Nonlinear Electromechanical Coupled Vibrations Of Switched Reluctance Motor

Switched reluctance motor(SRM)has been widely used in many fields such as textile,metallurgy and household appliances due to its simple structure,high-energy efficiency and low cost.Because of its unique double salient structure and magnetic saturation characteristics,the vibration problem of SRM is more prominent than other types of motor.When the stator windings of SRM are energized,the generated magnetic torque tends to pull the rotor to the minimum position of the reluctance,radial magnetic suction is also formed.Then the stator shell vibrates and produces noise under the action of radial electromagnetic force.Therefore,the research of radial vibration is of great significance for revealing the vibration mechanism of SRM and exploring the vibration reduction scheme.The present research focuses on the radial magnetic force of single tooth and the radial vibration of stator.However,there is strong coupling between radial magnetic force and vibration of stator and rotor during SRM running,the study of electromechanical coupling vibration of stator/rotor under radial magnetic force is seldom involved.Because analytical model of radial magnetic force during eccentric rotor running is still missing,it is very difficult to study the coupled vibration of stator and rotor.Therefore,analytical modeling of radial magnetic force and the stator/rotor coupling vibration response during the rotor running is focused in this paper,which provides a model and method for the vibration evaluation of SRM.In this paper,a 12/8 poles SRM is selected as the research object.Radial magnetic force of the single rotor tooth from unaligned position to aligned position is obtained through the technical parameters of the motor,based on the analytical methods such as equivalent magnetic circuit,Maxwell stress and series expansion.According to the function of air gap,winding currents and angle between stator and rotor teeth,the analytical models of radial magnetic resultant during eccentric rotor running are derived under ideal and overlap winding currents excitation,respectively.After consideration of the vibration displacement of stator and rotor,the model can be used to analyze coupling vibration of the stator and rotor.The finite element model of SRM body and control driving circuit during rotor rotation are built by electromagnetic software.The electromagnetic and force performance of SRM under static and transient state are simulated.By comparing the eccentric rotor index such as time history of radial magnetic resultant,resultant vector and amplitude spectrum,it is proved that analytical model reflects accurately the basic characteristics of radial magnetic resultant during rotor rotation.In consideration of rotor's vibration and neglect of stator's vibration,the transverse vibration model of eccentric rotor at constant speed is established.Modal analysis of the rotor bearing system at different rotational speed is carried out,and the critical whirl speed of the rotor is extracted from Campbell diagram.The transverse vibration response of the rotor under ideal currents or overlap current excition is studied,respectively.The solved results including time history waveform,resultant vector,displacement locus and amplitude spectrum show that the frequency distribution of magnetic resultant is closely related to rotational frequency,minimum common multiple of stator and rotor poles and current waveform.However,the frequency distribution of vibration displacement is also related to the first order critical whirl speed of the rotor.Magnetic resultant of the eccentric rotor could be modulated by vibration displacement,which makes resultant vector a blade shape or an overlap between the lobes.By analyzing the effect of rotating speed on the maximum vibration radius,the rotational speed of the rotor with transverse superharmonic resonance is determined.The displacement locus of the eccentric rotor at superharmonic speed is various.Several transverse superharmonic resonance bands exist due to the frequency sideband of magnetic resultant.Radial vibration of the stator shell is simulated by multiphysical field.The circumferential vibration modes of the stator shell are obtained by modal and harmonic response analysis.After radial magnetic force density is loaded to the stator teeth,the whole deformation,vibration displacement and acceleration of the key point on the stator are got under three phases and six phases mode,respectively.The stator vibration deformation depends on the spatial distribution of magnetic force density,and the frequency distribution of vibration acceleration is closely related to rotational frequency and rotor teeth numbers.When SRM runs by three phases,the fourth order square deformation is typical vibration mode of the stator shell.When SRM runs by six phases,the second order elliptical deformation is typical vibration mode.It is beneficial to reduce the amplitude of stator vibration by three phase's excition.Considering square and elliptical deformation modes of the stator and assumption of the rigid rotor,the strong nonlinear electromechanical coupling vibration model of the stator/rotor under magnetic forces in SRM is derived by using the Hamilton principle.The vibration response and frequency distribution of stator/rotor and radial magnetic force during SRM running are studied.Under different operating conditions,the coupling vibration response of stator/rotor and the radial magnetic force can be generated simultaneously.From the results of time history and amplitude spectrum,it is shown that the eccentricity of the rotor transforms the vibration of the stator to the coexistence of elliptical and square deformation.The corresponding superharmonic speed of the stator is determined by analyzing the effect of speed.When both stator and rotor are in superharmonic resonance,rotor vibration radius and stator vibration acceleration increase obviously.In conclusion,it has been studied that radial magnetic force and radial coupling vibration of stator/rotor in SRM through analytical modeling and numerical simulation.By magnetic force model,stator/rotor coupling vibration model and solution method introduced in this paper,radial magnetic force of eccentric rotor and the coupling vibration response of stator/rotor under any controlled windings currents can be solved quickly with the technical parameters of motor such as structure size,silicon steel and material properties.The analytical model and calculated results can be used to guide vibration evaluation and vibration reduction design of SRM.