Statistical energy analysis and noise prediction method for permanent magnet synchronous motor based on stator orthogonal anisotropy

Abstract

The invention belongs to the technical field of motor noise prediction, and particularly provides a permanent magnet synchronous motor statistical energy analysis and noise prediction method based on stator orthotropy. The method comprises the following steps: carrying out subsystem division on a motor structure, considering orthotropic characteristics of a stator and a winding, establishing an anisotropic cylindrical shell model, and deriving an analytical expression of a coupling loss factor between subsystems based on a first-order shear deformation theory; taking the electromagnetic force as input power, and constructing a statistical energy analysis model in combination with the internal loss factor; the average vibration energy of each subsystem is solved and obtained, the radiation sound power and the sound pressure level are calculated by combining a sound radiation efficiency model, and rapid and accurate prediction of the medium-high frequency vibration noise of the motor under the working conditions of the constant rotating speed and the variable speed is achieved. According to the method, effective estimation of the high-frequency noise of the motor can be realized in a design stage, and the problems that a traditional numerical method is large in calculation amount and an analytical method is not suitable for high-frequency statistical characteristics are solved.

Description

Technical Field

[0001] This invention belongs to the field of machine life prediction technology, specifically involving a statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) have advantages such as simple structure, reliable operation, low manufacturing cost, and good regulation performance, and are widely used in new energy vehicles and other fields. However, noise problems, especially electromagnetic noise, limit their application. Vibration and noise are key factors in designing low-noise PMSMs; therefore, research on motor vibration and noise prediction has significant theoretical and practical value. Currently, motor vibration and noise prediction mainly employs three methods: numerical methods, analytical methods, and statistical energy methods. Numerical methods are primarily based on finite element and boundary method simulations to predict electromagnetic noise under different operating conditions. Analytical methods, based on plate and shell theory or energy methods, perform numerical predictions of modal and electromagnetic vibration noise based on a moderately simplified stator model. Existing technologies have the following problems: 1. Since the motor is driven by SVPWM, the prediction of high-frequency noise near its switching frequency is limited by computing resources, and numerical methods are not sufficient to handle it.

[0003] 2. Analytical methods are difficult to handle complex geometric structures and are not well adapted to the statistical characteristics of structural uncertainties and high-frequency dense modes.

[0004] 3. Due to the complex and irregular structure of the motor and the unknown loss factor during the design stage, existing methods are difficult to efficiently predict high-frequency vibration and noise. In addition, existing SEA methods ignore the anisotropic material properties of the stator. Summary of the Invention

[0005] The purpose of this invention is to provide a statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy, so as to solve the problem of how to efficiently and accurately predict the electromagnetic vibration and noise of automotive permanent magnet synchronous motors (PMSMs) in the mid-to-high frequency range (especially near the switching frequency) without relying on prototype experiments during the motor design stage.

[0006] The present invention achieves the above objectives through the following technical solutions: This invention proposes a statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy. The method includes: Based on the structural characteristics of permanent magnet synchronous motors, subsystems are divided to obtain multiple structural subsystems, including the first subsystem of stator yoke and housing combination, the second subsystem of stator teeth, and the third and fourth subsystems of housings at both ends; Based on the subsystem division, a coupling loss factor matrix is ​​constructed to characterize the vibration energy transfer between subsystems; The electromagnetic force of the motor under specific operating conditions is obtained, and the excitation power is calculated and input to the corresponding subsystem based on the relationship between the electromagnetic force and the surface mobility function of the stator structure. The excitation power and the coupling loss factor matrix, combined with the preset internal loss factors of each subsystem, are used to jointly establish the statistical energy analysis energy balance equation of the permanent magnet synchronous motor. Solve the energy balance equation to obtain the average vibrational energy of each subsystem in time and space; Based on the average vibration energy and combined with the acoustic radiation efficiency model of the corresponding subsystem, the overall radiated acoustic power and sound pressure level of the motor are calculated to predict the high-frequency vibration noise.

[0007] As a preferred embodiment, the construction of the coupling loss factor matrix for characterizing vibration energy transfer between subsystems specifically includes: At least one structural subsystem is equivalent to an orthogonal anisotropic cylindrical shell model; Based on the first-order shear deformation theory and the orthogonal anisotropic constitutive relation, the vibration differential equation of the cylindrical shell model is established. Solve the vibration differential equation to obtain the dispersion curve characterizing the wave propagation properties; Based on the dispersion curve, the coupling loss factor between subsystems is calculated.

[0008] As a preferred embodiment, the coupling loss factor between the computational subsystems is achieved by the following formula: ; in, This is the coupling loss factor. For group velocity, Angular frequency, For subsystem area, is the energy transfer coefficient.

