A method for calculating magnetic flux distribution of tangential four-layer winding fractional slot permanent magnet motor

Abstract

The present invention discloses a method for calculating the magnetic flux distribution of a tangential four-layer winding fractional slot permanent magnet motor, including: equivalent each magnetic isolation bridge of the permanent magnet motor with a rectangular equivalent air gap; estimating the saturation degree of the iron core at the magnetic isolation bridge; calculating the initial value of the equivalent air gap length; dividing the motor area into five subdomains; establishing the vector magnetic potential equation in each subdomain and the boundary conditions on the interface; obtaining the magnetic flux expression of the permanent magnet motor and the error of the relative magnetic permeability by solving the unknown coefficients in the vector magnetic potential equation; iteratively calculating by updating the relative magnetic permeability of the iron core at the magnetic isolation bridge until the relative magnetic permeability error value obtained is less than the limit value, thereby obtaining the final magnetic flux result of the permanent magnet motor. The method of the present invention can accurately calculate the magnetic flux size of the permanent magnet motor considering the saturation of the iron core, and provides an efficient and accurate research method for the magnetic field calculation and performance analysis of the tangential four-layer winding fractional slot permanent magnet motor.

Description

Technical Field

[0001] The invention belongs to the technical field of permanent magnet motors, and in particular relates to a method for calculating magnetic flux density distribution of a tangential four-layer winding fractional-slot permanent magnet motor. Background Art

[0002] Electromagnetic field calculation is one of the important steps in motor design, and it is also the basis and premise for calculating and analyzing motor performance. Commonly used calculation methods include equivalent magnetic circuit method, finite element method and analytical method. Among them, the analytical method can obtain an intuitive relationship expression between motor performance and design parameters by solving the Laplace / Poisson equation of the magnetic potential in the motor. It is a fast and effective electromagnetic field calculation method, and has unique advantages in motor optimization design and parameter analysis. However, the premise of analytical modeling is the need for accurate mathematical description of the boundaries of each structure, which is difficult to achieve for motors with slightly complex structures. In addition, this method often assumes the magnetic permeability of the core to be infinite to simplify the problem analysis, so it is difficult to consider the problem of core saturation.

[0003] The tangential permanent magnet motor is a built-in motor whose rotor has good magnetic concentration performance and can provide large electromagnetic torque, so it has been widely used in the industrial field. However, the rotor structure of this motor is complex, mathematical modeling is relatively difficult, and there is leakage magnetic field and core saturation at the rotor magnetic isolation bridge. If the core saturation is not considered, it will lead to large errors in the subsequent magnetic field calculation. Therefore, in order to obtain the analytical expression of the magnetic field of the tangential four-layer winding permanent magnet motor, the core saturation problem at the magnetic isolation bridge must be solved. Summary of the invention

[0004] Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention provides a method for calculating the magnetic flux distribution of a tangential four-layer winding fractional-slot permanent magnet motor. In the method provided by the present invention, a research method is provided for the core saturation problem of the tangential structure permanent magnet motor through the equivalent air gap method, so as to facilitate more accurate mathematical modeling of the motor. The magnetic field calculation results obtained by this method can be further used to calculate other electromagnetic properties of the motor, providing a convenient and fast research means for the permanent magnet motor pole optimization design and motor performance analysis.

[0005] Technical solution: In the first aspect, the present invention provides a method for calculating the magnetic flux distribution of a tangential four-layer winding fractional slot permanent magnet motor, comprising the following steps:

[0006] Each magnetic isolation bridge in the permanent magnet motor rotor is treated equivalently using a rectangular air gap to obtain the actual width of a single magnetic isolation bridge.

[0007] The saturation degree of the core at the magnetic isolation bridge is estimated based on the actual width of a single magnetic isolation bridge, thereby obtaining the relative magnetic permeability value μ of the magnetic isolation bridge. r1 ;

[0008] The magnetic permeability value μ r1 As the initial value of the relative magnetic permeability of the core at the magnetic isolation bridge, μ r1 ;

[0009] According to the initial value μ of the relative magnetic permeability of the core at the magnetic isolation bridge r1 Calculate the corresponding equivalent rectangular air gap length l a1 ;

[0010] Based on the equivalent rectangular air gap length l a1 The motor magnetic field region is obtained and divided into five sub-domains; vector magnetic potential equations of the five sub-domains are established in the coordinate system of the motor magnetic field region;

[0011] According to Maxwell's theory, the magnetic field characteristics of the interfaces of each subdomain are established respectively, and the boundary conditions on the interfaces between the subdomains are obtained;

[0012] Substitute the vector magnetic potential equation of each subdomain into the boundary conditions, solve the unknown coefficients in the vector magnetic potential equation, obtain the vector magnetic potential of each subregion of the permanent magnet motor, and derive the magnetic flux density expression of each subdomain through the vector magnetic potential;

[0013] According to the magnetic density expression of each sub-domain, the relative magnetic permeability of the core at the magnetic isolation bridge in each sub-domain in this period is calculated. r1 ', and calculate the relative permeability error Δμ of this cycle r1 ;

[0014] Error Δμ based on the preset relative permeability s Judge and select to output the calculated value μ of relative permeability of each sub-domain rz ';

[0015] The relative permeability calculated value μ of each sub-domain is output rz 'The input motor magnetic field model finally analyzes the magnetic flux density distribution in each subdomain of the motor.

