A calculation and analysis method for the unbalanced electromagnetic force of an electric motor

Abstract

The present invention discloses a calculation and analysis method for unbalanced electromagnetic force acting on a motor rotor, comprising the following steps: establishing a hybrid eccentricity model, constructing a magnetomotive force and permeability matrix, extracting the unbalanced electromagnetic force, and analyzing the electromagnetic force characteristics, finally obtaining the time-domain signal and frequency spectrum characteristics of the unbalanced electromagnetic force. By applying the calculation and analysis method for unbalanced electromagnetic force of the motor of the present invention, the characteristics of the unbalanced electromagnetic force of the coupling between the motor equipment and the environment can be obtained, which has important theoretical significance for the state diagnosis, fault diagnosis of the motor, and the traceability of the unbalanced electromagnetic force.

Description

Technical Field

[0001] The present invention relates to the field of rotating machinery signal processing, and particularly to a method for calculating and analyzing the unbalanced electromagnetic force of an electric motor. Background Art

[0002] The unbalanced electromagnetic force of an electric motor stems from the asymmetry of the air-gap magnetic density, which is called air-gap eccentricity and can be divided into dynamic eccentricity and static eccentricity. Among them, the rotor position eccentricity caused by factors such as bearing wear, manufacturing tolerances, and misalignment is called static eccentricity; while the eccentricity caused by shaft bending due to mass imbalance or rotor shaft displacement caused by rotational vibration, which makes the rotor rotate around the center of the stator bore, is called dynamic eccentricity. In engineering practice, both types of eccentricity coexist, and this type of eccentricity is called mixed eccentricity. In addition, the electric motor is subject to eccentricity caused by various sources. For example, the relative condition between the rotor and the stator is not fixed axially, so the eccentricity rate change in the axial direction of the electric motor also needs to be considered. And even if the types of eccentricity are the same, the sources causing the eccentricity are not necessarily the same. For example, both shaft bending and shaft vibration can cause dynamic eccentricity. Therefore, establishing a method for calculating and analyzing the unbalanced electromagnetic force is particularly important for the analysis and traceability of the unbalanced electromagnetic force.

[0003] In the process of implementing the present invention, the inventors found that the prior art has at least the following disadvantages and deficiencies:

[0004] Regarding the method for calculating and analyzing the unbalanced electromagnetic force of an electric motor, extensive research has been done by domestic and foreign scholars. The main calculation methods include the Maxwell stress tensor method, the virtual work method, the conformal mapping method, the equivalent circuit method, etc. The virtual work method is mainly applied to the force analysis of local components in finite element analysis; while the Maxwell stress tensor method is the most widely used in analytical calculations, but when using this method for calculation, a series of preconditions often need to be established. For example, the relative condition between the axial rotor and the stator is fixed, and the flatness of the foundation is not considered, etc. Therefore, in actual engineering, the calculation accuracy of the unbalanced electromagnetic force beyond the set conditions is poor, and the existing methods for calculating and analyzing the unbalanced electromagnetic force need to be improved. Summary of the Invention

[0005] The present invention provides a method for calculating and analyzing the electromagnetic force of an unbalanced electric motor. By coupling the eccentricity variables caused by the stator-rotor system of the electric motor and environmental factors, the present invention improves the extraction accuracy of the unbalanced electromagnetic force. The method for calculating and analyzing the electromagnetic force includes the following steps:

[0006] A method for calculating and analyzing an unbalanced electromagnetic force, the method for calculating and analyzing the electromagnetic force includes the following steps:

[0007] Step 1: Establishing a mixed eccentricity model;

[0008] Step 2: Construct the magnetomotive force and permeability matrices;

[0009] Step 3: Extract the unbalanced electromagnetic force;

[0010] Step 4: Analyze the characteristics of the electromagnetic force.