[0009] As a preferred embodiment, the energy transfer coefficient Determined based on the geometric connection structure between subsystems: For the T-shaped connection between the stator teeth and the stator yoke, the energy transfer coefficient is a constant; For a line connection between collinear housing components that are in contact via a ring, the energy transfer coefficient is calculated using the following formula: ; in, Subsystems and density, Subsystems and The longitudinal wave velocity.

[0010] As a preferred embodiment, the calculation of excitation power based on the relationship between the electromagnetic force and the surface mobility function of the stator structure specifically includes: For the stator structure of the permanent magnet synchronous motor, based on its high-frequency vibration response characteristics under radial electromagnetic force excitation, its equivalent surface mobility function is established, where the real part of the equivalent surface mobility is... Approximated by the following formula: ; in, For the total mass of the stator, The excitation angular frequency; The total radial electromagnetic force spectrum F of the motor under the target operating condition is obtained and used as the excitation force input. The total radial electromagnetic force spectrum F is compared with the real part of the equivalent surface mobility. Substituting into the power input model shown in the following equation, the excitation power P2 input to the second subsystem is calculated: .

[0011] As a preferred embodiment, the statistical energy analysis energy balance equation is expressed in matrix form, and the average vibration energy vector E of each subsystem is solved by the following equation: ; Where P is the input power vector. The loss factor matrix is ​​a loss factor matrix. diagonal elements Off-diagonal elements This represents the internal loss factor of each subsystem.

[0012] As a preferred embodiment, the calculation of the overall radiated acoustic power of the motor based on the average vibration energy and in conjunction with the acoustic radiation efficiency model of the corresponding subsystem specifically includes: Determine the average acoustic radiation efficiency of each of the structural subsystems. ; Based on the average vibrational energy of each subsystem and subsystem quality ,according to Calculate its average vibration velocity ; The total radiated sound power of the motor is calculated according to the following formula. : ; in, air density, For the speed of sound, For subsystem The radiation surface area.

[0013] As a preferred embodiment, the determination of the average acoustic radiation efficiency of each of the structural subsystems is described. Specifically, it includes: For a subsystem equivalent to a flat plate structure, its acoustic radiation efficiency depends on its area. Harmony and wavelength Sure; For a subsystem equivalent to a cylindrical shell structure, its acoustic radiation efficiency is calculated using the following formula: Modal acoustic radiation efficiency. Then, modal averaging is performed to obtain: ; in, For circumferential mode number, For sound wave number, Where is the radius of the cylindrical shell. and Class I and Class II respectively Bessel function of order.

[0014] As a preferred embodiment, the preset internal loss factor of each subsystem The internal friction loss factor of the structural material Acoustic radiation damping loss factor and boundary connection damping loss factor The composition satisfies the following relationship: When predicting mid-to-high frequency vibration noise, the internal friction loss factor of the structural material is used. This serves as the basis for determining the value.

[0015] As a preferred embodiment, the method is applied in the motor design stage to predict the medium- and high-frequency electromagnetic vibration noise of automotive permanent magnet synchronous motors under constant speed or variable speed conditions.

[0016] The beneficial effects of this invention are as follows: This invention achieves accurate prediction of high-frequency vibration and noise in permanent magnet synchronous motors by establishing a statistical energy analysis model that incorporates the orthogonal anisotropy of the stator core and windings. In subsystem partitioning, this method models the stator teeth and yoke as independent subsystems and derives an analytical expression for the coupling loss factor of the anisotropic cylindrical shell based on first-order shear deformation theory, making the energy transfer model more consistent with actual physical characteristics. Compared to traditional methods that ignore anisotropy, the model of this invention significantly improves prediction accuracy in the mid-to-high frequency range, especially near the switching frequency. Simultaneously, the inherent high-frequency computational efficiency of the statistical energy analysis method allows for rapid evaluation of noise performance under multiple operating conditions during the motor design phase, providing an effective analytical tool for the structural optimization of low-noise motors. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating a statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy in this invention. Figure 2 This is another flowchart illustrating the statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy in this invention. Figure 3 This is a structural diagram of a permanent magnet synchronous motor in this invention; Figure 4 This is a schematic diagram of a three-dimensional statistical energy model in this invention; Figure 5 This is a schematic diagram of the statistical energy theory model in this invention; Figure 6 This is a schematic diagram of the stator yoke equivalent model in this invention; Figure 7 This is a schematic diagram of the wavenumber of the statistical energy subsystem in this invention; Figure 8 This is a schematic diagram of the coupling loss factor in this invention; Figure 9 This is a schematic diagram of the acoustic radiation efficiency in this invention; Figure 10 This is a schematic diagram of an electromagnetic two-dimensional finite element model in this invention; Figure 11 This is a schematic diagram of the 1600 rpm electromagnetic force in this invention; Figure 12 This is a schematic diagram of the 1800 rpm electromagnetic force in this invention; Figure 13 This is a schematic diagram of the 2000 rpm electromagnetic force in this invention; Figure 14 This is a schematic diagram of the 2200 rpm electromagnetic force in this invention; Figure 15 This is a schematic diagram of a motor stator winding in this invention; Figure 16 This is a schematic diagram of a motor noise test in this invention; Figure 17 is a schematic diagram comparing the noise of a 1600 rpm motor in this invention; Figure 18 This is a schematic diagram comparing the noise of a 1800 rpm motor in this invention; Figure 19 This is a schematic diagram comparing the noise of a 2000 rpm motor in this invention; Figure 20This is a schematic diagram comparing the noise of a 2000 rpm motor in this invention; Detailed Implementation

