A method for analyzing the Q-axis equivalent magnetic circuit of a permanent magnet motor with fractional slot distributed windings

Abstract

The present invention relates to the technical field of permanent magnet motors, and in particular to a method for analyzing the Q-axis equivalent magnetic circuit of a permanent magnet motor with a fractional slot distributed winding, comprising the following steps: determining two characteristic positions of the Q-axis magnetic circuit, and drawing the magnetic circuit model and its equivalent magnetic circuit of the two characteristic positions; determining the magnetic circuit flux expression of the magnetic resistance of each part and the magnetomotive force of the tooth under the two characteristic positions; obtaining the magnetomotive force of the tooth according to the arrangement of the stator winding of the motor; determining the number of teeth contained in each magnetic pole position, and respectively determining the characteristic position to which each magnetic pole position belongs and the magnetomotive force of the tooth contained in each magnetic pole position; calculating the magnetic resistance of each part; solving the magnetic circuit flux expression to obtain the magnetic circuit flux, and further obtaining the Q-axis inductance of the entire motor. The method can solve the problems of complex modeling, slow calculation speed, and inapplicability of the motor magnetic circuit calculation method of the fractional slot concentrated winding and the integer slot distributed winding in the prior art.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet motors, and in particular to a method for analyzing the Q-axis equivalent magnetic circuit of a permanent magnet motor with a fractional slot distributed winding. Background Art

[0002] A permanent magnet synchronous motor is a synchronous motor that generates a synchronous rotating magnetic field by excitation of a permanent magnet. The permanent magnet acts as a rotor to generate a rotating magnetic field. The three-phase stator winding induces a three-phase symmetrical current through armature reaction under the action of the rotating magnetic field. At this time, the rotor kinetic energy is converted into electrical energy, and the permanent magnet synchronous motor is used as a generator. In addition, when a three-phase symmetrical current is passed through the stator side, since the three-phase stator differs by 120 degrees in spatial position, the three-phase stator current generates a rotating magnetic field in space, and the rotor moves in the rotating magnetic field under the action of electromagnetic force. At this time, the electrical energy is converted into kinetic energy, and the permanent magnet synchronous motor is used as a motor.

[0003] Conventional motor magnetic circuit analysis methods mainly include finite element method and equivalent magnetic circuit method. In recent years, with the rapid development of computer software and hardware, finite element method has gradually become the mainstream of motor design due to its ultra-high calculation accuracy and low usage threshold, but it still has defects such as slow calculation and high requirements for computer hardware. The traditional equivalent magnetic circuit method has a long history and is widely used. It can quickly analyze and calculate the magnetic circuits of various motors and solve various parameters in the motor. Its accuracy is within the allowable error of the project and meets the design requirements.

[0004] In the existing magnetic circuit calculation methods, the analysis is often carried out for integer slot distributed windings and fractional slot concentrated windings. The number of slots corresponding to each pair of poles of integer slot distributed windings is fixed, that is, the magnetic circuit topology under all poles is basically the same, and the magnetic circuit only exists in one position; the magnetic circuit of fractional slot concentrated windings mainly requires solving the situation that one pole corresponds to one winding, and the position deviation is corrected by adding a coefficient, and the magnetic circuit generally only exists in one position. The magnetic circuit distribution of these two pole-slot combinations is independent of or has little relationship with the position, and the topological difference of this circuit caused by the position change is not considered in the calculation. The number of windings corresponding to each pole of the fractional slot distributed winding is a large fraction, that is, one pole corresponds to a few (distinguished from 1.0 of the fractional slot concentrated winding) slots, so the magnetic circuit under each pole of the rotor is different, and it is difficult to use a magnetic circuit topology to analyze the magnetic circuit situation at each position, so the motor magnetic circuit calculation method for fractional slot concentrated windings and integer slot distributed windings is not applicable. Summary of the invention

[0005] In view of the defects existing in the prior art, the purpose of the present invention is to provide a method for analyzing the Q-axis equivalent magnetic circuit of a permanent magnet motor with a fractional-slot distributed winding, which can solve the problems in the prior art of complex modeling, slow calculation speed, and the inapplicability of the motor magnetic circuit calculation methods for fractional-slot concentrated windings and integer-slot distributed windings.

[0006] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0007] The present invention provides a method for analyzing the Q-axis equivalent magnetic circuit of a permanent magnet motor with a fractional slot distributed winding, comprising the following steps:

[0008] Determine the two characteristic positions of the Q-axis magnetic circuit, and draw the magnetic circuit models and their equivalent magnetic circuits at the two characteristic positions;

[0009] According to the equivalent magnetic circuit of the magnetic circuit model at two characteristic positions, the magnetic circuit flux expressions of the magnetic resistance of each part and the magnetomotive force of the corresponding tooth at the two characteristic positions are determined;

[0010] According to the arrangement of the motor stator winding, the distribution of the stator magnetomotive force about the teeth is solved to obtain the stator tooth magnetomotive force;

[0011] Divide the half unit motor into a plurality of magnetic pole positions according to the number of poles contained in the half unit motor, determine the number of teeth contained in each magnetic pole position, and respectively determine the characteristic position to which each magnetic pole position belongs and the tooth magnetomotive force of the teeth contained in each magnetic pole position;

[0012] According to the specific structure of the motor stator and rotor, calculate the magnetic resistance of each part respectively;

[0013] Substitute the magnetic resistance of each part at the two characteristic positions and the tooth magnetomotive force of the teeth contained in each magnetic pole position into the magnetic circuit flux expression of the corresponding characteristic position, solve the magnetic circuit flux, and further obtain the Q-axis inductance of the entire motor.

[0014] In some optional solutions, the determining of two characteristic positions of the Q-axis magnetic circuit and drawing the magnetic circuit model of the two characteristic positions and their equivalent magnetic circuits include:

[0015] The rotor motor is analyzed to determine the two characteristic positions of the Q-axis magnetic circuit. The two characteristic positions are: one magnetic pole corresponds to slots and slots, where Z is the number of slots in the motor and p is the number of motor pole pairs;

[0016] According to the magnetic circuit analysis theory, the magnetic circuit models at two characteristic positions are drawn respectively;

[0017] The equivalent magnetic circuits at two characteristic positions are drawn based on the magnetic circuit model.

