CN104289524B - A kind of complex wave control method being suitable for four roller skin pass mill group - Google Patents

Abstract

Be suitable for a complex wave control method for four roller skin pass mill group, it mainly comprises the following step performed by computer: (1) collecting device parameter; (2) rolling technological parameter of product is collected; (3) asymmetric means are adopted to control complex wave: the 1. initial value of given upper and lower roll shifting amount process variable, roller amount of inclining and bending roller force Optimal Step Size, roll shifting amount Optimal Step Size, roller amount of inclining Optimal Step Size; 2. calculate upper and lower roll shifting amount, the left and right bending roller force of the best of roller amount of inclining, 3. calculate left and right bending roller force, the upper and lower roll shifting amount of the best of roller amount of inclining, 4. calculate left and right bending roller force, up and down the best of roll shifting amount and to incline roller amount; 5. export best left bending roller force, right bending roller force, upper roll shifting amount, lower roll shifting amount, roller amount of inclining, complex wave control is carried out to planisher.The present invention effectively can control the complex waves such as asymmetrical local shape wave, complex seas, improve finished product strip shape quality, has further promotion and use value.

Description

A kind of complex wave control method being suitable for four roller skin pass mill group

Technical field

The invention belongs to technical field of steel rolling, particularly a kind of control method of belt plate shape.

Background technology

In recent years, along with most of strip user is turned to high-end by low side, more and more higher requirement is proposed to the strip shape quality of band steel, smooth as the procedure closest to finished product in strip production, very important impact is played on the strip shape quality improving finished strip.With cold rolling and hot-rolled process is different, formation process drafts very little (generally all between 0.5% to 2%), therefore in the operation of rolling deformation heat and frictional heat little, roller heat convex degree learning is almost negligible, so the method for sub-sectional cooling cannot be adopted to finely control skin pass mill group plate shape.At present, for four roller skin pass mill group, the Strip Shape Control means of its routine mainly comprise the roller that inclines, symmetrical roller and symmetrical roll shifting etc. three kinds, the flatness defect that can control mainly contains monolateral wave, bilateral wave and middle wave, then helpless to complex waves such as asymmetrical local shape wave, complex seas.Like this, skin pass mill group how is utilized complex wave to be finely controlled to the emphasis just becoming site technology tackling key problem.

Bibliography:

[1] Lian Jiachuan, Liu Hongmin. AGC-ASC system [M]. weapon industry publishing house .1995

[2] Bai Zhenhua, Han Linfang, Li Jingzhou, the research of shape models during rolling abnormal etc. four-high mill. mechanical engineering journal, 2012,48

Summary of the invention

The object of the present invention is to provide a kind of complex wave control method being suitable for four roller skin pass mill group that can control the complex waves such as asymmetrical local shape wave, complex seas, improve finished product strip shape quality.The present invention mainly utilizes master data acquisition system and the plate shape mechanism model of milling train, propose a set of employing asymmetric structure and carry out alternative symmetrical structure, by Strip Shape Control means from the two-dimentional Strip Shape Control thought being increased to left roller, right roller, upper roll shifting, lower roll shifting and the roller that inclines etc. five and tieing up such as traditional symmetrical roller (symmetrical roll shifting), the roller that inclines, a set of complex wave control method being suitable for four roller skin pass mill group is established for target so that the difference of actual plate shape and target flatness is minimum

The present invention mainly comprises the following step performed by computer:

A the collection of () basic equipment parameter, mainly comprises the roller footpath D of working roll _w, backing roll roller footpath D _b, working roll barrel length L _w, backing roll barrel length L _b, working roll bending cylinder distance l _w, backing roll housing screw centre-to-centre spacing l _b, the maximum positive bending roller force that allows of milling train the maximum negative bending roller force that milling train allows the maximum roll shifting amount δ that milling train allows _max, the maximum roller amount η that inclines that allows of milling train _max;

B () collects the basic rolling technological parameter of ideal format product, mainly comprise thickness of strip H, width B, resistance of deformation k, roll-force P, mill speed v, percentage elongation entrance mean tension T ₀, outlet mean tension T ₁, target flatness coefficient a ₀, a ₁, a ₂, a ₃, a ₄;

(c) four roller skin pass mill group adopt asymmetric means to control the realization of complex wave, mainly comprise the following step performed by computer:

C1) given upper roll shifting amount δ _s, lower roll shifting amount δ _x, and the initial value of the roller amount η that inclines and bending roller force Optimal Step Size Δ S, roll shifting amount Optimal Step Size Δ δ, roller amount of inclining Optimal Step Size Δ η;

C2) calculating roll shifting amount is δ _s, lower roll shifting amount is δ _x, roller amount of inclining the best when being η left and right

Bending roller force S _zbest, S _ybest, mainly comprise the following step performed by computer:

C2-1) best roller computational process variable i is defined _s, j _s, object function initial value F ₀;

C2-2) i is made _s=0, j _s=0, get F ₀=10 ¹⁰;

