CN101898202B - Method for forecasting edge reduction in rolling strips of SMS-EDC rolling mill - Google Patents

Abstract

The invention provides a method for forecasting edge reduction in rolling strips of a SMS-EDC rolling mill, which comprises the following steps of: (a) collecting actual equipment parameters and rolled piece process parameters of the SMS-EDC rolling mill; (b) scattering a roll system and a rolled piece along the direction of a roll body; (c) assuming the shape of initial roll gap; (d) calculating rolling pressure in unit length and lateral distribution values of front tensile stress and rear tensile stress; (e) calculating pressure among rolls and an outlet thickness distribution value through the stress of the roll system and a deformation model; and (f) judging whether the maximum value of the lateral distribution variation of outlet thickness is converged or not, if the maximum value is converged, outputting a lateral distribution value of plate thickness, edge reduction, the convexity of a center plate and the like, and otherwise, returning to the step (d). The method has the advantages of distinct analysis thoughts, accurate and reliable calculation, capability of meeting the requirement of engineering accuracy and high forecasting accuracy on the edge reduction in the rolling strips of the SMS-EDC rolling mill, and is favorable for improving the control accuracy of plate shapes of the SMS-EDC rolling mill.

Description

A kind of forecasting procedure of SMS-EDC mill milling strip side portion attenuate amount

Technical field

The present invention relates to a kind of cold-rolling mill shape research and plate shape control field, particularly a kind of forecasting procedure of SMS-EDC mill milling strip side portion attenuate amount.

Background technology

Plate shape is one of important quality index of Strip, and it directly affects the lumber recovery of strip product and carrying out smoothly of follow-up deep processing.Along with the development of science and technology, the raising of social quality mind and the extensive use of new and high technology, good plate shape has become Strip user's eternal requirement, therefore, solves production board shape problem and just seems very important.The steel edge portion attenuate is a kind of defective common and the most rambunctious in the plate shape control theory.Edge thinning is with the important cross section quality index of steel, directly the size of damage is cut by decision limit section, with lumber recovery substantial connection is arranged, therefore strictly control the edge thinning phenomenon in the belt steel rolling, realization is with the rectangle of steel shape of cross section, being the requirement of representative high-end product in the present strip product, also is the difficult point in the following plate shape research and practice, simultaneously or the growing point of innovation theory and technology ^[1](platinum is blue for [1] Chang An, Di Hongshuan. affect the factor [J] of cold rolling edge thinning. and iron and steel, 2007, (10): 1-6).For the SMS-EDC milling train, because working roll (seeing Fig. 1) end has one than the circlet connected in star, increase working roll at the flexible of band zone and realize axial displacement, carrying roll gap aperture becomes large in the strip side portion zone, to improve edge thinning and to adapt to the rolling of different in width band ^[2]([2] Xu Lejiang. the control of plate shape and plate shape theoretical [M]. Beijing: metallurgical industry publishing house, 1986:138).SMS-EDC mill milling band control edge thinning does not have quantitative theory analysis, how rationally to set traversing amount and bending roller force, make it give play to greatest extent SMS-EDC Mill shape control potentiality, control steel edge portion attenuate amount is the Focal point and difficult point of SMS-EDC milling train operation technique.

Summary of the invention

In order to overcome the deficiency of the existing operation technique existence of SMS-EDC milling train, the invention provides a kind of forecasting procedure of SMS-EDC mill milling strip side portion attenuate amount.Consider the characteristics of SMS-EDC operation roll of mill flex region length, traversing and roller particularity, based on cutting apart influence function, set up accurate metal three-dimensional plastic model and roll elastic deformation model, for its edge drop control characteristic of research, improve edge thinning amount forecast precision, the edge drop control potentiality of giving full play to SMS-EDC mill milling band are significant.

To achieve these goals, the present invention has adopted following technical scheme, and described scheme may further comprise the steps:

(a) device parameter and the rolled piece technological parameter (seeing Fig. 2) of collection SMS-EDC milling train:

The barrel length L that comprises backing roll _b, barrel diameter D _b(radius R _b), roll neck diameter D _B1, elastic modulus E _b, Poisson's ratio v _b, working roll barrel length L _w, barrel diameter D _w(radius R _w), elastic modulus E _w, Poisson's ratio v _w, rolled piece supplied materials specification b * h * l _s, elastic modulus E _s, Poisson's ratio v _s, the total tension force T in front and back ₁, T ₀

(b) with roller system and rolled piece along body of roll discrete--direction (seeing Fig. 3):

