WO2022267111A1 - Magnetic field modulation type radial permanent magnet electric motor having high mechanical robustness, and multi-harmonic optimization design method therefor - Google Patents

Magnetic field modulation type radial permanent magnet electric motor having high mechanical robustness, and multi-harmonic optimization design method therefor Download PDF

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WO2022267111A1
WO2022267111A1 PCT/CN2021/106643 CN2021106643W WO2022267111A1 WO 2022267111 A1 WO2022267111 A1 WO 2022267111A1 CN 2021106643 W CN2021106643 W CN 2021106643W WO 2022267111 A1 WO2022267111 A1 WO 2022267111A1
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permanent magnet
torque
harmonic
magnetic field
rotor
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PCT/CN2021/106643
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French (fr)
Chinese (zh)
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陈前
廖继红
赵文祥
刘国海
徐高红
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江苏大学
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K1/00—Details of the magnetic circuit
    • H02K1/06—Details of the magnetic circuit characterised by the shape, form or construction
    • H02K1/22—Rotating parts of the magnetic circuit
    • H02K1/27—Rotor cores with permanent magnets
    • H02K1/2706—Inner rotors
    • H02K1/272—Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis
    • H02K1/274—Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis the rotor consisting of two or more circumferentially positioned magnets
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K1/00—Details of the magnetic circuit
    • H02K1/06—Details of the magnetic circuit characterised by the shape, form or construction
    • H02K1/22—Rotating parts of the magnetic circuit
    • H02K1/24—Rotor cores with salient poles ; Variable reluctance rotors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/05—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for damping motor oscillations, e.g. for reducing hunting
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
    • H02P21/28—Stator flux based control
    • H02P21/30—Direct torque control [DTC] or field acceleration method [FAM]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/10—Arrangements for controlling torque ripple, e.g. providing reduced torque ripple
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/14—Electronic commutators
    • H02P6/16—Circuit arrangements for detecting position
    • H02P6/18—Circuit arrangements for detecting position without separate position detecting elements
    • H02P6/182—Circuit arrangements for detecting position without separate position detecting elements using back-emf in windings
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K2201/00—Specific aspects not provided for in the other groups of this subclass relating to the magnetic circuits
    • H02K2201/03—Machines characterised by aspects of the air-gap between rotor and stator
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K2213/00—Specific aspects, not otherwise provided for and not covered by codes H02K2201/00 - H02K2211/00
    • H02K2213/03—Machines characterised by numerical values, ranges, mathematical expressions or similar information
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
    • Y02T10/64—Electric machine technologies in electromobility

Definitions

  • the invention relates to the design and optimization of a magnetic field modulation radial permanent magnet, in particular to a method for optimizing the mechanical strength of a rotor and the torque ripple of a motor, and belongs to the technical field of motor manufacturing.
  • magnetic field modulated permanent magnet motors have played a very important role in the fields of electric vehicles, aerospace, and rail transit. This is mainly due to the following salient features of magnetic field modulated permanent magnet motors, high output torque, high efficiency and high power density etc.
  • the magnetic field modulated permanent magnet motor uses a high magnetic energy product magnetic material to replace the traditional excitation winding, which not only eliminates the negative impact of the excitation winding, but also simplifies the mechanical structure of the motor, which improves the reliability of the motor and reduces the mechanical loss. Corresponding reduction.
  • stator permanent magnet type field modulated permanent magnet motor has attracted much attention due to its advantages of simple rotor structure, high mechanical strength, high efficiency and strong heat dissipation capacity, but it is worth noting that the permanent magnets and armature windings are located in the stator slots , which will reduce the area of the stator slot, thereby reducing the generation of electrical load and reducing the torque output capability of the motor. Therefore, in order to make full use of the rotor space, more and more scholars are devoting themselves to transferring the permanent magnets to the rotor, and propose a rotor permanent magnet magnetic field modulation permanent magnet motor.
  • Document CN104201852A proposes a winding complementary magnetic field modulation permanent magnet motor, which transfers the permanent magnet to the rotor, which will increase the area of the armature winding slot and improve the space utilization of the rotor. At the same time, the armature magnetic field and the permanent magnetic field are separated, The degree of magnetic saturation of the stator is alleviated, and the overload capacity of the motor is improved.
  • the document CN104201852A proposes a permanent magnet motor with complementary winding magnetic field modulation, which has the following disadvantages: the rotor module of the motor is provided with a magnetic modulation air gap, which makes the rotor structure separate, resulting in lower mechanical strength of the rotor; A rectangular magnetic block needs to be embedded inside the magnetic air gap. The magnetic block moves in the magnetic air gap.
  • a brush slip ring needs to be added on the rotor side to provide DC excitation current.
  • the brush slip ring has a complex structure and requires regular maintenance. ;
  • the torque ripple of the motor is large.
  • the existing torque ripple reduction methods mainly include rotor skew, optimized winding and adding virtual pole structure. These optimization methods will make the motor structure complicated, and the principle of torque ripple optimization is difficult to explain. Therefore, simplifying the structure of the motor and optimizing the torque ripple of the motor from the principle of torque ripple generation are the key research directions.
  • the purpose of the present invention is to propose a high mechanical robustness magnetic field modulation radial permanent magnet motor and its multi-harmonic optimization design method.
  • high mechanical robustness magnetic field modulation radial permanent magnet motor in order to improve the torque performance of the motor, an optimal design method of multi-air-gap harmonic motor is proposed.
  • the technical solution adopted in the present invention is: a highly mechanically robust magnetic field modulation type radial permanent magnet motor, including a stator and a rotor module inside the stator; the rotor module of the motor includes two rotor teeth and three permanent magnets,
  • the permanent magnet structure is an inverted T shape, which is regarded as a combination of a radial permanent magnet and a Halbach permanent magnet array; the two permanent magnets at the lower end are radially magnetized, and the magnetization direction is opposite, and the two permanent magnets are close to each other.
  • Radial permanent magnets are placed, with magnetic isolation bridges on both sides; or close to the rotor tooth wall, so that the magnetic isolation bridges are in the middle, and the radial permanent magnets in the middle are tangentially magnetized; at the same time, using the Halbach permanent magnet array at the lower end
  • the shielding effect prevents the permanent magnetic field from being closed in the rotor, and realizes the integrated processing of the rotor structure.
  • both the stator and the rotor of the motor have a salient pole structure, so both the permanent magnetic field and the armature reaction magnetic field are modulated by the salient poles of the stator and rotor, thereby generating more working harmonics.
  • Step 1 Perform permanent magnet air gap flux density and armature reaction air gap flux density analysis on the target motor, and determine the harmonic order and corresponding rotational speed of the permanent magnet air gap flux density and armature reaction air gap flux density;
  • Step 2 based on the air-gap magnetic field modulation principle, deduce the electromagnetic torque expression, and then derive the formulas of average torque and torque ripple;
  • Step 3 according to the average torque and torque ripple formula, analyze the influence of air gap harmonics on torque and torque ripple, and select the torque and torque ripple with greater influence as the optimization sub-goal;
  • Step 4 select key design parameters, and use finite element software to determine the range of parameters;
  • Step 5 using the Taguchi sensitivity analysis method to analyze the influence of the motor parameters on the sub-targets, and divide the design parameters into two layers according to the sensitivity;
  • Step 6 keep the low sensitivity parameters unchanged, and optimize the high sensitivity parameters by combining the response surface analysis method and the multi-objective backbone particle swarm optimization algorithm.
  • the electromagnetic torque in the step 2 is generated by the joint action of the electric load and the magnetic load with the same harmonic order and the same corresponding rotational speed, and the formula is expressed as follows:
  • D si is the inner diameter of the stator
  • l stk is the axial length of the motor
  • B gv is the magnetic load, that is, the amplitude of the v-th harmonic of the air-gap flux density of the permanent magnet
  • K sv is the v-th harmonic amplitude of the electric load, is the angle between the v-time magnetic load and the electric load; therefore, it is necessary to analyze the air-gap magnetic density generated by the permanent magnet and the air-gap magnetic density generated by the armature reaction respectively.
  • the permanent magnet air gap magnetic density in the step 1 can be obtained by the product of the magnetomotive force generated by the permanent magnet and the permeance of the stator side, wherein the magnetomotive force generated by the permanent magnet can be expressed as:
  • F RPMb and F RPMn are the Fourier coefficients of the magnetomotive force generated by the permanent magnet
  • n is the harmonic order of the magnetomotive force generated by the permanent magnet
  • P PM is the number of pole pairs of the permanent magnet
  • ⁇ is the phase angle
  • ⁇ 0 is the initial angle
  • ⁇ r is the angular velocity of the rotor
  • t is the time
  • the magnetic permeability of the stator side can be expressed as follows:
  • ⁇ s0 , ⁇ sb and ⁇ sk are the Fourier coefficients of the stator side permeance, k is the harmonic order of the stator side permeance, and P s is the number of stator slots; therefore, the air gap flux density produced by the permanent magnet Can be expressed as follows:
  • the air gap flux density is composed of two kinds of harmonics, namely the nP PM sub-harmonic with the speed of ⁇ r and
  • the air-gap magnetic density produced by the armature reaction in the step 1 can be obtained by the product of the magnetomotive force produced by the armature reaction and the permeance of the rotor side, wherein the air-gap magnetomotive force produced by the armature reaction can be obtained by Fu
  • the Liye decomposition is expressed as:
  • N RC is the number of turns of a phase winding
  • i is the harmonic order of the magnetomotive force generated by the armature reaction
  • ⁇ is the phase angle
  • D Ri is the Fourier coefficient of the magnetomotive force generated by the armature reaction
  • i A , i B , i C , i D , i E are the currents of A, B, C, D, and E phases respectively;
  • I Rmax is the current amplitude
  • P r is the number of rotor pole pairs
  • the Fourier expression of the air gap permeability on the rotor side is as follows:
  • ⁇ Rr0 , ⁇ Rrb , and ⁇ Rrp are the Fourier coefficients of the rotor-side air-gap permeance, and p is the harmonic order of the rotor-side permeance; therefore, the air-gap flux density generated by the armature reaction can be expressed as follows :
  • ⁇ 1 and ⁇ 2 can be expressed as :
  • ⁇ 1 and ⁇ 2 can be expressed as :
  • the speed of harmonic order 2i-1 is (P r ⁇ r /(2i-1)), and the harmonic order is (pP r +
  • the rotational speed of 2i-1) is ((p+1)P r ⁇ r /(pP r +(2i-1))), the harmonic order is
  • the rotational speed is (( p-1)P r ⁇ r /[pP r -(2i-1)]);
  • the harmonic order of 2i-1 is (-P r ⁇ r /(2i-1)), and the harmonic order is (2i-1+
  • the rotational speed of pPr) is ((p-1)P r ⁇ r /(pP r +(2i-1))), and the rotational speed of the harmonic order is
  • is ((p+ 1)P r ⁇ r /(pP r -(2i-1))).
