Solving method for electromagnetic design of surface-mounted permanent magnet motor with tooth socket and computer readable storage medium

Abstract

The invention relates to the technical field of permanent magnet motors, and discloses a solving method for the electromagnetic design of a surface-mounted permanent magnet motor with a tooth socket and a computer readable storage medium, and the method comprises the following steps: constructing an equivalent linear motor model through embedding an equivalent current sheet; dividing sub-domains, and establishing a magnetic field equation of each sub-domain including an undetermined coefficient; constructing a coupling equation set according to a physical condition at an interface of adjacent sub-domains, and integrating the coupling equation set into a unified multi-dimensional matrix equation about an undetermined coefficient; iterative solution is carried out based on a sub-domain method and a magnetic circuit method; according to the method, an actual nonlinear stator is converted into a linear stator model, a subdomain method is adopted to carry out refined area modeling and boundary coupling, local magnetic flux distortion and disturbance such as tooth tip saturation and notch magnetic leakage are captured, a closed-loop iteration process is constructed, and the performance parameters of the permanent magnet motor are calculated. Magnetic field changes caused by saturation are dynamically corrected, and it is ensured that key dynamic performance is highly matched with physical reality.

Description

Solution methods and computer-readable storage media for electromagnetic design of permanent magnet motors with surface-mount gauges and toothed gears. Technical Field

[0001] This invention relates to the field of permanent magnet motor technology, and more specifically to a solution method and a computer-readable storage medium for electromagnetic design of surface-mounted permanent magnet motors with tooth grooves. Background Technology

[0002] Permanent magnet motors, with their high power density, high efficiency, and excellent dynamic response characteristics, are widely used in industrial drives, servo control, and high-end equipment manufacturing. During motor development, accurate prediction of magnetic field distribution, torque output, and electromagnetic coupling processes typically requires the use of appropriate electromagnetic modeling tools. Different modeling methods vary significantly in terms of solution speed, structural description detail, and ability to handle nonlinearities; therefore, selecting the appropriate modeling method at different stages of motor design is crucial.

[0003] Currently, common modeling methods mainly include numerical finite element models and analytical models. Numerical models, such as the finite element method, can handle complex motor topologies and accurately characterize problems such as core saturation, magnetic nonlinearity, and local magnetic field distortion. However, its solution process is highly dependent on mesh generation and iterative calculation, and the computation time increases significantly with the size of the motor and the scale of the system, which is not conducive to parameter scanning and optimization design. One-dimensional analytical models directly describe the magnetic field distribution through mathematical expressions, have high computational efficiency, and can map geometric parameters to electromagnetic performance, making them suitable for the preliminary design stage. However, these models usually assume that the permeability of the stator and rotor cores is infinite, making it difficult to accurately handle material nonlinearity, and the prediction deviation is large under the condition of high core saturation. Magnetic network analytical models use equivalent magnetoresistive networks to characterize the magnetic flux relationship in the core. Although they can consider the nonlinear effects of the core to a certain extent, due to the discretization of the continuous electromagnetic field, it is difficult to accurately reproduce the magnetic flux disturbances in local areas such as slots and tooth tips.

[0004] In recent years, some studies have proposed analytical nonlinear material algorithms based on the slotless stator assumption. These algorithms eliminate slot effects by treating the stator's inner surface as a continuous circular ring structure, thereby further improving computational efficiency. Such "slotless" methods can quickly provide magnetic flux density distribution and output characteristics in the early design stages, offering a reference for optimizing pole arcs, air gap lengths, and permanent magnet structures. However, this model cannot reflect the periodic magnetic permeability modulation effects caused by the actual slotted structure. In particular, characteristics such as slotting torque, back EMF harmonics, and inductance variations with rotor position are closely related to slot type, tooth width, and slot opening shape. Therefore, models based on the slotless assumption often struggle to accurately predict flux linkage distortion, back EMF waveform distortion, and local core saturation in actual motors, limiting their applicability in medium- to high-precision design stages. Therefore, it is necessary to develop a nonlinear electromagnetic solution method directly addressing slotted stator structures, enabling it to accurately reflect key electromagnetic behaviors such as slot permeability abrupt changes, tooth tip leakage flux, local saturation, and spatial harmonic modulation while maintaining the efficiency of analytical solutions. Summary of the Invention

