Winding function enhanced wide-area high-efficiency permanent magnet brushless motor and design method thereof

Abstract

The invention relates to the technical field of motors, in particular to a winding function enhanced wide-area high-efficiency permanent magnet brushless motor and a design method thereof.The winding function enhanced wide-area high-efficiency permanent magnet brushless motor comprises a stator, a rotor and a rotating shaft, the rotor and the rotating shaft are concentrically connected through a key, and the rotor is sleeved with the stator; the stator and the rotor are formed by laminating silicon steel sheets with the same thickness, and the rotating shaft is made of a non-magnetic material; a plurality of pairs of neodymium iron boron permanent magnets are uniformly and fixedly embedded on the rotor along the circumferential direction; an outer arc-shaped segmented magnetic barrier, an elliptical magnetic barrier and an inner arc-shaped segmented magnetic barrier are respectively arranged between two adjacent pairs of neodymium-iron-boron permanent magnets; the outer arc-shaped segmented magnetic barrier, the elliptical magnetic barrier and the inner arc-shaped segmented magnetic barrier are sequentially arranged from outside to inside; each pair of neodymium-iron-boron permanent magnets is composed of two rectangular neodymium-iron-boron permanent magnets, the two rectangular neodymium-iron-boron permanent magnets are arranged in a V shape, and the opening of the V shape faces the air gap. On the basis of a winding function enhancement principle, winding arrangement is determined, direct-axis inductance is improved, and therefore the speed regulation range is widened.

Description

Technical Field

[0001] The present invention relates to the technical field of motors, and in particular to a winding function enhanced wide-area high-efficiency permanent magnet brushless motor and a design method thereof. Background Art

[0002] Driven by the global trend of intelligent and electrified vehicles, electric vehicles are booming, with global electric vehicle sales projected to reach 16.03 million units in 2024 alone. Electric vehicles often experience multiple operating conditions, including frequent acceleration and deceleration, hill climbing, and high-speed cruising. These conditions place stringent demands on the power density and speed range of the drive motor, their core power component.

[0003] The document with Chinese patent number CN202411652455.1 starts from the perspective of "variable permanent magnet source" and introduces permanent magnet materials (such as aluminum nickel cobalt) and magnetizing windings that can change the magnetization state online into permanent magnet motors. By applying a short-time demagnetization (or magnetization) current, the magnetization intensity of the permanent magnet material of the motor can be adjusted online, and the magnetic flux of the permanent magnet source can be changed to achieve flexible adjustment and control of the total magnetic field of the motor. However, in order to achieve effective regulation of the air gap flux under different working conditions, it is necessary to add a set or magnetizing windings and corresponding control circuits, which objectively increases the complexity of the motor system structure and reduces the power density and reliability of the motor to a certain extent. Chinese patent number CN202311691605.5 focuses on inductance characteristics and proposes a magnetic field enhanced permanent magnet motor, which reduces the q-axis inductance L by adding magnetic barriers on the q-axis. q Alternatively, add a magnetic bridge to the d-axis to increase the d-axis inductance L. d , thus achieving the inductance characteristic that the d-axis inductance is greater than the q-axis inductance (L d >L q ) and magnetic field enhancement effects. Due to the increased direct-axis inductance and reduced quadrature-axis inductance, this type of motor can broaden the speed regulation range and reduce copper loss in the high-speed, weak-field region, thereby improving the motor's efficiency in operating conditions such as high-speed cruising. However, it is undeniable that the difference between the direct and quadrature-axis inductances in this type of motor is small, resulting in low reluctance torque utilization, which limits its load-carrying capacity in the high-speed range.

