High torque density dual rotor permanent magnet fault-tolerant motor and pole arc coefficient optimization method thereof

Abstract

The application discloses a high-torque-density double-rotor permanent magnet fault-tolerant motor and a pole arc coefficient optimization method thereof, and comprises coaxially arranged inner rotor, stator and outer rotor; the axial end portions of the outer rotor and the inner rotor are fixedly connected, the stator is arranged between the inner rotor and the outer rotor and forms inner-layer air gaps and outer-layer air gaps with the inner rotor and the outer rotor respectively; the inner rotor and the outer rotor are both provided with Halbach arrays; the pole arc coefficient of the Halbach array is determined through an electromagnetic performance prediction model based on HO-GRNN and a pole arc coefficient optimization method of an improved sacred religion algorithm, the sum of the inner-layer air gap and the outer-layer air gap magnetic flux density fundamental wave amplitude is maximized, and the total harmonic distortion rate is minimized; and when the motor operates, the winding magnetic field simultaneously acts on the inner-layer air gap and the outer-layer air gap, and respectively interacts with the permanent magnet magnetic field of the inner rotor and the outer rotor, and the outer rotor and the inner rotor superimpose and output total torque.

Description

Technical Field

[0001] This invention belongs to the field of intelligent application of special motor design and calculation, specifically involving a high torque density dual-rotor permanent magnet fault-tolerant motor and its pole arc coefficient optimization method. Background Technology

[0002] As aircraft evolve from "more electric aircraft" to "all-electric aircraft" (AEA), the performance requirements for drive motors in aviation propulsion systems have become increasingly stringent. Unlike ground-based operations, aviation propulsion motors not only require extremely high power and torque densities to meet takeoff thrust demands, but also must maintain extremely high system reliability under extreme environments such as high temperatures, strong vibrations, and low air pressures. Currently, existing aviation motor designs often struggle to find a balance between lightweight design and high reliability, becoming a key issue hindering the commercial application of all-electric propulsion technology.

[0003] Currently, most aero propulsion motors adopt the traditional single-rotor radial magnetic field topology, which has limited air gap magnetic field utilization and relies on increasing volume or current to increase torque, making it difficult to achieve breakthroughs in motor power / torque density. To solve this problem, the dual-rotor motor structure has emerged. CN101243599A and CN114598071A both reveal solutions for improving aero motor performance from different perspectives, including improvements to fault-tolerant structures and motor thermal management.

[0004] In practical implementation, Halbach permanent magnet arrays are often used to enhance air gap magnetic flux density. However, while traditional Halbach arrays with equal pole widths can achieve a magnetic focusing effect, their air gap magnetic flux density waveform contains abundant high-order harmonic components. Under the high-speed operating conditions of aero-engines, these harmonic magnetic fields induce huge eddy current losses in the rotor sheath and inside the permanent magnets, causing a sharp rise in rotor component temperature. This not only reduces efficiency but may also cause irreversible demagnetization of the permanent magnets, seriously threatening system reliability.

[0005] To reduce harmonic losses and improve torque quality, it is typically necessary to optimize the pole arc coefficients of the primary and secondary magnetic poles of permanent magnets. However, optimizing the pole arc coefficients of a motor is a typical multivariate, nonlinear, and strongly coupled multi-objective optimization problem. Traditional optimization methods suffer from limitations such as low computational efficiency, insufficient model accuracy, and limited algorithmic optimization capabilities.

[0006] Therefore, we consider designing a novel motor topology that balances high torque density and high fault tolerance, and developing an intelligent multi-objective optimization method that can quickly and accurately determine the optimal pole arc coefficient. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention provides a high torque density dual-rotor permanent magnet fault-tolerant motor and its pole arc coefficient optimization method. The motor topology firstly combines the advantages of a dual-rotor structure, inner and outer double-layer air gaps, dual Halbach arrays, and fault-tolerant tooth isolation design. Without increasing the motor's size, it significantly improves the motor's power density and torque density by coaxially superimposing the output torque of the inner and outer rotors. Secondly, to address the thermal management challenges under high torque / power density and the reliability requirements in extreme environments, this invention employs high-temperature resistant permanent magnet materials to enhance the motor's anti-demagnetization capability. More importantly, the pole arc coefficient optimization method innovatively introduces a generalized regressive neural network (HO-GRNN) surrogate model based on the Hippo optimization algorithm and an improved DRA algorithm, achieving efficient shaping and harmonic suppression of the air gap magnetic flux density waveform.

[0008] The first aspect of this invention is to provide a high torque density dual-rotor permanent magnet fault-tolerant motor, including a stator and coaxially arranged inner and outer rotors;

[0009] The stator includes a stator core and a stator winding. The stator core has armature teeth and fault-tolerant teeth arranged alternately along the circumference, and the circumferential width of the armature teeth is greater than the circumferential width of the fault-tolerant teeth. The stator winding adopts a fractional slot concentrated winding, and the stator winding is only wound on the armature teeth.

[0010] The fault-tolerant teeth are exposed to form a physical and magnetic isolation barrier between adjacent phase windings;

[0011] The inner rotor and the outer rotor are fixedly connected at their axial ends by an end plate, forming a coaxial, rotating dual-rotor linkage structure, so as to superimpose the electromagnetic torque of the two and output it through a single common shaft.

