Parameter identification method of three-inductance equivalent circuit of induction heating based on numerical simulation

Abstract

The present invention belongs to the technical field of induction heating model structure design, and relates to parameter identification of a three-way mutual inductance circuit of an induction coil, a crucible, and a molten pool. Specifically, it is a parameter identification method of an induction heating three-way mutual inductance equivalent circuit based on numerical simulation, which can provide an equivalent circuit model for a control strategy, and can also provide support for the selection and design of an induction heating power supply, a coil, and a crucible.

Description

Technical Field

[0001] The present invention belongs to the technical field of induction heating model structure design, and relates to parameter identification of a three-way mutual inductance circuit of an induction coil, a crucible, and a molten pool. Specifically, it is a parameter identification method of an induction heating three-way mutual inductance equivalent circuit based on numerical simulation, which can provide an equivalent circuit model for a control strategy, and can also provide support for the selection and design of an induction heating power supply, a coil, and a crucible. Background Art

[0002] Induction heating technology is a non-contact electric heating method that uses the principle of electromagnetic induction to heat materials. In this method, heat is generated within the heated material without direct contact with the source. Electromagnetic induction heating technology has the characteristics of high heating efficiency, easy equipment maintenance, and high product purity. In recent years, induction heating technology has been continuously developed.

[0003] The induction heating model mainly includes three parts: induction heating power supply (including induction heating coil), water-cooled crucible, and molten pool. In addition to the resistance and inductance characteristics of these three parts, they also produce mutual inductance. If you want to better study the entire induction heating model, you need to consider the mutual influence between the three. Therefore, it is very meaningful to establish an equivalent circuit model that can describe the interaction between the three. It can provide support for the selection and design of induction heating power supply, coil, and crucible, and can also provide an equivalent circuit model reference for the control strategy.

[0004] The existing induction heating equivalent circuit models mainly include the series equivalent circuit model and the air-core transformer equivalent circuit model. The series equivalent circuit model regards the coil and the molten pool as a whole, and cannot accurately describe the interaction between the coil and the molten pool. The air-core transformer equivalent circuit model can better describe the mutual influence between the coil and the molten pool without a crucible, but it cannot describe the mutual influence between the coil, the crucible, and the molten pool under the condition of a crucible. Therefore, if you want to study the induction heating problem with a crucible in more depth, it is necessary to establish an equivalent circuit that can describe the interaction between the three, and use a reasonable method to identify the parameters of each part of the equivalent circuit. Summary of the invention

[0005] The purpose of the present invention is to establish an induction heating three-mutual inductance equivalent circuit model and provide a method for identifying the circuit parameters of the induction heating equivalent circuit model through numerical simulation technology. It can provide an equivalent circuit model for the control strategy and also provide support for the selection and design of the induction heating power supply, coil and crucible.

[0006] In order to achieve the above object, the present invention is implemented by the following technical solutions:

[0007] A method for identifying parameters of an induction heating three-mutual inductance equivalent circuit based on numerical simulation mainly includes the following steps:

[0008] (1) Establish an electromagnetic field model of induction heating under no-load conditions and calculate the resistance and inductance of the induction coil:

[0009] When no-load, only the induction coil works. Therefore, in the induction heating electromagnetic field simulation model that only contains the induction coil and the air domain, a sinusoidal AC excitation is applied to the coil to solve the induction coil resistance and inductance under no-load conditions.

[0010] (2) Establish an equivalent circuit model of a hollow transformer between the induction coil and the molten pool, use this circuit model to equate the electromagnetic field model between the two, and calculate the relevant parameters:

[0011] Set a sinusoidal AC excitation for the induction coil; refer to the air-core transformer model, take the excitation source, induction coil resistance, and induction coil inductance as the primary side, and the molten pool resistance and molten pool inductance as the secondary side, and calculate the total resistance and total inductance after the molten pool resistance and molten pool inductance are equivalent to the primary side, as well as the induced heat power and eddy current size of the molten pool; combine the induction coil resistance and induction coil inductance calculated in step (1) under no-load conditions to calculate the molten pool resistance, molten pool inductance, and the mutual inductance between the induction coil and the molten pool.

