A method for calculating performance of a squirrel cage induction motor based on a magnetic induction modulator

Abstract

This invention discloses a method for calculating the performance of a squirrel-cage induction motor based on a magnetic modulator, comprising: 1. calculating the spatial distribution function of the magnetic field of the squirrel-cage winding in the target squirrel-cage induction motor; 2. calculating the modulation air gap magnetomotive force; 3. calculating the magnetic field conversion coefficient C based on the modulation air gap magnetomotive force. vp This invention investigates the impact of phase shift and the specifications of the target squirrel-cage induction motor on motor performance. Based on magnetic field parameters, a modulation operator for the squirrel-cage induction motor is derived, facilitating a more intuitive understanding of the motor's operating principle. Simultaneously, it helps in studying the influence of changes in the structural parameters of the magnetic modulator on motor performance.

Description

Technical Field

[0001] This invention belongs to the field of motors and electrical appliances, and particularly relates to a method for calculating the performance of a squirrel-cage induction motor based on a magnetic modulator. Background Technology

[0002] According to the existing unified theory of air gap magnetic field modulation in motors, squirrel-cage induction motors achieve energy conversion through a short-circuit coil modulator. However, due to the lack of magnetic circuit parameters to understand the magnetic field modulation behavior in the short-circuit coil modulator, the air gap magnetomotive force generated on the rotor side is indirectly calculated by multiplying the winding function by the induced current. Therefore, the working principle of the short-circuit coil modulator cannot be directly understood from the perspective of the magnetic field. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a method for calculating the performance of a squirrel-cage induction motor based on a magnetic modulator. By equating the squirrel-cage winding of the motor to a magnetic modulator, the method directly analyzes the influence of the parameters of the magnetic modulator on the motor performance. In addition to calculating known amplitude modulation, this method can also calculate the phase shift unique to induction motors.

[0004] Technical solution: The present invention provides a method for calculating the performance of a squirrel-cage induction motor based on a magnetic modulator, comprising the following steps:

[0005] Step 1: Determine the specifications of the target squirrel-cage induction motor and the amplitude of a single magnetic modulator. And through specifications and amplitude Calculate the spatial distribution function of magnetic flux in the squirrel cage winding of the target squirrel cage induction motor.

[0006] Step 2: Determine the source air gap magnetomotive force f(φ,t) established by the stator winding and the permeability λ of the salient pole of the squirrel-cage induction motor rotor. RT (φ), and through the source air gap magnetomotive force f(φ,t) and the permeability function λ RT (φ) Calculate the modulation operator of the magnetic modulator, and obtain the modulated air gap magnetomotive force after modulation by the magnetic modulator;

[0007] Step 3: Calculate the magnetic field conversion coefficient C based on the modulated air gap magnetomotive force. vp and phase shift And the impact of the specifications of the target squirrel-cage induction motor on the motor performance.

[0008] Furthermore, in step 1, the spatial distribution function of the magnetic field of the squirrel cage winding in the target squirrel cage induction motor is... The calculation method is as follows:

[0009]

[0010] Where φ is the spatial electrical angle; N SC This represents the number of conductor bars per pair of pole cages on the rotor; Let C be the spatial distribution of the x-th magnetic modulator, occupying a range of C. Sx =[(x–1)2π / N SC –γ i π / p,(x–1)2π / N SC +γ i π / p], x = 1, 2, 3, ..., N SC p represents the number of pole pairs in the stator winding of the squirrel-cage induction motor; γ i The pitch of a single magnetic modulator; For the magnitude of the magnetic field of a single magnetic modulator, we have:

[0011]

[0012] Where N2 is the number of turns of the squirrel cage conductor bar; s is the slip of the squirrel cage induction motor; ω1 is the synchronous angular velocity of the source air gap magnetomotive force established by the stator winding of the squirrel cage induction motor; R2 and L2 are the equivalent resistance and equivalent inductance corresponding to a single squirrel cage conductor bar, respectively.

[0013]

[0014] Among them, R b With L b These represent the actual resistance and actual inductance of a single squirrel cage bar, respectively; R′ e With L′ e These are the equivalent resistance and equivalent inductance of the connecting end ring between two adjacent squirrel cage bars, respectively, and the calculation formula is as follows:

[0015]

[0016] Among them, R e With L e These represent the actual resistance and actual inductance of the connecting ring between two adjacent cage bars, respectively.

