Motor stator and winding equivalent material parameter identification method

Abstract

The invention discloses a motor stator and winding equivalent material parameter identification method, and belongs to the technical field of motor engineering, and the method comprises the steps: respectively obtaining the modal frequency and vibration mode of a stator core and a stator assembly through a modal test; establishing a stator core inherent frequency calculation theoretical model considering orthotropic material parameters; establishing a stator assembly inherent frequency calculation theoretical model considering orthotropic material parameters; identifying equivalent material parameters of the stator core; and identifying equivalent material parameters of the winding. According to the method, the relationship between the material parameters of the stator core and the stator assembly and the inherent frequency of the structure is disclosed based on the cylindrical shell theory, and the difference value between the test modal frequency and the theoretical calculation frequency is used as the optimization target by using the particle swarm optimization, so that the equivalent orthogonal anisotropic material parameters of the stator core and the winding can be conveniently and quickly identified; meanwhile, the inherent frequency of the stator core and the stator assembly under the free boundary condition can be rapidly calculated, and the method is worthy of being popularized and used.

Description

Technical Field

[0001] The invention belongs to the technical field of motor engineering, and in particular relates to a method for identifying equivalent material parameters of a motor stator and winding. Background Art

[0002] In recent years, electric motors have been widely used in automobiles. Since the NVH performance of the drive motor directly affects the comfort of electric vehicles, the vibration and noise of the motor have become a current research hotspot. If the radial electromagnetic force frequency is close to the natural frequency of the stator system, or the circumferential modal frequency of the motor is close to the frequency of the radial electromagnetic force wave of the corresponding order, resonance will occur. Therefore, it is very important to accurately identify the natural frequency of the motor.

[0003] Due to the axial lamination of silicon steel sheets, the radial stiffness of the stator core is significantly higher than the axial stiffness, while the motor winding is wound around the stator teeth with metal wires, and its radial stiffness is lower than the axial stiffness. The stator core and winding are not uniform rigid bodies, and have obvious orthogonal anisotropic characteristics, which poses an obstacle to the accurate modeling of the stator system. In order to solve the above problems, the stator core and winding are usually equivalent to homogeneous bodies during the modeling process, and the lamination effect is considered by assigning equivalent orthotropic material parameters to the solid structure. These material parameters usually include Young's modulus, shear modulus and Poisson's ratio. Therefore, obtaining accurate equivalent orthotropic material parameters is the basis for calculating the natural frequency of the motor. Most existing methods are based on finite element models, and the material parameters are continuously adjusted until the finite element simulation results are close to the experimental values, but it takes a lot of time to obtain equivalent material parameters. The analytical model can quickly obtain the complex nonlinear relationship between the orthotropic material parameters and the modal frequency. Therefore, there are some methods that calculate the orthotropic material parameters of the motor based on the analytical model. However, the analytical models currently established by this method are mostly based on the thin shell theory and a large number of simplifications are adopted. The motor as a whole is equivalent to a single-layer cylindrical shell, and it is difficult to obtain accurate stator core and winding equivalent material parameters at the same time. Summary of the invention

[0004] The purpose of the present invention is to provide a method for identifying motor stator and winding equivalent material parameters to solve the problems of existing motor stator core and winding equivalent material parameter acquisition methods being time-consuming and lacking in accuracy.

[0005] The present invention achieves the above-mentioned purpose through the following technical solutions:

[0006] The present invention proposes a method for identifying equivalent material parameters of a motor stator and winding, comprising:

[0007] S1. Obtain the modal vibration shape and corresponding modal natural frequency test results of the stator core and stator assembly through modal tests;

[0008] S2. Establish a theoretical model for calculating the natural frequency of the stator core, determine the nonlinear relationship between various anisotropic material parameters and the natural frequency of the stator core, and then calculate the natural frequency of the stator core;

[0009] S3. Establish a theoretical model for calculating the natural frequency of the stator assembly, determine the nonlinear relationship between the winding material parameters and the natural frequency of the stator assembly, and calculate the natural modal frequency of the stator assembly;

[0010] S4, substituting the natural frequency test result of the stator core and the natural frequency of the stator core into the fitness function of the particle swarm algorithm, and optimizing the elastic modulus, shear modulus and Poisson's ratio of the stator core by using the particle swarm algorithm until the set natural frequency error requirement is met, so as to identify the equivalent material parameters of the stator core;

[0011] S5. Substitute the natural frequency test results of the stator assembly and the natural modal frequency of the stator assembly into the fitness function of the particle swarm algorithm, and use the particle swarm algorithm to iteratively optimize the winding elastic modulus, shear modulus and Poisson's ratio until the set natural frequency error requirements are met, so as to identify the equivalent material parameters of the winding.

[0012] A further improvement is that the modal test in step S1 is specifically a hammering method, and the data processing of the modal test adopts LMS Testlab software.