[0012] (3) Establish an equivalent circuit model of a hollow transformer between the induction coil and the crucible, and use this circuit model to equate the electromagnetic field model between the two:

[0013] Set a sinusoidal AC excitation for the induction coil; refer to the hollow transformer model, take the excitation source, the induction coil resistance, and the induction coil inductance as the primary side, and the crucible resistance and the crucible inductance as the secondary side, calculate the total resistance and the total inductance after the crucible resistance and the crucible inductance are equivalent to the primary side, and the induced heat power of the crucible, and combine the coil resistance and the coil inductance under no-load condition calculated in step (1) to calculate the relationship between the crucible resistance, the crucible inductance and the mutual inductance between the induction coil and the crucible.

[0014] (4) Establish a three-way mutual inductance equivalent circuit model between the induction coil, crucible, and molten pool, and complete the equivalence of the electromagnetic field model of the entire induction heating system through the three-way mutual inductance equivalent circuit model:

[0015] By establishing an equivalent circuit model of the three mutual inductances between the induction coil, the crucible and the molten pool, and calculating the equivalent total resistance and the equivalent total inductance of the coil side after the three are coupled to each other according to the numerical simulation model, the equivalent total resistance and the equivalent total inductance are obtained. By combining the obtained equation group of the equivalent total resistance and the equivalent total inductance, and substituting the relationship between the crucible resistance, the crucible inductance and the mutual inductance between the induction coil and the crucible obtained in step (3) into the equation group, a binary equation group about the crucible resistance and the mutual inductance between the crucible and the molten pool can be simplified, and finally solving the equation group can obtain the crucible resistance, the mutual inductance between the crucible and the molten pool, and then obtain the crucible inductance and the mutual inductance between the induction coil and the crucible.

[0016] Beneficial effects of the invention: The invention establishes an equivalent circuit model that can better describe the relationship between the induction heating coil, crucible, and molten pool. The equivalent circuit parameters of this model are identified by numerical simulation methods to obtain the circuit parameters of each part of the induction heating, and the change law of the circuit parameters of each part of the induction heating model can also be obtained; the invention can provide an equivalent circuit model for the control strategy, and can also provide support for the selection and design of the induction heating power supply, coil, and crucible. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of specific implementation steps of the present invention.

[0018] Figure 2 This is a three-dimensional finite element simulation model diagram of the induction heating model, in which: 1 induction coil, 2 water-cooled crucible, 3 molten pool.

[0019] Figure 3 It is the equivalent circuit diagram of the induction heating model.

[0020] Figure 4 It is to establish a simulation model between the induction coil and the molten pool.

[0021] Figure 5 It is the equivalent circuit model of air-core transformer.

[0022] Figure 6 The primary side equivalent circuit model is obtained by equating the circuit parameters of the secondary side (molten pool side) in the transformer equivalent circuit model to the primary side (coil side).

[0023] Figure 7 It is the finite element simulation model between the induction coil and the crucible.

[0024] Figure 8 It is the equivalent circuit model of air-core transformer.

[0025] Fig. 9 The primary side equivalent circuit model is obtained by equating the secondary side (crucible side) circuit parameters in the transformer equivalent circuit model to the primary side (coil side).

[0026] Fig.10 It is an equivalent circuit model of three mutual inductances among the induction coil, water-cooled crucible and molten pool.

[0027] Fig.11 This is a simplified circuit model of the three-mutual inductance circuit equivalent to the coil side. DETAILED DESCRIPTION

[0028] The present invention will be further described below in conjunction with specific implementation methods, taking molten sodium chloride as a raw material as an example.

[0029] A method for identifying parameters of three-inductance equivalent circuit of induction heating based on numerical simulation, the flow chart is shown in Figure 1 , mainly including the following steps:

[0030] (1) Establish a three-dimensional electromagnetic field simulation model for induction heating, assign materials, set up the electromagnetic field, and divide the mesh model.

[0031] Taking molten sodium chloride as raw material, a three-dimensional electromagnetic field simulation model of the induction heating model is established. Figure 2 As shown. It consists of an induction coil 1, a water-cooled copper crucible 2, and a molten pool 3 (the heating raw material is molten sodium chloride). The induction coil has 2 turns, a winding inner diameter of 154mm, a winding outer diameter of 174mm, a coil radius of 5mm, a coil height of 25mm, a material conductivity of 59999999S / m, a relative magnetic permeability of 1, and is located in the center of the crucible. The water-cooled crucible has a height of 120mm, an inner diameter of 120mm, a conductivity of 39999999S / m, and a relative magnetic permeability of 1. The molten sodium chloride is a cylinder with a radius of 58mm and a height of 50mm, a conductivity of 1350S / m, a relative magnetic permeability of 1, and is located at the bottom of the crucible. An air domain of 1m*1m*1m is set outside. A sinusoidal alternating current of 500A and a frequency of 150kHz is set at the upper entrance of the induction coil, and a current outlet is set at the lower end of the induction coil. Since the skin effect has a significant impact on the parameter identification results, this model uses extremely fine grids for the induction coil, crucible, and molten sodium chloride to improve the calculation accuracy.