  • the electromagnetic torque can be expressed as follows:
  • ei and ii are the opposite potential and phase current of the winding respectively, and the subscript i is a, b, c, d, e; ⁇ is the mechanical angular velocity of the rotor; in order to calculate ei , the winding function is introduced:
  • N j is the number of turns of the armature winding of the jth harmonic
  • P a is the number of pole pairs of the armature winding
  • r g is the air gap length
  • L stk is the axial length
  • B g ( ⁇ , t) is the air gap flux density generated by the permanent magnet
  • N a ( ⁇ ) is the a-phase winding function
  • the calculated air-gap magnetic density that causes the secondary torque ripple is 9, 13, 29, 49, 53, and 71 times, according to the finite element analysis, it can be found that the torque ripple generated by the 29th air-gap magnetic density is larger. Combined with the previous torque analysis, the 9th and 11th air-gap magnetic density can be generated The torque of the torque and the torque ripple generated by the 29th air-gap magnetic density are used as optimization sub-objectives.
  • the response surface analysis method is used to establish a proxy model between the design high-sensitivity parameters and the sub-objectives:
  • the BBD sampling design method is used to obtain the combination of design parameters.
  • the sample points are brought into Maxwell software for parametric simulation, and then the sub-target values of each parameter combination are obtained, and then the response surface analysis is performed to obtain the high-sensitivity parameters and sub-targets.
  • the multi-objective backbone particle swarm optimization algorithm is used to optimize the agent model, and the function expression obtained by the response surface analysis is brought into the multi-objective backbone particle swarm algorithm program written by MATLAB, and the Pareto frontier diagram of the combination of the two sub-objectives can be obtained , and then the optimal sub-goal can be obtained.
  • the motor proposed by the present invention utilizes the magnetic field self-shielding effect of the Halbach permanent magnet array at the lower end to avoid the permanent magnetic field being closed in the rotor , Realize the integrated processing of the rotor, and the mechanical robustness of the rotor of the motor can be improved.
  • the T-shaped permanent magnet array proposed by the invention has multiple construction methods, and the radial permanent magnet and the Halbach permanent magnet can be placed together, and can also be isolated by an isolation bridge, which has flexibility.
  • Air slots are invented between the poles of the permanent magnets on the rotor, which is beneficial to the weight reduction of the rotor and improves the dynamic response capability of the motor.
  • the motor of the present invention has multiple working harmonics, and the source of the main components of torque and torque ripple is obtained. In the optimization process, only the main torque and torque ripple can be optimized to realize the overall Improved torque performance.
  • the motor optimization method based on air-gap harmonics proposed by the invention can analyze the motor output torque and the principle of torque ripple, and can reveal the reason for the decrease of torque ripple.
  • the relationship between all design parameters and sub-objectives can be considered at the same time, and the simulation time can be reduced.
  • Fig. 1 is the topological structure of the high mechanical robustness magnetic field modulation type radial permanent magnet motor proposed by the present invention.
  • Fig. 2 is a flow chart of the optimized design of the highly mechanically robust magnetic field modulated radial permanent magnet motor based on air gap harmonics in the present invention.
  • Figure 3 is the magnetomotive force generated by the permanent magnet-permeance model: (a) the magnetomotive force generated by the permanent magnet; (b) the stator side permeance.
  • Figure 4 shows the magnetomotive force-permeance model of the armature reaction: (a) the magnetomotive force generated by the armature reaction; (b) the permeance of the rotor side.
  • Figure 5 is a graph showing the contribution of the air gap magnetic density to the torque.
  • Fig. 6 is a parameter model diagram of a highly mechanically robust magnetic field modulated radial permanent magnet motor.
  • Figure 7 is the optimized Pareto frontier diagram.
  • Figure 8 is a comparison diagram of sub-objectives before and after optimization: (a) torque; (b) torque ripple.
  • Figure 9 is a comparison of the torque performance of the motor before and after optimization.
  • Figure 10 is a comparison of cogging torque before and after optimization.
  • the rotor module of the motor includes two rotor teeth and three permanent magnets, wherein the permanent magnet structure is an inverted T shape , which can be regarded as a combination of a radial permanent magnet and a Halbach permanent magnet array; the two permanent magnets at the lower end are radially magnetized in opposite directions, and the two permanent magnets can be placed close to the radial permanent magnet, separated by The magnetic bridge is on both sides and can be close to the tooth wall of the rotor, so that the magnetic isolation bridge is in the middle, and the radial permanent magnet in the middle is tangentially magnetized; at the same time, the self-shielding effect of the Halbach permanent magnet array at the lower end is used to avoid permanent magnetization.
  • the magnetic field is closed in the rotor to realize the integrated processing of the rotor structure.
  • both the stator and the rotor of the motor have a salient pole structure, so both the permanent magnetic field and the armature reaction magnetic field are modulated by the salient poles of the stator and rotor, thereby generating more working harmonics.
  • Step 1 Analyze the permanent magnet air-gap flux density and armature reaction air-gap flux density of the target motor, and determine the harmonic order and corresponding rotational speed of the permanent magnet air-gap flux density and armature reaction air-gap flux density.
  • Electromagnetic torque can be generated by the joint action of electric load and magnetic load with the same harmonic order and the same corresponding speed, and the formula is expressed as follows:
  • D si is the inner diameter of the stator
  • l stk is the axial length of the motor
  • B gv is the magnetic load, that is, the amplitude of the v-th harmonic of the permanent magnet air gap magnetic density
  • K sv is the v-th harmonic amplitude of the electric load
  • the air-gap magnetic density generated by the permanent magnet can be obtained by the product of the magnetomotive force generated by the permanent magnet and the magnetic permeability of the stator side, as shown in Figure 3 is the distribution diagram of the magnetomotive force generated by the permanent magnet and the magnetic permeability of the stator side, so , the air-gap magnetomotive force generated by the permanent magnet can be expressed by Fourier decomposition as:
  • F RPMb and F RPMn are the Fourier coefficients of the magnetomotive force generated by the permanent magnet
  • n is the harmonic order of the magnetomotive force generated by the permanent magnet
  • P PM is the number of pole pairs of the permanent magnet
  • ⁇ is the phase angle
  • ⁇ 0 is the initial angle
  • ⁇ r is the angular velocity of the rotor
  • t is the time.
  • the Fourier decomposition of the stator side permeance can be expressed as follows:
  • ⁇ s0 , ⁇ sb and ⁇ sk are the Fourier coefficients of the stator side permeance
  • k is the harmonic order of the stator side permeance
  • P s is the number of stator slots. Therefore, the air-gap flux density produced by the permanent magnet can be expressed as follows:
  • the air-gap flux density generated by the permanent magnet is composed of two harmonics, nP PM sub-harmonic and
  • the air-gap flux density generated by the armature reaction can be obtained by the product of the magnetomotive force generated by the armature reaction and the rotor-side permeance, as shown in Figure 4. Distribution.
  • the air-gap magnetomotive force generated by the armature reaction can be expressed by Fourier decomposition as:
  • N RC is the number of turns of a phase winding
  • i is the harmonic order of the magnetomotive force generated by the armature reaction
  • ⁇ is the phase angle
  • D Ri is the Fourier coefficient of the magnetomotive force generated by the armature reaction
  • i A , i B , i C , i D , i E are the currents of A, B, C, D, and E phases respectively;
  • I Rmax is the current amplitude
  • P r is the number of rotor pole pairs
  • ⁇ r is the angular velocity of the rotor
  • ⁇ Rr0 , ⁇ Rrb , and ⁇ Rrp are the Fourier coefficients of the rotor-side air-gap permeance
  • p is the harmonic order of the rotor-side permeance
  • P r is the number of rotor pole pairs
  • ⁇ 0 is the initial angle
  • ⁇ r is the angular velocity of the rotor
  • t is the time. Therefore, the air-gap flux density generated by the armature reaction can be expressed as follows:
  • ⁇ 1 and ⁇ 2 can be expressed as :
  • ⁇ 1 and ⁇ 2 can be expressed as :
  • the air-gap flux density harmonic order generated by the armature reaction can also be calculated by
  • the air-gap flux density harmonic order generated by the armature reaction.
  • the contribution ratio of the electromagnetic torque harmonics and then obtained the air gap flux density produced by the permanent magnet and the air gap flux density produced by the armature reaction.
  • the main working harmonics are 9th, 11th and 31st.
  • Step 2 based on the principle of air gap magnetic field modulation, the formulas of torque and torque ripple are derived.
  • the electromagnetic torque can be expressed as follows:
  • ei and ii are winding opposite potential and phase current respectively, ⁇ is rotor mechanical angular velocity.
  • ⁇ is rotor mechanical angular velocity.
  • N j is the number of turns of the armature winding of the jth harmonic
  • P a is the number of pole pairs of the armature winding
  • r g is the air gap length
  • B g ( ⁇ , t) is the air gap magnetic density generated by the permanent magnet
  • Step 3 according to the formula of torque and torque ripple, analyze the influence of air gap harmonics on torque and torque ripple.
  • the torque and torque ripple that have a greater influence are selected as optimization sub-objectives.
  • Step 4 select key design parameters, and use finite element analysis software to determine the range of parameters.
  • the selected design parameter model of the present invention is as shown in Figure 6, can obtain the initial value of design parameter and the scope of variation according to finite element analysis as follows:
  • Step 5 use the Taguchi sensitivity analysis method to analyze the influence of the motor parameters on the sub-objectives, and divide the design parameters into two layers according to the sensitivity.
  • an orthogonal table L 27 (3 7 ) with seven parameters and three levels is established for the seven parameters.
  • the design parameters and corresponding levels are as follows, where L represents the code of the orthogonal table, and 27 represents the number of rows of the orthogonal table. 3 means the number of levels, 7 means 7 parameters;
  • the response values of 27 parameter combinations are obtained through finite element simulation; finally, by calculating the influence degree of each parameter level on the target, the sensitivity value of each parameter can be obtained by variance analysis of the response value of each parameter level. Divide the parameters into two layers, the result is as follows:
  • Step 6 keep the low sensitivity parameters unchanged, and optimize the high sensitivity parameters by combining the response surface analysis method and the multi-objective backbone particle swarm optimization algorithm.
  • the low-sensitivity parameters have less influence on the sub-objective, the low-sensitivity parameters are kept constant and the high-sensitivity design parameters are optimized.
  • a proxy model between sub-objectives and design variables is established by using response surface analysis method. Then, a multi-objective backbone particle swarm optimization algorithm is employed to optimize the surrogate model. The optimization results are shown in the Pareto diagram in Figure 7. In order to see the changes of design parameters and sub-goals before and after optimization more intuitively, the comparison between design parameters and goals before and after optimization is listed:
  • the cogging torque of the motor before and after optimization is compared. It can be seen that after optimization, the cogging torque is reduced from the initial 309.1mNm to 264.4mNm, which shows that the proposed optimization method is effective.
  • the present invention discloses a magnetic field modulation radial permanent magnet motor with high mechanical robustness and a multi-harmonic optimization design method thereof.
  • the purpose of optimizing torque and torque ripple is achieved by introducing air gap harmonics as a bridge between the motor structure and the optimization target.

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Permanent Field Magnets Of Synchronous Machinery (AREA)
  • Permanent Magnet Type Synchronous Machine (AREA)

Abstract

Disclosed in the present invention are a magnetic field modulation type radial permanent magnet electric motor having high mechanical robustness, and a multi-harmonic optimization design method therefor. In order to enhance the mechanical robustness of a rotor of a traditional magnetic field modulation type radial permanent magnet electric motor, a magnetic field modulation type radial permanent magnet electric motor having an inverted T-shaped permanent magnet structure is provided. Since the proposed electric motor belongs to a magnetic field modulation electric motor having multiple operating harmonics, a multi-objective optimization design method based on air gap harmonics is provided. The specific implementation process comprises: analyzing an electric motor torque generation mechanism on the basis of a magnetic field modulation principle, and deducing formulae for torque and a torque ripple; according to the formulae for torque and a torque ripple, analyzing the contribution of air gap harmonics to the torque and the torque ripple, and selecting, as sub-objectives, a torque and a torque ripple generated by the air gap harmonics which have a relatively great effect; and then optimizing the sub-objectives by combining response surface analysis and a multi-objective bare-bones particle swarm algorithm, and finally, taking the optimization of the torque and the torque ripple of the electric motor both into consideration.

