CN112968582B - Low-vibration permanent magnet brushless motor optimization design method - Google Patents

Low-vibration permanent magnet brushless motor optimization design method Download PDF

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CN112968582B
CN112968582B CN202110243749.9A CN202110243749A CN112968582B CN 112968582 B CN112968582 B CN 112968582B CN 202110243749 A CN202110243749 A CN 202110243749A CN 112968582 B CN112968582 B CN 112968582B
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朱孝勇
朱庭辉
项子旋
周雪
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Jiangsu University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K29/00—Motors or generators having non-mechanical commutating devices, e.g. discharge tubes or semiconductor devices
    • H02K29/03—Motors or generators having non-mechanical commutating devices, e.g. discharge tubes or semiconductor devices with a magnetic circuit specially adapted for avoiding torque ripples or self-starting problems
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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Abstract

The invention discloses an optimized design method of a low-vibration permanent magnet brushless motor applied to an electric automobile, which designs the rotating speed of the motor to be more than five times of the basic speed, respectively changes single design variables in an initial range, sets other design variables except the single design variables as initial values, obtains stress sigma corresponding to the single design variables through simulation, compares the stress sigma with ultimate yield strength G, selects a maximum range meeting a constraint condition sigma smaller than or equal to G in the initial range of the single design variables as an accurate range, constructs an optimized model with the minimum radial harmonic order, the maximum torque and the minimum torque ripple by taking the minimum radial electromagnetic force harmonic order and the torque ripple as variable targets, ensures the high mechanical strength of a rotor, has the advantages of high efficiency, high efficiency and high reliability, high reliability of the motor is ensured, and low vibration characteristics are directly and efficiently realized while output performance is ensured.

Description

Low-vibration permanent magnet brushless motor optimization design method
Technical Field
The invention belongs to the field of motor design, and particularly relates to an optimal design method of a permanent magnet brushless motor applied to an electric automobile.
Background
Electric vehicles have become one of the important development directions in the automotive field in recent years due to their advantages of high efficiency, energy saving, environmental protection, etc. Because the driving motor in the electric automobile replaces the traditional internal combustion engine, the vibration noise is more obvious, and the whole noise, vibration and comfortable performance of the electric automobile are directly influenced, so that the requirements of high comfort and high reliability of the electric automobile put forward more rigorous performance requirements on the motor and a driving system thereof. At present, the permanent magnet brushless motor is widely applied to the field of electric vehicles due to the advantages of high power density, high efficiency and the like. However, the permanent magnet motor is designed to pursue high torque density and light weight, and the structural unreasonable problems of poor rigidity, high vibration noise and the like are caused, and the rigidity and the vibration noise determine the life cycle and the application occasion of the permanent magnet motor, so that the development of the permanent magnet motor in the field of electric automobiles is restricted to a certain extent.
Chinese patent No. 201620060777.1 proposes a novel low-vibration-noise fault-tolerant flux switching motor, which adopts a double-fault-tolerant tooth structure to reduce the vibration noise of the motor, however, the vibration noise is reduced, which not only results in the reduction of the output torque of the motor, but also consumes a lot of time for the design of the motor structure. The document "Design and optimization of a permanent magnet synchronous machine for low vibration and noise applications" (published in 2018, IEEE ICEMS, 280, 284, doi:10.23919/ICEMS.2018.8549128) proposes a parameter scanning motor optimization method, which reduces vibration and considers torque output capability, but the method changes the motor structure but does not consider the mechanical strength of the rotor, and easily causes the motor to have faults such as severe deformation and even breakage under the condition of high speed.
Therefore, the current motor optimization design method cannot be considered comprehensively, and the requirements of low vibration and high reliability of the vehicle driving motor are difficult to meet completely. Therefore, how to obtain a driving motor with low vibration and high reliability on the premise of ensuring the basic electromagnetic performance is still a problem to be solved in the field of driving motors for vehicles.
