A method for optimizing design of a hexagonal hollow cup winding of a brushless direct current motor

Abstract

The application discloses a kind of brushless DC motor hexagonal hollow cup winding optimization design method, which obtains the constraint condition of adjacent coil wire arrangement without structural interference under different wire diameter and hexagonal coil size parameter by establishing coil geometric shape model, deduces the coil design parameter for maximizing the winding ampere-turn magnetic flux, and is converted into control parameter in the process of coil winding process.The hollow cup winding optimized and designed by the application, the diagonal line segment is in a close arrangement state, so that the wire spacing is physically constrained, effectively limits the spatial position of the wire, avoids random displacement of the wire, can optimize the motor torque output performance and effectively improve the symmetry of three-phase winding electrical parameters, auxiliary hexagonal hollow cup winding design makes it scientific and standardized.

Description

Technical Field

[0001] This invention belongs to the field of motor design technology, specifically relating to an optimized design method for hexagonal hollow cup windings of a brushless DC motor. Background Technology

[0002] Hexagonal wound hollow cup winding is one of the mainstream hollow cup winding structures. The number of turns, wire diameter and the shape of each hexagonal winding are spatially constrained and all affect the electromagnetic performance of the motor.

[0003] Chinese patent application CN222750222U discloses a hollow cup winding structure, a micro motor, and a power device. While the hollow cup motor structure is the main invention, it lacks discussion of design methods for specific parameters such as the number of turns, layers, and wire diameter of the hollow cup winding. Chinese patent application CN120185261A discloses a design method for a hollow cup rhombic winding. It describes a method for deriving the design parameters of the hollow cup rhombic winding arrangement based on the physical structure relationship of the winding, allowing for predictive design of coil parameters. However, it does not establish a theoretical connection between winding parameters and the electromagnetic torque of the motor, nor does it involve the calculation of winding turn flux, making it difficult to reasonably optimize the coil shape.

[0004] It is evident that the current hollow cup winding design theory is incomplete, lacking a clear theoretical model to deduce the relationship between the hexagonal winding shape, number of turns, wire diameter, winding turn flux, and equivalent slot fill factor. This makes it difficult to unify the electromagnetic design scheme with the scheme that can be achieved in actual winding processing, resulting in the motor performance being difficult to achieve optimal and the motor design process being complicated and lengthy.

[0005] Therefore, constructing a theoretical model of the relationship between the geometry of hexagonal coils and hollow cup windings and the electromagnetic performance of motors, and developing accurate and efficient design methods have become urgent needs in the field of hollow cup motors. Summary of the Invention

[0006] In view of the above, the present invention provides an optimized design method for hexagonal hollow cup windings of brushless DC motors, which can assist in optimizing the electromagnetic performance of motors and accelerate the design and manufacturing iteration speed.

[0007] A method for optimizing the design of hexagonal hollow cup windings for brushless DC motors includes the following steps:

[0008] (1) Model the close arrangement of the winding conductors along the circumferential and radial directions respectively;

[0009] (2) Based on the winding geometric mathematical model obtained in step (1), establish the functional relationship between the equivalent slot fill factor of the motor and the winding shape;

[0010] (3) Model the winding turn flux to obtain the functional relationship between the winding turn flux and the winding shape;

[0011] (4) Determine the functional relationship between the electromagnetic torque of the motor and the winding shape based on the functional relationship obtained in steps (2) and (3);

[0012] (5) Based on the functional relationship obtained in step (4), the optimal solution of the winding shape is calculated under the design objective of improving electromagnetic torque, thereby calculating the overall design parameters of the winding.

[0013] For a single-turn coil, its shape is an axisymmetric hexagon with the pointed corner facing vertically. The two sides on the left and right sides, which are parallel to the axis of symmetry, are called straight segments, and the two straight segments are of equal length. The four inclined sides on the upper left, upper right, lower left, and lower right are called oblique segments, and the four oblique segments are of equal length. The left and right windings are divided into upper and lower layers along the central axis of the hexagon. In the winding arrangement, the upper and lower layers are located in different conductor arrangement layers. The upper layer is located in the inner layer closer to the motor's central axis, and the lower layer is located in the outer layer of the motor's central axis. The upper layer is only physically constrained by the upper layers of other turns, and the lower layer is only physically constrained by the lower layers of other turns. Since the upper and lower layers belong to different arrangement layers in the radial direction, there is no physical arrangement interference between them.

