Simulation and validation of the transmission error, meshing stiffness, and load sharing of planetary spur gear transmissions

• Model of transmission error and mesh stiffness for planetary gears is presented. • Influence of profile modification is considered. • Torque distribution among planets of sequentially phased planetary gears is obtained. • Influence of depth and length of modification is studied. • Length of modification for minimum amplitude of transmission error is obtained. Although the load sharing between planets of sequentially phased planetary gear transmissions has been studied in the past, the required solving techniques based on the Finite Element Method result in long time consuming and high computational cost. This limits the possibilities of undertaking extensive studies that take into consideration a high number of cases allowing optimal solutions to be sought or general conclusions drawn. In addition, the determination of the curves of transmission error, time-varying mesh stiffness, and load sharing among tooth pairs in simultaneous contact are also complicated. In this work an analytical model has been developed for the simulation of the time-varying mesh stiffness, quasi-static transmission error, and load sharing ratio between planets and tooth pairs of planetary spur gear transmissions. It is based on similar models for external and internal spur gears previously developed and has been validated by comparison with a hybrid model based on the Finite Element Method and theoretic-experimental correlation.