CN117634397A - Multi-objective optimization method and system based on two-dimensional equivalent model of axial flux permanent magnet motor - Google Patents
Multi-objective optimization method and system based on two-dimensional equivalent model of axial flux permanent magnet motor Download PDFInfo
- Publication number
- CN117634397A CN117634397A CN202311675268.0A CN202311675268A CN117634397A CN 117634397 A CN117634397 A CN 117634397A CN 202311675268 A CN202311675268 A CN 202311675268A CN 117634397 A CN117634397 A CN 117634397A
- Authority
- CN
- China
- Prior art keywords
- model
- dimensional
- equivalent
- optimization
- permanent magnet
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000005457 optimization Methods 0.000 title claims abstract description 142
- 230000004907 flux Effects 0.000 title claims abstract description 83
- 238000000034 method Methods 0.000 title claims abstract description 65
- 241000282461 Canis lupus Species 0.000 claims abstract description 96
- 238000013461 design Methods 0.000 claims abstract description 46
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 21
- 230000004044 response Effects 0.000 claims abstract description 17
- 238000012545 processing Methods 0.000 claims description 22
- 230000035945 sensitivity Effects 0.000 claims description 20
- 239000003795 chemical substances by application Substances 0.000 claims description 10
- 241000282421 Canidae Species 0.000 claims description 9
- 230000008569 process Effects 0.000 claims description 7
- 230000000739 chaotic effect Effects 0.000 claims description 6
- 238000012937 correction Methods 0.000 claims description 6
- 238000012795 verification Methods 0.000 claims description 6
- 238000004804 winding Methods 0.000 claims description 6
- 230000000694 effects Effects 0.000 claims description 5
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 3
- 239000004398 Ethyl lauroyl arginate Substances 0.000 claims description 3
- 239000004020 conductor Substances 0.000 claims description 3
- 239000004316 dimethyl dicarbonate Substances 0.000 claims description 3
- 230000010354 integration Effects 0.000 claims description 3
- 230000007246 mechanism Effects 0.000 claims description 3
- 239000002245 particle Substances 0.000 claims description 3
- 230000005855 radiation Effects 0.000 claims description 3
- 238000004364 calculation method Methods 0.000 abstract description 9
- 238000010206 sensitivity analysis Methods 0.000 abstract description 4
- 238000012360 testing method Methods 0.000 abstract description 4
- 238000010586 diagram Methods 0.000 description 3
- 230000004323 axial length Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000002028 premature Effects 0.000 description 1
- 230000010349 pulsation Effects 0.000 description 1
- 238000004904 shortening Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR 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; CALCULATING OR 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; CALCULATING OR 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; CALCULATING OR 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; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- General Physics & Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Geometry (AREA)
- Artificial Intelligence (AREA)
- Software Systems (AREA)
- Computing Systems (AREA)
- Biomedical Technology (AREA)
- General Health & Medical Sciences (AREA)
- Data Mining & Analysis (AREA)
- Computational Linguistics (AREA)
- Mathematical Physics (AREA)
- Biophysics (AREA)
- Molecular Biology (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Medical Informatics (AREA)
- Life Sciences & Earth Sciences (AREA)
- Health & Medical Sciences (AREA)
- Microelectronics & Electronic Packaging (AREA)
- Control Of Electric Motors In General (AREA)
- Feedback Control In General (AREA)
Abstract
The invention discloses a multi-objective optimization method and a system based on a two-dimensional equivalent model of an axial flux permanent magnet motor, wherein the axial flux permanent magnet motor is firstly unfolded and equivalent to be a two-dimensional linear motor along an equivalent radius, and then an equivalent coefficient equation is introduced based on the obtained two-dimensional linear motor and according to the error between the three-dimensional model and the two-dimensional equivalent model of the axial flux permanent magnet motor; the invention realizes the function of reducing multi-objective optimization time, shortens calculation time and ensures calculation precision by establishing a two-dimensional equivalent model and introducing equivalent coefficients, and uses sensitivity analysis to layer design parameters, thereby not only reducing the dimension of an optimization space, but also reducing the optimization difficulty, effectively reducing the test times by generating a proxy model through a response surface method, effectively improving global searching capability and searching speed by adopting a gray wolf optimization algorithm for optimizing, and being suitable for wide popularization and use.
Description
Technical Field
The invention relates to the technical field of axial flux permanent magnet motor optimization, in particular to a multi-objective optimization method and system based on a two-dimensional equivalent model of an axial flux permanent magnet motor.
Background
Axial flux permanent magnet motors have become an important choice for electric vehicles due to their high power density and high efficiency, and compared with conventional radial flux permanent magnet motors, axial flux permanent magnet motors have shorter axial lengths and higher torque densities, optimizing the structural and spatial arrangement of the electric vehicle system.
At present, the multi-objective optimization of the axial flux permanent magnet motor is a very important part of motor optimization design, most of the existing multi-objective optimization methods are aimed at radial permanent magnet motors or linear motors, and few multi-objective optimization methods aimed at the axial flux permanent magnet motors are adopted; because the magnetic field of the axial flux permanent magnet motor presents three-dimensional characteristics, a three-dimensional model must be established for analysis and optimization, however, a great deal of calculation time is required for multi-objective optimization by utilizing three-dimensional finite element analysis; therefore, a multi-objective optimization method and system based on a two-dimensional equivalent model of an axial flux permanent magnet motor are required to be designed.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a multi-objective optimization method and a system based on a two-dimensional equivalent model of an axial flux permanent magnet motor, which have the advantages of reducing the multi-objective optimization time, shortening the calculation time and ensuring the calculation accuracy by establishing the two-dimensional equivalent model and introducing the equivalent coefficient, layering design parameters by using sensitivity analysis, reducing the dimension of an optimization space, reducing the optimization difficulty by using a response surface method to generate a proxy model, effectively reducing the test times, and effectively improving the global searching capability and searching speed by using a gray wolf optimization algorithm for optimizing.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a multi-objective optimization method and system based on two-dimensional equivalent model of axial flux permanent magnet motor comprises the following steps,
step (A), expanding the axial flux permanent magnet motor along an equivalent radius to be equivalent to a two-dimensional linear motor;
step (B), based on the obtained two-dimensional linear motor, introducing an equivalent coefficient equation according to the error between the axial flux permanent magnet motor three-dimensional model and the two-dimensional equivalent model;
step (C), determining an optimization target, design parameters and constraint conditions according to the obtained equivalent coefficient equation;
step (D), dividing design parameters into significant parameters and non-significant parameters according to the sensitivity;
step (E), obtaining a proxy model of an optimization target for the significant parameters by using a response surface method, and optimizing the proxy model of the optimization target by adopting a gray wolf optimization algorithm;
step (F), optimizing the non-significant parameters by using parameter scanning, and obtaining optimal parameters;
and (G) performing finite element analysis on the optimized motor, comparing the comprehensive performances of the optimized motor and the original motor, and verifying the effectiveness of the optimization.
