CN115333302B - Method for analyzing and inhibiting stator core loss of magnetic field modulation permanent magnet motor - Google Patents

Method for analyzing and inhibiting stator core loss of magnetic field modulation permanent magnet motor Download PDF

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CN115333302B
CN115333302B CN202210909035.1A CN202210909035A CN115333302B CN 115333302 B CN115333302 B CN 115333302B CN 202210909035 A CN202210909035 A CN 202210909035A CN 115333302 B CN115333302 B CN 115333302B
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CN115333302A (en
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徐亮
孙志民
赵文祥
刘国海
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Jiangsu University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K15/00—Methods or apparatus specially adapted for manufacturing, assembling, maintaining or repairing of dynamo-electric machines
    • H02K15/0006—Disassembling, repairing or modifying dynamo-electric machines
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K21/00—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets
    • H02K21/02—Details
    • H02K21/021—Means for mechanical adjustment of the excitation flux
    • H02K21/028—Means for mechanical adjustment of the excitation flux by modifying the magnetic circuit within the field or the armature, e.g. by using shunts, by adjusting the magnets position, by vectorial combination of field or armature sections
    • 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

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Abstract

The invention discloses a method for analyzing and inhibiting the loss of a stator core of a magnetic field modulation permanent magnet motor. According to the magnetic density distribution characteristics on the stator, the influence of the core fundamental wave magnetic field on the stator core loss is analyzed, the permanent magnet and the armature magnetic field of the motor are decoupled, and corresponding air gap magnetic flux is deduced. Meanwhile, an equivalent magnetic circuit model is established according to the leakage magnetic flux path, and corresponding leakage magnetic flux is deduced. And (3) establishing the relation between the stator core loss and the air gap magnetic flux and the leakage magnetic flux, analyzing the influence of the magnetic field modulation effect and the modulation pole structure on the core loss, and obtaining useless magnetic flux generated by non-working air gap magnetic field harmonic wave and leakage magnetic flux. The harmonic wave and leakage magnetic suppression method of the non-working air gap magnetic field is provided, and useless magnetic flux is reduced, so that the stator core loss is reduced on the premise of ensuring the torque. The invention can provide clear thought and theoretical guidance for the suppression of the stator core loss of the magnetic field modulation permanent magnet motor.

Description

Method for analyzing and inhibiting stator core loss of magnetic field modulation permanent magnet motor
Technical Field
The invention relates to a method for analyzing and inhibiting the stator core loss of a magnetic field modulation permanent magnet motor, belongs to the field of motors, and is particularly suitable for motor systems requiring high torque and high efficiency, such as electric automobiles, ship propulsion, wind power generation, aerospace and the like.
Background
At present, the direct-drive permanent magnet motor has the advantages of high reliability, high efficiency and low vibration noise, and is applied to various industries including electric automobile driving motors, wind power generation, ship propulsion and aviation and aerospace fields. However, the rapid development of these electrical devices has also placed increasing demands on the performance of drive motor systems. For example, further reduction in size and weight is a development trend of driving motors of electric automobiles, and meanwhile, it is ensured that the driving motors can provide enough power for the electric automobiles under the condition, and the torque density of the driving motors is critical. In addition, in order to assist in achieving the peak-to-peak carbon neutralization goal, the efficiency of the motor needs to be considered with great importance, so high thrust density and high efficiency are major trends in motor design.
Along with the development of the magnetic field modulation theory, the magnetic field modulation permanent magnet motor is gradually researched by students as a high-performance motor, and the working principle of the magnetic field modulation permanent magnet motor is different from that of a conventional permanent magnet motor. The magnetic field modulation permanent magnet motor operates based on the magnetic gear effect, and can utilize various magnetic field harmonic components in an air gap, so that the magnetic field modulation permanent magnet motor has the advantage of high torque density, which is a main aspect different from the traditional permanent magnet motor. Research shows that the torque density of the magnetic field modulation permanent magnet motor under the same condition has obvious advantages compared with the conventional permanent magnet motor and the structure of the magnetic field modulation permanent magnet motor is relatively simple, so that the magnetic field modulation permanent magnet motor also has wide application prospect.
The magnetic field harmonic content of the magnetic field modulation permanent magnet motor is rich, multiple magnetic field harmonic waves can generate torque, and the average torque of the motor can be greatly improved under the cooperative work of the magnetic field harmonic wave magnetic fields. However, it should be noted that the harmonic magnetic field of the magnetic field modulation permanent magnet motor is rich and can cause the increase of the electromagnetic loss of the motor. The high loss of the motor can lead to the temperature rise of the motor, reduce the service life of the motor, and even cause irreversible demagnetization of the permanent magnet and burn out the motor, so that the motor can not stably run. Since stator core losses account for a significant portion of the total losses of a field modulated permanent magnet motor. The high stator core loss has an influence on the efficiency of the motor, and the analysis of the stator core loss has great significance.
