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CN103480651A - Roll profile curve design method for dual-frame four-roll leveling unit - Google Patents

Roll profile curve design method for dual-frame four-roll leveling unit Download PDF

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CN103480651A
CN103480651A CN201210194861.9A CN201210194861A CN103480651A CN 103480651 A CN103480651 A CN 103480651A CN 201210194861 A CN201210194861 A CN 201210194861A CN 103480651 A CN103480651 A CN 103480651A
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roll
roller
frame
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CN103480651B (en
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王天顺
申荣法
张青树
徐烨明
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Shanghai Meishan Iron and Steel Co Ltd
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Shanghai Meishan Iron and Steel Co Ltd
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Abstract

The invention relates to a roll profile curve design method for a dual-frame four-roll leveling unit. The method is characterized by comprising the following steps: (a) collecting equipment characteristic parameters of the dual-frame leveling unit; (b) collecting incoming material parameters of typical specification products in various specification ranges of strip steel; (c) setting the roll bending force and roll inclination of a first frame and a second frame in basic states; (d) setting roll profile curves of a working roll and a support roll by using roll profile curve parameters and an optimization variable; (e) optimally calculating roll profile curve parameters; (f) substituting an optimal roll profile curve parameter to obtain an optimal roll profile curve equation of the working roll and the support roll. According to the technical scheme, aberration is controlled under the consideration of a strip shape and the roll consumption, the obtained roll profile curves of the working roll and the support roll are optimized, the rolling pressure and pressure between the rolls can be distributed uniformly to the maximum extent, the probability of aberration is reduced; meanwhile, the requirements of strip shape and roll consumption are met, and greater economic benefit is brought to enterprises.

Description

The roller type curve design method of the smooth unit of a kind of Stand Mill four roller
Technical field
The present invention relates to the roller curve design field, relate in particular to a kind of roller type curve design method of smooth unit, particularly relate to the roller type curve design method of the smooth unit of a kind of Stand Mill four roller.
Background technology
The contact width of smoothing and rolling process tabularium and working roll generally all is less than the barrel length of working roll, under the roll-force effect, being positioned at working roll beyond plate width and backing roll body of roll contact zone is a harmful contact portion, it makes working roll produce additional distortion, cause working roll deflection by a relatively large margin, and then cause the uneven distribution of draught pressure and roll gap pressure, (as shown in Figure 1) finally to produce belt plate shape and the defects such as the roller consumption is excessive, aberration.For this technical problem, solution commonly used is to carry out the roll shape optimal design, weakens harmful contact of roller end, in the prior art, only considers the impact of plate shape and roller consumption during roll design, the aberration factor is not taken into account.And aberration is often to occur and have a strong impact on the defect of finished strip quality in smoothing and rolling process, therefore, how by roll design, effectively to prevent with the steel aberration the being focus of correlative study work, especially, for the smooth unit of Stand Mill four roller, key is, how, in the roll design that considers the conditions such as aberration, plate shape and roller consumption, realizes the coupling between Stand Mill.
In prior art, so-called aberration divides two kinds of strip surface aberration and roller surface aberration, and they are synergistic, both likely occurred making strip surface first occur that aberration affects roll because the draught pressure part is excessive, likely also because the roll contact pressure between rolls is inhomogeneous, local excessive, first at roller surface, aberration appears, then have influence on belt steel surface.In order to guarantee to produce qualified product, band and roller surface do not allow to occur the aberration problem, and both must the comprehensive regulation.In above analysis, the distribution of draught pressure and roll gap pressure can realize by optimizing roll shape, and should pay close attention to the problems such as plate shape and roller consumption in optimizing process simultaneously.For this reason, the present invention is on a large amount of field trials and theoretical research basis, take into full account the equipment and process characteristics of the smooth unit of Stand Mill four roller, by setting up belt steel surface Model for chromatic aberration and roller surface Model for chromatic aberration, smooth operation aberration Comprehensive Control object function has been proposed, and the factors such as board shape and roller consumption, finally established the roll shape optimal design object function of the smooth unit of Stand Mill four roller.Optimize gained working roll and backing roll roller curve, can at utmost make draught pressure and roll force distribution even, reduce the aberration probability of occurrence, guarantee that plate shape and roller consumption meet the demands simultaneously.
Summary of the invention
The present invention's defect such as, aberration excessive for belt plate shape in prior art and roller consumption just provides the roller type curve design method of the smooth unit of a kind of Stand Mill four roller.
In order to solve the problems of the technologies described above, technical scheme of the present invention is as follows: the roller type curve design method of the smooth unit of a kind of Stand Mill four roller is characterized in that said method comprising the steps of:
(a) collect the apparatus characteristic parameter of Two-stand Temper Mill group;
(b) the ideal format product supplied materials parameter of each description scope of collecting belt steel;
(c) set the bending roller force S of the first frame, the second frame 1, S 2, roller η inclines 1, η 2in ground state;
(d), with roller curve parameter and optimized variable, set the roller curve of working roll and backing roll;
(e) optimize and calculate the roller curve parameter;
(f) substitution of optimum roller curve parameter is obtained to the roller curve equation of optimum working roll and backing roll.
