Method for predicting the size of the central equiaxed zone of an ingot during rolling
By combining the Usatov broadening formula with the rolling method, the size of the equiaxed crystal zone at the center of the ingot during the rolling process can be quickly predicted, solving the problem of complex and time-consuming calculations in the existing technology. This enables precise control of the ingot morphology and is applicable to the production of precision machinery and silent engines.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- DAYE SPECIAL STEEL CO LTD
- Filing Date
- 2023-11-20
- Publication Date
- 2026-07-21
AI Technical Summary
Existing technologies are complex and time-consuming in predicting the size of the equiaxed crystal region at the center of the ingot during the rolling process. This makes it difficult to meet the precise control requirements of precision machinery and silent engines for the layered structure of the ingot, resulting in inconsistent finished products, affecting performance and causing economic losses.
By combining the Usatov widening formula with the rolling method, the size and frame ratio of the equiaxed crystal region at the center of the ingot can be quickly predicted during the rolling process by calculating the height and width of the cross section of the ingot and the central equiaxed crystal region. The height and width of the central equiaxed crystal region of the ingot after the nth rolling pass are calculated using formulas (1) and (2).
It enables rapid and simple prediction of the equiaxed crystal zone size at the ingot center, which can guide the rolling reduction process, improve the ingot morphology, and is suitable for actual on-site production, reducing calculation costs and time.
Smart Images
Figure CN117324369B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of steel rolling technology, and in particular to a method for predicting the size of the equiaxed crystal zone at the center of an ingot during the rolling process. Background Technology
[0002] Currently, most steel mills, both domestically and internationally, use continuous casting to produce square billets, with some using round billets. Both steel ingots and continuously cast billets belong to killed steel. Due to the characteristics of the solidification process, the microstructure of killed steel ingots (billets) generally consists of three layers from the outside in: an outer layer of fine equiaxed crystals (typically 5-15mm thick), a middle layer of columnar crystals, and a core layer of coarse equiaxed crystals. Figure 1 As shown.
[0003] The different layers of a cast ingot (billet) exhibit variations in composition, microstructure, and density. These differences inevitably lead to variations in properties between layers, such as strength, toughness, thermal expansion, and thermal conductivity. While these differences pose little problem for ordinary structural materials, they can significantly impact the manufacture of precision machinery, silent engines, and gearbox gears. Improper rolling can cause the large equiaxed grain region in the center of the billet to deform into an elliptical or rectangular shape with significant differences in the lengths of its major and minor axes (sides). Figure 2 Subsequently, when users forge gears, the microstructure in the circumferential direction of the gear will be inconsistent. In a ring-shaped region, some areas will only have columnar crystal structures, some only equiaxed crystal structures, and some areas will have both. This inconsistency in microstructure will cause uneven expansion and contraction of the gear during carburizing and quenching heat treatment. After heat treatment, the gear will deform excessively, making subsequent machining impossible and resulting in scrap, causing huge economic losses and a poor user experience. To meet the requirements of precision gear manufacturing and improve the user experience, this layered structure of the ingot (billet) must be well controlled during the rolling process so that the central equiaxed crystal region deforms into an approximately circular shape, such as... Figure 3 The ratio of the length of the long axis (side) to the short axis (side) of the frame in the central region (central equiaxed crystal region) (hereinafter referred to as "frame ratio") must be controlled within 1.1 (1≤frame ratio≤1.1). Therefore, it is necessary to design and standardize the pressing and turning system of each rolling pass according to the size of the central equiaxed crystal region of the ingot (billet) during the rolling process.
[0004] Currently, methods for predicting the square ratio of the central equiaxed crystal region generally include experimental analogy and numerical simulation. The experimental analogy method involves rolling a large batch of test billets into finished products, sampling and testing at different passes to determine the influence of deformation parameters on the change in the square ratio of the central equiaxed crystal region. The measured data is then used for deformation analogy. This method requires a large number of test billets and multiple trials. For reversible rolling, sampling can be taken from intermediate materials, but it is difficult to obtain intermediate pass samples during continuous rolling, making the operation difficult, time-consuming, and costly. The numerical simulation method uses large-scale nonlinear finite element software (such as DEFORM-3D) to simulate the deformation and square ratio changes at each pass, finding the optimal method for pass deformation allocation. This method requires reasonable modeling and server-level computing system hardware support; otherwise, simulating the process parameters for a single specification can take a month, and calculating the process parameters for dozens of specifications and varieties can take at least several months, which is not very convenient or cost-effective. Therefore, researching a new, simple, and fast-responding method for predicting the size (square ratio) of the central equiaxed crystal region of an ingot during the rolling process is of great significance. Summary of the Invention
[0005] To address the aforementioned shortcomings in the existing technology, the present invention aims to provide a method for predicting the size of the equiaxed crystal zone at the center of the billet during the rolling process. This method is simple to calculate, has a fast response, and can be well applied to actual production on site.
[0006] To achieve the above objectives, the present invention adopts the following technical solution:
[0007] In a first aspect, the present invention provides a method for predicting the size of the equiaxed crystal region at the center of an ingot during the rolling process, the method comprising the following steps:
[0008] S1. Obtain the height and width of the original ingot cross-section and the height and width of the equiaxed crystal region at the center of the original ingot;
[0009] S2. Based on the height and width of the original ingot cross-section, according to the rolling method, the height and width of the ingot cross-section after the nth rolling pass are determined using the Usatov width expansion formula, where n is an integer greater than or equal to 1.