[0016] In a further embodiment, each magnetic isolation bridge is subjected to equivalent processing to obtain the width of an equivalent rectangular air gap; the width of a single equivalent rectangular air gap is equal to the actual width of a single magnetic isolation bridge;

[0017] Then the equivalent air gap length l a1 The calculation formula is:

[0018] l a1 = l b / μ r1 (1)

[0019] In the formula, l b is the actual length of the magnetic isolation bridge, l azCalculated value for the equivalent air gap length.

[0020] In a further embodiment, the five types of sub-domains include: an equivalent air gap sub-domain, a permanent magnet sub-domain, an actual air gap sub-domain, a stator slot sub-domain, and a stator slot body sub-domain.

[0021] In a further embodiment, the equivalent air gap subdomain is set to region 1j and region 3j, the permanent magnet subdomain is set to region 2j, the actual air gap subdomain is set to region 4, the stator slot subdomain is set to region 5i, and the stator slot body subdomain is set to region 6i;

[0022] In a further embodiment, the calculation formula of the vector magnetic potential in the equivalent air gap region 1j is:

[0023]

[0024] In the formula, A z1 is the vector magnetic potential equation in the equivalent air gap region 1j, L p is the intermediate variable, PP is the number of motor poles;

[0025] Among them, L p is an intermediate variable, and the calculation formula is:

[0026]

[0027] The calculation formula of the vector magnetic potential in the permanent magnet region 2j is:

[0028]

[0029] In the formula, A z2 is the vector magnetic potential equation in the permanent magnet region 2j, U v is an intermediate variable;

[0030] U v The calculation formula is:

[0031]

[0032] The calculation formula of the vector magnetic potential in the equivalent air gap area 3j is:

[0033]

[0034] In the formula, A z3 is the vector magnetic potential equation in the equivalent air gap region 3j, Y q is an intermediate variable;

[0035] Y q The calculation formula is:

[0036]

[0037] The calculation formula of the vector magnetic potential in the air gap region 4 is:

[0038]

[0039] In the formula, A z4 is the vector magnetic potential equation in the air gap region 4;

[0040] The calculation formula of the vector magnetic potential in the stator slot area 5i is:

[0041]

[0042] In the formula, A z5i is the vector magnetic potential equation in the stator slot area 5i, F m is the intermediate variable, QQ is the number of motor slots;

[0043] F m The calculation formula is:

[0044]

[0045] The calculation formula of the vector magnetic potential in the stator slot area 6i is:

[0046]

[0047] In the formula, A z6i is the vector magnetic potential equation in the stator slot area 6i, E n is an intermediate variable;

[0048] E n The calculation formula is:

[0049]

[0050] In formulas (1)-(12), an arbitrary point in the motor is preset, r is the radius from the point to the center of the motor in the polar coordinate system, α is the mechanical position angle of the point, and A z is the axial component of the vector magnetic potential at this point, A z The corresponding subscripts 1j, 2j, 3j, 4, 5i and 6i are the regions to which the point belongs; p, v, q, k, m, n are the corresponding harmonic orders, P, V, Q, K, M, N are the maximum harmonic orders obtained in the calculation process of p, v, q, k, m, n, respectively, C 1j , D 1j , C 2j , D 2j , C 3j , D 3j , A4, B4, C4, D4, C 5i , D 5i , C 6i , D 6iis the unknown coefficient, β e1 is the central angle corresponding to the equivalent air gap width of the magnetic bridge at the bottom of the j-th magnetic pole, β j is the jth magnetic pole center position, β pm is the central angle corresponding to the pole width, β e2 is the central angle corresponding to the equivalent air gap width of the magnetic bridge at the top of the magnetic pole, β e1 , β j , β pm , β e2 All are in radians; α bo is the central angle corresponding to the slot width, α i is the center position of the i-th slot, α bs is the central angle corresponding to the slot width, α bo , α i , α bs All are in radians. p is the outer radius of the rotor core, R pmb The outer radius of the magnetic bridge at the bottom of the magnetic pole, R pmt Permanent magnet outer radius, R q The outer radius of the magnetic bridge at the top of the magnetic pole, R s is the inner radius of the stator core, R t R is the inner radius of the groove body sb is the inner and outer radius of the groove body.

