CN104588417A - Characteristic parameter identification method of lateral distribution of strip steel thickness on the basis of mechanism - Google Patents

Characteristic parameter identification method of lateral distribution of strip steel thickness on the basis of mechanism Download PDF

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CN104588417A
CN104588417A CN201510030087.1A CN201510030087A CN104588417A CN 104588417 A CN104588417 A CN 104588417A CN 201510030087 A CN201510030087 A CN 201510030087A CN 104588417 A CN104588417 A CN 104588417A
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abscissa
cross direction
strip steel
direction profiles
function
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CN104588417B (en
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王东城
吴燕林
刘宏民
张威
程晓丽
张龙
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Yanshan University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/16—Control of thickness, width, diameter or other transverse dimensions
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/16—Control of thickness, width, diameter or other transverse dimensions
    • B21B37/165—Control of thickness, width, diameter or other transverse dimensions responsive mainly to the measured thickness of the product
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B38/00—Methods or devices for measuring, detecting or monitoring specially adapted for metal-rolling mills, e.g. position detection, inspection of the product
    • B21B38/04—Methods or devices for measuring, detecting or monitoring specially adapted for metal-rolling mills, e.g. position detection, inspection of the product for measuring thickness, width, diameter or other transverse dimensions of the product

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Metal Rolling (AREA)

Abstract

The invention discloses a characteristic parameter identification method of the lateral distribution of strip steel thickness on the basis of a mechanism, and relates to the field of strip steel quality control. In the method, one function is adopted to describe the lateral distribution of the strip steel thickness in the whole width direction of the strip steel, the function consists of a basic mode based on an elastic flattening mechanism and a common polynomial, so that the function has few parameters and high precision, and strip steel edge drop can be favorably fitted. The characteristic parameter identification method has an important meaning on the aspects of identifying the section shape of strip materials, lowering influence on the plate shape of a finished product by the shape fluctuation of a material feeding section and improving the quality of the strip steel.