In working roll and backing roll contact length l scope, along body of roll direction, roller system is divided into m unit, rolled piece is divided into n unit, m=n+2d wherein, m, n are odd number, and d is body of roll end to the roller of homonymy rolled piece limit section is the dividing elements number.Depress fulcrum take a left side and be the origin of coordinates, cell width is Δ x _i(i=1,2 ..., m), the middle point coordinates of each unit is x _i(i=1,2 ..., m).The draught pressure, roll gap pressure and the roller system that act on the roll are out of shape also by the same unit discretization;

(c) suppose initial roll gap shape and roll rear roll gap shape:

C1) suppose that initial roll gap shape is:

$h_{0j}\left(x_j\right)=b_0+b_2{\left(\frac{{2x}_j}{B}\right)}^2+b_4{\left(\frac{{2x}_j}{B}\right)}^4$

B in the formula ₀-upper passage thickness cross direction profiles zero degree regression coefficient

b ₂-upper passage thickness cross direction profiles quadratic regression coefficient

b ₄-upper four regression coefficients of passage thickness cross direction profiles

C1) suppose to roll rear roll gap shape:

$h_{1j}\left(x_j\right)=b_{10}+b_{12}{\left(\frac{{2x}_j}{B}\right)}^2+b_{14}{\left(\frac{{2x}_j}{B}\right)}^4$

B in the formula ₁₀-outgoing gauge cross direction profiles zero degree regression coefficient

b ₁₂-outgoing gauge cross direction profiles quadratic regression coefficient

b ₁₄Four regression coefficients of-outgoing gauge cross direction profiles

(d) draught pressure of unit of account length and front and back tensile stress cross direction profiles comprise computer system execution in step (seeing Fig. 4):

D1) calculating parameter entrance average thickness

The outlet average thickness

D2) calculate each bar unit outlet lateral displacement amount;

D3) calculate the tensile stress cross direction profiles value σ that goes forward of bar unit _1j(x _j) rear tensile stress cross direction profiles value σ _0j(x _j);

D4) unit of account length roll-force p _j, calculate and finish.

J=1 in the above-mentioned computer system implementation, 2 ..., n.

(e) roller is stressed and distorted pattern calculating roll gap pressure and exit thickness distribution;

E1) utilize displacement coordination equation, work roll bending wind tunnel equilibrium equation between working roll and the backing roll to find the solution contact pressure between rolls

f _wi＝f _bi+δ _wbi+ΔD _i(i＝1，2，…，m)

$\left\{\begin{array}{c}{b}_{m+1}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{p}_i{\mathrm{\Δx}}_i+F_{\mathrm{wr}}+F_{\mathrm{wl}}\\ b_{m+2}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{p}_i{\mathrm{\Δxx}}_i+F_{\mathrm{wr}}(l+E)\end{array}\right.$

In the formula

$f_{\mathrm{wi}}=f_{\mathrm{wi}}^K+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\α}}_{\mathrm{wij}}{\mathrm{\Δx}}_i(p_{\mathrm{ij}}-q_j)-f_{\mathrm{wFri}}-f_{\mathrm{wFli}}(i=\mathrm{1,2},\·\·\·,m)$

$f_{\mathrm{wi}}^K=C_1+\frac{(C_2-C_1)}{l}(y_i-C)$

α wherein _Wij---working roller bending influence function coefficient, it is illustrated in x _jPoint action cell power is at x _iThe amount of deflection that point causes

Work as x _iDuring≤f≤xj, have

${\mathrm{\&alpha;}}_{\mathrm{wij}}=(l-x_j)x_i\left\{\frac{1}{E_w{I}_w{l}^2}\right[\frac{{\mathrm{lx}}_i^2-f^3}{3}+\frac{l(f^2-x_i^2)}{2}]+\frac{{\mathrm{\&alpha;}}_{s1}(l-f)}{G_w{A}_{\mathrm{<figure-callout\; id="2"\; label="w\; l"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">w</figure-callout>}}{l}^{}{}^2}+$

$\frac{1}{E_w{I}_{\mathrm{wr}}{l}^2}[\frac{l(x_i^2-f^2)}{2}-\frac{x_i^3-f^3}{3}+\frac{x_j{(l-x_j)}^2}{3}]+\frac{{\mathrm{\&alpha;}}_{s2}f}{G_w{A}_{\mathrm{wr}}{l}^2}\}$