[0018] In some optional schemes, the equivalent magnetic circuit of the magnetic circuit model at the two characteristic positions is used to determine the magnetic circuit flux expression for each part of the magnetic resistance and the magnetomotive force of the tooth at the two characteristic positions, including:

[0019] Kirchhoff's law is used to analyze and calculate the equivalent magnetic circuit of the magnetic circuit model at two characteristic positions, and Kirchhoff's equation of the magnetic circuit is listed, that is, the magnetic flux expression of the magnetic circuit for each part of the magnetic resistance and the magnetomotive force of the tooth at the two characteristic positions is obtained.

[0020] In some optional solutions, the calculation and solution of the partial magnetic resistance at two characteristic positions respectively according to the specific structure of the stator and rotor of the motor includes:

[0021] According to the size structure of each part of the stator and rotor, the magnetic resistance of each part of the magnetic circuit is analytically calculated to obtain the magnetic resistance of each part at two characteristic positions.

[0022] In some optional solutions, the magnetic resistance of each part of the magnetic circuit is analytically calculated according to the size structure of each part of the stator and rotor to obtain the magnetic resistance of each part at two characteristic positions, including:

[0023] The overall block of each magnetic resistance part is divided into rectangular areas and / or irregular areas;

[0024] For a rectangular region with a regular cross section, the rectangular region magnetic resistance is obtained according to the rectangular magnetic resistance calculation formula;

[0025] For any region with irregular cross-sectional area, the magnetic reluctance of the irregular region is calculated by integration;

[0026] This part of the magnetic resistance is obtained by integrating all the magnetic resistances in the rectangular area and the magnetic resistances in the irregular area according to the series-parallel relationship.

[0027] In some optional solutions, for any region with irregular cross-sectional area, the magnetic resistance of the irregular region is calculated by integration, including:

[0028] In the direction perpendicular to the magnetic flux cross section, the cross-sectional area S of the region with a length of l is written as a function S(x) related to the position. S(x) is a continuous function or a piecewise function.

[0029] The magnetic field density function at different positions is B(x) = Φ / S(x). According to the known μ r Functional relationship with B r =f(B), we can get the magnetic permeability function μ r (x)=f(B(x))=f(Φ / S(x)), μ r is the relative magnetic permeability, Φ is the magnetic flux;

[0030] According to the rectangular magnetic resistance calculation formula, the magnetic resistance expression of this area is obtained by integration: or Among them, l1, l2, ... l are the segment division positions in the length direction, μ0 is the vacuum permeability, μ ris the relative magnetic permeability of ferromagnetic material.

[0031] In some optional solutions, the half unit motor is divided into multiple positions according to the number of poles contained in the half unit motor, the number of teeth contained in each position is determined, and the characteristic positions to which each position belongs are determined, including:

[0032] Divide half of the unit motor into k equal parts to obtain k magnetic pole positions, k is The denominator after being reduced to the simplest fraction is the number of poles under half a unit motor;

[0033] The magnetomotive force is distributed according to the space proportion of the teeth at each magnetic pole position. When the number of teeth contained in the magnetic pole position is greater than or equal to When The characteristic magnetic circuit model calculates the magnetic pole position, otherwise it is calculated according to The characteristic magnetic circuit model calculates the magnetic pole position to determine the tooth magnetomotive force of each tooth in the k magnetic pole positions under half a unit motor.

[0034] In some optional schemes, according to the characteristic positions to which each position belongs, the partial magnetic resistances at the two characteristic positions and the tooth magnetomotive force at each position under the half unit motor are substituted into the magnetic circuit flux expression of the corresponding characteristic position, and the magnetic circuit flux is solved, and the Q-axis inductance of the entire motor can be further obtained, including:

[0035] According to the characteristic positions to which each position belongs, the partial magnetic resistances at the two characteristic positions and the tooth magnetomotive force of each tooth at the corresponding magnetic pole position under the half-unit motor are substituted into the magnetic circuit flux expression of the corresponding characteristic position, and the magnetic circuit flux expression is solved to obtain the main magnetic flux at each magnetic pole position in the half-unit motor;

[0036] According to the main magnetic flux of each magnetic pole position in the half unit motor, the Q-axis inductance of the half unit motor is obtained;

[0037] Based on the Q-axis inductance of half a unit motor, the Q-axis inductance of the entire motor is obtained by symmetry.

[0038] In some optional solutions, obtaining the Q-axis inductance of the half-unit motor according to the main magnetic flux at each magnetic pole position in the half-unit motor includes:

[0039] According to the formula Determine the flux Φ of a half-unit motor qh , where Φ qk is the main magnetic flux at each pole position;

[0040] According to the formula Determine the Q-axis inductance L of the half-unit motor qh , I qis the Q-axis current.

[0041] In some optional solutions, the Q-axis inductance of the entire motor is obtained by symmetry based on the Q-axis inductance of the half unit motor, including:

[0042] According to the formula L q =2ktL qh , the Q-axis inductance of the entire motor is obtained, where k is the number of poles under half a unit motor and t is the number of unit motors.

[0043] Compared with the prior art, the advantages of the present invention are: by selecting a permanent magnetic pole on the rotor for analysis, two characteristic positions are determined, magnetic circuit model diagrams and equivalent magnetic circuits at the two characteristic positions are drawn respectively, and magnetic circuit flux expressions at the two characteristic positions are analyzed; the magnetic resistance of each part at the two characteristic positions is solved; the half unit motor is divided into multiple magnetic pole positions according to the number of poles contained in the half unit motor, and the tooth magnetomotive force belonging to each magnetic pole position is solved; the calculated results of magnetic resistance and magnetomotive force are substituted into the magnetic circuit flux expression to obtain the magnetic flux Φ of k magnetic pole positions. qk The analytical solution is combined with the current to obtain the Q-axis inductance. Compared with the finite element simulation analysis, it has the advantages of simple modeling, greatly simplified calculation, and fast calculation speed. It avoids the complexity and huge workload of listing the magnetic circuit of each rotor position, as well as the problem that the calculation method of the motor magnetic circuit of fractional slot concentrated winding and integer slot distributed winding is not applicable. At the same time, the error is also within the allowable error range of the project. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0045] Figure 1 Schematic diagram of a Q-axis equivalent magnetic circuit analysis method for a permanent magnet motor with fractional slot distributed windings according to an embodiment of the present invention;

[0046] Figure 2(a) and 2(b) They are magnetic circuit model diagrams of the first characteristic position and the second characteristic position of an embodiment of the present invention respectively.

[0047] Figure 3(a) and 3(b) They are the equivalent magnetic circuit diagrams of the first characteristic position and the second characteristic position of the embodiments of the present invention respectively.

[0048] Figure 4 This is a diagram marking the structural parameters of a motor rotor according to an embodiment of the present invention.

