CN116191807A - Alternating pole magnetic flux reversing motor and analytic modeling method thereof - Google Patents

Alternating pole magnetic flux reversing motor and analytic modeling method thereof Download PDF

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CN116191807A
CN116191807A CN202310074742.8A CN202310074742A CN116191807A CN 116191807 A CN116191807 A CN 116191807A CN 202310074742 A CN202310074742 A CN 202310074742A CN 116191807 A CN116191807 A CN 116191807A
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倪有源
王佩
黄亚
曹帮恒
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Hefei University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K21/00—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets
    • H02K21/38—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with rotating flux distributors, and armatures and magnets both stationary
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    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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    • H02K1/16—Stator cores with slots for windings
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    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
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Abstract

The invention discloses an alternating pole magnetic flux reversing motor and an analytic modeling method thereof, wherein the motor comprises a rotor and a stator sleeved outside the rotor, the inner wall of the stator is provided with a plurality of stator teeth, stator slots are arranged between adjacent stator teeth, side magnetic poles are arranged in the anticlockwise and clockwise directions corresponding to the slots of each stator slot respectively, a central magnetic pole is arranged between two side magnetic poles of each stator tooth, the magnetization mode of the central magnetic pole is radial magnetization, and the side magnetic poles adopt a magnetization mode with a certain angle. The analytic method divides the motor into subfields, then solves a general solution expression of vector magnetic bits of each subfield, solves a direct current component and a harmonic component by utilizing boundary conditions of each subfield, and further obtains the motor air gap magnetic density and the electromagnetic torque. The average electromagnetic torque of the motor is obviously improved.

Description

Alternating pole magnetic flux reversing motor and analytic modeling method thereof
Technical Field
The invention relates to the field of motors, in particular to an alternating pole magnetic flux reversing motor and an analytic modeling method thereof.
Background
In recent years, a new type of permanent magnet brushless motor (i.e., stator-permanent magnet motor) has attracted great interest. The basic topological structure of the flux reversing permanent magnet motor is that two permanent magnets with opposite magnetizing directions are arranged on the surface of each stator tooth part facing to the air gap side, and the structure of the flux reversing permanent magnet motor is similar to that of a traditional rotor surface-mounted permanent magnet motor, and the permanent magnets are all arranged in the air gap. Compared with a rotor surface-mounted structure, the permanent magnet is arranged at the side of the stator, so that a complex process and measures are not needed to fix the permanent magnet, the effective length of an air gap of the motor can be obviously reduced, and the power density is improved. In order to reduce the cost and the use amount of the permanent magnets, the alternating-pole magnetic flux reversing motor is subjected to a plurality of researches, but the existing alternating-pole magnetic flux reversing motor still has the problem of non-ideal average electromagnetic torque. The invention changes the number and arrangement of the permanent magnets on the same stator tooth based on the research of the alternating pole magnetic flux reversing motor, thereby optimizing the performance of the motor.
Disclosure of Invention
The invention provides an alternating pole magnetic flux reversing motor and an analytic modeling method thereof, which are used for solving the problem of non-ideal average electromagnetic torque of the alternating pole magnetic flux reversing motor in the prior art.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
the alternating pole magnetic flux reversing motor comprises a rotor and a stator sleeved outside the rotor, wherein the inner wall of the stator is provided with a plurality of stator teeth distributed along the circumferential direction of the stator, stator grooves are formed between adjacent stator teeth in the circumferential direction, the notch of each stator groove is communicated with an air gap between the stator and the rotor, the side edge position of the stator tooth in the anticlockwise direction and the side edge position of the stator tooth in the clockwise direction corresponding to the notch of each stator groove are respectively provided with a side magnetic pole, and a central magnetic pole is arranged in the middle position between two side magnetic poles of each stator tooth; the magnetization mode of the central magnetic pole is radial magnetization, the magnetization angle of the side magnetic pole in the anticlockwise direction of the slot opening of each stator slot is an included angle between the magnetization direction of the side magnetic pole and the anticlockwise circumferential tangential direction, and the magnetization angle of the side magnetic pole in the clockwise direction of the slot opening of each stator slot is an included angle between the magnetization direction of the side magnetic pole and the clockwise circumferential tangential direction.
Further, the arrangement structure of the side magnetic poles and the stator slot openings is that the side magnetic poles in the anticlockwise and clockwise directions corresponding to each stator slot opening are symmetrical with respect to the geometric center of the stator slot opening.
Further, the side magnetic poles in the anticlockwise direction and the clockwise direction corresponding to the notch of each stator slot have symmetrical magnetization angles.