[0010] S3. Based on the height and width of the original ingot cross-section, the height and width of the equiaxed crystal region at the center of the original ingot, and the height and width of the ingot cross-section after the nth rolling pass, calculate the height and width of the equiaxed crystal region at the center of the ingot after the nth rolling pass using formulas (1) to (2):
[0011] h1=h*H1 / H(1)
[0012] b1=k*b*B1 / B(2)
[0013] In the formula, h1 represents the height of the equiaxed crystal region at the center of the ingot after the nth rolling pass; h represents the height of the cross-section of the ingot after the nth rolling pass; when n is 1, H represents the height of the original ingot cross-section; when n is an integer greater than 1, H represents the height of the ingot cross-section before the nth rolling pass, wherein the height of the ingot cross-section before the nth rolling pass is the height or width of the ingot cross-section after the (n-1)th rolling pass; when n is 1, H1 represents the height of the equiaxed crystal region at the center of the original ingot; when n is an integer greater than 1, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass, wherein the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height or width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass; b1 represents the height of the equiaxed crystal region at the center of the ingot after the nth rolling pass. The width of the equiaxed crystal region at the center of the ingot after rolling; b represents the width of the ingot cross-section after the nth rolling pass; when n is 1, B represents the width of the original ingot cross-section, and when n is an integer greater than 1, B represents the width of the ingot cross-section before the nth rolling pass, wherein the width of the ingot cross-section before the nth rolling pass is the height or width of the ingot cross-section after the (n-1)th rolling pass; when n is 1, B1 represents the width of the equiaxed crystal region at the center of the original ingot, and when n is an integer greater than 1, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass, wherein the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height or width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass; k is the coefficient of influence of the die shape on the frame shape in the rolling method.
[0014] S4. Based on the height and width of the equiaxed crystal region at the center of the ingot after the nth rolling pass, calculate the frame ratio of the equiaxed crystal region at the center of the ingot after the nth rolling pass.
[0015] This method is simple to calculate and has a fast response, making it well-suited for practical production in the field.
[0016] Furthermore, the step of determining the height and width of the ingot cross-section after the nth rolling pass, based on the height and width of the original ingot cross-section and using the Usatov width expansion formula, includes:
[0017] When n is 1, based on the height of the original ingot cross section, the height of the ingot cross section after the nth rolling pass is determined according to the rolling method. Based on the height and width of the original ingot cross section and the height of the ingot cross section after the nth rolling pass, the width of the ingot cross section after the nth rolling pass is determined using the Usatov width expansion formula.
[0018] When n is an integer greater than 1, the height of the ingot cross-section after the nth pass is determined based on the height or width of the ingot cross-section after the (n-1)th pass, according to the rolling method. Based on the height and width of the ingot cross-section after the (n-1)th pass and the height of the ingot cross-section after the nth pass, the width of the ingot cross-section after the nth pass is determined using the Usatov width expansion formula.
[0019] Furthermore, the Usatov broadening formula includes formulas (3) to (8):
[0020] β=λ -w (3)
[0021] W=10 -1.269*δ*ε^0.556 (4)
[0022] λ=h / H (5)
[0023] β=b / B (6)
[0024] δ=B / H (7)
[0025] ε=H / D (8)
[0026] In the formula, D is the working roll diameter;
[0027] When n is 1, h represents the height of the ingot cross-section after the nth rolling pass, determined according to the rolling method based on the height of the original ingot cross-section; H is the height of the original ingot cross-section; B is the width of the original ingot cross-section; and b is the width of the ingot cross-section after the nth rolling pass.
[0028] When n is an integer greater than 1, h represents the height of the ingot cross-section after the nth pass, determined according to the rolling method and based on the height or width of the ingot cross-section after the (n-1)th pass; H represents the height or width of the ingot cross-section after the (n-1)th pass; B represents the height or width of the ingot cross-section after the (n-1)th pass; and b represents the width of the ingot cross-section after the nth pass. Wherein, when the arrangement of the nth pass rolling is different from the arrangement of the (n-1)th pass rolling, H represents the height or width of the ingot cross-section after the (n-1)th pass rolling. The width of the ingot cross-section after rolling; when the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, H is the height of the ingot cross-section after the (n-1)th rolling pass; when the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, B is the height of the ingot cross-section after the (n-1)th rolling pass; when the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, B is the width of the ingot cross-section after the (n-1)th rolling pass.
[0029] Furthermore, when n is an integer greater than 1, determining the height of the ingot cross-section after the nth rolling pass based on the height or width of the ingot cross-section after the (n-1)th rolling pass includes:
[0030] When the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, the height of the ingot cross-section after the nth rolling pass is determined based on the width of the ingot cross-section after the (n-1)th rolling pass.
[0031] When the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, the height of the ingot cross-section after the nth rolling pass is determined based on the height of the ingot cross-section after the (n-1)th rolling pass.
[0032] Further, in step S3, when n is an integer greater than 1, H represents the height of the ingot cross-section before the nth rolling pass, and the height of the ingot cross-section before the nth rolling pass is the height or width of the ingot cross-section after the (n-1)th rolling pass, including:
[0033] When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, H represents the height of the ingot cross-section before the nth rolling pass, and the height of the ingot cross-section before the nth rolling pass is the width of the ingot cross-section after the (n-1)th rolling pass.
