CN112016172B - Air gap magnetic field prediction method and system of solid rotor induction motor - Google Patents

Air gap magnetic field prediction method and system of solid rotor induction motor Download PDF

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CN112016172B
CN112016172B CN202010966759.0A CN202010966759A CN112016172B CN 112016172 B CN112016172 B CN 112016172B CN 202010966759 A CN202010966759 A CN 202010966759A CN 112016172 B CN112016172 B CN 112016172B
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air gap
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solid rotor
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CN112016172A (en
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郭思源
陈远扬
柳永妍
陈道君
沈阳武
左剑
崔挺
王玎
孙杰懿
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Hunan Electric Power Co Ltd
State Grid Hunan Electric Power Co Ltd
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Hunan Electric Power Co Ltd
State Grid Hunan Electric Power Co Ltd
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Abstract

The invention relates to a method and a system for predicting an air gap field of a solid rotor induction motor, wherein the method comprises the following steps: acquiring magnetic flux density radial and tangential components in an air gap sub-domain based on a pre-acquired complex frequency domain vector magnetic potential expression of the air gap sub-domain of the solid rotor induction motor; the radial and tangential components of flux density in the air gap subdomain are the real parts of vector magnetic potential of the air gap subdomain; and judging whether the radial and tangential components of the magnetic flux density in the air gap sub-domain fall into a preset range or not, and determining whether the solid rotor induction motor meets the production conditions or not according to a judgment result.

Description

Air gap magnetic field prediction method and system of solid rotor induction motor
Technical Field
The invention relates to the technical field of motor electromagnetic field analytic calculation, in particular to a method and a system for predicting an air gap magnetic field of a solid rotor induction motor.
Background
The distribution of the air gap magnetic field of the motor is the key for designing and optimizing the electromagnetic performance, and the finite element method and the analytic method are mainly adopted for obtaining the air gap magnetic field distribution of the motor at present. The finite element method can process complex structures, has high calculation precision and consumes long time; the analytic method has the advantages of high speed, small calculated amount and clear physical concept, and is more beneficial to the initial design and optimization of the motor.
In recent years, a sub-domain analytical model based on a discrete variable method has gained precision comparable to that of a finite element in predicting electromagnetic performance of a motor, and thus has gained wide attention and use. However, the application of the sub-domain analytical model is mainly embodied in the analytical calculation of the constant magnetic field, wherein a rich technical effort is obtained in the permanent magnet motor. However, the sub-domain analytical model has little application in two-dimensional magnetic quasi-static fields. The solid rotor induction motor is used as an electromagnetic device with good starting and speed regulating performance, and a rotor iron core is a magnetic path and a current path. The eddy current distribution in a solid rotor is related to the stator current frequency, the rotor resistivity and the slip, and the magnetic field of the solid rotor is a typical quasi-static magnetic field. The main documents that can be found in the field analysis calculation of a solid rotor induction machine are:
(1) bell-good, layered impedance theory for double-layer solid rotor induction machines [ J ]. Proc. electrotechnical Commission, 1993, (2):18-20.
(2) Bell-good, two-layer transmission line comparative analysis of solid rotor induction machines [ J ]. Proc. electrotechnical Commission, 1995, (1):28-33.
(3) Study of additional loss of smooth-surface solid rotor induction motor based on two-dimensional analytical method [ J ]. proceedings of motor engineering in china, 2007, 21 (27): 83-88.
(4) Two-dimensional calculation method of equivalent circuit parameters of asynchronous motor with smooth solid rotor [ J ]. report of electrical engineering of china, 2016, 9 (36): 2505-2512.
(5) Equivalent circuit parameter calculation and performance analysis of a slotted solid rotor motor [ J ] reported in china motor engineering, 2017, 4 (37): 1208-1215.
