A method for identifying and suppressing coupled space-time harmonics of torque ripple and vibration noise

Abstract

The present invention discloses a method for identifying and suppressing coupled space-time harmonics of torque pulsation and vibration noise, relating to the field of air gap magnetic field harmonic analysis and optimization of permanent magnet motors. The method comprises: using a precise finite element model with a uniformly distributed air gap grid to obtain the two-dimensional space-time electromagnetic force and magnetic flux waveforms in the air gap; obtaining and identifying the physical characteristics of the space-time harmonics of the electromagnetic force and magnetic flux density in the air gap; determining the most critical space-time harmonics of the electromagnetic force; treating the space-time harmonics as vectors rotating with time and space, and identifying the coupled space-time harmonics based on the space-time invariance of the graph composed of vectors of the same order; suppressing the key coupled space-time harmonics without destroying the periodicity of the magnetic field; and verifying the torque pulsation and vibration noise of the optimized model through a multi-field coupling method. The present invention proposes for the first time a method for identifying the coupled space-time harmonics of torque pulsation and vibration noise in permanent magnet motors. By suppressing the key coupled space-time harmonics, the torque pulsation and vibration noise of permanent magnet motors can be simultaneously reduced.

Description

Technical Field

[0001] The present invention relates to the field of air gap magnetic field analysis and optimization of permanent magnet synchronous motors, in particular to a method for identifying and suppressing coupled space-time harmonics of torque pulsation and vibration noise of permanent magnet synchronous motors. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) are now widely used, playing a crucial role in numerous applications, from automotive to aerospace. This is primarily due to their significant advantages, including high torque density, high efficiency, and compact size. They utilize magnetic materials with high magnetic energy product to replace traditional field windings. This not only eliminates the negative effects of field windings but also simplifies the motor's mechanical structure, improving operational reliability and reducing mechanical losses.

[0003] Permanent magnet synchronous motors, especially rare earth permanent magnet synchronous motors with neodymium iron boron permanent magnet excitation, offer significant advantages such as simple structure, reliable operation, compact size, light weight, low losses, and high efficiency. Among them, spoke-type permanent magnet synchronous motors offer the advantages of high torque density and high efficiency, significantly improving permanent magnet utilization and saving material costs. However, their high air gap flux saturation and rich harmonics lead to significant torque ripple and vibration noise. This limits the application of spoke-type permanent magnet synchronous motors in applications with strict requirements for torque ripple and vibration noise, such as low-speed, high-torque direct-drive motors, high-precision servo motors, and high-coverage underwater vehicles. Therefore, research on suppressing torque ripple and vibration noise in spoke-type permanent magnet motors is extremely valuable. In recent years, many scholars at home and abroad have conducted extensive research on how to suppress torque ripple and vibration noise in spoke-type permanent magnet motors.

[0004] Currently, due to the unclear relationship between torque ripple and vibration noise, methods that can simultaneously reduce torque ripple in spoke-type permanent magnet synchronous motors without exacerbating vibration noise are very limited and understudied. Research on torque ripple and vibration noise in spoke-type permanent magnet synchronous motors often proceeds independently, focusing on either ripple alone or vibration noise alone. Traditional methods such as slot skew, winding optimization, and multi-objective optimization design remain applicable for suppressing torque ripple in spoke-type permanent magnet synchronous motors. More recently, methods such as adding unequal auxiliary poles to the rotor can also significantly reduce torque ripple. However, these methods do not guarantee simultaneous reductions in motor vibration noise, and some have even been shown to exacerbate vibration noise. Therefore, it is necessary to investigate the relationship between torque ripple and vibration noise and identify the sources that significantly contribute to both. Simultaneously suppressing torque ripple and vibration noise in spoke-type permanent magnet synchronous motors is a key research area. Summary of the Invention

[0005] The purpose of the present invention is to propose a method for identifying and suppressing the space-time harmonics of torque pulsation and vibration noise coupling, which mainly includes interpolation-free sampling of electromagnetic force and magnetic density space-time waves, acquisition of space-time harmonics and identification of their physical characteristics, determination of key electromagnetic force space-time harmonics, and identification and suppression of torque pulsation and vibration noise coupling space-time harmonics.