[0005] To address the technical problems of existing technologies, such as difficulty in accurately handling material nonlinearity, difficulty in accurately reproducing magnetic flux disturbances in local areas, and inability to accurately reflect key electromagnetic behaviors, this invention proposes a solution method and a computer-readable storage medium for the electromagnetic design of surface-mounted permanent magnet motors with cogging teeth. The technical solution is as follows:

[0006] Step 1: Simulate the nonlinear environment of the motor stator material by embedding equivalent current plates to construct an equivalent linear motor model;

[0007] Step 2: Divide the linear motor model into a permanent magnet subdomain, an air gap subdomain, a slot subdomain, and a slot opening subdomain. Establish the control equations and general solution expressions for each subdomain with vector magnetic potential as the variable. The general solution expressions include undetermined coefficients determined by the boundary conditions. The boundary conditions of the slot subdomain and the slot opening subdomain are related to the current density of the equivalent current sheet.

[0008] Step 3: Based on the physical condition that the tangential magnetic field strength and radial magnetic flux density are continuous at the interface of adjacent subdomains, construct a set of coupled equations and integrate the set of coupled equations into a unified multidimensional matrix equation about the undetermined coefficients.

[0009] Step 4: Iteratively solve the problem using a composite algorithm based on the subdomain method and the magnetic circuit method;

[0010] Step 5: Based on the magnetic field distribution obtained by the above iterative solution, calculate the performance parameters of the permanent magnet motor.

[0011] Furthermore, in step 1, the equivalent current sheet is specifically embedded in: the two sidewall surfaces of each slot, the bottom surface of each slot, and the two sidewall surfaces of each slot opening.

[0012] Furthermore, in step 2, the governing equations for the slot opening subdomain, the air gap subdomain, and the slot domain are Laplace's equations, while the governing equation for the permanent magnet subdomain is Poisson's equation.

[0013] Furthermore, in step 3, when constructing the unified multidimensional matrix equation, the field quantities on the interface between the slot opening subdomain and the air gap subdomain, and the interface between the slot opening subdomain and the slot subdomain, are expanded into Fourier series for processing.

[0014] Furthermore, the specific steps of step 4, the iterative solution, are as follows:

[0015] Step 4.1: Set the initial current density value for each equivalent current plate;

[0016] Step 4.2: Substitute the current equivalent current density as a boundary condition into the unified multidimensional matrix equation to solve for the magnetic field distribution under the current iteration;

[0017] Step 4.3: Based on the magnetic field distribution obtained above, calculate the magnetic flux entering each part of the stator core, construct an equivalent magnetic circuit model of the stator core, solve the magnetic circuit model to obtain the magnetic voltage drop of each part of the stator, and update the current density value of each equivalent current plate according to the magnetic voltage drop and the nonlinear BH curve of the stator material.

[0018] Step 4.4: Determine whether the difference between the equivalent current density before and after the update meets the preset convergence tolerance. If it does not meet the tolerance, return to step 4.2 with the updated equivalent current density for the next iteration. If it does meet the tolerance, proceed to step 5.

[0019] Further, in step 4.3, constructing the equivalent magnetic circuit model of the stator core specifically involves: constructing a magnetic circuit network based on the stator geometry; calculating the magnetic flux sources injected into each node of the magnetic circuit network by integrating the magnetic flux density of the air gap, slot opening, and slot based on the magnetic field distribution obtained in step 4.2; establishing the node equations of the magnetic circuit network according to Kirchhoff's magnetohydrodynamic law; and solving the equations in matrix form.

