Dynamic modeling and analysis of planetary S-gear train system considering time-varying pressure angle

In view of the time-varying pressure angle characteristics of S-gears, a dynamic model of planetary S-gear train which is closer to the actual working condition is established in this paper. Firstly, the machining method of internal and external S-gears is introduced and the equation of tooth surface is calculated. Subsequently, the pressure angle variation law of S-gears is derived according to the line-of-action (LOA) equation, then introducing it into the planetary S-gear train to establish a dynamic model considering time-varying pressure angle. Finally, the dynamic response of the planetary S-gear train is obtained by using the Runge–Kutta method, and the influence of time-varying pressure angle excitation on the dynamic characteristics of the system is revealed by comparing the dynamic mesh force (DMF), gear mesh deformation, and vibration displacement of components. The results clearly indicate that the time-varying pressure angle has a significant impact on the dynamic response of the planetary gear train, which cannot be ignored. The research results provide a useful source of reference for the dynamic design and vibration control of non-involute planetary gear trains.