An intermediate frequency furnace optimization design method based on equivalent circuit principle

Abstract

A method for optimizing the design of a medium-frequency furnace based on the equivalent circuit principle includes: obtaining the structural parameters of the medium-frequency furnace; obtaining the inductor energy consumption parameters of the medium-frequency furnace: the equivalent resistance value R1 of the inductor energy consumption; obtaining the eddy current energy consumption parameters of the medium-frequency furnace: the equivalent resistance value R2 and the inductance value L of the eddy current energy consumption; and obtaining the physical parameters of the furnace charge: C1, C2, Q, and T. C Obtain heating process parameters: T and t; Calculate the average heating power P of the furnace charge. T The heat dissipation power ΔP of the medium frequency furnace T R1, R2, L, and the capacitance C of the resonant capacitor; calculate the evaluation parameters U, I, P, P1, P2, η, η based on the circuit calculation model. t η u The design parameters of the intermediate frequency furnace are optimized by adjusting the parameters to determine the optimal parameter combination. Through actual testing, this invention establishes a complete design calculation method for intermediate frequency furnaces, making the design results more consistent with actual usage and effectively solving technical problems such as frequency mismatch and power mismatch that may occur during the use of intermediate frequency furnaces.

Description

Technical Field

[0001] This invention belongs to the field of induction heating technology, specifically relating to an optimized design method for a medium-frequency furnace based on the principle of equivalent circuits. Background Technology

[0002] Induction heating is characterized by its rapid heating speed, high thermal efficiency, and lack of pollution, and is widely used in the metal processing field. Examples include horizontal medium-frequency furnaces used for metal heat treatment and forging, and medium-frequency melting furnaces used for smelting metals. In 2020, the magazine *Metal Processing (Heat Treatment)* published a 12-issue series of lectures by Li Yunhao entitled "Induction Heating in the Foundry Industry," which provided a detailed introduction to the design of induction heating melting furnaces, representing the mainstream design methods for current medium-frequency melting furnaces.

[0003] The rated power allocation of the frequency converter power supply for the medium-frequency furnace includes: P -- output power of the frequency converter power supply; P1 -- power consumption of the inductor; P2 -- power consumption of the eddy current; ΔP T --Heat dissipation power through the sensor insulation layer (furnace lining) and the furnace opening and bottom; P T --The average heating power of the furnace charge from room temperature to its maximum temperature. The relationships between these various powers are as follows: P = P1 + P2, P2 = P T +ΔP T Define η = P T / P is called the overall efficiency of the sensor, defined as η. t =P2 / P is called the electrical efficiency of the sensor, defined as η. u =P T / P2 is referred to as thermal efficiency. However, in actual medium-frequency furnace design, P1, P2, and ΔP are not specifically calculated. T The size, but based on P T The total power P = P is calculated using empirical values ​​of η and η. T Regarding η, the text states that "η = 0.7~0.75 for smelting cast iron, and η = 0.65~0.70 for smelting cast steel; the upper limit is used for large-capacity electric furnaces, and the lower limit is used for small-capacity electric furnaces." Furthermore, the frequency f, inductor inner diameter D, height H, and number of turns n are also designed based on experience.

[0004] Therefore, the overall efficiency η of the inductor designed with existing technology may not reach its maximum value, meaning it may not achieve maximum overall efficiency. Since existing medium-frequency furnace designs are based on experience or empirical data, in some cases (where no experience is available), the designed medium-frequency furnace may encounter technical problems such as frequency mismatch or power mismatch. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides an optimized design method for medium-frequency furnaces based on the principle of equivalent circuits, aiming to improve the design efficiency and reliability of medium-frequency furnaces, increase overall efficiency through optimized design, and reduce energy consumption.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: an optimization design method for a medium-frequency furnace based on the equivalent circuit principle, comprising the following steps: S1, obtain the structural parameters of the medium frequency furnace, including the inner diameter of the inductor D, the height of the inductor H, the number of inductor turns n, the average inner diameter of the furnace d, the depth of the furnace H1, the average thermal conductivity λ of the insulation layer of the medium frequency furnace, and the rated capacity G of the medium frequency furnace. S2, Obtain the inductor energy consumption parameters of the medium frequency furnace: The inductor energy consumption parameters are the equivalent resistance value R1 of the inductor energy consumption; S3, Obtain the eddy current energy consumption parameters of the medium frequency furnace: the eddy current energy consumption parameters are the eddy current energy consumption equivalent resistance value R2 and inductance value L; S4, Obtain the physical parameters of the furnace charge, including the average solid-state specific heat C1, the average liquid-state specific heat C2, the latent heat of fusion Q, and the melting temperature T. c ; S5, obtain heating process parameters, including the maximum temperature T of the furnace charge and the heating time t from room temperature to the maximum temperature; S6, Calculate the average heating power P of the medium-frequency furnace charge. T The heat dissipation power ΔP of the medium frequency furnace T The circuit calculation model is used to calculate the following evaluation parameters: equivalent resistance R1 for inductor energy consumption, equivalent resistance R2 for eddy current energy consumption, inductance L, and capacitance C of the resonant capacitor. Based on the circuit calculation model, the following parameters are calculated: effective power output P, ​​effective voltage output U, effective current output I, inductor energy consumption P1, eddy current energy consumption P2, overall efficiency η, and electrical efficiency η0. t Thermal efficiency η u and energy consumption per unit of Pwh; S7. Optimize design parameters. By adjusting the design parameters of the medium-frequency furnace, including at least one of the structural parameters and heating process parameters, repeat step S6 to calculate the evaluation parameters and obtain the design parameter combination that optimizes the total efficiency or unit energy consumption.