In both the early stratified impedance theories (1) to (2) and the later two-dimensional linear analytical models (3) to (5), the stator slotting is replaced by the smooth surface, and the fundamental magnetomotive force synthesized by the three-phase winding current of the stator is equivalent to a fundamental sine current sheet distributed along the inner surface of the stator. Due to the assumption, the influence of stator slotting cannot be accurately considered by an analytic model, and leakage reactance generated by the stator slotting cannot be reflected in the analytic model.
In summary, the existing method for obtaining the air gap field distribution of the solid rotor induction motor has the defect that stator slotting cannot be considered, so that the obtained final obtained result is also inaccurate.
Disclosure of Invention
Technical problem to be solved
In view of the above-mentioned shortcomings and drawbacks of the prior art, the present invention provides a method and system for predicting an air-gap field of a solid rotor induction machine.
(II) technical scheme
In order to achieve the purpose, the invention adopts the main technical scheme that:
in a first aspect, an embodiment of the present invention provides a method for predicting an air-gap magnetic field of a solid rotor induction motor, including:
s1, acquiring a radial component and a tangential component of magnetic flux density in an air gap subdomain based on a complex frequency domain vector magnetic potential expression of the air gap subdomain of the solid rotor induction motor, which is acquired in advance;
the radial and tangential components of flux density in the air gap subdomain are the real parts of vector magnetic potential of the air gap subdomain;
s2, judging whether the radial and tangential components of the magnetic flux density in the air gap sub-domain fall into a preset range, and determining whether the solid rotor induction motor meets the production conditions according to the judgment result.
Preferably, before step S1, the method further includes the steps of:
s0, acquiring a complex frequency domain vector magnetic potential expression of an air gap sub-domain of the solid rotor induction motor based on the preset boundary condition of the stator slot sub-domain, the boundary condition of the air gap sub-domain and the boundary condition of the solid rotor sub-domain;
accordingly, the step S1 includes:
acquiring a magnetic flux density radial component and a tangential component in an air gap sub-domain according to a complex frequency domain vector magnetic potential expression of the air gap sub-domain of the solid rotor induction motor;
the radial and tangential components of the magnetic flux density in the air gap subdomain are the real parts of the vector magnetic potential of the air gap subdomain.
Preferably, the step S0 includes:
s01, establishing a solid rotor induction motor model in a two-dimensional polar coordinate plane (r, theta), and determining a slot subdomain, an air gap subdomain and a solid rotor subdomain of the solid rotor induction motor;
s02, respectively obtaining an initial complex vector magnetic potential expression of the slot sub-domain, an initial complex vector magnetic potential expression of the air gap sub-domain and an initial complex vector magnetic potential expression of the solid rotor sub-domain according to the preset boundary condition of the stator slot sub-domain, the boundary condition of the air gap sub-domain and the boundary condition of the solid rotor sub-domain;
the initial complex vector magnetic potential expression of the slot subdomain, the initial complex vector magnetic potential expression of the air gap subdomain and the initial complex vector magnetic potential expression of the solid rotor subdomain respectively have corresponding complex harmonic coefficients of each order;
and S03, respectively determining a specific numerical value of a complex harmonic coefficient corresponding to the initial complex vector magnetic potential expression of the slot sub-field, a specific numerical value of a complex harmonic coefficient corresponding to the initial complex vector magnetic potential expression of the air gap sub-field, and a specific numerical value of each order of complex harmonic coefficient to be solved corresponding to the initial complex vector magnetic potential expression of the solid rotor sub-field, and obtaining the complex vector magnetic potential expression of the slot sub-field, the complex vector magnetic potential expression of the air gap sub-field and the complex vector magnetic potential expression of the solid rotor sub-field.
