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

Abstract

A complex wave shape control method suitable for a four-roll skin pass unit, which mainly includes the following steps executed by a computer: (1) collecting equipment parameters; (2) collecting product rolling process parameters; (3) using asymmetric means Control the complex wave shape: ① Given the process variable of the up and down roll shifting amount, the initial value of the tilting amount, and the optimal step size of the bending force, the optimal step size of the roll shifting amount, and the optimal step size of the tilting amount; ② Calculate the up and down shifting amount The optimal left and right roll bending forces for the amount of rolls and tilting rolls, ③Calculate the left and right roll bending forces, and the optimal upper and lower roll shifting amounts for the amount of tilting rolls, ④Calculate the left and right bending forces, and the amount of up and down roll shifting Optimum roll tilting amount; ⑤ Output the best left bending roll force, right bending roll force, upper roll shifting amount, lower roll shifting amount, and roll tilting amount to control the complex wave shape of the skin pass mill. The present invention can effectively control complex wave shapes such as asymmetric local wave shapes and compound waves, improve the shape quality of finished products, and has further popularization and use value.

Description

A complex wave shape control method suitable for four-roll skin pass mill

technical field

The invention belongs to the technical field of steel rolling, in particular to a method for controlling the shape of a strip steel plate.

Background technique

In recent years, as most strip users have shifted from low-end to high-end, higher and higher requirements have been put forward for the quality of strip steel. Flattening, as a process closest to the finished product in strip production, has a great impact on improving the quality of finished strip steel. The quality of the plate shape plays a decisive role. Different from the cold rolling and hot rolling process, the reduction in the smoothing process is very small (generally between 0.5% and 2%), so the deformation heat and friction heat are very little during the rolling process, and the thermal crown of the roll can be almost ignored Therefore, it is impossible to finely control the plate shape of the leveling unit by means of subsection cooling. At present, for the four-roll skin pass unit, its conventional flatness control methods mainly include three types: tilting roll, symmetrical bending roll, and symmetrical roll shifting. The flatness defects that can be controlled mainly include unilateral waves, double-sided waves and middle waves, but it is helpless for complex wave shapes such as asymmetric partial waves and compound waves. In this way, how to use the leveling unit to finely control the complex wave shape has become the focus of on-site technical research.

references:

[1] Lian Jiachuang, Liu Hongmin. Plate Thickness and Shape Control [M]. Ordnance Industry Press. 1995

[2] Bai Zhenhua, Han Linfang, Li Jingzhou, et al. Research on flatness model of four-high rolling mill during abnormal rolling. Chinese Journal of Mechanical Engineering, 2012, 48

Contents of the invention

The object of the present invention is to provide a complex wave shape control method suitable for a four-roll skin pass unit that can control complex wave shapes such as asymmetric local wave shapes and compound waves, and improve the quality of the finished plate shape. The present invention mainly uses the basic data acquisition system and the shape mechanism model of the rolling mill to propose a set of asymmetric structure instead of the symmetrical structure, and change the shape control means from the traditional symmetrical bending roll (symmetrical roll shifting), tilting Rolls and other two-dimensional additions to the five-dimensional shape control idea of left bending roll, right bending roll, upper shifting roll, lower shifting roll and tilting roll, etc., aiming at the minimum difference between the actual shape and the target shape. A complex wave shape control method suitable for four-roll skin pass units,

The present invention mainly comprises the following steps carried out by the computer:

(a) Collection of basic equipment parameters, mainly including work roll diameter D _w , backup roll diameter D _b , work roll body length L _w , backup roll body length L _b , work roll bending cylinder The distance l _w , the distance between the center of the support roll pressing screw l _b , and the maximum positive roll bending force allowed by the rolling mill The maximum negative roll bending force allowed by the rolling mill The maximum roll shifting amount δ _max allowed by the rolling mill, and the maximum roll tilting amount η _max allowed by the rolling mill;

(b) Collect the basic rolling process parameters of typical specifications, mainly including strip thickness H, width B, deformation resistance k, rolling force P, rolling speed v, elongation Average inlet tension T ₀ , average outlet tension T ₁ , target shape coefficients a ₀ , a ₁ , a ₂ , a ₃ , a ₄ ;