[0020] Furthermore, in step 4.3, the current density values ​​of each equivalent current plate are updated based on the magnetic field strength of the corresponding iron core path obtained from the magnetic circuit model.

[0021] Furthermore, the value of the magnetic field strength is determined by the magnetic voltage drop of the core path and its length, and is associated with the nonlinear BH curve.

[0022] Furthermore, in step 5, the performance parameters of the permanent magnet motor are calculated, including flux linkage, back electromotive force, and cogging torque. The cogging torque is calculated using the Maxwell stress tensor method, selecting an integral loop within the air gap subdomain, and using the finally obtained radial and tangential magnetic flux density for calculation.

[0023] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the solution method for electromagnetic design of a surface-mount permanent magnet motor with toothed cogging as described above.

[0024] Beneficial effects:

[0025] This invention uses an equivalent current plate to represent the complex magnetic voltage drop generated by the nonlinear permeability iron core as the magnetic field generated by the current plate. This transforms the actual nonlinear stator into a linear stator model with infinite permeability, allowing for the direct application of the high-precision analytical subdomain method. The invention employs the subdomain method for refined region modeling and boundary coupling, precisely dividing the motor interior into four physical subdomains (permanent magnet, air gap, slot, and slot opening). Precise equations are established for each subdomain, strictly satisfying the magnetic field continuity condition at the interface between adjacent subdomains, thereby capturing local magnetic flux distortions and disturbances such as tooth tip saturation and slot leakage. Based on the subdomain method and the magnetic circuit method, this invention constructs a closed-loop iterative process to dynamically correct magnetic field changes caused by saturation, ensuring that the calculated back EMF waveform, tooth cogging torque peak value, and phase, among other key dynamic performance characteristics, are highly consistent with physical reality. Attached Figure Description

[0026] Figure 1 is a flowchart of the solution method for electromagnetic design of a surface-mounted permanent magnet motor with tooth grooves;

[0027] Figure 2 is a schematic diagram of solving the nonlinear stator permanent magnet motor model in an embodiment of the present invention;

[0028] Figure 3 is a schematic diagram of the linear stator permanent magnet motor model for solving the embedded equivalent current plate in an embodiment of the present invention.

[0029] Figure 4 is a diagram of the equivalent magnetic circuit model of the stator core constructed based on the magnetic circuit method in an embodiment of the present invention;

[0030] Figure 5 is a schematic diagram showing the relationship between the current density and magnetic voltage drop of the equivalent current sheet in an embodiment of the present invention;

[0031] Figure 6 is a schematic diagram of the A-phase magnetic flux predicted by the present invention compared with the prior art;

[0032] Figure 7 is a schematic diagram of the predicted back electromotive force A by the present invention compared with the prior art;

[0033] Figure 8 is a schematic diagram of the cogging torque predicted by the present invention compared with the prior art;

[0034] Figure 9 is a schematic diagram of the tangential magnetic flux density in the air gap predicted by the present invention compared with the prior art;

[0035] Figure 10 is a schematic diagram of the radial magnetic flux density in the air gap predicted by the present invention in comparison with the prior art. Detailed Implementation

[0036] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0037] As shown in Figure 1, the present invention provides a solution method for electromagnetic design of a surface-mounted permanent magnet motor with tooth grooves. This method uses embedded equivalent current plates to simulate the nonlinear environment of the motor stator material.

[0038] This invention first employs the equivalent current subdomain method for model building. Figures 2 and 3 illustrate the transformation of the subdomain method after considering the nonlinear permeability of the stator material. The nonlinear material stator is transformed into a linear material stator with equivalent current plates embedded around its outer edge. Like the traditional subdomain method, the linear material stator has infinite permeability, i.e., a linear environment. Therefore, the solution can be obtained using the traditional subdomain method approach. However, due to the embedded equivalent current plates, the boundary conditions change, which is the equivalent current subdomain method proposed in this invention.