[0004] Therefore, automotive permanent magnet motors still have challenges in wide speed ranges and high-speed efficiency, making it difficult to fully meet the diverse performance requirements of automotive drive motors under variable operating conditions. Therefore, addressing issues such as the difficulty in adjusting the air gap magnetic field, narrow speed range, and low efficiency in the high-speed field weakening region of permanent magnet motors is crucial to meet the diverse operating conditions of electric vehicles. Summary of the Invention

[0005] The purpose of the present invention is to address the shortcomings of the prior art and propose a winding function enhanced wide-area high-efficiency permanent magnet brushless motor and its design method. Based on the winding function enhancement principle, the winding arrangement is determined, the direct-axis inductance is improved, and the speed regulation range is widened.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A winding function-enhanced wide-area high-efficiency permanent magnet brushless motor comprises a stator, a rotor, and a rotating shaft. The rotor and the rotating shaft are concentrically connected via a key, and the stator is sleeved on the outside of the rotor. The stator has a plurality of stator slots evenly distributed in the circumferential direction; each stator slot is provided with an armature winding.

[0008] The stator and rotor are both made of laminated silicon steel sheets of equal thickness, and the rotating shaft is made of non-magnetic material;

[0009] The rotor is evenly and fixedly inlaid with a plurality of pairs of NdFeB permanent magnets along the circumferential direction; an outer arc segmented magnetic barrier, an elliptical magnetic barrier and an inner arc segmented magnetic barrier are respectively provided between two adjacent pairs of NdFeB permanent magnets; the outer arc segmented magnetic barrier, the elliptical magnetic barrier and the inner arc segmented magnetic barrier are arranged in sequence from the outside to the inside;

[0010] Each pair of NdFeB permanent magnets consists of two rectangular NdFeB permanent magnets, and the two rectangular NdFeB permanent magnets are placed in a V shape, with the V-shaped opening facing the air gap; an air groove is provided in the middle of the connection between the two rectangular NdFeB permanent magnets, and three layers of arc-shaped magnetic barriers are provided on both sides of the air groove, respectively. The three layers of arc-shaped magnetic barriers include a first layer of arc-shaped magnetic barrier, a second layer of arc-shaped magnetic barrier, and a third layer of arc-shaped magnetic barrier in sequence.

[0011] Preferably, the distances between the outer arc segmented magnetic barrier and the outer edge of the rotor, the distances between the outer arc segmented magnetic barrier and the elliptical magnetic barrier, and the distances between the elliptical magnetic barrier and the inner arc segmented magnetic barrier are w respectively. a 、w b and w c , and it satisfies: 0mm<w a ≤3mm, 0mm<w b ≤3mm, 0mm<w c ≤3mm.

[0012] Preferably, the distances from the first layer of arc-shaped magnetic barriers, the second layer of arc-shaped magnetic barriers and the third layer of arc-shaped magnetic barriers to the outer edge of the rotor are l a 、l b and l c , and it satisfies: 0mm<l a ≤4mm, 0mm<l b ≤3mm, 0mm<l c ≤2mm.

[0013] The present invention also provides a design method for a wide-area, high-efficiency permanent magnet brushless motor with enhanced winding function, comprising the following steps:

[0014] Step 1: First, clarify the concept of winding function enhancement:

[0015] Electric vehicle motors often require multiple design requirements, including high output torque, wide speed range, and high efficiency. In theory, the priority of each performance factor varies greatly under different operating conditions. For example, under the "low speed and heavy load" operating condition, output torque needs to be given priority; while under the "high speed and light load" operating condition, speed range is the key performance factor. Output torque T e and maximum speed ω max The formula is as follows:

[0016]

[0017] Where P is the number of pole pairs, ψ δ is the effective magnetic flux, L d is the d-axis inductance, L q is the q-axis inductance, U lim is the voltage limit, ψ pm is the permanent magnet flux, i s is the armature current, i d is the d-axis current, i q is the q-axis current;

[0018] It can be seen that in a permanent magnet motor, the maximum speed of the motor is related to the permanent magnet flux and the d-axis inductance, and is inversely proportional to the permanent magnet flux and directly proportional to the d-axis inductance. Therefore, in order to widen the motor speed regulation range while ensuring the output torque, the motor d-axis inductance can be increased. The d-axis inductance L of the permanent magnet motor d Often with the winding function N a (θ) has a close relationship, as shown in formula (2);

