A high-precision magnetic network modeling method suitable for a hybrid stator permanent magnet Vernier motor

Abstract

The application discloses a high-precision magnetic network modeling method suitable for a hybrid stator permanent magnet vernier motor, adopts a method combining an equivalent magnetic circuit model and a magnetic resistance network model, and realizes balance of model calculation time and calculation precision. For a complex magnetic flux distribution region, for example, a gap and a modulation tooth region, a magnetic resistance network method is adopted for modeling, and modeling precision and dynamic analysis efficiency are improved. A mixed medium grid is introduced, applicability of the model to motors with different topological structures is improved, modeling difficulty and workload are greatly reduced, a problem of irregular connection of stator and gap nodes caused by transient simulation is avoided, and simulation error is effectively reduced. A cubic spline interpolation method is adopted to update magnetic permeability, iteration speed is accelerated, and magnetic permeability updating precision is improved. An orthogonal decomposition model and a harmonic decomposition method are introduced, and a stator core loss is obtained through superposition, and calculation error of a classical loss separation model is reduced.

Description

Technical Field

[0001] This invention relates to a high-precision magnetic network modeling method applicable to hybrid stator permanent magnet vernier motors, belonging to the field of electromagnetic field calculation. Background Technology

[0002] Due to their low-speed, high-torque characteristics, permanent magnet vernier motors are now widely used in wind power generation, electric vehicles, and ship propulsion. The hybrid stator permanent magnet vernier motor in this invention employs a stator structure combining slotted teeth and open teeth. Compared to traditional permanent magnet vernier motors, this introduces multiple low-order harmonics into the air gap, significantly improving the motor's power factor. Furthermore, the multi-harmonic design helps increase the no-load back EMF, thereby improving the motor's output torque. By optimizing the permanent magnet thickness, armature tooth width, modulation tooth height, and permanent magnet pole arc coefficient, the motor's output torque and power factor can be effectively improved. To further study and analyze motor efficiency, based on the magnetization method of ferromagnetic materials, an orthogonal decomposition model is used, equating rotational magnetization to two alternating magnetic fields—radial and tangential—and, according to harmonic decomposition theory, superimposing them to obtain a more accurate result for stator core losses.

[0003] The Finite Element Method (FEM) is commonly used for analyzing the magnetic field of electric motors due to its ease of use, versatility, and high accuracy. However, the complex topology and magnetic field distribution of permanent magnet vernier motors necessitate extremely fine mesh generation for FEM simulations, making the solution process very time-consuming. Furthermore, processing large mesh sizes places extremely demanding requirements on computer performance. In contrast, the equivalent magnetic network method offers advantages such as simple principle, low computational cost, high simulation efficiency, and high accuracy. It can quickly analyze the electromagnetic characteristics of motors and is widely applicable in the initial stages of various motor designs. Summary of the Invention

[0004] The purpose of this invention is to provide a high-precision magnetic network modeling method suitable for hybrid stator permanent magnet vernier motors. This method mainly includes improved modeling methods for the motor air gap and modulation tooth region, as well as a solution algorithm for the model. The orthogonal decomposition model and harmonic decomposition method are combined with the constructed magnetic network model to accurately calculate stator core losses.

[0005] To achieve the above objectives, the technical solution adopted by this invention is: a high-precision magnetic network modeling method suitable for hybrid stator permanent magnet vernier motors, comprising the following steps:

[0006] Step 1: Establish an equivalent magnetic network model for a regular magnetic field region;

[0007] Step 2: Establish an equivalent magnetic network model for the air gap and modulation tooth region;

[0008] Step 3: Construct a complete magnetic network model and establish the magnetic permeability matrix equation;

[0009] Step 4: Using the nodal magnetomotive force method, solve the nonlinear equation system to obtain the nodal magnetomotive force and the magnetic flux of each permeability unit, and further calculate the magnetic density and permeability of each permeability unit.

[0010] Step 5: Retain the permeability of each permeability unit obtained in Step 4, and reset the permeability matrix accordingly; introduce the orthogonal decomposition model and harmonic decomposition method, and superimpose to obtain the stator core loss, thereby reducing the error of the classical loss separation model.

