A topology grid optimization method for permanent magnet flat wire motor based on micro-reluctance unit

Abstract

The present invention discloses a topological grid optimization method for a permanent magnet flat wire motor based on micro-reluctance units, establishes an equivalent model of a rotor, a stator and an air gap micro-reluctance network, obtains a complete rotor structure by symmetry and replication of a 1 / 16 magnetic pole region of the rotor; establishes a two-dimensional Gaussian basis function covering an optimized design region, obtains the material characteristic parameters of the micro-reluctance units on the optimized design region by weighted summation of the two-dimensional Gaussian basis function, aggregates the micro-reluctance units with the same material properties on the optimized design region to generate a new motor topology structure; calculates the average magnetic flux density of each micro-reluctance unit, the magnetic permeability of each iron core micro-reluctance unit and the magnetic permeability convergence coefficient; utilizes a genetic algorithm to optimize the weight coefficient of the Gaussian basis function, and adjusts the material distribution of the micro-reluctance units in the design region; the micro-reluctance unit network model adopted by the present invention is a multi-purpose model that combines motor structure generation and performance analysis, which can greatly improve the design freedom and ensure optimization efficiency.

Description

Technical Field

[0001] The present invention relates to a design method of a permanent magnet flat wire motor, in particular to a design method capable of realizing autonomous optimization of the topological structure of a permanent magnet flat wire motor, and belongs to the technical field of permanent magnet motors. Background Art

[0002] In the field of motor technology, permanent magnet flat wire motors (PMF motors) have been widely used in automotive drive motors due to their advantages, such as high torque density, high efficiency, and wide speed range. Generally speaking, the stator of a PMF motor uses flat wire windings, which improves motor efficiency and heat dissipation. The rotor utilizes an internal permanent magnet topology, which increases torque density while also improving speed regulation. The design of a PMF motor requires, on the one hand, a matching design between the electromagnetic field provided by the flat wire stator and the permanent magnetic field provided by the permanent magnet rotor to achieve optimal torque and efficiency output; on the other hand, consideration must be given to quality requirements such as motor torque ripple and vibration characteristics. Furthermore, due to the complex manufacturing process and high production difficulty of PMF motor stators, their design is subject to numerous constraints, such as the number of winding layers and end length. Therefore, developing an efficient optimization method for achieving near-limit design of PMF motors under multiple objectives and constraints has become a key technical challenge in this field.

[0003] In recent years, attempts have been made to improve the performance of permanent magnet flat-wire motors using techniques such as rotor topology optimization. These include layered permanent magnet placement, the addition of auxiliary slots, edge shaping, and pole skewing. However, these methods often require complex magnetic field analysis and multiple design iterations. Changes to basic motor specifications, such as size, split ratio, and pole-slot alignment, render these optimized designs ineffective and require readjustment. Consequently, attempts have been made to incorporate intelligent optimization methods into permanent magnet flat-wire motor design to address the complex multi-objective optimization problems faced by motors. For example, Chinese Patent Publication No. CN104517013B discloses a genetic algorithm-based multi-objective optimization design method for automotive motors. This method combines optimization methods such as genetic algorithms with electromagnetic field analysis. Through algorithms, key motor design parameters are continuously adjusted, and performance simulations are performed using finite element methods to rapidly optimize the motor structure. However, these optimization techniques typically require pre-design of the basic motor structure and parametric modeling of the structure, thus still requiring significant human involvement and multiple design iterations. In addition, these technologies can only optimize some structural parameter values ​​based on the initial structure of the motor, but cannot generate a new motor topology, resulting in limited improvement in the performance of the optimized motor. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems of high experience dependence and long design cycle in the design of permanent magnet flat wire motors. A topology grid optimization method for permanent magnet flat wire motors based on micro-reluctance units is proposed, which does not require structural design and parametric modeling. The method can realize parameter-free autonomous optimization of the rotor topology according to performance requirements under a given flat wire stator structure.

[0005] To achieve the above-mentioned purpose, the technical solution adopted by the topology grid optimization method of a permanent magnet flat wire motor based on micro-reluctance units of the present invention includes the following steps:

[0006] Step 1): The rotor of the motor is divided into a plurality of micro-reluctance units. The initial material properties of the micro-reluctance units on the rotor are assigned according to the position information of the center points of each micro-reluctance unit on the rotor to obtain the material properties of the permanent magnet, air or iron core, and the corresponding permanent magnet micro-reluctance unit, air micro-reluctance unit and iron core micro-reluctance unit are obtained, thereby establishing an equivalent model of the rotor micro-reluctance network;

[0007] The stator yoke, teeth, tooth shoes and armature winding are modeled in sequence to obtain the stator micro-reluctance network equivalent model;

[0008] The air gap is divided into air reluctance units using a network denser than the rotor's microreluctance units. The air reluctance units are then divided into two magnetic circuits: the outer magnetic circuit is connected to the equivalent magnetic circuit of the stator tooth shoe, and the inner magnetic circuit is connected to the equivalent magnetic circuit of the rotor, resulting in an equivalent model of the air gap microreluctance network.

[0009] Step 2): 1 / 16 of the rotor's magnetic pole area is used as the optimized design area, and the optimized design area is symmetrically and replicated to obtain a complete rotor structure;

[0010] Step 3): establishing a two-dimensional Gaussian basis function covering the entire optimized design area, obtaining material characteristic parameters of the micro-magnetoresistive unit in the optimized design area by weighted summation of the two-dimensional Gaussian basis function, and comparing the material characteristic parameters of the micro-magnetoresistive unit with a defined constant criterion to obtain the material properties of the air or iron core of the micro-magnetoresistive unit in the optimized design area;

[0011] Step 4): Aggregate the micro-magnetic resistance units with the same material properties in the optimized design area, aggregate the iron core micro-magnetic resistance units into the rotor iron core, and aggregate the air micro-magnetic resistance units into the rotor magnetic barrier, thereby generating a new motor topology.

