An optimal cooling combination parameter determination method for a wheel hub motor

Abstract

An optimal cooling combination parameter determination method for a wheel hub motor; at present, the wheel hub motor lacks a standard optimization processing mode, and there is no standard guide for the precise optimization of the stator water cooling flow channel cooperation in the wheel hub motor; in the present application, the optimal combination parameter determination method takes the air gap length, the permanent magnet thickness, the stator slot width, the stator slot bottom width and the stator slot height in the wheel hub motor as the optimization variables, generates sample points by using the optimal Latin hypercube experiment method, constructs a second-order response surface proxy model according to the sample points, and solves the second-order response surface proxy model based on the NSGA-II algorithm to obtain the determination process of the optimal combination parameters with the maximum average torque and the minimum torque ripple as the optimization objectives.

Description

Technical Field

[0001] This invention specifically relates to a method for determining the optimal cooling combination parameters for a hub motor. Background Technology

[0002] With the continuous development of new energy technologies, electric vehicles are becoming increasingly popular. The performance of an electric vehicle's drive system directly affects the vehicle's power performance and range, making it a key research focus for scholars and major automakers worldwide. Electric vehicle drive systems are mainly divided into two types: centralized drive and distributed drive. Centralized drive typically has a main drive motor that transmits power to the wheels via a drive shaft, differential, and other mechanical structures. Distributed drive, on the other hand, installs a drive motor on each drive wheel. Compared to centralized drive systems, it eliminates the need for drive shafts, differentials, and other mechanical transmission devices, resulting in a shorter transmission chain and higher efficiency. Therefore, distributed drive systems have become the development direction for next-generation electric vehicles. As the power core of a distributed drive system, the in-wheel motor needs to possess strong torque output capabilities to meet the demands of climbing and overtaking, while also adapting to wheel size and the space constraints within the wheel rim. This necessitates a high torque density from the in-wheel motor. On the other hand, hub motors need to have good sealing to avoid contamination and damage to the motor interior from mud and sand on the road. The motor interior is a closed space, so the motor cooling system needs to have strong cooling capacity to meet the heat dissipation requirements of the motor under various operating conditions, and avoid internal overheating that could lead to irreversible demagnetization of permanent magnets, insulation damage and other faults. At the same time, better heat dissipation conditions also help the motor output greater torque and power.

[0003] Axial flux motors are generally considered to have higher torque density than radial flux motors, and their flattened structure is better suited to the internal space of wheel rims. However, for hub systems, there is a lack of selection criteria based on motor torque density. Furthermore, after machining and assembly, it is difficult to directly observe the actual positional relationship between the stator and rotor inside the hub motor. Axial flux motors are prone to mechanical asymmetry due to bearing wear, machining deviations, and assembly errors, leading to increased vibration, increased bearing load, and even, in severe cases, rotor rubbing. This necessitates the urgent need to monitor the internal condition of the motor.

[0004] In the process of new energy vehicles developing towards electrification and intelligence, distributed drive electric vehicles have received widespread attention due to their good transmission efficiency, variable chassis, and excellent power response, and have obvious competitive advantages and development prospects in commercial vehicles and high-end passenger vehicles. As the core execution unit of the distributed drive system, the in-wheel motor highly integrates drive, braking, and load-bearing functions within the narrow space of the wheel rim, completely freeing up the vehicle body layout space and providing unprecedented possibilities for innovation in overall vehicle layout and chassis dynamics control. However, this highly integrated technical approach also brings extremely stringent engineering challenges: under the constraints of the limited and enclosed geometric space inside the wheel, the motor must simultaneously meet the vehicle's power demand for high torque density and the reliable heat dissipation requirements under extreme operating conditions. The contradiction between the two is particularly acute when the vehicle is operating at low speed and high torque.

[0005] When the vehicle's curb weight is 1900kg, the maximum load weight reaches 2400kg, and the maximum gradeability requirement is 30.5%, these vehicle parameters dictate that the hub motor must possess outstanding low-speed, high-torque output capabilities, with a peak torque requirement as high as 286.94 N·m. Under typical high-load conditions such as low-speed climbing or rapid acceleration, the motor's phase current increases sharply, and the stator winding copper losses increase quadratically with the current, resulting in a large amount of heat being generated and rapidly accumulated inside the motor in a short period of time. Due to the compact and enclosed structure of the hub motor, coupled with its installation position inside the wheel, the convective heat transfer conditions with the external environment are extremely limited. The difficulty in dissipating heat accumulation inside the stator has become a key bottleneck restricting the development of hub motors towards higher power density. If the heat inside the motor cannot be effectively dissipated in a timely manner, it will not only accelerate the thermal aging process of the stator winding insulation material, but may also cause the permanent magnet's operating point temperature to exceed its allowable limit, resulting in irreversible thermal demagnetization. This directly limits the duration of the motor's peak torque, severely weakening the vehicle's power performance and operational safety and reliability.

[0006] Although related research has made progress in improving in-slot cooling structures and thermal modeling methods, two main limitations remain unresolved. Firstly, the design of existing in-slot cooling structures is largely based on fixed electromagnetic design schemes, failing to achieve true synergistic optimization with the parameter variables from the electromagnetic design stage, especially the key dimensional parameters of the Halbach array magnetic circuit structure. For example, passively reducing the copper fill factor to embed DWHX directly leads to increased phase resistance and copper loss, and the interaction mechanism between this change and the altered internal loss distribution of the motor after Halbach array optimization has not been fully revealed and quantitatively analyzed. Secondly, there is a lack of targeted, low-cost, high-efficiency cooling structure design and optimization methods to address the unique engineering problem of obstructed axial heat conduction paths within the stator caused by the external rotor structure of hub motors.

[0007] With the continuous increase in the power density of automotive drive motors, the coupling effects between multiple physical fields such as electromagnetics, heat, and structure are becoming increasingly significant and complex. Existing single-discipline sequential design methods are no longer effective in obtaining the global optimal solution at the system level. Therefore, multi-objective, multi-physics collaborative optimization design methods have gradually become a cutting-edge technology direction in the field of motor R&D. Genetic algorithms, represented by NSGA-II, have been increasingly widely used in multi-objective optimization of motor structural parameters due to their powerful global search capabilities and effective approximation of Pareto fronts. However, there is a lack of corresponding processing methods for simultaneously incorporating the Halbach array magnetic circuit structural parameters and the geometric parameters of the cooling structure in the stator slots into the optimization variable space for collaborative optimization. The main reason is that there are differences in the time response scale and spatial resolution requirements of electromagnetic fields and temperature fields, resulting in high resource consumption for direct bidirectional coupling calculations, which is difficult to apply in practical engineering optimization iteration processes. Existing studies have largely employed coupling strategies based on unidirectional data transfer or simplified modeling methods based on lumped parameter thermal networks (LPTNs), which can address the problem to some extent. While these methods offer significant advantages in computational efficiency, they struggle to accurately capture the detailed temperature distribution in local hot spots within the stator slots and the three-dimensional characteristics of the cooling fluid flow and heat transfer. Therefore, there is currently no magnetic-thermal co-simulation modeling and multi-objective optimization framework that can balance computational accuracy and simulation efficiency. Hub motors lack standardized optimization methods, and there are no standardized guidelines for precise optimization of stator water-cooled flow channels in hub motors. Summary of the Invention

[0008] To overcome the shortcomings of existing technologies, a method for determining the optimal cooling combination parameters for hub motors is provided to solve the above problems.

[0009] A method for determining the optimal cooling combination parameters for a hub motor is proposed. The method involves using the air gap length, permanent magnet thickness, stator slot width, stator slot bottom width, and stator slot height in the hub motor as optimization variables, generating sample points using the optimal Latin hypercube experimental method, constructing a second-order response surface surrogate model based on the sample points, and solving the second-order response surface surrogate model using the NSGA-II algorithm to determine the optimal combination parameters with the dual optimization objectives of maximizing average torque and minimizing torque ripple.

[0010] As a preferred approach: using the air gap length, permanent magnet thickness, stator slot width, stator slot bottom width, and stator slot height in the hub motor as optimization variables, the optimal Latin hypercube experimental method is used to generate sample points. The process of constructing a second-order response surface surrogate model based on these sample points is as follows:

[0011] The air gap length is g, the slot opening width is bs1, the slot bottom width is bs2, the slot height is hs1, and the permanent magnet thickness is hpm. The air gap length g, slot opening width bs1, slot bottom width bs2, slot height hs1, and permanent magnet thickness hpm are used as optimization variables, with the average torque T as the metric. avg Maximize and torque ripple T ripple Minimization is the dual optimization objective. An optimal Latin hypercube experimental design is used to generate 40-60 sets of sample points. The response values ​​of each sample point are calculated using finite element simulation. Based on these response values, a second-order response surface surrogate model is constructed. The determination coefficients R0 for the corresponding average torque and torque ripple are then obtained using this second-order response surface surrogate model. 2 The two determining coefficients R corresponding to the average torque and torque ripple are used. 2 This indicates the model's fitting accuracy;

[0012] With the objectives of maximizing average torque and minimizing torque ripple, minT ripple For minimum torque ripple, maxT avg The formula for calculating the torque ripple corresponding to the maximum average torque is:

[0013]

[0014] The expression corresponding to the air gap length g, slot width bs1, slot bottom width bs2, slot height hs1, and permanent magnet thickness hpm as optimization variables is as follows:

[0015]

[0016] The range of values ​​for air gap length g, slot width bs1, slot bottom width bs2, slot height hs1, and permanent magnet thickness hpm is determined based on initial design parameters, electromagnetic performance requirements, and processing constraints.

