Novel alternating current motor pulsating magnetic potential harmonic wave analysis method

Abstract

The invention relates to a novel alternating current motor pulsating magnetic potential harmonic wave analysis method, which comprises the following steps of: defining an anti-clockwise direction of an air gap circumference as a positive direction of x, and expanding the air gap circumference along the anti-clockwise direction, so that the distribution of magnetic potential in the air gap circumference along the positive direction of x at a certain moment t accords with a cosx distribution rule; analyzing the magnetic potential of the single-phase integral pitch winding at the offset x; and solving a resultant magnetic field when each winding symmetrically shifts x. Mathematical analysis is simple and clear, graphical analysis is visual and easy to understand, firstly phasor decomposition is performed on fundamental wave components of pulsating magnetic potential based on a circuit theory, the phasor decomposition is simple, clear and easy to understand and master, the defects and ambiguity of related content in classical electromechanics are overcome, and the phasor decomposition can be used as a theoretical basis for subsequent analysis of a rotating magnetic field generation mechanism.

Description

Technical Field

[0001] The invention relates to the technical field of AC motors, and in particular to a novel method for analyzing harmonics of pulse magnetic potential of an AC motor. Background Art

[0002] Analysis of the magnetic potential of single-phase windings is the basis for studying the magnetic potential of three-phase AC motors. Single-phase full-pitch coil windings generate a pulsating magnetic potential distributed in a rectangular shape along the circumference of the air gap, such as Figure 1 shown.

[0003] Where x is the counterclockwise expansion of the air gap circumference, That is, at a fixed time t, the magnetic potential distribution along the circumference of the air gap in the counterclockwise direction is: the period is 2π and the height is Rectangular magnetic potential (time t is fixed, position x changes); at any fixed position x on the air gap circle, the variation law of magnetic potential is So, f p is a function of both x and ω.

[0004] f p (x, ω) is expanded by Fourier to obtain:

[0005] f p (x, ωt) = F p cosωt=f p1 +f p3 +f p5 +….

[0006] See Figure 2 Among them, f p1 =F p1 cosx cosωt is the fundamental wave, f p3 =F p3 cos3x cosωt、f p5 =F p5 cos5xcosωt, ... are the 3rd, 5th, ... harmonics respectively, F p1 =0.9N p I,

[0007] The following only uses the fundamental wave as an example to illustrate the deficiencies or ambiguities of the analysis methods in classical electrical engineering.

[0008] In classical electromechanics, the fundamental magnetic potential f p1 =F p1 The analysis of cos x cos ωt is as follows.

[0009] First, f p1 =F p1 The mathematical decomposition of cos x cosωt is as follows:

[0010]

[0011] And define So f p1 Can be decomposed into and Two parts, namely

[0012]

[0013] is a moving wave, the trajectory of its highest point is x-ωt=0, such as Figure 3 , that is, this is a rotating wave that rotates (transmits) counterclockwise along the circumference of the motor air gap, and the angular velocity of rotation is ω; similarly, It is also a motion wave, and the trajectory of its highest point is x+ωt=0, that is, it is a rotating wave that rotates (transmits) clockwise along the circumference of the motor air gap, and the rotation angular velocity is -ω.

[0014] This mathematical analysis method of fundamental wave magnetic potential is not easy to understand for electrical engineering students who do not have a theoretical foundation in wave transmission.

[0015] Another graphical analysis method given in classical electrical engineering is to use Directly diagram Figure 4 (a) Graphic Figure 4 (b).

[0016] This graphical analysis of the fundamental magnetic potential The -ω in the figure is a vector rotating counterclockwise. The +ω diagram in the figure shows a clockwise rotating vector, which is inconsistent with circuit theory. Summary of the invention

[0017] The purpose of the present invention is to provide a novel method for analyzing harmonics of pulse magnetic potential of an AC motor, the mathematical analysis of which is simple and clear, and the graphical analysis is intuitive and easy to understand.

[0018] To achieve the above-mentioned purpose, a novel AC motor pulse magnetic potential harmonic analysis method of the present invention comprises the following steps:

[0019] S1. Define the counterclockwise direction of the air gap circle as the positive direction of x, and expand the air gap circle in the counterclockwise direction. Then the distribution of the magnetic potential along the positive direction of x in the air gap circle at a certain time t conforms to the cos x distribution law;

[0020] S2, analyzing the magnetic potential of the single-phase full-pitch winding at the offset x;

[0021] S3. Assumptions

[0022] iA =I m cosωt

[0023] i B =I m cos(ωt-120°)

[0024] i c =I m cos(ωt-240°)

[0025] but

[0026] B A =B m cosωt

[0027] B B =B m cos(ωt-120°)

[0028] B c =B m cos(ωt-240°)

[0029] Find the resultant magnetic field when each winding is symmetrically offset by x.

