A method for controlling the bulging defect in continuously cast small square billets

Abstract

This invention discloses a method for controlling the bulging defect in continuously cast small square billets, belonging to the field of metallurgical technology. The method involves uniformly selecting several evaluation points along the distance from the crystallizer outlet to the last straightening roller of the straightening machine, numbering them sequentially, and then sequentially designing the roller conveyor process and water cooling process. By comparing the critical billet shell thickness for bulging with the estimated billet shell thickness, it can be determined whether the billet will develop a bulging defect. Based on the calculation results, the roller conveyor layout and cooling process of the continuous casting machine are designed, and the critical number of opening cooling water nozzles is optimized to maximize the billet's hot delivery temperature while preventing bulging defects. This data calculation method replaces the current method of gradually adjusting the number of opening cooling water nozzles through multiple field experiments. It has the advantages of fast calculation speed, high efficiency, low cost of adjusting the secondary cooling process in continuous casting, high accuracy, and improved automation and intelligent operation of continuous casting.

Description

Technical Field

[0001] This invention belongs to the field of metallurgical technology, specifically relating to a method for controlling the bulging defect in continuously cast small square billets. Background Technology

[0002] Small billets generally refer to billets with a cross-section of less than 200mm×200mm. They are widely used in the production of rebar. The compression ratio in the rebar production process is large, and the requirements for internal quality such as billet segregation and shrinkage are not high. The most important parameter for billets is the hot delivery temperature. Increasing the hot delivery temperature can reduce the gas consumption of the heating furnace and reduce costs. It is generally believed that every 10℃ increase in the hot delivery temperature of billets can reduce energy consumption costs by 0.5 yuan / ton of steel.

[0003] In the continuous casting process, after cooling in the crystallizer and secondary cooling in the secondary cooling chamber, the molten steel gradually solidifies into a billet. The heat of the billet is carried away by the cooling water. Therefore, the hot delivery temperature of the billet can be increased by reducing the amount of cooling water. However, too little cooling water will cause the billet to bulge.

[0004] Bulging of the billet occurs when the strength of the solidified billet shell is insufficient to withstand the static pressure of the molten steel, causing it to bulge into a convex surface. Current technology primarily involves on-site workers conducting experiments by gradually reducing the number of cooling water nozzles in operation. They observe and test the bulging defect at this number of nozzles. If no bulging defect is observed, the number of nozzles is further reduced until the billet begins to bulge. This method, which aims to determine the critical number of nozzles to prevent bulging, often requires dozens of trials. This approach suffers from high labor intensity, low efficiency, and poor adaptability to drastic changes in billet casting speed. Summary of the Invention

[0005] To address some or all of the technical problems existing in the prior art, the present invention provides a method for controlling the bulging defect in continuously cast small square billets.

[0006] The method for controlling the bulging defect in continuously cast small square billets provided by this invention includes:

[0007] Step S1: Select several evaluation points evenly along the distance from the outlet of the crystallizer to the last straightening roller of the straightening machine, and number them sequentially as S. 铸坯1 ~S 铸坯X ;

[0008] Step S2: Determine S based on the critical billet shell thickness and estimated billet shell thickness under the conditions of continuous casting machine operating at maximum design speed and continuous water cooling. 铸坯1 ~S 铸坯X The types of roller conveyors include dense roller conveyors and sparse roller conveyors.

[0009] Step S3: The billet is transferred from the crystallizer outlet to S 铸坯N The cooling water nozzles at the location are turned on, and the initial value of N is 1.

[0010] Step S4: Under the condition of the number of cooling water nozzles opened in step 3, calculate S respectively. 铸坯1 ~S 铸坯X The critical thickness of the billet shell at the bulging point, the estimated value of the billet shell thickness, and the estimated value of the billet shell thickness at the fixed-length cutting point of the billet;

[0011] Step S5: Calculate S in step S4. 铸坯1 ~S 铸坯X The critical billet shell thickness at the bulging point is compared with the estimated billet shell thickness. It is determined whether there is an evaluation point where the critical billet shell thickness at the bulging point is greater than the estimated billet shell thickness. If there is an evaluation point where the critical billet shell thickness at the bulging point is greater than the estimated billet shell thickness, the first loop instruction is output; otherwise, the first termination instruction is output.

[0012] Step S6: Compare the estimated value of the billet shell thickness at the fixed-length cutting point with 0.5 times the side length of the billet cross section. If the estimated value of the billet shell thickness at the fixed-length cutting point is equal to 0.5 times the side length of the billet cross section, output the second termination instruction; otherwise, output the second loop instruction.

[0013] Step S7: If a first loop instruction or a second loop instruction exists, return to step S3 and increment the value of N in step S3 by one;

[0014] Step S8: If both the first termination command and the second termination command exist simultaneously, the cooling water nozzle opening position range corresponding to step S3 at this time shall be taken as the actual cooling water nozzle opening position range.

