# Analysis of the dynamic response of three ring reducer

With the development of the research on three ring reducer, people begin to study its elastic dynamics. Without considering the influence of torque, inertia force of eccentric sleeve and the part outside the support at both ends of the input shaft, the input shaft is approximately regarded as a beam with constant cross-section. The vibration mechanical models of the input shaft in X and Y directions are obtained, and the natural frequency of the input shaft is calculated. It is pointed out that in the excitation force, the unbalanced inertia force is only a part of the excitation force; the excitation force is composed of a number of components with different frequencies, and the frequency of the excitation component is in multiple relationship with the input shaft angle frequency; the vibration can only be reduced and can not be eliminated; even if measures are taken to eliminate the inertia force, but can not solve the alternating problem of the engagement force, therefore, only a part of the vibration of the reducer can be reduced.

According to the shown offset three ring reducer, by analyzing its elastic deformation, the coordination condition of the elastic deformation of the three ring reducer is derived by using the vector closed equation method. By dividing the whole transmission system into input shaft subsystem, support shaft subsystem, output shaft subsystem and internal toothed plate subsystem, the motion differential equations of each subsystem are established, and each subsystem is assembled, Thus, the dynamic equation of the whole transmission system is derived. Then, the closed solution is used to solve the dynamic equation, and the natural frequency of the three ring reducer is calculated

The dynamic response of the three ring reducer, such as the acceleration response of the internal gear plate, the dynamic load of the gear, the dynamic load of the planetary bearing and the dynamic load of the box bearing, is analyzed, and the influence of the main design parameters on the dynamic response of the system is analyzed. So far, the dynamic model of the three ring reducer has been well established in this paper, but when the dynamic model is established, the internal gear plate is regarded as a rigid body, the change of the comprehensive stiffness in the gear engagement is ignored, and the gear engagement stiffness is regarded as a constant. Due to the large area of the internal gear plate, the influence of its deformation on the modeling of the three ring reducer needs further discussion. 