Design method of narrow face compensation type cavity of continuous casting crystallizer

Abstract

The application provides a design method of a narrow face compensation type cavity of a continuous casting crystallizer, and belongs to the technical field of continuous casting equipment and process collaborative design. The design method is based on full-process prediction of cooling shrinkage before pressing, thermal-mechanical coupling deformation in the pressing section, and cooling to the final temperature after pressing, to obtain a final state narrow face profile deviation distribution and a final state spread distribution. A compensation requirement is constructed with the final state narrow face flatness and / or spread uniformity as the target, a narrow face compensation profile is generated in the crystallizer outlet cross section, the compensation profile forms shrinkage near the two side corners, maintains the original width in the middle, and gradually changes along the drawing direction through a distribution function, to form a three-dimensional compensation type cavity inner surface. The final cavity parameters are determined through iterative checking. The design method provided by the application can reduce the maximum transverse spread after pressing, reduce the edge-to-center width difference and the narrow face peak-to-valley deviation, and help to reduce the pressing stress level, improve the rolling size adaptability and process stability.

Description

Technical Field

[0001] This invention relates to the field of co-design technology for continuous casting equipment and processes, and in particular to a design method for a narrow-face compensation cavity in a continuous casting crystallizer. Background Technology

[0002] In the continuous casting production of small square billets, a reduction process is often used to deform the billet in order to improve its internal quality, microstructure, and subsequent rolling conditions. However, complex thermo-mechanical coupling effects exist before and after reduction, including: 1) Temperature gradient and thermal contraction caused by cooling of the crystallizer and secondary cooling zone; 2) Plastic flow and lateral widening of the cross section caused by contact load and friction in the compression section; 3) Thermal contraction and stress redistribution that occur during the cooling process to the final temperature after compression.

[0003] Traditional crystallizers with narrow face cavities typically employ straight cavities or conventional tapered designs, failing to pre-compensate for the non-uniform widening of the cross-section caused by the pressing process. In practice, it has been found that under traditional crystallizer conditions, the narrow face of the cast billet after pressing often exhibits a distribution characteristic of "larger widening at both sides and smaller widening in the middle," and the final profile shows a non-straight shape of "high at both sides and low in the middle." This type of non-uniform widening leads to the following problems: • The maximum lateral width increases, making it easier to approach or exceed the upper limit of the mill's entry width; • The increased width difference between the edge and the center affects aperture matching and guide stability; • Increased peak and average compressive stress increase crack susceptibility; • Limiting the available reduction amount affects the process window and production line efficiency.

[0004] Therefore, a design method for a crystallizer narrow-face cavity structure is needed to compensate for the non-uniform widening of the narrow face caused by pressing and subsequent cooling, so as to improve the final cross-sectional morphology of the cast billet, enhance the adaptability of the rolling mill dimensions, and improve the process stability. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a design method for a narrow-face compensation cavity in a continuous casting mold that can compensate for the non-uniform widening of the narrow face caused by billet pressing and subsequent cooling.

[0006] To solve the above-mentioned technical problems, the present invention provides a design method for a narrow-face compensation cavity in a continuous casting mold, comprising the following steps: Obtain parameters including geometric and process parameters, thermal boundary and environmental parameters, contact parameters, and material and steel grade parameters; A predictive model for the entire process of billet cross-section evolution was established, including the pre-cooling thermal shrinkage sub-stage, the thermo-mechanical coupling deformation sub-stage during the pressing section, and the post-cooling to final temperature sub-stage. The final state narrow profile deviation distribution and final state widening distribution are obtained based on the full-process prediction model of billet cross-section evolution. The compensation demand is constructed with the final state narrow face flatness index and / or the final state widening uniformity index as the target, and a narrow face progressive compensation profile is generated in the crystallizer outlet cross section. The narrow-face progressive compensation profile generated in the cross-section of the crystallizer outlet is mapped along the billet pulling direction to the axial coordinate of the crystallizer through an assignment function to obtain the three-dimensional progressive compensation cavity inner surface; The three-dimensional progressively compensated cavity inner surface is substituted back into the full-process prediction model of the billet cross-section evolution for iterative calculation. The final cavity parameters are output after the final narrow face profile deviation distribution and / or the final widening distribution meet the preset threshold.