[0007] Furthermore, in step S2, the method for obtaining the equivalent resistance value R1 of the sensor energy consumption is as follows: without loading furnace charge, a bridge tester is used to measure the sensor at different test frequencies f in a series equivalent model. i The equivalent resistance R below i The test results are then processed according to the empirical formula: By performing a fitting, the values ​​of constants a, b, and α are obtained, and the empirical relationship for calculating R1 is derived as follows: .

[0008] Furthermore, in step S3, the method for obtaining the equivalent resistance value R2 of the sensor energy consumption is as follows: without loading furnace charge, use a bridge tester to test the sensor at different test frequencies f in a series equivalent model. i The equivalent resistance R below 1i With the furnace fully loaded, the inductor was tested at different frequencies f using a bridge tester in a series equivalent model. i The equivalent resistance R below i Then R 2i =R i -R 1i , will R 2i Based on empirical relationships: By performing a fitting operation, we obtain the values ​​of the constants c and β, and then derive the empirical relationship for calculating R²: .

[0009] Furthermore, in step S3, the method for obtaining the inductance value L is as follows: with the furnace fully loaded, the inductor is tested at different frequencies f using a bridge tester in a series equivalent model. i The inductance value Li is set below, and the inductance value Li is adjusted according to... By fitting the empirical relation, the constant K is obtained. L The value of k is used to derive the formula for calculating L: .

[0010] Furthermore, in step S6, when the medium-frequency furnace is a medium-frequency melting furnace, the average power P T Calculate using the following formula: .

[0011] Furthermore, in step S6, when the medium-frequency furnace is a medium-frequency through-firing furnace, the average power P T Calculate using the following formula: .

[0012] Furthermore, in step S6, when the medium-frequency furnace is a medium-frequency melting furnace, the heat dissipation power ΔP T Calculate using the following formula: .

[0013] Furthermore, in step S6, when the medium-frequency furnace is a medium-frequency through-firing furnace, the heat dissipation power ΔP T Calculate using the following formula: .

[0014] Furthermore, in step S6, the circuit calculation model for the optimized design of the medium-frequency furnace is a series resonant equivalent circuit model. The evaluation parameters are calculated based on the series resonant equivalent circuit model of the medium-frequency furnace, and each parameter is determined through the following relationship, where the frequency variable f substituted into the calculation is the resonant frequency of the medium-frequency furnace: (1) The capacitance value of the resonant capacitor: ; (2) Effective power output of the power supply: ; (3) Effective current output by the power supply: ; (4) Effective voltage of power supply output: ; (5) Sensor power consumption: ; (6) Eddy current energy consumption power: ; (7) Overall efficiency: ; (8) Electrical efficiency: ; (9) Thermal efficiency: ; (10) Unit energy consumption: .

[0015] Furthermore, in step S6, the frequency variable refers to the design frequency of the intermediate frequency furnace.

[0016] The medium-frequency furnace described in this invention includes a medium-frequency melting furnace and a medium-frequency through-firing furnace. The medium-frequency through-firing furnace is usually placed horizontally (hereinafter referred to as a horizontal medium-frequency furnace). The heated metal does not melt and is then forged or heat-treated.

[0017] The beneficial effects of this invention are: 1. Based on the principle of equivalent circuit, this invention establishes a complete design calculation method for medium-frequency furnaces through actual testing, making the design results more consistent with actual use and effectively solving technical problems such as frequency mismatch and power mismatch that may occur in the use of medium-frequency furnaces.

[0018] 2. This invention establishes a fitting formula for the relationship between the equivalent resistance value R1 of the inductor energy consumption, the equivalent resistance value R2 of the eddy current energy consumption, the inductance value L of the inductor, and the structural parameters and frequency variables of the medium-frequency furnace. This makes data processing and optimization design simpler and more practical, and improves work efficiency.

