Method and System for Calculating the No-Load Magnetic Field of Surface-Mounted Permanent Magnet Synchronous Motors with Unequal Thickness Poles

Abstract

This invention proposes a method and system for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal-thickness magnetic poles. Relating to the field of permanent magnet motor magnetic field calculation, the invention divides the solution domain of the surface-mounted permanent magnet synchronous motor into subdomains and determines the basic structural parameters of each subdomain. Using the separation of variables method, based on the basic structural parameters of each subdomain, a general solution expression for the vector magnetic potential containing undetermined coefficients is determined for each subdomain. Based on the general solution expression for the vector magnetic potential in each subdomain, combined with the boundary conditions of adjacent subdomains, the vector magnetic potential in each subdomain is iteratively calculated until the iteration stops, yielding the final vector magnetic potential in each subdomain. Based on the final vector magnetic potential in each subdomain, the no-load magnetic field of the motor is calculated. This invention considers the effects of stator slotting, unequal-thickness permanent magnets, and core saturation, accurately determining the magnetic field of each part of the motor, laying a theoretical foundation for subsequent calculations of motor electromagnetic parameters, motor optimization design, and electromagnetic vibration reduction.

Description

Technical Field

[0001] This invention belongs to the field of magnetic field calculation for permanent magnet motors, and particularly relates to a method and system for calculating the no-load magnetic field of a permanent magnet synchronous motor with surface-mounted poles of unequal thickness. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] In recent years, with the continuous expansion of the application scenarios of permanent magnet synchronous motors, high-performance, low-torsional-vibration, and low-noise permanent magnet synchronous motors have become increasingly popular. The vibration and noise levels of motors have become an important indicator for measuring motor performance. In high-speed and high-power applications where motor performance requirements are high, the torsional vibration of the motor will directly affect the overall system's operational stability and reliability. Improving motor performance and reducing motor torsional vibration have become key issues that urgently need to be addressed.

[0004] The interaction between the back EMF harmonics and the stator current in a permanent magnet synchronous motor generates electromagnetic torque fluctuations, which in turn excite torsional vibrations in the motor. Therefore, in the initial stage of motor design, an unequal-thickness magnetic pole structure can be used to weaken the back EMF harmonic components, thereby reducing the electromagnetic torque fluctuations and the torsional vibrations they generate, and improving the motor's operational stability. To determine the structural parameters of the unequal-thickness magnetic poles, an improved method for calculating the motor's magnetic field needs to be proposed to achieve rapid and accurate calculation of the magnetic field during the motor optimization process.

[0005] Currently, the calculation and analysis of motor magnetic fields mainly employ three methods: magnetomotive force-permeability method, analytical magnetic field method, and finite element method. The magnetomotive force-permeability method can directly obtain information such as the frequency, rotational speed, and phase of the air gap magnetic flux density, but it is difficult to accurately calculate the air gap permeability, making it more suitable for qualitative analysis of the magnetic field. Existing analytical magnetic field methods can quickly calculate the motor's magnetic field, but it is difficult to simultaneously consider the influence of factors such as stator slotting, unequal thickness magnetic pole structure, and core saturation, resulting in lower calculation accuracy. The finite element method can consider the influence of multiple factors such as core saturation and complex motor structure, and can accurately calculate the motor's magnetic field, but the calculation speed is slow, and it is difficult to directly embed into optimization algorithms, lacking convenience in the initial design stage of the motor. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, this invention provides a method and system for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles. Considering the effects of stator slotting, unequal thickness permanent magnets, and core saturation, the method accurately determines the magnetic field of each part of the motor, laying a theoretical foundation for subsequent calculation of motor electromagnetic parameters, motor optimization design, and electromagnetic vibration reduction.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0008] The first aspect of this invention provides a method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal-thickness magnetic poles.

[0009] The calculation method for the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles includes:

[0010] The solution domain for the magnetic field of a surface-mounted permanent magnet synchronous motor is divided into subdomains, and the basic structural parameters of each subdomain are determined.

[0011] Using the method of separation of variables, the vector magnetic potential general solution expression containing undetermined coefficients in each subdomain is determined based on the basic structural parameters of each subdomain;

[0012] Based on the general solution expression of the vector magnetic potential in each subdomain, and combined with the boundary conditions of adjacent subdomains, the vector magnetic potential in each subdomain is calculated iteratively until the iteration stopping condition is met, and the final vector magnetic potential in each subdomain is obtained.