As a modification of the present invention, described step (e) optimization calculates the roller curve parameter, specifically comprises the following steps:
E1) given initial curve parameter
Figure DEST_PATH_960253DEST_PATH_IMAGE001
;
E2) utilizing roller is elastic model, adopts the segmentation discrete method, by backing roll along barrel length be divided into the n section, band is divided into the m section, calculates the first frame, the second frame roll force distribution , roll-force distributes , the toe-out stress distribution ;
E3) calculate the first frame, the second frame strip surface aberration function
Figure DEST_PATH_118647DEST_PATH_IMAGE005
, its Mathematical Modeling is:
Figure DEST_PATH_383406DEST_PATH_IMAGE006
, k in formula 0for the standard resistance of deformation, get , the practical distortion drag that k is band, α is weight coefficient, α=0.6;
E4) judgement inequality
Figure DEST_PATH_814704DEST_PATH_IMAGE008
, k sband aberration critical value, k s=0.2 ~ 0.3, whether set up, if inequality is set up, proceed to step e5), otherwise, readjust the roller curve parameter, proceed to step e2);
E5) calculate the first frame, the second breast roller surface chromatic aberration function
Figure DEST_PATH_29654DEST_PATH_IMAGE009
, its Mathematical Modeling is:
Figure DEST_PATH_211236DEST_PATH_IMAGE010
, K in formula 0for standard roller surface hardness, get K 0=1100 ~ 1200Mpa, K wfor work roll surface actual hardness, K bfor the roll surface actual hardness;
E6) judged result is less than , k rroll aberration critical value, k swhether=0.4 ~ 0.5 set up, if inequality is set up, proceeds to step e7), otherwise, readjust the roller curve parameter, proceed to step e2);
E7) calculate the first frame, the second frame aberration Comprehensive Control function
Figure DEST_PATH_503995DEST_PATH_IMAGE012
, its Mathematical Modeling is , wherein β is weight coefficient,
E8) constraint IF condition
Figure DEST_PATH_106194DEST_PATH_IMAGE014
, whether λ is constant, gets 0.1-0.5, set up, if inequality is set up, proceeds to step e9); Otherwise, readjust the roller curve parameter, proceed to step e2);
E9) calculate the first frame, the second frame plate shape peak index
Figure DEST_PATH_420763DEST_PATH_IMAGE015
, k=1,2 represent shelf number, its Mathematical Modeling is
Figure DEST_PATH_542303DEST_PATH_IMAGE016
;
E10) judgement inequality
Figure DEST_PATH_912104DEST_PATH_IMAGE017
, k stbe to allow forward pull cross direction profiles peak-peak whether to set up, if inequality is set up, proceed to step e11), otherwise, readjust the roller curve parameter, proceed to step e2);
E11) calculate pressure peak index between the first frame, the second breast roll
Figure DEST_PATH_5962DEST_PATH_IMAGE018
, k=1,2 represent shelf number, its Mathematical Modeling is ;
E12) judgement inequality , k sqbe to allow roll force distribution cross direction profiles peak-peak whether to set up, if inequality is set up, proceed to step e13), otherwise, readjust the roller curve parameter, proceed to step e2);
E13) calculate the first frame, the second frame draught pressure peak index
Figure DEST_PATH_506717DEST_PATH_IMAGE021
, k=1,2 represent shelf number, its Mathematical Modeling is ;
E14) judgement inequality
Figure DEST_PATH_423037DEST_PATH_IMAGE023
, k sqbe to allow draught pressure distribution cross direction profiles peak-peak whether to set up, if inequality is set up, proceed to step e15), otherwise, readjust the roller curve parameter, proceed to step e2);
E15) calculate the Comprehensive Control function G of the first frame, the second frame plate shape and roller consumption 1(X), G 2(X), its Mathematical Modeling is
Figure DEST_PATH_519169DEST_PATH_IMAGE024
, α in formula 1, α 2, α 3for weight coefficient, meet α 1+ α 2+ α 3=1, g 1(X) represent plate shape uniformity index, g 2(X) represent roll gap pressure uniformity index, g 3(X) represent draught pressure uniformity index, its mathematic(al) representation is:
Figure DEST_PATH_230773DEST_PATH_IMAGE025
Figure DEST_PATH_44096DEST_PATH_IMAGE026
；
E16) constraint IF condition
Figure DEST_PATH_500803DEST_PATH_IMAGE028
, whether φ is constant, gets 0.1-0.5, set up, if inequality is set up, proceeds to step e17); Otherwise, readjust the roller curve parameter, proceed to step e2);
E17) calculate roll shape optimization aim function:
Figure DEST_PATH_953781DEST_PATH_IMAGE029
, in formula
Figure DEST_PATH_939054DEST_PATH_IMAGE030
be the weight coefficient of specification product in j, determined by the ratio of production output in total output of each specification product;
E18) judge whether the Powell condition is set up, if be false, adjust the roller curve parameter, repeating step e2) to e17), until the Powell condition is set up, finish to calculate, draw optimum roller curve parameter.
  
As a modification of the present invention, described step (a) is collected the apparatus characteristic parameter of Two-stand Temper Mill group, mainly comprises: the first frame, the second frame working roll and backing roll diameter D 1w, D 2w, D 1b, D 2b, working roll and backing roll barrel length L w1, L w2, L b1, L b2, working roll bending cylinder is apart from l 1, l 2, housing screw center square L 1, L 2, maximum positive bending roller force S + 1max, S + 2maxmaximum negative bending roller force S - 1max, S - 2max, the maximum roller amount of just inclining
Figure DEST_PATH_248813DEST_PATH_IMAGE031
, the maximum negative roller amount of inclining
Figure DEST_PATH_240908DEST_PATH_IMAGE032
, maximum rolling force
Figure DEST_PATH_294315DEST_PATH_IMAGE033
, maximum mill speed
Figure DEST_PATH_134095DEST_PATH_IMAGE034
, work roll surface actual hardness K w, roll surface actual hardness K b;
As a modification of the present invention, the ideal format product parameters of each description scope of described step (b) collecting belt steel, comprise strip width
Figure DEST_PATH_552438DEST_PATH_IMAGE035
, thickness
Figure DEST_PATH_110458DEST_PATH_IMAGE035
, yield limit , breaking elongation
Figure DEST_PATH_350258DEST_PATH_IMAGE037
, the first frame rolling force setup value
Figure DEST_PATH_1819DEST_PATH_IMAGE038
, the second frame sets the rolling force setup value , entrance tension force setting value
Figure DEST_PATH_114449DEST_PATH_IMAGE040
, intermediate tension setting value
Figure DEST_PATH_928821DEST_PATH_IMAGE041
, outlet tension force setting value
Figure DEST_PATH_938234DEST_PATH_IMAGE042
.