[0017] As a preferred approach, the process of generating sample points using the optimal Latin hypercube experimental method is as follows:

[0018] The range of values ​​for each optimization variable is evenly divided into several equally probable intervals. A sampling point is randomly selected within each interval to ensure that the samples are uniformly distributed across all dimensions of space. This process achieves better spatial coverage with a smaller number of samples. Another expression for the optimization variable is:

[0019]

[0020] In the above formula, k is the number of variables; the optimization variables include air gap length g, slot width bs1, slot bottom width bs2, slot height hs1, and permanent magnet thickness hpm. For each variable x i The calculation formula corresponding to its range of values ​​is:

[0021]

[0022] In Latin hypercube sampling, the range of values ​​for each variable is evenly divided into N sub-intervals. A sampling point is selected in each of the N sub-intervals. By randomly arranging and combining the sampling points of each variable, N sets of sample data are constructed, thus forming the experimental design matrix.

[0023]

[0024] In the process of optimizing the samples using the optimal Latin hypercube experimental method, the optimization criterion of maximum and minimum distance is introduced to ensure that the minimum distance between sample points is at the maximum value within the predetermined requirement range, thereby ensuring that the dispersion of the samples in the design space meets the predetermined requirements.

[0025] The expression for the optimization objective is:

[0026]

[0027] The above formula ensures that the minimum Euclidean distance between any two points in all sample points is maximized, thereby avoiding excessive concentration of sample points and ensuring the uniformity and representativeness of the experimental design.

[0028] As a preferred approach: the second-order response surface surrogate model is solved using the NSGA-II algorithm to determine the optimal combination parameters with the optimization objectives of maximizing average torque and minimizing torque ripple. This process involves solving the Pareto front using the NSGA-II algorithm, with the dual objectives of maximizing average torque and minimizing torque ripple. Given a range of design variables, N sets of sample points are generated. Finite element simulations are then performed on each set of samples using ANSYS Maxwell to obtain the corresponding motor performance indicators, which are the average torque Tavg and the torque ripple T. ripple Finally, the optimal solution was selected from the corresponding motor performance indicators to obtain the motor's average torque Tavg and torque ripple T. ripple The optimal value.

[0029] As a preferred option: the second-order response surface proxy model is solved based on the NSGA-II algorithm to obtain the processing result data. Based on the processing result data, the stator core loss formula is established based on the Bertotti iron loss separation model. The stator core loss formula, DC copper loss and AC copper loss are combined to calculate the winding copper loss. The permanent magnet eddy current loss is obtained by combining the winding copper loss with the three-dimensional transient finite element model.

[0030] As a preferred approach: Based on the processing results data and the Bertotti iron loss separation model, a stator core loss formula is established. The process of combining the stator core loss formula, DC copper loss, and AC copper loss to calculate the winding copper loss is as follows:

[0031] Winding copper losses include DC copper losses and AC copper losses. The formula corresponding to the DC resistance in winding copper losses is:

[0032]

[0033] In the above formula: For electrical conductivity, The length of each phase winding, This represents the cross-sectional area of ​​the winding.

[0034] The formula for DC copper loss in winding copper loss is:

[0035]

[0036] When an alternating current is passed through a conductor, the changing magnetic field around the conductor will induce a current in the conductor, causing the current in the wire to tend towards the surface. At this time, the current distribution is uneven and the skin effect occurs. When an alternating current is passed through adjacent conductors, the current distribution of each conductor will be affected by the adjacent magnetic field, resulting in the proximity effect. When the winding is in an alternating magnetic field, eddy current losses will be generated in the winding. The skin effect, proximity effect, and eddy current losses caused by the external magnetic field are collectively referred to as AC copper losses.

[0037] When the conductor is in a uniform magnetic field, and the magnetic field within the slot is parallel to the bottom of the slot, the formula for AC copper loss is:

[0038]

[0039] In the above formula, ω is the angular frequency of the current. For the conductor length, The diameter of the conductor. The resistivity of the conductor;

[0040] Under the constraints of the skin effect and proximity effect on AC copper loss, the formula for AC copper loss is:

[0041]

[0042] In the above formula, m1 represents the number of conductors. The distance between adjacent conductors. The resistivity between conductor chains is used to ultimately determine the copper loss of the motor windings.

[0043] As a preferred approach, the calculation process for permanent magnet eddy current losses, based on a combination of winding copper losses and a three-dimensional transient finite element model, is as follows:

[0044] After calculating the winding copper loss of the motor, the winding copper loss is combined with the three-dimensional transient finite element model for the following processing: The calculation process of permanent magnet eddy current loss of surface-mount or Halbach array permanent magnet motors is as follows:

[0045]

[0046] In the above formula, It is the eddy current density of the permanent magnet. It is the conductivity of the permanent magnet, V P It is the volume of the permanent magnet;

[0047] As shown in the above formula, the eddy current loss of a permanent magnet is directly proportional to the square of the eddy current density and is closely related to the material's conductivity. Eddy current loss is also affected by the frequency of magnetic flux density change, the size of the permanent magnet, and the segmentation method. Segmenting the permanent magnet or using materials with low conductivity can effectively suppress eddy current loss. The formula for calculating the eddy current density of a permanent magnet is:

[0048]

[0049] In the above formula, This represents the eddy current path length in the permanent magnet. It is the magnetic flux density of a permanent magnet. It is the area encompassed by the eddy current path of the permanent magnet;

[0050] After solving the motor operation process based on the three-dimensional transient finite element model, the eddy current density distribution in the permanent magnet region is directly extracted by processing. The eddy current loss is calculated by combining the eddy current density distribution in the permanent magnet region with the material conductivity parameters, providing reliable data for motor loss analysis and thermal design.

[0051] As a preferred approach: Analysis of the motor temperature rise mechanism is the foundation for establishing a temperature field model. Combining loss calculation results, temperature field simulation is performed on the axial flux hub motor to obtain data on the cooling system for controlling temperature rise. Specifically, the process of establishing a three-dimensional heat conduction differential equation based on the combination of permanent magnet eddy current losses and Fourier's law of heat conduction is as follows:

[0052] The heat sources inside the motor include stator core losses, winding copper losses, permanent magnet eddy current losses, and mechanical losses. Core losses include hysteresis losses and eddy current losses, and the magnitude of core losses is closely related to the magnetic field frequency, magnetic flux density amplitude, and core material properties. Winding copper losses are proportional to the square of the current and the winding resistance, and the resistance increases with increasing temperature. Permanent magnet eddy current losses are induced by harmonic components in the air gap magnetic field. Mechanical losses include bearing friction losses and wind resistance losses, and mechanical losses are proportional to the cube of the rotational speed. The stator core losses, winding copper losses, permanent magnet eddy current losses, and mechanical losses act on the corresponding components in the form of heat generation rate, becoming the source terms for temperature rise calculation.

[0053] The solution to the temperature field of the motor is based on Fourier's law of heat conduction and the law of conservation of energy. In a rectangular coordinate system, the three-dimensional steady-state differential equation of heat conduction is:

[0054]

[0055] In the above formula, k x k y k z These are the thermal conductivity of the material in the x, y, and z directions, respectively. For temperature; q v Let this be the volumetric heat generation rate; for transient temperature fields, a term needs to be added to the left-hand side of the equation, which is the product of density and specific heat capacity multiplied by the temperature's partial derivative with respect to time.

[0056]

[0057] Solving the above equation requires boundary conditions, which can be categorized into three types:

[0058] First type of boundary condition: ;

[0059] Second type of boundary condition: ;

[0060] Third type of boundary condition: ;

[0061] In motor temperature rise analysis, the first type of boundary condition corresponds to the working condition of a given temperature, the second type of boundary condition corresponds to the working condition of a given heat flux density, and the third type of boundary condition corresponds to the working condition of a given convective heat transfer. The convective heat transfer coefficient is W / (m²·K). The fluid temperature is used; for symmetrical structures, an adiabatic boundary condition is adopted, which is a special case of the second type of boundary condition. ;

[0062] In the temperature rise analysis, the lumped-parameter thermal network method is used to calculate the average temperature rise of each component of the motor. The motor is divided into several isothermal nodes, which are connected by thermal resistance. The node temperature equations are established based on thermal balance as follows:

[0063] ;

[0064] In the above formula, These are the temperatures of the first and second nodes, respectively, R ij For inter-node thermal resistance, P t Given the heat power input to the nodes, solving this system of linear equations yields the steady-state temperature of each node. For transient temperature rise, introducing the heat capacity C, we obtain the first-order thermal differential equation:

[0065] ;

[0066] The solution to the first-order thermal differential equation is:

[0067] ;

[0068] In the above formula, It is the thermal time constant, and the temperature rises exponentially with time. The temperature rises rapidly in the initial stage and then gradually reaches a steady state value.

