Rotor, magnetizing equipment, servo motor and structural parameter optimization method thereof

Abstract

The invention belongs to the technical field of permanent magnet servo motors, and particularly discloses a rotor, magnetizing equipment, a servo motor and a structural parameter optimization method of the servo motor. According to the invention, the overall magnetizing technology of assembling the magnetic steel first and then magnetizing is adopted, the non-magnetized permanent magnet blocks are assembled on the rotor, and the whole rotor is magnetized through the pulsed high-intensity magnetic field equipment, so that the assembling difficulty is reduced, and the assembling precision is improved. Compared with a traditional servo motor adopting a Halbach array, the Halbach array servo motor can obtain better performance under the condition of the same permanent magnet consumption, and is easy to process and manufacture. Based on an optimization result of a theoretical model, a finite element method is adopted to carry out more accurate optimization, and design parameters better than a Halbach array are obtained. On the premise that the number of the permanent magnets is not changed, the torque of the discrete magnetizing permanent magnet motor is remarkably increased, and the torque pulsation is remarkably reduced, so that the discrete magnetizing permanent magnet motor has higher competitiveness in the field of servo motors or more occasions and is expected to be a low-cost alternative scheme of the permanent magnet motor.

Description

Technical Field

[0001] The present application belongs to the technical field of permanent magnet servo motors, and more specifically, relates to a rotor, a magnetizing device, a servo motor, and a method for optimizing structural parameters thereof. Background Art

[0002] Servo motors are the core functional units in intelligent manufacturing equipment and play a key role in the performance and reliability of advanced manufacturing equipment. The performance of servo motors is mainly determined by indicators such as torque density, torque quality, and vibration noise.

[0003] In existing research, servo motors are mainly designed with bread-shaped poles, spoke-shaped poles or Halbach arrays. Bread-shaped poles are generally difficult to process and will waste permanent magnet materials during the processing. Spoke-shaped poles are more difficult to control the torque quality of the motor. Halbach arrays have the advantages of sinusoidal magnetic field distribution, self-shielding effect, high fundamental field, and low harmonic content. They are widely used in the field of servo motors. However, the torque quality of motors designed with Halbach arrays is relatively high, but there is still room for improvement. Summary of the invention

[0004] In view of the defects of the prior art, the purpose of this application is to provide a rotor, a magnetizing device, a servo motor and a method for optimizing its structural parameters, aiming to solve the problems of low torque density and high torque pulsation of existing servo motors, and low assembly accuracy and great assembly difficulty of traditional pre-magnetizing technology.

[0005] To achieve the above-mentioned objectives, in a first aspect, the present application provides a rotor, comprising: a rotor core and magnets, wherein the rotor core is provided with a plurality of poles along its circumferential surface, each pole is composed of a plurality of magnets, and the magnet combinations of different poles are the same; at least two magnets under the same pole have different central angles; the magnetization directions of all magnets under the same pole are different, and the magnetization direction of at least one magnet is radial.

[0006] Preferably, when the multiple magnetic steels under the same pole are of symmetrical structure, the magnetization directions of the magnetic steels of symmetrical structure are asymmetric.

[0007] Preferably, when the magnetization directions of multiple magnetic steels under the same pole are symmetrical, the central angles of the magnetic steels with symmetrical magnetization directions are different.

[0008] Preferably, the magnetization directions of the magnets in adjacent poles with radial magnetization directions are opposite, and the angles between the magnetization directions of the magnets in adjacent poles at the same position and the radial direction are equal.

[0009] Preferably, the magnetic steel has anisotropy and is oriented according to an optimally designed magnetization direction during the manufacturing stage.

[0010] To achieve the above-mentioned purpose, in a second aspect, the present application provides a magnetizing device for magnetizing the rotor as described in the first aspect, the magnetizing device comprising: a plurality of coils, the number of which is the same as the number of rotor pole pairs; the plurality of coils are evenly distributed circumferentially; each coil is a symmetrical structure; the inner diameter of the magnetizing device is larger than the outer diameter of the rotor.

[0011] Preferably, the coil is saddle-shaped.

[0012] Preferably, the magnetizing device further comprises a yoke; each coil is embedded in a groove of the yoke, and the midplane coincides with the midplane of the yoke.