[0013] A further improvement is that step S2 comprises:

[0014] S2.1. The stator core is equivalent to a stack of two isotropic materials, one of which is steel and the other is equivalent to a coating material. Parameters include E coat , μ coat and V coat , giving the material orthogonal anisotropy to consider the stacking effect, the anisotropic material parameters of the stator core are calculated by the following formula:

[0015]

[0016] E z =E θ =V steel E steel +V coat E coat (2)

[0017]

[0018] μ θx =V steel μ steel +V coat μ coat (5)

[0019] Where V steel and C coat Respectively represent the volume fraction of silicon steel and coating, μ xθ =μ θx E x / E θ ;

[0020] S2.2. The stator core can be equivalent to a cylindrical shell with longitudinal ribs. The dimensionless coordinate η is used in the axial direction, which is defined as η = x / L. The deformation of any point on the cylindrical shell at a distance z from the shell reference surface is expressed as:

[0021]

[0022] where u0, v0 and w0 are the axial, circumferential and radial displacements of the reference plane, respectively, and φ x and φ θ are the rotation angles in the x and θ directions respectively;

[0023] S2.3, the stress-strain relationship of cylindrical shell is expressed as:

[0024]

[0025] Where:

[0026] C 66 =G xθ ; C 55 =G xz ; C 44 =G θz ; where E x , E θ is the elastic modulus, G xθ , G xz and G θz is the shear modulus, μ xθ , μ θx is Poisson's ratio μ xθ E θ =μ θx E x ;

[0027] S2.4. According to the first-order shear deformation theory, the stress at any point on the cylindrical shell is:

[0028]

[0029] In the formula and Reference plane stress, κ x , κ θ and κ xθ is the surface curvature, and its expression is:

[0030]

[0031] S2.5. By integrating the stress and moment of the in-plane stress over the shell thickness, the results for force and moment are:

[0032]

[0033] Where N x 、N θ and N xθ is the resultant internal force, M x 、M θ and M xθ is the resultant force of bending moment and torque, Q x and Q θ is the resultant lateral shear force, κ is the shear correction factor, A ij , B ij and D ij are the tensile, coupling and bending stiffnesses, defined as:

[0034]

[0035] S2.6. Calculate the kinetic energy and potential energy of the cylindrical shell. The expressions are as follows:

[0036]

[0037] In the formula ρ is the stator core density.

[0038] S2.7. Calculate the potential energy and kinetic energy of the stator teeth and the axial stress ε of the longitudinal ribs x According to formula (8), ignoring the tangential deformation of the stator teeth, the potential energy and kinetic energy are expressed as follows:

[0039]

[0040] Where u r , v r and w r are the displacements of any point on the longitudinal rib, calculated according to formula (6), b s and d s are the longitudinal rib width and height, A r is the longitudinal rib area, N s is the number of longitudinal ribs, J is the torsion constant, which is defined as:

[0041]

[0042] S2.8. The displacement equation of the reference surface of a cylindrical shell with arbitrary boundary conditions is expressed as follows:

[0043]

[0044] Where n is the number of circumferential fluctuations, ω is the natural angular frequency U(η), V(η), W(η), Φ(η) and Ψ(η) are vibration mode functions, and Chebyshev polynomials are used as vibration mode functions, which are expressed as follows:

[0045]

[0046] Where M is the number of truncated Chebyshev polynomials a m , b m , c m , d m and e m is the corresponding weighting coefficient, T m (η) is the first kind of Chebyshev polynomial, and its recursive expression is as follows:

[0047] T0(η)=1,T1(η)=η,T m+1 (η)=2ηT m (η)-T m-1 (η), m≥2 (19)

[0048] η∈[0,1];

[0049] S2.9, use the Rayleigh-Ritz method to derive the stator motion equation, and substitute the displacement equation (17) into equations (12)-(15) to obtain the maximum potential energy and maximum kinetic energy The Lagrange equation L of the stator core is expressed as follows:

[0050]

[0051] The characteristic equation of the system can be obtained by solving the following equation:

[0052]

[0053] Where q m Respectively represent a m , b m , c m , d m and e m , the characteristic equation of the system is solved as:

[0054] (K-ω 2 M)q T =0 (22)

[0055] Where K and M are the stiffness matrix and mass matrix of the system respectively. The natural frequency of the stator core is obtained by solving the characteristic equation of the system.

[0056] A further improvement is that step S3 comprises:

[0057] S3.1. Assume that the winding in the stator slot is only composed of copper wire and insulating material stacked together, and then it is equivalent to a homogeneous body. The stacking effect is considered by giving the material orthogonal anisotropy. The equivalent winding material parameters of the winding are calculated as follows:

[0058] E x =V copper E copper +V insulation E insulation (twenty three)

[0059]

[0060] μ xθ =V copper μ copper +V insulation μ insulation (26)

[0061] Where V copper and V insulation Represent the volume fraction of copper and equivalent insulating material respectively. For winding material G θz Calculated by formula (4), μ θx =μ xθ E θ / E x ;