The rotor core loss analysis method cannot be applied to the analysis of stator core loss due to the difference in magnetic field variation between the stator and the rotor. Little research is currently done on the stator core loss of a field modulated permanent magnet motor, and the effect of the field modulation on the stator core loss of a permanent magnet synchronous motor has not been clearly explained. The motor also can cause difficulty in accurately analyzing the loss of the stator core due to abundant magnetic field harmonic waves and magnetic gear effects thereof. In addition, the number of the permanent magnets is large, and the stator slots are small, so that obvious slot magnetic leakage problem exists. Therefore, in analyzing the principle of stator core loss generation, not only is the influence of complex harmonic waves caused by magnetic field modulation effect deduced, but also the influence of armature leakage is considered according to the distribution situation of magnetic fields in a stator core, which also presents challenges for analyzing the stator core loss. However, when the suppression of the stator core loss is instructed, it is indispensable to ensure that the torque is not changed, and at the same time, the analysis method is ensured to be simple and quick as much as possible. Therefore, the invention provides a method capable of rapidly analyzing the stator core loss and verifying the effectiveness of the method by guiding two motor loss suppression cases.
Disclosure of Invention
The invention aims to provide an analysis and suppression method for stator core loss of a magnetic field modulation permanent magnet motor, aiming at the defects existing in the aspect of researching the stator core loss of the magnetic field modulation permanent magnet motor. According to the magnetic density distribution characteristics on the stator, the influence of the core fundamental wave magnetic field on the stator core loss is analyzed, the permanent magnet and the armature magnetic field of the motor are decoupled, and corresponding air gap magnetic flux is deduced. Meanwhile, an equivalent magnetic circuit model is established according to the leakage magnetic flux path, and corresponding leakage magnetic flux is deduced. And (3) establishing the relation between the stator core loss and the air gap magnetic flux and the leakage magnetic flux, analyzing the influence of the magnetic field modulation effect and the modulation pole structure on the core loss, and obtaining useless magnetic flux generated by non-working air gap magnetic field harmonic wave and leakage magnetic flux. The harmonic wave and leakage magnetic suppression method of the non-working air gap magnetic field is provided, and useless magnetic flux is reduced, so that the stator core loss is reduced on the premise of ensuring the torque. The invention can provide clear thought and theoretical guidance for the suppression of the stator core loss of the magnetic field modulation permanent magnet motor.
Specifically, the technical scheme of the invention comprises the following steps:
step 1: dividing a stator into a plurality of parts with the same magnetic flux path characteristics according to different magnetic flux path characteristics of a stator area, selecting representative points on each iron core according to the magnetic density distribution characteristics, calculating to obtain a curve of the magnetic density of each iron core changing along with time by using a finite element method, obtaining the amplitude of each magnetic density harmonic by using Fourier decomposition, substituting a classical iron core loss formula to calculate to obtain each part of iron core loss, obtaining the iron core loss of a stator tooth to occupy a very high proportion in the whole stator iron core loss, and selecting the suppression of the iron core loss of the stator tooth as a stator iron core loss suppression target;
step 2: comparing the contributions of the magnetic flux density harmonics of each secondary iron core to the stator tooth iron core loss, so that the fundamental wave of the magnetic flux density of the obtained iron core contributes most of the stator tooth iron core loss, wherein the stator tooth iron core loss is mainly generated by the fundamental wave magnetic flux passing through the stator iron core, and the fundamental wave component of the stator tooth magnetic flux is selected as a research object;
step 3: the fundamental wave is further expressed as a result of combining a permanent magnetic field component and an armature magnetic field component, and magnetic flux of the motor stator teeth is refined and decomposed and divided into magnetic flux of the stator teeth under independent actions of the permanent magnetic field and the armature magnetic field;
step 4: the analysis shows that the stator tooth magnetic flux under the action of the armature magnetic field has useless magnetic flux which does not contribute to torque and only generates loss, and the useless magnetic flux is formed by two parts according to the harmonic analysis of the air gap magnetic field under the action of the armature magnetic field and an equivalent magnetic circuit model, namely the air gap magnetic flux formed by the air gap magnetic field passing through the air gap, and the leakage magnetic flux which does not pass through the air gap and only links with the stator turns;
step 5: calculating the air gap flux density of the armature magnetic field generated by air gap magnetic field modulation, and deriving useless air gap magnetic flux of the stator teeth by integrating the air gap flux density in a range of the stator tooth pitch;
step 6: calculating to obtain the magnetic resistance of each part of the stator and the leakage magnetic flux of the stator teeth under the action of an armature magnetic field by using an equivalent magnetic circuit method according to the leakage magnetic flux path and the relevant size of the stator teeth;
step 7: the method is characterized in that the method is used for respectively aiming at the useless air gap flux and the leakage flux in the useless flux, reducing the non-working harmonic wave and the leakage flux on the stator teeth and reducing the useless flux, so that the stator core loss of the permanent magnet motor is restrained from being modulated by the magnetic field;
further, the calculation formula of the stator core loss in step 1 is:
Figure BDA0003773472600000031
wherein k is the harmonic frequency of the core density, f is the frequency, B core,k Is the magnetic density of k times harmonic wave, A e For the eddy current coefficient, A h Is a hysteresis coefficient.
Further, in the step 3, under the independent action of the permanent magnetic field and the armature magnetic field, the magnetic density expression of the stator core can be written as follows:
Figure BDA0003773472600000032
/>
in the method, in the process of the invention,
Figure BDA0003773472600000033
representing the magnetic density produced by the permanent magnetic field, +.>
Figure BDA0003773472600000034
Indicates the magnetic density produced by the armature magnetic field, +.>
Figure BDA0003773472600000035
Represents the k-order magnetic density produced by the permanent magnetic field,/->
Figure BDA0003773472600000036
The k-order flux density generated by the armature field, t representing time.