[0049] Figure 5 This is a diagram marking the structural parameters of the motor stator according to an embodiment of the present invention.

[0050] Figure 6 4 is a spatial distribution diagram of the winding functions of each phase according to an embodiment of the present invention.

[0051] Figure 7 Graph showing the synthetic magnetomotive force distribution of each tooth (slot) according to an embodiment of the present invention.

[0052] Figure 8 Schematic diagram of magnetic pole position and tooth (slot) distribution according to an embodiment of the present invention.

[0053] Fig. 9 R of the embodiment of the present invention t2 Schematic diagram of partial conduction magnetic resistance calculation analysis.

[0054] Fig.10 R of the embodiment of the present invention t1 Schematic diagram of partial conduction magnetic resistance calculation analysis. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0056] The embodiments of the present invention are further described in detail below with reference to the accompanying drawings.

[0057] like Figure 1 As shown, the present invention provides a method for analyzing the Q-axis equivalent magnetic circuit of a permanent magnet motor with a fractional slot distributed winding, comprising the following steps:

[0058] S1. Determine the two characteristic positions of the Q-axis magnetic circuit, and draw the magnetic circuit model of the two characteristic positions and their equivalent magnetic circuit.

[0059] Step S1 specifically includes:

[0060] S11. Analyze the motor and determine the two characteristic positions of the Q-axis magnetic circuit. The two characteristic positions are: one magnetic pole corresponds to slots and slots, where Z is the number of slots in the motor and p is the number of pole pairs in the motor.

[0061] Taking a 360-slot 84-pole permanent magnet motor as an example, calculate based on the number of poles and slots Rounding off, we determine that the two characteristic positions are one pole corresponding to 5 teeth (first characteristic position) and one pole corresponding to 4 teeth (second characteristic position). In this example, Round up.

[0062] S12. Based on the magnetic circuit analysis theory, draw the magnetic circuit models at two characteristic positions respectively.

[0063] Taking the 360-slot 84-pole permanent magnet motor as an example, two characteristic position magnetic circuit models are drawn, as shown in Figure 2(a), Figure 2(b) and Figure 5 shown.

[0064] Where: R c1 , R c2 , R c3 , R c4 is the magnetic resistance of the tooth; R e1 , R e2 , R e3 , R e4 is the stator yoke reluctance; F qs1 、F qs2 、F qs3 、F qs4 is the magnetomotive force of the tooth under the q-axis magnetic circuit; R g1 , R g2 , R g3 , R g4 is the air gap reluctance; R t1 , R t2 , R t3 , R t4 is the conduction magnetic resistance. q1 is the q-axis main magnetic flux, φ1, φ2, φ3, φ4 are the magnetic fluxes of the four magnetic circuit branches, and φ5 and φ6 are the magnetic fluxes of the other two magnetic circuit branches in Figure 2(b). The magnetomotive force of the corresponding tooth is the magnetomotive force of each stator tooth magnetomotive force in the corresponding magnetic pole position. If all are in the corresponding magnetic pole position, the magnetomotive force of the stator tooth is the magnetomotive force of the corresponding tooth, and the magnetic resistance of the corresponding tooth is also obtained in the same way.

[0065] S13. Draw the equivalent magnetic circuits of two characteristic positions based on the magnetic circuit model.

[0066] Taking the 360-slot 84-pole permanent magnet motor as an example, the corresponding equivalent magnetic circuits are drawn according to the magnetic circuit models at two characteristic positions, as shown in Figure 3(a) and Figure 3(b).

[0067] S2. According to the equivalent magnetic circuit of the magnetic circuit model at the two characteristic positions, determine the magnetic circuit flux expression for each part of the magnetic resistance and the magnetomotive force of the corresponding tooth at the two characteristic positions.

[0068] Step S2 specifically includes: using Kirchhoff's law to perform analytical calculation on the equivalent magnetic circuit of the magnetic circuit model at two characteristic positions, and writing the magnetic circuit Kirchhoff equation, that is, obtaining the magnetic circuit flux expression for each part of the magnetic resistance and the magnetomotive force of the tooth at the two characteristic positions.

[0069] Taking the 360-slot 84-pole permanent magnet motor as an example, the equation group for the first characteristic position is:

[0070] F qs1 -φ1(R c1 +R e1 +R g1 +R t1 )-(φ1+φ2)(R e2 +R e3 )-φ4(R c4 +R e4 +R g4 +R t4 )-F qs4 =0

[0071] F qs2 -φ2(R c2 +R e2 +R g2 +R t2 )-(φ1+φ2)(R e2 +R e3 )-φ3(R c3 +R g3 +R t3 )-F qs3 =0

[0072] φ q1 =φ1+φ2=φ3+φ4

[0073] φ1=φ2

[0074] φ3=φ4

[0075] The system of equations for the second characteristic position is:

[0076] F qs1 -(φ1-φ5)R t1 -φ1(R g1 +R c1 +R e1 )-(φ1+φ2)R e2 -φ4(R e3 +R c4 +R g4 )-F qs4 -(φ4-φ6)R t4 =0

[0077] φ4-φ6=φ1-φ5

[0078] F qs2 -(φ2+φ5)R t2 -φ2(R g2 +R c2 )-(φ1+φ2)R e2 -φ3(R c3 +R g3 )-F qs3 -(φ3+φ6)R t3 =0

[0079] φ3+φ6=φ2+φ5

[0080] φ1+φ2=φ3+φ4

[0081] (φ1-φ5)(R t1 +R t4 )+φ6R b2 -(φ3+φ6)(R t2 +R t3 )R e2 -φ5R b1 =0

[0082] Among them, R b1 and R b2 They are the magnetic resistance of the magnetic bridge in Figure 2(b) respectively.

[0083] Without considering the stator magnetic saturation, the magnetic resistance of the stator teeth and yoke is negligible, and we have:

[0084] R c1 =R c2 =R c3 =R c4 =0

[0085] R e1 =R e2 =R e3 =R e4 =0

[0086] The rotor structure has only one layer of permanent magnets, and the magnetic channel area is large, which is not easy to saturate, so the magnetic reluctance can also be ignored, that is:

[0087] R t1 =R t2 =R t3 =R t4 =0

[0088] If there are multiple layers of permanent magnets, the magnetic resistance of the magnetic paths between the permanent magnet layers cannot be ignored.

