Method for judging thickness of slab shell

Abstract

The invention belongs to the technical field of metallurgical machinery, and particularly provides a method for judging the thickness of a slab shell, which is based on data in two aspects of molten steel static pressure and yield strength of a corresponding steel grade at a target strain rate. According to the method, the shell thickness of the plate blank at different positions is judged by combining the geometric parameters of the roller array, the temperature field of the plate blank and other factors, the problem that the shell thickness of the plate blank cannot be accurately judged in the prior art is solved, the judgment result is closer to the real shell thickness, and the accuracy is high.

Description

Technical Field

[0001] The invention belongs to the technical field of metallurgical machinery, and in particular relates to a method for determining the thickness of a slab shell. Background Art

[0002] In recent years, slab continuous casting has been gradually developing towards high casting speed and high quality. Among them, accurate judgment of slab shell thickness has become an important link that cannot be ignored in restricting casting speed and internal quality.

[0003] Regarding increasing casting speed: As casting speed increases, the thickness of the slab shell at the mold exit decreases, becoming a key factor limiting casting speed. If the mold exit shell thickness is underestimated, fearing breakout accidents may occur, and a conservative lower casting speed is adopted, production efficiency is reduced. Conversely, if the mold exit shell thickness is overestimated and the casting speed is blindly increased, the risk of breakout increases dramatically, and may even lead to accidents. Therefore, accurately determining the slab shell thickness provides strong technical support for maximizing and rationally increasing casting speed.

[0004] In terms of improving the internal quality of slabs: using large reduction technology at the end of slab solidification is an effective means to improve the internal quality of slabs. When the sum of the thickness of the inner arc shell and the outer arc shell of the slab reaches the thickness of the slab, it is the solidification end point of the slab. If the judgment of the solidification end point is too early, the improvement of the internal quality of the slab (eliminating porosity, suppressing shrinkage holes, etc.) will not work, but may instead produce additional internal quality defects (middle cracks, etc.); conversely, if the judgment of the solidification end point is too late, the use of large reduction at the end of the slab solidification will not be implemented due to the excessive resistance of the slab to deformation. Therefore, accurate judgment of the slab shell thickness can provide effective theoretical guidance for implementing large reduction at the end of slab solidification in the correct range, and efficiently solving quality problems such as internal porosity and shrinkage holes. Summary of the Invention

[0005] The present invention provides a method for determining the thickness of a slab shell, aiming to overcome the problem in the prior art that the thickness of a slab shell cannot be accurately determined.

[0006] To this end, the present invention provides a method for determining the thickness of a slab shell, comprising the following steps:

[0007] S1. Determine the meniscus of the molten steel, the outer arc line between the meniscus and the end roller of the straightening zone, and the partition of the outer arc line;

[0008] S2. Establish the curvature function of any point on the outer arc;

[0009] S3. Obtain the original function of the curvature of any point on the outer arc according to the curvature function of any point on the outer arc;

[0010] S4. Convert the arc length from any point on the outer arc line to the meniscus to the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus;

[0011] 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 static pressure of the molten steel corresponding to the point;

[0012] S6. determining the yield strength function of the steel at the target strain rate, and calculating the inverse function of the yield strength function at the target strain rate;

[0013] S7, combining the parametric equation of step S5 and the inverse function of the yield strength function at the target strain rate of step S6, constructing a temperature equation for determining the shell thickness corresponding to a certain point on the neutral layer of the slab thickness;

[0014] S8. Divide the slab into slices and, in combination with the slab temperature field, determine the variation trend of the slab shell thickness in the drawing direction and the correct implementation range of the large reduction at the end of slab solidification.

[0015] Preferably, starting from the meniscus of the molten steel, the outer arc is divided into a plumb area, a curved area, an arc area, a straightening area and a horizontal area in sequence;

[0016] The curvature function of any point on the outer arc is

[0017]

[0018] Where: L0 is the arc length from the end of the plumb bob area on the outer arc to the meniscus;

[0019] L1 is the length of the arc from the end of the bending zone on the outer arc to the meniscus;

[0020] L2 is the length of the arc from the end of the arc area on the outer arc line to the meniscus;

[0021] L3 is the arc length from the end of the straightening zone on the outer arc to the meniscus;

[0022] L4 is the length of the arc from the end of the horizontal area on the outer arc line to the meniscus;

[0023] L is the length of the arc from any point on the outer arc to the meniscus;

[0024] R is the radius of the outer arc of the arc area;

[0025] Curvature_B(L) is the curvature of the bending area;

[0026] Curvature_S(L) is the curvature of the straightening area.