[0032] (2) Establish an induction heating no-load model and calculate the coil resistance R1 and coil inductance L1. In the initial model, the construction of the molten pool and the water-cooled crucible is cancelled, and a model containing only the induction coil and the air domain is established. The obtained induction heating no-load model is as follows: Figure 3 As shown. The coil resistance R1 and coil inductance L1 are obtained by numerical simulation software.

[0033] (3) Establish an electromagnetic field simulation model between the induction coil and the molten pool and an equivalent circuit model of the air-core transformer: The simulation model is as follows: Figure 4 As shown, the equivalent circuit model of the air-core transformer is as follows Figure 5As shown. Figure 5 , the Kirchhoff voltage equation of the circuit is as follows:

[0034]

[0035] in represents a voltage source, is the primary current, is the secondary current, j is the imaginary unit, and ω is the angular frequency. By equating the secondary side (molten pool side) circuit parameters in the air-core transformer equivalent circuit model to the primary side (coil side), the primary side equivalent circuit model can be obtained, as shown in Figure 6 As shown. By deducing from formula (3.1), we can get:

[0036]

[0037]

[0038] R eq =R1+R'2 (3.4)

[0039] L eq =L1-L'2 (3.5)

[0040] In the above equations, in the air-core transformer equivalent circuit model between the induction coil and the molten pool, R eq Indicates the equivalent primary side total resistance; L eq represents the equivalent primary side total inductance; R'2 is the resistance introduced on the primary side; L'2 is the inductance introduced on the primary side. eq , L eq It can be obtained by numerical simulation, combined with R1 and L1 obtained in step (2), R'2 and L'2 can be solved. The molten pool resistance R2 can be obtained by combining the numerical simulation molten pool power P2 (which can be obtained by the volume loss density volume of the electromagnetic), the molten pool induced eddy current I w2 (can be obtained by integrating the eddy current density of the molten pool cross section) and then derive the molten pool inductance L2 and the mutual inductance M1 between the induction coil and the molten pool. The calculation formula is as follows: w2 is the eddy current density of the molten pool, and S2 is the cross section of the molten pool.

[0041]

[0042]

[0043]

[0044] (4) Establish an electromagnetic field simulation model between the induction coil and the crucible and an equivalent circuit model of the hollow transformer: the simulation model is as follows: Figure 7As shown, the equivalent circuit model of the air-core transformer is as follows Figure 8 As shown. Figure 8 , the Kirchhoff voltage equation of the circuit is as follows:

[0045]

[0046] in represents a voltage source, is the primary current, is the secondary current. By converting the secondary side (crucible side) circuit parameters in the air-core transformer equivalent circuit model to the primary side (coil side), the primary side equivalent circuit model can be obtained, as shown in Fig. 9 As shown. By deducing from formula (3.9), we can get:

[0047]

[0048]

[0049] R eq2 =R1+R3' (3.12)

[0050] L eq2 =L1-L'3 (3.13)

[0051] In the above equations, in the air-core transformer equivalent circuit model between the induction coil and the crucible, R eq2 Indicates the equivalent primary side total resistance; L eq2 represents the equivalent primary side total inductance; R3' is the primary side introduced resistance; L'3 is the primary side introduced inductance. The relevant calculation formulas for the crucible resistance R3, the crucible inductance L3, and the mutual inductance M2 between the induction coil and the water-cooled crucible are as follows, where J w3 is the crucible eddy current density, and S3 is the crucible cross section.

[0052]

[0053]

[0054]

[0055] The calculation of relevant parameters is the same as the method described in step (3), but due to the complex structure of the crucible, it is impossible to directly obtain the crucible eddy current size I by the method of eddy current density surface integral. w3 , so the crucible resistance R3 cannot be directly obtained by equation (3.14). However, the relationship between the crucible resistance R3, the crucible inductance L3, and the mutual inductance M2 between the induction coil and the crucible can still be obtained by equations (3.15) and (3.16).

