The Magnetic Field And Flexspline Vibration Research Of Electormagnetic Harmonic Movable Teeth Trnsmission System

This paper is aimed to analyze the dynamic properties of a new type of reducer, which named electromechanical integrated electromagnetic harmonic movable teeth transmission system. This new system is the combination of traditional electromagnetic harmonic transmission system and movable teeth transmission system. It is the crystallization of elastics, mechanical kinematics, electromagnetics and other subjects. Comparing to traditional transmission system, this new one has an advantage of simple construction, small volume, small rotary inertia and high transmission ratio. It’s especially suitable for those high torques in addition low speed required situation.This paper starts with analyzing and optimizing about the air-gap magnetic field. Applying the finite element theory, the 2D finite element model was made, the air-gap magnetic field distribution map and the radial magnetic force distribution map of the flexspline was mapped, then the built model was improved through adding another magnetic conductor inside the air section of the flexspline, after the improvement, the distribution of the air-gap magnetic field and the radial force of the flexspline are much more matchable with the mathematical theory, parameter comparation illustrates that the improved model is more feasible, the feasibility was demonstrated by magnetic field and structure field coupling analysis.Based on the thin shell method, the flexspline is seemed as thin cylindrical shell, two kinds of kinetic equations of the flexspline are built. The first kind is satisfying the boundary conditions but without considering the effects of electromagnetic elasticity; the second one is considering both of them. In the first kind equations, the displacement depicted kinetic equations are achieved by using geometric equations, internal force equations, balance equations and constitutive equations. Then applying the Rayleigh-Ritz technique and the beam function method to solve the first kind kinetic equations, the varying patterns about the natural frequencies of the flexspline was analyzed, the response map and their laws were summarized.When solving the second type of kinetic equations, the whole issue includes the linearization about the induced magnetic field, the distribution laws about the electric field and the magnetic field and their connections, after all the kinetic equations of the flexspline among the transverse magnetic field were derived. This kind of vibration equations were solved using the beam function and multiple scale method. The vibration response map was depicted and the laws were summarized. These two types of kinetic response indicates that their response is almost same as the free vibration, while the second one’s frequency and amplitude is higher; but the forced vibration is absolutely different, the latter one has the obvious non-linear characters.