[0051] In a further embodiment, the boundary conditions on the interface between the sub-regions include:

[0052] The interface between the rotor core and the shaft must satisfy the formula:

[0053]

[0054] The interface between the equivalent air gap area 1j and the permanent magnet area 2j must satisfy the formula:

[0055]

[0056]

[0057] The interface between the permanent magnet region 2j and the equivalent air gap region 3j must satisfy the formula:

[0058]

[0059]

[0060] The interface between the equivalent air gap area 3j and the actual air gap area 4 must satisfy the formula:

[0061]

[0062]

[0063] The actual air gap area 4 and the stator slot area 5i interface must satisfy the formula:

[0064]

[0065]

[0066] The interface between the stator slot area 5i and the stator slot body area 6i must satisfy the formula:

[0067]

[0068]

[0069] In formulas (13)-(23), B r is the radial component of magnetic density B in polar coordinate system, B α is the tangential component of the magnetic density B in the polar coordinate system. The subscripts 1j, 2j, 3j, 4, 5i and 6i corresponding to B respectively indicate the region to which the variable belongs.

[0070] In a further embodiment, the method of obtaining the vector magnetic potential comprises:

[0071] The vector magnetic potential equations of each subdomain are substituted into the boundary conditions to solve the unknown coefficients C 1j , D 1j , C 2j , D 2j , C 3j , D 3j , A4, B4, C4, D4, C 5i , D 5i , C 6i , D 6i , and the vector magnetic potential of each subdomain is obtained in turn according to the solved vector magnetic potential equation.

[0072] In a further embodiment, the derivation of the magnetic density expression of each sub-domain by the vector magnetic potential includes: parsing the axial component A of the vector magnetic potential from the vector magnetic potential of each sub-domain z The calculation formula is: according to the axial component A of the vector magnetic potential of each subdomain z The calculation formula is used to calculate the radial component B of the magnetic flux density in each sub-domain of the motor again. r and the tangential component B α , and then the magnetic density expression of each subdomain is obtained, which is as follows:

[0073]

[0074]

[0075] In a further embodiment, the relative magnetic permeability calculated value μ of the core at the magnetic isolation bridge can be obtained by calculation according to the magnetic density expression: r1 ', and calculate the error Δμ of the relative permeability in this iteration r1 , the process is as follows:

[0076] According to the radial component B of the magnetic flux density r and the tangential component B α The magnetic flux amplitude B at the equivalent air gap of the permanent magnet motor is obtained, and its expression is:

[0077]

[0078] Then, according to the magnetization characteristic BH curve of the core material, the corresponding magnetic induction intensity H is found, and the relative magnetic permeability μ of the core at the magnetic isolation bridge is calculated according to the B and H values ​​at this time. r1 ';

[0079] Among them, the calculated value of the relative magnetic permeability of the core at the magnetic isolation bridge is μ r1 'The calculation formula is as follows:

[0080] μ r1 ′=B / H (27)

[0081] Enter the calculated value of the relative magnetic permeability of the core at the magnetic isolation bridge μ r1 ', derive the error Δμ of relative permeability r1 ;

[0082] Relative permeability error Δμ r1 The calculation formula is as follows:

[0083] Δμ r1 =μ r1 '-μ r1 (28).

[0084] In a further embodiment,

[0085] Error Δμ based on the preset relative permeability s , select to output the calculated value μ of relative permeability of each subdomain rz 'The process is as follows:

[0086] If the relative permeability error Δμ r1 Less than the set value Δμ s , output the calculated value μ of the relative permeability of each subdomain r1 ';

[0087] If the relative permeability error Δμ r1 Greater than the set value Δμ s , then the initial value μ of the relative magnetic permeability of the core at the magnetic isolation bridge in the next iteration is revisedr2 .

[0088] In a further embodiment, the initial value μ of the relative magnetic permeability of the core at the magnetic isolation bridge in the next iteration is revised. r2 The methods include:

[0089] Set the initial value of relative permeability μ r2 Recalculate the corresponding equivalent rectangular air gap length l a2 , according to the equivalent rectangular air gap length l a2 The vector magnetic potential equations of the five subdomains are updated respectively, and the updated vector magnetic potential equations are substituted into the boundary conditions to solve the unknown coefficients in the vector magnetic potential equations again, and the updated vector magnetic potential of each subdomain is obtained in turn according to the solved vector magnetic potential equations;

[0090] According to the vector magnetic potential of each subdomain, the magnetic density expression of each subdomain derived in the previous period is updated, and the calculated value μ of the relative magnetic permeability of each subdomain is re-output according to the updated magnetic density expression r2 ' and the error of relative permeability Δμ r2 ;