The multi-objective optimization method based on the two-dimensional equivalent model of the axial flux permanent magnet motor comprises the following steps of (A) expanding the axial flux permanent magnet motor along the equivalent radius to be equivalent to a two-dimensional linear motor,
step (A1), expanding the axial flux permanent magnet motor along an equivalent radius, wherein the equivalent radius is shown in a formula (1),
wherein r is k Represents equivalent radius, R out Represents the outer diameter of the motor, R in Representing the inner diameter of the motor;
step (A2), equivalent to a two-dimensional linear motor, wherein the thrust of the two-dimensional linear motor is converted into torque as shown in a formula (2),
T 2-D ＝r k ·F 2-D (2)
wherein T is 2-D Representing torque of two-dimensional linear motor, F 2-D Representing motor thrust.
The step (B) of the multi-objective optimization method based on the two-dimensional equivalent model of the axial flux permanent magnet motor introduces an equivalent coefficient equation based on the obtained two-dimensional linear motor according to the error between the three-dimensional model and the two-dimensional equivalent model of the axial flux permanent magnet motor, and the specific steps are as follows,
a step (B1) of constructing an average electromagnetic torque expression in which the effective conductors of the armature windings of the axial flux permanent magnet motor exhibit radial radiation in space, and the electric load of the motor varies with the variation of the radius, the specific average electromagnetic torque expression being constructed as follows,
a step (B11) of constructing an electric load peak value expression in which the electric load peak value is as shown in formula (3),
wherein A is m (r) represents an electrical load peak value, m 1 Representing the number of phases, N 1 Indicating the number of turns, I a Representing phase current, p representing the number of poles, τ (r) representing the pole pitch at different radii, r representing the radius;
a step (B12) of constructing a tangential force expression on the rotor disk, wherein the tangential force acting on the rotor disk is as shown in formula (4),
wherein dF x Represents tangential force acting on the rotor disk, dr represents unit radius, dS represents unit area, B g Representing the flux density component perpendicular to the permanent magnet in the breath;
a step (B13) of constructing an average electromagnetic torque expression in which the torques generated at different radii are as shown in formula (5),
dT＝rdF x ＝r[k w1 A(r)B avg dS]＝2m 1 I a N 1 k w1 B avg rdr (5)；
wherein dT represents the torque generated at different radii, for R in equation (5) from R out To R in When the integration is performed, the average electromagnetic torque is as shown in formula (6),
wherein T represents an average electromagnetic torque, k w1 Representing the winding coefficient, B avg Represents the average magnetic density at a certain radius;
step (B2), introducing an equivalent coefficient equation according to the error between the three-dimensional model and the two-dimensional equivalent model of the axial flux permanent magnet motor, specifically comprising the following steps of,
a step (B21) of dividing the axial flux permanent magnet motor into n equal two-dimensional segments, wherein the torque of the ith two-dimensional segment is shown as a formula (7),
T i ＝KLB avg-i r i ，
wherein T is i Represents the torque of the ith two-dimensional segment, K represents the sum of m 1 、I a 、N 1 、k w1 Related constants, B avg-i Represents the average flux density of the ith two-dimensional segment, R out-i Represents the outer diameter of the ith model, R in-i Represents the inner diameter of the ith model, L represents the radial thickness of each model, r i Representing the equivalent radius of the ith model;
step (B22) of obtaining the average magnetic density B of the model based on the torque of each model avg-i And r i The torque of the kth model is shown as a formula (8);
wherein T is k Representing the torque of the kth model, g k Represents an air gap correction coefficient, B avg-k Represents the average flux density of the kth two-dimensional segment, B avg 2-D Representing the average flux density of the two-dimensional equivalent model;
step (B23), the torque of the ith model is shown as a formula (9), the torques of the n models are summed to obtain a corrected torque which is shown as a formula (10),
wherein T is i Representing the torque of the ith model, T c Indicating corrected torque g l And the correction coefficient representing the end effect of the three-dimensional motor.
The foregoing method for optimizing multiple targets based on two-dimensional equivalent model of axial flux permanent magnet motor includes the steps of (C) determining optimization targets, design parameters and constraint conditions according to the obtained equivalent coefficient equation, wherein the optimization targets are output torque T avg Maximum, efficiency ηmaximum and torque ripple T rip Minimum is an optimization target; the optimized variable is the pole arc coefficient W of the permanent magnet PM Thickness H of permanent magnet PM Width B of notch s0 Groove width B s1 Slot height H s0 Height H of slot wedge s1 And groove depth H s2 Is a design parameter; the constraint is as shown in the formula (11),
the foregoing method for optimizing multiple targets based on two-dimensional equivalent model of axial flux permanent magnet motor includes (D) dividing design parameters into significant parameters and non-significant parameters according to sensitivity, wherein sensitivity index G j (x i ) And integrated sensitivity S (x i ) As shown in the formula (12) and the formula (13), respectively,
S(x i )＝λ j |G j (x i )| (13)
wherein x is i Representing design parameters, E (yj/xi) representing an optimization objective y j Average value of V (E (y) j /x i ) (1) represents E (y) j /x i ) Variance of (V) (y j ) Representing the variance, x of the optimization objective i Representing design parameters lambda j Representing the weights of the optimization targets.