Work as x _i≤ x _jDuring≤f, have

${\mathrm{\&alpha;}}_{\mathrm{wij}}=\frac{x_i}{E_w{I}_w{l}^2}\{\frac{(l-x_j)(l-x_i)x_i^2}{3}+(l-x_j)[\frac{l(x_j^2-x_i^2)}{2}-\frac{(x_j^3-x_i^3)}{3}]-\frac{x_j[{(l-f)}^3-{(l-x_j)}^3]}{3}\}$

$+\frac{x_j{x}_i{(l-f)}^2}{3E_w{I}_{\mathrm{<figure-callout\; id="2"\; label="wr\; l"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">wr</figure-callout>}}{l}^{}{}^2}+\frac{{\mathrm{\&alpha;}}_{s1}{x}_i}{G_w{A}_w{l}^2}[{(l-x_j)}^2+x_j(f-x_j)]+\frac{{\mathrm{\&alpha;}}_{s2}{x}_i{x}_j}{G_w{A}_{\mathrm{wr}}{l}^2}(l-f)$

As f≤x _i≤ x _jThe time, have

${\mathrm{\&alpha;}}_{\mathrm{wij}}=\frac{(l-x_j)}{E_w{I}_{\mathrm{wr}}{l}^2}[\frac{(l-x_i)(x_i^3-f^3)}{3}+x_i\frac{3l(x_j^2-x_i^2)-2(x_j^3-x_i^3)}{6}+\frac{{(l-x_j)}^2{x}_j{x}_i}{3}]+$

$\frac{(l-x_j)(l-x_i)f^3}{3E_w{I}_{\mathrm{<figure-callout\; id="2"\; label="w\; l"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">w</figure-callout>}}{l}^{}{}^2}+\frac{{\mathrm{\&alpha;}}_{s1}(l-x_j)(l-x_i)f}{G_w{A}_w^1{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">l</figure-callout>}}^2}+\frac{{\mathrm{\&alpha;}}_{s2}(l-x_j)}{G_w{A}_{\mathrm{wr}}{l}^2}({\mathrm{lx}}_i-\mathrm{lf}+{\mathrm{fx}}_i)$

As f≤x _j≤ x _iThe time, have

${\mathrm{\&alpha;}}_{\mathrm{wij}}=\frac{(l-x_i)}{E_w{I}_{\mathrm{wr}}{l}^2}[\frac{(l-x_j)(x_j^3-f^3)}{3}+x_j\frac{3l(x_i^2-x_j^2)-2(x_i^3-x_j^3)}{6}+\frac{{(l-x_i)}^2{x}_j{x}_i}{3}]+$

$\frac{(l-x_j)(l-x_i)f^3}{3E_w{I}_{\mathrm{<figure-callout\; id="2"\; label="w\; l"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">w</figure-callout>}}{l}^{}{}^2}+\frac{{\mathrm{\&alpha;}}_{s1}(l-x_j)(l-x_i)f}{G_w{A}_{\mathrm{<figure-callout\; id="2"\; label="w\; l"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">w</figure-callout>}}{l}^{}{}^2}+\frac{{\mathrm{\&alpha;}}_{s2}(l-x_i)}{G_w{A}_{\mathrm{wr}}{l}^2}({\mathrm{lx}}_j-\mathrm{fl}+{\mathrm{fx}}_j)$

Work as x _j≤ f≤x _iThe time, have

${\mathrm{\&alpha;}}_{\mathrm{wij}}=\frac{(l-x_i)x_j}{E_w{I}_w{l}^2}[\frac{{\mathrm{lx}}_j^2-f^3}{3}+\frac{l(f^2-x_j^2)}{2}]+\frac{{\mathrm{\&alpha;}}_{s1}(l-x_i)x_j(l-f)}{G_w{A}_{\mathrm{<figure-callout\; id="2"\; label="w\; l"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">w</figure-callout>}}{l}^{}{}^2}+$

$\frac{x_j(l-x_i)}{E_w{I}_{\mathrm{wr}}{l}^2}[\frac{l(x_j^2-f^2)}{2}-\frac{x_j^3-f^3}{3}+\frac{x_i{(l-x_i)}^2}{3}]+\frac{{\mathrm{\&alpha;}}_{s2}{x}_j(l-x_i)f}{G_w{A}_{\mathrm{<figure-callout\; id="2"\; label="wr\; l"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">wr</figure-callout>}}{l}^{}{}^2}$

Work as x _j≤ x _iDuring≤f, have

${\mathrm{\&alpha;}}_{\mathrm{wij}}=\frac{x_j}{E_w{I}_w{l}^2}\{\frac{(l-x_j)(l-x_i)x_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">j</figure-callout>}}^2}{3}+(l-x_i)[\frac{l(x_i^2-x_j^2)}{2}-\frac{(x_i^3-x_j^3)}{3}]-\frac{x_i[{(l-f)}^3-{(l-x_i)}^3]}{3}\}$