The analytical modeling method of the alternating pole magnetic flux reversing motor comprises the following steps:
step 1, dividing a motor solving domain into a stator slot subdomain, a side magnetic pole subdomain, a center magnetic pole subdomain, an air gap subdomain and a rotor slot subdomain by adopting an accurate subdomain model method;
step 2, obtaining a general solution expression of the vector magnetic potential A of each sub-field divided in the step 1 under the two-dimensional plane;
step 3, establishing a matrix equation to solve the direct current component and harmonic component coefficients in the general solution expression of the vector magnetic bit A of each subdomain obtained in the step 2 by utilizing boundary conditions among all subdomains;
and 4, obtaining the air gap density and the electromagnetic torque of the motor based on the direct current component and harmonic component coefficients of all the subfields obtained in the step 3.
In the division of all the subfields in the step 1, the stator slot subfields only comprise air areas between the outer radius of the magnetic poles and the inner radius of the stator slots, and the air areas between the inner radius of the stator and the outer radius of the magnetic poles and the side magnetic poles at two sides of the stator slot are divided into side magnetic pole subfields, so that the column writing of boundary conditions in the subfields and the solving of vector magnetic bits are facilitated.
Further, in step 2, partial differential equations are respectively built for the z-direction components of the vector magnetic bits a of the subfields obtained in step 1 based on ampere loop law and gaussian law of maxwell's equations, and then general solution expressions of the vector magnetic bits a of the subfields in the two-dimensional plane are deduced based on the built partial differential equations and boundary conditions.
Compared with the traditional alternating pole magnetic flux reversing motor, the novel alternating pole magnetic flux reversing motor structure has the advantage that the average electromagnetic torque is obviously improved under the condition that the same permanent magnet consumption is ensured. Meanwhile, the invention provides a new analytical modeling method for the alternating pole magnetic flux reversing motor, which uses an accurate subdomain model to carry out modeling analysis on the alternating pole magnetic flux reversing motor, improves the calculation precision and can accurately obtain the air gap flux density and the electromagnetic torque of the motor.
Drawings
FIG. 1 is a schematic diagram of an embodiment of the present invention.
Fig. 2 is a schematic diagram of a comparative object structure of a conventional alternating pole flux reversing motor employing concentrated windings.
Fig. 3 is a schematic diagram of a comparative object structure of a conventional alternating pole flux reversing motor employing distributed windings.
Fig. 4 is a graph showing the electromagnetic torque comparison result between two comparison objects according to the first embodiment of the present invention.
FIG. 5 is a graph comparing the air gap flux density analysis result with the finite element result of the motor under the modeling of the second embodiment of the invention.
Fig. 6 is a graph comparing electromagnetic torque analysis results and finite element results of a motor under modeling according to a second embodiment of the present invention.
Detailed Description
In order to make the technical solution of the present invention better understood by those skilled in the art, the following detailed description will be given with reference to the accompanying drawings and examples, by which the technical means are applied to solve the technical problem, and the implementation process for achieving the corresponding technical effects can be fully understood and implemented. The embodiment of the invention and the characteristics in the embodiment can be mutually combined on the premise of no conflict, and the formed technical scheme is within the protection scope of the invention.
It will be apparent that the described embodiments are merely some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It is noted that the terms "comprises" and "comprising," and any variations thereof, in the description and claims of the present invention and in the foregoing figures, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed or inherent to such process, method, article, or apparatus.
Example 1
As shown in fig. 1, the present embodiment discloses an alternating pole magnetic flux reversing motor, which comprises a rotor 2 and a stator 1 coaxially sleeved outside the rotor 2. The outer wall of the rotor 2 is provided with a plurality of rotor grooves 5 which are distributed at equal intervals along the circumferential direction of the rotor 2, the inner wall of the stator 1 is provided with a plurality of stator teeth 3 which are distributed at equal intervals along the circumferential direction of the stator 1, each stator tooth 3 is T-shaped, stator grooves 4 are arranged between adjacent stator teeth 3 in the circumferential direction, the notch 4.1 of each stator groove 4 is a necking with reduced groove width, and the notch 4.1 of each stator groove 4 is an air gap communicated between the stator 1 and the rotor 2.
The side of the stator tooth in the anticlockwise direction corresponding to the notch 4.1 of each stator slot 4 is provided with an edge magnetic pole 6.1, the side of the stator tooth in the clockwise direction corresponding to the notch 4.1 of each stator slot 4 is provided with an edge magnetic pole 6.2, each stator tooth 3 is provided with two edge magnetic poles 6.1 and 6.2, a central magnetic pole 6.3 is arranged between the two edge magnetic poles 6.1 and 6.2 of each stator tooth 3, and three sections of permanent magnetic poles (one central magnetic pole 6.2 and two edge magnetic poles 6.1 and 6.2) are arranged below each stator tooth 3, and the topological structure is named as N-Fe-N-Fe-N. The counter-clockwise side magnetic poles 6.1, 6.2 of the slot 4.1 of each stator slot 4 are symmetrical with respect to the geometric center of the slot 4.1 of that stator slot.