[0027] Preferably, the original function of the curvature of any point on the outer arc is

[0028]

[0029] Preferably, the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus is

[0030] ArcLength_Nt(L)=L-Slab_D / 2*(Curvature_prim(L)) Formula (3)

[0031] Where: Slab_D is the thickness of the slab.

[0032] Preferably, the relationship between the arc length from any point on the neutral layer of the slab thickness to the meniscus and the static pressure of the molten steel corresponding to the point is established by establishing a parametric equation through the arc length from any point on the outer arc line to the meniscus.

[0033] Preferably, the parametric equation is

[0034]

[0035] Where: L Nt (L) is the length of the arc from any point on the neutral layer of the slab thickness to the meniscus; ρ is the density of molten steel; g is the acceleration of gravity; Height(L) is the height of the molten steel pressure head at any point on the neutral layer of the slab thickness.

[0036] Preferably, the temperature equation for determining the shell thickness corresponding to a point on the neutral layer of the slab thickness is:

[0037]

[0038] Where: T shell (L) is the temperature basis for determining the thickness of the shell at a certain location.

[0039] Preferably, the slicing of the slab is divided into: cutting the slab into multiple slices along the casting strand direction, with each slice being perpendicular to the casting strand direction.

[0040] Preferably, the method of combining the temperature field of the slab to determine the changing trend of the shell thickness of the slab in the drawing direction is specifically as follows: first, the temperature used to determine the shell thickness of the corresponding slice is determined based on the temperature determination equation of the shell thickness corresponding to a point on the neutral layer of the slab thickness; then, the temperatures used to determine the shell thickness of the corresponding slice on all slices are connected in sequence according to the casting direction, and the connecting line is the changing trend of the shell thickness of the slab in the drawing direction.

[0041] Preferably, the correct implementation range of the large reduction at the end of slab solidification is: the intersection of the changing trend of the slab shell thickness in the drawing direction and the neutral layer of the slab thickness is A, the intersection 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 drawing direction is the correct implementation range of the large reduction at the end of slab solidification.

[0042] Beneficial effects of the present invention:

[0043] 1. The method for determining the shell thickness of a slab provided by the present invention is based on data on the static pressure of molten steel and the yield strength of the corresponding steel grade at a target strain rate. It combines multiple factors such as the geometric parameters of the roller array and the temperature field of the slab to determine the shell thickness of the slab at different positions. The judgment result is closer to the actual shell thickness and has high accuracy.

[0044] 2. The method provided by the present invention for determining the shell thickness of a slab and determining the shell thickness at the crystallizer outlet provides strong technical support for reasonably increasing the casting speed to the greatest extent.

[0045] 3. The method for determining the shell thickness of a slab provided by the present invention determines the correct implementation range of the large reduction at the end of solidification of the slab. Implementing the large reduction at the end of solidification in this range can effectively solve quality problems such as internal porosity and shrinkage holes. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The present invention will be described in further detail below with reference to the accompanying drawings.

[0047] Figure 1 It is a schematic diagram of the slab partition structure;

[0048] Figure 2 It is a graph showing the relationship between the arc length l from any point on the outer arc to the meniscus and the height of the molten steel pressure head at that point on the neutral layer of the slab thickness;

[0049] Figure 3 Is steel in 10 -5 Yield strength plots at different strain rates;

[0050] Figure 4 is a schematic diagram of slab slicing;

[0051] Figure 5 It is a relationship diagram between the arc length from the neutral layer of the slab thickness to the meniscus and its position to the surface of the slab. DETAILED DESCRIPTION

[0052] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0053] Example 1:

[0054] like Figure 1 As shown, a method for determining the shell thickness of a slab includes the following steps:

[0055] S1. Determine the meniscus of the molten steel, the outer arc line between the meniscus and the end roller of the straightening zone, and the partition of the outer arc line;

[0056] S2. Establish the curvature function of any point on the outer arc;

[0057] S3. Obtain the original function of the curvature of any point on the outer arc according to the curvature function of any point on the outer arc;

[0058] S4. Convert the arc length from any point on the outer arc line to the meniscus to the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus;

[0059] 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 static pressure of the molten steel corresponding to the point;

[0060] S6. determining the yield strength function of the steel at the target strain rate, and calculating the inverse function of the yield strength function at the target strain rate;

[0061] S7, combining the parametric equation of step S5 and the inverse function of the yield strength function at the target strain rate of step S6, constructing a temperature equation for determining the shell thickness corresponding to a certain point on the neutral layer of the slab thickness;

[0062] S8. Divide the slab into slices and, in combination with the slab temperature field, determine the variation trend of the slab shell thickness in the drawing direction and the correct implementation range of the large reduction at the end of slab solidification.