[0091] Again, the relative permeability error Δμ of the output r2 The error Δμ from the preset relative permeability s In contrast, if the relative permeability error Δμ r2 Greater than the set value Δμ s ;

[0092] Then the initial value of relative permeability is revised repeatedly until the relative permeability error value Δμ obtained by the zth iteration is rz Less than the set value Δμ s When the relative permeability calculated value μ of each sub-domain is output rz ';

[0093] Among them, the calculation formula for the initial value of the relative magnetic permeability of the core at the magnetic isolation bridge of the zth iteration is:

[0094] μ rz =(μ rz-1 +μ rz-1 ') / 2

[0095] In the formula, μ rz is the initial value of the relative permeability in the zth iteration.

[0096] Repeat the above steps until Δμ is calculated after the zth iteration. rz ≤Δμ s , then the vector magnetic potential equation obtained in this calculation is the final magnetic field calculation result of the motor, and the magnetic flux density distribution in each subdomain of the motor can be calculated based on the magnetic flux density expression.

[0097] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0098] (1) The equivalent air gap method provides a research method for the core saturation problem of tangential permanent magnet motors, which facilitates more accurate mathematical modeling of the motor and provides an effective analytical calculation method for motor researchers to calculate and analyze the magnetic field of tangential four-layer winding fractional slot permanent magnet motors considering the core saturation problem.

[0099] (2) By analyzing and calculating the magnetic field of the unit motor, the magnetic field characteristics of the entire motor can be further obtained.

[0100] (3) The magnetic field calculation results obtained by this method can be further used to calculate other electromagnetic properties of the motor, providing a convenient and fast research method for the optimization design of permanent magnet motor poles and motor performance analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 Schematic diagram of subdomain division of 1 / 2 tangential four-layer winding fractional-slot permanent magnet motor.

[0102] Figure 2 It is a flowchart of the specific steps of the subdomain analytical modeling method in the present invention.

[0103] Figure 3 This is the schematic diagram of the equivalent air gap method considering the saturation of the magnetic isolation bridge core.

[0104] Figure 4 Schematic diagram of the BH curve of the magnetization characteristics of a core material. DETAILED DESCRIPTION

[0105] In order to more fully understand the technical content of the present invention, the technical solution of the present invention is further introduced and illustrated in conjunction with specific embodiments below, but is not limited thereto.

[0106] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. Although the described embodiment is only for a tangential four-layer winding fractional slot permanent magnet motor with a pole slot match, the present invention can also be applied to other four-layer winding structure permanent magnet motors with a pole slot match.

[0107] Example 1

[0108] The steps include:

[0109] Step (1), treating each magnetic isolation bridge in the permanent magnet motor rotor with a rectangular equivalent air gap, wherein the width of the equivalent air gap is the same as the actual width of the magnetic isolation bridge;

[0110] Step (2), estimate the saturation degree of the core at the magnetic isolation bridge according to the actual width of a single magnetic isolation bridge, assuming that the relative magnetic permeability of the magnetic isolation bridge is μ r0 , which is the initial value of relative permeability in the first iteration calculation in step 3, namely μ r1 =μ r0 ;

[0111] Step (3), according to the initial value μ of the relative magnetic permeability of the core at the magnetic isolation bridge r1 Calculate the corresponding equivalent rectangular air gap length l a1 ;

[0112] Step (4), based on the equivalent rectangular air gap length l a1 The motor magnetic field area is obtained and divided into five sub-areas: equivalent air gap sub-area (area 1j and area 3j), permanent magnet sub-area (area 2j), actual air gap sub-area (area 4), stator slot sub-area (area 5i), and stator slot body sub-area (area 6i);

[0113] Step (5), respectively establishing vector magnetic potential equations of five sub-domains in the coordinate system of the motor magnetic field region;

[0114] Step (6), establishing the magnetic field characteristics of the interfaces of each subdomain respectively according to Maxwell theory, and obtaining the boundary conditions on the interfaces between the subdomains;

[0115] Step (7), substituting the vector magnetic potential equation of each subdomain into the boundary conditions, solving the unknown coefficients in the vector magnetic potential equation, obtaining the vector magnetic potential of each subregion of the permanent magnet motor, and deriving the magnetic flux density expression of each subdomain through the vector magnetic potential;

[0116] Step (8): According to the magnetic flux density expression, the relative magnetic permeability calculated value μ of the core at the magnetic isolation bridge can be obtained by calculation. r1 ', and calculate the error Δμ of the relative permeability in this iteration r1 ;

[0117] Step (9), if the relative permeability error Δμ r1 Greater than the set value Δμ s , then the initial value μ of the relative permeability at the magnetic isolation bridge in the next iteration is revised r2 ;

[0118] Step (9.1), the corrected initial value of relative permeability μ r2 Substitute into step (3) and repeat the solution process of steps (3) to (9) until the relative permeability error value μ obtained by the zth iteration is rz ' is less than the limit value Δμ s , step (10), at this time, the relative permeability calculated value μ of each sub-domain rz'The input motor magnetic field model finally analyzes the magnetic flux distribution in each subdomain of the motor, and the obtained motor magnetic flux is the final permanent magnet motor magnetic flux result.

