Investigation On Dynamic Characteristics Of Ring Structures

Ring structures are abundant in practice,such as rotating motors,micro-gyroscopes,ring gears,and bearings.In general,these structures can induce parametric vibration by the discrete/distributed or contact/non-contact traveling loads.This thesis examines the dynamic behaviors and presents the relationship between the key parameters and instabilities.The study provides a theoretical basis for parameters' selection.The main contents and conclusions are:(1)A magnetomechanical coupling dynamic model of a ring stator in the permanent magnet motor is developed by using the thin-ring assumption and energy method.The influences of the parameters,including pole-pair count,slot count,and the harmonic orders of rotating magnetic motive force and air-gap permeance,on the parametric vibration are indentified.Multi-scale method is employed to examine the relationship between the magnetomechanical parameters and instabilities.Based on these,this thesis also investigates the effect of parameters,including pole-arc ratio,slot pitch,slot width,air-gap average length and magnet thickness,on the unstable regions.(2)Based on the equivalence of the discrete and distributed loads,a dual-ring dynamic model is built up with the thin-ring assumption and energy method.This model can be used to indentify the dynamic characteristics of the dual-stationary-ring structure or moving-stationary-dual-ring structures through varying the rotating speeds of the inner ring and discrete supports.Moreover,the analytical model lays a foundation for the clarification of the relationship between structure parameters and vibration characteristics.(3)Based on the dual-stationary-ring model,this thesis examines the effects of the wavenumber and discrete support count on the parametric vibration.The numerical results show that some unstable boundaries are independent of the radial discrete supports,which is proved by the multi-scale method.According to the numerical results and structure parameters,the crossover points on the transition curves are predicted.In addition,the vibration patterns at those points are addressed.(4)Multi-scale method is also used to determine the possibility of the resonance manners and the corresponding unstable boundaries of the moving-stationary-dual-ring structure.The analytical results imply that there can be principal and additive combination resonances,but not difference combination resonance.The inner ring natural frequencies can split with the inner ring rotating.The splitting has effect on both the additive combination resonance and inner ring principal resonance,but has no effect on the outer ring principal resonance.The investigation on the speed ratio and stiffness ratio effects on the instabilities provides a reference during the parameters' selection.