A method for dynamic spray control of secondary cooling water in a continuous casting process of a casting blank

Abstract

A kind of secondary cooling water dynamic spraying control method of casting billet continuous casting process, for the section with free width cutting nozzle in secondary cooling control area, the calculation of periodic real-time dynamic spraying width in each section is established, and the control of corresponding dynamic spraying height of cooling nozzle in each section is formed according to the calculation.The secondary cooling water dynamic spraying control method of casting billet continuous casting process of the present application is based on real-time billet temperature tracking, and the calculation of real-time spraying width in each section is established for each secondary cooling section with free width cutting nozzle, and the dynamic adjustment of spraying height of cooling nozzle in corresponding section is realized based on this, to effectively avoid the purpose of overcooling of casting billet corner, thereby improving the uniformity of casting billet surface temperature.

Description

Technical Field

[0001] This invention belongs to the field of metallurgical production technology, specifically relating to a method for dynamic spray control of secondary cooling water in the continuous casting process of billets. Background Technology

[0002] In the continuous casting process, the section from the crystallizer outlet to the casting machine outlet is the secondary cooling water control zone. Within this zone, several cooling control areas are divided along the casting length, each consisting of several nozzles. During continuous casting production, the required water volume for each cooling area is calculated based on information such as the secondary cooling water process, casting speed, and measured temperature, thus achieving water volume setting control. Secondary cooling water control is one of the important process parameters for continuous casting billet quality control, and it is closely related to the formation of defects such as cracks in the billet. Secondary cooling water control is divided into two main categories: static control and dynamic control. Static control is an open-loop control method, generally calculated based on the actual casting speed or model, and the water volume in the secondary cooling control zone is directly calculated using a static water meter for water volume setting. Dynamic control is a closed-loop control method, with various dynamic control modes depending on the feedback object. The most common is billet surface temperature feedback control; in addition, modes based on billet shell thickness feedback control and billet surface temperature gradient feedback control have also been studied, but there are no mature application cases in China.

[0003] For cast slabs, excessively low corner temperatures can easily lead to corner cracks. Meanwhile, steel mills are actively promoting hot charging and delivery of continuously cast slabs, and excessively low temperatures at the edges or corners are detrimental to the efficient utilization of residual heat. Therefore, achieving high-precision temperature control along the width of the cast slab has become a technical problem that needs to be solved. Known patent literature mainly involves continuous casting cooling water control equipment, continuous casting cooling process control based on product characteristics, and automatic control methods for secondary cooling water based on online measurement of slab temperature and shell thickness. The online control methods for secondary cooling water involved here are basically zoned control along the length of the cast slab.

[0004] The invention application with application number CN201110431125.6 discloses "a method for controlling the secondary cooling water spray width of a slab continuous casting machine." It primarily uses the secondary cooling water spray width of slabs of different steel grades and widths, determined through simulation calculations of the temperature field in the secondary cooling zone and field experiments, as a basis to drive a guide device mainly composed of a support frame and a collection guide pipe. This device collects and discharges excess cooling water sprayed from the edge spray pipes of each row of spray pipes on the inner arc of the fan-shaped section, achieving precise online spray width control of the secondary cooling water spray width within the fan-shaped section. However, it only determines the secondary cooling water spray width of the inner arc of the fan-shaped section based on the specifications of the slab. Summary of the Invention

[0005] To address the above problems, this invention provides a method for dynamic spray control of secondary cooling water in the continuous casting process of billets, the specific technical solution of which is as follows:

[0006] A method for dynamic spray control of secondary cooling water in the continuous casting process of billets, characterized in that:

[0007] For the sections in the secondary cooling control zone equipped with free-width cutting nozzles, the periodic real-time dynamic spray width in each section is calculated, and the dynamic spray height of the cooling nozzles in each section is controlled accordingly.

[0008] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0009] The conversion from spray width to spray height is accomplished through linear transformation.

[0010] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0011] The linear transformation mentioned above is specifically as follows:

[0012]

[0013] In the formula,

[0014] h: Spray height, unit: m;

[0015] h min Minimum nozzle adjustment height, unit: m;

[0016] h max Maximum adjustable height of the nozzle, in meters (m).

[0017] W max : Maximum spray width corresponding to the maximum adjustable height of the nozzle, in meters;

[0018] W min Minimum spray width corresponding to the minimum nozzle adjustment height, in meters;

[0019] W: The currently calculated spray width, in meters.

