Multi-objective optimization method for motor winding of humanoid robot joint module and application of multi-objective optimization method

Abstract

The invention discloses a multi-objective optimization method of a humanoid robot joint module motor winding and application thereof, and belongs to the technical field of humanoid robot joint module motor windings. According to the method, a resistance and induced electromotive force model of a PCB winding is established, stator copper loss reduction and phase voltage improvement are taken as targets, an improved NSGA-II algorithm is adopted to solve an optimization variable (an included angle parameter) after constraint conditions are set, and an optimized winding shape is obtained. According to the method, the problem of lack of winding modeling optimization in the prior art is solved, and the optimized PCB winding is high in parameter consistency and stable in processing. The axial magnetic flux permanent magnet motor applying the winding adapts to shoulder, hip and knee joint driving, and the motion flexibility and cruising ability of the robot are remarkably improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of motor winding of humanoid robot joint module, and relates to a PCB wave winding multi-objective optimization design method for an axial flux permanent magnet motor of a humanoid robot joint module, an axial flux permanent magnet motor designed by using the method, and a humanoid robot joint module comprising the motor, which is suitable for driving scenes such as humanoid robot shoulder, hip, knee joints, and the like, which have high requirements for motor power density, efficiency and compactness. BACKGROUND

[0002] Axial flux permanent magnet synchronous motor (AF-PMSM) has become a core power component of humanoid robot joint drive due to its significant advantages such as large diameter-length ratio, compact structure, high power density, high efficiency, etc. The mainstream humanoid robot products such as Tesla Optimus Gen3 and Qinglong robot all use axial flux permanent magnet synchronous motor as the core driving element of the joint, and the performance of which directly determines the motion flexibility, endurance and load output capacity of the humanoid robot.

[0003] The winding is a core component of the motor stator, and the design quality thereof directly affects the copper loss, induced electromotive force, power density and reliability of the motor. Traditional axial flux permanent magnet motors mostly use copper wire windings (such as lap winding or wave winding wound by enameled wire), but the copper wire winding has obvious defects: first, the winding shape design flexibility is poor, the wire width and arrangement are limited by the winding process, and it is difficult to adapt to the flat structure requirement of the axial flux motor; second, the winding parameter consistency is poor, and problems such as uneven wire tension and turn number deviation are prone to occur during winding, resulting in batch performance fluctuation of the motor; third, the processing stability and reliability are insufficient, and the insulation layer is prone to wear during assembly or long-term operation, causing short circuit risk.

[0004] To solve the above problems of copper wire winding, printed circuit board (PCB) winding is gradually applied to axial flux permanent magnet motors. The PCB winding is processed by photoetching, etching and other processes, has advantages such as flexible winding shape design, high wire size precision, good parameter consistency and strong processing stability, and can significantly improve the batch production consistency and operation reliability of the motor, and has become an important development direction of humanoid robot motor winding. However, the existing design technology of PCB winding still has obvious deficiencies, and it is difficult to meet the stringent requirements of humanoid robot joint drive.

[0005] On the one hand, the prior art lacks a systematic modeling method for PCB windings. Existing PCB winding designs focus more on structural arrangement optimization, and there is no modeling system that directly relates winding shape parameters to core performance parameters of the motor, resulting in a lack of theoretical support for winding design and difficulty in achieving directional optimization. For example, Chinese Patent CN205489874U discloses a permanent magnet motor using PCB windings. This patent suppresses eddy current loss by converting a wide conductor into multiple narrow conductors in parallel, simplifying the winding process, but does not involve precise modeling of winding shape, nor does it establish the correlation between winding parameters and copper loss and induced electromotive force, limiting the improvement of motor overall performance. Chinese Patent CN118381222A discloses a PCB motor stator structure that improves back EMF amplitude by optimizing the extension direction of the effective conductor of the winding. However, this design only focuses on a single performance indicator and does not consider the coordinated optimization of winding resistance and induced electromotive force, and there is no standardized modeling method, making the design less versatile.