(c) The realization of the four-roll skin pass unit using asymmetric means to control the complex wave shape mainly includes the following steps executed by the computer:

c1) Given the initial values of the upper roll shifting amount δ _s , the lower roll shifting amount δ _x , and the tilting amount η, as well as the optimal step size of the bending force ΔS, the optimal step size of the roll shifting amount Δδ, and the optimal step size of the tilting amount Δη ;

c2) Calculate the best left and right when the upper roll shifting amount is δ _s , the lower roll shifting amount is δ _x , and the tilting roll amount is η

Roll bending force S _zbest , S _ybest mainly include the following steps executed by computer:

c2-1) Define the optimal roll bending calculation process variables i _S , j _S , and the initial value of the objective function F ₀ ;

c2-2) Make i _S =0, j _S =0, take F ₀ =10 ¹⁰ ;

c2-3) Let the left bending roller force be

c2-4) Let the right bending roller force be

c2-5) Calculate the front tension distribution of the strip when the upper roll shifting amount is δ _s , the lower roll shifting amount is δ _x , the tilting roll amount is η, the left bending roll force is S _z , and the right bending roll force is S _y value σ _1i ;

c2-6) Calculate the shape distribution value with I-Unit as the unit In the formula, E is the elastic modulus of the strip, and v is Poisson's ratio;

c2-7) Calculate the value of g ₁ (X) and g ₂ (X) of the plate shape control process function, where g ₂ (X)＝max(|α _i -β _i |), α _i is the target plate shape, i is the strip element number of the strip in the transverse direction, n is the total strip element number of the strip in the transverse direction, and x _i is the coordinate of the i-th strip element of the strip in the transverse direction;

c2-8) Calculate the value of the objective function F(X)=A·g ₁ (X)+(1-A)·g ₂ (X), wherein A is a weighting coefficient;

c2-9) Determine if the inequality F(X)<F ₀ holds true? If the inequality is true, set F ₀ =F(X), S _zbest =S _z , S _ybest =S _y , and go to step c2-10); if the inequality is not true, go to step c2-10);

c2-10) Judging inequality Is it established? If the inequality is established, then set j _s =j _s +1, and proceed to step c2-4); if the inequality is not established, then proceed to step c2-11);

c2-11) Judging inequality Is it established? If the inequality is established, then make i _s =i _s +1, and turn to step c2-3); if the inequality is not established, then turn to step c2-12);

c2-12) Get the best left and right bending forces S _zbest , S _ybest ;

c3) Calculating the optimal upper and lower shifting amounts δ _sbest and δ _xbest when the left bending force is S _zbest , the right bending force is S _ybest , and the tilting amount is η, mainly including the following steps that can be executed by a computer:

c3-1) Define the optimal roll shifting calculation process variables i _δ , j _δ , δ′ _s , δ′ _x ;

c3-2) let i _δ =0, j _δ =0;

c3-3) Let the upper roll shifting amount be δ′ _s =-δ _max +i _δ Δδ;

c3-4) Let the amount of roll shifting be δ′ _x = -δ _max +j _δ Δδ;

c3-5) Calculate the front of the strip when the upper shifting amount is δ′ _s , the lower shifting amount is δ′ _x , the tilting amount is η, the left bending force is S _zbest , and the right bending force is S _ybest Tension distribution value σ _1i ;

c3-6) Calculate the shape distribution value with I-Unit as the unit shape control process function g ₂ (X) = the value of max(|α _i -β _i |);

c3-7) Calculate the value of the objective function F(X)=A·g ₁ (X)+(1-A)·g ₂ (X);

c3-8) Determine whether the inequality F(X)<F ₀ holds true? If the inequality is true, set F ₀ =F(X), δ _sbest =δ′ _s , δ _xbest =δ′ _x , and turn to step c3-9); if the inequality is not true, then directly turn to step c3-9);

c3-9) Judging inequality Is it established? If the inequality is established, then let j _δ =j _δ +1, and proceed to step c3-4); if the inequality is not established, then proceed to step c3-10);

c3-10) Judging inequality Is it established? If the inequality is established, then let i _δ =i _δ +1, and proceed to step c3-3); if the inequality is not established, then proceed to step c3-11);

