WO2025213490A1 - 一种基于微磁阻单元的永磁扁线电机拓扑网格化优化方法 - Google Patents

一种基于微磁阻单元的永磁扁线电机拓扑网格化优化方法

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Publication number
WO2025213490A1
WO2025213490A1 PCT/CN2024/087924 CN2024087924W WO2025213490A1 WO 2025213490 A1 WO2025213490 A1 WO 2025213490A1 CN 2024087924 W CN2024087924 W CN 2024087924W WO 2025213490 A1 WO2025213490 A1 WO 2025213490A1
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Prior art keywords
micro
magnetic
reluctance
unit
rotor
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English (en)
French (fr)
Inventor
朱孝勇
武继奇
项子旋
樊德阳
杨张韦
韩春雷
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Jiangsu University
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Jiangsu University
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/373—Design optimisation
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/12—Computing arrangements based on biological models using genetic models
    • G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming

Definitions

  • 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.
  • PMF motors permanent magnet flat wire motors
  • 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.
  • the purpose of this 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 the parameter-free autonomous optimization of the rotor topology according to the performance requirements under a given flat wire stator structure. optimization.
  • 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:
  • 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;
  • 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 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 Furthermore, for the new motor topology described in step 4), the following steps are performed:
  • 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;
  • the rotor is divided into a number of sector-shaped micro-magnetic resistance units, each of which is 0.5deg ⁇ 0.5mm in size;
  • the permanent magnet micro-magnetic resistance unit whose material attribute is permanent magnet is composed of two symmetrical tangential equivalent magnetic resistances and tangential equivalent magnetic potentials connected in series and then connected to the central node;
  • the air micro-magnetic resistance unit whose material attribute is air It is composed of four radial air equivalent magnetic resistances and tangential air equivalent magnetic resistances connected to the central node;
  • the iron core micro-magnetic resistance unit whose material property is iron core is also composed of four radial air equivalent magnetic resistances and tangential air equivalent magnetic resistances connected to the central node;
  • the stator yoke equivalent magnetic resistance is represented by magnetic permeance, and the stator tooth equivalent magnetic resistance is represented by magnetic permeance:
  • the stator tooth shoe adopts the same multi-layer 0.5deg ⁇ 0.5mm air micro-magnetic resistance unit as the rotor to
  • 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 is the normalized form of the two-dimensional Gaussian basis function corresponding to G k(i,j) , wk is the weight coefficient, ⁇ is the standard deviation of the Gaussian basis function, and ( ⁇ k , ⁇ k ) is the center position of the kth Gaussian basis function.
  • Mn (i,j) is less than or equal to the criterion
  • the micromagnetoresistive unit is assigned air properties; when Mn (i,j) is greater than the criterion, the micromagnetoresistive unit is assigned iron core properties.
  • 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.
  • 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.
  • 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.
  • FIG1 is a three-dimensional schematic diagram of the initial structure of the permanent magnet flat wire motor targeted by the present invention.
  • FIG2 is an enlarged view of a partial structure of the rotor in the initial structure of the permanent magnet flat wire motor shown in FIG1 ;
  • FIG3 is a flow chart of a topology grid optimization method for a permanent magnet flat wire motor based on micro-reluctance units according to the present invention
  • FIG4 is a diagram of a micro-magnetic resistance unit equivalent to the permanent magnet material in FIG1 ;
  • FIG5 is a diagram of a micro-magnetoresistive unit equivalent to air material in FIG1 ;
  • FIG6 is a diagram of a micro-magnetic resistance unit equivalent to the iron core material in FIG1;
  • FIG7 is a schematic diagram of an equivalent micro-reluctance network of a magnetic pole where one of the permanent magnets of the rotor in FIG1 is located;
  • FIG8 is an equivalent model diagram of the flat wire stator micro-reluctance network in FIG1;
  • FIG9 is a diagram showing an equivalent model of the micro-magnetic resistance network of the stator teeth and tooth shoe in FIG1 ;
  • FIG10 is a diagram showing the magnetomotive force distribution of the flat wire stator A-phase winding in FIG1 ;
  • FIG11 is an equivalent model diagram of the air gap micro-magnetoresistive network in FIG1 ;
  • FIG12 is a schematic diagram of the connection mode of the air gap micro-reluctance unit when the rotor position angle is 0 degrees in FIG1;
  • FIG13 is a schematic diagram of the connection mode of the air gap reluctance unit when the rotor position angle is 0.5 degrees in FIG1;
  • FIG14 is a schematic diagram of the design area selected for the motor in FIG1 ;
  • FIG15 is a schematic diagram of the distribution of two-dimensional Gaussian basis functions constructed within the design area in FIG1 ;
  • FIG16 is a schematic diagram of the process of adjusting the material properties of the micro-magnetoresistive unit in the design area in FIG1 ;
  • FIG17 is a schematic diagram of the calculation of the tangential magnetic flux density of the micro-magnetoresistive unit in FIG1;
  • FIG18 is a schematic diagram of radial magnetic flux density calculation of the micro-magnetoresistive unit in FIG1 ;
  • FIG19 is a schematic diagram showing the calculation of the magnetic flux density of the stator tooth yoke reluctance unit
  • FIG20 is a schematic diagram of the B-H curve of the core material and the magnetic permeability iteration process of the core micro-magnetic resistance unit in FIG1;
  • FIG21 is a schematic diagram showing the changes in the topological structure and magnetic flux density distribution of the micro-magnetoresistive unit during the optimization process in FIG1 ;
  • FIG22 is a schematic diagram of the Pareto front and the selected candidate design solutions obtained through optimization in FIG1 ;
  • FIG23 is a schematic diagram of the magnetic barrier edge smoothing process of the final design scheme in FIG1;
  • FIG24 is a three-dimensional schematic diagram of the optimized topological structure in FIG1 ;
  • FIG25 is a comparison diagram of the no-load back EMF before and after optimization in FIG1;
  • Figure 26 is a comparison of no-load back EMF harmonic analysis before and after optimization in Figure 1;
  • FIG27 is a comparison diagram of the rated output torque before and after optimization in FIG1 ;
  • FIG28 is a comparison diagram of the cogging torque before and after optimization in FIG1 .
  • a 36-slot/8-pole permanent magnet flat wire motor includes a flat wire stator 01 and a rotor 02.
  • the stator 01 contains 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 contains 8 magnetic poles.
  • the permanent magnets of each pole are arranged in a V shape.
  • FIG. 2 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, located near the air gap, and its inner end connected to an inner magnetic barrier 023-2, located near the shaft.
  • the present invention optimizes the 1/4 model of the motor shown in Figure 1.
  • the optimization method is shown in Figure 3, specifically:
  • Step 1 Establish the equivalent model of the initial micro-reluctance network of the permanent magnet rotor of the motor.
  • 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 Cn (i,j) ( ⁇ , ⁇ ) is used to represent the position information of the center point of the corresponding sector-shaped micro-reluctance unit, where ⁇ is the distance between the center point of the sector-shaped micro-reluctance unit and the center of the rotor 02, and ⁇ is the position angle.