[0013] To achieve the above-mentioned purpose, in a third aspect, the present application provides a servo motor, comprising: a rotor as described in the first aspect.

[0014] Preferably, the servo motor is an inner rotor motor or an outer rotor motor.

[0015] To achieve the above-mentioned purpose, in a fourth aspect, the present application provides a method for optimizing the structural parameters of a servo motor as described in the third aspect, comprising: calculating the residual magnetization intensity vector of the servo motor at each moment based on a theoretical model; solving the electromagnetic torque of the servo motor at each moment according to the stator slot opening width of the servo motor and the residual magnetization intensity vector at each moment; calculating the electromagnetic torque average value and torque pulsation according to the electromagnetic torque of the servo motor at each moment; changing the central angle coefficient and magnetization angle of the magnetic steel and the stator slot opening width, repeating the above steps until the Pareto optimality is reached, and the corresponding structural parameter combination is the optimization result; the theoretical model is specifically as follows:

[0016]

[0017] in, is the residual magnetization vector, n is the summation variable in the Fourier series expansion, taking values ​​of 1, 2, …, ∞, M rn is the radial component of the residual magnetization, M θn is the circumferential component of the residual magnetization intensity, p is the number of rotor pole pairs, θ is the angle between the circumferential position of a point inside the magnetic steel and the center line of the magnetic steel with the magnetization direction radially outward, is the radial unit vector, is the circumferential unit vector;

[0018]

[0019] Among them, B r is the remanence of the magnetic steel, μ0 is the vacuum permeability, α i is the central angle of the i-th magnetic steel, γ i is the angle between the center line of the i-th magnetic steel and the center line of the magnetic steel with the magnetization direction radially outward, βi is the magnetization angle of the i-th magnetic steel, α i =a i α p , a i is the center angle coefficient of the i-th magnetic steel, α p is the pole pitch angle, i=1,2,…,m, and m is the number of magnetic steel blocks per pole.

[0020] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the prior art:

[0021] (1) The present application provides a rotor, comprising: a rotor core and a magnet, wherein the rotor core is provided with a plurality of poles along its circumferential surface, each pole is composed of a plurality of magnets, and the magnets of different poles have the same combination; at least two magnets under the same pole have different central angles; all magnets under the same pole have different magnetization directions, and at least one magnet has a radial magnetization direction. The present application adopts magnets of unequal width and a discrete magnetization method (the magnetization direction of each magnetic pole is discrete), so that the central angle and magnetization angle of each magnet are variable. Compared with the rotor of the existing structure, the rotor proposed in the present application has more variable parameters, which can improve the torque performance as much as possible while keeping the amount of permanent magnets unchanged.

[0022] (2) The present application provides a magnetizing device for magnetizing the rotor, the magnetizing device comprising: a plurality of coils, the number of which is the same as the number of rotor pole pairs; the plurality of coils are evenly distributed in the circumferential direction; each coil is a symmetrical structure; the inner diameter of the magnetizing device is larger than the outer diameter of the rotor. The present application adopts the overall magnetizing technology of assembling the magnetic steel first and then magnetizing, assembling the unmagnetized permanent magnet block onto the rotor, and magnetizing the rotor as a whole through the pulsed strong magnetic field equipment, thereby reducing the difficulty of assembly and improving the assembly accuracy.

[0023] (3) The present application provides a servo motor, including the rotor. The present application can achieve better performance than a traditional servo motor using a Halbach array under the condition of the same amount of permanent magnets, and is easy to process and manufacture.

[0024] (4) The present application provides a method for optimizing the structural parameters of the servo motor, including: calculating the residual magnetization intensity vector of the servo motor at each moment based on the theoretical model; solving the electromagnetic torque of the servo motor at each moment according to the stator slot opening width of the servo motor and the residual magnetization intensity vector at each moment; calculating the average electromagnetic torque, i.e., the average torque and torque pulsation, according to the electromagnetic torque of the servo motor at each moment; changing the center angle coefficient and magnetization angle of the magnetic steel and the stator slot opening width, repeating the above steps until the Pareto optimal stop, and the corresponding structural parameter combination is the optimization result. Based on the optimization results of the theoretical model, the present application uses the finite element method for more accurate optimization to obtain design parameters that are better than the Halbach array. Under the premise of keeping the amount of permanent magnets unchanged, the torque of the discrete magnetized permanent magnet motor is significantly improved and the torque pulsation is significantly reduced, so that the discrete magnetized permanent magnet motor has greater competitiveness in the field of servo motors or more occasions and is expected to become a lower-cost alternative to permanent magnet motors. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 A schematic diagram of the structure of a magnetizing device provided in this application.

