Novel magnetic flux switching motor with additional split magnet and modeling method thereof

Abstract

The invention discloses a novel magnetic flux switching motor with split magnets and an analytical modeling method thereof, the motor comprises a rotor, a stator, stator teeth, stator slots, stator slot permanent magnets, rotor slots and permanent magnets between the stator slots, and each permanent magnet is inserted into an iron core at the middle position and split into two sections of permanent magnets with equal arc angles; the permanent magnets of the stator slots are magnetized radially, and the permanent magnets among the stator slots are magnetized tangentially; the analysis modeling method comprises the following steps: firstly, dividing a motor into sub-domains to be solved, then deducing a vector magnetic potential general solution expression of each sub-domain, solving direct current and harmonic coefficients in the vector magnetic potential general solution expression according to boundary conditions among the sub-domains, and on the basis of the calculated magnetic potential expression, calculating the magnetic potential of the motor. And air-gap magnetic fields under an open-circuit field and an armature reaction field can be respectively obtained, so that the electromagnetic torque can be analyzed and calculated. Compared with a traditional motor structure, the motor has better electromagnetic performance, the analysis result of the method is basically consistent with the finite element result, and the correctness of an analysis model is verified.

Description

Technical Field

[0001] This invention relates to the field of motor technology, and in particular to a novel flux-switching motor with an additional split magnet and its modeling method. Background Technology

[0002] Flux-switched permanent magnet motors have a simple structure, with permanent magnets mounted on the stator side and a simple salient-pole iron core rotor. Due to the bipolar magnetic flux induced in the stator windings, this motor exhibits high power density and is suitable for low-to-high-speed operation, finding widespread application in industrial fields such as automotive manufacturing, wind turbines, and aerospace. However, existing flux-switched motors suffer from low average electromagnetic torque, and current technologies generally employ the finite element method for analytical analysis, which suffers from drawbacks such as long computation time and poor analytical accuracy. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a novel flux-switching motor with an additional split magnet and its modeling method, so as to solve the problems of low average electromagnetic torque and poor analytical accuracy of existing flux-switching motors.

[0004] This invention is achieved through the following technical solution:

[0005] A novel flux-switching motor with additional split magnets includes a rotor and a stator ringed around the rotor. Multiple stator teeth are formed on the inner annular surface of the stator, and stator slots are formed between adjacent stator teeth. The stator slots are connected to the space between the stator and the rotor through radially magnetized permanent magnets at the slot openings. Tangentially magnetized permanent magnets that penetrate the stator radially are provided between adjacent stator slots. Multiple rotor slots are formed on the circumferential outer surface of the rotor. Iron cores are provided in each radially magnetized permanent magnet and each tangentially magnetized permanent magnet. The iron cores are inserted radially into the radially magnetized permanent magnets and the tangentially magnetized permanent magnets to form split magnets.

[0006] The relative permeability of both the radially magnetized permanent magnet and the tangentially magnetized permanent magnet is 1.1, and the remanence is 1.23T. The current density of the armature winding in the flux-switching motor is 5.5 A / mm². 2 .

[0007] An analytical modeling method for a novel flux-switching motor with an additional split magnet includes the following steps:

[0008] Step (1): Using the precise subdomain model method, the solution domain of the novel flux-switching motor with additional split magnetic poles is divided into rotor slot subdomain I, internal air gap subdomain II, right radial magnetized magnet subdomain III, left radial magnetized magnet subdomain IV, left tangential magnetized magnet subdomain V, right tangential magnetized magnet subdomain VI, stator slot subdomain VII, and external air subdomain VIII.

[0009] Step (2): Determine the current density distribution in the stator slot subdomain VII, and the magnetization intensity of the right radial magnetized magnet subdomain III, the left radial magnetized magnetized magnet subdomain IV, the left tangential magnetized magnetized magnet subdomain V, and the right tangential magnetized magnetized magnet subdomain VI in one electric cycle;

[0010] Step (3): Based on the results obtained in step (2), the z-direction component of the vector magnetic potential A of each subdomain divided in step (1) is used as the solution variable of the partial differential equation. According to whether the stator slot subdomain VII has a current density component and whether the right radial magnetized magnet subdomain III, left radial magnetized magnet subdomain IV, left tangential magnetized magnet subdomain V and right tangential magnetized magnet subdomain VI have a magnetization intensity component, determine the Poisson equation of the stator slot subdomain VII, right radial magnetized magnet subdomain III, left radial magnetized magnet subdomain IV, left tangential magnetized magnet subdomain V and right tangential magnetized magnet subdomain VI with respect to the vector magnetic potential A, as well as the Laplace equation of the rotor slot subdomain I, internal air gap subdomain II and external air subdomain VIII with respect to the vector magnetic potential A, and solve the general solution expression of the vector magnetic potential A of each subdomain by means of separation of variables.

[0011] Step (4): Utilize the continuous relationship of the magnetic field between each subdomain to establish the boundary condition equations and obtain the matrix equations. Solve the DC component and harmonic component coefficients in the general solution expression of the vector magnetic potential A of each subdomain obtained in step (3) using the matrix equations.

[0012] Step (5): Substitute the DC component and harmonic component coefficients in the general solution expression of the vector magnetic potential A of each subdomain obtained in step (4) into the general solution expression of the vector magnetic potential A obtained in step (3) to obtain the complete expression of the vector magnetic potential A of each subdomain, and then calculate the air gap magnetic flux density and electromagnetic torque of the motor.

[0013] The specific details of step S2 are as follows:

[0014] (2.1) Current density distribution:

[0015] For a double-layer non-overlapping winding, J1 and J2 are the current densities on the left and right sides of the stator slot, respectively, and their corresponding expressions are as follows:

[0016] (1)

[0017] (2)

[0018] In the formula k s S is the winding fill factor. w Let C1 be the cross-sectional area of ​​the conductor, and I(t) be the matrix formed by the three-phase armature currents. Matrices C1 and C2 relate the three-phase currents to the current density of each stator slot. The correlation matrices C1 and C2 for the double-layer non-overlapping windings located on the left and right sides of the stator slots are as follows:

[0019] (3)

[0020] (4)

[0021] In the formula, C1 is the correlation matrix of the left winding and C2 is the correlation matrix of the right winding;

[0022] Therefore, the current density matrix on the left and right sides of the stator slot is represented as:

[0023] (5)

[0024] (6)

[0025] In the formula For the Nth s Current density of the left winding in each stator slot For the Nth s Current density of the right winding in each stator slot.

[0026] The Fourier expansion of the current density of each stator slot and its expansion coefficients are expressed as follows:

[0027] (7)

[0028] In the formula, θ is the mechanical angular position, and β s Let J be the central angle in radians corresponding to the stator slot subdomain, p be the harmonic order of the stator slot subdomain magnetic potential equation, and J be the value of J. j J is the current density of the j-th stator slot, and J is the DC component coefficient in the Fourier expansion of the current density of the j-th stator slot. j0 The AC component coefficient J in the Fourier expansion of the current density of the j-th stator slot jp and the center position angle of the j-th stator slot subdomain They are respectively:

[0029] (8)

[0030] (9)

[0031] (10)

[0032] In the formula θ j0 J is the position angle of the center of the first stator slot relative to the initial position. j1 Let J be the current density of the left winding in the j-th stator slot. j2 Let be the current density of the right winding in the j-th stator slot;

[0033] (2.2) Magnetization of permanent magnets:

[0034] In two-dimensional polar coordinates, the magnetization of a permanent magnet is represented by radial and tangential components:

[0035] M=M r e r +M θ e θ (11)

[0036] In the formula, M is the magnetization vector of the permanent magnet, e r and e θ M are unit vectors in the radial and tangential directions, respectively. r and M θ These are the radial and tangential components of the magnetization, respectively.

[0037] For the right radially magnetized magnet subdomain III, M g1r and M g1θ Let be the radial and tangential components of the magnetization, respectively, and their expressions are:

[0038] (12)

[0039] In the formula β g θ represents the central angle in radians corresponding to the magnetic pole of subdomain III of the radially magnetized magnet on the right. g1 M rv and M θv They are respectively:

[0040] (13)

[0041] In the formula θ g1 θ is the position angle of the g1th magnet center in the right radially magnetized magnet subdomain III. g10 The angle between the center of the first magnet in the right radial magnetization subdomain III and the initial position;

[0042] (14)

[0043] (15)

[0044] In the formula M rv and M θv, respectively, are the harmonic component coefficients in the Fourier expansions of the radial and tangential magnetization of the right radial magnetized magnet subdomain III, and v is the harmonic order of the magnetic potential equation of the right radial magnetized magnet subdomain III.

[0045] After mirroring the right-side radially magnetized magnet subdomain III, the expression for the magnetization intensity over one period is as follows:

[0046] (16)

[0047] (17)

[0048] In the formula B r μ0 is the remanence of the permanent magnet, and μ0 is the permeability of free space.

[0049] For the left radially magnetized magnet subdomain IV, M g2r and M g2θ Let be the radial and tangential components of the magnetization, respectively, and their expressions are:

[0050] (18)

[0051] In the formula θ g2 M rz and M θz They are respectively:

[0052] (19)

[0053] In the formula θ g2 θ is the position angle of the g2th magnet center in the left radially magnetized magnet subdomain IV. g20 The angle between the center of the first magnet in the left radially magnetized magnet subdomain IV and the initial position;

[0054] (20)

[0055] (twenty one)

[0056] In the formula M rz and M θz , respectively, are the harmonic component coefficients in the Fourier expansions of the radial and tangential magnetization of the left radially magnetized magnet subdomain IV magnet, and z is the harmonic order of the magnetic potential equation of the left radially magnetized magnet subdomain IV magnet.