[0019] 3. The optimized design method proposed in this invention can improve the overall efficiency of the medium-frequency furnace and reduce energy consumption. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the optimized design process of the present invention; Figure 2 This is a schematic diagram of the medium-frequency furnace structure of the present invention; Figure 3 This is the equivalent circuit diagram of an intermediate frequency furnace; Figure 4 This is the equivalent circuit diagram of a series resonant circuit for an intermediate frequency furnace. Figure 5 This is a graph showing the measured relationship between R1 and f in the example. Figure 6 This is a graph showing the measured relationship between R² and f in the example. Figure 7 This is a graph showing the measured relationship between L and f in the example. Figure 8 for Figure 7 A portion of the graph; Figure 9 This is a graph showing the relationship between the overall efficiency η and the frequency f in the embodiment. Figure 10 This is a graph showing the relationship between the overall efficiency η and the number of turns n in the example. Figure 11 This is a graph showing the relationship between the overall efficiency η and the sensor inner diameter D in the embodiment. Figure 12 This is a graph showing the relationship between the overall efficiency η and the thermal conductivity λ in the embodiment. The diagram shows: 1. Sensor, 2. Furnace charge, 3. AC power supply. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to the embodiments, but this should not be construed as limiting the invention in any way.

[0022] The symbols and units used in this invention are explained below: D -- Inner diameter of the inductor in the medium-frequency melting furnace, unit: mm; H -- Inductor height of the medium-frequency melting furnace, unit: mm; n -- Number of inductor turns in the medium-frequency melting furnace; d -- Average inner diameter of the furnace chamber of the medium-frequency melting furnace, unit: mm; H1 -- Depth of the furnace chamber in medium-frequency melting furnace, unit: mm; λ -- Average thermal conductivity of the insulation layer in a medium-frequency induction furnace, unit: W·mm -1 ·K -1 ; G -- Rated capacity of medium-frequency melting furnace, unit: kg; C1 -- Average solid-state specific heat of the furnace charge, unit: J·Kg -1 ·K -1 ; C2 -- Average liquid specific heat of the furnace charge, unit: J·Kg-1 ·K -1 ; Q -- Latent heat of fusion of the furnace charge, unit: J·Kg -1 ; T c -- Melting temperature of the furnace charge, in °C; T -- Maximum temperature of the furnace charge, unit: °C; t -- The time it takes for the furnace charge to rise from 20℃ to T, in seconds; P T --Average power for heating the furnace charge in the medium-frequency furnace, unit: W; Δ P T --Heat dissipation power of medium-frequency furnace, unit: W; R1 -- Equivalent resistance of the sensor power consumption, unit: Ω; R2 -- Equivalent resistance value of eddy current energy consumption, unit: Ω; L -- Inductance value of the sensor, unit: H; C -- The capacitance of the series resonant capacitor, in F (F). U -- Effective voltage of the power supply output, unit: V; I -- Effective current output by the power supply, unit: A; P -- Effective power output of the power supply, unit: W; P1 -- Sensor power consumption, unit: W; P2 -- Eddy current energy consumption power, unit: W; η -- Overall efficiency; η t --Electrical efficiency; η u --Thermal efficiency; Pwh -- Energy consumption per unit, unit: kwh / ton; In this invention, the frequency variable f has two meanings, which are distinguished according to the usage scenario: (1) In the parameter testing stage of steps S2 and S3, f refers to the test frequency of the LCR bridge tester, which is a continuously adjustable input parameter within a certain range, used to measure the equivalent resistance and inductance values ​​of the sensor at different frequencies. (2) In the design calculation stage of steps S8 and S9, f refers to the design frequency of the medium frequency furnace, that is, the frequency of the AC power supply or the resonant frequency of the furnace inductor, which is calculated from the inductance value and the resonant capacitance value of the inductor. (3) When the design frequency and the test frequency are equal, the measured inductance value and the equivalent resistance value are the same.

[0023] This invention provides an optimized design method for a medium-frequency furnace based on the principle of equivalent circuits. The medium-frequency furnace includes a medium-frequency melting furnace and a medium-frequency through-firing furnace. The medium-frequency through-firing furnace is usually placed horizontally (hereinafter referred to as a horizontal medium-frequency furnace). The heated metal does not melt and is forged or heat-treated after heating.

[0024] The present invention provides an optimized design method for a medium-frequency furnace based on the principle of equivalent circuits, the flowchart of which is attached. Figure 1 As shown, this design method includes 7 steps, which will be described in detail below.

[0025] S1. Obtain the structural parameters of the medium-frequency furnace, including the inductor inner diameter D, inductor height H, inductor turns n, average furnace inner diameter d, furnace depth H1, average thermal conductivity λ of the medium-frequency furnace insulation layer, and rated capacity G of the medium-frequency furnace. The insulation layer refers to the refractory material filling the space between the inner surface of the furnace chamber and the inner surface of the inductor; for medium-frequency melting furnaces, this is usually called the furnace lining, while for horizontal medium-frequency furnaces, it is often called the furnace tube. The rated capacity of the medium-frequency furnace, for medium-frequency melting furnaces, refers to the maximum liquid mass of one furnace; for horizontal medium-frequency furnaces, it refers to the maximum mass of metal rods that can be loaded into one furnace.

[0026] S2. Obtain the inductor energy consumption parameters of the medium frequency furnace: The inductor energy consumption parameter is the equivalent resistance value R1 of the inductor energy consumption. The calculation of the equivalent resistance value R1 of the inductor energy consumption is related to the inner diameter D of the inductor, the height H of the inductor, the number of turns n of the inductor, and the frequency variable f.