As a modification of the present invention, described step (c) is set the bending roller force S of the first frame, the second frame 1, S 2, roller η inclines 1, η 2in ground state,
Figure DEST_PATH_205267DEST_PATH_IMAGE043
As a modification of the present invention, two frames of described step (d) Two-stand Temper Mill group adopt identical roll shape, do not add differentiation here, with a, and b, c, k 1, δ, l z, k is roller curve parameter and optimized variable, sets respectively the curvilinear equation of working roll and backing roll.Wherein, the roller curve equation of setting working roll is:
Figure DEST_PATH_404168DEST_PATH_IMAGE044
The roller curve equation of setting backing roll is:
Figure DEST_PATH_10729DEST_PATH_IMAGE045
Above in two formulas:
D w---working roll green diameter (mm);
L w---working roll barrel length (mm);
D b---backing roll green diameter (mm);
L b---backing roll barrel length (mm);
A---work roll crown value;
B---cosine phase coefficient;
C---working roll high order curve partial safety factor;
K 1---working roll high order curve subitem index;
L z---backing roll roller curve sloping shoulders length (mm);
δ---the backing roll roller curve sloping shoulders degree of depth (mm);
K---backing roll roller curve index.
  
With respect to prior art, advantage of the present invention is as follows: when considering plate shape and roller consumption, take into account the control of aberration, optimize gained working roll and backing roll roller curve, can at utmost make draught pressure and roll force distribution even, reduce the aberration probability of occurrence, guarantee that plate shape and roller consumption meet the demands, for enterprise brings larger economic interests simultaneously.
The accompanying drawing explanation
Fig. 1 is the total design flow diagram of the present invention;
Fig. 2-1, Fig. 2-2 are roller curve optimizing flow chart;
Fig. 3 is embodiment 1 working roller schematic diagram;
Fig. 4 is the accurate curve map of embodiment 1 working roller;
Fig. 5 is embodiment 1 backing roll roller curve schematic diagram;
Fig. 6 is the accurate curve map of embodiment 1 backing roll roll shape;
Fig. 7 is embodiment 2 working roller schematic diagrames;
Fig. 8 is the accurate curve map of embodiment 2 working roller;
Fig. 9 is embodiment 2 backing roll roll shape schematic diagrames;
Figure 10 is the accurate curve map of embodiment 2 backing roll roll shape.
The specific embodiment
In order to deepen the understanding of the present invention, below in conjunction with accompanying drawing, 1-8 couples of the present invention are described in detail.
Referring to Fig. 1, Fig. 1 is the total design flow diagram of the present invention, and the roller type curve design method of the smooth unit of a kind of Stand Mill four roller is characterized in that said method comprising the steps of:
(a) collect the apparatus characteristic parameter of Two-stand Temper Mill group;
(b) the ideal format product supplied materials parameter of each description scope of collecting belt steel;
(c) set the bending roller force S of the first frame, the second frame 1, S 2, roller η inclines 1, η 2in ground state;
(d), with roller curve parameter and optimized variable, set the roller curve of working roll and backing roll;
(e) optimize and calculate the roller curve parameter;
(f) substitution of optimum roller curve parameter is obtained to the roller curve equation of optimum working roll and backing roll.
Referring to Fig. 2-1 and Fig. 2-2, be roller curve optimizing flow chart, specifically comprise the following steps:
E1) given initial curve parameter X 0={ a, b, c, k 1, δ, l z, k};
E2) utilizing roller is elastic model, adopts the segmentation discrete method, by backing roll along barrel length be divided into the n section, band is divided into the m section, calculates the first frame, the second frame roll force distribution , roll-force distributes , the toe-out stress distribution
Figure DEST_PATH_449429DEST_PATH_IMAGE048
;
E3) calculate the first frame, the second frame strip surface aberration function
Figure DEST_PATH_972815DEST_PATH_IMAGE049
, its Mathematical Modeling is:
Figure DEST_PATH_137080DEST_PATH_IMAGE006
, k in formula 0for the standard resistance of deformation, get K 0=1100 ~ 1200Mpa, the practical distortion drag that k is band, α is weight coefficient, α=0.6;
E4) judgement inequality
Figure DEST_PATH_316388DEST_PATH_IMAGE050
, k sband aberration critical value, k s=0.2 ~ 0.3, whether set up, if inequality is set up, proceed to step e5), otherwise, readjust the roller curve parameter, proceed to step e2);
E5) calculate the first frame, the second breast roller surface chromatic aberration function
Figure DEST_PATH_857091DEST_PATH_IMAGE009
, its Mathematical Modeling is:
Figure DEST_PATH_234983DEST_PATH_IMAGE051
, K in formula 0for standard roller surface hardness, get K 0=1100 ~ 1200Mpa, K wfor work roll surface actual hardness, K bfor the roll surface actual hardness;
E6) judged result is less than
Figure DEST_PATH_22679DEST_PATH_IMAGE011
, k rroll aberration critical value, k s=0.4 ~ 0.5, whether set up, if inequality is set up, proceed to step e7), otherwise, readjust the roller curve parameter, proceed to step e2);
E7) calculate the first frame, the second frame aberration Comprehensive Control function
Figure DEST_PATH_486021DEST_PATH_IMAGE012
, its Mathematical Modeling is
Figure DEST_PATH_830415DEST_PATH_IMAGE013
, wherein β is weight coefficient,
E8) constraint IF condition
Figure DEST_PATH_496DEST_PATH_IMAGE014
, whether λ is constant, gets 0.1-0.5, set up, if inequality is set up, proceeds to step e9); Otherwise, readjust the roller curve parameter, proceed to step e2);
E9) calculate the first frame, the second frame plate shape peak index
Figure DEST_PATH_772143DEST_PATH_IMAGE015
, k=1,2 represent shelf number, its Mathematical Modeling is
Figure DEST_PATH_722782DEST_PATH_IMAGE016
;
E10) judgement inequality
Figure DEST_PATH_293703DEST_PATH_IMAGE017
, k stbe to allow forward pull cross direction profiles peak-peak whether to set up, if inequality is set up, proceed to step e11), otherwise, readjust the roller curve parameter, proceed to step e2);
E11) calculate pressure peak index between the first frame, the second breast roll
Figure DEST_PATH_646187DEST_PATH_IMAGE018
, k=1,2 represent shelf number, its Mathematical Modeling is
Figure DEST_PATH_588735DEST_PATH_IMAGE019
;
E12) judgement inequality
Figure DEST_PATH_964352DEST_PATH_IMAGE020
, k sqbe to allow roll force distribution cross direction profiles peak-peak whether to set up, if inequality is set up, proceed to step e13), otherwise, readjust the roller curve parameter, proceed to step e2);
E13) calculate the first frame, the second frame draught pressure peak index
Figure DEST_PATH_650549DEST_PATH_IMAGE021
, k=1,2 represent shelf number, its Mathematical Modeling is ;
E14) judgement inequality , k sqbe to allow draught pressure distribution cross direction profiles peak-peak whether to set up, if inequality is set up, proceed to step e15), otherwise, readjust the roller curve parameter, proceed to step e2);
E15) calculate the Comprehensive Control function G of the first frame, the second frame plate shape and roller consumption 1(X), G 2(X), its Mathematical Modeling is , α in formula 1, α 2, α 3, be weight coefficient, meet α 1+ α 2+ α 3=1, g 1(X) represent plate shape uniformity index, g 2(X) represent roll gap pressure uniformity index, g 3(X) represent draught pressure uniformity index, its mathematic(al) representation is:
Figure DEST_PATH_245161DEST_PATH_IMAGE025
Figure DEST_PATH_572237DEST_PATH_IMAGE026
Figure DEST_PATH_591009DEST_PATH_IMAGE027
；
E16) constraint IF condition
Figure DEST_PATH_686092DEST_PATH_IMAGE028
, whether φ is constant, gets 0.1-0.5, set up, if inequality is set up, proceeds to step e17); Otherwise, readjust the roller curve parameter, proceed to step e2);
E17) calculate roll shape optimization aim function:
Figure DEST_PATH_714091DEST_PATH_IMAGE029
, in formula
Figure DEST_PATH_895673DEST_PATH_IMAGE030
be the weight coefficient of specification product in j, determined by the ratio of production output in total output of each specification product;
E18) judge whether the Powell condition is set up, if be false, adjust the roller curve parameter, repeating step e2) to e17), until the Powell condition is set up, finish to calculate, draw optimum roller curve parameter.