[0034] When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, H represents the height of the ingot cross-section before the nth rolling pass, and the height of the ingot cross-section before the nth rolling pass is the height of the ingot cross-section after the (n-1)th rolling pass.
[0035] Furthermore, in step S3, when n is an integer greater than 1, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass. The height of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height or width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass, including:
[0036] When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass.
[0037] When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass.
[0038] Furthermore, in step S3, when n is an integer greater than 1, B represents the width of the ingot cross-section before the nth rolling pass. The width of the ingot cross-section before the nth rolling pass is the height or width of the ingot cross-section after the (n-1)th rolling pass, including:
[0039] When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, B represents the width of the ingot cross-section before the nth rolling pass, and the width of the ingot cross-section before the nth rolling pass is the height of the ingot cross-section after the (n-1)th rolling pass.
[0040] When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, B represents the width of the ingot cross-section before the nth rolling pass, and the width of the ingot cross-section before the nth rolling pass is the width of the ingot cross-section after the (n-1)th rolling pass.
[0041] Further, in step S3, when n is an integer greater than 1, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height or width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass, including:
[0042] When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass.
[0043] When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass.
[0044] Furthermore, when the aperture is circular or box-shaped, k is 1; when the aperture is elliptical, k is 0.95-0.98.
[0045] Furthermore, the rolling process in the rolling method is carried out in two perpendicular directions.
[0046] Compared with the prior art, the beneficial effects of the present invention include at least one of the following:
[0047] (1) The method for predicting the size of the equiaxed crystal zone at the center of the ingot during the rolling process provided by the present invention is simple to calculate and has a fast response, and can be well applied to actual production on site.
[0048] (2) The method for predicting the size of the equiaxed crystal zone at the center of the ingot during the rolling process provided by the present invention can efficiently and quickly predict the size of the equiaxed crystal zone at the center of the ingot after deformation. It is not limited by the variety and billet specifications. By utilizing the rolling deformation principle and through experimental verification, the calculation results can be well matched with the actual results. It can be applied to guide the preparation of the rolling reduction system to achieve the purpose of improving the "frame" morphology. Attached Figure Description
[0049] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0050] Figure 1 This is a low-magnification microstructure diagram of the cross-section of the ingot;
[0051] Figure 2 A low-magnification microstructure of round steel obtained when the rolling process is improperly reduced;
[0052] Figure 3 A low-magnification microstructure of a round steel bar with an approximately circular morphology in the central equiaxed crystal region;
[0053] Figure 4 This is a schematic diagram of the deformation of the billet during the rolling process;
[0054] Figure 5 This is a low-magnification microstructure diagram of the round steel obtained in Example 1;
[0055] Figure 6 This is a low-magnification microstructure diagram of the round steel obtained in Example 2;
[0056] Figure 7 A trend comparison chart of the calculated and actual results of the central equiaxed crystal region size during the billet forming process;
[0057] Figure 8 This is a trend comparison chart of the calculated and actual results of the central equiaxed crystal region size during the billet forming process. Detailed Implementation
[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be clearly and completely described below in conjunction with the embodiments of this invention. Those skilled in the art should understand that the embodiments described are merely illustrative of the invention and should not be considered as specific limitations thereof. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. Process parameters not specifically specified in the following embodiments are generally performed under conventional conditions.
[0059] The endpoints and any values of the ranges disclosed in this invention are not limited to the precise ranges or values, and these ranges or values should be understood to include values close to these ranges or values. For numerical ranges, the endpoint values of the various ranges, the endpoint values of the various ranges and individual point values, and individual point values can be combined with each other to obtain one or more new numerical ranges, which should be considered as specifically disclosed in this invention.
[0060] This invention provides a method for predicting the size of the equiaxed crystal region at the center of an ingot during the rolling process, the method comprising the following steps:
[0061] S1. Obtain the height and width of the original ingot cross-section and the height and width of the equiaxed crystal region at the center of the original ingot;
[0062] S2. Based on the height and width of the original ingot cross-section, according to the rolling method, the height and width of the ingot cross-section after the nth rolling pass are determined using the Usatov width expansion formula, where n is an integer greater than or equal to 1.
[0063] S3. Based on the height and width of the original ingot cross-section, the height and width of the equiaxed crystal region at the center of the original ingot, and the height and width of the ingot cross-section after the nth rolling pass, calculate the height and width of the equiaxed crystal region at the center of the ingot after the nth rolling pass using formulas (1) to (2):
[0064] h1=h*H1 / H(1)
[0065] b1=k*b*B1 / B(2)
[0066] In the formula, h1 represents the height of the equiaxed crystal region at the center of the ingot after the nth rolling pass; h represents the height of the cross-section of the ingot after the nth rolling pass; when n is 1, H represents the height of the original ingot cross-section; when n is an integer greater than 1, H represents the height of the ingot cross-section before the nth rolling pass, wherein the height of the ingot cross-section before the nth rolling pass is the height or width of the ingot cross-section after the (n-1)th rolling pass; when n is 1, H1 represents the height of the equiaxed crystal region at the center of the original ingot; when n is an integer greater than 1, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass, wherein the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height or width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass; b1 represents the height of the equiaxed crystal region at the center of the ingot after the nth rolling pass. The width of the equiaxed crystal region at the center of the ingot after rolling; b represents the width of the ingot cross-section after the nth rolling pass; when n is 1, B represents the width of the original ingot cross-section, and when n is an integer greater than 1, B represents the width of the ingot cross-section before the nth rolling pass, wherein the width of the ingot cross-section before the nth rolling pass is the height or width of the ingot cross-section after the (n-1)th rolling pass; when n is 1, B1 represents the width of the equiaxed crystal region at the center of the original ingot, and when n is an integer greater than 1, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass, wherein the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height or width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass; k is the coefficient of influence of the die shape on the frame shape in the rolling method.