c3-11) Obtain the best upper and lower roll shifting amounts δ _sbest , δ _xbest ;

c4) Calculating the best tilting amount η _best when the left bending force is S _zbest , the right bending force is S _ybest , the upper shifting amount is δ _sbest , and the lower shifting amount is δ _xbest ;

c4-1) define the optimum tilting roll calculation process variable i _η , η';

c4-2) let i _η =0;

c4-3) make the amount of tilting roll be η'=-η _max +i _η Δη;

c4-4) Calculate the front tension of the strip when the upper roll shifting amount is δ _sbest , the lower roll shifting amount is δ _xbest , the tilting roll amount is η', the left bending roll force is S _zbest , and the right bending roll force is S _ybest Distribution value σ _1i ;

c4-5) Calculate the shape distribution value with I-Unit as the unit shape control process function g ₂ (X) = the value of max(|α _i -β _i |);

c4-6) Calculate the value of the objective function F(X)=A·g ₁ (X)+(1-A)·g ₂ (X);

c4-7) Determine whether the inequality F(X)<F ₀ holds true? If the inequality is established, then make F ₀ =F(X), η _best =η', and proceed to step c4-8); if the inequality is not established, then directly proceed to step c4-8);

c4-8) Judging inequality Is it established? If the inequality is established then make i _η =i _η +1, then proceed to step c4-3); if the inequality is not established, then proceed to step c4-9);

c4-9) obtain optimum tilting amount η _best ;

c5) judgment inequality $\sqrt{{({\mathrm{\&delta;}}_{\mathrm{the\; s}}-{\mathrm{\&delta;}}_{\mathrm{the\; s}be\mathrm{the\; s}t})}^2+{({\mathrm{\&delta;}}_x-{\mathrm{\&delta;}}_{xbe\mathrm{the\; s}t})}^2+{(\mathrm{\&eta;}-{\mathrm{\&eta;}}_{be\mathrm{the\; s}t})}^2}<0.001$ Is it established? If the inequality is not established, then give order δ _s =δ _sbest , δ _x =δ _xbest , η=η _best , and turn to step c2); if the inequality is established, turn to step c6);

c6) Output the best left bending force S _zbest , right bending force _Sybest , up shifting δ _sbest , down shifting δ _xbest , and tilting η _best to control the complex wave shape of the skin pass mill.

Compared with the prior art, the present invention has the following advantages and effects:

Through the optimal setting of plate shape control parameters such as left bending roll, right bending roll, upper shifting roll, lower shifting roll, and tilting roll, it can effectively control complex wave shapes such as asymmetrical local waves and compound waves, and improve the quality of finished boards. It makes up for the congenital deficiency of plate shape control caused by the inability to use fine cooling in the skin pass unit, and has further promotion and use value.

Description of drawings

Fig. 1 is the total calculation flowchart of the present invention;

Fig. 2 is the realization flowchart of asymmetric means control complex wave shape of the present invention;

Fig. 3 is a flow chart of calculation of roll shifting force optimization in the present invention;

Fig. 4 is a flow chart of calculation of roll shifting amount optimization in the present invention;

Fig. 5 is the optimization calculation flow chart of tilting amount of the present invention;

Fig. 6 is the pretension stress distribution figure in the optimization process of example 1 of the present invention;

Fig. 7 is the shape value distribution diagram in the optimization process of Example 1 of the present invention;

Fig. 8 is a comparison chart of shape values after optimization of Example 1 of the present invention;

Fig. 9 is the pretension stress distribution diagram in the optimization process of Example 2 of the present invention;

Fig. 10 is the shape value distribution diagram in the optimization process of Example 2 of the present invention;

Fig. 11 is a comparison chart of optimized plate shape values in Example 2 of the present invention.

detailed description

Example 1

A complex wave shape control method suitable for a four-roll skin pass unit, as shown in Figure 1, first, in step (a), the basic equipment parameters are collected, mainly including the roll diameter D _w of the working roll = 500mm, the support roll Roll diameter D _b = 1100mm, work roll body length L _w = 1450mm, back-up roll body length L _b = 1450mm, work roll bending cylinder distance l _w = 2300mm, back-up roll screw center distance l _b = 2300mm, the maximum positive roll bending force allowed by the rolling mill The maximum negative roll bending force allowed by the rolling mill The maximum roll shifting amount δ _max allowed by the rolling mill is 200 mm, and the maximum roll tilting amount η _max allowed by the rolling mill is 150 μm.