[0039] This invention divides the solution domain of the equivalent current subdomain method into permanent magnet, air gap, slot and slot opening. Indicates the rotor speed. and These represent the radial and tangential directions, respectively. , , , and These represent the radii of the bottom of the slot, the top of the slot, the stator, the permanent magnet, and the rotor yoke, respectively. and These represent the slot opening and the slot width angle, respectively. Then, the magnetic field equations for each subdomain are established, as follows:

[0040] 1) Magnetic field distribution in the slot opening:

[0041] The generalized equation satisfied by the magnetic potential vector at the slot opening is the Laplace equation:

[0042] (1.1)

[0043] in, is the magnetic potential vector in the slot opening.

[0044] The boundary conditions that must be satisfied in the slot opening are:

[0045] (1.2)

[0046] (1.3)

[0047] in, and It is in the The equivalent current density of the equivalent current plate at the corresponding position in each slot.

[0048] Based on the boundary conditions of equations 1.2 and 1.3, the first The general solution for the magnetic potential vector in each slot opening is:

[0049] (1.4)

[0050] in:

[0051] (1.5)

[0052] (1.6)

[0053] in:

[0054] (1.7)

[0055] (1.8)

[0056] (1.9)

[0057] (1.10)

[0058] in, , , and These are undetermined coefficients.

[0059] The radial and tangential magnetic flux density of the slot opening can be obtained from its vector magnetic potential:

[0060] (1.11)

[0061] (1.12)

[0062] Therefore, in the first Radial magnetic flux in each slot opening for:

[0063] (1.13)

[0064] Therefore, in the first Tangential magnetic flux in each slot opening for:

[0065] (1.14)

[0066] 2) Magnetic field distribution of slots, air gaps, and permanent magnets:

[0067] No. Regarding the magnetic potential vector in each slot Solving the equation yields the following expression:

[0068] (1.15)

[0069] in:

[0070] (1.16)

[0071] (1.17)

[0072] in:

[0073] (1.18)

[0074] (1.19)

[0075] (1.20)

[0076] (1.21)

[0077] in, and These are undetermined coefficients.

[0078] According to equations 1.11 and 1.12, the first... Radial magnetic flux density in each slot and tangential magnetic flux density They are respectively:

[0079] (1.22)

[0080] (1.23)

[0081] Regarding the magnetic potential vector in air gap and permanent magnet and Solving the equation yields the following expression:

[0082] (1.24)

[0083] (1.25)

[0084] According to equations 1.11 and 1.12, the radial magnetic flux density in the air gap and tangential magnetic flux density They are respectively:

[0085] (1.26)

[0086] (1.27)

[0087] in:

[0088] (1.28)

[0089] (1.29)

[0090] (1.30)

[0091] (1.31)

[0092] Tangential magnetic flux density in permanent magnets and radial magnetic flux density And respectively:

[0093] (1.32)

[0094] (1.33)

[0095] In the above formula , , , , and All are undetermined coefficients. , , and It is the correlation coefficient of permanent magnet magnetization, and the formula is as follows:

[0096] (1.34)

[0097] (1.35)

[0098] (1.36)

[0099] (1.37)

[0100] For radial magnetization:

[0101] (1.38)

[0102] (1.39)

[0103] For parallel magnetization:

[0104] (1.40)

[0105] (1.41)

[0106] (1.42)

[0107] (1.43)

[0108] in, It is the remanence coefficient of a permanent magnet. It is the ratio of the pole arc to the pole pitch of the permanent magnet. It is the number of pole pairs of the permanent magnet in the motor. It is the vacuum permeability. It is the initial angle of the rotor.