[0013] The no-load magnetic field of the motor is calculated based on the final vector magnetic potential in each subdomain.

[0014] The iterative calculation of the vector magnetic potential in each subdomain is based on the vector magnetic potential in each subdomain during the previous iteration. The value of the stator slot surface current used to characterize the effect of stator core saturation is calculated, and then the boundary conditions are reconstructed and the current vector magnetic potential in each subdomain is calculated.

[0015] Furthermore, the subdomains include permanent magnets, air gaps, stator slots, and stator slot openings.

[0016] Furthermore, determining the basic structural parameters of each subdomain specifically involves:

[0017] Based on the motor's structural dimensions, the stator slots and stator slot openings are transformed into radial sectors, and their main structural dimensions are determined. The air gap is transformed into an annular shape, and its main structural dimensions are determined. The permanent magnet is divided into a series of radial sectors, and the main structural dimensions of each sector are determined.

[0018] Furthermore, the specific calculation process of the vector magnetic potential general solution expression in each subdomain is as follows:

[0019] By using the method of separation of variables, the general solution expression of vector magnetic potential in each subdomain containing undetermined coefficients is obtained;

[0020] By solving the system of equations based on the boundary conditions, the specific values ​​of the undetermined coefficients in the general solution expression of the vector magnetic potential in each subdomain are determined, thus obtaining the final specific expression of the vector magnetic potential in each subdomain.

[0021] Furthermore, the vector magnetic potential solution expression within the permanent magnet is:

[0022]

[0023] Among them, A u B u C u D u r are undetermined coefficients. u and r u-1 These are the top and bottom radii of the permanent magnet subdomain u, respectively. pu For a particular solution related to the remanence of the permanent magnet and the corresponding pole arc coefficient, k = 1, 2, 3…;

[0024] The vector magnetic potential flux solution expression within the air gap is:

[0025]

[0026] Among them, A g B g C g D g r are undetermined coefficients. s and r U These are the top and bottom radii of the air gap subdomain, respectively.

[0027] Furthermore, the final vector magnetic potential within each subdomain is specifically as follows:

[0028] In the first iteration, the initial value of the added surface current is set to 0, and the vector magnetic potential in each subdomain is calculated. In the next iteration, the value of the added surface current and the vector magnetic potential are recalculated based on the vector magnetic potential obtained in the previous iteration. This iterative process is repeated until the rate of change of the surface current obtained in the previous two iterations is lower than the set rate of change threshold. Then, the vector magnetic potential obtained in this iteration is the final vector magnetic potential.

[0029] Furthermore, the surface current value added during the iteration process is calculated based on the motor's magnetic flux and magnetic reluctance, which are calculated based on the vector magnetic potential and the core magnetization curve.

[0030] The second aspect of the present invention provides a system for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles.

[0031] A system for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal-thickness poles includes a subdomain partitioning module, an expression determination module, a magnetic potential calculation module, and a magnetic field calculation module.

[0032] The subdomain partitioning module is configured to: partition the solution domain of the magnetic field of the surface-mounted permanent magnet synchronous motor into subdomains and determine the basic structural parameters of each subdomain;

[0033] The expression determination module is configured to: use the separation of variables method to determine the vector magnetic potential general solution expression containing undetermined coefficients in each subdomain based on the basic structural parameters of each subdomain;

[0034] The magnetic potential calculation module is configured to: iteratively calculate the vector magnetic potential in each subdomain based on the general solution expression of the vector magnetic potential in each subdomain and the boundary conditions of adjacent subdomains, until the iteration stopping condition is met, and obtain the final vector magnetic potential in each subdomain;

[0035] The magnetic field calculation module is configured to calculate the no-load magnetic field of the motor based on the final vector magnetic potential in each subdomain.

[0036] The iterative calculation of the vector magnetic potential in each subdomain is based on the vector magnetic potential in each subdomain during the previous iteration. The value of the stator slot surface current used to characterize the effect of stator core saturation is calculated, and then the boundary conditions are reconstructed and the current vector magnetic potential in each subdomain is calculated.

[0037] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in the method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal-thickness magnetic poles as described in the first aspect of the present invention.

[0038] The fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles as described in the first aspect of the present invention.