C2-3) left bending roller force is made to be

C2-4) right bending roller force is made to be

C2-5) calculating roll shifting amount is δ _s, lower roll shifting amount is δ _x, roller amount of inclining is η, left bending roller force is S _z, right bending roller force is S _ytime band forward pull Distribution Value σ _1i;

C2-6) plate shape Distribution Value in units of I-Unit is calculated in formula, E is the elastic modelling quantity of band, v is Poisson's ratio;

C2-7) Strip Shape Control procedure function g is calculated ₁(X), g ₂(X) value, wherein g ₂(X)=max (| α _i-β _i|), α _ifor target flatness, i is band in the bar unit number of transverse direction, n be band at laterally total bar unit number, x _ifor band is at the coordinate of horizontal i-th unit;

C2-8) objective function F (X)=Ag is calculated ₁(X)+(1-A) g ₂(X) value, wherein A is weight coefficient;

C2-9) inequality F (X) <F is judged ₀set up? if inequality is set up, make F ₀=F (X), S _zbest=S _z, S _ybest=S _y, proceed to step c2-10); If inequality is false, then directly proceed to step c2-10);

C2-10) inequality is judged set up? if inequality is set up, make j _s=j _s+ 1, proceed to step c2-4); If inequality is false, proceed to step c2-11);

C2-11) inequality is judged set up? if inequality is set up, make i _s=i _s+ 1, proceed to step c2-3); If inequality is false, proceed to step c2-12);

C2-12) best left and right bending roller force S is obtained _zbest, S _ybest;

C3) calculating left bending roller force is S _zbest, right bending roller force is S _ybest, the best upper and lower roll shifting amount δ of roller amount of inclining when being η _sbest, δ _xbest, mainly comprise the following step that can be performed by computer:

C3-1) best roll shifting computational process variable i is defined _δ, j _δ, δ ' _s, δ ' _x;

C3-2) i is made _δ=0, j _δ=0;

C3-3) in order, roll shifting amount is δ ' _s=-δ _max+ i _δΔ δ;

C3-4) the lower roll shifting amount of order is δ ' _x=-δ _max+ j _δΔ δ;

C3-5) calculating roll shifting amount is δ ' _s, lower roll shifting amount is δ ' _x, roller amount of inclining is η, left bending roller force is S _zbest, right bending roller force is S _ybesttime band forward pull Distribution Value σ _1i;

C3-6) plate shape Distribution Value in units of I-Unit is calculated strip Shape Control procedure function g ₂(X)=max (| α _i-β _i|) value;

C3-7) objective function F (X)=Ag is calculated ₁(X)+(1-A) g ₂(X) value;

C3-8) inequality F (X) <F is judged ₀set up? if inequality is set up, make F ₀=F (X), δ _sbest=δ ' _s, δ _xbest=δ ' _x, proceed to step c3-9); If inequality is false, directly proceed to step c3-9);

C3-9) inequality is judged set up? if inequality is set up, make j _δ=j _δ+ 1, proceed to step c3-4); If inequality is false, proceed to step c3-10);

C3-10) inequality is judged set up? if inequality is set up, make i _δ=i _δ+ 1, proceed to step c3-3); If inequality is false, proceed to step c3-11);

C3-11) best upper and lower roll shifting amount δ is obtained _sbest, δ _xbest;

C4) calculating left bending roller force is S _zbest, right bending roller force is S _ybest, upper roll shifting amount is δ _sbest, lower roll shifting amount is δ _xbesttime the best to incline roller amount η _best;

C4-1) define the best to incline roller computational process variable i _η, η ';

C4-2) i is made _η=0;

C4-3) roller amount of inclining is made to be η '=-η _max+ i _ηΔ η;

C4-4) calculating roll shifting amount is δ _sbest, lower roll shifting amount is δ _xbest, roller amount of inclining is η ', left bending roller force is S _zbest, right bending roller force is S _ybesttime band forward pull Distribution Value σ _1i;

C4-5) plate shape Distribution Value in units of I-Unit is calculated strip Shape Control procedure function g ₂(X)=max (| α _i-β _i|) value;

C4-6) objective function F (X)=Ag is calculated ₁(X)+(1-A) g ₂(X) value;

C4-7) inequality F (X) <F is judged ₀set up? if inequality is set up, make F ₀=F (X), η _best=η ', proceeds to step c4-8); If inequality is false, directly proceed to step c4-8);

C4-8) inequality is judged set up? if inequality is set up, make i _η=i _η+ 1, then proceed to step c4-3); If inequality is false, proceed to step c4-9);

C4-9) the best roller amount η that inclines is obtained _best;

C5) inequality is judged $\sqrt{{({\mathrm{\&delta;}}_s-{\mathrm{\&delta;}}_{sbest})}^2+{({\mathrm{\&delta;}}_x-{\mathrm{\&delta;}}_{xbest})}^2+{(\mathrm{\&eta;}-{\mathrm{\&eta;}}_{best})}^2}<0.001$ Set up? if inequality is false, to making δ _s=δ _sbest, δ _x=δ _xbest, η=η _best, proceed to step c2) and place; If inequality is set up and is proceeded to step c6);

C6) best left bending roller force S is exported _zbest, right bending roller force S _ybest, upper roll shifting amount δ _sbest, lower roll shifting amount δ _xbest, incline roller amount η _best, complex wave control is carried out to planisher.

