A method for determining a roll shape
By using a combination of high-order reverse curves and ramp curves in the hot continuous rolling process, a roll profile curve is generated, which solves the problems of edge drop and crown control, and improves rolling stability and profile quality.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIJING SHOUGANG CO LTD
- Filing Date
- 2023-08-22
- Publication Date
- 2026-06-05
AI Technical Summary
Existing technologies struggle to simultaneously and effectively reduce edge drop and control body crown during hot continuous rolling, and also suffer from wave problems.
The initial curve is edge-processed using a high-order reverse curve, and then connected with the ramp curve and the smooth superimposed curve to form a ramp body combined curve. Finally, a roller curve is generated by fitting and smoothing.
Without increasing costs, the edge drop effect was reduced and the body crown was controlled, improving rolling stability and profile quality, and solving the mid-wave problem.
Smart Images
Figure CN117102247B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to Rolling The technical field relates, in particular, to a method for determining the shape of a roller. Background Technology
[0002] In recent years, hot strip mills have been replacing cold rolling with hot rolling for high-value-added products such as silicon steel. The requirements for product crown, edge reduction, and contour control have been gradually strengthened. Therefore, reasonable and effective technologies are needed to support the rolling of ultra-flat products. Traditional roll shapes have waviness problems in use. The rolling of ultra-flat products on hot strip mill production lines requires reasonable roll shape, material, and process configuration to ensure that the target is achieved.
[0003] Hot rolling typically employs high-speed steel, conical roll profiles, rolling lubrication, and small-diameter rolls to control edge drop in ultra-flat products. However, each technology has its shortcomings and deficiencies. High-speed steel rolls have good wear resistance but poor accident resistance, generally preventing full-stand operation and making cost control difficult. Rolling lubrication primarily improves edge drop through wear control but lacks operational capability for edge drop control itself. Small-diameter rolls can only improve flattening by reducing rolling force. Traditional single-conical roll profiles offer significant edge drop control but lack crown control capabilities, resulting in center waviness issues during rolling, with more edge waviness than center waviness. In summary, existing technologies struggle to simultaneously reduce edge drop while controlling body crown and center waviness. Summary of the Invention
[0004] In view of the above problems, the present invention is proposed to provide a method for determining the roll shape that overcomes or at least partially solves the above problems.
[0005] A method for determining roller shape is provided, including:
[0006] Determine the initial curve of the roller surface;
[0007] The initial curve is edge-processed using a higher-order reverse curve to obtain a smooth superimposed curve;
[0008] On the operating side, a slope curve is determined, and the slope curve is connected with the smooth superimposed curve to form a slope body combined curve.
[0009] The combined curve of the slope body is fitted and smoothed to obtain a roller-shaped curve.
[0010] Optionally, the initial curve is a quadratic curve.
[0011] Optionally, the initial curve equation is y1 = a1x + a2x 2 a1 = -a2L, The independent variable x takes values in the range of [0, L], where L is the length of the roller body in mm; the dependent variable y takes values in the range of [-h, 0], where h is the crown of the roller in mm.
[0012] Optionally, the higher-order inverse curve equation is: The equation for the smooth superimposed curve is y3 = y1 + y2; where n is the degree of the higher-order reverse curve, taking the value of 4, 6 or 8, and k is a coefficient.
[0013] Optionally, the equation for the slope curve is: Among them l qd l is the x-coordinate value of the connection point between the slope curve and the smooth superimposed curve. cg The initial value for the skewed rollers, l c l is the rolling width value. sr For the depth measurement of the anti-warp curve, l fq For a rolling width of l c The depth is l sr The value of the anti-warping amount at time, l cg l c l sr l fq It is a constant, and the unit is mm.
[0014] Optionally, the equation for the combined curve of the slope body is:
[0015]
[0016] Optionally, the step of fitting and smoothing the combined curve of the slope body to obtain a roller curve includes:
[0017] Based on the equation of the slope's composite curve, several discrete points in the interval [0, L] are taken as independent variable values and input into the independent variable column of an Excel spreadsheet. The dependent variable values corresponding to these discrete points are input into the dependent variable column. The LINEST function is used for regression to obtain the regression coefficients. The roller curve expression is then generated using these regression coefficients. Where b n is the regression coefficient.
[0018] Optionally, n in the roller curve expression takes an integer value from 8 to 12.
[0019] The technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages:
[0020] The roll shape determination method provided in this invention employs high-order edge superposition smoothing, conical design, curve truncation combination, final smoothing, and control of stand usage based on the initial curve. This ensures that the conical roll reduces edge drop while simultaneously controlling the body convexity, controlling waviness, improving profile quality and rolling stability, and providing strong support for ultra-flat material rolling. It does not increase costs or change existing processes.