[0019]

[0020] Where, L aa (θ) is the self-inductance of phase A; M ab (θ) is the mutual inductance between phase A and phase B; r g is the air gap length; l eff is the motor shaft length; g -1 (θ) is the negative power function of the air gap, μ0 is the magnetic permeability;

[0021] It can be seen that the winding function enhancement design helps to improve the d-axis inductance, thereby widening the motor speed regulation range while ensuring the output torque;

[0022] Step 2: General form of the winding function and its direct relationship to the d-axis inductance:

[0023] The winding function of a permanent magnet motor is determined by the winding distribution, which is determined by the winding phase, such as Figure 3 The principle analysis of the motor winding function is given. Based on this, the general form of the winding function of the single-layer and double-layer winding motors when the slot angle is 40° is derived, as shown in Figure 4 As shown in Figure 2, it can be seen that the winding function is related to the number of winding layers, pitch, pole-slot coordination, etc.

[0024] according to Figure 4 The general form of the winding function and formula (2) can be used to obtain the dq axis inductance formula:

[0025]

[0026] Where N1 is the number of turns of a single-layer winding, N2 is the number of turns of a double-layer winding, τ is the span; μ0 is the magnetic permeability; r g is the air gap length; l eff is the motor shaft length; g -1 (θ) is the negative power function of the air gap.

[0027] Step 3: Design the winding based on the requirements of the winding function enhancement design:

[0028] In order to understand the relationship between the number of turns N1 of a single-layer winding and the number of turns N2 of a double-layer winding, first, the formula for the flux linkage of phase A expressed by the winding function is given:

[0029]

[0030] Where B(θ) is the magnetic field strength; B max is the magnetic field intensity amplitude;

[0031] Then, for simplicity, it is assumed that the motors with these two winding structures have the same flux linkage. So formula (4) is rewritten as:

[0032]

[0033] Where, Q is the number of slots; P is the number of poles; m is the number of phases; K w1c is the winding factor, C is the number of winding layers; r g is the air gap length; l eff is the motor shaft length;

[0034] Next, the formula for the winding factor is given:

[0035]

[0036] Where K p is the short distance coefficient; K dis the distribution factor; q is the number of slots per pole and phase, α is the slot pitch angle, Z is the number of slots, P is the number of poles, and τ is the span;

[0037] Therefore, when the motors with these two winding structures have the same flux linkage, the relationship between the number of turns N1 of the single-layer winding and the number of turns N2 of the double-layer winding can be obtained from the above formulas (4) to (6) as follows:

[0038]

[0039] Substituting formula (7) into formula (3), we can see that when the slot angle is 40°, the inductance relationship between the single-layer winding structure and the double-layer winding structure motor is as follows:

[0040]

[0041] Based on the above analysis, in order to improve the motor's d-axis inductance and widen the motor's speed regulation range, a single-layer, fractional-slot, distributed winding structure is selected.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] 1. The rotor of the present invention adopts a combination of a segmented permanent magnet structure and a multi-layer arc-shaped magnetic barrier structure of the cross-direct axis to form a multi-segment leakage magnetic circuit and multiple flux saturation areas, which helps to improve the flux control capability.

[0044] 2. The present invention adopts a segmented permanent magnet structure and a magnetic bridge connection method to reduce eddy current loss and improve motor efficiency. At the same time, multiple magnetic barriers such as an elliptical magnetic barrier and two layers of inner and outer arc-shaped magnetic barriers are set on the cross-axis to minimize the cross-axis inductance and ensure torque output.

[0045] 3. The present invention analyzes the relationship between direct-axis inductance and winding function, derives a general formula for winding function, and ultimately forms a universal relationship between inductance and winding function.