[0011] In Step 1, the method for establishing the hybrid eccentricity model is as follows:

[0012] Step 1-1: Synthesize the influences of dynamic eccentricity and static eccentricity of the air-gap eccentricity to obtain an eccentricity model after the superposition of the two eccentricities;

[0013] Step 1-2: Through the dynamic modeling and analysis of the motor frame and the stator as a whole, solve the vibration angle of the eccentricity model in Step 1-1 to obtain an eccentricity model under the influences of mechanical vibration and base flatness, etc.;

[0014] Step 1-3: Combine the two types of eccentricities in Step 1-1 and Step 1-2 to obtain an eccentricity model of the coupling between the motor equipment and the environment. Through this model, the eccentric conditions in actual engineering can be accurately simulated, and the calculation accuracy of the unbalanced electromagnetic force can be improved.

[0015] In Step 2, the specific process for constructing the magnetomotive force and permeability matrices is as follows:

[0016] Step 2-1: Select the corresponding formula according to the motor type, calculate the rotor and stator magnetomotive forces respectively, obtain the total magnetomotive force inside the air gap, and construct the motor air-gap magnetomotive force matrix;

[0017] Step 2-2: Combine the eccentricity model in Step 1 to construct the permeability matrix under the current eccentricity degree.

[0018] In Step 3, the method for extracting the unbalanced electromagnetic force is as follows:

[0019] Step 3-1: According to the magnetomotive force matrix and permeability matrix obtained in Step 2, multiply each element to obtain the axial micro-element air-gap magnetic density matrix;

[0020] Step 3-2: According to the micro-element air-gap magnetic density matrix obtained in Step 3, use the Maxwell stress tensor method to integrate the electromagnetic force density of the micro-element plane, so as to obtain the unbalanced electromagnetic force varying with time under the micro-element eccentricity model; when the relative conditions between the rotor and the stator change and the micro-element eccentricity model in the axial direction of the motor is no longer the same, repeat the operations in Steps 1 to 3, and accumulate the micro-element electromagnetic forces under different eccentricities in the axial direction of the motor. Finally, the unbalanced electromagnetic force in the radial direction of the entire motor is obtained.

[0021] In Step 4, the specific process for the analysis of the electromagnetic force characteristics is as follows: Perform Fourier transform spectrum analysis on the unbalanced electromagnetic force signal obtained in Step 3.

[0022] The beneficial effects of the technical solution provided by the present invention are as follows: The present invention realizes the extraction of the unbalanced electromagnetic force of the motor under the hybrid eccentricity condition, solves the accurate calculation of the unbalanced electromagnetic force under complex conditions such as hybrid eccentricity and shaft bending in engineering, and has important theoretical and engineering value for the analysis of motor vibration noise reduction. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic diagram of a method for calculating and analyzing the unbalanced electromagnetic force of a motor proposed by the present invention;

[0024] Figure 2 It is a schematic diagram of a hybrid eccentricity model;

[0025] Figure 3 It is a schematic diagram of a hybrid eccentricity model inside the motor;

[0026] Figure 4 It is a schematic diagram of an eccentricity model caused by the vibration of the frame structure;

[0027] Figure 5 It is a schematic diagram of a hybrid eccentricity permanent magnet synchronous motor model in an embodiment;

[0028] Figure 6 It is a schematic diagram of the result of the extracted micro-element unbalanced electromagnetic force;

[0029] Figure 7 It is a schematic diagram of the result of the extraction of the unbalanced electromagnetic force characteristics;

[0030] In the figure, 1. Rotor, 2. Stator, 3. Permanent magnet. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] To make the objectives, technical solutions, and advantages of the present invention clearer, the following further describes the embodiments of the present invention in detail.

[0032] In response to the problems in the background art, the present invention proposes a method for calculating and analyzing the unbalanced electromagnetic force of a motor. The present invention realizes the calculation and analysis of the unbalanced electromagnetic force of the motor, and solves the problem of calculating and analyzing the unbalanced electromagnetic force caused by various factors in engineering practice. See the following description for details.

[0033] S01, Establish a hybrid eccentricity model.