In this embodiment, the magnetization mode of the central magnetic pole 6.3 is radial magnetization, and the two side magnetic poles 6.1 and 6.2 adopt a magnetization mode with a certain angle, namely: the magnetizing angle of the side magnetic pole 6.1 in the anticlockwise direction of the notch 4.1 of each stator slot 4 is an included angle between the magnetizing direction of the side magnetic pole 6.1 and the anticlockwise circumferential tangential direction, and the magnetizing angle of the side magnetic pole 6.2 in the clockwise direction of the notch 4.1 of each stator slot 4 is an included angle between the magnetizing direction of the side magnetic pole 6.2 and the clockwise circumferential tangential direction. The side magnetic poles 6.1, 6.2 of the notch 4.1 of each stator slot 4 in the counter-clockwise direction and the clockwise direction have symmetrical magnetization angles.
Fig. 2 and 3 are schematic structural views of a conventional alternating-pole flux-reversing motor, as a comparison object of the present embodiment. Wherein, the concentrated windings are adopted in fig. 2, the distributed windings are adopted in fig. 3, and besides different winding connection modes, the structural dimensions of the two traditional motors in fig. 2 and 3 are completely consistent.
The alternating pole flux reversing machine of this embodiment employs 6 slot 14 poles, i.e. with 6 stator slots 4, 14 rotor slots 5. The concentrated winding comparison object in fig. 2 and the distributed winding comparison object in fig. 3 are both conventional 12-slot 14-pole flux reversing motors, i.e. with 12 stator slots 4 and 14 rotor slots 5.
In this embodiment, the rated rotation speeds of the concentrated winding comparison object in fig. 2 and the distributed winding comparison object in fig. 3 are 1200r/min, and the stator 1 and the rotor 2 are both made of 50WW470 silicon steel sheets. The outer radius of the stator 1 is 55mm, the outer radius of the stator slot 4 is 50mm, the inner radius of the stator slot 4 is 40.5mm, the inner radius of the stator 1 is 33.5mm, the inner radius of the rotor slot 5 is 26mm, the outer radius of the rotor 2 is 33mm, the angle of span of the rotor 2 is 11 degrees, and the axial length of the motor is 40mm.
In this embodiment, the same permanent magnet materials as the magnetic poles in the concentrated winding comparison object in fig. 2 and the distributed winding comparison object in fig. 3 are neodymium iron boron N35UH, the relative permeability of the permanent magnet is 1.05, and the remanence of the permanent magnet is 1.2T.
Under the condition of ensuring the same copper loss, the number of turns per coil in the embodiment is 100, the number of turns per coil of a concentrated winding comparison object in fig. 2 is 107, and the number of turns per coil of a distributed winding comparison object in fig. 3 is 65.
Under the condition that the magnetic pole outer radius is 36.5mm and the magnetic quantity is the same, the notch 4.1 crossing angle of the stator groove 4 is 6 degrees, the crossing angle of the stator groove 4 is 48 degrees, the crossing angle of the central magnetic pole 6.3 is 13 degrees, the crossing angles of the side magnetic poles 6.1 and 6.2 are 9 degrees and the magnetization angle is 70 degrees. In the concentrated winding comparison object in fig. 2 and the distributed winding comparison object in fig. 3, the outer radius of the magnetic pole is 37.2mm, the crossing angle of the magnetic pole is 12.44 degrees, the crossing angle of the stator notch 4.1 is 5.12 degrees, and the crossing angle of the stator slot 4 is 20 degrees.
Fig. 4 is a comparison of electromagnetic torque of the concentrated winding comparison object of the present embodiment and the distributed winding comparison object of fig. 3. When the permanent magnets are used in the same amount, compared with the traditional alternating-pole magnetic flux reversing motor adopting concentrated windings in fig. 2, the average electromagnetic torque of the proposed model is obviously improved and the torque pulsation is obviously reduced; the torque ripple is slightly increased within an acceptable range, but the average electromagnetic torque is significantly increased, as compared to the conventional alternating pole flux reversing motor of fig. 3 employing distributed windings.