[0089] Simplifying, we get:

[0090] The characteristic equation system for the first characteristic position:

[0091]

[0092]

[0093]

[0094] The characteristic equation system for the second characteristic position is:

[0095]

[0096]

[0097]

[0098] It should be noted that although the two characteristic position expressions are the same, they are different. In this calculation, because the core material is not saturated, R t1 =R t2 =R t3 =R t4 = 0, the two paths φ5 and φ6 added at the second characteristic position compared to the first characteristic position have no magnetic flux passing through. When the saturation phenomenon is more serious or other conditions where the rotor core magnetic resistance cannot be ignored, the magnetic flux expressions at the two positions of the q axis are different.

[0099] S3. According to the arrangement of the motor stator winding, solve the distribution of the stator magnetomotive force about the teeth and obtain the stator tooth magnetomotive force

[0100] According to the winding theory, draw the distribution diagram of the magnetomotive force under the unit motor according to the slot number:

[0101] Let the motor position be such that the rotor q-axis coincides with the maximum axis of the stator side A-phase winding magnetomotive force. At this time, id = 0, and the entire stator winding current is the q-axis current. According to the winding magnetomotive force theory, the winding arrangement is analyzed, and the A, B, and C three-phase winding function N(θ) is first calculated, and the following is obtained: Figure 6 The distribution diagram of each phase winding function about space is shown, and then the formula is:

[0102] F a =N(θ) a I a

[0103] F b =N(θ) b I b

[0104] F c =N(θ) c I c

[0105] Among them, I a,I b ,I c are the currents of the three phases A, B, and C in the motor respectively. F is the three-phase composite magnetomotive force, F a is the magnetomotive force of phase A, F b is the magnetomotive force of phase B, F c is the C phase magnetomotive force. Calculate the magnitude of each phase magnetomotive force, and then use:

[0106] F=F a +F b +F c

[0107] Calculate the spatial distribution of the synthetic magnetomotive force. Taking the 360-slot 84-pole permanent magnet motor as an example, we get Figure 7 The magnetomotive force distribution diagram of each tooth (slot) is shown, that is, the magnetomotive force of teeth No. 1 to No. 30 is F1-F 30 .

[0108] S4. Divide the half unit motor into multiple magnetic pole positions according to the number of poles contained in the half unit motor, determine the number of teeth contained in each magnetic pole position, and determine the characteristic positions to which each magnetic pole position belongs and the tooth magnetomotive force of each tooth at the corresponding magnetic pole position.

[0109] Step S3 specifically includes:

[0110] Divide half of the unit motor into k equal parts to obtain k magnetic pole positions, k is The denominator after being reduced to the simplest fraction is the number of poles in half a unit motor.

[0111] The magnetomotive force is distributed according to the space proportion of the teeth at each magnetic pole position. When the number of teeth contained in the magnetic pole position is greater than or equal to When The characteristic magnetic circuit model calculates the magnetic pole position, otherwise it is calculated according to The characteristic magnetic circuit model calculates the magnetic pole position to determine the tooth magnetomotive force of each tooth in the k magnetic pole positions under half a unit motor.

[0112] When dividing the magnetic pole position, when the number of teeth contained in the magnetic pole position is less than But greater than When the integer is rounded, the excess tooth magnetomotive force after rounding is added to the adjacent teeth in the magnetic pole position for calculation. When the intersection of two magnetic pole positions is located on the tooth, the magnetomotive force is distributed according to the space share of each position on the tooth, for example, Figure 8 As shown, the number of teeth contained in pole position 4 is greater than or equal to When The characteristic magnetic circuit model calculates the magnetic pole position, and the number of teeth contained in the adjacent magnetic pole position 5 is less than But greater than The division position is located at the junction of the two magnetic pole positions. The magnetic pole position 5 includes more than 4 teeth, but it is calculated according to the second characteristic position. The tooth magnetomotive force of the tooth shared with the magnetic pole position 4 is added to the adjacent tooth in the magnetic pole position 4 for calculation.

[0113] In motor theory, a unit motor is usually used to analyze waveforms such as magnetomotive force. The number of unit motors is represented by t, indicating that a motor contains t unit motors, and its magnetomotive force and other waveforms are also t repetitions of the unit motor. In a complete cycle of the magnetomotive force contained in a unit motor, the positive and negative half-cycles are the same in magnitude and opposite in polarity, and the flux generated is also the same in magnitude and opposite in direction. From the definition of the inductance formula, it can be seen that inductance is only related to the magnitude of flux, so when analyzing inductance, the situation under half a unit motor can be analyzed. The number of poles contained in half a unit motor is equal to k.

[0114] Taking the 360-slot 84-pole permanent magnet motor as an example, k=7

[0115] The stator and rotor space contained in half of the unit motor is divided equally according to the number of magnetic poles k. The number of slots occupied by each magnetic pole is Draw a diagram of the magnetic pole position distribution, such as Figure 8 shown.

[0116] In the figure, half of the magnetic pole space is divided into seven equal parts with the rotor permanent magnet as the center. The angle of the rotor position offset is a simplification to ensure that the q-axis is aligned with the A-phase magnetomotive force axis, which does not affect the entire analysis process. Here, the rotor is rotated 1° counterclockwise compared to the stator, so that the lower edge of the rotor at magnetic pole position 1 divides stator tooth 1 equally.

[0117] In this example, half of the motor unit occupies one twelfth of the circumference, that is, 30°. The stator has 30 slots (teeth), one slot plus a tooth is 1°, and the slots (teeth) from bottom to top are 1-30. Only 1-3 are marked in the figure. The same applies to the following. Similarly, half of the motor unit is divided into seven magnetic pole positions from bottom to top, that is, the positions when k=1-7. Each magnetic pole position occupies

[0118] According to this correspondence, it is easy to calculate the number of teeth corresponding to each pole position. When the number of teeth contained in the pole position is greater than or equal to When The characteristic magnetic circuit model calculates the position, otherwise it is calculated according to The characteristic magnetic circuit model calculates the position. In this way, the seven magnetic pole positions are calculated using the characteristic magnetic circuit model:

[0119] In this example, the magnetic circuit is symmetrically distributed and easy to calculate, that is, k = 1, 7 magnetic circuits are the same, k = 2, 6 magnetic circuits are the same, and k = 3, 5 magnetic circuits are the same. Among them, the magnetic pole positions 1, 4, and 7 are the first characteristic position magnetic circuits; 2, 3, 5, and 6 are the second characteristic position magnetic circuits. For the case where a tooth is on the boundary line between two magnetic pole positions, the magnetomotive force is distributed according to the spatial proportion of the tooth at each position, and the magnetomotive force F of a tooth on the boundary line between two magnetic pole positions in this example is calculated. MMF Distribution between teeth:

[0120] from Figure 8 It can be seen from the figure, or from the calculation, that teeth 1, 30, 14, and 18 need to be allocated with tooth magnetomotive force. Among them, teeth 1 and 30 are symmetrical, with the boundary line of the magnetic pole position in the middle of the tooth, and the tooth magnetomotive force is half on the left and half on the right; teeth 14 and 18 are calculated to occupy half of the slot on the left and half on the right. and The tooth magnetomotive force of each tooth at the corresponding magnetic pole position is the magnetomotive force divided by the space occupied by the magnetomotive force of each stator tooth at the corresponding magnetic pole position. If all are at the corresponding magnetic pole position, the magnetomotive force of the stator tooth is the magnetomotive force of the tooth.