  • the initial material properties An(i,j) of the sector-shaped micro-reluctance units are assigned according to the center point position information Cn (i,j) ( ⁇ , ⁇ ) of each sector-shaped micro-reluctance unit on the rotor 02.
  • the assignment rule is as follows:
  • ⁇ PM is the set permanent magnet area
  • ⁇ Air is the set air area
  • the initial material attribute An (i,j) of the sector-shaped micro-magnetoresistive unit is permanent magnet PM, air Air, or iron core Iron.
  • the initial material properties An (i,j) of the fan-shaped micro-magnetoresistive unit shown in Figure 4 are the permanent magnet micro-magnetoresistive unit 110 of the permanent magnet PM.
  • the permanent magnet micro-magnetoresistive 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, as well as two symmetrical radial equivalent magnetic resistances 113 and radial equivalent magnetic potentials 115 connected in series and then connected to the central node 111.
  • 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:
  • ⁇ PM is the magnetic permeability of the permanent magnet
  • l a is the axial length of the motor
  • ⁇ n(i,j) is the length from the center node of the permanent magnet micro-reluctance unit numbered n(i,j) to the motor axis
  • ⁇ n(i,j) is the height of the permanent magnet micro-reluctance unit
  • ⁇ n(i,j) is the tangential arc length of the permanent magnet micro-reluctance unit.
  • 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:.
  • Br is the remanence of the permanent magnet, are the magnetization direction and tangential angle of the permanent magnet; S ⁇ and S ⁇ represent the average cross-sectional area in the radial and tangential directions, respectively.
  • the initial material properties of the micro-magnetoresistive unit An (i,j) shown in FIG5 are the air micro-magnetoresistive unit 120 of air, which is a magnetic circuit model consisting of four radial air equivalent magnetic resistances 123 and tangential air equivalent magnetic resistances 122 connected to the central node 121.
  • Definition 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:
  • Air is the magnetic permeability of air.
  • the iron-core micro-magnetoresistive unit 130 has an initial material property An (i,j) of the iron core. Its structure is similar to the air micro-magnetoresistive unit 120.
  • the magnetic circuit model consists of four radial air equivalent magnetic resistors 133 and a tangential air equivalent magnetic resistor 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:
  • ⁇ Fe is the magnetic permeability of the core.
  • FIG7 shows an equivalent micro-magnetoresistance network of a magnetic pole where one of the permanent magnets 021 of the permanent magnet flat wire motor rotor is located, showing a permanent magnet equivalent micro-magnetoresistance unit 110 , an air equivalent micro-magnetoresistance unit 120 and an iron core equivalent micro-magnetoresistance unit 130 .
  • Step 2 At the same time as step 1, establish an equivalent model of the flat wire stator micro-reluctance network.
  • Figure 8 shows the equivalent reluctance network model of the motor's 1/4 flat wire stator 01.
  • stator yoke 012 and tooth 013 are equivalently modeled:
  • the reluctance model in the flat wire stator 01 can be simplified to improve solution efficiency.
  • the corresponding reluctance is represented by permeance.
  • the equivalent reluctance 220 of the stator yoke is represented by permeance Psy
  • the equivalent reluctance 230 of the stator teeth is represented by permeance Pst as follows:
  • ⁇ Fe is the core magnetic permeability
  • l a is the axis length
  • Rso is the stator outer diameter
  • Rsy is the stator yoke inner diameter
  • wst is the tooth width
  • hst is the tooth height.
  • 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.
  • 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.
  • armature winding 011 is equivalent to magnetic source 210 in the micro-reluctance network, providing magnetomotive force to the network. Because the motor uses an 8-layer hairpin winding structure, the magnetomotive force on each tooth is the superposition of the magnetomotive force generated by the 8 layers of three-phase windings. Taking the magnetomotive force generated by the A-phase winding as an example, its equivalent magnetomotive force matrix F sta on the stator teeth is expressed as follows:
  • Figure 10 shows the armature magnetomotive force distribution diagram from teeth 0 to 9, where ⁇ is the stator position angle.
  • the magnetomotive force calculation formula for the mth tooth is calculated according to the corresponding expression in the figure, n c is the number of flat wire winding layers, and I a is the A-phase current.
  • the matrix of the equivalent magnetic potential of the three-phase winding on the mth tooth is expressed as follows:
  • F sta is the magnetomotive force matrix of phase A
  • F stb is the magnetomotive force matrix of phase B
  • F stc is the magnetomotive force matrix of phase C.
  • Step 3 At the same time as step 2, establish an equivalent model of the air gap micro-magnetoresistance network.
  • Figures 11, 12, and 13 show the air gap micro-reluctance network model.
  • the air gap utilizes a denser air micro-reluctance grid, using 0.5deg x 0.25mm air reluctance units 120 for equivalent operation.
  • the air gap reluctance network is divided into two layers: the inner and outer magnetic circuits.
  • the outer magnetic circuit 310 connects to the stator tooth shoe 014 equivalent magnetic circuit, while the inner magnetic circuit 320 connects to the rotor 02 equivalent magnetic circuit.
  • Figure 12 shows a schematic diagram of the partial connection of the inner and outer magnetic circuits 320 and 310 branches when the rotor position is 0 degrees.
  • Figure 13 shows a schematic diagram of the partial connection of the inner and outer magnetic circuits 320 and 310 branches when the rotor position is 0.5 degrees.
  • 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.
  • 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
  • the air gap 03 is defined as layers 5 to 6.
  • the rotor 02 is defined as layers 7 to 57.
  • Table 1 The specific numbering rules are shown in Table 1:
  • Step 5 Select the optimal design area of the permanent magnet flat wire motor rotor.
  • the selected optimized design area 510 is a 1/16 area of the rotor, that is, the magnetic pole area occupied by a permanent magnet.
  • the complete rotor 02 structure can be obtained.
  • 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.
  • FIG15 is a schematic diagram of the two-dimensional Gaussian basis function distribution constructed in the optimized design region 510.
  • the material characteristic parameters M n(i,j) are defined for each micro-magnetoresistive unit 620 within the selected rotor optimized design region 510.
  • 6 ⁇ 6 two-dimensional Gaussian basis functions 610 are established to cover the entire optimized design region 510.
  • the material characteristic parameters of the micro-magnetoresistive units within the optimized design region 510 are assigned.
  • the material characteristic parameter Mn (i,j) of any micro-magnetoresistive unit 620 is calculated as follows:
  • the material characteristic parameter Mn (i,j) of the micro-magnetoresistive unit is obtained by weighted summation of 36 two-dimensional Gaussian basis functions, wk is the weight coefficient, is the normalized form of the two-dimensional Gaussian basis function corresponding to G k(i,j) .
  • the calculation formula of G k(i,j) is:
  • ⁇ is the standard deviation of the Gaussian basis function
  • ( ⁇ k , ⁇ k ) is the center position of the kth Gaussian basis function
  • a constant criterion c is defined.
  • the material properties of the corresponding micro-magnetoresistive unit are determined. The determination method is as follows:
  • a n(i, j) represents the material properties corresponding to the micro-magnetoresistive unit 620.
  • M n(i, j) is less than or equal to the criterion c
  • the micro-magnetoresistive unit 620 is assigned the air attribute