Description

A kind of characteristic parameter recognition methods of the belt steel thickness cross direction profiles based on mechanism
Technical field
The present invention relates to a kind of characteristic parameter recognition methods of belt steel thickness cross direction profiles, particularly a kind of characteristic parameter recognition methods of the belt steel thickness cross direction profiles based on mechanism, belongs to the technical field that computer controls strip quality.
Background technology
Rolling production is the subsequent process that iron and steel is produced, and rolled band steel is a part for Rolling production.Along with the development of the industries such as automobile making, had higher requirement in aspects such as being with the dimensional accuracy of steel and plate shape.
In belt steel rolling production process, edge there will be the phenomenon of local reduction, the reason of this phenomenon is caused to have a lot, comprise: on strip width direction, draught pressure skewness, can sharply reduce in edge roll-force, and the working roll elastic flattening caused due to roll-force also sharply reduces, the loading roll gap of roll is reduced, causes edge thinning; Under the effect of roll-force, working roll can produce certain amount of deflection, thus loading roll gap is reduced, and causes edge thinning; At steel edge portion, the resistance be subject to during metal lateral flow is less relative to middle part, easily lateral flow occurs, aggravation edge thinning etc.
By carrying out matching to belt steel thickness cross direction profiles, the section configuration characteristic parameter being with steel can be obtained, thus regulable control is carried out to production process, improve section and the strip shape quality of band steel.Therefore, belt steel thickness cross direction profiles matching whether accurate, has larger impact to the section of band steel and strip shape quality.
In existing open source literature, there is the research about belt steel thickness cross direction profiles.Be respectively: " the bar unit method of three-dimensional rolling therory and application thereof---analog rolling process ", Liu Hongmin work, Science Press, 1999, refer to by the thickness cross direction profiles high-order moment matching of band steel on whole width in book, the method cannot describe the edge thinning phenomenon of band steel; A kind of crown of strip detects recognition methods (Patent publication No is CN101908248A), detector is divided into three groups by this patent, corresponding strip width three sections interval matching three high-order moment functions respectively, the minimum method matching of sum of square of deviations functional value is adopted to obtain belt steel thickness cross direction profiles characteristic parameter, achieve good effect, but, the degree of polynomial that the method relates to higher (nine order polynomials), the characteristic parameter contained more (15).
Summary of the invention
The object of the invention is to: for the deficiency of existing belt steel thickness cross direction profiles characteristic parameter recognition methods, propose a kind of characteristic parameter recognition methods significantly improving the belt steel thickness cross direction profiles of fitting precision.In the method, whole width adopts a function be described belt steel thickness cross direction profiles, this function forms by based on the basic model of elastic flattening mechanism and common polynomial function, and parameter is less, accuracy is very high, can well matching steel edge portion thinning.Improvement can be optimized in fitting function to the equipment being provided with profiler, the equipment not installing profiler can be added up thickness cross direction profiles by off-line, after applying the rule that this invention draws statistically, be applied in online production again, and then improve section and the strip shape quality of band steel.
In order to achieve the above object, the characteristic parameter recognition methods of a kind of belt steel thickness cross direction profiles based on mechanism of the present invention mainly comprises the following steps:
A1: the abscissa of the n group initial data describing belt steel thickness cross direction profiles is demarcated as x by fore side successively to transmission side 1, x 2..., x n, wherein lateral coordinates x ithe actual measurement one-tenth-value thickness 1/10 at place is h i, wherein: n is natural number, value is 1,2,3,4 ..., i is natural number, 1≤i≤n;
A2: be normalized the abscissa of each eyeball, plate width is w, then have: x i=2x i/ w-1;
A3: the boundary point of setting abscissa is x s=-1, x e=1;
A4: according to elastic half-space theory, set the thickness cross direction profiles basic model based on elastic flattening mechanism, concrete functional form is as follows:
f m ( x ) = 2 Σ j = 0 m - 1 ( x e m - j - x s m - j ) x j + 1 ( m - j ) ( j + 1 ) - ( x m + 1 - x s m + 1 ) ln ( x - x s ) 2 + ( x e m + 1 - x m + 1 ) ln ( x e - x ) 2 m + 1 + 2 m + 1 Σ j = 0 m ( x m - j + 1 x s j m - j + 1 - x e m - j x j + 1 j + 1 )
In formula, m and j is natural number, and wherein, m gets 0 respectively, and 1,2,3,4,0≤j≤m;
A5: setting fitting function model, fitting function is thickness cross direction profiles basic model based on elastic flattening mechanism and ordinary polynomials function sum, and the fitting function form finally obtained is:
h(x)＝b -1+b 0f 0(x)+b 1f 1(x)+b 2f 2(x)+b 3f 3(x)+b 4f 4(x)+b 5x+b 6x 2+b 7x 3+b 8x 4
In formula, b -1..., b 8for the data obtained after carrying out matching to discrete point;
A6: according to step a4, by the abscissa x after normalization ivalue substitute into, obtain all subfunction values containing x item in step a5, be respectively: f 0(x i), f 1(x i), f 2(x i), f 3(x i), f 4(x i), x i, and with abscissa x icorresponding one-tenth-value thickness 1/10 h i;
A7: adopt least square method to carry out multilinear fitting to the numerical value that step a6 obtains;
A8: fitting coefficient b can be obtained according to step a7 -1, b 0, b 1, b 2, b 3, b 4, b 5, b 6, b 7, b 8,
Final fitting function can be drawn.
The invention has the beneficial effects as follows, whole width adopts a function be described belt steel thickness cross direction profiles, this function forms by based on the basic model of elastic flattening mechanism and common polynomial function, and parameter is less, accuracy is very high, can well matching steel edge portion thinning.Improvement can be optimized in Function Fitting to the equipment being provided with profiler, the equipment not installing profiler can be added up thickness cross direction profiles by off-line, after applying the rule that this invention draws statistically, be applied in online production again, and then improve section and the strip shape quality of band steel.
Accompanying drawing explanation
Fig. 1 is the comparison diagram (strip width is 1268mm) of curve and the discrete point adopting eight common order polynomial function matchings to obtain;
The comparison diagram (strip width is 1268mm) of Fig. 2 to be the present invention to belt steel thickness cross direction profiles carry out curve that piecewise fitting obtains and discrete point;
The comparison diagram (strip width is 1276mm) of Fig. 3 to be the present invention to belt steel thickness cross direction profiles carry out curve that matching obtains and discrete point.
Detailed description of the invention
Embodiment one:
Strip width is 1268mm, the abscissa of measurement point with corresponding thickness in table one.Concrete steps are as follows:
Table one belt steel thickness cross direction profiles measured data
i 1 2 3 4 5 6 7 8 9 10
x 3 5 7 10 15 20 25 30 50 75
h(mm) 4.434 4.453 4.494 4.517 4.538 4.538 4.548 4.541 4.531 4.528
i 11 12 13 14 15 16 17 18 19 20
x 100 125 200 300 634 968 1068 1143 1158 1193
h(mm) 4.529 4.532 4.538 4.528 4.554 4.528 4.516 4.505 4.505 4.503
i 21 22 23 24 25 26 27 28 29
x 1218 1238 1243 1248 1253 1258 1261 1263 1265
h(mm) 4.51 4.512 4.515 4.508 4.495 4.464 4.448 4.438 4.425
A1: the abscissa of the n group initial data describing belt steel thickness cross direction profiles is demarcated as x by fore side successively to transmission side 1, x 2..., x n, wherein lateral coordinates x ithe actual measurement one-tenth-value thickness 1/10 at place is h i;
A2: be normalized abscissa, plate width is w, then have: x i=2x i/ w-1; Concrete numerical value is:
x i＝-0.995268,-0.992114,-0.988959,-0.984227,-0.976341,-0.968454,-0.960568,-0.952681,-0.921136,-0.881703,-0.842271,-0.802839,-0.684543,-0.526814,0,0.526814,0.684543,0.802839,0.842271,0.881703,0.921136,0.952681,0.960568,0.968454,0.976341,0.984227,0.988959,0.992114,0.995268；