[0067] S4. Based on the height and width of the equiaxed crystal region at the center of the ingot after the nth rolling pass, calculate the frame ratio of the equiaxed crystal region at the center of the ingot after the nth rolling pass.
[0068] Here, rolling method refers to the method of rolling ingots (billets) into bars.
[0069] Height can refer to the length in the compression direction during rolling; width can refer to the length in the spreading direction during rolling.
[0070] The method for predicting the size of the equiaxed crystal zone at the center of the ingot during the rolling process provided by this invention is simple to calculate, has a fast response, and can be well applied to actual production on site.
[0071] The key to predicting the frame ratio using the method provided by this invention is to accurately calculate and predict the width spread of the rolled piece during rolling. The Usatov width spread formula is relatively accurate for bar rolling. Therefore, this invention mainly introduces a frame ratio prediction method based on the width spread calculated by the Usatov width spread formula.
[0072] This invention provides a computational model for efficiently predicting the deformation of the equiaxed crystal zone at the center of an ingot (billet) during the rolling process. It can efficiently and quickly predict the ingot segregation after the deformation of the equiaxed crystal zone at the center of the ingot (billet). By utilizing the rolling deformation principle and through experimental verification, the calculation results can match the actual situation well, guiding the formulation of the rolling reduction regime and achieving the purpose of improving the "frame" morphology.
[0073] In the above method for predicting the size of the equiaxed crystal region at the center of the ingot during the rolling process, as an optional implementation, determining the height and width of the ingot cross-section after the nth rolling pass, based on the height and width of the original ingot cross-section and using the Usatov width expansion formula, includes:
[0074] When n is 1, based on the height of the original ingot cross section, the height of the ingot cross section after the nth rolling pass is determined according to the rolling method. Based on the height and width of the original ingot cross section and the height of the ingot cross section after the nth rolling pass, the width of the ingot cross section after the nth rolling pass is determined using the Usatov width expansion formula.
[0075] When n is an integer greater than 1, the height of the ingot cross-section after the nth pass is determined based on the height or width of the ingot cross-section after the (n-1)th pass, according to the rolling method. Based on the height and width of the ingot cross-section after the (n-1)th pass and the height of the ingot cross-section after the nth pass, the width of the ingot cross-section after the nth pass is determined using the Usatov width expansion formula.
[0076] In the above method for predicting the size of the equiaxed crystal region at the center of the ingot during the rolling process, as an optional implementation, the Usatov broadening formula includes formulas (3) to (8):
[0077] β=λ -w (3)
[0078] W=10 -1.269*δ*ε^0.556 (4)
[0079] λ=h / H (5)
[0080] β=b / B (6)
[0081] δ=B / H (7)
[0082] ε=H / D (8)
[0083] In the formula, D is the working roll diameter;
[0084] When n is 1, h represents the height of the ingot cross-section after the nth rolling pass, determined according to the rolling method based on the height of the original ingot cross-section; H is the height of the original ingot cross-section; B is the width of the original ingot cross-section; and b is the width of the ingot cross-section after the nth rolling pass.
[0085] When n is an integer greater than 1, h represents the height of the ingot cross-section after the nth pass, determined according to the rolling method and based on the height or width of the ingot cross-section after the (n-1)th pass; H represents the height or width of the ingot cross-section after the (n-1)th pass; B represents the height or width of the ingot cross-section after the (n-1)th pass; and b represents the width of the ingot cross-section after the nth pass. Wherein, when the arrangement of the nth pass rolling is different from the arrangement of the (n-1)th pass rolling, H represents the height or width of the ingot cross-section after the (n-1)th pass rolling. The width of the ingot cross-section after rolling; when the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, H is the height of the ingot cross-section after the (n-1)th rolling pass; when the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, B is the height of the ingot cross-section after the (n-1)th rolling pass; when the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, B is the width of the ingot cross-section after the (n-1)th rolling pass.
[0086] Here, h can be obtained from H and the amount of reduction, and then h can be substituted into formulas (3) to (8) to calculate b.
[0087] D (work roll diameter) is a parameter related to the nominal diameter of the roll, the shape of the roll pass, the reduction, etc. It can be easily calculated according to the rolling process. The calculation method of D (work roll diameter) is common knowledge in this technical field.
[0088] In the above method for predicting the size of the equiaxed crystal region at the center of the billet during the rolling process, as an optional implementation, when n is an integer greater than 1, determining the height of the ingot cross-section after the nth rolling pass based on the height or width of the ingot cross-section after the (n-1)th rolling pass includes:
[0089] When the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, the height of the ingot cross-section after the nth rolling pass is determined based on the width of the ingot cross-section after the (n-1)th rolling pass.
[0090] When the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, the height of the ingot cross-section after the nth rolling pass is determined based on the height of the ingot cross-section after the (n-1)th rolling pass.
