Parametric life solution based on nonlinear vibration of a coupled planetary gear-bearing system

The fatigue life of bearings of a coupled planetary gear-bearing system based on Lundberg–Palmgren (LP) model is introduced in the current study. According to the nonlinear vibration of a coupled gear-bearing, eight nonlinear equations of motion of gears with dynamic mesh forces are derived using Lagrange theory. Finite difference method based on the fourth-order Runge–Kutta method was used to solve these equations in terms of time. A parametric solution was performed to show the effect of backlash, installation error, angular velocity and pressure angle on the life of bearings of sun and ring gears. The results show that the ring gear bearing is very sensitive to the changes of the mentioned parameters compared to the sun gear bearing. Furthermore, when the pressure angle is selected between 20° and 21°, the maximum and minimum service life for the ring and sun gears are observed, respectively. Moreover, it was observed that increasing backlash leads to drastic changes in bearing life ranging from 43% to 100% depending on the bearing position. In addition, it was observed that changes in installation error lead to changes in bearing life ranging from 21% to 54%.