[0015] Furthermore, the critical thickness of the bulging blank is calculated based on the following formula:

[0016] ;in, For S 铸坯_m The critical thickness of the billet shell at the bulge point is in meters (m); L is the side length of the billet cross-section, in meters (m). To determine the yield strength of the slab shell, based on high-temperature tensile test data, the yield strength R of the slab shell at the continuous casting drawing temperature is... eH The value is 2000000 Pa; For S 铸坯_m The pressure exerted by molten steel on the billet shell at a certain point, measured in Pa. ;in, This refers to the density of molten steel, expressed in kg / m³. 3 g is the acceleration due to gravity, in N / kg; h is the distance from the meniscus of the molten steel in the crystallizer to point S. 铸坯_mThe vertical distance between points S, in meters. 铸坯_m When you are behind the arc section of the continuous casting machine, When S 铸坯_m When in front of the arc section of the continuous casting machine, ;in, For the meniscus of the molten steel surface in the crystallizer and S 铸坯_m The distance between them is in meters (m). h1 is the distance between the meniscus of the molten steel in the crystallizer and the starting point of the arc segment of the continuous casting machine, in meters (m). r is the arc radius of the continuous casting machine, in meters (m).

[0017] Furthermore, the method for calculating the estimated thickness of the billet shell includes:

[0018] When S 铸坯_m When within the opening range of the water-cooled nozzle, S is calculated based on the following formula. 铸坯_m Estimated thickness of the blank shell at the location:

[0019] Where L is the side length of the billet cross section, in meters; For S 铸坯_m The estimated thickness of the billet shell at the location is given in meters. For the billet to travel from the crystallization outlet to S 铸坯_m The time taken at each location is in minutes. The solidification coefficient of the billet under water-cooling conditions is taken as 0.000529m. 2 ·min; For S 铸坯_m The first constant when the billet is within the opening range of the water-cooled nozzle is, based on production experience, the thickness of the billet exiting the bottom of the crystallizer is 11mm. Assuming the time at this point is 0 seconds, therefore, based on... Solving for;

[0020] When S 铸坯_m When not within the opening range of the water-cooled nozzle, calculate S based on the following steps. 铸坯_m Estimated thickness of the blank shell at the location:

[0021] Step G1: Based on production experience, the thickness of the billet exiting the crystallizer is 11mm. Assuming the time at this point is 0 seconds, therefore, based on... Solving ;

[0022] Step G2: Based on The estimated thickness of the billet shell when the billet leaves the opening range of the water-cooling nozzle is obtained, in meters. The estimated thickness of the billet shell when the billet leaves the opening range of the water-cooling nozzle, in meters; The time taken for the billet to travel from the crystallization outlet to the end of the water-cooling nozzle cooling position, expressed in tons (t). ,in, The distance traveled by the billet from the bottom of the crystallizer to the end of the water-cooling nozzle cooling position is expressed in meters (m); v is the billet casting speed, expressed in meters per minute (m / min).

[0023] Step G3: Based on Solving ,in, For S 铸坯_m The second constant when the water-cooled nozzle is not open. The solidification coefficient of the cast billet under water-free cooling conditions is taken as 0.000098m. 2 ·min;

[0024] Step G4: Based on Solving for S 铸坯_m Estimated thickness of billet shell at the location ,in, For the billet to move from the bottom of the crystallizer to S 铸坯_m The time taken at the location, in minutes. ,in, For the billet to move from the bottom of the crystallizer to S 铸坯_m The distance traveled at the location is in meters (m); v is the casting speed of the billet, in meters per minute (m / min).

[0025] when If there is no solution in the range of 0 to 0.5L, it indicates that the billet has completely solidified. At this point, take... =L / 2.

[0026] Further, step S2 includes:

[0027] When the continuous casting machine is at its highest design speed and the casting is cooled by water spray from the outlet of the crystallizer to a certain evaluation point on the billet, if the critical thickness of the billet shell at the evaluation point is greater than the estimated thickness of the billet shell, then a denser roller table is adopted at the evaluation point. The roller table diameter is 70-80mm and the roller spacing is 15-20mm.

[0028] When the continuous casting machine is at its highest design speed and the casting is cooled by water spray from the crystallizer outlet to a certain evaluation point on the billet, if the critical thickness of the billet shell at that evaluation point is equal to the estimated thickness of the billet shell, then that evaluation point is the termination point for the installation of the dense roller conveyor. The position after that evaluation point is a sparse roller conveyor with a roller diameter of 120-200mm and a roller spacing of 50-80mm.

[0029] Furthermore, the number of evaluation points in step S1 is 50.

[0030] The method for controlling the bulging defect in continuously cast small square billets of the present invention has the following advantages and beneficial effects:

[0031] By comparing the critical billet shell thickness for bulging with the estimated billet shell thickness, it is possible to determine whether the billet will develop a bulging defect. Based on the calculation results, the continuous casting machine roller arrangement and cooling process are designed, and the critical number of cooling water nozzles that can both prevent bulging defects and maximize the hot delivery temperature of the billet is optimized. This data calculation method replaces the current method of gradually adjusting the number of cooling water nozzles through multiple field experiments. It has the advantages of fast calculation speed, high efficiency, low cost of adjusting the secondary cooling process of continuous casting, high accuracy, and improved automation and intelligent operation level of continuous casting.