[0012] Furthermore, for the new motor topology described in step 4), the following steps are performed:

[0013] Step 41): Establish and solve the permeability matrix equation of the micro-magnetoresistive network, and calculate the average magnetic flux density of each micro-magnetoresistive unit, the permeability of each core micro-magnetoresistive unit, and the permeability convergence coefficient;

[0014] Step 42) When the maximum convergence coefficients of the magnetic permeabilities of all the core micro-reluctance units are less than the preset tolerance, the output torque is calculated and it is determined whether the output torque meets the design requirements; otherwise, the newly obtained magnetic permeability replaces the initial magnetic permeability or the last iterative magnetic permeability, and step 41) is executed again;

[0015] Step 43): When it is determined that the output torque meets the requirements, the regular shape scheme is selected as the final design scheme of the permanent magnet flat wire motor. Otherwise, the weight coefficient of the Gaussian basis function described in step 3) is optimized using a genetic algorithm, the distribution of the micro-reluctance unit material in the design area is adjusted, and the rotor topology is updated.

[0016] Furthermore, in step 1), the rotor is divided into several sector-shaped micro-reluctance units, each sector-shaped micro-reluctance unit is 0.5deg×0.5mm in size; the permanent magnet micro-reluctance unit whose material property is permanent magnet is composed of two symmetrical tangential equivalent reluctances and tangential equivalent magnetic potentials connected in series and then connected to the central node; the air micro-reluctance unit whose material property is air is composed of four radial air equivalent reluctances and tangential air equivalent reluctances connected to the central node; the iron core micro-reluctance unit whose material property is iron core is also composed of four radial air equivalent reluctances and tangential air equivalent reluctances connected to the central node; the equivalent reluctance of the stator yoke is represented by magnetic permeance, and the equivalent reluctance of the stator tooth is represented by magnetic permeance: the stator tooth shoe adopts the same multi-layer 0.5deg×0.5mm air micro-reluctance unit as the rotor to be equivalent to the 0.5deg×0.5mm iron core micro-reluctance unit; the armature winding is equivalent to the magnetic source.

[0017] Furthermore, in step 3), 6×6 two-dimensional Gaussian basis functions are established to cover the entire optimization design area, and the material characteristic parameters of any micro-magnetoresistive unit are It's G k(i,j) corresponds to the normalized form of the two-dimensional Gaussian basis function, w k is the weight coefficient, σ is the standard deviation of the Gaussian basis function, (ζ k ,τ k ) is the center position of the kth Gaussian basis function; when M n(i,j) Less than or equal to the criterion, the micro-magnetic resistance unit is given air properties; when M n(i,j) If the value is greater than the criterion, the micro-magnetic resistance unit is given the core property.

[0018] Beneficial effects of the present invention:

[0019] 1. The present invention abandons the process of rotor structure design and parameter optimization in the traditional motor design process. Under the given permanent magnet flat wire motor stator structure, it can independently generate the optimal design scheme of the motor rotor based on the motor performance, which is conducive to achieving the near-limit design of the motor and shortening the design cycle.

[0020] 2. The micro-reluctance unit network model adopted in the present invention is a multi-purpose model that combines motor structure generation and performance analysis. The model uses micro-reluctance units to grid the rotor topology of the permanent magnet flat wire motor design area, and generates different rotor topology structures with high design freedom by adjusting the material properties of the micro-reluctance units; at the same time, the model can quickly analyze the electromagnetic properties of the newly generated motor structure based on the path calculation principle, which can greatly improve the design freedom and is conducive to the near-limit design of the motor; at the same time, the micro-reluctance network is used to solve the corresponding motor electromagnetic performance, thereby ensuring optimized efficiency.

[0021] 3. This invention utilizes Gaussian basis functions to adjust the material properties of the micro-magnetoresistive units, ensuring that adjacent micro-magnetoresistive units are made of the same material, thereby generating a motor topology with continuous edges. This not only avoids the unmanufacturable porous structure created by directly adjusting the micro-magnetoresistive unit material, ensuring the manufacturability of the motor design, but also significantly reduces the number of design variables in the optimization process, thereby improving the effectiveness of the optimized design. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a three-dimensional schematic diagram of the initial structure of the permanent magnet flat wire motor targeted by the present invention;

[0023] Figure 2 for Figure 1 An enlarged view of the rotor local structure in the initial structure of the permanent magnet flat wire motor shown;

[0024] Figure 3 This is a flow chart of the topology grid optimization method of the permanent magnet flat wire motor based on micro-reluctance units of the present invention;

[0025] Figure 4 for Figure 1 Figure 2 shows the equivalent micro-magnetoresistance unit for permanent magnet materials;

[0026] Figure 5 for Figure 1 Figure 2 shows the micro-magnetoresistance unit used for the air material equivalent;

[0027] Figure 6 for Figure 1 Figure 2 shows the micro-magnetoresistance unit equivalent to the core material.

[0028] Figure 7 for Figure 1 Schematic diagram of the equivalent micro-reluctance network of the magnetic pole where one of the permanent magnets of the rotor is located;

[0029] Figure 8 for Figure 1 Diagram of the equivalent model of the flat wire stator micro-reluctance network;

[0030] Figure 9 for Figure 1 Equivalent model diagram of the micro-reluctance network of the stator teeth and tooth boots;

[0031] Figure 10 for Figure 1 Magnetomotive force distribution diagram of phase A winding of medium flat wire stator;

[0032] Figure 11 for Figure 1 Diagram of the equivalent model of the medium-gap micro-magnetoresistive network;

[0033] Figure 12 for Figure 1 Schematic diagram of the air gap micro-reluctance unit connection method when the rotor position angle is 0 degrees;

[0034] Figure 13 for Figure 1 Schematic diagram of the air gap reluctance unit connection method when the rotor position angle is 0.5 degrees;

[0035] Figure 14 for Figure 1 Schematic diagram of the design area selected for the motor;

[0036] Figure 15 for Figure 1 Schematic diagram of the two-dimensional Gaussian basis function distribution constructed in the designed area;

[0037] Figure 16 for Figure 1 Schematic diagram of the process of adjusting the material properties of the micro-magnetoresistive unit in the design area;