[0006] The technical solution adopted by the present invention comprises the following steps:

[0007] Step 1: Using the finite element method with uniform air gap grid distribution, the electromagnetic force and magnetic flux density waveforms in the air gap are obtained in two dimensions of space and time.

[0008] Step 2: Acquisition of the air gap electromagnetic force and magnetic field density space-time harmonics and identification of the physical characteristics of magnetic field density space-time harmonics;

[0009] Step 3: Determine the most critical electromagnetic force time-space harmonics based on the formation mechanism of torque ripple and vibration noise;

[0010] Step 4: Consider the spacetime harmonics as vectors that rotate with time and space. Based on the spacetime invariance of the graphs composed of vectors of the same order, study the magnetic density composition of the electromagnetic force and identify the coupled spacetime harmonics.

[0011] Step 5: Suppress the key coupled space-time harmonics without destroying the periodicity of the magnetic field;

[0012] Step 6: Verify the torque pulsation and vibration noise of the optimized model through the multi-field coupling method.

[0013] Furthermore, in step 1, the finite element method (FEM) with a uniformly distributed air gap mesh is used to obtain the two-dimensional electromagnetic force and magnetic flux density waveforms in the air gap in both time and space. This requires that the mesh and nodes in the air gap be uniformly distributed along the circumference, and there are limits on the number of mesh divisions. To accurately obtain harmonics with a time order of M−1 and a spatial order of N−1, the number of time steps should be no less than 2M, and the number of circumferential divisions of the air gap mesh should be no less than 2N, with both M and N being powers of 2.

[0014] Furthermore, the physical characteristics of the space-time harmonics in step 2 are identified, such as the two-dimensional harmonic expansion formula of magnetic density:

[0015]

[0016] in, B r ( θ, t )and B t ( θ, t ) represent radial magnetic flux density and tangential magnetic flux density respectively, i represents a spatial variable, t represents the time variable, B r𝛼,±f and f r𝛼,±f The spatial orders are 𝛼 , the time order is ±f of B r The amplitude and phase of the harmonics, B t𝛽,±𝜆 and f t𝛽,±𝜆 The spatial orders are 𝛽 , the time order is ±𝜆 of B t The amplitude and phase of the harmonics, p is the pole pair number, oh r is the angular velocity of rotation. 𝛼 、 f 、 𝛽 and 𝜆 are all natural numbers, indicating the number of cycles in time or space; the " ± " represents the rotation direction of the space-time wave," + " means clockwise rotation," − ” indicates counterclockwise rotation.

[0017] Furthermore, the torque pulsation formation mechanism in step 3 can be based on the following formula:

[0018]

[0019] in, T represents the output torque, L represents the effective axial length, R represents the air gap radius, F tk,±j and 𝜑 tk,±j They represent the spatial order in the air gap respectively. k , the time order is ± j The amplitude and phase of the tangential electromagnetic force harmonics. k ≠0 hours ， The integral result is 0, that is, it does not contribute to the average torque or torque ripple; when k =0 and j =0, the integral result is not 0 and does not contain time variables, that is, it contributes to the average torque but not to the torque ripple; when k =0 and j When ≠0, the integral term result contains time variables but the mean is 0, that is, it does not contribute to the average torque but contributes to the torque ripple.

[0020] Furthermore, the vibration noise formation mechanism in step 3 is based on the formula:

[0021]

[0022] in, m represents the order of radial force, 、 and They are 0-order radial force, 1-order radial force and m Step radial force, 、 and are respectively 、 and The amplitude of the stator deformation under the action of E is the Young's modulus of the stator, r i and N are the stator yoke average radius and stator inner radius respectively, h is the radial thickness of the stator yoke, l is the axial thickness, d is the shaft diameter, L b is the bearing distance. Aside from the special 0th- and 1st-order electromagnetic vibrations, the stator vibration level is proportional to the amplitude of the electromagnetic force and inversely proportional to the fourth power of the electromagnetic force order. This indicates that low-order electromagnetic forces play a dominant role in generating vibration noise in permanent magnet synchronous motors. Furthermore, the time-order characteristics of the two-dimensional electromagnetic force harmonics contributing to electromagnetic vibration are such that the closer their frequency is to the natural frequency, the greater the vibration response.

