CN114611315A - Calculation and analysis method for unbalanced electromagnetic force of motor - Google Patents

Calculation and analysis method for unbalanced electromagnetic force of motor Download PDF

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CN114611315A
CN114611315A CN202210285131.3A CN202210285131A CN114611315A CN 114611315 A CN114611315 A CN 114611315A CN 202210285131 A CN202210285131 A CN 202210285131A CN 114611315 A CN114611315 A CN 114611315A
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electromagnetic force
eccentricity
air gap
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宋永兴
刘正杨
侯瑞杰
张林华
张明阳
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Shandong Jianzhu University
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Abstract

The invention discloses a method for calculating and analyzing unbalanced electromagnetic force acting on a motor rotor, which comprises the following steps: establishing a mixed eccentric model, constructing a magnetomotive force and magnetic conductivity matrix, extracting unbalanced electromagnetic force, analyzing electromagnetic force characteristics, and finally obtaining time domain signals and frequency spectrum characteristics of the unbalanced electromagnetic force. The unbalanced electromagnetic force calculation and analysis method for the motor can obtain the characteristic of the unbalanced electromagnetic force coupling the motor equipment and the environment, and has important theoretical significance for state diagnosis, fault diagnosis and source tracing of the unbalanced electromagnetic force of the motor.

Description

Calculation and analysis method for unbalanced electromagnetic force of motor
Technical Field
The invention relates to the field of signal processing of rotating machinery, in particular to a calculation and analysis method for unbalanced electromagnetic force of a motor.
Background
The unbalanced electromagnetic force of the motor is derived from the asymmetry of air gap flux density, which is called air gap eccentricity and can be divided into dynamic eccentricity and static eccentricity. Wherein, the rotor position eccentricity caused by bearing abrasion, manufacturing tolerance, misalignment and other factors is called static eccentricity; and eccentricity of the rotor rotating around the center of the stator bore due to shaft bending caused by mass imbalance, or displacement of the rotor shaft caused by rotational vibration, is called dynamic eccentricity. In engineering practice, two eccentricities coexist, such eccentricities being referred to as mixed eccentricities. In addition, the motor may be subject to eccentricity caused by various sources, for example, the relative condition between the rotor and the stator is not fixed in the axial direction, and thus, the eccentricity change in the axial direction of the motor also needs to be considered. Also, even if the eccentricity types are the same, the eccentricity sources are not necessarily the same, for example, dynamic eccentricity is caused by both bending of the shaft and vibration of the shaft. Therefore, establishing a method for calculating and analyzing the unbalanced electromagnetic force is particularly important for analyzing and tracing the unbalanced electromagnetic force.
In the process of implementing the invention, the inventor finds that the prior art has at least the following disadvantages and shortcomings:
the method aims at the calculation and analysis method of the unbalanced electromagnetic force of the motor, and scholars at home and abroad make extensive research. The main calculation methods include Maxwell stress-strain method, virtual power method, angle-preserving mapping method, equivalent circuit method and the like. The virtual work method is mainly applied to stress analysis of local components in finite element analysis; the maxwell stress-strain method is most widely applied to analytical calculation, but when the method is used for calculation, a series of preconditions are often established, for example, the relative condition between an axial rotor and a stator is fixed, and the basic flatness is not considered. Therefore, the accuracy of calculating the unbalanced electromagnetic force beyond the set conditions in the actual engineering is poor, and the existing method for calculating and analyzing the unbalanced electromagnetic force needs to be improved.
Disclosure of Invention
The invention provides a method for calculating and analyzing unbalanced electromagnetic force of a motor, which improves the extraction precision of the unbalanced electromagnetic force by coupling a motor stator and rotor system with an eccentric variable caused by environmental factors, and comprises the following steps:
a method for computational analysis of unbalanced electromagnetic forces, the method comprising the steps of:
step 1: establishing a mixed eccentricity model;
step 2: constructing a magnetomotive force and magnetic conductivity matrix;
and step 3: extracting unbalanced electromagnetic force;
and 4, step 4: and (5) analyzing the electromagnetic force characteristics.