[0038] Figure 17 for Figure 1 Schematic diagram of tangential magnetic flux density calculation for medium and micro-magnetic resistance units;

[0039] Figure 18 for Figure 1 Schematic diagram of radial magnetic flux density calculation for medium and micro reluctance units;

[0040] Figure 19 This is a schematic diagram of the magnetic flux density calculation of the stator tooth yoke reluctance unit;

[0041] Figure 20 for Figure 1 Schematic diagram of the BH curve of the core material and the iterative process of the magnetic permeability of the core micro-reluctance unit;

[0042] Figure 21 for Figure 1Schematic diagram of the changes in topological structure and magnetic flux density distribution of micro-magnetoresistive units during the optimization process;

[0043] Figure 22 for Figure 1 Schematic diagram of the Pareto front obtained through optimization and the selected candidate design schemes;

[0044] Figure 23 for Figure 1 Schematic diagram of the magnetic barrier edge smoothing process for the final design;

[0045] Figure 24 for Figure 1 3D schematic diagram of the optimized topological structure;

[0046] Figure 25 for Figure 1 Comparison of no-load back EMF before and after optimization;

[0047] Figure 26 for Figure 1 Comparison of no-load back EMF harmonic analysis before and after optimization;

[0048] Figure 27 for Figure 1 Comparison of rated output torque before and after optimization;

[0049] Figure 28 for Figure 1 Comparison of cogging torque before and after optimization. DETAILED DESCRIPTION

[0050] The following, combined with the accompanying drawings of the embodiments of the present invention, uses a 36-slot, 8-pole permanent magnet flat wire motor as an example to clearly and completely describe the technical solution for improving the rotor structure of a permanent magnet flat wire motor using a topological grid optimization method based on micro-reluctance units. The embodiments described below with reference to the accompanying drawings are exemplary and intended only to explain the present invention and are not to be construed as limiting the present invention.

[0051] like Figure 1 The 36-slot / 8-pole permanent magnet flat wire motor shown includes a flat wire stator 01 and a rotor 02. The stator 01 includes 36 stator teeth and is wound with 8 layers of hairpin windings 011 with a span of 4. The rotor 02 is located inside the stator 01 and includes 8 magnetic poles. The permanent magnets of each pole are arranged in a V shape.

[0052] Figure 2 The figure shows the partial topology of rotor 02. NdFeB permanent magnets 021 are embedded in a V-shaped arrangement within rotor core 022, forming a single pole. Each NdFeB permanent magnet 021 has its outer end connected to an outer magnetic barrier 023-1 near the air gap and its inner end connected to an inner magnetic barrier 023-2 near the shaft.

[0053] In order to improve the design efficiency, the present invention Figure 1 The 1 / 4 model of the motor shown is optimized. The optimization method is shown in Figure 3 , specifically:

[0054] Step 1: Establish the equivalent model of the initial micro-reluctance network of the permanent magnet rotor of the motor.

[0055] First, the rotor 02 is divided into several sector-shaped micro-reluctance units, where the size of each sector-shaped micro-reluctance unit is 0.5deg×0.5mm, and n(i,j) is used to represent the sector-shaped micro-reluctance unit number on the rotor 02, where n is the number of sector-shaped micro-reluctance units, i is the tangential number, and j is the radial number; and C n(i,j) (ρ, θ) represents the position information of the center point of the corresponding sector-shaped micro-reluctance unit, ρ is the distance between the center point of the sector-shaped micro-reluctance unit and the center of the rotor 02, and θ is the position angle.

[0056] In the embodiment of the present invention, the rotor 02 is divided into 180×51 sector-shaped micro-reluctance units, so i=0, 1, 2, ..., 179, j=0, 1, 2, ..., 50.

[0057] Then, according to the center point position information C of each sector micro-reluctance unit on the rotor 02 n(i,j) (ρ,θ), the initial material properties A of the sector micro-magnetoresistive unit n(i,j) The allocation rules are as follows:

[0058]

[0059] Among them, Ω PM is the set permanent magnet area, Ω Air For the set air region, the initial material property A of the sector micro-magnetoresistive unit is obtained n(i,j) It is a permanent magnet PM, air Air or an iron core Iron.

[0060] like Figure 4 The initial material properties A of the sector-shaped micro-magnetoresistance unit are shown n(i,j) It is a permanent magnet micro-magnetic resistance unit 110 of a permanent magnet PM. The permanent magnet micro-magnetic resistance unit 110 is a magnetic circuit model composed of four magnetic potential sources and magnetic resistance phase series branches connected to the central node 111. It is composed of two symmetrical tangential equivalent magnetic resistances 112 and tangential equivalent magnetic potentials 114 connected in series and then connected to the central node 111, and two symmetrical radial equivalent magnetic resistances 113 and radial equivalent magnetic potentials 115 connected in series and then connected to the central node 111. In order to facilitate the subsequent solution, the corresponding magnetic resistance is represented by the magnetic permeance, and the definition is is the permeance of the tangential equivalent magnetic resistance of the permanent magnet micro-magnetoresistive unit numbered n(i,j), is the magnetic permeance of the radial equivalent magnetic resistance, and the specific calculation formula is as follows:

[0061]

[0062]

[0063] Among them, μ PM is the magnetic permeability of the permanent magnet, l a is the axial length of the motor, ρ n(i,j) is the distance from the center node of the permanent magnet micro-reluctance unit numbered n(i,j) to the motor axis, Δρ n(i,j) is the height of the permanent magnet micro-reluctance unit, Δθ n(i,j) is the tangential arc length of the permanent magnet micro-reluctance unit.

[0064] The tangential equivalent magnetic potential 114 is given by The radial equivalent magnetic potential 115 is expressed by Indicates that the specific calculation formula is as follows:.

[0065]

[0066] Among them, B r is the remanence of the permanent magnet, is the magnetization direction and tangential angle of the permanent magnet; S θ and S ρ represent the average cross-sectional area in the radial and tangential directions, respectively.