Description

一种高机械鲁棒性磁场调制式辐向永磁电机及其多谐波优化设计方法A high mechanical robustness magnetic field modulation radial permanent magnet motor and its multi-harmonic optimization design method 技术领域technical field
本发明涉及到磁场调制式辐向永磁的设计与优化，特别是优化转子机械强度和电机转矩脉动的方法，属于电机制造的技术领域。The invention relates to the design and optimization of a magnetic field modulation radial permanent magnet, in particular to a method for optimizing the mechanical strength of a rotor and the torque ripple of a motor, and belongs to the technical field of motor manufacturing.
背景技术Background technique
近年来，磁场调制式永磁电机在电动汽车、航空航天和轨道交通等领域都扮演着十分重要的角色，这主要得益于磁场调制式永磁电机具有以下显著特点，高输出转矩，高效率和高功率密度等。磁场调制式永磁电机采用了高磁能积的磁性材料取代了传统的励磁绕组，不仅消除了励磁绕组带来的负面影响，而且简化了电机的机械结构，使电机运行可靠性提高，机械损耗也相应的减小。In recent years, magnetic field modulated permanent magnet motors have played a very important role in the fields of electric vehicles, aerospace, and rail transit. This is mainly due to the following salient features of magnetic field modulated permanent magnet motors, high output torque, high efficiency and high power density etc. The magnetic field modulated permanent magnet motor uses a high magnetic energy product magnetic material to replace the traditional excitation winding, which not only eliminates the negative impact of the excitation winding, but also simplifies the mechanical structure of the motor, which improves the reliability of the motor and reduces the mechanical loss. Corresponding reduction.
定子永磁型磁场调制式永磁电机因其转子结构简单、机械强度高、效率高和散热能力强等优点而备受关注，但值得注意的是，永磁体和电枢绕组都位于定子槽内，这将减少定子槽面积，进而减少电负荷产生，降低电机的转矩输出能力。因此，为充分利用转子空间，越来越多的学者致力于将永磁体转移到转子上，提出转子永磁型磁场调制式永磁电机。文件CN104201852A提出一种绕组互补形磁场调制式永磁电机，将永磁体转移到转子上，这将增加电枢绕组槽面积，提高转子的空间利用率，同时，电枢磁场和永磁磁场分离，缓解了定子磁饱和程度，改善电机的过载能力。但是，文件CN104201852A提出一种绕组互补形磁场调制式永磁电机具有如下缺点：该电机的转子模块内部设有调磁气隙，使得转子结构分离，进而导致较低的转子机械强度；且在调磁气隙内部需要嵌入矩形调磁块，该调磁块在调磁气隙内运动，需要在转子侧加电刷滑环，提供直流励磁电流，而电刷滑环结构复杂，且需要定期维护；电机的转矩脉动较大。The stator permanent magnet type field modulated permanent magnet motor has attracted much attention due to its advantages of simple rotor structure, high mechanical strength, high efficiency and strong heat dissipation capacity, but it is worth noting that the permanent magnets and armature windings are located in the stator slots , which will reduce the area of the stator slot, thereby reducing the generation of electrical load and reducing the torque output capability of the motor. Therefore, in order to make full use of the rotor space, more and more scholars are devoting themselves to transferring the permanent magnets to the rotor, and propose a rotor permanent magnet magnetic field modulation permanent magnet motor. Document CN104201852A proposes a winding complementary magnetic field modulation permanent magnet motor, which transfers the permanent magnet to the rotor, which will increase the area of the armature winding slot and improve the space utilization of the rotor. At the same time, the armature magnetic field and the permanent magnetic field are separated, The degree of magnetic saturation of the stator is alleviated, and the overload capacity of the motor is improved. However, the document CN104201852A proposes a permanent magnet motor with complementary winding magnetic field modulation, which has the following disadvantages: the rotor module of the motor is provided with a magnetic modulation air gap, which makes the rotor structure separate, resulting in lower mechanical strength of the rotor; A rectangular magnetic block needs to be embedded inside the magnetic air gap. The magnetic block moves in the magnetic air gap. A brush slip ring needs to be added on the rotor side to provide DC excitation current. The brush slip ring has a complex structure and requires regular maintenance. ;The torque ripple of the motor is large.
目前存在的转矩脉动削弱方法主要有转子斜极、优化绕组和增添虚拟极结构，这些优化方法会使得电机结构变得复杂，并且转矩脉动优化原理难以解释。因此，简化电机结构，从转矩脉动产生原理上优化电机的转矩脉动是重点研究方向。The existing torque ripple reduction methods mainly include rotor skew, optimized winding and adding virtual pole structure. These optimization methods will make the motor structure complicated, and the principle of torque ripple optimization is difficult to explain. Therefore, simplifying the structure of the motor and optimizing the torque ripple of the motor from the principle of torque ripple generation are the key research directions.
发明内容Contents of the invention
本发明的目的是，提出了一种高机械鲁棒性磁场调制式辐向永磁电机及其多谐波优化设计方法。在高机械鲁棒性磁场调制式辐向永磁电机的基础上，为提高电机的转矩性能，提出一种多气隙谐波的电机优化设计方法。The purpose of the present invention is to propose a high mechanical robustness magnetic field modulation radial permanent magnet motor and its multi-harmonic optimization design method. On the basis of high mechanical robustness magnetic field modulation radial permanent magnet motor, in order to improve the torque performance of the motor, an optimal design method of multi-air-gap harmonic motor is proposed.
本发明采用的技术方案是：一种高机械鲁棒性磁场调制式辐向永磁电机，包括定子，以及定子内部的转子模块；该电机的转子模块包括两个转子齿和三块永磁体，其中永磁体结构为倒T型，视为一个辐向永磁体和一个Halbach永磁体阵列组合而成；下端的两块永磁体为径向充磁，且充磁方向相反，两块永磁体紧贴辐向永磁体放置，隔磁桥在两边；或者紧贴在转子齿壁，使隔磁桥在中间，中间的辐向永磁体为切向充磁；同时，利用下端的Halbach永磁体阵列的自屏蔽效应，避免了永磁磁场闭合在转子中，实现转子结构一体化加工。The technical solution adopted in the present invention is: a highly mechanically robust magnetic field modulation type radial permanent magnet motor, including a stator and a rotor module inside the stator; the rotor module of the motor includes two rotor teeth and three permanent magnets, The permanent magnet structure is an inverted T shape, which is regarded as a combination of a radial permanent magnet and a Halbach permanent magnet array; the two permanent magnets at the lower end are radially magnetized, and the magnetization direction is opposite, and the two permanent magnets are close to each other. Radial permanent magnets are placed, with magnetic isolation bridges on both sides; or close to the rotor tooth wall, so that the magnetic isolation bridges are in the middle, and the radial permanent magnets in the middle are tangentially magnetized; at the same time, using the Halbach permanent magnet array at the lower end The shielding effect prevents the permanent magnetic field from being closed in the rotor, and realizes the integrated processing of the rotor structure.
进一步，该电机的定子和转子均为凸极结构，因此永磁磁场和电枢反应磁场均受到定转子凸极的调制作用，从而产生更多工作谐波。Furthermore, both the stator and the rotor of the motor have a salient pole structure, so both the permanent magnetic field and the armature reaction magnetic field are modulated by the salient poles of the stator and rotor, thereby generating more working harmonics.
一种高机械鲁棒性磁场调制式辐向永磁电机的多谐波优化设计方法，将气隙谐波引入转矩和转矩脉动的优化中，实现步骤如下：A method for multi-harmonic optimization design of radial permanent magnet motor with high mechanical robustness and magnetic field modulation, which introduces air gap harmonics into the optimization of torque and torque ripple. The implementation steps are as follows:
步骤1，对目标电机进行永磁体气隙磁密和电枢反应气隙磁密分析，确定永磁体气隙磁密和电枢反应气隙磁密的谐波阶次及对应的转速；Step 1: Perform permanent magnet air gap flux density and armature reaction air gap flux density analysis on the target motor, and determine the harmonic order and corresponding rotational speed of the permanent magnet air gap flux density and armature reaction air gap flux density;
步骤2，基于气隙磁场调制原理，推导出电磁转矩表达式，进而推导平均转矩和转矩脉动的公式； Step 2, based on the air-gap magnetic field modulation principle, deduce the electromagnetic torque expression, and then derive the formulas of average torque and torque ripple;
步骤3，根据平均转矩和转矩脉动公式，分析气隙谐波对转矩和转矩脉动的影响，选择影响较大的转矩和转矩脉动为优化子目标； Step 3, according to the average torque and torque ripple formula, analyze the influence of air gap harmonics on torque and torque ripple, and select the torque and torque ripple with greater influence as the optimization sub-goal;
步骤4，选择关键设计参数，并利用有限元软件确定参数的范围； Step 4, select key design parameters, and use finite element software to determine the range of parameters;
步骤5，运用田口灵敏度分析方法分析电机参数对子目标的影响大小，并根据灵敏度大小将设计参数分为两层； Step 5, using the Taguchi sensitivity analysis method to analyze the influence of the motor parameters on the sub-targets, and divide the design parameters into two layers according to the sensitivity;
步骤6，保持低灵敏度参数不变，采用响应面分析方法和多目标骨干粒子群算法结合来优化高灵敏度参数。Step 6: keep the low sensitivity parameters unchanged, and optimize the high sensitivity parameters by combining the response surface analysis method and the multi-objective backbone particle swarm optimization algorithm.
进一步，所述步骤2中的电磁转矩由具有相同谐波阶次及对应的转速相同的电负荷和磁负荷共同作用产生，用公式表示如下：Further, the electromagnetic torque in the step 2 is generated by the joint action of the electric load and the magnetic load with the same harmonic order and the same corresponding rotational speed, and the formula is expressed as follows:
Figure PCTCN2021106643-appb-000001
Figure PCTCN2021106643-appb-000001
其中，D si是定子内径，l stk是电机轴向长度，B gv是磁负荷，即永磁体气隙磁密v次谐波的幅值，K sv是电负荷v次谐波幅值，
Figure PCTCN2021106643-appb-000002
是v次磁负荷和电负荷的夹角；因此，有必要分别分析永磁体产生气隙磁密和电枢反应产生气隙磁密。 Among them, D si is the inner diameter of the stator, l stk is the axial length of the motor, B gv is the magnetic load, that is, the amplitude of the v-th harmonic of the air-gap flux density of the permanent magnet, and K sv is the v-th harmonic amplitude of the electric load,
Figure PCTCN2021106643-appb-000002
is the angle between the v-time magnetic load and the electric load; therefore, it is necessary to analyze the air-gap magnetic density generated by the permanent magnet and the air-gap magnetic density generated by the armature reaction respectively.