[0012] The stator is disposed between the inner rotor and the outer rotor, forming an inner air gap and an outer air gap with them respectively; a Halbach array is disposed on the outer surface of the inner rotor and the inner surface of the outer rotor, the Halbach array being composed of main magnetic poles and auxiliary magnetic poles arranged alternately along the circumferential direction; wherein, the main magnetic poles are radially magnetized permanent magnets, the auxiliary magnetic poles are tangentially magnetized Halbach magnets, and both the permanent magnets and the Halbach magnets are made of samarium cobalt material;

[0013] Furthermore, the pole arc coefficient of the main magnetic pole in the Halbach array is determined by the pole arc coefficient optimization method based on the electromagnetic performance prediction model of HO-GRNN and the improved sacred religious algorithm, so that the motor can maximize the sum of the fundamental wave amplitude of the magnetic flux density of the inner air gap and the outer air gap and minimize the total harmonic distortion rate under fault-tolerant operation. Moreover, when the motor is running, the stator winding magnetic field acts on the inner and outer air gaps simultaneously, and interacts with the permanent magnet magnetic fields of the inner rotor and the outer rotor, respectively. The outer rotor and the inner rotor superimpose to output the total torque.

[0014] Furthermore, the gap between the inner surface of the stator and the outer surface of the inner rotor forms an inner air gap, and the gap between the outer surface of the stator and the inner surface of the outer rotor forms an outer air gap, and the inner air gap and the outer air gap are independent of each other.

[0015] More preferably, the air gap lengths of the inner air gap and the outer air gap are equal.

[0016] Furthermore, the stator core is formed by stacking high-permeability silicon steel sheets axially.

[0017] Furthermore, the stator winding adopts a fractional-slot concentrated winding configuration with 20 poles and 24 slots, and the stator winding does not cross the inner and outer air gaps, and the tooth tip has no modulated slot structure.

[0018] Furthermore, the permanent magnet has a thickness of 6.5 mm and is made of samarium cobalt material to enhance its resistance to demagnetization.

[0019] A second aspect of this invention is to provide a method for optimizing the pole arc coefficient, applied to a high torque density dual-rotor permanent magnet fault-tolerant motor as described above, comprising:

[0020] Step 1: Establish a parameterized finite element model of the dual-rotor permanent magnet fault-tolerant motor. Using the main magnetic pole arc coefficient as the key variable, collect sample data and perform electromagnetic field simulation using the Latin Hypercube Sampling (LHS) method. Construct a sample database containing the relationship between the main magnetic pole arc coefficient, the sum of the magnetic flux density fundamental wave amplitudes of the inner and outer air gaps, and the total harmonic distortion rate.

[0021] Step 2: Based on the sample database constructed in Step 1, a generalized regression neural network (GRNN) model is constructed as the electromagnetic performance prediction model. The polar arc coefficient of the main magnetic pole in the sample is used as the input variable of the electromagnetic performance prediction model, and the sum of the magnetic flux density fundamental wave amplitude and the total harmonic distortion rate of the corresponding inner and outer air gaps are used as the output variables to train the electromagnetic performance prediction model, establishing a nonlinear mapping relationship between the polar arc coefficient of the main magnetic pole and the magnetic flux density characteristics of the inner and outer air gaps. The Hippo optimization algorithm is introduced to adaptively optimize the smoothing factor of the GRNN model with the goal of minimizing the prediction error, resulting in the trained HO-GRNN prediction model.

[0022] Step 3: With the dual optimization objectives of maximizing the sum of the fundamental wave amplitudes of the air gap magnetic flux density and minimizing the total harmonic distortion rate, based on the HO-GRNN prediction model, a multi-objective optimization solution is performed using an improved sacred religious algorithm, and the Pareto optimal solution set is output.

[0023] Step 4: Select the point with the largest curvature on the Pareto front from the Pareto optimal solution set as the candidate solution for the front inflection point. Input the obtained candidate solution for the front inflection point into the HO-GRNN prediction model trained in Step 2 to verify its harmonic suppression effect on the air gap magnetic flux density waveform. The pole arc coefficient corresponding to the candidate solution that meets the preset harmonic suppression standard is taken as the optimal main magnetic pole pole arc coefficient.

[0024] Furthermore, step three includes:

[0025] S31: Two objective functions are defined with the dual optimization objectives of maximizing the sum of the fundamental wave amplitudes of the air gap magnetic flux density and minimizing the total harmonic distortion rate:

[0026]

[0027]

[0028] In the formula, The sum of the fundamental wave amplitudes is the air gap magnetic flux density, and THD is the total harmonic distortion rate. The main magnetic pole arc coefficient;

[0029] S32: The improved sacred religious algorithm is used to optimize the HO-GRNN prediction model trained in step two, and the initial population is generated using Tent chaotic mapping.

[0030] S33: By simulating the process of religious propagation, it evolves through iterative evolution, executing propaganda mechanisms for local development and miracle mechanisms for global exploration;

[0031] S34: Use a non-dominated sorting strategy to handle multi-objective competition, filter and output a set of non-dominated Pareto optimal solutions;

[0032] S35: Determine if the number of iterations has reached the preset value. If yes, proceed to step four; otherwise, return to S33 to continue iterating.

[0033] Furthermore, step four includes:

[0034] S41: Identify the point with the largest curvature on the leading edge of the Pareto optimal solution set output in step three as the candidate solution for the leading edge inflection point;

[0035] S42: Input the candidate solution of the leading edge inflection point into the HO-GRNN prediction model trained in step two to predict the amplitude of the third and fifth harmonics of its air gap magnetic flux density waveform.

