CN103157675A - Method of calculating external diameter of hot rolling checkered plate steel coil - Google Patents

Abstract

The invention discloses a method of calculating an external diameter of a hot rolling checkered plate steel coil. The method of calculating the external diameter of the hot rolling checkered plate steel coil includes the following steps: A. a hot rolling checkered plate steel coil finished product is sampled, and sample relevant coiling diameter data are measured; B. the compactness of a hot rolling checkered plate steel coil sample is calculated; C. a compactness mathematical model of the hot rolling checkered plate steel coil is established; D. a calculation formula of the external diameter of the hot rolling checkered plate steel coil is obtained according to the sample compactness and a compactness mathematical module; and E. the external diameter of the hot rolling checkered plate steel coil is calculated through the calculation formula of the external diameter of the hot rolling checkered plate steel coil. The method of calculating the external diameter of the hot rolling checkered plate steel coil starts from checkered coil external diameter actually measured data. Legendre polynomials are applied for a first time, a steel coil density calculation model is established, and then a novel method of checkered coil external diameter calculation is deduced. The method of calculating the external diameter of the hot rolling checkered plate steel coil is convenient and flexible to use, accurate in calculation result and capable of greatly improving the calculation accuracy of the checkered plate steel coil external diameter.

Description

A kind of method of calculating hot-rolled patterned steel sheet coil of strip external diameter

Technical field

The present invention relates to a kind of coil of strip method for computing data, specifically a kind of method of calculating hot-rolled patterned steel sheet coil of strip external diameter.

Background technology

Hot-rolled patterned steel sheet is different from common hot rolled coil, and with beans shape decorative pattern, its coil of strip external diameter is difficult to accurate calculating due to the surface.When the calculating of decorative pattern volume external diameter is excessive, help winding up roller and coil stripping car to put in advance the positional distance coil of strip excessive, in the time of can causing batching the throwing steel, magnetic tape trailer hits and helps winding up roller and coil stripping car, cause coil of strip not to be rolled tightly, coil stripping car runs to the time increase that contacts with coil of strip simultaneously, extend and unload the volume time, affected rolling rhythm; When the calculating of decorative pattern volume external diameter is too small, help winding up roller and coil stripping car to put in advance the positional distance coil of strip too small, can cause not batching complete coil of strip and be helped winding up roller and coil stripping car to block, cause the steel-fastening accident.As seen, when hot-rolled patterned steel sheet coil of strip external diameter computational accuracy is too low, gently influence of rolled rhythm and scroll quality, heavy cause the steel-fastening accident.

When conventional method is calculated hot-rolled patterned steel sheet coil of strip external diameter, with substrate thickness and the high sum of decorative pattern beans as equivalent thickness, calculate the coil of strip external diameter by calculating the coil of strip total length, because this method is not considered variation that in the operation of rolling, beans are high and the variation of coil of strip tight ness rating, the diameter error of calculation excessive (error can reach 50mm), not only influence of rolled rhythm and scroll quality, but also might cause the steel-fastening accident.

Summary of the invention

For above-mentioned deficiency, the invention provides a kind of method of calculating hot-rolled patterned steel sheet coil of strip external diameter, it can improve decorative pattern volume external diameter computational accuracy greatly, satisfies the needs of actual production.

The present invention solves the technical scheme that its technical problem takes: a kind of method of calculating hot-rolled patterned steel sheet coil of strip external diameter, it is characterized in that, and comprise the following steps:

A, hot-rolled patterned steel sheet coil of strip finished product is sampled, and measure the relevant coil diameter data of sample;

B, calculate the tight ness rating of hot-rolled patterned steel sheet coil of strip sample according to formula (1),

$t_i=\frac{H_0{W}_0{L}_0}{{\mathrm{\πW}}_1[{(d_i/2)}^2-{(d_0/2)}^2]}(i=\mathrm{1,2},...,N)---\left(1\right)$

In formula: t _iBe the tight ness rating of i hot-rolled patterned steel sheet coil of strip sample,

d _iBe the external diameter of i hot-rolled patterned steel sheet coil of strip sample,

d ₀Be the drum diameter of hot-rolled patterned steel sheet coil of strip,

H ₀Be the slab thickness of hot-rolled patterned steel sheet coil of strip,

W ₀Be the width of plate slab of hot-rolled patterned steel sheet coil of strip,

W ₁Be the finished width of hot-rolled patterned steel sheet coil of strip,

L ₀Be the slab length of hot-rolled patterned steel sheet coil of strip,

N is that the measurement of hot-rolled patterned steel sheet coil of strip is counted;

