first, to achieve adequate accuracy, the time domain is divided into very small time intervals then SL is utilized in each time step. For each time step an equivalent linear stiffness matrix is calculated and replacs the nonlinear stiffness matrix. The comparison between equivalent stiffness and linear stiffness at each step has shown a good agreement.