[0026] Figure 2 A flow chart of the overall magnetization technology of first assembling the magnetic steel and then magnetizing it provided in an embodiment of the present application.

[0027] Figure 3 A schematic diagram of the circumferential expansion of the rotor magnetic steel provided in an embodiment of the present application.

[0028] Figure 4 A schematic diagram of the inner rotor structure with 2 blocks provided in an embodiment of the present application.

[0029] Figure 5 A schematic diagram of the inner rotor structure with three blocks provided in an embodiment of the present application.

[0030] Figure 6 A schematic diagram of the inner rotor structure with 4 blocks provided in an embodiment of the present application.

[0031] Figure 7 A schematic diagram of the outer rotor structure with a block number of 2 provided in an embodiment of the present application.

[0032] Figure 8 This is the optimization result provided by the embodiment of the present application.

[0033] Fig. 9 Torque comparison diagram of the Halbach solution and the optimized solution provided in the embodiment of the present application. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0035] The term "and / or" in this article is a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. The symbol " / " in this article indicates that the associated objects are in an or relationship, for example, A / B means A or B.

[0036] The terms "first" and "second" in the specification and claims herein are used to distinguish different objects rather than to describe a specific order of the objects. For example, a first response message and a second response message are used to distinguish different response messages rather than to describe a specific order of the response messages.

[0037] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0038] In the description of the embodiments of the present application, unless otherwise specified, "multiple" means two or more than two. For example, multiple processing units refer to two or more processing units, etc.; multiple elements refer to two or more elements, etc.

[0039] Next, the technical solutions provided in the embodiments of the present application are introduced.

[0040] In a first aspect, the present application provides a rotor, comprising: a rotor core and magnets, wherein the rotor core is provided with a plurality of poles along its circumferential surface, each pole being composed of a plurality of magnets, and the magnet combinations of different poles are the same; at least two magnets under the same pole have different central angles; all magnets under the same pole have different magnetization directions, and at least one magnet has a radial magnetization direction.

[0041] Preferably, the number of blocks of magnetic steel under each pole can be 2, 3, 4 or more.

[0042] Preferably, when the multiple magnetic steels under the same pole are of symmetrical structure, the magnetization directions of the magnetic steels of symmetrical structure are asymmetric.

[0043] Preferably, when the magnetization directions of multiple magnetic steels under the same pole are symmetrical, the central angles of the magnetic steels with symmetrical magnetization directions are different.

[0044] Preferably, the magnetization directions of the magnets in adjacent poles with radial magnetization directions are opposite, and the angles between the magnetization directions of the magnets in adjacent poles at the same position and the radial direction are equal.

[0045] Preferably, the magnetic steel has anisotropy and is oriented according to an optimally designed magnetization direction during the manufacturing stage.

[0046] The traditional pre-magnetization technology for producing permanent magnet motors is to magnetize first and then assemble. That is, a small solenoid magnetizing coil is used to apply a pulsed strong magnetic field to the small non-magnetic permanent magnet block to saturate the magnetization, and then the small magnetic permanent magnet block is embedded or attached to the rotor to form the motor pole. The magnetic permanent magnet blocks have a huge attraction or repulsion force between each other, so the assembly is difficult and the assembly accuracy is not high.

[0047] In response to the above problems, the second aspect is Figure 1 As shown, the present application provides a magnetizing device for magnetizing the rotor as described in the first aspect, the magnetizing device comprising: a plurality of coils, the number of which is the same as the number of rotor pole pairs; the plurality of coils are evenly distributed circumferentially; each coil is a symmetrical structure; the inner aperture of the magnetizing device is larger than the outer diameter of the rotor.