[0067] like Figure 5 The initial material property A of the micro-magnetoresistance unit is shown n(i,j) The air micro-magnetic resistance unit 120 of Air is a magnetic circuit model consisting of four radial air equivalent magnetic resistances 123 and a tangential air equivalent magnetic resistance 122 connected to a central node 121. is the permeance of the tangential air equivalent magnetic resistance 122 numbered n(i,j), is the magnetic permeance of the radial air equivalent magnetic resistance 123, and the specific calculation formula is as follows:

[0068]

[0069] Among them, μ Air is the magnetic permeability of air.

[0070] like Figure 6 Shown is the initial material property A of the micro-magnetoresistance unit n(i,j) The iron core micro-magnetic resistance unit 130 has the same structure as the air micro-magnetic resistance unit 120. The magnetic circuit model consists of four radial air equivalent magnetic resistances 133 and tangential air equivalent magnetic resistances 132 connected to the central node 131. Definition is the permeance of the tangential air equivalent magnetic resistance 132 numbered n(i,j), is the magnetic permeance of the radial air equivalent magnetic resistance 133, and the specific calculation formula is as follows:

[0071]

[0072] Among them, μ Fe is the magnetic permeability of the core.

[0073] like Figure 7 The figure shows the equivalent micro-magnetoresistance network of the magnetic pole where one of the permanent magnets 021 of the permanent magnet flat wire motor rotor is located, showing the permanent magnet equivalent micro-magnetoresistance unit 110 , the air equivalent micro-magnetoresistance unit 120 and the iron core equivalent micro-magnetoresistance unit 130 .

[0074] Step 2: At the same time as step 1, establish an equivalent model of the flat wire stator micro-reluctance network.

[0075] like Figure 8 The figure shows the equivalent reluctance network model of the motor's 1 / 4 flat wire stator 01. First, the stator yoke 012 and tooth 013 are equivalently modeled:

[0076] Considering that the magnetic flux flows more regularly in the motor teeth and yoke, and that this part does not need to participate in the subsequent topology optimization process, the magnetic resistance model in the flat wire stator 01 can be simplified to improve the solution efficiency. In order to facilitate the subsequent solution, the corresponding magnetic resistance is represented by the magnetic permeance, and the equivalent magnetic resistance 220 of the stator yoke is represented by the magnetic permeance P. sy Indicates that the stator tooth equivalent magnetic resistance 230 is composed of the magnetic permeance P st It is expressed as follows:

[0077]

[0078] Among them, μ Fe is the magnetic permeability of the core, l a is the axis length, R so is the stator outer diameter, R sy is the inner diameter of the stator yoke; w st is the tooth width, h st is the tooth height.

[0079] Then, if Figure 9 As shown, a micro-reluctance unit equivalent model is established for the stator tooth shoe 014:

[0080] Because the stator tooth shoe 014 is close to the air gap, accurately analyzing the magnetic field in this area is crucial for calculating the motor's torque characteristics. To fully account for tooth tip saturation and tooth tip leakage, the stator tooth shoe 014 is equivalent to the rotor 02 using the same multi-layer 0.5deg×0.5mm air micro-reluctance unit 120 and 0.5deg×0.5mm iron core micro-reluctance unit 130. This is omitted for clarity, resulting in an equivalent model of the stator tooth shoe micro-reluctance unit.

[0081] Finally, the motor armature winding 011 is equivalently modeled:

[0082] like Figure 8 , the armature winding 011 is equivalent to the magnetic source 210 in the micro-reluctance network, providing magnetomotive force to the network. Because the motor adopts an 8-layer hairpin winding structure, the magnetomotive force on each tooth is the superposition of the magnetomotive force generated by the 8-layer three-phase winding. Taking the magnetomotive force generated by the A-phase winding as an example, its equivalent magnetomotive force matrix F on the stator tooth is sta The expression is as follows:

[0083]

[0084] in, is the armature equivalent magnetomotive force of the A-phase armature winding at the mth tooth.

[0085] like Figure 10 The figure shows the armature magnetomotive force distribution diagram from the 0th tooth to the 9th tooth, where θ is the stator position angle. The magnetomotive force calculation formula of the mth tooth is calculated according to the corresponding expression in the figure, n c is the number of flat wire winding layers, I a is the A phase current.

[0086] In addition, the equivalent magnetic potential matrix F of the B-phase armature winding and the C-phase armature winding on the stator teeth is stb With F stc The calculation method is the same as that of the A-phase armature winding F sta Similarly, the matrix of the equivalent magnetomotive force of the three-phase winding on the mth tooth is expressed as follows:

[0087]

[0088] in is the equivalent magnetomotive force generated by the armature winding on the mth tooth, F sta is the magnetomotive force matrix of phase A, F stb is the magnetomotive force matrix of phase B, F stc is the C-phase magnetomotive force matrix.

[0089] Step 3: At the same time as step 2, establish an equivalent model of the air gap micro-magnetoresistance network.

[0090] like Figure 11 、 Figure 12 and Figure 13The figure shows the air gap micro-reluctance network model. As the energy conversion site of the permanent magnet flat wire motor, the air gap magnetic field distribution will change with the change of the rotor 02 position angle and load. The air gap part adopts a denser air micro-reluctance grid, and uses 0.5deg×0.25mm air reluctance units 120 for equivalent. At the same time, the air gap reluctance network is divided into two layers of inner and outer magnetic circuits. The outer magnetic circuit 310 is connected to the stator tooth shoe 014 equivalent magnetic circuit, while the inner magnetic circuit 320 is connected to the rotor 02 equivalent magnetic circuit. When the position of the rotor 02 changes, the inner magnetic circuit 320 will rotate to the corresponding angle along the air gap centerline 330 and reconnect to the nearest outer magnetic circuit 310. As shown Figure 12 The figure shows the partial connection diagram of the inner and outer magnetic circuits 320 and 310 when the rotor position is 0 degrees; Figure 13 The figure shows a partial connection diagram of the inner and outer magnetic circuit branches 320 and 310 when the rotor position is 0.5 degrees.