[0056] (5) Establish the electromagnetic field simulation model between the induction coil, crucible and molten pool and the three-inductance equivalent circuit model. Figure 2 As shown, the equivalent circuit model is as follows Fig.10 As shown. Among them, R1 is the coil resistance, L1 is the coil inductance; R2 is the molten pool resistance, L2 is the molten pool inductance; R3 is the crucible resistance, L3 is the crucible inductance; M1 is the mutual inductance between the coil and the molten pool, M2 is the mutual inductance between the coil and the crucible, and M3 is the mutual inductance between the molten pool and the crucible; They are coil current, molten pool eddy current, and crucible eddy current respectively.

[0057] Kirchhoff's voltage equation for a three-way mutual inductance circuit based on a coil, a crucible, and a molten pool is shown below.

[0058]

[0059] The simple circuit model of the three-mutual inductance circuit equivalent to the coil side is as follows Fig.11 As shown. w ' is the load equivalent to the resistance of the coil side, L w ' is the inductance equivalent to the coil side of the load.

[0060]

[0061]

[0062] Where R w ' and L w The derivation formula of ' is shown in the above two equations. By subtracting the coil impedance under no-load condition from the coil impedance under electromagnetic field simulation load condition, R w ' and L w '. R2, L2, and M1 can be calculated by equations (3.6)-(3.8) in step (3), and the equivalent relationship between R3, L3, and M2 can be calculated by equations (3.14)-(3.16) in step (4). Therefore, two equations about R3 and M3 can be obtained by equations (3.17) and (3.18), and R3 and M3 can be obtained by solving the above two equations. And L3 and M2 can be obtained according to equations (3.15) and (3.16). So far, R2, L2, M1, R3, M3, L3, and M2 are all obtained.

Claims

1. A method for identifying parameters of an induction heating three-mutual inductance equivalent circuit based on numerical simulation, characterized in that: The following steps are involved: (1) Establish an electromagnetic field model of induction heating under no-load conditions and calculate the resistance and inductance of the induction coil: When no-load, only the induction coil works. Therefore, a sinusoidal AC excitation is applied to the coil in the induction heating electromagnetic field simulation model that only includes the induction coil and the air domain to solve the induction coil resistance and inductance under no-load conditions. (2) Establish an equivalent circuit model of a hollow transformer between the induction coil and the molten pool, use this circuit model to equate the electromagnetic field model between the two, and calculate the relevant parameters: Set a sinusoidal AC excitation for the induction coil; refer to the air-core transformer model, take the excitation source, the induction coil resistance, and the induction coil inductance as the primary side, and the molten pool resistance and the molten pool inductance as the secondary side, and calculate the total resistance and total inductance after the molten pool resistance and the molten pool inductance are equivalent to the primary side, as well as the induced heat power and eddy current size of the molten pool; combine the induction coil resistance and the induction coil inductance calculated in step (1) under no-load conditions to calculate the molten pool resistance, molten pool inductance, and the mutual inductance between the induction coil and the molten pool; (3) Establish an equivalent circuit model of a hollow transformer between the induction coil and the crucible, and use this circuit model to equate the electromagnetic field model between the two: Set a sinusoidal alternating current excitation for the induction coil; refer to the air-core transformer model, take the excitation source, the induction coil resistance, and the induction coil inductance as the primary side, and the crucible resistance and the crucible inductance as the secondary side, calculate the total resistance and the total inductance after the crucible resistance and the crucible inductance are equivalent to the primary side, and the induced heat power of the crucible, and combine the coil resistance and the coil inductance under no-load condition calculated in step (1) to calculate the relationship between the crucible resistance, the crucible inductance, and the mutual inductance between the induction coil and the crucible; (4) Establish a three-way mutual inductance equivalent circuit model between the induction coil, crucible, and molten pool, and complete the equivalence of the electromagnetic field model of the entire induction heating system through the three-way mutual inductance equivalent circuit model: By establishing an equivalent circuit model of the three mutual inductances among the induction coil, the crucible and the molten pool, the equivalent total resistance and the equivalent total inductance of the coil side after the three are coupled to each other are obtained according to the calculation of the numerical simulation model; the equation group of the equivalent total resistance and the equivalent total inductance is combined, and the relationship between the crucible resistance, the crucible inductance and the mutual inductance between the induction coil and the crucible obtained in step (3) is substituted into the equation group, and the binary equation group about the crucible resistance and the mutual inductance between the crucible and the molten pool is simplified, and finally the crucible resistance and the mutual inductance between the crucible and the molten pool are obtained by solving the equation group, and then the crucible resistance and the mutual inductance between the crucible and the molten pool are obtained, and then the crucible inductance and the mutual inductance between the induction coil and the crucible are obtained.