Subsequently, in step (b), the collection thickness is 0.22mm, width is 1220mm, the basic rolling process parameter of the typical specification product of SPCC, main deformation resistance k=300MPa, rolling force P=4200KN, rolling Speed v=600m/min, elongation The average inlet tension T ₀ =80MPa, the average outlet tension T ₁ =120MPa, and the target shape coefficients a ₀ =0, a ₁ =0, a ₂ =0, a ₃ =0, a ₄ =0.

Subsequently, in step (c), the four-roll skin pass unit uses asymmetric means to control the complex wave shape, and the calculation process is shown in Figure 2:

Firstly, in step (c1), the upper roll shifting amount process variable δ _s =0 mm, the lower roll shifting amount process variable δ _x =0 mm, and the roll tilting amount η=0 μm are given as initial values and the roll bending force optimization step Length ΔS=1KN, roll shifting amount optimization step length Δδ=5mm, tilting roll amount optimization step length Δη=2μm;

Subsequently, in step (c2), the optimum left and right roll bending forces S are calculated when the upper shifting amount is δ _s =0 mm, the lower shifting amount is δ _x =0 mm, and the tilting amount is η=0 μm _zbest and _Sybest mainly include the following steps that can be executed by a computer, as shown in Figure 3:

First, in step (c2-1), define the optimal roll bending calculation process variables i _S , j _S , and the initial value of the objective function F ₀ ;

Subsequently, in step (c2-2), let i _S =0, j _S =0, take F ₀ =10 ¹⁰ ;

Subsequently, in step (c2-3), let the left bending roller force be

Subsequently, in step (c2-4), let the right bending roller force be

Subsequently, in step (c2-5), the upper roll shifting amount is calculated as δ _s =0 mm, the lower roll shifting amount as δ _x =0 mm, the tilting roll amount as η=0 μm, and the left bending roll force as S _z =- The front tension distribution value σ _1i of the strip when the right bending roller force is S _y =-500KN at 500KN, its front tension distribution value is shown in the curve a in Figure 6;

Subsequently, in step (c2-6), calculate the shape distribution value with I-Unit as the unit In the formula, E=2.1×10 ⁵ MPa is the elastic modulus of the strip, v=0.3 is Poisson’s ratio, and its shape value is shown in curve a in Figure 7;

Subsequently, in step (c2-7), the values of g ₁ (X) and g ₂ (X) of the shape control process functions are calculated, where $g_1\left(x\right)=\frac{1}{\mathrm{no}}\sqrt{\underset{i=1}{\overset{\mathrm{no}}{\&Sigma;}}{\left({\mathrm{\&alpha;}}_i-{\mathrm{\&beta;}}_i\right)}^2}=\frac{1}{28}\sqrt{\underset{i=1}{\overset{28}{\&Sigma;}}{\left({\mathrm{\&beta;}}_i\right)}^2}=5.40---I$ , g ₂ (X)=max(|α _i -β _i |)=max(|β _i |)=8.90I, α _i is the target plate shape, i is the bar number of the strip in the horizontal direction, 28 is the total number of strips of the strip in the transverse direction, and x _i is the coordinate of the i-th bar of the strip in the transverse direction

Subsequently, in step (c2-8), from the formula F(X)=A·g ₁ (X)+(1-A)·g ₂ (X)=0.5×5.406+0.5×8.908=7.16I, where A=0.5 is the weighting coefficient;

Subsequently, in step (c2-9), the judgment condition F(X)=7.16<F ₀ =10 ¹⁰ is established, and the best objective function F ₀ =F(X)=7.16I and the best left, Right bending roller force S _zbest =S _z =-500KN, _Sybest =S _y =-500KN and then turn to step (c2-10);

Subsequently, in step (c2-10), it is judged that the condition Established, then j _s =j _s +1=0+1=1, then turn to step (c2-4);

