CN105013835A  Original roller seam setting method based on thermal crown in ultrathin strip rolling conducted by cold continuous rolling unit  Google Patents
Original roller seam setting method based on thermal crown in ultrathin strip rolling conducted by cold continuous rolling unit Download PDFInfo
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 CN105013835A CN105013835A CN201410165544.3A CN201410165544A CN105013835A CN 105013835 A CN105013835 A CN 105013835A CN 201410165544 A CN201410165544 A CN 201410165544A CN 105013835 A CN105013835 A CN 105013835A
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 238000005096 rolling process Methods 0.000 title claims abstract description 70
 238000000034 method Methods 0.000 claims abstract description 63
 229910000831 Steel Inorganic materials 0.000 claims abstract description 54
 239000010959 steel Substances 0.000 claims abstract description 54
 238000009826 distribution Methods 0.000 claims description 54
 239000000839 emulsion Substances 0.000 claims description 23
 238000001816 cooling Methods 0.000 claims description 16
 238000003801 milling Methods 0.000 claims description 10
 239000000463 material Substances 0.000 claims description 7
 238000005482 strain hardening Methods 0.000 claims description 7
 230000005489 elastic deformation Effects 0.000 claims description 6
 230000000875 corresponding Effects 0.000 claims description 5
 230000001050 lubricating Effects 0.000 claims description 5
 210000000481 Breast Anatomy 0.000 claims description 4
 101700050571 SUOX Proteins 0.000 claims description 4
 239000012530 fluid Substances 0.000 claims description 4
 238000004064 recycling Methods 0.000 claims description 3
 238000004364 calculation method Methods 0.000 abstract description 4
 238000010586 diagram Methods 0.000 description 5
 238000005516 engineering process Methods 0.000 description 5
 230000000694 effects Effects 0.000 description 3
 238000007796 conventional method Methods 0.000 description 2
 238000007630 basic procedure Methods 0.000 description 1
 239000002826 coolant Substances 0.000 description 1
 238000004519 manufacturing process Methods 0.000 description 1
 230000004048 modification Effects 0.000 description 1
 238000006011 modification reaction Methods 0.000 description 1
 238000005457 optimization Methods 0.000 description 1
 238000007668 thin rolling process Methods 0.000 description 1
Abstract
The invention provides an original roller seam setting method based on thermal crown in ultrathin strip rolling conducted by a cold continuous rolling unit. The method includes the steps that firstly, a roller twodimensional temperature field calculation model is established through a finite difference method; then, the dynamic change of the thermal crown of a roller is solved through an elasticplastic mechanics method; and finally, the original roller seam can be set. The step that the roller twodimensional temperature field calculation model is established includes the substep that relevant parameters and initial values of the parameters are acquired. The step that the dynamic change of the thermal crown of the roller is solved includes the substep that the thermal crown of various rack work rollers is determined. When the relevant parameters are acquired, main equipment and technological parameters of the 3+2 type fiverack continuous rolling unit are collected, and the parameters of the relevant process relating to the thermal crown calculation process are defined. According to the method, due to the fact that the dynamic thermal crown of the roller is accurately regressed, the original roller seam can be accurately set, the control precision of the plate shape and the plate thickness of the unit is achieved, the possibility of the situation that unqualified products exit is reduced, the quality of finished strip steel of the unit is improved, and large onsite economic benefits are generated.
Description
Technical field
The present invention relates to a kind of original intermesh determination method in tandem mills strip in razorthin operation of rolling.
Background technology
The five Stands Cold Tandem Mill groups (hereinafter referred to as 3+2 type five frame cold mill complex) that first three frame adopting fourhigh mill and latter two frame adopting sixhigh cluster mill form, compared with being all the unit of sixhigh cluster mill, 3+2 type five frame cold mill complex has saved cost of investment, both economical, and compared with being all the unit of 4 roller mills, the Strip Shape Control ability of 3+2 type five frame cold mill complex is more powerful, and it is also more outstanding to roll thin ability.But, along with belt steel thickness constantly diminishes, the requirement of unit gage and shape control precision is also improved gradually.In gage and shape control process, except needing to accurately calculate the elastic deformation of roller system, the roll thermal crown of roll also plays conclusive effect to the control accuracy of strip flatness and gauge.On the one hand, under the comprehensive function of being with steel and cooling medium, roll produces differential thermal expansion along body of roll direction, changes the roll gap shape of original start, directly the gage and shape control of impact outlet band steel; On the other hand, the inhomogeneous deformation of roll can compensate again the impact of roll elastic deformation and roll wear in the operation of rolling.In addition, the roll thermal crown change of working roll is except having an impact to the strip flatness and gauge of this frame band, also directly can have influence on the setting of followup milling train relevant parameter, if frame is due to the change of roll thermal crown above, cause the deviation of plate shape and strip crown beyond the ability of regulation and control of followup frame roller system parameter to plate shape and strip crown, then unit is difficult to produce qualified product, and this carries out integrated control with regard to needing scene to the impact of institute's organic frame roll thermal crown.Like this, in the paperthin strip operation of rolling, how accurately to return out the situation of change of each frame work roll thermal crown, realize the accurate setting to original roll gap, the gage and shape control precision improving finished strip just becomes the focus of site technology tackling key problem.