Example two
The embodiment discloses an analytical modeling method for an alternating pole flux reversing motor, which comprises the following steps:
and 1, dividing a motor solving domain into a stator slot subdomain, a side magnetic pole subdomain, a center magnetic pole subdomain, an air gap subdomain and a rotor slot subdomain by adopting an accurate subdomain model method. The process is as follows:
defining initial position as central position of first stator slot, and defining theta as the center line of stator slot subdomain, stator notch subdomain and side magnetic pole subdomain are coincident k For the central position angles of the three types of grooves, namely the included angle between the center line of the kth groove and the center line of the 1 st groove, the serial numbers are sequentially arranged into the 1 st … … kth groove by taking anticlockwise as the positive direction; a, a 0 For the position angle of the central magnetic pole relative to the initial position, a is defined k The central magnetic pole serial numbers are sequentially arranged into the kth central magnetic pole … … of the 1 st central magnetic pole by taking the anticlockwise direction as the positive direction for forming an included angle between the central line of the kth central magnetic pole and the central line of the 1 st central magnetic pole; θ 0 For the position angle of the rotor relative to the initial position, define θ i Rotor groove sequence for the included angle between the ith rotor groove center line and the 1 st rotor groove center lineThe numbers are sequentially arranged in the 1 st rotor groove … … ith rotor groove by taking the anticlockwise direction as the positive direction; obviously, for a single having N r Rotor grooves and N s Motor with stator slot, theta k 、a k And theta i The expressions of (2) are respectively:
Figure BDA0004065738240000051
and 2, respectively establishing partial differential equations for the z-direction components of the vector magnetic potential A of each subdomain obtained in the step 1 based on the ampere loop law and the Gaussian law of the Maxwell equation group, and then pushing the general solution expression of the vector magnetic potential A of each subdomain in the two-dimensional plane based on the established partial differential equations and boundary conditions. The process is as follows:
in a two-dimensional polar coordinate system, A is a function of radius r and angular position θ, and the radial component B of the magnetic field density vector r And tangential component B θ The relationship with magnetic bit a can be expressed as:
Figure BDA0004065738240000061
in the air region and magnetized linear media, the magnetic field strength and magnetic field density vectors are related by the following expression, where μ 0 Is vacuum permeability, mu r Is the medium relative permeability, M is the magnetization vector, H is the magnetic field vector, and B is the magnetic field density vector:
Figure BDA0004065738240000062
and obtaining the vector magnetic potential A of each subdomain and carrying out coefficient scaling by solving the poisson equation and the Laplace equation of each subdomain to obtain the final form of the vector magnetic potential A, wherein the method comprises the following steps of:
(1) Stator slot subdomain magnetic field analysis
In the stator slot sub-domain, when the current density distribution is 0, the vector magnetic level equation in two-dimensional polar coordinates can be expressed as follows:
Figure BDA0004065738240000063
k A s1 (r, θ) represents the z-component of the vector flux level a in the kth stator slot sub-domain, where k=1, 2,3 … N s ，R so For the inner radius of the stator groove, R s1 The radius of the stator slot is delta, and delta is radian of the fan-shaped stator slot corresponding to the central angle. The left and right boundaries of the stator slot subdomain are iron, so that the radial magnetic density at the boundary is 0. Solving the Laplace equation by a separation variable method to obtain the original form of the equation solution:
Figure BDA0004065738240000064
for facilitating subsequent calculation by scaling the coefficients
Figure BDA0004065738240000065
And->
Figure BDA0004065738240000066
The form transformation of the equation does not affect the final result. The solution of the stator slot subdomain vector magnetic bits after form transformation is as follows:
Figure BDA0004065738240000067
wherein: k W 1 ， k X 1 ，
Figure BDA0004065738240000068
and->
Figure BDA0004065738240000069
The direct current component coefficient and the harmonic component coefficient of the stator slot subdomain magnetic level equation are respectively, v is the harmonic order number of the stator slot subdomain magnetic level equation, and tau v The expression of (2) is:
Figure BDA00040657382400000610
(2) Stator slot subfield magnetic field analysis
The stator slot subdomain only comprises an air region between the outer radius of the magnetic pole and the inner radius of the stator slot, and when the current density distribution is 0 in the stator slot subdomain, the vector magnetic position equation under the two-dimensional polar coordinate can be expressed as follows:
Figure BDA0004065738240000071
k A so (r, θ) represents the z-component of the vector magnetic potential a in the kth stator slot subdomain, where k=1, 2,3 … N s ，R n The outer radius of the magnetic pole is beta, and beta is the radian of the slot opening of the sector stator corresponding to the central angle. The left and right boundaries of the stator slot subdomain are iron, so that the radial magnetic density at the boundary is 0. Solving the Laplace equation by a separation variable method, simultaneously scaling each coefficient, and solving the stator slot subfield vector magnetic position after form conversion as follows:
Figure BDA0004065738240000072
wherein: k W 2 ， k X 2 ，
Figure BDA0004065738240000073
and->
Figure BDA0004065738240000074
The direct current component coefficient and the harmonic component coefficient of the stator slot subfield magnetic level equation are respectively given, u is the harmonic order number of the stator slot subfield magnetic level equation, and τ u The expressions of (2) are respectively:
Figure BDA0004065738240000075
(3) Edge magnetic pole subdomain magnetic field analysis
In the side magnetic pole subdomain, the permanent magnets at two sides of the notch are symmetrical about the geometric center of the notch, and the magnetization mode of the magnetization angle in the embodiment I is adopted, the magnetization angle is symmetrical, and magnetization intensity components exist, so that a vector magnetic level equation under two-dimensional polar coordinates can be expressed as follows:
Figure BDA0004065738240000076
k A m (r, θ) represents the z-component of the vector magnetic potential a in the kth side magnetic pole sub-domain, where k=1, 2,3 … N s ，μ 0 Is vacuum permeability, R s Is the inner radius of the stator, and xi is the radian of the side magnetic pole area corresponding to the central angle, k M mr and k M mθ the radial and tangential components of the magnetization intensity of the permanent magnet are respectively shown as follows:
Figure BDA0004065738240000081
wherein: c, M rw And M θw The method comprises the following steps of:
Figure BDA0004065738240000082
the invention adopts alternate poles, and the magnetic poles are all N poles, so C is 1.