[0027] Specifically, without loading the furnace charge, an LCR bridge tester is used, with a series equivalent model selected, to test the inductor of the medium-frequency furnace at different test frequencies f on the LCR bridge tester. i The equivalent resistance R under (i.e., the aforementioned frequency variable) i The test results were then processed according to empirical formulas. By performing a fitting operation, the values ​​of constants a, b, and α are obtained, and the formula for calculating the equivalent resistance value R1 of the sensor energy consumption is then derived: (1) This empirical formula was established based on extensive testing using sensors with different D, H, and n values ​​wound from small-diameter copper tubes. Its more general form is... Where bDn is the DC resistance. In the empirical relationships given above for fitting, δ=1, γ=-1, and β=2.5. a and α are related to the material and cross-sectional shape of the inductor, and are independent of D, H, and n. b can be calculated based on resistivity and the cross-sectional area of ​​the copper tube, but it is still better to obtain it by fitting because resistivity will vary with different structures, and dimensional errors will also affect the calculation results.

[0028] S3. Obtain the eddy current energy consumption characteristic parameters of the medium-frequency furnace: The eddy current energy consumption parameters are the equivalent resistance value R2 and the inductance value L of the eddy current energy consumption. The calculation of the equivalent resistance value R2 of the eddy current energy consumption is related to the inner diameter D of the inductor, the height H of the inductor, the number of turns n of the inductor, the average inner diameter d of the furnace and the frequency variable f. The calculation of the inductance value L is related to the inner diameter D of the inductor, the height H of the inductor, the number of turns n of the inductor and the frequency variable f.

[0029] Specifically, without loading the furnace charge, an LCR bridge tester is used, with a series equivalent model selected, to test the inductor at different frequencies f. i The equivalent resistance R below 1i With the furnace fully loaded, the sensor was tested at different frequencies using an LCR bridge tester with a series equivalent model. i The equivalent resistance R below i And the inductance value Li, then R 2i =R i -R 1i , will R 2i According to empirical formulas By performing a fitting operation, we obtain the values ​​of the constants c and β, and then derive the empirical relationship for calculating R²: (2) This empirical formula was established based on extensive testing using inductors with different values ​​of D, H, and n, made by winding small-diameter copper tubes and placing low-carbon steel tubes of different diameters in between. c and β are constants mainly related to the magnetic conductivity of the furnace charge, the charge quantity, and the charge temperature. These factors include the carbon content of the steel, the content of alloying elements, the microstructure (ferrite, austenite), temperature (especially at the Curie temperature where magnetic properties change abruptly), and the state (solid, liquid). Therefore, these factors must be fully considered during testing.

[0030] The inductance value Li is adjusted according to By fitting the empirical relation, the constant K is obtained. L The k value, i.e. (3) The inductance value L mainly depends on the values ​​of n, D, and H; the magnetic yoke, furnace charge, temperature, and frequency also affect its magnitude. Induction heating is commonly used when only an inductor is present. The empirical formula for calculating inductance is used, but with a yoke and furnace charge, the inductance value not only changes but also depends on the frequency, rendering the formula inapplicable. Therefore, a correction factor K is added before the formula. L and (1-kf). K L The k value needs to be obtained through fitting based on the test results.

[0031] S4. Obtain the physical parameters of the furnace charge, including the average solid-state specific heat C1, the average liquid-state specific heat C2, the latent heat of fusion Q, and the melting temperature T.c .

[0032] S5. Obtain heating process parameters, including the highest temperature T of the furnace charge and the time t for the charge to rise from room temperature (20°C) to temperature T.

[0033] S6. Calculate the average heating power P of the medium-frequency furnace charge. T The heat dissipation power ΔP of the medium frequency furnace T The circuit calculation model is used to calculate evaluation parameters, including the equivalent resistance of the inductor power consumption R1, the equivalent resistance of the eddy current power consumption R2, the inductance value L, and the capacitance value C of the resonant capacitor. These parameters include the effective power output P, ​​the effective voltage output U, the effective current output I, the inductor power consumption P1, the eddy current power consumption P2, the overall efficiency η, and the electrical efficiency η. t Thermal efficiency η u And the unit energy consumption (Pwh). The circuit calculation model is the equivalent circuit model of a series resonant medium-frequency furnace.

[0034] Among them, the average heating power P of the medium-frequency furnace charge when heating the charge from room temperature (20℃) to the maximum temperature T is calculated. T The calculation formulas differ for medium-frequency melting furnaces and horizontal medium-frequency furnaces. The former needs to consider the latent heat of fusion, while the latter does not need to consider the latent heat of fusion and liquid state of the furnace charge.