Summary of the invention
The object of this invention is to provide the original intermesh determination method based on roll thermal crown in the rolling of a kind of tandem mills strip in razorthin, effectively can realize the setting of original roll gap, to improve outlet Strip Shape strip thickness control precision.
Based on the original intermesh determination method of roll thermal crown in tandem mills strip in razorthin of the present invention rolling, comprising: first adopt finite difference calculus to set up roll twodimensional temperature field computation model; The method of recycling plastoelasticity solves the dynamic change of roller heat convex degree learning; Finally realize the setting of original roll gap.
Wherein, set up roll twodimensional temperature field computation model and comprise acquisition relevant parameter, parameter initialize.
The dynamic change solving roller heat convex degree learning comprises determines each frame work roll thermal crown.
Wherein, obtain relevant parameter to comprise: collect capital equipment and the technological parameter of 3+2 type five Stands Cold Tandem Mill group, define relevant process parameters involved in roll thermal crown computational process;
Wherein, the capital equipment collecting 3+2 type five Stands Cold Tandem Mill group comprises to technological parameter: collect relevant roller system parameter, given band steel to be produced specification feature and technological parameter, collect main technique lubricating regime parameter, collect the relevant parameter related in heat transfer computational process;
Wherein, in definition roll thermal crown computational process, involved relevant process parameters comprises: belt steel rolling time t, roll along body of roll direction segments M, roll along direction, roller footpath segments N, process variable m=1,2, M, n=1,2 ... roll thermal crown distribution when N, the ith frame working roll temperature rolling
ith frame working roll Temperature Distribution initial value
t ith frame working roll Temperature Distribution
ith frame working roll reaches Temperature Distribution during stable state
the coefficientoffrictionμ of time search step delta t, process variable j, the ith frame
_{i}, the ith frame deformation heat
the frictional heat of the ith frame
the temperature of the ith frame band steel in deformed area
thermal expansion of the working roll factor beta
_{t}, the Poisson's ratio ν of working roll material, the original fixed value of roller slit H of each frame
_{i}, the best original fixed value of roller slit of each frame
Parameter initialize is the setting value H to the original roll gap of each frame
_{i}initialize.
Wherein, determine that each frame work roll thermal crown comprises:
D () order represents the process variable i=1 of shelf number;
E () gets each frame working roll
model carries out dividing elements, sets up twodimensional cell model that is radial and axis, each equal segments width along body of roll direction
along each equal segments width in direction, roller footpath
(f) preset time stepsize in search Δ t, roll initial temperature
process variable j=0, wherein should meet inequality according to the restrictive condition time search step delta t of two dimensions and unstable heat conduction
$\mathrm{\Δt}\≤\frac{1}{2\mathrm{\α}(\frac{1}{\mathrm{\Δ}{L}_{i}^{2}}+\frac{1}{\mathrm{\Δ}{r}_{i}^{2}})};$
G () uses finite difference calculus to calculate the ith frame working roll Temperature Distribution
Finite difference calculus is used to calculate the ith frame working roll Temperature Distribution
comprise the following step performed by computer:
G1) belt steel rolling time t=j Δ t is made;
G2) with the initial strength σ of band
_{s0}, strain hardening coefficient k
_{s}, the width B of band, inlet thickness be h
_{i1}, exit thickness is h
_{i}, entrance tension force is T
_{i1}, outlet tension force is T
_{i}, muzzle velocity is v
_{i}, concentration of emulsion used C, emulsion initial temperature setting value T
_{b}, the ith frame emulsion flow setting value W
_{i}for primary condition, under calculating current working, the coefficientoffrictionμ of the ith frame
_{i}, the deformation heat that produces because of resistance to deformation in the operation of rolling
the frictional heat produced owing to being with the relative sliding of steel and roll
G3) with the coefficientoffrictionμ of the ith frame
_{i}, the deformation heat that produces because of resistance to deformation in the operation of rolling
the frictional heat produced owing to being with the relative sliding of steel and roll