[0007] Furthermore, the establishment of the full-process prediction model for the evolution of the billet cross-section includes: During the pre-cooling thermal shrinkage stage before compression, the temperature field was calculated and the initial thermal shrinkage morphology of the compression inlet section was obtained; In the thermo-mechanical coupling deformation sub-stage of the pressing section, the contact and friction boundaries of the pressing roller are introduced based on the initial morphology and temperature field to calculate the cross-sectional widening and stress-strain distribution during the pressing process. In the cooling sub-stage after compression, the compressed section is further cooled to the final temperature to obtain the final cross-sectional geometry.

[0008] Furthermore, the final-state narrow face profile deviation distribution is the difference between the narrow face inner surface profile extracted at the final-state temperature and the target reference profile, i.e.

[0009] Where δ(y) is the final-state narrow-surface profile deviation distribution; x final (y) represents the narrow-face inner surface profile extracted at the final temperature; x ref (y) represents the target reference profile; y is the coordinate along the thickness direction of the narrow face within the cross-section of the crystallizer outlet, and x is the half-width coordinate in the width direction; The final-state broadening distribution is the width change calculated along the y-direction at the final-state temperature, i.e.

[0010] Where Δw(y) is the final-state broadened distribution; W final (y) represents the final state width, W in (y) represents the reference width of the pressure inlet; In the semi-model, the final-state broadening distribution can be equivalently represented as: .

[0011] Furthermore, the final-state narrow face flatness index includes one or more of the following: the maximum deviation of the final-state narrow face profile, the mean square deviation of the final-state narrow face profile, and the peak-valley difference of the final-state narrow face; the final-state widening uniformity index includes one or more of the following: the final-state widening range, the final-state widening standard deviation, and the maximum widening position offset, i.e., the widening difference between the edges.

[0012] Furthermore, the compensation demand c constructed with the final-state narrow-face flatness index and / or the final-state widening uniformity index as the target... raw (y) satisfies:

[0013] Where δ(x) is the final-state narrow profile deviation distribution, and Δw(x) is the final-state broadening distribution. (Δ w) represents the target broadening distribution or the target average broadening. λ and η are weighting coefficients; The compensation demand c raw (y) is smoothed and boundary / center constraints are applied to obtain the progressive compensation function c(y) used to generate the progressive compensation profile of the narrow face of the cavity: .

[0014] Furthermore, the progressive compensation profile satisfies at least one of the following: the two ends of the narrow face shrink inward relative to the original cavity reference surface; the middle region of the narrow face maintains the original width or close to the original width; the compensation profile is a continuous transition curve with continuous first derivative and / or continuous second derivative; and the compensation profile smoothly connects with the inner surface of the original cavity at the boundary.

[0015] Furthermore, the asymptotic compensation function c(y) along the casting direction is mapped to the crystallizer axial coordinate z using a continuous allocation function or a piecewise allocation function g(z) to obtain a three-dimensional compensation distribution: c(y,z)=g(z) c(y) Wherein, g(z) is used to control the compensation amplitude at different axial positions to achieve a smooth axial transition and / or a compensation distribution with a small inlet and a large outlet; The progressive compensation profile, within the cross-section of the crystallizer outlet, uses the coordinates y∈[0,H] along the thickness direction of the narrow face within the cross-section as the independent variable, and defines the normalized coordinate t=y / H. The progressive compensation amount distribution function is:

[0016] Where B is the maximum compensation on one side, and p is the shape index; The narrow inner surface profile at the outlet cross-section is as follows:

[0017] This causes the thickness to shrink near the two corners, while the thickness in the middle remains at its original width. Where x0 is the original narrow face half-width, i.e., x0=W / 2, and W is the original narrow face width of 153mm.

[0018] Furthermore, the inner surface of the three-dimensional progressively compensated cavity satisfies:

[0019] Where y is the coordinate along the thickness direction of the narrow face within the outlet cross section, and z is the coordinate between the pulling direction and the crystallizer axis.