[0048] Preferably, the coil is saddle-shaped.

[0049] The magnetizing device can be a coil with a yoke or a coil without a yoke.

[0050] Preferably, the magnetizing device further comprises a yoke, each coil is embedded in a groove of the yoke, and the midplane coincides with the midplane of the yoke. The yoke is made of laminated silicon steel sheets.

[0051] The magnetizing device of the present application is a set of coils with or without a yoke. The magnetizing device is used for magnetizing permanent magnets. The number of coils is the same as the number of rotor pole pairs. The overall magnetizing process is as follows: Figure 2 As shown: the unmagnetized magnetic steel and the rotor core are assembled, and then the magnetizing device is placed outside the outer surface of the rotor (inner rotor) or inside the inner surface (outer rotor), and the center of each coil is aligned with the N pole or S pole. A certain current is passed through the coil to generate a magnetic field that can saturate the permanent magnet to magnetize the permanent magnet.

[0052] In a third aspect, the present application provides a servo motor, comprising: a rotor as described in the first aspect.

[0053] Preferably, the servo motor is an inner rotor motor or an outer rotor motor.

[0054] In a fourth aspect, the present application provides a method for optimizing structural parameters of a servo motor as described in the third aspect, comprising:

[0055] Based on the theoretical model, the residual magnetization intensity vector of the servo motor at each moment is calculated;

[0056] According to the opening width of the servo motor stator slot and the residual magnetization intensity vector at each moment, the electromagnetic torque of the servo motor at each moment is solved;

[0057] According to the electromagnetic torque of the servo motor at each moment, the average electromagnetic torque, i.e., the average torque and the torque ripple, are calculated;

[0058] Change the magnetic steel's center angle coefficient (corresponding to the magnetic steel's center angle), magnetization angle, and stator slot opening width, and repeat the above steps until the Pareto optimality is reached. The corresponding structural parameter combination is the optimization result.

[0059] The theoretical model is as follows:

[0060]

[0061] in, is the residual magnetization vector, n is the summation variable in the Fourier series expansion, taking values ​​of 1, 2, …, ∞, M rn is the radial component of the residual magnetization, M θn is the circumferential component of the residual magnetization intensity, p is the number of rotor pole pairs, θ is the angle between the circumferential position of a point inside the magnetic steel and the center line of the magnetic steel with the magnetization direction radially outward, is the radial unit vector, is the circumferential unit vector. Expand the rotor magnet along the circumferential direction, as shown in Figure 3 shown.

[0062]

[0063] Among them, B r is the remanence of the magnetic steel, η0 is the vacuum permeability, α i is the central angle of the i-th magnetic steel, γ i is the angle between the center line of the i-th magnetic steel and the center line of the magnetic steel with the magnetization direction radially outward, β i is the magnetization angle of the i-th magnetic steel, α i =a i α p , a i is the center angle coefficient of the i-th magnetic steel, α p is the pole pitch angle, i=1,2,…,m, and m is the number of magnetic steel blocks per pole.

[0064] Example 1

[0065] like Figure 4As shown, the inner rotor has 2 blocks. The rotor core is provided with 4 poles along its circumferential surface, each pole is composed of 2 magnetic steels, and the magnetic steel combinations of different poles are the same. Figure 4 The middle part of the middle circle is a pole, and the center angles of the two magnets under the same pole are different, 54° and 36° respectively. The magnetization angles of all magnets under the same pole are different, one magnet has a magnetization angle of 0°, and the other magnet has a magnetization angle of 110°.

[0066] Example 2

[0067] like Figure 5 As shown, the inner rotor has 3 blocks. The rotor core is provided with 4 poles along its circumferential surface, each pole is composed of 3 magnetic steels, and the magnetic steel combinations of different poles are the same. Figure 5 The middle part of the middle circle is a pole, and the central angles of the three magnets under the same pole are different, namely 47.7°, 24.3° and 18°. The magnetization angles of all magnets under the same pole are different, the magnetization angle of the first magnet is 0°, the magnetization angle of the second magnet is 42°, and the magnetization angle of the third magnet is 147°.