[0035] (1) Calculate the average power P for heating and melting the charge in the medium-frequency melting furnace. T The calculation formula is: (4) (2) Calculate the average power P for heating and melting the charge in a horizontal medium-frequency furnace. T The calculation formula is: (4′) Similarly, in calculating the heat dissipation power ΔP of the intermediate frequency furnace... T The calculation formulas differ for medium-frequency melting furnaces and horizontal medium-frequency furnaces: (1) Calculate the heat dissipation power ΔP of the medium-frequency melting furnace. T The calculation formula is: (5) (2) Calculate the heat dissipation power ΔP of the horizontal medium-frequency furnace. T The calculation formula is: (5′) The derivation of these two formulas will be introduced later.

[0036] Other evaluation parameters can be determined through the following relationship, where the frequency variable f substituted into the calculation is the resonant frequency of the medium-frequency furnace.

[0037] (1) The capacitance value of the resonant capacitor: (6) (2) Effective power output of the power supply: (7) (3) Effective current output by the power supply: (8) (4) Effective voltage of power supply output: (9) (5) Sensor power consumption: (10) (6) Eddy current energy consumption power: (11) (7) Overall efficiency: (12) (8) Electrical efficiency: (13) (9) Thermal efficiency: (14) (10) Unit energy consumption: (15) S7. Optimize design parameters. By adjusting the design parameters of the medium-frequency furnace, including at least one of the structural parameters and heating process parameters, repeat step S6 to calculate the evaluation parameters and obtain the optimal combination of design parameters.

[0038] Specifically, this includes: (1) optimizing the power supply frequency variable f, inductor height H, and inductor turns n of the medium-frequency furnace, and repeating the calculation in step S6 after the change, so as to obtain the optimal values ​​of these three parameters; (2) optimizing the inductor inner diameter D, furnace average inner diameter d, furnace depth H1, and average thermal conductivity λ of the medium-frequency furnace insulation layer, and repeating the calculation in step S6 after the change, so as to obtain the optimal values ​​of these four parameters; (3) simultaneously changing the rated capacity G, furnace average inner diameter d, and furnace depth H1 of the medium-frequency furnace, or changing the process parameters: the maximum temperature T, the heating time t from room temperature to the maximum temperature, and repeating the calculation in step S6, so as to obtain the optimal values ​​of parameters such as the power supply frequency variable f, inductor inner diameter D, inductor height H, inductor turns n, furnace average inner diameter d, furnace depth H1, and average thermal conductivity λ of the medium-frequency furnace insulation layer after different rated capacity medium-frequency furnaces or process parameters.

[0039] The following points should be noted regarding the process of optimizing design parameters: (1) Evaluation parameters are the basis for evaluating design results. How to use these evaluation parameters for evaluation depends entirely on the designer's subjective will. That is, the so-called "optimal" is determined by the designer himself. There is no unified standard. It is possible not to optimize any design parameter, but only to perform calculations. If the designer believes that the design requirements have been met, then it is the optimal result. Of course, some basic principles should also be considered. First, the total efficiency or unit energy consumption should be taken as the most important evaluation parameter, because the higher the total efficiency, the less electrical energy is consumed. This is the most important technical indicator for both users and manufacturers. Second, an important evaluation indicator is the effective voltage of the power supply output. The higher the voltage value, the higher the insulation requirement of the sensor. Too high a voltage value may pose electrical safety problems. However, a higher voltage value reduces the current and increases the total efficiency. Therefore, the designer needs to consider all aspects. Finally, the electrical efficiency η needs to be considered. t and thermal efficiency η u The equilibrium problem involves a trade-off between the two factors; the overall efficiency is maximized when the two factors are close to each other, because η = η_0. t× η u This relationship requires changing the inner diameter D of the inductor. Alternatively, a refractory material with a low thermal conductivity λ can be selected as the insulation layer of the medium-frequency furnace, without reducing η. t Increasing η under the premise u This will ultimately increase η.

[0040] (2) Even if a parameter, such as the frequency variable f, is optimized, it is not necessary to obtain the mathematical optimum. For example, the optimized value of the frequency must also take into account the matching capacitor. Parameters related to size must also be considered to be at least without decimals. f must be optimized, and its optimized value must also take into account the capacitance value of the matching capacitor. In order to accurately match the capacitor, the value of the inductance L must also be considered. The value of L changes significantly compared to when the furnace charge is added. Only by matching the capacitor with the value of L after adding the furnace charge can the accurate calculated values ​​of voltage and current be obtained.

[0041] (3) In S7 parameter optimization, considering maintaining the original structural dimensions, the parameters that can be optimized include the frequency variable f and the average thermal conductivity λ, as well as the process parameters T and t. Reducing T and t will reduce the total power consumption, but this requires the approval of the intermediate frequency furnace user. When changing H1 and d, it is necessary to ensure that the furnace charge of mass G can be accommodated. When changing n and H, the spacing between the two turns needs to be considered. When changing G, in fact, when designing an intermediate frequency furnace with different capacities, H1 and d need to be changed simultaneously, but the cross-sectional dimensions of the copper tube used to wind the inductor cannot be changed.

[0042] Equations (1) to (15) above are all the calculation formulas used in the optimization design method of medium frequency furnace based on the principle of equivalent circuit. The names and units of the symbols used are described in the symbol and unit description section.

