Method for calculating magnetic circuit parameters of silicon steel sheet

Abstract

The application discloses a silicon steel sheet magnetic circuit parameter calculation method in the magnetic circuit theory application field, and the specific process is as follows: S1, the geometric size, electromagnetic parameters and lamination number of the silicon steel sheet are acquired; S2, the frequency and direction of the alternating magnetic flux in the silicon steel sheet are determined; S3, the magnetic circuit parameters of the silicon steel sheet are calculated according to the expression; the calculation method can quickly calculate the magnetic circuit parameters of the silicon steel sheet according to the geometric size, electromagnetic characteristics and lamination number of the silicon steel sheet, in combination with the frequency and direction of the alternating magnetic flux in the silicon steel sheet, draw the high-frequency magnetic circuit characteristics of the silicon steel sheet, and improve the work efficiency of researchers; the operation state of electromagnetic equipment can be evaluated, the behavior of the magnetic quantity in the magnetic circuit can be qualitatively analyzed, and the size of the magnetic circuit parameters can be quantitatively calculated.

Description

TECHNICAL FIELD

[0001] The application belongs to the application field of magnetic circuit theory, and particularly relates to a calculation method of magnetic circuit parameters of silicon steel sheets. BACKGROUND

[0002] Since the silicon steel sheet was invented by E. Gumlich in 1902, it has had a history of more than one hundred years, and it is an important soft magnetic alloy indispensable in motors, transformers and various electromagnetic devices, and its main function is to build a closed magnetic circuit with small eddy current loss and high permeability for electromagnetic devices. In the past analysis, people usually use circuit parameters such as resistance parameters and inductance parameters to qualitatively describe and quantitatively calculate the magnetic quantity change of the silicon steel sheet in the alternating magnetic field. For example, scholars such as SYR Hui and JG Zhu of the University of Sydney indirectly described the changes of the magnetomotive force and the magnetic flux in the magnetic circuit of the silicon steel sheet by establishing a circuit model of the silicon steel sheet. According to the measured experimental data, combined with the electric network theory, the scholar Xiaokang Liu proposed a high-order Debye circuit to simulate the changes of the circuit parameters in the magnetic circuit at different frequencies. In addition, combined with the electromagnetic field theory, the scholars such as Zhu Sa of the Hehai University proposed a frequency domain model of the iron loss generated by the PWM excitation in the magnetic circuit and low-frequency parameters, and used the circuit parameters to quantitatively evaluate the size of the iron loss in the laminated silicon steel sheet. However, in the existing circuit theory, the magnetic circuit variables are usually used as intermediate variables to participate in the circuit calculation, and the phase change is not considered. Therefore, the circuit parameter analysis of the silicon steel sheet cannot directly reflect the changes of the magnetic circuit parameters of the silicon steel sheet, and how to directly describe the magnetic quantity change in the silicon steel sheet through the magnetic circuit parameters has not been solved. SUMMARY

[0003] In view of the defects of the prior art, the purpose of the present application is to provide a calculation method of magnetic circuit parameters of silicon steel sheets to solve the problems in the background art.

[0004] The purpose of the present application can be achieved by the following technical solutions.

[0005] A calculation method of magnetic circuit parameters of silicon steel sheets, the specific process is as follows:

[0006] S1, the geometric size, electromagnetic parameters and the number of laminations of the silicon steel sheet are obtained;

[0007] The geometric size includes the thickness a, length b and width h of the silicon steel sheet, and the number of laminations is n;

[0008] The electromagnetic parameters include the conductivity σ, permeability μ and skin depth δ of the silicon steel sheet;

[0009] S2, the frequency f of the alternating magnetic flux in the silicon steel sheet and the direction thereof are determined;

[0010] S3: Finally, the magnetic circuit parameters of the silicon steel sheet are calculated according to the proposed expression.

