CN106547959B - One kind being based on the smallest CVC roller shape parameter optimized calculation method of roller diameter variance - Google Patents

Abstract

A CVC roll shape parameter optimization calculation method based on the minimum roll diameter variance, which includes the following steps performed by a computer: (1) collecting basic equipment parameters; (2) collecting product parameters of typical specification strip steel in production records; (3) ) Given the optimization interval [A _1min , A _1max ], and the optimization step size ΔA; (4) Define the intermediate parameter i in the optimization process of the best roll shape parameters, and the initial value of the objective function F ₀ ; (5) Calculate the outlet strip Pre-tension stress distribution value; (6) calculate the width value of the typical specification strip steel product under the roll shape parameter A _i ; (7) output the optimal roll shape parameter A _{1_best} , and draw the roll shape curve under the roll shape parameter . The invention reduces the roll diameter variance value of the upper and lower work rolls, alleviates the asynchronous rolling effect of the rolling mill caused by the difference in roll line speed caused by the difference in roll diameter of the upper and lower work rolls exceeding the standard, ensures the strip shape quality of the export strip, and solves the problem of The problem of ignoring the quality control of strip steel plate shape in the design and calculation process of roll shape parameters in the past is solved.

Description

An Optimal Calculation Method of CVC Roll Shape Parameters Based on Minimum Roll Diameter Variance

technical field

The invention relates to the flattening technology of cold-rolled strip steel, in particular to a calculation method for optimizing roll shape parameters.

Background technique

At present, in the field of strip steel temper rolling, the configuration types of roll profiles of rolling mills are becoming more and more diverse. The four-high CVC mill can quickly and continuously change the roll gap crown and adjust the strip profile according to the strip crown control requirements. The shape of the steel plate has a strong control ability, and it can realize free rolling of incoming strip steel of different steel types and specifications, and has been widely used. The upper and lower work rolls of the CVC mill are arranged anti-symmetrically. The rolling mill uses the upper and lower work rolls to shift the rolls in the roll axial direction with the same size and opposite direction to adjust the roll gap convexity to adapt to strip steel with different specifications and incoming material crowns. , the roll body curve _of a _{CVC mill} is ^S _{- shaped} , and the commonly used curve is a cubic ^polynomial . The expression of the roll shape curve is R _down (x) = R _up (Lx). On site, a reasonable roll shape curve of the work roll can be designed by optimizing the roll shape parameters of the roll. Seam convexity, to control the initial convexity of the incoming strip steel. However, in actual production, unreasonable roll body curves will lead to uneven wear of the rolls, which will greatly reduce the flatness control accuracy of the rolling mill and directly affect the flatness quality of the finished strip. Therefore, how to optimize and calculate the CVC roll body curve that satisfies the strip smoothing process on the production site according to the convexity and shape control requirements of the incoming strip steel, so as to improve the strip shape quality, has become the focus of on-site technical research. At present, the design calculation of the first-order coefficient of the roll shape parameters of the CVC mill is mainly determined from the angles of the axial force of the roll, the transverse thickness difference of the exit strip, and the change trend of the roll body curve, etc., without considering the influence of the exit strip. The influence of steel plate shape quality, and plate shape is an important indicator for downstream customers to judge the quality of strip steel products.

references

[1] Lian Jiachuang, Liu Hongmin. Plate Thickness and Shape Control [M]. Beijing: Ordnance Industry Press. 1995:1-90.

[2] Bai Zhenhua, Liu Hongmin, Li Xiujun, etc. Temper rolling process model [M]. Beijing: Metallurgical Industry Press. 2010: 1-100.

[3] Liu Guangming, Di Hongshuang, Chang An, et al. Discussion on design of roll profile curve and equivalent convexity of CVC mill [J]. Journal of Northeastern University (Natural Science Edition), 2008, 29(10): 1444-1446.

Contents of the invention

The object of the present invention is to provide a CVC roll shape parameter optimization calculation method based on the minimum roll diameter variance that can improve the strip shape quality and reduce the roll diameter variance of the upper and lower work rolls. The present invention fully considers the difference in the specifications of the incoming strip steel and the crown control requirements of the strip steel of different specifications, and sets the variance of the upper and lower work roll diameters of the CVC skin pass unit as the objective function for all typical specifications of the strip steel in the production site, and uses the output Good shape of the strip is the constraint condition. The first-order coefficient of roll shape grinding that satisfies the actual production is obtained by optimizing the calculation of the roll shape parameters. Shape quality.

The present invention comprises following computer-executed steps:

(a) Collect 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 distance l _w , screw center distance l _b of back-up roll, work roll bending force S _Qj (j=1,2,3...), variation range of roll shifting amount s of CVC skin pass unit [s _min ,s _max ] roll shape quadratic coefficient A ₂ , roll shape cubic coefficient A ₃ , roll initial radius parameter A ₀ , Q is the steel type code of the strip, and j is the serial number of the typical specification strip in the field statistics;

(b) Collect the products and rolling process parameters of typical strip steel in production records, mainly including the width value B _Qj of typical specification strip steel, strip steel thickness H _Qj , strip steel yield strength σ _Qs , total elongation ε _Qj , The total rolling pressure P _Qj of the tempering unit frame; the lateral distribution value L _Qi of the incoming plate shape, the front and rear tensions T _{Qj_1} and T _{Qj_0} of the tempering unit, and the rolling speed v _Qj , where i is the strip Sequence number i=1,2,3... of bar element divided in the width direction;

(c) define L as the work roll body length of the rolling mill, A ₁ is the roll shape parameter that needs to be optimized, and A _{1_best} is the optimal roll shape parameter linear term coefficient obtained by optimization;

(d) The optimization interval [A _1min , A _1max ] of the first-order coefficient A ₁ of the roll shape parameter is given, and the optimization step size ΔA;

(e) define the intermediate parameter i of the optimal roll shape parameter optimization process, and the initial value of the objective function F ₀ ;

(f) let i=0, get F ₀ =10 ¹⁰ ;

(g) Let the initial value of roll shape parameter optimization be A _i =A _1min +iΔA;

(h) Using the elastic deformation model of the roll system and the metal deformation model to calculate the pre-tension stress distribution value of the exit strip σ _1i = f(A _i , H _Qi , L _Qi , B _Qj , T _{Qj_0} , T _{Qj_1} ) (unit: MPa ), A _i determines the roll shape distribution of the roll;

(i) Calculate the shape distribution value with I-Unit as the unit

(j) Calculate the plate shape peak index g(X)=|max(α _i )-min(α _i )|(unit: I);

(k) Determine if the inequality g(X)≤g(X) _max (g(X) _max is the shape quality control parameter) holds true? If the inequality is established, then proceed to step (1) for calculation; if the inequality is not established, then proceed to step (g), re-determine the roll profile parameters, and calculate;

(l) Calculate the roll diameter variance corresponding to the width value B _Qj (j=1,2,3...) of a typical specification strip steel product under the roll shape parameter A _i (unit: μm):

(m) The maximum value of the variance of the roll diameter under the condition of the roll shape parameter A _i recorded as F (X) is the optimization calculation objective function of roll shape parameter;

(n) Determine whether the inequality F(X)<F ₀ (X) holds true? If the inequality is established, set F ₀ =F(X), A _{1_best} =A _i , and turn to step (o); if the inequality is not established, then directly turn to step (o);

(o) Judgment inequality Is it established? If inequality is established, make i=i+1, then proceed to step (g), continue to carry out the search of roll shape parameter; If inequality is not established, then directly proceed to step (p);

(p) Output the first-order parameter A _{1_best} of the optimal roll shape, and draw the roll shape curve under this roll shape parameter.

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

Fully consider the width variation range of different specifications of the strip steel at the production site, according to the convexity and shape control requirements of the incoming strip steel, and take the good shape of the strip steel strip at the exit as the constraint condition, and optimize the calculation of the roll shape parameters to meet the actual production requirements. Roll shape grinding parameters, on the basis of ensuring the equivalent crown control ability of the rolling mill, improve the flatness value of the exit strip, reduce the variance value of the roll diameter of the upper and lower work rolls, and help reduce the roll diameter difference caused by the upper and lower work rolls. The asynchronous rolling effect of the rolling mill caused by the difference in the roll line speed caused by exceeding the standard makes the roll wear more uniform, solves the problem that the strip steel shape quality control was ignored in the previous roll shape parameter design and calculation process, and improves the roll shape parameter design calculation of the CVC rolling mill The system has the value of further promotion and use.

Description of drawings

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

Fig. 2 is the T-2.5MA steel grade 0.305mm*998mm specification strip shape distribution diagram in the roll shape parameter optimization process in the embodiment 1 of the present invention;

Fig. 3 is the roll shape graph after the roll shape parameter optimization in the embodiment 1 of the present invention;

Fig. 4 is the shape distribution diagram of the strip steel plate of T-2MA steel type 0.315mm*786mm specification in the roll shape parameter optimization process in Example 2 of the present invention;

Fig. 5 is the roll shape curve figure after the roll shape parameter optimization in the embodiment 2 of the present invention;

Fig. 6 is a comparison chart of roll shape curves after optimization of roll shape parameters in Example 1 and Example 2 of the present invention.

Detailed ways

Example 1

A CVC roll shape parameter optimization calculation method based on the minimum roll diameter variance, the calculation process is shown in Figure 1, including the following steps:

(a) Collect basic equipment parameters, mainly including the roll diameter of the working roll D _w = 450mm, the roll diameter of the backup roll D _b = 1150mm, the roll body length of the work roll L _w = 1620mm, the roll body length of the backup roll L _b = 1380mm, working roll bending cylinder distance l _w = 2300mm, back-up roll pressing screw center distance l _b = 2300mm, rolling mill working roll bending force S = 200, 80, 120, 110, 110, 100, 50, 60 unit KN, change of roll shifting amount s in CVC mill Range [-120mm, 120mm], quadratic term coefficient A ₂ =-0.169563×10 ^-5 , roll shape cubic term coefficient A ₃ =0.635066×10 ^-9 , initial roll radius parameter A ₀ =225, statistics of two typical specifications The rolling process parameters of steel types MR T-3BA and MR T-2.5BA are shown in Table 1.

Table 1 Specifications and rolling process parameters of typical steel grades

(b) Collect the product parameters of typical strip steel in production records, mainly including the width value B _Qj (j=1,2,3...) of typical strip steel according to:

B _T3 = 780mm, 875mm, 994mm, 1105mm,

B _T2.5 = 725mm, 785mm, 870mm, 998mm;

Strip thickness values: H _T3 = 0.325mm, 0.285mm, 0.298mm, 0.304mm,

H _T2.5 = 0.298mm, 0.305mm, 0.285mm, 0.305mm;

Strip yield strength σ _{s_T2.5} = 250MPa, σ _{s_T3} = 270MPa, the total rolling pressure of the skin pass stand:

P _T3 = 2.2MN, 1.9MN, 2.0MN, 2.1MN,

P _T2.5 = 1.9MN, 2.4MN, 2.0MN, 1.8MN;

Total elongation ε _Qj = 0.9%, 1.0%, 1.05%, 1.1%, 0.9%, 1.0%, 1.05%, 1.1%; the lateral distribution value L _Qi = 0 of incoming plate tension:

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) define L as the work roll body length of the rolling mill, A ₁ is the roll shape parameter that needs to be optimized, and A _{1_best} is the optimal roll shape parameter linear term coefficient obtained by optimization;

(d) The optimization interval [0.126427×10 ^-2 ,0.146427×10 ^-2 ] of the first-order coefficient A ₁ of the given roll shape parameter, and the optimization step size ΔA=0.0002;

(e) define the intermediate parameter i of the optimal roll shape parameter optimization process, and the initial value of the objective function F ₀ ;

(f) let i=0, get F ₀ =10 ¹⁰ ;

(g) Let the initial value of roll shape parameter optimization be A _i =A _1min +iΔA=0.126427×10 ^-2 ;

(h) Using the elastic deformation model of the roll system and the metal deformation model to calculate the pre-tension stress distribution value σ _1i (i=1,2,3...) (unit: MPa) of the export strip;

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) Calculate the shape distribution value with I-Unit as the 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) Calculate the plate shape peak index g(X)=|max(α _i )-min(α _i )|=6.01 (unit: I)

(k) Judging whether the inequality g(X)≤g(X) _max (g(X) _max is the peak value of the shape quality control parameter, which is taken as g(X) _max = 10) is true, 6.01I<10I, the inequality Established, go to step (l);

(l) Calculate the roll diameter variance value corresponding to the strip product width value B _Qj (j=1,2,3...) of all typical specifications under the roll shape parameter A _i

in, (unit: μm)

(m) The maximum variance of the roll diameter under the roll shape parameter A _i recorded as At this time, the maximum variance of the roll diameter is F(X)=154.464μm;

(n) The inequality F(X)<10 ¹⁰ is established, let F ₀ =F(X), A _{1_best} =0.126427×10 ^-2 , and turn to step (o);

(o) Inequality Established, make i=i+1=1, then proceed to step (g); if the inequality is not established, then directly proceed to step (p);

(p) Output the optimal roll shape parameter A _{1_best} = 0.130623×10 ^-2 , and draw the roll shape curve under this roll shape parameter;

For the convenience of comparison, the roll diameter variance value after adopting the roll shape parameter optimization of the present invention is listed respectively to compare with the roll diameter variance value before optimization, as shown in table 2, the roll diameter variance value after optimization is by 149.889 μ m Reduced to 113.073μm; as shown in Figure 2, the calculated distribution of the flatness of the T-2.5MA steel grade 0.305mm*998mm strip steel in the optimization calculation process of the roll shape parameters is given, and the flatness value is 6.01I; As shown in Figure 3, the roll shape curve after the roll shape parameter optimization is given; the flatness statistics of other steel types and specifications are shown in Table 3, the maximum value of the flatness value of the exported strip is 7.36I, and the average The shape value is 5.595I, and the shape quality can be controlled at a relatively high level.

Table 2 Roll diameter variance before and after optimization of roll shape parameters

Table 3 Statistical values of strip shape during the optimization process of roll shape parameters

As shown in Figure 6, it can be seen that the optimized new roll shape curve has a more gentle change trend in the roll axial direction. On the premise of ensuring the shape quality of the export strip, the asynchronous rolling effect of the rolling mill is reduced, and more It is beneficial to the uniform wear of the roll and improves the service life of the roll.

Example 2

A CVC roll shape parameter optimization calculation method based on the minimum roll diameter variance, which includes the following computer-executed steps:

(a) Collect basic equipment parameters, mainly including the roll diameter of the working roll D _w = 450mm, the roll diameter of the backup roll D _b = 1150mm, the roll body length of the work roll L _w = 1620mm, the roll body length of the backup roll L _b = 1380mm, working roll bending cylinder distance l _w = 2300mm, back-up roll pressing screw center distance l _b = 2300mm, rolling mill working roll bending force S = 200, 80, 120, 110, 105, 40, 70, 80 units KN, roll shifting amount of CVC rolling mill s change range [-120mm, 120mm], quadratic term coefficient A ₂ =-0.169563×10 ^-5 , roll shape cubic term coefficient A ₃ =0.635066×10 ^-9 , roll initial radius parameter A ₀ =224.5, two kinds of statistics The rolling process parameters of typical steel types MR T-3BA and MR T-2BA are shown in Table 4.

Table 4 Specifications and rolling process parameters of typical steel grades

(b) Collect the product parameters of typical strip steel in production records, mainly including the width value B _Qj (j=1,2,3...) of typical strip steel according to:

B _T3 = 780mm, 875mm, 994mm, 1105mm,

B _T2 = 735mm, 786mm, 870mm, 934mm;

Strip thickness values: H _T3 = 0.325mm, 0.285mm, 0.298mm, 0.304mm,

H _T2 = 0.278mm, 0.315mm, 0.275mm, 0.285mm;

Strip yield strength σ _{s_T2} = 240MPa, σ _{s_T3} = 270MPa, the total rolling pressure of the skin pass stand:

P _T3 = 2.2MN, 1.9MN, 2.0MN, 2.1MN,

P _T2 = 1.7MN, 2.3MN, 2.1MN, 1.9MN;

Total elongation ε _Qj ＝0.9%, 1.0%, 1.05%, 1.1%, 0.8%, 0.9%, 1.0%, 1.05%, transverse distribution value L _Qi ＝0 of incoming plate shape, back tension of skin pass unit and front tension:

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) define L as the work roll body length of the rolling mill, A ₁ is the roll shape parameter that needs to be optimized, and A _{1_best} is the optimal roll shape parameter linear term coefficient obtained by optimization;

(d) The optimization interval [0.126427×10 ^-2 ,0.146427×10 ^-2 ] of the first-order coefficient A ₁ of the given roll shape parameter, and the optimization step size ΔA=0.0002;

(e) define the intermediate parameter i of the optimal roll shape parameter optimization process, and the initial value of the objective function F ₀ ;

(f) let i=0, get F ₀ =10 ¹⁰ ;

(g) Let the initial value of roll shape parameter optimization be A _i =A _1min +iΔA=0.126427×10 ^-2 ;

(h) Using the elastic deformation model of the roll system and the metal deformation model to calculate the pre-tension stress distribution value σ _1i (i=1,2,3...) (unit: MPa) of the export strip;

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) Calculate the shape distribution value with I-Unit as the 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) Calculate the plate shape peak index g(X)=|max(α _i )-min(α _i )|=5.09 (unit: I)

(k) Judging whether the inequality g(X)≤g(X) _max (g(X) _max is the peak value of the shape quality control parameter, which is taken as g(X) _max = 10) is true, 5.09I<10I, the inequality Established, go to step (l);

(l) Calculate the roll diameter variance value corresponding to the strip product width value B _Qj (j=1,2,3...) of all typical specifications under the roll shape parameter A _i

in, (unit: μm)

(m) The maximum variance of the roll diameter under the roll shape parameter A _i recorded as At this time, the maximum variance of the roll diameter is F(X)=153.409μm;

(n) The inequality F(X)<10 ¹⁰ is established, let F ₀ =F(X), A _{1_best} =0.126427×10 ^-2 , and turn to step (o);

(o) Inequality Established, make i=i+1=1, then proceed to step (g); if the inequality is not established, then directly proceed to step (p);

(p) Output the optimal roll shape parameter A _{1_best} = 0.129337×10 ^-2 , and draw the roll shape curve under this roll shape parameter;

For convenience of comparison, the roll diameter variance value after adopting the roll shape parameter optimization of the present invention is listed respectively to compare with the roll diameter variance value before optimization, as shown in table 5, the roll diameter variance value after optimization is by 149.889 μ m It is reduced to 111.376μm; as shown in Figure 4, the calculated distribution of the strip shape of the T-2MA steel grade 0.315mm*786mm in the process of optimizing the calculation of the roll shape parameters is given, and the shape value is 5.09I; As shown in Figure 5, the roll shape curve after the optimization of the roll shape parameters is given; the statistical values of the flatness of other steel types and specifications are shown in Table 6, the maximum value of the flatness of the exported strip is 7.65I, and the average flatness The shape value is 5.726I, and the shape quality can be controlled at a relatively high level.

As shown in Figure 6, it can be seen that the optimized new roll shape curve has a more gentle change trend in the roll axial direction. On the premise of ensuring the shape quality of the export strip, the asynchronous rolling effect of the rolling mill is reduced, and more It is beneficial to the uniform wear of the roll and improves the service life of the roll.

Table 5 Roll diameter variance before and after optimization of roll shape parameters

Table 6 Statistical values of strip shape during the optimization process of roll shape parameters

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_QjVariation range of roll shifting quantity s of CVC leveling unit_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 epsilon_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, A₁As a roll shape parameter, 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})，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)|；

(k) Judgment inequality g (X) is less than or equal to g (X)_maxWhether or not it holds, wherein, g (X)_maxIf the inequality is established, 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_QjCorresponding variance of roll diameter

(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 inequality F (X)<F₀(X) if true, if the inequality is true, 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 inequalityIf 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.