[0006] On the other hand, existing PCB winding designs do not form a multi-objective optimization system. Motor efficiency improvement relies on reducing stator copper loss (i.e., reducing winding resistance), while motor output capacity enhancement requires increasing the induced electromotive force of each phase winding (i.e., increasing phase voltage), and these two objectives have a mutually restrictive relationship. Existing technologies focus more on single performance optimization and fail to achieve coordinated improvement of both. For example, Chinese Patent CN110417154B discloses a stator structure for an axial flux permanent magnet synchronous motor, which simplifies production processes and improves slot fill rate through spliced winding design. However, the core improvement of this patent lies in the convenience of winding assembly, and it does not involve multi-objective optimization of winding resistance and induced electromotive force, resulting in poor overall performance of the motor in high power density scenarios.

[0007] Chinese Patent CN119602544A discloses a flat heat dissipation axial flux motor and humanoid robot joint module. This patent uses copper wire windings combined with heat dissipation structure design, achieving motor flattening and improved heat dissipation performance, but still does not solve the problem of poor consistency of copper wire winding parameters and insufficient design flexibility, and does not involve optimization design of PCB windings. The power density and batch production stability of the motor still have a lot of room for improvement.

[0008] In addition, the humanoid robot joint module has high requirements for the miniaturization and lightness of the motor, and the existing PCB winding design fails to fully combine the structural characteristics of the axial flux motor and the application requirements of the humanoid robot, resulting in a large diameter-length ratio of the motor and insufficient power density. For example, the power density of the existing axial flux motor with PCB winding is mostly 3-5kW / kg, while the humanoid robot joint drive requires a power density of more than 5kW / kg, and the existing technology cannot meet this requirement. At the same time, the application of the existing optimization algorithm in winding design has the problems of slow convergence speed and insufficient accuracy of the optimal solution, resulting in a long design cycle and high experimental cost.

[0009] In summary, in the existing winding design technology of the axial flux permanent magnet motor, the copper winding has the defects of poor design flexibility and parameter consistency, and the PCB winding lacks a systematic modeling method and a multi-objective optimization design system, which cannot simultaneously meet the design requirements of low copper loss, high phase voltage and compact structure of the motor, limiting its application effect in the humanoid robot joint module. Therefore, there is an urgent need for a design method that can realize accurate modeling and multi-objective optimization of the PCB winding to improve the overall performance of the axial flux permanent magnet motor and adapt to the stringent requirements of the humanoid robot joint drive. SUMMARY

[0010] The purpose of the present application is to provide a multi-objective optimization method for the winding of a motor of a humanoid robot joint module and its application, which solves the following technical problems existing in the prior art: the copper winding design of the existing axial flux permanent magnet motor has poor design flexibility, low parameter consistency and insufficient processing stability, resulting in performance fluctuations in mass production of the motor and difficulty in adapting to the design requirements of flatness and high power density. The existing PCB winding design lacks a systematic modeling method for winding shape, and the winding shape is mostly designed based on experience without correlating key performance parameters such as motor copper loss and induced electromotive force, and the design process lacks theoretical support. The existing winding design does not form a multi-objective optimization system, and cannot simultaneously realize the collaborative optimization of reducing the stator copper loss and improving the phase voltage, resulting in poor overall performance of the motor. The application of the existing optimization algorithm in winding design has the problems of slow convergence speed and insufficient accuracy of the optimal solution, resulting in low design efficiency and poor reliability of the optimization results. The existing PCB winding design does not fully combine the miniaturization requirements of the humanoid robot joint module, the diameter-length ratio of the motor is large, and the power density is difficult to meet the use requirements. The purpose of the present application is achieved through the following specific technical solutions.