[0109] The other coefficients in the above formula are shown below:

[0110] (1.44)

[0111] (1.45)

[0112] (1.46)

[0113] (1.47)

[0114] (1.48)

[0115] (1.49)

[0116] (1.50)

[0117] Then, the magnetic field equations at the interface between adjacent subdomains are established, as follows:

[0118] 1) The interface between the groove and the groove opening:

[0119] At the interface between the slot opening and the slot, the tangential magnetic flux density and vector magnetic potential of the two subdomains are continuous. Therefore, the equations can be set up and solved by assuming that the tangential magnetic flux density and vector magnetic potential at the interface are equal.

[0120] The interface between the slot and the slot opening, and the tangential magnetic flux density in the slot opening. The time was:

[0121] (1.51)

[0122] in:

[0123] (1.52)

[0124] (1.53)

[0125] (1.54)

[0126] Because the permeability of the stator core material is infinite, the magnetic flux density inside the slot is approximately equal to the radius outside the slot opening domain. The tangential components are all zero, and the tangential magnetic flux density within the slot opening is... At that time, it can be achieved through Fourier series transformation. Expanded to:

[0127] (1.55)

[0128] in:

[0129] (1.56)

[0130] (1.57)

[0131] in:

[0132] (1.58)

[0133] (1.59)

[0134] (1.60)

[0135] In radius At that time, the tangential magnetic flux density in the slot is:

[0136] (1.61)

[0137] (1.62)

[0138] (1.63)

[0139] Based on the interface conditions of the two subdomains, i.e. The following relation can be obtained:

[0140] (1.64)

[0141] (1.65)

[0142] According to Equation 1.64, the solution can be obtained as follows:

[0143] (1.66)

[0144] This invention solves for each undetermined coefficient using a multidimensional matrix, so equation 1.65 can be rewritten in the following matrix form:

[0145] (1.67)

[0146] in, , , They are respectively , , The matrix formed follows the following rules:

[0147] (1.68)

[0148] Other matrix parameters are as follows:

[0149] (1.69)

[0150] (1.70)

[0151] (1.71)

[0152] (1.72)

[0153] (1.73)

[0154] (1.74)

[0155] in:

[0156] (1.75)

[0157] (1.76)

[0158] (1.77)

[0159] (1.78)

[0160] (1.79)

[0161] (1.80)

[0162] (1.81)

[0163] (1.82)

[0164] (1.83)

[0165] In addition to having equal tangential magnetic flux density, the vector magnetic potentials of the two subdomains at the interface are also equal. At that time, the vector magnetic potential in the slot opening is:

[0166] (1.84)

[0167] exist At that time, the vector magnetic potential in the slot is:

[0168] (1.85)

[0169] in:

[0170] (1.86)

[0171] (1.87)

[0172] For ease of solution, It can be expanded into a Fourier series over the slot opening, that is... After unfolding:

[0173] (1.88)

[0174] (1.89)

[0175] (1.90)

[0176] in:

[0177] (1.91)

[0178] (1.92)

[0179] Based on the interface conditions of the two subdomains, i.e. The following results were obtained:

[0180] (1.93)

[0181] (1.94)

[0182] For ease of solution, equation 1.94 is rewritten as:

[0183] (1.95)

[0184] in:

[0185] (1.96)

[0186] (1.97)

[0187] (1.98)

[0188] (1.99)

[0189] (1.100)

[0190] (1.101)

[0191] 2) Interface between air gap and slot opening:

[0192] exist At that time, the tangential magnetic flux density at the slot opening is:

[0193] (1.102)

[0194] in:

[0195] (1.103)

[0196] (1.104)

[0197] Since the permeability of the stator core material is infinite, the tangential component at the stator edge outside the slot opening is zero. For ease of calculation, the tangential magnetic flux density in the slot opening region can be expanded into a Fourier series:

[0198] (1.105)

[0199] in:

[0200] (1.106)

[0201] (1.107)

[0202] (1.108)

[0203] (1.109)

[0204] (1.110)

[0205] (1.111)

[0206] exist At that time, the tangential magnetic flux density in the air gap is:

[0207] (1.112)