Figure BDA0004065738240000083
Figure BDA0004065738240000084
The left and right boundaries of the side magnetic pole subdomains are iron, so that the radial magnetic density at the boundary is 0. Solving the poisson equation by a separation variable method, and simultaneously scaling each coefficient, wherein the solution of the vector magnetic bit of the side magnetic pole subdomain after form conversion is as follows:
Figure BDA0004065738240000085
wherein: k W 3 ， k X 3 ，
Figure BDA0004065738240000086
and->
Figure BDA0004065738240000087
The direct current component coefficient and the harmonic component coefficient of the magnetic potential equation of the side magnetic pole subdomain are respectively, w is the harmonic order number of the magnetic potential equation of the side magnetic pole subdomain, and theta m Is the magnetization angle of the side magnetic pole. τ w And equation F w (r) are respectively:
Figure BDA0004065738240000091
/>
Figure BDA0004065738240000092
(4) Magnetic field analysis of central magnetic pole subdomain
In the central pole sub-domain, the permanent magnets are magnetized radially, and there is a magnetization component, so the vector magnetic potential equation in two dimensions of polar coordinates can be expressed as follows:
Figure BDA0004065738240000093
k A x (rθ) is the z-component of the vector flux position a in the kth central pole sub-domain, where k=1, 2,3 … N s ，μ 0 Is vacuum magnetic permeability, gamma is radian of central magnetic pole area corresponding to central angle, k M xr and k M xθ the radial and tangential components of the magnetization intensity of the permanent magnet are respectively shown as follows:
Figure BDA0004065738240000094
wherein: c, M rj And M θj The method comprises the following steps of:
Figure BDA0004065738240000095
the invention adopts alternate poles, and the magnetic poles are all N poles, so C is 1.
Figure BDA0004065738240000096
M θj ＝0 (23)
The left and right boundaries of the central magnetic pole subdomain are iron, so that the radial magnetic density at the boundary is 0. Solving the poisson equation by a separation variable method, and simultaneously scaling each coefficient, wherein the solution of the vector magnetic position of the central magnetic pole subdomain after form transformation is as follows:
Figure BDA0004065738240000101
wherein: k W 4 ， k X 4 ，
Figure BDA0004065738240000102
and->
Figure BDA0004065738240000103
Respectively is the middle partAnd j is the harmonic order of the magnetic level equation of the central magnetic pole subdomain. τ j And equation F j (r) are respectively:
Figure BDA0004065738240000104
/>
Figure BDA0004065738240000105
(5) Air gap sub-field magnetic field analysis
In the air gap sub-domain, there are no current and magnetization components, the solving domain is located at the rotor outer radius R o And the inner radius R of the stator s The annular region in between, and thus the vector magnetic potential equation in two dimensions of polar coordinates can be expressed as follows:
Figure BDA0004065738240000106
A a (r, θ) represents the z-component equation of the vector magnetic bit A of the air gap sub-field, and the Laplace equation is solved by using a separation variable method, and the original form of the solution is:
Figure BDA0004065738240000107
unlike the slot sub-region, the air gap sub-region is a connected annular region, so that the integral of the magnetic field strength at the circumference of any radius r in the air gap region is equal to the total current through the circumference range according to ampere's loop law, while the current through this region is always zero, so the solution of the differential equation should not contain a direct current component. Simplifying the solution of the equation and scaling the coefficient, and solving the air gap subdomain vector magnetic bits after form transformation into:
Figure BDA0004065738240000111
wherein: w (W) 5 ，X 5 ，
Figure BDA0004065738240000112
And->
Figure BDA0004065738240000113
The direct current component coefficient and the harmonic component coefficient of the air gap subdomain magnetic potential equation are respectively, and n is the harmonic order number of the air gap subdomain magnetic potential equation.