[0057] After mirroring the left radially magnetized magnet subdomain IV, the expression for the magnetization intensity over one period is as follows:

[0058] (twenty two)

[0059] (twenty three)

[0060] For the left-side tangentially magnetized subdomain V magnet, M k1r and M k1θ Let be the radial and tangential components of the magnetization, respectively, and their expressions are:

[0061] (twenty four)

[0062] In the formula β f θ represents the central angle in radians corresponding to the V-pole of the tangentially magnetized magnet subdomain on the left. k1 for:

[0063] (25)

[0064] In the formula θ k1 Let θ be the k1th center position angle of the left-side tangentially magnetized magnet subdomain V. k10 The angle between the center of the first magnet in the left-side tangentially magnetized magnet subdomain V and the initial position;

[0065] For the right-side tangentially magnetized magnet subdomain VI magnet, M k2r and M k2θ Let be the radial and tangential components of the magnetization, respectively, and their expressions are:

[0066] (26)

[0067] In the formula θ k2 for:

[0068] (27)

[0069] In the formula θ k2 Let θ be the k2th center position angle of the right-side tangentially magnetized magnet subdomain VI. k20 The angle between the center of the first magnet in the right-side tangentially magnetized magnet subdomain VI and the initial position.

[0070] The specific details of step S3 are as follows:

[0071] In a two-dimensional polar coordinate system, the z-direction component of the vector magnetic potential A is a function of the radius r and the angular position θ, and the radial component B of the magnetic field density vector B... r With tangential component B θ Represented as:

[0072] (28)

[0073] In air and in magnetized linear media, the magnetic field strength and magnetic field density vector are related by the following expression, where μ r is the relative permeability of the permanent magnet, and H is the magnetic field strength vector;

[0074] (29)

[0075] In the formula, μ0 is the magnetic permeability in vacuum;

[0076] (3.1) Magnetic field analysis of rotor slot subdomain I

[0077] In the rotor slot subdomain I, with no current or magnetization components, the Laplace equation for the vector magnetic potential in two-dimensional polar coordinates is:

[0078] (30)

[0079] In the formula A 1i It is the magnetic vector position of the i-th rotor slot, R1 is the inner radius of the rotor slot, R2 is the outer radius of the rotor slot, and β r Let θ be the radian of the central angle corresponding to the sector rotor slot, and θ be the center position angle of the i-th rotor slot subdomain. i The expression is:

[0080] (31)

[0081] In the formula θ i0 The angle of the first rotor slot subdomain relative to the initial position;

[0082] Since the left and right boundaries of the rotor slot subdomain are both iron cores, the radial magnetic field strength on both sides of the rotor slot is zero. Also, because the bottom boundary of the rotor slot subdomain is an iron core, the tangential magnetic field strength at the bottom of the rotor slot is zero. Therefore, the boundary conditions for rotor slot subdomain I are:

[0083] (32)

[0084] (33)

[0085] In the formula It is the tangential magnetic field strength of the i-th rotor slot. It is the radial magnetic field strength of the i-th rotor slot;

[0086] According to equations (32) and (33), the general solution of equation (30) is obtained as follows:

[0087] (34)

[0088] In the formula A im and A i0 , respectively, are the harmonic component and DC component coefficients of the general solution of the subdomain I magnetic potential equation, and m is the harmonic order of the subdomain I magnetic potential equation;

[0089] (3.2) Magnetic field analysis of the internal air gap subdomain II

[0090] The annular region located between the rotor outer radius R2 and the stator inner radius R3 is the internal air gap subdomain II. Internal air gap subdomain II has no current distribution or magnetization component. The Laplace equation for the vector magnetic potential in two-dimensional polar coordinates is:

[0091] (35)

[0092] In the formula, A2 is the magnetic vector potential of the internal air gap subdomain;

[0093] The periodicity condition for the existence of the internal air gap subdomain II is:

[0094] (36)

[0095] According to equation (36), the general solution can be obtained by solving equation (35):

[0096] (37)

[0097] In the formula B 1n B 2n B 3n and B 4n , respectively, are the harmonic component coefficients of the magnetic potential equation of the internal air gap subdomain II, and n is the harmonic order of the magnetic potential equation of the internal air gap subdomain II;

[0098] (3.3) Magnetic field analysis of right radial magnetized magnet subdomain III

[0099] The right-side radially magnetized magnet subdomain III has a magnetization vector; therefore, the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates is as follows:

[0100] (38)

[0101] In the formula A 3g1 R3 is the magnetic vector position of the g1-th magnet in the radially magnetized magnet subdomain III on the right side of the stator slot, R4 is the inner radius of the radially magnetized magnet subdomain III on the right side, and β is the outer radius of the radially magnetized magnet subdomain III on the right side. g The central angle of the permanent magnet in the radially magnetized subdomain III on the right side of the sector is in radians, and the magnetization vector M is... g1 radial component M g1r and tangential component M g1θ They are respectively:

[0102] (39)

[0103] The right radial magnetized magnet subdomain III is flanked by stator cores, therefore the radial magnetic field strength at both boundaries is zero. The boundary conditions at this point are:

[0104] (40)

[0105] In the formula It is the radial magnetic field strength of the g1th magnet in the right radially magnetized magnet subdomain III;

[0106] Solving equation (38) using the method of separation of variables, the solution to equation (40) is obtained as follows:

[0107] (41)

[0108] In the formula E g10 and F g10 E represents the DC component coefficient of the magnetic potential equation for the right-hand radially magnetized magnet subdomain III. g1v F g1v G represents the harmonic component coefficients of the magnetic potential equation for the right-hand radially magnetized magnet subdomain III, v represents the harmonic order of the magnetic potential equation for the right-hand radially magnetized magnet subdomain III, and G represents the harmonic component coefficients of the magnetic potential equation for the right-hand radially magnetized magnet subdomain III. g1v (r) is a particular solution produced by the radially magnetized magnet on the right, and its expression is:

[0109] (42)

[0110] (3.4) Analysis of the magnetic field of the left radial magnetized magnet subdomain IV

[0111] The left radially magnetized magnet subdomain IV has a magnetization vector, therefore the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates is as follows:

[0112] (43)

[0113] In the formula A 4g2 It is the magnetic vector position of the g2th magnet in the radially magnetized magnet subdomain IV on the left side of the stator slot, β g Simultaneously, the radian of the central angle corresponding to the permanent magnet IV subdomain of the radially magnetized magnet on the left side of the sector, and the magnetization vector M g2 radial component M g2r and tangential component M g2θ They are respectively:

[0114] (44)

[0115] The left radially magnetized magnet subdomain IV has iron cores on both sides, therefore the radial magnetic field strength at the two boundaries is zero. The boundary conditions at this time are:

[0116] (45)

[0117] In the formula It is the radial magnetic field strength of the g2th rotor slot in the left radially magnetized magnet subdomain IV;

[0118] Solving equation (43) using the method of separation of variables, the solution to the equation is obtained according to equation (45):

[0119] (46)

[0120] In the formula H g20 and Q g20 H represents the DC component coefficient of the potential equation for the left radially magnetized magnet subdomain IV. g2z Q g2z Let G be the harmonic component coefficient of the IV magnetic potential equation of the left radially magnetized magnet subdomain, z be the harmonic order of the IV magnetic potential equation of the left radially magnetized magnet subdomain, and G be the harmonic component coefficient of the IV magnetic potential equation of the left radially magnetized magnet subdomain. g2v (r) is a particular solution produced by the radially magnetized magnet on the right, and its expression is:

[0121] (47)

[0122] (3.5) Analysis of the magnetic field V in the left-side tangentially magnetized magnet subdomain

[0123] The left-side tangentially magnetized subdomain V contains a magnetization vector; therefore, the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates can be expressed as follows:

[0124] (48)

[0125] In the formula A 5k1 R3 is the magnetic vector position of the k1th magnet in the left-side tangentially magnetized magnet subdomain of the stator, R6 is the inner radius of the left-side tangentially magnetized magnet subdomain V, and β is the outer radius of the subdomain V. f The central angle of the permanent magnet V, the tangentially magnetized subdomain on the left side of the sector, is in radians, and the magnetization vector M is... k1 radial component M k1r and tangential component M k1θ Given by equation (24);

[0126] The left-side tangentially magnetized subdomain V is composed of iron cores on both sides, therefore the radial magnetic field strength at the two boundaries is zero. The boundary conditions are then expressed as:

[0127] (49)

[0128] In the formula It is the radial magnetic field strength of the k1th magnet in the tangentially magnetized magnet subdomain V on the left side of the stator;

[0129] Solving equation (48) using the method of separation of variables, the solution to equation (49) is obtained as follows:

[0130] (50)

[0131] In the formula D k10 and T k10 D represents the DC component coefficient of the magnetic potential equation for the V-field of the tangential magnetization subdomain on the left side of the stator. k1q T k1q q represents the harmonic component coefficients of the V magnetic potential equation of the tangential magnetization subdomain on the left side of the stator, and q represents the harmonic order of the V magnetic potential equation of the subdomain.

[0132] (3.6) Magnetic field analysis of the right-side tangential magnetized magnet subdomain VI

[0133] The right-side tangentially magnetized subdomain VI has a magnetization vector; therefore, the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates is as follows:

[0134] (51)

[0135] In the formula A 6k2 It is the magnetic vector position of the k2th magnet in the tangentially magnetized magnet subdomain on the right side of the stator, β f Simultaneously, the radian of the central angle corresponding to the permanent magnet VI subdomain tangentially magnetized on the right side of the sector, and the magnetization vector M. k2 radial component M k2r and tangential component M k2θ Given by equation (26);

[0136] The right-side tangentially magnetized magnet subdomain VI is flanked by stator cores, therefore the radial magnetic field strength at both boundaries is zero; the boundary conditions are as follows:

[0137] (52)

[0138] In the formula It is the radial magnetic field strength of the k2th magnet in the tangentially magnetized magnet subdomain on the right side of the stator;

[0139] By solving equation (51) using the method of separation of variables, the solution to the equation can be obtained from equation (52):

[0140] (53)

[0141] In the formula L k2s W k2s L k20 and W k20 , respectively, are the DC component coefficients and harmonic component coefficients of the magnetic potential equation of the right-side tangentially magnetized magnet subdomain VI, and s is the harmonic order of the magnetic potential equation of the right-side tangentially magnetized magnet subdomain VI.