[0208] according to The following relationship can be obtained:

[0209] (1.113)

[0210] (1.114)

[0211] Rewrite Equation 1.113 in matrix form:

[0212] (1.115)

[0213] (1.116)

[0214] in:

[0215] (1.117)

[0216] (1.118)

[0217] (1.119)

[0218] (1.120)

[0219] (1.121)

[0220] (1.122)

[0221] (1.123)

[0222] (1.124)

[0223] (1.125)

[0224] (1.126)

[0225] in:

[0226] (1.127)

[0227] (1.128)

[0228] (1.129)

[0229] (1.130)

[0230] (1.131)

[0231] (1.132)

[0232] (1.133)

[0233] (1.134)

[0234] (1.135)

[0235] (1.136)

[0236] (1.137)

[0237] (1.138)

[0238] (1.139)

[0239] (1.140)

[0240] exist At that time, the magnetic potential vector in the air gap can be converted into:

[0241] (1.141)

[0242] in:

[0243] (1.142)

[0244] (1.143)

[0245] Performing a Fourier transform on equation 1.141 yields the following formula:

[0246] (1.144)

[0247] in:

[0248] (1.145)

[0249] (1.146)

[0250] (1.147)

[0251] (1.148)

[0252] (1.149)

[0253] (1.150)

[0254] exist At that time, the magnetic potential vector in the slot opening is:

[0255] (1.151)

[0256] go through We can obtain the following formula:

[0257] (1.152)

[0258] (1.153)

[0259] Transform Equation 1.153 into matrix form:

[0260] (1.154)

[0261] (1.155)

[0262] (1.156)

[0263] (1.157)

[0264] (1.158)

[0265] (1.159)

[0266] (1.160)

[0267] (1.161)

[0268] (1.162)

[0269] (1.163)

[0270] 3) Interface between air gap and permanent magnet:

[0271] The equation for the interface condition matrix between the air gap and the permanent magnet is as follows:

[0272] (1.164)

[0273] (1.165)

[0274] (1.166)

[0275] (1.167)

[0276] in:

[0277] (1.168)

[0278] (1.169)

[0279] (1.170)

[0280] (1.171)

[0281] (1.172)

[0282] (1.173)

[0283] (1.174)

[0284] (1.175)

[0285] (1.176)

[0286] (1.177)

[0287] (1.178)

[0288] (1.179)

[0289] (1.180)

[0290] (1.181)

[0291] (1.182)

[0292] (1.183)

[0293] (1.184)

[0294] (1.185)

[0295] (1.186)

[0296] (1.187)

[0297] Among them, the column vectors relating to the magnetization components , , and Build in the same way, such as ,and It is the highest order of spatial harmonics considered in the air gap magnetic flux density.

[0298] The above matrix equations can be combined into the following:

[0299] (1.188)

[0300] Then, an iterative solution is performed based on a composite algorithm of the subdomain method and the magnetic circuit method, specifically:

[0301] First, assuming the initial current density of each equivalent current plate is zero, Equation 1.188 is solved to obtain the various unknowns. That is, the magnetic field distribution is solved based on the subdomain method under the linear assumption. Then, the convergent nodal magnetopotential matrix is ​​calculated through the magnetic circuit model, and the equivalent current density is updated. The subdomain method is then performed again using this current density to obtain the updated magnetic field distribution.

[0302] Next, the magnetic field within the stator core is calculated based on the new magnetic field distribution, and the difference between the current density obtained in this iteration and the previous iteration is checked to see if it meets the preset convergence tolerance. If not, the current magnetic field distribution is re-substituted into the magnetic circuit model, and the nodal magnetopotential matrix and its corresponding equivalent current density are solved again. The above steps are repeated until the current density iterative convergence is achieved. Finally, the converged current density is used to solve for the magnetic field distribution in the target subdomain.

