CN104588417B - A kind of characteristic parameter recognition methods of belt steel thickness cross direction profiles based on mechanism - Google Patents

Abstract

The present invention discloses the characteristic parameter recognition methods of a kind of belt steel thickness cross direction profiles based on mechanism, relates to strip quality control field.In the method, using a function to be described belt steel thickness cross direction profiles on the whole width of strip steel, this function is made up of basic model based on elastic flattening mechanism and common multinomial, and parameter is less, degree of accuracy is the highest, can well matching steel edge portion thinning.The present invention, for the section configuration identification of band, reduces the supplied materials section configuration fluctuation impact on production board shape, improves strip quality and be significant.

Description

A kind of characteristic parameter recognition methods of belt steel thickness cross direction profiles based on mechanism

Technical field

The present invention relates to the characteristic parameter recognition methods of a kind of belt steel thickness cross direction profiles, particularly to a kind of strip steel based on mechanism The characteristic parameter recognition methods of thickness cross direction profiles, belongs to the technical field being controlled strip quality by computer.

Background technology

Rolling production is the subsequent process that iron and steel produces, and rolled band steel is a part for Rolling production.Along with industries such as automobile makings Development, the aspects such as the dimensional accuracy of strip steel and plate shape are had higher requirement.

In belt steel rolling production process, edge there will be the phenomenon of local reduction, causes the reason of this phenomenon to have a lot, bag Include: on strip width direction, draught pressure skewness, can strongly reduce in edge roll-force, owing to roll-force causes Working roll elastic flattening also strongly reduces so that the loading roll gap of roll reduces, and causes edge thinning；Effect in roll-force Under, working roll can produce certain amount of deflection, so that loading roll gap reduces, causes edge thinning；At steel edge portion, metal is horizontal The resistance being subject to when flowing is less relative to middle part, is susceptible to horizontal mobility, aggravation edge thinning etc..

By belt steel thickness cross direction profiles is fitted, the section configuration characteristic parameter of strip steel can be obtained, thus to producing Journey is adjusted controlling, and improves section and the strip shape quality of strip steel.Therefore, belt steel thickness cross direction profiles matching whether accurate, Section and strip shape quality to strip steel have large effect.

In existing open source literature, it is related to the research of belt steel thickness cross direction profiles.It is respectively as follows: " three-dimensional rolling therory and should By the bar unit method of analog rolling process ", Liu Hongmin writes, Science Press, and 1999, book refer in whole width side Upwards by the thickness cross direction profiles high-order moment matching of strip steel, the method cannot describe the edge thinning phenomenon of strip steel；A kind of Crown of strip detection recognition methods (Patent publication No is CN101908248A), detector is divided into three groups by this patent, right Interval three the high-order moment functions of matching respectively of the strip width answered three sections, the method using sum of square of deviations functional value minimum is intended Conjunction has obtained belt steel thickness cross direction profiles characteristic parameter, achieves preferable effect, but, the multinomial that the method relates to Number higher (nine order polynomials), the characteristic parameter contained is more (15).

Summary of the invention

It is an object of the invention to: for the deficiency of existing belt steel thickness cross direction profiles characteristic parameter recognition methods, propose one aobvious Write the characteristic parameter recognition methods of the belt steel thickness cross direction profiles improving fitting precision.In the method, whole width is adopted Being described belt steel thickness cross direction profiles with a function, this function is by basic model based on elastic flattening mechanism and common Polynomial function form, parameter is less, and degree of accuracy is the highest, can well matching steel edge portion thinning.To being provided with profiler Equipment can be optimized improvement in terms of fitting function, can be with off-line to thickness cross direction profiles to the equipment not installing profiler Add up, after applying this invention to draw rule statistically, reapply in online production, so improve strip steel section with Strip shape quality.

In order to achieve the above object, the characteristic parameter recognition methods master of a kind of based on mechanism the belt steel thickness cross direction profiles of the present invention Comprise the following steps:

A1: the abscissa describing the n group initial data of belt steel thickness cross direction profiles is demarcated successively by operating lateral transmission side For x₁, x₂..., x_n, wherein abscissa x_iThe actual measurement one-tenth-value thickness 1/10 at place is h_i, wherein: n is natural number, value It 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: set the boundary point of abscissa as x_s=-1, x_e=1；

A4: according to elastic half-space theory, sets thickness cross direction profiles basic model based on elastic flattening mechanism, specifically Functional form as follows:

$\begin{array}{c}{f}_m\left(x\right)=2\underset{j=0}{\overset{m-1}{\mathrm{\Σ}}}\frac{(x_e^{m-j}-x_s^{m-j})x^{j+1}}{(m-j)(j+1)}-\frac{(x^{m+1}-x_s^{m+1})\ln {(x-x_s)}^2+(x_e^{m+1}-x^{m+1})\ln {(x_e-x)}^2}{m+1}\\ +\frac{2}{m+1}\underset{j=0}{\overset{m}{\mathrm{\Σ}}}(\frac{x^{m-j+1}{x}_s^j}{m-j+1}-\frac{x_e^{m-j}{x}^{j+1}}{j+1})\end{array}$