[0020] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0021] The calculation of the periodic real-time dynamic spray width within each section is specifically as follows:

[0022] First, the billet is divided into slices along its length, and real-time position tracking of each slice is established.

[0023] Then, at each cycle time, the slice closest to the end point of each segment at that time is determined;

[0024] Finally, the spray width of this slice in each section is calculated, and the calculation results are used to characterize the spray width of the corresponding section.

[0025] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0026] The spray width of the slice closest to the end of each section is determined based on the following formula:

[0027] W = 2 × (w1 + p),

[0028] in,

[0029] W: Spray width, unit: m;

[0030] w1: The distance from the solidification position along the slice width to the center of the slice, in meters;

[0031] p: Distance from the solidification endpoint in the slice width direction, determined by product characteristics, unit: m.

[0032] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0033] Real-time position tracking of each slice is performed using the following formula:

[0034] P i k =P i k-1 +v×t,

[0035] in,

[0036] P i k Position of slice i at time k, in meters;

[0037] P i k-1 : The position of slice i at time k-1, in meters;

[0038] t: Tracking period, in minutes;

[0039] v: Average billet pulling speed during the tracking period t, in m / min.

[0040] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0041] The distance w1 from the solidification position along the slice width to the center of the slice is determined according to the following steps:

[0042] S1: The slice is meshed based on the finite element method to form mesh nodes in the thickness and width directions;

[0043] S2: Calculate the temperature at each node based on the two-dimensional partial differential equation of heat conduction;

[0044] S3: By determining the temperature of each node in the width direction, the range where the solidification location is located is determined;

[0045] S4: Determine the solidification location using interpolation based on the node temperature, location coordinates, and solidus temperature of the interval.

[0046] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0047] The two-dimensional heat conduction partial differential equation in step S2 is based on the conservation of thermal energy considering the latent heat of phase change. In actual calculations, the latent heat is processed by the equivalent specific heat method. The two dimensions are based on the width and thickness directions.

[0048] The calculation of the temperatures at each node is based on the temperature of the molten steel in the tundish as the initial condition and the third type of boundary condition in heat transfer as the boundary condition.

[0049] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0050] The heat transfer coefficient of the spray zone is determined by the following formula:

[0051] h = A × F B +C,

[0052] For the heat transfer coefficient of the areas on the upper and lower surfaces of the billet that are not spray-cooled, the heat transfer coefficient is determined by the following formula:

[0053] h=τ×A×F B +C;

[0054] For the area on the side of the billet without spray cooling, the heat transfer coefficient is taken as 75 J / (m²). 2 Processing of .sk);

[0055] In the formula,

[0056] h: Heat transfer coefficient, unit: J / (m²) 2 .sk);

[0057] F: Nozzle water flow density, unit: l / min·m 2 ;

[0058] A, B, C: Regression coefficients;

[0059] τ; adjustment coefficient.

[0060] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0061] The adjustment coefficient τ ranges from [1 / 3, 1 / 2].

[0062] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0063] The regression coefficients can be determined based on the regression of historical data from continuous casting production, or by directly using the coefficients provided by the nozzle manufacturer.

[0064] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0065] Step S3 is specifically determined based on the following discriminant:

[0066]

[0067] in,

[0068] T(x1,(N+1) / 2): Calculated temperature of slice node (x1,(N+1) / 2), in °C;

[0069] T(x1+1,(N+1) / 2): Calculated temperature of slice node (x1+1,(N+1) / 2), unit: °C

[0070] T S Solidus temperature of the billet, unit: °C.

[0071] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0072] The grid is divided using a coordinate system with the center of the slice as the origin, the width direction as the X-axis, and the thickness direction as the Y-axis.

[0073] Step S3 is performed by determining the temperature of the nodes on the center line of the slice width direction.

[0074] According to the present invention, a method for dynamic spray control of secondary cooling water in the continuous casting process of billet is characterized in that:

[0075] The solidification location determined in step S4 is specifically based on the following formula:

[0076]

[0077] in,

[0078] w1: The distance from the solidification position along the slice width to the center of the slice, in meters;

[0079] W0: Slab width, unit: m;

[0080] x1: The x1th node in the width direction;

[0081] T(x1,(N+1) / 2): Calculated temperature of slice node (x1,(N+1) / 2), in °C;

[0082] T(x1+1,(N+1) / 2): Calculated temperature of slice node (x1+1,(N+1) / 2), unit: °C

[0083] T S Solidus temperature of the billet, unit: °C.