[0036] S43: If the candidate solution at the current leading edge inflection point meets the preset harmonic suppression criterion, output it as the main magnetic pole arc coefficient; otherwise, select the nearest solution along the Pareto leading edge for verification until a solution that meets the harmonic suppression criterion is found.

[0037] Furthermore, in the Halbach array of the inner rotor and the outer rotor, the pole arc coefficient of the auxiliary magnetic pole is determined based on the pole arc coefficient of the main magnetic pole, and the two satisfy the following relationship:

[0038] Auxiliary magnetic pole arc coefficient = 1 - Main magnetic pole arc coefficient

[0039] A third aspect of this application is to provide an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the polar arc coefficient optimization method as described above.

[0040] A fourth aspect of this application is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the polar arc coefficient optimization method as described above.

[0041] The fifth aspect of this application is to provide a computer program product, including a computer program that, when executed, is used to implement the polar arc coefficient optimization method as described above.

[0042] The beneficial effects of this invention are as follows:

[0043] The dual-rotor permanent magnet fault-tolerant motor of the present invention adopts an inner and outer dual-rotor, inner and outer double-layer air gap, and dual Halbach array structure, which makes full use of the space on both sides of the stator to achieve double-sided torque superposition output, significantly improving the torque and power density of the motor in the same volume.

[0044] The stator adopts a modular design with alternating armature teeth and fault-tolerant teeth, which has low mutual inductance and high leakage reactance characteristics, effectively suppresses fault propagation and short-circuit current, and has strong fault tolerance capability.

[0045] The Halbach array polar arc coefficient, determined by intelligent optimization methods, can effectively shape the air gap magnetic field and suppress the harmonic content (total harmonic distortion rate) to an extremely low level, thereby significantly reducing rotor eddy current loss and iron loss, and improving operating efficiency and stability.

[0046] Experiments show that the proposed HO-GRNN surrogate model, combined with the improved DRA optimization method, can accurately find the optimal combination of polar arc coefficients that satisfies the multi-objective competitive relationship at a speed far exceeding that of traditional finite element iteration, thus solving the problems of low efficiency and insufficient optimization capability of traditional design methods. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the radial cross-sectional structure of the high torque density dual-rotor permanent magnet fault-tolerant motor described in this invention;

[0048] Figure 2 for Figure 1 A partial enlarged view of the stator of the dual-rotor permanent magnet fault-tolerant motor shown;

[0049] Figure 3 This is a flowchart of the polar arc coefficient optimization method described in this invention;

[0050] Figure 4 This is a flowchart of the improved sacred religious algorithm described in this invention;

[0051] Figure 5 for Figure 1 The diagram shows the inner rotor torque of the dual-rotor permanent magnet fault-tolerant motor under rated operating conditions.

[0052] Figure 6 for Figure 1 The diagram shows the external rotor torque of the dual-rotor permanent magnet fault-tolerant motor under rated operating conditions.

[0053] Figure 7 This is the iron loss diagram under rated operating conditions, where 0~12ms is the transient process of magnetic field establishment, and the average value is calculated using data after 12ms.

[0054] Figure 8 This is the eddy current loss diagram under rated conditions, where 0~2ms is the transient process of magnetic field establishment, and the average value is calculated using data after 2ms.

[0055] Figure 9 It is the no-load back electromotive force of the motor at its rated speed.

[0056] Wherein: 1: stator; 2: inner rotor; 3: outer rotor; 4: permanent magnet; 5: armature tooth; 6: fault-tolerant tooth; 7: Halbach magnet; 8: stator winding. Detailed Implementation

[0057] To make the objectives, technical solutions, beneficial effects, and significant advancements of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings provided in the examples of the present invention. Obviously, all the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] In the description of this application, unless otherwise expressly specified and limited, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance; the term "multiple" refers to two or more; unless otherwise specified or explained, the terms "connected," "fixed," etc., should be interpreted broadly. For example, "connected" can be a fixed connection, a detachable connection, an integral connection, or an electrical connection; "connected" can be a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0059] like Figure 1 and Figure 2 As shown, a high torque density dual-rotor permanent magnet fault-tolerant motor is disclosed. The axial length of the motor is designed to be 100 mm. Within the radial space of the fault-tolerant motor, an inner rotor 2, a stator 1, and an outer rotor 3 are coaxially arranged from the inside to the outside along its central axis. The outer rotor 3 has an outer diameter of 360 mm and an inner diameter of 336 mm; the stator 1 has an outer diameter of 321 mm and an inner diameter of 240 mm; and the inner rotor 2 has an outer diameter of 225 mm and an inner diameter of 150 mm. The gap between the inner surface of the stator 1 and the outer surface of the inner rotor forms an inner air gap, and the gap between the outer surface of the stator and the inner surface of the outer rotor 3 forms an outer air gap. The inner and outer air gaps are independent of each other, and the length of both the inner and outer air gaps is 1 mm.

[0060] The stator 1 includes a stator core and a stator winding 8. The stator core is made of high-permeability silicon steel sheets stacked axially, forming the main magnetic circuit of the motor. Armature teeth 5 and fault-tolerant teeth 6 are alternately arranged along the circumference of the stator core, and the armature teeth 5 and fault-tolerant teeth 6 are of unequal width. The stator winding 8 adopts a 20-pole, 24-slot fractional-slot concentrated winding configuration. The stator winding is only concentrated on the armature teeth 5. The fault-tolerant teeth do not have windings and serve as physical isolation walls and magnetic circuit barriers. The armature teeth with stator windings are separated by the unwinding fault-tolerant teeth, forming physical and thermal isolation barriers between phases, enhancing the fault tolerance of the motor. Moreover, the fault-tolerant teeth 6, while isolating heat from adjacent windings, utilize their high leakage reactance characteristics to suppress short-circuit current.