[0091] In the above method for predicting the size of the equiaxed crystal region at the center of the billet during the rolling process, as an optional implementation, in step S3, when n is an integer greater than 1, H represents the height of the ingot cross-section before the nth rolling pass, and the height of the ingot cross-section before the nth rolling pass is the height or width of the ingot cross-section after the (n-1)th rolling pass, including:
[0092] When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, H represents the height of the ingot cross-section before the nth rolling pass, and the height of the ingot cross-section before the nth rolling pass is the width of the ingot cross-section after the (n-1)th rolling pass.
[0093] When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, H represents the height of the ingot cross-section before the nth rolling pass, and the height of the ingot cross-section before the nth rolling pass is the height of the ingot cross-section after the (n-1)th rolling pass.
[0094] In the above method for predicting the size of the equiaxed crystal region at the center of the billet during the rolling process, as an optional implementation, in step S3, when n is an integer greater than 1, H1 represents the height of the equiaxed crystal region at the center of the billet before the nth rolling pass. The height of the equiaxed crystal region at the center of the billet before the nth rolling pass is the height or width of the equiaxed crystal region at the center of the billet after the (n-1)th rolling pass, including:
[0095] When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass.
[0096] When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass.
[0097] In the above method for predicting the size of the equiaxed crystal region at the center of the billet during the rolling process, as an optional implementation, in step S3, when n is an integer greater than 1, B represents the width of the ingot cross-section before the nth rolling pass, wherein the width of the ingot cross-section before the nth rolling pass is the height or width of the ingot cross-section after the (n-1)th rolling pass, including:
[0098] When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, B represents the width of the ingot cross-section before the nth rolling pass, and the width of the ingot cross-section before the nth rolling pass is the height of the ingot cross-section after the (n-1)th rolling pass.
[0099] When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, B represents the width of the ingot cross-section before the nth rolling pass, and the width of the ingot cross-section before the nth rolling pass is the width of the ingot cross-section after the (n-1)th rolling pass.
[0100] In the above method for predicting the size of the equiaxed crystal region at the center of the billet during the rolling process, as an optional implementation, in step S3, when n is an integer greater than 1, B1 represents the width of the equiaxed crystal region at the center of the billet before the nth rolling pass, and the width of the equiaxed crystal region at the center of the billet before the nth rolling pass is the height or width of the equiaxed crystal region at the center of the billet after the (n-1)th rolling pass, including:
[0101] When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass.
[0102] When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass.
[0103] In the above method for predicting the size of the equiaxed crystal zone at the center of the billet during the rolling process, as an optional implementation, k is 1 when the die is circular or box-shaped; and k is 0.95-0.98 when the die is elliptical.
[0104] In the above-described method for predicting the size of the equiaxed crystal zone at the center of the billet during the rolling process, as an optional implementation, the rolling process in the rolling method is carried out in two perpendicular directions.
[0105] The present invention will now be described in further detail with reference to specific embodiments and comparative examples.
[0106] In the following embodiments:
[0107] Assuming the head and tail regions of the rolled piece (ingot) are removed, the rolled piece (ingot) is a rigid body, and rolling occurs in two perpendicular directions with perfectly symmetrical deformation. Because of this symmetrical deformation, it can be assumed that each particle moves only along its corresponding axis in the two perpendicular deformation directions (without considering extension). During vertical compression, points on the longitudinal axis move towards the origin, while points on the transverse axis move away from the origin due to widening. Conversely, during horizontal compression, points on the transverse axis move towards the origin, while points on the longitudinal axis move away from the origin. Furthermore, assuming the rolled piece (ingot) is perfectly symmetrical, and the point at the center of symmetry remains at the center, then the displacement of the center point is always zero. For example... Figure 4 The original billet (shown by the solid blue line): height * width = H * B, and its central equiaxed crystal region (shown by the dashed blue line): height * width = H1 * B1; after deformation, the original billet becomes (shown by the solid red line): height * width = h * b, and after deformation of the central equiaxed crystal region (shown by the dashed red line): height * width = h1 * b1.
[0108] Example 1
[0109] This embodiment provides a method for predicting the size of the equiaxed crystal region at the center of an ingot during the rolling process. The method includes the following steps:
[0110] S1. Obtain the height and width of the original ingot cross-section, as well as the height and width of the equiaxed crystal region at the center of the original ingot.
[0111] S2. When n is 1, based on the reduction amount in the rolling method, the height of the ingot cross section after the nth rolling pass is determined based on the height of the original ingot cross section. Based on the height and width of the original ingot cross section and the height of the ingot cross section after the nth rolling pass, the width of the ingot cross section after the nth rolling pass is determined using the Usatov widening formula (formulas (3) to (8)).
[0112] When n is an integer greater than 1 and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, the height of the ingot cross-section after the nth rolling pass is determined based on the reduction in the rolling method and the width of the ingot cross-section after the (n-1)th rolling pass; when n is an integer greater than 1 and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, the height of the ingot cross-section after the nth rolling pass is determined based on the reduction in the rolling method and the height of the ingot cross-section after the (n-1)th rolling pass; when n is an integer greater than 1, the width of the ingot cross-section after the nth rolling pass is determined based on the height and width of the ingot cross-section after the (n-1)th rolling pass and the height of the ingot cross-section after the nth rolling pass, using the Usatov widening formula (formulas (3) to (8)).