[0121] Calculate the magnetomotive force at the 1st and 7th magnetic pole positions from Figure 7 The magnetomotive force of teeth 1 to 30 can be obtained, and the magnetomotive force of teeth 31 can be obtained by symmetry. According to the above analysis, the magnetic circuit adopts the first characteristic position magnetic circuit.

[0122] For magnetic pole position 1 (the first magnetic pole position), calculate F qs1 ~F qs4 :

[0123] The magnetomotive force of the tooth No. 1 at the first magnetic pole position:

[0124]

[0125] F1 is the magnetomotive force of tooth 1, Nc is the number of turns of the coil, I is the current flowing through a coil, I=I q / a, a is the number of parallel branches, I q is the q-axis current.

[0126] The magnetomotive force of the tooth No. 2 at the first magnetic pole position:

[0127]

[0128] The magnetomotive force of the tooth belonging to the third tooth at the first magnetic pole position is 0;

[0129] The magnetomotive force of the tooth No. 4 at the first magnetic pole position:

[0130]

[0131] The magnetomotive force of the tooth No. 5 at the first magnetic pole position:

[0132]

[0133] Calculate the magnetomotive force at the 2nd and 6th pole positions. According to the above analysis, the magnetic circuit adopts the second characteristic position magnetic circuit.

[0134] For magnetic pole position 2, calculate F qs1 ~F qs4 :

[0135] The magnetomotive force of the tooth No. 6 at the second magnetic pole position:

[0136]

[0137] The magnetomotive force of the tooth No. 7 at the second magnetic pole position:

[0138]

[0139] The magnetomotive force of the tooth No. 8 at the second magnetic pole position:

[0140]

[0141] The magnetomotive force of the tooth No. 9 at the second magnetic pole position:

[0142]

[0143] Calculate the magnetomotive force at the 3rd and 5th pole positions. According to the above analysis, the magnetic circuit adopts the magnetic circuit corresponding to the second characteristic position, and the excess magnetomotive force needs to be converted.

[0144] For the magnetic pole position 3, calculate F qs1 ~F qs4 :

[0145] The magnetomotive force of the tooth No. 10 at the third magnetic pole position:

[0146]

[0147] The magnetomotive force of the tooth No. 11 at the third magnetic pole position:

[0148]

[0149] The magnetomotive force of the tooth of the twelfth tooth at the third magnetic pole position:

[0150]

[0151] The magnetomotive force of the 13th and 14th teeth at the third magnetic pole position:

[0152]

[0153] Calculate the magnetomotive force at the 4-pole position, and the magnetic circuit uses the magnetic circuit corresponding to the second characteristic position.

[0154] For the magnetic pole position 4, calculate F qs1 ~F qs4 :

[0155] The magnetomotive force of the tooth No. 14 at the 4th magnetic pole position:

[0156]

[0157] The magnetomotive force of the tooth No. 15 at the 4th magnetic pole position:

[0158]

[0159] The magnetomotive force of the tooth No. 17 at the 4th magnetic pole position:

[0160]

[0161] The magnetomotive force of the tooth No. 18 at the 4th magnetic pole position:

[0162]

[0163] S5. According to the specific structure of the motor stator and rotor, calculate and solve the magnetic resistance of each part at the two characteristic positions respectively.

[0164] In step S5, the magnetic resistance of each part is calculated and solved, specifically including: according to the size structure of each part of the stator and rotor, the magnetic resistance of each part of the magnetic circuit is analytically calculated to obtain the magnetic resistance of each part at two characteristic positions. Specifically:

[0165] S51: Divide the entire block of the partial magnetic resistance into rectangular areas and / or irregular areas.

[0166] In this example, for the stator tooth reluctance, stator yoke reluctance, air gap reluctance and conduction reluctance, the overall reluctance block itself is a regular rectangular area, and after being divided, it is also a regular block.

[0167] S52: For a rectangular driving region with a regular cross section, the rectangular region magnetic resistance is obtained according to a rectangular magnetic resistance calculation formula.

[0168] S53: For any region with irregular cross-sectional area, the magnetic resistance of the irregular region is calculated by integration.

[0169] S54: Obtain the partial magnetic resistance by connecting all the magnetic resistances in the rectangular area and the magnetic resistances in the irregular area according to the series-parallel relationship.

[0170] like Figure 4 , Fig. 9 and Fig.10 As shown in the figure, for the specific structure of a magnetic pole, for any region with irregular cross-sectional area, the magnetic resistance of the irregular region is calculated by integration. The magnetic resistance calculation formula of each part is as follows:

[0171] For non-rectangular regions, for example, the cross-sectional area of ​​the on-resistance is not a fixed value, resulting in different magnetic field densities at different locations. To calculate more accurately, the basic idea is:

[0172] Step 1: Write the cross-sectional area S of the region with a length of l as a function S(x) related to the position x in a direction perpendicular to the magnetic flux cross section. It can be a continuous function or a piecewise function.

[0173] Step 2: The magnetic field density function at different positions is B(x) = Φ / S(x), and then based on the known μ r Relationship with Bμ r =f(B), we can get μ r (x)=f(B(x))=f(Φ / S(x)), μ r is the relative magnetic permeability of ferromagnetic material, and Φ is the magnetic flux.

[0174] Step 3: Calculate the rectangular magnetic resistance according to the formula S is the cross-sectional area of ​​the rectangular area perpendicular to the magnetic flux, that is, the cross-sectional area of ​​the magnetic circuit, l is the length of the rectangular area perpendicular to the magnetic flux, that is, the length of the magnetic circuit, and the integral gives the magnetic resistance expression: or

[0175] Among them, l1, l2, ...l are the segment division positions in the length direction, and μ0 is the vacuum permeability.