The fundamental wave has a very high proportion in all iron core harmonics, the fundamental wave composite flux density on the stator teeth can be regarded as the superposition of the permanent magnetic fundamental wave flux density and the armature fundamental wave flux density, and the amplitude of the two fundamental wave magnetic fields has the following relation because the two fundamental wave magnetic fields differ by a quarter period in the time domain:
Figure BDA0003773472600000037
substituting the fundamental wave magnetic density relationship into an iron core loss calculation formula to obtain an algebraic sum of the iron core loss of the stator under the independent action of the permanent magnet and the armature magnetic field, wherein the iron core loss generated by the fundamental wave in the two magnetic fields can be decomposed into the algebraic sum of the iron core loss of the stator under the independent action of the permanent magnet and the armature magnetic field, and the algebraic sum can be expressed as:
Figure BDA0003773472600000038
in the method, in the process of the invention,
Figure BDA0003773472600000039
stator core loss due to the fundamental component of the flux density generated by the permanent magnetic field, < >>
Figure BDA00037734726000000310
Stator core losses due to the magnetically dense fundamental component generated for the armature field.
The stator core loss formula generated by the synthesized fundamental wave magnetic field is obtained by superposing the core losses generated by the armature magnetic field and the permanent magnetic field, and is the same as the classical core loss formula when k=1, and can be expressed as:
Figure BDA0003773472600000041
wherein P is core,1 Expressed as stator core consumption caused by magnetic density fundamental wave component under combined action of permanent magnet and armature, B core,1 Representing the magnetic density fundamental component of the core.
Since the fundamental magnetic field contributes most of the stator core loss, the stator core loss is approximately equal to the stator core loss generated by the fundamental magnetic field, and thus can be obtained:
Figure BDA0003773472600000042
the fundamental component of stator tooth magnetic flux synthesized by the permanent magnet and the armature magnetic field can be decomposed into the sum of the fundamental components of stator tooth magnetic flux under the independent action of the permanent magnet magnetic field and the armature magnetic field respectively, and is expressed as:
Figure BDA0003773472600000043
Figure BDA0003773472600000044
fundamental component of tooth flux representing the combination of permanent magnet and armature field,/->
Figure BDA0003773472600000045
Tooth magnetic flux fundamental component generated by permanent magnet, +.>
Figure BDA0003773472600000046
Fundamental component of tooth flux generated by the armature winding.
Further, in step 4, the permanent magnetic flux fundamental component is constituted by only the air-gap flux fundamental component, and the armature magnetic flux fundamental component is constituted by superimposing the air-gap flux fundamental component and the leakage magnetic flux fundamental component, which can be expressed as:
Figure BDA0003773472600000047
in the method, in the process of the invention,
Figure BDA0003773472600000048
fundamental component of stator tooth flux generated for permanent magnet air gap flux,/->
Figure BDA0003773472600000049
Fundamental component of stator tooth flux generated for armature air gap flux,/->
Figure BDA00037734726000000410
The leakage flux generated by the armature field is a fundamental component in the stator tooth flux.
Further, the specific process of step 5 may be expressed as:
step 5.1: the permanent magnet air gap flux density can be expressed as:
Figure BDA00037734726000000411
wherein m and n are respectively the harmonic orders of permanent magnet magnetomotive force and the harmonic orders of air gap magnetic permeability,
Figure BDA00037734726000000412
represents the air gap flux density generated by the permanent magnetic field, omega r For the mechanical rotational speed of the motor, lambda 0 Is the amplitude of the air gap flux guide of 0 times, Λ n For n air gap permeabilities of amplitude, P r Is the pole pair number of the permanent magnet, N s For the number of stator slots, C m The amplitude of the magnetomotive force of the permanent magnet air gap for m times is represented by θ, the circumferential position angle of the air gap is represented by t, and the time constant is represented by t.
Step 5.2: the armature air gap flux density can be expressed as:
Figure BDA0003773472600000051
wherein i and j are harmonic orders, omega of armature magnetomotive force r Is the rotation speed of the rotor, S i 、S j iP for armature magnetomotive force r And jP r Subharmonic amplitude.
Step 5.3: the flux on the stator teeth is obtained by integrating the permanent magnet and armature air gap flux densities, respectively, where the permanent magnet air gap flux on the stator teeth can be expressed as:
Figure BDA0003773472600000052
wherein r is δ Is the radius of the air gap, l s Is the axial length of the motor.
The armature air gap flux on the stator teeth can be expressed as:
Figure BDA0003773472600000053
step 5.4: further, the fundamental air gap flux generated on the stator teeth by the permanent magnet and the armature, respectively, acting alone, can be expressed as:
Figure BDA0003773472600000054
further, in step 6, by using the equivalent magnetic circuit method, the leakage magnetic flux generated by the armature magnetic field on the stator teeth can be calculated as:
Figure BDA0003773472600000055
wherein n is s For the number of turns of copper winding, I s Is the amplitude of the current, l s Mu, the axial length of the motor 0 Is vacuum permeability, h s Representing the height of the notch b s For the width of the notch, h w Is the groove height, b w For the width of the notch, P r Is the pole pair number omega of the permanent magnet r Is the mechanical rotational speed.
Further, step 7 may be expressed as finding out useless magnetic flux according to the modulation characteristics of the permanent magnet and the armature field of the field-modulated permanent magnet motor, and it may be roughly classified into two kinds, namely useless air gap flux generated by non-operating harmonics generated by the air gap field under the action of the armature field alone, and useless air gap flux generated by the leakage flux generated by the armature field alone.