Disclosure of Invention
The invention aims to solve the problems of the existing motor optimization design method, and provides a high-reliability low-vibration permanent magnet brushless motor optimization design method which can directly and efficiently realize low-vibration characteristics while ensuring output performance
In order to achieve the purpose, the invention discloses an optimal design method of a low-vibration permanent magnet brushless motor, which adopts the following technical scheme: determining a design variable to be optimized and an initial range of the design variable of the permanent magnet brushless motor, and obtaining the ultimate yield strength G of a silicon steel sheet according to the silicon steel sheet material of the motor, wherein the method further comprises the following steps:
step 1) designing the rotating speed of a motor to be more than five times of a basic speed, setting initial values of design variables, respectively enabling the single design variables to change in the initial ranges, setting the other design variables except the single design variable to be the initial values, and obtaining stress sigma corresponding to the single design variable through simulation;
step 2) comparing the stress sigma with the ultimate yield strength G, and selecting a maximum range which meets a constraint condition sigma and is not more than G in the initial range of a single design variable, wherein the maximum range is used as an accurate range of the design variable;
step 3) carrying out analytic derivation on the radial electromagnetic force of the motor to obtain the lowest order Q of harmonic waves of the radial electromagnetic forceth；
Step 4) leading the harmonic wave of the radial electromagnetic force to have the lowest order QthTorque T and torque ripple Tr as variable targets to construct the lowest order Q of harmonic of radial electromagnetic forcethThe minimum, the maximum and the minimum torque ripple Tr, and the constraint condition of the optimization model is that the design variable is in the accurate range.
Further, in step 1), the initial value of the design variable is an average value of the minimum value and the maximum value of the initial range.
Further, in the step 4), in the accurate range, the optimized design variables are determined through a multi-objective genetic algorithm.
Further, an initial population H [ H ] of the genetic algorithm is generated by simulation1,h2…he]In the initial population H [ H ]1,h2…he]Selecting, heredity and mutation to obtain non-inferior solution set conforming to the optimized model, wherein in the non-inferior solution set, the solution with the most occurrence times of the non-inferior solution is the optimized design variable, and h is1[Qth,T,Tr],h2[Qth,T,Tr]…he[Qth,T,Tr]Is the individual in the population, and e is the size of the population.
After the technical scheme is adopted, the invention has the beneficial effects that:
1. when the motor operates at a high speed of five times or more of the base speed, before optimization, the precise range of the design variable is determined according to the ultimate strength of the silicon steel sheet, the ultimate yield strength of the silicon steel sheet is used as a constraint condition to obtain the precise range of the design variable, and in the range, the high mechanical strength of the rotor is ensured, and the high reliability of the motor is ensured. The invention avoids the problems that the traditional optimization method does not conform to the mechanical strength after the optimization is completed and the work is repeated. The method solves the problems of incomplete consideration and time-consuming optimization in the traditional design optimization method.
2. The invention takes the optimized leading radial electromagnetic force harmonic amplitude as a means for optimizing vibration, directly and effectively reduces the vibration of the motor fundamentally, can directly and efficiently realize the low vibration characteristic while ensuring the output performance, overcomes the defects of repeated trial and error and time consumption in the traditional vibration reduction mode, and provides a general method for realizing the low vibration characteristic of the motor.
3. The invention introduces a multi-objective genetic algorithm, realizes the low-vibration and high-reliability performance of the motor, ensures the torque output capability of the motor, and improves the overall design optimization efficiency of the motor in the whole process.
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The invention is described in further detail below with reference to the figures and the detailed description;
FIG. 1 is a flow chart of an optimized design method for a low-vibration permanent magnet brushless motor according to the present invention;
FIG. 2 is a schematic diagram of an example of an interior permanent magnet brushless motor;
FIG. 3 is an enlarged view of the rotor of FIG. 2 showing the partial structure and design variables to be optimized;
FIG. 4 is a radial electromagnetic force harmonic profile of the motor of FIG. 2;
FIG. 5 is a schematic diagram of a non-inferior solution set based on a multi-objective optimization genetic algorithm;
in the figure: 1. a stator; 2. a rotor; 3. neodymium iron boron permanent magnet steel; 4. a magnetic barrier; 5. a rotating shaft.
Detailed Description
Referring to fig. 1, the design variables of the permanent magnet brushless motor to be optimized and the initial ranges of the corresponding design variables are first determined.