[0303] As shown in Figure 4, this invention utilizes an equivalent magnetic circuit model to accurately calculate the magnetic voltage drop in the stator teeth, slots, and yoke. The magnetic reluctance in this magnetic circuit model depends on the stator's geometry and the material's permeability, which needs to be determined through an iterative process combined with the material's BH curve.

[0304] Magnetic flux source entering the magnetic circuit , , and It is obtained by integrating the air gap, slot opening, and magnetic flux density in the slot as predicted by the subdomain method, as shown in the following formula:

[0305] (1.189)

[0306] (1.190)

[0307] (1.191)

[0308] (1.192)

[0309] (1.193)

[0310] (1.194)

[0311] (1.195)

[0312] (1.196)

[0313] in, , It's the number of slots. It is the axial length of the motor armature.

[0314] After identifying all magnetic flux sources, the nodal equations of the magnetic circuit can be established based on Kirchhoff's magnetohydrodynamic law to solve for the magnetopotential distribution at each node, thereby obtaining the magnetic field strength of each branch. Based on the magnetic field strength and the BH characteristic curve of the stator material, the permeability of the corresponding branch can be determined. Subsequently, the permeability of each part is calculated based on the permeability and geometric parameters. The above process can ultimately be expressed as the following matrix equation, used to solve for the nodal magnetopotential of the system, i.e. :

[0315] (1.197)

[0316] in, It is a correlation matrix. It is the magnetic permeability matrix of the magnetic circuit. It is the nodal magnetic potential matrix. It includes , , and The magnetic flux source matrix.

[0317] After obtaining the magnetopotential matrix that converges through iteration, the current plate and the magnetopotential of each node are shown in Figure 5. The current density on the corresponding equivalent current plate can be obtained based on the magnetic voltage drop of each part:

[0318] (1.198)

[0319] (1.199)

[0320] (1.200)

[0321] (1.201)

[0322] (1.202)

[0323] By solving Equation 1.188 using the current density on the equivalent current plate, we can obtain the various unknowns, the magnetic field distribution in the target subdomain, and then the performance parameters of the motor, including flux linkage, back electromotive force, and cogging torque, etc.

[0324] When a slot contains two coil sides and the windings are not overlapping, their flux linkages are as follows:

[0325] (1.203)

[0326] (1.204)

[0327] in:

[0328] (1.205)

[0329] (1.206)

[0330] in, It is the number of turns in each coil. It is the area of ​​the edge of a coil. It is the width of the coil edge. It is the axial length.

[0331] The solution for the back electromotive force is as follows:

[0332] (1.207)

[0333] in, Let be the magnetic flux linkage of a certain phase.

[0334] The algorithm for cogging torque is Maxwell's tensor method, that is:

[0335] (1.208)

[0336] As shown in Figures 6 to 10, by comparing the motor performance parameters predicted by the subdomain method, linear finite element method and nonlinear finite element method of the prior art, it can be seen that by using the above methods, the present invention can accurately capture local magnetic flux distortion and disturbance, dynamically correct the magnetic field changes caused by saturation, and obtain more accurate electromagnetic performance parameters.

[0337] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A solution method for the electromagnetic design of a surface-mounted permanent magnet motor with toothed slots, characterized in that: The process includes the following steps: Step 1: Simulate the nonlinear environment of the motor stator material by embedding equivalent current plates to construct an equivalent linear motor model; Step 2: Divide the linear motor model into a permanent magnet subdomain, an air gap subdomain, a slot subdomain, and a slot opening subdomain, and establish the governing equations and general solution expressions for each subdomain with vector magnetic potential as the variable. The general solution expressions include undetermined coefficients determined by boundary conditions. The boundary conditions of the slot subdomain and the slot opening subdomain are related to the current density of the equivalent current plates; Step 3: Based on the physical condition that the tangential magnetic field strength and radial magnetic flux density are continuous at the interface of adjacent subdomains, construct a set of coupled equations and integrate the set of coupled equations into a unified multidimensional matrix equation about the undetermined coefficients; Step 4: Iteratively solve the equations using a composite algorithm based on the subdomain method and the magnetic circuit method; Step 5: Calculate the performance parameters of the permanent magnet motor based on the magnetic field distribution obtained from the above iterative solution.