[0063] The present invention abandons the drawback of the traditional method of using the solidus line temperature as the standard to determine the shell thickness of the slab. It uses the static pressure of molten steel and the yield strength of the corresponding steel type at the target strain rate as the basis, and combines multiple factors such as the geometric parameters of the roller array and the temperature field of the slab to determine the shell thickness of the slab at different positions. The judgment result is closer to the actual shell thickness and has high accuracy. It provides strong technical support for reasonably improving the casting speed to the greatest extent. It provides effective theoretical guidance for implementing the large reduction in the correct range at the end of the solidification of the slab and efficiently solving quality problems such as internal porosity and shrinkage holes.

[0064] Example 2:

[0065] Based on Example 1, starting from the meniscus of the molten steel, the outer arc is divided into a plumb area, a curved area, an arc area, a straightening area and a horizontal area in sequence;

[0066] The curvature function of any point on the outer arc is

[0067]

[0068] Where: L0 is the arc length from the end of the plumb area (beginning of bending) on ​​the outer arc to the meniscus;

[0069] L1 is the length of the arc from the end of the bending zone (end of bending) on ​​the outer arc line to the meniscus;

[0070] L2 is the length of the arc from the end of the arc zone on the outer arc line (the beginning of straightening) to the meniscus;

[0071] L3 is the arc length from the end of the straightening zone (straightening end) on the outer arc line to the meniscus;

[0072] L4 is the length of the arc from the end of the horizontal area on the outer arc line to the meniscus;

[0073] L is the length of the arc from any point on the outer arc to the meniscus (variable);

[0074] R is the radius of the outer arc of the arc area;

[0075] Curvature_B(L) is the curvature of the bending area (L is a variable);

[0076] Curvature_S(L) is the curvature of the straightening zone (L is a variable).

[0077] Specifically, a segmented definition of the curvature function is adopted to avoid oversimplification of a single curvature model and better fit the dynamic deformation of the outer arc during the actual operation of the continuous casting machine; it ensures that the mechanical behavior of different process stages (such as molten steel flow and solidification shrinkage) is accurately modeled, thereby improving the accuracy of the shell thickness calculation.

[0078] Preferably, the original function of the curvature of any point on the outer arc is

[0079]

[0080] Specifically, the original function of the curvature of any point on the outer arc is integrated with the curvature function of formula (1), and the local curvature of each point on the outer arc is accumulated as a global geometric feature, avoiding the local error caused by relying solely on the instantaneous curvature, and more realistically reflecting the overall geometric changes of the slab during the continuous deformation process; providing a mathematically rigorous physical basis for the correction of the neutral layer arc length (Formula 3), ensuring that the neutral layer position correction value is consistent with the actual bending / straightening amount.

[0081] Preferably, the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus is

[0082] ArcLength_Nt(L)=L-Slab_D / 2*(Curvature_prim(L)) Formula (3)

[0083] Where: Slab_D is the thickness of the slab.

[0084] Specifically, the length of the arc from the corresponding point on the neutral layer of the slab thickness to the meniscus is calculated by this formula.

[0085] Preferably, the relationship between the arc length from any point on the neutral layer of the slab thickness to the meniscus and the static pressure of the molten steel corresponding to the point is established by establishing a parametric equation through the arc length from any point on the outer arc line to the meniscus.

[0086] Specifically, a parametric equation is established through the arc length from any point on the outer arc line to the meniscus, and the arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus is dynamically correlated with the static pressure of the molten steel. Relying on measurable parameters, real-time process optimization is supported to improve slab quality and production efficiency.

[0087] Preferably, the parametric equation is

[0088]

[0089] Where: ρ is the density of molten steel; g is the acceleration due to gravity; Height (L) is the height of the molten steel pressure head at any point on the neutral layer of the slab thickness.