[0046] 4. The present invention is based on the principle of winding function enhancement, determines the winding arrangement, improves the direct-axis inductance, and thus widens the speed regulation range. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 The flux-adjustable permanent magnet hub motor structure proposed by the present invention;

[0048] Figure 2 for Figure 1 A partial enlarged view of

[0049] Figure 3 This is a schematic diagram of the motor winding function principle analysis of the present invention;

[0050] Figure 4 The winding function of the single-layer and double-layer winding motor of the present invention;

[0051] Figure 5 The diagrams show the direct-axis inductance and speed regulation characteristics under single-layer and double-layer winding structures.

[0052] In the figure: 1. Stator; 2. Rotor; 3. Armature winding; 4. Rectangular NdFeB permanent magnet; 5. First layer of arc-shaped magnetic barrier; 6. Second layer of arc-shaped magnetic barrier; 7. Third layer of arc-shaped magnetic barrier; 8. Outer arc-shaped segmented magnetic barrier; 9. Elliptical magnetic barrier; 10. Inner arc-shaped segmented magnetic barrier; 11. Air slot; 12. Rotating shaft; 13. Stator slot. DETAILED DESCRIPTION

[0053] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings so that those skilled in the art can better understand the advantages and features of the present invention and thus more clearly define the scope of protection of the present invention. The embodiments described in the present invention are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making any creative work shall fall within the scope of protection of the present invention.

[0054] Reference Figure 1 A winding function-enhanced wide-area high-efficiency permanent magnet brushless motor comprises a stator 1, a rotor 2, and a rotating shaft 12. The rotor 2 and the rotating shaft 12 are concentrically connected by a key, and the stator 1 is sleeved on the outer portion of the rotor 2. The stator 1 has 36 stator slots 13 evenly distributed in the circumferential direction. Each stator slot 13 is provided with an armature winding 3.

[0055] The stator 1 and the rotor 2 are both laminated with silicon steel sheets having a thickness of 0.35 mm, and the lamination coefficient is 0.95; the rotating shaft 12 is made of non-magnetic material;

[0056] The rotor 2 is evenly and fixedly inlaid with a plurality of pairs of NdFeB permanent magnets along the circumferential direction; an outer arc segmented magnetic barrier 8, an elliptical magnetic barrier 9, and an inner arc segmented magnetic barrier 10 are respectively provided between two adjacent pairs of NdFeB permanent magnets; the outer arc segmented magnetic barrier 8, the elliptical magnetic barrier 9, and the inner arc segmented magnetic barrier 10 are arranged in sequence from the outside to the inside;

[0057] Each pair of NdFeB permanent magnets consists of two rectangular NdFeB permanent magnets 4, and the two rectangular NdFeB permanent magnets 4 are placed in a V shape with the V-shaped opening facing the air gap; an air groove 11 is provided in the middle of the connection between the two rectangular NdFeB permanent magnets 4, and three layers of arc-shaped magnetic barriers are provided on both sides of the air groove 11, and the three layers of arc-shaped magnetic barriers include a first layer of arc-shaped magnetic barrier 5, a second layer of arc-shaped magnetic barrier 6 and a third layer of arc-shaped magnetic barrier 7 in sequence.

[0058] Specifically, the distances between the outer arc segmented magnetic barrier 8 and the outer edge of the rotor 2, the distances between the outer arc segmented magnetic barrier 8 and the elliptical magnetic barrier 9, and the distances between the elliptical magnetic barrier 9 and the inner arc segmented magnetic barrier 10 are w respectively. a 、w b and w c , and it satisfies: 0mm<w a ≤3mm, 0mm<w b ≤3mm, 0mm<w c ≤3mm.

[0059] Specifically, the distances from the first layer of arc-shaped magnetic barriers 5, the second layer of arc-shaped magnetic barriers 6 and the third layer of arc-shaped magnetic barriers 7 to the outer edge of the rotor 2 are l and l, respectively. a 、l b and l c , and it satisfies: 0mm<l a ≤4mm, 0mm<l b ≤3mm, 0mm<l c ≤2mm.