[0039] The above one or more technical solutions have the following beneficial effects:

[0040] This invention provides a method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal-thickness poles. By employing an improved analytical method, the no-load magnetic field of this type of motor is calculated, significantly reducing computation time compared to finite element simulation. Furthermore, it can consider the influence of factors such as stator slotting, unequal-thickness permanent magnets, and core saturation on the motor's magnetic field, achieving higher calculation accuracy than general analytical methods. This disclosure facilitates the calculation of motor magnetic fields and electromagnetic parameters, laying the foundation for the electromagnetic design of permanent magnet synchronous motors.

[0041] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0042] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0043] Figure 1 This is a flowchart of the method in the first embodiment.

[0044] Figure 2 This is a schematic diagram of the unequal thickness magnetic pole structure in the first embodiment;

[0045] Figure 3 This is a schematic diagram of the unequal thickness magnetic pole structure division in the first embodiment;

[0046] Figure 4 This is a schematic diagram of the surface current added to the stator slot in the first embodiment;

[0047] Figure 5 The finite element simulation model of the surface-mounted permanent magnet synchronous motor in the first embodiment;

[0048] Figure 6 This is a schematic diagram of the circumferential distribution of the air gap magnetic flux density under one magnetic pole in the first embodiment;

[0049] Figure 7 shows the no-load back EMF curve of the motor in one electrical cycle of the first embodiment;

[0050] Figure 8 The electromagnetic torque curve of the motor under rated load conditions in the first embodiment is shown. Detailed Implementation

[0051] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0052] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0053] Example 1

[0054] In one or more embodiments, a method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal-thickness magnetic poles is disclosed, comprising the following steps:

[0055] Step S1: Divide the solution domain of the magnetic field of the surface-mounted permanent magnet synchronous motor into subdomains and determine the basic structural parameters of each subdomain;

[0056] Step S2: Using the method of separation of variables, determine the vector magnetic potential general solution expression containing undetermined coefficients in each subdomain based on the basic structural parameters of each subdomain;

[0057] Step S3: Based on the general solution expression of the vector magnetic potential in each subdomain and combined with the boundary conditions of adjacent subdomains, iteratively calculate the vector magnetic potential in each subdomain until the iteration stopping condition is met, and obtain the final vector magnetic potential in each subdomain.

[0058] Step S4: Calculate the no-load magnetic field of the motor based on the final vector magnetic potential in each subdomain;

[0059] The iterative calculation of the vector magnetic potential in each subdomain is based on the vector magnetic potential in each subdomain during the previous iteration. The value of the stator slot surface current used to characterize the effect of stator core saturation is calculated, and then the boundary conditions are reconstructed and the current vector magnetic potential in each subdomain is calculated.

[0060] The following is a detailed explanation of the implementation process of the no-load magnetic field calculation method for the surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles in this embodiment.

[0061] As described in the background section, with the continuous expansion of applications for permanent magnet synchronous motors (PMSMs), high-performance, low-torsional-vibration, and low-noise PMSMs are becoming increasingly popular. Motor vibration and noise levels have become important indicators for evaluating motor performance. In high-speed, high-power applications where motor performance is critical, torsional vibration directly affects the overall system's operational stability and reliability. Therefore, improving motor performance and reducing torsional vibration have become key issues that urgently need to be addressed.

[0062] In permanent magnet synchronous motors (PMSMs), the interaction between back EMF harmonics and stator current generates electromagnetic torque fluctuations, which in turn excite torsional vibration. Therefore, in the initial design stage of the motor, an unequal-thickness magnetic pole structure can be used to weaken the back EMF harmonic components, thereby reducing electromagnetic torque fluctuations and the torsional vibration they induce, and improving the motor's operational stability. To determine the structural parameters of the unequal-thickness magnetic poles, a method for calculating the motor's magnetic field needs to be proposed. An improved analytical method can be used to achieve rapid and accurate calculation of the magnetic field during the motor optimization process, such as... Figure 1 As shown, it includes the following steps:

[0063] (1) Divide each subdomain according to the motor structure parameters and determine the basic structure parameters corresponding to each subdomain.

[0064] For ease of analysis, it is stipulated that the axis of the permanent magnet coincides with the axis of the A-phase winding at the initial moment of the simulation. For example... Figure 2As shown, the thickness of the permanent magnet is not uniform, and the maximum thickness of the permanent magnet is h. max The minimum thickness is h min At this point, the thickness h(θ) of the permanent magnet can be calculated as follows:

[0065]

[0066] In the formula, r r r is the outer diameter of the rotor. h Let O be the distance between O and O1, and θ be the angle between O and the center line of the magnetic pole.