[0069] As a preferred option, the optimal combination parameter determination method also includes the process of constructing a T-shaped equivalent thermal resistance network model of the motor using the equivalent thermal network method, and establishing a fluid-structure interaction conjugate heat transfer model corresponding to the annular spiral water channel cooling structure built into the stator. The equivalent thermal network method discretizes the continuously distributed temperature field inside the motor into a finite number of nodes, and uses lumped parameter thermal resistance to replace the distributed thermal resistance, thereby constructing an equivalent model similar to an electrical network for temperature solution. The formation process of the T-shaped equivalent thermal resistance network of the annular cylinder in the method of temperature solution using the equivalent model is as follows:

[0070] The stator yoke, rotor yoke, and permanent magnet in the hub motor are all circular cylindrical structures with an outer diameter of r1, an inner diameter of r2, and an axial length of r1. When axial heat conduction and radial heat conduction are independent and there is no circumferential heat flow, the distributed parameter model is equivalent to a T-type lumped parameter network, where T is the lumped parameter network. m Let P represent the node with the average temperature of the cylinder, and P be the heat generated by the injected heat into that node. According to Fourier's law of heat conduction, the analytical expressions for the six thermal resistances in the network are:

[0071] ;

[0072] In the above formula: These are the axial and radial thermal conductivity of the material, respectively. The axial thermal resistance from the end face to the average temperature node. This is a negative thermal resistance term, used to correct for the location of the average temperature node; R 1r R 2r R is the radial thermal resistance from the inner and outer surfaces to the average temperature node. 3r This is the negative coupling thermal resistance between the inner and outer surfaces;

[0073] For the key heat exchange areas of the wheel hub motor, The convective heat transfer coefficient of the air gap between the stator and rotor, determined using empirical correlations, depends on the Nusselt number N. u And N u The convective heat transfer coefficient at the winding ends is related to the air gap geometry and Reynolds number Re; the convective heat transfer coefficient on the casing surface is determined by the external air velocity. For hub motors using axial ventilation cooling, a thermal pressure source model describing the temperature rise of the cooling medium is introduced, and the corresponding calculation process is as follows:

[0074] The cooling channel is divided into an inlet section, a middle section, and an outlet section. The average temperature rise of the cooling medium after absorbing heat loss from the components in each section is:

[0075]

[0076] In the above formula, P loss The total heat flow absorbed by the cooling medium in this section, and the equivalent flow resistance R. cf Defined as:

[0077]

[0078] In the above formula, For the density of the cooling fluid, For specific heat capacity at constant pressure, Volumetric flow rate;

[0079] The three thermal pressure source nodes represent the average temperatures of the cooling fluids in the inlet, middle, and outlet sections, respectively. average temperature The heat flow P absorbed at the inlet end ecl Heat flow P absorbed by the rotor yoke section yr Heat flow P absorbed at the outlet end ec2 The relation is:

[0080]

[0081] The above matrix equation couples the cooling medium temperature nodes with the solid component thermal network to form a complete three-dimensional equivalent thermal network;

[0082] Connecting the T-shaped thermal resistance network of each component to the thermal pressure source model of the cooling medium forms an overall thermal network with n nodes. According to Kirchhoff's heat flow law, the net heat flow injected into any node i is zero, that is:

[0083]

[0084] Written in matrix form:

[0085]

[0086] In the above formula, P is the column vector of node temperature rise; G is the column vector of node injection loss; The element expression of the thermal admittance matrix is ​​as follows:

[0087]

[0088] Substituting the constraint equations for the thermal pressure source of the cooling medium into the above equation, and then combining the matrices, we obtain the augmented equation set:

[0089]

[0090] In the above formula, the subscript Indicates a node of a solid component. The node represents the cooling fluid. Solving this system of equations will yield the axially asymmetric temperature distribution of the motor.

[0091] The beneficial effects of this invention are as follows:

[0092] This invention is essentially a collaborative processing method for the refined optimization of the structural parameters of the Halbach array and the efficient thermal management strategy within the stator slot. By deeply exploring the mutual feedback coupling mechanism between the Halbach magnetic circuit topology optimization variables and the space occupancy of the cooling structure within the slot, it resolves the strong correlation contradiction among electromagnetic performance, thermal load, and structural space in hub motors. This provides a systematic theoretical basis for realizing hub motors with high torque density, low torque ripple, and efficient heat dissipation capabilities. Through this invention, the optimal combination parameters with the dual optimization objectives of maximizing average torque and minimizing torque ripple can be derived, and the temperature distribution details and three-dimensional characteristics of the cooling fluid flow and heat transfer in local hot spots within the stator slot can be accurately captured, thus providing effective data to guide practical engineering.

[0093] This invention provides a precise processing method for electromagnetic optimization calculation and thermal management strategy of Halbach array axial flux hub motor. Based on three-dimensional finite element simulation and response surface proxy model, this invention completes the optimization processing of electromagnetic and thermal performance, provides a corresponding hub motor prototype for subsequent development of optimization schemes, and builds an electromagnetic performance test bench and thermal characteristic experimental platform to conduct actual measurements on key indicators such as no-load back electromotive force, load torque, efficiency, temperature rise distribution and cooling system pressure drop, in order to verify the accuracy of the simulation model and the effectiveness of the optimization scheme.

[0094] In the magnetothermal bidirectional coupling iterative analysis, this invention adopts a one-way data transfer strategy between electromagnetic calculation and thermal analysis, namely the conversion processing method of electromagnetic loss to temperature field source term. It also improves the transient thermal withstand capability of hub motor under extreme conditions by embedding micro heat pipe arrays in stator slots, using evaporative cooling technology or phase change material PC energy storage for heat equalization, and other novel enhanced heat transfer methods. Attached Figure Description

[0095] Figure 1 This is a schematic diagram of the overall structure of a hub motor.

[0096] Figure 2a This is a schematic diagram illustrating the quarter-air domain meshing process in the adaptive meshing process of the hub motor according to the present invention;

[0097] Figure 2b This is a schematic diagram of the mesh generation process for the quarter-stator yoke in the adaptive mesh generation process of the hub motor according to the present invention;

[0098] Figure 2c This is a schematic diagram of the overall mesh partitioning process of the hub motor in the adaptive mesh partitioning process of the present invention;

[0099] Figure 2d This is a schematic diagram of the quarter-band domain mesh partitioning process in the adaptive mesh partitioning process of the hub motor in this invention;

[0100] Figure 3 To obtain the curve of air gap magnetic flux density at the center line of the outer diameter and inner diameter of the motor;

[0101] Figure 4 A schematic diagram of harmonic orders;

[0102] Figure 5 This is a schematic diagram of the no-load back electromotive force waveform;

[0103] Figure 6 This is a schematic diagram of harmonic analysis of the no-load back electromotive force;

[0104] Figure 7 This is a schematic diagram of the external characteristic curves of the motor;

[0105] Figure 8 This is a schematic diagram of the Halbach permanent magnet array.

[0106] Figure 9 Schematic diagrams for magnetization at angles of 0, 30, 45, and 60 degrees;

[0107] Figure 10 This is a schematic diagram of the cogging torque curve;

[0108] Figure 11 This is a schematic diagram of the back electromotive force waveform;

[0109] Figure 12 This is a schematic diagram of the rated torque waveform;

[0110] Figure 13 This is a schematic diagram of the hysteresis loop.

[0111] Figure 14 The loss curves of silicon steel sheets at different frequencies;

[0112] Figure 15 This is a schematic diagram of the stator core loss curve;

[0113] Figure 16 This is a schematic diagram of rotor loss curves;

[0114] Figure 17 This is a schematic diagram of a T-type equivalent heat network;

[0115] Figure 18 This is a schematic diagram of the equivalent heat network model;

[0116] Figure 19 This is a schematic diagram comparing the steady-state temperature field under rated operating conditions before and after optimization of the present invention. Detailed Implementation

[0117] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0118] Specific implementation method one: Combining Figures 1 to 19This embodiment describes the method for determining the optimal combination parameters for the hub motor. The optimal combination parameters are determined using the air gap length, permanent magnet thickness, stator slot width, stator slot bottom width, and stator slot height as optimization variables. Sample points are generated using the optimal Latin hypercube experimental method. A second-order response surface surrogate model is constructed based on these sample points. The second-order response surface surrogate model is then solved using the NSGA-II algorithm to determine the optimal combination parameters with the dual optimization objectives of maximizing average torque and minimizing torque ripple.

[0119] This invention elaborates on the main technical parameters of the drive motor based on the analysis of vehicle driving resistance and power distribution. When a vehicle model's drive motor has a rated power of 16kW, a maximum power of 32kW, a rated torque of 95N·m, a maximum torque of 286.94N·m, a rated speed of 1600rpm, and a maximum operating speed of 3219rpm, a 36-slot, 40-pole fractional-slot concentrated winding scheme is adopted according to these requirements. A new single-stator, dual-rotor processing method is proposed. Furthermore, Halbach arrangement is used to improve the permanent magnet arrangement. A three-dimensional electromagnetic field finite element model is established to study and analyze the designed motor, demonstrating that it can ensure the motor has the characteristics of high torque at low speeds and stable, high-efficiency operation at medium and high speeds. This invention also compared the electromagnetic performance of four auxiliary permanent magnet magnetization angles (30°, 45°, 60°, and 90°). It was found that a 45° magnetization angle achieved the optimal balance between magnetization enhancement and torque ripple suppression. With maximizing average torque and minimizing torque ripple as optimization objectives, the air gap length, permanent magnet thickness, stator slot width, stator slot bottom width, and stator slot height were selected as optimization variables. An optimal Latin hypercube experimental design was used to generate sample points, and a second-order response surface surrogate model was constructed. The Pareto front was solved using the NSGA-II algorithm. After optimization, the average motor torque was 405.0 N·m, the torque ripple decreased from 12.58% to 9.00%, a reduction of 28.5%, and the efficiency increased from 91.8% to 93.2%.