[0084] The present invention discloses a dynamic spray control method for secondary cooling water in the continuous casting process of billet. Based on real-time billet temperature tracking, the method calculates the real-time spray width of each secondary cooling zone equipped with free-width cutting nozzles, and uses this as a basis to dynamically adjust the spray height of the cooling nozzles in the corresponding zone. This control method effectively avoids overcooling of the corners of the billet and thus improves the surface temperature uniformity of the billet. Attached Figure Description

[0085] Figure 1 This is a schematic diagram illustrating the steps of determining the distance w1 from the solidification position in the slice width direction to the slice center in this invention.

[0086] Figure 2 This is a schematic diagram of the overall control flow of the working principle of this invention;

[0087] Figure 3 This is a schematic diagram of the solidification state of a cross-section of the working principle of this invention;

[0088] Figure 4 This is a schematic diagram of the slice temperature distribution in an embodiment of the present invention;

[0089] Figure 5 This is a schematic diagram comparing the temperature distribution of the two types of cast billets before and after in an embodiment of the present invention. Detailed Implementation

[0090] The following is a detailed description of a dynamic spray control method for secondary cooling water in the continuous casting process of a billet according to the present invention, based on the accompanying drawings and specific embodiments.

[0091] A dynamic spray control method for secondary cooling water in the continuous casting process of billet is proposed. For the section in the secondary cooling control zone equipped with free-width cutting nozzles, the method establishes the calculation of the periodic real-time dynamic spray width in each section, and calculates the control of the dynamic spray height of the cooling nozzles in each section accordingly.

[0092] in,

[0093] The conversion from spray width to spray height is accomplished through linear transformation.

[0094] in,

[0095] The linear transformation mentioned above is specifically as follows:

[0096]

[0097] In the formula,

[0098] h: Spray height, unit: m;

[0099] h min Minimum nozzle adjustment height, unit: m;

[0100] h max Maximum adjustable height of the nozzle, in meters (m).

[0101] W max : Maximum spray width corresponding to the maximum adjustable height of the nozzle, in meters;

[0102] W min Minimum spray width corresponding to the minimum nozzle adjustment height, in meters;

[0103] W: The currently calculated spray width, in meters.

[0104] in,

[0105] The calculation of the periodic real-time dynamic spray width within each section is specifically as follows:

[0106] First, the billet is divided into slices along its length, and real-time position tracking of each slice is established.

[0107] Then, at each cycle time, the slice closest to the end point of each segment at that time is determined;

[0108] Finally, the spray width of this slice in each section is calculated, and the calculation results are used to characterize the spray width of the corresponding section.

[0109] in,

[0110] The spray width of the slice closest to the end of each section is determined based on the following formula:

[0111] W = 2 × (w1 + p),

[0112] in,

[0113] W: Spray width, unit: m;

[0114] w1: The distance from the solidification position along the slice width to the center of the slice, in meters;

[0115] p: Distance from the solidification endpoint in the slice width direction, determined by product characteristics, unit: m.

[0116] in,

[0117] Real-time position tracking of each slice is performed using the following formula:

[0118] P i k =P i k-1 +v×t,

[0119] in,

[0120] P i k Position of slice i at time k, in meters;

[0121] P i k-1 : The position of slice i at time k-1, in meters;

[0122] t: Tracking period, in minutes;

[0123] v: Average billet pulling speed during the tracking period t, in m / min.

[0124] in,

[0125] The distance w1 from the solidification position along the slice width to the slice center is determined according to the following steps (see...). Figure 1 ):

[0126] S1: The slice is meshed based on the finite element method to form mesh nodes in the thickness and width directions;

[0127] S2: Calculate the temperature at each node based on the two-dimensional partial differential equation of heat conduction;

[0128] S3: By determining the temperature of each node in the width direction, the range where the solidification location is located is determined;

[0129] S4: Determine the solidification location using interpolation based on the node temperature, location coordinates, and solidus temperature of the interval.

[0130] in,

[0131] The two-dimensional heat conduction partial differential equation in step S2 is based on the conservation of thermal energy considering the latent heat of phase change. In actual calculations, the latent heat is processed by the equivalent specific heat method. The two dimensions are based on the width and thickness directions.