[0020] Furthermore, the preset threshold includes one or more of the following: 1) The maximum width of the feed into the rolling mill shall not exceed the upper limit allowed by the rolling mill; 2) The width difference between the edge and the center does not exceed the preset value; 3) The peak-to-valley difference in the final narrow face does not exceed the preset value; 4) Compared to the uncompensated cavity, the flatness index and / or widening uniformity index are reduced by a preset percentage.

[0021] Furthermore, the maximum compensation amount B on one side is 0.1 to 5.0 mm; the shape index p is 0.5 to 3.0; and the allocation function g(z) takes values ​​in the range of 0 to 1 and satisfies the axial smooth transition constraint.

[0022] The present invention provides a design method for a narrow-face compensation cavity in a continuous casting crystallizer, which has the following beneficial effects: 1. Source compensation reduces non-uniform widening By pre-setting a compensation cavity shape with "contraction on both sides and original length in the middle" on the inner surface of the narrow face of the crystallizer, the excessive widening of the edge caused by pressing and subsequent cooling can be specifically offset.

[0023] 2. Improve the flatness of the final profile of narrow faces By pre-compensating the inner surface of the narrow face of the crystallizer, the final state peak-valley deviation of the narrow face can be reduced, making the unfavorable profile of "high on both sides and low in the middle" more straight and improving the consistency of cross-sectional morphology.

[0024] 3. Reduce the maximum transverse width to improve rolling mill adaptability. By pre-compensating the inner surface of the narrow face of the crystallizer, the maximum lateral widening and the difference between the width of the edge and the center can be reduced, making it easier for the billet to meet the rolling mill's entry width limit and expanding the available reduction process window.

[0025] 4. Reduce peak and average compressive stress. By optimizing geometric pre-compensation and load path, the peak and average stress during the pressing process can be reduced, stress concentration and crack sensitivity can be decreased, and the pressing quality of the billet can be improved.

[0026] 5. The method has strong generalizability. This invention adopts a process flow method of "full-process prediction - index quantification - reverse compensation - iterative verification", which can be applied to the design of crystallizer cavity with different cross-sectional specifications, different reduction amounts and different cooling regimes. Attached Figure Description

[0027] Figure 1 A flowchart illustrating a design method for a narrow-face compensation cavity in a continuous casting crystallizer, provided in an embodiment of the present invention; Figure 2 A schematic diagram of the narrow-face compensation cavity structure in a design method for a narrow-face compensation cavity of a continuous casting crystallizer provided in an embodiment of the present invention; Figure 3 The stress comparison diagram between the narrow-face compensation cavity crystallizer and the old-style crystallizer is provided by the design method of the narrow-face compensation cavity of the continuous casting crystallizer provided in the embodiment of the present invention. Detailed Implementation

[0028] See Figure 1 The present invention provides a design method for a narrow-face compensation cavity in a continuous casting crystallizer, comprising the following steps: Step 1) Obtain parameters including geometric and process parameters, thermal boundary and environmental parameters, contact parameters, and material and steel grade parameters.

[0029] The parameters mentioned above can be derived from production line process settings, equipment parameters, material databases, literature experience values, and / or experimental back-calibration. Specifically, these parameters include: 1) Geometric and process parameters: nominal cross-sectional dimensions of the billet, reduction amount, location of the reduction zone, and casting speed; 2) Thermal boundary parameters: heat transfer conditions of the crystallizer, heat transfer conditions of the secondary cooling zone, and ambient temperature; 3) Contact parameters: Contact parameters and friction parameters between the pressure roller and the billet; 4) Material parameters: density, specific heat, thermal conductivity, coefficient of thermal expansion and high-temperature constitutive parameters.

[0030] By obtaining the above parameters in advance, data support is provided for the next step of establishing a full-process prediction model of the evolution of the billet cross section during the pre-pressing stage of thermal shrinkage, the thermo-mechanical coupling deformation during the pressing stage, and the cooling process after pressing.

[0031] Step 2) Establish a full-process prediction model for the evolution of the billet cross section, including the pre-pressing cooling thermal shrinkage sub-stage, the pressing section thermo-mechanical coupling deformation sub-stage, and the post-pressing cooling to the final temperature sub-stage.