Preferably, the step S01 includes:
a stator slot i (i ═ 1 to Q) subfield, an air gap subfield, and a solid rotor subfield for a solid rotor induction machine; q is the total number of the stator slots; i is a preset number of the stator slot;
wherein the vector magnetic bit A of the slot sub-region1Comprises the following steps:
A1i＝A1i(r,θ,t)ez；
wherein the content of the first and second substances,
Figure BDA0002682613400000041
ω1is the fundamental angular frequency;
in which the vector magnetic bit A of the air-gap sub-field2Comprises the following steps:
A2＝A2(r,θ,t)ez；
wherein the content of the first and second substances,
Figure BDA0002682613400000042
wherein the vector magnetic potential A of the solid rotor subdomain3Comprises the following steps:
A3＝A3(r,θ,t)ez；
wherein
Figure BDA0002682613400000043
Preferably, the step S02 includes:
aiming at a stator slot subdomain, determining the ith slot vector magnetic potential by using a Poisson equation, which specifically comprises the following steps:
Figure BDA0002682613400000044
wherein the current density of the coil side in the slot is
Figure BDA0002682613400000045
And are uniformly distributed; the center position of the ith slot is:
Figure BDA0002682613400000046
beta is a groove width opening angle; mu.s0Is trueA null permeability;
Figure BDA0002682613400000047
the boundary conditions of the ith slot subfield are:
Figure BDA0002682613400000051
Figure BDA0002682613400000052
according to the separation variable method, the initial complex vector magnetic potential expression of the ith slot subdomain is as follows:
Figure BDA0002682613400000053
Figure BDA0002682613400000054
wherein
Figure BDA0002682613400000055
R1Is a solid rotor yoke surface radius, R2Radius of stator inner surface, R3Is the radius of the bottom surface of the stator slot, and R3>R2>R1(ii) a m is the harmonic order of the magnetic field of the stator slot sub-region and is a positive integer;
Figure BDA0002682613400000056
and
Figure BDA0002682613400000057
all the complex harmonic coefficients of each order to be solved in the ith slot sub-domain of the stator are obtained.
Preferably, the step S02 includes:
for an air gap sub-domain, a vector magnetic potential is determined by adopting a Laplace equation, which specifically comprises the following steps:
Figure BDA0002682613400000058
the boundary conditions are as follows:
Figure BDA0002682613400000059
Figure BDA0002682613400000061
according to the separation variable method, the initial complex vector magnetic potential expression of the air gap sub-domain is:
Figure BDA0002682613400000062
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002682613400000063
Figure BDA0002682613400000064
n is the harmonic order and is a positive integer;
Figure BDA0002682613400000065
and
Figure BDA0002682613400000066
all are the complex harmonic coefficients of each order to be solved for the air gap sub-field.
Preferably, the step S02 includes:
aiming at a solid rotor sub-domain, a vector magnetic potential is determined by adopting a Xuan-mholtz equation, which specifically comprises the following steps:
Figure BDA0002682613400000067
σRis the electrical conductivity;
μRmagnetic conductivity of a rotor core area;
the boundary conditions are as follows:
Figure BDA0002682613400000068
according to the separation variable method, the initial complex vector magnetic potential expression of the solid rotor subdomain is as follows:
Figure BDA0002682613400000069
n is a harmonic order and is a positive integer;
Figure BDA00026826134000000610
and
Figure BDA00026826134000000611
each order complex harmonic coefficient to be solved for the solid rotor subdomain; j. the design is a squaren(x) Is a Bessel function of the first type, s is the slip; wherein the complex propagation constant
Figure BDA0002682613400000071
Preferably, the S03 includes:
where R is R2The normal magnetic densities of two sub-fields of a stator slot and an air gap are equal; and where R is R1And according to the fact that the tangential magnetic field intensity of the air gap and the tangential magnetic field intensity of the two sub-fields of the solid rotor are equal, the harmonic orders M and N of the three sub-fields are taken as the finite orders M and N, harmonic coefficient equations in the form of GX-Y are solved, and the harmonic coefficients are obtained
Figure BDA0002682613400000072
Specific numerical values of the complex harmonic coefficients of each order;
wherein G is a coefficient matrix;
x is a column vector formed by harmonic coefficients of finite order to be solved in all subdomains when the harmonic order of each subdomain is taken as the finite order;
y is the excitation term produced by the stator current density in the magnetic field continuity equation.