[0067] The solution domain for the motor magnetic field is divided into subdomains such as permanent magnet, air gap, stator slot, and stator slot opening. The shape of each subdomain needs to be transformed into a radial sector or a ring: the stator slot and stator slot opening are transformed into radial sectors, the air gap is a ring, and the permanent magnet is transformed into a combination of a series of radial sectors.

[0068] Specifically, the permanent magnet under each pole is divided into U sector-shaped regions, and all the regions u under the poles constitute a permanent magnet subdomain u (here u = 1, 2, 3…U). The structural division diagram is shown below. Figure 3 As shown. Figure 3 As shown, the main structural parameters of the sector region u are as follows: r u-1 and r u These are the bottom radius and the top radius, respectively. The width angle can be calculated as b. u =α p π / p-2(u-1)·b0. Where, r u It can be calculated as:

[0069]

[0070] In the formula, θ u =α p π / (2p)-(u-0.5)·b0,α p Let r be the corresponding polar arc coefficient, p be the polar logarithm, and r0 = r r .

[0071] (2) Set the initial value of the added surface current to 0, and use the subdomain method to determine the vector magnetic potential in each subdomain of the motor under this state, so as to obtain the no-load magnetic field of the motor.

[0072] A surface current is added, which generates a magnetomotive force to counteract the magnetic voltage drop in the stator core. The basic principle is as follows: the effect of stator core saturation is characterized by adding a surface current within the stator slots. Figure 4 As shown. Figure 4 middle, I t2i and I t1(i+1) It is the line current added to both sides of the i-th stator tooth, I j1i and Ij2i It is the line current added to the inside of the i-th stator yoke. t2i and I t1(i+1) Generates a magnetomotive force to counteract the magnetic voltage drop of the i-th stator tooth; I j1i and I j2i A magnetomotive force is generated to counteract the magnetic voltage drop of the i-th stator yoke.

[0073] I t2i I t1(i+1) I j1i and I j2i The initial value is set to 0. In each subsequent iteration, it can be calculated as follows:

[0074]

[0075] In the formula, φ ti and φ ji R represents the magnetic flux flowing through the i-th stator tooth and the i-th stator yoke, respectively. ti and R ji These are the magnetic reluctances of the i-th stator tooth and the i-th stator yoke, respectively. The magnetic flux and magnetic reluctance can be calculated from the vector magnetic potential and the core magnetization curve.

[0076] The added surface current can be calculated as follows:

[0077] I 1i =I t1i +I y1i I 2i =I t2i +I y2i (4)

[0078] Calculate the surface current density J based on the surface current. 1i and J 2i This, in turn, changes the vector magnetic potential A within the stator slot subdomain. zs That is, the following formula (6).

[0079] Specifically, the vector magnetic potential within each subdomain of the motor is determined using the subdomain method, as follows:

[0080] By combining the subdomain method to calculate the vector magnetic potential within each subdomain, and then calculating the no-load magnetic field of the motor, A zu A represents the vector magnetic potential within the permanent magnet subdomain u. zsi A represents the vector magnetic potential within the i-th stator slot subdomain. zoi A represents the vector magnetic potential of the i-th stator slot. zg This represents the vector magnetic potential within the air gap subdomain.

[0081] Assuming linear demagnetization of the permanent magnet and neglecting the effects of eddy currents, the vector magnetic potential A within the permanent magnet subdomain u is... zu Satisfy the following equation:

[0082]

[0083] In the formula, r and α are the radial and tangential positions, respectively, μ0 is the free permeability, and M... r The magnetization intensity of the permanent magnet.

[0084] The vector magnetic potential A within the i-th stator slot subdomain zsi satisfy:

[0085]

[0086] In the formula, J i The surface current density, the current density in the i-th stator slot can be expanded as:

[0087]

[0088]

[0089] In the formula, n = 1, 2, 3, ..., E n =nπ / b sa b sa α is the stator slot width angle. i Let be the position angle of the center of the i-th stator slot in the stator polar coordinate system.

