CN106547959A - A kind of CVC roller shape parameter optimized calculation method minimum based on roll neck variance - Google Patents

Abstract

A kind of CVC roller shape parameter optimized calculation method minimum based on roll neck variance, it includes following the step of performed by computer：(1) collect basic equipment parameter；(2) product parameters of ideal format strip steel in the record of production are collected；(3) give optimization interval [A_1min,A_1max], and optimization step delta A；(4) optimal roller shape parameter searching process intermediate parameters i, object function initial value F are defined₀；(5) calculate the toe-out stress distribution numerical value of outlet strip steel；(6) calculate roller shape parameter A_iThe width numerical value of lower ideal format belt steel product；(7) export optimum roller shape first order parameter A_{1_best}, draw the roll shape curve under this roller shape parameter.Present invention decreases the roll neck variance value of upper working rolls and lower working rolls, alleviate the milling train asymmetrical rolling effect caused due to the exceeded caused roll linear velocity difference of upper working rolls and lower working rolls roll neck difference, the strip shape quality of outlet strip steel is ensure that, in solving the problems, such as conventional roller shape parameter design calculation process, ignores belt plate shape quality control.

Description

CVC (continuously variable crown) roll shape parameter optimization calculation method based on minimum roll diameter variance

Technical Field

The invention relates to a cold-rolled strip steel leveling technology, in particular to a calculation method for roll shape parameter optimization.

Background

At present, in the field of strip steel flat rolling, the roll shape configuration types of rolling mills are more and more diversified, and a four-roll CVC rolling mill can rapidly and continuously change the roll gap crown according to the crown control requirement of strip steel, has strong control capability on the strip steel shape, and can be widely applied to freely rolling the incoming strip steel with different steel types and specifications. The upper and lower working rolls of the CVC rolling mill are arranged in an antisymmetric manner, the rolling mill axially moves the rolls in opposite directions with equal size through the upper and lower working rolls to adjust the roll gap crown so as to adapt to strip steels with different specifications and incoming material crown, the roll body curve of the CVC rolling mill is S-shaped, the common curve is a cubic polynomial, and the roll shape curve expression of the upper working roll is R_up(x)＝A₀+A₁x+A₂x²+A₃x³The expression of the roll-shape curve of the lower working roll is R_down(x)＝R_up(L-x), a reasonable working roll shape curve can be designed by optimizing roll shape parameters on site, and the initial convexity of incoming strip steel is controlled by using the roll gap convexity formed in the roll shifting process of the upper and lower working rolls. However, in actual production, an unreasonable roll body curve can cause uneven wear of the roll, greatly reduce the plate shape control precision of the rolling mill, and directly influence the plate shape quality of the finished strip steel. Therefore, how to optimally calculate the CVC roll body curve meeting the strip steel leveling procedure in the production field according to the convexity and strip shape control requirements of incoming strip steel so as to improve the strip shape quality of the strip steelHas become the key point of field technical attack. At present, the design and calculation of the primary coefficient of the roll shape parameter of the CVC rolling mill are mainly determined from the angles of axial stress of a roll, the transverse thickness difference of outlet strip steel, the change trend of a roll body curve of the roll and the like, the influence on the shape quality of the outlet strip steel is not considered, and the shape is an important index for a downstream client to judge the quality of strip steel products.

Reference to the literature

[1] Even the family creation, liu hongmin, plate thickness and shape control [ M ]. beijing: weapon industry Press 1995:1-90.

[2] White shaghua, liu hongmin, li xijun, etc. planishing rolling process model [ M ]. beijing: publication of metallurgical industry 2010: 1-100.

[3] Liuguang, manhong shuang, changan, etc. CVC rolling mill roll shape curve design and equivalent crown discussion [ J ]. university of northeast (natural science edition), 2008, 29 (10): 1444-1446.

Disclosure of Invention

The invention aims to provide a CVC (continuously variable crown) roll forming parameter optimization calculation method based on minimum roll diameter variance, which can improve the strip shape quality of strip steel and reduce the roll diameter variance of upper and lower working rolls. The method fully considers the specification difference of incoming strip steel and the crown control requirement of strip steel with different specifications, sets the roll diameter variance of upper and lower working rolls of a CVC temper mill unit as an objective function aiming at all strip steel with typical specifications of a production field, takes the shape of the outlet strip steel as a constraint condition, obtains a roll shape grinding primary coefficient meeting the actual production by carrying out optimization calculation on roll shape parameters, is favorable for reducing the roll diameter variance value of the upper and lower working rolls of a rolling mill, and can ensure the shape quality of the outlet strip steel.