[0018] The following description provides specific application scenarios and requirements for this specification, intended to enable those skilled in the art to make and use the contents of this specification. Various partial modifications to the disclosed embodiments will be apparent to those skilled in the art, and the general principles defined herein can 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 rather to the widest scope consistent with the claims.

[0019] The terminology used herein is for the purpose of describing particular exemplary embodiments only and is not restrictive. For example, unless the context clearly indicates otherwise, the singular forms “a,” “an,” and “the” used herein may also include the plural forms. When used in this specification, the terms “comprising,” “including,” and / or “containing” mean that the associated integers, steps, operations, elements, and / or components are present, but do not exclude the presence 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 to the system / method.

[0020] Considering the following description, these and other features of this specification, as well as the operation and function of the related components of the structure, and the economy of assembly and manufacture of the parts, can be significantly improved. All of these form part of this specification with reference to the accompanying drawings. However, it should be clearly understood that the drawings are for illustrative and descriptive 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.

[0021] The flowcharts used in this specification illustrate operations implemented according to some embodiments of this specification. It should be clearly understood that the operations in the flowcharts may not be implemented in a sequential order. Instead, the operations may be implemented in reverse order or simultaneously. Furthermore, one or more additional operations may be added to the flowcharts. One or more operations may be removed from the flowcharts.

[0022] Example 1

[0023] Please see the appendix Figures 1-3 This embodiment proposes a statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy. The main components of the method are as follows: (1) Based on the structural characteristics of the permanent magnet synchronous motor, the system is divided into multiple structural subsystems, specifically including: a first subsystem consisting of the stator yoke and the housing, a second subsystem consisting of the stator teeth, and the housing portions located at both ends of the motor axis as the third and fourth subsystems. The above division method fully considers the differences in vibration modes and energy transfer characteristics of different structural components of the motor. In particular, the stator teeth and the stator yoke are treated as independent subsystems to more accurately reflect the influence of stator orthogonal anisotropy on vibration transmission.

[0024] (2) Based on the subsystem division, a coupling loss factor matrix is ​​constructed to characterize the vibration energy transfer relationship between each subsystem. The construction of the coupling loss factor matrix fully considers the orthogonal anisotropic material characteristics of the stator and winding. By equating the subsystem with a cylindrical shell structure having orthogonal anisotropic material parameters, and based on the first-order shear deformation theory and energy principle, a mathematical model of the coupling relationship between each subsystem is established, thereby more realistically depicting the transmission path and efficiency of vibration energy inside the motor.

[0025] Specifically, the subsystem division is based on the characteristics of the motor structure: such as Figure 3 As shown, for an 8-pole, 24-slot externally mounted permanent magnet synchronous motor, based on the modal test results, the middle and end portions embedded in the stator housing have different vibration characteristics. Therefore, the housing is divided into three parts. The stator teeth and stator yoke are respectively considered as independent subsystems (the first subsystem and the second subsystem), and the end housings are respectively considered as the third and fourth subsystems.

[0026] Specifically, a coupling loss factor matrix for characterizing vibration energy transfer between subsystems is constructed, which includes: equating at least one structural subsystem to an orthogonal anisotropic cylindrical shell model; establishing the vibration differential equation of the cylindrical shell model based on the first-order shear deformation theory and the orthogonal anisotropic constitutive relation; solving the vibration differential equation to obtain the dispersion curve characterizing wave propagation characteristics; and calculating the coupling loss factor between subsystems based on the dispersion curve.

[0027] The coupling loss factor between subsystems is calculated using the following formula: ; in, This is the coupling loss factor. For group velocity, Angular frequency, For subsystem area, is the energy transfer coefficient.

[0028] Specifically, energy transfer coefficient Determined based on the geometric connection structure between subsystems: For a T-type connection between stator teeth and stator yoke, the energy transfer coefficient is constant; for a line connection between collinear housing components connected by annular contact, the energy transfer coefficient is calculated using the following formula: ; in, Subsystems and density, Subsystems and The longitudinal wave velocity.