In formula, m and j is natural number, and wherein, m takes 0 respectively, 1,2,3,4,0≤j≤m；

A5: set fitting function model, fitting function be thickness cross direction profiles basic model based on elastic flattening mechanism with Ordinary polynomials function sum, the fitting function form finally given is:

H (x)=b_-1+b₀f₀(x)+b₁f₁(x)+b₂f₂(x)+b₃f₃(x)+b₄f₄(x)+b₅x+b₆x²+b₇x³+b₈x⁴

In formula, b_-1..., b₈For fitting coefficient；

A6: according to step a4, by the abscissa x after normalization_iValue substitute into, obtain all sons containing x item in step a5 Functional value, is respectively as follows: f₀(x_i), f₁(x_i), f₂(x_i), f₃(x_i), f₄(x_i), x_i,And With abscissa x_iCorresponding one-tenth-value thickness 1/10 h_i；

A7: use method of least square that the numerical value obtained by step a6 is carried out multilinear fitting；

A8: fitting coefficient b can be obtained according to step a7_-1, b₀, b₁, b₂, b₃, b₄, b₅, b₆, b₇, b₈, Final fitting function can be drawn.

The invention has the beneficial effects as follows, whole width uses a function belt steel thickness cross direction profiles is described, This function is made up of basic model based on elastic flattening mechanism and common polynomial function, and parameter is less, and degree of accuracy is the highest, Can well matching steel edge portion thinning.Equipment already installed with profiler can be optimized in terms of Function Fitting and change Enter, thickness cross direction profiles can be added up with off-line by the equipment not installing profiler, apply this invention to draw rule statistically After rule, reapply in online production, and then improve section and the strip shape quality of strip steel.

Accompanying drawing explanation

Fig. 1 is to use the comparison diagram of the curve that obtains of eight common order polynomial function matchings and discrete point (strip width is 1268mm)；

Fig. 2 is curve and the comparison diagram (band of discrete point that the present invention carries out that to belt steel thickness cross direction profiles piecewise fitting obtains Steel width is 1268mm)；

Fig. 3 is comparison diagram (the strip steel width that the present invention is fitted curve and the discrete point obtained to belt steel thickness cross direction profiles Degree is 1276mm).

Detailed description of the invention

Embodiment one:

Strip width is 1268mm, and the abscissa measuring point is shown in Table one with corresponding thickness.Specifically comprise the following steps that

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 describing the n group initial data of belt steel thickness cross direction profiles is demarcated successively by operating lateral transmission side For x₁, x₂..., x_n, wherein abscissa 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,-0.526814,0,0.52681 4,0.684543,0.802839,0.842271,0.881703,0.921136,0.952681,0.960568,0.968454,0. 976341,0.984227,0.988959,0.992114,0.995268；

A3: set the boundary point of abscissa as x_s=-1, x_e=1；

A4: according to elastic half-space theory, sets thickness cross direction profiles basic model based on elastic flattening mechanism, specifically Functional form as follows:

$\begin{array}{c}{f}_m\left(x\right)=2\underset{j=0}{\overset{m-1}{\mathrm{\Σ}}}\frac{(x_e^{m-j}-x_s^{m-j})x^{j+1}}{(m-j)(j+1)}-\frac{(x^{m+1}-x_s^{m+1})\ln {(x-x_s)}^2+(x_e^{m+1}-x^{m+1})\ln {(x_e-x)}^2}{m+1}\\ +\frac{2}{m+1}\underset{j=0}{\overset{m}{\mathrm{\Σ}}}(\frac{x^{m-j+1}{x}_s^j}{m-j+1}-\frac{x_e^{m-j}{x}^{j+1}}{j+1})\end{array}$

A5: set fitting function model, fitting function be thickness cross direction profiles basic model based on elastic flattening mechanism with Ordinary polynomials function sum, the fitting function form finally given is:

H (x)=b_-1+b₀f₀(x)+b₁f₁(x)+b₂f₂(x)+b₃f₃(x)+b₄f₄(x)+b₅x+b₆x²+b₇x³+b₈x⁴

A6: according to step a4, by the abscissa x after normalization_iValue substitute into, obtain all sons containing x item in step a5 Functional value, is respectively as follows: f₀(x_i), f₁(x_i), f₂(x_i), f₃(x_i), f₄(x_i), x_i,And With abscissa x_iCorresponding one-tenth-value thickness 1/10 h_i；

A7: use method of least square that the numerical value obtained by step a6 is carried out multilinear fitting；

A8: draw coefficient, b according to the equation matching that step a6 obtains_-1=4.55382, b₀=65.7754, b₁=-0.191995, b₂=-73.9525, b₃=0.106049, b₄=13.6673, b₅=0.620097, b₆=270.071, b₇=-0.3886, b₈=-64.6756, can draw final fitting function；

This fitting function is 0.00117738 with the value of the sum of square of deviations of measured value, has good fitting precision.