[0061] The axial ends of the outer rotor 3 and the inner rotor 2 in the same direction are fixedly connected by an end plate (not shown in the figure), and the outer rotor 3 and the inner rotor 2 rotate at the same speed. The outer rotor 3 and the inner rotor 2 output torque through a common output shaft. The outer rotor and the inner rotor can achieve pure physical superposition of torque under the same volume without relying on complex harmonic current injection or magnetic gear modulation.

[0062] Furthermore, both the outer rotor 3 and the inner rotor 2 are equipped with a main permanent magnet 4 and an auxiliary Halbach magnet 7, which together form a Halbach array. The inner and outer rotors are arranged in a Halbach array to form a hybrid magnetic structure, which can significantly enhance the working magnetic field acting on the air gap without increasing the amount of permanent magnets used. Moreover, the permanent magnet 4 is 6.5 mm thick, and both the permanent magnet 4 and the Halbach magnet 7 are made of samarium cobalt (SmCo28) material. Figure 1 and Figure 2 As shown, the blue magnet is the main magnetic pole (N pole) and is magnetized in the positive radial direction; the red magnet is the main magnetic pole (S pole) and is magnetized in the negative radial direction; the green and yellow magnets are auxiliary magnetic poles, with the green magnet being magnetized in the positive tangential direction and the yellow magnet being magnetized in the negative tangential direction.

[0063] When the motor is running, three-phase alternating current is applied to the stator windings to generate a rotating magnetic field. This magnetic field acts simultaneously on the inner and outer air gaps, interacting with the magnetic fields of the permanent magnets on the outer surface of the inner rotor and the inner surface of the outer rotor, respectively, to produce electromagnetic torque. Since the inner and outer rotors are mechanically connected and rotate at the same speed, their combined output torque significantly increases the torque density without increasing the motor's size.

[0064] To address the issues of high harmonic content and large rotor eddy current losses in traditional Halbach arrays with high air-gap magnetic flux density, this embodiment proposes a pole arc coefficient optimization method based on the HO-GRNN surrogate model and the Improved DRA algorithm. This method, through a combination of mathematical modeling and intelligent optimization, accurately determines the optimal pole arc coefficients for the primary and secondary magnetic poles. Figure 3 As shown, the specific implementation steps are as follows:

[0065] Step 1: Construct a parametric finite element model of the dual-rotor permanent magnet fault-tolerant motor, and use the Latin hypercube sampling method to sample and construct a sample database.

[0066] S11: Using electromagnetic field finite element analysis software, a fully parameterized simulation model of the high torque density dual-rotor permanent magnet fault-tolerant motor was established based on its topology, material properties, and dimensional parameters. In this model, the main magnetic pole arc coefficient, which directly affects the quality of the air gap magnetic field waveform, was selected. As a key design variable.

[0067] S12: Latin Hypercube Sampling (LHS) is used to collect sample data. For each sampling point (i.e., a set of determined main magnetic pole arc coefficients), the parameterized finite element model is run to perform electromagnetic field simulation. The sum of the fundamental wave amplitudes of the air gap magnetic flux density B1, the total harmonic distortion rate (THD), the sum of the third harmonic amplitudes B3, and the sum of the fifth harmonic amplitudes B5 are obtained for each sample point. This constructs a data sample library containing the correspondence between "input variables (determined main magnetic pole arc coefficients) - output response (sum of fundamental wave amplitudes of the air gap magnetic flux density and total harmonic distortion rate)".

[0068] Wherein, the sum of the fundamental wave amplitudes of the air gap magnetic flux density B1 refers to the sum of the fundamental wave amplitudes of the inner and outer air gap magnetic flux density, and the total harmonic distortion rate (THD) refers to the larger value of the distortion rate in the inner and outer air gaps.

[0069] Step 2: Construct a generalized regression neural network (GRNN) as an electromagnetic performance prediction model to establish a nonlinear mapping relationship between the main magnetic pole arc coefficient and the magnetic density characteristics of the inner and outer air gaps, and introduce the Hippo optimization algorithm to adaptively optimize the smoothing factor in the GRNN model.

[0070] A generalized regression neural network is established as a fast prediction model for electromagnetic properties. The prediction performance of the GRNN network is highly dependent on the smoothing factor, which is the most critical hyperparameter in the GRNN model and directly controls the smoothness and prediction accuracy of the model.

[0071] The data sample library of step one is divided into a training set and a test set. The main magnetic pole arc coefficient in the sample is used as the input variable of the GRNN network. The sum of the magnetic flux density fundamental wave amplitudes B1 of the corresponding inner air gap and outer air gap, the total harmonic distortion rate THD, and the amplitudes of the third and fifth harmonics B3 and B5 are used as output variables to train the network, thereby establishing a high-precision nonlinear mapping relationship between the main magnetic pole arc coefficient and the electromagnetic performance of the dual air gap.

[0072] To improve prediction accuracy, the model uses a Gaussian kernel function for the transfer function of the pattern layer neurons, and its mathematical expression is as follows:

[0073]

[0074] In the formula, The input variable for the network is the polar arc coefficient of the main magnetic pole. For the first One learning sample, This is a smoothing factor.