[0090] Specifically, the function of the molten steel head height (L) at any point on the neutral layer of the slab thickness in formula (4) is determined by the geometric parameters of the roller array. It is known at the beginning of the design of the slab continuous casting equipment that the relationship between the arc length L from any point on the outer arc line to the meniscus and the molten steel head height at that point on the neutral layer of the slab thickness is roughly as follows: Figure 2 When calculating the static pressure of molten steel, the height of the molten steel pressure head is matched with the length of the arc from the corresponding point on the neutral layer of the slab thickness to the meniscus to avoid pressure estimation errors caused by the curvature of the outer arc.

[0091] Preferably, the temperature equation for determining the shell thickness corresponding to a point on the neutral layer of the slab thickness is:

[0092]

[0093] Where: L Nt (L) is the arc length from any point on the neutral layer of the slab thickness to the meniscus; T shell (L) is the temperature basis for determining the thickness of the shell at a certain location.

[0094] Specifically, steel at 10 -5 The yield strength at the strain rate is approximately Figure 3 As shown, it is represented by the Strength(T) function, where T is the temperature of any point in the slab. The graph or function is slightly different for different steel grades. Through experiments or material software, the strength of a certain steel grade at 10-5 The yield strength under strain rate is presented in the form of a table. Taking a certain steel type as an example, the steel is -5 The yield strength at different strain rates is shown in Table 1. Strength(T) is used as an interpolation function.

[0095] Table 1

[0096]

[0097]

[0098] To facilitate the calculation of the corresponding temperature from the yield strength, the function Strength_inv(Stress) is defined as the inverse function of the Strength(T) function. Combining Equation (4), it can be deduced that the judgment temperature of the shell thickness corresponding to a point on the neutral layer of the slab thickness satisfies Equation (5).

[0099] Example 3:

[0100] On the basis of Example 2, the slab slicing is divided into: cutting the slab into multiple slices along the casting strand direction, with each slice being perpendicular to the casting strand direction.

[0101] Specifically, for the convenience of representation, the slab that has passed through the bending zone, the arc zone, and the straightening zone is flattened and represented as follows: Figure 4 As shown ( Figure 4 Only half of the slab thickness is shown in the figure. 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 final determination of the shell thickness trend and does not affect the expression of the determination method). Each slice can be divided into multiple cells, each of which has a node representing the cell temperature, and the spacing between nodes is Dis.

[0102] Preferably, the method of combining the temperature field of the slab to determine the changing trend of the shell thickness of the slab in the drawing direction is specifically as follows: first, the temperature used to determine the shell thickness of the corresponding slice is determined based on the temperature determination equation of the shell thickness corresponding to a point on the neutral layer of the slab thickness; then, the temperatures used to determine the shell thickness of the corresponding slice on all slices are connected in sequence according to the casting direction, and the connecting line is the changing trend of the shell thickness of the slab in the drawing direction.

[0103] During production, the temperature field of the slab can be calculated using a heat transfer model and can be considered a known quantity in the present invention. Figure 4 The calculation method for slice n is described as follows (without loss of generality).

[0104] Assume that there are k+1 nodes in slice n. The subscript of the node on the slab surface is represented by "0", the subscript of the node in the neutral layer of the slab thickness is represented by "k", and the middle nodes are "1", "2", ..., "k" along the slab surface toward the neutral layer of the slab thickness; the corresponding temperatures are represented by T[0], T[1], T[2], ..., T[k] respectively.

[0105] The temperature line determined by the present invention (see Figure 4 ) and the center line of slice n must be equal to T shell (L), its corresponding P shell (L) can be realized by expressing the logic of the pseudo code shown below,

[0106]

[0107] The pseudo code uses C++ language to express the implementation logic. In actual applications, using different languages ​​does not affect the implementation logic. The pseudo code shown shows the method for determining the intersection of the temperature line and any slice.

[0108] Similarly, the intersection of the temperature line determined by the present invention and any slice, and connecting all the intersections in sequence, is the change process of the shell thickness of the entire slab in the throwing direction, that is, the change trend of the shell thickness in the throwing direction.

[0109] Preferably, the correct implementation range of the large reduction at the end of slab solidification is: the intersection of the changing trend of the slab shell thickness in the drawing direction and the neutral layer of the slab thickness is A, the intersection 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 drawing direction is the correct implementation range of the large reduction at the end of slab solidification.

[0110] Compared with the traditional method of determining the shell thickness based on the solidus temperature, Figure 5 The difference between the temperature line of the present invention and the liquidus temperature isotherm and solidus temperature isotherm is shown. Implementing the final high pressure reduction in the correct implementation range of the final solidification of the slab can effectively solve the quality problems such as internal looseness and shrinkage.