[0011] Furthermore, the hybrid stator permanent magnet vernier motor is a 20-slot / 46-pole five-phase motor, comprising a rotor, stator, and air gap. The rotor is cylindrical, with permanent magnets attached to the inner wall of the rotor. It uses rare-earth neodymium iron boron material and radial magnetization, with alternating N and S poles arranged circumferentially. The pole arc coefficient is set to 0.86, achieving high power factor and high torque output while saving permanent magnet usage, reducing permanent magnet leakage, and lowering the difficulty of permanent magnet installation. The stator includes modulation teeth, stator teeth, armature windings, and a yoke. The stator teeth are staggered with armature teeth and fault-tolerant teeth, employing split-tooth and slotted structures respectively. The armature windings are designed as fractional-slot concentrated windings. Both the rotor and stator are made of silicon steel sheet DW465_50. The air gap, located between the stator and rotor, is 0.5mm thick and is the main site for magnetic field energy exchange.

[0012] Furthermore, in step 1, since the magnetic field distribution of the rotor yoke, stator pole shoes, stator teeth, and stator yoke is uniform and the magnetic lines of force are ordered, they can be equivalent to a unidirectional magnetic permeation unit based on their magnetic flux paths. The rotor yoke is uniformly divided into corresponding magnetic permeation units according to the number of permanent magnets, and the unit cross-section is fan-shaped. The stator pole shoes are divided into two magnetic permeation units symmetrical about the center line of the armature teeth according to the direction of magnetic flux flow, and the unit cross-section is approximately a right trapezoid. The cross-section of the stator tooth magnetic permeation unit is rectangular. The stator yoke is uniformly divided into corresponding magnetic permeation units according to the number of stator teeth, and the unit cross-section is fan-shaped. The permanent magnets are equivalent to a series structure of magnetic permeation and magnetomotive force. According to the current law, the energized winding is equivalent to an armature magnetomotive force source, which is connected in series with the armature tooth magnetic permeation.

[0013] In step 2, the hybrid stator permanent magnet vernier motor adopts a stator structure combining slotted and split teeth. Compared with traditional permanent magnet vernier motors, multiple harmonics are introduced into the air gap. Simultaneously, due to the influence of permanent magnet leakage and tooth tip leakage, the magnetic field distribution in the air gap and modulation tooth region is particularly complex. Considering both the magnetic field line distribution and the core saturation degree, the reluctance network method is used to model the air gap and modulation tooth region. The air gap model is similar to the finite element mesh generation method, containing a large number of cross-shaped mesh elements. The number of air gap mesh elements is 1840, a common multiple of the pole number and slot number, to provide sufficient modeling accuracy. All mesh elements have the same size and a defined air gap permeability. Only the changes in the node connection relationship between the air gap and the stator need to be considered. This improves the efficiency of dynamic model analysis, avoids the complex determination of magnetic permeability boundaries and calculation of magnetic permeability in the equivalent magnetic circuit method, and overcomes the drawback of the equivalent magnetic circuit method's inability to consider tangential magnetic flux, further improving model accuracy.

[0014] Due to the influence of the motor topology, the meshes of the air gap and the modulation tooth region overlap, lacking good connectivity. By introducing a hybrid dielectric mesh, the modulation tooth region can be divided into mesh cells of the same size along the circumference, thereby determining the node connection relationship between the stator and the air gap. This avoids the problem of irregular node connections caused by transient simulation, reducing simulation errors. In addition, the application of the hybrid dielectric mesh enhances the versatility of the equivalent magnetic network model, facilitating the optimized design of the motor.

[0015] Furthermore, in step 4, considering Matlab's advantage in calculating large-scale matrices, the nodal magnetomotive force method is used in Matlab to solve the magnetic permeability matrix equation: F = G -1 ·Ф, where F is the magnetomotive force matrix, G is the permeability matrix, and Ф is the flux matrix. Newton's iteration method is used for nonlinear iteration, with the flux density B as the iteration variable. To accelerate the convergence speed, the flux density B is modified as follows: B co =aB (k-1) +(1-a)B (k) Among them, B co B is the correction value for the magnetic flux density in the k-th iteration. (k-1) For the (k-1)th iteration, B (k) Let be the magnetic flux density of the k-th iteration, and 'a' be the relaxation factor, set to 0.5. After obtaining the magnetopotential of all nodes in the model, the magnetic flux density B of each magnetic permeability unit can be obtained through B = ΔF. ele ·G ele / S ele The calculation yields ΔF. ele For the magnetic potential drop of the permeability unit, G ele For the magnetic permeability unit, S eleThe effective cross-sectional area of ​​the magnetic permeability unit is given. The magnetic permeability is obtained by consulting the BH curve. Since the number of discrete sample points in the magnetization curve directly affects the accuracy of the magnetic permeability calculation, cubic spline interpolation is introduced to improve the smoothness of the BH curve, thereby improving the accuracy of the magnetic permeability calculation and further enhancing the iteration convergence speed.