Subsequently, in step (c2-11), it is judged that the condition Established, then i _s =i _s +1=0+1=1, then turn to step (c2-3);

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

Subsequently, in step (c3), calculate the best upper and lower shifting amount δ when the left bending force is S _zbest =-459KN, the right bending force is S _ybest -459KN, and the inclination amount is η=0μm _sbest and δ _xbest mainly include the following steps that can be executed by a computer, as shown in Figure 4;

Subsequently, in step (c3-1), define the optimal roll shifting calculation process variables i _δ , j _δ , δ′ _s , δ′ _x ;

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

Subsequently, in step (c3-3), the amount of upper roll shifting is δ′ _s =-δ _max +i _δ Δδ=-200+0×5=-200mm;

Subsequently, in step (c3-4), the roll shifting amount is ordered to be δ′ _x =-δ _max +j _δ Δδ=-200+0×5=-200mm;

Subsequently, in step (c3-5), the upper roll shifting amount is calculated as δ _s = -200mm, the lower roll shifting amount as δ _x = -200mm, the tilting roll amount as η = 0μm, and the left bending roll force as S _z =-459KN, the front tension distribution value σ _1i of the strip when the right bending roller force is S _y =-459KN, and its front tension distribution value is shown in the curve b in the accompanying drawing 6;

Subsequently, in step (c3-6), calculate the shape distribution value with I-Unit as the unit Its flatness value is shown in curve b in Fig. 7, and the flatness control process function $g_1\left(x\right)=\frac{1}{\mathrm{no}}\sqrt{\underset{i=1}{\overset{\mathrm{no}}{\&Sigma;}}{({\mathrm{\&alpha;}}_i-{\mathrm{\&beta;}}_i)}^2}=\frac{1}{28}\sqrt{\underset{i=1}{\overset{28}{\&Sigma;}}{\left({\mathrm{\&beta;}}_i\right)}^2}=16.21---I,$ g ₂ (X)=max(|α _i -β _i |)=max(|β _i |)=41.72I;

Subsequently, in step (c3-7), the value of the objective function F(X)=A·g ₁ (X)+(1-A)·g ₂ (X) is calculated, F(X)=0.5×16.219 +0.5×41.726=28.97I;

Subsequently, in step (c3-8), the judgment condition F(X)=28.97<F ₀ =6.28 is not established, and directly proceeds to step (c3-9);

Subsequently, in step (c3-9), it is judged that the condition Established, then j _δ =j _δ +1=0+1=1, then turn to step (c3-4);

Subsequently, in step (c3-10), it is judged that the condition Established, then i _δ =i _δ +1=0+1=1, then go to step (c3-3);

Subsequently, in step (c3-11), the best upper and lower roll shifting amounts δ _sbest =90mm, δ _xbest =-95mm are obtained;

Subsequently, in step (c4), it is calculated that the left bending force is S _zbest = -459KN, the right bending force is S _ybest = -459KN, the upper roll shifting amount is δ _sbest = 90mm, and the lower rolling roll shifting amount is δ _xbest The optimal tilting amount η _best when =-95mm, as shown in Figure 5;

Subsequently, in step (c4-1), define the optimal tilting roll calculation process variable i _η , η'generation;

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

Subsequently, in the step (c4-3), the tilting amount is set to be η'=-η _max +i _η Δη=-150+0×2=-150 μm;

Subsequently, in step (c4-4), it is calculated that the upper roll shifting amount is δ _sbest =90mm, the lower roll shifting amount is δ _xbest =-95mm, the tilting roll amount is η'=-150μm, and the left bending roll force is S _{When zbest} = -459KN and the right bending roll force is _Sybest = -459KN, the front tension distribution value σ _1i of the strip is shown in the curve c in Figure 6;

Subsequently, in step (c4-5), calculate the shape distribution value with I-Unit as the unit Its flatness value is shown in curve c in Fig. 7, and the flatness control process function $g_1\left(x\right)=\frac{1}{\mathrm{no}}\sqrt{\underset{i=1}{\overset{\mathrm{no}}{\&Sigma;}}{({\mathrm{\&alpha;}}_i-{\mathrm{\&beta;}}_i)}^2}=\frac{1}{28}\sqrt{\underset{i=1}{\overset{28}{\&Sigma;}}{\left({\mathrm{\&beta;}}_i\right)}^2}=10.88---I,$ g ₂ (X)=max(|α _i -β _i |)=max(|β _i |)=24.94I;