for primary condition, call band steel temperature rise computation model, determine the temperature of the ith frame band steel in deformed area
G4) ignore the circumferential heat conduction of roll, and deformation heat and frictional heat are passed to the heat that the part of working roll and cooling fluid take away and regard boundary condition as, according to the twodimentional heat conduction equation of roll, the difference expression can listing work roll thermal equilibrium equation is:
$[\frac{{T}_{m,n+1}^{i,t}2{T}_{m,n}^{i,t}+{T}_{m,n1}^{i,t}}{{\left(\mathrm{\Δ}{r}_{i}\right)}^{2}}+\frac{{T}_{m,n+1}^{i,t}{T}_{m,n1}^{i,t}}{2{r}_{m,n}^{i}\mathrm{\Δ}{r}_{i}}+\frac{{T}_{m+1,n}^{i,t}2{T}_{m,n}^{i,t}+{T}_{m1,n}^{i,t}}{{\left(\mathrm{\Δ}{L}_{i}\right)}^{2}}]=\left(\frac{{T}_{m,n}^{i,t+\mathrm{\Δt}}{T}_{m,n}^{i,t}}{\mathrm{\α\Δt}}\right),$ In formula
${r}_{m,n}^{i}=n\×\mathrm{\Δ}{r}_{i}$ Be the ith frame working roll m, the radius corresponding to n unit;
G5) according to principle of energy balance, with Newton's law of cooling obtain roll each several part boundary condition difference equation, by the cell node (m on the surface of roll for body of roll rolling section, n+1) heat transfer between internal node is no longer regarded as, but replaced by Newton's law of cooling, for the nonrolling section of the body of roll, heat transfer not with steel and roll shop building, for roller shoulder portion, cell node (the m+1 of roller shoulder portion, n) no longer as being heat transfer between internal node, but replaced by Newton's law of cooling; For symmetrical border, its thermograde should be zero, namely
G6) according to g2)g5), determine the thermo parameters method of the ith frame working roll t+ Δ t
G7) inequality is judged
set up? if inequality is set up, illustrate that the thermo parameters method of now working roll reaches stable state, order
proceed to step (h); If inequality is false, then make j=j+1, proceed to step g 1);
H () uses correlation technique described in elastic plastic theory, solve the roll thermal crown distribution of the ith frame working roll under stable state
$\mathrm{\Δ}{D}_{m}^{i}=4(1+v)\frac{{\mathrm{\β}}_{t}}{{D}_{\mathrm{iw}}}{\∫}_{0}^{{D}_{\mathrm{iw}}/2}({T}_{m,n}^{i}{T}_{B}){r}_{m,n}^{i}{\mathrm{dr}}_{i};$
Does i () judge that inequality i<6 sets up? if inequality is set up, then make i=i+1, proceed to step (d), calculate the roll thermal crown distribution of next frame; If inequality is false, then proceed to step (j).
Wherein, the setting realizing original roll gap comprises:
J () distributes and the spring equation of milling train, the elastic deformation model of milling train in conjunction with the roll thermal crown of the original roller type of roll, each breast roller, under solving current intermesh determination situation, and the exit thickness distribution h of last frame band steel
_{in}with plate shape distribution σ
_{5n}(n is bar unit number);
K () solves the object function of intermesh determination
$F={\mathrm{\α}}_{1}\left[\frac{\frac{1}{n}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{h}_{5j}{h}_{5}}{\mathrm{\Δh}}\right]+(1{\mathrm{\α}}_{1})\left[\frac{\frac{1}{n}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\σ}}_{5j}{\mathrm{\σ}}_{5}}{\mathrm{\Δ\σ}}\right],$ Wherein
strip crown relative deviation surplus, Target Board convexity relative deviation surplus is less, and strip crown is better;
be plate shape relative deviation surplus, target flatness relative deviation surplus is less, and plate shape is better; α
_{1}for the weight coefficient of merit plate shape and plate convexity, general α
_{1}=0.30.7;
Does l () judge that Powell condition is set up (namely judging that whether objective function F minimum)? if Powell condition is set up, then make best fixed value of roller slit
proceed to step (m), otherwise again original roll gap is set, proceed to step (c);
The roll thermal crown distribution of each frame working roll under (m) output current working
and the best original fixed value of roller slit of each frame
complete the original intermesh determination in the 3+2 type five Stands Cold Tandem Mill group strip in razorthin operation of rolling.
The invention has the beneficial effects as follows: by returning out the Dynamic Thermal convexity of roll accurately, realize the accurate setting of original roll gap, improve the gage and shape control precision of unit, plate Shape closed rate can be made to drop to 0.68% from 1.32% before application, meanwhile, strip crown is qualified reaches more than 98.5%, reduces the probability that substandard product occurs, improve the quality of unit finished strip, bring larger economic benefit to scene.