[0091] Step 4: After completing the establishment of the micro-reluctance network equivalent model of the rotor 02, flat wire stator 01 and air gap 03, all micro-reluctance units of the rotor 02, flat wire stator 01 and air gap 03 are uniformly numbered from the outside to the inside, starting from layer 0. Among them, the stator yoke 012 is defined as layer 0, the stator tooth 013 is defined as layer 1, the stator shoe 014 is defined as layers 2 to 4, and the air gap 03 is defined as layers 5 to 6. In the present invention, the rotor 02 is defined as layers 7 to 57. The specific numbering rules are shown in Table 1:

[0092] Table 1

[0093]

[0094] Step 5: Select the optimal design area of ​​the permanent magnet flat wire motor rotor.

[0095] like Figure 14 The optimized design region 510 shown is 1 / 16 of the rotor, i.e., the magnetic pole area occupied by a permanent magnet. Symmetrical and replicating operations can yield a complete rotor 02 structure. The optimized design region 510 contains 45 x 51 = 2295 micro-magnetic resistance units.

[0096] Step 6: Use the Gaussian basis function to readjust the material properties of the micro-reluctance unit in the optimized design region 510 to generate a new topology of the permanent magnet flat wire motor rotor.

[0097] like Figure 15 The figure shows a schematic diagram of a two-dimensional Gaussian basis function distribution constructed in the optimized design region 510. First, the material characteristic parameter M is defined for each micro-magnetic resistance unit 620 in the selected rotor optimized design region 510. n(i,j), and establish 6×6 two-dimensional Gaussian basis functions 610 covering the entire optimized design region 510, and assign values ​​to the material characteristic parameters of the micro-magnetoresistive unit in the optimized design region 510,

[0098] The material characteristic parameter M of any micro-magnetoresistive unit 620 n(i,j) The calculation formula is as follows:

[0099]

[0100] Among them, the material characteristic parameter M of the micro-magnetoresistance unit is n(i,j) Obtained by weighted summation of 36 two-dimensional Gaussian basis functions, w k is the weight coefficient, It's G k(i,j) Corresponding to the normalized form of the two-dimensional Gaussian basis function, G k(i,j) The calculation formula is:

[0101]

[0102] Where σ is the standard deviation of the Gaussian basis function, (ζ k ,τ k ) is the center position of the k-th Gaussian basis function.

[0103] Then, a constant criterion c is defined. By comparing the material characteristic parameters of the micro-magnetoresistive unit with the criterion c, the material properties of the corresponding micro-magnetoresistive unit are determined. The determination method is as follows:

[0104]

[0105] Among them, A n(i,j) Represents the material properties corresponding to the micro-magnetoresistive unit 620. n(i,j) is less than or equal to the criterion c, the micro-magnetic resistance unit 620 is given the air attribute; when M n(i,j) If the value is greater than criterion c, the micro-magnetic resistance unit 620 is assigned the iron core attribute. In addition, since permanent magnets do not participate in the topology optimization design, it is necessary to forcibly update the micro-magnetic resistance units in the permanent magnet area and re-assign them the permanent magnet attribute.

[0106] Finally, the micro-reluctance units 620 of the same type are aggregated, the iron core micro-reluctance units are aggregated into a rotor iron core structure, and the air micro-reluctance units are aggregated into a rotor magnetic barrier, thereby generating a new motor topology.

[0107] like Figure 16 What is shown is the process of generating a new structure of a permanent magnet flat wire motor using a micro-reluctance unit network model in the optimized design area 510, wherein 631 is the process of assigning material characteristic parameter values ​​to the micro-reluctance units, 632 is the process of determining the material characteristics of the micro-reluctance units, and 633 is the process of aggregating similar micro-reluctance units to generate a new rotor structure.

[0108] The generated new motor topology is further optimized as follows:

[0109] Step 7: Based on the new motor topology, use the micro-reluctance network to solve the electromagnetic performance of the new topology of the permanent magnet flat wire motor generated in step 6.

[0110] First, based on Kirchhoff's flux law, the magnetic permeability matrix equation of the micro-magnetoresistive network is established and solved:

[0111]

[0112] Among them, P 0-0 ~P 19-19 is the self-conductance and mutual conductance of the stator tooth nodes and stator yoke nodes, P 20-0 ~P 559-19 , P 0-20 ~P 19-559 is the mutual conductance between the stator tooth shoe nodes and the stator tooth nodes, P 20-20 ~P 559-559 is the self-conductance and mutual conductance of the stator tooth shoe node, P 20-560 ~P 559-919 , P 560-20 ~P 919-559 is the mutual conductance between the stator tooth shoe node and the air gap node, P 560-560 ~P 919-919 is the self-conductance and mutual conductance of the air gap node, P 560-920 ~P 919-10098 , P 920-560 ~P 10098-919 is the mutual conductance between the air gap node and the rotor node, P 920-920 ~P 10098-10098 are the rotor node self-conductance and mutual conductance; F0~F 19 is the magnetic potential of the nodes of the stator yoke, F 20 ~F 559 is the magnetic potential of the nodes of the stator tooth shoe, F 560 ~F 919 is the magnetic potential of the node in the air gap, F 920 ~F 10098 is the magnetic potential of the rotor node; Φ0~Φ 19 is the magnetic potential of the stator tooth yoke node, Φ 20 ~Φ 559 is the magnetic potential of the stator tooth shoe node, Φ 560 ~Φ 919 is the magnetic potential of the node in the air gap, Φ 920 ~Φ 10098 is the magnetic potential of the rotor node.

[0113] Subsequently, the super-relaxation iterative algorithm is used to solve the matrix equation. The iterative calculation formula is as follows:

[0114]

[0115] Among them, F i (k+1) is the k+1th iterative magnetic potential of node i, F i (k) is the k-th iterative magnetomotive force of node i, τ is the relaxation coefficient, P(i,i) is the node self-conductance, P(i,j) is the node mutual conductance, is the k+1-th iterative magnetomotive force of node j, is the k-th iterative magnetomotive force of node j, and Φ(i) is the magnetic flux of node i.