[0032] The billet shell thickness estimation method provided by this invention, compared with the existing billet shell thickness calculation formula, takes into account the influence of the different heat transfer areas of water spray cooling on the billet surface and the area of ​​the inner surface of the billet shell on the heat transfer efficiency, improves the billet shell thickness calculation method for small square billets, and improves the calculation accuracy of billet shell thickness. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for further understanding of the embodiments of the present invention and constitute a part of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0034] Figure 1 This is a process flow diagram of the method for controlling the bulging defect of small square billets in continuous casting according to the present invention;

[0035] Figure 2 This is a schematic diagram of the force exerted by the static pressure of molten steel on the billet shell in the method for controlling the bulging defect of continuously cast small square billets according to the present invention.

[0036] Figure 3 This is a schematic diagram of the bending moment of the molten steel static pressure on the billet shell in the method for controlling the bulging defect of continuously cast small square billets according to the present invention.

[0037] Figure 4 This is a schematic diagram of the internal stress of the billet shell in the method for controlling the bulging defect of continuously cast small square billets according to the present invention.

[0038] Figure 5 This is a schematic diagram of the billet shell resisting bending moment in the method for controlling the bulging defect of continuously cast small square billets according to the present invention. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0040] See Figure 1 The method for controlling the bulging defect in continuously cast small square billets provided by the present invention includes:

[0041] Step S1: Select 50 evaluation points evenly along the distance from the outlet of the crystallizer to the last straightening roller of the straightening machine, and number them sequentially as S. 铸坯1 ~S 铸坯X ;

[0042] Step S2: Determine S based on the critical billet shell thickness and estimated billet shell thickness under the conditions of continuous casting machine operating at maximum design speed and continuous water cooling. 铸坯1 ~S 铸坯X The types of roller conveyors include dense roller conveyors and sparse roller conveyors.

[0043] When the continuous casting machine is at its highest design speed and the casting is cooled by water spray from the outlet of the crystallizer to a certain evaluation point on the billet, if the critical thickness of the billet shell at the evaluation point is greater than the estimated thickness of the billet shell, then a denser roller table is adopted at the evaluation point. The roller table diameter is 70-80mm and the roller spacing is 15-20mm.

[0044] When the continuous casting machine is at its highest design speed and the casting is cooled by water spray from the crystallizer outlet to a certain evaluation point on the billet, if the critical thickness of the billet shell at that evaluation point is equal to the estimated thickness of the billet shell, then that evaluation point is the termination point for the installation of the dense roller conveyor. The position after that evaluation point is a sparse roller conveyor with a roller diameter of 120-200mm and a roller spacing of 50-80mm.

[0045] Step S3: The billet is transferred from the crystallizer outlet to S 铸坯N The cooling water nozzles at the location are turned on, and the initial value of N is 1.

[0046] Step S4: Under the condition of the number of cooling water nozzles opened in step 3, calculate S respectively. 铸坯1 ~S 铸坯X The critical thickness of the billet shell at the bulging point, the estimated value of the billet shell thickness, and the estimated value of the billet shell thickness at the fixed-length cutting point of the billet;

[0047] Step S5: Calculate S in step S4. 铸坯1 ~S铸坯X The critical billet shell thickness at the bulging point is compared with the estimated billet shell thickness. It is determined whether there is an evaluation point where the critical billet shell thickness at the bulging point is greater than the estimated billet shell thickness. If there is an evaluation point where the critical billet shell thickness at the bulging point is greater than the estimated billet shell thickness, the first loop instruction is output; otherwise, the first termination instruction is output.

[0048] Step S6: Compare the estimated value of the billet shell thickness at the fixed-length cutting point with 0.5 times the side length of the billet cross section. If the estimated value of the billet shell thickness at the fixed-length cutting point is equal to 0.5 times the side length of the billet cross section, output the second termination instruction; otherwise, output the second loop instruction.

[0049] Step S7: If a first loop instruction or a second loop instruction exists, return to step S3 and increment the value of N in step S3 by one;

[0050] Step S8: If both the first termination command and the second termination command exist simultaneously, the cooling water nozzle opening position range corresponding to step S3 at this time shall be taken as the actual cooling water nozzle opening position range.

[0051] By comparing the critical billet shell thickness for bulging with the estimated billet shell thickness, it is possible to determine whether the billet will develop a bulging defect. Based on the calculation results, the continuous casting machine roller arrangement and cooling process are designed, and the critical number of cooling water nozzles that can both prevent bulging defects and maximize the hot delivery temperature of the billet is optimized. This data calculation method replaces the current method of gradually adjusting the number of cooling water nozzles through multiple field experiments. It has the advantages of fast calculation speed, high efficiency, low cost of adjusting the secondary cooling process of continuous casting, high accuracy, and improved automation and intelligent operation level of continuous casting.