[0142] (3.7) Magnetic field analysis of stator slot subdomain VII

[0143] There is a current density distribution in the stator slot subdomain VII, and the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates is as follows:

[0144] (54)

[0145] In the formula A 7j R4 is the magnetic vector position of the j-th stator slot in stator slot subdomain VII, R5 is the inner radius of stator slot subdomain VII, and R5 is the outer radius of stator slot subdomain VII.

[0146] Since the left, right, and bottom boundaries of stator slot subdomain VII are all iron cores, the radial magnetic field strength on both sides of each slot and the tangential magnetic field strength at the bottom are zero; the boundary conditions are expressed as follows:

[0147] (55)

[0148] (56)

[0149] In the formula It is the tangential magnetic field strength of the j-th stator slot. It is the radial magnetic field strength of the j-th stator slot;

[0150] Solving equation (54) using the method of separation of variables, the solution to the equation is obtained from equations (55) and (56):

[0151] (57)

[0152] In the formula C jp and C j0 are the harmonic component coefficients and DC component coefficients of the magnetic potential equation for stator slot subdomain VII, respectively, where p is the harmonic order of the magnetic potential equation for stator slot subdomain VII, and V jp (t) is a particular solution generated by the current density, and its expression is:

[0153] (58)

[0154] (3.8) Magnetic field analysis of external air subdomain VIII

[0155] The annular region located between the stator outer radius R6 and the motor outer boundary radius R7 is the external air subdomain VIII. This subdomain has no current distribution and magnetization components, and its vector magnetic potential in two-dimensional polar coordinates is represented by the Laplace equation:

[0156] (59)

[0157] In the formula, A8 is the magnetic vector potential of the external air subdomain;

[0158] The outer boundary of the motor is a magnetically parallel boundary, therefore the radial magnetic field strength at the outer boundary of the motor is zero. Furthermore, similar to the internal air gap subdomain II, the external air subdomain VIII also exhibits periodic conditions. In this case, the boundary conditions of the motor are expressed as:

[0159] (60)

[0160] (61)

[0161] In the formula It is the radial magnetic field strength of the external air subdomain;

[0162] Solving equation (59) using the method of separation of variables, the solution to the equation is obtained from equations (60) and (61):

[0163] (62)

[0164] In the formula: F 1t and F 2t , respectively, are the harmonic component coefficients of the VIII magnetic potential equation of the external air subdomain, and t is the harmonic order of the VIII magnetic potential equation of the external air subdomain;

[0165] In summary, the general solutions to the magnetic potential equations containing unsolved coefficients for all six regions have been established, with a total of A... im A i0 B 1n B 2n B 3n B 4n E g1v F g1v E g10 F g10 H g2z Q g2z H g20 Q g20 D k1q T k1q D k10 T k10 L k2s W k2s L k20 W k20 C jp C j0 F 1t and F 2t The 26 sets of DC component and harmonic component coefficients to be solved are determined by the boundary conditions between each region.

[0166] The specific details of step S4 are as follows:

[0167] (4.1) At the interface between rotor slot subdomain I and internal air gap subdomain II, r = R2. Based on the equality of radial magnetic flux density and tangential magnetic field strength, the simultaneous equations are expressed as:

[0168] (63)

[0169] (64)

[0170] (4.2) At the interface between the right radially magnetized magnetic subdomain III, the left radially magnetized magnetic subdomain IV, the left tangentially magnetized magnetic subdomain V, the right tangentially magnetized magnetic subdomain VI, and the internal air gap subdomain II, r = R3. Based on the fact that the radial magnetic flux density of the right radially magnetized magnetic subdomain III and the internal air gap subdomain II are equal, the simultaneous equations are expressed as follows:

[0171] (65)

[0172] The radial magnetic flux density of the left radially magnetized magnet subdomain IV is equal to that of the internal air gap subdomain II. The simultaneous equations are expressed as follows:

[0173] (66)

[0174] The radial magnetic flux density of the left-side tangentially magnetized magnet subdomain V is equal to that of the internal air gap subdomain II. The simultaneous equations are expressed as follows:

[0175] (67)

[0176] The radial magnetic flux density of the right-side tangentially magnetized magnet subdomain VI is equal to that of the internal air gap subdomain II. The simultaneous equations are expressed as follows:

[0177] (68)

[0178] At the interface between the right radially magnetized magnetic subdomain III, the left radially magnetized magnetic subdomain IV, the left tangentially magnetized magnetic subdomain V, the right tangentially magnetized magnetic subdomain VI, and the internal air gap subdomain II, r = R3. Based on the boundary condition that the tangential magnetic field strength is equal, the simultaneous equations are expressed as:

[0179] (69)

[0180] (4.3) At the interface between the right radial magnetized magnet subdomain III and the left radial magnetized magnet subdomain IV and the stator slot subdomain VII, r = R4. Based on the fact that the radial magnetic flux density of the right radial magnetized magnet subdomain III and the stator slot subdomain VII are equal, the simultaneous equations are expressed as:

[0181] (70)

[0182] Based on the fact that the radial magnetic flux density of the left radial magnetized magnet subdomain IV is equal to that of the stator slot subdomain VII, the simultaneous equations can be expressed as follows:

[0183] (71)

[0184] At the interface between the right radial magnetized magnet subdomain III and the left radial magnetized magnet subdomain IV and stator slot subdomain VII, r = R4. Based on the boundary condition that the tangential magnetic field strength is equal, the simultaneous equations are expressed as:

[0185] (72)

[0186] (4.4) At the interface between the left tangentially magnetized magnetic subdomain V and the right tangentially magnetized magnetic subdomain VI and the external air subdomain VIII, r = R6. Based on the fact that the radial magnetic flux density of the left tangentially magnetized magnetic subdomain V and the external air subdomain VIII are equal, the simultaneous equations are expressed as follows:

[0187] (73)

[0188] Based on the fact that the radial magnetic flux density of the right-side tangentially magnetized magnet subdomain VI is equal to that of the external air subdomain VIII, the simultaneous equations can be expressed as follows:

[0189] (74)

[0190] At the interface between the left tangential magnetized magnetic subdomain V and the right tangential magnetized magnetic subdomain VI and the external air subdomain VIII, r = R6. Based on the boundary condition that the tangential magnetic field strengths are equal, the simultaneous equations are expressed as:

[0191] (75)

[0192] By combining equations (63) to (75), according to the properties of Fourier series, the above boundary conditions can all be written as the DC component and harmonic component coefficients being equal respectively. Thus, 26 sets of equations about the coefficients are obtained, and the 26 sets of unknown DC component and harmonic component coefficients of the magnetic potential equations of each region can be solved.

[0193] The specific details of step S5 are as follows:

[0194] First, substitute the magnetic potential flux solution (37) of the air gap region into equation (28) to obtain the radial component (76) and tangential component (77) of the air gap magnetic flux density of the motor. Set the armature current to zero and solve for the air gap magnetic flux density generated by the open circuit field under the action of only the permanent magnet. Then, set the permanent magnet to air and solve for the radial air gap magnetic flux density generated by the armature reaction field. and tangential air gap magnetic flux density ;

[0195] (76)

[0196] (77)

[0197] According to Maxwell's theory, electromagnetic torque is the result of the interaction between the open-circuit field and the armature reaction field. Given the air gap magnetic flux density of the open-circuit field and the armature reaction field, the instantaneous torque is obtained by integrating the magnetic stress on the closed surface of the air gap. The instantaneous electromagnetic torque is expressed as:

[0198] (78)

[0199] In the formula, T is the instantaneous electromagnetic torque, and R... x =(R2+R3) / 2 is the radius at the center of the internal air gap sub-domain, and L is the axial length of the motor. and These are the radial and tangential air gap magnetic flux densities of the open-circuit field, respectively. and These are the radial and tangential air gap magnetic flux densities of the armature reaction field, respectively.

[0200] The advantages of this invention are: under the condition of ensuring the same amount of permanent magnets, compared with the traditional flux-switching motor, the average electromagnetic torque of the structure of this invention is significantly improved, while the torque ripple is significantly reduced. The analytical modeling method for the novel flux-switching motor with additional split magnets proposed in this invention uses a two-dimensional precise subdomain model for modeling and analysis, which improves the accuracy and speed of calculation, and can accurately obtain the air gap magnetic flux density and electromagnetic torque of the motor. Attached Figure Description

[0201] Figure 1 This is a schematic diagram of the motor structure according to Embodiment 1 of the present invention.

[0202] Figure 2 This is a schematic diagram of motor subdomain partitioning in Embodiment 1 of the present invention.

[0203] Figure 3 This is a schematic diagram of a traditional flux-switching motor.

[0204] Figure 4 This is a schematic diagram of a flux switching motor structure based on a magnetic field splitting design.

[0205] Figure 5 This is a comparison diagram of the electromagnetic torque of the motor described in Embodiment 1 of Embodiment 2 of the present invention, a traditional flux-switching motor, and a flux-switching motor based on a split-magnet design.

[0206] Figure 6 This is a comparison diagram of the radial air gap magnetic flux density analytical results and finite element results of the open circuit field under the analytical modeling of the motor described in Example 1, in Example 2 of the present invention.

[0207] Figure 7 This is a comparison diagram of the radial air gap magnetic flux density analytical results and finite element results of the armature reaction field under the analytical modeling of the motor described in Example 1, in Example 2 of the present invention.

[0208] Figure 8 This is a comparison diagram of the electromagnetic torque analysis results and finite element results under the analytical modeling of the motor described in Example 1 in Example 2 of the present invention. Detailed Implementation

[0209] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0210] Example 1

[0211] like Figure 1 As shown, this embodiment discloses a novel flux-switching motor with additional split magnets, including a rotor 1 and a stator 2 coaxially ringed around the rotor 1. The inner ring surface of the stator 2 has six stator teeth 3, and the space between adjacent stator teeth 3 forms stator slots 5. Therefore, this embodiment has a total of six stator slots, with a span angle of 41.3° for each slot. Each stator slot 5 has two segments of equal-arc radially magnetized permanent magnets 8.1 and 8.2 facing the rotor 1, with an inserted iron core 9 between the two segments. The stator slot 5 is connected to the space between the stator 2 and the rotor 1 through the stator slot opening formed by the radially magnetized permanent magnets 8.1 and 8.2 and the intermediate iron core 9. The outer circumferential surface of the rotor 1 has eight rotor slots 4, thus forming a 6-slot, 8-pole motor structure.

