The Modal Analysis,Equivalent And Analytical Calculation Of The Stator Of Permanent Magnet Synchronous Motor

In recent years,permanent magnet synchronous motors(PMSMs)have been widely used in industrial production,artificial intelligence,aerospace and other fields due to their obvious advantages such as simple structure,reliable operation and high efficiency.With the continuous improvement of motor drive technology and the performance of PM materials,people have higher and higher requirements for PMSMs.The use of low-noise,high-efficiency permanent magnet synchronous motors has become a trend,and vibration and noise issues have become important indicators for measuring the performance of permanent magnet motors.As an important part of the vibration and noise of PMSMs,the calculation and analysis of electromagnetic vibration and noise are becoming more and more important.Electromagnetic vibration and noise are closely related to the electromagnetic parameters of the motor and the mode of the stator.When the frequency of the excitation force wave in the motor is close to the natural vibration frequency of the stator,resonance occurs,causing strong electromagnetic vibration and noise.Accurate prediction and reasonable adjustment of the natural vibration frequency of the permanent magnet synchronous motor stator can effectively avoid the excitation force wave frequency close to or equal to the stator natural vibration frequency,and provide a theoretical basis for weakening the vibration and noise of the motor.This article has made a systematic study on the vibration mode of the stator of the built-in permanent magnet synchronous motor.The main work and results achieved are as follows:1.Radial modal analysis of PMSMs’ statorIn the existing research on the modal analysis of the stator core finite element,the lamination structure of the core is usually ignored,and it is regarded as an isotropic whole.Although this method can quickly obtain the finite element model and material parameters,but It is inconsistent with the actual structure of the stator core and the calculation error is large.In view of the shortcomings of the traditional stator core finite element model,the actual lamination structure of the core is fully considered.In this paper,the laminated silicon steel sheet is equivalent to an anisotropic overall structure.By changing the material parameters of the three-dimensional model,the finite element calculation results converged to the measured values,and then the equivalent material parameters of the stator core were determined.Considering the complex structure of the stator core teeth,this paper analyzes the influence of the material parameters and structure parameters of the stator core teeth on the modal,and obtains the influence law of yoke thickness,slot number,tooth width,tooth height and other parameters on the modal.For the modeling of stator windings,existing studies add the end windings to the windings in the slot in the form of additional mass,but this method will make the mode pattern missing the vibration of the end windings and the resulting modal frequency is too small.In view of the above shortcomings,the windings in the stator slots are equivalent to approximate cylinders with the same mass,and the end windings are equivalent to concentric rings with the same axial length and equal inner and outer diameters.The natural vibration frequency and mode are obtained by finite element The vibration mode,and analyze the influence of the material parameters and structural parameters of the winding on the natural vibration frequency.Based on the above-mentioned iron and winding modeling work,finite element modeling is performed on the motor stator casing,the casing and the iron core,the casing and the winding iron core,and the stator as a whole,and the vibration modes of each model are analyzed.Finally,modal experiments are carried out on the stator core,windings and casing,to verify the accuracy of the above modeling and finite element analysis.2.Simplification and equivalent of the stator of PMSMsThe stator structure of the motor is complex and the modeling takes a long time,so the stator structure needs to be equivalent and simplified.In this paper,the finite element analysis method is used to make the structure of the motor stator equivalent and simplified under the premise that the radial modal frequency is basically unchanged,Considering the influence of tooth crests and pear-shaped slots,the stator teeth are regularized to simplify the stator core.Then the stator core is equivalent to a ring structure and compared with the finite element results to verify the correctness of the equivalent model.Then take the stator core slot number Q,the ratio of slot depth H to slot width Bt,the ratio of slot width Bt to tooth width Bs,the ratio of outer diameter D0 to inner diameter D1 as independent variables,and the equivalent outer diameter D0 of the ring The ratio of D1 ’is used as the dependent variable,and 15 representative models are selected as the calculation objects.Through the method of data fitting,the equivalent calculation formula of the stator core is obtained.Then,considering the actual extension length of the end winding,seven equivalent models of the winding are given,and the accuracy of the equivalent model is verified by the finite element method.Finally,combined with the results of finite element analysis,the casing,the core and the casing as a whole,the winding core and the casing as a whole,the end cover and the stator are equivalent,which provides an equivalent model for the following analytical calculation and quickly builds the motor stator.3.Analytical calculation of stator radial modalIn the existing research,when using the electromechanical analog method to calculate the stator modal frequency,the stator teeth are usually added to the stator yoke in the form of additional mass.This calculation method ignores the stator tooth stiffness,resulting in a large error in the analytical calculation results.In order to take into account the influence of the stator core teeth on the modal,this paper equivalently separates the stator teeth into concentric rings of equal mass.When calculating the modal frequency of the stator core,the stator teeth and the yoke form a double ring analytical model;when calculating the stator core with windings,it is equivalent to an analytical model with elastic coupling between the double rings;When the core and casing are integrated,the model is equivalent to a three-ring analytical model.According to the analytical model and the principle of electromechanical analogy,the modal expression and modal frequency can be obtained.The modal frequency calculated by this method is more accurate than the traditional method,which provides a theoretical basis for quickly estimating the low-order modal frequency of the stator.4.Analysis of the axial modal of the motor statorFor the modal analysis of the stator,most of them focus on the study of radial modal,and the axial modal analysis is less.During the operation of the motor,the axial vibration cannot be ignored.In this paper,the radial and tangential constraints are imposed on the two core models with or without windings.The axial modal frequency and vibration mode of the stator core are obtained by the finite element method.The slot width,tooth width,axial length,and yoke thickness are analyzed.,The number of slots,tooth height and other structural parameters on the axial modal,and use the modal experiment method to verify the correctness of the finite element analysis,which provides the basis of the finite element and experiment for the subsequent analytical calculation of the axial modal.It laid the foundation for a comprehensive analysis of the vibration of the motor stator.