[0014] Further, step (1) models the tightly arranged winding conductors along the circumferential direction. Specifically, it analyzes the spatial arrangement of winding elements in the same layer belonging to the upper edge. When the straight segments of adjacent coils are tightly arranged, the center distance between the two coils along the circumferential direction is d; when the oblique segments of adjacent coils are tightly arranged, the center distance between the two coils along the circumferential direction is d / sin(θ). It can be seen that the center distance between adjacent coils when the oblique segments are tightly arranged is greater than the center distance when the straight segments are tightly arranged. When the straight segments are tightly arranged, the oblique segments of the winding cannot be neatly arranged due to insufficient space. Based on the above analysis, the tightly arranged winding conductors along the circumferential direction are arranged tightly along the oblique segments. The expression of the winding geometric mathematical model is as follows:

[0015]

[0016] Where: n is the number of single-layer elements of the winding, r is the distribution radius of the innermost layer elements of the winding, d is the wire diameter, and θ is the angle between the winding's oblique segment and the horizontal direction.

[0017] Further, step (1) models the close arrangement of the winding conductors along the radial direction. Specifically: after the main magnetic circuit dimensions are determined, the available thickness of the winding in the radial direction is a constant, and the conductors should fill the space in the radial direction as much as possible; considering the winding process, the number of winding element arrangement layers is usually 2 or 6 layers. In order to make the winding close together along the radial direction, the expression of the winding geometric mathematical model is as follows:

[0018] d=(hd h ) / q

[0019]

[0020] Where: d h Here, n is the winding process margin, q is the number of single-layer elements in the winding, d is the wire diameter, r is the distribution radius of the innermost layer elements in the winding, h is the available thickness of the winding, and θ is the angle between the winding's oblique segment and the horizontal direction.

[0021] Furthermore, the functional relationship between the equivalent slot fill factor of the motor and the winding shape in step (2) is as follows:

[0022]

[0023] Where: K is the equivalent slot fill factor of the motor, h is the available thickness of the winding, and d h Here, r is the winding process allowance, r is the innermost element distribution radius of the winding, and θ is the angle between the winding oblique segment and the horizontal direction.

[0024] Further, the specific implementation of step (3) is as follows: First, it is assumed that the winding flux linkage changes sinusoidally when the rotor rotates at a constant speed, and the flux linkage amplitude is the flux linkage value when the N pole is directly opposite the positive direction of the winding. The circumferential distribution of the radial component of the rotor permanent magnet excitation magnetic field is approximately sinusoidal. When the rotor N pole is aligned with the central axis of the single-turn coil, the calculation expression of the single-turn coil flux linkage is as follows:

[0025]

[0026] in: Let L be the turn-chain flux of a single-turn coil, r be the axial length of the winding, r be the radius of the innermost element distribution of the winding, x be the length of the straight segment of the winding, p be the number of pole pairs of the motor, α be half the electrical angle of the winding span, and B be the total flux linkage flux. n This represents the effective value of the radial component of the air gap magnetic flux density;

[0027] The dimensions of the winding satisfy the following relationship:

[0028]

[0029] The expression for calculating the winding turn flux Φ is:

[0030]

[0031] Where: N c K represents the number of turns in the winding. w β is the winding distribution coefficient, and β is the electrical angle of continuous distribution coverage of a single-phase winding.

[0032] Furthermore, in step (4), based on the functional relationship between the equivalent slot fill factor of the motor and the winding flux linkage and the winding shape, it is derived through calculation that the electromagnetic torque of the motor is proportional to the product of the winding flux linkage Φ and the equivalent slot fill factor K of the motor. Thus, the functional relationship between the electromagnetic torque of the motor and the winding shape is obtained as follows:

[0033]

[0034] Where: T is the electromagnetic torque of the motor, L is the axial length of the winding, θ is the angle between the winding's inclined segment and the horizontal direction, r is the distribution radius of the innermost element of the winding, p is the number of pole pairs of the motor, α is half of the electrical angle of the winding span, and ∝ indicates proportional to.