[0029] (3) Obtain the electromagnetic force of the motor under specific operating conditions, and calculate and input the excitation power to the corresponding subsystem based on the functional relationship between the electromagnetic force and the surface mobility of the stator structure. The calculation process of the excitation power combines the spatial and frequency domain distribution characteristics of the electromagnetic force with the dynamic response characteristics of the structure, realizing an effective mapping from electromagnetic excitation to mechanical vibration energy input.

[0030] Specifically, the excitation power is calculated based on the relationship between electromagnetic force and the surface mobility function of the stator structure, including: For the stator structure of a permanent magnet synchronous motor, based on its high-frequency vibration response characteristics under radial electromagnetic force excitation, its equivalent surface mobility function is established, where the real part of the equivalent surface mobility is... Approximated by the following formula: ; in, For the total mass of the stator, The excitation angular frequency; Obtain the total radial electromagnetic force spectrum F of the motor under the target operating condition, and use it as the excitation force input; then, compare the total radial electromagnetic force spectrum F with the real part of the equivalent surface mobility. Substituting into the power input model shown in the following equation, the excitation power P2 input to the second subsystem is calculated: .

[0031] in, For equivalent excitation force, Let be the real part of the surface mobility. At high frequencies, the real part of the surface mobility can be approximated as: ; Where M is the total mass of the stator, The excitation angular frequency.

[0032] (4) The excitation power and the coupling loss factor matrix, combined with the preset internal loss factors of each subsystem, are used to jointly establish the statistical energy analysis energy balance equation of the permanent magnet synchronous motor. The energy balance equation, in matrix form, represents the dynamic balance relationship between the input energy, dissipated energy and transmitted energy of each subsystem, and constitutes the core equation set for solving the vibration response.

[0033] Specifically, the energy balance equation is: ; in, The average power of the input subsystem, For each subsystem, the internal loss factor is... For subsystem Passed to The average energy, The average vibrational energy of each subsystem in time and space.

[0034] (5) Solve the energy balance equation to obtain the average vibration energy of each subsystem in time and space. The solution process obtains the average energy distribution of each subsystem through matrix operations, providing key vibration state input for subsequent noise radiation calculation.

[0035] Specifically, Once the input energy, internal loss factor, and coupling loss factor between subsystems of each system are determined, the average vibration energy of each subsystem can be obtained by solving the above equations. Then, the average vibration velocity of each subsystem is obtained according to the following formula. in For the quality of each subsystem: .

[0036] As a preferred approach, the energy balance equations of statistical energy analysis are expressed in matrix form, and the average vibrational energy vector E of each subsystem is solved by the following equation: ; Where P is the input power vector. Here is the loss factor matrix. diagonal elements Off-diagonal elements This represents the internal loss factor of each subsystem.

[0037] (6) Based on the average vibration energy and combined with the acoustic radiation efficiency model of the corresponding subsystem, the overall radiated acoustic power and sound pressure level of the motor are calculated, thereby realizing the prediction of high-frequency vibration noise. The acoustic radiation efficiency model is established separately for different subsystem structural characteristics. For example, the radiation efficiency of the flat plate structure and the cylindrical shell structure are described by different physical models to ensure the accuracy of the noise prediction results.

[0038] Specifically, based on the average vibration energy and combined with the acoustic radiation efficiency model of the corresponding subsystem, the overall radiated acoustic power of the motor is calculated, including: Determine the average acoustic radiation efficiency of each structural subsystem. Based on the average vibrational energy of each subsystem and subsystem quality ,according to Calculate its average vibration velocity ; The total radiated sound power of the motor can be calculated using the following formula. : ; in, air density, For the speed of sound, For subsystem The radiation surface area.

[0039] Specifically, determine the average acoustic radiation efficiency of each structural subsystem. Specifically, it includes: For a subsystem equivalent to a flat plate structure, its acoustic radiation efficiency depends on its area. Harmony and wavelength Determined; for a subsystem equivalent to a cylindrical shell structure, its acoustic radiation efficiency is calculated using the following formula: Modal acoustic radiation efficiency. Then, modal averaging is performed to obtain: ; in, For circumferential mode number, For sound wave number, Where is the radius of the cylindrical shell. and Class I and Class II respectively Bessel function of order.

[0040] In a preferred embodiment, the preset internal loss factors of each subsystem are... The internal friction loss factor of the structural material Acoustic radiation damping loss factor and boundary connection damping loss factor The composition satisfies the following relationship: When predicting mid-to-high frequency vibration noise, the internal friction loss factor of the structural material is used. This serves as the basis for determining the value.