[0016]

[0017] In the formula, H ele and u new These represent the magnetic field strength and permeability of the updated magnetic permeability unit, respectively (H n B n ) and (H n+1 B n+1 ) represents two adjacent sample points on the BH curve.

[0018] Furthermore, in step 5, the permeability matrix is ​​recalculated based on the permeability of each permeability unit updated by cubic spline interpolation. Considering that ferromagnetic materials have two magnetization modes, alternating magnetization and rotational magnetization, an orthogonal decomposition model is adopted to calculate the stator core loss more accurately. The rotational magnetization is regarded as two alternating magnetic fields, radial and tangential. Based on the harmonic decomposition theory, the core losses generated by each harmonic in the radial and tangential directions are superimposed to obtain the stator core loss, thereby reducing the error of the classical loss separation model.

[0019] The present invention has the following beneficial effects:

[0020] 1. This invention employs a combination of equivalent magnetic circuit model and magnetoresistive network model. For regions with regular magnetic flux distribution, the equivalent magnetic circuit method is used for modeling, significantly reducing the number of nodes in the equivalent magnetic network model, decreasing computation time, and improving the model's analytical efficiency. Furthermore, the magnetoresistive network method fully considers local magnetic saturation of the stator core, permanent magnet leakage, and modulation tooth tip leakage, effectively improving model accuracy.

[0021] 2. In this invention, by introducing a hybrid dielectric mesh into the modulation tooth region, this region can be divided into mesh cells of the same size along the circumference, improving the versatility of the equivalent magnetic network model and providing good portability for permanent magnet vernier motors with different modulation tooth structures. Furthermore, the application of the hybrid dielectric mesh also determines the node connection relationship between the stator and the air gap, avoiding irregular node connections caused by transient simulation and reducing simulation errors.

[0022] 3. A cross-shaped mesh is used in the air gap region, avoiding the complex determination of magnetic permeability boundaries and calculations required by the equivalent magnetic circuit method. Furthermore, since the mesh elements in the air gap have the same geometric size, the air gap permeability does not change with the rotor position; dynamic analysis of the model can be achieved simply by changing the node connection relationship between the air gap and the stator.

[0023] 4. The magnetic permeability units in the model are all regular shapes such as sector, trapezoid and rectangle. The magnetic permeability calculation formula is simple, which meets the requirement of simplifying the processing of complex magnetic fields.

[0024] 5. The permeability update of ferromagnetic materials generally employs linear interpolation. The number of discrete samples in the magnetization curve directly affects the accuracy of this permeability update. Furthermore, when the magnetization curve is oversaturated, iterative linear interpolation struggles to converge and is prone to oscillations. Cubic spline interpolation inserts a cubic function between adjacent B values, thereby improving the smoothness of the BH curve. This effectively reduces the oscillation frequency of the iteration, accelerates the convergence speed, and enhances the accuracy of permeability updates. Attached Figure Description

[0025] Figure 1 (a) is the topology of the hybrid stator permanent magnet vernier motor according to an embodiment of the present invention;

[0026] Figure 1 (b) Dimensions of the hybrid stator permanent magnet vernier motor according to an embodiment of the present invention;

[0027] Figure 2 This is an equivalent magnetic network model for a region with regular magnetic flux distribution, as described in this embodiment of the invention.

[0028] Figure 3 This is an equivalent magnetic network model of the air gap and modulation tooth region in an embodiment of the present invention;

[0029] Figure 4 This refers to the hybrid medium grid cell used in the embodiments of the present invention;

[0030] Figure 5 This is a flowchart illustrating the iterative process of an embodiment of the present invention;

[0031] Figure 6 (a) shows the positional distribution of points A, B, and C on the stator core;

[0032] Figure 6 (b) shows the magnetic flux density waveforms at different positions of the stator core;

[0033] Figure 6 (c) is an improved model of the equivalent magnetic network of the stator pole shoes;

[0034] Figure 6 (d) Comparison of simulation results between the stator core loss separation model and the stator core loss improvement model;

[0035] Figure 7 (a) is the simulation waveform of the five-phase no-load flux linkage;

[0036] Figure 7 (b) shows the simulation waveform of the magnetic flux linkage under a five-phase load;

[0037] Figure 7 (c) is the simulated waveform of air gap magnetic flux density;

[0038] Figure 7 (d) is the frequency domain decomposition of the air gap magnetic flux density;

[0039] Figure 7 (e) is the simulated waveform of electromagnetic torque;

[0040] Figure 7 (f) shows the simulated waveform of the average torque as a function of current; Detailed Implementation