Embodiment 1: referring to Fig. 3,4,
At first, in step 1, collect the apparatus characteristic parameter of Two-stand Temper Mill group, mainly comprise: the first frame, the second frame working roll and backing roll diameter D 1w=D 2w=500mm, D 1b=D 2b=1100mm, working roll and backing roll barrel length L w1=L w2=L b1=L b2=1250mm, working roll bending cylinder is apart from l 1=l 2=2300mm, housing screw center square L 1=L 2=2300mm, maximum positive bending roller force S + 1max=S + 2max=1134kN, maximum negative bending roller force S - 1max=S - 2max=-1134kN, the maximum roller amount of just inclining
Figure DEST_PATH_288608DEST_PATH_IMAGE052
, the maximum negative roller amount of inclining
Figure DEST_PATH_922852DEST_PATH_IMAGE053
, maximum rolling force
Figure DEST_PATH_488963DEST_PATH_IMAGE054
, maximum mill speed
Figure DEST_PATH_977582DEST_PATH_IMAGE055
, work roll surface actual hardness K w=1200, roll surface actual hardness K b=1200;
Subsequently, in step 2, the ideal format product parameters of each description scope of collecting belt steel, comprise strip width
Figure DEST_PATH_603735DEST_PATH_IMAGE056
, thickness
Figure DEST_PATH_725275DEST_PATH_IMAGE056
, yield limit
Figure DEST_PATH_32759DEST_PATH_IMAGE057
, breaking elongation
Figure DEST_PATH_188934DEST_PATH_IMAGE058
, the first frame rolling force setup value
Figure DEST_PATH_985989DEST_PATH_IMAGE059
, the second frame sets the rolling force setup value
Figure DEST_PATH_283240DEST_PATH_IMAGE060
, entrance tension force setting value
Figure DEST_PATH_191154DEST_PATH_IMAGE061
, intermediate tension setting value
Figure DEST_PATH_201835DEST_PATH_IMAGE062
, outlet tension force setting value
Figure DEST_PATH_107474DEST_PATH_IMAGE063
.Specifically as shown in table 1.
Table 1 ideal format product
Sequence number 1 2 3 4 5 6 7 8
Yield limit/MPa 270 270 270 270 460 460 460 460
Width/mm 818 808 1018 1046 836 837 906 923
Speed/m/min 470 449 285 390 430 640 720 590
Thickness/mm 401 450 503 502 180 181 190 179
Outlet tension force/kN 3200 2600 3500 3650 3151 3000 3400 3200
Breaking elongation/% 1.92 1.32 1.31 1.21 1.08 1.07 1.36 1.36
1# roll-force/kN 3964 2456 2840 2987 8011 8015 7780 7911
The 2# roll-force 2500 2000 2001 2001 4649 5093 2580 2877
Entrance tension force/kN 3200 2600 3401 3550 1981 1950 2200 2100
Intermediate tension/kN 3400 2751 3450 3700 3652 3500 3900 3750
Subsequently, in step 3, set the bending roller force S of the first frame, the second frame 1, S 2, roller η inclines 1, η 2in ground state,
Figure DEST_PATH_203606DEST_PATH_IMAGE064
Figure DEST_PATH_915210DEST_PATH_IMAGE065
Subsequently, in step 4, two frames of Two-stand Temper Mill group adopt identical roll shape, do not add differentiation here.With a, b, c, k 1, δ, l z, k is roller curve parameter and optimized variable, sets respectively the curvilinear equation of working roll and backing roll.Wherein, the roller curve equation of setting working roll is:
Figure DEST_PATH_967349DEST_PATH_IMAGE044
The roller curve equation of setting backing roll is:
Figure DEST_PATH_106206DEST_PATH_IMAGE045
Subsequently, in step 5, given initial curve parameter
Figure DEST_PATH_627317DEST_PATH_IMAGE066
;
Subsequently, in step 6, utilizing roller is elastic model, adopts the segmentation discrete method, and backing roll is divided into along barrel length
Figure DEST_PATH_142612DEST_PATH_IMAGE067
section, band are divided into the n section, calculate the first frame, the second frame roll force distribution q bwil={ 7190.0,7440.2,7679.9,7943.2,8230.0,8539.6,8870.3,9170.1,9438.8,9676.7,9884.1,10061.8,10210.5,10330.9,10423.7,10489.6,10528.9,10542.0,10528.9,10489.6,10423.7,10330.9,10210.5,10061.8,9884.1,9676.7,9438.8,9170.1,8870.3,8539.6,8230.0,7943.2,7679.9,7440.2,7190.0}, q bwi2={ 4682.6,4722.6,4781.8,4860.3,4957.9,5073.9,5207.1,5329.6,5441.0,5540.8,5628.7,5704.7,5768.9,5821.1,5861.7,5890.6,5907.8,5913.6,5907.8,5890.6,5861.7,5821.1,5768.9,5704.7,5628.7,5540.8,5441.0,5329.6,5207.1,5073.9,4957.9,4860.3,4781.8,4722.6,4682.6}, the kN/m of unit;
Roll-force distribution q' i1={ 9026.6,8530.7,8093.3,7711.4,7382.1,7102.9,6871.2,6684.8,6541.8,6440.8,6380.6,6360.6,6380.6,6440.8,6541.8,6684.8,6871.2,7102.9,7382.1,7711.4,8093.3,8530.7,9026.6}, q' i2={ 4926.3,4728.0,4548.0,4386.8,4244.6,4121.5,4017.6,3932.8,3867.0,3820.1,3792.0,3782.6,3792.0,3820.1,3867.0,3932.8,4017.6,4121.5,4244.6,4386.8,4548.0,4728.0, the kN/m of 4926.3} unit;