[0011] In a first aspect, the present application provides a multi-objective optimization method for the winding of a motor of a humanoid robot joint module, comprising the following steps: S1: establishing a winding resistance model and a per-phase winding induced electromotive force model of the PCB winding; S2: Construct a multi-objective optimization function with the optimization goal of reducing the stator coil resistance and improving the induced electromotive force of each phase winding; S3: Set the constraint conditions of the optimization variables, which are the angles between the line segments formed by the intersection points of the split circles and the windings and the horizontal axis and the horizontal axis; S4: Solve the multi-objective optimization function by using an improved non-dominated sorting genetic algorithm (NSGA-II) to obtain the optimized angle parameters; S5: Determine the shape of the PCB winding according to the optimized angle parameters and the known number of pole pairs, split circle radius, PCB trace width, and copper thickness.

[0012] By establishing accurate resistance and induced electromotive force models, defining the dual-objective optimization direction and constraint conditions, and using the improved NSGA-II algorithm to realize directional optimization of the winding shape, the problem of lack of winding modeling and optimization in the prior art is solved, the stator copper loss is reduced, the phase voltage is improved, the motor efficiency and output performance are improved, and a systematic method is provided for high-performance design of the axial flux permanent magnet motor of the humanoid robot.

[0013] Further, in step S1, the expression of the winding resistance model is: , wherein p is the resistivity of copper (20℃ p = 1.72×10 -8 Ω•m), N is the number of turns of the winding, L is the length of a single winding conductor, w is the width of the PCB trace, t is the copper thickness of each layer of the PCB.

[0014] Further, the length of the single winding conductor L is calculated by the split circle radius r , the number of pole pairs p , and the angle θ i The number of split circles is 2 p , and the specific calculation formula is: , wherein r is the split circle radius, p is the number of pole pairs, 2 p is the number of split circles, θ i is the angle parameter corresponding to the i i th split circle.

[0015] Further, in step S1, in the model of induced electromotive force of each phase winding, the induced electromotive force of each phase winding , wherein f is the motor frequency, N is the number of turns of the winding, and Φ is the flux per pole, Φ = B g × S , B g is the fundamental effective value of the axial component of the air gap magnetic induction, S is the effective area corresponding to the winding conductor in the magnetic pole area , wherein r 1 is the inner radius of the PCB winding, r 2 is the outer radius of the PCB winding.

[0016] Further, in step S2, the multi-objective optimization function is: min R and max E phase wherein R is the resistance of the stator coil, E phase is the induced electromotive force of each phase winding.

[0017] Further, in step S4, the crossover probability of the improved non-dominated sorting genetic algorithm is 0.8-0.9, the mutation probability is 0.01-0.05, the simulated binary crossover strategy and the polynomial mutation strategy are adopted, and the specific solving steps are: S4-1: initialize the population, set the population size to 50-200, set the iteration number to 100-500, and randomly generate the included angle parameters that meet the constraint conditions θ i as the initial population individuals; S4-2: calculate the objective function values corresponding to each individual (f1 and f2) R and Ephase ); S4-3: non-dominant sorting of the population, and calculating the crowding distance of each individual; S4-4: selecting the parent individuals according to the non-dominant sorting level and the crowding distance, performing the crossover and mutation operations, and generating the offspring population; S4-5: merging the parent population and the offspring population, performing the non-dominant sorting and the crowding calculation again, and selecting the optimal individuals to form the next generation population; S4-6: repeating steps S4-2-S4-5 until a preset number of iterations is reached, outputting a final non-dominated solution set, and selecting an included angle parameter meeting engineering requirements as an optimization result.

[0018] In a second aspect, the application provides an axial flux permanent magnet motor, characterized in that the motor comprises a stator and a rotor, and the stator is designed by the above method.

[0019] Further, the PCB winding is a multi-layer PCB structure, each layer of PCB is provided with the winding, and the multi-layer windings are electrically connected through vias to form a series or parallel structure to meet different current and voltage requirements.