$+\frac{x_j{x}_i{(l-f)}^2}{3E_w{I}_{\mathrm{<figure-callout\; id="2"\; label="wr\; l"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">wr</figure-callout>}}{l}^{}{}^2}+\frac{{\mathrm{\&alpha;}}_{s1}{x}_j}{G_w{A}_w{l}^2}[{(l-x_i)}^2+x_i(f-x_i)]+\frac{{\mathrm{\&alpha;}}_{s2}{x}_i{x}_j}{G_w{A}_{\mathrm{wr}}{l}^2}(l-f)$

f _WFri---the right bending roller force of working roll causes the calculating of working roll amount of deflection

Work as x _iDuring 〉=f, have

$f_{\mathrm{wFri}}=\frac{M_r}{E_w{I}_w{l}^2}[\frac{{\mathrm{<figure-callout\; id="2"\; label="lf"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">lf</figure-callout>}}^2}{2}-\frac{f^3}{3}-\frac{{\mathrm{lx}}_i^2}{6}]+\frac{M_r{x}_i}{E_r{I}_{\mathrm{wr}}{l}^2}[\frac{l^3}{6}-\frac{{\mathrm{<figure-callout\; id="2"\; label="lf"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">lf</figure-callout>}}^2}{2}+\frac{f^3}{3}]$

Work as x _iDuring＜f, have

$f_{\mathrm{wFri}}=\frac{M_r(l-x_i)f^3}{3E_w{I}_{\mathrm{<figure-callout\; id="2"\; label="w\; l"\; filenames="HSA00000177551800022.png,HSA00000177551800023.png"\; state="\{\{state\}\}">w</figure-callout>}}{l}^{}{}^2}+\frac{M_r(l-x_i)}{E_w{I}_{\mathrm{wr}}{l}^2}[\frac{{\mathrm{lx}}_i(l+x_i)}{6}-\frac{f^3}{3}]$

$M_r=F_{\mathrm{wr}}(E+C+\frac{l_b-b}{2}+\mathrm{rx}+s)$

f _WFri---the left bending roller force of working roll causes the calculating of working roll amount of deflection

Work as x _iDuring＜f, have

$f_{\mathrm{wFli}}=\frac{M_l{x}_i}{6\mathrm{El}}\{\frac{[(l-x_i)l(2l-x_i)-2{(l-f)}^3]}{I_w}+\frac{2{(l-x_i)}^3}{I_{\mathrm{wr}}}\}$

Work as x _iDuring 〉=f, have

$f_{\mathrm{wFli}}=\frac{M_l(l-x_i)}{{6E}_w}[\frac{l^2}{I_w}+\frac{{2x}_{i}l-x_i^2-l^2}{I_{\mathrm{wr}}}]$

$M_l=F_{\mathrm{wl}}(l_w-l-E-C-\frac{l_b-b}{2}-\mathrm{rx}-s)$

Δ x in the formula _i---cell width, mm

p _j---unit width draught pressure, kN

q _j---the wide contact pressure between rolls of unit, kN

F _Wl---fore side work roll bending power, kN

F _Wr---transmission side work roll bending power, kN

C---backing roll is depressed half of difference of fulcrum and backing roll barrel length, mm

D---backing roll is depressed half of difference of fulcrum and working roll barrel length, mm

E---make half of difference that roll bending and backing roll are depressed fulcrum length, mm

---the rigid displacement of working roll axis, mm

C ₁---working roll body of roll left end shaft displacement of the lines, mm

C ₂---working roll body of roll right-hand member axis shift, mm

L---working roll and backing roll contact length, mm

α _S1---section factor, for the circular section,

α _S2---flex region section factor, α _S2=2

F---working roll solid section and backing roll contact length, mm

δ _Wbi---working roll and backing roll elastic flattening amount, mm

f _Wi---the total displacement of any unit axis of working roll, mm

f _Bi---the total displacement of any unit axis of backing roll, mm

Δ D _i---original gap or unloaded gap (convexity) between roller, mm

Rx---working roll flex region length, mm

S---work roll shifting amount, mm

G _w---the working roll coefficient of rigidity, MPa

I _w, I _Wr---working roll solid section elastic modelling quantity, flex region part elastic modelling quantity, mm ⁴

A _w, A _Wr---working roll solid section cross-sectional area, flex region part cross-sectional area, mm ²

