Research On Electromagnetic Force Waves And Electromagnetic Vibration Of PMSMs

Electromagnetic vibrations(EMVs)caused by electromagnetic force waves(EMFWs)are a key factor to give rise to noise for permanent magnet synchronous machines(PMSMs).Conducting in-depth study of EMFWs and EMVs can help to disclose the inherent laws of a machine's vibration,and thus has theoretical significance and engineering value for reducing the noise of machines.So far,numerous studies have been done on the vibration and noise issue of PMSMs by the scholars.However,due to the complexity of EMFWs and EMVs,there are still many problems worthy of in-depth analysis.This thesis conducts a study on the radial and tangential EMFWs and the vibrations induced by them in PMSMs,and make an analysis of the influences of torque ripple suppression measures,pole-slot combinations and winding layouts on the vibration of a machine.The radial and tangential EMFWs of PMSMs are studied.For surface-mounted machines,starting from the theoretical modeling of radial and tangential air-gap magnetic flux density harmonics,the expressions of radial and tangential EMFWs are derived,the harmonic characteristics of EMFWs are analyzed,and the relationship between tangential EMFWs and cogging torque and torque ripple is also established.A general cycle-analysis method is proposed and used to analyze the harmonic characteristics of the air-gap magnetic field and EMFWs of more complicated surface-insert and interior machines.The influence of permanent-magnets(PMs)embedding on the air-gap magnetic field and EMFWs is analyzed with a theoretical method and the finite element method(FEM).The research results show that the harmonic contents of tangential EMFWs are the same as those of radial EMFWs regardless of the structure type of a machine.The spatial orders are both the integral multiple of the greatest common divisor of the number of poles and the number of slots,and the temporal orders of the low-to-intermediate frequency contents are both even.Cogging torque and torque ripple are only related to the zero spatial-order(ZSO)tangential EMFWs.With the influence of the salient-pole effect and some other factors,PMs embedding can introduce additional armature reaction harmonics,change the amplitude of air-gap flux density harmonics,and then increase the amplitude of most EMFWs.The mechanism of vibration generation caused by radial and tangential EMFWs in PMSMs is analyzed,and the contributions of these two EMFWs to the vibration are compared.Vibration responses of the fractional-slot concentrated winding(FSCW)machines are calculated with the FEM,and then the microscopic model of the stator deformation is extracted and used to reveal the mechanism of vibration generation caused by these two kinds of EMFWs.A linear superposition method based on vibration transfer functions is proposed.With this method,the contribution of radial and tangential EMFWs is quantitatively analyzed.The results are verified by simulation and experiments.The above analysis is then extended to the machines with other pole-slot combinations to prove the universality of the conclusions.The effect of the ZSO tangential EMFW,i.e.,torque ripple,is also analyzed,and its specific influences on the vibration of the machine system are clarified.The research results show that the vibrational deformation caused by the nonZSO(NZSO)tangential EMFWs is similar to that of the radial EMFWs by the lever-arm effect of the stator teeth,and the contribution of NZSO tangential EMFWs to the vibration is comparable to that of the radial EMFWs.Similar to the radial EMFWs,the contribution of NZSO tangential EMFWs also decreases with the increase of spatial order.Torque ripple can cause the machine and the support to vibrate laterally,and exert fluctuant moment on the base to vibrate the machine system.The influences of torque ripple suppression meausres on raidal and lateral vibrations of PMSMs are studied.The suppression measures of torque ripple can be classified into asymmetric and symmetric methods,and the effects of these two kinds of methods are theoretically analyzed,simulated and experimentally studied,respectively.The relationship between torque ripple and ZSO radial EMFWs is also analyzed by a theoretical method,and simulations are performed to verify the findings.For an interior integral-slot distributed winding(ISDW)machine with a wide speed range,a study is conducted of the effect of torque ripple suppression on ZSO radial EMFWs and the vibration and noise induced by them.The research results show that asymmetric methods are prone to introduce unbalanced magnetic force(UMFs).When the speed of a machine is high,the benefit of the torque ripple reduction is far from able to compensate the effect of the UMFs on the machine's vibration and noise.Meanwhile,symmetric methods can only ensure the reduction of the ZSO tangential EMFW with the lowest temporal order,and cannot ensure the reduction of other EMFWs.When the speed of a machine is low,the change of the radial acceleration level of the machine depends on the overall variation trend of the NZSO EMFWs,and the change of lateral vibration corresponds to the variation of the torque ripple spectrum and the specific mounting conditions.Both the torque ripple and ZSO radial EMFWs are related to the periodic variation of the magnetic field,and the air-gap magnetic flux density harmonics contributing to them are the same.For the ISDW machine,the tooth harmonics of air-gap flux density have the greatest contribution to torque ripple and ZSO radial EMFWs,and thus these two kinds of EMFWs and the relevant vibration and noise can be simultaneously suppressed by weakening the tooth harmonics.The effects of pole-slot combinations and winding layouts on the radial vibration of PMSMs are studied when the least NZSO of EMFWs stays unchanged.A theoretical method and the FEM are used to analyze the influential factors of the significant harmonic components in the radial vibration spectrum of machines.It is found that the tooth harmonics of the winding magnetomotive force(MMF)have a vital influence on the vibration of a machine,and superposition or cancellation effect exists between the vibrations respectively caused by the radial and tangential EMFWs,both of which are formed with the participation of the tooth harmonics.Based on this finding,the influences of poleslot combinations and winding layouts are further studied.The research results show that when the number of poles stays unchanged,the larger the number of slots is,the easier it is to excite the low-order circumferential modes and cause the machine to resonate for ISDW machines.But FSCW machines do not have this feature.When the number of slots keeps the same,the vibration of the machine whose number of poles equals the number of slots minus 2 is usually larger than that of the machine whose number of poles equals the number of slots plus 2.When the least NZSO of EMFWs keeps the same,the larger the number of poles is,the higher the vibration amplitude of a machine will generally be.The increase in phase and layer numbers cannot reduce the tooth harmonics of the winding MMF,hence there is generally no substantial improvement in the radial vibration for the machines.Exceptions exist merely in the scarce cases where a single winding layer changes into double layers.