The beneficial effects are that:
after the design scheme is adopted, the invention has the following beneficial effects:
1. according to the invention, an analysis model of stator core loss is established according to the magnetic density distribution characteristics on the stator, and an analysis object is determined by researching the contribution of stator teeth and a core fundamental wave to the stator core loss. The method greatly simplifies the analysis process and shortens the calculated amount by using the traditional large-scale point-taking calculation method. By decoupling the internal magnetic field into the superposition of the permanent magnetic field and the armature magnetic field, the effect of each magnetic field on the stator core loss can be considered independently, and the subsequent analysis targets can be clearer and clearer.
2. The invention provides an analysis method for explaining loss by utilizing magnetic flux, which not only considers the influence of air gap harmonic wave, but also considers the influence of magnetic leakage on the loss of a stator core. The non-working harmonic wave and the magnetic leakage of the part which does not contribute to the torque and only generates the stator core loss generated by the internal magnetic field of the motor are respectively identified and independent through a simple technical means, and are uniformly calculated and summarized into useless magnetic flux. The motor internal magnetic field effect is divided more finely, and a clear guide is provided for suppressing the stator core loss.
3. The invention can apply the method in practical cases for investigation and analysis. The stator core loss is effectively inhibited from two angles of non-working harmonic wave generated under the independent action of the armature magnetic field and magnetic leakage generated under the independent action of the armature magnetic field; the method provides theoretical reference for the suppression of the stator core loss, and simultaneously can guide the design of the magnetic field modulation permanent magnet motor with better torque performance and higher efficiency.
Drawings
FIG. 1 is a cross-sectional view of an original motor in an embodiment of the present invention;
FIG. 2 is a cross-sectional view of an electric machine in an embodiment of the invention; (a) is a scheme one rotor open magnetic barrier motor sectional view; (b) a motor cross-sectional view for changing the shape of the stator teeth according to a second scheme;
FIG. 3 shows the magnetic density of the core on the stator of the original motor in an embodiment of the present invention;
FIG. 4 is a Fourier decomposition of the flux density of the primary motor core in an embodiment of the invention;
FIG. 5 is a graph showing the contribution of the original motor harmonics to stator core loss in an embodiment of the present invention;
FIG. 6 is an equivalent magnetic circuit of the armature field of the original motor under the independent action in the embodiment of the invention;
FIG. 7 is a chart of the air gap flux density spectrum of an original motor in an embodiment of the invention;
FIG. 8 is a diagram of the primary motor and case stator slot sizing in an embodiment of the present invention;
FIG. 9 shows phase angles of flux density harmonics of respective cores of an original motor in accordance with an embodiment of the present invention;
FIG. 10 is a comparison of air gap flux density spectra for an original motor and a case-motor in accordance with an embodiment of the present invention;
FIG. 11 is a diagram showing the magnetic field distribution of the original motor according to the embodiment of the present invention;
FIG. 12 is a diagram showing a magnetic field distribution of a case two motor according to an embodiment of the present invention;
FIG. 13 is a graph showing the flux contrast of an original motor, a case one motor, and a case two motor according to an embodiment of the present invention;
fig. 14 is a graph comparing stator core loss and torque of an original motor, a case one motor, a case two motor according to an embodiment of the present invention.
In the figure: 1. the motor comprises a motor stator, 2, a rotor, 3, stator teeth, 4, stator slots, 5, an armature winding, 6, split teeth, 7, a permanent magnet, 8 and a magnetic barrier.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
As shown in fig. 1, the embodiment of the invention is a five-phase magnetic field modulation permanent magnet motor, which comprises a motor stator 1 and a motor rotor 2, wherein an air gap is arranged between the motor stator 1 and the motor rotor 2, and armature windings 5 are wound on motor stator teeth 3; the motor stator 1 comprises 20 stator teeth 3, each stator tooth 3 is split into 2 split teeth 6, stator grooves 4 are formed in two sides of each stator tooth 3, and the motor stator 1 is provided with 40 split teeth 6 and 20 stator grooves 4 in total; the surface of the motor rotor 2 is stuck with permanent magnets 7 alternately magnetized in radial and tangential directions, 62 permanent magnets are all arranged on the surface of the motor rotor 2, and 31 pairs of poles are arranged on the surface of the motor rotor 2.
Fig. 2 is a cross-sectional view corresponding to two cases of motors listed in the embodiment of the present invention, wherein the cross-sectional views of the first case motor and the second case motor are shown in fig. 2 (a) and fig. 2 (b), respectively. Unlike the original motor structure shown in fig. 1, 31 magnetic barriers 8 are provided on the rotor 2 in fig. 2 (a), and the remaining structural dimensions remain unchanged. Fig. 2 (b) changes the structure of the stator split tooth 6, and other structural dimensions remain unchanged from the split tooth 6 of fig. 1 in shape.
The invention relates to a method for analyzing and inhibiting the stator core loss of a magnetic field modulation permanent magnet motor, which is specifically implemented as shown in figures 1-2 and comprises the following steps:
step 1: dividing a stator into a plurality of parts with the same magnetic flux path characteristics according to different magnetic flux path characteristics of a stator area, selecting representative points on each iron core according to the magnetic density distribution characteristics, calculating to obtain a curve of the magnetic density of each iron core changing along with time by using a finite element method, obtaining the amplitude value (fig. 3 and 4) of each magnetic density harmonic by using Fourier decomposition, substituting a classical iron core loss formula to calculate to obtain each part of iron core loss, obtaining the proportion of the iron core loss of a stator tooth occupying the whole stator iron core loss, and selecting the suppression of the iron core loss of the stator tooth as a target of stator iron core loss suppression.