The present invention compared with prior art tool has the following advantages and effect:

By the Optimal Setting of left roller, right roller, upper roll shifting, lower roll shifting and the Strip Shape Control parameters such as roller of inclining, effectively can control the complex waves such as asymmetrical local shape wave, complex seas, improve finished product strip shape quality, compensate for the congenital not enough problem of Strip Shape Control that skin pass mill group brings because adopting spray cooling, there is further promotion and use value.

Accompanying drawing explanation

Fig. 1 is the total calculation flow chart of the present invention;

Fig. 2 is the realization flow figure that the asymmetric means of the present invention control complex wave;

Fig. 3 is that roll shifting power of the present invention optimizes calculation flow chart;

Fig. 4 is that roll shifting amount of the present invention optimizes calculation flow chart;

Fig. 5 be the present invention incline roller amount optimize calculation flow chart;

Fig. 6 is the toe-out stress envelope in example 1 optimizing process of the present invention;

Fig. 7 is the plate shape Distribution value figure in example 1 optimizing process of the present invention;

Fig. 8 is the plate shape value comparison diagram after example 1 of the present invention is optimized;

Fig. 9 is the toe-out stress envelope in example 2 optimizing process of the present invention;

Figure 10 is the plate shape Distribution value figure in example 2 optimizing process of the present invention;

Figure 11 is the plate shape value comparison diagram after example 2 of the present invention is optimized.

Detailed description of the invention

Embodiment 1

Be suitable for a complex wave control method for four roller skin pass mill group, as shown in Figure 1, first, in step (a), collect basic equipment parameter, mainly comprise the roller footpath D of working roll _wthe roller footpath D of=500mm, backing roll _bthe barrel length L of=1100mm, working roll _wthe barrel length L of=1450mm, backing roll _b=1450mm, working roll bending cylinder distance l _w=2300mm, backing roll housing screw centre-to-centre spacing l _bthe maximum positive bending roller force that=2300mm, milling train allow the maximum negative bending roller force that milling train allows the maximum roll shifting amount δ that milling train allows _maxthe maximum roller amount η that inclines that=200mm, milling train allow _max=150 μm.

Subsequently, in step (b), collect the basic rolling technological parameter that thickness is 0.22mm, width is 1220mm, steel grade is the ideal format product of SPCC, primary deformable drag k=300MPa, roll-force P=4200KN, mill speed v=600m/min, percentage elongation entrance mean tension T ₀=80MPa, outlet mean tension T ₁=120MPa, target flatness coefficient a ₀=0, a ₁=0, a ₂=0, a ₃=0, a ₄=0.

Subsequently, in step (c), four roller skin pass mill group adopt asymmetric means to control complex wave, computational process as shown in Figure 2:

First, in step (c1), given upper roll shifting amount process variable δ _s=0mm, lower roll shifting amount process variable δ _x=0mm and roller amount η=0 μm of inclining are as initial value and bending roller force Optimal Step Size Δ S=1KN, roll shifting amount Optimal Step Size Δ δ=5mm, roller amount of inclining Optimal Step Size Δ η=2 μm;

Subsequently, in step (c2), calculating roll shifting amount is δ _s=0mm, lower roll shifting amount are δ _xthe left and right bending roller force S of the best when=0mm, roller amount of inclining are η=0 μm _zbest, S _ybest, mainly comprise the following step that can be performed by computer, as shown in Figure 3:

First, in step (c2-1), define best roller computational process variable i _s, j _s, object function initial value F ₀;

Subsequently, in step (c2-2), i is made _s=0, j _s=0, get F ₀=10 ¹⁰;

Subsequently, in step (c2-3), left bending roller force is made to be

Subsequently, in step (c2-4), right bending roller force is made to be

Subsequently, in step (c2-5), calculating roll shifting amount is δ _s=0mm, lower roll shifting amount are δ _x=0mm, roller amount of inclining are η=0 μm, left bending roller force is S _z=-500KN, right bending roller force are S _ythe forward pull Distribution Value σ of band during=-500KN _1i, its forward pull Distribution Value is as shown in curve a in accompanying drawing 6;

Subsequently, in step (c2-6), calculate plate shape Distribution Value in units of I-Unit e=2.1 × 10 in formula ⁵mPa is the elastic modelling quantity of band, v=0.3 is Poisson's ratio, and its plate shape value is as shown in curve a in Fig. 7;

Subsequently, in step (c2-7), calculate Strip Shape Control procedure function g ₁(X), g ₂(X) value, wherein $g_1\left(X\right)=\frac{1}{n}\sqrt{\underset{i=1}{\overset{n}{\&Sigma;}}{\left({\mathrm{\&alpha;}}_i-{\mathrm{\&beta;}}_i\right)}^2}=\frac{1}{28}\sqrt{\underset{i=1}{\overset{28}{\&Sigma;}}{\left({\mathrm{\&beta;}}_i\right)}^2}=5.40---I$ , g ₂(X)=max (| α _i-β _i|)=max (| β _i|)=8.90I, α _ifor target flatness, i is band in the bar unit number of transverse direction, 28 be band at the first number of laterally total bar, x _ifor band is at the coordinate of horizontal i-th unit