The multi-objective optimization method based on the two-dimensional equivalent model of the axial flux permanent magnet motor comprises the following steps of (E) obtaining an agent model of an optimization objective by using a response surface method for the significant parameters, optimizing the agent model of the optimization objective by adopting a gray wolf optimization algorithm,
step (E1), obtaining a proxy model of an optimization target for the significant parameters by using a response surface method, wherein the proxy model is specifically constructed by adopting a Box-Behnken Design method;
step (E2), adopting a gray wolf optimization algorithm to optimize the agent model of the optimization target, specifically comprising the following steps of,
step (E21), initializing the gray wolf population by using a Tent chaotic map, wherein the Tent chaotic map expression is shown in a formula (14),
wherein N represents the number of particles in the sequence, and rand (0, 1)/N represents a random variable;
a step (E22) of modifying the linear search process by using the nonlinear control parameter a, wherein the modified control parameter formula is shown as formula (15),
wherein a (t) represents the modified control parameter, t represents the current iteration number, and M represents the maximum iteration number;
step (E23), adding weight coefficients to alpha wolf, beta wolf and delta wolf in the Hunting of the wolf, wherein the weight coefficients are shown in a formula (16),
wherein θ i Representing the weight, ω, of each head wolf i Representing the ratio between the position of the individual wolf relative to the fitness of alpha wolf and delta wolf,f represents the fitness of the wolf;
in the step (E24), when the position of the head wolf is updated, an independent updating mode is adopted for the alpha wolf, the beta wolf and the delta wolf respectively, the specific updating mode is as follows,
step (E241), delta wolf is guided by alpha wolf and beta wolf, the updating mode of delta wolf is shown as formula (17),
X δ (t+1)＝D δ -X δ (t)，D δ ＝ρX δ (t)+(1-ρ)X α (t)+(1-ρ)X β (t) (17)
wherein X is δ (t+1) represents the position of δwolf after update; x is X α (t)、X β (t) and X δ (t) represents the current positions of alpha wolf, beta wolf and delta wolf, respectively, and ρ represents the distribution of [0,1 ]]Random numbers in (a);
step (E242), beta wolf is guided by alpha wolf, the position is updated by using a spiral update mechanism, the beta wolf update mode is shown in formula (18),
X β (t+1)＝|X α (t)-X β (t)|e bl cos(2pl)+ρX α (t) (18)
wherein X is β (t+1) represents the position of beta wolf after updating, b represents a logarithmic spiral shape function, and l represents [ -1,1 []Random numbers in (a);
step (E243), alpha wolf is not guided by other wolves, alpha wolf is updated by using the Levy flight method as shown in formula (19),
wherein X is best (t+1) represents the updated optimal position, μ represents a step size control factor,represents a dot product, and Levy (λ) represents a random search path.
The step (F) of the multi-objective optimization method based on the two-dimensional equivalent model of the axial flux permanent magnet motor is used for optimizing the non-significant parameter by using parameter scanning and obtaining the optimal parameter, wherein the non-significant parameter optimization is performed after the significant parameter optimization is completed.
The multi-objective optimization system based on the two-dimensional equivalent model of the axial flux permanent magnet motor comprises a two-dimensional equivalent module, an equivalent coefficient equation introduction module, a parameter determination module, a parameter distinguishing module, a first parameter processing module, a second parameter processing module and an optimization verification module, wherein the two-dimensional equivalent module is used for expanding and equivalent the axial flux permanent magnet motor into a two-dimensional linear motor along an equivalent radius; the equivalent coefficient equation introduction module is used for introducing an equivalent coefficient equation based on the obtained two-dimensional linear motor and according to the error between the axial flux permanent magnet motor three-dimensional model and the two-dimensional equivalent model; the parameter determining module is used for determining an optimization target, design parameters and constraint conditions according to the obtained equivalent coefficient equation; the parameter distinguishing module is used for dividing design parameters into significant parameters and non-significant parameters according to the sensitivity; the first parameter processing module is used for obtaining a proxy model of an optimization target for the significant parameters by using a response surface method, and optimizing the proxy model of the optimization target by adopting a gray wolf optimization algorithm; the second parameter processing module is used for optimizing the non-significant parameter using parameter scanning and obtaining an optimal parameter; the optimization verification module is used for carrying out finite element analysis on the optimized motor and comparing the comprehensive performance of the optimized motor and the original motor to verify the effectiveness of optimization.
The parameter distinguishing module distinguishes the design parameters determined by the parameter determining module and divides the design parameters into significant parameters and non-significant parameters according to the sensitivity.
In the multi-objective optimization system based on the two-dimensional equivalent model of the axial flux permanent magnet motor, the first parameter processing module is used for processing the significant parameters distinguished by the parameter distinguishing module, and the second parameter processing module is used for processing the non-significant parameters distinguished by the parameter distinguishing module.
The beneficial effects of the invention are as follows: according to the multi-objective optimization method and system based on the two-dimensional equivalent model of the axial flux permanent magnet motor, the axial flux permanent magnet motor is unfolded and equivalent to be a two-dimensional linear motor along the equivalent radius, the two-dimensional equivalent coefficient is introduced to reduce equivalent errors, then the response surface method is used for fitting the proxy model, and the gray wolf optimization algorithm is adopted for solving, so that the optimization method and system have the function of reducing multi-objective optimization time, the two-dimensional equivalent model is established, the equivalent coefficient is introduced, calculation time is shortened, calculation precision is guaranteed, design parameters are layered by using sensitivity analysis, the dimension of an optimization space is reduced, the optimization difficulty is reduced, the number of tests can be effectively reduced by generating the proxy model by the response surface method, the global search capability and the search speed can be effectively improved by adopting the gray wolf optimization algorithm, and the multi-objective optimization method has good application value in the optimization of the axial flux permanent magnet motor.
Drawings
FIG. 1 is an overall flow chart of the present invention;
FIG. 2 is an equivalent process diagram of the present invention;
FIG. 3 is a graph of torque versus current for the present invention;
FIG. 4 is a graph of design parameter sensitivity of the present invention;
FIG. 5 is a schematic diagram of the gray wolf optimization algorithm of the present invention;
fig. 6 is a pareto chart of the invention;
fig. 7 is an optimized torque waveform diagram of the present invention.
Detailed Description
The invention will be further described with reference to the drawings.