E2) with adjacent twice mean square deviation of contact pressure between rolls whether 0～1.0 * 10 ^-4Be convergence criterion within the N scope, if convergence enters step e3); Otherwise, revise contact pressure between rolls with the relaxation factor method, change step e1 over to) (seeing Fig. 5);

E3) rolled piece exit thickness cross direction profiles ^[3]([3] Liu Hongmin. three-dimensional rolling therory and application thereof [M]. Beijing: Science Press 1999:284-302) represents with following formula

$h_i=s_0+{2f}_{\mathrm{wi}}+2{\mathrm{\&delta;}}_{\mathrm{wi}}+f_{\mathrm{bbi}}^K$ (i＝1，2，…，m)

S in the formula ₀---initial fixed value of roller slit, mm

δ _Wi---the working roll elastic flattening amount that roll-force causes, mm

---the rigid displacement of upper lower support roll,

Be expressed as

$f_{\mathrm{bbi}}^K=\frac{F_{\mathrm{bl}}}{K_g}+\frac{F_{\mathrm{br}}-F_{\mathrm{bl}}}{K_g}\frac{x_i}{l_b}+\frac{s_{\mathrm{tilt}({2x}_i-l_b)}}{l_b}$

K in the formula _g---the rigidity of monolithic memorial archway, kN/mm

F _Bl---fore side backing roll bending roller force, kN

F _Br---transmission side backing roll bending roller force, kN

s _Tilt---the roller amount of inclining, mm

(f) take the maximum of the adjacent twice iteration variable quantity of exit thickness cross direction profiles as convergence criterion, precision is controlled in the 0.1 μ m.If it is equivalent that thickness of slab cross direction profiles value, edge thinning amount and central plate convexity are then exported in convergence; Do not restrain and then change step (d) over to.

The invention has the beneficial effects as follows: on a large amount of theoretical research bases, in conjunction with actual rolling situation, according to SMS-EDC operation roll of mill flex region and traversing characteristic, rationally set the bending roller force of SMS-EDC milling train, coupling metal pattern and roller are the edge thinning amount of distorted pattern forecast SMS-EDC mill milling band, are the higher forecasting procedures of a kind of precision.It is the order of accuarcy that distorted pattern calculates that the raising of edge thinning amount forecast precision not only is conducive to improve roller, and is conducive to improve SMS-EDC Mill shape control accuracy, thereby improves the utilization rate of strip product.

Description of drawings

Fig. 1 SMS-EDC operation roll of mill schematic diagram;

Fig. 2 SMS-EDC milling train mechanical model;

Fig. 3 is the work roll shifting schematic diagram;

Fig. 4 is the metal pattern flow chart;

Fig. 5 is total program flow diagram;

Fig. 6 is that working roll flex region internal diameter is on there being the impact of carrying roll gap;

Fig. 7 is that work roll bending is on there being the impact of carrying roll gap;

Fig. 8 is that work roll shifting is on there being the impact of carrying roll gap.

The specific embodiment

Below further describe the present invention by drawings and Examples.

Embodiment

Now take actual SMS-EDC mill milling parameter as example, by accompanying drawing certain specific band rolling forecasting process and relevant effect on the SMS-EDC milling train described, comprise the following step of being carried out by computer system:

(a) device parameter and the technological parameter of the actual SMS-EDC milling train of collection:

Barrel length 1200mm, the barrel diameter 1000mm, roll neck diameter 800mm, elastic modelling quantity 210GPa, the Poisson's ratio 0.3 that comprise backing roll, working roll barrel length 1600mm, barrel diameter 400mm, elastic modelling quantity 210GPa, Poisson's ratio 0.3, rolled piece supplied materials specification 2.35mm * 1000mm * 400mm, elastic modelling quantity 210GPa, Poisson's ratio 0.3, forward and backward total tension force 300kN, 200kN.

(b) with roller system and rolled piece along body of roll discrete--direction (seeing Fig. 3):

Roller system is divided into 103 unit, and rolled piece is divided into 99 unit.

(c) suppose initial roll gap shape:

The regression coefficient of supposing initial inlet thickness cross direction profiles be 2.35mm ,-0.0008mm, 0.004mm.

The regression coefficient of supposing initial exit thickness cross direction profiles be 1.56mm, 0.0004mm ,-0.00012mm.