  • M n(i, j) is greater than the criterion c
  • the micro-magnetoresistive unit 620 is assigned the iron core attribute.
  • 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.
  • the optimization design area 510 uses the micro-magnetic resistance unit network model to generate a new structure of the permanent magnet flat wire motor, wherein 631 is the process of assigning material characteristic parameter values to the micro-magnetic resistance unit, 632 is the process of determining the material characteristics of the micro-magnetic resistance unit, and 633 is the process of aggregating similar micro-magnetic resistance units to generate a new rotor structure.
  • the generated new motor topology is further optimized as follows:
  • 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.
  • P 0-0 to P 19-19 are the self-conductance and mutual conductance of the stator tooth node and the stator yoke node
  • P 20-0 to P 559-19 P 0-20 to P 19-559 are the mutual conductance of the stator tooth shoe node and the stator tooth node
  • P 20-20 to P 559-559 are the self-conductance and mutual conductance of the stator tooth shoe node
  • P 560-20 to P 919-559 are the mutual conductance of the stator tooth shoe node and the air gap node
  • P 560-560 to P 919-919 are the self-conductance and mutual conductance of the air gap node
  • P 560-920 to P 919-10098
  • P 920-560 to P 10098-919 are the mutual conductance between the air gap node and the rotor node
  • P 920-920 ⁇ P 10098-10098 are the self-conductance and mutual conductance of the rotor node
  • the iterative calculation formula is as follows:
  • Step 8 Calculate the average magnetic flux density Bn (i,j) of each micro-magnetoresistive unit in the micro-magnetoresistive network.
  • Fn (i,j) is the magnetic potential of the central node of n(i,j) micro-magnetoresistive unit 802, is the center of n(i,j-1) micro-magnetoresistance unit 801
  • Nodal magnetic potential is the magnetic potential of the central node of n(i,j+1) micro-magnetoresistance 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,
  • the radial magnetic flux density of the micro-magnetic resistance unit is calculated As shown in Figure 18, 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:
  • Fn (i,j) is the magnetic potential of the central node of n(i,j) micro-magnetoresistive unit 802, is the magnetic potential of the central node of the micro - magnetoresistive unit 812, is the magnetic potential of the central node of the n(i+1,j+ ⁇ j + ) micro-magnetoresistance unit 803; is the contact area between the n(i,j) micro-magnetoresistive unit 802 and the n(i-1,j+ ⁇ j ⁇ ) micro-magnetoresistive unit 801, is the contact area between the n(i,j) micro-magnetoresistive unit 802 and the n(i+1,j+ ⁇ j ⁇ ) 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
  • the corresponding calculation formula is as follows:
  • ⁇ is the motor position angle at time t.
  • 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 Bn (i,j) of the micro-magnetoresistive unit 801:
  • 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 19 shows the local magnetic circuit of the stator.
  • the average magnetic flux density calculation formula of the yoke magnetic resistance unit 830 and the tooth magnetic resistance unit 840 is as follows:
  • Fn (i,j) is the magnetic potential of the node on the left side 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 magnetic resistance unit 840; P sy is the magnetic permeance of the equivalent magnetic resistance 220 of the stator yoke magnetic resistance unit 830, P st is the magnetic permeance of the equivalent magnetic resistance 230 of the stator tooth magnetic resistance unit 840; R so is the stator outer diameter, R sy is the stator yoke inner diameter, and w st is the stator tooth width.
  • Step 9 Calculate the magnetic permeability of each core micro-magnetic resistance unit in the micro-magnetic resistance network.
  • Hn (i,j) is the corresponding magnetic field intensity obtained by looking up the BH curve of the iron core according to the micro-magnetic resistance unit.
  • the permeability convergence coefficient is defined as The corresponding calculation formula is:
  • 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.
  • FIG20 shows the BH curve of the core material and the iterative process of the magnetic permeability ⁇ n(i, j) of the core micro-magnetoresistive unit.
  • 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.
  • the output torque of the motor consists of electromagnetic torque Te and cogging torque Tcog :
  • W airgap represents the energy stored in the air gap when the motor is no-loaded and is calculated as follows:
  • ⁇ 0 is the magnetic permeability of air.
  • Step 11 Utilize a genetic algorithm to optimize the weight coefficient w k of the Gaussian basis function 610 in step 6, and adjust the material distribution of the micro-magnetic resistance unit in the design region 510 , thereby continuously updating the rotor topology and improving electromagnetic performance such as the motor load torque T rated .
  • the corresponding optimization model is established, in which the average value of the motor's rated torque, rated torque ripple, and the total amount of no-load back EMF harmonics are used as optimization targets, and the Gaussian basis function weight coefficient wk is used as the optimization variable.
  • the specific topology optimization model expression is:
  • ⁇ is the rated current angle
  • An (i,j) is the material property of the micromagnetoresistive unit
  • Cn (i,j) is the center node position of the micromagnetoresistive unit
  • ⁇ PM is the area where the permanent magnet is located.
  • Steps 6-11 are then repeated to calculate the load torque Trated of the new motor structure using the microreluctance network until the permanent magnet flat wire motor meets the torque design requirements or the maximum number of optimization iterations is reached.
  • Figure 21 shows the changes in the topological structure and magnetic flux density distribution of the 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.
  • Figure 22 shows the optimization results (Pareto front) obtained for the motor through step 11, along with the five candidate design solutions selected from them.
  • 501 represents 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 represents 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 represents 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 represents 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%
  • 505 represents 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%.
  • Step 12 Select a design and smooth it out.
  • 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.
  • the magnetic barrier edge of the scheme 1 is smoothed.
  • the smoothed magnetic barrier edge of the final scheme is Schematic diagram of the magnetic barrier structure. 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.
  • FIG24 shows a three-dimensional schematic diagram of the optimized structure of the permanent magnet flat wire motor.
  • Step 13 Performance verification and prototype processing.
  • Figures 25-28 show schematic diagrams comparing the electromagnetic performance of the motor before and after optimization using finite element analysis.
  • Figures 25 and 26 show the back EMF and corresponding spectrum analysis before and after optimization. It can be seen that the optimization method increases the back EMF amplitude from 56.2V to 66.2V, and the total harmonic frequency decreases from 16.9% to 3.09%, indicating that the optimized motor magnetic circuit design is more reasonable and the permanent magnet utilization rate is significantly improved.
  • Figure 27 compares the motor cogging torque before and after optimization. It can be seen that the optimization reduces the motor cogging torque from 612.84 mmNm to 201.90 mmNm, reaching approximately 70%.
  • Figure 28 compares the motor rated torque characteristics before and after optimization. It can be seen that the average output torque of the optimized motor increases from 31.38 Nm to 33.89 Nm, and the torque ripple decreases from 12.0% to 3.8%.