[0023] Furthermore, for the key electromagnetic force space-time harmonics in step 3, due to the modulation effect of the slotted stator, the high-order electromagnetic force in the air gap will be modulated to a low order by the stator teeth, and the order equivalence relationship can be expressed as follows:

[0024]

[0025] in, i stator and i air They are the order of the electromagnetic force after stator teeth modulation and the order of the electromagnetic force in the air gap that is not modulated by the stator teeth, n is a positive integer, Q s is the number of stator slots.

[0026] Furthermore, the analysis and identification of the coupled space-time waves in step 4 can be performed according to the formula:

[0027]

[0028] in, F r ( θ, t )and Ft ( θ, t ) represent the radial electromagnetic force density and tangential electromagnetic force in the air gap, is the magnetic permeability of air, B r ( θ, t )and B t ( θ, t ) represent radial magnetic flux density and tangential magnetic flux density respectively, i represents a spatial variable, t represents a time variable. Based on the principle of product and difference of trigonometric functions, the harmonic composition of the magnetic field density of a given order of electromagnetic force harmonics can be analyzed. Fourier harmonics can be viewed as rotating vectors. Rotating vectors of the same order rotate synchronously with time and space, and the vector graph they form exhibits time-space invariance. By calculating the projection ratio of the vector to the target vector, the contribution ratio can be determined. Furthermore, by analyzing the spatiotemporal harmonic composition of the magnetic field density of different electromagnetic forces, the coupled spatiotemporal harmonics of torque ripple and vibration noise can be identified.

[0029] Furthermore, the suppression of the key coupled space-time harmonics in step 5 is performed with the key coupled space-time harmonics identified in step 4 as the optimization target, using a structure that does not destroy the periodicity of the magnetic field and combining a multi-objective optimization method to perform parameter optimization.

[0030] Furthermore, the multi-field coupling method in step 6 verifies the torque pulsation and vibration noise of the optimized model, and its main steps are: first, verify the torque pulsation performance and calculate the electromagnetic force of the stator teeth in a two-dimensional electromagnetic field; then, the electromagnetic force calculated by the electromagnetic field is loaded as a load on the stator teeth of the three-dimensional mechanical field model, and the vibration response of the motor housing is calculated by the modal superposition method; finally, the vibration response calculated in the mechanical field is loaded as a load into the acoustic field model to solve the radiated noise.

[0031] The beneficial effects of the present invention are:

[0032] 1. The harmonic analysis method adopted in the present invention breaks through the limitation of traditional harmonic analysis that only considers spatial or temporal harmonics. It is based on the harmonics obtained by two-dimensional Fourier transform and considers the temporal and spatial properties of the harmonics at the same time, which can clearly and accurately reflect the formation mechanism of torque pulsation and vibration noise.

[0033] 2. In the present invention, the air gap magnetic field grid is required to be evenly divided, and the number of nodes is controlled to obtain accurate spatiotemporal waveforms, which helps to achieve a two-dimensional Fourier transform without interpolation errors.

[0034] 3. In the present invention, without destroying the periodicity of the magnetic field, by suppressing the coupled space-time harmonics, the effect of reducing torque pulsation and vibration noise can be achieved at the same time.

[0035] 4. In the present invention, the torque pulsation and vibration noise coupled spatiotemporal harmonic identification method proposed is based on the Maxwell stress tensor method and is applicable to other types of permanent magnet synchronous motors.

[0036] 5. In the present invention, by suppressing the coupled spatiotemporal harmonics of torque ripple and vibration noise, time-consuming multi-physics field coupling optimization is avoided, which helps to quickly and effectively achieve low torque ripple and low vibration noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a structural diagram of a traditional spoke-type permanent magnet synchronous motor (original motor).

[0038] FIG2 is a schematic diagram of the method for identifying and suppressing the coupled space-time harmonics of torque ripple and vibration noise in the present invention.

[0039] FIG3 is a structural diagram of the optimized harmonic injection auxiliary salient pole spoke permanent magnet motor (motor in the embodiment) in the present invention.

[0040] FIG4 is a schematic diagram of the identification of coupled space-time harmonics based on a vector diagram in the present invention.

[0041] FIG5 is a comparison diagram of the output torque of the original motor and the motor of the embodiment of the present invention.

[0042] FIG6 is a comparison diagram of the output torque harmonics of the original motor and the motor of the embodiment of the present invention.

