Development and verification of a computationally efficient stochastically linearized planetary gear train model with ring elasticity

Abstract This paper develops a hybrid dynamic model for the analysis of nonlinear stochastic vibration of a wind turbine’s planetary gear train (PGT) with an elastic ring gear. The elastic deformation of ring gear is considered and incorporated into the model through the finite element model. Moving loads are used to incorporate the meshing loads between the planet-ring gear pairs. In addition, the model includes both the stiffness variation and the backlash nonlinearity between meshing gears. The backlash is linearized using the statistical linearization technique, and a linear set of equations is obtained based on which simulation is carried out with PGT parameters in wind turbines. A parametric study is conducted, and the results demonstrate that the statistical linearization method is accurate enough to study the nonlinear stochastic PGT. The results reveal that the moving mesh has a strong effect on PGT when the ring gear elasticity is considered. The influence of rim thickness on PGT dynamics was analyzed, and the results show that the effect is significant. Monte Carlo simulations are used to verify the accuracy of the proposed method.