[0132] The calculation of the temperatures at each node is based on the temperature of the molten steel in the tundish as the initial condition and the third type of boundary condition in heat transfer as the boundary condition.

[0133] in,

[0134] The heat transfer coefficient of the spray zone is determined by the following formula:

[0135] h = A × F B +C,

[0136] For the heat transfer coefficient of the areas on the upper and lower surfaces of the billet that are not spray-cooled, the heat transfer coefficient is determined by the following formula:

[0137] h=τ×A×F B +C;

[0138] For the area on the side of the billet without spray cooling, the heat transfer coefficient is taken as 75 J / (m²). 2 Processing of .sk);

[0139] In the formula,

[0140] h: Heat transfer coefficient, unit: J / (m²) 2 .sk);

[0141] F: Nozzle water flow density, unit: l / min·m 2 ;

[0142] A, B, C: Regression coefficients;

[0143] τ; adjustment coefficient.

[0144] in,

[0145] The adjustment coefficient τ ranges from [1 / 3, 1 / 2].

[0146] in,

[0147] The regression coefficients can be determined based on the regression of historical data from continuous casting production, or by directly using the coefficients provided by the nozzle manufacturer.

[0148] in,

[0149] Step S3 is specifically determined based on the following discriminant:

[0150]

[0151] in,

[0152] T(x1,(N+1) / 2): Calculated temperature of slice node (x1,(N+1) / 2), in °C;

[0153] T(x1+1,(N+1) / 2): Calculated temperature of slice node (x1+1,(N+1) / 2), unit: °C

[0154] T S Solidus temperature of the billet, unit: °C.

[0155] in,

[0156] The grid is divided using a coordinate system with the center of the slice as the origin, the width direction as the X-axis, and the thickness direction as the Y-axis.

[0157] Step S3 is performed by determining the temperature of the nodes on the center line of the slice width direction.

[0158] in,

[0159] The solidification location determined in step S4 is specifically based on the following formula:

[0160]

[0161] in,

[0162] w1: The distance from the solidification position along the slice width to the center of the slice, in meters;

[0163] W0: Slab width, unit: m;

[0164] x1: The x1th node in the width direction;

[0165] T(x1,(N+1) / 2): Calculated temperature of slice node (x1,(N+1) / 2), in °C;

[0166] T(x1+1,(N+1) / 2): Calculated temperature of slice node (x1+1,(N+1) / 2), unit: °C

[0167] T S Solidus temperature of the billet, unit: °C.

[0168] Working principle

[0169] To facilitate understanding of this technical solution, the technical points involved are described below. For specific implementation processes, please refer to the embodiments and combine them with... Figure 2 .

[0170] This technical solution provides a dynamic spray control method for secondary cooling water in the continuous casting process of billets. By constructing a process control standard for the width direction of the billet under secondary cooling water, and based on the online tracking of the billet's 3D temperature, the method dynamically adjusts the cooling water volume and spray width of different cooling zones to achieve precise control of the billet's width direction temperature, improve the uniformity of the billet's surface temperature, and enhance the quality of the billet's corners.

[0171] Specifically, to avoid overcooling at the corners of the billet and improve the surface temperature uniformity of the billet, the secondary cooling zone of continuous casting adopts cooling nozzles with free slitting function. The spraying height of the cooling nozzles can be adjusted to achieve free control of the spraying width of the billet. A process control standard for the width direction of the billet is constructed. For each secondary cooling control zone, the spraying width of the corresponding cooling zone is defined according to formula (1):

[0172] W = 2 × (w1 + p) (1)

[0173] Where W is the spray width set in the current secondary cooling control zone, which needs to meet the constraints of the maximum and minimum spray width of the cooling device; w1 is the solidification position in the slice width direction at the end position of the current secondary cooling control zone; p is the distance from the solidification end point in the width direction of the billet, which is the process control parameter defined in this method and is related to the product characteristics.

[0174] like Figure 3 The image shows a cross-section of a cast billet, with the center of the slice as the origin. The area enclosed by the ellipse represents the liquid core in the cross-section of the billet, and w is the solidification location in the width direction of the slice.

[0175] Starting from the continuous casting crystallizer, a slice tracking system is established along the width and thickness of the billet. The slice temperature and solidification state are iteratively calculated, and combined with predefined control standards for the spraying process along the width of the billet, dynamic control of the secondary cooling water spray width is achieved. The specific implementation process is described below.