[0032] To establish a more accurate prediction model for the entire process of billet cross-section evolution, this invention does not only calculate the instantaneous deformation during compression, but also covers the following three stages: (1) Press down the previous stage The cooling process of the crystallizer and the secondary cooling zone is simulated to obtain the temperature field distribution and the initial geometric deviation before pressing caused by thermal contraction, which is used as the input state for the pressing section calculation.

[0033] (2) Pressing stage Based on the temperature field and initial geometry before pressing, the contact and friction of the pressing rollers are introduced to calculate the stress, strain and lateral widening behavior during the pressing process.

[0034] (3) Cooling stage after pressing The compressed section is further cooled to the final temperature (preferably room temperature or acceptance temperature), and the final section profile and final width distribution are calculated.

[0035] The finite element method was used to establish the prediction model for the entire process of billet cross-section evolution, and the model satisfies the following relationship: 1) Heat conduction equation:

[0036] 2) Equations of mechanical equilibrium:

[0037] 3) Thermal strain relationship:

[0038] 4) Contact friction conditions: τ≤μp Where ρ is density, c p σ is the specific heat, k is the thermal conductivity, Q is the volume heat source term, σ is the stress tensor, b is the volume force term, α is the coefficient of thermal expansion, μ is the coefficient of friction, and p is the contact pressure.

[0039] Step 3) Based on the full-process prediction model of billet cross-section evolution, obtain the final state narrow face profile deviation distribution and the final state widening distribution.

[0040] Among them, the final-state narrow face profile deviation distribution is the difference between the narrow face inner surface profile extracted at the final-state temperature and the target reference profile, i.e.

[0041] Where δ(y) is the final-state narrow-surface profile deviation distribution; x final (y) represents the narrow-face inner surface profile extracted at the final temperature; x ref(y) represents the target reference profile; y is the coordinate along the thickness direction of the narrow face within the cross-section of the crystallizer outlet, and x is the half-width coordinate in the width direction.

[0042] Wherein, the final-state broadening distribution is the width change calculated along the y-direction at the final-state temperature, i.e.

[0043] Where Δw(y) is the final-state broadened distribution; W final (y) represents the final state width, W in (y) represents the reference width of the pressure inlet.

[0044] In the semi-model, the final-state broadening distribution can be equivalently represented as: .

[0045] Of course, equivalent indices (including maximum broadening and the difference between the broadening at the edges and the middle) can also be used to characterize the final broadening distribution.

[0046] Step 4) Construct the compensation demand with the final state narrow face flatness index and / or final state widening uniformity index as the target, and generate the narrow face progressive compensation profile in the crystallizer outlet cross section.

[0047] Among them, the final state narrow face flatness index and the final state widening uniformity index shall each include at least one or more of the following.

[0048] 1) Final state narrow surface straightness indexes: maximum deviation max|δ(y)|, mean square deviation, peak-to-valley difference; 2) Final state widening uniformity index: widening range max(Δw)-min(Δw), widening standard deviation, maximum widening position offset, and side-to-side widening difference.

[0049] Among them, the compensation demand c is constructed with the final-state narrow face flatness index and / or the final-state widening uniformity index as the objectives. raw (y) satisfies:

[0050] The compensation demand is c raw (y) represents the original compensation requirement, that is, the compensation requirement before smoothing and before the corner and center constraints are forcibly satisfied.

[0051] Where δ(x) is the final-state narrow profile deviation distribution, and Δw(x) is the final-state broadening distribution. (Δ w) represents the target broadening distribution or the target average broadening. λ and η are weighting coefficients; Then, regarding the compensation demand c raw(y) is smoothed and boundary and center constraints are applied to obtain the progressive compensation function c(y) used to generate the progressive compensation profile of the narrow face of the cavity: .

[0052] Both can be written in the form of an "operator":

[0053] in, S ( Smoothing operators (such as moving average, spline fitting, low-pass filtering, etc.). P ( Projection / constraint operators (force the result to satisfy boundary conditions and continuity).

[0054] The progressive compensation profile satisfies at least one of the following constraints: 1) In the thickness direction region near the two corners, the compensation amount is larger, causing the inner surface of the narrow face to shrink inward relative to the reference narrow face cavity; 2) At the midpoint of the thickness direction, the compensation amount is zero, so that the midpoint maintains its original width; 3) The compensation profile is a continuous transition curve, and the first derivative is continuous and / or the second derivative is continuous; 4) The compensation contour smoothly connects with the wide-face cavity in the corner transition area.