Preferably, the radial and tangential components of flux density in the air gap sub-domain in step S1 are:
Figure BDA0002682613400000073
Figure BDA0002682613400000074
B2r(r, θ, t) is the flux density radial component within the air gap sub-domain; b is2θ(r, θ, t) is the flux density tangential component within the air gap sub-domain.
In a second aspect, an embodiment of the present invention provides a system for predicting an air-gap field of a solid rotor induction machine, including:
at least one processor; and
at least one memory communicatively coupled to the processor, wherein the memory stores program instructions executable by the processor, and wherein the processor invokes the program instructions to perform any of the solid rotor induction machine air-gap field prediction methods described above.
(III) advantageous effects
The beneficial effects of the invention are: according to the air gap field prediction method of the solid rotor induction motor, the solving area of the solid rotor induction motor magnetic field is divided into the stator slot sub-area, the air gap sub-area and the solid rotor sub-area in the air gap field prediction process of the solid rotor induction motor, so that the influence of stator slotting on the solid rotor induction motor magnetic field is considered, the obtained air gap field of the solid rotor induction motor is more accurate, and further, the quality of the produced solid rotor induction motor is better.
Drawings
FIG. 1 is a flow chart of a method of predicting an air gap field of a solid rotor induction machine in accordance with the present invention;
FIG. 2 is a subdomain analytical model of a solid rotor induction motor of the present invention;
FIG. 3 is a stator slot domain analytic model according to the present invention;
FIG. 4 is a diagram of stator winding connections within a pole range of a prototype solid rotor induction motor in accordance with an embodiment of the present invention;
FIG. 5 is a comparison graph of analytical models and finite element analysis results for the radial flux density of the air gap of the prototype of FIG. 4;
FIG. 6 is a graph comparing analytical modeling and finite element analysis results for the air gap tangential flux density of the prototype of FIG. 4.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
Referring to fig. 1, a method for predicting an air gap field of a solid rotor induction machine in this embodiment includes:
and S1, acquiring the radial and tangential components of the magnetic flux density in the air gap subdomain based on the pre-acquired complex frequency domain vector magnetic potential expression of the air gap subdomain of the solid rotor induction motor.
The radial and tangential components of magnetic density in the air gap subdomain are the real parts of the vector magnetic potential of the air gap subdomain.
S2, judging whether the radial and tangential components of the magnetic flux density in the air gap sub-domain fall into a preset range, and determining whether the solid rotor induction motor meets the production conditions according to the judgment result.
In this embodiment, it is preferable that before step S1, the method further includes the steps of:
and S0, acquiring a complex frequency domain vector magnetic potential expression of the air gap sub-domain of the solid rotor induction motor based on the preset boundary conditions of the stator slot sub-domain, the air gap sub-domain and the solid rotor sub-domain.
Accordingly, the step S1 includes:
and acquiring the radial and tangential components of magnetic flux density in the air gap subdomain according to the complex frequency domain vector magnetic potential expression of the air gap subdomain of the solid rotor induction motor.
The radial and tangential components of the magnetic flux density in the air gap subdomain are the real parts of the vector magnetic potential of the air gap subdomain.
Step S0 in this embodiment includes:
s01, establishing a model of the solid rotor induction motor on a two-dimensional polar coordinate plane (r, theta), dividing a magnetic field solving area into a slot sub-area, an air gap sub-area and a solid rotor sub-area, and enabling the cross section of the solid rotor induction motor to be seen in figure 2. R is1Is a solid rotor yoke surface radius, R2Radius of the stator inner surface, R3Is a radius of the bottom surface of the stator slot, and R3>R2>R1. There are the following basic assumptions in the analytical model:
1) the permeability μ of the stator core portion is ∞.
