CN109871590B - Hot rolled strip section profile reproduction method - Google Patents
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Abstract
The invention discloses a method for reproducing the profile of a section of a hot rolled strip, belonging to the field of stripsThe technical field of steel section shape control. The method adopts a piecewise quadratic function to reproduce the whole profile of the section of the hot rolled strip, the function uses few characteristic coefficients, and only three index parameters with practical physical significance are needed to solve, namely a measurement index C in the hot rolled strip control standard40And W40And the index C for representing the final edge part of the finishing coiling of the cold-rolled strip25The method has the advantages that the precision of the profile of the section of the strip reproduced by the method is high, the reproduction speed is high, and meanwhile, the introduction of the constraint equation ensures that the profile of the section of the strip reproduced is smooth and continuous and is more in line with the actual situation. The method for reproducing the profile of the section of the hot rolled strip has important significance for controlling the shape of the section of the hot rolled strip and improving the quality of the hot rolled strip.
Description
Technical Field
The invention belongs to the technical field of metallurgical rolling, and particularly relates to a method for reproducing a profile of a section of a hot rolled strip.
Background
With the high-speed development of the industry in China, the use requirement of high-quality strips is more and more large, for example, cold-rolled non-oriented silicon steel is widely applied to the fields of motors, transformers and the like, the larger the transverse thickness difference of silicon steel sheets is, the more easily the non-uniform lamination gap is caused, the lower the operation efficiency of equipment is, and the longer the service life of equipment is. As the incoming material of the cold-rolled strip, the section profile of the hot-rolled strip has direct influence on the section profile of a cold-rolled finished product, and in order to scientifically research the problem of the cold-rolled lateral thickness difference of the strip, firstly, the hot-rolled section profile of the strip must be scientifically described and reproduced, but at present, the section shape of the hot-rolled strip is generally described by only adopting a plurality of simple parameters such as convexity and wedge degree at a position 40mm away from the edge of the strip, convexity and wedge degree at a position 25mm away from the edge of the strip and the like, the whole section profile of the strip cannot be reproduced, and the comparison of the whole profiles of the front and. Therefore, the invention establishes the method for reproducing the profile of the section of the hot rolled strip, can reproduce the profile of the whole section of the strip by only three key parameters, and has important significance for controlling the shape of the section of the strip.
Some relevant documents are published in the field of the method for reproducing the section shape of the strip. For example: a strip steel section description method is provided in a characteristic parameter extraction method for transverse distribution of strip steel thickness (Chinese patent CN104550267B), but the method uses too many parameters, needs to be solved through more actual measurement point data, and the parameters lack practical physical significance. The strip steel section description method proposed in the mechanism-based strip steel thickness transverse distribution characteristic parameter identification method (Chinese patent CN104588417B) needs to combine a strip steel elastic flattening basic mode with a polynomial, has a complex calculation process, and can reproduce the section outline by also needing a large amount of actual measuring point thickness data (at least 9 points).
Disclosure of Invention
The invention aims to provide a quick hot-rolled strip section contour recurrence method with practical physical significance, the method can directly recur the whole section contour of the hot-rolled strip by only adopting three index parameters of convexity and wedge at a position 40mm away from the edge of the strip and convexity at a position 25mm away from the edge of the strip, the recurrence result has high precision and the recurrence process has high speed; the method adopts the piecewise quadratic function to reproduce the profile of the section of the strip, has less introduced characteristic coefficients and simple calculation, can ensure the smooth and continuous profile of the section of the strip after reproduction by introducing the constraint equation, is more in line with the actual situation, and has important significance for the research on the control of the shape and the quality of the section of the strip.
In order to achieve the above object, the present invention provides a method for reproducing a cross-sectional profile of a hot-rolled strip, comprising the steps of:
s1, collecting the section profile parameters of the hot rolled strip, wherein the parameters comprise: convexity C at a distance of 40mm from the edge of the strip40Degree of separation from wedge W40Convexity C at a distance of 25mm from the edge of the strip25And a strip width b;
s2, dividing the hot rolled strip into a left area, a center area and a right area along the width direction, defining the anti-symmetric distribution of the strip wedge about the center of the strip by taking the width center point of the strip as the origin of coordinates, and establishing a cross section profile recurrence equation of the hot rolled strip;
s3, determining the coordinates of the known points required for solving the coefficients m, n, c, d, e, f, g and h of the characteristic to be determined of the section profile of the strip in the recurring equation of the section profile of the strip, setting the known points according to the coordinates and the wedge in the step S2,
the coordinates at the location are:
s4, step S3 (x)1l，y1l)，(x1r，y1r) Substituting the two points into a recurrence equation B1 of the profile center area of the section of the strip to solve the profile characteristic waiting coefficients m and n of the section of the strip;
s5, introducing a constraint condition equation, and limiting the secondary curve of the central area and the secondary curve of the left side edge area to be in
The slope of the curve at the position is consistent and the center region secondary curve and the right side region secondary curve are at
The slope of the curve at the location is consistent;
and S6, calculating strip section profile feature undetermined coefficients c, d, e, f, g and h in an edge recurrence equation of the strip section profile.