Subsequently, in step (c2-8), by formula F (X)=Ag ₁(X)+(1-A) g ₂(X)=0.5 × 5.406+0.5 × 8.908=7.16I, wherein A=0.5 is weight coefficient;

Subsequently, in step (c2-9), Rule of judgment F (X)=7.16<F ₀=10 ¹⁰set up, record best objective function F ₀=F (X)=7.16I and best left and right bending roller force S _zbest=S _z=-500KN, S _ybest=S _ythen=-500KN proceeds to step (c2-10);

Subsequently, in step (c2-10), Rule of judgment set up, then j _s=j _s+ 1=0+1=1, then proceeds to step (c2-4);

Subsequently, in step (c2-11), Rule of judgment set up, then i _s=i _s+ 1=0+1=1, then proceeds to step (c2-3);

Subsequently, in step (c2-12), obtain best left and right bending roller force S _zbest=-459KN, S _ybest=-459KN;

Subsequently, in step (c3), calculating left bending roller force is S _zbest=-459KN, right bending roller force are S _ybestthe upper and lower roll shifting amount δ of the best when-459KN, roller amount of inclining are η=0 μm _sbest, δ _xbest, mainly comprise the following step that can be performed by computer, as shown in Figure 4;

Subsequently, in step (c3-1), define best roll shifting computational process variable i _δ, j _δ, δ ' _s, δ ' _x;

Subsequently, in step (c3-2), i is made _δ=0, j _δ=0;

Subsequently, in step (c3-3), in order, roll shifting amount is δ ' _s=-δ _max+ i _δΔ δ=-200+0 × 5=-200mm;

Subsequently, in step (c3-4), the lower roll shifting amount of order is δ ' _x=-δ _max+ j _δΔ δ=-200+0 × 5=-200mm;

Subsequently, in step (c3-5), calculating roll shifting amount is δ _s=-200mm, lower roll shifting amount are δ _x=-200mm, roller amount of inclining are η=0 μm, left bending roller force is S _z=-459KN, right bending roller force are S _ythe forward pull Distribution Value σ of band during=-459KN _1i, its forward pull Distribution Value is as shown in curve b in accompanying drawing 6;

Subsequently, in step (c3-6), calculate plate shape Distribution Value in units of I-Unit its plate shape is worth as shown in curve b in Fig. 7, Strip Shape Control procedure function $g_1\left(X\right)=\frac{1}{n}\sqrt{\underset{i=1}{\overset{n}{\&Sigma;}}{({\mathrm{\&alpha;}}_i-{\mathrm{\&beta;}}_i)}^2}=\frac{1}{28}\sqrt{\underset{i=1}{\overset{28}{\&Sigma;}}{\left({\mathrm{\&beta;}}_i\right)}^2}=16.21---I,$ g ₂(X)＝max(|α _i-β _i|)＝max(|β _i|)＝41.72I；

Subsequently, in step (c3-7), calculate objective function F (X)=Ag ₁(X)+(1-A) g ₂(X) value, F (X)=0.5 × 16.219+0.5 × 41.726=28.97I;

Subsequently, in step (c3-8), Rule of judgment F (X)=28.97<F ₀=6.28 are false, and directly proceed to step (c3-9);

Subsequently, in step (c3-9), Rule of judgment set up, then j _δ=j _δ+ 1=0+1=1, then proceeds to step (c3-4);

Subsequently, in step (c3-10), Rule of judgment set up, then i _δ=i _δ+ 1=0+1=1, then proceeds to step (c3-3);

Subsequently, in step (c3-11), obtain best upper and lower roll shifting amount δ _sbest=90mm, δ _xbest=-95mm;

Subsequently, in step (c4), calculating left bending roller force is S _zbest=-459KN, right bending roller force are S _ybest=-459KN, upper roll shifting amount are δ _sbest=90mm, lower roll shifting amount are δ _xbestthe best during=-95mm is inclined roller amount η _best, as shown in Figure 5;

Subsequently, in step (c4-1), definition the best is inclined roller computational process variable i _η, η ' generation;

Subsequently, in step (c4-2), i is made _η=0;

Subsequently, in step (c4-3), roller amount of inclining is made to be η '=-η _max+ i _ηΔ η=-150+0 × 2=-150 μm;

Subsequently, in step (c4-4), calculating roll shifting amount is δ _sbest=90mm, lower roll shifting amount are δ _xbest=-95mm, roller amount of inclining are η '=-150 μm, left bending roller force is S _zbest=-459KN, right bending roller force are S _ybestthe forward pull Distribution Value σ of band during=-459KN _1i, its forward pull Distribution Value is as shown in curve c in Fig. 6;