Step 2: comparing the contributions of the sub-core flux density harmonics to the stator tooth core loss, obtaining a stator tooth core loss (figure 5) of which the fundamental wave of the core flux density contributes most, wherein the stator tooth core loss is mainly generated by the fundamental wave magnetic flux passing through the stator core, and selecting the fundamental wave component of the stator tooth magnetic flux as a study object;
step 3: the fundamental wave is further expressed as a result of combining a permanent magnetic field component and an armature magnetic field component, and magnetic flux of the motor stator teeth is refined and decomposed and divided into magnetic flux of the stator teeth under independent actions of the permanent magnetic field and the armature magnetic field;
step 4: analysis shows that useless magnetic flux which does not contribute to torque and only generates loss exists in stator tooth magnetic flux under the action of an armature magnetic field, and according to the harmonic analysis of an air gap magnetic field and an equivalent magnetic circuit model (figure 6) under the action of the armature magnetic field, the useless magnetic flux is formed by two parts, namely, the air gap magnetic flux generated by non-working harmonic waves generated by the air gap magnetic field passing through an air gap, wherein the situation of each air gap harmonic wave is marked in figure 7; secondly, leakage magnetic flux which does not pass through an air gap and is only linked with the turn of the stator itself;
step 5: calculating the air gap flux density of the armature magnetic field generated by air gap magnetic field modulation, and deriving useless air gap magnetic flux of the stator teeth by integrating the air gap flux density in a range of the stator tooth pitch;
step 6: according to the leakage magnetic flux path and the relevant size of the stator teeth, the labeling of the size is shown in fig. 8, and the equivalent magnetic circuit method is utilized to calculate and obtain the magnetic resistance of each part of the stator and the leakage magnetic flux of the stator teeth under the action of the armature magnetic field;
step 7: the non-working harmonic wave is reduced, the magnetic leakage on the stator teeth is reduced, and the useless magnetic flux is reduced, so that the stator core loss of the permanent magnet motor is restrained from being modulated by the magnetic field.
Further, the specific calculation method of the steps 1-6 is as follows:
step 1: the calculation formula of the stator core loss is as follows:
Figure BDA0003773472600000081
wherein k is the harmonic frequency of the core density, f is the frequency, B core,k Is the magnetic density of k times harmonic wave, A e For the eddy current coefficient, A h Is a hysteresis coefficient.
The specific steps of the step 3 are as follows:
under the independent action of the permanent magnetic field and the armature magnetic field, the magnetic density expression of the stator core can be written as follows:
Figure BDA0003773472600000091
in the method, in the process of the invention,
Figure BDA0003773472600000092
representing the magnetic density produced by the permanent magnetic field, +.>
Figure BDA0003773472600000093
Indicates the magnetic density produced by the armature magnetic field, +.>
Figure BDA0003773472600000094
Represents the k-order magnetic density produced by the permanent magnetic field,/->
Figure BDA0003773472600000095
The k-order flux density generated by the armature field, t representing time.
Since the fundamental wave has a very high proportion in all the core harmonics, the fundamental wave composite flux density on the stator teeth can be regarded as a superposition of the permanent magnet flux density and the armature flux density, and since the two fundamental wave magnetic fields differ by a quarter period in the time domain (fig. 9), the magnitudes have the following relationship:
Figure BDA0003773472600000096
substituting the fundamental wave magnetic density relationship into an iron core loss calculation formula to obtain an algebraic sum of the iron core loss of the stator under the independent action of the permanent magnet and the armature magnetic field, wherein the iron core loss generated by the fundamental wave in the two magnetic fields can be decomposed into the algebraic sum of the iron core loss of the stator under the independent action of the permanent magnet and the armature magnetic field, and the algebraic sum can be expressed as:
Figure BDA0003773472600000097
in the method, in the process of the invention,
Figure BDA0003773472600000098
stator core loss due to the fundamental component of the flux density generated by the permanent magnetic field, < >>
Figure BDA0003773472600000099
Stator core losses due to the magnetically dense fundamental component generated for the armature field.
The stator core loss formula generated by the synthesized fundamental wave magnetic field is obtained by superposing the core losses generated by the armature magnetic field and the permanent magnetic field, and is the same as the classical core loss formula when k=1, and can be expressed as:
Figure BDA00037734726000000910
wherein P is core,1 Expressed as stator core consumption caused by magnetic density fundamental wave component under combined action of permanent magnet and armature, B core,1 Representing the magnetic density fundamental component of the core.
Since the fundamental magnetic field contributes most of the stator core loss, the stator core loss is approximately equal to the stator core loss generated by the fundamental magnetic field, and thus can be obtained:
Figure BDA00037734726000000911
the fundamental component of stator tooth magnetic flux synthesized by the permanent magnet and the armature magnetic field can be decomposed into the sum of the fundamental components of stator tooth magnetic flux under the independent action of the permanent magnet magnetic field and the armature magnetic field respectively, and is expressed as:
Figure BDA00037734726000000912
Figure BDA00037734726000000913
fundamental component of tooth flux representing the combination of permanent magnet and armature field,/->
Figure BDA00037734726000000914
Tooth magnetic flux fundamental component generated by permanent magnet, +.>
Figure BDA00037734726000000915
Fundamental component of tooth flux generated by the armature winding.