The invention includes the following computer-implemented steps:

(a) collecting basic equipment parameters, mainly including roll diameter D of working roll_wRoll diameter D of the support roll_bWorking rollLength L of the roll body_wLength L of the body of the support roll_bDistance l between the working roll and the roll bending cylinder_wCenter distance l of screw pressed by support roller_bBending force S of working roll of rolling mill_Qj(j ═ 1,2, 3.) variation range of roll shifting quantity s of CVC temper mill set [ s ]_min,s_max]Coefficient of quadratic term A of roll form₂Coefficient of cubic term of roller type A₃Initial radius parameter A of roller₀Q is the steel type code of the strip steel, and j is the serial number of the typical specification strip steel counted on site;

(b) collecting the products of typical specification strip steel and rolling process parameters in production record, mainly including width value B of typical specification strip steel_QjThickness H of strip steel_QjStrip steel yield strength sigma_QsTotal elongation of_QjTotal rolling pressure P of the frame of the temper mill_Qj(ii) a Transverse distribution value L of incoming material plate shape_QiFront and rear tension T of levelling machine set_Qj_₁、T_Qj_₀And rolling speed v_QjWherein, i is a serial number i of strip elements divided in the width direction of the strip steel, which is 1,2 and 3;

(c) l is defined as the length of the working roll barrel of the rolling mill, A₁To optimize the calculated roll shape parameters, A_{1_best}Obtaining the optimal roll shape parameter first-order coefficient for optimization;

(d) first order coefficient A of given roll shape parameter₁Optimized interval of [ A ]_1min,A_1max]And an optimization step Δ a;

(e) defining intermediate parameter i and initial value F of target function in optimum roll shape parameter optimizing process₀；

(f) Let i equal to 0, take F₀＝10¹⁰；

(g) Let the initial value of the optimization of the roll shape parameter be A_i＝A_1min+iΔA；

(h) Calculating the distribution value sigma of the tensile stress of the outlet strip steel by using the elastic deformation model and the metal deformation model of the roller system_1i＝f(A_i,H_Qi,L_Qi,B_Qj,T_Qj_₀,T_Qj_₁) (unit: MPa), A_iDetermining the roll profile distribution of the roll;

(i) calculating the distribution value of the plate shape by taking I-Unit as a Unit

(j) Calculating the sheet shape peak index g (X) ═ max (α)_i)-min(α_i) I (unit: I);

(k) judgment inequality g (X) is less than or equal to g (X)_max(g(X)_maxIs a quality control parameter for the panel shape)? If the inequality is true, the step (l) is carried out for calculation; if the inequality is not true, the step (g) is carried out, the roll shape curve parameters are determined again, and calculation is carried out;

(l) Calculating the roll shape parameter A_iWidth value B of lower typical specification strip steel product_Qj(j 1,2, 3.) corresponding variance of roll diameter(unit: μm):

(m) applying a roll shape parameter A_iMaximum value of variance of roll diameter under the conditionIs marked as(x) calculating an objective function for optimization of roll shape parameters;

(n) judgment of the inequality F (X) < F₀(X) is true? If the inequality holds, let F₀＝F(X)，A_{1_best}＝A_iAnd (f) turning to the step (o); if it is notIf the inequality is not true, directly switching to the step (o);

(o) judgment inequalityIs there any? If the inequality is true, making i equal to i +1, then turning to the step (g), and continuing to search the roll forming parameters; if the inequality is not true, directly turning to the step (p);

(p) outputting the optimal roll shape first order term parameter A_{1_best}And drawing a roll shape curve under the roll shape parameters.

Compared with the prior art, the invention has the following advantages:

the width variation range of different specifications of strip steel in a production field is fully considered, according to the convexity and plate shape control requirements of incoming strip steel, the plate shape of the outgoing strip steel is taken as a constraint condition, roll shape grinding parameters meeting actual production are obtained by performing optimization calculation on the roll shape parameters, on the basis of ensuring the equivalent convexity control capability of a rolling mill, the plate shape value of the outgoing strip steel is improved, the roll diameter variance value of upper and lower working rolls is reduced, the asynchronous rolling effect of the rolling mill caused by the linear speed difference of the rolls due to the fact that the roll diameter difference value of the upper and lower working rolls exceeds the standard is favorably relieved, the abrasion of the rolls is more uniform, the problem that the shape quality control of the strip steel is neglected in the roll shape parameter design calculation process in the prior art is solved, a roll shape parameter design calculation system of a CVC rolling mill.

Drawings

FIG. 1 is a total calculation flow diagram of the present invention;

FIG. 2 is a profile diagram of a T-2.5MA steel grade 0.305mm by 998mm specification strip steel in the roll shape parameter optimization process in example 1 of the present invention;

FIG. 3 is a graph showing the roll shape after optimization of roll shape parameters in example 1 of the present invention;

FIG. 4 is a profile distribution diagram of a strip steel with a specification of 0.315mm x 786mm in a T-2MA steel grade in the roll shape parameter optimization process in example 2 of the present invention;

FIG. 5 is a graph of roll shape after optimization of roll shape parameters in example 2 of the present invention;

FIG. 6 is a graph comparing the roll profile after optimization of the roll profile parameters in inventive example 1 and example 2.

Detailed Description

Example 1

A CVC roll forming parameter optimization calculation method based on minimum roll diameter variance is disclosed, the calculation flow of which is shown in figure 1, and the method comprises the following steps:

(a) collecting basic equipment parameters, mainly including roll diameter D of working roll_w450mm, roll diameter D of the support roll_b1150mm roll length L of work roll_w1620mm, roll body length L of the support roll_b1380mm, distance l of working roll bending cylinder_w2300mm, support roller screw down center distance l_b2300mm, bending force S of working roll of rolling mill 200,80,120,110, 100,50,60 KN, change range of roll shifting S of CVC rolling mill [ -120mm,120mm]Coefficient of quadratic term A₂＝-0.169563×10^-5Coefficient of cubic term of roller type A₃＝0.635066×10^-9Initial radius parameter A of roller₀The rolling process parameters of two typical specification steel grades MR T-3BA and MR T-2.5BA are counted as 225, which is shown in Table 1.

TABLE 1 Specifications and Rolling Process parameters for typical Steel grades

(b) Collecting product parameters of typical specification strip steel in production recordMainly comprises a width value B of the strip steel according to typical specifications_Qj(j＝1,2,3...)：

B_T3＝780mm,875mm,994mm,1105mm，

B_T2.5＝725mm,785mm,870mm,998mm；

The thickness value of the strip steel is as follows: h_T3＝0.325mm,0.285mm,0.298mm,0.304mm，

H_T2.5＝0.298mm,0.305mm,0.285mm,0.305mm；

Strip steel yield strength sigma_{s_T2.5}＝250MPa，σ_{s_T3}270MPa, total rolling pressure of the temper mill stand:

P_T3＝2.2MN,1.9MN,2.0MN,2.1MN，

P_T2.5＝1.9MN,2.4MN,2.0MN,1.8MN；

total elongation_Qj0.9%, 1.0%, 1.05%, 1.1%, 0.9%, 1.0%, 1.05%, 1.1%; transverse distribution value L of incoming material plate shape_Qi0, rear tension and front tension of the leveling unit:

T_{T3_0}＝85N·mm^-2,70N·mm^-2,94N·mm^-2,85N·mm^-2，

T_{T3_1}＝100N·mm^-2,90N·mm^-2,105N·mm^-2,98N·mm^-2，

T_{T2.5_0}＝90N·mm^-2,75N·mm^-2,85N·mm^-2,85N·mm^-2，

T_{T2.5_1}＝105N·mm^-2,85N·mm^-2,85N·mm^-2,100N·mm^-2；

and the rolling speed:

v_T3＝500m·min^-1,498m·min^-1,576m·min^-1,480m·min^-1，

v_T2.5＝520m·min^-1,510m·min^-1,480m·min^-1,476m·min^-1。

(c) l is defined as the length of the working roll barrel of the rolling mill, A₁To optimize the calculated roll shape parameters, A_{1_best}Obtaining the optimal roll shape parameter first-order coefficient for optimization;

(d) first order coefficient A of given roll shape parameter₁Optimization interval of [0.126427 × 10^-2,0.146427×10^-2]And the optimization step Δ a is 0.0002;

(e) defining intermediate parameter i and initial value F of target function in optimum roll shape parameter optimizing process₀；

(f) Let i equal to 0, take F₀＝10¹⁰；

(g) Let the initial value of the optimization of the roll shape parameter be A_i＝A_1min+iΔA＝0.126427×10-²；

(h) Calculating the distribution value sigma of the tensile stress of the outlet strip steel by using the elastic deformation model and the metal deformation model of the roller system_1i(i ═ 1,2, 3.) (unit: MPa);

σ_1i＝{13.64,10.06,6.99,4.47,2.50,1.10,0.27,0,0.30,1.17,2.60,

4.59,7.15,10.24,13.84}；

(i) calculating the distribution value of the plate shape by taking I-Unit as a Unit

α_i＝{3.64，2.09，0.75，-0.35，-1.2，-1.81，-2.17，-2.28，-2.16，-1.78，-1.15，

-0.29，0.82，2.16，3.73}；

(j) Calculating the sheet shape peak index g (X) ═ max (α)_i)-min(α_i) Equal to 6.01 (unit: I)

(k) Judgment inequality g (X) is less than or equal to g (X)_max(g(X)_maxTaking the value of the peak value of the plate-shaped quality control parameter as g (X)_max10), 6.01I < 10I, the inequality is true, and step (l) is performed;

(l) Calculating the roll shape parameter A_iWidth values of strip steel products of all typical specifications

B_Qj(j 1,2, 3.) corresponding roll diameter variance value

Wherein,

(unit: μm)

(m) applying a roll shape parameter A_iMaximum value of variance of lower roll diameterIs marked asThe maximum value of the variance of the roll diameter at this time was f (x) 154.464 μm;

(n) inequality F (X) < 10¹⁰Is established, let F₀＝F(X)，A_{1_best}＝0.126427×10^-2And (f) turning to the step (o);

(o) inequalityIf so, making i-i + 1-1, and then proceeding to step (g); if the inequality is not true, directly switching to the step (p);

(p) outputting the optimal roll shape first order term parameter A_{1_best}＝0.130623×10^-2Drawing a roll shape curve under the roll shape parameter;

for comparison, the roll diameter variance value after the optimization of the roll shape parameters is compared with the roll diameter variance value before the optimization, as shown in table 2, the roll diameter variance value after the optimization is reduced from 149.889 μm to 113.073 μm; as shown in fig. 2, the strip shape calculation distribution of the T-2.5MA steel grade 0.305mm × 998mm specification strip steel in the roll shape parameter optimization calculation process is given, and the strip shape value is 6.01I; as shown in fig. 3, a roll shape curve after optimization of the roll shape parameters is given; the plate shape statistics of the strip steels of other steel specifications are shown in Table 3, the maximum value of the plate shape value of the outlet strip steel is 7.36I, the average plate shape value is 5.595I, and the plate shape quality can be controlled at a higher level.

TABLE 2 roll diameter variance before and after optimization of roll shape parameters

TABLE 3 statistical values of strip shape during optimization of roll shape parameters

As shown in fig. 6, it can be seen that the change trend of the optimized new roll profile curve in the axial direction of the roll is more gradual, the asynchronous rolling effect of the rolling mill is reduced on the premise of ensuring the strip shape quality of the outlet strip steel, the uniform abrasion of the roll is facilitated, and the service life of the roll is prolonged.

Example 2

A CVC roll forming parameter optimization calculation method based on minimum roll diameter variance comprises the following steps executed by a computer:

(a) collecting basic equipment parameters, mainly including roll diameter D of working roll_w450mm, roll diameter D of the support roll_b1150mm roll length L of work roll_w1620mm, roll body length L of the support roll_b1380mm, distance l of working roll bending cylinder_w2300mm, support roller screw down center distance l_b2300mm, bending force S of working roll of rolling mill 200,80,120,110,105,40,70,80 KN, change range of roll shifting S of CVC rolling mill [ -120mm,120mm]Coefficient of quadratic term A₂＝-0.169563×10^-5Coefficient of cubic term of roller type A₃＝0.635066×10^-9Initial radius parameter A of roller₀The rolling process parameters of two typical specification steel grades MR T-3BA and MR T-2BA are counted as shown in Table 4.

TABLE 4 Specifications and Rolling Process parameters for typical Steel grades

(b) Collecting the product parameters of the typical specification strip steel in the production record, and mainly comprising the width value B of the strip steel according to the typical specification_Qj(j＝1,2,3...)：

B_T3＝780mm,875mm,994mm,1105mm，

B_T2＝735mm,786mm,870mm,934mm；

The thickness value of the strip steel is as follows: h_T3＝0.325mm,0.285mm,0.298mm,0.304mm，

H_T2＝0.278mm,0.315mm,0.275mm,0.285mm；

Strip steel yield strength sigma_{s_T2}＝240MPa，σ_{s_T3}270MPa, FlatThe total rolling pressure of the whole machine set frame is as follows:

P_T3＝2.2MN,1.9MN,2.0MN,2.1MN，

P_T2＝1.7MN,2.3MN,2.1MN,1.9MN；

total elongation_Qj0.9%, 1.0%, 1.05%, 1.1%, 0.8%, 0.9%, 1.0%, 1.05%, transverse distribution value L of the incoming sheet shape_Qi0, rear tension and front tension of the leveling unit:

T_{T3_0}＝85N·mm^-2,70N·mm^-2,94N·mm^-2,85N·mm^-2，

T_{T3_1}＝100N·mm^-2,90N·mm^-2,105N·mm^-2,98N·mm^-2，

T_{T2_0}＝85N·mm^-2,75N·mm^-2,80N·mm^-2,95N·mm^-2，

T_{T2_1}＝100N·mm^-2,95N·mm^-2,85N·mm^-2,105N·mm^-2；

and the rolling speed:

v_T3＝500m·min^-1,498m·min^-1,576m·min^-1,480m·min^-1，

v_T2＝510m·min^-1,510m·min^-1,498m·min^-1,486m·min^-1。

(c) l is defined as the length of the working roll barrel of the rolling mill, A₁To optimize the calculated roll shape parameters, A₁__bestObtaining the optimal roll shape parameter first-order coefficient for optimization;

(d) first order coefficient A of given roll shape parameter₁Optimization interval of [0.126427 × 10^-2,0.146427×10^-2]And the optimization step Δ a is 0.0002;

(e) statorIntermediate parameter i and initial value F of target function in the optimization process of sense-optimal roll shape parameter₀；

(f) Let i equal to 0, take F₀＝10¹⁰；

(g) Let the initial value of the optimization of the roll shape parameter be A_i＝A_1min+iΔA＝0.126427×10^-2；

(h) Calculating the distribution value sigma of the tensile stress of the outlet strip steel by using the elastic deformation model and the metal deformation model of the roller system_1i(i ═ 1,2, 3.) (unit: MPa);

σ_1i＝{11.56,8.53,5.92,3.79,2.12,0.93,0.23,0,0.25,0.99,2.2,

3.89,6.06,8.68,11.73}；

(i) calculating the distribution value of the plate shape by taking I-Unit as a Unit

α_i＝{3.08,1.77,0.64,-0.30,-1.02,-1.53,-1.83,-1.93,-1.83,-1.51,-0.97,

-0.25,0.69,1.83,3.16}；

(j) Calculating the sheet shape peak index g (X) ═ max (α)_i)-min(α_i) | ═ 5.09 (unit: I)

(k) Judgment inequality g (X) is less than or equal to g (X)_max(g(X)_maxTaking the value of the peak value of the plate-shaped quality control parameter as g (X)_max10), 5.09I < 10I, the inequality is true, and step (l) is performed;

(l) Calculating the roll shape parameter A_iWidth values of strip steel products of all typical specifications

B_Qj(j 1,2, 3.) corresponding roll diameter variance value

Wherein,

(unit: μm)

(m) applying a roll shape parameter A_iMaximum value of variance of lower roll diameterIs marked asThe maximum value of the variance of the roll diameter at this time was f (x) 153.409 μm;

(n) inequality F (X) < 10¹⁰Is established, let F₀＝F(X)，A_{1_best}＝0.126427×10^-2And (f) turning to the step (o);

(o) inequalityIf so, making i-i + 1-1, and then proceeding to step (g); if the inequality is not true, directly switching to the step (p);

(p) outputting the optimal roll shape first order term parameter A_{1_best}＝0.129337×10^-2Drawing a roll shape curve under the roll shape parameter;

for comparison, the roll diameter variance value after optimization by using the roll shape parameters of the invention is compared with the roll diameter variance value before optimization, and as shown in table 4, the roll diameter variance value after optimization is reduced from 149.889 μm to 111.376 μm; as shown in fig. 4, the strip shape calculation distribution of the T-2MA steel grade 0.315mm × 786mm specification strip steel in the roll shape parameter optimization calculation process is given, and the strip shape value is 5.09I; as shown in fig. 5, a roll shape curve after optimization of the roll shape parameters is given; the plate shape statistics of the strip steels of other steel specifications are shown in Table 5, the maximum value of the plate shape value of the outlet strip steel is 7.65I, the average plate shape value is 5.726I, and the plate shape quality can be controlled at a higher level.

As shown in fig. 6, it can be seen that the change trend of the optimized new roll profile curve in the axial direction of the roll is more gradual, the asynchronous rolling effect of the rolling mill is reduced on the premise of ensuring the strip shape quality of the outlet strip steel, the uniform abrasion of the roll is facilitated, and the service life of the roll is prolonged.

TABLE 4 roll diameter variance before and after optimization of roll shape parameters

TABLE 5 strip shape statistics in roll shape parameter optimization

Claims (1)

1. A CVC roll forming parameter optimization calculation method based on minimum roll diameter variance is characterized in that: it includes the following steps executed by computer:

(a) collecting basic equipment parameters, mainly including roll diameter D of working roll_wRoll diameter D of the support roll_bLength L of working roll body_wLength L of the body of the support roll_bDistance l between the working roll and the roll bending cylinder_wCenter distance l of screw pressed by support roller_bBending force S of working roll of rolling mill_Qj(j ═ 1,2, 3.) variation range of roll shifting quantity s of CVC temper mill set [ s ]_min,s_max]Coefficient of quadratic term A of roll form₂Coefficient of cubic term of roller type A₃Initial radius parameter A of roller₀Q is the steel type code of the strip steel, and j is the serial number of the typical specification strip steel counted on site;

(b) collecting the products of typical specification strip steel and rolling process parameters in production record, mainly including width value B of typical specification strip steel_QjThickness H of strip steel_QjStrip steel yield strength sigma_QsTotal elongation of_QjTotal rolling pressure P of the frame of the temper mill_Qj(ii) a Transverse distribution value L of incoming material plate shape_QiFront and rear tension T of levelling machine set_{Qj_1}、T_{Qj_0}And rolling speed v_QjWherein, i is a serial number i of strip elements divided in the width direction of the strip steel, which is 1,2 and 3;

(c) l is defined as the length of the working roll barrel of the rolling mill, A₁For the patent of the invention, the roll shape parameters to be calculated are optimized, A_{1_best}The optimal roll shape parameter primary term coefficient obtained for optimization:

(d) first order coefficient A of given roll shape parameter₁Optimized interval of [ A ]_1min,A_1max]And an optimization step Δ a;

(e) defining intermediate parameter i and initial value F of target function in optimum roll shape parameter optimizing process₀；

(f) Let i equal to 0, take F₀＝10¹⁰；

(g) Let the initial value of the optimization of the roll shape parameter be A_i＝A_1min+iΔA；

(h) Calculating the distribution value sigma of the tensile stress of the outlet strip steel by using the elastic deformation model and the metal deformation model of the roller system_1i＝f(A_i,H_Qi,L_Qi,B_Qj,T_{Qj_0},T_{Qj_1}) (unit: MPa), A_iDetermining the roll profile distribution of the roll;

(i) calculating the distribution value of the plate shape by taking I-Unit as a Unit

(j) Calculating the sheet shape peak index g (X) ═ max (α)_i)-min(α_i) I (unit: I);

(k) judgment inequality g (X) is less than or equal to g (X)_max(g(X)_maxIs a quality control parameter for the panel shape)? If the inequality is true, the step (l) is carried out for calculation; if the inequality is not true, the step (g) is carried out, the roll shape curve parameters are determined again, and calculation is carried out;

(l) Calculating the roll shape parameter A_iWidth value B of lower typical specification strip steel product_Qj(j 1,2, 3.) corresponding variance of roll diameter(unit: μm):

${\mathrm{\&Delta;R}}_j^i=\sqrt{\frac{{\&Integral;}_{\frac{L}{2}-\frac{B_{Qj}}{2}}^{\frac{L}{2}+\frac{B_{Qj}}{2}}{\&lsqb;R_{up}\left(x\right)-R_{down}\left(x\right)\&rsqb;}^{2}dx}{B_{Qj}}};$

(m) applying a roll shape parameter A_iMaximum value of variance of roll diameter under the conditionIs marked as(x) calculating an objective function for optimization of roll shape parameters;

(n) judgment of the inequality F (X) < F₀(X) is true? If the inequality holds, let F₀＝F(X)，A_{1_best}＝A_iAnd (f) turning to the step (o); if the inequality is not true, directly turning to the step (o);

(o) judgment inequalityIs there any? If the inequality is true, making i equal to i +1, then turning to the step (g), and continuing to search the roll forming parameters; if the inequality is not true, directly turning to the step (p);

(p) outputting the optimal roll shape first order term parameter A_{1_best}Drawing a roll profile curve under the roll profile parameters。