For a permanent magnet brushless motor with a basic structure, determining the design variable to be optimized as m1，m2,…miAnd i is the number of design variables. For example, the design variables may be the permanent magnet length, width, the size of the magnetic separation bridge between two permanent magnets, the size of the magnetic ribs, the size of the magnetic barriers, etc. In the initial stage of motor design, according to design power requirements and design experience, the initial range corresponding to each design variable is obtained as [ a ]1，b1]，[a2，b2],…[ai，bi]I.e. design variable miHas an initial range of [ a ]i，bi]，aiAnd biThe minimum and maximum values of the initial range of design variables, respectively.
The silicon steel sheet material of the permanent magnet brushless motor is a known selected model, and the ultimate yield strength of the silicon steel sheet is found to be G in MPa in the existing literature data. Determining each design variable m by using the ultimate yield strength G of the silicon steel sheet as a constraint1，m2,…miThe precise range of (2). The rated rotating speed of the permanent magnet brushless motor is n revolutions per minute, the high rotating speed generally meets more than five times of the basic speed, and due to the fact that the risk of deformation and breakage exists in the motor rotor at high speed, in order to ensure the reliability of the motor, the accurate range of the design variable is further obtained. In a Static structure module (Static structure) of the Ansys Workbench software, the rotating speed of a motor is set to Xn revolutions per minute, X is an integer greater than or equal to 5, and stress is set to sigma [ m ]1，m2,…mi]。
Design variable m1，m2,…miThe initial value given is the average of the minimum and maximum values of the initial range of the design variable, i.e. the initial value is (a)1+b1)/2，(a2+b2)/2…(ai+bi)/2. For a single design variable miIn the initial range [ a ]i，bi]Inner variation, other than the single design variable miThe external design variables are all set as initial values, and the design variable m corresponding to the single design variable is obtained through software simulationiStress of (a) [ (a)1+b1)/2,(a2+b2)/2,…mi]And miThe variation relationship of (a).
Judging the single design variable m by using the ultimate yield strength G as a constraintiCorresponding stress σ [ (a)1+b1)/2,(a2+b2)/2,…mi]And the ultimate yield strength G, and comparing the two, when the stress is sigma [ (a)1+b1)/2,(a2+b2)/2,…mi]When the stress is less than or equal to G, namely the corresponding stress is less than or equal to the ultimate yield strength G, the requirement of mechanical strength is met, and a single design variable miInitial range of [ a ]i，bi]Inner selection satisfies constraint condition sigma [ (a)1+b1)/2,(a2+b2)/2,…mi]The maximum range less than or equal to G is the design variable miPrecise range of [ c ]i，di]。
Similarly, the initial range [ a ] can be set1，b1]，[a2，b2],…[ai-1，bi-1]Reducing to obtain the precise range of the design variable correspondingly as [ c1，d1]，[c2，d2],…[ci-1，di-1]. In the precise range [ c1，d1]，[c2，d2],…[ci，di]The mechanical strength of the motor is ensured, the range is narrowed, and the time is saved for the following optimization.
On the premise of ensuring the high reliability of the motor, the vibration performance of the motor is optimally designed. The radial electromagnetic force is the main reason for generating vibration, and the harmonic wave lowest order Q of the radial electromagnetic force for generating motor vibration is obtained by analyzing and deducing the radial electromagnetic forcethAnd takes it as one of the optimization objectives. The derivation process does not need to quantitatively calculate the specific amplitude of the radial electromagnetic force, and only needs to qualitatively determine the lowest order Q of the harmonic wave of the radial electromagnetic forceth。
Radial electromagnetic force P according to Maxwell stress-strain methodr(θ, t) is:
Figure BDA0002963301960000041
in the formula, br(θ, t) is the radial air gap flux density, br 2(θ, t) is brSquare of (theta, t), bt(θ, t) is the tangential air gap flux density, bt 2(θ, t) is the square of b due to the tangential air gap flux densitytThe smaller amplitude of (theta, t) is generally ignored, theta is the mechanical angle, t is the time, and the vacuum permeability mu0＝4π×10-7。
Radial air gap flux density br(θ, t) is:
br(θ,t)＝[fPM(θ,t)+fARM(θ,t)]×Λs(θ) (2)
Figure BDA0002963301960000042
Figure BDA0002963301960000043
Figure BDA0002963301960000044
in the formula (f)PM(θ,t),fARM(theta, t) are the permanent magnet magnetomotive force and the armature magnetomotive force, respectively, mu and v are the magnetomotive force harmonic orders of the permanent magnet field and the armature field, respectively, FμAnd FνThe amplitude of the mu-th order permanent magnetic field magnetomotive force harmonic wave and the amplitude of the v-th order armature field magnetomotive force harmonic wave are respectively, p and alpha are respectively the number of pole pairs and the number of units of the motor, omega is the current angular frequency, SνRepresenting the rotation direction of the motor (1 is positive direction, -1 is reverse direction), z is the number of slots of the stator of the motor, and Λs(theta) is the air gap permeance, Lambda, taking into account the notching effect0Is the average permeance value, ΛkThe k-th harmonic permeance amplitude is defined as an integer of 1,2,3 ….