Step 4 may be further expressed as:
the permanent magnetic flux fundamental component is composed of only the air-gap flux fundamental component, and the armature magnetic flux fundamental component is composed of an air-gap flux fundamental component and a leakage magnetic flux fundamental component which are superimposed, and can be expressed as:
Figure BDA0003773472600000101
in the method, in the process of the invention,
Figure BDA0003773472600000102
fundamental component of stator tooth flux generated for permanent magnet air gap flux,/->
Figure BDA0003773472600000103
Fundamental component of stator tooth flux generated for armature air gap flux,/->
Figure BDA0003773472600000104
The leakage flux generated by the armature field is a fundamental component in the stator tooth flux.
Further, the specific steps of the step 5 are as follows:
step 5.1: the permanent magnet air gap flux density can be expressed as:
Figure BDA0003773472600000105
wherein m and n are respectively the harmonic orders of permanent magnet magnetomotive force and the harmonic orders of air gap magnetic permeability,
Figure BDA0003773472600000106
represents the air gap flux density generated by the permanent magnetic field, omega r For the mechanical rotational speed of the motor, lambda 0 Is the amplitude of the air gap flux guide of 0 times, Λ n For n air gap permeabilities of amplitude, P r Is the pole pair number of the permanent magnet, N s For the number of stator slots, C m The amplitude of the magnetomotive force of the permanent magnet air gap for m times is represented by θ, the circumferential position angle of the air gap is represented by t, and the time constant is represented by t.
Step 5.2: the armature air gap flux density can be expressed as:
Figure BDA0003773472600000107
/>
wherein i and j are harmonic orders, omega of armature magnetomotive force r Is the rotation speed of the rotor, S i 、S j iP for armature magnetomotive force r And jP r Subharmonic amplitude.
Step 5.3: the flux on the stator teeth is obtained by integrating the permanent magnet and armature air gap flux densities, respectively, where the permanent magnet air gap flux on the stator teeth can be expressed as:
Figure BDA0003773472600000111
wherein r is δ Is the radius of the air gap, l s For the axial length of the motor。
The armature air gap flux on the stator teeth can be expressed as:
Figure BDA0003773472600000112
step 5.4: further, the fundamental air gap flux generated on the stator teeth by the permanent magnet and the armature, respectively, acting alone, can be expressed as:
Figure BDA0003773472600000113
step 6, using the equivalent magnetic circuit method, the leakage magnetic flux generated by the armature magnetic field on the stator teeth can be calculated as:
Figure BDA0003773472600000114
wherein n is s For the number of turns of copper winding, I s Is the amplitude of the current, l s Mu, the axial length of the motor 0 Is vacuum permeability, h s Representing the height of the notch b s For the width of the notch, h w Is the groove height, b w For the width of the notch, P r Is the pole pair number omega of the permanent magnet r Is the mechanical rotational speed.
Further, the specific method in the step 7 is as follows: the unwanted magnetic flux is found out according to the modulation characteristics of the permanent magnet and the armature field of the field-modulated permanent magnet motor, and can be roughly divided into two types, namely, unwanted air gap magnetic flux generated by non-working harmonic waves generated by the air gap field under the independent action of the armature field, and unwanted leakage magnetic flux generated by the independent action of the armature field. The correctness of this analysis method is verified by two cases, namely: case one: the stator core loss is suppressed by suppressing non-operating harmonics of a specific order generated in the air gap by providing the same number of magnetic barriers as the number of pairs of rotor poles on the motor rotor (fig. 2 (a)). Case two: the stator slot shape is appropriately changed (fig. 2 (b)), slot reluctance is increased, slot leakage is reduced, and thus stator core loss is reduced.
Fig. 10 is a comparison of air gap harmonics of an original motor and a case-open-barrier motor in accordance with an embodiment of the present invention. As shown in the figure, the designed rotor magnetic flux barrier structure effectively inhibits the generation of high-hazard harmonics (1 st harmonic), while other harmonics are not affected basically. Fig. 11 and 12 are magnetic field line comparisons of an original motor and a case two motor with a slot shape change in an embodiment of the present invention. As shown in the figure, by increasing the opening of the notch, the magnetic leakage at the notch of the magnetic field modulation permanent magnet motor is reduced. Fig. 13 is a comparison of the magnetic fluxes of an original motor, a case one motor, and a case two motor in an embodiment of the present invention. As shown, the magnetic flux of both cases is significantly reduced compared to the original motor. To further evaluate the effects of the original motor and the two cases, the stator core loss and the torque of the two-scheme motor were compared with the original motor, respectively, as shown in fig. 14. As shown, the stator core losses of the original motor, the first motor and the second motor were 68.4w,61.4w and 53.9w, respectively, while the torque was maintained substantially constant around 23 Nm. Under the guidance of the method provided by the invention, the stator core loss can be restrained under the premise of ensuring that the motor torque density is unchanged.
In summary, the invention discloses a method for analyzing and inhibiting the stator core loss of a magnetic field modulation permanent magnet motor. According to the magnetic density distribution characteristics on the stator, the influence of the core fundamental wave magnetic field on the stator core loss is analyzed, the permanent magnet and the armature magnetic field of the motor are decoupled, and corresponding air gap magnetic flux is deduced. Meanwhile, an equivalent magnetic circuit model is established according to the leakage magnetic flux path, and corresponding leakage magnetic flux is deduced. And (3) establishing the relation between the stator core loss and the air gap magnetic flux and the leakage magnetic flux, analyzing the influence of the magnetic field modulation effect and the modulation pole structure on the core loss, and obtaining useless magnetic flux generated by non-working air gap magnetic field harmonic wave and leakage magnetic flux. The harmonic wave and leakage magnetic suppression method of the non-working air gap magnetic field is provided, and useless magnetic flux is reduced, so that the stator core loss is reduced on the premise of ensuring the torque. The invention can provide clear thought and theoretical guidance for the suppression of the stator core loss of the magnetic field modulation permanent magnet motor.