进一步，所述步骤1中永磁体气隙磁密可由永磁体产生的磁动势和定子侧磁导的乘积得到，其中，由永磁体产生的磁动势可通过傅里叶分解表示为：Further, the permanent magnet air gap magnetic density in the step 1 can be obtained by the product of the magnetomotive force generated by the permanent magnet and the permeance of the stator side, wherein the magnetomotive force generated by the permanent magnet can be expressed as:
Figure PCTCN2021106643-appb-000003
Figure PCTCN2021106643-appb-000003
其中，F RPMb和F RPMn为永磁体产生磁动势的傅里叶系数，n为永磁体产生的磁动势的谐波次数，P PM为永磁体极对数，θ为相位角，θ 0为初始角，ω r为转子角速度，t为时间；定子侧磁导可表示如下： Among them, F RPMb and F RPMn are the Fourier coefficients of the magnetomotive force generated by the permanent magnet, n is the harmonic order of the magnetomotive force generated by the permanent magnet, P PM is the number of pole pairs of the permanent magnet, θ is the phase angle, and θ 0 is the initial angle, ω r is the angular velocity of the rotor, and t is the time; the magnetic permeability of the stator side can be expressed as follows:
Figure PCTCN2021106643-appb-000004
Figure PCTCN2021106643-appb-000004
其中，Λ s0，Λ sb和Λ sk为定子侧磁导的傅里叶系数，k为定子侧磁导的谐波次数，P s为定子槽数；因此，由永磁体产生的气隙磁密可表示如下： Among them, Λ s0 , Λ sb and Λ sk are the Fourier coefficients of the stator side permeance, k is the harmonic order of the stator side permeance, and P s is the number of stator slots; therefore, the air gap flux density produced by the permanent magnet Can be expressed as follows:
Figure PCTCN2021106643-appb-000005
Figure PCTCN2021106643-appb-000005
由上式可以看出，气隙磁密由两种谐波组成，即转速为ω r的nP PM子谐波和转速为nP PMω r/(nP PM±kP s)的|nP PM±kP s|子谐波。 It can be seen from the above formula that the air gap flux density is composed of two kinds of harmonics, namely the nP PM sub-harmonic with the speed of ω r and |nP PM ±kP with the speed of nP PM ω r /(nP PM ±kP s ) s | subharmonic.
进一步，所述步骤1中电枢反应产生的气隙磁密可由电枢反应产生的磁动势和转子侧磁导的乘积得到，其中，由电枢反应产生的气隙磁动势可通过傅里叶分解表示为：Further, the air-gap magnetic density produced by the armature reaction in the step 1 can be obtained by the product of the magnetomotive force produced by the armature reaction and the permeance of the rotor side, wherein the air-gap magnetomotive force produced by the armature reaction can be obtained by Fu The Liye decomposition is expressed as:
Figure PCTCN2021106643-appb-000006
Figure PCTCN2021106643-appb-000006
其中，N RC为一相绕组匝数，i为电枢反应产生磁动势的谐波次数，θ为相位角，D Ri为电枢反应产生磁动势的傅里叶系数，i A，i B，i C，i D，i E分别为A，B，C，D，E相的电流； Among them, N RC is the number of turns of a phase winding, i is the harmonic order of the magnetomotive force generated by the armature reaction, θ is the phase angle, D Ri is the Fourier coefficient of the magnetomotive force generated by the armature reaction, i A , i B , i C , i D , i E are the currents of A, B, C, D, and E phases respectively;
当i＝5r，r＝1，2，...When i=5r, r=1, 2, ...
Figure PCTCN2021106643-appb-000007
Figure PCTCN2021106643-appb-000007
当i＝5r-1，i＝5r-2，i＝5r-3，r＝1，2，...，F＝0.When i=5r-1, i=5r-2, i=5r-3, r=1, 2, ..., F=0.
当i＝5r-4，r＝1，2，...，When i=5r-4, r=1, 2, ...,
Figure PCTCN2021106643-appb-000008
Figure PCTCN2021106643-appb-000008
其中，I Rmax为电流幅值，P r为转子极对数；转子侧气隙磁导的傅里叶表达式如下： Among them, I Rmax is the current amplitude, P r is the number of rotor pole pairs; the Fourier expression of the air gap permeability on the rotor side is as follows:
Figure PCTCN2021106643-appb-000009
Figure PCTCN2021106643-appb-000009
其中，Λ Rr0，Λ Rrb，和Λ Rrp为转子侧气隙磁导的傅里叶系数，p为转子侧磁导的谐波次数；因此，由电枢反应产生的气隙磁密可表示如下： Among them, Λ Rr0 , Λ Rrb , and Λ Rrp are the Fourier coefficients of the rotor-side air-gap permeance, and p is the harmonic order of the rotor-side permeance; therefore, the air-gap flux density generated by the armature reaction can be expressed as follows :
当i＝5r，r＝1，2，...，When i=5r, r=1, 2, ...,
Figure PCTCN2021106643-appb-000010
Figure PCTCN2021106643-appb-000010
其中，β 1和β 2可表示为： Among them, β1 and β2 can be expressed as :
Figure PCTCN2021106643-appb-000011
Figure PCTCN2021106643-appb-000011
当i＝5r-4，r＝1，2，...，When i=5r-4, r=1, 2, ...,
Figure PCTCN2021106643-appb-000012
Figure PCTCN2021106643-appb-000012
其中，β 1和β 2可表示为： Among them, β1 and β2 can be expressed as :
Figure PCTCN2021106643-appb-000013
Figure PCTCN2021106643-appb-000013
因此，基于以上电枢反应产生的气隙磁密公式，可得到电枢反应产生气隙磁密的谐波特性：Therefore, based on the air-gap flux density formula generated by the armature reaction above, the harmonic characteristics of the air-gap flux density generated by the armature reaction can be obtained:
当i＝5r-4，r＝1，2，...，谐波阶次为2i-1的转速为(P rω r/(2i-1))，谐波阶次为(pP r+2i-1)的转速为((p+1)P rω r/(pP r+(2i-1)))，谐波阶次为|pP r-(2i-1)|的转速为((p-1)P rω r/[pP r-(2i-1)])； When i=5r-4, r=1, 2,..., the speed of harmonic order 2i-1 is (P r ω r /(2i-1)), and the harmonic order is (pP r + The rotational speed of 2i-1) is ((p+1)P r ω r /(pP r +(2i-1))), the harmonic order is |pP r -(2i-1)| the rotational speed is (( p-1)P r ω r /[pP r -(2i-1)]);
当i＝5r，r＝1，2，...，谐波阶次为2i-1的转速为(-P rω r/(2i-1))，谐波阶次为(2i-1+pPr)的转速为((p-1)P rω r/(pP r+(2i-1)))，谐波阶次为|pP r-(2i-1)|的转速为((p+1)P rω r/(pP r-(2i-1)))。 When i=5r, r=1, 2,..., the harmonic order of 2i-1 is (-P r ω r /(2i-1)), and the harmonic order is (2i-1+ The rotational speed of pPr) is ((p-1)P r ω r /(pP r +(2i-1))), and the rotational speed of the harmonic order is |pP r -(2i-1)| is ((p+ 1)P r ω r /(pP r -(2i-1))).
进一步，所述步骤2中，电磁转矩可表示如下：Further, in the step 2, the electromagnetic torque can be expressed as follows:
Figure PCTCN2021106643-appb-000014
Figure PCTCN2021106643-appb-000014
其中，e i和i i分别为绕组相反电势和相电流，下标i为a、b、c、d、e；Ω为转子机械角速度；为计算e i，引入绕组函数： Among them, ei and ii are the opposite potential and phase current of the winding respectively, and the subscript i is a, b, c, d, e; Ω is the mechanical angular velocity of the rotor; in order to calculate ei , the winding function is introduced:
Figure PCTCN2021106643-appb-000015
Figure PCTCN2021106643-appb-000015
其中，N j是第j次谐波的电枢绕组匝数，P a为电枢绕组极对数；因此，可以推导出a相反电势公式如下： Among them, N j is the number of turns of the armature winding of the jth harmonic, and P a is the number of pole pairs of the armature winding; therefore, the formula for the opposite potential of a can be derived as follows:
Figure PCTCN2021106643-appb-000016
Figure PCTCN2021106643-appb-000016
其中，r g为气隙长度，L stk为轴向长度，B g(θ，t)为永磁体产生气隙磁密，N a(θ)为a相绕组函数； Among them, r g is the air gap length, L stk is the axial length, B g (θ, t) is the air gap flux density generated by the permanent magnet, and N a (θ) is the a-phase winding function;
然后，电磁转矩公式可得出如下：Then, the electromagnetic torque formula can be derived as follows:
Figure PCTCN2021106643-appb-000017
Figure PCTCN2021106643-appb-000017
进而可得，平均转矩T avg和转矩脉动T ripple的公式分别表示如下： Furthermore, the formulas of the average torque T avg and the torque ripple T ripple can be expressed as follows:
Figure PCTCN2021106643-appb-000018
Figure PCTCN2021106643-appb-000018
Figure PCTCN2021106643-appb-000019
Figure PCTCN2021106643-appb-000019
进一步，从转矩脉动T ripple的公式看出，产生转矩脉动的阶次n＝5r±1，5r±3；同时对所提出电机进行转矩谐波分析，发现主要转矩脉动谐波为2，11，20次，可推算出n＝1，3，10，12，19，21，均满足转矩脉动公式中的n的取值。 Further, from the formula of torque ripple T ripple , it can be seen that the order of torque ripple is n=5r±1, 5r±3; at the same time, the torque harmonic analysis of the proposed motor shows that the main torque ripple harmonic is 2, 11, 20 times, it can be deduced that n=1, 3, 10, 12, 19, 21, all of which satisfy the value of n in the torque ripple formula.
进一步，所述步骤3中，为降低二次转矩脉动，有n＝1，3，k＝1，2，3...，计算的引起二次转矩脉动的气隙磁密有9，13，29，49，53，71次，根据有限元分析可以发现29次气隙磁密产生的转矩脉动更大，结合之前的转矩分析，可以将9次、11次气隙磁密产生的转矩和29次气隙磁密产生的转矩脉动作为优化子目标。Further, in the step 3, in order to reduce the secondary torque ripple, there are n=1, 3, k=1, 2, 3..., the calculated air-gap magnetic density that causes the secondary torque ripple is 9, 13, 29, 49, 53, and 71 times, according to the finite element analysis, it can be found that the torque ripple generated by the 29th air-gap magnetic density is larger. Combined with the previous torque analysis, the 9th and 11th air-gap magnetic density can be generated The torque of the torque and the torque ripple generated by the 29th air-gap magnetic density are used as optimization sub-objectives.