2) Magnetic permeability of rotor core region is muRElectrical conductivity of σR。
3) Neglecting the effect of the end effect of the motor.
4) Referring to fig. 3, the stator slots are radial sector structures; current density of coil side in slot is JiAnd are uniformly distributed.
Referring to fig. 2, in the present embodiment, Q is the total number of slots of the stator, and β is the slot width opening angle. Taking the center of the 1 st slot of the stator as the initial position of the circumferential direction of the stator slot, the center position of the ith slot is as follows:
Figure BDA0002682613400000101
referring to fig. 2, in the solid rotor induction machine of the present embodiment, there are three sub-regions of stator slot i (i ═ 1 to Q), air gap, and solid rotor.
The air gap sub-region in the present embodiment refers to R in a solid rotor induction machine1≤r≤R 20 is not less than theta not less than 2 pi, and the circular ring area.
The stator slot region in this embodiment refers to a solid rotor induction machine R2≤r≤R3,
Figure BDA0002682613400000102
And (4) a region.
In the embodiment, the solid rotor subdomain refers to that R is more than or equal to 0 and less than or equal to R of the solid rotor induction motor1And theta is more than or equal to 0 and less than or equal to 2 pi.
Taking the vector magnetic potential A as a solving variable of three types of subdomain magnetic field constraint equations (wherein t is a time parameter):
Figure BDA0002682613400000103
wherein the mathematical relationship between the time domain and the frequency domain of the vector magnetic potential is as follows, omega1Is the fundamental angular frequency:
Figure BDA0002682613400000104
s02, respectively obtaining an initial complex vector magnetic potential expression of the slot sub-domain, an initial complex vector magnetic potential expression of the air gap sub-domain and an initial complex vector magnetic potential expression of the solid rotor sub-domain according to the magnetic field boundary condition, and specifically comprising the following steps:
1) for a stator slot subdomain, the ith slot vector magnetic potential equation is a Poisson equation due to the stator current:
Figure BDA0002682613400000105
the current density on the end face of each conductor becomes a sinusoidal alternating variable changing along with time, and the three phases respectively have a phase difference of 120 degrees;
Figure BDA0002682613400000111
the boundary condition of the ith slot sub-field can be expressed as:
Figure BDA0002682613400000112
Figure BDA0002682613400000113
according to the separation variable method, the initial complex vector magnetic potential expression of the ith slot sub-field is as follows:
Figure BDA0002682613400000114
Figure BDA0002682613400000115
wherein m is the harmonic order of the magnetic field of the stator slot sub-region and is a positive integer;
Figure BDA0002682613400000116
Figure BDA0002682613400000117
all the complex harmonic coefficients of each order to be solved in the ith slot sub-domain of the stator are obtained.
To facilitate the solution of the harmonic coefficients, the following functions are cited:
Figure BDA0002682613400000118
that is, in the initial complex vector magnetic potential expression of the ith slot sub-field
Figure BDA0002682613400000119
2) For the air gap sub-domain, the vector magnetic potential equation is the Laplace equation:
Figure BDA00026826134000001110
the boundary conditions are as follows:
Figure BDA0002682613400000121
Figure BDA0002682613400000122
according to the separation variable method, the initial complex vector magnetic potential of the air gap sub-region is expressed as follows
Figure BDA0002682613400000123
Wherein n is a harmonic order and is a positive integer;
Figure BDA0002682613400000124
all are the complex harmonic coefficients of each order to be solved in the air gap sub-field.