[0116] Step 8: Calculate the average magnetic flux density B of each micro-magnetoresistive unit in the micro-magnetoresistive network n(i,j) .

[0117] First, calculate the tangential magnetic flux density of the micro-magnetoresistive unit like Figure 17 The figure shows the n(i,j) micro-magnetoresistive unit 802 and the tangentially adjacent n(i,j-1) micro-magnetoresistive unit 801 and n(i,j+1) micro-magnetoresistive unit 803, where 800 is the tangential magnetic flux density of the n(i,j) micro-magnetoresistive unit. The corresponding calculation formula is as follows:

[0118]

[0119] Among them, F n(i,j) is the magnetic potential of the central node of the n(i,j) micro-magnetoresistance unit 802, is the magnetic potential of the central node of n(i,j-1) micro-magnetoresistance unit 801, is the magnetic potential of the central node of n(i,j+1) micro-magnetoresistance unit 803; is the contact area between the n(i,j) micro-magnetoresistive unit 802 and the n(i,j-1) micro-magnetoresistive unit 801, is the contact area between the n(i,j) micro-magnetoresistive unit 802 and the n(i,j+1) micro-magnetoresistive unit 803; is the magnetic permeance between the central node of the n(i,j) micro-magnetoresistive unit 802 and the central node of the n(i,j-1) micro-magnetoresistive unit 801, is the magnetic permeance between the central node of the n(i,j) micro-magnetoresistive unit 802 and the central node of the n(i,j+1) micro-magnetoresistive unit 803.

[0120] Then, the radial magnetic flux density of the micro-magnetic resistance unit is calculated like Figure 18 The figure shows the n(i,j) micro-magnetoresistive unit 802 and the radially adjacent n(i-1,j) micro-magnetoresistive unit 801 and n(i,j+1) micro-magnetoresistive unit 803, where 800 is the tangential magnetic flux density of the n(i,j) micro-magnetoresistive unit. The corresponding calculation formula is as follows:

[0121]

[0122] Among them, F n(i,j) is the magnetic potential of the central node of the n(i,j) micro-magnetoresistance unit 802, is n(i-1,j+Δj - ) The magnetic potential of the central node of the micro-magnetoresistive unit 812, is n(i+1,j+Δj + ) magnetic potential of the central node of the micro-magnetoresistive unit 803; is n(i,j) micro-magnetoresistance unit 802 and n(i-1,j+Δj - ) The contact area between the micro-magnetoresistive units 801, is n(i,j) micro-magnetoresistance unit 802 and n(i+1,j+Δj - ) the contact area between the micro-magnetoresistive units 803; is the magnetic permeance between the central node of the n(i,j) micro-magnetoresistive unit 802 and the central node of the n(i,j-1) micro-magnetoresistive unit 801, is the center node of n(i,j) micro-magnetoresistance unit 802 and n(i+1,j+Δj + )The magnetic conductivity between the central nodes of the micro-magnetoresistive unit 803.

[0123] It is worth noting that the connection mode of the micro-reluctance units in the air gap region (i=5, i=6) will change with the rotor position angle, so Δj + and Δj - It is used to adjust the displacement parameter of the micro-magnetic resistance unit above and below the air gap. The corresponding calculation formula is as follows:

[0124]

[0125] Where Δθ is the motor position angle at time t.

[0126] Finally, the radial magnetic flux density of the micro-magnetic resistance unit 800 and tangential magnetic flux density The vector sum 810 is used as the average magnetic flux density B of the micro-magnetic resistance unit 801 n(i,j) :

[0127]

[0128] In addition, since the stator yoke of the motor adopts a simplified equivalent magnetic circuit, the magnetic flux density of the stator yoke reluctance unit is and the magnetic flux density of the stator tooth reluctance unit The calculation method is different from that of the micro-magnetic resistance unit. Figure 19The figure shows the local magnetic circuit of the stator. The average magnetic flux density of the yoke reluctance unit 830 and the tooth reluctance unit 840 is calculated as follows:

[0129]

[0130] Among them, F n(i,j) is the magnetic potential of the left node of the stator yoke reluctance unit 830 and the magnetic potential of the node above the stator tooth reluctance unit 840, is the magnetic potential of the node on the right side of the magnetoresistive unit 830, is the magnetic potential of the node below the magnetoresistive unit 840; sy is the permeance of the stator yoke reluctance unit 830 equivalent reluctance 220, P st is the magnetic permeance of the stator tooth reluctance unit 840 equivalent reluctance 230; R so is the stator outer diameter, R sy is the inner diameter of the stator yoke, w st is the stator tooth width.

[0131] Step 9: Calculate the magnetic permeability of each core micro-magnetic resistance unit in the micro-magnetic resistance network.

[0132] First, traverse all the iron core micro-magnetic resistance units in the magnetoresistive network, and according to the adopted silicon steel hysteresis (BH) curve and the magnetic density B obtained in step 8, n(i,j) Calculate the corresponding magnetic permeability μ n(i,j) , the corresponding calculation formula is:

[0133]

[0134] Among them, H n(i,j) It is the corresponding magnetic field strength obtained by looking up the BH curve of the iron core based on the micro-magnetic resistance unit.

[0135] Then, the convergence of the micro-magnetic resistance unit permeability is determined. The permeability convergence coefficient is defined as The corresponding calculation formula is:

[0136]

[0137] in, represents the permeability of n(i,j) micro-magnetoresistance unit in the kth iteration, represents the permeability of n(i,j) micro-magnetoresistance unit in the k-1th iteration. When k=1, is the initial magnetic permeability.

[0138] When the maximum convergence coefficient of all core reluctance units If both are less than the preset tolerance (5% in the present invention), the iteration is completed and step 10 is executed. Otherwise, the newly obtained magnetic permeability Replacement initial or the last iteration permeability Update the magnetic permeability, update the micro-magnetic resistance network, and repeat step 7. Figure 20 Shown is the BH curve of the core material and the magnetic permeability μ of the core micro-reluctance unit n(i,j) Iterative process.

[0139] Step 10: Calculate the torque characteristics of the new topology of the permanent magnet flat wire motor and determine whether the torque meets the design requirements.