C, the tight ness rating Mathematical Modeling of setting up the hot-rolled patterned steel sheet coil of strip are seen formula (2),

t(h)＝c ₀+c ₁p ₁(h)+c ₂p ₂(h)+c ₃p ₃(h)+c ₄p ₄(h) （2）

In formula: c _i(i=0,1,2,3,4) are the tight ness rating coefficient,

p _i(h) (i=1,2,3,4) are Legnedre polynomial,

H is hot-rolled patterned steel sheet thickness;

D, the computing formula that can draw hot-rolled patterned steel sheet coil of strip external diameter by formula (1) and formula (2) are seen formula (3):

$d\left(h\right)=2\sqrt{{\left(\frac{d_0}{2}\right)}^2+\frac{H_0{W}_0{L}_0}{\mathrm{\π}{W}_{1}t\left(h\right)}}---\left(3\right)$

In formula: d (h) is hot-rolled patterned steel sheet coil of strip external diameter,

d ₀Be the drum diameter of hot-rolled patterned steel sheet coil of strip,

H ₀Be the slab thickness of hot-rolled patterned steel sheet coil of strip,

W ₀Be the width of plate slab of hot-rolled patterned steel sheet coil of strip,

W ₁Be the finished width of hot-rolled patterned steel sheet coil of strip,

L ₀Be the slab length of hot-rolled patterned steel sheet coil of strip,

T (h) is hot-rolled patterned steel sheet coil of strip tight ness rating,

H is hot-rolled patterned steel sheet thickness;

E, through type (3) calculate hot-rolled patterned steel sheet coil of strip external diameter.

In said method, described hot-rolled patterned steel sheet coil of strip sample coil diameter data comprise external diameter, width and the drum diameter of hot-rolled patterned steel sheet slab thickness, width and length and hot-rolled patterned steel sheet coil of strip.

In said method, the step of the described tight ness rating Mathematical Modeling of setting up the hot-rolled patterned steel sheet coil of strip is as follows:

C1, select once, secondary, three times and four Legnedre polynomials be as the basic model of tight ness rating;

C2, find the solution the tight ness rating coefficient by returning decomposition method based on the Legnedre polynomial of the principle of least square;

C3, determine tight ness rating mathematical modulo pattern (2) according to the tight ness rating coefficient.

The invention has the beneficial effects as follows: the present invention is from decorative pattern volume external diameter measured data, the first Application Legnedre polynomial, set up coil of strip density calculation model, and then derive decorative pattern and roll up outer new method as calculated, the method easy to use and flexible, result of calculation are accurate, have greatly improved the computational accuracy of diamond plate coil of strip external diameter.

Description of drawings

Fig. 1 is method flow diagram of the present invention;

Fig. 2 is the tight ness rating calculated of the present invention and the comparison diagram as a result of actual measurement tight ness rating.

The specific embodiment

Below in conjunction with its accompanying drawing, the present invention will be described in detail.

As shown in Figure 1, a kind of method of calculating hot-rolled patterned steel sheet coil of strip external diameter of the present invention, it comprises the following steps:

A, hot-rolled patterned steel sheet coil of strip finished product is sampled, and measure the relevant coil diameter data of sample, described hot-rolled patterned steel sheet coil of strip sample coil diameter data comprise external diameter, width and the drum diameter of hot-rolled patterned steel sheet slab thickness, width and length and hot-rolled patterned steel sheet coil of strip.

B, calculate the tight ness rating of hot-rolled patterned steel sheet coil of strip sample according to formula (1),

$t_i=\frac{H_0{W}_0{L}_0}{{\mathrm{\πW}}_1[{(d_i/2)}^2-{(d_0/2)}^2]}(i=\mathrm{1,2},...,N)---\left(1\right)$

In formula: t _iBe the tight ness rating of i hot-rolled patterned steel sheet coil of strip sample, d _iBe the external diameter of i hot-rolled patterned steel sheet coil of strip sample, d ₀Be the drum diameter of hot-rolled patterned steel sheet coil of strip, H ₀Be the slab thickness of hot-rolled patterned steel sheet coil of strip, W ₀Be the width of plate slab of hot-rolled patterned steel sheet coil of strip, W ₁Be the finished width of hot-rolled patterned steel sheet coil of strip, L ₀Be the slab length of hot-rolled patterned steel sheet coil of strip, N is that the measurement of hot-rolled patterned steel sheet coil of strip is counted;

C, set up the tight ness rating Mathematical Modeling of hot-rolled patterned steel sheet coil of strip

C1, select once, secondary, three times and four Legnedre polynomials be as the basic model of tight ness rating, each time curve representation formula is as follows:

(1.1) Legnedre polynomials:

p ₁(y)＝y

(1.2) secondary Legnedre polynomial:

$p_2\left(y\right)=\frac{3}{2}{y}^2-\frac{1}{2}$

(1.3) three Legnedre polynomials:

$p_3\left(y\right)=\frac{1}{2}({5y}^3-3y)$

(1.4) four Legnedre polynomials:

$p_4\left(y\right)=\frac{1}{8}({35y}^4-{30y}^2+3)$

C2, find the solution the tight ness rating coefficient by returning decomposition method based on the Legnedre polynomial of the principle of least square, namely seek a function P (y _i), satisfy

$\min \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{[P\left(y_i\right)-d_i]}^2$

In formula, P (y)=c ₀+ c ₁p ₁(y)+c ₂p ₂(y)+c ₃p ₃(y)+c ₄p ₄(y),

Be converted into and ask the function of many variables:

$\mathrm{\φ}(c_0,c_1,c_2,c_3,c_4)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{[\underset{j=0}{\overset{4}{\mathrm{\Σ}}}{c}_j{p}_j\left(y_i\right)-d_i]}^2---\left(2.1\right)$

Extreme-value problem.

Necessary condition according to function of many variables extreme value has

$\frac{\∂\mathrm{\φ}}{{\∂c}_k}=2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}[\underset{j=0}{\overset{4}{\mathrm{\Σ}}}{c}_j{p}_j\left(y_i\right)-d_i]p_k\left(y_i\right)=0(k=\mathrm{0,1,2,3,4})---\left(2.2\right)$

If order

$a_{\mathrm{jk}}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{p}_j\left(y_i\right)p_k\left(y_i\right)$

$b_k=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{p}_k\left(y_i\right)d_i(k=\mathrm{0,1,2,3,4})$

Formula (2.1) can be write as

$\underset{j=0}{\overset{4}{\mathrm{\Σ}}}{a}_{\mathrm{jk}}{c}_j=b_k(k=\mathrm{0,1,2,3,4})$

Being write as matrix form is

AC＝B (2.3)

In formula, C=[c ₀, c ₁, c ₂, c ₃, c ₄] ^T,

B＝[b ₀,b ₁,b ₂,b ₃,b ₄] ^T,

$A=\left[\begin{array}{ccccc}{a}_{00}& a_{01}& a_{02}& a_{03}& a_{04}\\ a_{10}& a_{11}& a_{12}& a_{13}& a_{14}\\ a_{20}& a_{21}& a_{22}& a_{23}& a_{24}\\ a_{30}& a_{31}& a_{32}& a_{33}& a_{34}\\ a_{40}& a_{41}& a_{42}& a_{43}& a_{44}\end{array}\right]$

Solving equation (2.3) obtains C, and this moment, the value of C was namely the optimal solution of equation (2.2), the element c in C _i(i=0,1,2,3,4) are tight ness rating computation model coefficient.

C3, determine tight ness rating mathematical modulo pattern (2) according to the tight ness rating coefficient:

t(h)＝c ₀+c ₁p ₁(h)+c ₂p ₂(h)+c ₃p ₃(h)+c ₄p ₄(h) （2）

In formula: c _i(i=0,1,2,3,4) are the tight ness rating coefficient, p _i(h) (i=1,2,3,4) are Legnedre polynomial, and h is hot-rolled patterned steel sheet thickness;

D, the computing formula that can draw hot-rolled patterned steel sheet coil of strip external diameter by formula (1) and formula (2) are seen formula (3):

$d\left(h\right)=2\sqrt{{\left(\frac{d_0}{2}\right)}^2+\frac{H_0{W}_0{L}_0}{{\mathrm{\πW}}_{1}t\left(h\right)}}---\left(3\right)$

In formula: d (h) is hot-rolled patterned steel sheet coil of strip external diameter, d ₀Be the drum diameter of hot-rolled patterned steel sheet coil of strip, H ₀Be the slab thickness of hot-rolled patterned steel sheet coil of strip, W ₀Be the width of plate slab of hot-rolled patterned steel sheet coil of strip, W ₁Be the finished width of hot-rolled patterned steel sheet coil of strip, L ₀Be the slab length of hot-rolled patterned steel sheet coil of strip, t (h) is hot-rolled patterned steel sheet coil of strip tight ness rating, and h is hot-rolled patterned steel sheet thickness;

E, through type (3) calculate hot-rolled patterned steel sheet coil of strip external diameter.