To facilitate the solution of the harmonic coefficients, two functions are cited:
Figure BDA0002682613400000125
that is to say the initial complex vector magnetic potential expression of its air gap sub-domain:
Figure BDA0002682613400000126
Figure BDA0002682613400000127
3) for the solid rotor subdomain, the vector magnetic potential equation is the Schlemm Hotz equation:
Figure BDA0002682613400000128
the boundary conditions are as follows:
Figure BDA0002682613400000131
according to the separation variational method, the analytical solution for the solid rotor subdomain is as follows:
Figure BDA0002682613400000132
n is the harmonic order and is a positive integer;
Figure BDA0002682613400000133
all the harmonic coefficients of each order to be solved of the solid rotor subdomain are complex harmonic coefficients of each order to be solved; j. the design is a squaren(x) Is a Bessel function of the first kind, s is the slip, where the complex propagation constant:
Figure BDA0002682613400000134
and S03, solving complex harmonic coefficients of the three sub-fields by using the magnetic field continuous relation between two adjacent sub-fields with different radiuses R-R in the R direction, thereby obtaining complex frequency domain vector magnetic potential expressions of the three sub-fields. The method specifically comprises the following steps: where R is R2The normal magnetic densities of two sub-regions of a stator slot and an air gap are equal; and where R is R1And according to the fact that the tangential magnetic field intensity of the two sub-fields of the air gap and the solid rotor is equal, the harmonic orders M and N of the three sub-fields are taken as the finite orders M and N, harmonic coefficient equation solution in the form of GX-Y is carried out, and the harmonic coefficient equation is obtained
Figure BDA0002682613400000135
Specific numerical values of the complex harmonic coefficients of each order;
wherein G is a coefficient matrix.
And X is a column vector formed by harmonic coefficients of finite order to be solved in all the subdomains when the harmonic order of each subdomain is taken as the finite order.
Y is an excitation term generated by the current density of the stator in a magnetic field continuous relation equation (the normal magnetic densities of the two types of sub-fields are equal, the tangential magnetic field strengths of the two types of sub-fields are equal, and the excitation term is that the current density is JiA known quantity prior to solving the equation).
In this embodiment, after the complex vector magnetic potential of the air gap sub-domain is solved, the radial and tangential components of magnetic flux density in the air gap sub-domain in step S1 are:
Figure BDA0002682613400000136
Figure BDA0002682613400000141
B2r(r, θ, t) is the flux density radial component within the air gap sub-domain; b is2θ(r, θ, t) is the flux density tangential component within the air gap sub-domain.
In the method for predicting the air gap field of the solid rotor induction motor in the embodiment, the solving area of the solid rotor induction motor field is divided into the stator slot sub-area, the air gap sub-area and the solid rotor sub-area in the process of predicting the air gap field of the solid rotor induction motor, so that the influence of stator slots on the solid rotor induction motor field is considered, the obtained air gap field of the solid rotor induction motor is more accurate, and the quality of the produced solid rotor induction motor is better.
In this embodiment, in order to verify the accuracy of the method for predicting the air gap field of the solid rotor induction motor in this embodiment, a single-layer winding solid rotor induction motor is taken as an example to perform calculation. The prototype parameters are shown in Table 1, and the winding distribution is shown in FIG. 4.
TABLE 1 solid rotor induction motor prototype parameters
Figure BDA0002682613400000142
In this embodiment, FIG. 5 and FIG. 6 are Ia＝I1，Ib＝IcWhen t is 0, the air gap center position at the time when t is 0, R, is (R)2+R3) Radial and tangential component analytical models and finite of flux density at/2And comparing the meta-analysis results. The results show that the resolution of the radial component of the air gap magnetic flux density is higher in goodness of fit with the time harmonic finite element, and the resolution of the tangential component is basically consistent with the trend of the time harmonic finite element.
Since the system described in the above embodiment of the present invention is a system used for implementing the method in the above embodiment of the present invention, a person skilled in the art can understand the specific structure and the modification of the system based on the method described in the above embodiment of the present invention, and thus the detailed description is omitted here. All systems/devices employed in the method of the above embodiment of the present invention are within the scope of the present invention.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, systems and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions.
It should be noted that in the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word "comprising" does not exclude the presence of elements or steps not listed in a claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The invention can be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In the claims enumerating several means, several of these means may be embodied by one and the same item of hardware. The use of the terms first, second, third and the like are for convenience only and do not denote any order. These words are to be understood as part of the name of the component.