[0060] In this embodiment, three leakage magnetic paths are formed inside the outer arc segmented magnetic barrier 8, the elliptical magnetic barrier 9 and the inner arc segmented magnetic barrier 10, and the widths of the magnetic bridges are w a , w b and w c ,like Figure 2 As shown, its size directly affects the unique variable flux leakage characteristics of the motor of the present invention. The multiple magnetic barriers structure increases the q-axis magnetic resistance, reduces the q-axis inductance, and lowers the motor's salient pole ratio. Furthermore, the rectangular NdFeB permanent magnets 4 adopt a segmented structure, which helps reduce eddy current losses and improve motor performance. Air slots 11 are used to reduce flux leakage at the connection points of the rectangular NdFeB permanent magnets 4. The first, second, and third layers of arc-shaped magnetic barriers 5, 6, and 7 provide a layered permanent magnet circuit.

[0061] Reference Figure 3 A design method for a wide-area high-efficiency permanent magnet brushless motor with enhanced winding function comprises the following steps:

[0062] Step 1: First, clarify the concept of winding function enhancement:

[0063] Electric vehicle motors often require multiple design requirements, including high output torque, wide speed range, and high efficiency. In theory, the priority of each performance factor varies greatly under different operating conditions. For example, under the "low speed and heavy load" operating condition, output torque needs to be given priority; while under the "high speed and light load" operating condition, speed range is the key performance factor. Output torque T e and maximum speed ω max The formula is as follows:

[0064]

[0065] Where P is the number of pole pairs, ψ δ is the effective magnetic flux, L d is the d-axis inductance, L q is the q-axis inductance, U lim is the voltage limit, ψ pm is the permanent magnet flux, i s is the armature current, i d is the d-axis current, i q is the q-axis current;

[0066] It can be seen that in a permanent magnet motor, the maximum speed of the motor is related to the permanent magnet flux and the d-axis inductance, and is inversely proportional to the permanent magnet flux and directly proportional to the d-axis inductance. Therefore, in order to widen the motor speed regulation range while ensuring the output torque, the motor d-axis inductance can be increased. The d-axis inductance L of the permanent magnet motor d Often with the winding function N a (θ) has a close relationship, as shown in formula (2);

[0067]

[0068] Where, L aa (θ) is the self-inductance of phase A; M ab (θ) is the mutual inductance between phase A and phase B; r g is the air gap length; l eff is the motor shaft length; g -1 (θ) is the negative power function of the air gap, μ0 is the magnetic permeability;

[0069] It can be seen that the winding function enhancement design helps to improve the d-axis inductance, thereby widening the motor speed regulation range while ensuring the output torque;

[0070] Step 2: General form of the winding function and its direct relationship to the d-axis inductance:

[0071] The winding function of a permanent magnet motor is determined by the winding distribution, which is determined by the winding phase, such as Figure 3 The principle analysis of the motor winding function is given. Based on this, the general form of the winding function of the single-layer and double-layer winding motors when the slot angle is 40° is derived, as shown in Figure 4 As shown in Figure 2, it can be seen that the winding function is related to the number of winding layers, pitch, pole-slot coordination, etc.

[0072] according to Figure 4 The general form of the winding function and formula (2) can be used to obtain the dq axis inductance formula:

[0073]

[0074] Where N1 is the number of turns of a single-layer winding, N2 is the number of turns of a double-layer winding, τ is the span; μ0 is the magnetic permeability; r g is the air gap length; l eff is the motor shaft length; g -1 (θ) is the negative power function of the air gap.