进一步，所述步骤6中，由于低灵敏度参数对子目标的影响很小，因此保持低灵敏度参数不变；响应面分析方法用于建立设计高灵敏度参数与子目标之间的代理模型：Further, in the step 6, since the low-sensitivity parameters have little influence on the sub-objectives, the low-sensitivity parameters are kept unchanged; the response surface analysis method is used to establish a proxy model between the design high-sensitivity parameters and the sub-objectives:
首先，采用BBD采样设计方法得出设计参数的组合，其次，将样本点带入Maxwell软件进行参数化仿真，进而得到各参数组合的子目标值，然后进行响应面分析得到高灵敏度参数与子目标的函数表达式；First, the BBD sampling design method is used to obtain the combination of design parameters. Secondly, the sample points are brought into Maxwell software for parametric simulation, and then the sub-target values of each parameter combination are obtained, and then the response surface analysis is performed to obtain the high-sensitivity parameters and sub-targets. the function expression of
然后，多目标骨干粒子群算法用于优化代理模型，将响应面分析所得的函数表达式带入MATLAB编写的多目标骨干粒子群算法的程序中，可得到两个子目标组合的帕累托前沿图，进而可得到最优子目标。Then, the multi-objective backbone particle swarm optimization algorithm is used to optimize the agent model, and the function expression obtained by the response surface analysis is brought into the multi-objective backbone particle swarm algorithm program written by MATLAB, and the Pareto frontier diagram of the combination of the two sub-objectives can be obtained , and then the optimal sub-goal can be obtained.
本发明得到的有益效果是：The beneficial effect that the present invention obtains is:
1.1.
传统的需要非导体支撑件，转子分离式的磁场调制式辐向永磁电机相比，本发明提出的电机利用下端的Halbach永磁体阵列的磁场自屏蔽效应，避免了永磁磁场闭合在转子里、实现转子一体化加工，电机的转子机械鲁棒性得以提升。Compared with the traditional magnetic field modulation radial permanent magnet motor that requires non-conductive supports and the rotor is separated, the motor proposed by the present invention utilizes the magnetic field self-shielding effect of the Halbach permanent magnet array at the lower end to avoid the permanent magnetic field being closed in the rotor , Realize the integrated processing of the rotor, and the mechanical robustness of the rotor of the motor can be improved.
2.2.
发明所提的T型永磁阵列具有多种构造方式，可以将辐向永磁体和Halbach永磁体 放置在一起，也可由隔离桥隔离，具有灵活性。The T-shaped permanent magnet array proposed by the invention has multiple construction methods, and the radial permanent magnet and the Halbach permanent magnet can be placed together, and can also be isolated by an isolation bridge, which has flexibility.
3.3.
发明转子上各永磁磁极间有空气槽，利于转子减重、提高电机动态响应能力。Air slots are invented between the poles of the permanent magnets on the rotor, which is beneficial to the weight reduction of the rotor and improves the dynamic response capability of the motor.
4.4.
于磁场调制原理揭示出本发明电机具有多工作谐波，且获取了转矩和转矩脉动的主要成分来源，进而在优化过程中，只需优化主要转矩和转矩脉动，便能实现整体转矩性能提升。Based on the principle of magnetic field modulation, it is revealed that the motor of the present invention has multiple working harmonics, and the source of the main components of torque and torque ripple is obtained. In the optimization process, only the main torque and torque ripple can be optimized to realize the overall Improved torque performance.
5.5.
发明提出的基于气隙谐波的电机优化方法，能够分析电机输出转矩和转矩脉动产生原理，并能够揭示转矩脉动下降的原因。The motor optimization method based on air-gap harmonics proposed by the invention can analyze the motor output torque and the principle of torque ripple, and can reveal the reason for the decrease of torque ripple.
6.6.
用响应面分析建立设计参数与子目标的代理模型，能够同时考虑设计所有设计参数与子目标之间的关系，同时减少仿真时间。Using response surface analysis to establish a surrogate model of design parameters and sub-objectives, the relationship between all design parameters and sub-objectives can be considered at the same time, and the simulation time can be reduced.
附图说明Description of drawings
图1为本发明提出的高机械鲁棒性磁场调制式辐向永磁电机的拓扑结构。Fig. 1 is the topological structure of the high mechanical robustness magnetic field modulation type radial permanent magnet motor proposed by the present invention.
图2为本发明基于气隙谐波的高机械鲁棒性磁场调制式辐向永磁电机的优化设计流程图。Fig. 2 is a flow chart of the optimized design of the highly mechanically robust magnetic field modulated radial permanent magnet motor based on air gap harmonics in the present invention.
图3为永磁体产生的磁动势-磁导模型：(a)永磁体产生的磁动势；(b)定子侧磁导。Figure 3 is the magnetomotive force generated by the permanent magnet-permeance model: (a) the magnetomotive force generated by the permanent magnet; (b) the stator side permeance.
图4为电枢反应磁动势-磁导模型：(a)电枢反应产生的磁动势；(b)转子侧磁导。Figure 4 shows the magnetomotive force-permeance model of the armature reaction: (a) the magnetomotive force generated by the armature reaction; (b) the permeance of the rotor side.
图5为气隙磁密对转矩的贡献图。Figure 5 is a graph showing the contribution of the air gap magnetic density to the torque.
图6为高机械鲁棒性磁场调制式辐向永磁电机的的参数模型图。Fig. 6 is a parameter model diagram of a highly mechanically robust magnetic field modulated radial permanent magnet motor.
图7为优化后的帕累托前沿图。Figure 7 is the optimized Pareto frontier diagram.
图8为优化前后子目标的比较图：(a)转矩；(b)转矩脉动。Figure 8 is a comparison diagram of sub-objectives before and after optimization: (a) torque; (b) torque ripple.
图9为优化前后电机的转矩性能比较。Figure 9 is a comparison of the torque performance of the motor before and after optimization.
图10为优化前后齿槽转矩比较。Figure 10 is a comparison of cogging torque before and after optimization.
具体实施方式detailed description
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention.
如图1所示为本发明提出的一种高机械鲁棒性磁场调制式辐向永磁电机，该电机的转子模块包括两个转子齿和三块永磁体，其中永磁体结构为倒T型，可以看做是一个辐向永 磁体和一个Halbach永磁体阵列组合而成；下端的两块永磁体为方向相反的径向充磁，两块永磁体既可紧贴辐向永磁体放置，隔磁桥在两边，又可紧贴在转子齿壁，使隔磁桥在中间，中间的辐向永磁体为切向充磁；同时，利用下端的Halbach永磁体阵列的自屏蔽效应，避免了永磁磁场闭合在转子中，实现转子结构一体化加工。As shown in Figure 1, it is a highly mechanically robust magnetic field modulation radial permanent magnet motor proposed by the present invention. The rotor module of the motor includes two rotor teeth and three permanent magnets, wherein the permanent magnet structure is an inverted T shape , which can be regarded as a combination of a radial permanent magnet and a Halbach permanent magnet array; the two permanent magnets at the lower end are radially magnetized in opposite directions, and the two permanent magnets can be placed close to the radial permanent magnet, separated by The magnetic bridge is on both sides and can be close to the tooth wall of the rotor, so that the magnetic isolation bridge is in the middle, and the radial permanent magnet in the middle is tangentially magnetized; at the same time, the self-shielding effect of the Halbach permanent magnet array at the lower end is used to avoid permanent magnetization. The magnetic field is closed in the rotor to realize the integrated processing of the rotor structure.
进一步地，该电机的定子和转子均为凸极结构，因此永磁磁场和电枢反应磁场均受到定转子凸极的调制作用，从而产生更多工作谐波。Furthermore, both the stator and the rotor of the motor have a salient pole structure, so both the permanent magnetic field and the armature reaction magnetic field are modulated by the salient poles of the stator and rotor, thereby generating more working harmonics.
在高机械鲁棒性磁场调制式辐向永磁电机的基础上，提出一种基于多气隙谐波优化方法，优化流程如图2所示，其具体实施步骤如下：Based on the highly mechanically robust magnetic field modulation radial permanent magnet motor, a harmonic optimization method based on multi-air gaps is proposed. The optimization process is shown in Figure 2. The specific implementation steps are as follows:
步骤1，对目标电机进行永磁体气隙磁密和电枢反应气隙磁密分析，确定永磁体气隙磁密和电枢反应气隙磁密的谐波阶次及对应的转速。Step 1: Analyze the permanent magnet air-gap flux density and armature reaction air-gap flux density of the target motor, and determine the harmonic order and corresponding rotational speed of the permanent magnet air-gap flux density and armature reaction air-gap flux density.
电磁转矩可由具有相同谐波阶次及对应的转速相同的电负荷和磁负荷共同作用产生，用公式表示如下：Electromagnetic torque can be generated by the joint action of electric load and magnetic load with the same harmonic order and the same corresponding speed, and the formula is expressed as follows:
Figure PCTCN2021106643-appb-000020
Figure PCTCN2021106643-appb-000020
其中，D si是定子内径，l stk是电机轴向长度，B gv是磁负荷，即永磁气隙磁密v次谐波的幅值，K sv是电负荷v次谐波幅值，
Figure PCTCN2021106643-appb-000021
是v次磁负荷和电负荷的夹角。因此，为分析电机的转矩产生机理，有必要对目标电机进行永磁体产生气隙磁密和电枢反应气隙磁密分析 Among them, D si is the inner diameter of the stator, l stk is the axial length of the motor, B gv is the magnetic load, that is, the amplitude of the v-th harmonic of the permanent magnet air gap magnetic density, K sv is the v-th harmonic amplitude of the electric load,
Figure PCTCN2021106643-appb-000021
is the angle between the magnetic load and the electric load for v times. Therefore, in order to analyze the torque generation mechanism of the motor, it is necessary to analyze the air gap flux density of the permanent magnet and the armature reaction air gap flux density of the target motor
进一步地，由永磁体产生的气隙磁密可由永磁体产生的磁动势和定子侧磁导的乘积得到，如图3所示为永磁体产生磁动势和定子侧磁导分布图，因此，由永磁体产生的气隙磁动势可通过傅里叶分解表示为：Further, the air-gap magnetic density generated by the permanent magnet can be obtained by the product of the magnetomotive force generated by the permanent magnet and the magnetic permeability of the stator side, as shown in Figure 3 is the distribution diagram of the magnetomotive force generated by the permanent magnet and the magnetic permeability of the stator side, so , the air-gap magnetomotive force generated by the permanent magnet can be expressed by Fourier decomposition as:
Figure PCTCN2021106643-appb-000022
Figure PCTCN2021106643-appb-000022
其中，F RPMb和F RPMn为永磁体产生磁动势的傅里叶系数，n为永磁体产生的磁动势的谐波次数，P PM为永磁体极对数，θ为相位角，θ 0为初始角，ω r为转子角速度，t为时间。定子侧磁导的傅里叶分解可表示如下： Among them, F RPMb and F RPMn are the Fourier coefficients of the magnetomotive force generated by the permanent magnet, n is the harmonic order of the magnetomotive force generated by the permanent magnet, P PM is the number of pole pairs of the permanent magnet, θ is the phase angle, and θ 0 is the initial angle, ω r is the angular velocity of the rotor, and t is the time. The Fourier decomposition of the stator side permeance can be expressed as follows:
Figure PCTCN2021106643-appb-000023
Figure PCTCN2021106643-appb-000023
其中，Λ s0，Λ sb和Λ sk为定子侧磁导的傅里叶系数，k为定子侧磁导的谐波次数，P s为定子槽数。因此，由永磁体产生的气隙磁密可表示如下： Among them, Λ s0 , Λ sb and Λ sk are the Fourier coefficients of the stator side permeance, k is the harmonic order of the stator side permeance, and P s is the number of stator slots. Therefore, the air-gap flux density produced by the permanent magnet can be expressed as follows:
Figure PCTCN2021106643-appb-000024
Figure PCTCN2021106643-appb-000024
由此公式可以看出，永磁体产生的气隙磁密由两种谐波组成，nP PM子谐波和|nP PM±kP s|子谐波，气隙磁密谐波及对应的转速如下： It can be seen from this formula that the air-gap flux density generated by the permanent magnet is composed of two harmonics, nP PM sub-harmonic and |nP PM ±kP s | sub-harmonic, the air-gap flux density harmonic and the corresponding speed are as follows :
Figure PCTCN2021106643-appb-000025
Figure PCTCN2021106643-appb-000025
进一步地，由电枢反应产生的气隙磁密可由电枢反应产生的磁动势和转子侧磁导的乘积得到，如图4所示为电枢反应产生的磁动势和转子侧磁导分布图。由电枢反应产生的气隙磁动势可通过傅里叶分解表示为：Furthermore, the air-gap flux density generated by the armature reaction can be obtained by the product of the magnetomotive force generated by the armature reaction and the rotor-side permeance, as shown in Figure 4. Distribution. The air-gap magnetomotive force generated by the armature reaction can be expressed by Fourier decomposition as:
Figure PCTCN2021106643-appb-000026
Figure PCTCN2021106643-appb-000026
其中，N RC为一相绕组匝数，i为电枢反应产生磁动势的谐波次数，θ为相位角，D Ri为电枢反应产生磁动势的傅里叶系数，i A，i B，i C，i D，i E分别为A，B，C，D，E相的电流； Among them, N RC is the number of turns of a phase winding, i is the harmonic order of the magnetomotive force generated by the armature reaction, θ is the phase angle, D Ri is the Fourier coefficient of the magnetomotive force generated by the armature reaction, i A , i B , i C , i D , i E are the currents of A, B, C, D, and E phases respectively;
当i＝5r，r＝1，2，...When i=5r, r=1, 2, ...