[0120] Specific Implementation Method Two: This implementation method is a further limitation of Specific Implementation Method One. In this implementation method, the air gap length, permanent magnet thickness, stator slot width, stator slot bottom width, and stator slot height in the hub motor are used as optimization variables. The optimal Latin hypercube experimental method is used to generate sample points, and the process of constructing a second-order response surface surrogate model based on the sample points is as follows:

[0121] The air gap length is g, the slot opening width is bs1, the slot bottom width is bs2, the slot height is hs1, and the permanent magnet thickness is hpm. The air gap length g, slot opening width bs1, slot bottom width bs2, slot height hs1, and permanent magnet thickness hpm are used as optimization variables, with the average torque T as the metric. avg Maximize and torque ripple T rippleMinimization is the dual optimization objective. An optimal Latin hypercube experimental design is used to generate 40-60 sets of sample points. The response values ​​of each sample point are calculated using finite element simulation. Based on these response values, a second-order response surface surrogate model is constructed. The determination coefficients R0 for the corresponding average torque and torque ripple are then obtained using this second-order response surface surrogate model. 2 The two determining coefficients R corresponding to the average torque and torque ripple are used. 2 This indicates the model's fitting accuracy;

[0122] With the objectives of maximizing average torque and minimizing torque ripple, minT ripple For minimum torque ripple, maxT avg The formula for calculating the torque ripple corresponding to the maximum average torque is:

[0123]

[0124] The expression corresponding to the air gap length g, slot width bs1, slot bottom width bs2, slot height hs1, and permanent magnet thickness hpm as optimization variables is as follows:

[0125]

[0126] The range of values ​​for air gap length g, slot width bs1, slot bottom width bs2, slot height hs1, and permanent magnet thickness hpm is determined based on the initial design parameters, electromagnetic performance requirements, and processing constraints. That is, the range of values ​​for each variable is determined under the premise of ensuring the rationality of the optimization process and the engineering feasibility of the results.

[0127] In this embodiment, the main dimensions of the motor are:

[0128] Table 1 Motor Design Parameters

[0129]

[0130] Formula for calculating motor winding coefficient:

[0131]

[0132] In the above formula: This refers to the coil short-pitch factor; The coil distribution coefficient; The minimum effective angle for each cell's electrical angle, in degrees; This represents the number of coils per phase within the basic winding unit; The value represents the electrical angle per slot of the motor, in degrees.

[0133] Slot-pole configuration is a core parameter in the electromagnetic design of permanent magnet synchronous motors, directly determining the winding distribution and significantly impacting the motor's torque characteristics, back EMF sinusoidal nature, cogging torque, torque density, and additional losses. A reasonable slot-pole configuration can significantly reduce torque ripple and improve low-speed operation smoothness. To address the requirements of low-speed, high-torque, and high-smoothness hub motors, this paper prioritizes a fractional-slot concentrated winding structure. After comprehensively comparing various combinations of stator 36-48 slots and 18-24 pole pairs, considering both the winding coefficient Kdp and the least common multiple (LCM) of the slot-pole ratio, and taking into account manufacturing difficulty and cost, a 36-slot, 40-pole configuration was ultimately selected. This configuration offers the best overall performance in suppressing cogging torque, optimizing back EMF waveform, and improving torque output capability, fully meeting the design requirements of axial flux hub motors. The corresponding winding parameters are shown in the table below.

[0134] Table 2 Winding coefficient Kdp

[0135]

[0136] Table 3 Least Common Multiple (LCM)

[0137]

[0138]

[0139] Considering the manufacturing difficulty and cost, a 36-slot, 40-pole motor was ultimately selected.

[0140] Table 4 Winding Parameters

[0141]

[0142] A permanent magnet brushless disc DC motor is essentially a permanent magnet synchronous AC motor. A permanent magnet brushless disc DC motor is one where the inverter converts DC power into a rectangular wave current for driving, while a permanent magnet brushless disc AC motor is one where the inverter converts DC power into a sinusoidal wave current for driving.

[0143] The stator outer diameter is a key basic parameter in motor design and can be calculated based on motor design performance indicators and dimensional equations. The motor output power is:

[0144]

[0145] Rate waveform coefficient; The winding distribution factor; For current waveform coefficients; This is the polar arc coefficient; T represents the air gap magnetic flux density, measured in tons (T); A represents the electrical load of the motor, measured in A / cm. This is the ratio of the inner and outer diameters of the motor stator; Motor outer diameter, in cm; if outer diameter D m and maximum electrical load A max The armature diameter ratio of a disc permanent magnet motor is constant. Maximum output power can be obtained at this time. Considering factors such as copper usage, efficiency, and leakage flux, the calculated outer diameter of the motor stator is 320mm and the inner diameter is 191mm, which are the most suitable dimensions for the inner and outer diameters of the permanent magnet body of the motor.

[0146] Specific Implementation Method Three: This implementation method is a further limitation of Specific Implementation Method One or Two. In this implementation method, the process of generating sample points using the optimal Latin hypercube experimental method involves uniformly dividing the value range of each optimization variable into several equally probable intervals, and randomly selecting a sampling point within each interval. This ensures that the samples are uniformly distributed in all dimensions of space, thus achieving better spatial coverage with a smaller number of samples. Another expression for the optimization variable is:

[0147]

[0148] In the above formula, k is the number of variables; the optimization variables include air gap length g, slot width bs1, slot bottom width bs2, slot height hs1, and permanent magnet thickness hpm. For each variable x i The calculation formula corresponding to its range of values ​​is:

[0149]

[0150] In Latin hypercube sampling, the range of values ​​for each variable is evenly divided into N sub-intervals. A sampling point is selected in each of the N sub-intervals. By randomly arranging and combining the sampling points of each variable, N sets of sample data are constructed, thus forming the experimental design matrix.

[0151]

[0152] In the process of optimizing the samples using the optimal Latin hypercube experimental method, the optimization criterion of maximum and minimum distance is introduced to ensure that the minimum distance between sample points is at the maximum value within the predetermined requirement range, thereby ensuring that the dispersion of the samples in the design space meets the predetermined requirements.

[0153] The expression for the optimization objective is:

[0154]

[0155] The above formula ensures that the minimum Euclidean distance between any two points in all sample points is maximized, thereby avoiding excessive concentration of sample points and ensuring the uniformity and representativeness of the experimental design.

[0156] Specific Implementation Method Four: This implementation method further defines Specific Implementation Methods One, Two, or Three. In this method, the process of determining the optimal combination parameters with the optimization objectives of maximizing average torque and minimizing torque ripple is based on solving the second-order response surface surrogate model using the NSGA-II algorithm. This involves solving the Pareto front using the NSGA-II algorithm, with the dual objectives of maximizing average torque and minimizing torque ripple. Given a range of design variables, N sets of sample points are generated. Finite element simulation calculations are performed on each set of samples using ANSYS Maxwell to obtain the corresponding motor performance indicators. The motor performance indicators are the average torque Tavg and the torque ripple T. ripple Finally, the optimal solution was selected from the corresponding motor performance indicators to obtain the motor's average torque Tavg and torque ripple T. ripple The optimal value.

[0157] Specific Implementation Method Five: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, or Four, combined with... Figures 8 to 18 As shown, in this embodiment, the stator core loss of the motor can be solved using Maxwell software. The curve showing the change of stator core loss over time is illustrated. The area of ​​the hysteresis loop reflects the magnitude of the hysteresis loss, and its area is proportional to the loss. The motor core is in an alternating magnetic field, which induces an electromotive force, generating eddy currents and thus causing eddy current losses. Hysteresis loss and eddy current loss are affected by frequency, magnetic flux density amplitude, and the volume of the core material. Currently, silicon steel sheets are commonly used in core manufacturing, and the processing technology mostly employs lamination. This is because silicon steel has good magnetic permeability and high resistivity, which can effectively reduce eddy current losses. Additional iron losses do not depend on the core material itself, but rather on the core's structure and manufacturing process.

[0158] The core loss separation model proposed by Bertotti et al. is used, and the specific Bertotti iron loss calculation formula is as follows:

[0159]

[0160] Hysteresis loss is the energy loss caused by hysteresis during the magnetization process of a permanent magnet material, and is calculated by the following formula:

[0161]

[0162] Eddy current loss is the energy loss caused by eddy currents generated in the iron core in a changing magnetic field. The flow of these eddy currents in the conductor creates a Joule heating effect. It is calculated by the following formula.

[0163]

[0164] The formula for calculating additional losses is:

[0165]

[0166] In the above formula: To find the hysteresis loss coefficient, This is the eddy current loss coefficient. This is the additional loss factor.

[0167] The second-order response surface proxy model is solved using the NSGA-II algorithm to obtain the processed data. Based on the processed data, the stator core loss formula is established using the Bertotti iron loss separation model. The winding copper loss is calculated by combining the stator core loss formula, DC copper loss and AC copper loss. The permanent magnet eddy current loss is obtained by combining the winding copper loss with the three-dimensional transient finite element model.

[0168] Specific Implementation Method Six: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, Four, or Five. In this implementation method, based on the processing result data and the Bertotti iron loss separation model, a stator core loss formula is established. The process of calculating the winding copper loss by combining the stator core loss formula, DC copper loss, and AC copper loss is as follows:

[0169] Winding copper losses include DC copper losses and AC copper losses. The formula corresponding to the DC resistance in winding copper losses is:

[0170]

[0171] In the above formula: For electrical conductivity, The length of each phase winding, This represents the cross-sectional area of ​​the winding.

[0172] The formula for DC copper loss in winding copper loss is:

[0173]

[0174] When an alternating current is passed through a conductor, the changing magnetic field around the conductor will induce a current in the conductor, causing the current in the wire to tend towards the surface. At this time, the current distribution is uneven and the skin effect occurs. When an alternating current is passed through adjacent conductors, the current distribution of each conductor will be affected by the adjacent magnetic field, resulting in the proximity effect. When the winding is in an alternating magnetic field, eddy current losses will be generated in the winding. The skin effect, proximity effect, and eddy current losses caused by the external magnetic field are collectively referred to as AC copper losses.

[0175] When the conductor is in a uniform magnetic field, and the magnetic field within the slot is parallel to the bottom of the slot, the formula for AC copper loss is:

[0176]

[0177] In the above formula, ω is the angular frequency of the current. d is the conductor length, and d is the conductor diameter. The resistivity of the conductor;

[0178] Under the constraints of the skin effect and proximity effect on AC copper loss, the formula for AC copper loss is:

[0179]

[0180] In the above formula, m1 represents the number of conductors. ρ is the distance between adjacent conductors. ss The resistivity between conductor chains is used to ultimately determine the copper loss of the motor windings.