Accompanying drawing explanation
Fig. 1 is the general flow chart based on the original intermesh determination method of roll thermal crown in the tandem mills strip in razorthin rolling of one embodiment of the invention;
Fig. 2 is the roll thermal crown forecast host computer flow chart of method in the 3+2 type five Stands Cold Tandem Mill group strip in razorthin operation of rolling of Fig. 1 embodiment;
Fig. 3 is working roll dividing elements figure in the roll thermal crown forecast host computer flow chart of Fig. 2;
Working roll Temperature calculating block diagram in determination each frame work roll thermal crown step of the method for Fig. 4 Fig. 1;
Fig. 5 is the first frame work roll thermal crown measured value and the calculated value correlation curve figure adopting the inventive method;
Fig. 6 is the second frame work roll thermal crown measured value and the calculated value correlation curve figure adopting the inventive method;
Fig. 7 is the 3rd frame work roll thermal crown measured value and the calculated value correlation curve figure adopting the inventive method;
Fig. 8 is the 4th frame work roll thermal crown measured value and the calculated value correlation curve figure adopting the inventive method;
Fig. 9 is the 5th frame work roll thermal crown measured value and the calculated value correlation curve figure adopting the inventive method;
Figure 10 is the inventive method and conventional method plate shape comparison diagram;
Figure 11 is the inventive method and conventional method strip crown comparison diagram.
Detailed description of the invention
For abovementioned purpose of the present invention, feature and advantage can be become apparent, below in conjunction with accompanying drawing, the specific embodiment of the present invention is elaborated.First it should be noted that, the present invention is not limited to following detailed description of the invention, and the spirit that those skilled in the art should embody from following embodiment is to understand the present invention, and each technical term can do the most wide in range understanding based on Spirit Essence of the present invention.Reference numeral identical in the accompanying drawings represents identical part.
Based on the original intermesh determination method of roll thermal crown in tandem mills strip in razorthin of the present invention rolling, comprising: first adopt finite difference calculus to set up roll twodimensional temperature field computation model; The method of recycling plastoelasticity solves the dynamic change of roller heat convex degree learning; Finally realize the setting of original roll gap.In one embodiment, as shown in Figure 1, set up roll twodimensional temperature field computation model and comprise acquisition relevant parameter, parameter initialize.The dynamic change solving roller heat convex degree learning comprises determines each frame work roll thermal crown.
The computational process of roll thermal crown as shown in Figure 2, comprising: a. collects capital equipment and the technological parameter of unit; B. the relevant process parameters related in computational process is defined; C. to initial roll gap initialize; D. order represents the process variable i=1 of shelf number; E. dividing elements is carried out to working roll; F. preset time stepsize in search Δ t; G. frame working roll Temperature Distribution is determined
h. the roll thermal crown distribution of frame working roll is determined
i.i<6?, then i=i+1 turn back to step e in this way, as otherwise j. solves the strip flatness and gauge distribution of finished strip; K. intermesh determination object function is solved; Is l.Powell condition set up?, be that m. exports best fixed value of roller slit, otherwise change fixed value of roller slit, return step c.
Wherein, obtain relevant parameter to comprise: collect capital equipment and the technological parameter of 3+2 type five Stands Cold Tandem Mill group, define relevant process parameters involved in roll thermal crown computational process;
Wherein, the capital equipment collecting 3+2 type five Stands Cold Tandem Mill group comprises to technological parameter: collect relevant roller system parameter, given band steel to be produced specification feature and technological parameter, collect main technique lubricating regime parameter, collect the relevant parameter related in heat transfer computational process;
Wherein, in definition roll thermal crown computational process, involved relevant process parameters comprises: belt steel rolling time t, roll along body of roll direction segments M, roll along direction, roller footpath segments N, process variable m=1,2, M, n=1,2 ... roll thermal crown distribution when N, the ith frame working roll temperature rolling
ith frame working roll Temperature Distribution initial value
t ith frame working roll Temperature Distribution
ith frame working roll reaches Temperature Distribution during stable state
the coefficientoffrictionμ of time search step delta t, process variable j, the ith frame
_{i}, the ith frame deformation heat
the frictional heat of the ith frame
the temperature of the ith frame band steel in deformed area
thermal expansion of the working roll factor beta
_{t}, the Poisson's ratio ν of working roll material, the original fixed value of roller slit H of each frame
_{i}, the best original fixed value of roller slit of each frame
Parameter initialize comprises: to the setting value H of the original roll gap of each frame
_{i}initialize.