[0212] Between every two stator slots 5, there are two radially penetrating tangentially magnetized permanent magnets, 6.1 and 6.2, with equal arc angles, and an iron core 7 inserted in between. The arc angles of the tangentially magnetized permanent magnets 6.1 and 6.2 are 4.2°, and the arc angle of the inserted iron core 7 is 10.5°. At the stator slot opening, the arc angles of the two radially magnetized permanent magnets 8.1 and 8.2 are 2.05°, and the arc angle of the intermediate iron core 9 is 2°. The relative permeability of the permanent magnets is 1.1, and the remanence is 1.23 T. The current density of the motor's armature windings is 5.5 A / mm². 2 .

[0213] Example 2

[0214] This embodiment discloses an analytical modeling method for analytically modeling a novel flux-switching motor with an additional split magnet as described in Embodiment 1, comprising the following steps:

[0215] Step 1: Using the precise subdomain model method, the solution domain of the two-segment inserted alternating pole flux reverse motor described in Example 1 is divided into 8 subdomains: rotor slot subdomain I, internal air gap subdomain II, right radial magnetized magnet subdomain III, left radial magnetized magnet subdomain IV, left tangential magnetized magnet subdomain V, right tangential magnetized magnet subdomain VI, stator slot subdomain VII, and external air subdomain VIII. Clearly, for a motor with N... r One rotor slot and N s A motor with one stator slot, comprising the right radial magnetized magnet subdomain III, the left radial magnetized magnet subdomain IV, the left tangential magnetized magnet subdomain V, the right tangential magnetized magnet subdomain VI, and N stator slot subdomains. s N rotor slots r There is one internal air gap subdomain and one external air subdomain.

[0216] Step 2: Determine the current density distribution within the stator slot sub-domain VII, and the magnetization intensity of the right radially magnetized magnet sub-domain III, the left radially magnetized magnet sub-domain IV, the left tangentially magnetized magnet sub-domain V, and the right tangentially magnetized magnet sub-domain VI within one electrical cycle. The process is as follows:

[0217] (2.1) Current density distribution:

[0218] For a double-layer non-overlapping winding, J1 and J2 are the current densities on the left and right sides of the stator slot, respectively, and their corresponding expressions are as follows:

[0219] (1)

[0220] (2)

[0221] In the formula k s S is the winding fill factor. w Let I(t) be the cross-sectional area of ​​the conductor, and I(t) be the matrix formed by the three-phase armature currents. Matrices C1 and C2 relate the three-phase currents to the current density of each stator slot. For the double-layer non-overlapping windings located on the left and right sides of the stator slots in Example 1, the correlation matrices C1 and C2 are as follows:

[0222] (3)

[0223] (4)

[0224] In the formula, C1 is the correlation matrix of the left winding and C2 is the correlation matrix of the right winding.

[0225] Therefore, the current density matrix on the left and right sides of the stator slot can be expressed as:

[0226] (5)

[0227] (6)

[0228] In the formula For the Nth s Current density of the left winding in each stator slot For the Nth s Current density of the right winding in each stator slot.

[0229] The Fourier expansions of the current densities in each tank and their expansion coefficients can be expressed as follows:

[0230] (7)

[0231] In the formula, θ is the mechanical angular position, and β s Let be the central angle in radians corresponding to the stator slot subdomain, and p be the harmonic order of the magnetic potential equation of the stator slot subdomain. j J is the current density of the j-th stator slot, and J is the DC component coefficient in the Fourier expansion of the current density of the j-th stator slot. j0 The AC component coefficient J in the Fourier expansion of the current density of the j-th stator slot jp and the center position angle of the j-th stator slot subdomain They are respectively:

[0232] (8)

[0233] (9)

[0234] (10)

[0235] In the formula θ j0 J is the position angle of the center of the first stator slot relative to the initial position. j1 Let J be the current density of the left winding in the j-th stator slot. j2 Let be the current density of the right winding in the j-th stator slot.

[0236] (2.2) Magnetization of permanent magnets:

[0237] In two-dimensional polar coordinates, the magnetization of a permanent magnet is represented by radial and tangential components:

[0238] M=M r e r +M θ e θ (11)

[0239] In the formula, M is the magnetization vector of the permanent magnet, e r and e θ M are unit vectors in the radial and tangential directions, respectively. r and M θThese are the radial and tangential components of the magnetization, respectively.

[0240] For the tangentially magnetized subdomain III, M g1r and M g1θ Let be the radial and tangential components of the magnetization, respectively, and their expressions are:

[0241] (12)

[0242] In the formula β g θ is the central angle in radians corresponding to the magnetic pole of subdomain III. g1 M rv and M θv They are respectively:

[0243] (13)

[0244] In the formula θ g1 Let θ be the position angle of the center of the g1th magnet in subdomain III. g10 The angle between the center of the first magnet in subdomain III and the initial position.

[0245] (14)

[0246] (15)

[0247] In the formula M rv and M θv , respectively, are the harmonic component coefficients in the Fourier expansions of the radial and tangential magnetization of subdomain III magnet, and v is the harmonic order of the magnetic potential equation of subdomain III magnet.

[0248] After mirroring the subdomain III magnet, the expression for the magnetization intensity over one period is as follows:

[0249] (16)

[0250] (17)

[0251] In the formula B r μ0 is the remanence of a permanent magnet, and μ0 is the permeability of free space.

[0252] For the radially magnetized subdomain IV, M g2r and M g2θ Let be the radial and tangential components of the magnetization, respectively, and their expressions are:

[0253] (18)

[0254] In the formula θ g2 M rz and M θz They are respectively:

[0255] (19)

[0256] In the formula θ g2 Let θ be the position angle of the center of the g2th magnet in subdomain IV. g20 The angle between the center of the first magnet in subdomain IV and the initial position.

[0257] (20)

[0258] (twenty one)

[0259] In the formula M rz and M θz , respectively, are the harmonic component coefficients in the Fourier expansions of the radial and tangential magnetization of subdomain IV magnet, and z is the harmonic order of the magnetic potential equation of subdomain IV magnet.

[0260] After mirroring the subdomain IV magnet, the expression for the magnetization intensity over one period is as follows:

[0261] (twenty two)

[0262] (twenty three)

[0263] For a tangentially magnetized subdomain V magnet, M k1r and M k1θ Let be the radial and tangential components of the magnetization, respectively, and their expressions are:

[0264] (twenty four)

[0265] In the formula β f Let θ be the central angle in radians corresponding to the V magnetic pole of the subdomain. k1 for:

[0266] (25)

[0267] In the formula θ k1 Let θ be the angle of the k1th center position of subdomain V. k10 Let be the angle between the center of the first magnet in subdomain V and the initial position.

[0268] For a tangentially magnetized subdomain VI magnet, M k2r and M k2θ Let be the radial and tangential components of the magnetization, respectively, and their expressions are:

[0269] (26)

[0270] In the formula θ k2 for:

[0271] (27)

[0272] In the formula θ k2 Let θ be the angle of the k2th center position of subdomain VI. k20 The angle between the center of the first magnet in subdomain VI and the initial position.

[0273] Step 3: Based on Ampere's circuital law and Gauss's law of Maxwell's equations, the z-direction components of the vector magnetic potential A of each subdomain obtained in step (1) are used as the solution variables of the partial differential equations. Poisson's equation or Laplace's equation for each subdomain is established, and then the general solution expression for the z-direction components of the vector magnetic potential A of each subdomain in the two-dimensional plane is derived through the method of separation of variables and boundary conditions. The process is as follows:

[0274] In a two-dimensional polar coordinate system, the z-direction component of A is a function of the radius r and the angular position θ, and the radial component of the magnetic field density vector B is Br. r With tangential component B θ It can be represented as:

[0275] (28)

[0276] In air and in magnetized linear media, the magnetic field strength and magnetic field density vector are related by the following expression, where μ r H is the relative permeability of the permanent magnet, and H is the magnetic field strength vector.

[0277] (29)

[0278] (3.1) Magnetic field analysis of rotor slot subdomain I

[0279] In the rotor slot subdomain I, with no current or magnetization components, the Laplace equation for the vector magnetic potential in two-dimensional polar coordinates is:

[0280] (30)

[0281] In the formula, R1 is the inner radius of the rotor slot, R2 is the outer radius of the rotor slot, and β r Let θ be the radian of the central angle corresponding to the sector rotor slot, and θ be the center position angle of the i-th rotor slot subdomain. i The expression is:

[0282] (31)

[0283] In the formula θ i0 The angle of the first rotor slot subdomain relative to the initial position.

[0284] Since the left and right boundaries of the subdomain are both the rotor core, the radial magnetic field strength on both sides of the rotor slot is zero. Also, because the bottom boundary of the subdomain is the rotor core, the tangential magnetic field strength at the bottom of the rotor slot is zero. Therefore, the boundary conditions for subdomain I are:

[0285] (32)

[0286] (33)

[0287] According to equations (32) and (33), the general solution of equation (30) is obtained as follows:

[0288] (34)

[0289] In the formula A im and A i0 , respectively, are the harmonic component and DC component coefficients of the general solution of the magnetic potential equation of subdomain I, and m is the harmonic order of the magnetic potential equation of subdomain I.

[0290] (3.2) Magnetic field analysis of the internal air gap subdomain II

[0291] The annular region located between the rotor outer radius R2 and the stator inner radius R3 is the internal air gap subdomain II. This subdomain has no current distribution and magnetization component. The Laplace equation for the vector magnetic potential in two-dimensional polar coordinates is:

[0292] (35)

[0293] The periodicity condition for the existence of subdomain II is:

[0294] (36)

[0295] According to equation (36), the general solution can be obtained by solving equation (35):

[0296] (37)

[0297] In the formula B 1n B 2n B 3n and B 4n , , are the harmonic component coefficients of the subdomain II magnetic potential equation, and n is the harmonic order of the subdomain II magnetic potential equation.