[0176] 1. Online tracking of billet slice position

[0177] The position tracking of the slab slices is achieved in a periodic manner.

[0178] P i k =P i k-1 +v×t (2)

[0179] Among them, P i k P i k-1 , respectively, represent the positions of slice i at time k and time k-1, in meters; t is the calculation period, in minutes; v is the average throwing speed within the calculation period t, in meters per minute.

[0180] 2. Calculate the temperature distribution of the slices

[0181] The temperature distribution of all slab slices along the length of the slab is calculated iteratively using a 2D partial differential equation of heat conduction, enabling 3D online temperature tracking in the length, thickness, and width directions of the slab.

[0182]

[0183] Where T = T(x,y,t), M and N are the number of grid nodes in the width and thickness directions, respectively, and are odd numbers;

[0184] ρ: Density [kg / m³] 3 c: Specific heat [kcal / kg] 0 C];λ:thermal conductivity [kcal / m·hr] 0 C];

[0185] Q t (x,t) represents the heat flow absorbed by the upper surface of the cast billet, Q. b (x,t) represents the heat flow absorbed by the lower surface of the billet, Q. r (y,t) represents the heat flow absorbed by the right side of the billet, Q. l (y,t) represents the heat flow absorbed by the left side of the billet; Q* represents the latent heat of solidification of the billet. In the calculation, the influence of the latent heat of solidification of the billet is compensated by the specific heat of the billet.

[0186] In the calculation, the effect of the latent heat of solidification Q* of the billet is compensated by the specific heat of the billet.

[0187] The initial condition is the temperature of the molten steel in the tundish, and the boundary condition is the third type of boundary condition.

[0188] Heat transfer on the surface of the cast billet involves various methods, including water cooling, heat transfer through contact with the casting rolls, and thermal radiation, but water cooling is the primary method. Therefore, the heat transfer boundary conditions are simplified here, and only the simplified heat exchange is considered for the cooling zone. The heat transfer coefficient is further considered separately as follows:

[0189] For the heat transfer coefficient of the spray area, formula (4) is used for simplified calculation:

[0190] h = A × F B +C (4)

[0191] Where A, B, and C are regression coefficients, F is the nozzle water flow density, and h is the heat transfer coefficient;

[0192] For the heat transfer coefficient of the areas on the upper and lower surfaces of the billet that are not spray-cooled, the heat transfer coefficient is determined by the following formula:

[0193] h=τ×A×F B +C,

[0194] τ; adjustment coefficient, with a value range of [1 / 3, 1 / 2];

[0195] For the area on the side of the billet without spray cooling, the heat transfer coefficient is taken as 75 J / (m²). 2 Processing of .sk).

[0196] Solving two-dimensional partial differential equations of heat conduction is a mature technique, which will not be elaborated here.

[0197] 3. Calculate the solidification position of the billet in the width direction at the end of each cooling zone.

[0198] Select the section of the billet that is closest to the end of each cooling zone. The solidification endpoint in the width direction of the billet is as follows: Figure 3 The vertex of the liquid core in the slice shown is located in the width direction, which is approximately taken as the solidification endpoint on the center line of the billet thickness. Specifically, starting from the center of the slice, the node temperature on the right side of the slice is determined. If there are nodes (x1, N+1 / 2) and (x1+1, N+1 / 2) that satisfy formula (5), then the solidification position in the width direction of the billet is calculated by formula (6); otherwise, it means that the billet at this slice position has been completely solidified, and w = 0.

[0199]

[0200]

[0201] Among them, T S : Solidus temperature of the billet (°C); W0: Width of the billet (m); T(x1,(N+1) / 2) represents the calculated temperature of node (x1,(N+1) / 2) within the slice. Wherein, the formula... This represents the distance between nodes in the width direction.

[0202] 4. Dynamically determine the spray width of the secondary cooling zone based on process control standards.

[0203] Formula (1) is used to calculate the spray width of different secondary cooling zones.

[0204] When specifying process control standards, the process control parameter p needs to be designed in conjunction with the product cooling control requirements. In the secondary cooling water distribution process, the water volume in the cooling zone before the billet completely solidifies is large, while the water volume in the subsequent cooling zone is small. For steel grades sensitive to crack temperature, precise control of the water volume before the billet completely solidifies is crucial.