[0041] Understandably, this method is particularly suitable for predicting mid-to-high frequency electromagnetic vibration and noise of automotive permanent magnet synchronous motors (PMSMs) under constant speed or variable speed conditions during the motor design phase. This prediction process spans several key stages in the early stages of motor design, enabling effective evaluation and optimization of the motor's acoustic performance before physical prototype manufacturing.

[0042] Specifically, during the design phase, engineers first construct the aforementioned subsystem division and statistical energy analysis model based on the preliminary structural design parameters of the motor (such as stator inner and outer diameters, core length, slot-pole fit, etc.). The material parameters required for this model, including the orthotropic elastic modulus, shear modulus, and Poisson's ratio exhibited by the stator silicon steel lamination structure and windings, can be equivalent parameters obtained through experiments or high-precision simulation. Subsequently, the target rotational speed is obtained based on electromagnetic design software or finite element simulation. The air gap magnetic flux density and radial electromagnetic force wave spectrum are used as the input source of the excitation power.

[0043] By running the statistical energy analysis model established by this method, the vibration energy level and final radiated sound pressure level spectrum of each subsystem of the motor under the target operating condition can be quickly obtained. The prediction results can clearly reveal the frequency components of the main noise peaks (especially the frequency bands related to the switching frequency and its sidebands) and their contribution magnitude, so that designers can make targeted adjustments to electromagnetic parameters (such as pole arc coefficient, winding form), control strategies (such as modulation method, switching frequency), or mechanical structures (such as stator stiffness, shell reinforcement arrangement) to suppress noise from the source or the transmission path.

[0044] The statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy proposed in the above embodiments will be described and explained below with reference to a specific implementation procedure.

[0045] 1. Subsystem Division A typical motor includes a stator, rotor, housing, end covers, etc. Specifically, this motor is an 8-pole, 24-slot externally mounted permanent magnet synchronous motor, such as... Figure 3As shown. Based on the modal test results, the middle and end portions embedded in the stator housing have different vibration characteristics, so the housing is divided into three parts. Previously, the stator was often treated as a single subsystem. The orthogonal anisotropy of the stator has a crucial impact on the accurate prediction of motor vibration and noise. Now, the stator teeth and stator yoke are considered separately: the stator and the portion of the housing immediately adjacent to it are subsystem 1; the stator teeth are subsystem 2; and the two portions of the housing indirectly connected to the stator at both ends are subsystems 3 and 4, respectively. The end caps only provide boundary conditions for the housing and are ignored in the modeling process; simulation is performed using boundary conditions. Simultaneously, the rotor, which is only effective in the low-frequency range, is ignored because its acoustic power is relatively small compared to the structural vibration power. This simplification and neglect will not lead to significant errors in the final results. The statistical energy three-dimensional model is shown below. Figure 4 As shown.

[0046] Figure 5 The theoretical model for statistical energy analysis of permanent magnet synchronous motors is established based on the above subsystem division. The four boxes represent four subsystems. The average power of the input subsystem, The average vibrational energy of each subsystem in time and space. For each subsystem, the internal loss factor is... For subsystem Passed to The average energy. According to the model, Figure 5 The energy balance equation for the SEA model of the motor shown can be written as: (1) In the formula: (2) The average power of the input subsystem, The average vibrational energy of each subsystem in time and space. For each subsystem, the internal loss factor is... For subsystem Passed to The average energy.

[0047] As can be seen from equations (1) and (2), once the input energy, internal loss factor, and coupling loss factor between subsystems of each system are determined, the average vibration energy of each subsystem can be obtained by solving equation (1). Then, the average vibration velocity of each subsystem is obtained according to equation (3). ,in For the quality of each subsystem.

[0048] (3) 2. Input power To predict the vibration response of a motor structure using equation (1), the electromagnetic force calculation results under specific operating conditions must be input into the mechanical power of the stator. In vibration and acoustic analysis, mobility is often used to characterize the ability of a structure to respond to excitation forces. If the mobility and total excitation force are known, the transmitted power can be easily calculated. The surface loads of permanent magnet synchronous motors have the same characteristics, and their equivalent surface mobility can be obtained through the equivalent excitation force. Therefore, the input power can be obtained corresponding to the equivalent excitation force F. With structural surface mobility The real part of the functional relationship indicates that all motors have the same load and the same input power. With the surface mobility of a structure The real part is related to the excitation force F: (4) The electromagnetic noise of an electric motor is mainly caused by the interaction of electromagnetic forces applied to the rotor and stator. Motor vibration is primarily dominated by bending vibration. For the stator's vibration response under electromagnetic force wave excitation, the amplitude of the stator core radial acceleration can be expressed as: (5) The circumferential mode number m and its corresponding natural frequency can be expressed as: (6) In the formula: This refers to the stator core angular frequency. In the high-frequency range, the modal overlap coefficient is high, meaning the natural frequencies of adjacent vibration modes are quite close. Therefore, at a frequency of... The vibration response under excitation can be determined by its nearby natural frequencies. The response at that point is approximate. Substituting equation (6) into equation (5), we can obtain an approximate expression for the real part of the surface mobility: (7) In the formula: Let be the total mass of the stator. Equation (7) shows that, under the excitation of electromagnetic force waves, the real part of the equivalent surface mobility of the cylindrical shell in the high-frequency band is inversely proportional to the structural mass and frequency.