Toe-out stress distribution σ 1i1={ 146.2,162.8,176.9,188.7,198.5,206.7,213.3,218.5,222.5,225.3,226.9,227.5,226.9,225.3,222.5,218.5,213.3,206.7,198.5,188.7,176.9,162.8,146.2}, σ 1i2={ 181.2,186.2,190.8,194.9,198.6,201.9,204.7,206.9,208.7,210.0,210.7,211.0,210.7,210.0,208.7,206.9,204.7,201.9,198.6,194.9,190.8,186.2,181.2}, units MPa;
Subsequently, in step 7, calculate the first frame, the second frame strip surface aberration function
Figure DEST_PATH_862306DEST_PATH_IMAGE068
;
Subsequently, in step 8, the judgement inequality set up? obviously inequality 0.294<0.3 is set up, and proceeds to step 9; Otherwise, readjust the roller curve parameter, proceed to step 6;
Subsequently, in step 9, calculate the first frame, the second breast roller surface chromatic aberration function
Figure DEST_PATH_931205DEST_PATH_IMAGE070
;
Subsequently, in step 10, judged result is less than
Figure DEST_PATH_984611DEST_PATH_IMAGE071
set up? obviously inequality 0.344<0.5 is set up, and proceeds to step 11; Otherwise, readjust the roller curve parameter, proceed to step 6;
Subsequently, in step 11, calculate the first frame, the second frame aberration Comprehensive Control function
Figure DEST_PATH_762074DEST_PATH_IMAGE072
, get weight coefficient β=0.6 in this embodiment.
Subsequently, in step 12, the constraint IF condition
Figure DEST_PATH_242734DEST_PATH_IMAGE073
set up? obviously inequality 0.395<0.4 is set up, and proceeds to step 13; Otherwise, readjust the roller curve parameter, proceed to step 6, in this embodiment, get λ=0.4;
Subsequently, in step 13, calculate the first frame, the second frame plate shape peak index
Figure DEST_PATH_987705DEST_PATH_IMAGE074
;
Subsequently, in step 14, the judgement inequality
Figure DEST_PATH_579224DEST_PATH_IMAGE017
set up? obviously inequality 0.407<0.45 is set up, and proceeds to step 15, otherwise, readjust the roller curve parameter, proceed to step 6, in this embodiment, get k st=0.45;
Subsequently, in step 15, calculate pressure peak index between the first frame, the second breast roll
Figure DEST_PATH_273510DEST_PATH_IMAGE075
;
Subsequently, in step 16, the judgement inequality
Figure DEST_PATH_128334DEST_PATH_IMAGE020
set up? obviously inequality 0.363≤0.4 is set up, and proceeds to step 17, otherwise, readjust the roller curve parameter, proceed to step 6, in this embodiment, get k sq=0.4;
Subsequently, in step 17, calculate the first frame, the second frame draught pressure peak index
Figure DEST_PATH_908071DEST_PATH_IMAGE076
;
Subsequently, in step 18, the judgement inequality
Figure DEST_PATH_303280DEST_PATH_IMAGE077
set up? obviously inequality 0.365<0.4 is set up, and proceeds to step 19, otherwise, readjust the roller curve parameter, proceed to step 6, in this embodiment, get k sq'=0.4;
Subsequently, in step 19, calculate the Comprehensive Control function of the first frame, the second frame plate shape and roller consumption
Figure DEST_PATH_806068DEST_PATH_IMAGE078
, in this embodiment, get ;
Subsequently, in step 20, the constraint IF condition
Figure DEST_PATH_895564DEST_PATH_IMAGE080
set up? obviously inequality sets up 0.392<0.45, proceeds to step 21; Otherwise, readjust the roller curve parameter, proceed to step 6, get φ=0.45 in this embodiment;
Subsequently, in step 21, calculate roll shape optimization aim function E (X)=0.98;
Do you subsequently, in step 22, judge that the Powell condition sets up? if be false, adjust the roller curve parameter, repeating step 6 to 21, until the Powell condition is set up, finishes to calculate, and draws optimum roller curve parameter.
Finally, in step 23, by optimum roller curve parameter
Figure DEST_PATH_32147DEST_PATH_IMAGE081
Figure DEST_PATH_701026DEST_PATH_IMAGE082
the roller curve equation of substitution working roll and the roller curve equation of backing roll obtain the roller curve equation of optimum working roll:
Figure DEST_PATH_881340DEST_PATH_IMAGE083
The roller curve equation of optimum backing roll is:
Figure DEST_PATH_635670DEST_PATH_IMAGE084
。
embodiment 2: referring to Fig. 5-Fig. 8.