[0043] Unlike existing technologies, this invention is based on the equivalent circuit principle. It models the intermediate frequency furnace and obtains the specific parameters of the equivalent circuit through equivalent resistance testing. Using the equivalent circuit, the relationship between voltage, current, power, and other parameters of the intermediate frequency furnace is calculated. Then, by changing the parameters in the model, the optimal design parameters are obtained. The basic principles of this invention are described in detail below, and the equivalent resistance testing and optimization design process is illustrated with specific examples.

[0044] As attached Figure 2 As shown, a medium-frequency furnace is abstracted as an inductor 1, furnace charge 2, and AC power supply 3. The inner diameter of the inductor is D, the number of turns is n, and the height is H; the outer diameter of the furnace charge (inner diameter of the furnace chamber) is d, and the height is H1 (see attached diagram). Figure 1 (Not shown in the diagram); the inner side of the inductor is separated from the furnace charge by a heat insulation layer with a thickness of (Dd) / 2; an AC current with frequency f and voltage U is connected to both ends of the inductor, and its equivalent circuit diagram is attached. Figure 3 As shown, R1 is the equivalent resistance of the inductor loss, and its calculation formula is as shown in formula (1), R2 is the equivalent resistance of the eddy current loss, and its calculation formula is as shown in formula (2), and L is the inductance value after the furnace charge is applied, and its calculation formula is as shown in formula (3). Figure 3 This is also a series model tested by a bridge tester. When using a bridge tester, either R (resistance) or L (inductance) can be selected. When L (inductance) is used, the inductance value and equivalent resistance value can be measured simultaneously, as well as X (reactance), D (loss factor), Q (quality factor), and θ (impedance angle). ESR is the equivalent resistance value referred to in this invention. In this industry, Q is commonly used as a calculation parameter, but Q cannot be used in circuit calculations. This invention first tests the equivalent resistance R1 without charge, then measures the equivalent resistance with charge; the difference between the two is the equivalent resistance R2 of the charge eddy current. Once the equivalent resistance value is obtained, it can be calculated according to… Figure 3 Optimize the model, or follow Figure 4 The model is optimized, and the difference between the two lies in the method used. Figure 3 Optimization involves a power factor issue, which is the same as or similar to what is currently being used.

[0045] Equations (6) to (15) in the evaluation parameters are based on the appendix Figure 4 The calculation formula obtained from the model is attached. Figure 4 With appendix Figure 3 Compared to adding a resonant capacitor with a capacitance of C, the resonance condition is reached when the power supply frequency f and C satisfy equation (6). When the resonance condition is reached, the load can be equivalent to a purely resistive load with a resistance of R1 + R2. Let the effective value of the current be I, then P1 = I. 2 R1, P2 = I 2 R2, i.e., equations (10) and (11). Since the eddy current energy consumption power P2 = the average power of furnace charge heating and melting P...T +Heat dissipation power ΔP T Therefore, That is, equation (8). Since the power output power P = P1 + P2, we get equation (7). From P = IU, we get the expression for U (9). P, I, and U are used as power supply design parameters after adding appropriate margins.

[0046] Calculating heat dissipation power is a complex problem. For a hollow cylinder with an inner diameter of d and an outer diameter of D, assuming the inner surface temperature is T, and considering that the sensor is water-cooled, the outer surface temperature is set to 100℃, and the average thermal conductivity of the insulation layer is λ, according to the steady-state heat transfer principle of a cylindrical surface, the power dissipated per unit area from the inner surface to the outside can be obtained as follows: (16) Therefore, the area of ​​the inner cylindrical surface is πdH1, and its heat dissipation power is... .

[0047] For horizontal medium-frequency furnaces, the common working mode is a continuous working mode in which steel bars (furnace charge) enter from one end and exit from the other end. The highest temperature on the inner surface of the cylinder is T, while the lowest temperature is close to room temperature. Therefore, T / 2 is taken in the calculation, and the heat dissipation at both ends is ignored, which gives equation (5′).

[0048] For medium-frequency melting furnaces, heat dissipation of the bottom surface and furnace opening also needs to be calculated. Heat dissipation of the furnace opening is more complicated. As an approximation, the area is calculated based on the three bottom areas, resulting in equation (5).

[0049] Example: The following example uses a 3000kg medium-frequency induction melting furnace as an example to perform calculations and provide necessary explanations and analyses. This example is a 3-ton furnace designed and manufactured by a company according to existing technology, used for melting medium carbon steel, with a designed frequency of 700Hz. The inductor is wound with a 30×45×5 rectangular T2 copper tube.

[0050] S1, the structural parameters of the medium-frequency melting furnace are obtained as follows: D=840mm H=1031mm n=17 d=660mm H1=1450mm λ=0.003 w·mm -1 ·K -1 G = 3000 kg.