By adopting a kind of method of calculating hot-rolled patterned steel sheet coil of strip external diameter proposed by the invention, be that example has been carried out computational analysis to certain 1700mm four roller continuous hot-rolling mill diamond plate rolling data, slab thickness is 135mm, and drum diameter is 762mm, and steel grade is Q235B.Chosen 19 typical decorative pattern volume data, finished product thickness according to computational methods of the present invention, has determined that tight ness rating computation model coefficient is at 3～8mm:

C=[-0.33425,0.902168,-0.18475,0.015229,-0.00043] ^T

According to above-mentioned tight ness rating computation model coefficient, the diameter of actual production 8 volume diamond plate coil of strips to be calculated, result is as shown in table 1, can see that coil of strip external diameter calculated value and measured value coincide better, and computational accuracy is higher, has satisfied the needs of actual production.

Table 1 decorative pattern volume external diameter result of calculation

The above is the preferred embodiment of the present invention, for those skilled in the art, under the prerequisite that does not break away from the principle of the invention, can also make some improvements and modifications, and these improvements and modifications also are regarded as protection scope of the present invention.

Claims (3)

1. a method of calculating hot-rolled patterned steel sheet coil of strip external diameter, is characterized in that, comprises the following steps:

A, hot-rolled patterned steel sheet coil of strip finished product is sampled, and measure the relevant coil diameter data of sample;

B, calculate the tight ness rating of hot-rolled patterned steel sheet coil of strip sample according to formula (1),

$t_i=\frac{H_0{W}_0{L}_0}{{\mathrm{\πW}}_1[{(d_i/2)}^2-{(d_0/2)}^2]}(i=\mathrm{1,2},...,N)---\left(1\right)$

In formula: t _iBe the tight ness rating of i hot-rolled patterned steel sheet coil of strip sample,

d _iBe the external diameter of i hot-rolled patterned steel sheet coil of strip sample,

d ₀Be the drum diameter of hot-rolled patterned steel sheet coil of strip,

H ₀Be the slab thickness of hot-rolled patterned steel sheet coil of strip,

W ₀Be the width of plate slab of hot-rolled patterned steel sheet coil of strip,

W ₁Be the finished width of hot-rolled patterned steel sheet coil of strip,

L ₀Be the slab length of hot-rolled patterned steel sheet coil of strip,

N is that the measurement of hot-rolled patterned steel sheet coil of strip is counted;

C, the tight ness rating Mathematical Modeling of setting up the hot-rolled patterned steel sheet coil of strip are seen formula (2),

t(h)＝c ₀+c ₁p ₁(h)+c ₂p ₂(h)+c ₃p ₃(h)+c ₄p ₄(h) （2）

In formula: c _i(i=0,1,2,3,4) are the tight ness rating coefficient,

p _i(h) (i=1,2,3,4) are Legnedre polynomial,

H is hot-rolled patterned steel sheet thickness;

D, the computing formula that can draw hot-rolled patterned steel sheet coil of strip external diameter by formula (1) and formula (2) are seen formula (3):

$d\left(h\right)=2\sqrt{{\left(\frac{d_0}{2}\right)}^2+\frac{H_0{W}_0{L}_0}{\mathrm{\π}{W}_{1}t\left(h\right)}}---\left(3\right)$

In formula: d (h) is hot-rolled patterned steel sheet coil of strip external diameter,

d ₀Be the drum diameter of hot-rolled patterned steel sheet coil of strip,

H ₀Be the slab thickness of hot-rolled patterned steel sheet coil of strip,

W ₀Be the width of plate slab of hot-rolled patterned steel sheet coil of strip,

W ₁Be the finished width of hot-rolled patterned steel sheet coil of strip,

L ₀Be the slab length of hot-rolled patterned steel sheet coil of strip,

T (h) is hot-rolled patterned steel sheet coil of strip tight ness rating,

H is hot-rolled patterned steel sheet thickness;

E, through type (3) calculate hot-rolled patterned steel sheet coil of strip external diameter.

2. a kind of method of calculating hot-rolled patterned steel sheet coil of strip external diameter according to claim 1, it is characterized in that, described hot-rolled patterned steel sheet coil of strip sample coil diameter data comprise external diameter, width and the drum diameter of hot-rolled patterned steel sheet slab thickness, width and length and hot-rolled patterned steel sheet coil of strip.

3. a kind of method of calculating hot-rolled patterned steel sheet coil of strip external diameter according to claim 1, is characterized in that, the step of the described tight ness rating Mathematical Modeling of setting up the hot-rolled patterned steel sheet coil of strip is as follows:

C1, select once, secondary, three times and four Legnedre polynomials be as the basic model of tight ness rating;

C2, find the solution the tight ness rating coefficient by returning decomposition method based on the Legnedre polynomial of the principle of least square;

C3, determine tight ness rating mathematical modulo pattern (2) according to the tight ness rating coefficient.

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