[0298] (3.3) Magnetic field analysis of right radial magnetized magnet subdomain III

[0299] The right-side radially magnetized magnet subdomain III has a magnetization vector; therefore, the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates can be expressed as follows:

[0300] (38)

[0301] In the formula, R3 is the inner radius of subdomain III, R4 is the outer radius of subdomain III, and β g Let M be the radian of the central angle corresponding to the sector subdomain III permanent magnet, and the magnetization vector M. g1 radial component M g1r and tangential component M g1θ They are respectively:

[0302] (39)

[0303] Subdomain III is flanked by stator cores on both sides, therefore the radial magnetic field strength at the two side boundaries is zero. The boundary conditions at this point are:

[0304] (40)

[0305] By solving equation (38) using the method of separation of variables, the solution to the equation can be obtained according to equation (40):

[0306] (41)

[0307] In the formula E g1v F g1v E g10 and F g10 , respectively, are the DC component coefficients and harmonic component coefficients of the subdomain III magnetic potential equation, v is the harmonic order of the subdomain III magnetic potential equation, and G g1v (r) is a particular solution produced by the radially magnetized magnet on the right, and its expression is:

[0308] (42)

[0309] (3.4) Analysis of the magnetic field of the left radial magnetized magnet subdomain IV

[0310] Since subdomain IV has a magnetization vector, the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates can be expressed as follows:

[0311] (43)

[0312] In the formula β g Simultaneously, the magnetization vector M corresponds to the radian of the central angle of the sector subdomain IV permanent magnet. g2 radial component M g2r and tangential component M g2θ They are respectively:

[0313] (44)

[0314] Subdomain IV is flanked by stator cores on both sides, therefore the radial magnetic field strength at the two side boundaries is zero. The boundary conditions at this point are:

[0315] (45)

[0316] By solving equation (43) using the method of separation of variables, the solution to the equation can be obtained according to equation (45):

[0317] (46)

[0318] In the formula H g2z Q g2z H g20 and Q g20 Let be the DC component coefficients and harmonic component coefficients of the subdomain IV magnetic potential equation, respectively, and let z be the harmonic order of the subdomain IV magnetic potential equation. g2v (r) is a particular solution produced by the radially magnetized magnet on the right, and its expression is:

[0319] (47)

[0320] (3.5) Analysis of the magnetic field V in the left-side tangentially magnetized magnet subdomain

[0321] Since the subdomain V has a magnetization vector, the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates can be expressed as follows:

[0322] (48)

[0323] In the formula, R3 is the inner radius of subdomain V, R6 is the outer radius of subdomain V, and β f Let M be the radian of the central angle corresponding to the sector-shaped subdomain V permanent magnet, and the magnetization vector M. k1 radial component M k1r and tangential component M k1θ It is given by equation (24).

[0324] Since the subdomain V is flanked by stator cores, the radial magnetic field strength at both boundaries is zero. The boundary conditions are then expressed as:

[0325] (49)

[0326] Solving equation (48) using the method of separation of variables, the solution to the equation can be obtained from equation (49):

[0327] (50)

[0328] In the formula D k1q T k1q D k10 and T k10are the DC component coefficients and harmonic component coefficients of the subdomain V magnetic potential equation, respectively, and q is the harmonic order of the subdomain V magnetic potential equation.

[0329] (3.6) Magnetic field analysis of the right-side tangential magnetized magnet subdomain VI

[0330] Since subdomain VI has a magnetization vector, the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates can be expressed as follows:

[0331] (51)

[0332] In the formula β f Simultaneously, the magnetization vector M corresponds to the radian of the central angle of the sector subdomain VI permanent magnet. k2 radial component M k2r and tangential component M k2θ It is given by equation (26).

[0333] Subdomain VI is flanked by stator cores on both sides, therefore the radial magnetic field strength at the two boundary points is zero. The boundary conditions are then expressed as:

[0334] (52)

[0335] By solving equation (51) using the method of separation of variables, the solution to the equation can be obtained from equation (52):

[0336] (53)

[0337] In the formula L k2s W k2s L k20 and W k20 , respectively, are the DC component coefficients and harmonic component coefficients of the subdomain VI magnetic potential equation, and s is the harmonic order of the subdomain VI magnetic potential equation.

[0338] (3.7) Magnetic field analysis of stator slot subdomain VII

[0339] In subdomain VII, there is a current density distribution. The Poisson equation for the vector magnetic potential in two-dimensional polar coordinates can be expressed as follows:

[0340] (54)

[0341] In the formula, R4 is the inner radius of subdomain VII, and R5 is the outer radius of subdomain VII.

[0342] Subdomain VII's left and right boundaries and bottom boundary are both stator cores; therefore, the radial magnetic field strength on both sides of each slot and the tangential magnetic field strength at the bottom are zero. The boundary conditions are then expressed as:

[0343] (55)

[0344] (56)

[0345] Solving equation (54) using the method of separation of variables, the solution to the equation can be obtained from equations (55) and (56):

[0346] (57)

[0347] In the formula C jp and C j0 are the harmonic component coefficients and DC component coefficients of the magnetic potential equation of subdomain VII, respectively, where p is the harmonic order of the magnetic potential equation of subdomain VII, and V jp (t) is a particular solution generated by the current density, and its expression is:

[0348] (58)

[0349] (3.8) Magnetic field analysis of external air subdomain VIII

[0350] The annular region located between the stator outer radius R6 and the motor outer boundary radius R7 is subdomain VIII. This subdomain has no current distribution and magnetization component. The Laplace equation for the vector magnetic potential in two-dimensional polar coordinates is:

[0351] (59)

[0352] The outer boundary of the motor is a magnetically parallel boundary, therefore the radial magnetic field strength at the outer boundary is zero. Furthermore, similar to the internal air gap subdomain II, subdomain VIII also exhibits periodic conditions. The boundary conditions of the motor are then expressed as:

[0353] (60)

[0354] (61)

[0355] Solving equation (59) using the method of separation of variables, the solution to the equation can be obtained from equations (60) and (61):

[0356] (62)

[0357] In the formula: F 1t and F 2t , , are the harmonic component coefficients of the VIII magnetic potential equation of the subdomain, and t is the harmonic order of the VIII magnetic potential equation of the subdomain.

[0358] In summary, the general solutions to the magnetic potential equations containing unsolved coefficients for all six regions have been established. Among them, there are A... im A i0 B 1n B2n B 3n B 4n E g1v F g1v E g10 F g10 H g2z Q g2z H g20 Q g20 D k1q T k1q D k10 T k10 L k2s W k2s L k20 W k20 C jp C j0 F 1t and F 2t The 26 sets of DC component and harmonic component coefficients to be solved will be determined by the boundary conditions between each region.

[0359] Step 4: Using the magnetic field continuity relationship between the subdomains at the four positions r=R2, R3, R4, R5 (i.e., equal radial magnetic flux density and equal tangential magnetic field strength as boundary conditions), establish matrix equations for the coefficients, solve for the coefficients in the general solution of the magnetic potential equations for each subdomain in Step 3, and thus obtain the air gap magnetic flux density and electromagnetic torque. Specifically:

[0360] (4.1) At the interface between rotor slot subdomain I and internal air gap subdomain II (r=R2), based on the equality of radial magnetic flux density and tangential magnetic field strength, the simultaneous equations can be expressed as:

[0361] (63)

[0362] (64)

[0363] (4.2) At the interface (r=R3) between the right radial magnetized magnetic subdomain III, the left radial magnetized magnetic subdomain IV, the left tangential magnetized magnetic subdomain V, the right tangential magnetized magnetic subdomain VI, and the internal air gap subdomain II, based on the equality of the radial magnetic flux density of the right radial magnetized magnetic subdomain III and the internal air gap subdomain II, the simultaneous equations can be expressed as:

[0364] (65)

[0365] The radial magnetic flux density of the left radially magnetized magnet subdomain IV is equal to that of the internal air gap subdomain II. The simultaneous equations can be expressed as:

[0366] (66)

[0367] The radial magnetic flux density of the left-side tangentially magnetized magnet subdomain V is equal to that of the internal air gap subdomain II. The simultaneous equations can be expressed as:

[0368] (67)

[0369] The radial magnetic flux density of the right-side tangentially magnetized magnet subdomain VI is equal to that of the internal air gap subdomain II. The simultaneous equations can be expressed as:

[0370] (68)

[0371] At the interface (r=R3) between the right radial magnetized magnetic subdomain III, the left radial magnetized magnetic subdomain IV, the left tangential magnetized magnetic subdomain V, the right tangential magnetized magnetic subdomain VI, and the internal air gap subdomain II, based on the boundary condition that the tangential magnetic field strength is equal, the simultaneous equations can be expressed as:

[0372] (69)

[0373] (4.3) At the interface between the right radial magnetized magnet subdomain III and the left radial magnetized magnet subdomain IV and the stator slot subdomain VII (r=R4), based on the fact that the radial magnetic flux density of the right radial magnetized magnet subdomain III and the stator slot subdomain VII are equal, the simultaneous equations can be expressed as:

[0374] (70)

[0375] Based on the fact that the radial magnetic flux density of the left radial magnetized magnet subdomain IV is equal to that of the stator slot subdomain VII, the simultaneous equations can be expressed as:

[0376] (71)

[0377] At the interface between the right radial magnetized magnet subdomain III and the left radial magnetized magnet subdomain IV and the stator slot subdomain VII (r=R4), based on the boundary condition that the tangential magnetic field strength is equal, the simultaneous equations can be expressed as:

[0378] (72)

[0379] (4.4) At the interface between the left tangentially magnetized magnetic subdomain V and the right tangentially magnetized magnetic subdomain VI and the external air subdomain VIII (r=R6), based on the fact that the radial magnetic flux density of the left tangentially magnetized magnetic subdomain V and the external air subdomain VIII are equal, the simultaneous equations can be expressed as:

[0380] (73)

[0381] Based on the fact that the radial magnetic flux density of the right-side tangentially magnetized magnet subdomain VI is equal to that of the external air subdomain VIII, the simultaneous equations can be expressed as:

[0382] (74)

[0383] At the interface between the left tangential magnetized magnetic subdomain V and the right tangential magnetized magnetic subdomain VI and the external air subdomain VIII (r=R6), based on the boundary condition that the tangential magnetic field strength is equal, the simultaneous equations can be expressed as:

[0384] (75)

[0385] By combining equations (63) to (75), according to the properties of Fourier series, the above boundary conditions can all be written as the DC component and harmonic component coefficients being equal respectively. Therefore, 26 sets of equations about the coefficients can be obtained, and the 26 sets of unknown DC component and harmonic component coefficients of the magnetic potential equations of each region can be solved.