Wherein, determine that each frame work roll thermal crown comprises:
D. order represents the process variable i=1 of shelf number;
E. each frame working roll is got
model carries out dividing elements, sets up twodimensional cell model that is radial and axis, as shown in Figure 3, and each equal segments width along body of roll direction
along each equal segments width in direction, roller footpath
$\mathrm{\Δ}{r}_{i}=\frac{{D}_{\mathrm{iw}}}{2N};$
F. preset time stepsize in search Δ t, roll initial temperature
process variable j=0, wherein should meet inequality according to the restrictive condition time search step delta t of two dimensions and unstable heat conduction
G. finite difference calculus is used to calculate the ith frame working roll Temperature Distribution
Finite difference calculus is used to calculate the ith frame working roll Temperature Distribution
comprise the following step performed by computer, as shown in Figure 4:
G1) belt steel rolling time t=j Δ t is made;
G2) with the initial strength σ of band
_{s0}, strain hardening coefficient k
_{s}, the width B of band, inlet thickness be h
_{i1}, exit thickness is h
_{i}, entrance tension force is T
_{i1}, outlet tension force is T
_{i}, muzzle velocity is v
_{i}, concentration of emulsion used C, emulsion initial temperature setting value T
_{b}, the ith frame emulsion flow setting value W
_{i}for primary condition, under calculating current working, the coefficientoffrictionμ of the ith frame
_{i}, the deformation heat that produces because of resistance to deformation in the operation of rolling
the frictional heat produced owing to being with the relative sliding of steel and roll
G3) with the coefficientoffrictionμ of the ith frame
_{i}, the deformation heat that produces because of resistance to deformation in the operation of rolling
the frictional heat produced owing to being with the relative sliding of steel and roll
for primary condition, call band steel temperature rise computation model, determine the temperature of the ith frame band steel in deformed area
G4) ignore the circumferential heat conduction of roll, and deformation heat and frictional heat are passed to the heat that the part of working roll and cooling fluid take away and regard boundary condition as, according to the twodimentional heat conduction equation of roll, the difference expression can listing work roll thermal equilibrium equation is:
$[\frac{{T}_{m,n+1}^{i,t}2{T}_{m,n}^{i,t}+{T}_{m,n1}^{i,t}}{{\left(\mathrm{\Δ}{r}_{i}\right)}^{2}}+\frac{{T}_{m,n+1}^{i,t}{T}_{m,n1}^{i,t}}{2{r}_{m,n}^{i}\mathrm{\Δ}{r}_{i}}+\frac{{T}_{m+1,n}^{i,t}2{T}_{m,n}^{i,t}+{T}_{m1,n}^{i,t}}{{\left(\mathrm{\Δ}{L}_{i}\right)}^{2}}]=\left(\frac{{T}_{m,n}^{i,t+\mathrm{\Δt}}{T}_{m,n}^{i,t}}{\mathrm{\α\Δt}}\right),$ In formula
${r}_{m,n}^{i}=n\×\mathrm{\Δ}{r}_{i}$ Be the ith frame working roll m, the radius corresponding to n unit;
G5) according to principle of energy balance, with Newton's law of cooling obtain roll each several part boundary condition difference equation, wherein it should be noted that, by the cell node (m on the surface of roll for body of roll rolling section, n+1) heat transfer between internal node is no longer regarded as, but replaced by Newton's law of cooling, for the nonrolling section of the body of roll, heat transfer not with steel and roll shop building, for roller shoulder portion, the cell node (m+1, n) of roller shoulder portion no longer as being heat transfer between internal node, but is replaced by Newton's law of cooling; For symmetrical border, its thermograde should be zero, namely
G6) according to g2)g5), determine the thermo parameters method of the ith frame working roll t+ Δ t
G7) inequality is judged
set up? if inequality is set up, illustrate that the thermo parameters method of now working roll reaches stable state, order
proceed to step (h); If inequality is false, then make j=j+1, proceed to step g 1);
H. use correlation technique described in elastic plastic theory, solve the roll thermal crown distribution of the ith frame working roll under stable state
$\mathrm{\Δ}{D}_{m}^{i}=4(1+v)\frac{{\mathrm{\β}}_{t}}{{D}_{\mathrm{iw}}}{\∫}_{0}^{{D}_{\mathrm{iw}}/2}({T}_{m,n}^{i}{T}_{B}){r}_{m,n}^{i}{\mathrm{dr}}_{i};$
I. do you judge that inequality i<6 sets up? if inequality is set up, then make i=i+1, proceed to step (d), calculate the roll thermal crown distribution of next frame; If inequality is false, then proceed to step (j).
Below the detail of abovedescribed embodiment is further described, understands the present invention so that clearer.