[0119] Figure 1 It is a 10-pole 12-slot tangential four-layer winding fractional slot permanent magnet motor. The basic parameters of the motor are shown in Table 1. Taking this motor as an example, according to Figure 2 The basic flow chart shown adopts the method of the present invention to solve and calculate the armature reaction field distribution and permanent magnet eddy current loss of the tangential four-layer winding fractional slot permanent magnet motor.

[0120] Table 1 Basic parameters of permanent magnet motor

[0121]

[0122]

[0123] Each magnetic isolation bridge in the permanent magnet motor rotor is equivalent to a rectangular equivalent air gap. The equivalent schematic diagram is shown in the figure. Figure 3 As shown, in this example, the actual width of the rotor core magnetic isolation bridge in step (3) is l b =2mm, assuming that the initial value of the relative magnetic permeability of the magnetic isolation bridge is μ r1 = 10, then the length of the equivalent air gap in the first iteration is l a1 for

[0124] l a1 = l b / μ r1 =2 / 10=0.2mm (1)

[0125] like Figure 1 As shown, in step (5), the motor area is divided into five sub-areas, namely, equivalent air gap area 1j and area 3j, permanent magnet area 2j, actual air gap area 4, stator slot area 5i, and stator slot body area 6i. In this example, the number of permanent magnet poles PP=10, the number of motor slots QQ=12, j=1,2,3,...,10, i=1,2,3,...,12.

[0126] In the polar coordinate system, the Laplace / Poisson equation of the vector magnetic potential equation in each subdomain of the unit motor is established; in this example, K=100, P=20, V=20, Q=20, M=15, and N=15 are taken.

[0127] The vector magnetic potential equations of each subdomain are:

[0128] (1) The vector magnetic potential A in the equivalent air gap region 1j z1 The equation is

[0129]

[0130] Among them, L p is the intermediate variable, and the calculation formula is

[0131]

[0132] (2) Vector magnetic potential A in permanent magnet region 2j z2 The equation is

[0133]

[0134] Among them, U v is the intermediate variable, and the calculation formula is

[0135]

[0136] (3) The vector magnetic potential A in the equivalent air gap region 3j z3 The equation is

[0137]

[0138] Among them, Y q is the intermediate variable, and the calculation formula is

[0139]

[0140] (4) Vector magnetic potential A in air gap region 4 z4 The equation is

[0141]

[0142] (5) The vector magnetic potential A in the stator slot area 5i z5i The equation is

[0143]

[0144] Among them, F m is the intermediate variable, and the calculation formula is

[0145]

[0146] (6) Vector magnetic potential A in stator slot area 6i z6i The equation is

[0147]

[0148] Among them, E n is an intermediate variable, specifically

[0149]

[0150] In the formula, for any point in the motor, in the polar coordinate system, r represents the radius from the point to the center of the motor, α represents the mechanical position angle of the point, and A z is the vector magnetic potential at the point, and its subscripts 1j, 2j, 3j, 4, 5i and 6i distinguish the area at the point; p, v, q, k, m, n are the corresponding harmonic orders, and P, V, Q, K, M, N are the maximum harmonic orders obtained in the calculation process of p, v, q, k, m, n respectively; C 1j , D 1j , C 2j , D 2j , C 3j , D 3j , A4, B4, C4, D4, C 5i , D 5i , C 6i and D 6i is the unknown coefficient; β e1 is the central angle corresponding to the equivalent air gap width of the magnetic bridge at the bottom of the j-th magnetic pole, β j is the jth magnetic pole center position, β e2 is the central angle corresponding to the equivalent air gap width of the magnetic bridge at the top of the magnetic pole, β e1 , β j , β pm , β e2 All are in radians; α bo is the central angle corresponding to the slot width, α i is the center position of the i-th slot, α bs is the central angle corresponding to the slot width, α bo , α i , α bs All are in radians. p , R pmb , R pmt , R q , R s are the outer radius of the rotor core, the outer radius of the magnetic pole bottom isolation bridge, the outer radius of the permanent magnet, the outer radius of the magnetic pole top isolation bridge and the inner radius of the stator core; μ0 is the vacuum permeability; R t , R sb They are the inner radius and outer radius of the groove body respectively.