[0062] S3.2. The motor stator core and winding assembly are equivalent to a double-layer cylindrical shell structure, the outer layer represents the stator yoke, the inner layer represents the teeth and windings, and the distance h0 from the inner surface of the composite cylindrical shell to the neutral layer is calculated according to the following formula:

[0063]

[0064] Where E k is the tangential elastic modulus of the k-th cylindrical shell, N is the number of cylindrical shell layers, where N is 2, H0 = 0;

[0065] S3.3. According to the thin film model method of composite material theory, the elastic model and shear modulus along the parallel direction are calculated as follows:

[0066]

[0067] V i The volume fraction of stator teeth and windings is shown in the table. The elastic model and shear modulus along the series direction are calculated as follows:

[0068]

[0069] S3.4. The kinetic energy and potential energy of the equivalent double-layer composite cylindrical shell of the stator core and winding assembly are expressed as follows:

[0070]

[0071] Where L is the total length of the equivalent composite cylindrical shell;

[0072] The multilayer composite cylindrical shell I0, I1, I2, A ij , B ij , D ij Written in the following form:

[0073]

[0074] Where z k-1 and z k denote the coordinates of the bottom and top surfaces of the k-th cylindrical shell in the reference coordinate system, ρ k is the equivalent density of the kth layer;

[0075] S3.5 uses the Rayleigh-Ritz method to derive the stator motion equation, and writes the displacement equation of the multilayer cylindrical shell reference plane into the form of equation (17). Substituting the displacement equation into (32), (33) obtains the maximum potential energy and maximum kinetic energy The Lagrange equation L of the stator assembly is expressed as follows:

[0076]

[0077] Substituting equation (36) into equation (21) yields the characteristic equation of the stator core and winding assembly system. The natural modal frequency of the stator assembly is obtained by solving the characteristic equation.

[0078] A further improvement is that step S4 comprises:

[0079] S4.1. Calculate fitness, fitness function f err The definition is as follows:

[0080]

[0081] Where f acm，i and f test，i They represent the modal frequencies of the i-th order motor stator core obtained by analytical calculation and modal test respectively;

[0082] S4.2. Add constraints:

[0083]

[0084] S4.3. By evaluating the fitness function, the elastic modulus E of the equivalent coating is identified by the PSO algorithm.coat , Poisson's ratio μ coat and its volume fraction V coat , and then calculate the equivalent material parameters of the stator core according to equations (1)-(5).

[0085] A further improvement is that the step S5 comprises: based on the fitness function f err Calculate the fitness and add the constraints, and identify the elastic modulus E of the equivalent insulation through the PSO algorithm. insulation , Poisson's ratio μ insulation and its volume fraction V insulation , and then calculate the equivalent material parameters of the winding through equations (23)-(26).

[0086] The beneficial effects of the present invention are:

[0087] The stator core and winding equivalent material parameter identification method proposed in the present invention is based on a theoretical model and a particle swarm optimization algorithm. It can not only quickly, conveniently and accurately identify the equivalent material parameters, but also quickly and accurately calculate the natural frequencies of the stator core and stator assembly under free boundary conditions, providing a theoretical basis for modal frequency calculation, which is of great significance to the optimization design of motor vibration and noise reduction. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 It is a flow chart of the equivalent material parameter identification method in the present invention;

[0089] Figure 2 It is a structural schematic diagram of a motor in an example of the present invention;

[0090] Figure 3 The figure is a modal test diagram of the stator core and the stator assembly in the example of the present invention;

[0091] Figure 4 It is the equivalent schematic diagram of stator core material;

[0092] Figure 5 Schematic diagram of the stator core equivalent model in the method of the present invention;

[0093] Figure 6 It is the equivalent schematic diagram of winding materials;

[0094] Figure 7 Schematic diagram of a double-layer cylindrical shell equivalent to the stator assembly in the method of the present invention.

[0095] Figure 8 This is the principle diagram of the particle swarm algorithm. DETAILED DESCRIPTION

[0096] The following description provides specific application scenarios and requirements of this specification, with the purpose of enabling those skilled in the art to make and use the contents of this specification. Various local modifications to the disclosed embodiments will be apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of this specification. Therefore, this specification is not limited to the embodiments shown, but to the widest scope consistent with the claims.

[0097] The terms used herein are only used for the purpose of describing specific example embodiments and are not restrictive. For example, unless the context clearly indicates otherwise, as used herein, the singular forms "a", "an" and "the" may also include plural forms. When used in this specification, the terms "include", "comprise" and / or "contain" mean that the associated integers, steps, operations, elements and / or components exist, but do not exclude the existence of one or more other features, integers, steps, operations, elements, components and / or groups or that other features, integers, steps, operations, elements, components and / or groups may be added in the system / method.

[0098] In view of the following description, these and other features of the present specification, as well as the operation and function of the related elements of the structure, and the economy of the combination and manufacture of the parts can be significantly improved. Reference is made to the accompanying drawings, all of which form a part of this specification. However, it should be clearly understood that the drawings are for illustration and description purposes only and are not intended to limit the scope of this specification. It should also be understood that the drawings are not drawn to scale.