Based on an original intermesh determination technology for roll thermal crown in the 3+2 type tandem mills strip in razorthin operation of rolling, comprise the following step (computing block diagram is as shown in Figure 1) performed by computer:
(1) relevant parameter is obtained
A () collects capital equipment and the technological parameter of 3+2 type five Stands Cold Tandem Mill group, mainly comprise the following steps:
A1) collect relevant roller system parameter, mainly comprise: each frame working roll body of roll section diameter D
_{iw}, i=1,2 ... 5, each frame working roll body of roll partiallength L
_{iw};
A2) the specification feature of given band steel to be produced and technological parameter, mainly comprise: the initial strength σ of band
_{s0}, strain hardening coefficient k
_{s}, the width B of band, the thickness h of supplied materials
_{0}, each rack outlet thickness h
_{i}, each frame muzzle velocity v
_{i}, each frame outlet tension force σ
_{i}, uncoiling tension σ
_{0}, each frame draught pressure setting value P
_{i}, plate shape allows maximum deviation Δ σ, Target Board convexity to allow maximum deviation Δ h;
A3) collect main technique lubricating regime parameter, mainly comprise: concentration of emulsion used C, emulsion initial temperature setting value T
_{b}, each frame emulsion flow setting value W
_{i};
A4) collect the relevant parameter related in heat transfer computational process, mainly comprise: air themperature T
_{c}, strip steel at entry temperature
working roll temperature diffusivity α, heat exchange coefficient α between working roll and rolled piece
_{a}, heat exchange coefficient α between working roll and emulsion
_{b}, heat exchange coefficient α between working roll and air
_{c}, working roll specific heat C
_{p}, working roll thermal conductivity factor k, working roll density p;
Relevant process parameters involved in (b) definition roll thermal crown computational process, mainly comprise: belt steel rolling time t, roll are along body of roll direction segments M, roll along direction, roller footpath segments N, process variable m=1,2, M, n=1,2 ... roll thermal crown distribution when N, the ith frame working roll temperature rolling
ith frame working roll Temperature Distribution initial value
moment ith frame working roll Temperature Distribution
ith frame working roll reaches Temperature Distribution during stable state
the coefficientoffrictionμ of time search step delta t, process variable j, the ith frame
_{i}, the ith frame deformation heat
the frictional heat of the ith frame
the temperature of the ith frame band steel in deformed area
thermal expansion of the working roll factor beta
_{t}, the Poisson's ratio ν of working roll material, the original fixed value of roller slit H of each frame
_{i}, the best original fixed value of roller slit of each frame
(2) parameter initialize
C () is to the setting value H of the original roll gap of each frame
_{i}initialize;
(3) each frame work roll thermal crown is determined
D () order represents the process variable i=1 of shelf number;
E () considers the symmetry of temperature field to middle section, and ignore the heat transfer between roll and bearing, gets each frame working roll
model carries out dividing elements (as shown in Figure 3), sets up twodimensional cell model that is radial and axis, each equal segments width along body of roll direction
along each equal segments width in direction, roller footpath
$\mathrm{\Δ}{r}_{i}=\frac{{D}_{\mathrm{iw}}}{\mathrm{wN}};$
(f) preset time stepsize in search Δ t, roll initial temperature
process variable j=0, wherein should meet inequality according to the restrictive condition time search step delta t of two dimensions and unstable heat conduction
$\mathrm{\Δt}\≤\frac{1}{2\mathrm{\α}(\frac{1}{\mathrm{\Δ}{L}_{i}^{2}}+\frac{1}{\mathrm{\Δ}{r}_{i}^{2}})};$
G () uses finite difference calculus to calculate the ith frame working roll Temperature Distribution
mainly comprise the following step (computing block diagram is as shown in Figure 4) performed by computer:
G1) belt steel rolling time t=j Δ t is made;
G2) with the initial strength σ of band
_{s0}, strain hardening coefficient k
_{s}, the width B of band, inlet thickness be h
_{i1}, exit thickness is h
_{i}, entrance tension force is T
_{i1}, outlet tension force is T
_{i}, muzzle velocity is v
_{i}, concentration of emulsion used C, emulsion initial temperature setting value T
_{b}, the ith frame emulsion flow setting value W
_{i}for primary condition, under calculating current working, the coefficientoffrictionμ of the ith frame
_{i}, the deformation heat that produces because of resistance to deformation in the operation of rolling