[0035] Furthermore, in step (5), according to the functional relationship between the electromagnetic torque of the motor and the shape of the winding, as the included angle θ increases, the equivalent slot fill factor K of the motor gradually increases, but the winding chain flux Φ decreases nonlinearly. The product of the two terms will reach a maximum value during the change of θ. The θ value corresponding to this maximum value is obtained by numerical solution so that the electromagnetic torque T of the motor reaches the maximum value. This θ value is the optimal solution of the winding shape. Then, the overall design parameters of the winding are calculated based on this θ value.

[0036] Furthermore, the overall design parameters of the winding include the winding axial length, winding inner diameter, winding outer diameter, winding span, winding straight section length, wire diameter, number of element arrangement layers, and number of winding turns.

[0037] A computer device includes a memory and a processor, wherein the memory stores a computer program and the processor executes the computer program to implement the above-described method for optimizing the design of hexagonal hollow cup windings for brushless DC motors.

[0038] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described optimized design method for hexagonal hollow cup windings of a brushless DC motor.

[0039] The present invention provides an optimized design method for hexagonal hollow cup windings in brushless DC motors, comprising five parts: the first part is a mathematical model of the conductor arrangement in the hollow cup winding; the second part is the calculation of the equivalent slot fill factor; the third part is the calculation of the winding turn flux; the fourth part is the calculation of the motor's electromagnetic torque; and the fifth part is the deduction of the hexagonal winding shape and overall design parameters of the hollow cup winding from the torque calculation results. The theories in each part are derived from real-world physics and motor design theories. The application and logical analysis of the theory for hexagonal wound hollow cup windings constitute the core of this invention. The optimization process for hollow cup windings with similar structures but different parameters, based on the analytical logic and mathematical model of this invention, is covered within the scope of the claims of this patent.

[0040] The hollow cup winding optimized by the method of this invention has a closely arranged oblique line segment, which physically constrains the spacing between the conductors, effectively restricts the spatial position of the conductors, avoids random displacement of the conductors, optimizes the torque output performance of the motor, and effectively improves the symmetry of the electrical parameters of the three-phase winding. It also assists in the scientific and standardized design of the hexagonal hollow cup winding. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the electromagnetic structure of a brushless DC permanent magnet hollow cup motor. In the diagram, 1 is the hollow cup winding, 2 is the stator core, 3 is the rotor magnet, and 4 is the shaft.

[0042] Figure 2 The diagram shows a hexagonal wound hollow cup winding structure. In the diagram, (a) is the planar state of the hexagonal winding, and (b) is the hollow cup winding formed after the winding process.

[0043] Figure 3 This is a schematic diagram showing the structure of a single-turn hexagonal coil and its geometric dimensions.

[0044] Figure 4 This is a schematic diagram of a hexagonal coil tightly wound along the radial direction.

[0045] Figure 5 This is a schematic diagram of the three-dimensional model of the hollow cup winding structure calculated in an embodiment of the present invention. Detailed Implementation

[0046] To describe the present invention in more detail, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] This invention summarizes the effects of hexagonal winding shape, wire diameter, and number of turns on motor torque output performance as influences on both the equivalent slot fill factor K and the winding turn flux Φ. Under the constraint of constant conductor current density, the motor electromagnetic torque is proportional to the product of the equivalent slot fill factor and the winding turn flux amplitude. The calculation methods for the equivalent slot fill factor K and the winding turn flux Φ will be described in detail below, and a method for calculating motor torque will be given, leading to an optimized winding design method. This invention is applicable to... Figure 1 The brushless DC motor shown here has an electromagnetic component that mainly includes a hollow cup winding 1, a stator core 2, a rotor magnet 3, and a rotating shaft 4.

[0048] like Figure 2 The hexagonal wound hollow cup winding shown has a hexagonal shape that is an axisymmetric figure with the line connecting opposite vertices as the axis of symmetry. The four sides connected to the axis of symmetry are of equal length, and the two sides not connected to the axis of symmetry are of equal length and parallel to the axis of symmetry. The hexagonal shape is a mathematical model and abstract generalization of the winding. The actual coil shape is not strictly hexagonal and is a three-dimensional entity. The hexagonal coil and winding of this invention and its analysis method cover all coils and windings that can be considered to have approximate shapes. The main processing technology of the winding is as follows: a hexagonal hollow solenoid is wound on a hexagonal core rod. The hexagonal solenoid is flattened into a flat hexagonal wire array through a flattening process. The flat hexagonal wire array is rolled into a cylindrical hollow cup coil through a rolling process. After the wires on the left and right sides of the hexagonal coil are flattened and rolled, the coil can be divided into upper and lower sides along the axis of symmetry. The arrangement of conductors in hexagonal wound hollow cup windings can be divided into radial arrangement and circumferential arrangement. Radial arrangement refers to the arrangement of the upper and lower conductors of the hexagonal coil along the radial direction, with each layer of conductors consisting entirely of the upper or lower edge of a single hexagonal coil. Circumferential arrangement refers to the arrangement where adjacent conductors in each element layer have the same shape after being flattened and rolled, and are arranged in parallel along the circumferential direction.