Subsequently, in step (c4-5), calculate plate shape Distribution Value in units of I-Unit its plate shape is worth as shown in curve c in Fig. 7, Strip Shape Control procedure function $g_1\left(X\right)=\frac{1}{n}\sqrt{\underset{i=1}{\overset{n}{\&Sigma;}}{({\mathrm{\&alpha;}}_i-{\mathrm{\&beta;}}_i)}^2}=\frac{1}{28}\sqrt{\underset{i=1}{\overset{28}{\&Sigma;}}{\left({\mathrm{\&beta;}}_i\right)}^2}=10.88---I,$ g ₂(X)＝max(|α _i-β _i|)＝max(|β _i|)＝24.94I；

Subsequently, in step (c4-6), calculate objective function F (X)=Ag ₁(X)+(1-A) g ₂(X) value F (X)=0.5 × 10.887+0.5 × 24.948=17.92I;

Subsequently, in step (c4-7), Rule of judgment F (X)=17.92<F ₀=5.76 are false, and directly proceed to step (c4-8);

Subsequently, in step (c4-8), Rule of judgment set up, then i _η=i _η+ 1=0+1=1, then proceeds to step (c4-3);

Subsequently, in step (c4-9), obtain the roller amount η that inclines of current the best _best=0 μm;

Subsequently, in step (c5), Rule of judgment (δ ' _s-δ _sbest) ²+ (δ ' _x-δ _xbest)+(η '-η _best) ²=(0-90) ²+ (0-(-95)) ²+ (0-0) ²=17125< ε ₀=0.01 is false then given δ _s=δ _sbest=90mm, δ _x=δ _xbest=-95mm, η=η _best=0 μm proceeds to step (c2) place as initial value.

Finally, in step (c6), exporting best left bending roller force is S _zbest=236KN, best right bending roller force are S _ybestin=-500KN, the best, roll shifting amount is δ _sbest=125mm, best lower roll shifting amount are δ _xbest=-40mm, the best roller amount of inclining is η _best=112 μm are carried out complex wave control to planisher, and as shown in Figure 8, in figure, curve c is best plate shape target function value F (X)=3.69I; In figure, curve b is plate shape target function value F (the X)=5.84I of the best that conventional means controls, and compared with conventional control means, the object function of the present embodiment reduces 36.8%; In figure, curve a is the plate shape distribution not adding control device, and plate shape is the poorest.

Embodiment 2

First, in step (a), collect basic equipment parameter, mainly comprise the roller footpath D of working roll _wthe roller footpath D of=500mm, backing roll _bthe barrel length L of=1100mm, working roll _wthe barrel length L of=1450mm, backing roll _b=1450mm, working roll bending cylinder distance l _w=2300mm, backing roll housing screw centre-to-centre spacing l _bthe maximum positive bending roller force that=2300mm, milling train allow the maximum negative bending roller force that milling train allows the maximum roll shifting amount δ that milling train allows _maxthe maximum roller amount η that inclines that=200mm, milling train allow _max=150 μm.

Subsequently, in step (b), collect the basic rolling technological parameter that thickness is 0.22mm, width is 1220mm, steel grade is the ideal format product of SPCD, mainly comprise deformation of strip drag k=300MPa, roll-force P=4200KN, mill speed v=600m/min, percentage elongation entrance mean tension T ₀=80MPa, outlet mean tension T ₁=120MPa, target flatness coefficient a ₀=0, a ₁=0, a ₂=0, a ₃=0, a ₄=0.

Subsequently, in step (c), four roller skin pass mill group adopt asymmetric means to control complex wave:

First, in step (c1), given upper roll shifting amount process variable δ _s=0mm, lower roll shifting amount process variable δ _x=0mm and roller amount η=0 μm of inclining are as initial value and bending roller force Optimal Step Size Δ S=1KN, roll shifting amount Optimal Step Size Δ δ=5mm, roller amount of inclining Optimal Step Size Δ η=2 μm;

Subsequently, in step (c2), calculating roll shifting amount is δ _s=0mm, lower roll shifting amount are δ _xthe left and right bending roller force S of the best when=0mm, roller amount of inclining are η=0 μm _zbest, S _ybest, mainly comprise the following step that can be performed by computer:

First, in step (c2-1), define best roller computational process variable i _s, j _s, object function initial value F ₀;

Subsequently, in step (c2-2), i is made _s=0, j _s=0, get F ₀=10 ¹⁰;

Subsequently, in step (c2-3), left bending roller force is made to be

Subsequently, in step (c2-4), right bending roller force is made to be

Subsequently, in step (c2-5), calculating roll shifting amount is δ _s=0mm, lower roll shifting amount are δ _x=0mm, roller amount of inclining are η=0 μm, left bending roller force is S _z=-500KN, right bending roller force are S _ythe forward pull Distribution Value σ of band during=-500KN _1i, its toe-out stress distribution is as shown in curve a in Fig. 9;

Subsequently, in step (c2-6), calculate plate shape Distribution Value in units of I-Unit e=2.1 × 10 in formula ⁵mPa is the elastic modelling quantity of band, v=0.3 is Poisson's ratio, and its plate shape Distribution Value is as shown in curve a in Figure 10;