[0017] Furthermore, in step 1, the specifications of the target squirrel-cage induction motor include the number of squirrel-cage rotor bars, the material used, the embedding depth, the number of stator slots, the pitch of the magnetic modulator, the number of stator winding pole pairs, the slip, the number of series turns per phase of the winding, the stator outer radius, the stator inner radius, the rotor outer radius, the rotor inner radius, the air gap length, the motor stacking length, and the synchronous angular velocity.

[0018] Furthermore, step 2 specifically involves:

[0019] The modulation operator of the magnetic modulator is:

[0020]

[0021] Where f(φ,t) is the source air gap magnetomotive force established by the stator winding; λ RT (φ) is the magnetic permeability function of the salient pole of the rotor of the squirrel-cage induction motor; And λ are respectively and λ RT The amplitude of (φ), after being modulated by the magnetic induction modulator in the motor, yields the modulated air gap magnetomotive force as follows:

[0022]

[0023] Where F1 is the amplitude of the source air gap magnetomotive force f(φ,t) established by the stator side winding; C vp C sum and C dif p-pole, (lN) SC -p) polar and (lN SC +p) The magnetic field conversion coefficients of the poles are respectively:

[0024]

[0025]

[0026]

[0027] Furthermore, in step 3, the magnetic field conversion coefficient C vp for:

[0028]

[0029] Phase shift for:

[0030]

[0031] Furthermore, by equating the squirrel-cage winding of the motor to a magnetic modulator, the influence of the magnetic modulator's parameters on the performance of the squirrel-cage induction motor is directly analyzed using magnetic induction elements. Based on the mathematical expression of magnetic induction, the effects of the number of conductor bars, the materials used, and the embedding depth on the motor performance of the squirrel-cage induction motor can be obtained.

[0032] Furthermore, the motor performance includes air gap magnetic flux density, winding flux linkage, winding inductance, and average torque.

[0033] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0034] Based on the concept of magnetic sensing elements, this invention proposes a method for calculating the performance of a squirrel-cage induction motor based on a magnetic sensing modulator.

[0035] This invention derives a modulation operator for a squirrel-cage induction motor based on magnetic field parameters, which is beneficial for intuitively understanding the working principle of the motor.

[0036] This invention can help study the impact of changes in the structural parameters of a magnetic modulator on motor performance;

[0037] This invention effectively illustrates the vector modulation unique to magnetic modulators, enabling not only accurate calculation of motor performance but also simultaneous study of amplitude modulation and phase shift in squirrel-cage induction motors. Attached Figure Description

[0038] Figure 1 This is an analysis of the magnetic field modulation behavior of a magnetic modulator for a squirrel-cage induction motor.

[0039] Figure 2 This is a flowchart illustrating the implementation steps of the calculation method proposed in this invention;

[0040] Figure 3 This is the physical topology diagram of a cage rotor;

[0041] Figure 4 This is the equivalent topology diagram of a cage rotor;

[0042] Figure 5 This is a spatial distribution diagram of the magnetic field of the squirrel cage winding;

[0043] Figure 6 The magnetic field conversion coefficient C is calculated based on the method proposed in this invention. vp and phase shift Curve showing the variation in the number of rotor bars;

[0044] Figure 7 This is a comparison chart of the calculation results of the effect of the number of rotor bars on torque performance based on the method proposed in this invention and the finite element method;

[0045] Figure 8 The magnetic field conversion coefficient C is calculated based on the method proposed in this invention. vp and phase shift Curve relating to the variation of radial depth of rotor bars;

[0046] Figure 9 This is a comparison chart of the calculation results of the influence of rotor guide bar radial depth on torque performance based on the method proposed in this invention and the finite element method;

[0047] Figure 10 It is the magnetic field conversion coefficient C throughout the entire slip range. vp and phase shift Change curve;

[0048] Figure 11 This is a comparison chart of the electromagnetic torque calculation results over the entire slip range;

[0049] Figure 12 These are the topology parameters on the rotor side. Detailed Implementation

[0050] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0051] The invention will be further described below with reference to the accompanying drawings. This invention proposes a method for calculating the performance of a squirrel-cage induction motor based on a magnetic modulator. The modulation behavior of the magnetic modulator in the squirrel-cage induction motor is analyzed as follows: Figure 1 As shown in Table 1, the specifications of the squirrel-cage induction motor in this embodiment are shown in Table 1. The implementation steps of the performance calculation method for a squirrel-cage induction motor based on a magnetic modulator proposed in this invention are as follows: Figure 2 As shown, the specific description is as follows:

[0052] Table 1 Specifications of Squirrel-Cage Induction Motors

[0053]

[0054]

[0055] Step 1: Calculate the mathematical expression for magnetic induction:

[0056] Figure 3 The diagram shows the topology of a cage rotor. Where R... b L b and I b These represent the actual resistance, actual inductance, and actual current flowing through a single squirrel cage bar, respectively; R e L e and I e These represent the actual resistance, actual inductance, and actual current flowing through the connecting ring between two adjacent squirrel-cage bars. The rotor-side topology parameters of the squirrel-cage induction motor in this implementation example are shown below. Figure 12 .

[0057] To account for the influence of the current on the common end ring on the air gap magnetic field, the cage rotor is equivalent to, for example, Figure 4 As shown. Where, I′ e R′ is the equivalent current on the connecting ring between two adjacent squirrel cage bars; e With L′ e These are the equivalent resistance and equivalent inductance of the connecting end ring between two adjacent squirrel cage bars, respectively, and the calculation formula is as follows:

[0058]

[0059] Where, N SC denoted by , where is the number of conductor bars per pole pair in the squirrel cage on the rotor; p is the number of pole pairs in the stator winding of the squirrel cage induction motor.

[0060] The equivalent resistance R2 and equivalent inductance L2 of a single squirrel cage conductor are:

[0061]

[0062] Amplitude of a single magnetic modulator for:

[0063]

[0064] Where N2 is the number of turns of the squirrel cage conductor bar; s is the slip of the squirrel cage induction motor; and ω1 is the synchronous angular velocity of the source air gap magnetomotive force established by the stator winding of the squirrel cage induction motor.

[0065] Spatial distribution function of magnetic field of squirrel cage winding for:

[0066]

[0067] Where φ is the spatial electrical angle; Let C be the spatial distribution of the x-th magnetic modulator, occupying a range of C. Sx =[(x–1)2π / N SC –γ i π / p,(x–1)2π / N SC +γ i π / p], x = 1, 2, 3, ..., N SC ;γ i The pitch of a single magnetic modulator.

[0068] Based on the above, based on N SC =26, calculated as R b It is 0.154mΩ, R e It is 0.184mΩ, R′ e It is 3.2mΩ. 38.57Ω -1 The resulting spatial distribution of magnetic flux density in the squirrel-cage winding is as follows: Figure 5 As shown, with N SC Taking N = 6, 18, and 26 as examples, it can be seen that the peak value and sinusoidal intensity of the distribution function of the magnetic modulator increase with N. SC The increase in N indicates that the increase in N... SC The quantity is beneficial to improving the performance of squirrel-cage induction motors.

[0069] Step 2: Calculate the modulated air gap magnetomotive force:

[0070] The modulation operator of the magnetic modulator is:

[0071]

[0072] Where f(φ,t) is the source air gap magnetomotive force established by the stator winding; λ RT (φ) is the magnetic permeability function of the salient pole of the rotor of the squirrel-cage induction motor; And λ are respectively and λ RT The amplitude of (φ).

[0073] In this implementation example, f(φ,t) is represented as:

[0074]

[0075] Where F1 is the amplitude of the source air gap magnetomotive force f(φ,t) established by the stator winding; m1 is the number of phases of the stator winding; k w I is the stator winding coefficient; m Current is passed through the stator winding.

[0076] In this implementation case, λ RT (φ) is represented as:

[0077]

[0078] Where μ0 is the vacuum permeability; g is the air gap length.

[0079] After modulation by the magnetic induction modulator in the motor, the modulated air gap magnetomotive force is:

[0080]

[0081] Among them, C vp C sum and C dif p-pole, (lN) SC -p) polar and (lN SC +p) The magnetic field conversion coefficients of the poles are respectively:

[0082]

[0083]

[0084]

[0085] The amplitude modulation of p under the pole is determined by the magnetic field conversion coefficient C. vp This indicates phase shift. for:

[0086]

[0087] Step 3: Calculate the performance of the squirrel-cage induction motor:

[0088] Based on the modulated air gap magnetomotive force obtained in step 2, the motor performance can be analyzed and calculated. In this implementation case, taking electromagnetic torque as an example, the corresponding calculation formula is as follows:

[0089]

[0090] Where, r g Where is the air gap radius.