[0049] This invention, based on the hexagonal wound hollow cup winding conductor arrangement and the basic design concept of motor torque enhancement, determines the constraints on the conductor arrangement in the circumferential and radial directions (ensuring no overlap or interference between conductors given their physical volume) and the mathematical model. Based on this, it calculates the functional relationship between the motor's equivalent slot fill factor, the winding turn flux, and the hexagonal coil shape. This leads to the functional relationship between the motor's electromagnetic torque and the shape of the hexagonal single-turn winding. Under the design objective of improving electromagnetic torque, the optimal solution for the winding shape can be calculated, and finally, the overall design parameters of the hollow cup winding are derived. The specific implementation process is as follows:

[0050] First, this invention models the equivalent slot fill factor of the motor. Generally, the higher the slot fill factor of the motor, the higher the torque it can achieve under certain temperature rise and efficiency constraints, i.e., better torque output performance. The more tightly the hollow cup windings are arranged along the circumferential and radial directions, the higher the equivalent slot fill factor and the better the torque output performance. To calculate the maximum equivalent slot fill factor of the hollow cup windings, it is necessary to model the tight arrangement of the conductors in the circumferential and radial directions separately. The mathematical models for conductor arrangement in the circumferential and radial directions are conductor arrangement rules constructed under the conditions of increasing motor torque optimization design objectives and conductor arrangement constraints. They are one of the theoretical models constructed in this invention. The mathematical model for conductor arrangement in the circumferential direction is: within the same conductor element layer, the center-to-center distance between adjacent coils along the circumferential direction reaches the minimum value to avoid physical interference. Specifically, the oblique segments of adjacent hexagonal coils are arranged in a seamless and tightly packed state. The mathematical model for conductor arrangement in the radial direction is: there is no misalignment of the elements in each layer in the radial direction, and process and installation margins are reserved in the space occupied by the conductors in the radial direction. Under the traction of the torque optimization objective, the conductor diameter is made as large as possible and fully occupies the conductor layer space.

[0051] For a single-turn coil, its shape is an axisymmetric hexagon with the pointed corner facing vertically. The two sides on the left and right sides, which are parallel to the axis of symmetry, are called straight segments, and the two straight segments are of equal length. The four inclined sides on the upper left, upper right, lower left, and lower right are called oblique segments, and the four oblique segments are of equal length. The left and right windings are divided into upper and lower layers along the central axis of the hexagon. In the winding arrangement, the upper and lower layers are located in different conductor arrangement layers. The upper layer is located in the inner layer closer to the motor's central axis, and the lower layer is located in the outer layer of the motor's central axis. The upper layer is only physically constrained by the upper layers of other turns, and the lower layer is only physically constrained by the lower layers of other turns. Since the upper and lower layers belong to different arrangement layers in the radial direction, there is no physical arrangement interference between them.

[0052] Modeling the close arrangement of windings along the circumference is performed. Specifically, the spatial arrangement of winding elements belonging to the same layer on the upper edge is analyzed. When the straight segments of adjacent coils are closely arranged, the center distance between the two coils along the circumference is one wire diameter d; when the oblique segments of adjacent coils are closely arranged, the center distance between the two coils along the circumference is d / sin(θ), where θ is the angle between the oblique segment and the horizontal direction. It is easy to see that the center distance between adjacent windings when the oblique segments are closely arranged is greater than the center distance when the straight segments are closely arranged, indicating that when the straight segments are closely arranged, the oblique segments of the windings cannot be neatly arranged due to insufficient space. Based on the above modeling, the conclusion regarding the close arrangement of windings along the circumference can be drawn: the most compact arrangement of coils along the circumference is when the oblique segments are closely arranged, and the straight segments are sparsely arranged, such as... Figure 4As shown. At this point, the relationships between the number of single-layer components n, the distribution radius r of the innermost layer components, the wire diameter d, and the angle θ between the oblique line segment and the horizontal direction are:

[0053]

[0054] Modeling is performed for a close arrangement of the windings along the radial direction. Specifically: after determining the main magnetic circuit dimensions, the available thickness h of the windings in the radial direction is a constant, and the conductors should fill the radial space as much as possible. Considering the winding process, the number of element layers in a hollow cup winding is usually 2 or 6. To ensure a close arrangement of the windings along the radial direction, the wire diameter should be taken as the available thickness minus the winding process allowance divided by the length of the element layer. The wire diameter d can be determined by the available winding thickness h and the winding process allowance d. h The number of component arrangement layers q is calculated as follows:

[0055] d=(hd h ) / q

[0056]

[0057] The functional relationship between the equivalent slot fill factor and the hexagonal coil shape is derived using a mathematical model of the hexagonal coil shape and wire arrangement. This model shows the change in center distance between adjacent coils with different hexagonal shapes, and further calculates the equivalent slot fill factor within a complete circle. Combining this with the above formula, it can be seen that the equivalent slot fill factor K is a function of θ, and the expression for K is:

[0058]

[0059] Next, this invention models the winding turn flux. The functional relationship between the winding turn flux and the shape of the hexagonal coil is calculated by integrating along the circumferential direction to calculate the flux of the air gap radial magnetic flux generated by the rotor permanent magnet excitation within the hexagonal coil. Then, the product of the single-turn flux, the number of turns per phase winding, and the winding coefficient is calculated to obtain the phase winding turn flux.

[0060] To simplify the problem, we assume that the winding flux changes sinusoidally when the rotor rotates at a constant speed, and the flux amplitude is the value of the winding flux when the N pole is directly opposite the positive direction of the winding. The circumferential distribution of the radial component of the excitation magnetic field of the rotor permanent magnet is approximately sinusoidal.

[0061] Calculate the turn flux of a single-turn hexagonal coil: (e.g.) Figure 3 As shown, let the total axial length of the hexagonal winding be L, the length of the straight segment be x, the winding span electrical angle be 2α, neglecting the wire thickness, and the number of motor pole pairs be p. When the rotor's N pole is aligned with the central axis of a single-turn hexagonal coil, the coil coil flux linkage is calculated as follows:

[0062]

[0063] The dimensions of the hexagonal winding satisfy the following relationship:

[0064]

[0065] Eliminating x, we get:

[0066]

[0067] The winding chain flux Φ is expressed as:

[0068]

[0069] In the formula: B n N is the effective value of the radial component of the air gap magnetic flux density. c K represents the number of turns in the winding. w K is the winding distribution coefficient. If we take the continuous distribution of a single-phase winding covering an electrical angle of β, then K w The calculation is as follows:

[0070]

[0071] Combining the above equations, we can see that the winding coil flux Φ is also a function of θ.

[0072] The functional relationship between the electromagnetic torque of the motor and the shape of the hexagonal coil requires the use of a motor input-output active power balance torque calculation model. This model shows that the electromagnetic torque is proportional to the product of the effective value of the current and the effective value of the no-load back EMF. Using the motor temperature rise constraint, the effective value of the current is directly proportional to the equivalent slot fill factor. The no-load back EMF has a time differential relationship with the winding turn flux, and its fundamental effective value is directly proportional. In summary, the electromagnetic torque is directly proportional to the product of the equivalent slot fill factor and the winding turn flux, thus revealing the functional relationship between the electromagnetic torque and the hexagonal winding shape.

[0073] Under the maximum torque per unit current strategy control, the electromagnetic torque T of the motor based on active power energy conversion is calculated as follows:

[0074] T = mEI / ω

[0075] In the formula: m is the number of phases, E is the effective value of the no-load induced electromotive force of the phase winding, I is the effective value of the phase current, and ω is the mechanical speed. For E and I, the following formulas apply:

[0076]

[0077] In the formula: ρ is the effective value of the current density at the conductor cross-section. Substituting into the above formula, we obtain the formula for calculating the electromagnetic torque T:

[0078]

[0079] The above analysis leads to the conclusion that the electromagnetic torque T is proportional to the flux amplitude of a single-turn winding. The product of the torque and the equivalent slot fill factor K, and T is also a function of θ. The torque calculation formula is simplified by omitting constants:

[0080]

[0081] As θ increases, the equivalent slot fill factor K of the motor gradually increases, but the nonlinearity of the winding chain flux decreases. The product of the two terms will reach a maximum value during the change of θ, which can be solved numerically. This maximum value corresponds to θ that can make the electromagnetic torque T reach the maximum value, which is the optimal solution for motor torque optimization.