(d) draught pressure of unit of account length and front and back tensile stress cross direction profiles (seeing Fig. 4);

(e) roller is stressed and distorted pattern calculating roll gap pressure and exit thickness distribution (seeing Fig. 5);

(f) take the maximum of exit thickness cross direction profiles variable quantity as convergence criterion, precision is controlled in the 0.1 μ m.If it is equivalent that thickness of slab cross direction profiles value, edge thinning amount and central plate convexity are then exported in convergence; Do not restrain and then change step (d) over to.

Fig. 6 is under above-mentioned parameter, by changing working roll flex region internal diameter to the impact of carrying roll gap is arranged; Fig. 7 is under above-mentioned parameter, by changing work roll bending to the impact of carrying roll gap is arranged; Fig. 8 is under above-mentioned parameter, by work roll shifting on the impact of carrying roll gap is arranged.

Claims (3)

1. the forecasting procedure of a SMS-EDC mill milling strip side portion attenuate amount is characterized in that: may further comprise the steps:

(a) device parameter and the rolled piece technological parameter of collection SMS-EDC milling train;

(b) with roller system and rolled piece along body of roll discrete--direction;

(c) suppose initial roll gap shape and roll rear roll gap shape;

C1) suppose initial roll gap shape;

C2) suppose to roll rear roll gap shape;

(d) draught pressure of unit of account length and front and back tensile stress cross direction profiles;

D1) calculating parameter entrance average thickness

The outlet average thickness

D2) calculate each bar unit outlet lateral displacement amount;

D3) calculate the tensile stress cross direction profiles value σ that goes forward of bar unit _1j(x _j), rear tensile stress cross direction profiles value σ _0j(x _j);

D4) unit of account length roll-force p _j, calculate and finish;

(e) roller is stressed and distorted pattern calculating roll gap pressure and exit thickness cross direction profiles;

E1) utilize displacement coordination equation, work roll bending wind tunnel equilibrium equation between working roll and the backing roll to find the solution contact pressure between rolls; Displacement coordination equation between working roll and the backing roll:

f _wi＝f _bi+δw _bi+ΔD _i

In the formula

$f_{\mathrm{wi}}=f_{\mathrm{wi}}^K+\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{\mathrm{wij}}\mathrm{\&Delta;}{x}_i(p_j-q_j)-f_{\mathrm{wFri}}-f_{\mathrm{wFli}}$

i＝1，2，…，m

$f_{\mathrm{wi}}^K=C_1+\frac{(C_2-C_1)}{l}(x_i-C)$

α wherein _Wij---working roller bending influence function coefficient, it is illustrated in x _jPoint action cell power is at x _iThe amount of deflection that point causes

Work as x _i≤ f≤x _jThe time, have

${\mathrm{\&alpha;}}_{\mathrm{wij}}=(l-x_j)x_i\left\{\frac{1}{E_w{I}_w{l}^2}\right[\frac{{\mathrm{lx}}_i^2-f^3}{3}+\frac{l(f^2-x_i^2)}{2}]+\frac{{\mathrm{\&alpha;}}_{s1}(l-f)}{G_w{A}_w{l}^2}\text{+}$

$\frac{1}{E_w{I}_{\mathrm{wr}}{l}^2}[\frac{l(x_i^2-f^2)}{2}-\frac{x_i^3-f^3}{3}+\frac{x_j{(l-x_j)}^2}{3}]+\frac{{\mathrm{\&alpha;}}_{s2}f}{G_w{A}_{\mathrm{wr}}{l}^2}\}$

Work as x _i≤ x _jDuring≤f, have

${\mathrm{\&alpha;}}_{\mathrm{wij}}=\frac{x_i}{E_w{I}_w{l}^2}\{\frac{(l-x_j)(l-x_i)x_i^2}{3}+(l-x_j)[\frac{l(x_j^2-x_i^2)}{2}-\frac{(x_j^3-x_i^3)}{3}]-\frac{x_j[{(l-f)}^3-{(l-x_j)}^3]}{3}\}$

$+\frac{x_j{x}_i{(l-f)}^2}{3E_w{I}_{\mathrm{wr}}{l}^2}+\frac{{\mathrm{\&alpha;}}_{s1}{x}_i}{G_w{A}_w{l}^2}[{(l-x_j)}^2+x_j(f-x_j)]+\frac{{\mathrm{\&alpha;}}_{s2}{x}_i{x}_j}{G_w{A}_{\mathrm{wr}}{l}^2}(l-f)$

As f≤x _i≤ x _jThe time, have

${\mathrm{\&alpha;}}_{\mathrm{wij}}=\frac{(l-x_j)}{E_w{I}_{\mathrm{wr}}{l}^2}[\frac{(l-x_i)(x_i^3-f^3)}{3}+x_i\frac{3l(x_j^2-x_i^2)-2(x_j^3-x_i^3)}{6}+\frac{{(l-x_j)}^2{x}_j{x}_i}{3}]+$