As shown in fig. 1, the multi-objective optimization method and system based on the two-dimensional equivalent model of the axial flux permanent magnet motor of the invention comprises the following steps,
step (A), the axial flux permanent magnet motor is unfolded and equivalent to a two-dimensional linear motor along the equivalent radius, the specific steps are as follows,
step (A1), expanding the axial flux permanent magnet motor along an equivalent radius, wherein the equivalent radius is shown in a formula (1),
wherein r is k Represents equivalent radius, R out Represents the outer diameter of the motor, R in Representing the inner diameter of the motor;
step (A2), equivalent to a two-dimensional linear motor, wherein the thrust of the two-dimensional linear motor is converted into torque as shown in a formula (2),
T 2-D ＝r k ·F 2-D (2)
wherein T is 2-D Representing torque of two-dimensional linear motor, F 2-D Representing motor thrust.
Step (B), based on the obtained two-dimensional linear motor, introducing an equivalent coefficient equation according to the error between the three-dimensional model and the two-dimensional equivalent model of the axial flux permanent magnet motor, specifically comprising the following steps of,
a step (B1) of constructing an average electromagnetic torque expression in which the effective conductors of the armature windings of the axial flux permanent magnet motor exhibit radial radiation in space, and the electric load of the motor varies with the variation of the radius, the specific average electromagnetic torque expression being constructed as follows,
a step (B11) of constructing an electric load peak value expression in which the electric load peak value is as shown in formula (3),
wherein A is m (r) represents an electrical load peak value, m 1 Representing the number of phases, N 1 Indicating the number of turns, I a Representing phase current, p representing the number of poles, τ (r) representing the pole pitch at different radii, r representing the radius;
a step (B12) of constructing a tangential force expression on the rotor disk, wherein the tangential force acting on the rotor disk is as shown in formula (4),
dF x ＝I a (dr×B g )＝A(r)(dS×B g )，
wherein dF x Representing tangential force acting on the rotor disk, dr representing unit radius, dS representing unit area, bg representing the flux density component perpendicular to the permanent magnets in the breath;
a step (B13) of constructing an average electromagnetic torque expression in which the torques generated at different radii are as shown in formula (5),
dT＝rdF x ＝r[k w1 A(r)B avg dS]＝2m 1 I a N 1 k w1 B avg rdr (5)；
wherein dT represents the torque generated at different radii, for R in equation (5) from R out To R in When the integration is performed, the average electromagnetic torque is as shown in formula (6),
wherein T represents an average electromagnetic torque, k w1 Representing the winding coefficient, B avg Represents the average magnetic density at a certain radius;
step (B2), introducing an equivalent coefficient equation according to the error between the three-dimensional model and the two-dimensional equivalent model of the axial flux permanent magnet motor, specifically comprising the following steps of,
a step (B21) of dividing the axial flux permanent magnet motor into n equal two-dimensional segments, wherein the torque of the ith two-dimensional segment is shown as a formula (7),
T i ＝KLB avg-i r i ，
wherein T is i Represents the torque of the ith two-dimensional segment, K represents the sum of m 1 、I a 、N 1 、k w1 Related constants, B avg-i Represents the average flux density of the ith two-dimensional segment, R out-i Represents the outer diameter of the ith model, R in-i Representing the ith modelL represents the radial thickness of each model, r i Representing the equivalent radius of the ith model;
step (B22) of obtaining the average magnetic density B of the model based on the torque of each model avg-i And r i The torque of the kth model is shown as a formula (8);
wherein T is k Representing the torque of the kth model, g k Represents an air gap correction coefficient, B avg-k Represents the average flux density of the kth two-dimensional segment, B avg 2-D Representing the average flux density of the two-dimensional equivalent model;
step (B23), the torque of the ith model is shown as a formula (9), the torques of the n models are summed to obtain a corrected torque which is shown as a formula (10),
wherein T is i Representing the torque of the ith model, T c Indicating corrected torque g l And the correction coefficient representing the end effect of the three-dimensional motor.
Step (C) of determining an optimization target, a design parameter and a constraint condition based on the obtained equivalent coefficient equation, wherein the optimization target is a torque T avg Maximum, efficiency ηmaximum and torque ripple T rip Minimum is an optimization target; the optimized variable is the pole arc coefficient W of the permanent magnet PM Thickness H of permanent magnet PM Width B of notch s0 Groove width B s1 Slot height H s0 Height H of slot wedge s1 And groove depth H s2 Is a design parameter; the constraint is as shown in the formula (11),
step (D), dividing the design parameters into significant parameters and non-significant parameters according to the sensitivity, wherein the sensitivity index G j (x i ) And integrated sensitivity S (x i ) As shown in the formula (12) and the formula (13), respectively,
S(x i )＝λ j |G j (x i )| (13)
wherein x is i Representing design parameters, E (yj/xi) representing an optimization objective y j Average value of V (E (y) j /x i ) (1) represents E (y) j /x i ) Variance of (V) (y j ) Representing the variance, x of the optimization objective i Representing design parameters lambda j Representing the weights of the optimization targets.
Step (E), obtaining an agent model of an optimization target for the significant parameters by using a response surface method, optimizing the agent model of the optimization target by adopting a gray wolf optimization algorithm, specifically comprising the following steps of,
step (E1), obtaining a proxy model of an optimization target for the significant parameters by using a response surface method, wherein the proxy model is specifically constructed by adopting a Box-Behnken Design method;
step (E2), adopting a gray wolf optimization algorithm to optimize the agent model of the optimization target, specifically comprising the following steps of,
step (E21), initializing the gray wolf population by using a Tent chaotic map, wherein the Tent chaotic map expression is shown in a formula (14),
wherein N represents the number of particles in the sequence, and rand (0, 1)/N represents a random variable;
a step (E22) of modifying the linear search process by using the nonlinear control parameter a, wherein the modified control parameter formula is shown as formula (15),
wherein a (t) represents the modified control parameter, t represents the current iteration number, and M represents the maximum iteration number;
step (E23), adding weight coefficients to alpha wolf, beta wolf and delta wolf in the Hunting of the wolf, wherein the weight coefficients are shown in a formula (16),
wherein θ i Representing the weight, ω, of each head wolf i Representing the ratio between the position of the individual wolf relative to the fitness of alpha wolves and delta wolves, f representing the fitness of the wolves;
in the step (E24), when the position of the head wolf is updated, an independent updating mode is adopted for the alpha wolf, the beta wolf and the delta wolf respectively, the specific updating mode is as follows,
step (E241), delta wolf is guided by alpha wolf and beta wolf, the updating mode of delta wolf is shown as formula (17),
X δ (t+1)＝D δ -X δ (t)，D δ ＝ρX δ (t)+(1-ρ)X α (t)+(1-ρ)X β (t) (17)
wherein X is δ (t+1) represents the position of δwolf after update; x is X α (t)、X β (t) and X δ (t) represents the current positions of alpha wolf, beta wolf and delta wolf, respectively, and ρ represents the distribution of [0,1 ]]Random numbers in (a);
step (E242), beta wolf is guided by alpha wolf, the position is updated by using a spiral update mechanism, the beta wolf update mode is shown in formula (18),
X β (t+1)＝|X α (t)-X β (t)|e bl cos(2pl)+ρX α (t) (18)
wherein X is β (t+1) represents the position of beta wolf after updating, b represents a logarithmic spiral shape function, and l represents [ -1,1 []Random numbers in (a);
step (E243), alpha wolf is not guided by other wolves, alpha wolf is updated by using the Levy flight method as shown in formula (19),
wherein X is best (t+1) represents the updated optimal position, μ represents a step size control factor,represents a dot product, and Levy (λ) represents a random search path.