A3: the boundary point of setting abscissa is x s=-1, x e=1;
A4: according to elastic half-space theory, set the thickness cross direction profiles basic model based on elastic flattening mechanism, concrete functional form is as follows:
f m ( x ) = 2 Σ j = 0 m - 1 ( x e m - j - x s m - j ) x j + 1 ( m - j ) ( j + 1 ) - ( x m + 1 - x s m + 1 ) ln ( x - x s ) 2 + ( x e m + 1 - x m + 1 ) ln ( x e - x ) 2 m + 1 + 2 m + 1 Σ j = 0 m ( x m - j + 1 x s j m - j + 1 - x e m - j x j + 1 j + 1 )
A5: setting fitting function model, fitting function is thickness cross direction profiles basic model based on elastic flattening mechanism and ordinary polynomials function sum, and the fitting function form finally obtained is:
h(x)＝b -1+b 0f 0(x)+b 1f 1(x)+b 2f 2(x)+b 3f 3(x)+b 4f 4(x)+b 5x+b 6x 2+b 7x 3+b 8x 4
A6: according to step a4, by the abscissa x after normalization ivalue substitute into, obtain all subfunction values containing x item in step a5, be respectively: f 0(x i), f 1(x i), f 2(x i), f 3(x i), f 4(x i), x i, and with abscissa x icorresponding one-tenth-value thickness 1/10 h i;
A7: adopt least square method to carry out multilinear fitting to the numerical value that step a6 obtains;
A8: draw coefficient, b according to the equation matching that step a6 obtains -1=4.55382, b 0=65.7754, b 1=-0.191995, b 2=-73.9525, b 3=0.106049, b 4=13.6673, b 5=0.620097, b 6=270.071, b 7=-0.3886, b 8=-64.6756, final fitting function can be drawn;
The value of the sum of square of deviations of this fitting function and measured value is 0.00117738, has good fitting precision.
Embodiment two:
Width with steel is 1276mm, the abscissa of measurement point with corresponding thickness in table two.Concrete steps are as follows:
Table two belt steel thickness cross direction profiles measured data
i 1 2 3 4 5 6 7 8 9 10
x 3 5 7 10 15 20 25 30 50 75
h(mm) 2.485 2.491 2.497 2.495 2.502 2.512 2.531 2.534 2.541 2.543
i 11 12 13 14 15 16 17 18 19 20
x 100 125 200 300 638 976 1076 1151 1176 1201
h(mm) 2.547 2.551 2.555 2.566 2.575 2.566 2.558 2.551 2.552 2.547
i 21 22 23 24 25 26 27 28 29
x 1226 1246 1251 1256 1261 1266 1269 1271 1273
h(mm) 2.541 2.539 2.538 2.528 2.516 2.494 2.483 2.47 2.46
A1: the abscissa of the n group initial data describing belt steel thickness cross direction profiles is demarcated as x by fore side successively to transmission side 1, x 2..., x n, wherein lateral coordinates x ithe actual measurement one-tenth-value thickness 1/10 at place is h i;
A2: be normalized abscissa, plate width is w, then have: x i=2x i/ w-1; Concrete numerical value is:
x i＝-0.995298,-0.992163,-0.989028,-0.984326,-0.976489,-0.968652,-0.960815,-0.952978,-0.92163,-0.882445,-0.84326,-0.804075,-0.68652,-0.529781,0,0.529781,0.68652,0.804075,0.84326,0.882445,0.92163,0.952978,0.960815,0.968652,0.976489,0.984326,0.989028,0.992163,0.995298；
A3: the boundary point of setting abscissa is x s=-1, x e=1;
A4: according to elastic half-space theory, set the thickness cross direction profiles basic model based on elastic flattening mechanism, concrete functional form is as follows:
f m ( x ) = 2 Σ j = 0 m - 1 ( x e m - j - x s m - j ) x j + 1 ( m - j ) ( j + 1 ) - ( x m + 1 - x s m + 1 ) ln ( x - x s ) 2 + ( x e m + 1 - x m + 1 ) ln ( x e - x ) 2 m + 1 + 2 m + 1 Σ j = 0 m ( x m - j + 1 x s j m - j + 1 - x e m - j x j + 1 j + 1 )
A5: setting fitting function model, fitting function is thickness cross direction profiles basic model based on elastic flattening mechanism and ordinary polynomials function sum, and the fitting function form finally obtained is:
h(x)＝b -1+b 0f 0(x)+b 1f 1(x)+b 2f 2(x)+b 3f 3(x)+b 4f 4(x)+b 5x+b 6x 2+b 7x 3+b 8x 4
A6: according to step a4, by the abscissa x after normalization ivalue substitute into, obtain all subfunction values containing x item in step a5, be respectively: f 0(x i), f 1(x i), f 2(x i), f 3(x i), f 4(x i), x i, and with abscissa x icorresponding one-tenth-value thickness 1/10 h i;
A7: adopt least square method to carry out multilinear fitting to the numerical value that step a6 obtains;
A8: draw coefficient, b according to the equation matching that step a6 obtains -1=2.57466, b 0=0.608792, b 1=0.777202, b 2=1.39254, b 3=-0.467523, b 4=-1.06049, b 5=-2.44899, b 6=-0.829575, b 7=1.49899, b 8=2.35986, final fitting function can be drawn; The value of the sum of square of deviations of this fitting function and measured value is 0.000528475, has good fitting precision.