[0091] Based on the above formula, the performance of the squirrel-cage induction motor was calculated, and the results are shown in Table 2. Figure 6 – Figure 11 As shown, by utilizing the concept of magnetic induction elements, the influence of the magnetic modulator parameters on motor performance can be directly analyzed, and the calculation results of the method proposed in this invention are accurate. It should also be noted that the magnetic field conversion coefficient C... vp and phase shift All of these factors will affect the performance of the motor and cannot be ignored in the performance calculation of squirrel-cage induction motors.

[0092] Table 2 Comparison of calculation results when using different materials for the squirrel cage rotor.

[0093]

Claims

1. A method for calculating the performance of a squirrel-cage induction motor based on a magnetic modulator, characterized in that, Includes the following steps: Step 1: Determine the specifications of the target squirrel-cage induction motor and the amplitude of a single magnetic modulator. And through specifications and amplitude Calculate the spatial distribution function of magnetic flux in the squirrel cage winding of the target squirrel cage induction motor. ; In step 1, the spatial distribution function of the magnetic field of the squirrel cage winding in the target squirrel cage induction motor. The calculation method is as follows: ； in, N is the electrical angle in space. SC This represents the number of conductor bars per pair of pole cages on the rotor; Let C be the spatial distribution of the x-th magnetic modulator, occupying a range of C. Sx =[(x–1)2π / N SC –γ i π / p, (x–1)2π / N SC +γ i π / p], x=1, 2, 3, …, N SC p represents the number of pole pairs in the stator winding of the squirrel-cage induction motor; γ i The pitch of a single magnetic modulator; For the magnitude of the magnetic field of a single magnetic modulator, we have: ； Where N2 is the number of turns of the squirrel cage conductor bar; s is the slip of the squirrel cage induction motor; ω1 is the synchronous angular velocity of the source air gap magnetomotive force established by the stator winding of the squirrel cage induction motor; R2 and L2 are the equivalent resistance and equivalent inductance corresponding to a single squirrel cage conductor bar, respectively. ； wherein R b and L b are the actual resistance and inductance of a single squirrel cage bar; R′ e and L′ e are the equivalent resistance and inductance of the connection ring between two adjacent squirrel cage bars, and the calculation formula is: ； Among them, R e With L e These are the actual resistance and actual inductance of the connecting ring between two adjacent cage bars, respectively. Step 2: Determine the source air gap magnetomotive force established by the stator winding. The magnetic permeability of the rotor salient pole of a squirrel-cage induction motor And through the source air gap magnetomotive force and magnetic permeability Calculate the modulation operator of the magnetic modulator, and obtain the modulated air gap magnetomotive force after modulation by the magnetic modulator; Step 3: Calculate the magnetic field conversion coefficient C based on the modulated air gap magnetomotive force. vp The influence of phase offset φ and the specifications of the target squirrel-cage induction motor on motor performance.

2. The method for calculating the performance of a squirrel-cage induction motor based on a magnetic modulator according to claim 1, characterized in that, In step 1, the specifications of the target squirrel-cage induction motor include the number of squirrel-cage rotor bars, the material used, the embedding depth, the number of stator slots, the pitch of the magnetic modulator, the number of stator winding pole pairs, the slip, the number of series turns per phase of the winding, the stator outer radius, the stator inner radius, the rotor outer radius, the rotor inner radius, the air gap length, the motor stacking length, and the synchronous angular velocity.

3. The method for calculating the performance of a squirrel-cage induction motor based on a magnetic modulator according to claim 1, characterized in that, Step 2 is as follows: The modulation operator of the magnetic modulator is: ； in, The source air gap magnetomotive force established for the stator side winding; is the permeability function of the salient pole of the rotor of a squirrel-cage induction motor; And λ are respectively and The amplitude of the magnetomotive force, after being modulated by the magnetic induction modulator in the motor, is as follows: ； Wherein, F1 is the source air gap magnetomotive force established by the stator side winding. amplitude; C vp C sum and C dif p-pole, polar and The magnetic field conversion coefficients of the opposite poles are respectively: ； ； ； 4. The method for calculating the performance of a squirrel-cage induction motor based on a magnetic modulator according to claim 1, characterized in that, In step 3, the magnetic field conversion coefficient C vp for: ； The phase offset φ is: 。 5. The method for calculating the performance of a squirrel-cage induction motor based on a magnetic modulator according to claim 1, characterized in that, In step 3, the motor performance includes air gap magnetic flux density, winding flux linkage, winding inductance, and average torque.

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