[0099] The flowcharts used in this specification illustrate the operations implemented by the system according to some embodiments in this specification. It should be clearly understood that the operations of the flowcharts may not be implemented in sequence. On the contrary, the operations may be implemented in reverse order or simultaneously. In addition, one or more other operations may be added to the flowchart. One or more operations may be removed from the flowchart.

[0100] Example 1

[0101] like Figure 1 As shown, this embodiment proposes a method for identifying equivalent material parameters of a motor stator and winding. Figure 2 This is a schematic diagram of a motor used in an embodiment of the present invention. The main structural dimensions of the motor are shown in Table 1:

[0102] Table 1 Main structural dimensions of motor stator

[0103]

[0104]

[0105] The identification method includes the following steps:

[0106] S1. Obtain the modal vibration shapes and corresponding modal natural frequency test results of the stator core and stator assembly respectively through modal tests;

[0107] More specifically, step S1 includes the following:

[0108] S1.1、Modal test Figure 3 As shown in the figure, use a marker pen to mark and number the force hammer excitation points on the stator surface, as well as the acceleration sensor position mark. The motor stator core and stator assembly are suspended with elastic ropes to simulate free boundary conditions. The acceleration sensor is attached to the middle right position of the stator outer surface. The force hammer is moved to excite the test points on the stator surface, and the test data is collected through LMS SCADAS.

[0109] S1.2. The data is post-processed by LMS Testlab software to obtain the modal vibration shapes and corresponding modal frequencies of the stator core and stator assembly, and finally the 2nd to 4th order modal vibration shapes and modal frequencies of the stator core and stator assembly are obtained as shown in Table 2 and Table 3:

[0110] Table 2 Test stator core modes

[0111]

[0112] Table 3 Test stator assembly modes

[0113]

[0114]

[0115] S2. Establish a theoretical model for calculating the natural frequency of the stator core considering the orthogonal anisotropic material parameters. After determining the nonlinear relationship between the anisotropic material parameters and the natural frequency of the stator core, calculate the natural frequency of the stator core:

[0116] More specifically, step S2 includes the following:

[0117] S2.1. Stator core material equivalence. The density of the stator core can be obtained by actually measuring the mass of the stator core, and by establishing its geometric model to calculate its volume, and finally the density of the stator core. The stator core is formed by stacking silicon steel sheets. In order to prevent short circuits between the core laminations and increase eddy current losses, there is usually a coating on the surface of the silicon steel sheets. Finally, the material parameters of the stator core are orthogonal anisotropic. In order to simplify the analysis, the stator core is equivalent to the stacking of two isotropic materials, one material is steel, and the other equivalent coating material parameters include E coat , μ coat and V coat, in order to facilitate analysis, it is regarded as a homogeneous body, and then the material is given orthotropic anisotropy to consider the stacking effect. Its equivalent schematic diagram is as follows Figure 4 As shown. The anisotropic material parameters of the stator core can be calculated by the following formula:

[0118]

[0119] E z =E θ =V steel E steel +V coat E coat (2)

[0120]

[0121] μ θx =V steel μ steel +V coat μ coat (5)

[0122] Where V steel and V coat Respectively represent the volume fraction of silicon steel and coating, μ xθ =μ θx E x / E θ .

[0123] S2.2. When modeling, the motor stator yoke is equivalent to an ideal cylindrical shell, and the stator teeth are equivalent to the longitudinal ribs attached to the inner surface of the stator yoke. Therefore, the stator core can be equivalent to a cylindrical shell with longitudinal ribs. The equivalent schematic diagram is as follows: Figure 5 As shown, the axial direction uses a dimensionless coordinate η, which is defined as η = x / L. The deformation of any point on the cylindrical shell at a distance z from the shell reference surface can be expressed as:

[0124]

[0125] where u0, v0 and w0 are the axial, circumferential and radial displacements of the reference plane, respectively, and φ x and φ θ are the rotation angles in the x and θ directions respectively.

[0126] S2.3. The stress-strain relationship of cylindrical shell can be expressed as:

[0127]

[0128] Where:

[0129] C 66 =G xθ ; C 55 =Gxz ; C 44 =G θz ; where E x , E θ is the elastic modulus, G xθ , G xz and G θz is the shear modulus, μ xθ , μ θx is Poisson's ratio μ xθ E θ =μ θx E x .

[0130] S2.4. According to the first-order shear deformation theory, the stress at any point on the cylindrical shell is:

[0131]

[0132] In the formula and Reference plane stress, κ x , κ θ and κ xθ is the surface curvature, and its expression is

[0133]

[0134] S2.5. By integrating the stress and moment of the in-plane stress over the shell thickness, the results for force and moment are:

[0135]

[0136] Where N x 、N θ and N xθ is the resultant internal force, M x 、M θ and M xθ is the resultant force of bending moment and torque, Q x and Q θ is the resultant lateral shear force, κ is the shear correction factor, A ij , B ij and D ij are the tensile, coupling and bending stiffnesses, defined as:

[0137]

[0138] S2.6. Calculate the kinetic energy and potential energy of the cylindrical shell. The expressions are as follows:

[0139]

[0140] In the formula ρ is the stator core density.