Substituting the formulas (2), (3), (4) and (5) into the formula (1) to obtain the radial electromagnetic force PrThe expansion of (θ, t) is:
Figure BDA0002963301960000051
to distinguish partial items, e.g. FμMultiplying by the square, and then expanding, wherein mu is mu1And mu2(μ1＝μ2) Or (mu)1≠μ2)，ν1V and v2，k1And k2Similarly, v is v1V and v2K is k1And k2. By the development analysis of the formula, the radial electromagnetic force P can be derivedrThe main sources of (theta, t) are the permanent magnet field, the armature field and the stator slotThe effect is generated, and the harmonic order expression is as follows:
μp±να±kz (7)
in the formula (7), the harmonic lowest order Q of the radial electromagnetic force is further obtainedthAnd because the amplitude of the vibration is inversely proportional to the fourth power of the harmonic order of the radial electromagnetic force, the lower the harmonic order of the radial electromagnetic force is, the greater the influence on the vibration is. Obtaining radial electromagnetic force through maxwell finite element software simulation, carrying out FFT decomposition, and confirming QthThe harmonic of the radial electromagnetic force of the order is the harmonic of the lowest order, and Q is confirmedthThe order radial electromagnetic force harmonics are one of the optimization objectives.
And finally, in order to ensure the torque output performance of the motor while having the characteristics of low vibration and high reliability, an optimization model is constructed, and the optimal size of the motor is determined through a multi-objective genetic algorithm. Leading radial electromagnetic force harmonic Q in maxwell softwarethTorque T and torque ripple Tr are set as variable targets that are in the precise range [ c ] with i design variables1，d1],[c2，d2],…[ci，di]Internal variation, simulation generation of initial population H [ H ] of genetic algorithm1,h2…he]Wherein h is1[Qth,T,Tr],h2[Qth,T,Tr]…he[Qth,T,Tr]Is the individual in the population, and e is the size of the population. According to design requirements, harmonic lowest order Q of radial electromagnetic forcethThe smaller the motor vibration, the better the torque T, and the better the torque ripple Tr, thereby constructing the lowest order Q of the harmonic wave of the radial electromagnetic forcethAn optimized model with minimum torque, maximum torque and minimum torque ripple Tr and the constraint condition of the optimized model is a design variable m1，m2,…miIn the precise range [ c1，d1]，[c2，d2],…[ci，di]And (4) the following steps. The optimization model and constraint conditions are as follows:
Figure BDA0002963301960000052
in the multi-objective optimization problem, it is difficult to simultaneously achieve the optimization by a plurality of optimization objectives, and even a unique optimal solution does not exist, so the multi-objective optimization needs to balance each objective. Further, a genetic algorithm is adopted to perform the initial population H [ H ]1,h2…he]And (4) selecting, heredity and mutation to finally obtain a non-inferior solution set C which accords with the optimization model. And in the non-inferior solution set C, selecting a solution with the most occurrence times of non-inferior solutions, and determining the size of the optimized design variable of the motor by combining with actual design requirements, thereby obtaining a final motor optimized structure.