[0075] This embodiment introduces the Hippo Optimization (HO) algorithm to adjust the smoothing factor. Adaptive optimization is performed to minimize the mean squared error of prediction (MSE) by iteratively updating candidate solutions (i.e., different smoothing factors). The optimal smoothing factor that minimizes MSE is found by locating the value of the HO-GRNN prediction model. Through this process, a HO-GRNN prediction model with high prediction accuracy is trained, thereby establishing a high-precision nonlinear mapping model between the pole arc coefficient and motor performance, replacing the time-consuming finite element iterative calculation.

[0076] Step 3: Based on the trained HO-GRNN prediction model, solve the multi-objective collaborative optimization problem between high torque output and low harmonic loss, and use the improved Sacred Religion algorithm to solve it, outputting the Pareto optimal solution set.

[0077] S31: To achieve optimal overall electromagnetic performance, the optimization problem of the main magnetic pole arc coefficient is formalized into a dual-objective optimization problem, namely, the coordinated optimization of high torque output and low harmonic loss. The following two competing objective functions are defined:

[0078]

[0079]

[0080] In the formula, The sum of the fundamental wave amplitudes is the air gap magnetic flux density, and THD is the total harmonic distortion rate. This is the polar arc coefficient of the main magnetic pole. Its calculation formula is:

[0081]

[0082] In the formula, B n It represents the amplitude of the nth harmonic of the air gap magnetic flux density waveform.

[0083] S32: The improved Divine Religion Algorithm (Improved DRA) is used to optimize the trained HO-GRNN prediction model, such as... Figure 4 As shown. The improved Sacred Religion algorithm is based on the original Sacred Religion algorithm, introducing Tent chaotic mapping to initialize the population, executing propaganda and miracle mechanisms in the simulated religious propagation process to achieve dual evolution, and employing a non-dominated sorting strategy to handle the competitive relationship between multiple objectives of the objective function.

[0084] In the improved sacred religious algorithm described in this invention, to achieve multi-objective collaborative optimization, the optimization process in mathematical space is mapped to a rigorous religious hierarchical structure and propagation behavior. For clarity and rigor in the specification, the metaphorical roles in the algorithm are defined mathematically and physically as follows:

[0085] Faith Level: Corresponding to the fitness of an individual in multi-objective optimization, it is determined by the individual's non-dominant ranking level in the population. The higher the level, the higher the faith level.

[0086] Religion Leader: Corresponds to the non-dominated optimal solution selected from the external Pareto archive. It represents the best physical compromise found by the current algorithm and is responsible for guiding the evolutionary direction of the entire population.

[0087] Missionary: Corresponds to the top 50% of dominant individuals in the internal population based on their faith level. They have high fitness and undertake the task of "local development".

[0088] Ordinary Believers: These correspond to the bottom 50% of individuals in the internal population. They have low fitness and are tasked with "global exploration" to find new feasible domains.

[0089] Believers: refers to all individuals within the internal population, that is, missionaries and ordinary believers collectively.

[0090] To overcome the shortcomings of traditional random initialization, which easily leads to uneven population distribution and the algorithm getting trapped in local optima, this invention introduces Tent chaotic mapping to initialize the population.

[0091] First, set the initial parameters for the algorithm: population size. Maximum number of iterations The decision variable dimension dim=1 (corresponding to the primary magnetic pole arc coefficient). Maximum capacity of the external Pareto archive set. The search space for the polar arc coefficient is set to a lower bound. Upper Realm Initial maximum step size weight Minimum step size weight in the final stage Tent chaotic mapping parameters =0.499.

[0092] The one-dimensional discrete iterative equation for the initial principal magnetic pole arc coefficient sequence is:

[0093]

[0094] In the formula, For the first Chaotic variables in the next iteration; To avoid getting stuck in a fixed point, the chaotic parameter is taken as follows in this embodiment. .generate After considering the chaotic variables, they are transformed into the initial physical population of the main magnetic pole arc coefficients using the following carrier mapping formula. :

[0095]

[0096] In the formula, For the first The initial principal polar arc coefficient solution for each individual.

[0097] Then, the HO-GRNN prediction model is used to evaluate the initial physical population, obtaining two objective function values ​​for each individual: the sum of the magnetic flux density fundamental wave amplitudes of the inner and outer air gaps (corresponding to maximizing B1) and the total harmonic distortion (THD), which constitute the initial fitness matrix. An empty external Pareto optimal solution archive set and its corresponding fitness archive are initialized.

[0098] S33: For the current population, the improved DRA algorithm simulates the religious propagation process in each iteration. In the process, the current non-dominant ranking level of each population is calculated, its "faith level" is assessed, and the internal population dynamics are divided into two classes: "missionaries" and "ordinary believers" based on this, and propaganda and miracle mechanisms are executed accordingly.

[0099] Specifically, at the start of each iteration, a non-dominated sort is first performed on the fitness of the current internal population, and the crowding distance within the same level is calculated. The internal population is then sorted according to the non-dominated sort level and the crowding distance. Adaptive iterative weights are introduced. The expression for controlling step size decay is:

[0100]

[0101] In the formula, and These are the initial maximum step size weight and the final minimum step size weight, respectively, with the optimal value set as follows: , .