[0052] Furthermore, the critical thickness of the bulging blank is calculated based on the following formula:

[0053] ;in, For S 铸坯_m The critical thickness of the billet shell at the bulge point is in meters (m); L is the side length of the billet cross-section, in meters (m). To determine the yield strength of the slab shell, based on high-temperature tensile test data, the yield strength R of the slab shell at the continuous casting drawing temperature is... eH The value is 2000000 Pa; For S 铸坯_m The pressure exerted by molten steel on the billet shell at a certain point, measured in Pa. ;in, This refers to the density of molten steel, expressed in kg / m³. 3 g is the acceleration due to gravity, in N / kg; h is the distance from the meniscus of the molten steel in the crystallizer to point S. 铸坯_mThe vertical distance between points S, in meters. 铸坯_m When you are behind the arc section of the continuous casting machine, When S 铸坯_m When in front of the arc section of the continuous casting machine, ;in, For the meniscus of the molten steel surface in the crystallizer and S 铸坯_m The distance between them is in meters (m). h1 is the distance between the meniscus of the molten steel in the crystallizer and the starting point of the arc segment of the continuous casting machine, in meters (m). r is the arc radius of the continuous casting machine, in meters (m).

[0054] The derivation of the above formula is as follows:

[0055] According to mechanical calculation formulas, the maximum bending moment generated by the static pressure of molten steel on the billet shell is located at 1 / 2 the width of the billet. The resulting bending moment is:

[0056] ;in, is the maximum bending moment generated by the static pressure of molten steel on the billet shell; F is the static pressure of molten steel; H is the distance from the point of application of the static pressure on both sides of the billet at half the width of the billet.

[0057] Since the static pressure of molten steel is the product of pressure and area, the static pressure on both sides of half the width of the billet is:

[0058] Where F is the static pressure of the molten steel; P is the pressure of the molten steel. L is the length of the billet shell; D is the side length of the billet cross-section; and D is the thickness of the billet shell.

[0059] The distance from the point of application of the static pressure on both sides of the billet at half its width to the billet width is:

[0060] Where H is the distance from the point of application of the static pressure on both sides of the billet at half the width of the billet; L is the side length of the billet cross section; and D is the thickness of the billet shell.

[0061] In summary, the maximum bending moment generated by the static pressure of molten steel on the billet shell is:

[0062] ;in, The maximum bending moment generated by the static pressure of molten steel on the billet shell; P is the molten steel pressure. L is the length of the billet shell; D is the side length of the billet cross-section; and D is the thickness of the billet shell.

[0063] Under the hydrostatic pressure of molten steel, the billet shell tends to bulge and deform, generating a force acting on its cross-section. To resist this deformation, the billet shell generates resistance stress. This resistance moment is equal in magnitude and opposite in direction to the bending moment generated by the hydrostatic pressure of the molten steel. The resistance force includes compressive stress on the inner surface of the billet shell and tensile stress on the outer surface.

[0064] When the tensile or compressive stress exceeds the yield strength, the billet will bulge. The maximum resisting moment of the billet shell against bending deformation is the moment generated at the cross-section of the billet shell by the stress that causes the billet shell to yield. At this time, the resisting moment generated by the yield strength of the billet shell is equal to the moment generated by the hydrostatic pressure of the molten steel.

[0065] According to the calculation formula of mechanics of materials, the bending moment resisted by stress in the thickness direction of the billet shell is the same. This application takes the maximum resisting moment against bending deformation at 1 / 2 thickness of the billet shell (for example, the thickness of the billet shell is 35mm, and the 1 / 2 thickness of the billet shell is 17.5mm away from the surface of the billet) as an example to briefly introduce the calculation method of the maximum resisting moment.

[0066] The maximum moment resisting bending deformation by the yield strength of the cast billet shell is the sum of the bending moments generated by compressive stress and tensile stress, i.e. ;in, The maximum resisting moment against bending deformation is the yield strength of the billet shell. The bending moment is caused by compressive stress; The bending moment generated by tensile stress;

[0067] Along the thickness direction of the billet shell, the compressive stress decreases linearly from the inner surface of the billet shell to half its thickness, where the pressure at the inner surface of the billet shell is R. eH From the inner surface of the billet shell to half the thickness of the billet shell, the compressive stress per unit area is increased by R. eH As the tensile stress decreases linearly to zero, it increases linearly from half the thickness of the billet shell to the outer surface of the billet shell, generating tensile stress. The tensile stress per unit area increases linearly from zero to R. eH According to the definition of moment and the integral formula, the bending moment generated by compressive stress is:

[0068] Where D is the thickness of the billet shell; The compressive stress is measured at different points from the inner surface of the billet shell to half its thickness. The distance between the point of application of compressive stress at different locations from the inner surface of the billet to 1 / 2 thickness and the location of 1 / 2 thickness of the billet shell;

[0069] According to the formula: Pressure equals Intensity multiplied by Area, we have:

[0070] ;in, This refers to the pressure exerted on the inner surface of the billet shell at different locations up to 1 / 2 thickness due to compressive stress. S represents the compressive stress at different points from the inner surface of the billet shell to half its thickness; S is the area of ​​the pressure action.