$\frac{(l-x_j)(l-x_i)f^3}{3E_w{I}_w{l}^2}+\frac{{\mathrm{\&alpha;}}_{s1}(l-x_j)(l-x_i)f}{G_w{A}_w{l}^2}+\frac{{\mathrm{\&alpha;}}_{s2}(l-x_j)}{G_w{A}_{\mathrm{wr}}{l}^2}({\mathrm{lx}}_i-\mathrm{lf}+{\mathrm{fx}}_i)$

As f≤x _j≤ x _iThe time, have

${\mathrm{\&alpha;}}_{\mathrm{wij}}=\frac{(l-x_j)}{E_w{I}_{\mathrm{wr}}{l}^2}[\frac{(l-x_j)(x_j^3-f^3)}{3}+x_j\frac{3l(x_i^2-x_j^2)-2(x_i^3-x_j^3)}{6}+\frac{{(l-x_i)}^2{x}_j{x}_i}{3}]+$

$\frac{(l-x_j)(l-x_i)f^3}{3E_w{I}_w{l}^2}+\frac{{\mathrm{\&alpha;}}_{s1}(l-x_j)(l-x_i)f}{G_w{A}_w{l}^2}+\frac{{\mathrm{\&alpha;}}_{s2}(l-x_i)}{G_w{A}_{\mathrm{wr}}{l}^2}({\mathrm{lx}}_j-\mathrm{lf}+{\mathrm{fx}}_j)$

Work as x _j≤ f≤x _iThe time, have

${\mathrm{\&alpha;}}_{\mathrm{wij}}=\frac{(l-x_i)x_j}{E_w{I}_w{l}^2}[\frac{{\mathrm{lx}}_j^2-f^3}{3}+\frac{l(f^2-x_j^2)}{2}]+\frac{{\mathrm{\&alpha;}}_{s1}(l-x_i)x_j(l-f)}{G_w{A}_w{l}^2}+$

$\frac{x_j(l-x_i)}{E_w{I}_{\mathrm{wr}}{l}^2}[\frac{l(x_j^2-f^2)}{2}-\frac{x_j^3-f^3}{3}+\frac{x_i{(l-x_i)}^2}{3}]+\frac{{\mathrm{\&alpha;}}_{s2}{x}_j(l-x_i)f}{G_w{A}_{\mathrm{wr}}{l}^2}$

Work as x _j≤ x _iDuring≤f, have

${\mathrm{\&alpha;}}_{\mathrm{wij}}=\frac{x_j}{E_w{I}_w{l}^2}\{\frac{(l-x_j)(l-x_i)x_j^2}{3}+(l-x_i)[\frac{l(x_i^2-x_j^2)}{2}-\frac{(x_i^3-x_j^3)}{3}]-\frac{x_i[{(l-f)}^3-{(l-x_i)}^3]}{3}\}$

$+\frac{x_j{x}_i{(l-f)}^2}{3E_w{I}_{\mathrm{wr}}{l}^2}+\frac{{\mathrm{\&alpha;}}_{s1}{x}_j}{G_w{A}_w{l}^2}[{(l-x_i)}^2+x_i(f-x_i)]+\frac{{\mathrm{\&alpha;}}_{s2}{x}_i{x}_j}{G_w{A}_{\mathrm{wr}}{l}^2}(l-f)$

f _WFri---the right bending roller force of working roll causes the calculating of working roll amount of deflection

Work as x _iDuring 〉=f, have

$f_{\mathrm{wFri}}=\frac{M_r}{E_w{I}_w{l}^2}[\frac{{\mathrm{lf}}^2}{2}-\frac{f^3}{3}-\frac{{\mathrm{lx}}_i^2}{6}]+\frac{M_r{x}_i}{E_w{I}_{\mathrm{wr}}{l}^2}[\frac{l^3}{6}-\frac{{\mathrm{lf}}^2}{2}+\frac{f^3}{3}]$

Work as x _iDuring＜f, have

$f_{\mathrm{wFri}}=\frac{M_r(l-x_i)f^3}{3E_w{I}_w{l}^2}+\frac{M_r(l-x_i)}{E_w{I}_{\mathrm{wr}}{l}^2}[\frac{{\mathrm{lx}}_i(l+x_i)}{6}-\frac{f^3}{3}]$