[0049] 3. Internal loss factor and coupling loss factor As can be seen from equation (1), the loss factor is an important parameter for measuring the damping characteristics of a system and determining its vibration energy dissipation capability. Therefore, it is also called the damping loss factor, which includes the internal loss factor. and coupling loss factor The internal loss factor is a quantity that reflects the damping characteristics of a system, while the coupling loss factor is an important parameter used in statistical energy analysis to characterize the energy exchange between coupled systems.

[0050] (a) Internal loss factor Structural subsystem Internal loss factor Composed of three independent damping mechanisms (8) In the formula It is the structural loss factor caused by the internal friction of the material in the structural subsystem itself; It is the loss factor formed by the vibration acoustic radiation damping of the structural subsystem; It is the loss factor formed by the boundary connection damping of the structural subsystem.

[0051] In mid-to-high frequency analysis Mainly, and Negligible, based on literature. and It is 0.0001. and It is 0.0002.

[0052] (b) Analytical modeling of coupling loss factor The motor subsystem 3 mainly consists of a stator yoke and a connected housing, as shown in the schematic diagram below. Figure 3 As shown. During modeling, subsystem 3 can be equivalently represented as a cylindrical shell, with the mass of the outer shell's longitudinal ribs added to the cylindrical shell. For example... Figure 6 As shown, the cylindrical shell has radius R, length L, and thickness h. Using a cylindrical coordinate system fixed to the neutral plane of the shell as a reference, the axial, circumferential, and radial displacements of the shell are represented by u, v, and w, respectively. The axial direction uses dimensionless coordinates, defined as... .

[0053] According to the first-order shear deformation theory, the displacement of any point on the cylindrical shell at a distance from any point on the shell is: (9) In the formula , and These represent the axial, circumferential, and radial displacements of the reference plane, respectively. and They are respectively and Directional rotation angle. Ignoring stress in the direction perpendicular to the neutral plane of the cylindrical shell, the stress-strain relationship of the cylindrical shell can be expressed as: (10) in ;in For elastic modulus, and For shear modulus, Poisson's ratio According to the first-order shear deformation theory, the stress at any point on the cylindrical shell is... (11)

[0054] (12)

[0055] According to the first-order shear deformation theory, by integrating the stress and bending moment of the in-plane stress over the shell thickness, the results of the force and bending moment are obtained as follows: (13) in the formula For the resultant force of in-plane forces, The resultant force of bending moment and torque, Here, k represents the resultant transverse shear force, and k is the shear correction factor. For tensile, coupling and bending stiffness (14) Incorporating internal forces into the shell's five force balance equations based on FSDT: (15) in This can be derived to the equilibrium differential equation: (16) Differential operators Elements: (17) (18) (19) (20) (twenty one) Then the displacement field generated by a single wave: Substituting into the equilibrium differential equation yields the corresponding dispersion equation, and the second-order time derivative and spatial derivative are calculated: (twenty two) Therefore, the original dynamic equation is: (twenty three) Substituting the plane wave solution, it becomes: (twenty four) Determinant It is about The 10th-order polynomial has three effective characteristic wavenumbers within a finite frequency band, corresponding to bending wave (F), shear wave (S), and longitudinal wave (L), respectively. Its dispersion curve is calculated as follows: Figure 7 As shown.

[0056] Based on the dispersion curve of the cylindrical shell, the group velocity and phase velocity of the bending wave (F), shear wave (S), and longitudinal wave (L) are obtained according to the following formulas. For the cylindrical shell in SEA high-frequency analysis, the bending mode plays a dominant role, and only the bending mode can be considered for analysis. (25) Substituting into equation (26), we can solve for the coupling loss factor. The same method was used to obtain and like Figure 8 As shown.

[0057] (26) in For the transfer factor, for the teeth and stator connected in a “T”-like manner, the transfer factor is 8 / 27

[20] , and for the two curved panels or circular shells connected along the annulus by a line connection, the following is true: (27) in shell and density, shell and The longitudinal wave velocity.