Subsequently, in step (c2-7), calculate Strip Shape Control procedure function g ₁(X), g ₂(X) value, wherein $g_1\left(X\right)=\frac{1}{n}\sqrt{\underset{i=1}{\overset{n}{\&Sigma;}}{({\mathrm{\&alpha;}}_i-{\mathrm{\&beta;}}_i)}^2}=\frac{1}{28}\sqrt{\underset{i=1}{\overset{28}{\&Sigma;}}{\left({\mathrm{\&beta;}}_i\right)}^2}=5.71---I,$ G ₂(X)=max (| α _i-β _i|)=max (| β _i|)=12.68I, α _ifor target flatness, i is band in the bar unit number of transverse direction, 28 be band at the first number of laterally total bar, x _ifor band is at the coordinate of horizontal i-th unit

Subsequently, in step (c2-8), by formula F (X)=Ag ₁(X)+(1-A) g ₂(X)=0.5 × 5.406+0.5 × 8.908=9.20I, wherein A=0.5 is weight coefficient;

Subsequently, in step (c2-9), Rule of judgment F (X)=9.20<F ₀=10 ¹⁰set up, record best objective function F ₀=F (X)=9.20I and best left and right bending roller force S _zbest=S _z=-500KN, S _ybest=S _ythen=-500KN proceeds to step (c2-10);

Subsequently, in step (c2-10), Rule of judgment $j_s=0<\frac{S_{max}^{+}-S_{max}^{-}}{\mathrm{\&Delta;}S}=\frac{500-(-500)}{1}=1000$ Set up, then j _s=j _s+ 1=0+1=1, then proceeds to step (c2-4);

Subsequently, in step (c2-11), Rule of judgment $i_s=0<\frac{S_{max}^{+}-S_{max}^{-}}{\mathrm{\&Delta;}S}=\frac{500-(-500)}{1}=1000$ Set up, then i _s=i _s+ 1=0+1=1, then proceeds to step (c2-3);

Subsequently, in step (c2-12), obtain best left and right bending roller force S _zbest=-100KN, S _ybest=95KN;

Subsequently, in step (c3), calculating left bending roller force is S _zbest=-100KN, right bending roller force are S _ybestthe upper and lower roll shifting amount δ of the best when=95KN, roller amount of inclining are η=0 μm _sbest, δ _xbest, mainly comprise the following step that can be performed by computer;

Subsequently, in step (c3-1), define best roll shifting computational process variable i _δ, j _δ, δ ' _s, δ ' _x;

Subsequently, in step (c3-2), i is made _δ=0, j _δ=0;

Subsequently, in step (c3-3), in order, roll shifting amount is δ ' _s=-δ _max+ i _δΔ δ=-200+0 × 5=-200mm;

Subsequently, in step (c3-4), the lower roll shifting amount of order is δ ' _x=-δ _max+ j _δΔ δ=-200+0 × 5=-200mm;

Subsequently, in step (c3-5), calculating roll shifting amount is δ _s=-200mm, lower roll shifting amount are δ _x=-200mm, roller amount of inclining are η=0 μm, left bending roller force is S _z=-100KN, right bending roller force are S _ythe forward pull Distribution Value σ of band during=95KN _1i, the distribution of its forward pull is as shown in curve b in Fig. 9;

Subsequently, in step (c3-6), calculate plate shape Distribution Value in units of I-Unit its plate shape Distribution Value as shown in curve b in Figure 10, Strip Shape Control procedure function $g_1\left(X\right)=\frac{1}{n}\sqrt{\underset{i=1}{\overset{n}{\&Sigma;}}{({\mathrm{\&alpha;}}_i-{\mathrm{\&beta;}}_i)}^2}=\frac{1}{28}\sqrt{\underset{i=1}{\overset{28}{\&Sigma;}}{\left({\mathrm{\&beta;}}_i\right)}^2}=24.89---I,$ g ₂(X)＝max(|α _i-β _i|)＝max(|β _i|)＝47.31I；

Subsequently, in step (c3-7), calculate objective function F (X)=Ag ₁(X)+(1-A) g ₂(X) value, F (X)=0.5 × 24.895+0.5 × 47.31=36.10I;

Subsequently, in step (c3-8), Rule of judgment F (X)=28.97<F ₀=8.18 are false, and directly proceed to step (c3-9);

Subsequently, in step (c3-9), Rule of judgment set up, then j _δ=j _δ+ 1=0+1=1, then proceeds to step (c3-4);

Subsequently, in step (c3-10), Rule of judgment set up, then i _δ=i _δ+ 1=0+1=1, then proceeds to step (c3-3);

Subsequently, in step (c3-11), obtain best upper and lower roll shifting amount δ _sbest=30mm, δ _xbest=-60mm;

Subsequently, in step (c4), calculating left bending roller force is S _zbest=-100KN, right bending roller force are S _ybest=95KN, upper roll shifting amount are δ _sbest=30mm, lower roll shifting amount are δ _xbestthe best during=-60mm is inclined roller amount η _best;