Subsequently, in step (c4-6), the value F(X)=0.5×10.887+ of the objective function F(X)=A·g ₁ (X)+(1-A)·g ₂ (X) is calculated 0.5×24.948=17.92I;

Subsequently, in step (c4-7), the judgment condition F(X)=17.92<F ₀ =5.76 is not established, and directly proceeds to step (c4-8);

Subsequently, in step (c4-8), it is judged that the condition Set up, then i _η =i _η +1=0+1=1, then proceed to step (c4-3);

Subsequently, in step (c4-9), obtain current optimum tilting amount η _best =0 μm;

Subsequently, in step (c5), the judgment condition (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 not established, then given δ _s ＝δ _sbest ＝90mm, δ _x ＝δ _xbest ＝-95mm, η＝η _best ＝0μm as initial values Enter step (c2).

Finally, in step (c6), the best left bending force is S _zbest =236KN, the best right bending force is S _ybest =-500KN, the best upper shifting amount is δ _sbest =125mm, the best lower The roll shifting amount is δ _xbest = -40mm, and the optimal roll tilting amount is η _best = 112μm to control the complex wave shape of the tempering machine, as shown in Figure 8, the curve c in the figure is the best plate shape objective function value F (X)=3.69I; Among the figure, curve b is the best plate shape objective function value F(X)=5.84I controlled by conventional means, compared with conventional control means, the objective function of the present embodiment reduces 36.8%; Curve a in the figure is the shape distribution without control means, and the shape is the worst.

Example 2

First, collect the basic equipment parameters in step (a), mainly including the roll diameter D _w of the work roll = 500mm, the roll diameter D _b of the backup roll = 1100mm, the roll body length L _w of the work roll = 1450mm, the roll diameter of the backup roll Body length L _b = 1450mm, work roll bending cylinder distance l _w = 2300mm, back-up roll screw center distance l _b = 2300mm, maximum positive roll bending force allowed by the rolling mill The maximum negative roll bending force allowed by the rolling mill The maximum roll shifting amount δ _max allowed by the rolling mill is 200 mm, and the maximum roll tilting amount η _max allowed by the rolling mill is 150 μm.

Subsequently, in step (b), collecting thickness is 0.22mm, width is 1220mm, and the basic rolling process parameter of the typical specification product of SPCD mainly comprises strip deformation resistance k=300MPa, rolling force P=4200KN, Rolling speed v=600m/min, elongation The average inlet tension T ₀ =80MPa, the average outlet tension T ₁ =120MPa, and the target shape coefficients a ₀ =0, a ₁ =0, a ₂ =0, a ₃ =0, a ₄ =0.

Subsequently, in step (c), the four-roll skin pass unit uses asymmetric means to control the complex wave shape:

Firstly, in step (c1), the upper roll shifting amount process variable δ _s =0 mm, the lower roll shifting amount process variable δ _x =0 mm, and the roll tilting amount η=0 μm are given as initial values and the roll bending force optimization step Length ΔS=1KN, roll shifting amount optimization step length Δδ=5mm, tilting roll amount optimization step length Δη=2μm;

Subsequently, in step (c2), the optimum left and right roll bending forces S are calculated when the upper shifting amount is δ _s =0 mm, the lower shifting amount is δ _x =0 mm, and the tilting amount is η=0 μm _zbest and _Sybest mainly include the following steps that can be executed by a computer:

First, in step (c2-1), define the optimal roll bending calculation process variables i _S , j _S , and the initial value of the objective function F ₀ ;

Subsequently, in step (c2-2), let i _S =0, j _S =0, take F ₀ =10 ¹⁰ ;

Subsequently, in step (c2-3), let the left bending roller force be

Subsequently, in step (c2-4), let the right bending roller force be

Subsequently, in step (c2-5), the upper roll shifting amount is calculated as δ _s =0 mm, the lower roll shifting amount as δ _x =0 mm, the tilting roll amount as η=0 μm, and the left bending roll force as S _z =- The front tension distribution value σ _1i of the strip when the right bending roller force is S _y =-500KN at 500KN, the front tension stress distribution is shown in curve a in Figure 9;