[0058] 4. Noise prediction results of permanent magnet synchronous motor Based on the internal loss factor obtained above and coupling loss factor The vibration energy of each subsystem is obtained by combining equation (1). Based on this, the radiated sound power of the motor can be further solved by combining the sound radiation efficiency of each subsystem, and then the sound pressure level can be determined. The sound radiation efficiency of subsystem 2 is obtained according to formula (28) and the sound radiation efficiency of subsystems 1, 3 and 4 is obtained according to (29).

[0059] (28) in The area of ​​one side of the flat plate. The wavelength of the sound wave.

[0060] (29) In the formula and These are Bessel equations of the first kind, of order n and n+1, respectively. and These are the nth and (n+1)th order Bessel equations of the second kind. For radius, denoted as the sound wave number, and m as the circumferential mode.

[0061] The modal average radiated power can be obtained from the following formula for each subsystem: (30) Using the electromagnetic force under various working conditions as input, the average vibration velocity of each subsystem is obtained based on equation (3). and the average acoustic radiation efficiency of each subsystem The radiated sound power of the entire motor is calculated using the shell: (31) The sound pressure level of an electric motor can be described by the following formula: (32) The following simulation experiment will be used to evaluate the feasibility of the proposed method, thereby providing proof of the effectiveness of the underlying theoretical framework.

[0062] 1. Input power Since it is difficult to experimentally measure the radial force of a permanent magnet synchronous motor during operation, this application uses JMAG electromagnetic simulation software to perform two-dimensional modeling of an 8-pole, 24-slot permanent magnet synchronous motor based on its actual structure. The finite element model is as follows: Figure 10 As shown, the three-phase current corresponding to the test conditions below is then input to simulate and obtain the frequency spectrum waveform of the radial force. Figures 11-14 The spectrum of radial force of a motor with a switching frequency of 12500kHz at no-load speeds of 1600 r / min, 1800 r / min, 2000 r / min, and 2200 r / min is given. The input power of the motor can then be obtained.

[0063] 2. Stator anisotropic material parameters The previous section considered that the anisotropic calculation of the coupling loss factor of the stator core can be equivalent to a composite material formed by two isotropic materials, where the parameters of one material (steel) are known, while the parameters of the other equivalent material (coating) are unknown. We identify the elastic modulus of the coating through an optimization algorithm. Poisson's ratio and its volume fraction The results of the stator core parameter identification for these three parameters are shown in Table 1-3.

[0064] Table 1 Equivalent Material Parameters ; Table 2 Equivalent stator core material parameters ; Table 3 Equivalent winding material parameters ; 3. Comparison of noise prediction results with experimental results (a) Noise test In the noise experiment, the host computer established communication with the inverter via a USB CAN card, and the motor was powered by a DC power supply. The motor was driven by the inverter, the load was provided by a magnetic powder brake, and a torque sensor recorded the output torque. A microphone was fixed 10cm to the side of the motor, and a current clamp was installed on the three-phase windings. The microphone and current clamp respectively collected noise and current signals, and the data were processed by Siemens data acquisition equipment. Due to experimental limitations, this experiment was not conducted in a semi-anechoic chamber; therefore, a relatively quiet time period was selected to reduce environmental noise interference. The noise experiment is as follows: Figure 16 As shown.

[0065] (b) Comparison of prediction noise results The internal loss factor and coupling loss factor obtained in the previous section, combined with the input power and acoustic radiation efficiency, are used to solve for the noise sound pressure level of the permanent magnet synchronous motor at different speeds, as shown in the figure. Figures 17-19 As shown in the figure. To verify the accuracy of the prediction results, under the same operating parameters, the noise sound pressure level of the motor was measured at the corresponding operating conditions of electromagnetic force, namely no-load 1600 r / min, 1800 r / min, 2000 r / min, and 2200 r / min. The figure shows that the predicted sound pressure level in the mid-to-high frequency noise range, especially near the switching frequency, is in good agreement with the measured values, indicating that statistical energy analysis is effective in predicting the vibration and noise of permanent magnet synchronous motors.

[0066] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features disclosed in this disclosure that have similar functions.

[0067] Furthermore, while the operations are described in a specific order, this should not be construed as requiring these operations to be performed in the specific order shown or in a sequential order. In certain environments, multitasking and parallel processing may be advantageous. Similarly, while several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of this disclosure. Certain features described in the context of individual embodiments may also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment may also be implemented individually or in any suitable sub-combination in multiple embodiments.