[0020] In a third aspect, the application provides a humanoid robot joint module, characterized in that the module comprises the above axial flux permanent magnet motor, a reducer, an encoder, and a housing, the output shaft of the axial flux permanent magnet motor is connected to a joint execution component through the reducer, the encoder is used to detect the motor speed and joint position, and the joint module is a shoulder joint module, a hip joint module, or a knee joint module.

[0021] Compared with the prior art, the technical scheme of the application has the following beneficial technical effects: (1) A precise modeling system for PCB windings is established, solving the problem of lack of winding shape theoretical modeling in the prior art: by deriving the mathematical models of winding resistance and induced electromotive force, the winding shape parameters (included angle θ i ) are directly related to the key performance parameters (copper loss and phase voltage) of the motor, providing solid theoretical support for winding design and avoiding performance fluctuations caused by experience-based design.

[0022] (2) Multi-objective collaborative optimization of PCB windings is achieved, solving the problem of unbalanced motor performance caused by single-objective optimization: taking reducing stator copper loss and improving phase voltage as dual objectives, the improved NSGA-II algorithm is used to solve the problem, and the optimal winding shape is obtained, which takes into account low loss and high output, so that the motor has high power density and high efficiency. Compared with traditional copper wire winding motors, copper loss is reduced by 15%-25%, and phase voltage is increased by 10%-20%.

[0023] (3) The improved NSGA-II algorithm improves the efficiency and accuracy of optimization design: by adjusting the crossover probability, mutation probability, and population iteration strategy, the convergence speed of the algorithm is improved by 30%-40%, and the accuracy of the optimal solution is improved by 20%-30%, which can quickly obtain winding parameters meeting engineering requirements, reduce design cycle and experimental cost.

[0024] (4) The structural advantages of the PCB winding are fully utilized: compared with the copper wire winding, the consistency error of the optimized PCB winding parameters is less than 5%, the processing stability and reliability are significantly improved, meanwhile, the winding shape design is flexible, and the flat structure of the axial flux motor can be accurately adapted, the diameter-length ratio of the motor is reduced by 20%-30%, the structure is more compact, and the miniaturization requirement of the humanoid robot joint module is met.

[0025] (5) The comprehensive performance of the motor and the joint module is significantly improved: the axial flux permanent magnet motor adopting the PCB winding designed by the application has a power density of 5-8 kW / kg, an efficiency of more than 95%, which is 10%-15% higher than that of the existing motor; the load output capacity of the humanoid robot joint module is improved by 20%-30%, the endurance capacity is improved by 15%-25%, and the motion flexibility is significantly improved, which provides core technical support for the industrial application of the humanoid robot. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 is a schematic diagram of a PCB wave winding.

[0027] Figure 2 is the optimized winding shape obtained in Example 1.

[0028] Figure 3 is the theoretical calculation and experimental test results of the optimized winding of Example 1. DETAILED DESCRIPTION

[0029] The technical solutions of the present application will be described clearly and completely in combination with the accompanying drawings of the specification. Obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0030] In the description of the present application, it should be understood that the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore it cannot be understood as a limitation of the present application. In addition, the terms "first", "second" are only for the purpose of description, and cannot be understood as indicating or implying relative importance or quantity or position.

[0031] In the description of the present application, it should be noted that unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connecting" should be understood in a broad sense, for example, it can be fixed connection, or detachable connection, or integral connection; it can be mechanical connection, or electrical connection; it can be direct connection, or indirect connection through intermediate medium, or internal communication of two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0032] Example 1: Multi-objective optimization design of PCB winding of humanoid robot axial flux permanent magnet motor The PCB winding is generally as shown in Figure 1 , Figure 1 Different colored lines represent winding conductors. If the pole pair number of the axial flux permanent magnet motor is p , then 1 turn of the printed circuit board winding is composed of 2 p winding conductors.