[0041] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0042] To more concisely illustrate the beneficial effects of the present invention, a detailed description is provided below using a specific hybrid stator permanent magnet vernier motor as an example: Figure 1 (a) is a topology diagram of the motor, where 1 is the rotor, 2 is the surface-mounted permanent magnet, 3 is the modulation tooth, 4 is the armature tooth, 5 is the fault-tolerant tooth, 6 is the stator, and 7 is the armature winding. This embodiment of the invention is a 20-slot / 46-pole five-phase motor, comprising a rotor, stator, and air gap. The rotor is cylindrical, with the permanent magnets surface-mounted on the inner wall of the rotor. Rare-earth neodymium iron boron material and radial magnetization are used, with alternating N and S poles arranged circumferentially. The pole arc coefficient is set to 0.86 to achieve a high power factor. While providing high torque output, it saves on the amount of permanent magnets used, reduces permanent magnet leakage, and lowers the difficulty of permanent magnet installation. The stator includes modulation teeth, stator teeth, armature windings, and a yoke. The stator teeth are staggered with armature teeth and fault-tolerant teeth, using split tooth and slotted structures respectively. The armature windings are designed as fractional-slot concentrated windings. Both the rotor and stator are made of silicon steel sheet DW465_50. The air gap, located between the stator and rotor, is 0.5mm thick and is the main site for magnetic field energy exchange. Figure 1 (b) shows the dimensions of the motor.

[0043] Step 1: Establish an equivalent magnetic network model for a region with regular magnetic flux distribution.

[0044] Figure 2This is a schematic diagram of the uniform magnetic field distribution region model according to an embodiment of the present invention. The rotor yoke is divided into 46 magnetic permeability units based on the number of surface-mounted permanent magnets and the magnetization center line of the permanent magnets. The cross-section of each magnetic permeability unit is fan-shaped. The leakage permeability between stator slots is extremely small and can be ignored. Due to the regular topological structure and magnetic flux distribution of the stator teeth, each stator tooth can be equivalent to a single magnetic permeability unit with a rectangular cross-section. The stator yoke is divided into 20 magnetic permeability units based on the number of stator teeth and the center line of the stator teeth. The cross-section of each magnetic permeability unit is fan-shaped. The stator pole shoes are divided into two magnetic permeability units based on the magnetic flux flow direction. These units are symmetrical about the center line of the armature teeth and have a right-angled trapezoidal cross-section. The formula for calculating the magnetic permeability of the rotor yoke is:

[0045]

[0046] In the formula, G ry For the rotor yoke magnetic permeability, N pm Let u0 and u be the number of permanent magnets. r W represents the vacuum permeability and relative permeability, respectively. ry R is the rotor yoke width. ri h is the inner diameter of the rotor. pm The height of the permanent magnet is given; the formula for calculating the magnetic permeability of the stator teeth is:

[0047]

[0048] In the formula, G st For stator tooth permeability, W st and W sy These are the stator tooth width and stator yoke width, respectively, L d R is the axial length of the motor. st Let be the stator tooth radius; the formula for calculating the magnetic permeability of the stator yoke is:

[0049]

[0050] In the formula, G sy For the stator yoke magnetic permeability, N slot R is the number of stator slots. si Where is the stator inner diameter; the formula for calculating the stator pole shoe permeability is:

[0051]

[0052] In the formula, G sh For the stator pole shoe magnetic permeability, θ sho R is the radius corresponding to the outer diameter of the pole shoe. sho h0 is the outer diameter of the pole shoe, h1 is the height of the pole shoe, and h1 is the height of the slot wedge.

[0053] In this embodiment of the invention, the permanent magnet is equivalent to a magnetomotive force and permeability connected in series. Considering the multi-pole pairs of the permanent magnet vernier motor and the surface-mounted permanent magnet structure, there is a large amount of permanent magnet leakage flux in the air gap. Since the air gap is divided into a large number of cross-shaped grids, there is no need to consider the inter-pole leakage flux of the permanent magnet separately. The corresponding formulas for calculating the magnetomotive force and permeability of the permanent magnet are as follows:

[0054]

[0055] In the formula F pm For the magnetomotive force of a permanent magnet, G pm For permanent magnet permeability, B r For permanent magnet remanence, μ0 is the free permeability, and μ pm w is the relative permeability of the permanent magnet. pm and l pm These represent the width and length of the permanent magnet, respectively; the winding is a fractional-slot concentrated winding design. According to the current law, the line integral of the magnetic field strength vector along any closed loop is equal to the algebraic sum of the currents passing through the area enclosed by the closed loop; since the magnetic flux path generated by the current-carrying conductor all passes through the armature teeth, the equivalent magnetomotive force is placed on the armature teeth, and its direction is determined according to the right-hand screw rule, and its magnitude is:

[0056]

[0057] In the formula, F s H is the magnetomotive force of the winding, H is the magnetic field strength, l is the closed path of the magnetic flux, and N is the magnetic flux density. s denoted as the number of turns in the armature winding, and i as the armature winding current.