[0205] 5. The PLC dynamically adjusts the nozzle position according to the spray width.

[0206] Step (4) calculates the spray width of each control zone and sends it to the secondary cooling water PLC control system to realize the adjustment control of the corresponding nozzle height. The conversion function between nozzle height and spray width is an inherent parameter of the spray equipment, and an approximate linear conversion method can be used in actual control.

[0207]

[0208] Among them, h min h max These are the minimum and maximum adjustment heights of the nozzle, respectively; W min W max These are the minimum spray width and maximum spray width corresponding to the minimum and maximum adjustment heights of the nozzle, respectively.

[0209] Example

[0210] Assuming a continuous casting production line with the top of the crystallizer as the origin, the crystallizer height is 0.8m, and the casting machine has 13 secondary cooling control zones with the following configuration information: Secondary cooling control zones without free-cutting nozzles have their spray width controlled at the maximum spray width of 1.8m; secondary cooling control zones with free-cutting nozzles have a spray width range of [0.8m, 1.8m] and a nozzle height adjustment range of [0.15m, 0.30m]. Secondary cooling control zones 1 and 2 are equipped with cooling nozzles on their sides, while the other secondary cooling control zones only allow water cooling control on the upper and lower surfaces of the cast billet.

[0211] Secondary cooling control area End position of length (m) Free sectional 1 1.1 NO 2 1.6 NO 3 2.7 YES 4 4.4 YES 5 6.4 YES 6 10.3 YES 7 14.4 YES 8 16.5 YES 9 21.1 YES 10 25.7 NO 11 30.2 NO 12 34.8 NO 13 39.3 NO

[0212] For a given product with a billet size of 1200mm × 250mm, define the process control standards for the width direction of the billet:

[0213] Secondary cooling control area Width-direction position control parameter p(m) 3 0.05 4 0.05 5 0.05 6 0.05 7 0.00 8 0.00 9 0.00

[0214] 1. Online tracking of billet slice position

[0215] Along the casting direction of the billet, cross-sectional slices of the billet are taken at 50mm intervals for online tracking of the billet. The tracking calculation cycle is 10s, and the continuous casting speed is 1.2m / min.

[0216] Assume the slice position tracking information from the previous period is as follows:

[0217]

[0218]

[0219] The billet moves a distance of v×t in one cycle: v×t=1.2×10 / 60=0.2m. The newly formed tracking queue is as follows: the slices of the previous tracking sequence correspond to indices 5 to 804 in the new sequence. The slice indices 1 to 4 in the new sequence are the newly generated tracking slices in this calculation cycle. By continuously scrolling and refreshing, the dynamic tracking of the slice position is achieved. Generally, when the slice reaches the billet flame cutting position, it can be deleted from the tracking queue.

[0220] Slice Index Slice position m Corresponding casting length m 1 0.05 200.2 2 0.1 200.15 3 0.15 200.1 4 0.2 200.05 5 0.25 200 6 0.3 199.95 7 0.35 199.9 8 0.4 199.85 9 0.45 199.8 10 0.5 199.75 …… …… 199.7 799 39.95 199.65 800 40 199.6 801 40.05 199.55 802 40.1 199.5 803 40.15 199.45 804 40.2 199.4

[0221] 2. Calculate the temperature distribution of the slices

[0222] Without loss of generality, taking parameters A = 8.9, B = 0.795, C = 95, tundish steel temperature 1560℃, solidus temperature TS = 1510℃, liquidus temperature TLL = 1540℃, and assuming the spray water flow density of each cooling zone nozzle at a billet drawing speed of 1.2 m / min is as shown in the table below, the formula h = A × F is used. B +C, where the vertical sections (zones 1, 2, 3, and 4) are adjusted by a multiplicative correction factor of 0.85 based on the calculated heat exchange coefficient. The calculated heat exchange coefficients for each cooling zone's spray area are shown below:

[0223]

[0224]

[0225] For the heat transfer coefficient of the areas on the upper and lower surfaces of the billet that are not spray-cooled, the heat transfer coefficient is determined by the following formula:

[0226] h=τ×A×F B +C; In this embodiment, the value of τ is uniformly taken as 0.5; The value of τ for the area on the side of the billet without spray cooling is 75 J / (m 2 .sk).