And (F) optimizing the non-significant parameter by using parameter scanning, and obtaining the optimal parameter, wherein the non-significant parameter optimization is performed after the significant parameter optimization is completed.
And (G) performing finite element analysis on the optimized motor, comparing the comprehensive performances of the optimized motor and the original motor, and verifying the effectiveness of the optimization.
The multi-objective optimization system based on the two-dimensional equivalent model of the axial flux permanent magnet motor comprises a two-dimensional equivalent module, an equivalent coefficient equation introduction module, a parameter determination module, a parameter distinguishing module, a first parameter processing module, a second parameter processing module and an optimization verification module, wherein the two-dimensional equivalent module is used for expanding and equivalent the axial flux permanent magnet motor into a two-dimensional linear motor along an equivalent radius; the equivalent coefficient equation introduction module is used for introducing an equivalent coefficient equation based on the obtained two-dimensional linear motor and according to the error between the axial flux permanent magnet motor three-dimensional model and the two-dimensional equivalent model; the parameter determining module is used for determining an optimization target, design parameters and constraint conditions according to the obtained equivalent coefficient equation; the parameter distinguishing module is used for dividing design parameters into significant parameters and non-significant parameters according to the sensitivity; the first parameter processing module is used for obtaining a proxy model of an optimization target for the significant parameters by using a response surface method, and optimizing the proxy model of the optimization target by adopting a gray wolf optimization algorithm; the second parameter processing module is used for optimizing the non-significant parameter using parameter scanning and obtaining an optimal parameter; the optimization verification module is used for carrying out finite element analysis on the optimized motor and comparing the comprehensive performance of the optimized motor and the original motor to verify the effectiveness of optimization.
Specifically, the parameter distinguishing module distinguishes the design parameters determined by the parameter determining module and divides the design parameters into significant parameters and non-significant parameters according to the sensitivity.
Specifically, the first parameter processing module processes the significant parameters distinguished by the parameter distinguishing module, and the second parameter processing module processes the non-significant parameters distinguished by the parameter distinguishing module.
To better illustrate the effect of the present invention, a specific embodiment of the present invention is described below;
an axial flux permanent magnet machine to which this embodiment is applied is shown in fig. 2.
As shown in fig. 3, in this embodiment, the corrected torque-to-current curve graph is obtained by using the equivalent coefficient, and it can be seen that the errors of the initial model and the corrected model and the three-dimensional model are 12.1% and 4.9%, respectively, and the error is reduced by 7.2%.
As shown in FIG. 4, for the sensitivity of the design parameters of this embodiment, a significant parameter W is obtained PM ，B s0 ，H s1 And H s2 Non-salient parameter H PM ，B s1 And H s0 。
In the embodiment, finite element software simulation is adopted to simulate generation of sample points for significant parameters by using a Box-Behnken Design method and construction of a proxy model, and simulation results are shown in table 1.
TABLE 1 Box-Behnken Design method Design Table and finite element analysis results
As shown in table 1, the variances of the torque, torque ripple, and efficiency proxy models were 0.9973,0.9453 and 0.9913, respectively, indicating high accuracy of the proxy models.
The resulting torque has a surrogate model as shown in equation (20), the resulting torque ripple has a surrogate model as shown in equation (21), the resulting efficiency has a surrogate model as shown in equation (22),
wherein x is 1 Is W PM ，x 2 Is B s0 ，x 3 Is H s1 ，x 4 Is H s2 。
As shown in fig. 5, the gray wolf optimization algorithm adopted in the embodiment solves the problems of premature convergence and local optimum sinking of the existing gray wolf optimization algorithm;
as shown in fig. 6, for the pareto solution set obtained by optimizing the agent model of the optimization target by using a wolf optimization algorithm in this embodiment, an optimal solution is selected;
as shown in fig. 7, the optimized torque waveform is shown in fig. 7, and compared with the original motor, the optimized motor torque is increased from 601.3Nm to 670.9Nm, and is increased by 11.8%; the efficiency is improved from 91.6% to 92.1%, and is improved by 0.5%; the torque pulsation is reduced from 3.9% to 2.25%, and is reduced by 1.65%, and the optimization effect is obvious.
In summary, the multi-objective optimization method and system based on the two-dimensional equivalent model of the axial flux permanent magnet motor firstly unfolds the axial flux permanent magnet motor along the equivalent radius to be equivalent to a two-dimensional linear motor, then introduces an equivalent coefficient equation based on the obtained two-dimensional linear motor and according to the error between the three-dimensional model and the two-dimensional equivalent model of the axial flux permanent magnet motor, then determines an optimization objective, design parameters and constraint conditions according to the obtained equivalent coefficient equation, then divides the design parameters into significant parameters and non-significant parameters according to the sensitivity, then uses a response surface method to obtain a proxy model of the optimization objective for the significant parameters, then uses a gray wolf optimization algorithm to optimize the proxy model of the optimization objective, finally uses parameter scanning to optimize the non-significant parameters, obtains optimal parameters, performs finite element analysis on the optimized motor, compares the comprehensive performances of the optimized motor and the original motor, and verifies the effectiveness of the optimization; the invention realizes the function of reducing multi-objective optimization time, shortens calculation time and ensures calculation precision by establishing a two-dimensional equivalent model and introducing equivalent coefficients, and uses sensitivity analysis to layer design parameters, thereby not only reducing the dimension of an optimization space, but also reducing the optimization difficulty, effectively reducing the test times by generating a proxy model through a response surface method, and effectively improving global searching capability and searching speed by adopting a gray wolf optimization algorithm for optimizing.