At first, in step 1, collect the apparatus characteristic parameter of Two-stand Temper Mill group, mainly comprise: the first frame, the second frame working roll and backing roll diameter D 1w=D 2w=450mm, D 1b=D 2b=1100mm, working roll and backing roll barrel length L w1=L w2=L b1=L b2=1450mm, working roll bending cylinder is apart from l 1=l 2=2400mm, housing screw center square L 1=L 2=2400mm, maximum positive bending roller force S + 1max=S + 2max=800kN, maximum negative bending roller force S - 1max=S - 2max=-800kN, the maximum roller amount of just inclining
Figure DEST_PATH_372681DEST_PATH_IMAGE085
, the maximum negative roller amount of inclining
Figure DEST_PATH_833750DEST_PATH_IMAGE086
, maximum rolling force
Figure DEST_PATH_263594DEST_PATH_IMAGE087
, maximum mill speed
Figure DEST_PATH_211213DEST_PATH_IMAGE088
, work roll surface actual hardness K w=1100, roll surface actual hardness K b=1200;
Subsequently, in step 2, the ideal format product parameters of each description scope of collecting belt steel, comprise strip width
Figure DEST_PATH_486337DEST_PATH_IMAGE056
, thickness
Figure DEST_PATH_129808DEST_PATH_IMAGE056
, yield limit
Figure DEST_PATH_402657DEST_PATH_IMAGE057
, breaking elongation , the first frame rolling force setup value
Figure DEST_PATH_210393DEST_PATH_IMAGE059
, the second frame sets the rolling force setup value
Figure DEST_PATH_895321DEST_PATH_IMAGE060
, entrance tension force setting value
Figure DEST_PATH_666968DEST_PATH_IMAGE061
, intermediate tension setting value , outlet tension force setting value
Figure DEST_PATH_437795DEST_PATH_IMAGE063
.Specifically as shown in table 1.
Table 2 ideal format product
Sequence number 1 2 3 4 5 6 7 8
Yield limit/MPa 230 230 230 230 420 420 420 420
Width/mm 1050 1002 983 930 837 876 905 938
Speed/m/min 439 475 360 300 628 740 700 690
Thickness/μ m 253 351 402 502 181 201 242 250
Outlet tension force/kN 3200 3500 3500 3300 3099 3500 3999 4000
Breaking elongation/% 1.32 1.37 1.32 1.39 1.27 1.32 1.34 1.33
1# roll-force/kN 3121 2806 2252 2003 5420 7075 7233 6498
The 2# roll-force 2051 2002 2002 2004 2450 2501 2501 2500
Entrance tension force/kN 3200 3400 3401 3300 1950 2230 2849 2850
Intermediate tension/kN 3350 3450 3450 3500 3499 4000 4578 4581
Subsequently, in step 3, set the bending roller force S of the first frame, the second frame 1, S 2, roller η inclines 1, η 2in ground state,
Subsequently, in step 4, two frames of Two-stand Temper Mill group adopt identical roll shape, do not add differentiation here.With a, b, c, k 1, δ, l z, k is roller curve parameter and optimized variable, sets respectively the curvilinear equation of working roll and backing roll.Wherein, the roller curve equation of setting working roll is:
Figure DEST_PATH_859177DEST_PATH_IMAGE091
The roller curve equation of setting backing roll is:
Figure DEST_PATH_279794DEST_PATH_IMAGE045
Subsequently, in step 5, given initial curve parameter ;
Subsequently, in step 6, utilizing roller is elastic model, adopts the segmentation discrete method, and backing roll is divided into along barrel length
Figure DEST_PATH_803497DEST_PATH_IMAGE067
section, band are divided into
Figure DEST_PATH_728727DEST_PATH_IMAGE092
section, calculate the first frame, the second frame roll force distribution q bwil={ 6073.2,6231.8,6414.1,6620.4,6850.2,7102.2,7374.6,7623.5,7848.1,8048.1,8223.5,8374.5,8501.3,8604.5,8684.2,8740.9,8774.7,8786.0,8774.7,8740.9,8684.2,8604.5,8501.3,8374.5,8223.5,8048.1,7848.1,7623.5,7374.6,7102.2,6850.2,6620.4,6414.1,6231.8,6073.2}, q bwi2={ 7644.1,7635.8,7661.3,7720.8,7814.1,7939.9,8096.4,8241.2,8373.4,8492.3,8597.4,8688.4,8765.4,8828.2,8877.0,8911.7,8932.5,8939.5,8932.5,8911.7,8877.0,8828.2,8765.4,8688.4,8597.4,8492.3,8373.4,8241.2,8096.4,7939.9,7814.1,7720.8,7661.3,7635.8,7644.1}, the kN/m of unit;
Roll-force distribution q' i1={ 7651.0,7276.1,6938.8,6639.0,6376.6,6150.9,5961.3,5807.3,5688.3,5603.6,5553.0,5536.1,5553.0,5603.6,5688.3,5807.3,5961.3,6150.9,6376.6,6639.0,6938.8,7276.1,7651.0}, q' i2={ 7293.9,7023.9,6778.0,6557.3,6362.2,6193.1,6050.1,5933.2,5842.5,5777.7,5738.9,5725.9,5738.9,5777.7,5842.5,5933.2,6050.1,6193.1,6362.2,6557.3,6778.0,7023.9, the kN/m of 7293.9} unit;
Toe-out stress distribution σ 1i1={ 185.4,195.3,204.3,212.4,219.6,225.8,231.1,235.3,238.7,241.0,242.5,242.9,242.5,241.0,238.7,235.3,231.1,225.8,219.6,212.4,204.3,195.3,185.4}, σ 1i2={ 168.7,175.3,181.5,187.1,192.1,196.5,200.3,203.3,205.7,207.5,208.5,208.8,208.5,207.5,205.7,203.3,200.3,196.5,192.1,187.1,181.5,175.3,168.7}, units MPa;
Subsequently, in step 7, calculate the first frame, the second frame strip surface aberration function
Figure DEST_PATH_139986DEST_PATH_IMAGE093
;
Subsequently, in step 8, the judgement inequality
Figure DEST_PATH_201483DEST_PATH_IMAGE069
set up? obviously inequality 0.292<0.3 is set up, and proceeds to step 9; Otherwise, readjust the roller curve parameter, proceed to step 6;
Subsequently, in step 9, calculate the first frame, the second breast roller surface chromatic aberration function
Figure DEST_PATH_423517DEST_PATH_IMAGE094
;
Subsequently, in step 10, judged result is less than
Figure DEST_PATH_836044DEST_PATH_IMAGE071
set up? obviously inequality 0.343<0.5 is set up, and proceeds to step 11; Otherwise, readjust the roller curve parameter, proceed to step 6;
Subsequently, in step 11, calculate the first frame, the second frame aberration Comprehensive Control function
Figure DEST_PATH_864043DEST_PATH_IMAGE095
, in this embodiment, get weight coefficient
Figure DEST_PATH_734041DEST_PATH_IMAGE096
.