[0034] For motors in actual engineering, various forms of eccentricity coexist. Considering both dynamic eccentricity and static eccentricity, this method establishes a hybrid eccentricity model that comprehensively considers the coupling between the motor and the environment. In this demonstration, a hybrid eccentricity permanent magnet synchronous motor model is used (as shown in Figure 5 ), and according to the internal hybrid eccentricity of the motor, an internal hybrid eccentricity model of the motor can be established (as shown in Figure 2 , Figure 3As shown in the figure, the obtained mathematical model is as follows:

[0035]

[0036] Through dynamic modeling, the vibration angle θ of the motor frame frame (t) can be solved, and an eccentric model of the motor frame structure is established (as Figure 4 shown in the figure), and the obtained mathematical model is as follows:

[0037]

[0038] By combining the two eccentric models, the eccentric model of the coupling between the motor equipment and the environment is obtained as follows:

[0039]

[0040] In the formula, e cp , e st , e dy , e frame are the eccentricity of the coupling between the motor equipment and the environment, the static eccentricity, the dynamic eccentricity, and the eccentricity of the motor frame caused by mechanical vibration respectively; the horizontal and vertical displacements caused by the motor vibration are x frame , y frame respectively, and the azimuth angles corresponding to the internal eccentricity of the motor are θ st , θ dy ; the deflection angles of the motor frame in the horizontal and vertical directions caused by vibration are θ frame,x , θ frame,y .

[0041] S02, construct the magnetomotive force and magnetic permeability matrix.

[0042] The air-gap magnetomotive force of the motor is jointly determined by the rotor and the stator. Since the calculation methods of the magnetomotive forces of various motors are different, taking the permanent magnet synchronous motor as an example (as Figure 5 shown in the figure), its air-gap magnetomotive force is as follows:

[0043]

[0044] In the formula, F PMSM is the air-gap magnetomotive force of the permanent magnet synchronous motor; F sm , F rm are the magnetomotive force generated by the stator of the motor and the magnetomotive force generated by the rotor respectively; is the power factor angle; ω is the electrical angular velocity; p is the number of pole pairs.

[0045] The air-gap magnetic permeability is jointly determined by the air-gap medium and the actual air-gap length. In this embodiment, the air-gap medium is air, and the actual air-gap length is determined by the eccentric model. The relational expression of the air-gap magnetic permeability can be obtained as follows:

[0046]

[0047] In the formula, Λ is the air-gap magnetic permeability; μ 0 is the magnetic permeability of the air-gap medium; δ is the actual air-gap length; since the circumferential actual air-gap lengths are not the same, the air-gap magnetic permeability matrix is defined as ΛM.

[0048] Furthermore, the magnetomotive force and magnetic permeability at each time and each space inside the motor air-gap are obtained, and their cumulant matrices are constructed respectively as follows:

[0049]

[0050] In the formula, FM MMF is the total magnetomotive force matrix of n×m; ΛM is the air-gap magnetic permeability matrix of n×m; α 1 , α 2 , …, α n are the azimuth angles of the points inside the positioning air-gap; t 1 , t 2 , …, t n are the times.

[0051] S03, Unbalanced electromagnetic force extraction.

[0052] According to the magnetomotive force cumulant matrix and magnetic permeability cumulant matrix extracted in S02, multiplying element by element can obtain the air-gap magnetic flux density matrix BM as follows:

[0053]

[0054] In the formula, BM is the air-gap magnetic flux density matrix of the micro-element surface; Λ(α i , t j ), F(α i , t j ) are the magnetic permeability and magnetomotive force at the air-gap at the angle α j at the time t i .

[0055] According to the extracted air-gap magnetic flux density cumulant matrix of the micro-element surface, using Maxwell stress tensor analysis, the horizontal and vertical components of the unbalanced electromagnetic force on the micro-element surface are obtained as follows.

[0056]

[0057] In the formula, the horizontal and vertical components of the axial micro-element unbalanced electromagnetic force are respectively f ump,x , f ump,y ; B is the air-gap magnetic flux density; r i is the direction angle of α iThe air-gap radius above. According to the change in the axial stator-rotor relationship caused by the shaft bending in this embodiment, return to S01, continue to solve the electromagnetic force on the next axial micro-element, and finally accumulate the unbalanced electromagnetic forces on each micro-element length. The results are as follows:

[0058]

[0059] In the formula, the horizontal and vertical components of the motor unbalanced electromagnetic force are F ump,x , F ump,y ; l j is the axial length of the j-th micro-element.

[0060] S04, Electromagnetic force characteristic analysis.