[0090] The vector magnetic potential A in the i-th stator slot and air gap subdomain zoi and A zg satisfy:

[0091]

[0092] The method of separation of variables is used to solve the problem, and the general solution expression for the vector magnetic potential in each subdomain is obtained. The vector magnetic potential A in the permanent magnet subdomain u is... zu The expression is:

[0093]

[0094] By combining the boundary conditions and solving the system simultaneously, the specific values ​​of the undetermined coefficients in the general solution expression of the vector magnetic potential in each subdomain are determined, thereby obtaining the specific expression of the vector magnetic potential.

[0095] The tangential component of the magnetic field strength at the interface between the permanent magnet subdomain 1 and the rotor core is 0. Combining with formula (10), the following equation can be obtained:

[0096]

[0097] The tangential components of the vector magnetic potential and magnetic field strength at the interface between the permanent magnet subdomains u and u+1 (where u = 1, 2, 3…U-1) are continuous, therefore the following equation can be obtained:

[0098]

[0099]

[0100] The vector magnetic potential A within the air gap is obtained by using the method of separation of variables. zg The expression is:

[0101]

[0102] The tangential components of the vector magnetic potential and magnetic field strength at the interface between the permanent magnet subdomain U and the air gap subdomain are continuous, therefore the following equation can be obtained:

[0103]

[0104]

[0105] Using the method of separation of variables, the general solution expression A for the vector magnetic potential of the i-th stator slot and the stator slot opening can be obtained. zsi and A zoi , respectively

[0106]

[0107]

[0108] In the formula, r t and r sb These are the top and bottom radii of the stator slot, respectively, B. si D si These are coefficients to be determined.

[0109]

[0110] In the formula, m = 1, 2, 3, ..., F m =mπ / b oa A oi B oi C oi and D oi r are undetermined coefficients. s Let b be the inner radius of the stator. oa The width angle of the stator slot.

[0111] Based on the boundary conditions at the interfaces between the stator slots and the stator slot openings, as well as between the stator slot openings and the air gap, the correlation between the undetermined coefficients in the general solution expressions for the vector magnetic potential within the stator slots, stator slot openings, and air gap is obtained, but will not be elaborated upon here.

[0112] The above relational equations are integrated into the form of the following matrix equations, and numerical solutions are used to obtain the specific values ​​of the undetermined coefficients in the general solution expression of the vector magnetic potential in each subdomain. Based on the vector magnetic potential, the magnetic field in each subdomain is calculated.

[0113] TA·[A u B u C u D u …A g B g C g D g ] T =TY (20)

[0114] Among them, TA and TY are coefficient matrices obtained by simplifying the equations derived from the boundary conditions.

[0115] By solving formula (20), the specific expressions for the vector magnetic potential in each subdomain are obtained.

[0116] (3) Based on the vector magnetic potential in each subdomain obtained in step (2), use iterative calculation of the vector magnetic potential as the initial value; during the iteration process, combine the magnetic circuit method to calculate the specific value of the added surface current and replace the original value to recalculate the vector magnetic potential in each subdomain. When the rate of change of the surface current obtained in the previous two iterations is lower than the set rate of change threshold, the iteration stops. Based on the final vector magnetic potential in each subdomain, calculate and output the unloaded magnetic field. In this embodiment, the rate of change threshold is set to 1%.

[0117] The above method is an improved analytical method. The improvement lies in the fact that, during the iterative calculation process, the influence of stator core saturation is characterized by adding surface current in the stator slots. The influence of factors such as stator slotting, unequal thickness permanent magnets, and core saturation on the motor magnetic field is considered, thereby improving the calculation accuracy of the motor magnetic field.

[0118] The accuracy of this magnetic field calculation method was verified using the finite element method.

[0119] To verify the accuracy of the above analytical calculation method for the magnetic field, a 6-pole, 36-slot surface-mounted permanent magnet synchronous motor with unequal-thickness magnetic poles is selected as an example for analysis. Its main structural dimensional parameters are shown in Table 1, and the finite element simulation model is as follows. Figure 5 As shown.

[0120] Table 1 Main structural dimensions of surface-mounted permanent magnet synchronous motor

[0121]

[0122] Figure 5The figure shows the finite element simulation model of the motor. The magnetic field is calculated using the proposed analytical magnetic field calculation method, and the Maxwell 2D static field solver is used for simulation analysis. The distribution of the air gap magnetic flux density along the circumferential direction under one magnetic pole is shown below. Figure 6 As shown, Figure 6 The analytical calculation results of the air gap magnetic flux density are also given without considering core saturation. Analytical method 1 considers core saturation, while analytical method 2 does not. Figure 6 It can be seen that, considering core saturation, the analytical calculation results of the unloaded air gap magnetic flux density are in good agreement with the finite element simulation results, verifying the accuracy of the proposed analytical calculation method. Furthermore, from... Figure 6 It can be seen that core saturation has a significant impact on the air gap magnetic field. The air gap magnetic flux density obtained without considering core saturation is significantly larger. This indicates that the proposed analytical calculation method for the magnetic field has higher calculation accuracy compared with the existing analytical method that does not consider core saturation.