[0011] Preferably, the magnetic reluctance parameter expression of the silicon steel sheet in S3 is as follows:

[0012]

[0013] The expression of the magnetic inductance parameter is as follows:

[0014]

[0015] In the formula, σ is the conductivity of the silicon steel sheet, μ is the permeability of the silicon steel sheet, and δ is the skin depth of the silicon steel sheet magnetic flux;

[0016] The expression of the magnetic flux skin depth is as follows:

[0017]

[0018] In the formula, f is the frequency of the alternating magnetic flux in the silicon steel sheet, and ρ is the resistivity of the silicon steel sheet.

[0019] Preferably, the electromagnetic parameter in S3 is when the magnetic flux skin depth δ >> a, the expression of the magnetic reluctance parameter is as follows:

[0020]

[0021] The expression of the magnetic inductance parameter is as follows:

[0022]

[0023] Preferably, the electromagnetic parameter in S3 is when n silicon steel sheets are mutually insulated and stacked into a closed magnetic circuit along the magnetic flux direction, which is equivalent to n silicon steel magnetic circuits being connected in parallel, the expression of the magnetic reluctance parameter is as follows:

[0024]

[0025] The expression of the equivalent magnetic inductance parameter is as follows:

[0026]

[0027] Preferably, the magnetic reactance, magnetic impedance, and magnetic impedance angle of the silicon steel sheet can be determined according to the magnetic reluctance parameter and the magnetic inductance parameter in S3.

[0028] The expression of the magnetic reactance of the silicon steel sheet is as follows:

[0029]

[0030] The expression of the magnetic impedance of the silicon steel sheet is as follows:

[0031]

[0032] The magnetic impedance angle expression of the silicon steel sheet is as follows:

[0033]

[0034] Preferably, the magnetic flux expression of the silicon steel sheet is as follows:

[0035]

[0036] In the formula, H m is the amplitude of the magnetic flux intensity in the silicon steel sheet.

[0037] Preferably, the magnetic field energy expression of the silicon steel sheet is as follows:

[0038]

[0039] The active power expression of the silicon steel sheet is as follows:

[0040]

[0041] Preferably, the calculation method is applied to calculate the magnetic circuit parameters of a magnetic material with the same geometric shape.

[0042] Preferably, the magnetic material includes materials such as nickel-iron, cobalt-iron, amorphous metal alloy, and ferrite that can form a closed magnetic circuit.

[0043] Advantages of the present application:

[0044] 1. The calculation method of the present application can quickly calculate the magnetic circuit parameters of the silicon steel sheet, draw the high-frequency magnetic circuit characteristics of the silicon steel sheet, and improve the work efficiency of researchers according to the geometric size, electromagnetic characteristics, and the number of laminations of the silicon steel sheet, combined with the frequency and direction of the alternating magnetic flux in the silicon steel sheet.

[0045] 2. The calculation method of the present application can evaluate the running state of the electromagnetic equipment, both qualitatively analyze the behavior of the magnetic quantity in the magnetic circuit and quantitatively calculate the size of the magnetic circuit parameters. BRIEF DESCRIPTION OF DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows. Obviously, for those skilled in the art, other drawings can also be obtained based on these drawings without creative labor.

[0047] Figure 1 is a three-dimensional mathematical model diagram of the silicon steel sheet in the present application;

[0048] Figure 2 This is a three-dimensional mathematical model diagram of the laminated silicon steel sheets in this invention;

[0049] Figure 3 This is the equivalent magnetic circuit diagram of the laminated silicon steel sheets in this invention;

[0050] Figure 4 This is a flowchart of the calculation method of the present invention;

[0051] Figure 5 This is a diagram of the experimental setup for verifying the calculation method in this invention;

[0052] Figure 6 These are the experimental results of the magnetoresistive parameters calculated using the method of this invention;

[0053] Figure 7 These are the experimental results of the magnetic field parameters calculated by the method of this invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] This invention proposes a method for calculating the magnetic circuit parameters of silicon steel sheets. The core of the method is to calculate the magnetic circuit parameters of silicon steel sheets based on their geometric dimensions, electromagnetic properties, number of stacked sheets, and the frequency and direction of the alternating magnetic flux in the silicon steel sheets.