[0021] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description
[0022] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:
[0023] Figure 1 This is a flowchart of the roller shape determination method in an embodiment of the present invention;
[0024] Figure 2 This is a schematic diagram of the initial curve in an embodiment of the present invention;
[0025] Figure 3 This is a schematic diagram of a smooth overlay curve in an embodiment of the present invention;
[0026] Figure 4 This is a schematic diagram of the combined curve of the slope body in an embodiment of the present invention;
[0027] Figure 5 This is a schematic diagram of the roller curve in an embodiment of the present invention. Detailed Implementation
[0028] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings.
[0029] The accompanying drawings illustrate various structural schematics according to embodiments of the present disclosure. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.
[0030] To better understand the above technical solutions, the following will describe the above technical solutions in detail with reference to specific implementation methods. It should be understood that the embodiments of this disclosure and the specific features in the embodiments are detailed descriptions of the technical solutions of this application, rather than limitations on the technical solutions of this application. In the absence of conflict, the embodiments of this application and the technical features in the embodiments can be combined with each other.
[0031] This invention provides a method for determining roller shape; please refer to [the relevant documentation]. Figure 1 , Figure 1 The flowchart of the roller shape determination method in this embodiment of the invention includes:
[0032] S1, determine the initial curve of the roller surface;
[0033] S2, use a higher-order reverse curve to perform edge processing on the initial curve to obtain a smooth superimposed curve;
[0034] S3, determine the ramp curve on the operation side, and connect the ramp curve with the smooth superimposed curve to form a ramp body combined curve;
[0035] S4. Fit and smooth the combined curve of the slope body to obtain a roller curve.
[0036] The following examples and... Figure 2-5 The implementation process steps of this embodiment are described in detail below:
[0037] The design requirements are: roller body length 1880mm, design width 1880mm, width convexity -0.2, smoothing times 4, smoothing ratio 0.5, anti-warping width 1000, anti-warping amount 0.04, anti-warping insertion depth 100, upper roller starting point shifting roller -150, and taper slope 0.0004.
[0038] like Figure 2 As shown, when performing operation S1, the initial roll shape of the finishing mill's work roll adopts a concave-convex initial curve, and the initial curve equation is y1=a1x+a2x. 2 a1 = -a2L, The independent variable x takes values in the range [0, L], where L is the length of the roller body. Figure 2 In this example, L is set to 1880 mm, and the dependent variable y ranges from -h to 0, where h is the roll crown value, which can range from 0 to 1. Figure 2 In the example, the value of h is taken as 0.2 mm.
[0039] like Figure 3 As shown, operation S2 is performed to design an edge smoothing curve. A higher-order inverse curve is directly used for edge processing of the initial curve. The processing method involves superimposing the higher-order curve and the initial curve. The equation for the higher-order inverse curve is: The equation of the smoothed composite curve is y3 = y1 + y2. Edge smoothing is achieved through curve superposition. Here, n represents the degree of the higher-order inverse curve, taking values of 4, 6, or 8, indicating that the higher-order curves are designed using 4th, 6th, or 8th order curves. The higher the degree, the closer to the edge. k is a coefficient, with the curve convexity ranging from 10% to 60% of the -h convexity. The larger the value of k, the more of the initial curve is retained in the smoothed composite curve. Figure 3 In the high-order inverse curve shown, the value of k is taken as 10%.
[0040] Execute operation S3, employing the connection method to design the ramp curve. Connect the main curve (higher-order reverse curve) and the conical section. The equation for the ramp curve of the conical section is: Among them l qd The x-coordinate value of the junction point between the slope curve and the smooth overlay curve. cg The initial roll shift value ranges from -150 to 150, and the unit is mm. c This is the rolling width value, usually a constant less than L, and the unit is mm. sr The depth measurement of the anti-warp curve, ranging from [0, 100], is expressed in mm. fq For a rolling width of l c The depth is l sr The anti-warping value at that time ranges from [0, 1], and the unit is mm. qd The value represents the midpoint of the roller body minus half the width specification of the anti-warping design, plus the initial insertion amount of the design cone.
[0041] like Figure 4 As shown, the equation for the combined curve of the slope body is:
[0042]
[0043] from Figure 4 As can be seen from this, after the curve is truncated and combined, x is in the range of 0 to 1. qd Use equation y4 within the range, in l qd Use equation y3 within the range of ~1. Figure 4 Point S is the starting point of the operating side roller profile, and point E, corresponding to point S, is the ending point of the drive side roller profile. Since point S is the junction of the ramp curve and the smooth superimposed curve, the y5 curve has a strong transition point (abrupt inflection point) at this point, and cannot be directly used for production.