Subsequently, in step (c4-1), definition the best is inclined roller computational process variable i _η, η ' generation;

Subsequently, in step (c4-2), i is made _η=0;

Subsequently, in step (c4-3), roller amount of inclining is made to be η '=-η _max+ i _ηΔ η=-150+0 × 2=-150 μm;

Subsequently, in step (c4-4), calculating roll shifting amount is δ _sbest=30mm, lower roll shifting amount are δ _xbest=-60mm, roller amount of inclining are η '=-150 μm, left bending roller force is S _zbest=-100KN, right bending roller force are S _ybestthe forward pull Distribution Value σ of band during=95KN _1i, its forward pull Distribution Value is as shown in c in Fig. 9;

Subsequently, in step (c4-5), calculate plate shape Distribution Value in units of I-Unit its plate shape Distribution Value as shown in c in Figure 10, Strip Shape Control procedure function $g_1\left(X\right)=\frac{1}{n}\sqrt{\underset{i=1}{\overset{n}{\&Sigma;}}{({\mathrm{\&alpha;}}_i-{\mathrm{\&beta;}}_i)}^2}=\frac{1}{28}\sqrt{\underset{i=1}{\overset{28}{\&Sigma;}}{\left({\mathrm{\&beta;}}_i\right)}^2}=24.89---I.$ g ₂(X)＝max(|α _i-β _i|)＝max(|β _i|)＝47.31I；

Subsequently, in step (c4-6), calculate objective function F (X)=Ag ₁(X)+(1-A) g ₂(X) value F (X)=0.5 × 24.895+0.5 × 47.31=36.10I;

Subsequently, in step (c4-7), Rule of judgment F (X)=36.10<F ₀=7.66 are false, and directly proceed to step (c4-8);

Subsequently, in step (c4-8), Rule of judgment set up, then i _η=i _η+ 1=0+1=1, then proceeds to step (c4-3);

Subsequently, in step (4-9), obtain the roller amount η that inclines of current the best _best=10 μm;

Subsequently, in step (c5), Rule of judgment (δ ' _s-δ _sbest) ²+ (δ ' _x-δ _xbest)+(η '-η _best) ²=(0-30) ²+ (0-(-60)) ²+ (0-10) ²=4600< ε ₀=0.01 is false then given δ _s=δ _sbest=30mm, δ _x=δ _xbest=-60mm, η=η _best=10 μm proceed to step (c2) place as initial value.

Finally, in step (c6), exporting best left bending roller force is S _zbest=196KN, best right bending roller force are S _ybestin=136KN, the best, roll shifting amount is δ _sbest=50mm, best lower roll shifting amount are δ _xbest=10mm, the best roller amount of inclining is η _best=42 μm, carry out complex wave control to planisher, as shown in Figure 11, in figure, curve c is best plate shape target function value F (X)=1.84I; In figure, curve b is plate shape target function value F (X)=2.66I best after the asymmetrical control of conventional means control, and compared with conventional control means, object function reduces 30.8%; In figure, curve a is the plate shape distribution map not adding control device, and plate shape is the poorest.

Claims (1)

1. be suitable for a complex wave control method for four roller skin pass mill group, it is characterized in that: it mainly comprises the following step performed by computer:

A the collection of () basic equipment parameter, mainly comprises the roller footpath D of working roll _w, backing roll roller footpath D _b, working roll barrel length L _w, backing roll barrel length L _b, working roll bending cylinder distance l _w, backing roll housing screw centre-to-centre spacing l _b, the maximum positive bending roller force that allows of milling train the maximum negative bending roller force that milling train allows the maximum roll shifting amount δ that milling train allows _max, the maximum roller amount η that inclines that allows of milling train _max;

B () collects the basic rolling technological parameter of ideal format product, mainly comprise thickness of strip H, width B, resistance of deformation k, roll-force P, mill speed v, percentage elongation entrance mean tension T ₀, outlet mean tension T ₁, target flatness coefficient a ₀, a ₁, a ₂, a ₃, a ₄;

(c) four roller skin pass mill group adopt asymmetric means to control the realization of complex wave, mainly comprise the following step performed by computer:

C1) given upper roll shifting amount δ _s, lower roll shifting amount δ _x, and the initial value of the roller amount η that inclines and bending roller force Optimal Step Size Δ S, roll shifting amount Optimal Step Size Δ δ, roller amount of inclining Optimal Step Size Δ η;

C2) calculating roll shifting amount is δ _s, lower roll shifting amount is δ _x, roller amount of inclining the best when being η left and right bending roller force S _zbest, S _ybest, mainly comprise the following step performed by computer:

C2-1) best roller computational process variable i is defined _s, j _s, object function initial value F ₀;

C2-2) i is made _s=0, j _s=0, get F ₀=10 ¹⁰;

C2-3) left bending roller force is made to be

C2-4) right bending roller force is made to be

C2-5) calculating roll shifting amount is δ _s, lower roll shifting amount is δ _x, roller amount of inclining is η, left bending roller force is S _z, right bending roller force is S _ytime band forward pull Distribution Value σ _1i;