(6) Rotor slot subdomain magnetic field analysis
In the rotor slot subzone, the vector magnetic level equation in two dimensions of polar coordinates, without current and magnetization components, can be expressed as follows:
Figure BDA0004065738240000114
i A z (r, θ) is the z-component of the vector magnetic flux level a in the ith rotor slot subzone, where i=1, 2,3 … N r ，R r The radius of the rotor groove is eta, and the radian of the fan-shaped rotor groove corresponding to the central angle. The left and right boundaries of the rotor groove subdomain are iron, so that the radial magnetic density at the boundary is 0. Solving the Laplace equation by a separation variable method to obtain the original form of the equation solution:
Figure BDA0004065738240000115
for facilitating subsequent calculation by scaling the coefficients
Figure BDA0004065738240000116
And->
Figure BDA0004065738240000117
The form transformation of the equation does not affect the final result. The solution of the rotor slot subdomain vector magnetic bits after form transformation is as follows: />
Figure BDA0004065738240000118
Wherein: i W 6 ， i X 6 ，
Figure BDA0004065738240000119
and->
Figure BDA00040657382400001110
The direct current component coefficient and the harmonic component coefficient of the rotor groove subdomain magnetic level equation are respectively, s is the harmonic order number of the rotor groove subdomain magnetic level equation, and tau s The expression of (2) is:
Figure BDA00040657382400001111
in summary, magnetic potential equations including coefficients to be solved for the six regions are established. Wherein the method comprises the steps of k W 1 ， k X 1 ，
Figure BDA00040657382400001112
k W 2 ， k X 2 ，/>
Figure BDA00040657382400001113
k W 3 ， k X 3 ，/>
Figure BDA00040657382400001114
k W 4 ， k X 4 ，/>
Figure BDA00040657382400001115
Figure BDA0004065738240000121
And->
Figure BDA0004065738240000122
Series of 24 groupsThe number (including the direct current component coefficient and the harmonic component coefficient) will be determined by the boundary conditions between the regions.
And 3, establishing a matrix equation to solve the direct current component and harmonic component coefficients in the general solution expression of the vector magnetic bit A of each subdomain obtained in the step 2 by utilizing boundary conditions among all subdomains. The process is as follows:
used at r=r r ，R o ，R s ，R m ，R so ，R s1 And (3) establishing a matrix equation to solve each harmonic component coefficient in each sub-field magnetic potential equation under boundary conditions of six positions, and obtaining the air gap flux density and the electromagnetic torque. Because the bottom surface of the stator slot, the bottom surface of the central magnetic pole and the bottom surface of the rotor slot are all ferromagnetic boundaries with infinite magnetic permeability, the tangential magnetic field intensity of the stator slot bottom is 0, and then the magnetic potential equation of the subdomain is simplified. The method comprises the following steps:
(1) For the stator slot subdomain, r=r at its radial position s1 The boundary conditions of (2) can be expressed as:
Figure BDA0004065738240000123
substituting equation (6) into equation (34) can be solved:
k X 1 ＝0 (35)
Figure BDA0004065738240000124
substituting equations (35) and (36) into equation (6), and simplifying the stator slot subfield magnetic potential equation into:
Figure BDA0004065738240000125
in the following, the expression for the stator slot subdomain is operated by using the expression (37).
(2) For the central pole sub-region, r=r at its radial position m The boundary conditions of (2) can be expressed as:
Figure BDA0004065738240000126
substituting equation (24) into equation (38) can be solved:
k X 4 ＝0 (39)
Figure BDA0004065738240000127
substituting equations (39) and (40) into equation (24) reduces the central pole subfield magnetic potential equation to:
Figure BDA0004065738240000131
in the following, expressions for the central pole subfields are all calculated using expression (41).
(3) For the rotor slot subdomain, r=r at its radial position r The boundary conditions of (2) can be expressed as:
Figure BDA0004065738240000132
substituting equation (32) into equation (42) can be solved:
i X 6 ＝0 (43)
Figure BDA0004065738240000133
substituting equations (43) and (44) into equation (32) reduces the rotor slot subfield magnetic potential equation to:
Figure BDA0004065738240000134
in the following, the expression for the rotor groove sub-region is calculated using the expression (45).
(4) On the basis of obtaining six types of sub-field general solutions, the related harmonic coefficients are required to be obtained according to the magnetic field continuous relation among all sub-fields in the radial direction, namely, the radial magnetic densities are equal, and the tangential magnetic field strengths are equal.