Subsequently, in step 12, the constraint IF condition
Figure DEST_PATH_923714DEST_PATH_IMAGE073
set up? obviously inequality 0.38<0.4 is set up, and proceeds to step 13; Otherwise, readjust the roller curve parameter, proceed to step 6, in this embodiment, get
Figure DEST_PATH_823536DEST_PATH_IMAGE097
;
Subsequently, in step 13, calculate the first frame, the second frame plate shape peak index
Figure DEST_PATH_327330DEST_PATH_IMAGE098
;
Subsequently, in step 14, the judgement inequality
Figure DEST_PATH_628998DEST_PATH_IMAGE017
set up? obviously inequality 0.259<0.45 is set up, and proceeds to step 15, otherwise, readjust the roller curve parameter, proceed to step 6, in this embodiment, get
Figure DEST_PATH_989573DEST_PATH_IMAGE099
;
Subsequently, in step 15, calculate pressure peak index between the first frame, the second breast roll
Figure DEST_PATH_563642DEST_PATH_IMAGE100
;
Subsequently, in step 16, the judgement inequality
Figure DEST_PATH_933444DEST_PATH_IMAGE020
set up? obviously inequality 0.343<0.4 is set up, and proceeds to step 17, otherwise, readjust the roller curve parameter, proceed to step 6, in this embodiment, get
Figure DEST_PATH_824039DEST_PATH_IMAGE101
;
Subsequently, in step 17, calculate the first frame, the second frame draught pressure peak index
Figure DEST_PATH_558777DEST_PATH_IMAGE102
;
Subsequently, in step 18, the judgement inequality
Figure DEST_PATH_167613DEST_PATH_IMAGE077
set up? obviously inequality 0.333<0.4 is set up, and proceeds to step 19, otherwise, readjust the roller curve parameter, proceed to step 6, in this embodiment, get
Figure DEST_PATH_341105DEST_PATH_IMAGE103
;
Subsequently, in step 19, calculate the Comprehensive Control function of the first frame, the second frame plate shape and roller consumption
Figure DEST_PATH_40202DEST_PATH_IMAGE104
, in this embodiment, get
Figure DEST_PATH_8158DEST_PATH_IMAGE079
;
Subsequently, in step 20, the constraint IF condition
Figure DEST_PATH_41973DEST_PATH_IMAGE080
set up? obviously inequality sets up 0.346<0.45, proceeds to step 21; Otherwise, readjust the roller curve parameter, proceed to step 6, in this embodiment, get
Figure DEST_PATH_753577DEST_PATH_IMAGE105
;
Subsequently, in step 21, calculate roll shape optimization aim function
Figure DEST_PATH_618765DEST_PATH_IMAGE106
;
Do you subsequently, in step 22, judge that the Powell condition sets up? if be false, adjust the roller curve parameter, repeating step 6 to 21, until the Powell condition is set up, finishes to calculate, and draws optimum roller curve parameter.
Finally, in step 23, by optimum roller curve parameter
Figure DEST_PATH_944573DEST_PATH_IMAGE081
Figure DEST_PATH_528001DEST_PATH_IMAGE107
the roller curve equation of substitution working roll and the roller curve equation of backing roll obtain the roller curve equation of optimum working roll:
The roller curve equation of optimum backing roll is:
。
  
It should be noted that above-described embodiment is only preferred embodiment of the present invention, is not that protection scope of the present invention is as the criterion with claims for limiting protection scope of the present invention.

Claims (5)

1. the roller type curve design method of the smooth unit of Stand Mill four roller is characterized in that said method comprising the steps of:
(a) collect the apparatus characteristic parameter of Two-stand Temper Mill group;
(b) the ideal format product supplied materials parameter of each description scope of collecting belt steel;
(c) set the bending roller force of the first frame, the second frame
Figure 219512DEST_PATH_IMAGE001
, roller inclines
Figure 478455DEST_PATH_IMAGE002
in ground state;
(d), with roller curve parameter and optimized variable, set the roller curve of working roll and backing roll;
(e) optimize and calculate the roller curve parameter;
(f) substitution of optimum roller curve parameter is obtained to the roller curve equation of optimum working roll and backing roll.
2. the roller type curve design method of the smooth unit of Stand Mill four roller according to claim 1 is characterized in that: described step (e) optimization calculates the roller curve parameter, specifically comprises the following steps:
E1) given initial curve parameter
Figure 904888DEST_PATH_IMAGE003
;
E2) utilizing roller is elastic model, adopts the segmentation discrete method, and backing roll is divided into along barrel length
Figure 907479DEST_PATH_IMAGE004
section, band are divided into
Figure 867083DEST_PATH_IMAGE005
section, calculate the first frame, the second frame roll force distribution
Figure 969031DEST_PATH_IMAGE006
, roll-force distributes
Figure 210656DEST_PATH_IMAGE007
, the toe-out stress distribution
Figure 689042DEST_PATH_IMAGE008
;
E3) calculate the first frame, the second frame strip surface aberration function , its Mathematical Modeling is:
Figure 605363DEST_PATH_IMAGE010
, in formula for the standard resistance of deformation, get
Figure 849317DEST_PATH_IMAGE012
,
Figure 284977DEST_PATH_IMAGE013
for the practical distortion drag of band,
Figure 791045DEST_PATH_IMAGE014
for weight coefficient,
Figure 944946DEST_PATH_IMAGE015
;
E4) judgement inequality
Figure 765134DEST_PATH_IMAGE016
, band aberration critical value,
Figure 230806DEST_PATH_IMAGE018
, whether set up, if inequality is set up, proceed to step e5), otherwise, readjust the roller curve parameter, proceed to step e2);
E5) calculate the first frame, the second breast roller surface chromatic aberration function
Figure 606423DEST_PATH_IMAGE019
, its Mathematical Modeling is: , in formula
Figure 437293DEST_PATH_IMAGE021
for standard roller surface hardness, get
Figure 550743DEST_PATH_IMAGE022
,
Figure 413656DEST_PATH_IMAGE023
for the work roll surface actual hardness, for the roll surface actual hardness;
E6) judged result is less than
Figure 418837DEST_PATH_IMAGE025
,
Figure 640871DEST_PATH_IMAGE026