[0030] Specifically, in step S1, since i=I m cosωt, so at a fixed position x on the circumference of the air gap, f p1 =F p1 cos x cos ωt.

[0031] Specifically, in step S2, for a single-phase full-pitch winding, f p1 =F p1 cosωt cos x, in the complex coordinate system, is equivalent to the length F on the real axis p1 cosωt is the vector of cos x, and at the offset x

[0032]

[0033] in,

[0034]

[0035]

[0036] That is, at any time t at offset x, f p1 This is equivalent to starting from the vector e jx Starting from, the length of the clockwise rotation at angular velocity ω is The rotation vector With from vector e jx The length of the counterclockwise rotation at the angular velocity ω is The rotation vector The vector sum of .

[0037] Specifically, in step S3, for phase A, B A =B m cosωt cos x, in the complex coordinate system, is equivalent to the length B on the real axis m cosωtcos x is the vector of x, and at the offset x;

[0038]

[0039] in,

[0040]

[0041]

[0042] That is, at any time t at offset x, B A This is equivalent to starting from the vector e jx Starting from, the length of the clockwise rotation at angular velocity ω is The rotation vector With from vector e jx The length of the counterclockwise rotation at the angular velocity ω is The rotation vector The vector sum of .

[0043] Further, in step S3, for phase B, B B =B m cos(ωt-120°)cos x, in the complex coordinate system, is equivalent to being located at e j(x-120°) Position and length are B m cos(ωt-120°)cos x is the vector of x, while at the offset x;

[0044]

[0045] in,

[0046]

[0047]

[0048] That is, at any time t at offset x, This is equivalent to starting from the vector e jx , the length of the clockwise rotation at the angular velocity ω is The rotation vector With from vector e j(x+120°) The length of the counterclockwise rotation at the angular velocity ω is The rotation vector The vector sum of .

[0049] Furthermore, for phase C, B C =B m cos(ωt-240°)cos x, in the complex coordinate system, is equivalent to being located at the vector e j(x-240°) Position and length are B m cos(ωt-240°)cos x is the vector of x, while at the offset x;

[0050]

[0051] in,

[0052]

[0053]

[0054] That is, at any time t at offset x, This is equivalent to starting from the vector e jx Starting from, the length of the clockwise rotation at angular velocity ω is The rotation vector With from vector e j(x-120°) Starting from, the length of the counterclockwise rotation at angular velocity ω is The rotation vector The vector sum of

[0055] The synthetic magnetic field is:

[0056]

[0057] Furthermore, the resultant magnetic field when the three-phase windings are symmetrically offset by x is given by the vector e jx Start, rotate clockwise with angular velocity ω, magnitude 1.5B m The rotating magnetic field of cos x, that is, the synthetic magnetic field, is a cosine wave that moves forward clockwise at an angular velocity ω.

[0058] The novel AC motor pulsating magnetic potential harmonic analysis method provided by the present invention has the following advantages compared with the prior art:

[0059] (1) First, the fundamental component of the pulsating magnetic potential is decomposed into phase components based on circuit theory. This is simple and easy to understand and master, which solves the shortcomings and ambiguities of related content in classical electrical machinery and can serve as a theoretical basis for subsequent analysis of the generation mechanism of the rotating magnetic field.

[0060] (2) The mathematical analysis is simple and clear, and the graphical analysis is intuitive and easy to understand. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1A pulsating magnetomotive force diagram with rectangular distribution along the circumference of the air gap is generated for the single-phase full-pitch coil winding in the background technology;

[0062] Figure 2 It is a schematic diagram in the background technology;

[0063] Figure 3 It is a schematic diagram in the background technology;

[0064] Figure 4 (a) is a schematic diagram of the background technology;

[0065] Figure 4 (b) is a schematic diagram of the background technology;

[0066] Figure 5 (a) is a schematic diagram of this embodiment;

[0067] Figure 5 (b) is a schematic diagram of this embodiment;

[0068] Figure 6 Schematic diagram of magnetic potential distribution of single-phase full-pitch winding in this embodiment;

[0069] Figure 7 is a distribution diagram of the magnetic potential in the present embodiment along the positive x direction in the air gap circumference at a certain time t;

[0070] Figure 8 Schematic diagram of magnetic potential of a single-phase full-pitch winding at an offset x in this embodiment;

[0071] Fig. 9 Schematic diagram of a three-phase AC asynchronous motor in this embodiment. DETAILED DESCRIPTION

[0072] The present invention is further described below in conjunction with specific embodiments.