Furthermore, it should be noted that in the description of the present specification, the description of the term "one embodiment", "some embodiments", "examples", "specific examples" or "some examples", etc., means that a specific feature, structure, material or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Moreover, various embodiments or examples and features of various embodiments or examples described in this specification can be combined and combined by one skilled in the art without being mutually inconsistent.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, the claims should be construed to include preferred embodiments and all such variations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention should also include such modifications and variations.

Claims (2)

1. A method of predicting an air gap field in a solid rotor induction machine, comprising:
s0, acquiring a complex frequency domain vector magnetic potential expression of an air gap sub-domain of the solid rotor induction motor based on the preset boundary condition of the stator slot sub-domain, the boundary condition of the air gap sub-domain and the boundary condition of the solid rotor sub-domain; the method specifically comprises the following steps:
s01, establishing a solid rotor induction motor model in a two-dimensional polar coordinate plane (r, theta), and determining a slot subdomain, an air gap subdomain and a solid rotor subdomain of the solid rotor induction motor; the method comprises the following steps:
a stator slot i (i ═ 1 to Q) sub-region, an air gap sub-region, and a solid rotor sub-region for a solid rotor induction machine; q is the total number of the stator slots; i is a preset number of the stator slot;
wherein the vector magnetic potential A of the slot sub-region1Comprises the following steps:
A1i＝A1i(r,θ,t)ez；
wherein the content of the first and second substances,
Figure FDA0003665854110000011
ω1is the fundamental angular frequency;
in which the vector magnetic potential A of the air-gap sub-field2Comprises the following steps:
A2＝A2(r,θ,t)ez；
wherein the content of the first and second substances,
Figure FDA0003665854110000012
wherein the vector magnetic potential A of the solid rotor subdomain3Comprises the following steps:
A3＝A3(r,θ,t)ez；
wherein
Figure FDA0003665854110000013
S02, respectively obtaining an initial complex vector magnetic potential expression of the slot subdomain, an initial complex vector magnetic potential expression of the air gap subdomain and an initial complex vector magnetic potential expression of the solid rotor subdomain according to preset boundary conditions of the stator slot subdomain, the air gap subdomain and the solid rotor subdomain;
the initial complex vector magnetic potential expression of the slot subdomain, the initial complex vector magnetic potential expression of the air gap subdomain and the initial complex vector magnetic potential expression of the solid rotor subdomain are respectively provided with corresponding complex harmonic coefficients of various orders;
aiming at a stator slot subdomain, determining the ith slot vector magnetic bit by adopting a Poisson equation, which specifically comprises the following steps:
Figure FDA0003665854110000021
wherein the current density of the coil side in the slot is
Figure FDA0003665854110000022
And are uniformly distributed; the center position of the ith slot is:
Figure FDA0003665854110000023
beta is a groove width opening angle; mu.s0Is a vacuum magnetic conductivity;
Figure FDA0003665854110000024
the boundary conditions for the ith slot sub-region are:
Figure FDA0003665854110000025
Figure FDA0003665854110000026
according to the separation variable method, the initial complex vector magnetic potential expression of the ith slot sub-field is as follows:
Figure FDA0003665854110000027
Figure FDA0003665854110000028
wherein
Figure FDA0003665854110000029
R1Is a solid rotor yoke surface radius, R2Radius of the stator inner surface, R3Is a radius of the bottom surface of the stator slot, and R3>R2>R1(ii) a m is the harmonic order of the magnetic field of the stator slot subdomain and is a positive integer; a1i 0, B1i 0 and A1im are complex harmonic coefficients of each order to be solved in the ith slot domain of the stator;
for an air gap sub-domain, a vector magnetic potential is determined by adopting a Laplace equation, which specifically comprises the following steps:
Figure FDA0003665854110000031
the boundary conditions are as follows:
Figure FDA0003665854110000032
Figure FDA0003665854110000033