[0141] S2.7. Calculate the potential energy and kinetic energy of the stator teeth and the axial stress ε of the longitudinal ribs x According to formula (8), ignoring the tangential deformation of the stator teeth, the potential energy and kinetic energy are expressed as follows:

[0142]

[0143] Where u r , v r and w r are the displacements of any point on the longitudinal rib, calculated according to formula (6), b s and d s are the longitudinal rib width and height, A r is the longitudinal rib area, N s is the number of longitudinal ribs, J is the torsion constant, which is defined as:

[0144]

[0145] S2.8. The displacement equation of the reference surface of a cylindrical shell with arbitrary boundary conditions can be expressed as follows:

[0146]

[0147] Where n is the number of circumferential fluctuations, ω is the natural angular frequency U(η), V(η), W(η), Φ(η) and Ψ(η) are vibration mode functions, and Chebyshev polynomials are used as vibration mode functions, which are expressed as follows:

[0148]

[0149] Where M is the number of truncated Chebyshev polynomials a m , b m , c m , d m and e m is the corresponding weighting coefficient, T m (η) is the first kind of Chebyshev polynomial, and its recursive expression is as follows:

[0150] T0(η)=1,T1(η)=η,T m+1 (η)=2ηT m (η)-T m-1 (η), m≥2 (19)

[0151] It should be noted that the use of Chebyshev polynomials requires the conversion of coordinates from to , because Chebyshev polynomials are defined on the interval [-1, 1], η∈[0, 1].

[0152] S2.9. Using the Rayleigh-Ritz method to derive the equation of motion of the stator core, substituting the displacement equation (17) into equations (12)-(15) yields the maximum potential energy: and maximum kinetic energy The Lagrange equation L of the stator core is expressed as follows:

[0153]

[0154] The characteristic equation of the system can be obtained by solving the following equation:

[0155]

[0156] Where q m Respectively represent a m , b m , c m , d m and e m , the characteristic equation of the system is solved as:

[0157] (K-ω 2 M)q T =0 (22)

[0158] Where K and M are the stiffness matrix and mass matrix of the system respectively. The natural frequency of the stator core is obtained by solving equation (22).

[0159] S3. Establish a theoretical model for calculating the natural frequency of the stator assembly taking into account the orthotropic material parameters, determine the nonlinear relationship between the winding material parameters and the natural frequency of the stator assembly, and calculate the natural modal frequency of the stator assembly;

[0160] Step S3 specifically includes the following:

[0161] S3.1. Simplified winding material. The stator slot is made of copper, insulation and air. The insulation material cannot fill all the gaps between the copper wires. To simplify the analysis, it is assumed that the winding in the slot is only stacked with copper wires and insulation materials, and then it is equivalent to a homogeneous body. The stacking effect is considered by giving the material orthogonal anisotropy. The equivalent schematic diagram is shown below. Figure 6 As shown, the equivalent winding material parameters of the winding are calculated as follows:

[0162] E x =V copper E copper +V insulation E insulation (twenty three)

[0163]

[0164] μxθ =V copper μ copper +V insulation μ insulation (26)

[0165] Where V copper and V insulation Represent the volume fraction of copper and equivalent insulating material respectively. For winding material G θz It can still be calculated by formula (4), μ θx =μ xθ E θ / E x .

[0166] S3.2, Simplify the stator assembly, ignore the influence of the end winding structure, and add the mass of the end winding to the winding in the slot. The motor winding is wound on the stator teeth, which limits the lateral movement of the stator teeth. The motor stator core and winding assembly are equivalent to a double-layer cylindrical shell structure, with the outer layer representing the stator yoke and the inner layer representing the teeth and windings. The equivalent schematic diagram is shown below. Figure 7 As shown in the figure, h0 is the distance from the inner surface of the composite cylindrical shell to the neutral layer, which can be expressed as:

[0167]

[0168] Where E k is the tangential elastic modulus of the kth cylindrical shell, N is the number of cylindrical shell layers, where N is 2, and H0=0.

[0169] S3.3. Simplification of stator teeth and winding layers. The combination of stator teeth and windings is equivalent to an inner cylindrical shell. The stator teeth and windings are connected in series along the tangential direction and in parallel along the axial direction. The combination of stator teeth and windings is homogenized and then given orthotropic material parameters. According to the thin film model method of composite material theory, the elastic model and shear modulus along the parallel direction are calculated as follows:

[0170]

[0171] V i The volume fraction of stator teeth and windings is shown in the table. The elastic model and shear modulus along the series direction are calculated as follows:

[0172]

[0173] S3.4. Calculate the potential energy and kinetic energy of the equivalent double-layer cylindrical shell. The kinetic energy and potential energy of the equivalent double-layer composite cylindrical shell of the stator core and winding assembly can be expressed as follows:

[0174]

[0175] Where L is the total length of the equivalent composite cylindrical shell.