[0068] Example 3

[0069] like Figure 6 As shown, the inner rotor has 4 blocks. The rotor core is provided with 4 poles along its circumferential surface, each pole is composed of 4 magnetic steels, and the magnetic steel combinations of different poles are the same. Figure 6 The middle part of the middle circle is a pole, and the four magnets under the same pole have different central angles, which are 52.2°, 11.7°, 15.75° and 10.35° respectively. The magnetization angles of all magnets under the same pole are different, the magnetization angle of the first magnet is 0°, the magnetization angle of the second magnet is 42°, the magnetization angle of the third magnet is 106°, and the magnetization angle of the fourth magnet is 147°.

[0070] Example 4

[0071] like Figure 7 As shown, the outer rotor has 2 blocks. The rotor core is provided with 42 poles along its circumferential surface, each pole is composed of 2 magnetic steels, and the magnetic steel combinations of different poles are the same. Figure 7 The middle part of the middle circle is a pole, and the center angles of the two magnets under the same pole are different, 6.51° and 2.06° respectively. The magnetization angles of all magnets under the same pole are different, one magnet has a magnetization angle of 0°, and the other magnet has a magnetization angle of 130°.

[0072] Example 5

[0073] The main parameters of the motor involved in this embodiment are shown in Table 1.

[0074] Table 1 Main parameters of the motor

[0075] parameter value Stator outer diameter / mm 122.5 Stator inner diameter / mm 83 Stack length / mm 34 Number of stator slots 12 Pole pairs 5 Air gap length / mm 0.7 Magnetic steel thickness / mm 3

[0076] Taking a discrete magnetization permanent magnet motor with an inner rotor and 4 magnets per pole (m=4) as an example, the optimization results of the analytical method are as follows: Figure 8 As shown in Figure 2, it can be seen that the torque ripple of the optimization scheme is reduced compared with the Halbach scheme.

[0077] The parameters and performance of the analytical optimization scheme and the Halbach scheme are compared, and the results are shown in Tables 2 and 3.

[0078] Table 2 Parameter comparison between analytical optimization scheme and Halbach scheme

[0079] Halbach solution Optimization plan <![CDATA[β2 / °]]> -45 -21.117 <![CDATA[β3 / °]]> -90 -53.661 <![CDATA[β4 / °]]> -135 -167.07 <![CDATA[a2]]> 0.25 0.1888 <![CDATA[a3]]> 0.25 0.1498 <![CDATA[a4]]> 0.25 0.3237 <![CDATA[w so / mm]]> 2.5 2.1066

[0080] Table 3 Comparison of analytical solutions of the performance of the optimization scheme and the Halbach scheme

[0081] Halbach solution Optimization plan Average torque / Nm 6.23 7.01 Torque ripple / % 0.625 0.144

[0082] The analytical method ignores the influence of inter-pole leakage, pole edge effect and saturation effect, and cannot accurately predict the torque, but it can predict the change law of the torque. Therefore, the analytical method can be used for preliminary optimization, and then based on the optimization results of the analytical method, the finite element method can be used for more accurate optimization. The optimization results of the finite element method are shown in Table 4.

[0083] Table 4 Parameter comparison between the finite element method optimization scheme and the Halbach scheme

[0084] Halbach solution Optimization plan <![CDATA[β2 / °]]> -45 -41.7 <![CDATA[β3 / °]]> -90 -106.35 <![CDATA[β4 / °]]> -135 -146.5 <![CDATA[a2]]> 0.25 0.13 <![CDATA[a3]]> 0.25 0.175 <![CDATA[a4]]> 0.25 0.115 <![CDATA[w so / mm]]> 2.5 2.89

[0085] Table 5 Comparison of finite element results of the performance of the optimization scheme and the Halbach scheme

[0086] Halbach solution Optimization plan Average torque / Nm 5.98 6.66 Torque ripple / % 2.28 1.20

[0087] The torque comparison between the optimization scheme and the Halbach scheme is as follows: Fig. 9 As shown in Figure 2, it can be seen that the average torque of the optimization scheme is significantly improved compared with the Halbach scheme.

[0088] The comparison of the finite element results of the two schemes shows that the torque of the optimized discrete magnetization permanent magnet motor is higher than that of the Halbach scheme, and the torque pulsation is lower, that is, the performance of the discrete magnetization permanent magnet motor is better than that of the Halbach scheme.