[0113] β=λ -w (3)
[0114] W=10 -1.269*δ*ε^0.556 (4)
[0115] λ=h / H (5)
[0116] β=b / B (6)
[0117] δ=B / H (7)
[0118] ε=H / D (8)
[0119] In the formula, D is the working roll diameter;
[0120] When n is 1, h represents the height of the ingot cross-section after the nth rolling pass, determined according to the rolling method based on the height of the original ingot cross-section; H is the height of the original ingot cross-section; B is the width of the original ingot cross-section; and b is the width of the ingot cross-section after the nth rolling pass.
[0121] When n is an integer greater than 1, h represents the height of the ingot cross-section after the nth pass, determined according to the rolling method and based on the height or width of the ingot cross-section after the (n-1)th pass; H represents the height or width of the ingot cross-section after the (n-1)th pass; B represents the height or width of the ingot cross-section after the (n-1)th pass; and b represents the width of the ingot cross-section after the nth pass. Wherein, when the arrangement of the nth pass rolling is different from the arrangement of the (n-1)th pass rolling, H represents the height or width of the ingot cross-section after the (n-1)th pass rolling. The width of the ingot cross-section after rolling; when the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, H is the height of the ingot cross-section after the (n-1)th rolling pass; when the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, B is the height of the ingot cross-section after the (n-1)th rolling pass; when the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, B is the width of the ingot cross-section after the (n-1)th rolling pass.
[0122] S3. Based on the height and width of the original ingot cross-section, the height and width of the equiaxed crystal region at the center of the original ingot, and the height and width of the ingot cross-section after the nth rolling pass, calculate the height and width of the equiaxed crystal region at the center of the ingot after the nth rolling pass using formulas (1) to (2):
[0123] h1=h*H1 / H(1)
[0124] b1=k*b*B1 / B(2)
[0125] In the formula, h1 represents the height of the equiaxed crystal region at the center of the ingot after the nth rolling pass; h represents the height of the ingot cross-section after the nth rolling pass; when n is 1, H represents the height of the original ingot cross-section; when n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, H represents the height of the ingot cross-section before the nth rolling pass, where the height of the ingot cross-section before the nth rolling pass is the width of the ingot cross-section after the (n-1)th rolling pass; when n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, H represents the height of the ingot cross-section before the nth rolling pass. The height of the ingot cross-section before the nth rolling pass is the same as the height of the ingot cross-section after the (n-1)th rolling pass. When n is 1, H1 represents the height of the equiaxed crystal region at the center of the original ingot. When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass, where the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the same as the width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass. When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass. The height of the equiaxed crystal region at the center of the ingot before rolling is the same as the height of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass; b1 represents the width of the equiaxed crystal region at the center of the ingot after the nth rolling pass; b represents the width of the cross-section of the ingot after the nth rolling pass; when n is 1, B represents the width of the original ingot cross-section; when n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, B represents the width of the cross-section of the ingot before the nth rolling pass, where the width of the cross-section of the ingot before the nth rolling pass is the same as the height of the cross-section of the ingot after the (n-1)th rolling pass; when n is an integer greater than 1... When the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, B represents the width of the ingot cross-section before the nth rolling pass, and the width of the ingot cross-section before the nth rolling pass is the width of the ingot cross-section after the (n-1)th rolling pass; when n is 1, B1 represents the width of the equiaxed crystal region at the center of the original ingot; when n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass;When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass; when the die shape in the rolling method is circular or box-shaped, k is 1; when the die shape is elliptical, k is 0.97.
[0126] S4. Based on the height and width of the equiaxed crystal region at the center of the ingot after the nth rolling pass, calculate the frame ratio of the equiaxed crystal region at the center of the ingot after the nth rolling pass.
[0127] The method provided in this embodiment is used to predict the change in the size of the central equiaxed crystal region during the rolling process of a 300X400mm square billet ingot (the central square frame size is 210*130mm) into φ80mm 20CrMnTi round steel in 16 passes. The arrangement, pass shape and size change of the central equiaxed crystal region during the rolling process are shown in Table 1.
[0128] Table 1
[0129]
[0130]
[0131] Predicted results: The dimensions of the central region (central equiaxed crystal region) of a 300x400mm square billet after 16 passes of flat and vertical rolling are 37.8mm on the long axis and 33.65mm on the short axis, with a ratio of long axis to short axis (square ratio) of 1.12.
[0132] Following the rolling method shown in Table 1, a 300x400mm square billet (center square frame dimensions length*width = 210*130mm) was rolled into φ80mm 20CrMnTi round steel through 16 passes of flat and vertical rolling. The low-magnification microstructure of the φ80mm 20CrMnTi round steel is shown below. Figure 5 As shown, the dimensions of the central region (central equiaxed crystal region) of the φ80mm 20CrMnTi round steel were measured on-site. The major axis was 38mm and the minor axis was 34mm. The ratio of the major axis to the minor axis was 1.118. The predicted value was very close to the actual value, and the deviation of the ratio of the major axis to the minor axis was small.
[0133] Example 2
[0134] The method for predicting the size of the equiaxed crystal zone at the center of the ingot during the rolling process provided in this embodiment is basically the same as that in Embodiment 1. The difference is that in step S3, when the hole shape is elliptical, k is 0.975.
[0135] The method provided in this embodiment is used to predict the change in the size of the central equiaxed crystal region during the 16-pass flat and vertical rolling of a φ390mm round billet (center square size φ210mm) into a φ80mm 20CrMnTi round steel. The arrangement, pass shape and size change of the central equiaxed crystal region during the rolling process are shown in Table 2.