2. The method for identifying parameters of an induction heating three-mutual inductance equivalent circuit based on numerical simulation according to claim 1 is characterized in that: The step (2) establishes an electromagnetic field simulation model between the induction coil and the molten pool and an equivalent circuit model of an air-core transformer, and obtains the Kirchhoff voltage equation of the circuit as follows: in represents a voltage source, is the primary current, is the secondary current, j is an imaginary unit, and ω is the angular frequency; the circuit parameters of the secondary side, i.e., the molten pool side, in the air-core transformer equivalent circuit model are equivalent to the primary side, i.e., the coil side, and the primary side equivalent circuit model is obtained. By deducing from formula (3.1), we can get: R eq =R1+R′2 (3.4) L eq =L1-L′2 (3.5) In the above equations, in the air-core transformer equivalent circuit model between the induction coil and the molten pool, R eq Indicates the equivalent primary side total resistance; L eq represents the equivalent primary side total inductance; R′2 is the resistance introduced on the primary side; L′2 is the inductance introduced on the primary side; R eq , L eq The numerical simulation results show that R′2 and L′2 are obtained by combining R1 and L1 obtained in step (1). The molten pool resistance R2 is combined with the numerical simulation molten pool power P2 and the molten pool induced eddy current I w2 It is deduced that the molten pool inductance L2 and the mutual inductance M1 between the induction coil and the molten pool are derived; the calculation formula is as follows, where J w2 is the eddy current density of the molten pool, S2 is the cross section of the molten pool; The step (3) establishes an electromagnetic field simulation model between the induction coil and the crucible and an equivalent circuit model of the hollow transformer, and obtains the Kirchhoff voltage equation of the circuit as follows: in represents a voltage source, is the primary current, is the secondary current; the circuit parameters of the secondary side, i.e. the crucible side, in the air-core transformer equivalent circuit model are equivalent to the primary side, i.e. the coil side, to obtain the primary side equivalent circuit model. By deducing from formula (3.9), we can obtain: R eq2 =R1+R′3 (3.12) L eq2 =L1-L′3 (3.13) In the air-core transformer equivalent circuit model between the induction coil and the crucible, R eq2 Indicates the equivalent primary side total resistance; L eq2 represents the equivalent primary side total inductance; R′3 is the primary side introduced resistance; L′3 is the primary side introduced inductance; the relevant calculation formulas for the crucible resistance R3, the crucible inductance L3, and the mutual inductance M2 between the induction coil and the water-cooled crucible are as follows, where J w3 is the crucible eddy current density, S3 is the crucible cross section; The calculation of related parameters is the same as the method described in step (2). The crucible resistance R3 cannot be directly obtained using formula (3.14); however, the relationship between the crucible resistance R3, the crucible inductance L3, and the mutual inductance M2 between the induction coil and the crucible can be obtained using formulas (3.15) and (3.16); The step (4) establishes an electromagnetic field simulation model and a three-mutual inductance equivalent circuit model between the induction coil, the crucible, and the molten pool; wherein R1 is the coil resistance, L1 is the coil inductance; R2 is the molten pool resistance, L2 is the molten pool inductance; R3 is the crucible resistance, L3 is the crucible inductance; M1 is the mutual inductance between the coil and the molten pool, M2 is the mutual inductance between the coil and the crucible, and M3 is the mutual inductance between the molten pool and the crucible; They are coil current, molten pool eddy current, and crucible eddy current respectively; Kirchhoff's voltage equation based on the three-way mutual inductance circuit of coil, crucible and molten pool is as follows: Where R w ' is the load equivalent to the resistance of the coil side, L w ' is the inductance equivalent to the coil side of the load; By using electromagnetic field simulation, the coil impedance under load is subtracted from the coil impedance under no-load condition to obtain R w ' and L w '; R2, L2, and M1 can be calculated by formulas (3.6)-(3.8), and the equivalent relationship between R3, L3, and M2 can be calculated by formulas (3.14)-(3.16); therefore, two equations about R3 and M3 are obtained by formulas (3.17) and (3.18), and R3 and M3 are obtained by solving the above two equations; and L3 and M2 are obtained according to formulas (3.15) and (3.16); so far, R2, L2, M1, R3, M3, L3, and M2 are all obtained.

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