[0058] Step 2: Establish an equivalent magnetic network model for the air gap and modulation tooth region.

[0059] A schematic diagram of the equivalent magnetic network model of the air gap and modulation tooth region in this embodiment of the invention is shown below. Figure 3As shown, in order to improve the accuracy of air gap modeling, the air gap model adopts a mesh generation method similar to that of finite element method, dividing the air gap into a large number of cross-shaped mesh elements. The mesh generation process strictly follows the following principles: (1) all cross-shaped mesh elements have the same size; (2) the number of cross-shaped mesh elements is controlled within the range of 1500-2000; (3) the radial arrangement of cross-shaped mesh elements does not exceed two layers. Mesh elements of the same size have a definite air gap permeability, avoiding complex permeability calculations caused by the rotor position. At the same time, only the stator and air gap need to be changed. By establishing the node connection relationships, dynamic analysis of the motor can be quickly achieved; all mesh elements have the same size and a defined air gap permeability, requiring only consideration of changes in the node connection relationships between the air gap and the stator; this avoids the complex permeability boundary determination and permeability calculation of the equivalent magnetic circuit method, while overcoming the drawback of the equivalent magnetic circuit method's inability to consider tangential magnetic flux, further improving model accuracy; when the number of mesh layers in the air gap exceeds two, the model accuracy does not significantly improve. Therefore, to balance the model's timing and computational accuracy, the air gap is divided into single-layer cross-shaped mesh elements, and the air gap permeability calculation formula is:

[0060]

[0061] In the formula G t_air and G r_air These are the air gap tangential and radial magnetic permeabilities, respectively, N air W represents the number of air gap mesh elements. air R is the air gap width. so The outer diameter of the stator is used. To avoid abrupt changes in the connection relationship between the stator and air gap nodes caused by transient simulation of the equivalent magnetic network model, a hybrid dielectric mesh is introduced. This divides the modulation tooth region into mesh elements of equal size along the circumferential direction, thereby determining the node connection relationship between the two and reducing simulation errors. The hybrid dielectric mesh element is as follows: Figure 4 As shown, the corresponding formula for calculating magnetic permeability is:

[0062]

[0063] In the formula, Gr and Gt are the radial and tangential magnetic permeabilities of the hybrid dielectric mesh element, respectively, and u i Let u be the permeability of the iron core, g be the height of the hybrid dielectric grid cell, and R be the inner diameter of the hybrid dielectric grid cell. i >>u0, therefore, the magnetic permeability formula for the hybrid dielectric mesh can be simplified to:

[0064] Due to the influence of the motor topology, the meshes of the air gap and the modulation tooth region overlap and lack good connectivity. By introducing a hybrid medium mesh, the modulation tooth region can be divided into mesh cells of the same size along the circumference, thereby determining the node connection relationship between the stator and the air gap. This avoids the problem of irregular node connection caused by transient simulation and reduces simulation error. In addition, the application of the hybrid medium mesh also enhances the versatility of the equivalent magnetic network model, which is conducive to the optimized design of the motor.

[0065] Step 3: Construct the complete magnetic network model.

[0066] The magnetic flux distribution regular region model, air gap and modulation tooth region model of the present invention are connected by air nodes to form a complete magnetic network model, and each node of the equivalent magnetic network model is numbered, with a total of 6668 nodes.

[0067] Step 4: Establish and solve the magnetic permeability matrix equation.