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Abstract

本发明公开一种基于微磁阻单元的永磁扁线电机拓扑网格化优化方法，建立转子、定子和气隙微磁阻网络等效模型，对转子的1/16磁极区域通过对称和复制得到完整的转子结构；建立二维高斯基函数覆盖优化设计区域，由二维高斯基函数加权求和获得优化设计区域上的微磁阻单元材料特性参数，将优化设计区域上的材料属性相同的微磁阻单元进行聚合生成新的电机拓扑结构；计算各微磁阻单元的平均磁密、各铁芯微磁阻单元磁导率和磁导率收敛系数；利用遗传算法优化高斯基函数的权重系数，调整设计区域内微磁阻单元材料分布；本发明采用的微磁阻单元网络模型是一种兼具电机结构生成与性能分析的多用途模型，能够极大提高设计自由度，保证优化效率。

Description

一种基于微磁阻单元的永磁扁线电机拓扑网格化优化方法 技术领域
本发明涉及一种永磁扁线电机的设计方法，尤其是一种能够实现永磁扁线电机拓扑结构自主优化的设计方法，属于永磁电机技术领域。
背景技术
在电机技术领域，永磁扁线电机凭借其高转矩密度、高效率和宽调速等优势，在车用驱动电机领域得到了广泛应用。一般而言，永磁扁线电机定子采用扁线绕组，能够提升电机效率及散热性能；转子采用内置式永磁拓扑结构，能够在提高电机转矩密度同时改善电机调速特性。在永磁扁线电机设计过程中，一方面需要保证扁线定子提供的电磁场和永磁转子提供的永磁磁场的匹配设计，实现最佳转矩及效率输出；另一方面，需要兼顾电机转矩脉动、振动特性等品质需求。同时，由于永磁扁线电机定子工艺复杂，生产难度大，其设计存在众多限制条件，如绕组层数、端部长度等。因此，在多目标多限制条件下，设计一种实现永磁扁线电机近限设计的高效优化设计方法成为该领域的一个关键技术问题。
近年来，尝试采用转子拓扑优化等技术手段来改善永磁扁线电机性能，例如永磁体分层排布、添加辅助槽、边缘修型、斜极等，然而，这些方法往往需要进行复杂的磁场分析和多次迭代设计，一旦电机有基本规格发生变化，如尺寸、裂比和极槽配合等，这些优化设计会失效，需要进行重新调整；对此，尝试将智能优化法引入到永磁扁线电机设计中解决电机多目标复杂优化问题。例如：中国专利公开号CN104517013B的文献公开的一种基于遗传算法的车用电机多目标优化设计方法，是一种将遗传算法等优化方法与电磁场分析相结合的优化方法，通过算法不断调整电机关键设计设计参数并利用有限元进行性能仿真，实现对电机结构实现快速寻优。然而，这些优化技术通常需要预先设计电机的基本结构，并对结构进行参数化建模，因此，仍需要人为高度参与和多次迭代设计。此外，这些技术只能在电机初始结构的基础上优化部分结构参数值，而无法生成新的电机拓扑结构，导致优化后的电机性能的改善也是有限的。
发明内容
本发明的目的是为了解决永磁扁线电机设计中存在的经验依赖度高、设计周期长等问题，提出一种无需结构设计和参数化建模的基于微磁阻单元的永磁扁线电机拓扑网格化优化方法，实现电机在给定扁线定子结构下，直接根据性能要求对转子拓扑进行无参数自主 优化。
为实现上述目的，本发明一种基于微磁阻单元的永磁扁线电机拓扑网格化优化方法采用的技术方案包括以下步骤：
步骤1)：对电机的转子划分为若干个微磁阻单元，根据转子上的各微磁阻单元中心点位置信息对转子上的微磁阻单元初始材料属性进行分配得到永磁体、空气或铁芯的材料属性，以及得到相应的永磁体微磁阻单元、空气微磁阻单元和铁芯微磁阻单元，由此建立转子微磁阻网络等效模型；
依次对定子轭部、齿部、齿靴部和电枢绕组等效建模，得到定子微磁阻网络等效模型；
采用比转子的微磁阻单元更密集的网络划分气隙部分得到空气磁阻单元，将空气磁阻单元分为内外两层磁路；外层磁路连接定子齿靴的等效磁路，内层磁路连接转子的等效磁路，得到气隙微磁阻网络等效模型；
步骤2)：将转子的1/16磁极区域作为优化设计区域，对所述的优化设计区域通过对称和复制得到完整的转子结构；
步骤3)：建立二维高斯基函数覆盖整个所述的优化设计区域，由二维高斯基函数加权求和获得所述的优化设计区域上的微磁阻单元材料特性参数，将该微磁阻单元材料特性参数与定义的常数判据相比较，得到所述的优化设计区域上的微磁阻单元的空气或者铁芯的材料属性；
步骤4)：将所述的优化设计区域上的材料属性相同的微磁阻单元进行聚合，铁芯微磁阻单元聚合为转子铁芯，空气微磁阻单元聚合为转子磁障，生成新的电机拓扑结构。
进一步地，针对步骤4)中所述的新的电机拓扑结构，再执行以下步骤：
步骤41)：建立并求解微磁阻网络磁导矩阵方程，计算各微磁阻单元的平均磁密、各铁芯微磁阻单元磁导率和磁导率收敛系数；
步骤42)当所有铁芯微磁阻单元磁导率的最大收敛系数均小于预先设定公差时，计算输出转矩并判断输出转矩是否满足设计需求，否则新获得的磁导率替代初始磁导率或上次迭代磁导率，重新执行步骤41)；
步骤43)：当判断出输出转矩满足要求，则选择形状规则的方案作为永磁扁线电机最终设计方案，否则，利用遗传算法优化步骤3)中所述的高斯基函数的权重系数，调整设计区域内微磁阻单元材料分布，更新转子拓扑结构。
更进一步地，步骤1)中，将转子划分为若干个扇形微磁阻单元，每个扇形微磁阻单元的大小为0.5deg×0.5mm；材料属性是永磁体的永磁体微磁阻单元是由对称的两个切向等效磁阻和切向等效磁势相串联后连接到中心节点构成；材料属性是空气的空气微磁阻单元 是由四个径向空气等效磁阻和切向空气等效磁阻连接到中心节点构成；材料属性是铁芯的铁芯微磁阻单元也是由四个径向空气等效磁阻和切向空气等效磁阻连接到中心节点构成；定子轭部等效磁阻由磁导表示，定子齿部等效磁阻由磁导表示：定子齿靴部采用与转子相同的多层0.5deg×0.5mm空气微磁阻单元与0.5deg×0.5mm铁芯微磁阻单元进行等效；电枢绕组等效为磁源。
更进一步地，步骤3)中，建立6×6个二维高斯基函数覆盖整个优化设计区域，任意微磁阻单元的材料特性参数 是Gk(i,j)对应二维高斯基函数的归一化形式，wk是权重系数，σ为高斯基函数标准差，(ζk,τk)为第k个高斯基函数中心位置；当Mn(i,j)小于等于判据，微磁阻单元被赋予空气属性；当Mn(i,j)大于判据，微磁阻单元被赋予铁芯属性。
本发明的有益效果：
1.本发明摈弃了传统电机设计过程中转子结构设计与参数优化的过程，能够在给定永磁扁线电机定子结构情况下，以电机性能为导向，自主生成电机转子最优设计方案，有利于实现电机的近限设计，缩短设计周期。
2.本发明采用的微磁阻单元网络模型，是一种兼具电机结构生成与性能分析的多用途模型，该模型利用微磁阻单元将将永磁扁线电机设计区域转子拓扑进行网格化划分，并通过调整微磁阻单元材料属性，生成具备高设计自由度的不同转子拓扑结构；同时该模型能够基于路算原理，快速分析新生成电机结构的电磁性能，能够极大提高设计自由度，有利于实现电机的近限设计；同时，微磁阻网络被用来求解对应电机电磁性能，从而保证优化效率。
3.本发明利用高斯基函数来调整微磁阻单元材料属性，能够使相邻微磁阻单元具备相同材料，从而生成具有连续边缘的电机拓扑结构。不仅避免直接调整微磁阻单元材料生成无法加工的多孔结构，保证电机设计方案的可制造性；同时极大程度减少了优化过程中设计变量数量，有利于提升优化的设计有效性。
附图说明
图1为本发明针对的永磁扁线电机初始结构三维示意图；
图2为图1所示永磁扁线电机初始结构中的转子局部结构放大图；
图3为本发明的基于微磁阻单元的永磁扁线电机拓扑网格化优化方法的流程图；
图4为图1中用于永磁体材料等效的微磁阻单元图；
图5为图1中用于空气材料等效的微磁阻单元图；
图6为图1中用于铁芯材料等效的微磁阻单元图；
图7为图1中的转子其中一块永磁体所在磁极的等效微磁阻网络示意图；
图8为图1中扁线定子微磁阻网络等效模型图；
图9为图1中定子齿部及齿靴部微磁阻网络等效模型图；
图10为图1中扁线定子A相绕组磁动势分布图；
图11为图1中气隙微磁阻网络等效模型图；
图12为图1中转子位置角为0度时气隙微磁阻单元连接方式示意图；
图13为图1中转子位置角为0.5度时气隙磁阻单元连接方式示意图；
图14为图1中电机所选取的设计区域示意图；
图15为图1中设计区域内所构建二维高斯基函数分布示意图；
图16为图1中设计区域内微磁阻单元材料属性的调整过程示意图；
图17为图1中微磁阻单元切向磁密计算示意图；
图18为图1中微磁阻单元径向磁密计算示意图；
图19为定子齿轭部磁阻单元磁密计算示意图；
图20为图1中铁芯材料B-H曲线及铁芯微磁阻单元磁导率迭代过程示意图；
图21为图1中优化过程中拓扑结构及微磁阻单元磁密分布变化示意图；
图22为图1中通过优化获得的帕累托前沿及所选择的候选设计方案示意图；
图23为图1中最终设计方案的磁障边缘平滑处理过程示意图；
图24为图1中优化后的拓扑结构三维示意图；
图25为图1中优化前后空载反电势对比图；
图26为图1中优化前后空载反电势谐波分析对比图；
图27为图1中优化前后额定输出转矩对比图；
图28为图1中优化前后齿槽转矩对比图。
具体实施方式
下面将结合本发明实施例中的附图，以一款36槽8极永磁扁线电机为例，对本发明实施例中利用基于微磁阻单元的拓扑网格化优化方法改进永磁扁线电机转子结构的技术方案进行清楚、完整的描述。下面通过参考附图描述的实施例是示例性的，仅用于解释本发明， 而不能理解为对本发明的限制。
如图1所示的一台36槽/8极的永磁扁线电机，包括电机扁线定子01和转子02，定子01上包含36个定子齿，绕有8层跨距为4的发卡绕组011；转子02在定子01内侧，转子02上包含8个磁极，每个磁极永磁体呈V型排列。
图2所示是转子02的局部拓扑结构，转子铁芯022中嵌有V型排列的钕铁硼永磁体021，形成一极。每块钕铁硼永磁体021的外端连接靠近气隙侧的外磁障023-1，内端连接靠近转轴侧的内磁障023-2。
为了提高设计效率，本发明对图1所示电机的1/4模型进行优化。优化方法参见图3，具体是：
步骤1：建立电机永磁转子初始微磁阻网络等效模型。
首先，将转子02划分为若干个扇形微磁阻单元，其中每个扇形微磁阻单元的大小为0.5deg×0.5mm，并用n(i,j)表示转子02上的扇形微磁阻单元编号，n是扇形微磁阻单元的个数，i是切向编号，j是径向编号；并用Cn(i,j)(ρ,θ)代表对应的扇形微磁阻单元中心点的位置信息，ρ是扇形微磁阻单元中心点距离转子02中心的距离，θ是位置角度。
本发明实施例中转子02划分出180×51个扇形微磁阻单元，因此i＝0,1,2,…,179，j＝0,1,2,…,50。
随后，根据转子02上的各扇形微磁阻单元中心点位置信息Cn(i,j)(ρ,θ)，对扇形微磁阻单元的初始材料属性An(i,j)进行分配，分配规则如下：
其中，ΩPM为设定的永磁体区域，ΩAir为设定的空气区域，得到扇形微磁阻单元初始材料属性An(i,j)是永磁体PM、空气Air或者是铁芯Iron。
如图4所示的扇形微磁阻单元初始材料属性An(i,j)是永磁体PM的永磁体微磁阻单元110，永磁体微磁阻单元110是由四个磁势源和磁阻相串联支路共同连接到中心节点111构成的磁路模型，由对称的两个切向等效磁阻112和切向等效磁势114相串联后连接到中心节点111，以及对称的两个径向等效磁阻113和径向等效磁势115相串联后连接到中心节点111。为了便于后续求解，相应的磁阻由磁导表示，定义为编号n(i,j)的永磁体微磁阻单元切向等效磁阻的磁导，为径向等效磁阻的磁导，具体计算公式如下：

