Nonlinear Vibration Analysis of Rotor considering Cogging and Harmonic Effects

Shanle Li,Haijun Song,Hongyan Wang,Kuilong Yu,Feng Liu,Chengzhi Shi

doi:10.1155/2021/6685588

Abstract

This paper aims to investigate nonlinear vibration characteristics of rotor system considering cogging and harmonic effects. Firstly, relative permeance with eccentric was established and then corrected by correction factor caused by the cogging effect. Based on the new formula of relative permeance, the expression of unbalanced magnetic force was obtained, and the coefficient of cogging effect was defined. Motion equations of rotor system were established, and Runge–Kutta method was used to solve the equations. Results showed that errors between finite and analytical results were smaller considering cogging and harmonic effects. When the harmonics were taken into consideration, the vibration of rotor increases sharply. When the cogging and harmonics were taken into consideration simultaneously, the vibration of rotor decreased instead, which means that stator slots have the effect of reducing vibration in rotor system. Rotor vibration was axis symmetry with static eccentricity rather than central symmetry with no eccentricity, and double, four times, and six times supply frequency always existed in the components of main frequency with eccentric.

Highlights

Introduction e existence of eccentric is rather common in electric machinery, and issues with unbalanced magnetic pull (UMP) caused by eccentric have been investigated for many years [1]
U 2n−1 where v is the harmonic order of the stator magnetomotive force, u is the harmonic order of the rotor magnetomotive force, and Fsv and Fru are the amplitude of the magnetomotive force of the stator windings and the permanent magnet
It shows that the analytical results with cogging and harmonic effects taken into consideration are in great consistency with the finite element analytical (FEA) results

Summary

Cogging effect considered Cogging effect ignored

Tooth, which is more like the actual relative permeance between the stator and rotor. E relative permeance with stator slots can be obtained by introducing correction factor of stator slots It can be expressed as follows: Λ(α, t) λ(α, t)Λe(α, t),. U 2n−1 where v is the harmonic order of the stator magnetomotive force, u is the harmonic order of the rotor magnetomotive force, and Fsv and Fru are the amplitude of the magnetomotive force of the stator windings and the permanent magnet They can be expressed as follows: Fsv. Brhm μ0 sin􏼒u αp π 􏼓, where I1 is amplitude of the current of the stator windings, p is the number of pole-pair numbers, N1 is the number of the stator turns in series per phase, kdp v is the winding factor for the v − th harmonic, Br is the magnet remanence, hm is the magnet thickness, αp is the pole-arc/pole-pitch ratio, and μ0is the vacuum permeability. It shows that the airgap flux density is nonuniform due to cogging and harmonic effects.

With harmonic and cogging effects No harmonic and cogging effects

Static eccentricity

Amplitude of x

Conclusions