[0111] In the description of the present invention, it should be understood that if there is a term indicating an orientation or positional relationship, it is 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 used for illustrative purposes and cannot be understood as limiting the present invention.

[0112] The above examples are merely illustrative of the present invention and do not limit the scope of protection of the present invention. Any design that is identical or similar to the present invention falls within the scope of protection of the present invention.

Claims

1. A method for determining the thickness of a slab shell, characterized by: The steps include: S1. Determine the meniscus of the molten steel, the outer arc line between the meniscus and the end roller of the straightening zone, and the partition of the outer arc line; S2. Establish the curvature function of any point on the outer arc; S3. Obtain the original 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 line 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 static pressure of the molten steel corresponding to the point; S6. determining the yield strength function of the steel at the target strain rate, and calculating the inverse function of the yield strength function at the target strain rate; S7, combining the parametric equation of step S5 and the inverse function of the yield strength function at the target strain rate of step S6, constructing a temperature equation for determining the shell thickness corresponding to a certain point on the neutral layer of the slab thickness; S8. Divide the slab into slices and, in combination with the slab temperature field, determine the variation trend of the slab shell thickness in the drawing direction and the correct implementation range of the large reduction at the end of slab solidification.

2. The method for determining the thickness of a slab shell according to claim 1, wherein: The outer arc is divided into a plumb area, a curved area, an arc area, a straightening area and a horizontal area starting from the meniscus of the molten steel; The curvature function of any point on the outer arc is Where: L0 is the arc length from the end of the plumb bob area on the outer arc to the meniscus; L1 is the length of the arc from the end of the bending zone on the outer arc to the meniscus; L2 is the length of the arc from the end of the arc area on the outer arc line to the meniscus; L3 is the arc length from the end of the straightening zone on the outer arc to the meniscus; L4 is the length of the arc from the end of the horizontal area on the outer arc line to the meniscus; L is the length of the arc from any point on the outer arc to the meniscus; R is the radius of the outer arc of the arc area; Curvature_B(L) is the curvature of the bending area; Curvature_S(L) is the curvature of the straightening area.

3. The method for determining the slab shell thickness according to claim 2, wherein: The original function of the curvature of any point on the outer arc is 4. The method for determining the thickness of a slab shell according to claim 3, wherein: The arc length from the corresponding point on the neutral layer of the slab thickness to the meniscus is ArcLength_Nt(L)=L-Slab_D / 2*(Curvature_prim(L)) Formula (3) Where: Slab_D is the thickness of the slab.

5. The method for determining the thickness of a slab shell according to claim 4, wherein: The relationship between the arc length from any point on the neutral layer of the slab thickness to the meniscus and the static pressure of the molten steel corresponding to the point is established by using the arc length from any point on the outer arc line to the meniscus to establish a parametric equation.

6. The method for determining the thickness of a slab shell according to claim 5, wherein: The parametric equation is Where: L Nt (L) is the length of the arc from any point on the neutral layer of the slab thickness to the meniscus; ρ is the density of molten steel; g is the acceleration of gravity; Height(L) 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 a slab shell according to claim 6, wherein: The temperature equation for determining the shell thickness at a point on the neutral layer of the slab thickness is: Where: T shell (L) is the temperature basis for determining the thickness of the shell at a certain location.

8. The method for determining the thickness of a slab shell according to claim 7, wherein: The slab slicing is divided into: cutting the slab into multiple slices along the casting strand direction, with each slice being perpendicular to the casting strand direction.

9. The method for determining the thickness of a slab shell according to claim 8, wherein: The variation trend of the slab shell thickness in the drawing direction is determined by combining the slab temperature field as follows: First, the temperature used to determine the shell thickness of the corresponding slice is determined based on the temperature equation for determining the shell thickness corresponding to a point on the neutral layer of the slab thickness. Then, the temperatures used to determine the shell thickness of the corresponding slice on all slices are connected in sequence along the casting direction. The connecting line represents the changing trend of the shell thickness of the slab in the casting direction.

10. The method for determining the thickness of a slab shell according to claim 9, wherein: The correct implementation range of the large reduction at the end of slab solidification is: the intersection of the changing trend of the slab shell thickness in the drawing direction and the neutral layer of the slab thickness is A, the intersection 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 drawing direction is the correct implementation range of the large reduction at the end of slab solidification.

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