[0176] During specific calculations, the position x can be divided into n equal-length portions. When n is larger, each portion can be approximated as a rectangle, and the calculation accuracy is higher.

[0177] A specific embodiment of solving magnetic resistance is given below:

[0178] For example, the upper half of the conduction reluctance is divided into equal R t2 and R t3 , as shown in Figure 2(a) and Figure 3(a), where R t2 The on-resistance of the part is calculated as follows:

[0179] like Fig. 9 As shown, R t2The part is divided into regions 1, 2, and 3 in the figure, that is, the dotted lines in the figure divide the regions region ①, region ②, and region ③. Region ① and region ③ are rectangular, and the cross-sectional area along the magnetic flux direction remains unchanged. The relative magnetic permeability μ r Unchanged, combined Figure 4 , so by We can get:

[0180]

[0181]

[0182] Among them, w b1 for Fig. 9 The width of the rectangular area in region①, l a5 The central axis and Fig. 9 The distance between the right vertical side of the upper left air barrier, l a1 for Fig. 9 The length of the upper side of the air magnetic barrier in the upper left center; l a3 for Fig. 9 The length of the upper side of the air magnetic barrier in the middle, that is, Fig. 9 w is twice the width of the rectangular area in region ③; a4 like Figure 4 The length of the label is shown in .

[0183] For region 2, if Fig. 9 As shown in the figure, along the direction of magnetic flux, only the size of the cross-sectional area changes. The cross-sectional area of ​​region ② corresponding to position x changes along S x It can be expressed as the following piecewise function form, where S max The corresponding position l1 is the segmentation point of the piecewise function:

[0184]

[0185] Among them, S max =(l a5 -0.5l a3 +w a4 / (2cos(α)))cos(α)l st , l st is the axial length of the motor, Fig. 9 The angle between the central axis of the left permanent magnet pole or the outer lower side line of the left permanent magnet pole, S max for Fig. 9 The maximum cross-sectional area of ​​region ②, S x is the cross-sectional area of ​​region② corresponding to position x, x is Fig. 9 The distance from the upper right edge of the left permanent magnet pole to its upper left edge, l1 is Fig. 9 The distance between the upper left edge of the left permanent magnet pole and the maximum cross-sectional area of ​​region ②.

[0186] Then the magnetic resistance expression of region 2 can be obtained as:

[0187]

[0188] Among them, l m for Fig. 9 The length of the upper right side of the left permanent magnet pole is Φ, which is the magnetic flux.

[0189] According to the series-parallel relationship of R1, R2 and R3, we can get R t2 =R1+R2+R3

[0190] For example, the lower half of the conduction magnetic resistance is divided into equal R t1 and R t4 , as shown in Figure 2(a) and Figure 3(a), where R t1 The on-resistance of the part is calculated as follows:

[0191] like Fig.10 As shown, R t1 The part is divided into regions 1, 2, and 3 in the figure, namely region ①, region ②, and region ③ marked with dotted lines in the figure. Region ① is divided according to the above Fig.10 The method is used to divide it into two rectangles and one triangle. Similarly, region ③ is divided into a rectangle and a triangle.

[0192] For the Q-axis magnetic circuit, the magnetic flux direction passes through regions 1-2-3, and the magnetic flux direction changes from the rotor radial direction to the magnet direction to the rotor radial direction, as shown by the orange arrow in the figure above. Therefore, for the rectangular parts of regions 1 and 3, along the magnetic flux direction, the size and normal direction of the cross-sectional area S remain unchanged, μ r Unchanged, use The calculation can be done. However, in the triangular parts of area 1 and area 3, the direction of the magnetic flux changes from time to time, and the size of the cross-sectional area S and the direction of the normal change at the same time, so it is impossible to directly use the formula or simple integration to calculate. Since the two triangular areas are small, during the process of the change of the normal direction of the cross-sectional area S, it can be approximately considered that the size of the cross-sectional area S remains unchanged, and the effective length l in the normal direction is approximately half of the length of the triangular area. In summary, by The magnetic resistance expression of regions 1 and 3 is obtained as follows:

[0193]

[0194]

[0195] Among them, w b1 for Fig. 9 The width of the rectangular area in region① is Fig.10 w in b1 Same, w p is the distance between adjacent upper air magnetic barriers, w a2 for Fig.10 The length of the air magnetic barrier at the upper middle part at the maximum cross-sectional area along the length direction of the corresponding permanent magnet pole; and so on. a5 、w m and w a7 The length of Figure 4 , Fig. 9 and Fig.10 As shown in the markings.

[0196] Similarly, for region 2, Fig.10 As shown in the figure, along the direction of magnetic flux, only the size of the cross-sectional area S changes. The cross-sectional area S corresponding to position x x It can be expressed as the following piecewise function form, where the cross-sectional area corresponding to position x = 0 is S0, and the cross-sectional area corresponding to position x = l m The cross-sectional area is The position l1 shown in the figure is the segmentation point of the piecewise function.

[0197]

[0198] Where S0=(w p / 2cos(α)-(w m -l a2 -w a1 tan(α)))l st and S lm =(w a7 / sin(α))l st .

[0199] Then the magnetic resistance expression of region 2 can be obtained as:

[0200]

[0201] Where Φ is the magnetic flux.

[0202] According to the series-parallel relationship of R1, R2 and R3, we can get R t1 =R1+R2+R3.

[0203] According to the above method, the magnetic resistance of each part is obtained as follows:

[0204]

[0205] In this example, characteristic position 1 is the first characteristic position, and characteristic position 2 is the second characteristic position. Wherein μ0 is the vacuum magnetic permeability, w p is the distance between the air magnetic barriers above the adjacent poles (e.g. Figure 4 γ is the angle between the axis of any pole and the line connecting the motor axis and the lower right corner of the right magnet in the pole (as shown in Figure 4 β is the angle between the axis of any pole and the line connecting the motor axis and the upper right corner of the right magnet in the pole (as shown in Figure 4 shown).

[0206]

[0207]

[0208]

[0209] Since the rotor structure has nothing to do with the characteristic position, and the stator side core is not saturated, there is R c1 =R c2 =R c3 =R c4 =0, R e1 =R e2 =R e3 =R e4 =0, so the magnetic resistance expressions of the two characteristic positions are the same.

[0210] Where g' is the equivalent air gap length, which is calculated according to the Karlsruhe coefficient k c Correcting the air gap length yields:

[0211]

[0212] g′=k c g

[0213] Where g is the air gap length and b0 is the slot opening width.