[0051] S2, obtain the circuit energy consumption characteristic parameters of the medium-frequency melting furnace. The test results of R1 are as follows: Figure 5 As shown in the figure, the unit of R1 is mΩ, and the horizontal axis is f. 0.88The figure also shows the fitting relationship between the two, which, combined with equation (1), yields: Therefore, a = 1.504 × 10 -8 b = 1.718 × 10 -7 ,Right now .

[0052] by Figure 5 Taking the illustrated embodiment as an example, the coefficients a, b, and α in the empirical formula for the equivalent resistance value R1 of the sensor are determined as follows: Different test frequencies f measured by the LCR bridge tester and their corresponding measured R1 values ​​are entered into a Microsoft Excel worksheet. The first column, i.e., the horizontal axis shown in the figure, represents f. α , R1~f α Based on linear fitting, different α values ​​are selected, and the linear correlation coefficient R0... 2 When the value is maximized, the optimal fitting equation is obtained: Y = 0.0146x(f 0.88 +2.453, R 2 =0.9988. Empirical formula with R1. The above result is obtained (×10) -3 (This is a unit conversion.)

[0053] S3, obtain the eddy current energy consumption characteristic parameters of the medium-frequency melting furnace. The test results of R2 are as follows: Figure 6 As shown in the figure, the unit of R2 is mΩ, and the horizontal axis is f. 0.54 The figure also shows the fitting relationship between the two, which, combined with equation (2), yields... Therefore, c = 9.797 × 10 -6 ,Right now The relationship between L and f is as follows: Figure 7 As shown, when f < 200Hz, L decreases rapidly with increasing f. Since the design frequency of this furnace is 700Hz, the data with f < 200Hz are discarded before fitting, and the results are as follows. Figure 8 As shown, combining equation (3) yields Therefore, K L =5.972×10 -8 k = 9.978 × 10 -5 ,Right now .

[0054] S4, obtain the physical parameters of the furnace charge. The physical parameters of commonly used medium carbon steel are as follows: C1 = 700 J·Kg -1 ·K -1 C2 = 816 J·Kg -1 ·K -1 Q = 272000 J·Kg -1 T c =1510℃.

[0055] S5, the heating process parameters are as follows: T=1650℃, t=3000s.

[0056] S6, calculate the average power P of heating the furnace charge from room temperature (20°C) to the maximum temperature T. T Calculate according to formula (4): Calculate the heat dissipation power ΔP of the medium-frequency furnace. T Calculated according to formula (5), that is Calculate other evaluation parameters, taking the design frequency as f=700, and substitute them into equations (6) to (15). The complete calculation results are as follows: P T =1429240W ΔP T =235518W R1 = 0.00711Ω R2 = 0.04428Ω L = 7.92 × 10 -5 H C = 6.524 × 10 -4 F P=1932058W I=6131.5A U=315.1V P1=267300W P2=1664758W η=0.73975 η t =0.86165 η u =0.85853 Pwh = 536.7 kWh / ton.

[0057] S7, Optimize Design Parameters. As mentioned above, optimizing design parameters requires comprehensive evaluation. The following example only considers the impact of changes in a single parameter (while keeping other parameters constant) on the overall efficiency.

[0058] Example 1: The relationship between overall efficiency η and frequency variable f, the results are shown in the appendix. Figure 9 It can be seen that the overall efficiency η is highest, approximately 74%, when the frequency variable f is between 500 and 650 Hz. The design frequency of 700 Hz is slightly too high. Subsequent calculations will use f = 600 Hz.

[0059] Example 2: The relationship between overall efficiency η and the number of sensor turns n is shown in the appendix. Figure 10 As can be seen, the overall efficiency η increases with the number of turns n. Subsequent calculations use n=17.

[0060] Example 3: The relationship between the overall efficiency η and the sensor inner diameter D is shown in the appendix. Figure 11 It can be seen that the overall efficiency η has a maximum value as D changes, which is about 76%. Subsequent calculations use D=940mm, which is 100mm larger than the original design value.

[0061] Example 4: The relationship between the overall efficiency η and the average thermal conductivity λ of the insulation layer is shown in the appendix. Figure 12 (The length unit in the figure is m). It can be seen that the overall efficiency η increases monotonically as λ decreases. When λ=0.0015, the results are compared with the original design calculation results in the table below, which lists all parameters.

[0062] After the above optimization, the energy consumption per ton decreased from 536.7 kWh to 523.4 kWh and 497.0 kWh respectively, demonstrating a significant energy-saving effect.

[0063] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Those skilled in the art should understand that modifications or equivalent substitutions can be made to the specific implementation of the present invention with reference to the above embodiments. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention are within the protection scope of the pending claims.