[0140] The output torque of the motor is determined by the electromagnetic torque T e and cogging torque T cog composition:

[0141]

[0142] Among them, θ is the electrical angle of the motor rotation, θ mech is the mechanical angle of the motor, P is the number of rotor poles, i A 、i B 、i C and ψ A , ψ B , ψ C Represents three-phase current and magnetic flux respectively; W airgap Represents the energy stored in the air gap when the motor is no-loaded. The calculation formula is:

[0143]

[0144] Where μ0 is the magnetic permeability of air.

[0145] Determine whether the torque meets the design requirements. If so, proceed to step 12; otherwise, proceed to step 11.

[0146] Step 11: Use genetic algorithm to optimize the weight coefficient w of Gaussian basis function 610 in step 6 k , adjust the distribution of micro-magnetic resistance unit materials in the design area 510, thereby continuously updating the rotor topology and improving the motor load torque T rated And other electromagnetic properties.

[0147] First, the corresponding optimization model is established, in which the average value of the motor rated torque, rated torque ripple, and the total amount of no-load back EMF harmonics are taken as optimization targets, and the Gaussian basis function weight coefficient w k is used as the optimization variable. The specific topology optimization model expression is:

[0148]

[0149] Among them, i s is the rated current amplitude, β is the rated current angle; A n(i,j)is the material property of the micro-magnetoresistance unit, C n(i,j) is the central node position of the micro-magnetoresistive unit, Ω PM is the area where the permanent magnet is located.

[0150] Then, the genetic algorithm is used to select, crossover, and mutation operations to optimize the weight value w of each Gaussian basis function. k , update the material characteristic parameters M of the micro-magnetoresistance unit n(i,j) Generate a new rotor topology and repeat steps 6-11 to calculate the load torque T of the new motor structure using the micro-reluctance network. rated , until the permanent magnet flat wire motor meets the torque design requirements or reaches the maximum number of optimization iterations.

[0151] like Figure 21 The figure shows the change of topological structure and magnetic flux density distribution of micro-reluctance unit during the motor optimization process, where 461 is the result of the first iteration, 462 is the result of the tenth iteration, and 463 is the result of the fortieth iteration.

[0152] like Figure 22 The figure shows the optimized results (Pareto front) obtained by step 11 and the five candidate design solutions selected from them. Among them, 501 is solution 1, with an average torque of 34.2 Nm, a torque ripple of 3.6%, and a no-load back EMF total harmonic content of 4.3%; 502 is solution 2, with an average torque of 35.3 Nm, a torque ripple of 6.2%, and a no-load back EMF total harmonic content of 4.7%; 503 is solution 3, with an average torque of 34.9 Nm, a torque ripple of 4.6%, and a no-load back EMF total harmonic content of 4.2%; 504 is solution 4, with an average torque of 35.1 Nm, a torque ripple of 4.0%, and a no-load back EMF total harmonic content of 4.2%; and 505 is solution 5, with an average torque of 33.1 Nm, a torque ripple of 3.8%, and a no-load back EMF total harmonic content of 3.5%.

[0153] Step 12: Select a design and smooth it out.

[0154] First, the scheme with a more regular shape is selected from the candidate schemes as the final design scheme for the permanent magnet flat wire motor.

[0155] Then, the edge of the magnetic barrier of Scheme 1 is smoothed. Figure 23 The figure shows the final magnetic barrier edge smoothing process. 623-1 and 623-2 are the sawtooth magnetic barrier structures before smoothing, and 723-1 and 723-2 are the magnetic barrier structures after smoothing.

[0156] Finally, if Figure 24 Shown is a three-dimensional schematic diagram of the optimized structure of the permanent magnet flat wire motor.

[0157] Step 13: Performance verification and prototype processing.

[0158] First, the performance of the permanent magnet flat wire motor design scheme determined above is evaluated through finite element analysis.

[0159] like Figures 25-28 The figure shows a comparison of the electromagnetic performance of the motor before and after optimization using finite element method. Figure 25 and Figure 26 The comparison of the motor back EMF and the corresponding spectrum analysis before and after optimization is shown. It can be seen that through the optimization method, the back EMF amplitude is increased from 56.2 volts to 66.2 volts, and the total harmonic order is reduced from 16.9% to 3.09%, indicating that the motor magnetic circuit design is more reasonable after optimization and the permanent magnet utilization rate is significantly improved. Figure 27 Comparison of the motor cogging torque before and after optimization shows that the motor cogging torque has decreased from 612.84 mmNm to 201.90 mmNm through optimization, reaching about 70%; Figure 28 Comparing the rated torque characteristics of the motor before and after optimization, it can be seen that the average output torque of the optimized motor is increased from 31.38 Nm to 33.89 Nm, and the torque ripple is reduced from 12.0% to 3.8%.

[0160] Finally, the prototype is processed according to the design plan and relevant tests are carried out to further verify the motor structure.

Claims

1. A topology grid optimization method for permanent magnet flat wire motor based on micro-reluctance unit, characterized by The following steps are involved: Step 1): The rotor of the motor is divided into a plurality of micro-reluctance units. The initial material properties of the micro-reluctance units on the rotor are assigned according to the position information of the center points of each micro-reluctance unit on the rotor to obtain the material properties of the permanent magnet, air or iron core, and the corresponding permanent magnet micro-reluctance unit, air micro-reluctance unit and iron core micro-reluctance unit are obtained, thereby establishing an equivalent model of the rotor micro-reluctance network; The stator yoke, teeth, tooth shoes and armature winding are modeled in sequence to obtain the stator micro-reluctance network equivalent model; The air gap is divided into air reluctance units using a network denser than the rotor's microreluctance units. The air reluctance units are then divided into two magnetic circuits, the inner and outer magnetic circuits. The outer magnetic circuit is connected to the equivalent magnetic circuit of the stator tooth shoe, while the inner magnetic circuit is connected to the equivalent magnetic circuit of the rotor, resulting in an equivalent model of the air gap microreluctance network. Step 2): 1 / 16 of the rotor's magnetic pole area is used as the optimized design area, and the optimized design area is symmetrically and replicated to obtain a complete rotor structure; Step 3): establishing a two-dimensional Gaussian basis function covering the entire optimized design area, obtaining material characteristic parameters of the micro-magnetoresistive unit in the optimized design area by weighted summation of the two-dimensional Gaussian basis function, and comparing the material characteristic parameters of the micro-magnetoresistive unit with a defined constant criterion to obtain the material properties of the air or iron core of the micro-magnetoresistive unit in the optimized design area; Step 4): Aggregate the micro-magnetic resistance units with the same material properties in the optimized design area, aggregate the iron core micro-magnetic resistance units into the rotor iron core, and aggregate the air micro-magnetic resistance units into the rotor magnetic barrier, thereby generating a new motor topology.