[0214] Taking the 360-slot 84-pole permanent magnet motor as an example, the 1st, 4th, and 7th pole positions are the first characteristic position magnetic circuit; the 2nd, 3rd, 5th, and 6th pole positions are the second characteristic position magnetic circuit.

[0215] When the 1st, 4th and 7th pole positions are the first characteristic position magnetic circuit, the magnetic resistance of each part is:

[0216]

[0217]

[0218] The 2nd, 3rd, 5th and 6th pole positions are the second characteristic position magnetic circuit, and the magnetic resistance of each part is:

[0219]

[0220]

[0221] In the formula, t is the number of unit motors, w is s is the tooth width, w sp is the slot distance, l t is the tooth length, R s is the difference between the inner and outer diameters of the stator, μ r is the magnetic permeability of silicon steel sheet, D r is the rotor outer diameter, l st is the motor axial length, μ r is the relative magnetic permeability of ferromagnetic materials, such as Figure 5 S6. Substitute the magnetic resistance of each part at the two characteristic positions and the magnetomotive force of each tooth at each magnetic pole position into the magnetic flux expression of the corresponding characteristic position, solve the magnetic flux, and further obtain the Q-axis inductance of the entire motor.

[0222] Step S6 specifically includes:

[0223] S61: According to the characteristic positions to which each position belongs, the partial magnetic resistances at the two characteristic positions and the tooth magnetomotive force of each tooth at the corresponding magnetic pole position under the half-unit motor are substituted into the magnetic circuit flux expression of the corresponding characteristic position, and the magnetic circuit flux expression is solved to obtain the main magnetic flux Φ of each magnetic pole position in the half-unit motor. qk .

[0224] Solve the magnetic flux expression of the magnetic circuit to obtain the main magnetic flux Φ at each pole position in the half unit motor qk Specifically include:

[0225] Solve the flux expressions of each magnetic circuit to obtain the flux φ of each branch corresponding to each pole position in the half unit motor. k , the maximum value of the branch flux at the i-th magnetic pole position is the main magnetic flux φq at that magnetic pole position i .

[0226] For the 1st magnetic pole position:

[0227] Solve for the magnetic flux in the magnetic circuit branch:

[0228]

[0229]

[0230] Solve:

[0231] is the main magnetic flux at the first magnetic pole position, Φ qi is the main magnetic flux at the i-th magnetic pole position.

[0232] For the second magnetic pole position:

[0233] Solve for the magnetic flux in the magnetic circuit branch:

[0234]

[0235]

[0236] Solve:

[0237]

[0238] For the 3rd pole position:

[0239] Solve for the magnetic flux in the magnetic circuit branch:

[0240]

[0241]

[0242] Solve:

[0243]

[0244] For the 4th pole position:

[0245] Solve for the magnetic flux in the magnetic circuit branch:

[0246]

[0247]

[0248] Solve:

[0249] In this example, the magnetic circuits are symmetrically distributed, that is, k = 1, 7 magnetic circuits are the same, k = 2, 6 magnetic circuits are the same, k = 3, 5 magnetic circuits are the same. From the above calculation, we can get Φ q1 -Φ q7 .

[0250] S62: Obtain the Q-axis inductance of the half-unit motor according to the main magnetic flux at each magnetic pole position in the half-unit motor.

[0251] According to the formula Determine the flux Φ of a half-unit motor qh , where Φ qk is the main magnetic flux at each pole position; according to the formula Determine the Q-axis inductance L of the half-unit motor qh , I q is the q-axis current.

[0252] S63: Based on the Q-axis inductance of half of the unit motor, the Q-axis inductance of the entire motor is obtained by symmetry.

[0253] According to the formula L q =2ktL qh , the Q-axis inductance of the entire motor is obtained, where k is the number of poles under half a unit motor and t is the number of unit motors.

[0254] In summary, the Q-axis magnetic circuit model and equivalent magnetic circuit analysis method of a fractional slot distribution winding permanent magnet motor of the present invention take into account that although the number of slots in each pole of the rotor is different, the distribution is symmetrical, and the distribution in the minimum symmetrical unit is also regular. By selecting a permanent magnet pole on the rotor for analysis, two characteristic positions are determined, and the magnetic circuit model diagram and the equivalent magnetic circuit at the two characteristic positions are drawn respectively, and the magnetic circuit flux expressions of the two characteristic positions are analyzed; the magnetic resistance of each part at the two characteristic positions is solved; the half unit motor is divided into multiple (k) magnetic pole positions according to the number of poles contained in the half unit motor, and the tooth magnetomotive force belonging to the k magnetic pole positions is solved; the magnetic resistance and magnetomotive force calculation results are substituted into the magnetic circuit flux expression to obtain the magnetic flux Φ of the k positions. qk The analytical solution is combined with the current to obtain the Q-axis inductance. Compared with the finite element simulation analysis, it has the advantages of simple modeling, greatly simplified calculation, and fast calculation speed. It avoids the complexity and huge workload of listing the magnetic circuit of each rotor position, as well as the problem that the calculation method of the motor magnetic circuit of fractional slot concentrated winding and integer slot distributed winding is not applicable. At the same time, the error is also within the allowable error range of the project.

[0255] The above description is only a specific implementation of the present application, so that those skilled in the art can understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest range consistent with the principles and novel features applied for herein.

Claims

1. A method for analyzing the Q-axis equivalent magnetic circuit of a permanent magnet motor with fractional slot distributed windings, characterized in that: The following steps are involved: Determine the two characteristic positions of the Q-axis magnetic circuit, and draw the magnetic circuit models and their equivalent magnetic circuits at the two characteristic positions; According to the equivalent magnetic circuit of the magnetic circuit model at two characteristic positions, the magnetic circuit flux expressions of the magnetic resistance of each part and the magnetomotive force of the corresponding tooth at the two characteristic positions are determined; According to the arrangement of the motor stator winding, the distribution of the stator magnetomotive force about the teeth is solved to obtain the stator tooth magnetomotive force; Divide the half unit motor into a plurality of magnetic pole positions according to the number of poles contained in the half unit motor, determine the number of teeth contained in each magnetic pole position, and respectively determine the characteristic position to which each magnetic pole position belongs and the tooth magnetomotive force of the teeth contained in each magnetic pole position; According to the specific structure of the motor stator and rotor, calculate the magnetic resistance of each part respectively; Substitute the magnetic resistance of each part at the two characteristic positions and the tooth magnetomotive force of the teeth contained in each magnetic pole position into the magnetic circuit flux expression of the corresponding characteristic position, solve the magnetic circuit flux, and further obtain the Q-axis inductance of the entire motor.