according to the separation variable method, the initial complex vector magnetic potential expression of the air gap sub-domain is:
Figure FDA0003665854110000034
wherein the content of the first and second substances,
Figure FDA0003665854110000035
Figure FDA0003665854110000036
n is the harmonic order and is a positive integer; a2 n, B2 n, C2 n and D2 n are allEach order complex harmonic coefficient to be solved by the air gap sub-field;
aiming at a solid rotor sub-domain, a vector magnetic potential is determined by adopting a Xuan-mholtz equation, which specifically comprises the following steps:
Figure FDA0003665854110000037
σRis the electrical conductivity;
μRmagnetic conductivity of a rotor core area;
the boundary conditions are as follows:
Figure FDA0003665854110000041
according to the separation variable method, the initial complex vector magnetic potential expression of the solid rotor subdomain is as follows:
Figure FDA0003665854110000042
n is the harmonic order and is a positive integer; a3 n and B3 n are complex harmonic coefficients of each order to be solved of the solid rotor subdomain; j is a unit ofn(x) Is a Bessel function of the first type, s is the slip; wherein the complex propagation constant
Figure FDA0003665854110000043
S03, respectively determining a specific numerical value of a complex harmonic coefficient corresponding to the initial complex vector magnetic potential expression of the slot sub-field, a specific numerical value of a complex harmonic coefficient corresponding to the initial complex vector magnetic potential expression of the air gap sub-field, and a specific numerical value of each order of complex harmonic coefficient to be solved corresponding to the initial complex vector magnetic potential expression of the solid rotor sub-field, and obtaining the complex vector magnetic potential expression of the slot sub-field, the complex vector magnetic potential expression of the air gap sub-field and the complex vector magnetic potential expression of the solid rotor sub-field;
where R is R2According to the prescriptionThe normal magnetic densities of two sub-fields of the sub-slot and the air gap are equal; and when R ═ R1Taking the harmonic orders M and N of the three types of sub-fields as finite orders M and N according to the fact that the tangential magnetic field strength of the air gap and the tangential magnetic field strength of the two types of sub-fields of the solid rotor are equal, and solving a harmonic coefficient equation in a GX-Y form to obtain specific numerical values of complex harmonic coefficients of the orders A1i 0, B1i 0, A1i M, A2N, B2N, C2N, D2N, A3N and B3N;
wherein G is a coefficient matrix;
x is a column vector formed by harmonic coefficients of finite order to be solved in all the subdomains when the harmonic order of each subdomain is taken as the finite order;
y is the excitation term produced by the stator current density in the magnetic field continuity equation;
s1, acquiring radial and tangential components of flux density in an air gap sub-domain based on a pre-acquired complex frequency domain vector magnetic potential expression of the air gap sub-domain of the solid rotor induction motor; the method comprises the following steps:
acquiring a magnetic flux density radial component and a tangential component in an air gap subdomain of the solid rotor induction motor according to a complex frequency domain vector magnetic potential expression of the air gap subdomain;
the radial and tangential components of flux density in the air gap subdomain are the real parts of vector magnetic potential of the air gap subdomain;
the radial and tangential components of magnetic density in the air gap sub-domain are:
Figure FDA0003665854110000051
Figure FDA0003665854110000052
B2r(r, θ, t) is the flux density radial component within the air gap sub-domain; b is2θ(r, θ, t) is the flux density tangential component within the air gap sub-domain;
s2, judging whether the radial and tangential components of the magnetic flux density in the air gap sub-domain fall into a preset range, and determining whether the solid rotor induction motor meets the production conditions according to the judgment result.
2. A system for predicting an air-gap field of a solid rotor induction machine, comprising:
at least one processor; and
at least one memory communicatively coupled to the processor, wherein the memory stores program instructions executable by the processor to invoke the program instructions to perform the solid rotor induction machine air-gap field prediction method of claim 1.
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