[0123] Compared with finite element simulation, the analytical method is faster. When performing static field simulation of this motor, the analytical method takes about 1 second, while the finite element simulation takes more than 20 seconds. The comparison results show that the proposed analytical calculation method has a significant advantage in terms of calculation speed.

[0124] Figure 7 shows the no-load back EMF curve of the A-phase winding of the unequal-thickness pole motor within one electrical cycle, and also shows the corresponding no-load back EMF curve of the A-phase winding of the motor with uniform permanent magnet thickness. As shown in Figure 7(a), when using the unequal-thickness pole structure, the back EMF curve is approximately sinusoidal with very low harmonic content; Figure 7(b) shows that when the permanent magnet thickness is uniform, the harmonic content of the motor's back EMF is relatively high.

[0125] According to the law of conservation of energy, the electromagnetic torque is generated by the interaction between the back EMF and the stator current of the surface-mounted permanent magnet synchronous motor. Figure 8 The electromagnetic torque of the two motors under rated load conditions was compared. Motor 1 had a uniform permanent magnet thickness, while Motor 2 had an uneven permanent magnet thickness. Figure 8 It is known that the back EMF harmonic content of the unequal-thickness magnetic pole motor is very low, thus its electromagnetic torque fluctuation is significantly reduced. Electromagnetic torque fluctuation excites torsional vibration in the motor; therefore, torsional vibration can be reduced by employing an unequal-thickness magnetic pole structure.

[0126] Example 2

[0127] In one or more embodiments, a system for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal-thickness magnetic poles is disclosed, including a subdomain partitioning module, an expression determination module, a magnetic potential calculation module, and a magnetic field calculation module:

[0128] The subdomain partitioning module is configured to: partition the solution domain of the magnetic field of the surface-mounted permanent magnet synchronous motor into subdomains and determine the basic structural parameters of each subdomain;

[0129] The expression determination module is configured to: use the separation of variables method to determine the vector magnetic potential general solution expression containing undetermined coefficients in each subdomain based on the basic structural parameters of each subdomain;

[0130] The magnetic potential calculation module is configured to: iteratively calculate the vector magnetic potential in each subdomain based on the general solution expression of the vector magnetic potential in each subdomain and the boundary conditions of adjacent subdomains, until the iteration stopping condition is met, and obtain the final vector magnetic potential in each subdomain;

[0131] The magnetic field calculation module is configured to calculate the no-load magnetic field of the motor based on the final vector magnetic potential in each subdomain.

[0132] The iterative calculation of the vector magnetic potential in each subdomain is based on the vector magnetic potential in each subdomain during the previous iteration. The value of the stator slot surface current used to characterize the effect of stator core saturation is calculated, and then the boundary conditions are reconstructed and the current vector magnetic potential in each subdomain is calculated.

[0133] Example 3

[0134] The purpose of this embodiment is to provide a computer-readable storage medium.

[0135] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal-thickness magnetic poles as described in Embodiment 1 of this disclosure.

[0136] Example 4

[0137] The purpose of this embodiment is to provide an electronic device.

[0138] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles as described in Embodiment 1 of this disclosure.

[0139] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal-thickness magnetic poles, characterized in that, include: The solution domain for the magnetic field of a surface-mounted permanent magnet synchronous motor is divided into subdomains, and the basic structural parameters of each subdomain are determined. Using the method of separation of variables, the vector magnetic potential general solution expression containing undetermined coefficients in each subdomain is determined based on the basic structural parameters of each subdomain; Based on the general solution expression of the vector magnetic potential in each subdomain, and combined with the boundary conditions of adjacent subdomains, the vector magnetic potential in each subdomain is calculated iteratively until the iteration stopping condition is met, and the final vector magnetic potential in each subdomain is obtained. The no-load magnetic field of the motor is calculated based on the final vector magnetic potential in each subdomain. The iterative calculation of the vector magnetic potential in each subdomain is based on the vector magnetic potential in each subdomain during the previous iteration. The value of the stator slot surface current used to characterize the effect of stator core saturation is calculated, and then the boundary conditions are reconstructed and the current vector magnetic potential in each subdomain is calculated.