Preferably, step S2 specifically includes the following steps:
s21, establishing a recurring equation B1 of the central area of the profile of the section of the strip:
s22, establishing a recurring equation B2 of the left edge region of the section profile of the strip:
s23, establishing a recurring equation B3 of the right part area of the profile of the strip:
wherein: m, n, c, d, e, f, g and h are respectively strip section profile characteristic predetermined coefficients.
Preferably, step S5 specifically includes the following steps:
s51, introducing a left region constraint condition equation E1:
s52, introducing a right side region constraint condition equation E2:
preferably, step S6 specifically includes the following steps:
s61, step S3 (x)1l，y1l)，(x2l，y2l) Substituting the two points into a recurring equation B2 of the left edge part area of the profile of the section of the strip to obtain 2 solving equations F1:
s62, step S3 (x)1r，y1r)，(x2r，y2r) Substituting the two points into the right part area of the profile of the section of the strip to reproduce an equation B3 to obtain 2 solving equations F2:
s63, mixing
And substituting m and n solved in the step S4 into the left side region constraint equation E1 in the step S51 to obtain 1 solution equation F3:
2cx1l+d＝2mx1l+n；
s64, mixing
And substituting m and n solved in the step S4 into the right side region constraint equation E2 in the step S52 to obtain 1 solved equation F4:
2fx1r+g＝2mx1r+n；
s65, simultaneous equations F1 and F3 solve c, d and e;
s66, solving F, g and h by simultaneous equations F2 and F4;
and S67, substituting the values of m, n, c, d, e, f, g and h into equations B1, B2 and B3 to obtain a concrete expression of a recurrence equation, and directly drawing the profile curve of the section of the strip according to the concrete expression of the recurrence equation.
Compared with the prior art, the invention has the following characteristics:
firstly, compared with the prior hot rolled strip section profile which is generally described by only adopting a few simple parameters, the hot rolled strip section profile reproduction method only needs to be based on C40、W40、C25The three parameters can directly reproduce the whole section profile of the hot rolled strip, the reproduction result precision is high, and the speed of the reproduction process is high.
Secondly, the sectional quadratic function adopted by the method is used for reproducing the profile of the section of the strip steel, the introduced characteristic coefficients are few, the calculation is simple, and the method is very practical.
And finally, the method ensures that the profile of the cross section of the reproduced strip is smoother and continuous by introducing a constraint equation, is more in line with the actual situation and has important significance for the research on the shape and quality control of the cross section of the strip.
Drawings
FIG. 1 is a schematic cross-sectional profile of a hot rolled strip of the present invention;
FIG. 2 is a hot rolled strip profile coordinate profile of the present invention;
FIG. 3 is a flow chart of a method of reproducing the profile of a hot rolled strip section according to the invention;
FIG. 4 is a profile of a hot rolled strip section according to an embodiment of the present invention;
FIG. 5 is a cross-sectional profile of a hot rolled strip according to a second embodiment of the present invention.
Detailed Description
Exemplary embodiments, features and aspects of the present invention will be described in detail below with reference to the accompanying drawings. In the drawings, like reference numbers can indicate functionally identical or similar elements. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.
The invention relates to a method for reproducing the profile of a hot-rolled strip section, as shown in figure 3, comprising the following steps:
s1, collecting the section profile parameters of the hot rolled strip, wherein the parameters comprise: convexity C at a distance of 40mm from the edge of the strip40Degree of separation from wedge W40Convexity C at a distance of 25mm from the edge of the strip25And a strip width b;
s2, dividing the hot rolled strip into a left area 2, a center area 1 and a right area 3 along the width direction as shown in figure 1, and establishing a reproduction equation of the cross section profile of the hot rolled strip by taking the width center point of the strip as a coordinate origin and limiting the wedge shape of the strip to be in anti-symmetric distribution about the center of the strip as shown in figure 2; the left side region 2 is the operating side region and the right side region 3 is the drive side region.