roll aberration critical value,
Figure 787818DEST_PATH_IMAGE027
, whether set up, if inequality is set up, proceed to step e7), otherwise, readjust the roller curve parameter, proceed to step e2);
E7) calculate the first frame, the second frame aberration Comprehensive Control function
Figure 753500DEST_PATH_IMAGE028
, its Mathematical Modeling is , wherein for weight coefficient,
E8) constraint IF condition
Figure 227841DEST_PATH_IMAGE031
,
Figure 230170DEST_PATH_IMAGE032
for constant, get 0.1-0.5, whether set up, if inequality is set up, proceed to step e9); Otherwise, readjust the roller curve parameter, proceed to step e2);
E9) calculate the first frame, the second frame plate shape peak index
Figure 266259DEST_PATH_IMAGE033
,
Figure 830095DEST_PATH_IMAGE034
represent shelf number, its Mathematical Modeling is
Figure 951635DEST_PATH_IMAGE035
;
E10) judgement inequality
Figure 259120DEST_PATH_IMAGE036
,
Figure 415295DEST_PATH_IMAGE037
be to allow forward pull cross direction profiles peak-peak whether to set up, if inequality is set up, proceed to step e11), otherwise, readjust the roller curve parameter, proceed to step e2);
E11) calculate pressure peak index between the first frame, the second breast roll
Figure 150032DEST_PATH_IMAGE038
,
Figure 758868DEST_PATH_IMAGE034
represent shelf number, its Mathematical Modeling is
Figure 103000DEST_PATH_IMAGE039
;
E12) judgement inequality
Figure 113681DEST_PATH_IMAGE040
, be to allow roll force distribution cross direction profiles peak-peak whether to set up, if inequality is set up, proceed to step e13), otherwise, readjust the roller curve parameter, proceed to step e2);
E13) calculate the first frame, the second frame draught pressure peak index
Figure 115452DEST_PATH_IMAGE042
,
Figure 827056DEST_PATH_IMAGE034
represent shelf number, its Mathematical Modeling is ;
E14) judgement inequality
Figure 34364DEST_PATH_IMAGE044
,
Figure 289896DEST_PATH_IMAGE041
be to allow draught pressure distribution cross direction profiles peak-peak whether to set up, if inequality is set up, proceed to step e15), otherwise, readjust the roller curve parameter, proceed to step e2);
E15) calculate the Comprehensive Control function of the first frame, the second frame plate shape and roller consumption
Figure 805191DEST_PATH_IMAGE045
, its Mathematical Modeling is , in formula
Figure 536441DEST_PATH_IMAGE047
for weight coefficient, meet
Figure 341586DEST_PATH_IMAGE048
,
Figure 332676DEST_PATH_IMAGE049
represent plate shape uniformity index,
Figure 172456DEST_PATH_IMAGE050
represent roll gap pressure uniformity index, represent draught pressure uniformity index, its mathematic(al) representation is:
Figure 148819DEST_PATH_IMAGE052
Figure 678020DEST_PATH_IMAGE053
Figure 637886DEST_PATH_IMAGE054
；
E16) constraint IF condition
Figure 731525DEST_PATH_IMAGE055
, for constant, get 0.1-0.5, whether set up, if inequality is set up, proceed to step e17); Otherwise, readjust the roller curve parameter, proceed to step e2);
E17) calculate roll shape optimization aim function:
Figure 906471DEST_PATH_IMAGE057
, in formula
Figure 658527DEST_PATH_IMAGE058
be the weight coefficient of specification product in j, determined by the ratio of production output in total output of each specification product;
E18) judge whether the Powell condition is set up, if be false, adjust the roller curve parameter, repeating step e2) to e17), until the Powell condition is set up, finish to calculate, draw optimum roller curve parameter.
3. the roller type curve design method of the smooth unit of Stand Mill four roller according to claim 1 and 2, it is characterized in that: described step (a) is collected the apparatus characteristic parameter of Two-stand Temper Mill group, mainly comprises: the first frame, the second frame working roll and backing roll diameter
Figure 480989DEST_PATH_IMAGE059
, working roll and backing roll barrel length
Figure 685706DEST_PATH_IMAGE060
, the working roll bending cylinder distance
Figure 884606DEST_PATH_IMAGE061
, housing screw center square , maximum positive bending roller force
Figure 484532DEST_PATH_IMAGE063
,
Figure 675079DEST_PATH_IMAGE064
maximum negative bending roller force
Figure 677670DEST_PATH_IMAGE065
, the maximum roller amount of just inclining
Figure 201055DEST_PATH_IMAGE066
, the maximum negative roller amount of inclining
Figure 303004DEST_PATH_IMAGE067
, maximum rolling force
Figure 544629DEST_PATH_IMAGE068
, maximum mill speed , the work roll surface actual hardness , the roll surface actual hardness
Figure 939335DEST_PATH_IMAGE024
.
4. the roller type curve design method of the smooth unit of Stand Mill four roller according to claim 1 and 2, it is characterized in that: the ideal format product parameters of each description scope of step (b) collecting belt steel comprises strip width
Figure 402678DEST_PATH_IMAGE070
, thickness
Figure 747072DEST_PATH_IMAGE070
, yield limit
Figure 415688DEST_PATH_IMAGE071
, breaking elongation
Figure 187335DEST_PATH_IMAGE072
, the first frame rolling force setup value
Figure 75656DEST_PATH_IMAGE073
, the second frame sets the rolling force setup value , entrance tension force setting value , intermediate tension setting value
Figure 190877DEST_PATH_IMAGE076
, outlet tension force setting value
Figure 628812DEST_PATH_IMAGE077
.
5. the roller type curve design method of the smooth unit of Stand Mill four roller according to claim 1 and 2 is characterized in that: the roller curve equation of setting working roll in described step (d) is:
Figure 252691DEST_PATH_IMAGE078
The roller curve equation of setting backing roll is:
Figure 459681DEST_PATH_IMAGE079
。
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CN116000258A (en) * 2023-02-01 2023-04-25 东北大学 Hole pattern manufacturing method for continuous casting round billet solidification tail end pressing
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