其中，μPM是永磁体的磁导率，la是电机的轴向长度，ρn(i,j)是编号为n(i,j)的永磁体微磁阻单元中心节点距离电机轴心的长度，Δρn(i,j)是永磁体微磁阻单元高度，Δθn(i,j)是永磁体微磁阻单元切向弧长。
切向等效磁势114由表示，径向等效磁势115由表示，具体计算公式如下：。

其中，Br为永磁体剩磁，为永磁体磁化方向与切向角度；Sθ和Sρ分别表示从径向和切向方向的平均横截面积。
如图5所示的微磁阻单元初始材料属性An(i,j)是空气Air的空气微磁阻单元120，其为由四个径向空气等效磁阻123和切向空气等效磁阻122连接到中心节点121构成的磁路模型。定义为编号n(i,j)的切向空气等效磁阻122的磁导，为径向空气等效磁阻123的磁导，具体计算公式如下：

其中，μAir是空气的磁导率。
如图6所示的是微磁阻单元初始材料属性An(i,j)是铁芯Iron的铁芯微磁阻单元130，其结构与空气微磁阻单元120雷同。由四个径向空气等效磁阻133和切向空气等效磁阻132连接到中心节点131构成的磁路模型。定义为编号n(i,j)的切向空气等效磁阻132的磁导，为径向空气等效磁阻133的磁导，具体计算公式如下：