[0176] For multilayer composite cylindrical shells I0, I1, I2, A ij , B ij , D ij It can be written as follows

[0177]

[0178] Where z k-1 and z k denote the coordinates of the bottom and top surfaces of the k-th cylindrical shell in the reference coordinate system, ρ k is the equivalent density of the kth layer.

[0179] S3.5. Using the Rayleigh-Ritz method to derive the stator motion equation, the displacement equation of the reference plane of the multilayer cylindrical shell can still be written in the form of equation (17). Substituting the displacement equation into (32), (33) we can get the maximum potential energy and maximum kinetic energy The Lagrange equation L of the stator assembly is expressed as follows

[0180]

[0181] Substituting equation (36) into equation (21) can obtain the characteristic equation of the stator core and winding assembly system. By solving the characteristic equation, the natural modal frequency of the stator core and winding assembly can be obtained.

[0182] S4. Identification of equivalent material parameters of stator core: Substitute the natural frequency test results of the stator core and the natural frequency of the stator core into the fitness function of the particle swarm algorithm, and use the particle swarm algorithm to iteratively optimize the elastic modulus, shear modulus and Poisson's ratio of the stator core until the set natural frequency error requirements are met, so as to identify the equivalent material parameters of the stator core.

[0183] The particle swarm algorithm (PSO) is used to identify the orthogonal anisotropic materials of the motor stator. The schematic diagram is shown in the figure. Figure 8 As shown, the difference between the natural frequency of the core obtained by the modal test and the natural frequency calculated by the theoretical model is used as the optimization target, and the equivalent material parameters of the stator core are finally output.

[0184] S4.1. Fitness calculation, fitness function f err The definition is as follows:

[0185]

[0186] Where f acm，i and f test，i They represent the modal frequencies of the i-th order motor stator core obtained by analytical calculation and modal test respectively.

[0187] S4.2. Adding constraints When performing parameter identification, it is necessary to limit the value range of the parameters to be identified. The constraints can be written as:

[0188]

[0189] S4.3. By evaluating the fitness function, the role of the PSO algorithm is to calculate the fitness of the entire particle group, select the particle with the best position, that is, the particle with the smallest fitness function value to participate in the next speed update, and then recalculate the position of the particle group. This cycle continues until the fitness function approaches 0 or the number of iterations reaches the upper limit, that is, the calculation is stopped, and the optimal particle in the group is considered to be the true value of the system.

[0190] The particle swarm algorithm parameters are set as follows: population number is 30, iteration number is 50. The stator core can be equivalent to the stack of silicon steel and coating. Due to the different processing methods and trace element contents, the elastic modulus of silicon steel will change. Therefore, the appropriate elastic modulus, shear modulus and Poisson's ratio of silicon steel are selected first, and then the elastic modulus E of the equivalent coating is identified through the optimization algorithm. coat , Poisson's ratio μ coat and its volume fraction V coat These three parameters are then used to calculate the equivalent material parameters of the stator core according to equations (1)-(5) as shown in the following table:

[0191] Table 4 Equivalent stator core material parameters

[0192]

[0193] Table 5 shows the comparison of the natural frequencies of the stator core calculated by modal test, analytical calculation based on identification of material parameters, and finite element calculation. In the table, (m, n) represents the modal order, m represents the axial order, and n represents the circumferential order. As can be seen from Table 4, the modal frequency errors calculated by both the analytical model and the finite element model are less than 2%, meeting the engineering requirements.

[0194] Table 5 Stator core natural frequency

[0195]

[0196] S5. Identification of winding material parameters: Substitute the natural frequency test results of the stator core and the natural frequency of the stator core into the fitness function of the particle swarm algorithm, and use the particle swarm algorithm to iteratively optimize the elastic modulus, shear modulus and Poisson's ratio of the stator core until the set natural frequency error requirements are met, so as to identify the equivalent material parameters of the stator core.

[0197] The basic steps of the winding equivalent material parameter identification are basically the same as those of the core material identification. The particle swarm algorithm parameters remain the same as those of the stator core material parameter identification in the previous article. The fitness function and constraints are shown in equations (34) and (35). The winding is equivalent to a stack of insulators and copper wires. Due to the different processing methods and trace element content, the elastic modulus of copper will change. Therefore, the appropriate elastic modulus, shear modulus and Poisson's ratio of copper are first selected, and then the elastic modulus E of the equivalent insulation is identified through the optimization algorithm. insulation , Poisson's ratio μ insulation and its volume fraction V insulation These three parameters are then used to calculate the equivalent material parameters of the windings as shown in Table 6 using equations (23)-(26). Table 7 shows the comparison of the natural frequencies of the stator core and winding assembly calculated by the modal test and the analytical calculation of the identified material parameters and the finite element calculation. It can be seen from Table 7 that the modal frequency errors calculated by both the analytical model and the finite element model are less than 3%, indicating the accuracy of the proposed method.