In the description of the present specification, reference to the terms "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.

Claims (7)

1. The method for analyzing and inhibiting the stator core loss of the magnetic field modulation permanent magnet motor is characterized by comprising the following steps of:
step 1: dividing a stator into a plurality of parts with the same magnetic flux path characteristics according to different magnetic flux path characteristics of a stator area, selecting representative points on each iron core according to the magnetic density distribution characteristics, calculating to obtain a curve of the magnetic density of each iron core changing along with time by using a finite element method, obtaining the amplitude of each magnetic density harmonic by using Fourier decomposition, substituting an iron core loss formula to calculate to obtain each part of iron core loss, and obtaining that the iron core loss of a stator tooth occupies a high proportion in the whole stator iron core loss, so that the suppression of the iron core loss of the stator tooth is selected as a target of stator iron core loss suppression;
step 2: comparing the contributions of the magnetic flux density harmonics of each secondary iron core to the stator tooth iron core loss, so that the fundamental wave of the magnetic flux density of the obtained iron core contributes most of the stator tooth iron core loss, wherein the stator tooth iron core loss is mainly generated by the fundamental wave magnetic flux passing through the stator iron core, and the fundamental wave component of the stator tooth magnetic flux is selected as a research object;
step 3: the fundamental wave is further expressed as a result of combining a permanent magnetic field component and an armature magnetic field component, and magnetic flux of the motor stator teeth is refined and decomposed and divided into magnetic flux of the stator teeth under independent actions of the permanent magnetic field and the armature magnetic field;
step 4: the stator tooth permanent magnetic flux fundamental component is only composed of an air gap flux fundamental component, and the stator tooth armature magnetic flux fundamental component is composed of an air gap flux fundamental component and a leakage flux fundamental component in a superposition mode; the analysis shows that the stator tooth magnetic flux under the action of the armature magnetic field has useless magnetic flux which does not contribute to torque and only generates loss, and the useless magnetic flux is formed by two parts according to the harmonic analysis of the air gap magnetic field under the action of the armature magnetic field and an equivalent magnetic circuit model, namely the air gap magnetic flux formed by the air gap magnetic field passing through the air gap, and the leakage magnetic flux which does not pass through the air gap and only links with the stator turns;
step 5: calculating the air gap flux density of the armature magnetic field generated by air gap magnetic field modulation, and deriving useless air gap magnetic flux of the stator teeth by integrating the air gap flux density in a range of the stator tooth pitch;
step 6: calculating to obtain the magnetic resistance of each part of the stator and the leakage magnetic flux of the stator teeth under the action of an armature magnetic field by using an equivalent magnetic circuit method according to the leakage magnetic flux path and the relevant size of the stator teeth;
step 7: the non-working harmonic wave is reduced, the magnetic leakage on the stator teeth is reduced, and the useless magnetic flux is reduced, so that the stator core loss of the permanent magnet motor is restrained from being modulated by the magnetic field.
2. The method for analyzing and suppressing the core loss of a stator of a magnetic field modulation permanent magnet motor according to claim 1, wherein in step 1: the calculation formula of the stator core loss is as follows:
Figure FDA0004149173100000011
wherein v is the number of blocks divided by the stator, k is the harmonic frequency of the magnetic density of the iron core, f is the frequency, B core,k Is the magnetic density of k times harmonic wave, A e For the eddy current coefficient, A h Is a hysteresis coefficient.