其中，μFe是铁芯的磁导率。
如图7所示的是永磁扁线电机转子其中一块永磁体021所在磁极的等效微磁阻网络，显示出永磁体等效微磁阻单元110、空气等效微磁阻单元120和铁芯等效微磁阻单元130。
步骤2：与步骤1的同时，建立扁线定子微磁阻网络等效模型。
如图8所示的是电机1/4扁线定子01等效磁阻网络模型，首先，对定子轭部012和齿部013进行等效建模：
考虑磁通在电机齿、轭处流动较为规则，同时，该部分不需要参与后续的拓扑优化过程。因此，可简化扁线定子01中的磁阻模型，以提高求解效率。为了便于后续求解，相应的磁阻由磁导表示，定子轭部等效磁阻220由磁导Psy表示，定子齿部等效磁阻230由磁导Pst表示如下：

其中，μFe为铁芯磁导率，la为轴长，Rso为定子外径，Rsy为定子轭内径；wst为齿宽，hst为齿高。
随后，如图9所示，对定子齿靴部014建立微磁阻单元等效模型：
由于定子齿靴部014靠近气隙，因此准确分析该区域的磁场对于计算电机的转矩特性至关重要。为了充分考虑到齿尖饱和与齿尖漏磁，定子齿靴部014采用与转子02相同的多层0.5deg×0.5mm空气微磁阻单元120与0.5deg×0.5mm铁芯微磁阻单元130进行等效，因此不再赘述，得到定子齿靴部微磁阻单元等效模型。
最后，对电机电枢绕组011进行等效建模：
如图8，电枢绕组011在微磁阻网络中等效为磁源210，向网络提供磁动势。因电机采用8层发卡绕组结构，每个齿上的磁势是8层三相绕组产生的磁势的叠加。以A相绕组产生的磁动势为例，其在定子齿上的等效磁动势矩阵Fsta表达式如下：
其中，是A相电枢绕组在第m齿的电枢等效磁动势。
如图10所示的是第0齿到第9齿的电枢磁动势分布图，其中θ为定子位置角度，第m齿的磁动势计算公式根据图中对应的表达式计算，nc为扁线绕组层数，Ia为A相电流。
此外，B相电枢绕组、C相电枢绕组在定子齿上的等效磁势矩阵Fstb与Fstc计算方式与A相电枢绕组Fsta雷同，因此三相绕组在第m齿上等效磁动势的矩阵表示如下：
其中为电枢绕组在第m齿上产生的等效磁动势，Fsta为A相磁动势矩阵，Fstb为B相磁动势矩阵，Fstc为C相磁动势矩阵。
步骤3：与步骤2同时，建立气隙微磁阻网络等效模型。
如图11、图12和图13所示的是气隙微磁阻网络模型。作为永磁扁线电机的能量转换场所，气隙磁场分布将随转子02位置角度和负载的变化而变化。气隙部分采用了更密集的空气微磁阻网格，使用了0.5deg×0.25mm的空气磁阻单元120来进行等效。同时，气隙磁阻网络分为内外两层磁路。外层磁路310连接到定子齿靴014等效磁路，而内层磁路320连接到转子02等效磁路。当转子02位置改变时，内层磁路320将沿气隙中线330旋转到相应的角度，并重新连接到最近的外层磁路310。如图12所示的是转子位置为0度时，内外两层磁路320、310支路局部连接示意图；如图13所示的是转子位置为0.5度时，内外两层磁路320、310支路局部连接示意图。
步骤4：在完成转子02、扁线定子01和气隙03的微磁阻网络等效模型的建立后，对转子02、扁线定子01和气隙03的全部微磁阻单元由外到内进行统一编号，从第0层开始编号。其中定子轭部012定义为第0层，定子齿部013定义为第1层，定子靴部014定义为第2～4层，气隙03定义为第5～6层，在本发明中，转子02定义为第7～57层。具体编号规则如表1：
表1
步骤5：选择永磁扁线电机转子的优化设计区域。
如图14所示的所选取的优化设计区域510，该优化区域为转子的1/16区域，即一块永磁体所占的磁极区域，通过对称和复制操作可以得到完整的转子02结构。优化设计区域 510内包含45×51＝2295个微磁阻单元。
步骤6：利用高斯基函数重新调整优化设计区域510内微磁阻单元材料属性，生成永磁扁线电机转子新拓扑。
如图15所示是在优化设计区域510所构建的二维高斯基函数分布示意图，首先，为所选取的转子优化设计区域510内的各微磁阻单元620定义材料特性参数Mn(i,j)，并建立6×6个二维高斯基函数610覆盖整个优化设计区域510，对优化设计区域510内微磁阻单元材料特性参数进行赋值，
任意微磁阻单元620的材料特性参数Mn(i,j)计算公式如下：

其中，微磁阻单元材料特性参数Mn(i,j)由36个二维高斯基函数加权求和获得，wk是权重系数，是Gk(i,j)对应二维高斯基函数的归一化形式，Gk(i,j)计算公式为：
其中，σ为高斯基函数标准差，(ζk,τk)为第k个高斯基函数中心位置。
然后，定义一个常数判据c，通过比较微磁阻单元的材料特性参数和判据c大小，判断对应微磁阻单元材料属性，判断方式如下：
其中，An(i,j)代表微磁阻单元620对应材料属性。当Mn(i,j)小于等于判据c，微磁阻单元620被赋予空气属性；当Mn(i,j)大于判据c，微磁阻单元620被赋予铁芯属性。此外，由于永磁体不参与拓扑优化设计，需要强制更新永磁体区域内微磁阻单元，为其重新赋予为永磁体属性。
最后，将同类型微磁阻单元620进行聚合，铁芯微磁阻单元聚合为转子铁芯结构，空气微磁阻单元聚合为转子磁障，从而生成新的电机拓扑结构。
如图16所示的是优化设计区域510利用微磁阻单元网络模型生成永磁扁线电机新结构的过程，其中631是微磁阻单元赋材料特性参数值的过程，632是判断微磁阻单元材料特性的过程，633是同类微磁阻单元聚合生成转子新结构的过程。
以下对生成的新的电机拓扑结构作进一步优化：
步骤7：针对新的电机拓扑结构，利用微磁阻网络求解步骤6中永磁扁线电机新生成拓扑的电磁性能。
首先，基于基尔霍夫磁通定律，建立并求解微磁阻网络磁导矩阵方程：
其中，P0-0～P19-19为定子齿部节点和定子轭部节点的自导和互导，P20-0～P559-19，P0-20～P19-559为定子齿靴部节点与定子齿部节点互导，P20-20～P559-559为定子齿靴部节点的自导和互导，P20-560～P559-919，P560-20～P919-559为定子齿靴部节点与气隙节点互导，P560-560～P919-919为气隙节点自导与互导，P560-920～P919-10098，P920-560～P10098-919为气隙节点与转子节点互导，P920-920～P10098-10098为转子节点自导与互导；F0～F19为定子齿轭部分节点磁势，F20～F559为定子齿靴部分节点磁势，F560～F919为气隙部节点磁势，F920～F10098为转子部节点磁势；Φ0～Φ19为定子齿轭部节点磁势，Φ20～Φ559为定子齿靴部节点磁势，Φ560～Φ919为气隙部节点磁势，Φ920～Φ10098为转子部节点磁势。
随后，利用超松弛迭代算法求解矩阵方程，迭代计算公式如下：
其中，为节点i第k+1次的迭代磁势，为节点i第k次的迭代磁动势，τ是松弛系数，P(i,i)为节点自导，P(i,j)为节点互导，为节点j第k+1次的迭代磁势，为节点j第k次的迭代磁势，Φ(i)为节点i磁通。
步骤8：计算微磁阻网络中各微磁阻单元平均磁密Bn(i,j)。
首先，计算微磁阻单元切向磁密如图17所示的是n(i,j)微磁阻单元802与切向左右相邻n(i,j-1)微磁阻单元801与n(i,j+1)微磁阻单元803，其中800为n(i,j)微磁阻单元切向磁密对应计算公式如下：
其中，Fn(i,j)为n(i,j)微磁阻单元802中心节点磁势，为n(i,j-1)微磁阻单元801中心 节点磁势，为n(i,j+1)微磁阻单元803中心节点磁势；是n(i,j)微磁阻单元802与n(i,j-1)微磁阻单元801之间的接触面积，是n(i,j)微磁阻单元802与n(i,j+1)微磁阻单元803之间的接触面积；是n(i,j)微磁阻单元802中心节点与n(i,j-1)微磁阻单元801中心节点之间的磁导，是n(i,j)微磁阻单元802中心节点与n(i,j+1)微磁阻单元803中心节点之间的磁导。
随后，计算微磁阻单元径向磁密如图18所示的是n(i,j)微磁阻单元802与径向上下相邻n(i-1,j)微磁阻单元801与n(i,j+1)微磁阻单元803，其中800为n(i,j)微磁阻单元切向磁密对应计算公式如下：
其中，Fn(i,j)为n(i,j)微磁阻单元802中心节点磁势，为n(i-1,j+Δj-)微磁阻单元812中心节点磁势，为n(i+1,j+Δj+)微磁阻单元803中心节点磁势；是n(i,j)微磁阻单元802与n(i-1,j+Δj-)微磁阻单元801之间的接触面积，是n(i,j)微磁阻单元802与n(i+1,j+Δj-)微磁阻单元803之间的接触面积；是n(i,j)微磁阻单元802中心节点与n(i,j-1)微磁阻单元801中心节点之间的磁导，是n(i,j)微磁阻单元802中心节点与n(i+1,j+Δj+)微磁阻单元803中心节点之间的磁导。
值得注意的是，气隙区域内(i＝5,i＝6)微磁阻单元连接方式会随转子位置角发生变化，因此Δj+和Δj-是用于调整气隙上下微磁阻单元的位移参数，对应计算公式如下：