[0198] Table 6 Equivalent winding material parameters

[0199]

[0200] Table 7 Stator assembly natural frequency

[0201]

[0202] According to the above-mentioned embodiment of the present invention, the method for identifying equivalent material parameters of the stator core and winding of the above-mentioned embodiment can conveniently and quickly identify the equivalent material parameters of the core and winding, reveal the nonlinear relationship between material parameters and structural modes, and facilitate the rapid calculation of vibration and noise, and is worthy of being promoted and used.

[0203] The above description is only a preferred embodiment of the present disclosure and an explanation of the technical principles used. Those skilled in the art should understand that the scope of disclosure involved in the present disclosure is not limited to the technical solutions formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above disclosed concept. For example, the above features are replaced with the technical features with similar functions disclosed in the present disclosure (but not limited to) by each other to form a technical solution.

[0204] In addition, although each operation is described in a specific order, this should not be understood as requiring these operations to be performed in the specific order shown or in a sequential order. Under certain circumstances, multitasking and parallel processing may be advantageous. Similarly, although some specific implementation details are included in the above discussion, these should not be interpreted as limiting the scope of the present disclosure. Some features described in the context of a separate embodiment can also be implemented in a single embodiment in combination. On the contrary, the various features described in the context of a single embodiment can also be implemented in multiple embodiments individually or in any suitable sub-combination mode.

[0205] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for identifying equivalent material parameters of a motor stator and winding, characterized in that: include: S1. Obtain the modal vibration shape and corresponding modal natural frequency test results of the stator core and stator assembly through modal tests; S2. Establish a theoretical model for calculating the natural frequency of the stator core, determine the nonlinear relationship between various anisotropic material parameters and the natural frequency of the stator core, and then calculate the natural frequency of the stator core; S3. Establish a theoretical model for calculating the natural frequency of the stator assembly, determine the nonlinear relationship between the winding material parameters and the natural frequency of the stator assembly, and calculate the natural modal frequency of the stator assembly; S4, substituting the natural frequency test result of the stator core and the natural frequency of the stator core into the fitness function of the particle swarm algorithm, and optimizing the elastic modulus, shear modulus and Poisson's ratio of the stator core by using the particle swarm algorithm until the set natural frequency error requirement is met, so as to identify the equivalent material parameters of the stator core; S5. Substitute the natural frequency test results of the stator assembly and the natural modal frequency of the stator assembly into the fitness function of the particle swarm algorithm, and use the particle swarm algorithm to iteratively optimize the winding elastic modulus, shear modulus and Poisson's ratio until the set natural frequency error requirements are met, so as to identify the equivalent material parameters of the winding.

2. The method for identifying equivalent material parameters of a motor stator and winding according to claim 1, characterized in that: The modal test in step S1 is specifically a hammer test, and the data processing of the modal test adopts LMS Testlab software.

3. The method for identifying equivalent material parameters of a motor stator and winding according to claim 1, characterized in that: The step S2 comprises: S2.

1. The stator core is equivalent to a stack of two isotropic materials, one of which is steel and the other is equivalent to a coating material. Parameters include E coat , μ coat and V coat , giving the material orthogonal anisotropy to consider the stacking effect, the anisotropic material parameters of the stator core are calculated by the following formula: E z =E θ =V steel E steel +V coat E coat (2) m θx =V steel m steel +V coat m coat (5) Where V steel and V coat Respectively represent the volume fraction of silicon steel and coating, μ xθ =μ θx E x / E θ ; S2.

2. The stator core can be equivalent to a cylindrical shell with longitudinal ribs. The dimensionless coordinate η is used in the axial direction, which is defined as η = x / L. The deformation of any point on the cylindrical shell at a distance z from the shell reference surface is expressed as: where u0, v0 and w0 are the axial, circumferential and radial displacements of the reference plane, respectively, and φ x and φ θ are the rotation angles in the x and θ directions respectively; S2.3, the stress-strain relationship of cylindrical shell is expressed as: Where: C 66 =G xθ ; C 55 =G xz ; C 44 =G θz ; where E x , E θ is the elastic modulus, G xθ , g xz and G θz is the shear modulus, μ xθ , μ θx is Poisson's ratio μ xθ E θ =μ θx E x ; S2.

4. According to the first-order shear deformation theory, the stress at any point on the cylindrical shell is: In the formula and Reference plane stress, κ x , κ θ and κ xθ is the surface curvature, and its expression is: S2.

5. By integrating the stress and moment of the in-plane stress over the shell thickness, the results for force and moment are: Where N x 、N θ and N xθ is the resultant internal force, M x 、M θ and M xθ is the resultant force of bending moment and torque, Q x and Q θ is the resultant lateral shear force, κ is the shear correction factor, A ij , B ij and D ij are the tensile, coupling and bending stiffnesses, defined as: S2.

6. Calculate the kinetic energy and potential energy of the cylindrical shell. The expressions are as follows: In the formula ρ is the stator core density. S2.