Step S2 specifically includes the following steps:
s21, establishing a recurring equation B1 of the central area of the profile of the section of the strip:
s22, establishing a recurring equation B2 of the left edge region of the section profile of the strip:
s23, establishing a recurring equation B3 of the right part area of the profile of the strip:
wherein: m, n, c, d, e, f, g and h are respectively strip section profile characteristic predetermined coefficients.
S3, determining the coordinates of the known points required for solving the coefficients m, n, c, d, e, f, g and h of the characteristic to be determined of the section profile of the strip in the recurring equation of the section profile of the strip, defining according to the coordinates and the wedge in S2,
the coordinates at the location are:
s4, step S3 (x)1l，y1l)，(x1r，y1r) Substituting the two points into a recurrence equation B1 of the profile center area of the section of the strip to solve the profile characteristic waiting coefficients m and n of the section of the strip;
s5, introducing a constraint condition equation, and limiting the secondary curve of the central area and the secondary curve of the left side edge area to be in
The slope of the curve at the position is consistent and the center region secondary curve and the right side region secondary curve are at
The slope of the curve at the location is consistent.
Step S5 specifically includes the following steps:
s51, left region constraint equation E1:
s52, right edge region constraint condition equation E2:
and S6, calculating strip section profile feature undetermined coefficients c, d, e, f, g and h in an edge recurrence equation of the strip section profile.
Step S6 specifically includes the following steps:
s61, step S3 (x)1l，y1l)，(x2l，y2l) Substituting the two points into a recurring equation B2 of the left edge part area of the profile of the section of the strip to obtain 2 solving equations F1:
s62, step S3 (x)1r，y1r)，(x2r，y2r) Substituting the two points into the right part area of the profile of the section of the strip to reproduce an equation B3 to obtain 2 solving equations F2:
s63, mixing
And substituting m and n solved in the step S4 into the left side region constraint equation E1 in the step S51 to obtain 1 solution equation F3:
2cx1l+d＝2mx1l+n；
s64, mixing
And substituting m and n solved in the step S4 into the right side region constraint equation E2 in the step S52 to obtain 1 solved equation F4:
2fx1r+g＝2mx1r+n；
s65, simultaneous equations F1 and F3 solve c, d and e;
s66, solving F, g and h by simultaneous equations F2 and F4;
and S67, substituting the values of m, n, c, d, e, f, g and h into equations B1, B2 and B3 to obtain a concrete expression of a recurrence equation, and directly drawing the profile curve of the section of the strip according to the concrete expression of the recurrence equation.
The first embodiment is as follows:
s1, collecting the section shape parameters of the hot rolled strip, wherein the parameters mainly comprise: convexity C at a distance of 40mm from the edge of the strip400.01mm and a wedge W400.01mm, convexity C at a distance of 25mm from the edge of the strip250.01333mm, and 1200mm of strip width b;
s2, establishing a strip section profile recurrence equation, which specifically comprises the following steps:
s21, establishing a recurring equation B1 of the central area of the profile of the section of the strip: y isc＝mx2+nx(-560≤x≤560)；
S22, establishing a recurring equation B2 of the left edge region of the section profile of the strip: y isl＝cx2+dx+e(x≤-560)；
S23, establishing a recurring equation B3 of the right part area of the profile of the strip: y isr＝fx2+gx+h(x≥560)；
S3, determining the coordinates of the known points required for solving the coefficients m, n, c, d, e, f, g and h of the strip section profile feature to be determined in the recurrence equation:
x1l＝-560，y1l＝-0.005；x1r＝560，y1r＝-0.015；
x2l＝-575，y2l＝-0.00833；x2r＝575，y2r＝-0.01833；
s4, substituting the two points (-560, -0.005), (560, -0.015) in the step S3 into a center region recurrence equation B1 to solve the strip profile characteristic coefficient:
m＝-3.188775510204082×10-8、n＝-8.92857142857143×10-6；
s5, introducing a constraint condition equation, namely that the slope of the curve of the center region secondary curve is consistent with that of the left region secondary curve at the position of-560 mm, and the slope of the curve of the center region secondary curve is consistent with that of the right region secondary curve at the position of 560mm, and specifically comprising the following steps:
s51, left constraint equation E1:
2c×(-560)+d＝2m(-560)+n；
s52, right constraint equation E2:
2f×(560)+g＝2m(560)+n；
s6, calculating strip section contour feature undetermined coefficients c, d, e, f, g and h in an edge recurrence equation of the strip section contour, and specifically comprising the following steps:
s61, substituting the two points (-560, -0.005), (-575, -0.00833) in the step S3 into the left region to reproduce the equation B2, and obtaining 2 solving equations F1:
s62, substituting the two points (560, -0.015) and (575, -0.01833) in step S3 into the right edge region recurring equation B3, so as to obtain 2 solving equations F2:
s63, mixing x1lSubstituting-560 and m, n solved in step S4 into equation E1, yields 1 solved equation F3:
2c×(-560)+d＝2×(-3.188775510204082×10-8)×(-560)-8.92857142857143×10-6
s64, mixing x1rSubstituting 560 and m, n solved in step S4 into E2, yields 1 solution equation F4:
2f×560+g＝2×(-3.188775510204082×10-8)×560-8.92857142857143×10-6
s65, simultaneous equations F1 and F3:
c＝-1.301428571428572×10-5、d＝-0.014549214285714、e＝-4.071280000000002；
s66, simultaneous equations F2 and F4:
f＝-1.182380952380951×10-5、g＝+0.013198023809524、h＝-3.697946666666665；
s67, the hot rolled strip profile recurrence equation therefore is:
according to the concrete expression of the recurrence equation, the whole profile curve of the section of the hot rolled strip can be directly drawn, as shown in FIG. 4.