Figure PCTCN2021106643-appb-000027
Figure PCTCN2021106643-appb-000027
当i＝5r-1，i＝5r-2，i＝5r-3，r＝1，2，...，F＝0.When i=5r-1, i=5r-2, i=5r-3, r=1, 2, ..., F=0.
当i＝5r-4，r＝1，2，...，When i=5r-4, r=1, 2, ...,
Figure PCTCN2021106643-appb-000028
Figure PCTCN2021106643-appb-000028
其中，I Rmax为电流幅值，P r为转子极对数，ω r为转子角速度；转子侧气隙磁导的傅里叶表达式如下： Among them, I Rmax is the current amplitude, P r is the number of rotor pole pairs, and ω r is the angular velocity of the rotor; the Fourier expression of the air gap permeance on the rotor side is as follows:
Figure PCTCN2021106643-appb-000029
Figure PCTCN2021106643-appb-000029
其中，Λ Rr0，Λ Rrb，和Λ Rrp为转子侧气隙磁导的傅里叶系数，p为转子侧磁导的谐波次数，P r为转子极对数，θ 0为初始角，ω r为转子角速度，t为时间。因此，由电枢反应产生的气隙磁密可表示如下： Among them, Λ Rr0 , Λ Rrb , and Λ Rrp are the Fourier coefficients of the rotor-side air-gap permeance, p is the harmonic order of the rotor-side permeance, P r is the number of rotor pole pairs, θ 0 is the initial angle, ω r is the angular velocity of the rotor, and t is the time. Therefore, the air-gap flux density generated by the armature reaction can be expressed as follows:
当i＝5r，r＝1，2，...，When i=5r, r=1, 2, ...,
Figure PCTCN2021106643-appb-000030
Figure PCTCN2021106643-appb-000030
其中，β 1和β 2可表示为： Among them, β1 and β2 can be expressed as :
Figure PCTCN2021106643-appb-000031
Figure PCTCN2021106643-appb-000031
当i＝5r-4，r＝1，2，...，When i=5r-4, r=1, 2, ...,
Figure PCTCN2021106643-appb-000032
Figure PCTCN2021106643-appb-000032
其中，β 1和β 2可表示为： Among them, β1 and β2 can be expressed as :
Figure PCTCN2021106643-appb-000033
Figure PCTCN2021106643-appb-000033
因此，基于上述电枢反应产生气隙磁密公式，可得到电枢反应产生气隙磁密的谐波特性：Therefore, based on the above formula of air-gap flux density generated by armature reaction, the harmonic characteristics of air-gap flux density generated by armature reaction can be obtained:
Figure PCTCN2021106643-appb-000034
Figure PCTCN2021106643-appb-000034
当i＝5r-4，
Figure PCTCN2021106643-appb-000035
其中r为偶数； When i=5r-4,
Figure PCTCN2021106643-appb-000035
where r is an even number;
当i＝5r时，
Figure PCTCN2021106643-appb-000036
其中r为奇数。 When i=5r,
Figure PCTCN2021106643-appb-000036
where r is an odd number.
因此电枢反应产生的气隙磁密谐波次数也可由|nP PM±kP s|计算，对于本发明的设计的20槽11极的电机，基于麦克斯韦应力张量法，可以求得如图5所示的电磁转矩谐波贡献比例，进而得到永磁体产生气隙磁密和电枢反应产生的气隙磁密主要工作谐波为9次、11次和31次。 Therefore, the air-gap flux density harmonic order generated by the armature reaction can also be calculated by |nP PM ±kP s |. For the motor with 20 slots and 11 poles designed in the present invention, based on the Maxwell stress tensor method, it can be obtained as shown in Figure 5 The contribution ratio of the electromagnetic torque harmonics, and then obtained the air gap flux density produced by the permanent magnet and the air gap flux density produced by the armature reaction. The main working harmonics are 9th, 11th and 31st.
步骤2，基于气隙磁场调制原理，推导出转矩和转矩脉动的公式。电磁转矩可表示如下：Step 2, based on the principle of air gap magnetic field modulation, the formulas of torque and torque ripple are derived. The electromagnetic torque can be expressed as follows:
Figure PCTCN2021106643-appb-000037
Figure PCTCN2021106643-appb-000037
其中，e i和i i分别为绕组相反电势和相电流，Ω为转子机械角速度。为计算e i，引入绕组函数： Among them, ei and ii are winding opposite potential and phase current respectively, Ω is rotor mechanical angular velocity. To calculate e i , the winding function is introduced:
Figure PCTCN2021106643-appb-000038
Figure PCTCN2021106643-appb-000038
其中，N j是第j次谐波的电枢绕组匝数，P a为电枢绕组极对数。因此，可以推导出a相反电势公式如下： Among them, N j is the number of turns of the armature winding of the jth harmonic, and P a is the number of pole pairs of the armature winding. Therefore, the formula of a reverse potential can be deduced as follows:
Figure PCTCN2021106643-appb-000039
Figure PCTCN2021106643-appb-000039
其中，r g为气隙长度，L stk轴向长度，B g(θ，t)为永磁体产生气隙磁密；然后，电磁转矩公式可得出如下： Among them, r g is the air gap length, L stk axial length, B g (θ, t) is the air gap magnetic density generated by the permanent magnet; then, the electromagnetic torque formula can be obtained as follows:
Figure PCTCN2021106643-appb-000040
Figure PCTCN2021106643-appb-000040
然后，平均转矩T avg和转矩脉动T ripple的公式可分别表示如下： Then, the formulas of the average torque T avg and the torque ripple T ripple can be respectively expressed as follows:
Figure PCTCN2021106643-appb-000041
Figure PCTCN2021106643-appb-000041
Figure PCTCN2021106643-appb-000042
Figure PCTCN2021106643-appb-000042
进一步地，从转矩脉动公式看出，产生转矩脉动的n＝5r±1，5r±3；同时对所提出电机进行转矩谐波分析，发现主要转矩脉动谐波为2，11，20次，可推算出n＝1，3，10，12，19，21，均满足转矩脉动公式中的n的取值。Further, from the torque ripple formula, it can be seen that n=5r±1, 5r±3 for the torque ripple; at the same time, the torque harmonic analysis of the proposed motor shows that the main torque ripple harmonics are 2, 11, 20 times, it can be deduced that n=1, 3, 10, 12, 19, 21, all of which satisfy the value of n in the torque ripple formula.
步骤3，根据转矩和转矩脉动公式，分析气隙谐波对转矩和转矩脉动的影响。选择影响较大的转矩和转矩脉动为优化子目标。 Step 3, according to the formula of torque and torque ripple, analyze the influence of air gap harmonics on torque and torque ripple. The torque and torque ripple that have a greater influence are selected as optimization sub-objectives.
为降低二次转矩脉动，有n＝1，3，k＝1，2，3...，计算的引起二次转矩脉动的气隙磁密有9，13，29，49，53，71次，根据有限元分析可以发现29次气隙磁密产生的转矩脉动更大，结合之前的转矩分析，可以将9次、11次气隙磁密产生的转矩和29次气隙磁密产生的转矩脉动作为优化子目标。In order to reduce the secondary torque ripple, there are n=1, 3, k=1, 2, 3..., and the calculated air gap magnetic density that causes the secondary torque ripple is 9, 13, 29, 49, 53, 71 times, according to the finite element analysis, it can be found that the torque ripple generated by the air-gap magnetic density of the 29th time is larger. Combined with the previous torque analysis, the torque generated by the 9th and 11th air-gap magnetic density and the The torque ripple generated by magnetic density is used as the optimization sub-objective.
步骤4，选择关键设计参数，并利用有限元分析软件确定参数的范围。 Step 4, select key design parameters, and use finite element analysis software to determine the range of parameters.
本发明所选择的设计参数模型如图6所示，根据有限元分析可得到设计参数的初值及变化范围如下：The selected design parameter model of the present invention is as shown in Figure 6, can obtain the initial value of design parameter and the scope of variation according to finite element analysis as follows:
Figure PCTCN2021106643-appb-000043
Figure PCTCN2021106643-appb-000043
步骤5，运用田口灵敏度分析方法分析电机参数对子目标的影响大小，并根据灵敏度 大小将设计参数分为两层。 Step 5, use the Taguchi sensitivity analysis method to analyze the influence of the motor parameters on the sub-objectives, and divide the design parameters into two layers according to the sensitivity.
首先对七个参数建立七参数三水平的正交表L 27(3 7)，设计参数和相应的水平数如下表，其中L表示正交表的代码，27表示正交表的行数，3表示水平数，7表示7个参数； Firstly, an orthogonal table L 27 (3 7 ) with seven parameters and three levels is established for the seven parameters. The design parameters and corresponding levels are as follows, where L represents the code of the orthogonal table, and 27 represents the number of rows of the orthogonal table. 3 means the number of levels, 7 means 7 parameters;
Figure PCTCN2021106643-appb-000044
Figure PCTCN2021106643-appb-000044
然后通过有限元仿真得到27个参数组合的响应值；最后通过计算各参数水平对目标的影响程度，对各参数水平的响应值进行方差分析可以得到各个参数的灵敏度值，根据综合灵敏度的值可将参数分为两层，结果如下：Then, the response values of 27 parameter combinations are obtained through finite element simulation; finally, by calculating the influence degree of each parameter level on the target, the sensitivity value of each parameter can be obtained by variance analysis of the response value of each parameter level. Divide the parameters into two layers, the result is as follows:
Figure PCTCN2021106643-appb-000045
Figure PCTCN2021106643-appb-000045
步骤6，保持低灵敏度参数不变，采用响应面分析方法和多目标骨干粒子群算法结合来优化高灵敏度参数。Step 6: keep the low sensitivity parameters unchanged, and optimize the high sensitivity parameters by combining the response surface analysis method and the multi-objective backbone particle swarm optimization algorithm.