[0151] In order to solve the unknown coefficients in equations (2) to (12), the following boundary conditions are established in step (6) according to the magnetic field characteristics of the interfaces of each region:

[0152] (1) The interface between the rotor core and the shaft must satisfy the following formula:

[0153]

[0154] (2) The interface between the equivalent air gap area 1j and the permanent magnet area 2j must satisfy the formula:

[0155]

[0156]

[0157] (3) The interface between the permanent magnet region 2j and the equivalent air gap region 3j must satisfy the following formula:

[0158]

[0159]

[0160] (4) The interface between the equivalent air gap area 3j and the actual air gap area 4 must satisfy the formula:

[0161]

[0162]

[0163] (5) The interface between the actual air gap area 4 and the stator slot area 5i must satisfy the formula:

[0164]

[0165]

[0166] (6) The interface between the stator slot area 5i and the stator slot body area 6i must satisfy the formula:

[0167]

[0168]

[0169] In the formula, B r is the radial component of magnetic density B in polar coordinate system, B α is the tangential component of the magnetic density B in the polar coordinate system. The subscripts 1j, 2j, 3j, 4, 5i and 6i corresponding to B respectively indicate the region to which the variable belongs.

[0170] In step (7), the vector magnetic potential equations of each sub-domain are transformed and substituted into the boundary conditions on the interface between each sub-domain to solve the unknown coefficient C 1j , D 1j , C 2j , D 2j , C 3j , D 3j , A4, B4, C4, D4, C 5i , D 5i , C 6i , D 6i, and the vector magnetic potential of each subdomain is obtained in turn according to the solved vector magnetic potential equation.

[0171] The axial component A of the vector magnetic potential is obtained by analyzing the vector magnetic potential of each subdomain. z The calculation formula of

[0172] According to the axial component A of the vector magnetic potential z The calculation formula is used to calculate the radial component B of the magnetic flux density in each sub-domain of the motor again. r and the tangential component B α , and then the magnetic density expression is obtained, the magnetic density expression formula is as follows:

[0173]

[0174]

[0175] In step (8), the relative magnetic permeability of the core at the magnetic isolation bridge can be calculated based on the magnetic density expression: r1 ', and calculate the error Δμ of the relative permeability in this iteration rz The process is as follows:

[0176] According to the radial component B of the magnetic flux density r and the tangential component B α The magnetic flux amplitude B at the equivalent air gap of the permanent magnet motor is obtained, and its expression is:

[0177]

[0178] According to the permanent magnet motor magnetic flux expression obtained in step (7), the magnetic flux amplitude B at the equivalent air gap is calculated, and then the corresponding magnetic induction intensity H is found according to the magnetization characteristic BH curve of the core material; and the relative magnetic permeability μ of the core at the magnetic isolation bridge is calculated according to the B and H values ​​at this time. rz ';

[0179] Among them, μ r1 'The calculation formula is as follows:

[0180] μ r1 ′=B / H (27)

[0181] Input relative magnetic permeability μ r1 ', derive the error Δμ of relative permeability r1 ;

[0182] Relative permeability error Δμ r1 The calculation formula is as follows:

[0183] Δμ r1 =μ r1 '-μ r1 (28)

[0184] The formula for calculating the initial value of the z iteration in step (9.1) is:

[0185] μ rz =(μ rz-1 +μ rz-1 ') / 2 (29)

[0186] In the formula, μ rz is the initial value of the relative permeability in the zth iteration.

[0187] Repeat the above steps until Δμ is calculated after the zth iteration. rz ≤Δμ s , then the vector magnetic potential equation obtained in this calculation is the final magnetic field calculation result of the motor, and the magnetic flux density distribution in each subdomain of the motor can be calculated based on the magnetic flux density expression.

[0188] The present invention provides a research method for the core saturation problem of tangential structure permanent magnet motor through the equivalent air gap method, so as to facilitate more accurate mathematical modeling of the motor, and provides an effective analytical calculation method for motor researchers to calculate and analyze the magnetic field of tangential four-layer winding fractional slot permanent magnet motor considering the core saturation problem; secondly, by analyzing and calculating the magnetic field of the unit motor, the magnetic field characteristics of the entire motor can be further obtained; finally, the magnetic field calculation results obtained by this method can be further used to calculate other electromagnetic properties of the motor, providing a convenient and fast research means for the permanent magnet motor pole optimization design and motor performance analysis.