[0227] Based on dynamic tracking of the billet slices, iterative calculations using the 2D partial differential heat conduction equation were performed on all slices. In this case, the number of nodes N=7 in the billet thickness direction and M=17 in the width direction were used. The obtained temperature information is as follows: Figure 4 As shown in the figure, the horizontal axis represents the slice location, and the vertical axis represents the temperature.

[0228] 3. Calculate the solidification position of the billet in the width direction at the end of each cooling zone.

[0229] The above temperature calculation results are used to determine the solidification position of the billet in the width direction at the end of each cooling zone. This will be illustrated using secondary cooling control zone 3 as an example.

[0230] The end position of the secondary cooling control zone 3 is 2.7m, and the slice index of the nearest slice to this position is 54. It should be noted that during the initial or final pouring, if the billet has not yet reached the end position of the control zone or has already left the control zone, continuous casting will use the corresponding initial or final pouring cooling control strategy, and this method will not be used. In this case, the billet surface uses a symmetrical heat exchange coefficient, and the calculated temperature exhibits symmetry. The temperature node is taken as 1 / 4 area of ​​the slice.

[0231] node 9 10 11 12 13 14 15 16 17 1 867.5 867.5 867.5 867.5 867.5 867.5 867.2 858.0 722.8 2 1534.6 1534.6 1534.6 1534.6 1534.6 1534.6 1534.6 1530.1 1224.7 3 1554.3 1554.3 1554.3 1554.3 1554.3 1554.3 1553.5 1542.3 1308.9 4 1558.3 1558.3 1558.3 1558.3 1558.3 1558.2 1557.2 1542.8 1318.3

[0232] Temperature along the center line of the billet thickness is:

[0233]

[0234]

[0235] The solidus temperature of the cast billet is 1510℃, according to the following formula:

[0236]

[0237] We arrive at x1 = 16, using the formula:

[0238]

[0239]

[0240] In the same way, calculate the solidification position of the billet in the width direction in other secondary cooling control zones.

[0241] Secondary cooling control area Position along the casting length (m) Solidification position (m) in the width direction of the cast billet 3 2.7 0.536 4 4.4 0.535 5 6.4 0.534 6 10.3 0.532 7 14.4 0.530 8 16.5 0.528 9 21.1 0.461

[0242] 4. Dynamically determine the spray width of the secondary cooling zone based on process control standards.

[0243] Formula (1) is used to calculate the spray width of different secondary cooling zones.

[0244] For the secondary cooling control zone 3, the process control standard specifies p = 0.05m. Calculate the spray width using the formula:

[0245] W=2×(w+p)=2×(0.536+0.05)=1.172m

[0246] Similarly, the spray width information for the other several secondary cooling control zones is calculated as follows:

[0247]

[0248] 5. The PLC dynamically adjusts the nozzle position according to the spray width.

[0249] Step (4) calculates the spray width of each control zone and sends it to the secondary cooling water PLC control system to realize the adjustment control of the corresponding nozzle height. The conversion function between nozzle height and spray width is an inherent parameter of the spray equipment, and an approximate linear conversion is used in actual control.

[0250] For example, the secondary cooling control zone 3 is calculated using a formula.

[0251]

[0252] Similarly, the free-width nozzle height adjustment for other secondary cooling control zones is calculated as follows:

[0253]

[0254] After adjusting the spray width, the temperature tracking comparison of the cast billet slices is as follows: Figure 5 As can be seen, by adjusting the spray width, the temperature at the corner of the billet increases and the uniformity of the surface temperature is significantly improved. Therefore, the dynamic adjustment method for the cooling width of the billet provided by this method is beneficial to the continuous casting production control of products with special temperature control requirements.

Claims

1. A method for dynamic spray control of secondary cooling water in the continuous casting process of billets, characterized in that: For sections of the secondary cooling control zone equipped with free-cutting nozzles, the periodic real-time dynamic spray width within each section is calculated, and based on this, the dynamic spray height of the cooling nozzles within each section is controlled. The conversion from spray width to spray height is achieved through linear transformation. The linear transformation mentioned above is specifically as follows: ， In the formula, h: Spray height, unit: m; h min Minimum nozzle adjustment height, unit: m; h max Maximum adjustable height of the nozzle, in meters (m). W max : Maximum spray width corresponding to the maximum adjustable height of the nozzle, in meters; W min Minimum spray width corresponding to the minimum nozzle adjustment height, in meters; W: The currently calculated spray width, in meters. The calculation of the periodic real-time dynamic spray width within each section is specifically as follows: First, the billet is divided into slices along its length, and real-time position tracking of each slice is established. Then, at each cycle time, the slice closest to the end point of each segment at that time is determined; Finally, the spray width of this slice in each section is calculated, and the calculation results are used to characterize the spray width of the corresponding section. The spray width of the slice closest to the end of each section is determined based on the following formula: ， in, Spray width, unit: m; : The distance from the solidification position along the width of the slice to the center of the slice, in meters; : The distance from the solidification endpoint in the width direction of the slice, determined by the product characteristics, in meters.