由于低灵敏度参数对子目标的影响较小，因此保持低灵敏度参数不变，优化高灵敏度设计参数。为减少仿真次数，采用响应面分析方法建立子目标与设计变量之间的代理模型。然后，采用多目标骨干粒子群算法来优化代理模型。优化结果如图7所示的Pareto图。为更加直观的看出优化前后设计参数与子目标的变化情况，列出了优化前后的设计参数与目标的对比：Since the low-sensitivity parameters have less influence on the sub-objective, the low-sensitivity parameters are kept constant and the high-sensitivity design parameters are optimized. In order to reduce the number of simulations, a proxy model between sub-objectives and design variables is established by using response surface analysis method. Then, a multi-objective backbone particle swarm optimization algorithm is employed to optimize the surrogate model. The optimization results are shown in the Pareto diagram in Figure 7. In order to see the changes of design parameters and sub-goals before and after optimization more intuitively, the comparison between design parameters and goals before and after optimization is listed:
Figure PCTCN2021106643-appb-000046
Figure PCTCN2021106643-appb-000046
Figure PCTCN2021106643-appb-000047
Figure PCTCN2021106643-appb-000047
优化之后，子目标的变化如图8所示，最终的转矩波形比较如图9所示，可以看出优化之后输出转矩由6.78Nm提升至7.77Nm，转矩脉动由7％降低至3.1％。从图8和图9可以看出，所提出的基于气隙谐波的优化设计方法是有效的。After optimization, the change of the sub-target is shown in Figure 8, and the comparison of the final torque waveform is shown in Figure 9. It can be seen that after optimization, the output torque increases from 6.78Nm to 7.77Nm, and the torque ripple decreases from 7% to 3.1 %. It can be seen from Fig. 8 and Fig. 9 that the proposed optimal design method based on air-gap harmonics is effective.
如图10所示比较了优化前后电机的齿槽转矩，可以看出优化之后，齿槽转矩有所降低，由最初的309.1mNm降低到264.4mNm，说明所提出的优化方法是有效的。As shown in Figure 10, the cogging torque of the motor before and after optimization is compared. It can be seen that after optimization, the cogging torque is reduced from the initial 309.1mNm to 264.4mNm, which shows that the proposed optimization method is effective.
综上，本发明公开了一种高机械鲁棒性磁场调制式辐向永磁电机及其多谐波优化设计方法。在高机械鲁棒性磁场调制式辐向永磁电机的基础上，通过引入气隙谐波作为电机结构与优化目标联系的桥梁，进而达到优化转矩和转矩脉动的目的。To sum up, the present invention discloses a magnetic field modulation radial permanent magnet motor with high mechanical robustness and a multi-harmonic optimization design method thereof. On the basis of high mechanical robustness magnetic field modulation radial permanent magnet motor, the purpose of optimizing torque and torque ripple is achieved by introducing air gap harmonics as a bridge between the motor structure and the optimization target.
在本说明书的描述中，参考术语“一个实施例”、“一些实施例”、“示意性实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中，对上述术语的示意性表述不一定指的是相同的实施例或示例。而且，描述的具体特征、结构、材料或者特点可以在任何的一个或多个实施例或示例中以合适的方式结合。In the description of this specification, reference to the terms "one embodiment," "some embodiments," "exemplary embodiments," "example," "specific examples," or "some examples" is intended to mean that the implementation A specific feature, structure, material, or characteristic described by an embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
尽管已经示出和描述了本发明的实施例，本领域的普通技术人员可以理解：在不脱离本发明的原理和宗旨的情况下可以对这些实施例进行多种变化、修改、替换和变型，本发明的范围由权利要求及其等同物限定。Although the embodiments of the present invention have been shown and described, those skilled in the art can understand that various changes, modifications, substitutions and modifications can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the invention is defined by the claims and their equivalents.

Claims (10)

  1. 一种高机械鲁棒性磁场调制式辐向永磁电机，其特征在于，包括定子，以及定子内部的转子模块；该电机的转子模块包括两个转子齿和三块永磁体，其中永磁体结构为倒T型，视为一个辐向永磁体和一个Halbach永磁体阵列组合而成；下端的两块永磁体为径向充磁，且充磁方向相反，两块永磁体紧贴辐向永磁体放置，隔磁桥在两边；或者紧贴在转子齿壁，使隔磁桥在中间，中间的辐向永磁体为切向充磁；同时，利用下端的Halbach永磁体阵列的自屏蔽效应，避免了永磁磁场闭合在转子中，实现转子结构一体化加工。A radial permanent magnet motor with high mechanical robustness magnetic field modulation is characterized in that it includes a stator and a rotor module inside the stator; the rotor module of the motor includes two rotor teeth and three permanent magnets, wherein the permanent magnet structure It is an inverted T shape, which is regarded as a combination of a radial permanent magnet and a Halbach permanent magnet array; the two permanent magnets at the lower end are radially magnetized, and the magnetization direction is opposite, and the two permanent magnets are close to the radial permanent magnet. Place the magnetic isolation bridge on both sides; or close to the rotor tooth wall, so that the magnetic isolation bridge is in the middle, and the radial permanent magnet in the middle is tangentially magnetized; at the same time, the self-shielding effect of the Halbach permanent magnet array at the lower end is used to avoid The permanent magnetic field is closed in the rotor, and the integrated processing of the rotor structure is realized.
  2. 根据权利要求1所述的高机械鲁棒性磁场调制式辐向永磁电机，其特征在于，该电机的定子和转子均为凸极结构，因此永磁磁场和电枢反应磁场均受到定转子凸极的调制作用，从而产生更多工作谐波。The high mechanical robustness magnetic field modulation type radial permanent magnet motor according to claim 1 is characterized in that, the stator and the rotor of the motor are salient pole structures, so the permanent magnet magnetic field and the armature reaction magnetic field are both affected by the stator and rotor The modulation effect of the salient pole produces more working harmonics.
  3. 一种高机械鲁棒性磁场调制式辐向永磁电机的多谐波优化设计方法，其特征在于，将气隙谐波引入转矩和转矩脉动的优化中，实现步骤如下：A multi-harmonic optimization design method for a highly mechanically robust magnetic field modulation type radial permanent magnet motor, characterized in that air gap harmonics are introduced into the optimization of torque and torque ripple, and the implementation steps are as follows:
    步骤1，对目标电机进行永磁体气隙磁密和电枢反应气隙磁密分析，确定永磁体气隙磁密和电枢反应气隙磁密的谐波阶次及对应的转速；Step 1: Perform permanent magnet air gap flux density and armature reaction air gap flux density analysis on the target motor, and determine the harmonic order and corresponding rotational speed of the permanent magnet air gap flux density and armature reaction air gap flux density;
    步骤2，基于气隙磁场调制原理，推导出电磁转矩表达式，进而推导平均转矩和转矩脉动的公式；Step 2, based on the air-gap magnetic field modulation principle, deduce the electromagnetic torque expression, and then derive the formulas of average torque and torque ripple;
    步骤3，根据转矩和转矩脉动公式，分析气隙谐波对转矩和转矩脉动的影响，选择影响较大的平均转矩和转矩脉动为优化子目标；Step 3, according to the formula of torque and torque ripple, analyze the influence of air gap harmonics on torque and torque ripple, and select the average torque and torque ripple with greater influence as the optimization sub-goal;
    步骤4，选择关键设计参数，并利用有限元软件确定参数的范围；Step 4, select key design parameters, and use finite element software to determine the range of parameters;
    步骤5，运用田口灵敏度分析方法分析电机参数对子目标的影响大小，并根据灵敏度大小将设计参数分为两层；Step 5, using the Taguchi sensitivity analysis method to analyze the influence of the motor parameters on the sub-targets, and divide the design parameters into two layers according to the sensitivity;
    步骤6，保持低灵敏度参数不变，采用响应面分析方法和多目标骨干粒子群算法结合来优化高灵敏度参数。Step 6: keep the low sensitivity parameters unchanged, and optimize the high sensitivity parameters by combining the response surface analysis method and the multi-objective backbone particle swarm optimization algorithm.
  4. 根据权利要求3所述的一种高机械鲁棒性磁场调制式辐向永磁电机多谐波优化设计方法，其特征在于：所述步骤2中的电磁转矩由具有相同谐波阶次及对应的转速相同的电负荷和磁负荷共同作用产生，用公式表示如下：A method for multi-harmonic optimization design of a highly mechanically robust magnetic field-modulated radial permanent magnet motor according to claim 3, characterized in that: the electromagnetic torque in the step 2 consists of the same harmonic order and The electric load and the magnetic load corresponding to the same rotating speed are jointly generated, and the formula is expressed as follows:
    Figure PCTCN2021106643-appb-100001
    Figure PCTCN2021106643-appb-100001
    其中，D si是定子内径，l stk是电机轴向长度，B gv是磁负荷，即永磁体气隙磁密v次谐波的幅值，K sv是电负荷v次谐波幅值，
    Figure PCTCN2021106643-appb-100002
    是v次磁负荷和电负荷的夹角；因此，有必要分别分析 永磁体产生气隙磁密和电枢反应产生气隙磁密。     Among them, D si is the inner diameter of the stator, l stk is the axial length of the motor, B gv is the magnetic load, that is, the amplitude of the v-th harmonic of the air-gap flux density of the permanent magnet, and K sv is the v-th harmonic amplitude of the electric load,
    Figure PCTCN2021106643-appb-100002
    is the angle between the v-time magnetic load and the electric load; therefore, it is necessary to analyze the air-gap magnetic density generated by the permanent magnet and the air-gap magnetic density generated by the armature reaction respectively.
  5. 根据权利要求3所述的一种高机械鲁棒性磁场调制式辐向永磁电机多谐波优化设计方法，其特征在于：所述步骤1中永磁体气隙磁密可由永磁体产生的磁动势和定子侧磁导的乘积得到，其中，由永磁体产生的磁动势可通过傅里叶分解表示为：According to claim 3, a high mechanical robustness magnetic field modulation radial permanent magnet motor multi-harmonic optimization design method, characterized in that: in the step 1, the air gap flux density of the permanent magnet can be generated by the permanent magnet The product of the momentum and the permeance on the stator side is obtained, where the magnetomotive force generated by the permanent magnet can be expressed by Fourier decomposition as:
    Figure PCTCN2021106643-appb-100003
    Figure PCTCN2021106643-appb-100003
    其中，F RPMb和F RPMn为永磁体产生磁动势的傅里叶系数，n为永磁体产生的磁动势的谐波次数，P PM为永磁体极对数，θ为相位角，θ 0为初始角，ω r为转子角速度，t为时间；定子侧磁导可表示如下： Among them, F RPMb and F RPMn are the Fourier coefficients of the magnetomotive force generated by the permanent magnet, n is the harmonic order of the magnetomotive force generated by the permanent magnet, P PM is the number of pole pairs of the permanent magnet, θ is the phase angle, and θ 0 is the initial angle, ω r is the angular velocity of the rotor, and t is the time; the magnetic permeability of the stator side can be expressed as follows:
    Figure PCTCN2021106643-appb-100004
    Figure PCTCN2021106643-appb-100004
    其中，Λ s0，Λ sb和Λ sk为定子侧磁导的傅里叶系数，k为定子侧磁导的谐波次数，P s为定子槽数；因此，由永磁体产生的气隙磁密可表示如下： Among them, Λ s0 , Λ sb and Λ sk are the Fourier coefficients of the stator side permeance, k is the harmonic order of the stator side permeance, and P s is the number of stator slots; therefore, the air gap flux density produced by the permanent magnet Can be expressed as follows:
    Figure PCTCN2021106643-appb-100005
    Figure PCTCN2021106643-appb-100005
    由上式可以看出，气隙磁密由两种谐波组成，即转速为ω r的nP PM子谐波和转速为nP PMω r/(nP PM±kP s)的|nP PM±kP s|子谐波。 It can be seen from the above formula that the air gap flux density is composed of two kinds of harmonics, namely the nP PM sub-harmonic with the speed of ω r and |nP PM ±kP with the speed of nP PM ω r /(nP PM ±kP s ) s | subharmonic.