the frictional heat produced owing to being with the relative sliding of steel and roll
G3) with the coefficientoffrictionμ of the ith frame
_{i}, the deformation heat that produces because of resistance to deformation in the operation of rolling
the frictional heat produced owing to being with the relative sliding of steel and roll
for primary condition, call band steel temperature rise computation model, determine the temperature of the ith frame band steel in deformed area
G4) ignore the circumferential heat conduction of roll, and deformation heat and frictional heat are passed to the heat that the part of working roll and cooling fluid take away and regard boundary condition as, according to the twodimentional heat conduction equation of roll, the difference expression can listing work roll thermal equilibrium equation is:
$[\frac{{T}_{m,n+1}^{i,t}2{T}_{m,n}^{i,t}+{T}_{m,n1}^{i,t}}{{\left(\mathrm{\Δ}{r}_{i}\right)}^{2}}+\frac{{T}_{m,n+1}^{i,t}{T}_{m,n1}^{i,t}}{2{r}_{m,n}^{i}\mathrm{\Δ}{r}_{i}}+\frac{{T}_{m+1,n}^{i,t}2{T}_{m,n}^{i,t}+{T}_{m1,n}^{i,t}}{{\left(\mathrm{\Δ}{L}_{i}\right)}^{2}}]=\left(\frac{{T}_{m,n}^{i,t+\mathrm{\Δt}}{T}_{m,n}^{i,t}}{\mathrm{\α\Δt}}\right),$ In formula
${r}_{m,n}^{i}=n\×\mathrm{\Δ}{r}_{i}$ Be the ith frame working roll m, the radius corresponding to n unit;
G5) according to principle of energy balance, with Newton's law of cooling obtain roll each several part boundary condition difference equation, wherein it should be noted that, by the cell node (m on the surface of roll for body of roll rolling section, n+1) heat transfer between internal node is no longer regarded as, but replaced by Newton's law of cooling, for the nonrolling section of the body of roll, heat transfer not with steel and roll shop building, for roller shoulder portion, the cell node (m+1, n) of roller shoulder portion no longer as being heat transfer between internal node, but is replaced by Newton's law of cooling; For symmetrical border, its thermograde should be zero, namely
G6) according to g2)g5), determine the thermo parameters method of the ith frame working roll t+ Δ t
G7) inequality is judged
set up? if inequality is set up, illustrate that the thermo parameters method of now working roll reaches stable state, order
proceed to step (h); If inequality is false, then make j=j+1, proceed to step g 1);
H () uses correlation technique described in elastic plastic theory, solve the roll thermal crown distribution of the ith frame working roll under stable state
$\mathrm{\Δ}{D}_{m}^{i}=4(1+v)\frac{{\mathrm{\β}}_{t}}{{D}_{\mathrm{iw}}}{\∫}_{0}^{{D}_{\mathrm{iw}}/2}({T}_{m,n}^{i}{T}_{B}){r}_{m,n}^{i}{\mathrm{dr}}_{i};$
Does i () judge that inequality i<6 sets up? if inequality is set up, then make i=i+1, proceed to step (d), calculate the roll thermal crown distribution of next frame; If inequality is false, then proceed to step (j);
(4) the original intermesh determination of each frame is completed
J () distributes and the spring equation of milling train, the elastic deformation model of milling train in conjunction with the roll thermal crown of the original roller type of roll, each breast roller, under solving current intermesh determination situation, and the exit thickness distribution h of last frame band steel
_{in}with plate shape distribution σ
_{5n}(n is bar unit number);
K () solves the object function of intermesh determination
$F={\mathrm{\α}}_{1}\left[\frac{\frac{1}{n}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{h}_{5j}{h}_{5}}{\mathrm{\Δh}}\right]+(1{\mathrm{\α}}_{1})\left[\frac{\frac{1}{n}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\σ}}_{5j}{\mathrm{\σ}}_{5}}{\mathrm{\Δ\σ}}\right],$ Wherein
strip crown relative deviation surplus, Target Board convexity relative deviation surplus is less, and strip crown is better;
be plate shape relative deviation surplus, target flatness relative deviation surplus is less, and plate shape is better; α
_{1}for the weight coefficient of merit plate shape and plate convexity, general α
_{1}=0.30.7;
Does l () judge that Powell condition is set up (namely judging that whether objective function F minimum)? if Powell condition is set up, then make best fixed value of roller slit
proceed to step (m), otherwise again original roll gap is set, proceed to step (c);
The roll thermal crown distribution of each frame working roll under (m) output current working
and the best original fixed value of roller slit of each frame
complete the original intermesh determination in the 3+2 type five Stands Cold Tandem Mill group strip in razorthin operation of rolling.
Below enumerate the implementation process that an application example illustrates such scheme of the present invention.