[0075] Step 3: Design the winding based on the requirements of the winding function enhancement design:

[0076] In order to understand the relationship between the number of turns N1 of a single-layer winding and the number of turns N2 of a double-layer winding, first, the formula for the flux linkage of phase A expressed by the winding function is given:

[0077]

[0078] Where B(θ) is the magnetic field strength; B max is the magnetic field intensity amplitude;

[0079] Then, for simplicity, it is assumed that the motors with these two winding structures have the same flux linkage. So formula (4) is rewritten as:

[0080]

[0081] Where, Q is the number of slots; P is the number of poles; m is the number of phases; K w1c is the winding factor, C is the number of winding layers; r g is the air gap length; l eff is the motor shaft length;

[0082] Next, the formula for the winding factor is given:

[0083]

[0084] Where K p is the short distance coefficient; K d is the distribution factor; q is the number of slots per pole and phase, α is the slot pitch angle, Z is the number of slots, P is the number of poles, and τ is the span;

[0085] Therefore, when the motors with these two winding structures have the same flux linkage, the relationship between the number of turns N1 of the single-layer winding and the number of turns N2 of the double-layer winding can be obtained from the above formulas (4) to (6) as follows:

[0086]

[0087] Substituting formula (7) into formula (3), we can see that when the slot angle is 40°, the inductance relationship between the single-layer winding structure and the double-layer winding structure motor is as follows:

[0088]

[0089] Based on the above analysis, in order to improve the motor's d-axis inductance and widen the motor's speed regulation range, a single-layer, fractional-slot, distributed winding structure is selected.

[0090] See also Figure 5 , are the direct-axis inductance and speed regulation characteristics of the single-layer and double-layer winding structures of the present invention. It can be seen that the motor with a single-layer winding structure has a larger d-axis inductance and a wider speed regulation range.

[0091] In summary, the present invention determines the winding arrangement based on the principle of winding function enhancement, improves the direct-axis inductance, and thus widens the speed regulation range.

[0092] The descriptions and practices disclosed in this invention are easy to understand and comprehend for those skilled in the art, and modifications and refinements may be made without departing from the principles of the invention. Therefore, modifications and improvements made without departing from the spirit of the invention should also be considered within the scope of protection of this invention.

Claims

1. A winding function enhanced wide-area high-efficiency permanent magnet brushless motor, comprising a stator (1), a rotor (2) and a rotating shaft (12), characterized in that: The rotor (2) and the rotating shaft (12) are concentrically connected via a key, and the stator (1) is sleeved on the outside of the rotor (2); a plurality of stator slots (13) are evenly distributed in the circumferential direction of the stator (1); and an armature winding (3) is provided on each stator slot (13); The stator (1) and the rotor (2) are both formed by laminating silicon steel sheets of equal thickness, and the rotating shaft (12) is made of non-magnetic material; The rotor (2) is evenly and fixedly inlaid with a plurality of pairs of NdFeB permanent magnets along the circumferential direction; an outer arc segmented magnetic barrier (8), an elliptical magnetic barrier (9), and an inner arc segmented magnetic barrier (10) are respectively provided between two adjacent pairs of NdFeB permanent magnets; the outer arc segmented magnetic barrier (8), the elliptical magnetic barrier (9), and the inner arc segmented magnetic barrier (10) are arranged in sequence from the outside to the inside; Each pair of NdFeB permanent magnets consists of two rectangular NdFeB permanent magnets (4), and the two rectangular NdFeB permanent magnets (4) are placed in a V-shape, with the V-shaped opening facing the air gap; an air slot (11) is provided in the middle of the connection between the two rectangular NdFeB permanent magnets (4), and three layers of arc-shaped magnetic barriers are respectively provided on both sides of the air slot (11), and the three layers of arc-shaped magnetic barriers sequentially include a first layer of arc-shaped magnetic barriers (5), a second layer of arc-shaped magnetic barriers (6), and a third layer of arc-shaped magnetic barriers (7).

2. The winding function enhanced wide-area high-efficiency permanent magnet brushless motor according to claim 1, characterized in that: The distances between the outer arc segmented magnetic barrier (8) and the outer edge of the rotor (2), the outer arc segmented magnetic barrier (8) and the elliptical magnetic barrier (9), and the elliptical magnetic barrier (9) and the inner arc segmented magnetic barrier (10) are w respectively. a 、w b and w c , and it satisfies: 0mm<w a ≤3mm, 0mm<w b ≤3mm, 0mm<w c ≤3mm.