[0056] The specific process of the calculation method for magnetic circuit parameters of silicon steel sheets proposed in this invention is as follows:

[0057] S1: Obtain the geometric dimensions, electromagnetic parameters, and number of laminates of silicon steel sheets according to requirements;

[0058] S2: Determine the frequency and direction of the alternating magnetic flux in the silicon steel sheet;

[0059] S3: Calculate the magnetic circuit parameters of the silicon steel sheet according to the formula.

[0060] Please see Figure 1 As shown, Figure 1 The three-dimensional mathematical model of the silicon steel sheet is given, where the thickness of the silicon steel sheet is a, the length is b, and the width is h. When the sinusoidal magnetomotive force of the silicon steel sheet... When the frequency f is constant, the alternating magnetic flux formed flows into the silicon steel sheet along the positive y-axis. According to Faraday's law of electromagnetic induction, eddy currents that oppose the change of magnetic flux will be formed in the silicon steel sheet in the z-direction.

[0061] The expression of the silicon steel sheet reluctance parameter is as follows:

[0062]

[0063] The expression of the silicon steel sheet permeance parameter is as follows:

[0064]

[0065] In the formula, σ is the conductivity of the silicon steel sheet, μ is the permeability of the silicon steel sheet, and δ is the skin depth of the silicon steel sheet magnetic flux.

[0066] When the frequency of the alternating magnetic flux is low, that is, the skin depth δ of the magnetic flux is much larger than a, it is considered that the magnetic flux is uniformly distributed in the silicon steel sheet. At this time, the expression of the silicon steel sheet reluctance parameter can be simplified as The expression of the silicon steel sheet permeance parameter can be simplified as

[0067] When n silicon steel sheets are mutually insulated and stacked into a closed magnetic circuit along the magnetic flux direction, as shown in Figure 2 The equivalent magnetic circuit of the n silicon steel sheets is shown in Figure 3 At this time, the expression of the equivalent reluctance parameter of the parallel magnetic circuit is as follows:

[0068]

[0069] The expression of the equivalent permeance parameter is as follows:

[0070]

[0071] The expression of the magnetic flux skin depth is as follows:

[0072]

[0073] In the formula, f is the frequency of the alternating magnetic flux in the silicon steel sheet, and ρ is the resistivity of the silicon steel sheet.

[0074] The expression of the silicon steel sheet magnetic reactance is as follows:

[0075]

[0076] The expression of the silicon steel sheet magnetic impedance is as follows:

[0077]

[0078] The expression of the silicon steel sheet magnetic impedance angle is as follows:

[0079]

[0080] The expression of the silicon steel sheet magnetic flux is as follows:

[0081]

[0082] H m is the amplitude of the magnetic flux density in the silicon steel sheet.

[0083] The expression of the magnetic field energy of the silicon steel sheet is as follows:

[0084]

[0085] The expression of the active power of the silicon steel sheet

[0086]

[0087] The calculation method is not only limited to the silicon steel sheet, but also applicable to other magnetic materials with the same geometric structure and capable of forming a magnetic circuit, such as nickel-iron (Mop), cobalt-iron (Perminvar), amorphous metal alloy, and ferrite.

[0088] Please refer to Figure 4 The calculation method of the magnetic circuit parameters of the silicon steel sheet according to the present application is verified according to the flowchart, and the verification device is as shown in Figure 5 The verification device is composed of a programmable AC power supply, a temperature detector, an Epstein coil, a power analyzer, a voltage differential probe, a high-frequency current probe, and a wave recorder. The Epstein coil is made of 35 pieces of 0.5 mm silicon steel sheets stacked along the magnetic flux direction, and the silicon steel sheet model is B50A470. The primary side coil of the Epstein coil is ZR-BVR-2.5, with 152 turns and a resistance value of 0.1044 Ω. The secondary side coil is made of polyester enameled copper wire with a diameter of 0.88 mm, with 152 turns and a resistance value of 0.484 Ω.