[0055] See Figure 2 The compensation profile preferably adopts a bell-shaped compensation form with "contraction at both sides and original length in the middle" to reduce the maximum lateral widening after compression and improve the difference in widening between the edges and the middle. The compensation requirement is constructed from the final narrow face profile deviation distribution δ(y) and / or the final widening distribution Δw(y), and after smoothing and boundary constraints, an asymptotic compensation function c(y) is obtained, where c(y) represents the single-sided compensation distribution along the width direction coordinate y within the crystallizer outlet cross-section.

[0056] The middle section retains its original width. c(H / 2)=0 The contraction is greater (compensation is greater) near the corners: c(y) takes a larger value in the region close to y=0 and y=H; The compensation amount is non-negative (the shrinkage amount should not be negative), that is: c(y)≥0 Continuous transition: c(y) is continuous, preferably continuous first derivative (second derivative is optional).

[0057] In this way, the narrow - face progressive compensation profile obtained by the present invention is symmetrically arranged with respect to the center line of the narrow face, and is continuously transitioned with the wide - face cavity in the corner transition region and smoothly connected to the reference narrow - face cavity.

[0058] Step 5) Map the generated narrow - face progressive compensation profile along the casting direction and the crystallizer axial coordinate through a distribution function to obtain the three - dimensional progressive compensation cavity inner surface.

[0059] Specifically, the progressive compensation amount function c(y) is mapped along the casting direction and the crystallizer axial coordinate z through a continuous distribution function or a piece - wise distribution function g(z) to obtain the three - dimensional compensation amount distribution: c(y,z)=g(z) c(y) Among them, g(z) is used to control the compensation amplitude at different axial positions to achieve axial smooth transition and / or a compensation distribution with a small entrance and a large exit; Among them, in the cross - section of the crystallizer outlet, with the coordinate y ∈ [0, H] along the narrow - face thickness direction in the cross - section as the independent variable, the normalized coordinate t = y / H is defined, and the progressive compensation amount distribution function is:

[0060] Among them, B is the maximum unilateral compensation amount, and p is the shape index, which is used to control the speed of the compensation curve recovering from the edge to the middle; when p increases, the compensation amount grows more concentrated near the middle; when p decreases, the compensation amount distribution is flatter.

[0061] The profile of the narrow - face inner surface in the outlet cross - section is:

[0062] It makes the thickness - direction positions near the two corners shrink, while the middle part in the thickness direction maintains the original width; Among them, x0 is the original half - width of the narrow face, that is, x0 = W / 2, and W is the original narrow - face width of 153 mm.

[0063] It can be seen from this: When y = 0 or y = H, Δx = 0, and x(y)=x_0 - B, corresponding to the shrinkage at both ends of the narrow face; When y = H / 2, Δx = B, and x(y)=x_0, corresponding to the middle part of the narrow face maintaining the original width; In the range of 0 < y < H, the profile is a continuous transition curve, forming a narrow - face progressive compensation cavity type with "shrinkage at both sides and original length in the middle".

[0064] The present invention relates to a narrow-face progressive compensation cavity system, which refers to a pre-compensation geometry constructed to address the non-uniform widening trend of the narrow face after compression, characterized by "high on both sides and low in the middle". The actual cavity is characterized by pre-contraction at both ends of the narrow face and preservation of the width in the middle, in order to offset the excessive widening of the side after compression.

[0065] In this invention, the narrow-faceted progressive compensation profile can use different B and / or p values ​​at different height segments of the crystallizer to form a continuously varying or segmented compensation distribution.

[0066] Among them, the three-dimensional progressively compensated cavity inner surface satisfies:

[0067] Where y is the coordinate along the thickness direction of the narrow face within the outlet cross section, z is the coordinate between the pulling direction and the crystallizer axis, and H is the height of the narrow face.

[0068] Wherein, the maximum compensation amount B on one side is 0.1 to 5.0 mm; the shape index p is 0.5 to 3.0; and the allocation function g(z) takes values ​​in the range of 0 to 1 and satisfies the axial smooth transition constraint.