At the stator slot sub-domain and stator slot sub-domain interface, i.e. r=r so Where, according to the boundary condition, the tangential magnetic field strength is equal, it can be expressed as:
Figure BDA0004065738240000135
let r=r so Substituting, considering the boundary condition equation (46), the properties of the dc coefficient and harmonic component coefficient of the fourier series can be obtained:
k X 2 ＝0 (47)
Figure BDA0004065738240000141
(5) At the stator slot sub-domain and stator slot sub-domain interface, i.e. r=r so Where, according to the boundary condition, the radial magnetic densities are equal, it can be expressed as:
Figure BDA0004065738240000142
let r=r so Substituting, considering the boundary condition expression (49), the properties of the dc coefficient and harmonic component coefficient of the fourier series can be obtained:
Figure BDA0004065738240000143
Figure BDA0004065738240000144
(6) At the interface of stator slot sub-region and side magnetic pole sub-region, i.e. r=r m Where, according to the boundary condition, the tangential magnetic field strength is equal, it can be expressed as:
Figure BDA0004065738240000145
let r=r n Substituting, considering the boundary condition expression (52), the properties of the DC coefficient and harmonic component coefficient of the Fourier series can be obtained:
k X 3 ＝0 (53)
Figure BDA0004065738240000151
(7) At the interface of stator slot sub-region and side magnetic pole sub-region, i.e. r=r m Where, according to the boundary condition, the radial magnetic densities are equal, it can be expressed as:
Figure BDA0004065738240000152
let r=r m Substituting, considering the boundary condition expression (55), the properties of the DC coefficient and harmonic component coefficient of the Fourier series can be obtained:
Figure BDA0004065738240000153
Figure BDA0004065738240000154
(8) At the boundary between the side pole sub-region and the air gap sub-region, i.e. r=r s Where, according to the boundary condition, the radial magnetic densities are equal, it can be expressed as:
Figure BDA0004065738240000155
let r=r s Substitution intoConsidering the boundary condition equation (58), from the nature of the DC coefficient and harmonic component coefficient of the Fourier series, it is possible to obtain:
Figure BDA0004065738240000156
Figure BDA0004065738240000161
(9) At the interface of the central pole sub-region and the air gap sub-region, i.e. r=r s Where, according to the boundary condition, the radial magnetic densities are equal, it can be expressed as:
Figure BDA0004065738240000162
let r=r s Substituting, considering the boundary condition expression (61), the properties of the DC coefficient and harmonic component coefficient of the Fourier series can be obtained:
Figure BDA0004065738240000163
Figure BDA0004065738240000164
(10) At the boundary between the side magnetic, central magnetic pole sub-region and the air gap sub-region, i.e. r=r s Where, according to the boundary condition, the tangential magnetic field strength is equal, it can be expressed as:
Figure BDA0004065738240000165
let r=r s Substituting, considering the boundary condition expression (64), the properties of the harmonic component coefficients of the fourier series can be obtained:
Figure BDA0004065738240000166
Figure BDA0004065738240000171
(11) At the rotor slot sub-region and air gap sub-region interface, i.e. r=r o Where, according to the boundary condition, the tangential magnetic field strength is equal, it can be expressed as:
Figure BDA0004065738240000172
let r=r o Substituting, considering the boundary condition expression (67), the properties of the harmonic component coefficients of the fourier series can be obtained:
Figure BDA0004065738240000173
Figure BDA0004065738240000174
(12) At the rotor slot sub-region and air gap sub-region interface, i.e. r=r o Where, according to the boundary condition, the radial magnetic densities are equal, it can be expressed as:
Figure BDA0004065738240000175
let r=r o Substituting, considering the boundary condition expression (70), the properties of the DC coefficient and harmonic component coefficient of the Fourier series can be obtained:
Figure BDA0004065738240000176
Figure BDA0004065738240000177
the 24 sets of direct current component coefficients and harmonic component coefficients of the magnetic potential equations of each region can be solved by 24 sets of equations in total of the combination formula (35), formula (36), formula (39), formula (40), formula (43), formula (44), formula (47), formula (48), formula (50), formula (51), formula (53), formula (54), formula (56), formula (57), formula (59), formula (60), formula (62), formula (63), formula (65), formula (66), formula (68), formula (69), formula (71) and formula (72).
And 4, obtaining the air gap density and the electromagnetic torque of the motor based on the direct current component and harmonic component coefficients of all the subfields obtained in the step 3.
First, the air gap area magnetic potential equation A a And (r, theta) is substituted into the formula (2), and the air gap flux density of the motor is obtained by solving.
Then, the induced electromotive force and the electromagnetic torque can be solved according to the vector magnetic potential in the stator slot, and the following specific solving process is as follows: for any rotor position, the flux linkage of a coil is equal to the difference between the average vector flux levels of the upper and lower edges of the coil, which can be expressed as:
ψ x ＝ψ x+ -ψ x- (73)
Figure BDA0004065738240000181
wherein: l is the axial length of the motor, N c For the number of turns of the coil, S is the transverse section area of the upper layer edge or the lower layer edge of the coil, and the expression is as follows:
Figure BDA0004065738240000182
for any one phase winding N λ The coils are connected in series, and then the total flux linkage of the phase is as follows:
Figure BDA0004065738240000183
the no-load induced electromotive force of this phase is:
Figure BDA0004065738240000184
the electromagnetic torque expression of the three-phase motor is:
Figure BDA0004065738240000185
wherein: t is time, ω is motor speed; e (E) A ，E B ，E c Is the induced electromotive force of each phase; i.e A ，i B And i c Is a three-phase symmetric armature current.