  6. 根据权利要求3所述的一种高机械鲁棒性磁场调制式辐向永磁电机多谐波优化设计方法，其特征在于：所述步骤1中电枢反应产生的气隙磁密可由电枢反应产生的磁动势和转子侧磁导的乘积得到，其中，由电枢反应产生的气隙磁动势可通过傅里叶分解表示为：According to claim 3, a high mechanical robustness magnetic field modulation type radial permanent magnet motor multi-harmonic optimization design method is characterized in that: the air gap magnetic density generated by the armature reaction in the step 1 can be obtained by the armature The product of the magnetomotive force generated by the reaction and the permeance of the rotor side is obtained, where the air gap magnetomotive force generated by the armature reaction can be expressed by Fourier decomposition as:
    Figure PCTCN2021106643-appb-100006
    Figure PCTCN2021106643-appb-100006
    其中，N RC为一相绕组匝数，i为电枢反应产生磁动势的谐波次数，θ为相位角，D Ri为电枢反应产生磁动势的傅里叶系数，i A，i B，i C，i D，i E分别为A，B，C，D，E相的电流； Among them, N RC is the number of turns of a phase winding, i is the harmonic order of the magnetomotive force generated by the armature reaction, θ is the phase angle, D Ri is the Fourier coefficient of the magnetomotive force generated by the armature reaction, i A , i B , i C , i D , i E are the currents of A, B, C, D, and E phases respectively;
    当i＝5r，r＝1，2，...When i=5r, r=1, 2, ...
    Figure PCTCN2021106643-appb-100007
    Figure PCTCN2021106643-appb-100007
    当i＝5r-1，i＝5r-2，i＝5r-3，r＝1，2，...，F＝0.When i=5r-1, i=5r-2, i=5r-3, r=1, 2, ..., F=0.
    当i＝5r-4，r＝1，2，...，When i=5r-4, r=1, 2, ...,
    Figure PCTCN2021106643-appb-100008
    Figure PCTCN2021106643-appb-100008
    其中，I Rmax为电流幅值，P r为转子极对数；转子侧气隙磁导的傅里叶表达式如下： Among them, I Rmax is the current amplitude, P r is the number of rotor pole pairs; the Fourier expression of the air gap permeability on the rotor side is as follows:
    Figure PCTCN2021106643-appb-100009
    Figure PCTCN2021106643-appb-100009
    其中，Λ Rr0，Λ Rrb，和Λ Rrp为转子侧气隙磁导的傅里叶系数，p为转子侧磁导的谐波次数；因此，由电枢反应产生的气隙磁密可表示如下： Among them, Λ Rr0 , Λ Rrb , and Λ Rrp are the Fourier coefficients of the rotor-side air-gap permeance, and p is the harmonic order of the rotor-side permeance; therefore, the air-gap flux density generated by the armature reaction can be expressed as follows :
    当i＝5r，r＝1，2，...，When i=5r, r=1, 2, ...,
    Figure PCTCN2021106643-appb-100010
    Figure PCTCN2021106643-appb-100010
    其中，β 1和β 2可表示为： Among them, β1 and β2 can be expressed as :
    Figure PCTCN2021106643-appb-100011
    Figure PCTCN2021106643-appb-100011
    当i＝5r-4，r＝1，2，...，When i=5r-4, r=1, 2, ...,
    Figure PCTCN2021106643-appb-100012
    Figure PCTCN2021106643-appb-100012
    其中，β 1和β 2可表示为： Among them, β1 and β2 can be expressed as :
    Figure PCTCN2021106643-appb-100013
    Figure PCTCN2021106643-appb-100013
    因此，基于以上电枢反应产生的气隙磁密公式，可得到电枢反应产生气隙磁密的谐波特性：Therefore, based on the air-gap flux density formula generated by the armature reaction above, the harmonic characteristics of the air-gap flux density generated by the armature reaction can be obtained:
    当i＝5r-4，r＝1，2，...，谐波阶次为2i-1的转速为(P rω r/(2i-1))，谐波阶次为(pP r+2i-1)的转速为((p+1)P rω r/(pP r+(2i-1)))，谐波阶次为|pP r-(2i-1)|的转速为((p-1)P rω r/[pP r-(2i-1)])； When i=5r-4, r=1, 2,..., the speed of harmonic order 2i-1 is (P r ω r /(2i-1)), and the harmonic order is (pP r + The rotational speed of 2i-1) is ((p+1)P r ω r /(pP r +(2i-1))), the harmonic order is |pP r -(2i-1)| the rotational speed is (( p-1)P r ω r /[pP r -(2i-1)]);
    当i＝5r，r＝1，2，...，谐波阶次为2i-1的转速为(-P rω r/(2i-1))，谐波阶次为(2i-1+pPr)的转速为((p-1)P rω r/(pP r+(2i-1)))，谐波阶次为|pP r-(2i-1)|的转速为((p+1)P rω r/(pP r-(2i-1)))。 When i=5r, r=1, 2,..., the harmonic order of 2i-1 is (-P r ω r /(2i-1)), and the harmonic order is (2i-1+ The rotational speed of pPr) is ((p-1)P r ω r /(pP r +(2i-1))), the harmonic order is |pP r -(2i-1)| the rotational speed is ((p+ 1)P r ω r /(pP r -(2i-1))).
  7. 根据权利要求3所述的一种高机械鲁棒性磁场调制式辐向永磁电机多谐波优化设计方法，其特征在于：所述步骤2中，电磁转矩可表示如下：According to claim 3, a high mechanical robustness magnetic field modulation radial permanent magnet motor multi-harmonic optimization design method is characterized in that: in the step 2, the electromagnetic torque can be expressed as follows:
    Figure PCTCN2021106643-appb-100014
    Figure PCTCN2021106643-appb-100014
    其中，e i和i i分别为绕组相反电势和相电流，下标i为a、b、c、d、e；Ω为转子机械角速度；为计算e i，引入绕组函数： Among them, ei and ii are the opposite potential and phase current of the winding respectively, and the subscript i is a, b, c, d, e; Ω is the mechanical angular velocity of the rotor; in order to calculate ei , the winding function is introduced:
    Figure PCTCN2021106643-appb-100015
    Figure PCTCN2021106643-appb-100015
    其中，N j是第j次谐波的电枢绕组匝数，P a为电枢绕组极对数；由此推导出a相反电势公式、电磁转矩公式、平均转矩T avg和转矩脉动T ripple的公式。 Among them, N j is the number of turns of the armature winding of the jth harmonic, and P a is the number of pole pairs of the armature winding; from this, the formula of a reverse potential, the formula of electromagnetic torque, the average torque T avg and the torque ripple are derived Tripple 's formula.
  8. 根据权利要求7所述的一种高机械鲁棒性磁场调制式辐向永磁电机多谐波优化设计方法，其特征在于：从转矩脉动T ripple的公式看出，产生转矩脉动的阶次n＝5r±1，5r±3； 同时对所提出电机进行转矩谐波分析，发现主要转矩脉动谐波为2，11，20次，可推算出n＝1，3，10，12，19，21，均满足转矩脉动公式中的n的取值。 According to claim 7, a high mechanical robustness magnetic field modulation type radial permanent magnet motor multi-harmonic optimization design method is characterized in that: from the formula of torque ripple T ripple , the order of torque ripple is generated Order n=5r±1, 5r±3; At the same time, the torque harmonic analysis of the proposed motor is found, and the main torque ripple harmonics are found to be 2, 11, 20 orders, and n=1, 3, 10, 12 can be deduced , 19, 21, all satisfy the value of n in the torque ripple formula.
  9. 根据权利要求3所述的一种高机械鲁棒性磁场调制式辐向永磁电机多谐波优化设计方法，其特征在于：所述步骤3中，为降低二次转矩脉动，有n＝1，3，k＝1，2，3…，计算的引起二次转矩脉动的气隙磁密有9，13，29，49，53，71次，根据有限元分析可以发现29次气隙磁密产生的转矩脉动更大，结合之前的转矩分析，可以将9次、11次气隙磁密产生的转矩和29次气隙磁密产生的转矩脉动作为优化子目标。According to claim 3, a high mechanical robustness magnetic field modulation type radial permanent magnet motor multi-harmonic optimization design method is characterized in that: in the step 3, in order to reduce the secondary torque ripple, n= 1, 3, k=1, 2, 3..., the calculated air gap magnetic density that causes the secondary torque ripple has 9, 13, 29, 49, 53, 71 times, and 29 air gaps can be found according to the finite element analysis The torque ripple generated by the flux density is larger. Combined with the previous torque analysis, the torque generated by the 9th and 11th air-gap flux density and the torque ripple generated by the 29th air-gap flux density can be used as optimization sub-objectives.
  10. 根据权利要求3所述的一种高机械鲁棒性磁场调制式辐向永磁电机多谐波优化设计方法，其特征在于：所述步骤6中，由于低灵敏度参数对子目标的影响很小，因此保持低灵敏度参数不变；响应面分析方法用于建立设计高灵敏度参数与子目标之间的代理模型：A method for multi-harmonic optimization design of radial permanent magnet motor with high mechanical robustness magnetic field modulation according to claim 3, characterized in that: in said step 6, due to the low sensitivity parameter has little influence on the sub-objective , so the low sensitivity parameters are kept constant; the response surface analysis method is used to establish a surrogate model between the design high sensitivity parameters and the sub-goals:
    首先，采用BBD采样设计方法得出设计参数的组合，其次，将样本点带入Maxwell软件进行参数化仿真，进而得到各参数组合的子目标值，然后进行响应面分析得到高灵敏度参数与子目标的函数表达式；First, the BBD sampling design method is used to obtain the combination of design parameters. Secondly, the sample points are brought into Maxwell software for parametric simulation, and then the sub-target values of each parameter combination are obtained, and then the response surface analysis is performed to obtain the high-sensitivity parameters and sub-targets. the function expression of
    然后，多目标骨干粒子群算法用于优化代理模型，将响应面分析所得的函数表达式带入MATLAB编写的多目标骨干粒子群算法的程序中，可得到两个子目标组合的帕累托前沿图，进而可得到最优子目标。Then, the multi-objective backbone particle swarm optimization algorithm is used to optimize the agent model, and the function expression obtained by the response surface analysis is brought into the multi-objective backbone particle swarm algorithm program written by MATLAB, and the Pareto frontier diagram of the combination of the two sub-objectives can be obtained , and then the optimal sub-goal can be obtained.
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