[0068] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for statistical energy analysis and noise prediction of permanent magnet synchronous motors based on stator orthogonal anisotropy, characterized in that, The methods include: Based on the structural characteristics of the permanent magnet synchronous motor, the subsystems are divided into multiple structural subsystems, including the first subsystem of the stator yoke and housing combination, the second subsystem of stator teeth, and the third and fourth subsystems of the housings at both ends; Based on the subsystem division, a coupling loss factor matrix is ​​constructed to characterize the vibration energy transfer between subsystems; The electromagnetic force of the motor under specific operating conditions is obtained, and the excitation power is calculated and input to the corresponding subsystem based on the relationship between the electromagnetic force and the surface mobility function of the stator structure. The excitation power and the coupling loss factor matrix, combined with the preset internal loss factors of each subsystem, are used to jointly establish the statistical energy analysis energy balance equation of the permanent magnet synchronous motor. Solve the energy balance equation to obtain the average vibrational energy of each subsystem in time and space; Based on the average vibration energy and combined with the acoustic radiation efficiency model of the corresponding subsystem, the overall radiated acoustic power and sound pressure level of the motor are calculated to predict the high-frequency vibration noise.

2. The statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy as described in claim 1, characterized in that, The construction of the coupling loss factor matrix for characterizing vibrational energy transfer between subsystems specifically includes: At least one structural subsystem is equivalent to an orthogonal anisotropic cylindrical shell model; Based on the first-order shear deformation theory and the orthogonal anisotropic constitutive relation, the vibration differential equation of the cylindrical shell model is established. Solve the vibration differential equation to obtain the dispersion curve characterizing the wave propagation properties; Based on the dispersion curve, the coupling loss factor between subsystems is calculated.

3. The statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy as described in claim 2, characterized in that, The coupling loss factor between the computational subsystems is achieved by the following formula: ； in, This is the coupling loss factor. For group velocity, Angular frequency, Let i be the area of ​​subsystem i. is the energy transfer coefficient.

4. The statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy as described in claim 3, characterized in that, The energy transfer coefficient Determined based on the geometric connection structure between subsystems: For a T-type connection between the stator teeth and the stator yoke, the energy transfer coefficient is constant. For a line connection between collinear housing components that are in contact via a ring, the energy transfer coefficient is calculated using the following formula: ； in, Subsystems and density, Subsystems and The longitudinal wave velocity.

5. The statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy as described in claim 1, characterized in that, The calculation of excitation power based on the relationship between the electromagnetic force and the surface mobility function of the stator structure specifically includes: For the stator structure of the permanent magnet synchronous motor, based on its high-frequency vibration response characteristics under radial electromagnetic force excitation, its equivalent surface mobility function is established, where the real part of the equivalent surface mobility is... Approximated by the following formula: ； in, For the total mass of the stator, The excitation angular frequency; The total radial electromagnetic force spectrum F of the motor under the target operating condition is obtained and used as the excitation force input. The total radial electromagnetic force spectrum F is compared with the real part of the equivalent surface mobility. Substituting into the power input model shown in the following equation, the excitation power P2 input to the second subsystem is calculated: 。 6. The statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy as described in claim 1, characterized in that, The statistical energy analysis energy balance equation is expressed in matrix form, and the average vibrational energy vector E of each subsystem is solved by the following formula: ； Where P is the input power vector. The loss factor matrix is ​​a loss factor matrix. diagonal elements Off-diagonal elements , This represents the internal loss factor of each subsystem.

7. The statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy as described in claim 1, characterized in that, The calculation of the overall radiated acoustic power of the motor based on the average vibration energy and the acoustic radiation efficiency model of the corresponding subsystem specifically includes: Determine the average acoustic radiation efficiency of each of the structural subsystems. ; Based on the average vibrational energy of each subsystem and subsystem quality ,according to Calculate its average vibration velocity ; The total radiated sound power of the motor is calculated according to the following formula. : ； in, air density, For the speed of sound, For subsystem The radiation surface area.

8. The statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy as described in claim 7, characterized in that, The determination of the average acoustic radiation efficiency of each of the structural subsystems Specifically, it includes: For a subsystem equivalent to a flat plate structure, its acoustic radiation efficiency depends on its area. Harmony and wavelength Sure; For a subsystem equivalent to a cylindrical shell structure, its acoustic radiation efficiency is calculated using the following formula: Modal acoustic radiation efficiency. Then, modal averaging is performed to obtain: ； in, For circumferential mode number, For sound wave number, Where is the radius of the cylindrical shell. and Class I and Class II respectively Bessel function of order.

9. The statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy according to claim 1, characterized in that, The preset internal loss factors of each subsystem The internal friction loss factor of the structural material Acoustic radiation damping loss factor and boundary connection damping loss factor The composition satisfies the following relationship: When predicting mid-to-high frequency vibration noise, the internal friction loss factor of the structural material is used. This serves as the basis for determining the value.

10. The statistical energy analysis and noise prediction method for permanent magnet synchronous motors based on stator orthogonal anisotropy according to claim 1, characterized in that, The method is applied in the motor design stage to predict the mid-to-high frequency electromagnetic vibration noise of automotive permanent magnet synchronous motors under constant speed or variable speed conditions.

Images