3. The method for analyzing and suppressing the core loss of the stator of the magnetic field modulation permanent magnet motor according to claim 1, wherein in step 3:
under the independent action of the permanent magnetic field and the armature magnetic field, the magnetic density expression of the stator core can be written as follows:
Figure FDA0004149173100000021
in the method, in the process of the invention,
Figure FDA0004149173100000022
representing the magnetic density produced by the permanent magnetic field, +.>
Figure FDA0004149173100000023
Indicates the magnetic density produced by the armature magnetic field, +.>
Figure FDA0004149173100000024
Represents the magnitude of the k-order magnetic density produced by the permanent magnetic field,/->
Figure FDA0004149173100000025
Represents the magnitude of the k-order magnetic density produced by the armature magnetic field,/->
Figure FDA0004149173100000026
Represents the k-order magnetic density phase angle produced by the permanent magnetic field,/->
Figure FDA0004149173100000027
The phase angle of the k-order flux density generated by the armature magnetic field, t represents time, and f represents frequency;
the fundamental wave composite flux density on the stator teeth can be regarded as the superposition of the permanent magnetic flux density and the armature fundamental wave flux density due to the high ratio of the fundamental wave in all iron core harmonics, and meanwhile, the amplitude of the two fundamental wave magnetic fields is in the following relation due to the fact that the two fundamental wave magnetic fields differ by a quarter period in the time domain:
Figure FDA0004149173100000028
substituting the fundamental wave magnetic density relationship into an iron core loss calculation formula to obtain an algebraic sum of the iron core loss of the stator under the independent action of the permanent magnet and the armature magnetic field, wherein the iron core loss generated by the fundamental wave in the two magnetic fields can be decomposed into the algebraic sum of the iron core loss of the stator under the independent action of the permanent magnet and the armature magnetic field, and the algebraic sum can be expressed as:
Figure FDA0004149173100000029
in the method, in the process of the invention,
Figure FDA00041491731000000210
stator core loss due to the fundamental component of the flux density generated by the permanent magnetic field, < >>
Figure FDA00041491731000000211
Stator core loss due to the magnetic density fundamental component generated for the armature magnetic field;
the stator core loss formula generated by the synthesized fundamental wave magnetic field obtained by superposing the core losses generated by the armature magnetic field and the permanent magnetic field is the same as the core loss formula when k=1, and can be expressed as:
Figure FDA00041491731000000212
wherein P is core,1 Expressed as stator core consumption caused by magnetic density fundamental wave component under combined action of permanent magnet and armature, B core,1 Representing the magnetic density fundamental component of the iron core;
since the fundamental magnetic field contributes most of the stator core loss, the stator core loss is approximately equal to the stator core loss generated by the fundamental magnetic field, and thus can be obtained:
Figure FDA0004149173100000031
the fundamental component of stator tooth magnetic flux synthesized by the permanent magnet and the armature magnetic field can be decomposed into the sum of the fundamental components of stator tooth magnetic flux under the independent action of the permanent magnet magnetic field and the armature magnetic field respectively, and is expressed as:
Figure FDA0004149173100000032
Figure FDA0004149173100000033
fundamental component of tooth flux representing the combination of permanent magnet and armature field,/->
Figure FDA0004149173100000034
The tooth magnetic flux fundamental component generated by the permanent magnet,
Figure FDA0004149173100000035
fundamental component of tooth flux generated by the armature winding.
4. The method for analyzing and suppressing the core loss of the stator of the magnetic field modulation permanent magnet motor according to claim 1, wherein the specific process of the step 4 is as follows:
the stator tooth permanent magnet flux fundamental component is composed of only the air gap flux fundamental component, and the stator tooth armature flux fundamental component is composed of the air gap flux fundamental component and the leakage flux fundamental component in superposition, which can be expressed as:
Figure FDA0004149173100000036
in the method, in the process of the invention,
Figure FDA0004149173100000037
is a permanent magnetic air gap magnetic fieldFundamental component of the stator tooth magnetic flux generated by, < >>
Figure FDA0004149173100000038
Fundamental component of stator tooth flux generated for armature air gap flux,/->
Figure FDA0004149173100000039
The leakage flux generated by the armature field is a fundamental component in the stator tooth flux.
5. The method for analyzing and suppressing the core loss of the stator of the magnetic field modulation permanent magnet motor according to claim 1, wherein the specific process of the step 5 is as follows:
step 5.1: the permanent magnet air gap flux density can be expressed as:
Figure FDA00041491731000000310
wherein m and n are respectively the harmonic orders of permanent magnet magnetomotive force and the harmonic orders of air gap magnetic permeability,
Figure FDA00041491731000000311
represents the air gap flux density generated by the permanent magnetic field, omega r For the mechanical rotational speed of the motor, lambda 0 Is the amplitude of the air gap flux guide of 0 times, Λ n For n air gap permeabilities of amplitude, P r Is the pole pair number of the permanent magnet, N s For the number of stator slots, C m The amplitude value of the magnetomotive force of the permanent magnet air gap for m times is represented by θ, the circumferential position angle of the air gap is represented by t, and the time constant is represented by t;
step 5.2: the armature air gap flux density can be expressed as:
Figure FDA0004149173100000041
wherein i and j are harmonic orders, omega of armature magnetomotive force r Is the rotation speed of the rotor, S i 、S j Armature magnet respectivelyiP of electromotive force r And jP r Subharmonic amplitude;
step 5.3: the flux on the stator teeth is obtained by integrating the permanent magnet and armature air gap flux densities, respectively, where the permanent magnet air gap flux on the stator teeth can be expressed as:
Figure FDA0004149173100000042
wherein r is δ Is the radius of the air gap, l s Is the axial length of the motor;
the armature air gap flux on the stator teeth can be expressed as:
Figure FDA0004149173100000043
step 5.4: further, the fundamental air gap flux generated on the stator teeth by the permanent magnet and the armature, respectively, acting alone, can be expressed as:
Figure FDA0004149173100000044
6. the method for analyzing and suppressing the core loss of the stator of the magnetic field modulation permanent magnet motor according to claim 1, wherein in step 6: the magnetic resistance of each part of the stator under the action of the armature magnetic field and the leakage magnetic flux of the stator teeth can be calculated by an equivalent magnetic circuit method as follows:
Figure FDA0004149173100000051
wherein n is s For the number of turns of copper winding, I s Is the amplitude of the current, l s Mu, the axial length of the motor 0 Is vacuum permeability, h s Representing the height of the notch b s For the width of the notch, h w Is the groove height, b w For the width of the notch, P r Is the pole pair number omega of the permanent magnet r Is the mechanical rotational speed.
7. The method for analyzing and suppressing the core loss of a stator of a magnetic field modulated permanent magnet motor according to claim 1, wherein the useless magnetic flux in the step 7 is divided into two types: one is the unwanted air gap flux generated by non-working harmonics generated by the air gap field under the action of the armature field alone; the other is leakage magnetic flux generated by the armature magnetic field alone.
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