The second embodiment is as follows:
s1, collecting the section shape parameters of the hot rolled strip, which mainly comprises: convexity C at a distance of 40mm from the edge of the strip400.02mm and a wedge W400.04mm, convexity C at a distance of 25mm from the edge of the strip250.04mm, and 1000mm of strip width b;
s2, establishing a strip section wheel recurrence equation, which specifically comprises the following steps:
s21, establishing a recurring equation B1 of the central area of the profile of the section of the strip: y isc＝mx2+nx(-460≤x≤460)；
S22, establishing a recurring equation B2 of the left edge region of the section profile of the strip: y isl＝cx2+dx+e(x≤-460)
S23, establishing a recurring equation B3 of the right part area of the profile of the strip: y isr＝fx2+gx+h(x≥460)
S3, determining the coordinates of the known points required for solving the coefficients m, n, c, d, e, f, g and h of the strip section profile feature to be determined in the recurrence equation:
x1l＝-460，y1l＝0；x1r＝460，y1r＝-0.04；
x2l＝-475，y2l＝-0.02；x2r＝475，y2r＝-0.06；
s4, substituting the two points of (-460,0), (460, -0.04) in the step S3 into a central region recurrence equation B1 to solve the strip section profile characteristic waiting coefficient:
m＝-9.45179584120983×10-8、n＝-4.347826086956522×10-5；
s5, introducing a constraint equation, that is, the slope of the curve of the center area secondary curve is consistent with that of the left area secondary curve at the position of-460 mm, and the slope of the curve of the center area secondary curve is consistent with that of the right area secondary curve at the position of 460mm, specifically including:
s51, left constraint equation E1:
2c×(-460)+d＝2m(-460)+n；
s52, right constraint equation E2:
2f×(460)+g＝2m(460)+n；
s6, calculating strip section contour feature undetermined coefficients c, d, e, f, g and h in an edge recurrence equation of the strip section contour, and specifically comprising the following steps:
s61, substituting the two points (-460,0), (-475, -0.02) in step S3 into the left region recurring equation B2, resulting in 2 solving equations F1:
s62, substituting the two points (460, -0.04), (475, -0.06) in step S3 into the right edge region recurrence equation B3, resulting in 2 solution equations F2:
s63, mixing x1lSubstituting m, n solved in-460 and S4 into E1, yields 1 solution equation F3:
2c×(-460)+d＝2×(-9.45179584120983×10-8)×(-460)-4.347826086956522×10-5
s64, mixing x1rSubstituting m, n solved in 460 and S4 into E2, yields 1 solved equation F4:
2f×460+g＝2×(-9.45179584120983×10-8)×460-4.347826086956522×10-5
s65, simultaneous equations F1 and F3:
c＝-8.599033816425121×10-5、d＝-0.079067632850242、e＝-18.175555555555555；
s66, simultaneous equations F2 and F4:
f＝-8.019323671497585×10-5、g＝0.073647342995169、h＝-16.948888888888888；
s67, the hot rolled strip profile description equation is:
according to the concrete expression of the recurrence equation, the whole profile curve of the section of the hot rolled strip can be directly drawn, as shown in FIG. 5.