The foregoing has outlined and described the basic principles, features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (10)
1. A multi-objective optimization method based on a two-dimensional equivalent model of an axial flux permanent magnet motor is characterized by comprising the following steps of: comprises the steps of,
step (A), expanding the axial flux permanent magnet motor along an equivalent radius to be equivalent to a two-dimensional linear motor;
step (B), based on the obtained two-dimensional linear motor, introducing an equivalent coefficient equation according to the error between the axial flux permanent magnet motor three-dimensional model and the two-dimensional equivalent model;
step (C), determining an optimization target, design parameters and constraint conditions according to the obtained equivalent coefficient equation;
step (D), dividing design parameters into significant parameters and non-significant parameters according to the sensitivity;
step (E), obtaining a proxy model of an optimization target for the significant parameters by using a response surface method, and optimizing the proxy model of the optimization target by adopting a gray wolf optimization algorithm;
step (F), optimizing the non-significant parameters by using parameter scanning, and obtaining optimal parameters;
and (G) performing finite element analysis on the optimized motor, comparing the comprehensive performances of the optimized motor and the original motor, and verifying the effectiveness of the optimization.
2. The multi-objective optimization method based on the two-dimensional equivalent model of the axial flux permanent magnet motor according to claim 1, wherein the method comprises the following steps: step (A), the axial flux permanent magnet motor is unfolded and equivalent to a two-dimensional linear motor along the equivalent radius, the specific steps are as follows,
step (A1), expanding the axial flux permanent magnet motor along an equivalent radius, wherein the equivalent radius is shown in a formula (1),
wherein r is k Represents equivalent radius, R out Represents the outer diameter of the motor, R in Representing the inner diameter of the motor;
step (A2), equivalent to a two-dimensional linear motor, wherein the thrust of the two-dimensional linear motor is converted into torque as shown in a formula (2),
T 2-D ＝r k ·F 2-D (2)
wherein T is 2-D Representing rotation of a two-dimensional linear motorMoment, F 2-D Representing motor thrust.
3. The multi-objective optimization method based on the two-dimensional equivalent model of the axial flux permanent magnet motor according to claim 2, wherein the method comprises the following steps: step (B), based on the obtained two-dimensional linear motor, introducing an equivalent coefficient equation according to the error between the three-dimensional model and the two-dimensional equivalent model of the axial flux permanent magnet motor, specifically comprising the following steps of,
a step (B1) of constructing an average electromagnetic torque expression in which the effective conductors of the armature windings of the axial flux permanent magnet motor exhibit radial radiation in space, and the electric load of the motor varies with the variation of the radius, the specific average electromagnetic torque expression being constructed as follows,
a step (B11) of constructing an electric load peak value expression in which the electric load peak value is as shown in formula (3),
wherein A is m (r) represents an electrical load peak value, m 1 Representing the number of phases, N 1 Indicating the number of turns, I a Representing phase current, p representing the number of poles, τ (r) representing the pole pitch at different radii, r representing the radius;
a step (B12) of constructing a tangential force expression on the rotor disk, wherein the tangential force acting on the rotor disk is as shown in formula (4),
wherein dF x Represents tangential force acting on the rotor disk, dr represents unit radius, dS represents unit area, B g Representing the flux density component perpendicular to the permanent magnet in the breath;
a step (B13) of constructing an average electromagnetic torque expression in which the torques generated at different radii are as shown in formula (5),
dT＝rdF x ＝r[k w1 A(r)B avg dS]＝2m 1 I a N 1 k w1 B avg rdr (5)；
wherein dT represents the torque generated at different radii, for R in equation (5) from R out To R in When the integration is performed, the average electromagnetic torque is as shown in formula (6),
wherein T represents an average electromagnetic torque, k w1 Representing the winding coefficient, B avg Represents the average magnetic density at a certain radius;
step (B2), introducing an equivalent coefficient equation according to the error between the three-dimensional model and the two-dimensional equivalent model of the axial flux permanent magnet motor, specifically comprising the following steps of,
a step (B21) of dividing the axial flux permanent magnet motor into n equal two-dimensional segments, wherein the torque of the ith two-dimensional segment is shown as a formula (7),
wherein T is i Represents the torque of the ith two-dimensional segment, K represents the sum of m 1 、I a 、N 1 、k w1 Related constants, B avg-i Represents the average flux density of the ith two-dimensional segment, R out-i Represents the outer diameter of the ith model, R in-i Represents the inner diameter of the ith model, L represents the radial thickness of each model, r i Representing the equivalent radius of the ith model;
step (B22) of obtaining the average magnetic density B of the model based on the torque of each model avg-i And r i The torque of the kth model is shown as a formula (8);
wherein T is k Representing the torque of the kth model, g k Represents an air gap correction coefficient, B avg-k Represents the average flux density of the kth two-dimensional segment, B avg 2-D Representing the average flux density of the two-dimensional equivalent model;
step (B23), the torque of the ith model is shown as a formula (9), the torques of the n models are summed to obtain a corrected torque which is shown as a formula (10),
wherein T is i Representing the torque of the ith model, T c Indicating corrected torque g l And the correction coefficient representing the end effect of the three-dimensional motor.