[0386] Step 5: Based on the DC component and harmonic component coefficients of each subdomain obtained in Step 4, calculate the air gap magnetic flux density and electromagnetic torque of the motor.

[0387] First, substitute the magnetic potential solution (37) of the air gap region into equation (28) to obtain the radial component (76) and tangential component (77) of the air gap magnetic flux density of the motor. In order to facilitate the subsequent calculation of electromagnetic torque, the armature current can be set to zero first, and the air gap magnetic flux density generated by the open circuit field under the action of only the permanent magnet can be solved; then the permanent magnet can be set to air, and the air gap magnetic flux density generated by the armature reaction field can be solved.

[0388] (76)

[0389] (77)

[0390] According to Maxwell's theory, electromagnetic torque is the result of the interaction between the open-circuit field and the armature reaction field. Given the air gap magnetic flux density of the open-circuit field and the armature reaction field, the instantaneous torque can be obtained by integrating the magnetic stress on the closed surface of the air gap. The instantaneous electromagnetic torque can be expressed as:

[0391] (78)

[0392] In the formula R x =(R2+R3) / 2 is the radius at the center of the internal air gap sub-domain, and L is the axial length of the motor. and These are the radial and tangential air gap magnetic flux densities of the open-circuit field, respectively. and These are the radial and tangential air gap magnetic flux densities of the armature reaction field, respectively.

[0393] This embodiment uses, as follows Figure 1As shown in Embodiment 1, the novel flux-switching motor with an additional split magnet is analyzed as an example. Figure 3 , Figure 4 The 6-slot (6 stator slots) 8-pole (8 rotor slots) motor shown is used as a comparative example to illustrate the performance of the novel flux-switching motor with additional split magnets described in Embodiment 1.

[0394] like Figure 3 , Figure 4 The conventional 6-slot 8-pole flux-switching motor shown, and the novel flux-switching motor with additional split magnets described in Embodiment 1, both include a rotor 1, a stator 2, stator teeth 3, a rotor slot 4, and a stator slot 5. The difference lies in... Figure 3 In the conventional 6-slot 8-pole flux-switching motor shown, the 6th pole is a non-split tangential magnetized pole, and as... Figure 3 , Figure 4 The motor shown does not have stator slot radial magnetized permanent magnet 8.1 and radial magnetized permanent magnet 8.2, nor iron core 9.

[0395] In this embodiment, as Figure 1 The novel flux-switching motor with an additional split magnet as shown in Embodiment 1, and as... Figure 3 , Figure 4 The three 6-slot 8-pole flux-switching motors shown all have a rated speed of 600 r / min. The rotor 1 and stator 2 of all three are made of 50WW470 silicon steel sheets, and the permanent magnets are all made of neodymium iron boron (NdFe35). The relative permeability of the permanent magnets is 1.1, the remanence is 1.23 T, and the current density is 5.5 A / mm². 2 The inner radius of rotor slot 4 in all three components is 20 mm, and the outer radius of rotor slot 4 is 29.2 mm. Figure 1 and Figure 3 The rotor 1 has a convex iron span angle of 7°. Figure 3 and Figure 4 The convex iron span angles of rotor 1 are 17.5° and 17.25° respectively. The outer radius of stator 2 of all three is 50 mm, the inner radius of stator 2 is 30 mm, and the axial length of the motor is 50 mm.

[0396] Under the premise of ensuring the same utilization rate of magnets, such as Figure 1 In the novel flux-switching motor with additional split magnets described in Embodiment 1, the outer radius of radially magnetized permanent magnet 8.1 and radially magnetized permanent magnet 8.2 is 33 mm, the span angle is 4.2°, the span angle of stator slot 5 is 41.3°, and the span angle of tangentially magnetized magnets 6.1 and 6.2 is 2.05°. Figure 3 In the conventional 6-slot 8-pole flux-switching motor shown, the span angle of pole 6 is 9.7°, the inner radius of stator slot 5 is 30 mm, and the span angle is 31.6°. For example... Figure 3In the conventional 6-slot 8-pole flux-switching motor shown, the span angle of the tangential magnets 6.1 and 6.2 is 3.4°, the inner radius of the stator slot 5 is 30 mm, and the span angle is 31.2°.

[0397] Under the premise of ensuring the same copper loss, such as Figure 1 In the novel flux-switching motor with an additional split magnet described in Embodiment 1, each coil has 72 turns. Figure 3 and Figure 4 In the 6-slot 8-pole flux-switching motor shown, each coil has 72 turns.

[0398] Figure 5 Is it like this? Figure 1 The novel flux-switching motor with an additional split magnet as shown in Embodiment 1, and as... Figure 3 , Figure 4 The comparison results of the electromagnetic torque of the flux-switching motor are shown. With the same amount of permanent magnets, the average electromagnetic torque of this embodiment is significantly improved, and the torque ripple is lower, indicating that the torque performance is significantly better than that of the traditional structure.

[0399] Figure 6 Is it like this? Figure 1 The radial air gap magnetic flux density of the open field at the middle of the air gap calculated under analytical modeling in Embodiment 2 of the novel flux switching motor with an additional split magnet described in Embodiment 1 is compared with the finite element results. Figure 7 This figure compares the analytical results of the radial air gap magnetic flux density of the armature reaction field at the middle of the air gap with the finite element method results. As can be seen from the figure, the results calculated using the exact subdomain model method are in almost perfect agreement with the finite element results.

[0400] Figure 8 Is it like this? Figure 1 The electromagnetic torque calculated by the novel flux-switching motor with an additional split magnet described in Embodiment 1, as shown in Embodiment 2, is compared with the finite element results under analytical modeling. Within the allowable error range, the waveforms of the two are highly consistent. Figure 6 , Figure 7 and Figure 8 The correctness of the analytical modeling presented was verified.

[0401] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. These embodiments are merely descriptions of preferred embodiments and are not intended to limit the scope or concept of the invention. The specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. Such combinations, as long as they do not violate the spirit of the present invention, should also be considered as part of this disclosure. To avoid unnecessary repetition, the present invention will not further describe the various possible combinations.

[0402] This invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of this invention and without departing from the design idea of ​​this invention, all modifications and improvements made by those skilled in the art to the technical solutions of this invention should fall within the protection scope of this invention. The technical content for which protection is sought in this invention has been fully described in the claims.

Claims

1. A novel flux switching motor with an additional split magnet, characterized in that: The device includes a rotor and a stator that is ringed around the rotor. Multiple stator teeth are formed on the inner ring surface of the stator, and stator slots are formed between adjacent stator teeth. The stator slots are connected to the space between the stator and the rotor through radially magnetized permanent magnets at the slot openings. Tangentially magnetized permanent magnets that penetrate the stator radially are provided between adjacent stator slots. Multiple rotor slots are formed on the circumferential outer surface of the rotor. An iron core is provided in each radially magnetized permanent magnet and each tangentially magnetized permanent magnet. The iron core is inserted into the radially magnetized permanent magnet and the tangentially magnetized permanent magnet respectively to form a split magnet.

2. A novel flux switching motor with an additional split magnet according to claim 1, characterized in that: The relative permeability of the radially magnetized permanent magnet and the tangentially magnetized permanent magnet are both 1.1, the residual magnetism is 1.23 T, and the current density of the armature winding in the flux-switched motor is 5.5 A / mm². 2 .

3. An analytical modeling method for a novel flux-switching motor with an additional split magnet, characterized in that: Specifically, the following steps are included: Step (1): Using the precise subdomain model method, the solution domain of the novel flux-switching motor with additional split magnetic poles is divided into rotor slot subdomain I, internal air gap subdomain II, right radial magnetized magnet subdomain III, left radial magnetized magnet subdomain IV, left tangential magnetized magnet subdomain V, right tangential magnetized magnet subdomain VI, stator slot subdomain VII, and external air subdomain VIII. Step (2): Determine the current density distribution in the stator slot subdomain VII, and the magnetization intensity of the right radial magnetized magnet subdomain III, the left radial magnetized magnetized magnet subdomain IV, the left tangential magnetized magnetized magnet subdomain V, and the right tangential magnetized magnetized magnet subdomain VI in one electric cycle; Step (3): Based on the results obtained in step (2), the z-direction component of the vector magnetic potential A of each subdomain divided in step (1) is used as the solution variable of the partial differential equation. According to whether the stator slot subdomain VII has a current density component and whether the right radial magnetized magnet subdomain III, left radial magnetized magnet subdomain IV, left tangential magnetized magnet subdomain V and right tangential magnetized magnet subdomain VI have a magnetization intensity component, determine the Poisson equation of the stator slot subdomain VII, right radial magnetized magnet subdomain III, left radial magnetized magnet subdomain IV, left tangential magnetized magnet subdomain V and right tangential magnetized magnet subdomain VI with respect to the vector magnetic potential A, as well as the Laplace equation of the rotor slot subdomain I, internal air gap subdomain II and external air subdomain VIII with respect to the vector magnetic potential A, and solve the general solution expression of the vector magnetic potential A of each subdomain by means of separation of variables. Step (4): Utilize the continuous relationship of the magnetic field between each subdomain to establish the boundary condition equations and obtain the matrix equations. Solve the DC component and harmonic component coefficients in the general solution expression of the vector magnetic potential A of each subdomain obtained in step (3) using the matrix equations. Step (5): Substitute the DC component and harmonic component coefficients in the general solution expression of the vector magnetic potential A of each subdomain obtained in step (4) into the general solution expression of the vector magnetic potential A obtained in step (3) to obtain the complete expression of the vector magnetic potential A of each subdomain, and then calculate the air gap magnetic flux density and electromagnetic torque of the motor.