[0102] Based on the current population's non-dominated ranking, the top 50% of individuals are selected to form a dominant subpopulation, i.e., "missionaries," while the bottom 50% are selected to form "ordinary believers." A propaganda mechanism is implemented on the top 50% of individuals, simulating the behavior of highly devout "missionaries" closely following the "leader" and proselytizing within a localized area. An optimal non-dominated solution from an external archive is selected as the "leader." Individual missionaries perform highly precise neighborhood searches by absorbing information from the leader:

[0103]

[0104] In the formula, This is the latest optimized solution. It is the best individual in the current population. and for Random numbers that are uniformly distributed between each other. A nonlinear oscillation factor was introduced, which enabled missionaries to fine-tune in multiple directions when moving closer to the leader, thus accelerating convergence to the Pareto front.

[0105] The Miracle Mechanism is applied to all populations after the propaganda mechanism update, simulating the random epiphany behavior of believers. This mechanism gives individuals trapped in local optima the possibility of escaping their current region:

[0106]

[0107] In the formula, for The random number between these values ​​is multiplied by a decay term, which ensures that the insight range covers the entire population in the early stages of iteration and gradually converges in the later stages, effectively maintaining the diversity of the population space.

[0108] To prevent the generated principal magnetic pole arc coefficient from losing its physical meaning, an out-of-bounds handling strategy is adopted for the newly generated solution:

[0109]

[0110] In the formula, This outbound handling strategy is better at maintaining population diversity and preventing believers from accumulating at the boundary than a simple cutoff strategy.

[0111] S34: Due to the requirement to simultaneously maximize the fundamental wave of the air gap magnetic flux density And minimize the total harmonic distortion rate The newly generated population individuals are input into the HO-GRNN prediction model to obtain a dual-objective performance evaluation.

[0112] After completing the position update and boundary crossing handling, a new generation of population is obtained. The HO-GRNN prediction model is called to evaluate the bi-objective fitness values ​​of all individuals in the new population, and a new fitness matrix is ​​obtained for the next iteration.

[0113] Update the external archive set using Pareto dominance logic: for any two individuals and If satisfied and If at least one of them is strictly unequal, then it is determined that... Dominate .

[0114] To prevent solutions from becoming too concentrated on the Pareto front, a crowding distance is introduced. A truncation selection is performed. For individuals at the same non-dominated level, their crowding degree is calculated as follows:

[0115]

[0116] In the formula, , and , These represent the objective function in the current set of non-dominated solutions. and Maximum and minimum values.

[0117] When updating external archives, prioritize retaining archives with high non-dominance levels and high crowding distances. Large individuals, thus outputting a set of uniformly distributed and non-dominant Pareto optimal solutions.

[0118] S35: Determine if the current iteration count has reached the preset 200 iterations. If yes, proceed to step four; otherwise... Return to S33 and continue iterating until the condition is met.

[0119] After the main loop of the algorithm ends, the external archive set stores a set of Pareto optimal main magnetic pole arc coefficient solutions obtained by optimization, as well as the sum of the magnetic flux density fundamental wave amplitude values ​​B1 and the THD prediction values ​​of the corresponding inner and outer air gaps.

[0120] In other embodiments, the judgment condition of step S35 can also be set to consider the iteration requirement as met when the prediction mean square error is less than the preset convergence accuracy threshold of 0.0001.

[0121] Step 4: Select the leading edge inflection point solution from the output Pareto optimal solution set. Verify the suppression effect of the 3rd and 5th harmonics using the selected leading edge inflection point solution. Use its corresponding pole arc coefficient as the final design scheme and output the optimal pole arc coefficient. Through optimization decision-making, determine the pole arc coefficient of the main magnetic pole and derive the corresponding pole arc coefficient of the auxiliary magnetic pole accordingly.

[0122] S41: Based on the distribution of solutions in the Pareto optimal solution set output in step three, plot the Pareto front in a coordinate system with the sum of the fundamental wave amplitudes of the air-gap magnetic flux density (B1) as the vertical axis and the total harmonic distortion (THD) as the horizontal axis. Use geometric criteria to identify the inflection point on this front, i.e., the point with the largest curvature on the Pareto front curve. This point represents the optimal marginal compromise between the sum of the fundamental wave amplitudes of the air-gap magnetic flux density and the total harmonic distortion (THD) of the objective function, thus obtaining candidate solutions for the front inflection point.

[0123] S42: Input the obtained candidate solutions for the leading edge inflection point into the HO-GRNN prediction model trained in step two for rapid prediction, predict its air gap magnetic flux density waveform, and extract its 3rd and 5th harmonic amplitudes.

[0124] S43: According to the standard setting verification criteria for torque smoothness of aviation electric propulsion systems, the ratio of the third harmonic amplitude to the fundamental amplitude must be less than 2%, and the ratio of the fifth harmonic amplitude to the fundamental amplitude must be less than 2%.

[0125] If the current candidate solution at the inflection point of the Pareto front satisfies the above harmonic suppression criteria, the current candidate solution at the inflection point is output as the optimal principal magnetic pole arc coefficient; otherwise, along the Pareto front, the next non-dominated solution is selected in the direction with lower total harmonic distortion, and the process returns to S42 for verification until the verification criteria of S43 are met, and it is output as the optimal pole arc coefficient.

[0126] S44: Based on the main magnetic pole arc coefficient output from S43, according to the following formula:

[0127]

[0128] Thus, the auxiliary magnetic pole arc coefficient is obtained.

[0129] Finite element simulation was performed on the determined pole arc coefficient under the conditions of rated current 300A and rated speed 3000r / min to verify the relationship between the sinusoidal waveform of air gap magnetic flux density and rotor eddy current loss and torque pulsation.