Finally, it should be noted that: the above-mentioned embodiments are only used for illustrating the technical solution of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (2)
1. A method for reproducing the profile of the cross section of a hot rolled strip is characterized in that: which comprises the following steps:
s1, collecting the section profile parameters of the hot rolled strip, wherein the parameters comprise: convexity C at a distance of 40mm from the edge of the strip40Degree of separation from wedge W40Convexity C at a distance of 25mm from the edge of the strip25And a strip width b;
s2, dividing the hot rolled strip into a left area, a center area and a right area along the width direction, defining the anti-symmetric distribution of the strip wedge about the center of the strip by taking the width center point of the strip as the origin of coordinates, and establishing a cross section profile recurrence equation of the hot rolled strip;
the method specifically comprises the following steps:
s21, establishing a recurring equation B1 of the central area of the profile of the section of the strip:
s22, establishing a recurring equation B2 of the left edge region of the section profile of the strip:
s23, establishing a recurring equation B3 of the right part area of the profile of the strip:
wherein: m, n, c, d, e, f, g and h are respectively strip section profile characteristic pending coefficients;
s3, determining the coordinates of the known points required for solving the coefficients m, n, c, d, e, f, g and h of the characteristic to be determined of the section profile of the strip in the recurring equation of the section profile of the strip, setting the known points according to the coordinates and the wedge in the step S2,
the coordinates at the location are:
s4, step S3 (x)1l,y1l)，(x1r,y1r) Substituting the two points into a recurrence equation B1 of the profile center area of the section of the strip to solve the profile characteristic waiting coefficients m and n of the section of the strip;
s5, introducing a constraint condition equation, and limiting the secondary curve of the central area and the secondary curve of the left side edge area to be in
The slope of the curve at the position is consistent and the center region secondary curve and the right side region secondary curve are at
The slope of the curve at the position is consistent, and the method comprises the following specific steps:
s51, left region constraint equation E1:
s52, right edge region constraint condition equation E2:
and S6, calculating strip section profile feature undetermined coefficients c, d, e, f, g and h in an edge recurrence equation of the strip section profile.
2. A hot rolled strip profile hot rolling method as claimed in claim 1 wherein: step S6 specifically includes the following steps:
s61, step S3 (x)1l,y1l)，(x2l,y2l) Substituting the two points into a recurring equation B2 of the left edge part area of the profile of the section of the strip to obtain 2 solving equations F1:
s62, step S3 (x)1r,y1r)，(x2r,y2r) Substituting the two points into the right part area of the profile of the section of the strip to reproduce an equation B3 to obtain 2 solving equations F2:
s63, mixing
And substituting m and n solved in the step S4 into the left side region constraint equation E1 in the step S51 to obtain 1 solution equation F3:
2cx1l+d＝2mx1l+n；
s64, mixing
And substituting m and n solved in the step S4 into the right side region constraint equation E2 in the step S52 to obtain 1 solved equation F4:
2fx1r+g＝2mx1r+n；
s65, simultaneous equations F1 and F3 solve c, d and e;
s66, solving F, g and h by simultaneous equations F2 and F4;
s67, substituting the numerical values of m, n, c, d, e, f, g and h into equations B1, B2 and B3 to obtain a concrete expression of a recurrence equation, and directly drawing the profile curve of the section of the strip according to the concrete expression of the recurrence equation.
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| CN101905248B (en) * | 2010-07-27 | 2015-03-18 | 上海梅山钢铁股份有限公司 | Strip steel section shape detecting and identifying method |
| JP5862247B2 (en) * | 2011-12-01 | 2016-02-16 | Ｊｆｅスチール株式会社 | Metal strip rolling method |
| CN102650879B (en) * | 2012-04-13 | 2014-05-14 | 燕山大学 | Method for reproducing and analyzing section properties of finished product for hot continuous rolling unit |
| CN104550267B (en) * | 2014-12-30 | 2017-01-18 | 燕山大学 | Strip steel thickness lateral distribution characteristic parameter extraction method |
| CN104588417B (en) * | 2015-01-21 | 2016-10-05 | 燕山大学 | A kind of characteristic parameter recognition methods of belt steel thickness cross direction profiles based on mechanism |
| EP3271092B1 (en) * | 2015-03-16 | 2019-06-19 | SMS group GmbH | Method for producing metal strips |
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Effective date of registration: 20201217 Address after: No.3, Dongtinghu Road, economic and Technological Development Zone, Qinhuangdao City, Hebei Province Patentee after: QINHUANGDAO CHANLINE PHOTOVOLTAIC ELECTRONICS Co.,Ltd. Address before: No.438, west section of Hebei Street, Haigang District, Qinhuangdao City, Hebei Province Patentee before: Yanshan University |