Claims

1. A method for optimizing the design of a medium-frequency furnace based on the principle of equivalent circuits, characterized in that, Includes the following steps: S1, obtain the structural parameters of the medium frequency furnace, including the inner diameter of the inductor D, the height of the inductor H, the number of inductor turns n, the average inner diameter of the furnace d, the depth of the furnace H1, the average thermal conductivity λ of the insulation layer of the medium frequency furnace, and the rated capacity G of the medium frequency furnace. S2, Obtain the inductor energy consumption parameters of the medium frequency furnace: The inductor energy consumption parameters are the equivalent resistance value R1 of the inductor energy consumption; S3, Obtain the eddy current energy consumption parameters of the medium frequency furnace: the eddy current energy consumption parameters are the eddy current energy consumption equivalent resistance value R2 and inductance value L; S4, Obtain the physical parameters of the furnace charge, including the average solid-state specific heat C1, the average liquid-state specific heat C2, the latent heat of fusion Q, and the melting temperature T. c ; S5, obtain heating process parameters, including the maximum temperature T of the furnace charge and the heating time t from room temperature to the maximum temperature; S6, Calculate the average heating power P of the medium-frequency furnace charge. T The heat dissipation power ΔP of the medium frequency furnace T The circuit calculation model is used to calculate evaluation parameters, including the equivalent resistance R1 of the inductor energy consumption, the equivalent resistance R2 of the eddy current energy consumption, the inductance L, and the capacitance C of the resonant capacitor. These parameters include the effective power output P of the power supply, the effective voltage U of the power supply output, the effective current I of the power supply output, the inductor energy consumption P1, the eddy current energy consumption P2, the overall efficiency η, and the electrical efficiency η. t Thermal efficiency η u and energy consumption per unit of Pwh; S7. Optimize design parameters. By adjusting the design parameters of the medium-frequency furnace, including at least one of the resonant frequency f, structural parameters, and heating process parameters, repeat step S6 to calculate the evaluation parameters and obtain the design parameter combination that optimizes the total efficiency or unit energy consumption.

2. The medium-frequency furnace optimization design method according to claim 1, characterized in that, In step S2, the method for obtaining the equivalent resistance value R1 of the sensor energy consumption is as follows: without loading furnace charge, a bridge tester is used to measure the sensor at different test frequencies f in a series equivalent model. i The equivalent resistance R below i The test results are then processed according to the empirical formula: By performing a fitting, the values ​​of constants a, b, and α are obtained, and the empirical relationship for calculating R1 is derived as follows: .

3. The medium-frequency furnace optimization design method according to claim 1, characterized in that, In step S3, the method for obtaining the equivalent resistance value R2 of the sensor energy consumption is as follows: without loading furnace charge, use a bridge tester to test the sensor at different test frequencies f in a series equivalent model. i The equivalent resistance R below 1i With the furnace fully loaded, the inductor was tested at different frequencies f using a bridge tester in a series equivalent model. i The equivalent resistance R below i Then R 2i =R i -R 1i , will R 2i Based on empirical relationships: By performing a fitting operation, we obtain the values ​​of the constants c and β, and then derive the empirical relationship for calculating R²: .

4. The medium-frequency furnace optimization design method according to claim 1, characterized in that, In step S3, the method for obtaining the inductance value L is as follows: with the furnace fully loaded, the inductor is tested at different frequencies f using a bridge tester in a series equivalent model. i The inductance value L i The inductance value L i according to By fitting the empirical relation, the constant K is obtained. L The value of k is used to derive the formula for calculating L: .

5. The medium-frequency furnace optimization design method according to claim 1, characterized in that, In step S6, when the medium-frequency furnace is a medium-frequency melting furnace, the average heating power P of the furnace charge is... T Calculate using the following formula: 。 6. The method for optimizing the design of a medium-frequency furnace according to claim 1, characterized in that, In step S6, when the medium-frequency furnace is a medium-frequency through-firing furnace, the average heating power P of the furnace charge is... T Calculate using the following formula: 。 7. The medium-frequency furnace optimization design method according to claim 1, characterized in that, In step S6, when the medium-frequency furnace is a medium-frequency melting furnace, the heat dissipation power ΔP of the medium-frequency furnace is... T Calculate using the following formula: 。 8. The method for optimizing the design of a medium-frequency furnace according to claim 1, characterized in that, In step S6, when the medium-frequency furnace is a medium-frequency through-firing furnace, the heat dissipation power ΔP of the medium-frequency furnace is... T Calculate using the following formula: 。 9. The method for optimizing the design of a medium-frequency furnace according to claim 1, characterized in that, In step S6, the circuit calculation model is a series resonant equivalent circuit model. The evaluation parameters are calculated based on the series resonant equivalent circuit model of the medium-frequency furnace, and each parameter is determined through the following relationship, where the frequency variable f substituted into the calculation is the resonant frequency of the medium-frequency furnace: (1) The capacitance value of the resonant capacitor: ; (2) Effective power output of the power supply: ; (3) Effective current output by the power supply: ; (4) Effective voltage of power supply output: ; (5) Sensor power consumption: ; (6) Eddy current energy consumption power: ; (7) Overall efficiency: ; (8) Electrical efficiency: ; (9) Thermal efficiency: ; (10) Unit energy consumption: .

10. The method for optimizing the design of a medium-frequency furnace according to claim 1, characterized in that, In step S6, the frequency variable refers to the design frequency of the medium-frequency furnace.

Images