2. The solution method for electromagnetic design of surface-mounted permanent magnet motors with toothed cogging as described in claim 1, characterized in that: In step 1, the equivalent current sheet is specifically embedded in: the two sidewall surfaces of each slot, the bottom surface of each slot, and the two sidewall surfaces of each slot opening.

3. The solution method for electromagnetic design of surface-mounted permanent magnet motors with toothed cogging as described in claim 1, characterized in that: In step 2, the governing equations for the slot opening subdomain, the air gap subdomain, and the slot domain are the Laplace equation, and the governing equation for the permanent magnet subdomain is the Poisson equation.

4. The solution method for electromagnetic design of surface-mounted permanent magnet motors with toothed grooves as described in claim 1, characterized in that: In step 3, when constructing the unified multidimensional matrix equation, the field quantities on the interface between the slot opening subdomain and the air gap subdomain, and the interface between the slot opening subdomain and the slot domain, are expanded into Fourier series for processing.

5. The solution method for electromagnetic design of surface-mounted permanent magnet motors with toothed cogging as described in claim 1, characterized in that: The specific steps of the iterative solution in step 4 are as follows: Step 4.1: Set the initial value of the current density of each equivalent current plate; Step 4.2: Substitute the current equivalent current density as the boundary condition into the unified multidimensional matrix equation for solution to obtain the magnetic field distribution under the current iteration; Step 4.3: Based on the magnetic field distribution obtained above, calculate the magnetic flux entering each part of the stator core, construct the equivalent magnetic circuit model of the stator core, solve the magnetic circuit model to obtain the magnetic voltage drop of each part of the stator, and update the current density value of each equivalent current plate according to the magnetic voltage drop and the nonlinear BH curve of the stator material; Step 4.4: Determine whether the difference between the equivalent current density before and after the update meets the preset convergence tolerance. If it does not meet the tolerance, return to step 4.2 with the updated equivalent current density for the next iteration. If it meets the tolerance, proceed to step 5.

6. The solution method for electromagnetic design of surface-mounted permanent magnet motors with toothed cogging, as described in claim 5, is characterized in that: In step 4.3, constructing the equivalent magnetic circuit model of the stator core specifically involves: constructing a magnetic circuit network based on the stator geometry; calculating the magnetic flux sources injected into each node of the magnetic circuit network by integrating the magnetic flux density of the air gap, slot opening, and slot based on the magnetic field distribution obtained in step 4.2; establishing the node equations of the magnetic circuit network according to Kirchhoff's magnetohydrodynamic law; and solving the equations in matrix form.

7. The solution method for electromagnetic design of surface-mounted permanent magnet motors with toothed cogging as described in claim 6, characterized in that: In step 4.3, the current density values ​​of each equivalent current plate are updated based on the magnetic field strength of the corresponding iron core path obtained from the magnetic circuit model.

8. The solution method for electromagnetic design of surface-mounted permanent magnet motors with toothed cogging as described in claim 7, characterized in that: The value of the magnetic field strength is determined by the magnetic voltage drop of the core path and its length, and is related to the nonlinear BH curve.

9. The solution method for electromagnetic design of surface-mounted permanent magnet motors with toothed cogging as described in claim 1, characterized in that: In step 5, the performance parameters of the permanent magnet motor are calculated, including flux linkage, back electromotive force and cogging torque. The cogging torque is calculated using Maxwell's stress tensor method, selecting an integral loop in the air gap subdomain, and using the finally obtained radial and tangential magnetic flux density for calculation.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the solution method for electromagnetic design of a surface-mount permanent magnet motor with tooth grooves as described in any one of claims 1 to 9.

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