[0069] In this invention, the allocation function g(z) is a linear function, a monotonically increasing function, or a piecewise increasing function, which can make the compensation amplitude near the crystallizer inlet region smaller than the compensation amplitude near the crystallizer outlet region.

[0070] Step 6) Substitute the three-dimensional progressive compensation cavity inner surface back into the full-process prediction model of the billet cross-section evolution for iterative calculation. Output the final cavity parameters after the final narrow face profile deviation distribution and / or final widening distribution meet the preset threshold.

[0071] The preset threshold includes one or more of the following: 1) The maximum width of the feed into the rolling mill shall not exceed the upper limit allowed by the rolling mill; 2) The width difference between the edge and the center does not exceed the preset value; 3) The peak-to-valley difference in the final narrow face does not exceed the preset value; 4) Compared to the uncompensated cavity, the flatness index and / or widening uniformity index are reduced by a preset percentage.

[0072] This invention calibrates the whole-process prediction model of billet cross-section evolution by using measured width data and / or final cross-sectional profile data, so that the deviation between the prediction results and the measured results is less than a preset calibration threshold.

[0073] The present invention provides a design method for a narrow-face compensation cavity of a continuous casting crystallizer. Without adding a complex mechanism, it achieves a reduction in the maximum lateral width expansion after pressing, a reduction in the width difference between the sides and the center, and an optimization of the stress level by directly optimizing the geometry of the inner surface of the narrow face of the crystallizer. It has significant engineering application value.

[0074] The following examples illustrate the design method of a narrow-face compensation cavity for a continuous casting crystallizer provided by the present invention.

[0075] Example 1: Model building, calibration and identification of traditional crystallizer problems (1) Object and working conditions Taking a 168×153 mm small square billet from a certain enterprise as the object, the steel grade is GCr15, and the reference drawing speed is 2000 mm / min. Finite element analysis is performed using a half-bill symmetric model, which covers the entire process of thermal shrinkage before pressing, thermo-mechanical coupling deformation during pressing, and cooling to room temperature after pressing.

[0076] (2) Model calibration By calibrating the thermal shrinkage parameters through on-site measurement of cold billet dimensions, the model can reasonably reproduce the measured widening trend and dimensional changes under uncompensated or traditional cavity conditions.

[0077] (3) Verification under 10 mm compression condition When the reduction is 10 mm, the model calculates that the maximum transverse width of the cold billet is about 2.36 mm, which is consistent with the 2-3 mm range observed on site, indicating that the model can be used for subsequent cavity compensation design.

[0078] (4) Problems with traditional cavities under 15 mm compression conditions Under conventional crystallizer cavity conditions, when the reduction is 15 mm, the model shows that the maximum transverse width of the billet is close to or exceeds the mill entry limit (e.g., 158 mm), and the width difference between the edge and center increases significantly, posing a risk of exceeding the entry size limit.

[0079] (5) Upper limit identification of compression amount Based on the fitting of multiple sets of reduction simulation results, the upper limit constraint of the reduction of this specification of billet under the traditional crystallizer cavity condition can be obtained (for example, about 13 mm), indicating that the traditional cavity limits the reduction process window.

[0080] Example 2: Construction of Narrow Face Compensation Profile (1) Compensation Target To address the final state characteristics of the cross-section after compression under traditional crystallizer conditions, which are characterized by "larger width at the edges and smaller width in the middle" and "higher at both sides and lower in the middle" in the narrow face profile, a narrow face compensation cavity is constructed to reduce the maximum lateral width and improve the difference in width between the edges and the middle.

[0081] (2) Design concept A narrow-face compensation cavity design with "contraction at both ends and original length in the middle" is adopted. That is, appropriate contraction is set at both ends of the narrow face of the crystallizer in the height direction, while the original width is maintained in the middle. It is connected by a continuous transition curve to pre-compensate for excessive widening of the edges caused by compression.

[0082] (3) Parameter definition and function expression For a 168×153 mm small square billet, take: 1) Original narrow face half-width x0 = 153 / 2 = 76.5mm; 2) Narrow face height H = 168 mm; 3) The maximum shrinkage on one side is B = 0.85 mm (corresponding to an equivalent compensation of approximately 1.7 mm across the entire width). 4) Shape index p This is an adjustable parameter.

