Method for determining round billet continuous casting secondary cooling target surface temperature

Abstract

The invention relates to the technical field of metallurgy, in particular to a method for determining a round billet continuous casting secondary cooling target surface temperature, which comprises the following steps: firstly, establishing a round billet continuous casting one-dimensional solidification heat transfer mathematical model; deducing an ideal heat flux density expression in the solidification process of the round billet according to the solidification rule of the round billet; an ideal heat flux density expression obtained through derivation is adopted as a boundary condition of a one-dimensional solidification heat transfer mathematical model, and the target surface temperature under the conditions of different steel types, sections and pulling speeds is calculated, so that the method for determining the secondary cooling target surface temperature of the round billet can be clearly, quantitatively and rapidly adapted to different production conditions; according to the method, the quality stability of the continuous casting blank is effectively improved, the defects of the casting blank are reduced, and the technical problems that in the prior art, a quantitative temperature curve cannot be obtained according to the method, the difference of target surface temperatures formulated by different researchers is large, and the target surface temperatures under different process conditions cannot be formulated in a targeted mode are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of metallurgy, and particularly to a method for determining the target surface temperature of secondary cooling in round billet continuous casting. Background Art

[0002] During the continuous casting process, secondary cooling plays a key role in the quality of the cast billet. The secondary cooling regime directly affects quality problems such as surface cracks and bulging deformation of the cast billet. At present, continuous casting production mainly adopts dynamic secondary cooling water distribution based on the target surface temperature, that is, a process control technology that preset the surface temperature distribution curve of the cast billet and dynamically adjusts the secondary cooling water volume to achieve precise temperature control. Therefore, setting a reasonable target surface temperature for the continuous casting billet is the premise of dynamic secondary cooling water distribution. Traditional methods usually determine the target surface temperature based on metallurgical criteria. These metallurgical criteria mainly include:

[0003] Surface temperature criterion in the secondary cooling zone: The surface temperature distribution of the cast billet in the secondary cooling zone should adapt to the high-temperature characteristics of the steel grade. When straightening, the surface temperature of the cast billet should avoid the low ductility zone of the steel grade, and the temperature should be controlled in the temperature range with higher ductility of the steel to avoid transverse cracks on the surface of the cast billet during straightening; usually, the surface temperature of the cast billet during straightening should be greater than 900 °C. For low-alloy steels containing Nb, V, and Ti, the surface temperature of the cast billet in the straightening zone should be higher.

[0004] Criterion for the change rate of the surface temperature of the cast billet: In order to avoid cracks caused by excessive temperature fluctuations, generally, the cooling rate along the length direction of the continuous casting billet is required not to exceed 200 °C / m, and the temperature rise rate is not greater than 100 °C / m.

[0005] However, the above metallurgical criteria for determining the target surface temperature cannot obtain a quantitative temperature curve based on them. The target surface temperatures formulated by different researchers vary greatly, and it is also impossible to specifically formulate the target surface temperature under different process conditions. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for determining the target surface temperature of secondary cooling in round billet continuous casting, aiming to solve the technical problems in the prior art that a quantitative temperature curve cannot be obtained based on it, the target surface temperatures formulated by different researchers vary greatly, and it is also impossible to specifically formulate the target surface temperature under different process conditions.

[0007] To achieve the above purpose, a method for determining the target surface temperature of secondary cooling in round billet continuous casting adopted by the present invention includes the following steps:

[0008] Establish a one-dimensional solidification heat transfer mathematical model for round billet continuous casting;

[0009] According to the solidification law of the round billet, derive the expression of the ideal heat flux density during the solidification process of the round billet;

[0010] The ideal heat flux density expression obtained by derivation is used as the boundary condition of the one-dimensional solidification heat transfer mathematical model to calculate the target surface temperature under different steel grades, cross-sections, and drawing speeds.

[0011] Among them, the ideal heat flux density expression obtained by derivation is:

[0012]

[0013] In the formula, q is the heat flux density, kW·m -2 ; ρ is the density, kg·m -3 ; L is the latent heat of solidification, J·kg -1 ; K R is the solidification coefficient of the round billet, taking 21mm·min -1 / 2 ; R is the radius of the round billet, mm; r is the inner diameter of the solidified shell.

[0014] Among them, the calculation formula for the inner diameter r of the solidified shell is:

[0015]

[0016] In the formula, t is the solidification time, and the unit is min.

[0017] A method for determining the target surface temperature of secondary cooling in round billet continuous casting according to the present invention, in specific use, the present invention first establishes a one-dimensional solidification heat transfer mathematical model for round billet continuous casting; according to the solidification law of the round billet, the ideal heat flux density expression during the solidification process of the round billet is derived; the ideal heat flux density expression obtained by derivation is used as the boundary condition of the one-dimensional solidification heat transfer mathematical model to calculate the target surface temperature under different steel grades, cross-sections, and drawing speeds, so that the present invention can clearly, quantitatively and quickly adapt to the method for determining the target surface temperature of secondary cooling of round billets under different production conditions, effectively improving the stability of the quality of continuous casting billets, reducing billet defects, optimizing the production process, and solving the technical problems in the prior art that it is impossible to obtain a quantitative temperature curve therefrom, the target surface temperatures formulated by different researchers vary greatly, and it is also impossible to specifically formulate the target surface temperature under different process conditions. Brief Description of the Drawings

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for description in the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0019] Figure 1 It is a schematic diagram of the solidification cross-section of the round billet.