[0068] Based on the similarity between circuits and magnetic circuits, circuit analysis methods, such as Kirchhoff's voltage law and current law, are also applicable to solving equivalent magnetic network models, thus simplifying magnetic circuit analysis. The magnetic permeability matrix equation can be expressed as:

[0069] F = G -1 ·Φ (10)

[0070] In the formula:

[0071] and

[0072] F = [F(1),F(2),...,F(n)] T

[0073] Φ = [Φ(1), Φ(2), ..., Φ(n)] T

[0074] Based on the Matlab platform, the magnetic flux density between node i and node j can be calculated as follows:

[0075]

[0076] In the formula, B new Let F(i) and F(j) be the magnetomotive forces at nodes i and j, respectively, and G(i,j) be the magnetic permeability between nodes i and j. Let S be the new magnetic flux density. ij W represents the cross-sectional area of ​​the mesh cells between node i and node j. eleThe width of the grid cell is given; the magnetic permeability matrix equation (10) is a nonlinear equation, which requires nonlinear iteration using Newton's iteration method. In this embodiment, magnetic flux density is used as the iteration variable, and the influence of the magnetic flux density calculation result in the previous iteration step on the magnetic flux density calculation result in the current iteration step is considered. The iteration format is as follows:

[0077] B co =aB pre +(1-a)B new (12)

[0078] In the formula B pre The magnetic flux density value obtained in the previous iteration step; according to B co Update the permeability by using cubic spline interpolation on the BH curve:

[0079]

[0080] The iterative process flowchart is as follows: Figure 5 As shown.

[0081] Step 5: Application of the improved model for stator core loss.

[0082] Retain the permeability of the nonlinear magnetic permeability unit obtained in each iteration step of step 4, recalculate the permeability matrix, and proceed to the next iteration. To prevent the iteration from entering an infinite loop, pre-set error limits and the number of iterations. Once the termination condition, i.e., B, is reached, the iteration will terminate. co The iteration ends when the following relationship is satisfied:

[0083]

[0084] In the formula, B co (k+1) and B co (k) The values ​​are the magnetic flux density values ​​after the (k+1)th and kth corrections, respectively. ε is the error limit, set to 0.0001 to ensure sufficient convergence of the iteration. If the inequality holds, the equivalent magnetic network model moves to the next rotor position and re-performs the iteration calculation. Finite element calculations show that the stator core loss and rotor core loss are 45W and 2W, respectively. The stator core loss is significantly greater than the rotor core loss. Therefore, adopting an improved stator core loss model will enhance the equivalent magnetic network model's ability to predict and analyze motor loss characteristics. Since the variation patterns and amplitudes of magnetic flux density vary in different regions of the core, the stator core is divided into four parts: modulation teeth, pole shoes, stator teeth (armature teeth, fault-tolerant teeth), and stator yoke. Furthermore, considering the influence of rotational magnetization on ferromagnetic materials, an orthogonal decomposition model is introduced, treating the rotating magnetic field as two alternating magnetic fields, radial and tangential. Figure 6(b) shows the magnetic flux density waveforms at points A, B, and C on the stator core in 6(a) over one electrical cycle. It can be observed that the radial magnetic flux density amplitude at point A, the stator pole shoe, is 0.63T, and the tangential magnetic flux density amplitude is 0.99T. Therefore, both alternating magnetization and rotational magnetization affect the stator pole shoe. The radial magnetic flux density amplitude at point B, the armature tooth, is 1.54T, and the tangential magnetic flux density amplitude is 0.01T. Therefore, the magnetization of the armature tooth can be approximated as alternating magnetization, and the effect of rotational magnetization at this point can be ignored. The radial magnetic flux density amplitude at point C, the fault-tolerant tooth, is 1.07T, and the tangential magnetic flux density amplitude is 0.02T. Therefore, the magnetization of the fault-tolerant tooth can be approximated as alternating magnetization. Based on the above analysis, the stator teeth and stator pole shoes are modeled using the equivalent magnetic circuit method and the reluctance network method, respectively. Figure 6 (c) is an improved model of the stator pole shoe, which is divided into three parts. The corresponding magnetic permeability calculation formulas for each part are as follows:

[0085]

[0086]

[0087]

[0088]

[0089] In the formula, G r_left and G t_right The radial and tangential magnetic permeabilities of region I are respectively, G r_mid and G t_mid The radial and tangential magnetic permeabilities of region II are respectively, R shi and R sho Let θ1 be the inner and outer diameters of the pole shoe, θ2 and θ3 be the radians corresponding to the height in region I, θ2 and θ3 be the radians corresponding to the lower and upper bases in region II, h0 be the pole shoe height, and h1 be the slot wedge height. The magnetic flux density waveforms in each region are approximately sinusoidal, but they exhibit varying degrees of higher harmonics. According to Fourier decomposition theory, any periodic function can be decomposed into a superposition of a finite number of simple harmonic functions with different amplitudes and frequencies. Furthermore, since the core is simultaneously affected by both the magnetic flux density amplitude and frequency, the losses caused by higher harmonics cannot be ignored. The stator core loss is obtained by superimposing the core losses generated by each harmonic after decomposition. Based on the classical loss separation model, the improved stator core loss model adopts the following formula:

[0090]

[0091] In the formula, P fe K represents the stator core loss density. h K c and K eThese represent the hysteresis loss coefficient, eddy current loss coefficient, and additional loss coefficient, respectively, where f is the motor frequency, k is the harmonic order, and B is the frequency. kr and B kt These are the radial and tangential magnetic flux density amplitudes of the k-th harmonic, respectively. Figure 6 (d) compares the stator core loss model and the finite element calculation results before and after the improvement. It can be observed that the calculation results of the improved stator core loss model are closer to the finite element calculation results. Under the premise of increasing the number of nodes and mesh elements by a small amount, the calculation efficiency of the model is guaranteed, and the calculation accuracy of the core loss of the equivalent magnetic network model is significantly improved.

[0092] Step 7: Compare and analyze the errors between the calculation results.

[0093] To verify the accuracy of the modeling method in this embodiment of the invention, Figure 7 (a)~7(f) show the error comparison between the equivalent magnetic network calculation results and the finite element calculation results.

[0094] Figure 7 (a) shows the no-load flux linkage waveform of the motor. The calculation results of the equivalent magnetic network are in high agreement with the finite element calculation results, which verifies the accuracy and effectiveness of the equivalent magnetic network model. Figure 7 (b) shows the magnetic flux waveform of the motor load (current amplitude is 10A). The equivalent magnetic network model and the finite element calculation results are still very close.

[0095] Figure 7 (c) and Figure 7 (d) shows the simulation waveform and frequency domain decomposition results of the air gap magnetic flux density, respectively. It can be found that the magnetic network has smaller errors in the simulation waveform and harmonic amplitude compared with the finite element method. Furthermore, due to the use of a hybrid structure of toothed and slotted stator, a variety of low-order working harmonics are introduced into the air gap, which effectively improves the power factor and output torque of the motor.

[0096] Figure 7 (e) By comparing the motor output torque, it can be seen that the output torque waveforms obtained from the equivalent magnetic network and the finite element calculation are almost identical. The magnetic network, based on the principle of virtual work, can be used to calculate the output torque as follows:

[0097]

[0098] In the formula, T e For output torque, p r ψ is the number of pole pairs of the permanent magnet. d and ψ q These are the direct and quadrature axis flux linkages, I d and I q These are the direct and quadrature axis currents, respectively; W is the magnetic field energy; θ is the magnetic field energy. e and θ mThe rotor positions are expressed in electrical and mechanical angles, respectively; considering dψ d / dθ e ,dψ q / dθ e and dW / dθ m It does not contribute to the average torque; therefore, the average torque formula can be simplified to:

[0099]

[0100] In the formula, T avg This is the average torque; Figure 7 (f) shows the average torque of the motor under different winding currents. It is easy to see that the equivalent magnetic network and the finite element calculation results are very close, achieving good accuracy.

[0101] In summary, this invention provides a high-precision magnetic network modeling method for hybrid stator permanent magnet vernier motors. This method combines an equivalent magnetic circuit model and a magnetoresistive network model, achieving a balance between model calculation time and computational accuracy. Considering both the motor topology and magnetic field distribution, the equivalent magnetic circuit method is used for regions with regular magnetic flux distribution to reduce model analysis time. For regions with complex magnetic flux distribution, such as the air gap and modulation tooth regions, the magnetoresistive network method is used, fully considering the leakage flux from the permanent magnets and tooth tips. This overcomes the complex determination of magnetic permeability boundaries and calculations required by the equivalent magnetic circuit method, improving modeling accuracy and dynamic analysis efficiency. Introducing a hybrid dielectric mesh enhances the model's applicability to motors with different topologies, significantly reducing modeling difficulty and workload. It also avoids irregular connections between stator and air gap nodes caused by transient simulations, effectively reducing simulation errors. Cubic spline interpolation is used to update the permeability, accelerating the iteration speed and improving the accuracy of permeability updates. Considering the influence of rotational magnetization on ferromagnetic materials, an orthogonal decomposition model and harmonic decomposition method are introduced, and the stator core loss is obtained by superposition, reducing the calculation error of the classical loss separation model. The accuracy of the model was verified by comparing the magnetic network calculation results with the finite element calculation results. This invention is the first to implement magnetic network modeling for a hybrid stator permanent magnet vernier motor, and the proposed scheme can provide a reference for later research on magnetic network modeling of this type of motor.