[0181] Specific Implementation Method Seven: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, Four, Five, or Six. In this implementation method, a three-dimensional heat conduction differential equation is established based on the combination of permanent magnet eddy current loss and Fourier's law of heat conduction. An equivalent thermal network model of the motor is constructed using the equivalent thermal network method. Finally, an annular spiral water channel cooling structure built into the stator is designed, and a fluid-structure interaction conjugate heat transfer model is established.

[0182] Combination Figures 3 to 7 As shown, under rated load conditions, the motor operates at rated current, with an average electromagnetic torque of 95.09 N·m, corresponding to an effective back electromotive force of 133.23 V and an effective current of 59 A. This result reflects the theoretical output capability of the motor under continuous operating conditions. The calculated relationship shows that torque and current exhibit essentially linear changes, indicating that the motor's magnetic circuit design has not entered a significant saturation state near the rated operating point, and the electromagnetic parameter matching is relatively reasonable. The external characteristic curve shows that the torque remains essentially constant below the base speed, indicating that the motor operates in the constant torque region.

[0183] Under peak torque conditions, the calculated motor current is 275A, corresponding to an average torque of 285.79 N·m, which is three times the rated torque, and the effective value of the back electromotive force is 176.94 V. This result indicates that, theoretically, the motor possesses strong short-term overload capacity, meeting the requirements of vehicle start-up and transient acceleration. However, it should be noted that this conclusion is based on an ideal electromagnetic model and does not consider the effects of temperature rise and material nonlinearity; in actual operation, its duration will be limited by thermal conditions.

[0184] Under peak power conditions, as the motor speed increases, the calculated average torque decreases to 47.45 N·m, the effective value of the back electromotive force increases to 208.74 V, and the effective value of the current is 25.1 A. This trend conforms to the basic operating law of permanent magnet synchronous motors, namely, as the speed increases, the back electromotive force gradually approaches the power supply voltage limit, requiring field weakening control to reduce the air gap flux linkage, thereby allowing the motor to enter the constant power operating region. Although control strategy simulation has not yet been introduced at this stage, the calculation results preliminarily indicate that the motor has the potential to expand its high-speed operating range.

[0185] Based on the theoretical calculation results of the above three operating conditions, it can be seen that the motor exhibits typical "low speed high torque - high speed constant power" operating characteristics at the design level, which can meet the drive requirements within a wide speed range.

[0186] Specific Implementation Method Eight: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, Four, Five, Six, or Seven. In this implementation method, the calculation process for the permanent magnet eddy current loss is obtained by combining the winding copper loss with the three-dimensional transient finite element model as follows:

[0187] After calculating the winding copper loss of the motor, the winding copper loss is combined with the three-dimensional transient finite element model for the following processing: The calculation process of permanent magnet eddy current loss of surface-mount or Halbach array permanent magnet motors is as follows:

[0188]

[0189] In the above formula, J P It is the eddy current density of the permanent magnet. It is the conductivity of the permanent magnet, V P It is the volume of the permanent magnet;

[0190] As shown in the above formula, the eddy current loss of a permanent magnet is directly proportional to the square of the eddy current density and is closely related to the material's conductivity. Eddy current loss is also affected by the frequency of magnetic flux density change, the size of the permanent magnet, and the segmentation method. Segmenting the permanent magnet or using materials with low conductivity can effectively suppress eddy current loss. The formula for calculating the eddy current density of a permanent magnet is:

[0191]

[0192] In the above formula, l is the eddy current path length in the permanent magnet, and B P It is the magnetic flux density of a permanent magnet, S P It is the area contained in the eddy current path of the permanent magnet; after completing the solution of the motor operation process based on the three-dimensional transient finite element model, the eddy current density distribution of the permanent magnet region is directly extracted by processing, and the eddy current loss is calculated by combining the eddy current density distribution of the permanent magnet region with the material conductivity parameters, so as to provide reliable data basis for motor loss analysis and thermal design.

[0193] Combination Figures 8 to 12 As shown in the figure, the rated torque waveforms of the motor under different Halbach schemes are presented in this embodiment, and the average torque and torque ripple values ​​of each scheme are compared. The analysis results show that, compared with the prototype motor, the average torque of each scheme is improved to varying degrees after adopting the Halbach array, verifying the effectiveness of the Halbach array's unilateral magnetic focusing effect in enhancing the air gap magnetic flux density. Among them, the average torque increase is most significant when the magnetization angle of the auxiliary permanent magnet is 30° and 45°, both of which are better than the 0° and 60° schemes. However, further comparison of the torque ripple index reveals that the torque ripple at a magnetization angle of 45° is significantly less than that at 30°. This is because the 45° magnetization direction can more effectively smooth the air gap magnetic permeability distribution, weaken the interaction between the harmonic magnetic field and the stator slots, thereby reducing torque ripple.

[0194] After a comprehensive evaluation of the cogging torque, the sinusoidal waveform of the no-load back EMF, and the average torque, the 45° magnetization angle scheme exhibits good balance in all performance indicators: the cogging torque amplitude is the smallest, the back EMF harmonic distortion rate is low, and the average torque is significantly improved, ensuring the smooth operation of the motor under high torque pulsation, balancing the compensation degree of the control system, and having a positive impact on ride comfort.

[0195] In this embodiment, the segmented Halbach array significantly improves the overall performance of the motor. Comparing the optimization effects of four auxiliary permanent magnet magnetization angles (0°, 30°, 45°, and 60°), it was found that a 45° magnetization angle achieves the best balance between enhanced magnetization efficiency and torque ripple suppression. Compared to the prototype, this structure reduces the motor cogging torque by 0.235 N·m, increases the peak no-load back EMF by 16.53 V, increases the fundamental amplitude by 34.15 V, and increases the average load torque by 64.8 N·m. It also improves the sinusoidal nature of the back EMF, verifying the applicability of the Halbach array's advantages of single-sided magnetization and reduced leakage flux in axial flux motors.

[0196] The combination of response surface methodology and genetic algorithm can efficiently solve the multi-objective optimization problem of axial flux motors. A high-precision response surface model was constructed using the Latin hypercube sampling method, and the Pareto optimal front was obtained based on the non-dominated sorting genetic algorithm. Considering the priority requirements of power and ride comfort for electric vehicle hub motors, a torque density weight of 0.7 and a torque ripple weight of 0.3 were set, and the optimal design scheme was selected through comprehensive evaluation coefficients. After optimization, the average torque of the motor increased by 232.09 N·m, torque ripple decreased by 28.5%, torque density increased by 22.8%, and efficiency increased by 1.746 percentage points, achieving a synergistic improvement in torque output capability, operational stability, and energy conversion efficiency.

[0197] Specific Implementation Method Nine: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, Four, Five, Six, Seven, or Eight. In this implementation method, the analysis of the motor temperature rise mechanism is the basis for establishing a temperature field model. Combined with the loss calculation results, a temperature field simulation is performed on the axial flux hub motor to obtain data sources for the cooling system to control the temperature rise. Specifically, the process of establishing a three-dimensional heat conduction differential equation based on the combination of permanent magnet eddy current loss and Fourier's law of heat conduction is as follows:

[0198] The heat sources inside the motor include stator core losses, winding copper losses, permanent magnet eddy current losses, and mechanical losses. Core losses include hysteresis losses and eddy current losses, and the magnitude of core losses is closely related to the magnetic field frequency, magnetic flux density amplitude, and core material properties. Winding copper losses are proportional to the square of the current and the winding resistance, and the resistance increases with increasing temperature. Permanent magnet eddy current losses are induced by harmonic components in the air gap magnetic field. Mechanical losses include bearing friction losses and wind resistance losses, and mechanical losses are proportional to the cube of the rotational speed. The stator core losses, winding copper losses, permanent magnet eddy current losses, and mechanical losses act on the corresponding components in the form of heat generation rate, becoming the source terms for temperature rise calculation.

[0199] The solution to the temperature field of the motor is based on Fourier's law of heat conduction and the law of conservation of energy. In a rectangular coordinate system, the three-dimensional steady-state differential equation of heat conduction is:

[0200]

[0201] In the above formula, k x k y k z These are the thermal conductivity of the material in the x, y, and z directions, respectively. For temperature; Let this be the volumetric heat generation rate; for transient temperature fields, a term needs to be added to the left-hand side of the equation, which is the product of density and specific heat capacity multiplied by the temperature's partial derivative with respect to time.

[0202]

[0203] Solving the above equation requires boundary conditions, which can be categorized into three types:

[0204] First type of boundary condition: ;

[0205] Second type of boundary condition: ;

[0206] Third type of boundary condition: ;

[0207] In the analysis of motor temperature rise, the first type of boundary condition corresponds to the working condition of a given temperature, the second type of boundary condition corresponds to the working condition of a given heat flux density, and the third type of boundary condition corresponds to the working condition of a given convective heat transfer. The convective heat transfer coefficient is W / (m²·K). The fluid temperature is used; for symmetrical structures, an adiabatic boundary condition is applied, which is a special case of the second type of boundary condition. ;

[0208] In the temperature rise analysis, the lumped-parameter thermal network method is used to calculate the average temperature rise of each component of the motor. The motor is divided into several isothermal nodes, which are connected by thermal resistance. The node temperature equations are established based on thermal balance as follows:

[0209] ;

[0210] In the above formula, These are the temperatures of the first and second nodes, respectively. For inter-node thermal resistance, Given the thermal power input to the nodes, solving this system of linear equations yields the steady-state temperature of each node. For transient temperature rise, introducing the heat capacity C, we obtain the first-order thermal circuit differential equation:

[0211] ;

[0212] The solution to the first-order thermal differential equation is:

[0213] ;

[0214] In the above formula, It is the thermal time constant, and the temperature rises exponentially with time. The temperature rises rapidly in the initial stage and then gradually reaches a steady state value.