C2-6) plate shape Distribution Value in units of I-Unit is calculated in formula, E is the elastic modelling quantity of band, v is Poisson's ratio;

C2-7) Strip Shape Control procedure function g is calculated ₁(X), g ₂(X) value, wherein g ₂(X)=max (| α _i-β _i|), α _ifor target flatness, i is band in the bar unit number of transverse direction, n be band at laterally total bar unit number, x _ifor band is at the coordinate of horizontal i-th unit;

C2-8) objective function F (X)=Ag is calculated ₁(X)+(1-A) g ₂(X) value, wherein A is weight coefficient;

C2-9) inequality F (X) <F is judged ₀set up? if inequality is set up, make F ₀=F (X), S _zbest=S _z, S _ybest=S _y, proceed to step c2-10); If inequality is false, then directly proceed to step c2-10);

C2-10) inequality is judged set up? if inequality is set up, make j _s=j _s+ 1, proceed to step c2-4); If inequality is false, proceed to step c2-11);

C2-11) inequality is judged set up? if inequality is set up, make i _s=i _s+ 1, proceed to step c2-3); If inequality is false, proceed to step c2-12);

C2-12) best left and right bending roller force S is obtained _zbest, S _ybest;

C3) calculating left bending roller force is S _zbest, right bending roller force is S _ybest, the best upper and lower roll shifting amount δ of roller amount of inclining when being η _sbest, δ _xbest, mainly comprise the following step that can be performed by computer:

C3-1) best roll shifting computational process variable i is defined _δ, j _δ, δ ' _s, δ ' _x;

C3-2) i is made _δ=0, j _δ=0;

C3-3) in order, roll shifting amount is δ ' _s=-δ _max+ i _δΔ δ;

C3-4) the lower roll shifting amount of order is δ ' _x=-δ _max+ j _δΔ δ;

C3-5) calculating roll shifting amount is δ ' _s, lower roll shifting amount is δ ' _x, roller amount of inclining is η, left bending roller force is S _zbest, right bending roller force is S _ybesttime band forward pull Distribution Value σ _1i;

C3-6) plate shape Distribution Value in units of I-Unit is calculated strip Shape Control procedure function g ₂(X)=max (| α _i-β _i|) value;

C3-7) objective function F (X)=Ag is calculated ₁(X)+(1-A) g ₂(X) value;

C3-8) inequality F (X) <F is judged ₀set up? if inequality is set up, make F ₀=F (X), δ _sbest=δ ' _s, δ _xbest=δ ' _x, proceed to step c3-9); If inequality is false, directly proceed to step c3-9);

C3-9) inequality is judged set up? if inequality is set up, make j _δ=j _δ+ 1, proceed to step c3-4); If inequality is false, proceed to step c3-10);

C3-10) inequality is judged set up? if inequality is set up, make i _δ=i _δ+ 1, proceed to step c3-3); If inequality is false, proceed to step c3-11);

C3-11) best upper and lower roll shifting amount δ is obtained _sbest, δ _xbest;

C4) calculating left bending roller force is S _zbest, right bending roller force is S _ybest, upper roll shifting amount is δ _sbest, lower roll shifting amount is δ _xbesttime the best to incline roller amount η _best;

C4-1) define the best to incline roller computational process variable i _η, η ';

C4-2) i is made _η=0;

C4-3) roller amount of inclining is made to be η '=-η _max+ i _ηΔ η;

C4-4) calculating roll shifting amount is δ _sbest, lower roll shifting amount is δ _xbest, roller amount of inclining is η ', left bending roller force is S _zbest, right bending roller force is S _ybesttime band forward pull Distribution Value σ _1i;

C4-5) plate shape Distribution Value in units of I-Unit is calculated strip Shape Control procedure function g ₂(X)=max (| α _i-β _i|) value;

C4-6) objective function F (X)=Ag is calculated ₁(X)+(1-A) g ₂(X) value;

C4-7) inequality F (X) <F is judged ₀set up? if inequality is set up, make F ₀=F (X), η _best=η ', proceeds to step c4-8); If inequality is false, directly proceed to step c4-8);

C4-8) inequality is judged set up? if inequality is set up, make i _η=i _η+ 1, then proceed to step c4-3); If inequality is false, proceed to step c4-9);

C4-9) the best roller amount η that inclines is obtained _best;

C5) inequality is judged $\sqrt{{({\mathrm{\&delta;}}_s-{\mathrm{\&delta;}}_{sbest})}^2+{({\mathrm{\&delta;}}_x-{\mathrm{\&delta;}}_{xbest})}^2+{(\mathrm{\&eta;}-{\mathrm{\&eta;}}_{best})}^2}<0.001$ Set up? if inequality is false, to making δ _s=δ _sbest, δ _x=δ _xbest, η=η _best, proceed to step c2) and place; If inequality is set up and is proceeded to step c6);

C6) best left bending roller force S is exported _zbest, right bending roller force S _ybest, upper roll shifting amount δ _sbest, lower roll shifting amount δ _xbest, incline roller amount η _bestcomplex wave control is carried out to planisher.