One embodiment of the invention is provided below:
in order to clearly illustrate the optimal design method of the present invention and facilitate understanding of those skilled in the art, the present invention takes a conventional interior permanent magnet brushless motor as an example, and describes the optimal design method of the low vibration permanent magnet brushless motor in detail. The structure of the built-in permanent magnet brushless motor is shown in figure 2, the motor comprises an outer stator 1 and an inner rotor 2, the inner rotor 2 is coaxially sleeved outside a rotating shaft 5, and permanent magnets 3 arranged in a V shape are embedded in the inner rotor 2 and provided with magnetic barriers 4. In a radial section, the permanent magnet 3 is provided with magnetic barriers 4 on both sides in the length direction, and the magnetic barrier 4 on the inner side is close to the rotating shaft 5, and the magnetic barrier 4 on the outer side is opposite to the magnetic barrier 4 on the inner side. The permanent magnets 3 are arranged in a V shape to increase the air gap flux density, and the magnetic barriers 4 are designed to reduce the flux leakage and further increase the utilization rate of the permanent magnets 3. The outer stator 1 and the inner rotor 2 adopt a 36-pole/8-slot combination mode, the outer stator 1 is wound with a three-phase winding, and the three-phase winding adopts a double-layer distributed mode, so that the electromagnetic performance is improved. The optimal design process for the interior permanent magnet brushless motor shown in fig. 2 includes the following steps:
step 1: and determining the design variable to be optimized of the built-in permanent magnet brushless motor. As shown in fig. 3, after determining the initial structure of the motor, the length of the permanent magnet 3 in the radial section is selected to be Lpm, the width of the permanent magnet 3 in the radial section is selected to be Hpm, and the width of the magnetic separation bridge between two permanent magnets 3 is selected to be O1Magnetic rib thickness of D1(i.e. the minimum distance between the outer barriers 4 and the outer wall of the inner rotor 2), the width between the two outer barriers 4 is Rib, and the inner magnetic fieldThe minimum distance between the barrier 4 and the outer wall of the rotating shaft 5 is O2As design variables to be optimized, their initial ranges, determined from previous design experience and references, are Lpm of [8, 13 ] respectively]And Hpm is [3, 5 ]]，O1Is [0, 4 ]]，D1Is [0, 3 ]]Rib is [2, 6 ]]，O2Is [7, 13 ]]In mm.
Step 2: and determining the ultimate yield strength of the silicon steel sheet used for the motor. The model of the silicon steel sheet for the motor is DW470, and the ultimate yield strength G of the silicon steel sheet of the material is 235MPa by inquiring relevant information.
And step 3: and determining the accurate range of each design variable through the ultimate yield strength G of the silicon steel sheet. The rated rotating speed of the motor is designed to be 1200 rpm, the high speed generally meets over five times of the basic speed, and the embodiment selects 6000 rpm. The simulation was performed in the Ansys Workbench with a speed of 6000 rpm and stress σ [ Lpm, Hpm, O1,D1,Rib,O2]. Design variables Lpm, Hpm, O1，D1，Rib，O2The initial values given are the average values of the corresponding initial ranges, respectively, 10.5,4, 2,1.5,4, 10. For the design variable Lpm, in the initial range [8, 13 ]]Internal variation, other design variables except Lpm are set to initial values, i.e. Hpm, O1，D1，Rib，O2Initial values of 4,2,1.5,4,10, respectively. Obtaining the stress sigma [ Lpm,4,2,1.5,4,10 of the design variable Lpm through software simulation]In relation to Lpm change, stress σ [ Lpm,4,2,1.5,4,10, with an ultimate yield strength G of 235MPa as a constraint]When compared to ultimate yield strength G, stress σ [ Lpm,4,2,1.5,4,10]When the pressure is less than or equal to 235Mpa, the requirement of mechanical strength is met, and the initial range is [8, 13 ]]The maximum range of the internal selection satisfying the constraint condition G is [8.3, 12.5 ]]I.e. the precise range of the design variable Lpm.
Similarly, for design variable Hpm, at the initial range [3, 5 ]]The internal variables, other than Hpm, are set to initial values, Lpm, O1，D1，Rib，O2The initial values given are 10.5, 2,1.5,4,10, respectively, thus yielding a stress σ [10.5, Hpm,2,1.5,4,10 ] for the design variable Hpm]In a varying relationship with respect to Hpm,stress sigma [10.5, Hpm,2,1.5,4,10 ]]The maximum range of design variable Hpm was found to be [3.2, 5 ] compared to the ultimate yield strength G]。
Repeating the design to obtain a design variable O1，D1，Rib，O2Are in respective precise ranges of [0.5, 4 ]]，[0.5，3]，[3，5]，[8，13]. The initial range of the design variable is reduced to obtain respective accurate range, the mechanical strength of the motor is guaranteed in the accurate range, the range is reduced, and time is saved for later optimization.