[0020] Figure 2 It is a schematic diagram of the growth law of the solidified shell in round and square billet continuous casting.

[0021] Figure 3 It is a schematic diagram of the change of the ideal heat flux density with time calculated by a specific embodiment of the present invention.

[0022] Figure 4 It is a schematic diagram of the change of the target surface temperature with time calculated by a specific embodiment of the present invention.

[0023] Figure 5 It is a schematic diagram of the change of the target surface temperature with distance calculated by a specific embodiment of the present invention. Detailed implementation manners

[0024] The embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the drawings. The embodiments described below by referring to the drawings are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

[0025] Please refer to Figure 1 and Figure 2 , Figure 1 It is a schematic diagram of the solidification section of the round billet. Figure 2 It is a schematic diagram of the growth law of the solidified shell in round and square billet continuous casting.

[0026] The present invention provides a method for determining the target surface temperature of secondary cooling in round billet continuous casting, including the following steps:

[0027] Establish a one-dimensional solidification heat transfer mathematical model for round billet continuous casting;

[0028] According to the solidification law of the round billet, derive an expression for the ideal heat flux density during the solidification process of the round billet;

[0029] Use the derived expression for the ideal heat flux density as the boundary condition of the one-dimensional solidification heat transfer mathematical model to calculate the target surface temperature under different steel grades, cross-sections, and casting speeds.

[0030] For this specific implementation manner, the method for deriving the expression for the ideal heat flux density during the solidification process of the round billet according to the solidification law of the round billet is as follows:

[0031] Based on Figure 1 , Figure 1 It is a schematic diagram of the solidification section of the round billet. Applying the solution of the Fourier heat conduction equation on the circular cylinder, the expression for the heat Q flowing out of the surface of the casting per unit time per unit length is:

[0032]

[0033] In Equation 1, T surf is the surface temperature of the casting, °C; Ts is the solidus temperature, in °C; R is the radius of the round billet, in m; r is the inner diameter of the solidified shell, in m;

[0034] In addition, at the solidification front, the inner diameter of the solidified billet shell increases by dr within the time dt, and the latent heat of solidification released on the circumferential surface per unit length of the continuous casting billet is:

[0035]

[0036] Making the two equations of Equation 1 and Equation 2 equal, and since the growth direction of the solidified billet shell is opposite to the heat transfer direction, then:

[0037]

[0038] Define K R as the solidification coefficient of the round billet, and let:

[0039]

[0040] And write Equation 3 in differential form as:

[0041]

[0042] Since r = R when t = 0, integrating Equation 5 to solve, we can get:

[0043]

[0044] The function given by Equation 6 is in the form of t = f(r), which is not convenient to use, and it is a transcendental equation, making it difficult to directly solve the function in the form of r = f(t) required for practical applications. Therefore, further analysis is needed. Let:

[0045]

[0046] In the formula, t' is the dimensionless solidification time, r' is the dimensionless inner diameter of the solidified shell, and d' is the dimensionless thickness of the solidified billet shell. Rewrite Equation 6 as:

[0047] t′ = (1 - d′) 2 [ln(1 - d′) - 0.5] + 0.5; Equation 8

[0048] In the above formula, the value range of d' is [0, 1]. Plot t' - d' and perform data fitting to obtain the fitting formula as:

[0049]

[0050] Based on Figure 2 , Figure 2 is a schematic diagram of the growth law of the solidified billet shell in round-square billet continuous casting. At Figure 2Among them, a large number of measured data of the solidified shell thickness are summarized. These measured data are processed into dimensionless data by Equation 7, and it is found that when K R = 22, the distribution of the dimensionless data is in good agreement with Equation 9.

[0051] Substituting Equation 7 into Equation 9, the growth law of the shell thickness d is obtained as:

[0052]

[0053] Since r = R - d, there is:

[0054]

[0055] In Equation 11, the units of d and R are mm; the unit of t is min; the unit of K R is mm·min -1 / 2 .

[0056] The ideal heat flux density distribution is the change of the heat flux density that conforms to the growth law of the solidified shell. From

[0057] Equation 2, the heat flux density q of the round billet is:

[0058]

[0059] From Equation 5, there is:

[0060]

[0061] Substituting Equation 13 into Equation 12, we get:

[0062]

[0063] The expression of Equation 14 adopts Equation 11. Specific embodiments:

[0065] Please refer to Figures 3 to 5 , Figure 3 which is a schematic diagram of the change of the ideal heat flux density with time calculated by the specific embodiment of the present invention. Figure 4 which is a schematic diagram of the change of the target surface temperature with time calculated by the specific embodiment of the present invention. Figure 5 which is a schematic diagram of the change of the target surface temperature with distance calculated by the specific embodiment of the present invention.