Embodiment two:

The width of strip steel is 1276mm, and the abscissa measuring point is shown in Table two with corresponding thickness.Specifically comprise the following steps that

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 describing the n group initial data of belt steel thickness cross direction profiles is demarcated successively by operating lateral transmission side For x₁, x₂..., x_n, wherein abscissa 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: set the boundary point of abscissa as x_s=-1, x_e=1；

A4: according to elastic half-space theory, sets thickness cross direction profiles basic model based on elastic flattening mechanism, specifically Functional form as follows:

$\begin{array}{c}{f}_m\left(x\right)=2\underset{j=0}{\overset{m-1}{\mathrm{\Σ}}}\frac{(x_e^{m-j}-x_s^{m-j})x^{j+1}}{(m-j)(j+1)}-\frac{(x^{m+1}-x_s^{m+1})\ln {(x-x_s)}^2+(x_e^{m+1}-x^{m+1})\ln {(x_e-x)}^2}{m+1}\\ +\frac{2}{m+1}\underset{j=0}{\overset{m}{\mathrm{\Σ}}}(\frac{x^{m-j+1}{x}_s^j}{m-j+1}-\frac{x_e^{m-j}{x}^{j+1}}{j+1})\end{array}$

A5: set fitting function model, fitting function be thickness cross direction profiles basic model based on elastic flattening mechanism with Ordinary polynomials function sum, the fitting function form finally given is:

H (x)=b_-1+b₀f₀(x)+b₁f₁(x)+b₂f₂(x)+b₃f₃(x)+b₄f₄(x)+b₅x+b₆x²+b₇x³+b₈x⁴

A6: according to step a4, by the abscissa x after normalization_iValue substitute into, obtain all sons containing x item in step a5 Functional value, is respectively as follows: f₀(x_i), f₁(x_i), f₂(x_i), f₃(x_i), f₄(x_i), x_i,And With abscissa x_iCorresponding one-tenth-value thickness 1/10 h_i；

A7: use method of least square that the numerical value obtained by step a6 is carried out multilinear fitting；

A8: draw coefficient, b according to the equation matching that step a6 obtains_-1=2.57466, b₀=0.608792, b₁=0.777202, b₂=1.39254, b₃=-0.467523, b₄=-1.06049, b₅=-2.44899, b₆=-0.829575, b₇=1.49899, b₈=2.35986, final fitting function can be drawn；

This fitting function is 0.000528475 with the value of the sum of square of deviations of measured value, has good fitting precision.

Claims (1)

1. a characteristic parameter recognition methods for belt steel thickness cross direction profiles based on mechanism, is characterized in that: comprise the following steps:

A1: the abscissa describing the n group initial data of belt steel thickness cross direction profiles is demarcated as successively by operating lateral transmission side x₁, x₂..., x_n, wherein abscissa 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: set the boundary point of abscissa as x_s=-1, x_e=1；

A4: according to elastic half-space theory, sets thickness cross direction profiles basic model based on elastic flattening mechanism, specifically Functional form as follows:

$\begin{array}{c}{f}_m\left(x\right)=2\underset{j=0}{\overset{m-1}{\Σ}}\frac{(x_e^{m-j}-x_s^{m-j})x^{j+1}}{(m-j)(j+1)}-\frac{(x^{m+1}-x_s^{m+1})\ln {(x-x_s)}^2+(x_e^{m+1}-x^{m+1})\ln {(x_e-x)}^2}{m+1}\\ +\frac{2}{m+1}\underset{j=0}{\overset{m}{\Σ}}(\frac{x^{m-j+1}{x}_s^j}{m-j+1}-\frac{x_e^{m-j}{x}^{j+1}}{j+1})\end{array}$

In formula, m and j is natural number, and wherein, m takes 0 respectively, 1,2,3,4,0≤j≤m；

A5: set fitting function model, fitting function be thickness cross direction profiles basic model based on elastic flattening mechanism with Ordinary polynomials function sum, the fitting function form finally given is:

H (x)=b_-1+b₀f₀(x)+b₁f₁(x)+b₂f₂(x)+b₃f₃(x)+b₄f₄(x)+b₅x+b₆x²+b₇x³+b₈x⁴

In formula, b_-1..., b₈For fitting coefficient；

A6: according to step a4, by the abscissa x after normalization_iValue substitute into, obtain all sons containing x item in step a5 Functional value, is respectively as follows: f₀(x_i), f₁(x_i), f₂(x_i), f₃(x_i), f₄(x_i), x_i,And with Abscissa x_iCorresponding one-tenth-value thickness 1/10 h_i；

A7: use method of least square that the numerical value obtained by step a6 is carried out multilinear fitting；

A8: fitting coefficient b can be obtained according to step a7_-1, b₀, b₁, b₂, b₃, b₄, b₅, b₆, b₇, b₈, Draw final fitting function.