[0089] It can be understood that the detailed functional implementation of each of the above-mentioned units / modules can be found in the introduction of the aforementioned method embodiment, and will not be repeated here.

[0090] It should be understood that the above-mentioned device is used to execute the method in the above-mentioned embodiment. The implementation principle and technical effect of the corresponding program module in the device are similar to those described in the above-mentioned method. The working process of the device can refer to the corresponding process in the above-mentioned method, which will not be repeated here.

[0091] It should be understood that the various numerical numbers involved in the embodiments of the present application are only used for the convenience of description and are not used to limit the scope of the embodiments of the present application.

[0092] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A rotor, comprising: A rotor core and magnetic steel, wherein the rotor core is provided with a plurality of poles along its circumferential surface, each pole being composed of a plurality of magnetic steels, characterized in that: The combination of magnetic steels of different poles is the same; There are at least two magnets with different central angles under the same pole; The magnetization directions of all the magnets under the same pole are different, and the magnetization direction of at least one magnet is radial.

2. The rotor according to claim 1, characterized in that When multiple magnetic steels under the same pole are of symmetrical structure, the magnetization directions of the symmetrical magnetic steels are asymmetrical.

3. The rotor according to claim 1, characterized in that When the magnetization directions of multiple magnets under the same pole are symmetrical, the central angles of the magnets with symmetrical magnetization directions are different.

4. The rotor according to claim 1, characterized in that The magnets with radial magnetization directions in adjacent poles have opposite magnetization directions, and the magnets with the same adjacent poles have the same angle with the radial direction.

5. The rotor according to claim 1, characterized in that The magnetic steel has anisotropy and is oriented according to an optimally designed magnetization direction during the manufacturing stage.

6. A magnetizing device, characterized in that: Used to magnetize the rotor according to any one of claims 1 to 5, the magnetizing device comprising: a plurality of coils, the number of which is the same as the number of rotor pole pairs; The multiple coils are evenly distributed in the circumferential direction; Each coil is a symmetrical structure; The inner diameter of the magnetizing device is larger than the outer diameter of the rotor.

7. The magnetizing device according to claim 6, characterized in that: The magnetizing device also includes a yoke; each coil is embedded in a groove of the yoke, and the middle plane coincides with the middle plane of the yoke.

8. A servo motor, characterized in that: include: A rotor as claimed in any one of claims 1 to 5.

9. The servo motor according to claim 8, characterized in that: The servo motor is an inner rotor motor or an outer rotor motor.

10. A method for optimizing the structural parameters of a servo motor according to claim 8 or 9, characterized in that: include: Based on the theoretical model, the residual magnetization intensity vector of the servo motor at each moment is calculated; According to the opening width of the servo motor stator slot and the residual magnetization intensity vector at each moment, the electromagnetic torque of the servo motor at each moment is solved; According to the electromagnetic torque of the servo motor at each moment, the average electromagnetic torque, i.e., the average torque and the torque ripple, are calculated; Change the center angle coefficient and magnetization angle of the magnetic steel and the width of the stator slot opening, and repeat the above steps until the Pareto optimality is reached. The corresponding combination of structural parameters is the optimization result. The theoretical model is as follows: in, is the residual magnetization vector, n is the summation variable in the Fourier series expansion, and takes values ​​of 1, 2, ..., ∞, M rn is the radial component of the residual magnetization, M θn is the circumferential component of the residual magnetization intensity, p is the number of rotor pole pairs, θ is the angle between the circumferential position of a point inside the magnetic steel and the center line of the magnetic steel with the magnetization direction radially outward, is the radial unit vector, is the circumferential unit vector; Among them, B r is the remanence of the magnetic steel, η0 is the vacuum permeability, α i is the central angle of the i-th magnetic steel, γ i is the angle between the center line of the i-th magnetic steel and the center line of the magnetic steel with the magnetization direction radially outward, β i is the magnetization angle of the i-th magnetic steel, α i =a i α p , a i is the center angle coefficient of the i-th magnetic steel, α p is the pole pitch angle, i=1,2,…,m, and m is the number of magnetic steel blocks per pole.

Images