[0083] Define the normalized coordinates t = y / H, and the compensation function is:

[0084] The compensated narrow face profile is as follows:

[0085] Among them, y=0 and y=168mm correspond to the two ends of the narrow face, and y=84mm corresponds to the middle of the narrow face.

[0086] (4) Parameter meaning B This represents the maximum shrinkage on one side, which can be determined based on empirical values ​​of the maximum widening on one side under traditional cavity design or simulation results. p The shape index controls how quickly the compensation curve recovers from the edge to the center and the shape of the central contour.

[0087] (5) Parameter optimization By different p Comparative simulations were conducted, and considering the maximum lateral width, the difference between the widths at the edges and the final state straightness index, the optimal value was p=1.2.

[0088] Example 3: Comparison and verification between compensated cavity and traditional cavity (1) Comparison settings Under the same steel grade, drawing speed, cooling regime, and pressing conditions, the compensation cavity constructed in Example 2 was compared and analyzed with the traditional crystallizer cavity.

[0089] (2) Comparison of dimensions under 15 mm pressing conditions When the reduction is 15 mm, the maximum transverse width of the billet under the conventional crystallizer cavity exceeds or approaches the mill entry limit; after using the compensation cavity of the present invention, the maximum transverse width is reduced, which can meet the entry size limit.

[0090] (3) Comparison of the difference in width between sides Under conventional crystallizer cavity conditions, the difference in width between the edge and the center is relatively large (e.g., about 1.59 mm); after using the compensation cavity of the present invention, the difference in width between the edge and the center can be reduced to less than 0.4 mm.

[0091] (4) Comparison of stress effects See Figure 3 From the stress comparison between the narrow-face compensation cavity mold designed by the embodiment of the present invention and the old-style mold, it can be seen that the compensation cavity of the present invention can significantly reduce the peak and average stress in the key area of ​​the narrow face and reduce the range of high stress area, indicating that it is beneficial to reduce stress concentration and crack sensitivity.

[0092] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A design method for a narrow-face compensation cavity in a continuous casting crystallizer, characterized in that, Includes the following steps: Obtain parameters including geometric and process parameters, thermal boundary and environmental parameters, contact parameters, and material and steel grade parameters; A predictive model for the entire process of billet cross-section evolution was established, including the pre-cooling thermal shrinkage sub-stage, the thermo-mechanical coupling deformation sub-stage during the pressing section, and the post-cooling to final temperature sub-stage. The final state narrow profile deviation distribution and final state widening distribution are obtained based on the full-process prediction model of billet cross-section evolution. The compensation demand is constructed with the final state narrow face flatness index and / or the final state widening uniformity index as the target, and a narrow face progressive compensation profile is generated in the crystallizer outlet cross section. The generated narrow-face progressive compensation profile is mapped along the billet pulling direction to the axial coordinates of the crystallizer through an assignment function to obtain the three-dimensional progressive compensation cavity inner surface; The three-dimensional progressively compensated cavity inner surface is substituted back into the full-process prediction model of the billet cross-section evolution for iterative calculation. The final cavity parameters are output after the final narrow face profile deviation distribution and / or the final widening distribution meet the preset threshold.

2. The design method for the narrow-face compensation cavity of the continuous casting crystallizer according to claim 1, characterized in that, The establishment of the full-process prediction model for the evolution of the billet cross-section includes: During the pre-pressing cooling thermal contraction sub-stage, the temperature field was calculated and the initial thermal contraction morphology of the pressing inlet section was obtained. In the thermo-mechanical coupling deformation sub-stage of the pressing section, the contact and friction boundaries of the pressing roller are introduced based on the initial morphology and temperature field to calculate the cross-sectional widening and stress-strain distribution during the pressing process; In the cooling sub-stage after compression, the compressed section is further cooled to the final temperature to obtain the final cross-sectional geometry.