[0215] Specific Implementation Method Ten: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, Four, Five, Six, Seven, Eight, or Nine. The optimal combination parameter determination method in this implementation method also includes the process of constructing a T-shaped equivalent thermal resistance network model of the motor using the equivalent thermal network method, and establishing a fluid-structure interaction conjugate heat transfer model corresponding to the annular spiral water channel cooling structure built into the stator. The equivalent thermal network method discretizes the continuously distributed temperature field inside the motor into a finite number of nodes, uses lumped parameter thermal resistance to replace the distributed thermal resistance, and thus constructs an equivalent model similar to an electrical network for temperature calculation. The formation process of the T-shaped equivalent thermal resistance network of the annular cylinder in the method of temperature calculation using the equivalent model is as follows:

[0216] Mesh generation is crucial for the accuracy of finite element analysis of electromagnetic fields. While increasing the mesh size improves the computational accuracy of Maxwell simulations, it also significantly increases the computational scale and solution time. Therefore, a reasonable trade-off between computational accuracy and computational cost must be struck in practical modeling to determine the appropriate mesh generation scheme.

[0217] Combination Figure 2a , 2b As shown in Figures 2c and 2d, the model was discretized using a combination of manual mesh generation and local refinement. The stator teeth have a relatively uniform magnetic flux distribution and are a fixed structure, therefore the mesh is relatively sparse, with an element size of 2mm. The permanent magnets and rotor support, as moving parts, have complex magnetic field variations; to improve computational accuracy, they are appropriately refined, with an element size of 1mm. The air gap region, as a critical area for electromagnetic energy conversion, experiences drastic magnetic field changes and has the highest accuracy requirements; therefore, a high-density mesh is used, with an element size of 0.5mm. Furthermore, to improve the accuracy of cogging torque calculation, the number of mesh layers in the air gap region is further increased. For the outer regions of the solution domain, where magnetic field changes are relatively gentle, a larger mesh size can be used to reduce the computational scale.

[0218] After mesh generation, the solution type needs to be set. This invention primarily employs a static field solution method for electromagnetic analysis, and uses a band region at the air gap to realize the relative motion between the rotor and stator. All other parameters use the software default settings. After completing the above settings, electromagnetic performance simulation analysis of the motor model can be performed.

[0219] The stator yoke, rotor yoke, and permanent magnet in the hub motor are all circular cylindrical structures with an outer diameter of r1, an inner diameter of r2, and an axial length of r1. When axial heat conduction and radial heat conduction are independent and there is no circumferential heat flow, the distributed parameter model is equivalent to a T-type lumped parameter network, where T is the lumped parameter network. m This represents the node representing the average temperature of the column. This represents the heat generation power injected into this node. According to Fourier's law of heat conduction, the analytical expressions for the six thermal resistances in the network are:

[0220] ;

[0221] In the above formula: These are the axial and radial thermal conductivity of the material, respectively. The axial thermal resistance from the end face to the average temperature node. This is a negative thermal resistance term, used to correct for the location of the average temperature node; R 1r R 2r R is the radial thermal resistance from the inner and outer surfaces to the average temperature node.3r This is the negative coupling thermal resistance between the inner and outer surfaces;

[0222] For the key heat exchange areas of the wheel hub motor, The convective heat transfer coefficient of the air gap between the stator and rotor, determined using empirical correlations, depends on the Nusselt number N. u And N u With air gap geometry and Reynolds number Related; the convective heat transfer coefficient at the winding ends is affected by the cooling air velocity; the convective heat transfer coefficient on the casing surface is determined by the external air velocity. For hub motors using axial ventilation cooling, a thermal pressure source model describing the temperature rise of the cooling medium is introduced, and the corresponding calculation process is as follows:

[0223] The cooling channel is divided into an inlet section, a middle section, and an outlet section. The average temperature rise of the cooling medium after absorbing heat loss from the components in each section is:

[0224]

[0225] In the above formula, P loss The total heat flow absorbed by the cooling medium in this section, and the equivalent flow resistance R. cf Defined as:

[0226]

[0227] In the above formula, For the density of the cooling fluid, For specific heat capacity at constant pressure, Volumetric flow rate;

[0228] The three thermal pressure source nodes represent the average temperatures of the cooling fluids in the inlet, middle, and outlet sections, respectively. average temperature The heat flow P absorbed at the inlet end ecl Heat flow P absorbed by the rotor yoke section yr Heat flow P absorbed at the outlet end ec2 The relation is:

[0229]

[0230] The above matrix equation couples the cooling medium temperature nodes with the solid component thermal network to form a complete three-dimensional equivalent thermal network;

[0231] Connecting the T-shaped thermal resistance network of each component to the thermal pressure source model of the cooling medium forms an overall thermal network with n nodes. According to Kirchhoff's heat flow law, the net heat flow injected into any node i is zero, that is:

[0232]

[0233] Written in matrix form:

[0234]

[0235] In the above formula, Let P be the column vector of node temperature rise; let G be the column vector of node injection loss; let G be the n×n dimensional thermal admittance matrix, whose element expression is:

[0236]

[0237] Substituting the constraint equations for the thermal pressure source of the cooling medium into the above equation, and then combining the matrices, we obtain the augmented equation system:

[0238]

[0239] In the above formula, the subscript 's' represents a solid component node. The node represents the cooling fluid. Solving this system of equations will yield the axially asymmetric temperature distribution of the motor.

[0240] Combination Figure 19 As shown, the temperature distribution of the motor before optimization exhibits obvious local concentration. The high-temperature area is mainly distributed in the stator winding slots and near the teeth, with a large temperature gradient and uneven circumferential distribution.

[0241] In the optimized structure, the overall temperature level of the stator is significantly reduced, the high-temperature area is significantly shrunk, the concentration of hot spots is weakened, and the temperature distribution is more uniform. This is mainly attributed to the more reasonable fluid distribution after the optimization of the cooling channel structure, which enhances the local heat exchange capacity of the high-heat area, thereby reducing the degree of heat accumulation. The temperature of the stator core area has also decreased, indicating that the efficiency of heat transfer from the winding to the cooling system has been improved, and the overall thermal resistance level has been reduced.

[0242] Specific Implementation Method Eleven: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, Four, Five, Six, Seven, Eight, Nine, or Ten. In this implementation method, during the process of determining the optimal combination parameters, when the motor is running, the rotors on both sides drive the air in the air gap to rotate, forming a complex flow state. The convective heat transfer in the air gap is equivalent to solid heat conduction, and an equivalent thermal conductivity (kg / kg) is introduced. The corresponding processing procedure is as follows:

[0243] First, calculate the air gap Reynolds number Re to determine the flow state:

[0244]

[0245] In the above formula, ν r ν is the linear velocity of the rotor rotation; g is the air gap length; air Let be the kinematic viscosity of air; the formula for calculating the critical Reynolds number is:

[0246]

[0247] In the above formula, d si The outer diameter is the stator diameter; calculations show that the air in the air gap is in a turbulent state, with an equivalent thermal conductivity k. g The calculation formula is:

[0248]

[0249] In the above formula, r is the ratio of the stator inner diameter to the rotor inner diameter. si r is the inner diameter of the stator. o Given the rotor's inner diameter, the equivalent thermal conductivity k of the air gap is calculated. g =0.0796W / (m·K);

[0250] The winding is composed of copper conductors, insulation layer and epoxy resin potting material, and adopts an isotropic equivalent model. The equivalent density ρ of the equivalent model is... eq Equivalent specific heat capacity c eq and equivalent thermal conductivity k eq The calculation formulas are as follows:

[0251] ;

[0252] In the above formula, ρ i c i k i V i l i Let be the density, specific heat capacity, thermal conductivity, volume, and length in the heat flow direction of the i-th material, respectively.

[0253] The fluid domain is the coolant within an annular spiral water channel. The physical property of the coolant is its density ρ. eq =998.2kg / m 3 Thermal conductivity k = 0.641 W / (m·K), specific heat capacity c = 4182 J / (kg·K), dynamic viscosity μ = 0.001003 Pa·s;

[0254] The process of selecting the turbulence model and determining the boundary conditions is as follows:

[0255] The formula for estimating the Reynolds number Re of the coolant flowing within the water channels is:

[0256] ;

[0257] The calculations above show that when Re > 2300, the flow is in a turbulent state. The standard k-ε turbulence model is selected, and its transport equation is:

[0258] The turbulent kinetic energy k equation is:

[0259] ;

[0260] The equation for the turbulent dissipation rate ε is:

[0261]

[0262] In the above formula, G k G is the turbulent kinetic energy production term caused by the average velocity gradient. b μ is the term for turbulent kinetic energy generation caused by buoyancy. t The viscosity is turbulent; the model constant is taken as the standard value C. 1ε =1.44, C 2ε =1.92, C 3ε =0.09, C 4ε =1.3;

[0263] The boundary conditions are: velocity inlet, turbulence intensity turbulent length scale Pressure outlet, relative static pressure is 0 Pa; when there is no slipping wall, the standard wall function is used to handle the near-wall flow; a coupled heat transfer boundary is set at the interface between the solid and fluid domains, ensuring continuous heat flow; the outer surface of the motor is set as a natural convection boundary, and the ambient temperature is... The convective heat transfer coefficient can be calculated using empirical formulas.