[0189] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for calculating the magnetic flux distribution of a tangential four-layer winding fractional slot permanent magnet motor, characterized in that: The following steps are involved: Each magnetic isolation bridge in the permanent magnet motor rotor is treated equivalently using a rectangular air gap to obtain the actual width of a single magnetic isolation bridge. The saturation degree of the core at the magnetic isolation bridge is estimated based on the actual width of a single magnetic isolation bridge, thereby obtaining the relative magnetic permeability value of the magnetic isolation bridge. ; The magnetic permeability value As the initial value of the relative magnetic permeability of the core at the magnetic isolation bridge ; According to the initial value of the relative magnetic permeability of the core at the magnetic isolation bridge Calculate the corresponding equivalent rectangular air gap length ; Based on the equivalent rectangular air gap length The motor magnetic field region is obtained and divided into five sub-domains; vector magnetic potential equations of the five sub-domains are established in the coordinate system of the motor magnetic field region; According to Maxwell's theory, the magnetic field characteristics of the interfaces of each subdomain are established respectively, and the boundary conditions on the interfaces between the subdomains are obtained; Substitute the vector magnetic potential equation of each subdomain into the boundary conditions, solve the unknown coefficients in the vector magnetic potential equation, obtain the vector magnetic potential of each subregion of the permanent magnet motor, and derive the magnetic flux density expression of each subdomain through the vector magnetic potential; According to the magnetic density expression of each sub-domain, the relative magnetic permeability of the core at the magnetic isolation bridge in each sub-domain in this period is calculated. , and calculate the error of relative permeability in this cycle ; Error based on preset relative permeability Judge and select to output the calculated value of relative permeability of each sub-domain ; The calculated relative permeability values ​​of each subdomain will be output The input motor magnetic field model finally analyzes the magnetic flux density distribution in each subdomain of the motor; The five sub-domains include: an equivalent air gap sub-domain, a permanent magnet sub-domain, an actual air gap sub-domain, a stator slot sub-domain, and a stator slot body sub-domain; The equivalent air gap subdomain is set to the region and Region , the permanent magnet subdomain is set to the region , the actual air gap subdomain is set to region 4, and the stator slot subdomain is set to region , the stator slot body subdomain is set as region ; The equivalent air gap area The calculation formula of the vector magnetic potential inside is: The vector magnetic potential A in the equivalent air gap region 1j z1 The equation is: （1） Among them, L p is an intermediate variable, and the calculation formula is: （2） The vector magnetic potential A in the permanent magnet region 2j z2 The equation is: （3） Among them, U v is an intermediate variable, and the calculation formula is: （4） The vector magnetic potential A in the equivalent air gap region 3j z3 The equation is: （5） Among them, Y q is an intermediate variable, and the calculation formula is: （6） The vector magnetic potential A in the air gap region 4 z4 The equation is: （7） The vector magnetic potential A in the stator slot area 5i z5i The equation is: （8） Among them, F m is an intermediate variable, and the calculation formula is: （9） The vector magnetic potential A in the stator slot area 6i z6i The equation is: （10） Among them, E n is an intermediate variable, and the calculation formula is: （11） In formulas (1)-(12), any point in the motor is assumed to be is the radius from this point to the center of the motor in the polar coordinate system, is the mechanical position angle of the point, is the axial component of the vector magnetic potential at this point, The corresponding corner marks , , 、4、 as well as is the area to which the point belongs, is the number of motor poles, is the number of motor slots; p, , , , , is the corresponding harmonic order, , , , , , They are , , , , , The maximum harmonic order obtained during the calculation process, , , , , , , , , , , , , , is the coefficient to be determined, For the The central angle corresponding to the equivalent air gap width of the magnetic bridge at the bottom of the pole is: For the The magnetic pole center position, is the central angle corresponding to the magnetic pole width, is the central angle corresponding to the equivalent air gap width of the magnetic bridge at the top of the pole, , , , All are in radians; is the central angle corresponding to the slot width, For the The center position of the slot body, is the central angle corresponding to the slot width, , , All are in radians; is the outer radius of the rotor core, The outer radius of the magnetic bridge at the bottom of the magnetic pole, Permanent magnet outer radius, The outer radius of the magnetic bridge at the top of the magnetic pole, is the inner radius of the stator core, is the inner radius of the groove body, is the inner and outer radius of the groove body.

2. The method for calculating the magnetic flux distribution of a tangential four-layer winding fractional slot permanent magnet motor according to claim 1 is characterized in that: Each magnetic isolation bridge is processed equivalently to obtain the width of an equivalent rectangular air gap; the width of a single equivalent rectangular air gap is equal to the actual width of a single magnetic isolation bridge; Then the equivalent rectangular air gap length The calculation formula is: （12） In the formula, is the actual length of the magnetic isolation bridge, Calculate the value for the equivalent rectangular air gap length.