Claims (1)

1., based on a characteristic parameter recognition methods for the belt steel thickness cross direction profiles of mechanism, it is characterized in that: comprise the following steps:
A1: the abscissa of the n group initial data describing belt steel thickness cross direction profiles is demarcated as x by fore side successively to transmission side 1, x 2..., x n, wherein lateral coordinates x ithe actual measurement one-tenth-value thickness 1/10 at place is h i, wherein: n is natural number, value is 1,2,3,4 ..., i is natural number, 1≤i≤n;
A2: be normalized the abscissa of each eyeball, plate width is w, then have: x i=2x i/ w-1;
A3: the boundary point of setting abscissa is x s=-1, x e=1;
A4: according to elastic half-space theory, set the thickness cross direction profiles basic model based on elastic flattening mechanism, concrete functional form is as follows:
f m ( x ) = 2 Σ j = 0 m - 1 ( x e m - j - x s m - j ) x j + 1 ( m - j ) ( j + 1 ) - ( x m + 1 - x s m + 1 ) ln ( x - x s ) 2 + ( x e m + 1 - x m + 1 ) ln ( x e - x ) 2 m + 1 + 2 m + 1 Σ j = 0 m ( x m - j + 1 x s j m - j + 1 - x e m - j x j + 1 j + 1 )
In formula, m and j is natural number, and wherein, m gets 0 respectively, and 1,2,3,4,0≤j≤m;
A5: setting fitting function model, fitting function is thickness cross direction profiles basic model based on elastic flattening mechanism and ordinary polynomials function sum, and the fitting function form finally obtained is:
h(x)＝b -1+b 0f 0(x)+b 1f 1(x)+b 2f 2(x)+b 3f 3(x)+b 4f 4(x)+b 5x+b 6x 2+b 7x 3+b 8x 4
In formula, b -1..., b 8for the data obtained after carrying out matching to discrete point;
A6: according to step a4, by the abscissa x after normalization ivalue substitute into, obtain all subfunction values containing x item in step a5, be respectively: f 0(x i), f 1(x i), f 2(x i), f 3(x i), f 4(x i), x i, and with abscissa x icorresponding one-tenth-value thickness 1/10 h i;
A7: adopt least square method to carry out multilinear fitting to the numerical value that step a6 obtains;
A8: fitting coefficient b can be obtained according to step a7 -1, b 0, b 1, b 2, b 3, b 4, b 5, b 6, b 7, b 8, final fitting function can be drawn.
CN201510030087.1A 2015-01-21 2015-01-21 A kind of characteristic parameter recognition methods of belt steel thickness cross direction profiles based on mechanism Expired - Fee Related CN104588417B (en)

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Cited By (4)

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CN107138540A (en) * 2017-04-06 2017-09-08 首钢总公司 The approximating method and evaluation method of a kind of strip section plate profile shape
CN108188184A (en) * 2018-02-13 2018-06-22 中冶南方工程技术有限公司 A kind of method of determining crown of strip
CN109871590A (en) * 2019-01-23 2019-06-11 燕山大学 A kind of hot-rolled band profiled outline reproducing method
CN116371942A (en) * 2023-06-05 2023-07-04 东北大学 Transverse thickness distribution prediction method based on uneven transverse strength of strip steel

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Publication number Priority date Publication date Assignee Title
CN107138540A (en) * 2017-04-06 2017-09-08 首钢总公司 The approximating method and evaluation method of a kind of strip section plate profile shape
CN108188184A (en) * 2018-02-13 2018-06-22 中冶南方工程技术有限公司 A kind of method of determining crown of strip
CN108188184B (en) * 2018-02-13 2019-09-03 中冶南方工程技术有限公司 A kind of method of determining crown of strip
CN109871590A (en) * 2019-01-23 2019-06-11 燕山大学 A kind of hot-rolled band profiled outline reproducing method
CN116371942A (en) * 2023-06-05 2023-07-04 东北大学 Transverse thickness distribution prediction method based on uneven transverse strength of strip steel
CN116371942B (en) * 2023-06-05 2023-10-20 东北大学 Transverse thickness distribution prediction method based on uneven transverse strength of strip steel

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