[0264] This invention establishes a mathematical expression for stator core loss based on the Bertotti iron loss separation model, calculates winding copper loss using a combination of DC and AC copper loss methods, and extracts permanent magnet eddy current losses through a three-dimensional transient finite element model. A three-dimensional heat conduction differential equation is established based on Fourier's law of heat conduction, and a T-type equivalent thermal resistance network model of the motor is constructed using the equivalent thermal network method. Finally, a fluid-structure interaction conjugate heat transfer model is established using a ring-shaped spiral water channel cooling structure integrated into the stator.

[0265] Simulation results show that, under rated operating conditions, the optimized motor's maximum temperature decreased from 278.936℃ to 156.719℃, and the temperature difference decreased from 62.204℃ to 21.103℃; under peak torque transient conditions, the peak temperature rise rate decreased from 4.2℃ / s to 1.8℃ / s, and the steady-state time shortened from 38.5s to 21.2s; the flow channel pressure drop decreased from 12.7kPa to 5.3kPa.

[0266] This invention addresses the problems of enclosed installation space and poor heat dissipation conditions in hub motors by establishing a built-in annular spiral water channel cooling structure within the stator. A fluid-structure interaction conjugate heat transfer model is established, with equivalent thermal conductivity applied to the air gap region and an isotropic equivalent thermal model established for the winding region. The steady-state temperature field distribution and transient temperature rise characteristics of the motor are analyzed under rated and peak torque conditions. The highest temperature, temperature difference, and channel pressure drop are used as evaluation indicators to assess the cooling performance, evaluating the heat dissipation effect of the annular spiral water channel. The results are compared with a waterless natural cooling scheme to verify the effectiveness of the proposed cooling structure in reducing hot spot temperatures and improving temperature uniformity. The Halbach array optimization design and stator water-cooled channel co-optimization method proposed in this invention can effectively improve the electromagnetic and thermal management performance of axial flux hub motors, providing a systematic theoretical basis and engineering-feasible design method for realizing hub motors with high torque density, low torque ripple, and efficient heat dissipation capabilities.

Claims

1. A method for determining the optimal cooling combination parameters for a hub motor, characterized in that: The optimal combination parameter determination method is as follows: the air gap length, permanent magnet thickness, stator slot width, stator slot bottom width, and stator slot height in the hub motor are used as optimization variables. The optimal Latin hypercube experimental method is used to generate sample points. A second-order response surface surrogate model is constructed based on the sample points. The second-order response surface surrogate model is solved based on the NSGA-II algorithm to obtain the process of determining the optimal combination parameters with the dual optimization objectives of maximizing average torque and minimizing torque ripple.

2. The method for determining the optimal combination parameters for a hub motor according to claim 1, characterized in that: Using the air gap length, permanent magnet thickness, stator slot width, stator slot bottom width, and stator slot height in the hub motor as optimization variables, the optimal Latin hypercube experimental method is used to generate sample points. The process of constructing a second-order response surface surrogate model based on the sample points is as follows: The air gap length is g The width of the slot is bs 1. The width of the bottom of the trough is bs 2. The height of the groove is hs 1. The thickness of the permanent magnet is hpm, air gap length g Groove width bs 1. Groove bottom width bs 2. Tank height hs 1 and permanent magnet thickness hpm As an optimization variable, average torque T avg Maximize and torque ripple T ripple Minimization is the dual optimization objective. An optimal Latin hypercube experimental design is used to generate 40-60 sets of sample points. The response values ​​of each sample point are calculated through finite element simulation. Based on the response values ​​of each sample point, a second-order response surface surrogate model is constructed. The determination coefficients of the corresponding average torque and torque ripple are obtained from the second-order response surface surrogate model. R 2 Through the two determining coefficients corresponding to the average torque and torque ripple. R 2 This indicates the model's fitting accuracy; With the goal of maximizing average torque and minimizing torque ripple, minT ripple For minimum torque pulsation, maxT avg The formula for calculating the torque ripple corresponding to the maximum average torque is: Air gap length g Groove width bs 1. Groove bottom width bs 2. Tank height hs 1 and permanent magnet thickness hpm One expression corresponding to the optimization variable is: Air gap length g Groove width bs 1. Groove bottom width bs 2. Tank height hs 1 and permanent magnet thickness hpm The range of values ​​is determined based on the initial design parameters, electromagnetic performance requirements, and processing constraints.

3. The method for determining the optimal combination parameters for a hub motor according to claim 2, characterized in that: The process of generating sample points using the optimal Latin hypercube experimental method is as follows: The range of values ​​for each optimization variable is evenly divided into several equally probable intervals. A sampling point is randomly selected within each interval to ensure that the samples are uniformly distributed across all dimensions of space. This process achieves better spatial coverage with a smaller number of samples. Another expression for the optimization variable is: In the above formula, k The number of variables; optimization variables include air gap length. g Groove width bs 1. Groove bottom width bs 2. Tank height hs 1 and permanent magnet thickness hpm For each variable x i The calculation formula corresponding to its range of values ​​is: In Latin hypercube sampling, the range of values ​​for each variable is evenly divided into N sub-intervals. A sampling point is selected in each of the N sub-intervals. By randomly arranging and combining the sampling points of each variable, N sets of sample data are constructed, thus forming the experimental design matrix. In the process of optimizing the samples using the optimal Latin hypercube experimental method, the optimization criterion of maximum and minimum distance is introduced to ensure that the minimum distance between sample points is at the maximum value within the predetermined requirement range, thereby ensuring that the dispersion of the samples in the design space meets the predetermined requirements. The expression for the optimization objective is: The above formula ensures that the minimum Euclidean distance between any two points in all sample points is maximized, thereby avoiding excessive concentration of sample points and ensuring the uniformity and representativeness of the experimental design.

4. The method for determining the optimal combination parameters for a hub motor according to claim 1, 2, or 3, characterized in that: The process of determining the optimal combination parameters with the optimization objectives of maximizing average torque and minimizing torque ripple is based on solving the second-order response surface surrogate model using the NSGA-II algorithm. This involves solving the Pareto front using the NSGA-II algorithm, with the dual objectives of maximizing average torque and minimizing torque ripple, generating N sets of sample points within a given design variable range, and using ANSYS Maxwell to perform finite element simulation calculations on each set of samples to obtain the corresponding motor performance indicators. The motor performance indicators are the average torque Tavg and the torque ripple T. ripple Finally, the optimal solution was selected from the corresponding motor performance indicators to obtain the motor's average torque Tavg and torque ripple T. ripple The optimal value.

5. The method for determining the optimal combination parameters for a hub motor according to claim 1, characterized in that: The second-order response surface proxy model is solved using the NSGA-II algorithm to obtain the processed data. Based on the processed data, the stator core loss formula is established using the Bertotti iron loss separation model. The winding copper loss is calculated by combining the stator core loss formula, DC copper loss and AC copper loss. The permanent magnet eddy current loss is obtained by combining the winding copper loss with the three-dimensional transient finite element model.

6. The method for determining the optimal combination parameters for a hub motor according to claim 5, characterized in that: Based on the processed data and the Bertotti iron loss separation model, a stator core loss formula is established. The process of calculating the winding copper loss by combining the stator core loss formula, DC copper loss, and AC copper loss is as follows: Winding copper losses include DC copper losses and AC copper losses. The formula corresponding to the DC resistance in winding copper losses is: In the above formula: ρ For electrical conductivity, The length of each phase winding, This represents the cross-sectional area of ​​the winding. The formula for DC copper loss in winding copper loss is: When an alternating current is passed through a conductor, the changing magnetic field around the conductor will induce a current in the conductor, causing the current in the wire to tend towards the surface. At this time, the current distribution is uneven and the skin effect occurs. When an alternating current is passed through adjacent conductors, the current distribution of each conductor will be affected by the adjacent magnetic field, resulting in the proximity effect. When the winding is in an alternating magnetic field, eddy current losses will be generated in the winding. The skin effect, proximity effect, and eddy current losses caused by the external magnetic field are collectively referred to as AC copper losses. When the conductor is in a uniform magnetic field, and the magnetic field within the slot is parallel to the bottom of the slot, the formula for AC copper loss is: In the above formula, ω It is the angular frequency of the current. l For the conductor length, d The diameter of the conductor. ρ c The resistivity of the conductor; Under the constraints of the skin effect and proximity effect on AC copper loss, the formula for AC copper loss is: In the above formula, m 1 represents the number of conductors. p The distance between adjacent conductors. ρ ss The resistivity between conductor chains is used to ultimately determine the copper loss of the motor windings.

7. The method for determining the optimal combination parameters for a hub motor according to claim 6, characterized in that: The calculation process for permanent magnet eddy current loss, based on the combination of winding copper loss and three-dimensional transient finite element model, is as follows: After calculating the winding copper loss of the motor, the winding copper loss is combined with the three-dimensional transient finite element model for the following processing: The calculation process of permanent magnet eddy current loss of surface-mount or Halbach array permanent magnet motors is as follows: In the above formula, J P It is the eddy current density of the permanent magnet. It is the conductivity of the permanent magnet. V P It is the volume of the permanent magnet; As shown in the above formula, the eddy current loss of a permanent magnet is directly proportional to the square of the eddy current density and is closely related to the material's conductivity. Eddy current loss is also affected by the frequency of magnetic flux density change, the size of the permanent magnet, and the segmentation method. Segmenting the permanent magnet or using materials with low conductivity can effectively suppress eddy current loss. The formula for calculating the eddy current density of a permanent magnet is: In the above formula, l This represents the eddy current path length in the permanent magnet. B P It is the magnetic flux density of a permanent magnet. S P It is the area encompassed by the eddy current path of the permanent magnet; After solving the motor operation process based on the three-dimensional transient finite element model, the eddy current density distribution in the permanent magnet region is directly extracted by processing. The eddy current loss is calculated by combining the eddy current density distribution in the permanent magnet region with the material conductivity parameters, providing reliable data for motor loss analysis and thermal design.

