An analytical determining the internal ring gear rim stiffness for practical purpose

Internal ring gears have a wide application in planetary gearboxes and transmission systems. The mesh stiffness of planetary gearboxes is an essential parameter for dynamic and vibration analysis. No direct practical method for calculating the stiffness of the internal ring gear rim has been investigated yet to the authors' knowledge. For the first time in this research, a practical method is presented to determine the stiffness of the internal ring gear rim with an appropriate accuracy based on strain energy. To accomplish this goal, every part of the internal ring gear rim, which is between two consecutive pins or bolts, is modeled as a curved beam. The deflection of the curved beam is determined according to Castigliano's theorem. Then, the stiffness of the internal ring gear rim is obtained through this deflection. Fourier's series of deflections are calculated to make analytical results more comfortable to use. Finally, the analytical results are validated by FEM using ABAQUS software.