[0061] Based on the unbalanced electromagnetic force signal obtained in S03, draw the time-domain signal (as shown in Figure 6 ), and perform Fourier transform spectrum analysis on the electromagnetic force signal (as shown in Figure 7 ).

[0062] In summary, by using the hybrid eccentricity model iteration to calculate and analyze the unbalanced electromagnetic force under complex eccentricity faults, the problem of poor accuracy in extracting the characteristics of the unbalanced electromagnetic force signal in engineering is overcome. Therefore, the calculation and analysis method of the motor unbalanced electromagnetic force adopted by the present invention can obtain a better extraction effect.

[0063] Those skilled in the art can understand that the drawings are only schematic diagrams of a preferred embodiment, and the serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0064] The above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A calculation and analysis method for the unbalanced electromagnetic force of an electric motor, characterized in that, the calculation of the electromagnetic force includes the following steps: Step 1: Establish a hybrid eccentricity model; The method for establishing the model in Step 1 is to extract the relative eccentricity of each point inside the air gap. The specific process for extracting the relative eccentricity of each point inside the air gap is as follows: Step 1-1: For the hybrid eccentricity caused by the relative relationship between the stator and rotor inside the motor, the established mathematical model is as follows: where e mix , e st , e dy are the combined eccentricity, static eccentricity, and dynamic eccentricity, respectively; the azimuth angles corresponding to the eccentricities are θ mix , θ st , θ dy ; Step 1-2: For the eccentricity caused by the stator displacement generated by the motor vibration, the established mathematical model is as follows: where, e frame is the eccentricity of the motor frame caused by mechanical vibration; l part is the axial length of the vibrating part of the motor frame; the horizontal and vertical displacements caused by the motor vibration are x frame , y frame , and the deflection angles of the motor frame in the horizontal and vertical directions caused by the vibration are θ frame，x , θ frame，y ; Step 1-3: Combine the two eccentricity models in Step 1-1 and Step 1-2 to obtain the eccentricity model of the coupling between the motor equipment and the environment as follows: where, e cp is the eccentricity of the coupling between the motor equipment and the environment; Step 2: Construct the magnetomotive force and permeability matrix; The specific process of Step 2 is as follows: Step 2-1: Solve the magnetomotive force and magnetic permeability according to the relative eccentricity in Step 1, and define the total magnetomotive force matrix under the action of the rotor and stator as FM MMF , and the constructed magnetomotive force matrix is as follows: where, FM MMF is the total magnetomotive force matrix of n×m, α 1 , α 2 , …, α n are the angles of the positions of the points in the positioning air gap, t 1 , t 2 , …, t n are the times; Step 2-2: According to the eccentricity model established in Step 1, obtain the actual length of the air gap, determine the air-gap permeability matrix ΛM, and the constructed permeability matrix is: In the formula, ΛM is an n×m air-gap permeability matrix; Step 3: Extract the unbalanced electromagnetic force; The specific process of Step 3 is as follows: Step 3-1: According to the total magnetomotive force matrix FM in Step 2 MMF , and the air-gap permeability matrix ΛM, multiplying element by element can obtain the air-gap magnetic flux density matrix BM: In the formula, BM is an n×m air-gap magnetic flux density matrix; Step 3-2: According to the differential air-gap magnetic flux density matrix in Step 3-1, the horizontal and vertical components of the unbalanced electromagnetic force of the jth differential element can be obtained by using the Maxwell stress tensor method. Superimpose the axial-section differential element electromagnetic forces with different hybrid eccentricities caused by the change of the relative conditions between the stator and rotor. The unbalanced electromagnetic force of the whole motor is as follows: In the formula, the horizontal and vertical components of the unbalanced electromagnetic force of the motor are F ump,x , F ump,y ; B(α i , t) is the air-gap magnetic density at a certain moment; r i is the air-gap radius at the direction angle α i ; l j is the axial length of the j-th microelement; Step 4: Analyze the characteristics of the electromagnetic force; The specific process of Step 4 is as follows: According to the unbalanced electromagnetic force signal obtained in Step 3, its time-domain waveform can be plotted, and the spectral analysis of the unbalanced electromagnetic force signal can be realized through Fourier transform.

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