8. The method for determining the optimal combination parameters for a hub motor according to claim 5, characterized in that: The analysis of the motor temperature rise mechanism is the foundation for establishing a temperature field model. Combining loss calculation results, a temperature field simulation is performed on an axial flux hub motor to obtain data on the cooling system for controlling temperature rise. Specifically, the process of establishing a three-dimensional heat conduction differential equation based on the combination of permanent magnet eddy current losses and Fourier's law of heat conduction is as follows: The heat sources inside the motor include stator core losses, winding copper losses, permanent magnet eddy current losses, and mechanical losses. Core losses include hysteresis losses and eddy current losses, and the magnitude of core losses is closely related to the magnetic field frequency, magnetic flux density amplitude, and core material properties. Winding copper losses are proportional to the square of the current and the winding resistance, and the resistance increases with increasing temperature. Permanent magnet eddy current losses are induced by harmonic components in the air gap magnetic field. Mechanical losses include bearing friction losses and wind resistance losses, and mechanical losses are proportional to the cube of the rotational speed. The stator core losses, winding copper losses, permanent magnet eddy current losses, and mechanical losses act on the corresponding components in the form of heat generation rate, becoming the source terms for temperature rise calculation. The solution to the temperature field of the motor is based on Fourier's law of heat conduction and the law of conservation of energy. In a rectangular coordinate system, the three-dimensional steady-state differential equation of heat conduction is: In the above formula, k x , k y , k z These are the thermal conductivity of the material in the x, y, and z directions, respectively. T For temperature; Let this be the volumetric heat generation rate; for transient temperature fields, a term needs to be added to the left-hand side of the equation, which is the product of density and specific heat capacity multiplied by the temperature's partial derivative with respect to time. Solving the above equation requires boundary conditions, which can be categorized into three types: First type of boundary condition: ; Second type of boundary condition: ; Third type of boundary condition: ; In motor temperature rise analysis, the first type of boundary condition corresponds to the working condition of a given temperature, the second type of boundary condition corresponds to the working condition of a given heat flux density, and the third type of boundary condition corresponds to the working condition of a given convective heat transfer. The convective heat transfer coefficient is W / (m²·K). The fluid temperature is used; for symmetrical structures, an adiabatic boundary condition is adopted, which is a special case of the second type of boundary condition. ; In the temperature rise analysis, the lumped-parameter thermal network method is used to calculate the average temperature rise of each component of the motor. The motor is divided into several isothermal nodes, which are connected by thermal resistance. The node temperature equations are established based on thermal balance as follows: ； In the above formula, T i , T j These are the temperatures of the first and second nodes, respectively. R ij For inter-node thermal resistance, P t The steady-state temperature of each node can be obtained by solving the linear equations, where the heat power is the input to the node. For transient temperature rise, heat capacity is introduced. C The first-order thermal differential equation is obtained as follows: ； The solution to the first-order thermal differential equation is: ； In the above formula, It is the thermal time constant, and the temperature rises exponentially with time. The temperature rises rapidly in the initial stage and then gradually reaches a steady state value.

9. The method for determining the optimal combination parameters for a hub motor according to claim 8, characterized in that: The method for determining the optimal combination parameters also includes constructing a T-shaped equivalent thermal resistance network model of the motor using the equivalent thermal network method, and establishing a fluid-structure interaction conjugate heat transfer model corresponding to the annular spiral water channel cooling structure built into the stator. The equivalent thermal network method discretizes the continuously distributed temperature field inside the motor into a finite number of nodes, and uses lumped parameter thermal resistance to replace the distributed thermal resistance, thereby constructing an equivalent model similar to an electrical network for temperature solution. The formation process of the T-shaped equivalent thermal resistance network of the annular cylinder in the method of temperature solution using the equivalent model is as follows: The stator yoke, rotor yoke, and permanent magnet in the hub motor are all circular ring-cylinder structures, with an outer diameter of [missing information]. r 1. Inner diameter is r 2. Axial length is When axial heat conduction and radial heat conduction are independent and there is no circumferential heat flow, the distributed parameter model is equivalent to... T Lumped parameter network, in which the network is based on T m This represents the node representing the average temperature of the column. P This refers to the heat generation power injected into this node. According to Fourier's law of thermal conduction, the analytical expressions for the six thermal resistances in the network are: ； In the above formula: These are the axial and radial thermal conductivity of the material, respectively. The axial thermal resistance from the end face to the average temperature node. This is a negative thermal resistance term, used to correct the location of the average temperature node; R 1r , R 2r The radial thermal resistance from the inner and outer surfaces to the average temperature node is denoted as . R 3r This is the negative coupling thermal resistance between the inner and outer surfaces; For the key heat exchange areas of the wheel hub motor, The convective heat transfer coefficient of the air gap between the stator and rotor, determined using empirical correlations, depends on the Nusselt number. N u ,and N u With air gap geometry and Reynolds number Re Related; the convective heat transfer coefficient at the winding ends is affected by the cooling air velocity; the convective heat transfer coefficient on the casing surface is determined by the external air velocity. For hub motors using axial ventilation cooling, a heat pressure source model describing the temperature rise of the cooling medium is introduced, and the corresponding calculation process is as follows: The cooling channel is divided into an inlet section, a middle section, and an outlet section. The average temperature rise of the cooling medium after absorbing heat loss from the components in each section is: In the above formula, P loss The total heat flow absorbed by the cooling medium in this section, and the equivalent flow resistance. Defined as: In the above formula, ρ For the density of the cooling fluid, C p For specific heat capacity at constant pressure, q Volumetric flow rate; The three thermal pressure source nodes represent the average temperatures of the cooling fluids in the inlet, middle, and outlet sections, respectively. average temperature Heat flow absorbed at the inlet end P ecl Heat flow absorbed by the rotor yoke section P yr Heat flow P absorbed at the outlet end ec2 The relation is: The above matrix equation couples the cooling medium temperature nodes with the solid component thermal network to form a complete three-dimensional equivalent thermal network; Connect the T-shaped thermal resistance network of each component to the thermal pressure source model of the cooling medium to form a system containing... n A global thermal network with nodes, according to Kirchhoff's heat flux law, is injected into any node. i The net heat flow is zero, that is: Written in matrix form: In the above formula, This is the column vector of node temperature rise; P Inject a loss column vector into the node; G for n × n The element expression of the thermal admittance matrix is ​​as follows: Substituting the constraint equations for the thermal pressure source of the cooling medium into the above equation, and then combining the matrices, we obtain the augmented equation system: In the above formula, the subscript Indicates a node of a solid component. The node represents the cooling fluid. Solving this system of equations will yield the axially asymmetric temperature distribution of the motor.

10. The method for determining the optimal combination parameters for a hub motor according to any one of claims 1, 2, 3, 5, 6, 7, 8, or 9, characterized in that: During the process of determining the optimal combination parameters, when the motor is running, the rotors on both sides drive the air in the air gap to rotate, forming a complex flow state. The convective heat transfer in the air gap is equivalent to solid heat conduction, and an equivalent thermal conductivity (kg) is introduced. kg, The corresponding processing procedure is as follows: First, calculate the air gap Reynolds number Re to determine the flow state: In the above formula, The linear velocity of the rotor rotation; g This is the air gap length; ν air Let be the kinematic viscosity of air; the formula for calculating the critical Reynolds number is: In the above formula, d si for Stator outer diameter; calculations show that the air in the air gap is in a turbulent state, with an equivalent thermal conductivity of k g The calculation formula is: In the above formula, It is the ratio of the stator inner diameter to the rotor inner diameter. r si Stator inner diameter r o Given the rotor's inner diameter, the equivalent thermal conductivity of the air gap is calculated. k g =0.0796W / (m·K); The winding is composed of copper conductors, insulation layer, and epoxy resin potting material, and adopts an isotropic equivalent model. The equivalent density of the equivalent model is... ρ eq Equivalent specific heat capacity c eq and equivalent thermal conductivity k eq The calculation formulas are as follows: ； In the above formula, ρ i , c i , k i , V i , l i The first i The density, specific heat capacity, thermal conductivity, volume, and length of the heat flow direction of the material; The fluid domain is the coolant within an annular spiral water channel, and the coolant's physical properties include density. ρ eq = 998.2 kg / m 3 thermal conductivity k =0.641 W / (m·K), specific heat capacity c =4182 J / (kg·K), dynamic viscosity μ =0.001003 Pa·s; The process of selecting the turbulence model and determining the boundary conditions is as follows: The formula for estimating the Reynolds number Re of the coolant flowing within the water channels is: ； The above formula shows that when Re > 2300, the flow is in a turbulent state. Therefore, a standard is selected. k - ε Turbulence model, standard k - ε The transport equations for the turbulent model are: Turbulent kinetic energy k The equation is: ； Turbulent dissipation rate The equation is: In the above formula, G k This is the turbulent kinetic energy production term caused by the average velocity gradient. G b The term representing the turbulent kinetic energy generated by buoyancy. μ t The viscosity is turbulent; the model constants are taken as standard values. C 1ε =1.44, C 2ε =1.92, C 3ε =0.09, C 4ε =1.3; The boundary conditions are: velocity inlet, turbulence intensity Turbulent length scale 0.07 d g =0.48mm; pressure outlet, relative static pressure is 0Pa; when there is no slipping wall, the standard wall function is used to handle the near-wall flow; a coupled heat transfer boundary is set at the interface between the solid and fluid domains, and the heat flow is continuous; the outer surface of the motor is set as a natural convection boundary, and the ambient temperature is... T ∞ =20℃, the convective heat transfer coefficient can be calculated using empirical formulas.

Images