[0071] Based on the principle that area equals the length of the blank multiplied by its thickness:

[0072] ;in, is the length of the billet shell; x is the distance from the inner surface of the billet shell in the thickness direction. The area under pressure;

[0073] Since the compressive stress from the inner surface of the billet shell to half its thickness decreases linearly, the pressure at a distance x meters from the inner surface of the billet shell is:

[0074] Among them, R eH denoted as , where is the yield strength of the billet shell at the continuous casting drawing temperature; x is the distance from the inner surface of the billet shell in the thickness direction; and D is the thickness of the billet shell. denoted as , where is the pressure exerted at different points from the inner surface of the billet shell to half its thickness due to compressive stress; x is the distance from the inner surface of the billet shell in the thickness direction.

[0075] The distance between a position x meters away from the inner surface of the billet shell and the position at half the thickness of the billet shell is:

[0076] Where D is the thickness of the billet shell; x is the distance from the inner surface of the billet shell in the thickness direction; H is the distance from the point of application of the compressive stress at 1 / 2 thickness from the inner surface of the billet shell to 1 / 2 thickness.

[0077] In summary, by combining the above formulas and transforming them, we obtain:

[0078] ;

[0079] Integrating x from 0 to D / 2 in the above equation, we get:

[0080] ;in, R is the bending moment caused by compressive stress; D is the thickness of the billet shell; eH The yield strength of the billet shell at the continuous casting drawing temperature; The length of the blank;

[0081] The bending moment generated by tensile stress from half the thickness of the billet shell to the outer surface is the same as the bending moment generated by compressive stress, therefore:

[0082] ;in, R is the bending moment caused by tensile stress; D is the thickness of the billet shell; eH The yield strength of the cast billet shell; The length of the blank;

[0083] Further results were obtained:

[0084] ;

[0085] Since the direction of the torque is determined by the right-hand rule and is not reflected in the sign, we can conclude from the fact that the bending moment generated by the hydrostatic pressure of molten steel on the billet shell and the bending moment generated by the internal stress of the billet shell are equal in magnitude:

[0086] ;in, This represents the maximum bending moment generated by the static pressure of molten steel on the billet shell. The bending moment is caused by compressive stress;

[0087] Will and Substituting into the above equation and simplifying, we get:

[0088] ;in, For S 铸坯_m The critical thickness of the billet shell at the bulge point is in meters (m); L is the side length of the billet cross-section, in meters (m). To determine the yield strength of the slab shell, based on high-temperature tensile test data, the yield strength R of the slab shell at the continuous casting drawing temperature is... eH The value is 2000000 Pa; For S 铸坯_m The pressure exerted by molten steel on the billet shell at a certain point, measured in Pa. ;in, This refers to the density of molten steel, expressed in kg / m³. 3 g is the acceleration due to gravity, in N / kg; h is the distance from the meniscus of the molten steel in the crystallizer to point S. 铸坯_m The vertical distance between points S, in meters. 铸坯_m When you are behind the arc section of the continuous casting machine, When S 铸坯_m When in front of the arc section of the continuous casting machine, ;in, For the meniscus of the molten steel surface in the crystallizer and S 铸坯_m The distance between them is in meters (m). h1 is the distance between the meniscus of the molten steel in the crystallizer and the starting point of the arc segment of the continuous casting machine, in meters (m). r is the arc radius of the continuous casting machine, in meters (m).

[0089] Furthermore, the method for calculating the estimated thickness of the billet shell includes:

[0090] When S 铸坯_m When within the opening range of the water-cooled nozzle, S is calculated based on the following formula. 铸坯_m Estimated thickness of the blank shell at the location:

[0091] Where L is the side length of the billet cross section, in meters; For S 铸坯_m The estimated thickness of the billet shell at the location is given in meters. For the billet to travel from the crystallization outlet to S 铸坯_m The time taken at each location is in minutes. The solidification coefficient of the billet under water-cooling conditions is taken as 0.000529m. 2 ·min; For S 铸坯_m The first constant when the billet is within the opening range of the water-cooled nozzle is, based on production experience, the thickness of the billet exiting the bottom of the crystallizer is 11mm (0.011m). Assuming the time at this point is 0 seconds, therefore, based on... Solving for;

[0092] When S 铸坯_m When not within the opening range of the water-cooled nozzle, calculate S based on the following steps. 铸坯_m Estimated thickness of the blank shell at the location:

[0093] Step G1: Based on production experience, the thickness of the billet exiting the crystallizer is 11mm (0.011m). Assuming the time at this point is 0 seconds, therefore, based on... Solving ;

[0094] Step G2: Based on The estimated thickness of the billet shell when the billet leaves the opening range of the water-cooling nozzle is obtained, in meters. The estimated thickness of the billet shell when the billet leaves the opening range of the water-cooling nozzle, in meters; The time taken for the billet to travel from the crystallization outlet to the end of the water-cooling nozzle cooling position, expressed in tons (t). ,in, The distance traveled by the billet from the bottom of the crystallizer to the end of the water-cooling nozzle cooling position is expressed in meters (m); v is the billet casting speed, expressed in meters per minute (m / min).

[0095] Step G3: Based on Solving ,in, For S 铸坯_m The second constant when the water-cooled nozzle is not open. The solidification coefficient of the cast billet under water-free cooling conditions is taken as 0.000098m. 2 ·min;

[0096] Step G4: Based on Solving for S 铸坯_m Estimated thickness of billet shell at the location ,in, For the billet to move from the bottom of the crystallizer to S 铸坯_m The time taken at the location, in minutes. ,in, For the billet to move from the bottom of the crystallizer to S 铸坯_m The distance traveled at the location is in meters (m); v is the casting speed of the billet, in meters per minute (m / min).

[0097] when If there is no solution in the range of 0 to 0.5L, it indicates that the billet has completely solidified. At this point, take... =L / 2.

[0098] The basic formula for estimating the thickness of the billet shell is as follows: Where D is the billet shell thickness; L is the side length of the square billet cross-section; t is the time taken for the billet to travel from the bottom of the crystallizer to a certain position; K is the solidification coefficient of the billet; in this application, under water cooling, the value of K is 0.000529m. 2 •min; In the absence of water cooling, the K value is 0.000098m 2 ·min; C is a constant;

[0099] The derivation process of the basic formula for estimating the thickness of the billet shell is as follows:

[0100] According to Fourier's law:

[0101] ;in, t is the proportionality coefficient; t is the time it takes for the billet to travel from the bottom of the crystallizer to a certain position. The temperature of the molten steel inside the billet; D is the outer surface temperature of the billet; D is the thickness of the billet shell. L is the length of the billet; L is the side length of the billet cross section. The heat transferred from molten steel to the surface of the billet;

[0102] According to the exothermic formula for the solidification process of molten steel, we get:

[0103] ;in, ρ is the latent heat of solidification; L is the density of molten steel; D is the side length of the billet cross section; and D is the thickness of the billet shell. This represents the variation in the thickness of the billet shell. The length of the cast billet; The heat released when molten steel solidifies;

[0104] According to the heat transfer rate = latent heat of solidification derived from the solidification of molten steel into a cast billet, ( = (and transform both sides of the equation).

[0105] ;in, ρ is the latent heat of solidification; L is the density of molten steel; D is the side length of the billet cross section; and D is the thickness of the billet shell. This represents the variation in the thickness of the billet shell. This is the proportionality coefficient; The time taken for the cast billet to solidify; The temperature of the molten steel inside the billet; This refers to the outer surface temperature of the cast billet.

[0106] because During the secondary cooling stage of continuous casting, K1 and K are basically fixed values. 潜热 , It is also a fixed value, therefore let In this application, with water cooling, the K value is 0.000529m. 2 ·min, in the absence of water cooling, the K value is 0.000098m 2 ·min;

[0107] Then, simplified, we get:

[0108] ;

[0109] Let D be a variable. For another variable, use the following three integral formulas:

[0110] ;

[0111] ;

[0112] ;

[0113] Integrating both sides of the above equation, we get:

[0114] Where D is the billet shell thickness; L is the side length of the square billet cross-section; t is the time taken for the billet to travel from the bottom of the crystallizer to a certain position; K is the solidification coefficient of the billet; in this application, under water cooling, the value of K is 0.000529m. 2 •min; In the absence of water cooling, the K value is 0.000098m 2 ·min; C is a constant;

[0115] The above equation is a cubic equation in one variable, solved using Cardin's formula. Since the left side of the equation is within the range of 0 to 0.5L... The value of D increases monotonically, therefore the number of solutions for D in the range of 0 to 0.5 × L is less than or equal to 1. Since the thickness of the billet shell must be within the range of 0 to 0.5 times the side length of the square billet cross-section (0.5 × L), solving the equation according to Cardan's formula yields 3 roots. The root within the range of 0 to 0.5 × L is taken as the solution for D when t is known. If there is no solution in the range of 0 to 0.5L, it indicates that the billet has completely solidified. At this point, take... =L / 2.

[0116] The billet shell thickness estimation method provided by this invention, compared with the existing billet shell thickness calculation formula, takes into account the influence of the different heat transfer areas of water spray cooling on the billet surface and the area at the inner surface of the billet shell (solid-liquid interface area) on the heat transfer efficiency, improves the billet shell thickness calculation method for small square billets, and improves the calculation accuracy of billet shell thickness.

[0117] The method for controlling the bulging defect in continuously cast small square billets according to the present invention is further illustrated below with reference to specific embodiments.

[0118] Example 1

[0119] The billet produced in Embodiment 1 of the present invention is a square billet with a specification of 160mm×160mm. The maximum casting speed of the continuous casting design is 5m / min, the arc radius of the continuous casting machine is 10m, the distance from the meniscus of the molten steel in the crystallizer to the lower opening of the crystallizer is 0.9m, the lower opening of the crystallizer is the starting point of the arc segment of the continuous casting, and the distance from the lower opening of the crystallizer to the fixed length cutting position is 36m.