2. The Q-axis equivalent magnetic circuit analysis method of a permanent magnet motor with fractional slot distributed winding according to claim 1, characterized in that: The method of determining two characteristic positions of the Q-axis magnetic circuit and drawing the magnetic circuit model of the two characteristic positions and its equivalent magnetic circuit includes: The motor is analyzed to determine the two characteristic positions of the Q-axis magnetic circuit. The two characteristic positions are: one magnetic pole corresponds to slots and slots, where Z is the number of slots in the motor and p is the number of motor pole pairs; According to the magnetic circuit analysis theory, the magnetic circuit models at two characteristic positions are drawn respectively; The equivalent magnetic circuits at two characteristic positions are drawn based on the magnetic circuit model.

3. The Q-axis equivalent magnetic circuit analysis method of a permanent magnet motor with fractional slot distributed winding according to claim 1, characterized in that: The equivalent magnetic circuit of the magnetic circuit model at the two characteristic positions is used to determine the magnetic circuit flux expression of each part of the magnetic resistance and the corresponding tooth magnetomotive force at the two characteristic positions, including: Kirchhoff's law is used to analyze and calculate the equivalent magnetic circuit of the magnetic circuit model at two characteristic positions, and Kirchhoff's equation of the magnetic circuit is listed, that is, the magnetic flux expression of the magnetic circuit for each part of the magnetic resistance and the magnetomotive force of the tooth at the two characteristic positions is obtained.

4. The Q-axis equivalent magnetic circuit analysis method of a permanent magnet motor with fractional slot distributed winding according to claim 1, characterized in that: The method of calculating and solving the magnetic resistance of each part at two characteristic positions according to the specific structure of the motor stator and rotor includes: According to the size structure of each part of the stator and rotor, the magnetic resistance of each part of the magnetic circuit is analytically calculated to obtain the magnetic resistance of each part at two characteristic positions.

5. The Q-axis equivalent magnetic circuit analysis method of a permanent magnet motor with fractional slot distributed winding according to claim 4, characterized in that: According to the size structure of each part of the stator and rotor, the magnetic resistance of each part of the magnetic circuit is analyzed and calculated to obtain the magnetic resistance of each part at two characteristic positions, including: The overall block of each magnetic resistance part is divided into rectangular areas and / or irregular areas; For a rectangular region with a regular cross section, the rectangular region magnetic resistance is obtained according to the rectangular magnetic resistance calculation formula; For any region with irregular cross-sectional area, the magnetic reluctance of the irregular region is calculated by integration; This part of the magnetic resistance is obtained by integrating all the magnetic resistances in the rectangular area and the magnetic resistances in the irregular area according to the series-parallel relationship.

6. The Q-axis equivalent magnetic circuit analysis method of a permanent magnet motor with fractional slot distributed winding according to claim 5, characterized in that: For any region with irregular cross-sectional area, the magnetic resistance of the irregular region is calculated by integration, including: In the direction perpendicular to the magnetic flux cross section, the cross-sectional area S of the region with a length of l is written as a function S(x) related to the position. S(x) is a continuous function or a piecewise function. The magnetic field density function at different positions is B(x) = Φ / S(x). According to the known μ r Functional relationship with B r =f(B), we can get the magnetic permeability function μ r (x)=f(B(x))=f(Φ / S(x)), μ r is the relative magnetic permeability, Φ is the magnetic flux; According to the rectangular magnetic resistance calculation formula, the magnetic resistance expression of this area is obtained by integration: or Among them, l1, l2, ... l are the segment division positions in the length direction, μ0 is the vacuum permeability, μ r is the relative magnetic permeability of ferromagnetic material.

7. The Q-axis equivalent magnetic circuit analysis method of a permanent magnet motor with fractional slot distributed winding according to claim 1, characterized in that: The method of dividing the half unit motor into a plurality of positions according to the number of poles contained in the half unit motor, determining the number of teeth contained in each position, and determining the characteristic positions to which each position belongs, includes: Divide half of the unit motor into k equal parts to obtain k magnetic pole positions, k is The denominator after being reduced to the simplest fraction is the number of poles under half a unit motor; The magnetomotive force is distributed according to the space proportion of the teeth at each magnetic pole position. When the number of teeth contained in the magnetic pole position is greater than or equal to When The characteristic magnetic circuit model calculates the magnetic pole position, otherwise it is calculated according to The characteristic magnetic circuit model calculates the magnetic pole position to determine the tooth magnetomotive force of each tooth in the k magnetic pole positions under half a unit motor.

8. The Q-axis equivalent magnetic circuit analysis method of a permanent magnet motor with fractional slot distributed winding according to claim 1, characterized in that: According to the characteristic positions to which each position belongs, the magnetic resistance of each part under the two characteristic positions and the tooth magnetomotive force of each position under the half unit motor are substituted into the magnetic flux expression of the corresponding characteristic position, and the magnetic flux is solved to further obtain the Q-axis inductance of the entire motor, including: According to the characteristic positions to which each position belongs, the partial magnetic resistances at the two characteristic positions and the tooth magnetomotive force of each tooth at the corresponding magnetic pole position under the half-unit motor are substituted into the magnetic circuit flux expression of the corresponding characteristic position, and the magnetic circuit flux expression is solved to obtain the main magnetic flux at each magnetic pole position in the half-unit motor; According to the main magnetic flux of each magnetic pole position in the half unit motor, the Q-axis inductance of the half unit motor is obtained; Based on the Q-axis inductance of half a unit motor, the Q-axis inductance of the entire motor is obtained by symmetry.

9. The Q-axis equivalent magnetic circuit analysis method of a permanent magnet motor with fractional slot distributed winding according to claim 8, characterized in that: The method of obtaining the Q-axis inductance of the half-unit motor according to the main magnetic flux of each magnetic pole position in the half-unit motor includes: According to the formula Determine the flux Φ of a half-unit motor qh , where Φ qk is the main magnetic flux at each pole position; According to the formula Determine the Q-axis inductance L of the half-unit motor qh , I q is the Q-axis current.

10. The Q-axis equivalent magnetic circuit analysis method of a permanent magnet motor with fractional slot distributed winding according to claim 8, characterized in that: The method of obtaining the Q-axis inductance of the entire motor by symmetry based on the Q-axis inductance of the half-unit motor includes: According to the formula L q =2ktL qh , the Q-axis inductance of the entire motor is obtained, where k is the number of poles under half a unit motor and t is the number of unit motors.

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