3. The winding function enhanced wide-area high-efficiency permanent magnet brushless motor according to claim 1, characterized in that: The distances from the first layer of arc-shaped magnetic barriers (5), the second layer of arc-shaped magnetic barriers (6) and the third layer of arc-shaped magnetic barriers (7) to the outer edge of the rotor (2) are respectively l a 、l b and l c , and it satisfies: 0mm<l a ≤4mm, 0mm<l b ≤3mm, 0mm<l c ≤2mm.

4. The design method of a winding function enhanced wide-area high-efficiency permanent magnet brushless motor according to claim 1, characterized in that: The steps include: Step 1: First, clarify the concept of winding function enhancement: Electric vehicle motors require multiple design requirements, such as high output torque, wide speed range, and high efficiency. Under low-speed and heavy-load conditions, output torque needs to be given priority; under high-speed and light-load conditions, speed range is the key performance, and output torque T e and maximum speed ω max The formula is as follows: Where P is the number of pole pairs, ψ δ is the effective magnetic flux, L d is the d-axis inductance, L q is the q-axis inductance, U lim is the voltage limit, ψ pm is the permanent magnet flux, i s is the armature current, i d is the d-axis current, i q is the q-axis current; In a permanent magnet motor, the maximum motor speed is related to the permanent magnet flux and the d-axis inductance, and is inversely proportional to the permanent magnet flux and directly proportional to the d-axis inductance. The d-axis inductance L of the permanent magnet motor is d With the winding function N a (θ) has a close relationship, as shown in formula (2); Where, L aa (θ) is the self-inductance of phase A; M ab (θ) is the mutual inductance between phase A and phase B; r g is the air gap length; l eff is the motor shaft length; g -1 (θ) is the negative power function of the air gap, μ0 is the magnetic permeability; It can be seen that the winding function enhancement design helps to improve the d-axis inductance, while ensuring the output torque and widening the motor speed regulation range; Step 2: General form of the winding function and its direct relationship to the d-axis inductance: The winding function of a permanent magnet motor is determined by the winding distribution, which in turn is determined by the winding phase. Based on this, the general form of the winding function for single-layer and double-layer winding motors with a slot angle of 40° is derived. According to the general form of the winding function and formula (2), the dq-axis inductance formula is obtained: Where N1 is the number of turns of a single-layer winding, N2 is the number of turns of a double-layer winding, τ is the span; μ0 is the magnetic permeability; r g is the air gap length; l eff is the motor shaft length; g -1 (θ) is the negative power function of the air gap; Step 3: Design the winding based on the requirements of the winding function enhancement design: The flux formula of phase A expressed by winding function is given as: Where B(θ) is the magnetic field strength; B max is the magnetic field intensity amplitude; P is the pole pair number; Then, for simplicity, assuming that the motors with these two winding structures have the same flux linkage, formula (4) can be rewritten as: Where, Q is the number of slots; P is the number of poles; m is the number of phases; K w1c is the winding factor, C is the number of winding layers; r g is the air gap length; l eff is the motor shaft length; Next, the formula for the winding factor is given: Where K p is the short distance coefficient; K d is the distribution factor; q is the number of slots per pole and phase, α is the slot pitch angle, Z is the number of slots, P is the number of poles, and τ is the span; Therefore, when the motors with these two winding structures have the same flux linkage, the relationship between the number of turns N1 of the single-layer winding and the number of turns N2 of the double-layer winding can be obtained from the above formulas (4) to (6) as follows: Substituting formula (7) into formula (3), we can see that when the slot angle is 40°, the inductance relationship between the single-layer winding structure and the double-layer winding structure motor is as follows: Based on the above analysis, in order to improve the motor's d-axis inductance and widen the motor's speed regulation range, a single-layer, fractional-slot, distributed winding structure is selected.

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