2. The topology grid optimization method for a permanent magnet flat wire motor according to claim 1 is characterized by: For the new motor topology described in step 4), perform the following steps: Step 41): Establish and solve the permeability matrix equation of the micro-magnetoresistive network, and calculate the average magnetic flux density of each micro-magnetoresistive unit, the permeability of each core micro-magnetoresistive unit, and the permeability convergence coefficient; Step 42) When the maximum convergence coefficients of the magnetic permeabilities of all the core micro-reluctance units are less than the preset tolerance, the output torque is calculated and it is determined whether the output torque meets the design requirements; otherwise, the newly obtained magnetic permeability replaces the initial magnetic permeability or the last iterative magnetic permeability, and step 41) is executed again; Step 43): When it is determined that the output torque meets the requirements, the regular shape scheme is selected as the final design scheme of the permanent magnet flat wire motor. Otherwise, the weight coefficient of the Gaussian basis function described in step 3) is optimized using a genetic algorithm, the distribution of the micro-reluctance unit material in the design area is adjusted, and the rotor topology is updated.

3. The topology grid optimization method for a permanent magnet flat wire motor according to claim 1 or 2, characterized in that: In step 1), the rotor is divided into several sector-shaped micro-reluctance units, and the size of each sector-shaped micro-reluctance unit is 0.5deg×0.5mm; the permanent magnet micro-reluctance unit whose material property is permanent magnet is composed of two symmetrical tangential equivalent reluctances and tangential equivalent magnetic potentials connected in series and then connected to the central node; the air micro-reluctance unit whose material property is air is composed of four radial air equivalent reluctances and tangential air equivalent reluctances connected to the central node; the iron core micro-reluctance unit whose material property is iron core is also composed of four radial air equivalent reluctances and tangential air equivalent reluctances connected to the central node; the equivalent reluctance of the stator yoke is represented by magnetic permeance, and the equivalent reluctance of the stator tooth is represented by magnetic permeance: the stator tooth boot adopts the same multi-layer 0.5deg×0.5mm air micro-reluctance unit as the rotor to be equivalent to the 0.5deg×0.5mm iron core micro-reluctance unit; the armature winding is equivalent to the magnetic source.

4. The topology grid optimization method for a permanent magnet flat wire motor according to claim 1 or 2, characterized in that: In step 3), a 6×6 two-dimensional Gaussian basis function is established to cover the entire optimization design area, and the material characteristic parameters of any micro-magnetoresistive unit are It's G k(i,j) corresponds to the normalized form of the two-dimensional Gaussian basis function, w k is the weight coefficient, σ is the standard deviation of the Gaussian basis function, (ζ k ,τ k ) is the center position of the kth Gaussian basis function; when M n(i,j) Less than or equal to the criterion, the micro-magnetic resistance unit is given air properties; when M n(i,j) If the value is greater than the criterion, the micro-magnetic resistance unit is given the core property.

5. The topology grid optimization method for a permanent magnet flat wire motor according to claim 2, characterized in that: In step 41), the magnetic permeability matrix equation of the micro-magnetoresistive network is established and solved based on Kirchhoff's flux law: the tangential magnetic flux density of the micro-magnetoresistive unit is calculated first, then the radial magnetic flux density of the micro-magnetoresistive unit is calculated, and finally the vector sum of the radial magnetic flux density and the tangential magnetic flux density of the micro-magnetoresistive unit is taken as the average magnetic flux density.

6. The topology grid optimization method for a permanent magnet flat wire motor according to claim 5, characterized in that: In step 41), the magnetic permeability The magnetic permeability convergence coefficient B n(i,j) is the average magnetic flux density, H n(i,j) It is the corresponding magnetic field strength obtained by looking up the BH curve of the iron core based on the micro-magnetic resistance unit. represents the permeability of n(i,j) micro-magnetoresistance unit in the kth iteration, represents the permeability of n(i,j) micro-magnetoresistance unit in the k-1th iteration. When k=1, is the initial magnetic permeability.

7. The topology grid optimization method for a permanent magnet flat wire motor according to claim 6, characterized in that: In step 42), the output torque is determined by the electromagnetic torque T e and cogging torque T cog composition, θ is the electrical angle of motor rotation, θ mech is the mechanical angle of the motor, P is the number of rotor poles, i A 、i B 、i C and ψ A , ψ B , ψ C Represents three-phase current and magnetic flux respectively; W airgap is the energy stored in the air gap when the motor is no-load, μ0 is the magnetic permeability of air, 8. The topology grid optimization method for a permanent magnet flat wire motor according to claim 7, characterized in that: In step 43), the rated torque average value, rated torque pulsation and total no-load back EMF harmonics are used as optimization targets, and the Gaussian basis function weight coefficient is used as the optimization variable. The genetic algorithm selection, crossover and mutation operations are used to optimize the weight value of each Gaussian basis function, and the material characteristic parameters of the micro-reluctance unit are updated to generate a new rotor topology structure.

9. The topology grid optimization method for a permanent magnet flat wire motor according to claim 8, characterized in that: In step 43), the magnetic barrier edge of the final design is smoothed.

10. The topology grid optimization method for a permanent magnet flat wire motor according to claim 8, characterized in that: The performance of the smoothed design was evaluated using finite element analysis.

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