4. A multi-objective optimization method based on a two-dimensional equivalent model of an axial flux permanent magnet motor according to claim 3, wherein: step (C) of determining an optimization target, a design parameter and a constraint condition based on the obtained equivalent coefficient equation, wherein the optimization target is a torque T avg Maximum, efficiency ηmaximum and torque ripple T rip Minimum is an optimization target; the optimized variable is the pole arc coefficient W of the permanent magnet PM Thickness H of permanent magnet PM Width B of notch s0 Groove width B s1 Slot height H s0 Height H of slot wedge s1 And groove depth H s2 Is a design parameter; the constraint is as shown in the formula (11),
5. the multi-objective optimization method based on the two-dimensional equivalent model of the axial flux permanent magnet motor according to claim 4, wherein the method comprises the following steps: step (D), dividing the design parameters into significant parameters and non-significant parameters according to the sensitivity, wherein the sensitivity index G j (x i ) And integrated sensitivity S (x i ) As shown in the formula (12) and the formula (13), respectively,
S(x i )＝λ j |G j (x i )| (13)
wherein x is i Representing design parameters, E (yj/xi) representing an optimization objective y j Average value of V (E (y) j /x i ) (1) represents E (y) j /x i ) Variance of (V) (y j ) Representing the variance, x of the optimization objective i Representing design parameters lambda j Representing the weights of the optimization targets.
6. The multi-objective optimization method based on the two-dimensional equivalent model of the axial flux permanent magnet motor according to claim 5, wherein the method comprises the following steps: step (E), obtaining an agent model of an optimization target for the significant parameters by using a response surface method, optimizing the agent model of the optimization target by adopting a gray wolf optimization algorithm, specifically comprising the following steps of,
step (E1), obtaining a proxy model of an optimization target for the significant parameters by using a response surface method, wherein the proxy model is specifically constructed by adopting a Box-Behnken Design method;
step (E2), adopting a gray wolf optimization algorithm to optimize the agent model of the optimization target, specifically comprising the following steps of,
step (E21), initializing the gray wolf population by using a Tent chaotic map, wherein the Tent chaotic map expression is shown in a formula (14),
wherein N represents the number of particles in the sequence, and rand (0, 1)/N represents a random variable;
a step (E22) of modifying the linear search process by using the nonlinear control parameter a, wherein the modified control parameter formula is shown as formula (15),
wherein a (t) represents the modified control parameter, t represents the current iteration number, and M represents the maximum iteration number;
step (E23), adding weight coefficients to alpha wolf, beta wolf and delta wolf in the Hunting of the wolf, wherein the weight coefficients are shown in a formula (16),
wherein θ i Representing the weight, ω, of each head wolf i Representing the ratio between the position of the individual wolf relative to the fitness of alpha wolves and delta wolves, f representing the fitness of the wolves;
in the step (E24), when the position of the head wolf is updated, an independent updating mode is adopted for the alpha wolf, the beta wolf and the delta wolf respectively, the specific updating mode is as follows,
step (E241), delta wolf is guided by alpha wolf and beta wolf, the updating mode of delta wolf is shown as formula (17),
X δ (t+1)＝D δ -X δ (t)，D δ ＝ρX δ (t)+(1-ρ)X α (t)+(1-ρ)X β (t) (17)
wherein X is δ (t+1) represents the position of δwolf after update; x is X α (t)、X β (t) and X δ (t) represents the current positions of alpha wolf, beta wolf and delta wolf, respectively, and ρ represents the distribution of [0,1 ]]Random numbers in (a);
step (E242), beta wolf is guided by alpha wolf, the position is updated by using a spiral update mechanism, the beta wolf update mode is shown in formula (18),
X β (t+1)＝|X α (t)-X β (t)|e bl cos(2πl)+ρX α (t) (18)
wherein X is β (t+1) represents the position of beta wolf after updating, b represents a logarithmic spiral shape function, and l represents [ -1,1 []Random numbers in (a);
step (E243), alpha wolf is not guided by other wolves, alpha wolf is updated by using the Levy flight method as shown in formula (19),
wherein X is best (t+1) represents the updated optimal position, μ represents a step size control factor,represents a dot product, and Levy (λ) represents a random search path.
7. The multi-objective optimization method based on the two-dimensional equivalent model of the axial flux permanent magnet motor according to claim 6, wherein the method comprises the following steps: and (F) optimizing the non-significant parameter by using parameter scanning, and obtaining the optimal parameter, wherein the non-significant parameter optimization is performed after the significant parameter optimization is completed.
8. A multi-objective optimization system based on a two-dimensional equivalent model of an axial flux permanent magnet motor, wherein the operation process of the optimization system adopts the optimization method based on claims 1-7, and the multi-objective optimization system is characterized in that: the system comprises a two-dimensional equivalent module, an equivalent coefficient equation introduction module, a parameter determination module, a parameter distinguishing module, a first parameter processing module, a second parameter processing module and an optimization verification module, wherein the two-dimensional equivalent module is used for expanding and equivalent an axial flux permanent magnet motor into a two-dimensional linear motor along an equivalent radius;
the equivalent coefficient equation introduction module is used for introducing an equivalent coefficient equation based on the obtained two-dimensional linear motor and according to the error between the axial flux permanent magnet motor three-dimensional model and the two-dimensional equivalent model;
the parameter determining module is used for determining an optimization target, design parameters and constraint conditions according to the obtained equivalent coefficient equation;
the parameter distinguishing module is used for dividing design parameters into significant parameters and non-significant parameters according to the sensitivity;
the first parameter processing module is used for obtaining a proxy model of an optimization target for the significant parameters by using a response surface method, and optimizing the proxy model of the optimization target by adopting a gray wolf optimization algorithm;
the second parameter processing module is used for optimizing the non-significant parameter using parameter scanning and obtaining an optimal parameter;
the optimization verification module is used for carrying out finite element analysis on the optimized motor and comparing the comprehensive performance of the optimized motor and the original motor to verify the effectiveness of optimization.
9. The multi-objective optimization system based on a two-dimensional equivalent model of an axial flux permanent magnet motor according to claim 8, wherein: the parameter distinguishing module is used for distinguishing the design parameters determined by the parameter determining module and separating the design parameters into significant parameters and non-significant parameters according to the sensitivity.