[0089] The temperature of the Epstein coil is maintained at about 24℃, and the magnetic flux with a frequency range of 10Hz-5000Hz and a magnetic flux density of 0.01T is passed through the closed magnetic circuit of the silicon steel sheet. The active power and reactive power of the Epstein coil at different frequencies are recorded by the power analyzer. After removing the primary winding loss, the magnetic resistance value and magnetic inductance value of the Epstein coil at different frequencies are solved by the magneto-electric power law. The theoretical analysis and experimental measurement results are as shown in Figure 6 、 Figure 7 It can be seen that the proposed calculation method can not only quantitatively evaluate the size of the magnetic circuit parameters at different frequencies, but also qualitatively describe the law of the magnetic circuit parameters changing with the frequency. The experimental results prove the feasibility and effectiveness of the present application.

[0090] In the description of the specification, the description of the terms "one embodiment", "an example", "a specific example" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Also, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0091] The basic principles, main features and advantages of the present application are shown and described above. Those skilled in the art should understand that the present application is not limited by the above embodiments, and the above embodiments and descriptions in the specification are only to illustrate the principles of the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application.

Claims

1. A method of calculating a magnetic circuit parameter of a silicon steel sheet, characterized by, The specific process is as follows: S1, first obtain the geometric size, electromagnetic parameters, and the number of laminations of the silicon steel sheet; The geometric size includes the thickness a, length b, and width h of the silicon steel sheet, and the number of laminations is n; The electromagnetic parameters include the conductivity σ, permeability μ, and skin depth δ of the magnetic flux of the silicon steel sheet; S2, then determine the frequency f of the alternating magnetic flux in the silicon steel sheet and the direction thereof; S3: Finally, the magnetic circuit parameters of the silicon steel sheet are calculated according to the proposed expression, when the sinusoidal magnetomotive force When the frequency f is constant, the magnetic resistance parameter expression of the silicon steel sheet is as follows: The expression of the magnetic inductance parameter is as follows: In the formula, σ is the conductivity of the silicon steel sheet, μ is the permeability of the silicon steel sheet, and δ is the skin depth of the magnetic flux of the silicon steel sheet; The expression of the magnetic flux skin depth is as follows: In the formula, f is the frequency of the alternating magnetic flux in the silicon steel sheet, and ρ is the resistivity of the silicon steel sheet.

2. The method of claim 1, wherein, When the electromagnetic parameters in S3 are δ >> a, the expression of the magnetic reluctance parameter is as follows: The expression of the magnetic inductance parameter is as follows:

3. The method for calculating magnetic circuit parameters of silicon steel sheets according to claim 1, characterized in that, When the electromagnetic parameters in S3 are n silicon steel sheets mutually insulated, stacked into a closed magnetic circuit along the direction of the magnetic flux, and equivalent to n silicon steel magnetic circuits mutually connected in parallel, the expression of the magnetic reluctance parameter is as follows: The expression of the equivalent magnetic inductance parameter is as follows:

4. The method of claim 1, wherein, Determine the magnetic reactance, magnetic impedance, and magnetic impedance angle of the silicon steel sheet according to the magnetic reluctance parameter and the magnetic inductance parameter: The expression of the magnetic reactance of the silicon steel sheet is as follows: The expression of the magnetic impedance of the silicon steel sheet is as follows: The expression of the magnetic impedance angle of the silicon steel sheet is as follows:

5. The method of calculating the magnetic circuit parameters of a silicon steel sheet according to claim 1, characterized in that, The expression of the magnetic flux of the silicon steel sheet is as follows: In the formula, H m is the amplitude of the magnetic flux in the silicon steel sheet.

6. The method of calculating the magnetic circuit parameters of a silicon steel sheet according to claim 5, characterized in that, The expression of the magnetic field energy of the silicon steel sheet is as follows: The expression of the active power of the silicon steel sheet is as follows:

7. The method of calculating the magnetic circuit parameters of a silicon steel sheet according to claim 1, characterized in that, The calculation method can be applied to calculate the magnetic circuit parameters of magnetic materials with the same geometric shape.

8. The method of calculating the magnetic circuit parameters of a silicon steel sheet according to claim 7, characterized in that, The magnetic materials include nickel iron, cobalt iron, amorphous metal alloy, and ferrite.

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