3. The method for calculating the magnetic flux distribution of a tangential four-layer winding fractional slot permanent magnet motor according to claim 1 is characterized in that: The boundary conditions on the interface between subdomains include the following: At the interface between the rotor core and the shaft: （13） At the interface between the equivalent air gap region 1j and the permanent magnet region 2j, the following conditions are satisfied: （14） （15） At the interface between the permanent magnet region 2j and the equivalent air gap region 3j, the following conditions are satisfied: （16） （17） At the interface between the equivalent air gap region 3j and the actual air gap region 4, the following is satisfied: （18） （19） At the interface between the actual air gap area 4 and the stator slot area 5i, the following conditions are satisfied: （20） （21） At the interface between the stator slot area 5i and the stator slot body area 6i, the following conditions are satisfied: （22） （23） In formulas (13)-(23), Magnetic density The radial component in polar coordinates is Magnetic density The tangential component in polar coordinates is The corresponding subscripts , , 、4、 as well as The region to which the variable belongs.

4. The method for calculating the magnetic flux distribution of a tangential four-layer winding fractional slot permanent magnet motor according to claim 3 is characterized in that: Methods for obtaining vector magnetic potential include: Substitute the vector magnetic potential equations of each subdomain into the boundary conditions and solve for the unknown coefficients , , , , , , , , , , , , , , and the vector magnetic potential of each subdomain is obtained in turn according to the solved vector magnetic potential equation.

5. The method for calculating the magnetic flux distribution of a tangential four-layer winding fractional slot permanent magnet motor according to claim 4, characterized in that: The method of deriving the magnetic density expression of each sub-domain by using the vector magnetic potential includes: analyzing the axial component of the vector magnetic potential from the vector magnetic potential of each sub-domain. The calculation formula is: according to the axial component of the vector magnetic potential of each subdomain The calculation formula is used to calculate the radial component B of the magnetic flux density in each sub-domain of the motor again. r and the tangential component B α , and then the magnetic density expression of each subdomain is obtained, which is as follows: （24） （25） In the formula, B r Represents the radial component of magnetic flux density in a certain area, B α Represents the tangential component of the magnetic density in a certain area.

6. The method for calculating the magnetic flux distribution of a tangential four-layer winding fractional slot permanent magnet motor according to claim 5, characterized in that: The relative magnetic permeability of the core at the magnetic isolation bridge is calculated based on the magnetic density expression. , and calculate the error of relative permeability in this cycle The process is as follows: According to the radial component B of the magnetic flux density r and the tangential component B α The magnetic flux amplitude B at the equivalent air gap of the permanent magnet motor is obtained, and its expression is: （26） Then, according to the BH curve of the magnetization characteristics of the core material, the corresponding magnetic induction intensity H is found, and the relative magnetic permeability of the core at the magnetic isolation bridge is calculated according to the B and H values ​​at this time. ; Among them, the calculated value of the relative magnetic permeability of the core at the magnetic isolation bridge is The calculation formula is as follows: （27） Calculated value of relative magnetic permeability of the core at the input magnetic isolation bridge , and thus derive the corresponding relative permeability error ; Error in relative permeability The calculation formula is as follows: （28）。 7. The method for calculating the magnetic flux distribution of a tangential four-layer winding fractional slot permanent magnet motor according to claim 1, characterized in that: Error based on preset relative permeability , select to output the calculated relative permeability of each subdomain The process is as follows: If the relative permeability error Less than the set value , output the calculated value of relative permeability of each subdomain ; If the relative permeability error Greater than the set value , then the initial value of the relative magnetic permeability of the core at the magnetic isolation bridge in the next iteration is revised .

8. The method for calculating the magnetic flux distribution of a tangential four-layer winding fractional slot permanent magnet motor according to claim 7, characterized in that: Re-determine the initial value of the relative magnetic permeability of the core at the magnetic isolation bridge for the next iteration The method includes: setting the initial value of relative magnetic permeability Recalculate the corresponding equivalent rectangular air gap length , according to the equivalent rectangular air gap length The vector magnetic potential equations of the five subdomains are updated respectively, and the updated vector magnetic potential equations are substituted into the boundary conditions to solve the unknown coefficients in the vector magnetic potential equations again, and the updated vector magnetic potential of each subdomain is obtained in turn according to the solved vector magnetic potential equations; Update the magnetic density expression of each subdomain derived in the previous period according to the vector magnetic potential of each subdomain, and re-output the calculated value of the relative magnetic permeability of each subdomain according to the updated magnetic density expression and the relative permeability error ; Again, the relative permeability error of the output Deviation from the preset relative permeability In contrast, if the relative permeability error Greater than the set value ; Then the initial value of relative permeability is revised repeatedly until the relative permeability error value obtained by the zth iteration is Less than the set value When , the calculated relative permeability of each subdomain is output ; Among them, the calculation formula for the initial value of the relative magnetic permeability of the core at the magnetic isolation bridge of the zth iteration is: In the formula, is the initial value of the relative permeability in the zth iteration.

Images