[0043] FIG. 7 is a comparison diagram of the vibration acceleration of the housing surface of the Zhongyuan motor and the motor of the embodiment of the present invention.

[0044] FIG8 is a comparison diagram of the radiated sound pressure levels of the original motor and the motor of the embodiment of the present invention. DETAILED DESCRIPTION

[0045] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention.

[0046] The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0047] like Figure 1 As shown, the traditional spoke-type permanent magnet synchronous motor includes an outer stator 1, an inner rotor 2, and permanent magnets 4; the outer stator 1 includes 40 stator slots and a single-layer integer slot distributed winding 3 embedded therein; the inner rotor 2 includes 8 rotor cores and 8 permanent magnets 4, and the excitation direction of the permanent magnets is shown in the figure.

[0048] like Figure 2As shown, first, a precise finite element model with uniformly distributed air gap grids is used to obtain the two-dimensional space-time electromagnetic force and magnetic density waveforms in the air gap; then a two-dimensional Fourier transform is performed on the space-time waves to obtain the air gap electromagnetic force and magnetic density space-time harmonics, and their physical characteristics are identified at the same time; then, based on the formation mechanism of torque pulsation and vibration noise, the most critical electromagnetic force space-time harmonics are determined; then, the space-time harmonics are regarded as vectors rotating with time and space, and based on the space-time invariance of the graphics composed of vectors of the same order, the magnetic density composition of the electromagnetic force is studied and coupled space-time harmonics are identified; finally, without destroying the periodicity of the magnetic field, the key coupled space-time harmonics are suppressed, and the performance of the optimized model is verified. The final optimization is as follows Figure 3 The harmonic injection-assisted salient pole spoke permanent magnet motor shown in the figure includes an outer stator 1, an inner rotor 2, and permanent magnets 4. The outer stator 1 includes 40 stator slots and a single-layer integer-slot distributed winding 3 embedded therein. The inner rotor 2 is additionally provided with harmonic injection-assisted salient poles 5, forming eight convex rotor cores and eight permanent magnets 4. The excitation directions of the permanent magnets are shown in the figure.

[0049] Taking a 40-slot 8-pole spoke permanent magnet synchronous motor as an example, the method and steps are as follows.

[0050] Step 1: Use the finite element method with uniform air gap grid distribution to obtain the two-dimensional electromagnetic force and magnetic flux density waveforms in the air gap in time and space.

[0051] To avoid errors caused by interpolation, the mesh and nodes in the air gap are evenly distributed along the circumference. In addition, to accurately obtain harmonics with a time order of M-1 and a spatial order of N-1, the number of time steps should be no less than 2M, and the number of air gap mesh divisions along the circumference should be no less than 2N, with both M and N being powers of 2.

[0052] Step 2: Acquisition of air gap electromagnetic force and magnetic field density space-time harmonics and identification of the physical characteristics of magnetic field density space-time harmonics.

[0053] Performing a two-dimensional Fourier transform on the air gap electromagnetic force and magnetic density space-time waves can obtain a series of harmonics with both time and space orders, such as the two-dimensional Fourier harmonic expansion formula of magnetic density:

[0054]

[0055] in, B r ( θ, t )and B t ( θ, t ) represent the radial flux density and tangential flux density in the air gap, i represents a spatial variable, t represents the time variable, B r𝛼,±f and fr𝛼,±f The spatial orders are 𝛼 , the time order is ±f of B r The amplitude and phase of the harmonics, B t𝛽,±𝜆 and f t𝛽,±𝜆 The spatial orders are 𝛽 , the time order is ±𝜆 of B t The amplitude and phase of the harmonics, p is the pole pair number, oh r is the angular velocity of rotation. 𝛼 、 f 、 𝛽 and 𝜆 are all natural numbers, indicating the number of cycles in time or space; the " ± " represents the rotation direction of the space-time wave," + " means clockwise," − ” means counterclockwise. Similarly, the radial electromagnetic force of the air gap can be obtained F r and air gap tangential electromagnetic force F t In order to distinguish the time order and space order of harmonics, the time-related order is described in terms of frequency, that is, the mechanical rotation frequency. f r The spatial order is expressed as a multiple of , while the spatial order is expressed as a number.