2. The method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles as described in claim 1, characterized in that, The subdomains include permanent magnets, air gaps, stator slots, and stator slot openings.

3. The method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles as described in claim 2, characterized in that, The determination of the basic structural parameters of each subdomain is specifically as follows: Based on the motor's structural dimensions, the stator slots and stator slot openings are transformed into radial sectors, and their main structural dimensions are determined. The air gap is transformed into an annular shape, and its main structural dimensions are determined. The permanent magnet is divided into a series of radial sectors, and the main structural dimensions of each sector are determined.

4. The method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles as described in claim 2, characterized in that, The specific calculation process of the vector magnetic potential general solution expression in each subdomain is as follows: By using the method of separation of variables, the general solution expression of vector magnetic potential in each subdomain containing undetermined coefficients is obtained; By solving the system of equations based on the boundary conditions, the specific values ​​of the undetermined coefficients in the general solution expression of the vector magnetic potential in each subdomain are determined, thus obtaining the final specific expression of the vector magnetic potential in each subdomain.

5. The method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles as described in claim 4, characterized in that, The vector magnetic potential flux expression within the permanent magnet is: Among them, A u B u C u D u r are undetermined coefficients. u and r u-1 These are the top and bottom radii of the permanent magnet subdomain u, respectively. pu For a particular solution related to the remanence of the permanent magnet and the corresponding pole arc coefficient, k = 1, 2, 3…; The vector magnetic potential flux solution expression within the air gap is: Among them, A g B g C g D g r are undetermined coefficients. s and r U These are the top and bottom radii of the air gap subdomain, respectively.

6. The method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles as described in claim 1, characterized in that, The final vector magnetic potential within each subdomain is specifically as follows: In the first iteration, the initial value of the added surface current is set to 0, and the vector magnetic potential in each subdomain is calculated. In the next iteration, the value of the added surface current and the vector magnetic potential are recalculated based on the vector magnetic potential obtained in the previous iteration. This iterative process is repeated until the rate of change of the surface current obtained in the previous two iterations is lower than the set rate of change threshold. Then, the vector magnetic potential obtained in this iteration is the final vector magnetic potential.

7. The method for calculating the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles as described in claim 6, characterized in that, The surface current value added during the iteration process is calculated based on the motor's magnetic flux and magnetic reluctance, which are calculated based on the vector magnetic potential and the core magnetization curve.

8. A calculation system for the no-load magnetic field of a surface-mounted permanent magnet synchronous motor with unequal thickness magnetic poles, characterized in that, It includes a subdomain partitioning module, an expression determination module, a magnetic potential calculation module, and a magnetic field calculation module: The subdomain partitioning module is configured to: partition the solution domain of the magnetic field of the surface-mounted permanent magnet synchronous motor into subdomains and determine the basic structural parameters of each subdomain; The expression determination module is configured to: use the separation of variables method to determine the vector magnetic potential general solution expression containing undetermined coefficients in each subdomain based on the basic structural parameters of each subdomain; The magnetic potential calculation module is configured to: iteratively calculate the vector magnetic potential in each subdomain based on the general solution expression of the vector magnetic potential in each subdomain and the boundary conditions of adjacent subdomains, until the iteration stopping condition is met, and obtain the final vector magnetic potential in each subdomain; The magnetic field calculation module is configured to calculate the no-load magnetic field of the motor based on the final vector magnetic potential in each subdomain. The iterative calculation of the vector magnetic potential in each subdomain is based on the vector magnetic potential in each subdomain during the previous iteration. The value of the stator slot surface current used to characterize the effect of stator core saturation is calculated, and then the boundary conditions are reconstructed and the current vector magnetic potential in each subdomain is calculated.

9. An electronic device, characterized in that it comprises: Memory is used to store computer-readable instructions in a non-transitory manner. as well as Processor, for executing the computer-readable instructions, When the computer-readable instructions are executed by the processor, they perform the method described in any one of claims 1-7.

10. A storage medium, characterized in that, The computer-readable instructions are stored non-transitory, wherein when the non-transitory computer-readable instructions are executed by a computer, the instructions of the method according to any one of claims 1-7 are executed.

Images