[0073] Example 1

[0074] The present invention proposes a new harmonic analysis method for the pulse magnetic potential of an AC motor. The mathematical analysis is simple and clear, and the graphical analysis is intuitive and easy to understand. The specific technical solution is (taking the fundamental magnetic potential as an example):

[0075] 1. Mathematical analysis method

[0076]

[0077] definition So f p1 Can be decomposed into and Two parts, namely

[0078]

[0079] According to circuit theory, it is clear that The amplitude is A vector that rotates at an angular velocity ω (i.e., counterclockwise) along the circumference of the motor air gap, The amplitude is A vector that rotates at an angular velocity of -ω (i.e., clockwise) along the circumference of the motor air gap.

[0080] 2. Graphical analysis method

[0081] Here is still Directly diagram Figure 5 (a) Graphic Figure 5 (b) but The vector represented is no longer the vector in classical electrical engineering.

[0082] The schematic diagram of magnetic potential distribution of single-phase full-pitch winding is as follows Figure 6 shown.

[0083] Define the counterclockwise direction of the air gap circumference as the positive direction of x, and expand the air gap circumference in the counterclockwise direction. Then the distribution of the magnetic potential along the positive direction of x in the air gap circumference at a certain time t is as follows: Figure 7 As shown, it conforms to the cos x distribution law. Since i = I m cosωt, so at a fixed position x on the circumference of the air gap, f p1 =f p1 cos x cos ωt.

[0084] Now analyze the magnetic potential of the single-phase full-pitch winding at the offset x, as Figure 8 shown.

[0085] For a single-phase full-pitch winding, f p1 =F p1 cosωtcos x, in the complex coordinate system, is equivalent to the length F on the real axis p1 cosωt is the vector of cos x, and at the offset x

[0086]

[0087] in,

[0088]

[0089]

[0090] That is, at any time t at offset x, f p1 This is equivalent to starting from the vector e jx Starting from, the length of the clockwise rotation at angular velocity ω is The rotation vector With from vector e jx The length of the counterclockwise rotation at the angular velocity ω is The rotation vector The vector sum of .

[0091] The above method is used to analyze the generation mechanism of the rotating magnetic field of the three-phase AC asynchronous motor, which is simple and clear and easy to understand and master. Fig. 9 Assume

[0092] i A =I m cosωt

[0093] i B =I m cos(ωt-120°)

[0094] i C =I m cos(ωt-240°)

[0095] but

[0096] B A =B m cosωt

[0097] B B =B m cos(ωt-120°)

[0098] B c =B m cos(ωt-240°)

[0099] Now find the resultant magnetic field when the windings are symmetrically offset by x.

[0100] For phase A, B A =B m cosωt cos x, in the complex coordinate system, is equivalent to the length B on the real axis m cosωtcos x is the vector of x, and at the offset x.

[0101]

[0102] in,

[0103]

[0104]

[0105] That is, at any time t at offset x, This is equivalent to starting from the vector e jx Starting from, the length of the clockwise rotation at angular velocity ω is The rotation vector With from vector e jx The length of the counterclockwise rotation at the angular velocity ω is The rotation vector The vector sum of .

[0106] For phase B, B =B m cos(ωt-120°)cos x, in the complex coordinate system, is equivalent to being located at e j(x-120°) Position and length are B m cos(ωt-120°)cos x is the vector at offset x.

[0107]

[0108]

[0109] in,

[0110]

[0111]

[0112] That is, at any time t at offset x, This is equivalent to starting from the vector e jx , the length of the clockwise rotation at the angular velocity ω is The rotation vector With from vector e j(x+120°) The length of the counterclockwise rotation at the angular velocity ω is The rotation vector The vector sum of .

[0113] For phase C, B c =B m cos(ωt-240°)cos x, in the complex coordinate system, is equivalent to being located at the vector e j(x-240°) Position and length are B m cos(ωt-240°)cos x is the vector at offset x.