Subsequently, in step (c2-6), calculate the shape distribution value with I-Unit as the unit In the formula, E=2.1×10 ⁵ MPa is the elastic modulus of the strip, v=0.3 is the Poisson’s ratio, and its plate shape distribution value is shown in curve a in Figure 10;

Subsequently, in step (c2-7), the values of g ₁ (X) and g ₂ (X) of the shape control process functions are calculated, where $g_1\left(x\right)=\frac{1}{\mathrm{no}}\sqrt{\underset{i=1}{\overset{\mathrm{no}}{\&Sigma;}}{({\mathrm{\&alpha;}}_i-{\mathrm{\&beta;}}_i)}^2}=\frac{1}{28}\sqrt{\underset{i=1}{\overset{28}{\&Sigma;}}{\left({\mathrm{\&beta;}}_i\right)}^2}=5.71---I,$ g ₂ (X)＝max(|α _i -β _i |)＝max(|β _i |)＝12.68I, α _i is the target plate shape, i is the bar number of the strip in the horizontal direction, 28 is the total number of strips of the strip in the transverse direction, and x _i is the coordinate of the i-th bar of the strip in the transverse direction

Subsequently, in step (c2-8), from the formula F(X)=A·g ₁ (X)+(1-A)·g ₂ (X)=0.5×5.406+0.5×8.908=9.20I, where A=0.5 is the weighting coefficient;

Subsequently, in step (c2-9), the judgment condition F(X)=9.20<F ₀ =10 ¹⁰ is established, and the best objective function F ₀ =F(X)=9.20I and the best left, Right bending roller force S _zbest =S _z =-500KN, _Sybest =S _y =-500KN and then turn to step (c2-10);

Subsequently, in step (c2-10), it is judged that the condition $j_{\mathrm{the\; s}}=0<\frac{S_{max}^{+}-S_{max}^{-}}{\mathrm{\&Delta;}S}=\frac{500-(-500)}{1}=1000$ Established, then j _s =j _s +1=0+1=1, then turn to step (c2-4);

Subsequently, in step (c2-11), it is judged that the condition $i_{\mathrm{the\; s}}=0<\frac{S_{max}^{+}-S_{max}^{-}}{\mathrm{\&Delta;}S}=\frac{500-(-500)}{1}=1000$ Established, then i _s =i _s +1=0+1=1, then turn to step (c2-3);

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

Subsequently, in step (c3), calculate the optimum upper and lower roll shifting amounts δ when the left bending force is S _zbest = -100KN, the right bending force is S _ybest = 95KN, and the inclination amount is η = 0 μm _sbest and δ _xbest mainly include the following steps that can be executed by a computer;

Subsequently, in step (c3-1), define the optimal roll shifting calculation process variables i _δ , j _δ , δ′ _s , δ′ _x ;

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

Subsequently, in step (c3-3), the amount of upper roll shifting is δ′ _s =-δ _max +i _δ Δδ=-200+0×5=-200mm;

Subsequently, in step (c3-4), the roll shifting amount is ordered to be δ′ _x =-δ _max +j _δ Δδ=-200+0×5=-200mm;

Subsequently, in step (c3-5), the upper roll shifting amount is calculated as δ _s = -200mm, the lower roll shifting amount as δ _x = -200mm, the tilting roll amount as η = 0μm, and the left bending roll force as S _z =-100KN, the front tension distribution value σ _1i of the strip when the right bending roller force is S _y =95KN, its front tension distribution is shown in curve b in Figure 9;

Subsequently, in step (c3-6), calculate the shape distribution value with I-Unit as the unit The flatness distribution value is shown in the curve b in Fig. 10, and the flatness control process function $g_1\left(x\right)=\frac{1}{\mathrm{no}}\sqrt{\underset{i=1}{\overset{\mathrm{no}}{\&Sigma;}}{({\mathrm{\&alpha;}}_i-{\mathrm{\&beta;}}_i)}^2}=\frac{1}{28}\sqrt{\underset{i=1}{\overset{28}{\&Sigma;}}{\left({\mathrm{\&beta;}}_i\right)}^2}=24.89---I,$ g ₂ (X)=max(|α _i -β _i |)=max(|β _i |)=47.31I;