其中，Δθ是t时刻电机位置角度。
最后，将微磁阻单元径向磁密800与切向磁密磁810矢量和作为微磁阻单元801磁密平均值Bn(i,j)：
此外，由于电机定子齿轭部采用简化等效磁路，因此定子轭部磁阻单元磁密和定子齿部磁阻单元磁密计算方式和微磁阻单元有所差异。如图19所示的是定子局部磁路，轭部磁阻单元830和齿部磁阻单元840平均磁密计算公式如下：

其中，Fn(i,j)为n(i,j)定子轭部磁阻单元830左侧节点磁势及定子齿部磁阻单元840上方节点磁势，为磁阻单元830右侧节点磁势，为磁阻单元840下方节点磁势；Psy为定子轭部磁阻单元830等效磁阻220的磁导，Pst为定子齿部磁阻单元840等效磁阻230的磁导；Rso为定子外径，Rsy为定子轭内径，wst为定子齿宽。
步骤9：计算微磁阻网络中各铁芯微磁阻单元磁导率。
首先，遍历磁阻网络中全部铁芯微磁阻单元，根据所采用的硅钢磁滞(B-H)曲线，以及步骤8所获得的磁密Bn(i,j)求取对应磁导率μn(i,j)，对应计算公式为：
其中，Hn(i,j)是根据微磁阻单元通过铁芯B-H曲线查表获得的对应磁场强度。
随后，判断微磁阻单元磁导率收敛性。定义磁导率收敛系数对应计算公式为：
其中，代表n(i,j)微磁阻单元在第k次迭代中磁导率，代表n(i,j)微磁阻单元在第k-1次迭代中磁导率，当k＝1时，为初始磁导率。
当所有铁芯磁阻单元最大收敛系数均小于预先设定公差(本发明为5％)，则完成迭代，执行步骤10。否则，新获得的磁导率替代初始或上次迭代磁导率更新磁导率，更新微磁阻网络，重新执行步骤7。如图20所示的是铁芯材料B-H曲线及铁芯微磁阻单元磁导率μn(i,j)迭代过程。
步骤10：计算永磁扁线电机新拓扑转矩特性并判断转矩是否满足设计需求。
电机的输出转矩由电磁转矩Te和齿槽转矩Tcog组成：
其中，θ为电机转动电角度，θmech为电机转动机械角度，P为转子极对数，iA、iB、iC和ψA、ψB、ψC分别代表三相电流和磁链；Wairgap代表电机处于空载情况下气隙中储存的能量，其计算公式为：
其中，μ0为空气磁导率。
判断转矩是否满足设计需求，如果满足则执行步骤12，否则执行步骤11。
步骤11：利用遗传算法优化步骤6中高斯基函数610权重系数wk，调整设计区域510内微磁阻单元材料分布，从而不断更新转子拓扑结构，改善电机负载转矩Trated等电磁性能。
首先，建立对应的优化模型，其中电机额定转矩平均值、额定转矩脉动、以及空载反电势谐波总量被作为优化目标，高斯基函数权重系数wk被作为优化变量。具体的拓扑优化模型表达式为：
其中，is为额定电流幅值，β为额定电流角；An(i,j)为微磁阻单元材料属性，Cn(i,j)为微磁阻单元中心节点位置，ΩPM为永磁体所在区域。
随后，利用遗传算法选择、交叉、变异操作优化每个高斯基函数的权重值wk，更新微磁阻单元的材料特性参数Mn(i,j)产生新的转子拓扑结构，并重复执行步骤6-步骤11利用微磁阻网络计算电机新结构负载转矩Trated，直到永磁扁线电机满足转矩设计需求或达到最大优化迭代次数。
如图21所示的是电机优化过程中拓扑结构及微磁阻单元磁密分布变化示意图，其中461为第1次迭代结果，462为第10次迭代结果，463为第40次迭代结果。
如图22所示的是电机通过步骤11所获得的优化结果(帕累托前沿)以及从中选取5个候选设计方案。其中，501为方案一，其平均转矩为34.2牛米、转矩脉动为3.6％、空载反电势总谐波含量为4.3％；502为方案二，其平均转矩为35.3牛米、转矩脉动为6.2％、空载反电势总谐波含量为4.7％；503为方案三，其平均转矩为34.9牛米、转矩脉动为4.6％、空载反电势总谐波含量为4.2％；504为方案四，其平均转矩为35.1牛米、转矩脉动为4.0％、空载反电势总谐波含量为4.2％；505为方案五，其平均转矩为33.1牛米、转矩脉动为3.8％、空载反电势总谐波含量为3.5％。
步骤12：选择设计方案并进行平滑处理。
首先，从候选方案中选择形状较规则的方案一作为为永磁扁线电机最终设计方案。
随后，对方案一的磁障边缘进行平滑处理。如图23所示的是最终方案磁障边缘平滑处 理示意图。其中，623-1、623-2为平滑处理前锯齿形磁障结构，723-1、723-2为平滑处理后磁障结构。
最后，如图24所示的是永磁扁线电机优化后的结构三维示意图。
步骤13：性能验证与样机加工。
首先，通过有限元分析对上述确定的永磁扁线电机设计方案性能进行评估。
如图25-图28所示的是利用有限元对实施例电机优化前后电磁性能进行对比示意图，其中图25和图26展示了优化前后电机反电势及相应的频谱分析对比，可以看出通过所述优化方法，反电势幅值从56.2伏特提升至66.2伏特，总谐波次数从16.9％下降至3.09％，表明优化后电机磁路设计更加合理，永磁利用率获得明显改善。图27为优化前后电机齿槽转矩对比，可以看出通过优化，电机齿槽转矩从612.84毫牛米下降到201.90毫牛米，达到约70％；图28为优化前后电机额定转矩特性对比，可以看出，优化后的电机平均输出转矩从31.38牛米提升至33.89牛米，转矩脉动从12.0％下降至3.8％。
最后，根据设计方案进行样机加工并进行相关测试，进一步验证电机结构。