[0136] Table 2
[0137]
[0138]
[0139] Predicted results: After 16 passes of flat and vertical rolling, the dimensions of the central region (central equiaxed crystal region) of the φ390mm round billet are as follows: major axis 43.96mm, minor axis 39.45mm, and the ratio of major axis to minor axis (square ratio) is 1.11.
[0140] Following the rolling method shown in Table 2, a φ390mm round billet (center square size φ210mm) ingot was rolled into φ80mm 20CrMnTi round steel through 16 passes of flat and vertical rolling. The low-magnification microstructure of the φ80mm 20CrMnTi round steel is shown below. Figure 6 As shown, the dimensions of the central region (central equiaxed crystal region) of the φ80mm 20CrMnTi round steel were measured on-site. The major axis was 43mm and the minor axis was 38mm. The ratio of the major axis to the minor axis was 1.13. The predicted value was very close to the actual value, and the deviation of the ratio of the major axis to the minor axis was small.
[0141] Example 3
[0142] A square billet with dimensions of 300mm*400mm is put into production and rolled into... Round steel bars, after being formed, are sampled for low-magnification inspection. The major and minor axis dimensions of the center frame (central equiaxed crystal region) are measured and recorded. These dimensions are compared with data calculated using the method provided in Example 1 for predicting the dimensions of the equiaxed crystal region at the center of the ingot during the rolling process, based on on-site rolling data. The results are as follows: Figure 7 As shown, the horizontal axis represents the specifications of the round steel, and the vertical axis represents the characteristic dimensions of the center frame (central equiaxed crystal region), in mm. Figure 7 From left to right, the corresponding steel specifications are as follows: arrive It can be seen that the calculated results of the square frame size of the billet (the long axis size and short axis size of the central equiaxed crystal region) are consistent with the actual results, and the difference is within a small range. After experimental verification, the prediction method provided in Example 1 can predict the change of the square frame size of the central equiaxed crystal region of the rolled piece in a good way during the rolling process, and can provide guidance for the design of the pressing system on site.
[0143] Example 4
[0144] The φ390mm round billet is put into production and rolled into... Round steel bars, after being formed, are sampled for low-magnification inspection. The major and minor axis dimensions of the center frame (central equiaxed crystal region) are measured and recorded. These dimensions are compared with data calculated using the method provided in Example 2 for predicting the dimensions of the equiaxed crystal region at the center of the ingot during the rolling process, based on on-site rolling data. The results are as follows: Figure 8 As shown, the horizontal axis represents the specifications of the round steel, and the vertical axis represents the characteristic dimensions of the center frame (central equiaxed crystal region), in mm. Figure 8 From left to right, the corresponding steel specifications are as follows: arrive It can be seen that the calculated results of the square frame size of the round billet are consistent with the actual results, and the difference is within a small range. After experimental verification, the prediction method provided in Example 2 can predict the changes in the square frame size (long axis size and short axis size of the central equiaxed crystal region) of the rolled piece during the rolling process, and can provide guidance for the design of the pressing system on site.
[0145] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for predicting the size of the equiaxed crystal region at the center of an ingot during rolling, characterized in that, The method includes the following steps: S1. Obtain the height and width of the original ingot cross-section and the height and width of the equiaxed crystal region at the center of the original ingot; S2. Based on the height and width of the original ingot cross-section, according to the rolling method, the height and width of the ingot cross-section after the nth rolling pass are determined using the Usatov width expansion formula, where n is an integer greater than or equal to 1. S3. Based on the height and width of the original ingot cross-section, the height and width of the equiaxed crystal region at the center of the original ingot, and the height and width of the ingot cross-section after the nth rolling pass, calculate the height and width of the equiaxed crystal region at the center of the ingot after the nth rolling pass using formulas (1)~(2): h1=h*H1 / H(1) b1=k*b*B1 / B(2) In the formula, h1 represents the height of the equiaxed crystal region at the center of the ingot after the nth rolling pass; h represents the height of the cross-section of the ingot after the nth rolling pass; when n is 1, H represents the height of the original ingot cross-section; when n is an integer greater than 1, H represents the height of the ingot cross-section before the nth rolling pass, wherein the height of the ingot cross-section before the nth rolling pass is the height or width of the ingot cross-section after the (n-1)th rolling pass; when n is 1, H1 represents the height of the equiaxed crystal region at the center of the original ingot; when n is an integer greater than 1, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass, wherein the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height or width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass; b1 represents the height of the equiaxed crystal region at the center of the ingot after the nth rolling pass. The width of the equiaxed crystal region at the center of the ingot after rolling; b represents the width of the ingot cross-section after the nth rolling pass; when n is 1, B represents the width of the original ingot cross-section, and when n is an integer greater than 1, B represents the width of the ingot cross-section before the nth rolling pass, wherein the width of the ingot cross-section before the nth rolling pass is the height or width of the ingot cross-section after the (n-1)th rolling pass; when n is 1, B1 represents the width of the equiaxed crystal region at the center of the original ingot, and when n is an integer greater than 1, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass, wherein the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height or width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass; k is the coefficient of influence of the die shape on the frame shape in the rolling method. S4. Based on the height and width of the equiaxed crystal region at the center of the ingot after the nth rolling pass, calculate the frame ratio of the equiaxed crystal region at the center of the ingot after the nth rolling pass. When the aperture is circular or box-shaped, k is 1; when the aperture is elliptical, k is 0.95-0.
98.