[0056] Step 3: According to the generation mechanism of torque pulsation and vibration noise, analyze the electromagnetic harmonic sources of torque pulsation and vibration noise in turn. The two-dimensional electromagnetic harmonic sources that contribute to torque pulsation can be calculated according to the following formula:

[0057]

[0058] in, L represents the effective axial length, R represents the air gap radius, F tk,±j and 𝜑 tk,±j They represent the spatial order in the air gap respectively. k , the time order is ± j The amplitude and phase of the tangential electromagnetic force harmonics. k ≠0 hours ， The integral result is 0, that is, it does not contribute to the average torque or torque ripple; when k =0 and j=0, the integral result is not 0 and does not contain time variables, that is, it contributes to the average torque but not to the torque ripple; when k =0 and j When ≠0, the integral term contains time variables but the mean is 0, that is, it does not contribute to the average torque, but contributes to the torque ripple. Therefore, the electromagnetic force harmonic characteristics that contribute to the torque ripple are: the spatial order is 0 and the time order is not 0 f r The electromagnetic force harmonics that contribute to the original motor's various harmonic torques are listed in Table 1. The order is 0 f r Harmonic torque is the average torque, and the remaining harmonic torques together constitute the torque ripple.

[0059] Table 1 Electromagnetic force harmonics contributing to harmonic torque

[0060]

[0061] Next, we analyze the two-dimensional electromagnetic force harmonics that contribute to electromagnetic vibration, according to the stator deformation formula:

[0062]

[0063] in, m represents the order of radial force, 、 and They are 0-order radial force, 1-order radial force and m Step radial force, 、 and are respectively 、 and The amplitude of the stator deformation under the action of E is the Young's modulus of the stator, r i and N are the stator yoke average radius and stator inner radius respectively, h is the radial thickness of the stator yoke, l is the axial thickness, d is the shaft diameter, L b is the bearing distance. Except for special 0th- and 1st-order electromagnetic vibrations, the stator vibration level is proportional to the amplitude of the electromagnetic force and inversely proportional to the fourth power of the electromagnetic force order. This means that low-order electromagnetic forces play a dominant role in generating vibration noise in permanent magnet synchronous motors. Due to the modulation effect of the slotted stator, high-order electromagnetic forces in the air gap are modulated to low-order forces by the stator teeth. The order equivalence relationship can be expressed as follows:

[0064]

[0065] in, i stator and i air They are the order of the electromagnetic force after stator teeth modulation and the order of the electromagnetic force in the air gap that is not modulated by the stator teeth, n is a positive integer, Q s is the number of slots in the stator. Therefore, even high-order air-gap electromagnetic harmonics cannot be ignored, but generally, only the main air-gap electromagnetic harmonics need to be considered. In addition, the time-order characteristics of the two-dimensional electromagnetic harmonics that contribute to electromagnetic vibration are that the closer their frequency is to the natural frequency, the greater the vibration response will be. The original motor is a symmetrical motor, and the lowest non-zero order of its electromagnetic force wave is equal to the greatest common divisor of the number of slots and the number of poles, which is 8. Its impact on vibration noise can be ignored. Therefore, the main contributor to the vibration noise of the original motor is the zero-order electromagnetic force wave. According to the above rules, the two-dimensional electromagnetic force harmonics that contribute most to vibration noise can be found. The radial electromagnetic force wave that contributes most to the vibration noise of the original motor is listed in Table 2. It is worth noting that both radial electromagnetic force waves and tangential electromagnetic force waves will contribute to vibration noise, and tangential electromagnetic force waves of the same order also need to be considered.

[0066] Table 2 Radial electromagnetic force waves that contribute most to vibration noise

[0067]

[0068] Step 4: Analyze the magnetic density harmonic composition of electromagnetic force harmonics based on the vector diagram, and identify the coupled space-time harmonics of torque pulsation and vibration noise according to the formula:

[0069]