And 4, step 4: by selecting the target to be optimized, and by performing the development analysis on the formula (6) of the radial electromagnetic force, it can be deduced that the main source of the radial electromagnetic force is generated by the interaction of the permanent magnetic field, the armature field and the stator slot, and the harmonic order expression is formula (7): μ p ± ν α ± kz. Taking the 36 slot/8 pole motor as an example, the number z of the stator slots is 36, the number P of the pole pairs is 4, the number α of the motor units is 4, the harmonic order μ of the magnetomotive force of the permanent magnet field is 2m +1, m is 0,1,2 …, the harmonic order v of the magnetomotive force of the armature field is 3n +1, n is 0, ± 1, ± 2 …, and the 4 th order is the lowest order radial electromagnetic force harmonic appearing in the formula by substituting specific numerical values, for example: μ ═ 3, ν ═ 2, k ═ 0, μ p ± ν α ± kz ═ 3 × 4+ (-2) × 4+0 ═ 4. And because the amplitude of the vibration is inversely proportional to the fourth power of the harmonic order of the radial electromagnetic force, the lower the harmonic order of the radial electromagnetic force is, the greater the influence on the vibration is, and therefore the lowest order is dominant order 4th. As shown in fig. 4, radial electromagnetic force harmonic distribution is obtained through maxwell finite element software simulation, and the 4 th order radial electromagnetic force harmonic is the lowest order harmonic, which is consistent with theoretical derivation. The 4 th order radial electromagnetic force harmonic was identified as one of the optimization objectives.
And 5: and determining the optimal size of the motor through a multi-target genetic algorithm. Leading radial electromagnetic force harmonic 4 in maxwell softwarethTorque T and torque ripple Tr are set as variable sweep targets that vary as the variables change, 6 design variables Lpm, Hpm, O1，D1，Rib，O2In the precise range [8.3, 12.5 ]]，[3.2，5]，[0.5，4]，[0.5，3]，[3，5]，[8，13]Internal variation, simulation generationInitial population of genetic algorithm H [ H ]1,h2…he]Wherein h is1[4th,T,Tr],h2[4th,T,Tr]…he[4th,T,Tr]The population size e is set to 100 for the individuals in the population. According to design requirements, radial electromagnetic force harmonic 4 is dominantthThe smaller the motor vibration is, the larger the torque T is, the better the torque T is, and the smaller the torque pulse Tr is, the better the torque pulse Tr is, so that the constructed optimization model and the constraint conditions are as follows:
Figure BDA0002963301960000081
in the multi-objective optimization problem, it is difficult to simultaneously achieve the optimization by a plurality of optimization objectives, and even a unique optimal solution does not exist, so the multi-objective optimization needs to balance each objective. Further, a genetic algorithm is adopted to perform the initial population H [ H ]1,h2…he]The non-inferior solution set C which accords with the optimization model is finally obtained by selection, heredity and mutation, and is shown in figure 5. In the non-inferior solution set C, selecting a solution with the most occurrence times of non-inferior solutions, and finally determining the design variable size after the motor optimization by combining the actual design requirements as follows: lpm 11mm Hpm 3.5mm O1Is 2mm D11mm, Rib 4mm, O2Is 2 mm. At the moment, the amplitude of the fourth-order radial electromagnetic force of the motor is 22445N/m2The torque was 28.67Nm and the torque ripple was 12.1%. The optimized motor has the characteristics of low vibration and high reliability while ensuring the torque performance.
The optimization design method in the present invention has been described above with the motor in fig. 2 as an example, but the present invention is not limited to the motor in fig. 2, and is also applicable to motors having other configurations.

Claims (8)

1. An optimization design method of a low-vibration permanent magnet brushless motor determines a design variable to be optimized and an initial range of the design variable of the permanent magnet brushless motor, and obtains ultimate yield strength G of a silicon steel sheet according to a silicon steel sheet material of the motor, and is characterized by further comprising the following steps of:
step 1) designing the rotating speed of a motor to be more than five times of a basic speed, setting initial values of design variables, respectively enabling the single design variables to change in the initial ranges, setting the other design variables except the single design variable to be the initial values, and obtaining stress sigma corresponding to the single design variable through simulation;
step 2) comparing the stress sigma with the ultimate yield strength G, and selecting a maximum range which meets a constraint condition sigma and is not more than G in the initial range of a single design variable, wherein the maximum range is used as an accurate range of the design variable;
step 3) carrying out analytic derivation on the radial electromagnetic force of the motor to obtain the lowest order Q of harmonic waves of the radial electromagnetic forceth；
Step 4) leading the harmonic wave of the radial electromagnetic force to have the lowest order QthTorque T and torque ripple Tr as variable targets to construct the lowest order Q of harmonic of radial electromagnetic forcethThe minimum, the maximum and the minimum torque ripple Tr, and the constraint condition of the optimization model is that the design variable is in the accurate range.