[0082] Based on the calculation formula above, the shape and number of turns of the hexagonal winding can be calculated using the optimal solution θ, thereby determining the optimized design parameters of the motor winding, including the axial length of the hollow cup coil, the inner diameter of the hollow cup coil, the outer diameter of the hollow cup coil, the span of the hexagonal coil, the length of the straight segment of the hexagonal coil, the wire diameter, the number of conductor element layers, and the number of winding turns.

[0083] Example

[0084] This embodiment takes a coreless motor as an example. After magnetic circuit design, the main dimensions involved in the motor's magnetic circuit structure are determined as follows: stator inner diameter 10mm, motor axial length 20mm, permanent magnet rotor outer diameter 7mm, single-sided air gap length 0.3mm, and motor pole pair number p is 1. At this time, the winding parameters can be determined as follows: the available winding thickness h is 1.2mm, the total axial length L is 20mm, and the winding inner diameter is 7.6mm.

[0085] Take the winding process margin d h The wire diameter is 0.5mm, the number of winding elements is 2 layers, and the wire diameter d is calculated to be 0.35mm based on the principle of close arrangement in the direction of the winding radius. The distribution radius r of the inner layer elements is 3.98mm. The winding is designed as a full-pitch winding, and α is π / 2.

[0086] Substituting the above parameters into the simplified torque expression, we get:

[0087]

[0088] The maximum value of the above equation, calculated numerically, corresponds to θ of 34.2°. Substituting this value into the formula for the length x of the straight segment of the hexagonal winding:

[0089] x=20-2×3.98×π÷2×tan(34.2°)=11.5(mm)

[0090] Calculate the number of elements n in a single layer of the winding:

[0091] n=2π×3.98÷(1.2-0.5)×2×sin(34.2°)=40.16

[0092] Considering the actual situation of three-phase windings, the number of elements is rounded down to a multiple of 3, and the number of elements per layer n is taken as 39. At this time, the number of turns N per phase winding is... c It is 13.

[0093] Through the above calculation steps, the determined winding structure and design parameters are obtained, and its three-dimensional model is as follows: Figure 5 As shown. This completes the optimized design of the hexagonal wound hollow cup winding for a brushless DC permanent magnet motor using the method of this invention. This design enables the motor to achieve optimal output torque. Furthermore, by... Figure 5 As can be seen, the closely spaced oblique segments of the conductors effectively constrain the spatial position of the conductors, prevent random movement of the conductors, improve the symmetry of the electrical parameters of the three-phase windings, and enable the electromagnetic torque of the motor in this embodiment to reach its maximum value.

[0094] The above description of the embodiments is provided to enable those skilled in the art to understand and apply the present invention. Those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention.

Claims

1. A method for optimizing the design of hexagonal hollow cup windings for a brushless DC motor, characterized in that, Includes the following steps: (1) Model the close arrangement of the winding conductors along the circumferential direction and the radial direction respectively. The close arrangement along the circumferential direction is a close arrangement along the oblique line segment without gaps. (2) Based on the winding geometric mathematical model obtained in step (1), the functional relationship between the equivalent slot fill factor of the motor and the winding shape is established as follows: in: K This represents the equivalent slot fill factor of the motor. h For the available thickness of the winding, d h To allow for winding process margins, r The innermost element distribution radius of the winding. θ The angle between the inclined segment of the winding and the horizontal direction; (3) Model the winding coil flux to obtain the functional relationship between the winding coil flux and the winding shape; the calculation expression of the winding coil flux is: in: Φ For winding turn flux, p This represents the number of pole pairs of the motor. For the turn-chain flux of a single-turn coil, N c The number of turns in the winding. K w The winding distribution factor, β The electrical angle is continuously distributed and covered by single-phase windings; (4) Based on the functional relationship obtained in steps (2) and (3) and the fact that the electromagnetic torque of the motor is proportional to the winding flux, Φ Equivalent slot fill factor of motor K The product of these factors determines the functional relationship between the electromagnetic torque of the motor and the shape of the windings; (5) Based on the functional relationship between the electromagnetic torque of the motor and the winding shape, the optimal solution for the winding shape is calculated under the design objective of increasing the electromagnetic torque, that is, as the included angle... θ Increase, motor equivalent slot fill factor K Gradually increasing, but the winding turn flux Φ The nonlinearity decreases, and the product of the two terms is... θ During the process of change, a maximum value will appear. The value corresponding to this maximum value can be obtained by numerical method. θ Value makes the motor electromagnetic torque T When the maximum value is reached, the θ The value is the optimal solution for the winding shape, and then based on this... θ The overall design parameters of the winding are calculated.