[0070] in, F r ( θ, t )and F t ( θ, t ) represent the radial electromagnetic force density and tangential electromagnetic force in the air gap, is the magnetic permeability of air, B r ( θ, t )and B t ( θ, t ) represent radial magnetic flux density and tangential magnetic flux density respectively, i represents a spatial variable, t Represents the time variable. According to the principle of product and difference of trigonometric functions, the magnetic density harmonics that contribute to a certain order of electromagnetic force harmonics can be obtained. For example, the order is (A f r,B) are generated by the interaction of magnetic density harmonics with a time order sum (difference) of A and a space order sum (difference) of B. Two-dimensional Fourier harmonics can be viewed as a series of rotating vectors. Rotating vectors of the same order rotate synchronously with time and space. The vector graphics they form have time and space invariance. By calculating the projection ratio of the vector to the target vector, the contribution ratio can be determined. Furthermore, by analyzing the time and space harmonic composition of magnetic density of different electromagnetic forces, the coupled time and space harmonics of torque pulsation and vibration noise can be identified. Figure 4 Shows the order (-40 f r ,0) F r and the order is (-40 f r ,0) F t The magnetic density harmonic composition. It can be seen that the contribution order is (-40 f r ,0) F r and F t The main magnetic density harmonics of the harmonics are almost the same, which is (-36 f r ,36)、(-44 f r ,44)、(4 f r ,36) and (-4 f r ,44) B r Harmonics, they are also 40 f r The main sources of harmonic torque and vibration noise are determined to be 40 f r The coupled space-time harmonics of torque ripple and vibration noise at the same frequency can be identified. Similarly, the coupled space-time harmonics of torque ripple and vibration noise at other key frequencies can be identified.

[0071] Step 5: Use the modified auxiliary salient pole rotor combined with the multi-objective optimization method to suppress the magnetic density harmonics found in step 4 that significantly contribute to both torque pulsation and vibration noise. The multi-objective optimization method used is fast and effective. The mathematical model obtained by response surface fitting is used instead of the time-consuming finite element calculation. The intelligent optimization algorithm is combined to perform parameter optimization to obtain the optimal solution. In order to ensure that the torque pulsation and vibration noise are reduced at the same time without reducing the torque density, the (-4 f r ,4) B r Harmonics as a constraint, suppressing (-36 f r,36) and (-44 f r ,44) B r Harmonics is used as the optimization target, and the final optimization result is as follows Figure 3 The harmonic injection auxiliary salient pole spoke permanent magnet motor. The comparison of the magnetic flux harmonic amplitude of the original motor and the embodiment motor is shown in Table 3. f r ,4) is the main source of the average torque, and the other magnetic density harmonics are 40 f r , 80 f r and 120 f r The main source of harmonic torque and vibration noise. The performance changes after optimization can be predicted from the change amplitude: the average torque remains almost unchanged, the torque ripple is greatly reduced, and the vibration noise of each order is significantly reduced.

[0072] Table 3 Comparison of radial magnetic flux harmonics before and after optimization

[0073]

[0074] Step 6: Verify the torque ripple and vibration noise of the optimized motor by using the multi-field coupling method of electromagnetic field, mechanical field and acoustic field.

[0075] Figure 5 and Figure 6 The figure shows the comparison between the original motor and the embodiment motor in terms of final output torque and harmonic analysis. Figure 5 As shown in FIG, compared with the original motor, the average torque of the motor of the embodiment remains almost unchanged, while the torque ripple is significantly reduced. Figure 6 As shown, compared with the original motor, the torque of the embodiment motor is 0 f r The order is slightly reduced, and 40 f r , 80 f r and 120 f r The order is significantly reduced. Compared with the original motor, the average torque of the motor in the embodiment is reduced from 6.31Nm to 6.23Nm, and the torque ripple is reduced from 72.9% to 8.55%.

[0076] Figure 7 The figure is a comparison of the vibration acceleration of the motor housing surface of the original motor and the motor of the embodiment of the present invention. Figure 7 As shown in the figure, the vibration acceleration of the motor in the embodiment is significantly reduced compared with the original motor. f rThe vibration acceleration of the order is 0.202m / s 2 Reduced to 0.060m / s 2 , 80 f r The vibration acceleration of the order is 0.177m / s 2 Reduced to 0.027m / s 2 , 120 f r The vibration acceleration of the order is 0.161m / s 2 Reduced to 0.007m / s 2 .

[0077] Figure 8 This is a comparison of the sound pressure levels at a point 40 cm outside the housing of the original motor and the motor of the embodiment of the present invention. Figure 8 As shown in the figure, the sound pressure level of the motor in the embodiment is significantly reduced compared with the original motor. f r The sound pressure level of the order is reduced from 53.68dB to 42.36dB, 80 f r The sound pressure level of the order is reduced from 47.24dB to 30.56dB, 120 f r The sound pressure level of the order is reduced from 44.88dB to 17.48dB.