[0130] The performance simulation data and analysis are as follows:

[0131] like Figure 5 As shown, the average torque of the inner rotor is 108.87 Nm, the maximum torque is 110.10 Nm, the minimum torque is 107.68 Nm, and the torque pulsation is about 2.22%, which is extremely small and close to an ideal constant torque source.

[0132] like Figure 6 As shown, the average torque of the outer rotor is 153.25 Nm, the maximum torque is 155.55 Nm, and the minimum torque is 149.27 Nm. The torque fluctuation is about 4.10%. Although the outer rotor is limited by a large radius lever arm and the pulsation is slightly higher, it still meets the requirements of the aerospace propulsion system for torque stability (pulsation <5%).

[0133] The torques of the inner and outer rotors are superimposed, resulting in a total average output torque of approximately 262.12 Nm. The calculation formula is as follows:

[0134]

[0135] in, This refers to the output torque of the motor's internal rotor. The output torque of the motor's outer rotor. This represents the total output torque of the motor.

[0136] This invention innovatively embeds an inner rotor in the radial space, contributing an additional torque of 108.87 Nm. Under the premise of keeping the overall size (volume) of the motor unchanged, its total output torque and power density are greatly improved. The extremely low torque ripple of the motor makes the mechanical vibration of the motor during operation very small, which can effectively reduce the risk of aircraft fuselage resonance, reduce mechanical fatigue of the transmission system, and improve the quietness and stealth of the system.

[0137] The formula for calculating motor output power is:

[0138]

[0139] in, This refers to the motor's output power. This represents the total output torque of the motor. ω is the angular velocity of the motor, and n is the rotational speed of the motor.

[0140] The motor output power is approximately 82.34kW. Traditional single-rotor motors of the same size are limited by stator yoke saturation and heat dissipation, making it difficult for their power to exceed 60kW. Compared to high-performance single-rotor aircraft motors of the same size, this motor increases output power by about 30%.

[0141] Calculations show that the motor's volumetric torque density is approximately 25.75 Nm / L, which is higher than that of a high-performance single-rotor motor of the same volume in aviation, which has a torque density of approximately 18~22 Nm / L. This represents a 30% increase in torque density and a higher utilization rate of takeoff weight.

[0142] Loss characteristics:

[0143] like Figure 7 As shown, after the motor is powered on and started, it undergoes a magnetic field transient establishment process of approximately 12ms, during which the iron loss value gradually increases from 0. After 12ms, the magnetic field enters a steady state, and the iron loss stabilizes at approximately 58W, with minimal fluctuation, demonstrating the motor's excellent electromagnetic performance. Figure 8 As shown, during the startup phase from 0ms to 2ms, the loss increases linearly with the establishment of the air gap magnetic flux density; after 2ms, it enters a steady state with an average eddy current loss of approximately 18W. This low-loss characteristic verifies the rationality of the dual-rotor structure and magnetic circuit design described in this invention. For 82kW-class motors, eddy current losses in the magnets are usually the main risk source leading to rotor overheating and demagnetization. This design controls the eddy current loss to an extremely low level of 18W, indicating that the harmonic content of the air gap magnetic field is extremely low, resulting in less rotor heat generation. This significantly reduces the dependence on the rotor cooling system and improves the thermal stability of the motor under all operating conditions.

[0144] Figure 9 The waveform of the three-phase no-load back EMF of the high torque density dual-rotor permanent magnet fault-tolerant motor described in this embodiment at a rated speed of 3000 r / min is shown in the time domain. The three phases are 120° electrical angle apart, the amplitude is balanced, the sinusoidal degree is excellent and there is no obvious distortion, which confirms the harmonic suppression effect of the pole arc coefficient optimization design.

[0145] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style of the specification is merely for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in the embodiments can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A high torque density dual-rotor permanent magnet fault-tolerant motor, comprising an inner rotor (2), a stator (1), and an outer rotor (3) coaxially arranged; the stator (1) comprises a stator core and a stator winding (8), the stator core having armature teeth (5) and fault-tolerant teeth (6) arranged alternately in the circumferential direction, and the circumferential width of the armature teeth (5) is greater than the circumferential width of the fault-tolerant teeth (6); characterized in that, The stator winding (8) adopts a fractional slot concentrated winding, and the stator winding (8) is only wound on the armature teeth (5); the fault-tolerant teeth (6) are exposed to form a physical and magnetic circuit isolation barrier between adjacent phase windings. The outer rotor (3) and the inner rotor (2) are fixedly connected at the axial ends by end plates to form a coaxial, same-speed rotating dual-rotor linkage structure, so as to superimpose the electromagnetic torque of the two and output it through a single common shaft. The stator (1) is disposed between the inner rotor (2) and the outer rotor (3), and forms an inner air gap and an outer air gap with the two respectively; wherein, the gap between the inner surface of the stator (1) and the outer surface of the inner rotor (2) forms the inner air gap, and the gap between the outer surface of the stator (1) and the inner surface of the outer rotor (3) forms the outer air gap, and the inner air gap and the outer air gap are independent of each other; Halbach arrays are provided on the outer surface of the inner rotor (2) and the inner surface of the outer rotor (3). The Halbach arrays are composed of main magnetic poles and auxiliary magnetic poles arranged alternately along the circumferential direction. The main magnetic poles are radially magnetized permanent magnets (4), and the auxiliary magnetic poles are tangentially magnetized Halbach magnets (7). Both the permanent magnets (4) and the Halbach magnets (7) are made of samarium cobalt material. Furthermore, the polar arc coefficient of the main magnetic pole in the Halbach array is determined by the polar arc coefficient optimization method based on the electromagnetic performance prediction model of HO-GRNN and the improved sacred religious algorithm, so that the motor can maximize the sum of the fundamental wave amplitude of the inner air gap and the outer air gap magnetic flux density and minimize the total harmonic distortion rate under fault-tolerant operation. In addition, when the motor is running, the magnetic field of the stator winding (8) acts on the inner and outer air gaps at the same time, and interacts with the permanent magnet magnetic fields of the inner rotor and the outer rotor respectively. The outer rotor (3) and the inner rotor (2) superimpose to output the total torque.