$M_r=F_{\mathrm{wr}}(E+C+\frac{l_b-b}{2}+\mathrm{rx}+s)$

f _WFli---the left bending roller force of working roll causes the calculating of working roll amount of deflection

Work as x _iDuring＜f, have

$f_{\mathrm{wFli}}=\frac{M_l{x}_i}{{6E}_{w}l}\{\frac{[(l-x_i)l(2l-x_i)-2{(l-f)}^3]}{I_{\text{w}}}+\frac{2{(l-x_i)}^3}{I_{\mathrm{wr}}}\}$

Work as x _iDuring 〉=f, have

$f_{\mathrm{wFli}}=\frac{M_l(l-x_i)}{{6E}_w}[\frac{l^2}{I_w}+\frac{2x_{i}l-x_i^2-l^2}{I_{\mathrm{wr}}}]$

$M_l=F_{\mathrm{wl}}(l_w-l-E-C-\frac{l_b-b}{2}-\mathrm{rx}-s)$

Δ x in the formula _i---cell width, mm

p _j---unit width draught pressure, kN

q _j---the wide contact pressure between rolls of unit, kN

F _Wl---fore side work roll bending power, kN

F _Wr---transmission side work roll bending power, kN

C---backing roll is depressed half of difference of fulcrum and backing roll barrel length, mm

D---backing roll is depressed half of difference of fulcrum and working roll barrel length, mm

E---work roll bending and backing roll are depressed half of difference of fulcrum length, mm

---the rigid displacement of working roll axis, mm

C ₁---working roll body of roll left end shaft displacement of the lines, mm

C ₂---working roll body of roll right-hand member axis shift, mm

L---working roll and backing roll contact length, mm

α _S1---section factor, for the circular section,

α _S2---flex region section factor, α _S2=2

F---working roll solid section and backing roll contact length, mm

δ _Wbi---working roll and backing roll elastic flattening amount, mm

f _Wi---the total displacement of any unit axis of working roll, mm

f _Bi---the total displacement of any unit axis of backing roll, mm

_ΔD _i---original gap or unloaded gap between roller, mm

Rx---working roll flex region length, mm

S---work roll shifting amount, mm

M _r---working roll flex region moment, Nmm

M _l---working roll solid section moment, Nmm

G _w---the working roll coefficient of rigidity, MPa

I _w, I _Wr---working roll solid section elastic modelling quantity, flex region part elastic modelling quantity, mm ⁴

A _w, A _Wr---working roll solid section cross-sectional area, flex region part cross-sectional area, mm ²

E2) with the mean square deviation of adjacent twice iteration of contact pressure between rolls whether 0～1.0 * 10 ^-4Be convergence criterion within the N scope, if convergence enters step e3); Otherwise, revise contact pressure between rolls with the relaxation factor method, change step e1 over to);

E3) calculate rolled piece exit thickness cross direction profiles;

(f) take the maximum of the adjacent twice iteration variable quantity of exit thickness cross direction profiles as convergence criterion, precision is controlled in the 0.1 μ m; If it is equivalent that thickness of slab cross direction profiles value, edge thinning amount and central plate convexity are then exported in convergence; Do not restrain and then change step (d) over to.

2. the forecasting procedure of SMS-EDC mill milling strip side portion attenuate amount as claimed in claim 1 is characterized in that, described step (a) is collected device parameter and the rolled piece technological parameter of SMS-EDC milling train: backing roll barrel length L _b, backing roll barrel diameter D _b, backing roll body of roll radius R _b, roll neck diameter D _B1, elastic modulus E _b, Poisson's ratio v _b, working roll barrel length l _w, working roll roller barrel diameter D _w, working roll roller body of roll radius R _w, elastic modulus E _w, Poisson's ratio v _w, rolled piece supplied materials specification b * h * l _s, elastic modulus E _s, Poisson's ratio v _s, the total tension force T in front and back ₁, T ₀

3. the forecasting procedure of SMS-EDC mill milling strip side portion attenuate amount as claimed in claim 1, it is characterized in that, described step (b) with roller system and rolled piece along body of roll discrete--direction: in working roll and backing roll contact length l scope, along body of roll direction, roller system is divided into m unit, rolled piece is divided into n unit, wherein m=n+2d, m, n are odd number, and d is body of roll end to the roller of homonymy rolled piece limit section is the dividing elements number; Depress fulcrum take a left side and be the origin of coordinates, cell width is Δ x _i, the middle point coordinates of each unit is x _i, i=1 wherein, 2 ..., m; The draught pressure, roll gap pressure and the roller system that act on the roll are out of shape also by the same unit discretization.

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