[0078] In summary, the present invention discloses a method for identifying and suppressing coupled space-time harmonics of torque pulsation and vibration noise, which relates to the field of harmonic analysis and optimization of the air gap magnetic field of permanent magnet motors. This method breaks through the limitation of traditional harmonic analysis that only considers one-dimensional spatial or temporal harmonics, and conducts research based on harmonics obtained by two-dimensional Fourier transform. The proposed method includes: using a precise finite element model with a uniform air gap grid to obtain the two-dimensional space-time electromagnetic force and magnetic flux waveforms in the air gap; obtaining and identifying the physical characteristics of the space-time harmonics of the electromagnetic force and magnetic flux density in the air gap; determining the most critical space-time harmonics of the electromagnetic force based on the formation mechanism of torque pulsation and vibration noise; treating the space-time harmonics as vectors that rotate with time and space, and based on the spatial and temporal invariance of the graph composed of vectors of the same order, studying the magnetic flux density composition of the electromagnetic force and identifying coupled space-time harmonics; suppressing the key coupled space-time harmonics without destroying the periodicity of the magnetic field; and verifying the torque pulsation and vibration noise of the optimized model through a multi-field coupling method. This method can accurately identify the coupled space-time harmonics of torque pulsation and electromagnetic vibration, thereby making it possible to simultaneously suppress torque pulsation and vibration noise. By using a modified auxiliary salient-pole rotor combined with a multi-objective optimization method to suppress critical coupled spatiotemporal harmonics, time-consuming multi-physics field optimization is avoided, allowing for rapid and effective reduction of torque ripple and vibration noise. Furthermore, the proposed method for identifying coupled spatiotemporal harmonics of torque ripple and vibration noise, based on the Maxwell stress tensor method, is applicable to other types of permanent magnet synchronous motors.

[0079] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, illustrative uses of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0080] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

Claims

1. A method for identifying and suppressing torque ripple and vibration noise coupled spatiotemporal harmonics, characterized in that: The following steps are involved: Step 1: Using the finite element method with uniform air gap grid distribution, the electromagnetic force and magnetic flux density waveforms in the air gap are obtained in two dimensions of space and time. Step 2: Acquisition of the air gap electromagnetic force and magnetic field density space-time harmonics and identification of the physical characteristics of magnetic field density space-time harmonics; Step 3: Determine the most critical electromagnetic force time-space harmonics based on the formation mechanism of torque ripple and vibration noise; Step 4: Consider the spacetime harmonics as vectors that rotate with time and space. Based on the spacetime invariance of the graphs composed of vectors of the same order, study the magnetic density composition of the electromagnetic force and identify the coupled spacetime harmonics. Step 5: Suppress the key coupled space-time harmonics without destroying the periodicity of the magnetic field; Step 6: Verify the torque ripple and vibration noise of the optimized model through the multi-field coupling method; The physical characteristics identification process of the magnetic field density space-time harmonics in step 2 is: according to the two-dimensional harmonic expansion formula of the magnetic field density, the following is obtained: Among them, B r (θ, t) and B t (θ, t) represent radial magnetic flux density and tangential magnetic flux density respectively, θ represents spatial variable, t represents time variable, B rα,±f and They are B with spatial order α and time order ±f respectively. r Amplitude and phase of harmonics, B tβ,±λ and They are B with spatial order β and time order ±λ respectively. t The amplitude and phase of the harmonics, p is the number of pole pairs, ω r is the angular velocity of rotation, α, f, β and λ are all natural numbers, indicating the number of cycles in time or space; the "±" before the time order indicates the rotation direction of the space-time wave, "+" indicates clockwise rotation, and "-" indicates counterclockwise rotation; The torque pulsation formation mechanism in step 3 is obtained according to the following formula: Among them, T represents the output torque, L represents the effective axial length, R represents the air gap radius, and F tk,±j and They represent the amplitude and phase of the tangential electromagnetic force harmonics with spatial order k and time order ±j in the air gap, respectively. When k≠0, the integral term is 0, which means it does not contribute to the average torque or torque ripple. When k=0 and j=0, the integral term is not 0 and does not contain time variables, which means it contributes to the average torque but not to the torque ripple. When k=0 and j≠0, the integral term contains time variables but the mean is 0, which means it does not contribute to the average torque but contributes to the torque ripple. θ represents the spatial variable, t represents the time variable, p is the pole pair number, ω r is the angular velocity of rotation; The coupled space-time harmonics in step 4 are identified according to the following formula: Among them, F r (θ, t) and F t (θ, t) represent the radial electromagnetic force density and tangential electromagnetic force in the air gap, μ0 is the magnetic permeability of air, B r (θ, t) and B t (θ, t) represent radial magnetic flux density and tangential magnetic flux density, respectively, θ represents spatial variable, and t represents time variable; According to the principle of product and difference of trigonometric functions, the harmonic composition of the magnetic density of a certain order of electromagnetic force harmonics is analyzed. Fourier harmonics can be regarded as rotating vectors. Rotating vectors of the same order rotate synchronously with time and space. The vector graphics they constitute have time and space invariance. By calculating the projection ratio of the vector to the target vector, the contribution ratio is determined. Furthermore, by analyzing the time and space harmonic composition of the magnetic density of different electromagnetic forces, the coupled time and space harmonics of torque pulsation and vibration noise are identified.