In step 1, the method for establishing the hybrid eccentricity model comprises the following steps:
step 1-1, the influence of dynamic eccentricity and static eccentricity of air gap eccentricity is synthesized, and two eccentric models with eccentricity superposed are obtained.
Step 1-2, performing dynamic modeling analysis on the whole motor frame and the stator to solve the vibration angle of the eccentric model in the step 1-1 to obtain the eccentric model under the influence of factors such as mechanical vibration and base flatness;
step 1-3, combining the two types of eccentricity in the step 1-1 and the step 1-2 to obtain an eccentric model of the motor equipment coupled with the environment, and accurately simulating the eccentric working condition in the actual engineering through the model to improve the calculation accuracy of the unbalanced electromagnetic force;
in step 2, the specific process of constructing the magnetomotive force and magnetic permeability matrix is as follows: and selecting a corresponding formula according to the type of the motor, respectively calculating the magnetomotive force of the rotor and the stator, calculating the total magnetomotive force in the air gap, and constructing an air gap magnetomotive force matrix of the motor. Constructing a magnetic permeability matrix under the current eccentricity degree by combining the eccentric model in the step 1;
in step 3, the extraction method of the unbalanced electromagnetic force comprises the following steps:
step 3-1, multiplying element by element according to the magnetomotive force matrix and the magnetic conductivity matrix obtained in the step 2 to obtain an axial infinitesimal air gap flux density matrix;
step 3-2, according to the infinitesimal air gap magnetic density matrix obtained in the step 3, integrating the electromagnetic force density of the infinitesimal plane by adopting a Maxwell stress-strain method, so as to obtain unbalanced electromagnetic force which changes along with time under the infinitesimal eccentric model; and (3) when the relative conditions of the rotor and the stator are changed, the axial infinitesimal eccentric model of the motor is not the same, the operations from the step 1 to the step 3 are repeated, and the infinitesimal electromagnetic forces under different eccentricities in the axial direction of the motor are accumulated to finally obtain the unbalanced electromagnetic force of the whole motor in the radial direction.
In step 4, the electromagnetic force characteristic analysis comprises the following specific processes: and performing Fourier transform spectrum analysis according to the unbalanced electromagnetic force signal obtained in the step 3.
The technical scheme provided by the invention has the beneficial effects that: the method realizes extraction of the unbalanced electromagnetic force of the motor under the mixed eccentric working condition, solves the problem of accurate calculation of the unbalanced electromagnetic force under the complex working conditions of mixed eccentricity, rotating shaft bending and the like in engineering, and has important theoretical and engineering values for vibration noise reduction analysis of the motor.
Drawings
Fig. 1 is a schematic diagram of a method for calculating and analyzing unbalanced electromagnetic force of a motor according to the present invention;
FIG. 2 is a schematic diagram of a hybrid eccentric model;
FIG. 3 is a schematic diagram of a hybrid eccentricity model within an electric machine;
FIG. 4 is a schematic diagram of an eccentric model caused by vibration of a frame structure;
FIG. 5 is a schematic diagram of a hybrid eccentric permanent magnet synchronous motor model according to an embodiment;
FIG. 6 is a diagram illustrating the results of the extracted infinitesimal unbalanced electromagnetic force;
FIG. 7 is a diagram illustrating the feature extraction result of unbalanced electromagnetic force;
in the figure, 1 is a rotor, 2 is a stator, and 3 is a permanent magnet.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
The problems existing in the prior art are solved. The invention provides a method for calculating and analyzing the unbalanced electromagnetic force of a motor, which realizes the calculation and analysis of the unbalanced electromagnetic force of the motor, solves the problem of calculation and analysis of the unbalanced electromagnetic force caused by various factors in engineering practice, and is described in detail as follows:
and S01, establishing a mixed eccentricity model.
For the motor in practical engineering, various eccentric forms coexist. The dynamic eccentricity and the static eccentricity are comprehensively considered, and a hybrid eccentricity model comprehensively considering the coupling of the motor and the environment is established. In the demonstration, a mixed eccentric permanent magnet synchronous motor model (as shown in fig. 5) is adopted, a mixed eccentric model (as shown in fig. 2 and 3) in the motor can be established according to the mixed eccentricity in the motor, and the vibration angle theta of the motor frame can be measured through dynamic modelingframeAnd (t) solving, and establishing an eccentric model of the motor frame structure (as shown in figure 4). Combining the two eccentric models to obtain the eccentric model of the coupling of the motor equipment and the environment as follows:
Figure 465265DEST_PATH_IMAGE001
in the formula, ecp，est，edy，eframeRespectively the eccentricity of the coupling of the motor equipment and the environment, the static eccentricity, the dynamic eccentricity and the eccentricity of a motor frame caused by mechanical vibration; the horizontal and vertical displacement caused by the vibration of the motor is respectively xframe，yframeThe azimuth angles corresponding to the static eccentricity and the dynamic eccentricity in the motor are thetast，θdy(ii) a The deflection angles of the motor frame in the horizontal and vertical directions caused by vibration are thetaframe，x，θframe，y；
S02, constructing a magnetomotive force and magnetic permeability matrix.
The air gap magnetomotive force of the motor is determined by the rotor and the stator together, and because the calculation methods of the air gap magnetomotive force of various motors are different, taking a permanent magnet synchronous motor as an example (as shown in fig. 5), the air gap magnetomotive force is as follows:
Figure 223006DEST_PATH_IMAGE002
in the formula, FPMSMIs the air gap magnetomotive force of the permanent magnet synchronous motor; fsm，FrmThe magnetomotive force generated by the stator of the motor and the magnetomotive force generated by the rotor are respectively; phi is a power factor angle; omega is the electrical angular velocity; p is the number of pole pairs.
The air gap permeability is determined by the air gap medium and the actual air gap length, in this embodiment, the air gap medium is air, the actual air gap length is determined by the eccentric model, and the relationship of the air gap permeability is obtained as follows:
Figure 730210DEST_PATH_IMAGE003
in the formula, Λ is air gap permeability; mu.s0Air gap medium permeability; delta is the actual air gap length; and defining the air gap permeability matrix as Lambda M due to different circumferential actual air gap lengths.
Further obtaining the magnetomotive force and the magnetic conductivity in each time and each space in the air gap of the motor, and respectively constructing the cumulant matrixes as follows:
Figure 208596DEST_PATH_IMAGE004
Figure 117646DEST_PATH_IMAGE005
in the formula, FMMMFIs a total magnetomotive force matrix of n x M, and Lambda M is an air gap permeability matrix of n x M, alpha1，α2，α3…，αnTo locate the azimuth angle of the point inside the air gap, t1，t2，…，tmIs time.
And S03, extracting unbalanced electromagnetic force.
The air gap flux density matrix BM is obtained by multiplying the magnetomotive force accumulation matrix and the magnetic permeability accumulation matrix extracted in S02 element by element as follows.
Figure 780709DEST_PATH_IMAGE006
Wherein BM is a infinitesimal-surface air-gap flux density matrix of n x m. Λ (α)i，tj)， F(αi，tj) Are each tjTime alphaiMagnetic permeability and magnetomotive force at the air gap at an angle.
According to the extracted infinitesimal surface air gap magnetic density accumulative matrix, the horizontal component and the vertical component of the unbalanced electromagnetic force on the infinitesimal surface are obtained by Maxwell stress tensor analysis.
Figure 775210DEST_PATH_IMAGE007
Figure 57287DEST_PATH_IMAGE008
According to the axial stator-rotor relationship change caused by the shaft bending in the embodiment, the process returns to S01, the electromagnetic force on the next axial infinitesimal element is continuously solved, and finally the unbalanced electromagnetic force on the length of each infinitesimal element is accumulated, and the result is as follows.
Figure 820843DEST_PATH_IMAGE009
In the formula, the horizontal and vertical components of the axial infinitesimal unbalanced electromagnetic force are respectively fump,x，fump,yThe horizontal and vertical components of the unbalanced electromagnetic force of the motor are respectively Fump,x，Fump,y， B(αi，t) is the air gap flux density at a certain moment,
Figure 920386DEST_PATH_IMAGE010
the length is the air gap radius and the direction angle is alphaiVector of (a) < i >jIs the axial length of the jth element.
And S04, electromagnetic force characteristic analysis.
Time domain signal mapping is performed according to the unbalanced electromagnetic force signal obtained in the step S03 (as shown in fig. 6), and fourier transform spectrum analysis is performed on the electromagnetic force signal (as shown in fig. 7).
In conclusion, the unbalanced electromagnetic force under the complex eccentric fault is calculated and analyzed by utilizing the mixed eccentric model iteration, and the problem of poor characteristic accuracy of the unbalanced electromagnetic force signal extracted in the engineering is solved, so that the motor unbalanced electromagnetic force calculation and analysis method adopted by the invention can obtain a better extraction effect.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (8)