[0066] Taking the production of 45 steel, the casting speed (Vc) of 0.28 m / min, and the Φ600 mm round billet as an example, the specific implementation steps for determining the target surface temperature by the method of the present invention are as follows:

[0067] S1. Establish a one-dimensional transient mathematical model for the solidification heat transfer of the round billet continuous casting;

[0068] For this specific embodiment, in the continuous casting heat transfer model, it is assumed that the meniscus temperature is the pouring temperature (ignoring the convective heat transfer of the submerged nozzle impinging flow), only considering the radial heat transfer of the round billet (ignoring the axial / circumferential heat flux and the joule heat of electromagnetic stirring), and equivalent the convective effect of the molten steel to a pure heat conduction process with an increased thermal conductivity. By setting the circumferential temperature field to be uniformly distributed, the one-dimensional solidification heat transfer control equation for round billet continuous casting can be constructed:

[0069]

[0070] In Equation 15, ρ is the density of the molten steel; λ is the thermal conductivity; T is the temperature; t is the solidification time; r is the coordinate in the radial direction; C eq is the equivalent specific heat capacity:

[0071]

[0072] In Equation 16, C p is the specific heat capacity of steel, J·kg -1 ·K -1 ; f S is the solid fraction, and in the solid-liquid two-phase region:

[0073]

[0074] In Equation 17, T liq is the liquidus temperature, °C; T melt is the melting point of pure iron, °C; k0 is the liquidus slope.

[0075] S2. Determine the physical property parameters of the specific steel grade;

[0076] For this specific embodiment, the density of the molten steel ρ = 7200 kg·m -3 , the latent heat of solidification L = 2.7×10 5 J·kg -1 , the radius of the round billet R = 0.3 m, the solidification coefficient K R = 21 mm·min -1 / 2 , the liquidus temperature T liq = 1492 °C; the melting point of pure iron T melt = 1538 °C; the liquidus slope k0 = 0.39, the specific heat capacity of steel C p = 740 J·kg -1 ·K -1 , the thermal conductivity of steel λ = 35 W·m -1 ·K -1 .

[0077] S3. Determine the ideal heat flux density of round billet solidification;

[0078] For this specific embodiment, based on the process conditions and physical property parameters given in this embodiment, the relationship between the heat flux density and the casting time can be calculated using Equation 14 and Equation 11, as shown in Figure 3 .

[0079] S4. Determine the target surface temperature

[0080] Using the ideal heat flux density expression determined above as the boundary condition, solve the one-dimensional solidification heat transfer equation established by Equations 15 - 17, and the target surface temperature under the conditions of this embodiment can be obtained, as shown in Figure 4 .

[0081] If it is necessary to rewrite the time t as a function of the distance Z to the meniscus, since t = Z / V c , then the result is as shown in Figure 5 .

[0082] When using a method for determining the target surface temperature of secondary cooling in round billet continuous casting according to this embodiment, in specific use, the present invention first establishes a one-dimensional solidification heat transfer mathematical model for round billet continuous casting; according to the solidification law of round billets, an ideal heat flux density expression during the solidification process of round billets is derived; the derived ideal heat flux density expression is used as the boundary condition of the one-dimensional solidification heat transfer mathematical model to calculate the target surface temperature under different steel grades, cross-sections, and casting speeds, enabling the present invention to be a method for determining the target surface temperature of secondary cooling in round billets that can clearly, quantitatively, and quickly adapt to different production conditions, effectively improving the stability of the quality of continuous casting billets, reducing billet defects, and optimizing the production process, thereby solving the technical problems in the prior art that a quantitative temperature curve cannot be obtained therefrom, the target surface temperatures formulated by different researchers vary greatly, and the target surface temperature under different process conditions cannot be formulated specifically.

[0083] The above-disclosed is only a preferred embodiment of the present invention, and of course, it cannot be used to limit the scope of rights of the present invention. Those of ordinary skill in the art can understand the entire or partial processes of implementing the above embodiments, and the equivalent changes made according to the claims of the present invention still fall within the scope covered by the invention.

Claims

1. A method for determining the target surface temperature of secondary cooling in round billet continuous casting, characterized in that: It includes the following steps: Establish a one-dimensional solidification heat transfer mathematical model for round billet continuous casting; According to the solidification law of round billets, derive the expression of ideal heat flux density during the solidification process of round billets; Use the derived expression of ideal heat flux density as the boundary condition of the one-dimensional solidification heat transfer mathematical model to calculate the target surface temperature under different steel grades, cross-sections, and casting speeds.

2. The method for determining the target surface temperature of secondary cooling in round billet continuous casting according to claim 1, characterized in that: The derived expression of ideal heat flux density is: where q is the heat flux density, kW·m -2 ; ρ is the density, kg·m -3 ; L is the latent heat of solidification, J·kg -1 ; K R is the solidification coefficient of the round billet, taken as 21 mm·min -1 / 2 ; R is the radius of the round billet, mm; r is the inner diameter of the solidified shell.

3. The method for determining the target surface temperature of secondary cooling in round billet continuous casting according to claim 2, characterized in that: The calculation formula for the inner diameter r of the solidified shell is: In the formula, t is the solidification time, with the unit of min.

Images