Subsequently, in step (c3-7), the value of the objective function F(X)=A·g ₁ (X)+(1-A)·g ₂ (X) is calculated, F(X)=0.5×24.895 +0.5×47.31=36.10I;

Subsequently, in step (c3-8), the judgment condition F(X)=28.97<F ₀ =8.18 is not established, and directly proceeds to step (c3-9);

Subsequently, in step (c3-9), it is judged that the condition Established, then j _δ =j _δ +1=0+1=1, then turn to step (c3-4);

Subsequently, in step (c3-10), it is judged that the condition Established, then i _δ =i _δ +1=0+1=1, then go to step (c3-3);

Subsequently, in step (c3-11), the best upper and lower roll shifting amounts δ _sbest =30mm, δ _xbest =-60mm are obtained;

Subsequently, in step (c4), it is calculated that the left bending roll force is S _zbest =-100KN, the right bending roll force is S _ybest =95KN, the upper roll shifting amount is δ _sbest =30mm, and the lower roll shifting amount is δ _xbest = The best tilting amount η _best when -60mm;

Subsequently, in step (c4-1), define the optimal tilting roll calculation process variable i _η , η'generation;

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

Subsequently, in the step (c4-3), the tilting amount is set to be η'=-η _max +i _η Δη=-150+0×2=-150 μm;

Subsequently, in step (c4-4), the upper roll shifting amount is calculated as δ _sbest =30mm, the lower roll shifting amount as δ _xbest =-60mm, the tilting roll amount as η'=-150μm, and the left bending roll force as S _{When zbest} = -100KN and the right bending roll force is _Sybest = 95KN, the front tension distribution value σ _1i of the strip is shown as c in Figure 9;

Subsequently, in step (c4-5), calculate the shape distribution value with I-Unit as the unit The flatness distribution value is shown as c in Fig. 10, and the flatness control process function $g_1\left(x\right)=\frac{1}{\mathrm{no}}\sqrt{\underset{i=1}{\overset{\mathrm{no}}{\&Sigma;}}{({\mathrm{\&alpha;}}_i-{\mathrm{\&beta;}}_i)}^2}=\frac{1}{28}\sqrt{\underset{i=1}{\overset{28}{\&Sigma;}}{\left({\mathrm{\&beta;}}_i\right)}^2}=24.89---I.$ g ₂ (X)=max(|α _i -β _i |)=max(|β _i |)=47.31I;

Subsequently, in step (c4-6), the value F(X)=0.5×24.895+ of the objective function F(X)=A·g ₁ (X)+(1-A)·g ₂ (X) is calculated 0.5×47.31=36.10I;

Subsequently, in step (c4-7), the judgment condition F(X)=36.10<F ₀ =7.66 is not established, and directly proceeds to step (c4-8);

Subsequently, in step (c4-8), the judgment condition Set up, then i _η =i _η +1=0+1=1, then proceed to step (c4-3);

Subsequently, in step (4-9), obtain current optimum tilting amount η _best =10 μm;

Subsequently, in step (c5), the judgment condition (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 not established, then given δ _s ＝δ _sbest ＝30mm, δ _x ＝δ _xbest ＝-60mm, η＝η _best ＝10μm as initial values Enter step (c2).

Finally, in step (c6), the best left bending force is S _zbest = 196KN, the best right bending force is S _ybest = 136KN, the best upward shifting amount is δ _sbest = 50mm, the best downward shifting The amount of rolls is δ _x best = 10mm, the best tilting amount is η _best = 42 μm, and the complex wave shape control is performed on the skin pass mill, as shown in Figure 11, the curve c in the figure is the best plate shape objective function value F (X)=1.84I; Curve b in the figure is the best plate shape objective function value F(X)=2.66I after the asymmetric control controlled by conventional means, compared with conventional control means, the objective function is reduced by 30.8%; Curve a in the figure is the flatness distribution diagram without control means, and the flatness is the worst.

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.