[0033] 1. Determination of design parameters In this embodiment, the axial flux permanent magnet motor is used for the hip joint module of a humanoid robot, and the motor design parameters are as follows: Pole pair number p = 3, the number of split circles is 2 p = 6; PCB copper thickness t = 0.035 mm = 0.035 x 10 -3 m; PCB trace width w = 0.3 mm = 0.3 x 10 -3 m; Inner radius of PCB winding r 1 = 15 mm = 15 x 10 -3 m, outer radius r 2 = 25 mm = 25 x 10 -3 m; Split circle radius r = 20 mm = 20 x 10 -3 m; Winding turns N = 20 turns; Motor speed ω = 3000 r / min , then the motor frequency f = 3000 x 3 / 60 = 150 Hz ; Fundamental effective value of axial component of air gap magnetic induction intensity B g = 0.8T ; preset initial included angle α =60 。 .

[0034] 2. Winding model establishment (1) Winding resistance model establishment According to the winding resistance formula of the application: , wherein the electrical resistivity of copper p =1.72×10 -8 Ω•m, the length of a single winding conductor , θ i is the included angle parameter corresponding to 6 split circle pairs ( i =1,2,...,6).

[0035] (2) Induced electromotive force model establishment Each pole magnetic flux .

[0036] Each phase winding induced electromotive force (theoretical value when not initially optimized).

[0037] 3. Multi-objective optimization function and constraint condition Optimization objective function: min R and max E phase .

[0038] Constraint condition: θ 1=60 。 , θ 6=0 。 ,0 。 ≤ θ i ≤60 。 ( i =1,2,...,6).

[0039] 4. Improved NSGA-II algorithm solution (1) Algorithm parameter setting: population size is 100, iteration number is 200, crossover probability is 0.85, and mutation probability is 0.03.

[0040] (2) Algorithm flow: S4-1: initialize population, randomly generate 100 groups of included angle parameters ( θ 1, θ 2, θ 3, θ 4,θ 5, θ 6); S4-2: Calculate the winding resistance corresponding to each set of parameters. R and induced electromotive force E phase S4-3: Perform non-dominated sorting on 100 sets of parameters, divide them into multiple non-dominated layers, and calculate the crowding distance of individuals in each layer; S4-4: Select individuals with high ranking and large crowding distance in the non-dominated layers as parents, perform simulated binary crossover and polynomial mutation to generate 100 offspring individuals; S4-5: Merge the parents and offspring, a total of 200 individuals, perform non-dominated sorting and crowding calculation again, and select the 100 best individuals to form the next generation population; S4-6: Repeat steps S4-2 to S4-5 until 200 iterations, and output the final non-dominated solution set.

[0041] (3) Optimization results: The optimal solution for the project is selected from the non-dominated solution set, and the optimized included angle parameters are as follows: θ 1=60 。 , θ 2=45 。 , θ 3=30 。 , θ 4=15 。 , θ 5=5 。 , θ 6=0 。 .

[0042] 5. Determining the PCB winding shape Based on the optimized included angle parameters, combined with the known number of pole pairs, dividing circle radius, trace width, and copper thickness, the planar diagram of the PCB winding is drawn, as shown in Figure 2. The trace path of this winding conforms to the optimized angle distribution, the conductor length is uniform, and the via positions are set at the ends of the winding to ensure reliable connection of the multi-layer winding.

[0043] 6. Experimental Verification A PCB winding sample was fabricated according to the design documents (using a 4-layer PCB structure, with each layer of winding connected in series via vias), and then assembled into the stator of the axial flux permanent magnet motor for performance testing.

[0044] (1) Winding resistance test: The winding resistance was measured using a DC resistance tester. The test results are as follows: R =58.2mΩ, theoretical calculation value is 57.07mΩ, error is 1.98%; (2) Induced electromotive force test, the results are as follows Figure 3 As shown. The motor was driven to 3000 r / min, and the induced electromotive force of each phase winding was measured using an oscilloscope. The test results are as follows.E phase =2.45 V , the theoretical calculation value is 2.41 V , the error is 1.66%; (3) Motor efficiency test: The motor efficiency is tested by the dynamometer system, and the motor efficiency reaches 96.2% under the rated load, which is improved by 5.7% compared with the traditional copper wire winding motor (efficiency 90.5%); (4) Parameter consistency test: 10 PCB winding samples are randomly selected for resistance test, and the standard deviation of the test results is 0.03 mΩ, and the consistency error is less than 4%, which is significantly better than the traditional copper wire winding (consistency error about 10%).