2. The method for predicting the size of the equiaxed crystal region at the center of an ingot during the rolling process according to claim 1, characterized in that, The step of determining the height and width of the ingot cross-section after the nth rolling pass, based on the height and width of the original ingot cross-section using the Usatov width expansion formula, includes: When n is 1, based on the height of the original ingot cross section, the height of the ingot cross section after the nth rolling pass is determined according to the rolling method. Based on the height and width of the original ingot cross section and the height of the ingot cross section after the nth rolling pass, the width of the ingot cross section after the nth rolling pass is determined using the Usatov width expansion formula. When n is an integer greater than 1, the height of the ingot cross-section after the nth pass is determined based on the height or width of the ingot cross-section after the (n-1)th pass, according to the rolling method. Based on the height and width of the ingot cross-section after the (n-1)th pass and the height of the ingot cross-section after the nth pass, the width of the ingot cross-section after the nth pass is determined using the Usatov width expansion formula.
3. The method for predicting the size of the equiaxed crystal region at the center of an ingot during the rolling process according to claim 1, characterized in that, The Usatov broadening formula includes formulas (3) to (8): β=λ -w (3) W=10 -1.269*δ*ε^0.556 （4） λ=h / H (5) β=b / B (6) δ=B / H (7) ε=H / D (8) In the formula, D is the working roll diameter; When n is 1, h represents the height of the ingot cross-section after the nth rolling pass, determined according to the rolling method based on the height of the original ingot cross-section; H is the height of the original ingot cross-section; B is the width of the original ingot cross-section; and b is the width of the ingot cross-section after the nth rolling pass. When n is an integer greater than 1, h represents the height of the ingot cross-section after the nth pass, determined according to the rolling method and based on the height or width of the ingot cross-section after the (n-1)th pass; H represents the height or width of the ingot cross-section after the (n-1)th pass; B represents the height or width of the ingot cross-section after the (n-1)th pass; and b represents the width of the ingot cross-section after the nth pass. Wherein, when the arrangement of the nth pass rolling is different from the arrangement of the (n-1)th pass rolling, H represents the height or width of the ingot cross-section after the (n-1)th pass rolling. The width of the ingot cross-section after rolling; when the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, H is the height of the ingot cross-section after the (n-1)th rolling pass; when the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, B is the height of the ingot cross-section after the (n-1)th rolling pass; when the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, B is the width of the ingot cross-section after the (n-1)th rolling pass.
4. The method for predicting the size of the equiaxed crystal region at the center of the ingot during the rolling process according to claim 2, characterized in that, When n is an integer greater than 1, determining the height of the ingot cross-section after the nth rolling pass based on the height or width of the ingot cross-section after the (n-1)th rolling pass includes: When the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, the height of the ingot cross-section after the nth rolling pass is determined based on the width of the ingot cross-section after the (n-1)th rolling pass. When the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, the height of the ingot cross-section after the nth rolling pass is determined based on the height of the ingot cross-section after the (n-1)th rolling pass.
5. The method for predicting the size of the equiaxed crystal region at the center of an ingot during the rolling process according to claim 1, characterized in that, In step S3, when n is an integer greater than 1, H represents the height of the ingot cross-section before the nth rolling pass, and the height of the ingot cross-section before the nth rolling pass is the height or width of the ingot cross-section after the (n-1)th rolling pass, including: When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, H represents the height of the ingot cross-section before the nth rolling pass, and the height of the ingot cross-section before the nth rolling pass is the width of the ingot cross-section after the (n-1)th rolling pass. When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, H represents the height of the ingot cross-section before the nth rolling pass, and the height of the ingot cross-section before the nth rolling pass is the height of the ingot cross-section after the (n-1)th rolling pass.
6. The method for predicting the size of the equiaxed crystal region at the center of an ingot during the rolling process according to claim 1, characterized in that, In step S3, when n is an integer greater than 1, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass. The height of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height or width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass, including: When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass. When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, H1 represents the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the height of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass.
7. The method for predicting the size of the equiaxed crystal region at the center of an ingot during the rolling process according to claim 1, characterized in that, In step S3, when n is an integer greater than 1, B represents the width of the ingot cross-section before the nth rolling pass. The width of the ingot cross-section before the nth rolling pass is the height or width of the ingot cross-section after the (n-1)th rolling pass, including: When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, B represents the width of the ingot cross-section before the nth rolling pass, and the width of the ingot cross-section before the nth rolling pass is the height of the ingot cross-section after the (n-1)th rolling pass. When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, B represents the width of the ingot cross-section before the nth rolling pass, and the width of the ingot cross-section before the nth rolling pass is the width of the ingot cross-section after the (n-1)th rolling pass.
8. The method for predicting the size of the equiaxed crystal region at the center of an ingot during the rolling process according to claim 1, characterized in that, In step S3, when n is an integer greater than 1, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass. The width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height or width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass, including: When n is an integer greater than 1, and the arrangement of the nth rolling pass is different from that of the (n-1)th rolling pass, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the height of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass. When n is an integer greater than 1, and the arrangement of the nth rolling pass is the same as that of the (n-1)th rolling pass, B1 represents the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass, and the width of the equiaxed crystal region at the center of the ingot before the nth rolling pass is the width of the equiaxed crystal region at the center of the ingot after the (n-1)th rolling pass.
9. The method for predicting the size of the equiaxed crystal region at the center of an ingot during the rolling process according to claim 1, characterized in that, The rolling process in the rolling method is carried out in two perpendicular directions.