7. Calculate the potential energy and kinetic energy of the stator teeth and the axial stress ε of the longitudinal ribs x According to formula (8), ignoring the tangential deformation of the stator teeth, the potential energy and kinetic energy are expressed as follows: Where u r , v r and w r are the displacements of any point on the longitudinal rib, calculated according to formula (6), b s and d s are the longitudinal rib width and height, A r is the longitudinal rib area, N s is the number of longitudinal ribs, J is the torsion constant, which is defined as: S2.

8. The displacement equation of the reference surface of a cylindrical shell with arbitrary boundary conditions is expressed as follows: Where n is the number of circumferential fluctuations, ω is the natural angular frequency U(η), V(η), W(η), Φ(η) and Ψ(η) are vibration mode functions, and Chebyshev polynomials are used as vibration mode functions, which are expressed as follows: Where M is the number of truncated Chebyshev polynomials a m , b m , c m , d m and e m is the corresponding weighting coefficient, T m (η) is the first kind of Chebyshev polynomial, and its recursive expression is as follows: T0(n)=1,T1(n)=n,T m+1 (η)=2ηT m (h)-T m-1 (n), m≥2 (19) η∈[0,1]; S2.9, use the Rayleigh-Ritz method to derive the stator motion equation, and substitute the displacement equation (17) into equations (12)-(15) to obtain the maximum potential energy and maximum kinetic energy The Lagrange equation L of the stator core is expressed as follows: The characteristic equation of the system can be obtained by solving the following equation: Where q m Respectively represent a m , b m , c m , d m and e m , the characteristic equation of the system is solved as: (K-ωω 2 M) q T =0(22) Where K and M are the stiffness matrix and mass matrix of the system respectively. The natural frequency of the stator core is obtained by solving the characteristic equation of the system.

4. The method for identifying equivalent material parameters of a motor stator and winding according to claim 1, characterized in that: The step S3 comprises: S3.

1. Assume that the winding in the stator slot is only composed of copper wire and insulating material stacked together, and then it is equivalent to a homogeneous body. The stacking effect is considered by giving the material orthogonal anisotropy. The equivalent winding material parameters of the winding are calculated as follows: E x =V copper E copper +V insulation E insulation (23) m xθ =V copper m copper +V insulation m insulation (26) Where V copper and V insulation Represent the volume fraction of copper and equivalent insulating material respectively. For winding material G θz Calculated by formula (4), μ θx =μ xθ E θ / E x ; S3.

2. The motor stator core and winding assembly are equivalent to a double-layer cylindrical shell structure, the outer layer represents the stator yoke, the inner layer represents the teeth and windings, and the distance h0 from the inner surface of the composite cylindrical shell to the neutral layer is calculated according to the following formula: Where E k is the tangential elastic modulus of the k-th cylindrical shell, N is the number of cylindrical shell layers, where N is 2, H0 = 0; S3.

3. According to the thin film model method of composite material theory, the elastic model and shear modulus along the parallel direction are calculated as follows: V i The volume fraction of stator teeth and windings is shown in the table. The elastic model and shear modulus along the series direction are calculated as follows: S3.

4. The kinetic energy and potential energy of the equivalent double-layer composite cylindrical shell of the stator core and winding assembly are expressed as follows: Where L is the total length of the equivalent composite cylindrical shell; The multilayer composite cylindrical shell I0, I1, I2, A ij , B ij , D ij Written in the following form: Where z k-1 and z k denote the coordinates of the bottom and top surfaces of the k-th cylindrical shell in the reference coordinate system, ρ k is the equivalent density of the kth layer; S3.5 uses the Rayleigh-Ritz method to derive the stator motion equation, and writes the displacement equation of the multilayer cylindrical shell reference plane into the form of equation (17). Substituting the displacement equation into (32), (33) obtains the maximum potential energy and maximum kinetic energy The Lagrange equation L of the stator assembly is expressed as follows: Substituting equation (36) into equation (21) yields the characteristic equation of the stator core and winding assembly system. The natural modal frequency of the stator assembly is obtained by solving the characteristic equation.

5. The method for identifying equivalent material parameters of a motor stator and winding according to claim 1, characterized in that: Step S4 includes: S4.

1. Calculate fitness, fitness function f err The definition is as follows: Where f acm，i and f test，i They represent the modal frequencies of the i-th order motor stator core obtained by analytical calculation and modal test respectively; S4.

2. Add constraints: S4.

3. By evaluating the fitness function, the elastic modulus E of the equivalent coating is identified by the particle swarm algorithm. coat , Poisson's ratio μ coat and its volume fraction V coat , and then calculate the equivalent material parameters of the stator core according to equations (1)-(5).

6. The method for identifying equivalent material parameters of a motor stator and winding according to claim 5, characterized in that: The step S5 comprises: based on the fitness function f err Calculate the fitness and add the constraints, and identify the elastic modulus E of the equivalent insulation through the particle swarm algorithm. insulation , Poisson's ratio μ insulation and its volume fraction V iinsulation , and then calculate the equivalent material parameters of the winding through equations (23)-(26).

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