2. A method for identifying and suppressing torque ripple and vibration noise coupled spatiotemporal harmonics according to claim 1, characterized in that: In step 1, the grids and nodes in the air gap are required to be evenly distributed along the circumferential direction, and there is a limit on the number of grid divisions. In order to accurately obtain harmonics with a time order of M-1 and a spatial order of N-1, the number of time steps should be no less than 2M, and the number of air gap grid divisions along the circumferential direction should be no less than 2N, and both M and N are exponential powers of 2.

3. The method for identifying and suppressing torque ripple and vibration noise coupled spatiotemporal harmonics according to claim 1, characterized in that: The vibration noise formation mechanism in step 3 is obtained according to the formula: Where m represents the order of radial force, σ0, σ1 and σ m They are 0-order radial force, 1-order radial force and m-order radial force, Y0, Y1 and Y m≥2 are affected by σ0, σ1 and σ m The amplitude of the stator deformation under the action, E is the Young's modulus of the stator, r i and N are the average radius of the stator yoke and the inner radius of the stator, h is the radial thickness of the stator yoke, l is the axial thickness, d is the diameter of the shaft, L b is the bearing distance. Except for the special 0th-order and 1st-order electromagnetic vibrations, the stator vibration level is proportional to the amplitude of the electromagnetic force and inversely proportional to the fourth power of the electromagnetic force order. That is, the low-space-order electromagnetic force plays a dominant role in the generation of vibration noise in the permanent magnet synchronous motor. In addition, the time-order characteristic of the two-dimensional electromagnetic force harmonics that contribute to the electromagnetic vibration is that the closer its frequency is to the natural frequency, the greater the vibration response will be.

4. The method for identifying and suppressing torque ripple and vibration noise coupled spatiotemporal harmonics according to claim 1, characterized in that: The key electromagnetic force space-time harmonics in step 3 are modulated by the stator teeth to low order due to the modulation effect of the slotted stator. The order equivalence relationship can be expressed as follows: Among them, i stator and i air They are the order of the electromagnetic force after stator tooth modulation and the order of the electromagnetic force in the air gap that is not modulated by the stator teeth, n is a positive integer, Q s is the number of stator slots.

5. The method for identifying and suppressing torque ripple and vibration noise coupled spatiotemporal harmonics according to claim 1, characterized in that: The process of suppressing the key coupled space-time harmonics in step 5 is as follows: taking the coupled space-time harmonics identified in step 4 as the optimization target, using a structure that does not destroy the periodicity of the magnetic field, and combining a multi-objective optimization method to perform parameter optimization.

6. The method for identifying and suppressing coupled space-time harmonics of torque ripple and vibration noise according to claim 1, characterized in that: The specific steps of step 6 are: first, verify the torque pulsation performance and calculate the electromagnetic force of the stator teeth in a two-dimensional electromagnetic field; then, load the electromagnetic force calculated in the electromagnetic field as a load onto the stator teeth of the three-dimensional mechanical field model, and calculate the vibration response of the motor housing by the modal superposition method; finally, load the vibration response calculated in the mechanical field as a load into the acoustic field model to solve the radiated noise.

Images