Fig. 5 is a comparison of the analytical results and finite element results of radial air gap flux densities for one revolution of an alternating pole flux reversing motor designed in this embodiment at an air gap intermediate position. As can be seen from fig. 5, the results calculated by the accurate subfield modeling method are substantially identical to the finite element results within the error tolerance range, verifying the correctness of the analytical modeling in question.
Fig. 6 is a comparison of the result of the analysis of the electromagnetic torque of the alternating pole flux reversing motor designed in this embodiment and the result of the finite element. As can be seen from fig. 6, both remain substantially identical within the tolerance limits. The errors mainly originate from insufficient harmonic frequencies and the defects of the method for calculating the torque.
The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings, and the examples described herein are merely illustrative of the preferred embodiments of the present invention and are not intended to limit the spirit and scope of the present invention. The individual technical features described in the above-described embodiments may be combined in any suitable manner without contradiction, and such combination should also be regarded as the disclosure of the present invention as long as it does not deviate from the idea of the present invention. The various possible combinations of the invention are not described in detail in order to avoid unnecessary repetition.
The present invention is not limited to the specific details of the above embodiments, and various modifications and improvements made by those skilled in the art to the technical solution of the present invention should fall within the protection scope of the present invention without departing from the scope of the technical concept of the present invention, and the technical content of the present invention is fully described in the claims.

Claims (6)

1. The alternating pole magnetic flux reversing motor comprises a rotor and a stator sleeved outside the rotor, wherein the inner wall of the stator is provided with a plurality of stator teeth distributed along the circumferential direction of the stator, stator grooves are formed between adjacent stator teeth in the circumferential direction, and the notch of each stator groove is communicated with an air gap between the stator and the rotor; the magnetization mode of the central magnetic pole is radial magnetization, the magnetization angle of the side magnetic pole in the anticlockwise direction of the slot opening of each stator slot is an included angle between the magnetization direction of the side magnetic pole and the anticlockwise circumferential tangential direction, and the magnetization angle of the side magnetic pole in the clockwise direction of the slot opening of each stator slot is an included angle between the magnetization direction of the side magnetic pole and the clockwise circumferential tangential direction.
2. An alternate pole flux reversing machine according to claim 1, wherein the arrangement of side magnetic poles and stator slot slots is such that the counter-clockwise side magnetic pole corresponding to each stator slot is symmetrical about the geometric centre of the stator slot.
3. An alternate pole flux reversing machine according to claim 1, wherein the counter-clockwise side poles of each stator slot have symmetrical magnetization angles.
4. A method of analytical modeling of an alternating pole flux reversing machine according to any one of claims 1 to 3, comprising the steps of:
step 1, dividing a motor solving domain into a stator slot subdomain, a side magnetic pole subdomain, a center magnetic pole subdomain, an air gap subdomain and a rotor slot subdomain by adopting an accurate subdomain model method;
step 2, obtaining vector magnetic potential of each sub-field divided in step 1 under two-dimensional planeAA general solution expression of (2);
step 3, establishing a matrix equation to solve the vector magnetic bits of all the subfields obtained in the step 2 by utilizing boundary conditions among all the subfieldsADirect current component and harmonic component coefficients in the general solution expression of (a);
and 4, obtaining the air gap density and the electromagnetic torque of the motor based on the direct current component and harmonic component coefficients of all the subfields obtained in the step 3.
5. The analytical modeling method of alternating pole flux reversing motor of claim 4, wherein in the dividing of each sub-field in step 1, the stator slot sub-field only comprises an air area between the outer radius of the magnetic pole and the inner radius of the stator slot, and the air area between the inner radius of the stator and the outer radius of the magnetic pole and the side magnetic poles on both sides of the stator slot are divided into side magnetic pole sub-fields, so that the column writing of boundary conditions in the sub-field and the solving of vector magnetic bits are facilitated.
6. The analytical modeling method of alternating pole flux reversing motor according to claim 4, wherein in step 2, based on ampere loop law and gaussian law of maxwell's equations, vector magnetic potential of each subfield is obtained for step 1AA kind of electronic devicezThe direction components respectively establish partial differential equations, and then the vector magnetic potential of each subdomain under the two-dimensional plane is deduced based on the established partial differential equations and boundary conditionsAIs a general solution expression of (2).
CN202310074742.8A 2023-01-16 2023-01-16 Alternating pole magnetic flux reversing motor and analytic modeling method thereof Pending CN116191807A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117828244A (en) * 2024-03-06 2024-04-05 华中科技大学 Linear induction motor chain type equivalent circuit and characteristic analysis method

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117828244A (en) * 2024-03-06 2024-04-05 华中科技大学 Linear induction motor chain type equivalent circuit and characteristic analysis method
CN117828244B (en) * 2024-03-06 2024-05-14 华中科技大学 Linear induction motor chain type equivalent circuit and characteristic analysis method

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