4. The analytical modeling method for a novel flux-switching motor with an additional split magnet according to claim 3, characterized in that: The specific details of step S2 are as follows: (2.1) Current density distribution: For a double-layer non-overlapping winding, J1 and J2 are the current densities on the left and right sides of the stator slot, respectively, and their corresponding expressions are as follows: In the formula k s S is the winding fill factor. w Let C1 be the cross-sectional area of ​​the conductor, and I(t) be the matrix formed by the three-phase armature currents. Matrices C1 and C2 relate the three-phase currents to the current density of each stator slot. The correlation matrices C1 and C2 for the double-layer non-overlapping windings located on the left and right sides of the stator slots are as follows: In the formula, C1 is the correlation matrix of the left winding and C2 is the correlation matrix of the right winding; Therefore, the current density matrix on the left and right sides of the stator slot is represented as: In the formula For the Nth s Current density of the left winding in each stator slot For the Nth s Current density of the right winding in each stator slot; The Fourier expansion of the current density of each stator slot and its expansion coefficients are expressed as follows: In the formula, θ is the mechanical angular position, and β s Let J be the central angle in radians corresponding to the stator slot subdomain, p be the harmonic order of the stator slot subdomain magnetic potential equation, and J be the value of J. j J is the current density of the j-th stator slot, and J is the DC component coefficient in the Fourier expansion of the current density of the j-th stator slot. j0 The AC component coefficient J in the Fourier expansion of the current density of the j-th stator slot jp and the center position angle of the j-th stator slot subdomain They are respectively: In the formula θ j0 J is the position angle of the center of the first stator slot relative to the initial position. j1 Let J be the current density of the left winding in the j-th stator slot. j2 Let be the current density of the right winding in the j-th stator slot; (2.2) Magnetization of permanent magnets: In two-dimensional polar coordinates, the magnetization of a permanent magnet is represented by radial and tangential components: M=M r e r +M θ e θ In the formula, M is the magnetization vector of the permanent magnet, e r and e θ M are unit vectors in the radial and tangential directions, respectively. r and M θ These are the radial and tangential components of the magnetization, respectively. For the right radially magnetized magnet subdomain III, M g1r and M g1θ Let be the radial and tangential components of the magnetization, respectively, and their expressions are: In the formula β g θ represents the central angle in radians corresponding to the magnetic pole of subdomain III of the radially magnetized magnet on the right. g1 M rv and M θv They are respectively: In the formula θ g1 θ is the position angle of the g1th magnet center in the right radially magnetized magnet subdomain III. g10 The angle between the center of the first magnet in the right radial magnetization subdomain III and the initial position; In the formula M rv and M θv , respectively, are the harmonic component coefficients in the Fourier expansions of the radial and tangential magnetization of the right radial magnetized magnet subdomain III, and v is the harmonic order of the magnetic potential equation of the right radial magnetized magnet subdomain III. After mirroring the right-side radially magnetized magnet subdomain III, the expression for the magnetization intensity over one period is as follows: In the formula B r μ0 is the remanence of the permanent magnet, and μ0 is the permeability of free space. For the left radially magnetized magnet subdomain IV, M g2r and M g2θ Let be the radial and tangential components of the magnetization, respectively, and their expressions are: In the formula θ g2 M rz and M θz They are respectively: In the formula θ g2 θ is the position angle of the g2th magnet center in the left radially magnetized magnet subdomain IV. g20 The angle between the center of the first magnet in the left radially magnetized magnet subdomain IV and the initial position; In the formula M rz and M θz , respectively, are the harmonic component coefficients in the Fourier expansions of the radial and tangential magnetization of the left radially magnetized magnet subdomain IV magnet, and z is the harmonic order of the magnetic potential equation of the left radially magnetized magnet subdomain IV magnet. After mirroring the left radially magnetized magnet subdomain IV, the expression for the magnetization intensity over one period is as follows: For the left-side tangentially magnetized subdomain V magnet, M k1r and M k1θ Let be the radial and tangential components of the magnetization, respectively, and their expressions are: In the formula β f θ represents the central angle in radians corresponding to the V-pole of the tangentially magnetized magnet subdomain on the left. k1 for: In the formula θ k1 Let θ be the k1th center position angle of the left-side tangentially magnetized magnet subdomain V. k10 The angle between the center of the first magnet in the left-side tangentially magnetized magnet subdomain V and the initial position; For the right-side tangentially magnetized magnet subdomain VI magnet, M k2r and M k2θ Let be the radial and tangential components of the magnetization, respectively, and their expressions are: In the formula θ k2 for: In the formula θ k2 Let θ be the k2th center position angle of the right-side tangentially magnetized magnet subdomain VI. k20 The angle between the center of the first magnet in the right-side tangentially magnetized magnet subdomain VI and the initial position.