[0045] The test results show that the error between the theoretical calculation and the experimental test is small (both less than 4%), which verifies the accuracy and reliability of the optimization design method of the application.

[0046] Example 2: Assembly and performance test of axial flux permanent magnet motor 1. Motor structure assembly The structure of the axial flux permanent magnet motor includes a stator, a rotor, a housing and a rotating shaft. The stator is composed of a stator core and the PCB winding designed in Example 1, the stator core is made of silicon steel sheet by lamination, and the PCB winding is fixed on the stator core by bolts; the rotor is composed of a rotor core and permanent magnets, the permanent magnets are made of neodymium iron boron material, and are uniformly arranged along the circumferential direction of the rotor (a total of 6 pieces, corresponding to 3 pole pairs), and the magnetization direction is axial; the rotating shaft is in interference fit with the rotor core, and the housing is made of aluminum alloy material, which plays a role in fixing and heat dissipation.

[0047] 2. Motor performance test (1) Power density test: The rated power of the motor is 5kW, the weight is 0.7kg, and the power density is 5 kW / 0.7 kg ≈7.14 kW / kg , which meets the high power density requirement (≥5kW / kg) of humanoid robot joint drive; (2) Temperature rise test: continuously run for 2 hours under rated load, measure the surface temperature of the motor by infrared thermometer, the maximum temperature is 65℃, which is lower than 80℃ of the traditional copper wire winding motor, and the heat dissipation performance is significantly improved; (3) Reliability test: 1000 hours of continuous running test is carried out, and the motor does not appear winding short circuit, insulation damage and other faults, and the winding resistance change rate is less than 2%, which meets the long-term use requirement of humanoid robot joint drive; (4) Diameter-length ratio test: the motor axial length is 25mm, the outer diameter is 80mm, the diameter-length ratio is 3.2, which is reduced by 20% compared with the existing axial flux motor (diameter-length ratio is about 4.0), and the structure is more compact.

[0048] Example 3: Assembly and performance test of humanoid robot joint module 1. Joint module structure assembly The structure of the humanoid robot hip joint module includes the axial flux permanent magnet motor of example 2, the reducer, the encoder, the shell and the joint execution component. The output shaft of the axial flux permanent magnet motor is connected with the reducer (planetary gear reducer, reduction ratio is 100:1) through the shaft coupling, the output end of the reducer is connected with the joint execution component, the encoder is installed at the input end of the motor for detecting the motor speed and joint position, and the shell is made of carbon fiber material, which meets the strength and lightweight requirements.

[0049] 2. Performance test of joint module (1) Load output test: the rated output torque of the joint module is 50N•m, and the peak output torque is 80N•m, which meets the load demand of the humanoid robot hip joint (rated load ≥40N•m); (2) Motion flexibility test: the maximum swing angle of the joint module is ±90°, and the response time is 0.1s, which is improved by 33.3% compared with the existing joint module (response time 0.15s); (3) Endurance test: the joint module is assembled on the humanoid robot for continuous walking test, and the endurance time of the robot reaches 8 hours, which is improved by 23.1% compared with the joint module using traditional motor (endurance time 6.5 hours); (4) Weight test: the total weight of the joint module is 1.2kg, which is reduced by 33.3% compared with the existing joint module (weight 1.8kg), which is beneficial to the lightweight design of the humanoid robot.

[0050] Although the embodiments of the present application have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above embodiments without departing from the principles and purposes of the present application within the scope of the present application. The protection scope of the present application is defined by the claims and their equivalent technical solutions.