[0044] like Figure 5 As shown, operation S4 is performed to smooth the curve. For curve y5, a smoothing method is used to remove sharp inflection points. Several discrete points in the interval [0, L] are taken as independent variable values and input into column a of the Excel spreadsheet. The dependent variable values corresponding to these discrete points are input into column b of the dependent variable. The LINEST function is used for regression to obtain regression coefficients b1 to b2. n The expression for generating the roller curve using the regression coefficients is as follows: n takes an integer value between 8 and 12. Smoothing uses 8 to 12 iterations of fitting; a lower iteration will not fully represent the curve. The y6 curve is applied to the later stands of the finishing mill (F4, F5, F6), but not to the last stand. Following the above operation, with a roll body length of 1880mm, a design width of 1880mm, a width crown of -0.2, 4 iterations of smoothing, a smoothing ratio of 0.5, a warp width of 1000, a warp amount of 0.04, a warp insertion depth of 100, an upper roll starting point offset of -150, and a taper slope of 0.0004, the regression coefficient obtained after 8 iterations of fitting is: b1 = 8.51278757788914E-04.
[0045] b2=-4.83566886442397E-06, b3=2.01129006182079E-08,
[0046] b4=-3.99227939051505E-11, b5=4.15102739281312E-14,
[0047] b6=-2.3536348031836E-17,b7=6.92429695992194E-21,
[0048] b8 = -8.29967751953829E-25. The roller curve is generated using the regression coefficients b1 to b7 as shown below. Figure 5 As shown.
[0049] The technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages:
[0050] The roll shape determination method provided in this invention adopts high-order edge superposition smoothing, conical design, curve interception combination, final smoothing, and control of stand usage on the basis of the initial curve. While ensuring the effect of tapered rolls in reducing edge drop, it also achieves body crown control and improves rolling stability, providing strong support for ultra-flat material rolling.
[0051] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.
[0052] Similarly, it should be understood that, in order to simplify this disclosure and aid in understanding one or more of the various aspects of the invention, in the above description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof. However, this method of disclosure should not be construed as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as reflected in the following claims, inventive aspects lie in fewer than all features of a single foregoing disclosed embodiment. Therefore, the claims following the detailed description are hereby expressly incorporated into this detailed description, wherein each claim itself is a separate embodiment of the invention.
[0053] It should be noted that the above embodiments are illustrative of the invention and not restrictive, and that those skilled in the art can devise alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The invention can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer.
Claims
1. A method for determining roller shape, characterized in that, include: Determine the initial curve of the roller surface; The initial curve is edge-processed using a higher-order reverse curve to obtain a smooth superimposed curve; On the operating side, a slope curve is determined, and the slope curve is connected with the smooth superimposed curve to form a slope body combined curve. The combined curve of the slope body is fitted and smoothed to obtain a roller-shaped curve; The step of fitting and smoothing the combined curve of the slope body to obtain a roller curve includes: Based on the equation of the slope's composite curve, several discrete points in the interval [0, L] are taken as independent variable values and input into the independent variable column of an Excel spreadsheet. The dependent variable values corresponding to these discrete points are input into the dependent variable column. The LINEST function is used for regression to obtain the regression coefficients. The roller curve expression is then generated using these regression coefficients. ,in As the regression coefficient, n in the expression for the roller curve takes an integer value between 8 and 12.
2. The roller shape determination method as described in claim 1, characterized in that, The initial curve is a quadratic curve.
3. The roller shape determination method as described in claim 2, characterized in that, The initial curve equation is: , The independent variable x ranges from [0, L], where L is the length of the roller body in mm; the dependent variable y ranges from [-h, 0], where h is the roll crown in mm.
4. The roller shape determination method as described in claim 3, characterized in that, The equation for the higher-order inverse curve is: The equation for the smooth superimposed curve is: Where n is the degree of the higher-order inverse curve, which takes the value of 4, 6 or 8, and k is a coefficient.
5. The roller shape determination method as described in claim 4, characterized in that, The equation for the slope curve is: , ,in The x-coordinate value of the junction point between the slope curve and the smooth superimposed curve. This is the initial roll shift value. This is the rolling width value. The depth measurement of the anti-warp curve, For the rolling width is , depth of measurement The value of the anti-warping amount at that time.
6. The roller shape determination method as described in claim 5, characterized in that, The equation for the combined curve of the slope body is: 。