5. The analytical modeling method for a novel flux-switching motor with an additional split magnet according to claim 4, characterized in that: The specific details of step S3 are as follows: In a two-dimensional polar coordinate system, the z-direction component of the vector magnetic potential A is a function of the radius r and the angular position θ, and the radial component B of the magnetic field density vector B... r With tangential component B θ Represented as: In air and in magnetized linear media, the magnetic field strength and magnetic field density vector are related by the following expression, where μ r is the relative permeability of the permanent magnet, and H is the magnetic field strength vector; In the formula, μ0 is the magnetic permeability in vacuum; (3.1) Magnetic field analysis of rotor slot subdomain I In the rotor slot subdomain I, with no current or magnetization components, the Laplace equation for the vector magnetic potential in two-dimensional polar coordinates is: In the formula A 1i It is the magnetic vector position of the i-th rotor slot, R1 is the inner radius of the rotor slot, R2 is the outer radius of the rotor slot, and β r Let θ be the radian of the central angle corresponding to the sector rotor slot, and θ be the center position angle of the i-th rotor slot subdomain. i The expression is: In the formula θ i0 The angle of the first rotor slot subdomain relative to the initial position; Since the left and right boundaries of the rotor slot subdomain are both iron cores, the radial magnetic field strength on both sides of the rotor slot is zero. Also, because the bottom boundary of the rotor slot subdomain is an iron core, the tangential magnetic field strength at the bottom of the rotor slot is zero. Therefore, the boundary conditions for rotor slot subdomain I are: In the formula It is the tangential magnetic field strength of the i-th rotor slot. It is the radial magnetic field strength of the i-th rotor slot; According to equations (32) and (33), the general solution of equation (30) is obtained as follows: In the formula A im and A i0 , respectively, are the harmonic component and DC component coefficients of the general solution of the subdomain I magnetic potential equation, and m is the harmonic order of the subdomain I magnetic potential equation; (3.2) Magnetic field analysis of the internal air gap subdomain II The annular region located between the rotor outer radius R2 and the stator inner radius R3 is the internal air gap subdomain II. Internal air gap subdomain II has no current distribution or magnetization component. The Laplace equation for the vector magnetic potential in two-dimensional polar coordinates is: In the formula, A2 is the magnetic vector potential of the internal air gap subdomain; The periodicity condition for the existence of the internal air gap subdomain II is: According to equation (36), the general solution can be obtained by solving equation (35): In the formula B 1n B 2n B 3n and B 4n , respectively, are the harmonic component coefficients of the magnetic potential equation of the internal air gap subdomain II, and n is the harmonic order of the magnetic potential equation of the internal air gap subdomain II; (3.3) Magnetic field analysis of right radial magnetized magnet subdomain III The right-side radially magnetized magnet subdomain III has a magnetization vector; therefore, the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates is as follows: In the formula A 3g1 R3 is the magnetic vector position of the g1-th magnet in the radially magnetized magnet subdomain III on the right side of the stator slot, R4 is the inner radius of the radially magnetized magnet subdomain III on the right side, and β is the outer radius of the radially magnetized magnet subdomain III on the right side. g The central angle of the permanent magnet in the radially magnetized subdomain III on the right side of the sector is in radians, and the magnetization vector M is... g1 radial component M g1r and tangential component M g1θ They are respectively: The right radial magnetized magnet subdomain III is flanked by stator cores, therefore the radial magnetic field strength at both boundaries is zero. The boundary conditions at this point are: In the formula It is the radial magnetic field strength of the g1th magnet in the right radially magnetized magnet subdomain III; Solving equation (38) using the method of separation of variables, the solution to equation (40) is obtained as follows: In the formula E g10 and F g10 E represents the DC component coefficient of the magnetic potential equation for the right-hand radially magnetized magnet subdomain III. g1v F g1v G represents the harmonic component coefficients of the magnetic potential equation for the right-hand radially magnetized magnet subdomain III, v represents the harmonic order of the magnetic potential equation for the right-hand radially magnetized magnet subdomain III, and G represents the harmonic component coefficients of the magnetic potential equation for the right-hand radially magnetized magnet subdomain III. g1v (r) is a particular solution produced by the radially magnetized magnet on the right, and its expression is: (3.4) Analysis of the magnetic field of the left radial magnetized magnet subdomain IV The left radially magnetized magnet subdomain IV has a magnetization vector, therefore the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates is as follows: In the formula A 4g2 It is the magnetic vector position of the g2th magnet in the radially magnetized magnet subdomain IV on the left side of the stator slot, β g Simultaneously, the radian of the central angle corresponding to the permanent magnet IV subdomain of the radially magnetized magnet on the left side of the sector, and the magnetization vector M g2 radial component M g2r and tangential component M g2θ They are respectively: The left radially magnetized magnet subdomain IV has iron cores on both sides, therefore the radial magnetic field strength at the two boundaries is zero. The boundary conditions at this time are: In the formula It is the radial magnetic field strength of the g2th rotor slot in the left radially magnetized magnet subdomain IV; Solving equation (43) using the method of separation of variables, the solution to the equation is obtained according to equation (45): In the formula H g20 and Q g20 H represents the DC component coefficient of the potential equation for the left radially magnetized magnet subdomain IV. g2z Q g2z Let G be the harmonic component coefficient of the IV magnetic potential equation of the left radially magnetized magnet subdomain, z be the harmonic order of the IV magnetic potential equation of the left radially magnetized magnet subdomain, and G be the harmonic component coefficient of the IV magnetic potential equation of the left radially magnetized magnet subdomain. g2v (r) is a particular solution produced by the radially magnetized magnet on the right, and its expression is: (3.5) Analysis of the magnetic field V in the left-side tangentially magnetized magnet subdomain The left-side tangentially magnetized subdomain V contains a magnetization vector; therefore, the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates can be expressed as follows: In the formula A 5k1 R3 is the magnetic vector position of the k1th magnet in the left-side tangentially magnetized magnet subdomain of the stator, R6 is the inner radius of the left-side tangentially magnetized magnet subdomain V, and β is the outer radius of the subdomain V. f The central angle of the permanent magnet V, the tangentially magnetized subdomain on the left side of the sector, is in radians, and the magnetization vector M is... k1 radial component M k1r and tangential component M k1θ Given by equation (24); The left-side tangentially magnetized subdomain V is composed of iron cores on both sides, therefore the radial magnetic field strength at the two boundaries is zero. The boundary conditions are then expressed as: In the formula It is the radial magnetic field strength of the k1th magnet in the tangentially magnetized magnet subdomain V on the left side of the stator; Solving equation (48) using the method of separation of variables, the solution to equation (49) is obtained as follows: In the formula D k10 and T k10 D represents the DC component coefficient of the magnetic potential equation for the V-field of the tangential magnetization subdomain on the left side of the stator. k1q T k1q q represents the harmonic component coefficients of the V magnetic potential equation of the tangential magnetization subdomain on the left side of the stator, and q represents the harmonic order of the V magnetic potential equation of the subdomain. (3.6) Magnetic field analysis of the right-side tangential magnetized magnet subdomain VI The right-side tangentially magnetized subdomain VI has a magnetization vector; therefore, the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates is as follows: In the formula A 6k2 It is the magnetic vector position of the k2th magnet in the tangentially magnetized magnet subdomain on the right side of the stator, β f Simultaneously, the radian of the central angle corresponding to the permanent magnet VI subdomain tangentially magnetized on the right side of the sector, and the magnetization vector M. k2 radial component M k2r and tangential component M k2θ Given by equation (26); The right-side tangentially magnetized magnet subdomain VI is flanked by stator cores, therefore the radial magnetic field strength at both boundaries is zero; the boundary conditions are as follows: In the formula It is the radial magnetic field strength of the k2th magnet in the tangentially magnetized magnet subdomain on the right side of the stator; By solving equation (51) using the method of separation of variables, the solution to the equation can be obtained from equation (52): In the formula, L k20 and W k20 L represents the DC component coefficient of the magnetic potential equation for the right-hand tangentially magnetized magnet subdomain VI. k2s W k2s denoted as the harmonic component coefficients of the VI magnetic potential equation of the right-side tangentially magnetized magnet subdomain, and s is the harmonic order of the VI magnetic potential equation of the right-side tangentially magnetized magnet subdomain. (3.7) Magnetic field analysis of stator slot subdomain VII There is a current density distribution in the stator slot subdomain VII, and the Poisson equation for the vector magnetic potential in two-dimensional polar coordinates is as follows: In the formula A 7j R4 is the magnetic vector position of the j-th stator slot in stator slot subdomain VII, R5 is the inner radius of stator slot subdomain VII, and R5 is the outer radius of stator slot subdomain VII. Since the left, right, and bottom boundaries of stator slot subdomain VII are all iron cores, the radial magnetic field strength on both sides of each slot and the tangential magnetic field strength at the bottom are zero; the boundary conditions are expressed as follows: In the formula It is the tangential magnetic field strength of the j-th stator slot. It is the radial magnetic field strength of the j-th stator slot; Solving equation (54) using the method of separation of variables, the solution to the equation is obtained from equations (55) and (56): In the formula C jp and C j0 are the harmonic component coefficients and DC component coefficients of the magnetic potential equation for stator slot subdomain VII, respectively, where p is the harmonic order of the magnetic potential equation for stator slot subdomain VII, and V jp (t) is a particular solution generated by the current density, and its expression is: (3.8) Magnetic field analysis of external air subdomain VIII The annular region located between the stator outer radius R6 and the motor outer boundary radius R7 is the external air subdomain VIII. This subdomain has no current distribution and magnetization components, and its vector magnetic potential in two-dimensional polar coordinates is represented by the Laplace equation: In the formula, A8 is the magnetic vector potential of the external air subdomain; The outer boundary of the motor is a magnetically parallel boundary, therefore the radial magnetic field strength at the outer boundary of the motor is zero. Furthermore, similar to the internal air gap subdomain II, the external air subdomain VIII also exhibits periodic conditions. In this case, the boundary conditions of the motor are expressed as: In the formula It is the radial magnetic field strength of the external air subdomain; Solving equation (59) using the method of separation of variables, the solution to the equation is obtained from equations (60) and (61): In the formula: F 1t and F 2t , respectively, are the harmonic component coefficients of the VIII magnetic potential equation of the external air subdomain, and t is the harmonic order of the VIII magnetic potential equation of the external air subdomain; In summary, the general solutions to the magnetic potential equations containing unsolved coefficients for all six regions have been established, with a total of A... im A i0 B 1n B 2n B 3n B 4n E g1v F g1v E g10 F g10 H g2z Q g2z H g20 Q g20 D k1q T k1q D k10 T k10 L k2s W k2s L k20 W k20 C jp C j0 F 1t and F 2t The 26 sets of DC component and harmonic component coefficients to be solved are determined by the boundary conditions between each region.

6. The analytical modeling method for a novel flux-switching motor with an additional split magnet according to claim 5, characterized in that: The specific details of step S4 are as follows: (4.1) At the interface between rotor slot subdomain I and internal air gap subdomain II, r = R2. Based on the equality of radial magnetic flux density and tangential magnetic field strength, the simultaneous equations are expressed as: (4.2) At the interface between the right radially magnetized magnetic subdomain III, the left radially magnetized magnetic subdomain IV, the left tangentially magnetized magnetic subdomain V, the right tangentially magnetized magnetic subdomain VI, and the internal air gap subdomain II, r = R3. Based on the fact that the radial magnetic flux density of the right radially magnetized magnetic subdomain III and the internal air gap subdomain II are equal, the simultaneous equations are expressed as follows: The radial magnetic flux density of the left radially magnetized magnet subdomain IV is equal to that of the internal air gap subdomain II. The simultaneous equations are expressed as follows: The radial magnetic flux density of the left-side tangentially magnetized magnet subdomain V is equal to that of the internal air gap subdomain II. The simultaneous equations are expressed as follows: The radial magnetic flux density of the right-side tangentially magnetized magnet subdomain VI is equal to that of the internal air gap subdomain II. The simultaneous equations are expressed as follows: At the interface between the right radially magnetized magnetic subdomain III, the left radially magnetized magnetic subdomain IV, the left tangentially magnetized magnetic subdomain V, the right tangentially magnetized magnetic subdomain VI, and the internal air gap subdomain II, r = R3. Based on the boundary condition that the tangential magnetic field strength is equal, the simultaneous equations are expressed as: (4.3) At the interface between the right radial magnetized magnet subdomain III and the left radial magnetized magnet subdomain IV and the stator slot subdomain VII, r = R4. Based on the fact that the radial magnetic flux density of the right radial magnetized magnet subdomain III and the stator slot subdomain VII are equal, the simultaneous equations are expressed as: Based on the fact that the radial magnetic flux density of the left radial magnetized magnet subdomain IV is equal to that of the stator slot subdomain VII, the simultaneous equations can be expressed as follows: At the interface between the right radial magnetized magnet subdomain III and the left radial magnetized magnet subdomain IV and stator slot subdomain VII, r = R4. Based on the boundary condition that the tangential magnetic field strength is equal, the simultaneous equations are expressed as: (4.4) At the interface between the left tangentially magnetized magnetic subdomain V and the right tangentially magnetized magnetic subdomain VI and the external air subdomain VIII, r = R6. Based on the fact that the radial magnetic flux density of the left tangentially magnetized magnetic subdomain V and the external air subdomain VIII are equal, the simultaneous equations are expressed as follows: Based on the fact that the radial magnetic flux density of the right-side tangentially magnetized magnet subdomain VI is equal to that of the external air subdomain VIII, the simultaneous equations can be expressed as follows: At the interface between the left tangential magnetized magnetic subdomain V and the right tangential magnetized magnetic subdomain VI and the external air subdomain VIII, r = R6. Based on the boundary condition that the tangential magnetic field strengths are equal, the simultaneous equations are expressed as: By combining equations (63) to (75), according to the properties of Fourier series, the above boundary conditions can all be written as the DC component and harmonic component coefficients being equal respectively. Thus, 26 sets of equations about the coefficients are obtained, and the 26 sets of unknown DC component and harmonic component coefficients of the magnetic potential equations of each region can be solved.

7. The analytical modeling method for a novel flux-switching motor with an additional split magnet according to claim 6, characterized in that: The specific details of step S5 are as follows: First, substitute the magnetic potential flux solution (37) of the air gap region into equation (28) to obtain the radial component (76) and tangential component (77) of the air gap magnetic flux density of the motor. Set the armature current to zero and solve for the air gap magnetic flux density generated by the open circuit field under the action of only the permanent magnet. Then, set the permanent magnet to air and solve for the radial air gap magnetic flux density generated by the armature reaction field. and tangential air gap magnetic flux density ; According to Maxwell's theory, electromagnetic torque is the result of the interaction between the open-circuit field and the armature reaction field. Given the air gap magnetic flux density of the open-circuit field and the armature reaction field, the instantaneous torque is obtained by integrating the magnetic stress on the closed surface of the air gap. The instantaneous electromagnetic torque is expressed as: In the formula, T is the instantaneous electromagnetic torque, and R... x =(R2+R3) / 2 is the radius at the center of the internal air gap sub-domain, and L is the axial length of the motor. and These are the radial and tangential air gap magnetic flux densities of the open-circuit field, respectively. and These are the radial and tangential air gap magnetic flux densities of the armature reaction field, respectively.

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