2. The method for dynamic spray control of secondary cooling water in the continuous casting process of billet according to claim 1, characterized in that: Real-time position tracking of each slice is performed using the following formula: ， in, Position of slice i at time k, in meters; : The position of slice i at time k-1, in meters; Tracking period, in minutes; : Average billet pulling speed during the tracking period t, in m / min.

3. The method for dynamic spray control of secondary cooling water in the continuous casting process of billet according to claim 1, characterized in that: Distance of the solidification position from the center of the slice along its width Specifically, it is determined according to the following steps: S1: The slice is meshed based on the finite element method to form mesh nodes in the thickness and width directions; S2: Calculate the temperature at each node based on the two-dimensional partial differential equation of heat conduction; S3: By determining the temperature of each node in the width direction, the range where the solidification location is located is determined; S4: Determine the solidification location using interpolation based on the node temperature, location coordinates, and solidus temperature of the interval.

4. The method for dynamic spray control of secondary cooling water in the continuous casting process of billet according to claim 3, characterized in that: The two-dimensional heat conduction partial differential equation in step S2 is based on the conservation of thermal energy considering the latent heat of phase change. In actual calculations, the latent heat is processed by the equivalent specific heat method. The two dimensions are based on the width and thickness directions. The calculation of the temperatures at each node is based on the temperature of the molten steel in the tundish as the initial condition and the third type of boundary condition in heat transfer as the boundary condition.

5. The method for dynamic spray control of secondary cooling water in the continuous casting process of billet according to claim 4, characterized in that: The heat transfer coefficient of the spray zone is determined by the following formula: ， For the heat transfer coefficient of the areas on the upper and lower surfaces of the billet that are not spray-cooled, the heat transfer coefficient is determined by the following formula: ； For the area on the side of the billet without spray cooling, the heat transfer coefficient is taken as 75 J / (m²). 2 Processing of .sk); In the formula, Heat transfer coefficient, unit: J / (m³) 2 .sk); Nozzle water flow density, unit: ; A, B, C: Regression coefficients; ; Adjustment coefficient.

6. The method for dynamic spray control of secondary cooling water in the continuous casting process of billet according to claim 5, characterized in that: Adjustment coefficient The value range is [1 / 3, 1 / 2].

7. The method for dynamic spray control of secondary cooling water in the continuous casting process of billet according to claim 5, characterized in that: The regression coefficients can be determined based on the regression of historical data from continuous casting production, or by directly using the coefficients provided by the nozzle manufacturer.

8. The method for dynamic spray control of secondary cooling water in the continuous casting process of billet according to claim 2, characterized in that: Step S3 is specifically determined based on the following discriminant: ， in, N is the number of nodes in the thickness direction of the slab slice. Slice node The calculated temperature, in °C; Slice node Calculated temperature, unit: ℃ Solidus temperature of the billet, unit: °C.

9. The method for dynamic spray control of secondary cooling water in the continuous casting process of billet according to claim 3, characterized in that: The grid is divided using a coordinate system with the center of the slice as the origin, the width direction as the X-axis, and the thickness direction as the Y-axis. Step S3 is performed by determining the temperature of the nodes on the center line of the slice width direction.

10. The method for dynamic spray control of secondary cooling water in the continuous casting process of billet according to claim 7, characterized in that: The solidification location determined in step S4 is specifically based on the following formula: ， in, M: Number of nodes in the width direction of the billet slice. N is the number of nodes in the thickness direction of the slab slice. : The distance from the solidification position along the width of the slice to the center of the slice, in meters; : Slab width, unit: m; : the first in the width direction One node; Slice node The calculated temperature, in °C; Slice node Calculated temperature, unit: ℃ Solidus temperature of the billet, unit: °C.

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