2. The high torque density dual-rotor permanent magnet fault-tolerant motor according to claim 1, characterized in that, The widths of the inner and outer air gaps are equal.

3. The high torque density dual-rotor permanent magnet fault-tolerant motor according to claim 1, characterized in that, The stator winding (8) adopts a fractional slot concentrated winding configuration with 20 poles and 24 slots.

4. A method for optimizing the pole arc coefficient, applied to the high torque density dual-rotor permanent magnet fault-tolerant motor as described in claim 1, characterized in that, include: Step 1: Establish a parameterized finite element model of the dual-rotor permanent magnet fault-tolerant motor. Using the main magnetic pole arc coefficient as the key variable, the Latin hypercube sampling method is used to collect sample data and perform electromagnetic field simulation. Construct a sample database containing the relationship between the main magnetic pole arc coefficient and the sum of the magnetic flux density fundamental wave amplitudes of the inner and outer air gaps, as well as the total harmonic distortion rate. Step 2: Based on the sample database constructed in Step 1, a generalized regression neural network (GRNN) model is constructed as the electromagnetic performance prediction model. The polar arc coefficient of the main magnetic pole in the sample is used as the input variable of the electromagnetic performance prediction model, and the sum of the magnetic flux density fundamental wave amplitude and the total harmonic distortion rate of the corresponding inner and outer air gaps are used as the output variables to train the GRNN model, thereby establishing a nonlinear mapping relationship between the polar arc coefficient of the main magnetic pole and the magnetic flux density characteristics of the inner and outer air gaps. Furthermore, the Hippo optimization algorithm is introduced to adaptively optimize the smoothing factor of the electromagnetic performance prediction model with the goal of minimizing the prediction error, thereby obtaining the trained HO-GRNN prediction model. Step 3: With the dual optimization objectives of maximizing the sum of the fundamental wave amplitudes of the air gap magnetic flux density and minimizing the total harmonic distortion rate, based on the HO-GRNN prediction model, a multi-objective optimization solution is performed using an improved sacred religious algorithm, and the Pareto optimal solution set is output. Step 4: Select the point with the largest curvature on the Pareto front from the Pareto optimal solution set as the candidate solution for the front inflection point. Input the obtained candidate solution for the front inflection point into the HO-GRNN prediction model trained in Step 2 to verify its harmonic suppression effect on the air gap magnetic flux density waveform. The pole arc coefficient corresponding to the candidate solution that meets the preset harmonic suppression standard is taken as the optimal main magnetic pole pole arc coefficient.

5. The polar arc coefficient optimization method according to claim 4, characterized in that, Step three includes: S31: Two objective functions are defined with the dual optimization objectives of maximizing the sum of the fundamental wave amplitudes of the air gap magnetic flux density and minimizing the total harmonic distortion rate: In the formula, It is the sum of the fundamental wave amplitudes of the air gap magnetic flux density. THD Total harmonic distortion (THD) The main magnetic pole arc coefficient; S32: The improved sacred religious algorithm is used to optimize the HO-GRNN prediction model trained in step two, and the initial population is generated using Tent chaotic mapping. S33: By simulating the process of religious propagation, it evolves through iterative evolution, executing propaganda mechanisms for local development and miracle mechanisms for global exploration; S34: Use a non-dominated sorting strategy to handle multi-objective competition, filter and output a set of non-dominated Pareto optimal solutions; S35: Determine if the number of iterations has reached the preset value. If yes, proceed to step four; otherwise, return to S33 to continue iterating.

6. The polar arc coefficient optimization method according to claim 4, characterized in that, Step four includes: S41: Identify the point with the largest curvature on the leading edge of the Pareto optimal solution set output in step three as the candidate solution for the leading edge inflection point; S42: Input the candidate solution of the leading edge inflection point into the HO-GRNN prediction model trained in step two to predict the amplitude of the third and fifth harmonics of its air gap magnetic flux density waveform. S43: If the candidate solution at the current leading edge inflection point meets the preset harmonic suppression criterion, output it as the main magnetic pole arc coefficient; otherwise, select the nearest solution along the Pareto leading edge for verification until a solution that meets the harmonic suppression criterion is found.

7. The polar arc coefficient optimization method according to claim 6, characterized in that, In the Halbach array of the inner rotor (2) and the outer rotor (3), the pole arc coefficient of the auxiliary magnetic pole is determined based on the pole arc coefficient of the main magnetic pole, and the two satisfy the following relationship: Auxiliary magnetic pole arc coefficient = 1 - Main magnetic pole arc coefficient.

8. A computer-readable storage medium storing a computer program, characterized in that, When the program is executed by the processor, it implements the polar arc coefficient optimization method according to any one of claims 4-7.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed, it is used to implement the polar arc coefficient optimization method according to any one of claims 4-7.

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