10. The multi-objective optimization system based on a two-dimensional equivalent model of an axial flux permanent magnet motor according to claim 9, wherein: the first parameter processing module is used for processing the significant parameters distinguished by the parameter distinguishing module, and the second parameter processing module is used for processing the non-significant parameters distinguished by the parameter distinguishing module.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311675268.0A CN117634397B (en) | 2023-12-01 | 2023-12-01 | Multi-objective optimization method and system based on two-dimensional equivalent model of axial flux permanent magnet motor |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311675268.0A CN117634397B (en) | 2023-12-01 | 2023-12-01 | Multi-objective optimization method and system based on two-dimensional equivalent model of axial flux permanent magnet motor |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN117634397A true CN117634397A (en) | 2024-03-01 |
| CN117634397B CN117634397B (en) | 2024-05-28 |
Family
ID=90026690
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202311675268.0A Active CN117634397B (en) | 2023-12-01 | 2023-12-01 | Multi-objective optimization method and system based on two-dimensional equivalent model of axial flux permanent magnet motor |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN117634397B (en) |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111327170A (en) * | 2018-12-14 | 2020-06-23 | 南京理工大学 | Modeling method for equivalent magnetic circuit of hybrid excitation axial flux switching motor |
| CN112861427A (en) * | 2021-01-15 | 2021-05-28 | 湖南科技大学 | Permanent magnet synchronous motor parameter identification method based on improved wolf optimization algorithm |
| US20220043950A1 (en) * | 2020-05-27 | 2022-02-10 | Jiangsu University | Parametric equivalent magnetic network modeling method for multi objective optimization of permanent magnet motor |
| CN114726284A (en) * | 2022-04-28 | 2022-07-08 | 南京信息职业技术学院 | Construction method of surface-mounted bearingless permanent magnet motor rotor displacement estimator |
| CN114757112A (en) * | 2022-06-16 | 2022-07-15 | 佛山仙湖实验室 | Motor parameter design method and system based on Hui wolf algorithm |
| CN116257724A (en) * | 2023-02-13 | 2023-06-13 | 南京师范大学 | Calculation method for end effect of surface-mounted permanent magnet motor |
| CN116822095A (en) * | 2023-07-13 | 2023-09-29 | 东南大学 | Magnetic circuit modeling method for double-stator single-rotor axial permanent magnet motor |
-
2023
- 2023-12-01 CN CN202311675268.0A patent/CN117634397B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111327170A (en) * | 2018-12-14 | 2020-06-23 | 南京理工大学 | Modeling method for equivalent magnetic circuit of hybrid excitation axial flux switching motor |
| US20220043950A1 (en) * | 2020-05-27 | 2022-02-10 | Jiangsu University | Parametric equivalent magnetic network modeling method for multi objective optimization of permanent magnet motor |
| CN112861427A (en) * | 2021-01-15 | 2021-05-28 | 湖南科技大学 | Permanent magnet synchronous motor parameter identification method based on improved wolf optimization algorithm |
| CN114726284A (en) * | 2022-04-28 | 2022-07-08 | 南京信息职业技术学院 | Construction method of surface-mounted bearingless permanent magnet motor rotor displacement estimator |
| CN114757112A (en) * | 2022-06-16 | 2022-07-15 | 佛山仙湖实验室 | Motor parameter design method and system based on Hui wolf algorithm |
| CN116257724A (en) * | 2023-02-13 | 2023-06-13 | 南京师范大学 | Calculation method for end effect of surface-mounted permanent magnet motor |
| CN116822095A (en) * | 2023-07-13 | 2023-09-29 | 东南大学 | Magnetic circuit modeling method for double-stator single-rotor axial permanent magnet motor |
Non-Patent Citations (1)
| Title |
|---|
| 刘细平 等: ""基于转子永磁分段优化的轴向磁通永磁电机涡流损耗分析与试验研究"", 《电工技术学报》, 4 August 2023 (2023-08-04) * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN117634397B (en) | 2024-05-28 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| WO2020108411A1 (en) | Method for evaluating electromagnetic properties of permanent magnet motor | |
| Yan et al. | Design and multi‐objective optimisation of switched reluctance machine with iron loss | |
| Diao et al. | Robust-oriented optimization of switched reluctance motors considering manufacturing fluctuation | |
| CN112600375A (en) | Multi-objective optimization method of novel alternating-pole brushless hybrid excitation motor | |
| Yu et al. | Torque performance improvement for slotted limited-angle torque motors by combined SMA application and GA optimization | |
| Dianati et al. | Analytical design of axial-flux induction motors | |
| Sun et al. | Multiobjective optimization of IPMSM with FSCW applying rotor notch design for torque performance improvement | |
| Abdollahi et al. | A multi-objective optimization framework for the design of a high power-density switched reluctance motor | |
| JP5884160B2 (en) | Performance analysis method of motor for hybrid vehicle | |
| CN117634397B (en) | Multi-objective optimization method and system based on two-dimensional equivalent model of axial flux permanent magnet motor | |
| Shao et al. | Design and optimisation of energy‐efficient PM‐assisted synchronous reluctance machines for electric vehicles | |
| Chen et al. | A computationally efficient multi-physics optimization technique for permanent magnet machines in electric vehicle traction applications | |
| CN113420386A (en) | Vehicle driving motor robustness optimization design method based on interpolation model and multi-objective genetic algorithm | |
| CN113434958A (en) | Magnetic suspension flywheel motor multi-target optimization method based on heterogeneous integrated proxy model | |
| Verma et al. | Integrated Taguchi method‐assisted polynomial Metamodelling & Genetic Algorithm based optimisation of a surface inset permanent synchronous motor for performance improvement | |
| Nobahari et al. | Optimal Shaping of Non-Conventional Permanent Magnet Geometries for Synchronous Motors via Surrogate Modeling and Multi-Objective Optimization Approach. | |
| Sardar et al. | Robust Design Optimization of an IPM Synchronous Motor for Electric Vehicle Applications | |
| Wang et al. | Sensitivity analysis for performance and power density improvements in salient-pole synchronous generators | |
| CN111859574B (en) | Synchronous reluctance motor rotor optimization design method for reducing torque pulsation | |
| Ruzbehi et al. | Hybrid Structure Optimization of a PMSM Using Global and Local Methods for Higher Torque and Lower Volume | |
| Li et al. | Improving thermal analysis accuracy of LPTN for vehicle claw-pole alternator by calibrating forced convection coefficients based on experimental results | |
| Msaddek et al. | Optimal design and cogging torque minimization of a permanent magnet motor for an electric vehicle | |
| Mazloum et al. | Wound field synchronous drive cycle current parameters optimization: A metamodel-based approach | |
| Sardar et al. | State-of-the-Art Design Optimization of an IPM Synchronous Motor for Electric Vehicle Applications | |
| Xu et al. | Rotor topology optimization of a synchronous reluctance motor based on deep neural network model |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |