Method for judging thickness of slab shell
By combining hydrostatic pressure and yield strength data of steel, combined with roller geometric parameters and temperature field, the thickness of the slab shell is accurately determined, which solves the slab pulling speed and internal quality problems, and improves production efficiency and quality.
Patent Information
- Application Number
- CN202510559124.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-30
- Publication Date
- 2025-07-29
AI Technical Summary
The prior art is difficult to accurately judge the thickness of the slab shell, which leads to pulling speed and internal quality problems, affecting production efficiency and quality.
The hydrostatic pressure of the steel and the yield strength data of the corresponding steel grade at the target strain rate are used, combined with the roller geometric parameters and the slab temperature field, and the outer arc curvature function and parameter equation are established to determine the thickness of the slab at different positions.
It improves the accuracy of judging the thickness of the slab shell, supports the maximum reasonable increase in the rolling speed, and solves quality problems such as internal looseness and shrinkage holes.
Smart Images
Figure CN120382138A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of metallurgical machinery, and particularly relates to a method for determining the thickness of a slab shell. Background Art
[0002] In recent years, the production of slab continuous casting has been gradually developing towards high casting speed and high quality. Among them, the accurate judgment of the slab shell thickness has become an important link that cannot be ignored in restricting the casting speed and internal quality.
[0003] In terms of increasing the casting speed: As the casting speed increases, the thickness of the slab shell at the mold outlet will continuously decrease, which has become a key factor restricting the casting speed. If the thickness of the slab shell at the mold outlet is estimated too thin, fearing a breakout accident and conservatively using a lower casting speed for production, the production efficiency will be reduced; conversely, if the thickness of the slab shell at the mold outlet is estimated too thick and the drawing speed is blindly increased, the risk of breakout will increase sharply and even an accident will occur. Therefore, the accurate judgment of the slab shell thickness can provide strong technical support for reasonably increasing the drawing speed to the greatest extent.
[0004] In terms of improving the internal quality of the slab: The large reduction technology for the end of slab solidification is an effective means to improve the internal quality of the slab. When the sum of the thicknesses of the inner arc slab shell and the outer arc slab shell reaches the slab thickness, it is the solidification end point of the slab. If the judgment of the solidification end point is too early, the improvement of the slab internal quality (eliminating porosity, suppressing shrinkage cavities, etc.) will not work, and instead, additional internal quality defects (such as intermediate cracks) may be generated; conversely, if the judgment of the solidification end point is too late, the large reduction for the end of slab solidification cannot be implemented due to the excessive deformation resistance of the slab. Therefore, the accurate judgment of the slab shell thickness can provide effective theoretical guidance for the large reduction at the end of slab solidification to be implemented in the correct range and efficiently solve quality problems such as internal porosity and shrinkage cavities. Summary of the Invention
[0005] In view of the above problems, the purpose of the present invention is to provide a method for determining the thickness of a slab shell. This method is based on data from two aspects: the hydrostatic pressure of molten steel and the yield strength of the corresponding steel grade at the target strain rate, and combines various factors such as the geometric parameters of the roll train and the temperature field of the slab to determine the thickness of the slab shell at different positions. The judgment result is closer to the actual slab shell thickness and has high accuracy.
[0006] The technical solution of the present invention is as follows: A method for determining the thickness of a slab shell includes the following steps: S1. Determine the meniscus of the molten steel, the outer arc between the meniscus and the end roller of the straightening zone, and the partition of the outer arc; S2. Establish a curvature function for any point on the outer arc; S3. Obtain the primitive function of the curvature at any point on the outer arc according to the curvature function at any point on the outer arc; S4. Convert the arc length from any point on the outer arc to the meniscus into the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus; S5. Establish a parametric equation for the relationship between the arc length from any point on the neutral layer of the slab thickness to the meniscus and the hydrostatic pressure of the molten steel at this point; S6. Determine the yield strength function of steel at the target strain rate and calculate the inverse function of the yield strength function at the target strain rate; S7. Combine the parametric equation in step S5 and the inverse function of the yield strength function at the target strain rate in step S6 to construct a determination temperature equation for the shell thickness corresponding to a certain point on the neutral layer of the slab thickness; S8. Divide the slab slices, combine the temperature field of the slab, determine the shell thickness of the slab and its change trend in the casting direction, and determine the correct implementation interval of large reduction at the solidification end of the slab according to the change of the shell thickness of the slab.
[0007] In the said step S1, starting from the meniscus of the molten steel, the partition of the outer arc is successively the plumb zone, the bending zone, the arc zone, the straightening zone and the horizontal zone; in the said step S2, the curvature function at any point on the outer arc is: Equation (1) Where: is the arc length from the end of the plumb zone on the outer arc to the meniscus; is the arc length from the end of the bending zone on the outer arc to the meniscus; is the arc length from the end of the arc zone on the outer arc to the meniscus; is the arc length from the end of the straightening zone on the outer arc to the meniscus; is the arc length from the end of the horizontal zone on the outer arc to the meniscus; is the arc length from any point on the outer arc to the meniscus; is the radius of the outer arc of the arc zone; is the curvature of the bending zone; is the curvature of the straightening zone.
[0008] In the said step S3, the primitive function of the curvature at any point on the outer arc is: Equation (2).
[0009] In the said step S4, the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus is: Equation (3) Where: is the thickness of the slab.
[0010] In step S5, a parametric equation is established for the relationship between the arc length from any point on the neutral layer of the slab thickness to the meniscus and the hydrostatic pressure of the molten steel corresponding to this point through the arc length from any point on the outer arc to the meniscus.
[0011] The parametric equation is as follows: Equation (4) Where: is the arc length from any point on the neutral layer of the slab thickness to the meniscus; is the density of the molten steel; is the acceleration due to gravity; is the height of the hydrostatic head of the molten steel at any point on the neutral layer of the slab thickness.
[0012] In step S7, the judgment temperature equation for the thickness of the shell corresponding to a certain point on the neutral layer of the slab thickness is: Equation (5) Where: is the temperature basis for judging the thickness of the shell at a certain place.
[0013] In step S8, the slab is sliced as follows: the slab is cut into multiple slices along the casting direction, and each slice is perpendicular to the casting direction.
[0014] Combined with the temperature field of the slab, the specific change trend of the shell thickness of the slab in the casting direction is as follows: First, determine the temperature for judging the shell thickness of the corresponding slice according to the judgment temperature equation for the shell thickness corresponding to a certain point on the neutral layer of the slab thickness; then, connect the temperatures for judging the shell thickness of the corresponding slices on all slices in sequence along the casting direction, and this connection line is the change trend of the shell thickness of the slab in the casting direction.
[0015] The correct implementation interval for the large reduction at the end of slab solidification is: the intersection point of the change trend of the shell thickness of the slab in the casting direction and the neutral layer of the slab thickness is A, the intersection point of the solidus temperature isotherm and the neutral layer of the slab thickness is B, and the interval between point A and point B in the casting direction is the correct implementation interval for the large reduction at the end of slab solidification.
[0016] The technical effects of the present invention are as follows: 1. Based on the data of the hydrostatic pressure of molten steel and the yield strength of the corresponding steel grade at the target strain rate, and considering various factors such as the geometric parameters of the roll arrangement and the temperature field of the slab, the present invention determines the shell thickness of the slab at different positions, and the judgment result is closer to the actual shell thickness with high accuracy; 2. The shell thickness at the mold outlet determined by the present invention provides strong technical support for reasonably increasing the casting speed to the greatest extent; 3. The correct implementation interval of the large reduction at the solidification end of the slab determined by the present invention can effectively solve quality problems such as internal porosity and shrinkage cavity when the large reduction at the solidification end is implemented within this interval.
[0017] The following will be further described with reference to the accompanying drawings. Brief Description of the Drawings
[0018] Figure 1 It is a schematic diagram of the slab zoning structure.
[0019] Figure 2 It is a relationship diagram between the arc length L from any point on the outer arc to the meniscus and the height of the molten steel head at this point on the neutral layer of the slab thickness.
[0020] Figure 3 It is the yield strength diagram of steel at 10 -5 strain rate.
[0021] Figure 4 It is a schematic diagram of the slab slice.
[0022] Figure 5 It is a relationship diagram between the arc length from the neutral layer of the slab thickness to the meniscus and the position to the surface of the continuous casting billet. Detailed Embodiment
[0023] The principle and features of the present invention will be described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention. Embodiment 1
[0024] As Figures 1 to 5 shown, a method for determining the shell thickness of a slab includes the following steps: S1. Determine the meniscus of the molten steel, the outer arc between the meniscus and the end roller of the straightening zone, and the zoning of the outer arc; S2. Establish the curvature function of any point on the outer arc; S3. Obtain the primitive function of the curvature of any point on the outer arc according to the curvature function of any point on the outer arc; S4. Convert the arc length from any point on the outer arc to the meniscus to the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus; S5. Establish a parametric equation for the relationship between the arc length from an arbitrary point on the neutral layer of the slab thickness to the meniscus and the hydrostatic pressure of the molten steel corresponding to this point; S6. Determine the yield strength function of steel at the target strain rate and calculate the inverse function of the yield strength function at the target strain rate; S7. Combine the parametric equation in step S5 and the inverse function of the yield strength function at the target strain rate in step S6 to construct a determination temperature equation for the shell thickness corresponding to a certain point on the neutral layer of the slab thickness; S8. Divide the slab slices, combine the temperature field of the slab, determine the shell thickness of the slab and its change trend in the casting direction, and determine the correct implementation interval of large reduction at the end of slab solidification according to the change of the shell thickness of the slab.
[0025] The present invention abandons the drawback of using the solidus temperature as the standard to determine the shell thickness in the traditional method. Based on the data of the hydrostatic pressure of the molten steel and the yield strength of the corresponding steel grade at the target strain rate, and combining various factors such as the geometric parameters of the roll train and the temperature field of the slab, it determines the shell thickness of the slab at different positions. The judgment result is closer to the actual shell thickness, with high accuracy; it provides strong technical support for reasonably increasing the casting speed to the greatest extent; and it provides effective theoretical guidance for the correct implementation of large reduction at the end of slab solidification to efficiently solve quality problems such as internal porosity and shrinkage.
[0026] In step S1, starting from the meniscus of the molten steel, the outer arc is divided into a vertical zone, a bending zone, an arc zone, a straightening zone, and a horizontal zone in sequence; in step S2, the curvature function of any point on the outer arc is: Equation (1) Where: is the arc length from the end of the vertical zone on the outer arc to the meniscus; is the arc length from the end of the bending zone on the outer arc to the meniscus; is the arc length from the end of the arc zone on the outer arc to the meniscus; is the arc length from the end of the straightening zone on the outer arc to the meniscus; is the arc length from the end of the horizontal zone on the outer arc to the meniscus; is the arc length from an arbitrary point on the outer arc to the meniscus; is the radius of the outer arc of the arc zone; is the curvature of the bending zone; is the curvature of the straightening zone.
[0027] Specifically, a piecewise-defined curvature function is adopted to avoid the over-simplification of a single curvature model, which is more in line with the dynamic deformation of the outer arc in the actual operation of the continuous caster; ensure that the mechanical behaviors in different process stages (such as molten steel flow and solidification shrinkage) are accurately modeled, and improve the accuracy of shell thickness calculation.
[0028] In step S3, the primitive function of the curvature at any point on the outer arc is: Equation (2).
[0029] Specifically, the primitive function of the curvature at any point on the outer arc accumulates the local curvature of each point on the outer arc into a global geometric feature by integrating the curvature function in Equation (1), avoiding local errors caused by relying solely on instantaneous curvature, and more truly reflecting the overall geometric changes of the slab during the continuous deformation process; it provides a mathematically rigorous physical basis (Equation 3) for the correction of the neutral layer arc length, ensuring that the correction value of the neutral layer position is consistent with the actual bending / straightening amount.
[0030] In step S4, the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus is: Equation (3) Where: is the thickness of the slab.
[0031] Specifically, the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus calculated by this formula.
[0032] In step S5, a parametric equation is established for the relationship between the arc length from any point on the neutral layer of the slab thickness to the meniscus and the hydrostatic pressure of the molten steel at this point through the arc length from any point on the outer arc to the meniscus.
[0033] Specifically, a parametric equation is established through the arc length from any point on the outer arc to the meniscus, dynamically correlating the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus with the hydrostatic pressure of the molten steel, relying on measurable parameters to support real-time process optimization and improve the quality and production efficiency of the slab.
[0034] The parametric equation is: Equation (4) Where: is the arc length from any point on the neutral layer of the slab thickness to the meniscus; is the density of the molten steel; is the acceleration due to gravity; is the height of the molten steel head at any point on the neutral layer of the slab thickness.
[0035] Specifically, the function Height(L) of the height of the molten steel head at any point on the neutral layer of the slab thickness in Equation (4) is determined by the geometric parameters of the roll arrangement and is known at the beginning of the design of the slab continuous casting equipment. The relationship between the arc length L from any point on the outer arc to the meniscus and the height of the molten steel head at this point on the neutral layer of the slab thickness is approximately as Figure 2As shown in the figure. When calculating the hydrostatic pressure of molten steel, the height of the molten steel head is matched with the arc length position from the corresponding point on the neutral layer of the slab thickness to the meniscus to avoid the pressure estimation deviation caused by the curvature of the outer arc.
[0036] In the step S7, the determination temperature equation of the shell thickness corresponding to a certain point on the neutral layer of the slab thickness is: Equation (5) Where: is the temperature basis for determining the shell thickness at a certain place.
[0037] Specifically, the yield strength of steel at a strain rate of 10 -5 is approximately as Figure 3 shown, and is represented by the function, where is the temperature at any point of the slab. The image or function of different steel grades is slightly different. The yield strength of a certain steel grade at a strain rate of 10 -5 can be obtained through experiments or material software and presented in the form of a table. Taking a certain steel grade as an example, the yield strength of steel at a strain rate of 10 -5 is shown in Table 1. When in use, is used as the interpolation function.
[0038] Table 1 Temperature, °C <![CDATA[10 -5 Yield strength at strain rate, MPa]]> 1515 0 1510 0.01 1505 0.04 1500 0.07 1495 0.12 1490 0.16 1485 0.26 1480 1.22 1475 1.94 1470 2.07 1465 2.7 1460 2.78 1455 2.84 1450 2.9 To facilitate calculating the corresponding temperature from the yield strength, the function is specifically defined as the inverse function of the
[0039] function. Combining with Equation (4), it can be deduced that the determination temperature of the shell thickness corresponding to a certain point on the neutral layer of the slab thickness satisfies Equation (5).
[0040] Specifically, for convenience of representation, the slab that has experienced the bending zone, arc zone, and straightening zone is flattened and shown as Figure 4 shown ( Figure 4 only shows half of the slab thickness of the flattened slab). Starting from the meniscus of the molten steel, the slab is divided into multiple slices (the number of slices is only related to the accuracy of the trend of the finally determined shell thickness and does not affect the expression of the determination method). Each slice can be divided into multiple cells, and each cell has nodes representing the temperature of the cell. The distance between the nodes is .
[0041] The specific process of combining the temperature field of the slab to determine the change trend of the shell thickness of the slab in the casting direction is as follows: First, determine the temperature for judging the shell thickness of the corresponding slice according to the judgment temperature equation of the shell thickness corresponding to a certain point on the neutral layer of the slab thickness; then, connect the temperatures for judging the shell thickness of the corresponding slice on all slices in sequence along the casting flow direction, and this connection line is the change trend of the shell thickness of the slab in the casting direction.
[0042] In production, the temperature field of the slab can be calculated through a heat transfer model and can be regarded as a known quantity in the present invention. For Figure 4 the middle slice n, the calculation method is described as follows (without loss of generality).
[0043] It is assumed that there are nodes in slice n. The subscript of the node on the slab surface is represented by "0", the subscript of the node on the neutral layer of the slab thickness is represented by "k", and the intermediate nodes are successively "1", "2",..., "k" along the direction from the slab surface to the neutral layer of the slab thickness; the corresponding temperatures are represented by T[0], T[1], T[2],..., T[k] respectively.
[0044] The temperature at the intersection of the temperature line determined by the present invention (see Figure 4 ) and the center line of slice n must be equal to , and its corresponding can be realized through the expression logic of the following pseudo-code.
[0045] The said pseudo-code uses the C++ language to represent the implementation logic. In actual applications, using different languages does not affect the implementation logic. The shown pseudo-code indicates the method for determining the intersection of the temperature line and any slice.
[0046] Similarly, for the intersection of the temperature line determined by the present invention and any slice, connecting all the intersections in sequence is the change process of the shell thickness of the entire slab in the casting direction, that is, the change trend of the shell thickness in the casting direction.
[0047] The correct implementation interval of the large reduction at the solidification end of the slab is: the intersection of the change trend of the shell thickness of the slab in the casting direction and the neutral layer of the slab thickness is point A, the intersection of the solidus temperature isotherm and the neutral layer of the slab thickness is point B, and the interval between point A and point B in the casting direction is the correct implementation interval of the large reduction at the solidification end of the slab.
[0048] Compared with the traditional method of judging the shell thickness by taking the solidus temperature as the standard, Figure 5 shows the differences between the temperature line of the present invention and the liquidus temperature isotherm and the solidus temperature isotherm. Implementing the large reduction at the solidification end in the correct implementation interval of the large reduction at the solidification end of the slab can efficiently solve quality problems such as internal porosity and shrinkage cavity.
[0049] In the description of the present invention, it should be understood that if there are terms indicating the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the drawings are only for illustrative purposes and should not be construed as a limitation of the present invention.
[0050] The above examples are merely illustrative of the present invention and do not constitute a limitation on the scope of protection of the present invention. Any design identical or similar to the present invention falls within the scope of protection of the present invention.
Claims
1. A method for determining the shell thickness of a slab, characterized by: It includes the following steps: S1. Determine the meniscus of the molten steel, the outer arc between the meniscus and the end roller of the straightening zone, and the division of the outer arc; S2. Establish the curvature function of any point on the outer arc; S3. Obtain the primitive function of the curvature of any point on the outer arc according to the curvature function of any point on the outer arc; S4. Convert the arc length from any point on the outer arc to the meniscus to the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus; S5. Establish a parametric equation for the relationship between the arc length from any point on the neutral layer of the slab thickness to the meniscus and the hydrostatic pressure of the molten steel corresponding to this point; S6. Determine the yield strength function of steel at the target strain rate and calculate the inverse function of the yield strength function at the target strain rate; S7. Combine the parametric equation in step S5 and the inverse function of the yield strength function at the target strain rate in step S6 to construct a determination temperature equation for the shell thickness corresponding to a certain point on the neutral layer of the slab thickness; S8. Divide the slab into slices, combine the temperature field of the slab, determine the shell thickness of the slab and its change trend in the casting direction, and determine the correct implementation interval of large reduction at the solidification end of the slab according to the change of the shell thickness of the slab; 2. The method for determining the slab shell thickness according to claim 1, wherein: In step S1, starting from the meniscus of the molten steel, the divisions of the outer arc are successively the plumb zone, the bending zone, the arc zone, the straightening zone, and the horizontal zone; in step S2, the curvature function of any point on the outer arc is: Formula (1) Wherein: is the arc length from the end of the plumb area on the outer arc to the meniscus; is the arc length from the end of the bending area on the outer arc to the meniscus; is the arc length from the end of the arc area on the outer arc to the meniscus; is the arc length from the end of the straightening area on the outer arc to the meniscus; is the arc length from the end of the horizontal area on the outer arc to the meniscus; is the arc length from any point on the outer arc to the meniscus; is the radius of the outer arc of the arc area; is the curvature of the bending area; is the curvature of the straightening area.
3. The method for determining the thickness of a slab shell according to claim 2, wherein: In step S3, the original function of the curvature of any point on the outer arc is: Formula (2).
4. The method for determining the slab shell thickness according to claim 3, wherein: In the step S4, the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus is: Equation (3) Wherein: is the thickness of the slab.
5. The method for determining the thickness of a slab shell according to claim 4, characterized in that: In step S5, a parametric equation is established for the relationship between the arc length from any point on the neutral layer of the slab thickness to the meniscus and the hydrostatic pressure of the molten steel corresponding to this point through the arc length from any point on the outer arc to the meniscus; 6. The method for determining the slab shell thickness according to claim 5, wherein: The parametric equation is: Formula (4) Wherein: is the arc length from any point on the neutral layer of the slab thickness to the meniscus; is the density of molten steel; is the acceleration due to gravity; is the height of the molten steel pressure head at any point on the neutral layer of the slab thickness.
7. The method for determining the thickness of the slab shell according to claim 6, wherein: In the step S7, the determination temperature equation of the shell thickness corresponding to a certain point on the neutral layer of the slab thickness is: Equation (5) Wherein: is the temperature basis for determining the thickness of the shell at a certain location.
8. A method for determining the thickness of a slab shell as described in claim 7, characterized in that: In step S8, the slab is divided into slices as follows: the slab is cut into multiple slices along the casting direction, and each slice is perpendicular to the casting direction; 9. The method for determining the thickness of a slab shell according to claim 8, characterized in that: The specific method for combining the temperature field of the slab to determine the change trend of the shell thickness of the slab in the casting direction is: First, determine the temperature for determining the shell thickness of the corresponding slice according to the determination temperature equation for the shell thickness corresponding to a certain point on the neutral layer of the slab thickness; then, connect the temperatures for determining the shell thickness of the corresponding slices on all slices in sequence along the casting direction, and this connection line is the change trend of the shell thickness of the slab in the casting direction; 10. The method for determining the thickness of the slab shell as described in claim 9, characterized in that: The correct implementation interval of large reduction at the solidification end of the slab is: the intersection point of the change trend of the shell thickness of the slab in the casting direction and the neutral layer of the slab thickness is point A, the intersection point of the solidus temperature isotherm and the neutral layer of the slab thickness is point B, and the interval between point A and point B in the casting direction is the correct implementation interval of large reduction at the solidification end of the slab.