2. The method for optimally designing the low-vibration permanent magnet brushless motor according to claim 1, wherein the method comprises the following steps of: in the step 1), the initial value of the design variable is the average value of the minimum value and the maximum value of the initial range.
3. The method for optimally designing the low-vibration permanent magnet brushless motor according to claim 1, wherein the method comprises the following steps of: and 4) determining the optimized design variable through a multi-objective genetic algorithm in the accurate range.
4. The method for optimally designing the low-vibration permanent magnet brushless motor according to claim 3, wherein the method comprises the following steps of: simulation generation of initial population H [ H ] of genetic algorithm1,h2...he]In the initial population H [ H ]1,h2...he]Selecting, heredity and mutation to obtain non-inferior solution set in the optimized modelAnd (c) concentrating the solution with the highest occurrence frequency of the non-inferior solutions as the optimized design variable, wherein h is1[Qth,T,Tr],h2[Qth,T,Tr]...he[Qth,T,Tr]Is the individual in the population, and e is the size of the population.
5. The method for optimally designing the low-vibration permanent magnet brushless motor according to claim 1, wherein the method comprises the following steps of: in the step 3), the radial electromagnetic force harmonic wave lowest order Q is obtained by the expression mu p +/-v alpha +/-kz of the radial electromagnetic force harmonic wave orderthMu and v are respectively the magnetomotive force harmonic orders of the permanent magnetic field and the armature field, p and alpha are respectively the number of pole pairs and the number of units of the motor, z is the number of slots of the stator of the motor, and k is the kth harmonic.
6. The method for optimally designing the low-vibration permanent magnet brushless motor according to claim 5, wherein the method comprises the following steps of: radial electromagnetic force
Figure FDA0003326007880000011
br(θ, t) is the radial air gap flux density,
Figure FDA0003326007880000012
is brSquare of (theta, t), bt(θ, t) is the tangential air gap flux density, bt 2(θ, t) is btSquare of (theta, t), tangential air gap flux density btThe (theta, t) amplitude is small and ignored, theta is the mechanical angle, t is the time, and the vacuum permeability mu0＝4π×10-7。
7. The method for optimally designing the low-vibration permanent magnet brushless motor according to claim 6, wherein the method comprises the following steps of: in step 3), the radial air gap flux density br(θ,t)＝[fPM(θ,t)+fARM(θ,t)]×Λs(theta), wherein, among others,
Figure FDA0003326007880000021
fPM(θ,t),fARM(θ, t) are eachIs a permanent magnet magnetomotive force and an armature magnetomotive force,
Figure FDA0003326007880000022
mu and v are the magnetomotive harmonic orders of the permanent magnetic field and the armature field, respectively, FμAnd FνThe amplitude of the mu-th order permanent magnetic field magnetomotive force harmonic wave and the amplitude of the v-th order armature field magnetomotive force harmonic wave are respectively, p and alpha are respectively the number of pole pairs and the number of units of the motor, omega is the current angular frequency, SνRepresenting the rotation direction of the motor, 1 is positive direction, -1 is reverse direction, z is the number of slots of the stator of the motor, and Λs(theta) is the air gap permeance, Lambda, taking into account the notching effect0Is the average permeance value, ΛkIs the k-th harmonic permeance amplitude.
8. The method for optimally designing the low-vibration permanent magnet brushless motor according to claim 7, wherein the method comprises the following steps of: radial electromagnetic force PrThe expansion of (θ, t) is:
Figure FDA0003326007880000023
obtaining a harmonic order expression mu p +/-v alpha +/-kz through an expansion formula, wherein mu is mu1And mu2V is v1V and v2K is k1And k2。
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