2. The optimized design method for hexagonal hollow cup windings of a brushless DC motor according to claim 1, characterized in that: Step (1) involves modeling the close arrangement of the winding conductors along the circumferential direction. Specifically, it analyzes the spatial arrangement of each winding element belonging to the same layer on the upper edge. When the straight segments of adjacent coils are closely arranged, the center distance between the two coils along the circumferential direction is... d When the oblique segments of adjacent coils are closely arranged, the center distance between the two coils along the circumferential direction is... d / sin θ Therefore, it can be seen that the center distance between adjacent coils when the diagonal segments are closely arranged is greater than the center distance when the straight segments are closely arranged. When the straight segments are closely arranged, the diagonal segments of the winding cannot be neatly arranged due to insufficient space. Based on the above analysis, the most compact arrangement of the winding wires along the circumference is when they are closely arranged along the diagonal segments. The expression of the geometric mathematical model of the winding at this time is as follows: in: n This refers to the number of elements in a single layer of the winding. d This refers to the wire diameter.

3. The optimized design method for hexagonal hollow cup windings of a brushless DC motor according to claim 1, characterized in that: Step (1) involves modeling the close arrangement of the winding conductors along the radial direction. Specifically, after the main magnetic circuit dimensions are determined, the available thickness of the winding in the radial direction is a constant, and the conductors should fill the radial space as much as possible. Considering the winding process, the number of winding element layers is usually 2 or 6. To ensure that the windings are closely arranged along the radial direction, the expression of the winding geometric mathematical model is as follows: in: n This refers to the number of elements in a single layer of the winding. q The number of layers for the element arrangement in the winding. d This refers to the wire diameter.

4. The optimized design method for hexagonal hollow cup windings of a brushless DC motor according to claim 1, characterized in that: The specific implementation of step (3) is as follows: First, it is assumed that the winding flux linkage changes sinusoidally when the rotor rotates at a constant speed, and the flux linkage amplitude is the flux linkage value when the N pole is directly opposite the positive direction of the winding. The circumferential distribution of the radial component of the rotor permanent magnet excitation magnetic field is approximately sinusoidal. When the rotor N pole is aligned with the central axis of the single-turn coil, the single-turn coil flux linkage is... The calculation expression is as follows: in: L This is the axial length of the winding. x The length of the straight segment of the winding. α It is half the electrical angle of the winding span. B n This represents the effective value of the radial component of the air gap magnetic flux density; The dimensions of the winding satisfy the following relationship: 。 5. The optimized design method for hexagonal hollow cup windings of a brushless DC motor according to claim 1, characterized in that: In step (4), based on the functional relationship between the equivalent slot fill factor of the motor and the winding flux linkage and the winding shape, it is derived through calculation that the electromagnetic torque of the motor is proportional to the winding flux linkage. Φ Equivalent slot fill factor of motor K The product of these factors yields the following functional relationship between the motor's electromagnetic torque and the winding shape: in: L This is the axial length of the winding. α It is half the electrical angle of the winding span, and ∝ means proportional to.

6. The optimized design method for hexagonal hollow cup windings of a brushless DC motor according to claim 1, characterized in that: The overall design parameters of the winding include the winding axial length, winding inner diameter, winding outer diameter, winding span, winding straight section length, conductor diameter, number of element arrangement layers, and number of winding turns.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: The processor is used to execute the computer program to implement the brushless DC motor hexagonal hollow cup winding optimization design method as described in any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by the processor, it implements the brushless DC motor hexagonal hollow cup winding optimization design method as described in any one of claims 1 to 6.

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