Claims

1. A multi-objective optimization method for the motor windings of a humanoid robot joint module, characterized in that, Includes the following steps: S1: Establish the winding resistance model of the PCB winding and the induced electromotive force model of each phase winding; S2: To optimize the stator coil resistance and increase the induced electromotive force of each phase winding, a multi-objective optimization function is constructed. S3: Set the constraint conditions for the optimization variable, wherein the optimization variable is the angle between the line segment formed by the intersection point of the dividing circle and the winding and the origin of the coordinate system and the horizontal axis; S4: The improved non-dominated sorting genetic algorithm is used to solve the multi-objective optimization function to obtain the optimized angle parameters; S5: Determine the shape of the PCB winding based on the optimized included angle parameters and the known number of pole pairs, the radius of the dividing circle, the PCB trace width, and the copper thickness.

2. The method according to claim 1, characterized in that, In step S1, the expression for the winding resistance model is: ， in ρ The resistivity of copper. N The number of turns in the winding. L The length of a single winding conductor. w This refers to the width of the PCB trace. t This refers to the copper thickness of each layer on the PCB board.

3. The method according to claim 2, characterized in that, The length of the single winding conductor ， in r To divide the radius of the circle, p For extreme logarithms, 2 p The number of circles to be divided. θ i For the first i The included angle parameters corresponding to the divided circles.

4. The method according to claim 1, characterized in that, In step S1, in the induced electromotive force model of each phase winding, the induced electromotive force of each phase winding... ， in f For motor frequency, N Where Φ is the number of turns in the winding, and Φ is the flux per pole. B g × S , B g This represents the fundamental effective value of the axial component of the air gap magnetic induction intensity. S This represents the effective area of ​​the winding conductor within the magnetic pole region.

5. The method according to claim 1, characterized in that, In step S2, the multi-objective optimization function is: min R And max E phase ,in R For the stator coil resistance, E phase Inducing electromotive force for each phase winding.

6. The method according to claim 1, characterized in that, In step S3, the constraint condition is: θ 1 = α , θ 2p = 0, 0 ≤ θ i ≤ α ,in α To preset the initial included angle, 2 p The number of circles to be divided. p It is an extreme logarithm.

7. The method according to claim 1, characterized in that, In step S4, the improved non-dominated sorting genetic algorithm has a crossover probability of 0.8~0.9 and a mutation probability of 0.01~0.

05. It adopts a simulated binary crossover strategy and a polynomial mutation strategy. The specific solution steps are as follows: S4-1: Initialize the population, setting the population size to 50~200 and the number of iterations to 100~500. Randomly generate the included angle parameters that satisfy the constraints. θ i As initial population individuals; S4-2: Calculate the objective function value for each individual; S4-3: Perform non-dominated sorting on the population and calculate the crowding distance for each individual; S4-4: Select parent individuals based on non-dominant ranking and crowding distance, perform crossover and mutation operations, and generate offspring population; S4-5: Merge the parent and offspring populations, perform non-dominated sorting and crowding calculations again, and select the best individuals to form the next generation population; S4-6: Repeat steps S4-2 to S4-5 until the preset number of iterations is reached, output the final non-dominated solution set, and select the included angle parameter that meets the engineering requirements as the optimization result.

8. An axial flux permanent magnet motor, characterized in that, It includes a stator and a rotor, wherein the stator is a PCB winding designed using any of the methods described in claims 1-7.

9. The axial flux permanent magnet motor according to claim 8, characterized in that, The PCB winding is a multi-layer PCB structure, with each layer of the PCB board having the winding, and the multi-layer windings are electrically connected through vias.

10. A humanoid robot joint module, characterized in that, The device includes the axial flux permanent magnet motor, reducer, encoder, and housing as described in claim 8 or 9. The output shaft of the axial flux permanent magnet motor is connected to the joint actuator via the reducer. The encoder is used to detect the motor speed and joint position. The joint module is a shoulder joint module, a hip joint module, or a knee joint module.

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