1. A method for calculating and analyzing unbalanced electromagnetic force of a motor is characterized in that the calculation of the electromagnetic force comprises the following steps:
step 1: establishing a mixed eccentricity model: and extracting the relative eccentricity of each point in the air gap.
2. Step 1-1: aiming at the mixed eccentricity caused by the relative relation of a stator and a rotor in the motor, the established mathematical model is as follows:
Figure 460899DEST_PATH_IMAGE001
in the formula, emix，est，edyRespectively, the mixed eccentricity, the static eccentricity and the dynamic eccentricity; the azimuth angles corresponding to the eccentricity are thetamix，θst，θdy；
Step 1-2: aiming at the eccentricity caused by the stator displacement generated by the vibration of the motor, the established mathematical model is as follows:
Figure 608984DEST_PATH_IMAGE002
in the formula, eframeThe eccentricity of the motor frame caused by mechanical vibration; lpartThe axial length of the vibration part of the motor frame; the horizontal vertical displacement caused by the vibration of the motor is xframe，yframeThe deflection angles of the motor frame in the horizontal and vertical directions caused by vibration are thetaframe，x，θframe，y；
Step 1-3: combining the two eccentric models in the step 1-1 to obtain the eccentric model of the coupling of the motor equipment and the environment as follows:
Figure 289364DEST_PATH_IMAGE003
in the formula, ecpEccentricity of the coupling of the motor device with the environment;
step 2: constructing magnetomotive force and magnetic permeability matrix
Solving the magnetomotive force and the magnetic conductivity according to the relative eccentricity in the step 1, and defining the total magnetomotive force matrix under the action of the rotor and the stator as FMMMF。
3. The constructed magnetomotive force matrix is as follows:
Figure 497491DEST_PATH_IMAGE004
in the formula, FMMMFIs a total magnetomotive force matrix of n x m, alpha1，α2，…，αnTo locate the angle of position of a point in the air gap, t1，t2，…，tnIs time.
4. And (4) obtaining the actual length of the air gap according to the eccentric model established in the step (1), and determining an air gap magnetic permeability matrix Lambda M.
5. The permeability matrix is constructed as follows:
Figure 138688DEST_PATH_IMAGE005
in the formula, Lambda M is an n multiplied by M air gap permeability matrix.
6. And step 3: extraction of unbalanced electromagnetic forces
Step 3-1: according to the total magnetomotive force matrix FM in step 2MMFAir gap permeability matrix lambdam, element-by-element multiplicationThe air gap flux density matrix BM can be obtained as follows:
Figure 824884DEST_PATH_IMAGE006
wherein BM is an n × m air gap flux density matrix.
7. Step 3-2: according to the infinitesimal air-gap magnetic density matrix in the step 3-1, a Maxwell stress tensor method is adopted to obtain a horizontal component and a vertical component of the jth infinitesimal unbalanced electromagnetic force, the axial slicing infinitesimal electromagnetic forces with different mixed eccentricities caused by the change of relative conditions of the stator and the rotor are superposed, and the unbalanced electromagnetic force of the whole motor is as follows:
Figure 123885DEST_PATH_IMAGE007
Figure 502914DEST_PATH_IMAGE008
in the formula, the horizontal and vertical components of the unbalanced electromagnetic force of the motor are respectively Fump,x，Fump,y，B(aiT) is the air gap flux density at a certain time, riThe length is the air gap radius and the direction angle is aiVector of (a) < i >jIs the axial length of the jth element.
8. And 4, step 4: electromagnetic force signature analysis
And (4) according to the unbalanced electromagnetic force signal obtained in the step (3), drawing a time domain wave pattern of the unbalanced electromagnetic force signal, and realizing the spectrum analysis of the unbalanced electromagnetic force signal through Fourier transform.
CN202210285131.3A 2022-03-23 2022-03-23 Calculation and analysis method for unbalanced electromagnetic force of motor Pending CN114611315A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117171493A (en) * 2023-11-01 2023-12-05 华能澜沧江水电股份有限公司 Electromagnetic vibration calculation method and system for stator of hydraulic generator

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117171493A (en) * 2023-11-01 2023-12-05 华能澜沧江水电股份有限公司 Electromagnetic vibration calculation method and system for stator of hydraulic generator
CN117171493B (en) * 2023-11-01 2024-03-01 华能澜沧江水电股份有限公司 Electromagnetic vibration calculation method and system for stator of hydraulic generator

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