3. The design method for the narrow-face compensation cavity of the continuous casting crystallizer according to claim 1, characterized in that, The final-state narrow face profile deviation distribution is the difference between the narrow face inner surface profile extracted at the final-state temperature and the target reference profile, i.e. Where δ(y) is the final-state narrow-surface profile deviation distribution; x final (y) represents the narrow-face inner surface profile extracted at the final temperature; x ref (y) represents the target reference profile; y is the coordinate along the thickness direction of the narrow face within the cross-section of the crystallizer outlet, and x is the half-width coordinate in the width direction; The final-state broadening distribution is the width change calculated along the y-direction at the final-state temperature, i.e. Where Δw(y) is the final-state broadened distribution; W final (y) represents the final state width, W in (y) represents the reference width of the pressure inlet; In the semi-model, the final-state broadening distribution can be equivalently represented as: 。 4. The design method for the narrow-face compensation cavity of the continuous casting crystallizer according to claim 1, characterized in that, The final-state narrow face flatness index includes one or more of the following: the maximum deviation of the final-state narrow face profile, the mean square deviation of the final-state narrow face profile, and the peak-valley difference of the final-state narrow face. The final-state widening uniformity index includes one or more of the following: the final-state widening range, the final-state widening standard deviation, the maximum widening position offset, and the edge-to-center widening difference.

5. The design method for the narrow-face compensation cavity of the continuous casting crystallizer according to claim 1, characterized in that, The compensation demand c raw (y) satisfies: Where δ(y) is the final-state narrow profile deviation distribution, and Δw(y) is the final-state broadening distribution. (Δ w) represents the target broadening distribution or the target average broadening. λ and η are weighting coefficients; The compensation demand c raw (y) is smoothed and boundary / center constraints are applied to obtain the progressive compensation function c(y) used to generate the progressive compensation profile of the narrow face of the cavity: 。 6. The design method for the narrow-face compensation cavity of the continuous casting crystallizer according to claim 5, characterized in that, The progressive compensation profile satisfies at least one of the following: the two ends of the narrow face shrink inward relative to the original cavity reference surface; the middle area of ​​the narrow face maintains the original width or close to the original width; the compensation profile is a continuous transition curve with continuous first derivative and / or continuous second derivative; and the compensation profile smoothly connects to the inner surface of the original cavity at the boundary.

7. The design method for the narrow-face compensation cavity of the continuous casting crystallizer according to claim 6, characterized in that, The asymptotic compensation function c(y) is related to the casting direction and the crystallizer axial coordinate. The three-dimensional compensation distribution is obtained by mapping using either a continuous allocation function or a piecewise allocation function g(z): Wherein, g(z) is used to control the compensation amplitude at different axial positions to achieve a smooth axial transition and / or a compensation distribution with a small inlet and a large outlet; The progressive compensation profile, within the cross-section of the crystallizer outlet, uses the coordinates y∈[0,H] along the thickness direction of the narrow face within the cross-section as the independent variable, and defines the normalized coordinate t=y / H. The progressive compensation amount distribution function is: Where B is the maximum compensation on one side, and p is the shape index; The inner surface profile of the narrow face within the outlet cross-section is as follows: This causes the thickness to shrink near the two corners, while the thickness in the middle remains at its original width. Where x0 is the original narrow face half-width, i.e., x0=W / 2, and W is the original narrow face width of 153mm.

8. The design method for the narrow-face compensation cavity of the continuous casting crystallizer according to claim 7, characterized in that, The three-dimensional progressively compensated cavity inner surface satisfies: Where y is the coordinate along the thickness direction of the narrow face within the outlet cross section, and z is the coordinate between the pulling direction and the crystallizer axis.

9. The design method for the narrow-face compensation cavity of the continuous casting crystallizer according to claim 8, characterized in that, The preset threshold includes one or more of the following: 1) The maximum width of the feed into the rolling mill shall not exceed the upper limit allowed by the rolling mill; 2) The width difference between the edge and the center does not exceed the preset value; 3) The peak-to-valley difference in the final narrow face does not exceed the preset value; 4) Compared to the uncompensated cavity, the flatness index and / or widening uniformity index are reduced by a preset percentage.

10. The design method for the narrow-face compensation cavity of the continuous casting crystallizer according to claim 9, characterized in that, The maximum compensation amount B on one side is 0.1 to 5.0 mm; the shape index p is 0.5 to 3.0; the allocation function g(z) takes values ​​in the range of 0 to 1 and satisfies the axial smooth transition constraint.

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