Claims (10)

  1. 一种基于微磁阻单元的永磁扁线电机拓扑网格化优化方法，其特征是包括以下步骤：
    步骤1)：对电机的转子划分为若干个微磁阻单元，根据转子上的各微磁阻单元中心点位置信息对转子上的微磁阻单元初始材料属性进行分配得到永磁体、空气或铁芯的材料属性，以及得到相应的永磁体微磁阻单元、空气微磁阻单元和铁芯微磁阻单元，由此建立转子微磁阻网络等效模型；
    依次对定子轭部、齿部、齿靴部和电枢绕组等效建模，得到定子微磁阻网络等效模型；
    采用比转子的微磁阻单元更密集的网络划分气隙部分得到空气磁阻单元，将空气磁阻单元分为内外两层磁路；外层磁路连接定子齿靴的等效磁路，内层磁路连接转子的等效磁路，得到气隙微磁阻网络等效模型；
    步骤2)：将转子的1/16磁极区域作为优化设计区域，对所述的优化设计区域通过对称和复制得到完整的转子结构；
    步骤3)：建立二维高斯基函数覆盖整个所述的优化设计区域，由二维高斯基函数加权求和获得所述的优化设计区域上的微磁阻单元材料特性参数，将该微磁阻单元材料特性参数与定义的常数判据相比较，得到所述的优化设计区域上的微磁阻单元的空气或者铁芯的材料属性；
    步骤4)：将所述的优化设计区域上的材料属性相同的微磁阻单元进行聚合，铁芯微磁阻单元聚合为转子铁芯，空气微磁阻单元聚合为转子磁障，生成新的电机拓扑结构。
  2. 根据权利要求1所述的永磁扁线电机拓扑网格化优化方法，其特征是：针对步骤4)中所述的新的电机拓扑结构，再执行以下步骤：
    步骤41)：建立并求解微磁阻网络磁导矩阵方程，计算各微磁阻单元的平均磁密、各铁芯微磁阻单元磁导率和磁导率收敛系数；
    步骤42)当所有铁芯微磁阻单元磁导率的最大收敛系数均小于预先设定公差时，计算输出转矩并判断输出转矩是否满足设计需求，否则新获得的磁导率替代初始磁导率或上次迭代磁导率，重新执行步骤41)；
    步骤43)：当判断出输出转矩满足要求，则选择形状规则的方案作为永磁扁线电机最终设计方案，否则，利用遗传算法优化步骤3)中所述的高斯基函数的权重系数，调整设计区域内微磁阻单元材料分布，更新转子拓扑结构。
  3. 根据权利要求1或2所述的永磁扁线电机拓扑网格化优化方法，其特征是：步骤1)中，将转子划分为若干个扇形微磁阻单元，每个扇形微磁阻单元的大小为0.5deg×0.5mm；材料属性是永磁体的永磁体微磁阻单元是由对称的两个切向等效磁阻和切向等效磁势相串 联后连接到中心节点构成；材料属性是空气的空气微磁阻单元是由四个径向空气等效磁阻和切向空气等效磁阻连接到中心节点构成；材料属性是铁芯的铁芯微磁阻单元也是由四个径向空气等效磁阻和切向空气等效磁阻连接到中心节点构成；定子轭部等效磁阻由磁导表示，定子齿部等效磁阻由磁导表示：定子齿靴部采用与转子相同的多层0.5deg×0.5mm空气微磁阻单元与0.5deg×0.5mm铁芯微磁阻单元进行等效；电枢绕组等效为磁源。
  4. 根据权利要求1或2所述的永磁扁线电机拓扑网格化优化方法，其特征是：步骤3)中，建立6×6个二维高斯基函数覆盖整个优化设计区域，任意微磁阻单元的材料特性参数 是Gk(i,j)对应二维高斯基函数的归一化形式，wk是权重系数，σ为高斯基函数标准差，(ζk,τk)为第k个高斯基函数中心位置；当Mn(i,j)小于等于判据，微磁阻单元被赋予空气属性；当Mn(i,j)大于判据，微磁阻单元被赋予铁芯属性。
  5. 根据权利要求2所述的永磁扁线电机拓扑网格化优化方法，其特征是：步骤41)中，基于基尔霍夫磁通定律建立并求解微磁阻网络磁导矩阵方程：先计算微磁阻单元切向磁密，再计算微磁阻单元径向磁密，最后将微磁阻单元径向磁密与切向磁密磁的矢量和作为平均磁密。
  6. 根据权利要求5所述的永磁扁线电机拓扑网格化优化方法，其特征是：步骤41)中，所述的磁导率所述的磁导率收敛系数Bn(i,j)是所述的平均磁密，Hn(i,j)是根据微磁阻单元通过铁芯B-H曲线查表获得的对应磁场强度，代表n(i,j)微磁阻单元在第k次迭代中磁导率，代表n(i,j)微磁阻单元在第k-1次迭代中磁导率，当k＝1时，为初始磁导率。
  7. 根据权利要求6所述的永磁扁线电机拓扑网格化优化方法，其特征是：步骤42)中，输出转矩由电磁转矩Te和齿槽转矩Tcog组成，θ为电机转动电角度，θmech为电机转动机械角度，P为转子极对数，iA、iB、iC和ψA、ψB、ψC分别代表三相电流和磁链；Wairgap 是电机处于空载情况下气隙中储存的能量，μ0为空气磁导率，
  8. 根据权利要求7所述的永磁扁线电机拓扑网格化优化方法，其特征是：步骤43)中，以额定转矩平均值、额定转矩脉动以及空载反电势谐波总量作为优化目标，高斯基函数权重系数作为优化变量，利用遗传算法选择、交叉、变异操作优化每个高斯基函数的权重值，更新微磁阻单元的材料特性参数产生新的转子拓扑结构。
  9. 根据权利要求8所述的永磁扁线电机拓扑网格化优化方法，其特征是：步骤43)中，对最终设计方案的磁障边缘进行平滑处理。
  10. 根据权利要求8所述的永磁扁线电机拓扑网格化优化方法，其特征是：通过有限元分析对平滑处理后的设计方案性能进行评估。
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