[0102] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0103] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A high-precision magnetic network modeling method suitable for hybrid stator permanent magnet vernier motors, characterized in that, Includes the following steps: Step 1: Establish an equivalent magnetic network model for a region with regular magnetic flux distribution; Step 2: Establish an equivalent magnetic network model for the air gap and modulation tooth region; Step 3: Construct a complete magnetic network model and establish the magnetic permeability matrix equation; Step 4: Using the nodal magnetomotive force method, solve the nonlinear equation system to obtain the nodal magnetomotive force and the magnetic flux of each permeability unit, and further calculate the magnetic density and permeability of each permeability unit. Step 5: Retain the permeability of each permeability unit obtained in Step 4, and reset the permeability matrix accordingly; introduce the orthogonal decomposition model and harmonic decomposition method, and superimpose to obtain the stator core loss. In step 2, the hybrid stator permanent magnet vernier motor adopts a stator structure combining slotted and split teeth. The air gap and modulation tooth regions are modeled using a magnetoresistive network method. The number of cross-shaped mesh elements is controlled within the range of 1500-2000, which is a common multiple of the pole number and slot number. All mesh elements have the same size and a defined air gap permeability. The meshes in the air gap and modulation tooth regions overlap. By introducing a hybrid dielectric mesh, the modulation tooth region can be divided into mesh elements of the same size along the circumference, thus determining the node connection relationship between the stator and the air gap. The permeability calculation formula for the hybrid dielectric mesh element is: ； In the formula, Gr and Gt are the radial and tangential magnetic permeabilities of the hybrid dielectric mesh element, respectively, and u i Let u0 be the permeability of the iron core, u0 be the permeability of free space, and L be the permeability of the iron core. d denoted as axial length of the motor, g as height of the mixed medium grid cell, and R as inner diameter of the mixed medium grid cell.

2. The high-precision magnetic network modeling method for hybrid stator permanent magnet vernier motors according to claim 1, characterized in that, The hybrid stator permanent magnet vernier motor is a 20-slot / 46-pole five-phase motor, comprising a rotor, stator, and air gap. The rotor is cylindrical, with permanent magnets attached to the inner wall of the rotor. It uses rare-earth neodymium iron boron material and radial magnetization, with alternating N and S poles arranged circumferentially. The pole arc coefficient is set to 0.

86. The stator includes modulation teeth, stator teeth, armature winding, and yoke. The stator teeth are staggered with armature teeth and fault-tolerant teeth, using split-tooth and slotted structures respectively. The armature winding is a fractional-slot concentrated winding design. Both the rotor and stator are made of silicon steel sheet DW465_50. The air gap, located between the stator and rotor, is 0.5mm thick and is the main site for magnetic field energy exchange.

3. The high-precision magnetic network modeling method for hybrid stator permanent magnet vernier motors according to claim 1, characterized in that, In step 1, the magnetic fields of the rotor yoke, stator pole shoes, stator teeth, and stator yoke are equivalent to a unidirectional magnetic permeation unit according to their magnetic flux paths; the rotor yoke is uniformly divided into corresponding magnetic permeation units according to the number of permanent magnets, and the unit cross-section is fan-shaped; the stator pole shoes are divided into two magnetic permeation units symmetrical about the center line of the armature teeth according to the direction of magnetic flux flow, and the unit cross-section is approximately right trapezoidal; the cross-section of the stator tooth magnetic permeation unit is rectangular; the stator yoke is uniformly divided into corresponding magnetic permeation units according to the number of stator teeth, and the unit cross-section is fan-shaped; the permanent magnets are equivalent to a magnetic permeation and magnetomotive force series structure; according to Ampere's law, the energized winding is equivalent to an armature magnetomotive force source, which is connected in series with the armature tooth magnetic permeation.

4. The high-precision magnetic network modeling method for hybrid stator permanent magnet vernier motors according to claim 1, characterized in that, In step 3, the air gap is divided into cross-shaped grid cells. The upper radial magnetic permeability of the air gap is connected to the permanent magnet, and the lower radial magnetic permeability is connected to the modulation tooth region, thus forming a complete equivalent magnetic network model. The nodes of the equivalent magnetic network model are numbered, and the magnetic permeability matrix equation is established according to Kirchhoff's voltage law.

5. The high-precision magnetic network modeling method for hybrid stator permanent magnet vernier motors according to claim 1, characterized in that, In step 5, the permeability of each permeability unit is updated according to the cubic spline interpolation method, and the permeability matrix is ​​recalculated. An orthogonal decomposition model is adopted to regard the rotational magnetization as two alternating magnetic fields in the radial and tangential directions. According to the harmonic decomposition theory, the core losses generated by the radial and tangential harmonics are superimposed to obtain the stator core loss.

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