[0120] The method for controlling the bulging defect in continuously cast small square billets in Example 1 includes:

[0121] Fifty evaluation points were evenly selected along the distance from the outlet of the crystallizer to the last straightening roller of the straightening machine in the continuous casting billet, and numbered sequentially as S. 铸坯1 ~S 铸坯50 ;

[0122] Roller conveyor design: At the highest continuous casting speed, when the billet length pulled out from the bottom of the crystallizer is 3.14m, the estimated billet shell thickness is 0.0326m, and the critical billet shell thickness for bulging is 0.0323m. The estimated billet shell thickness at this point is approximately equal to the critical billet shell thickness for bulging. Therefore, the section from the crystallizer outlet to 3.14m is designed as a dense roller conveyor with a roller diameter of 80mm and a roller spacing of 20mm. The section after 3.14m from the crystallizer outlet is arranged as a sparse roller conveyor with a roller diameter of 120mm and a roller spacing of 50mm.

[0123] Water-cooling process design: In this embodiment, the maximum casting speed is used. At this maximum speed, the billet is pulled out from the bottom of the crystallizer and cooled using water-cooling nozzles until the billet length reaches 3.768m. At this point, the estimated shell thickness is 0.0360m, and the critical shell thickness for billet bulging is 0.0336m. Even if air cooling is used from the billet length onwards, the critical shell thickness for bulging of the billet from 3.7684m onwards is still less than the estimated shell thickness. The difference between the critical bulging shell thickness and the estimated shell thickness of the cast billet 3.7684m downstream of the crystallizer first decreases and then increases. The smallest difference is found at a distance of 7.536m from the bottom of the crystallizer, where the estimated shell thickness is 0.0397m and the critical bulging shell thickness is 0.0388m, with a difference of 0.0009m. Therefore, water cooling is designed for the section from the crystallizer outlet to 3.768m, while air cooling is designed for the section downstream of the crystallizer outlet. Under this cooling mode, C1 = 8.79267 × 10⁻⁶. -6 C2 = 6.07596 × 10 -5 In this cooling mode, when the billet is 34.854m from the bottom of the crystallizer, the estimated thickness of the billet shell is 80mm, which is 0.5 times the side length of the square billet cross-section (0.5×L). The billet is completely solidified, and the length of the billet is less than the distance from the bottom of the crystallizer to the fixed-length cutting position (36m). Therefore, the billet is completely solidified at the fixed-length cutting position, and there will be no cutting leakage accident.

[0124] Example 1 is S 铸坯1 ~S 铸坯50 The estimated blank shell thickness, critical blank shell thickness for bulging, roller conveyor type, and water cooling process are shown in Table 1.

[0125] Table 1 S 铸坯1 ~S 铸坯50 Estimated billet shell thickness, critical billet shell thickness for bulging, roller conveyor type, and water cooling process.

[0126]

[0127]

[0128]

[0129] In summary, by comparing the critical billet shell thickness for bulging with the estimated billet shell thickness, it is possible to determine whether the billet will develop a bulging defect. Based on the calculation results, the continuous casting machine roller arrangement and cooling process can be designed, and the optimal number of critical cooling water nozzles that can both prevent bulging defects and maximize the hot delivery temperature of the billet can be selected. This data calculation method replaces the current method of gradually adjusting the number of cooling water nozzles through multiple field experiments. It has the advantages of fast calculation speed, high efficiency, low cost of adjusting the secondary cooling process of continuous casting, high accuracy, and improved automation and intelligent operation level of continuous casting.

[0130] It should be noted that, unless otherwise specified, the terms used herein have the meanings commonly understood by those skilled in the art. Furthermore, when a numerical range is disclosed herein, the range is considered continuous and includes the minimum and maximum values ​​of the range, as well as every value between such minimum and maximum. Further, when the range refers to integers, it includes every integer between the minimum and maximum values ​​of the range. Moreover, when multiple ranges are provided to describe features, the ranges may be combined. In other words, unless otherwise specified, all ranges disclosed herein should be understood to include any and all subranges to which they are incorporated.

[0131] It should also be noted that, in this document, the term "comprising" or any other variation thereof is intended to cover non-exclusive inclusion, such that an article or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such an article or device.

[0132] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the present invention.