[0114]

[0115] in,

[0116]

[0117]

[0118] That is, at any time t at offset x, This is equivalent to starting from the vector e jxStarting from, the length of the clockwise rotation at angular velocity ω is The rotation vector With from vector e j(x-120°) Starting from, the length of the counterclockwise rotation at angular velocity ω is The rotation vector The vector sum of .

[0119] The synthetic magnetic field is:

[0120]

[0121] That is, the resultant magnetic field when the three-phase windings are symmetrically offset by x is jx Start, rotate clockwise with angular velocity ω, magnitude 1.5B m The rotating magnetic field of cos x, that is, the synthetic magnetic field, is a cosine wave that moves forward clockwise at an angular velocity ω.

[0122] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A novel method for analyzing harmonics of pulse magnetic potential of AC motor, characterized in that: The following steps are included: S1. Define the counterclockwise direction of the air gap circumference as the positive direction of x, and expand the air gap circumference in the counterclockwise direction. Then the distribution of the magnetic potential along the positive direction of x in the air gap circumference at a certain time t conforms to the cosx distribution law; S2, analyzing the magnetic potential of the single-phase full-pitch winding at the offset x; S3. Assumptions i A =I m cosωt i B =I m cos(ωt-120°) i c =I m cos(ωt-240°) but B A =B m cosωt B B =B m cos(ωt-120°) B C =B m cos(ωt-240°) Find the resultant magnetic field when each winding is symmetrically offset by x.

2. A novel AC motor pulsating magnetic potential harmonic analysis method according to claim 1, characterized in that: In step S1, since i=I m cosωt, so at a fixed position x on the circumference of the air gap, f p1 =F p1 cosxcosωt。 3. A novel AC motor pulsating magnetic potential harmonic analysis method according to claim 1, characterized in that: In step S2, for a single-phase full-pitch winding, f p1 =F p1 cosωtcosx, in the complex coordinate system, is equivalent to the length F on the real axis p1 cosωtcosx is the vector of the offset x in, That is, at any time t at offset x, f p1 This is equivalent to starting from the vector e jx Starting from, the length of the clockwise rotation at angular velocity ω is The rotation vector With from vector e jx The length of the counterclockwise rotation at the angular velocity ω is The rotation vector The vector sum of .

4. A novel AC motor pulsating magnetic potential harmonic analysis method according to any one of claims 1 to 3, characterized in that: In step S3, for phase A, B A =B m cosωtcosx, in the complex coordinate system, is equivalent to the length B on the real axis m cosωtcosx is the vector of offset x; in, That is, at any time t at offset x, This is equivalent to starting from the vector e jx Starting from, the length of the clockwise rotation at angular velocity ω is The rotation vector With from vector e jx The length of the counterclockwise rotation at the angular velocity ω is The rotation vector The vector sum of .

5. A novel AC motor pulsating magnetic potential harmonic analysis method according to claim 4, characterized in that: In step S3, for phase B, B E =B m cos(ωt-120°)cosx, in the complex coordinate system, is equivalent to being located at e j(x-120°) Position and length are B m The vector of cos(ωt-120°)cosx, while at the offset x; in, That is, at any time t at offset x, This is equivalent to starting from the vector e jx , the length of the clockwise rotation at the angular velocity ω is The rotation vector With from vector e j(x+120°) The length of the counterclockwise rotation at the angular velocity ω is The rotation vector The vector sum of .

6. A novel AC motor pulsating magnetic potential harmonic analysis method according to claim 5, characterized in that: For phase C, B C =B m cos(ωt-240°)cosx, in the complex coordinate system, is equivalent to being located at the vector e j(x-240°) Position and length are B m The vector of cos(ωt-240°)cosx, while at the offset x; in, That is, at any time t at offset x, This is equivalent to starting from the vector e jx Starting from, the length of the clockwise rotation at angular velocity ω is The rotation vector With from vector e j(x-120°) Starting from, the length of the counterclockwise rotation at angular velocity ω is The rotation vector The vector sum of The synthetic magnetic field is:

7. A novel AC motor pulse magnetic potential harmonic analysis method according to claim 6, characterized in that: The resultant magnetic field when the three-phase winding is symmetrically offset by x is given by vector e jx Start, rotate clockwise with angular velocity ω, magnitude 1.5B m The rotating magnetic field of cosx, that is, the synthetic magnetic field, is a cosine wave that moves forward clockwise at an angular velocity ω.

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