Claims

1. A method for controlling the bulging defect in continuously cast small square billets, characterized in that, include: Step S1: Select several evaluation points evenly along the distance from the outlet of the crystallizer to the last straightening roller of the straightening machine, and number them sequentially as S. 铸坯1 ~S 铸坯X ; Step S2: Determine S based on the critical billet shell thickness and estimated billet shell thickness under the conditions of continuous casting machine operating at maximum design speed and continuous water cooling. 铸坯1 ~S 铸坯X The types of roller conveyors include dense roller conveyors and sparse roller conveyors. Step S3: The billet is transferred from the crystallizer outlet to S 铸坯N The cooling water nozzles at the location are turned on, and the initial value of N is 1. Step S4: Under the condition of the number of cooling water nozzles opened in step 3, calculate S respectively. 铸坯1 ~S 铸坯X The critical thickness of the billet shell at the bulging point, the estimated value of the billet shell thickness, and the estimated value of the billet shell thickness at the fixed-length cutting point of the billet; Step S5: Calculate S in step S4. 铸坯1 ~S 铸坯X The critical billet shell thickness at the bulging point is compared with the estimated billet shell thickness. It is determined whether there is an evaluation point where the critical billet shell thickness at the bulging point is greater than the estimated billet shell thickness. If there is an evaluation point where the critical billet shell thickness at the bulging point is greater than the estimated billet shell thickness, the first loop instruction is output; otherwise, the first termination instruction is output. Step S6: Compare the estimated value of the billet shell thickness at the fixed-length cutting point with 0.5 times the side length of the billet cross section. If the estimated value of the billet shell thickness at the fixed-length cutting point is equal to 0.5 times the side length of the billet cross section, output the second termination instruction; otherwise, output the second loop instruction. Step S7: If a first loop instruction or a second loop instruction exists, return to step S3 and increment the value of N in step S3 by one; Step S8: If both the first termination command and the second termination command exist simultaneously, the range of the opening position of the cooling water nozzle corresponding to step S3 at this time shall be taken as the actual range of the opening position of the cooling water nozzle. The critical thickness of the bulging blank is calculated based on the following formula: ;in, For S 铸坯_m The critical thickness of the billet shell at the bulge point is in meters (m); L is the side length of the billet cross-section, in meters (m). The yield strength of the cast billet shell is taken as 2,000,000 Pa; For S 铸坯_m The pressure exerted by molten steel on the billet shell at a certain point, measured in Pa. ;in, This refers to the density of molten steel, expressed in kg / m³. 3 g is the acceleration due to gravity, in N / kg; h is the distance from the meniscus of the molten steel in the crystallizer to point S. 铸坯_m The vertical distance between points S, in meters. 铸坯_m When you are behind the arc section of the continuous casting machine, When S 铸坯_m When in front of the arc section of the continuous casting machine, ;in, For the meniscus of the molten steel surface in the crystallizer and S 铸坯_m The distance between them is in meters (m); h1 is the distance between the meniscus of the molten steel in the crystallizer and the starting point of the arc segment of the continuous casting machine, in meters; r is the arc radius of the continuous casting machine, in meters. The calculation method for the estimated thickness of the billet shell includes: When S 铸坯_m When within the opening range of the water-cooled nozzle, S is calculated based on the following formula. 铸坯_m Estimated thickness of the blank shell at the location: Where L is the side length of the billet cross section, in meters; For S 铸坯_m The estimated thickness of the billet shell at the location is given in meters. For the billet to travel from the crystallization outlet to S 铸坯_m The time taken at each location is in minutes. The solidification coefficient of the billet under water-cooling conditions is taken as 0.000529m. 2 ·min; For S 铸坯_m The first constant when within the opening range of the water-cooled nozzle is based on Solving for; When S 铸坯_m When not within the opening range of the water-cooled nozzle, calculate S based on the following steps. 铸坯_m Estimated thickness of the blank shell at the location: Step G1: Based on Solving ; Step G2: Based on The estimated thickness of the billet shell when the billet leaves the opening range of the water-cooling nozzle is obtained, in meters. The estimated thickness of the billet shell when the billet leaves the opening range of the water-cooling nozzle, in meters; The time taken for the billet to travel from the crystallization outlet to the end of the water-cooling nozzle cooling position, expressed in tons (t). ,in, The distance traveled by the billet from the bottom of the crystallizer to the end of the water-cooling nozzle cooling position is expressed in meters (m); v is the billet casting speed, expressed in meters per minute (m / min). Step G3: Based on Solving ,in, For S 铸坯_m The second constant when the water-cooled nozzle is not open. The solidification coefficient of the cast billet under water-free cooling conditions is taken as 0.000098m. 2 ·min; Step G4: Based on Solving for S 铸坯_m Estimated thickness of billet shell at the location ,in, For the billet to move from the bottom of the crystallizer to S 铸坯_m The time taken at the location, in minutes. ,in, For the billet to move from the bottom of the crystallizer to S 铸坯_m The distance traveled at the location is in meters (m); v is the casting speed of the billet, in meters per minute (m / min). when If there is no solution in the range of 0 to 0.5L, it indicates that the billet has completely solidified. At this point, take... =L / 2.

2. The method for controlling the bulging defect in continuously cast small square billets according to claim 1, characterized in that, Step S2 includes: When the continuous casting machine is at its highest design speed and the casting is cooled by water spray from the outlet of the crystallizer to a certain evaluation point on the billet, if the critical thickness of the billet shell at the evaluation point is greater than the estimated thickness of the billet shell, then a denser roller table is adopted at the evaluation point. The roller table diameter is 70-80mm and the roller spacing is 15-20mm. When the continuous casting machine is at its highest design speed and the casting is cooled by water spray from the crystallizer outlet to a certain evaluation point on the billet, if the critical thickness of the billet shell at that evaluation point is equal to the estimated thickness of the billet shell, then that evaluation point is the termination point for the installation of the dense roller conveyor. The position after that evaluation point is a sparse roller conveyor with a roller diameter of 120-200mm and a roller spacing of 50-80mm.

3. The method for controlling the bulging defect in continuously cast small square billets according to claim 1, characterized in that, The number of evaluation points in step S1 is 50.

Images