In order to the application process of correlation technique of the present invention is described, existing for certain 14203+2 type five Stands Cold Tandem Mill group, introduce the basic procedure of intermesh determination in certain 14203+2 type five Stands Cold Tandem Mill group strip in razorthin operation of rolling in detail:
First, in step 1, collect capital equipment and the technological parameter of 3+2 type five Stands Cold Tandem Mill group, mainly comprise: each frame working roll body of roll section diameter D
_{iw}={ 482.89,486.32,459.24,386.21,394.5}mm, each frame working roll body of roll partiallength L
_{iw}={ 1510,1510,1510,1350,1350}mm;
Subsequently, in step 2, the specification feature of given band steel to be produced and technological parameter, mainly comprise: the initial strength σ mainly comprising band
_{s0}=350MPa, strain hardening coefficient k
_{s}=1.3, the width B=812mm of band, the thickness h of supplied materials
_{0}=2.01mm, each rack outlet thickness h
_{i}={ the muzzle velocity v of 1.186,0.68,0.472,0.271,0.182}mm, each frame
_{i}={ 168.80,284.41,474.42,738.75,1100}m/min; The tension distribution value σ of each frame
_{i}={ 110,125,132,125,68}MPa; Uncoiling tension σ
_{0}=65MPa; The draught pressure setting value P of each frame
_{i}=(778.7,857.4,859.6,603.6,690.3) t, plate shape allow maximum deviation Δ σ=15I, Target Board convexity permission maximum deviation Δ h=3.5 μm;
Subsequently, in step 3, collect main technique lubricating regime parameter, mainly comprise: concentration of emulsion used C=4.2%, emulsion initial temperature setting value T
_{b}=58 DEG C, each frame emulsion flow setting value W
_{i}={ 1010,1250,1100,950,1200}L/min;
Subsequently, in step 4, collect the relevant parameter related in heat transfer computational process, mainly comprise: air themperature T
_{c}=25 DEG C, strip steel at entry temperature
working roll temperature diffusivity α=8.08*10
^{6}m
^{2}/ s, heat exchange coefficient α between working roll and rolled piece
_{a}=350J/ (m
^{2}s DEG C), heat exchange coefficient α between working roll and emulsion
_{b}=9820J/ (m
^{2}s DEG C), heat exchange coefficient α between working roll and air
_{c}=60J/ (m
^{2}s DEG C), the specific heat C of working roll
_{p}density p=the 7800kg/m of=460J/ (kg DEG C), working roll thermal conductivity factor k=29J/ (ms DEG C), working roll
^{3}, thermal expansion of the working roll factor beta
_{t}poisson's ratio ν=0.3 of=10 (1/ DEG C), working roll material;
Subsequently, in steps of 5, relevant process parameters involved in definition roll thermal crown computational process, mainly comprise: belt steel rolling time t=0, roll are along body of roll direction segments M=20, roll along direction, roller footpath segments N=10, process variable m=1,2 ... M, n=1,2 ... roll thermal crown distribution when N, the ith frame working roll temperature rolling
ith frame working roll Temperature Distribution initial value
t ith frame working roll Temperature Distribution
ith frame working roll reaches Temperature Distribution during stable state
the coefficientoffrictionμ of time search step delta t, process variable j, the ith frame
_{i}, the ith frame deformation heat
the frictional heat of the ith frame
the temperature of the ith frame band steel in deformed area
Subsequently, in step 6, to the setting value initialize of the original roll gap of each frame, and initial value is H
_{i}=(0.156 ,1.783 ,0.429 ,0.334 ,0.621) mm;
Subsequently, in step 7, order represents the process variable i=1 of shelf number;
Subsequently, in step 8, consider the symmetry of temperature field to middle section, and ignore the heat transfer between roll and bearing, get the 1st frame working roll
model carries out dividing elements, sets up twodimensional cell model that is radial and axis, each equal segments width along body of roll direction
along each equal segments width in direction, roller footpath
$\mathrm{\Δ}{r}_{1}=\frac{{D}_{1w}}{2N}=\frac{482.89}{20}=24.1445;$
Subsequently, in step 9, preset time stepsize in search Δ t=3s, roll initial temperature
process variable j=0;
Subsequently, in step 10, belt steel rolling time t=j Δ t=0 is made;
Subsequently, in a step 11, with initial strength σ
_{s0}=350MPa, strain hardening coefficient k
_{s}=1.3, the width B=812mm of band, inlet thickness are h
_{0}=2.01mm, exit thickness are h
_{1}=1.186mm, entrance tension force are T
_{0}=65MPa, outlet tension force are T
_{1}=110MPa, muzzle velocity are v
_{1}=168.80m/min, concentration of emulsion used C=4.2%, emulsion initial temperature setting value T
_{b}=58 DEG C, the first frame emulsion flow setting value W
_{1}=1010L/min is primary condition, under calculating current working, and the coefficientoffrictionμ of the ith frame
_{1}=0.0717, the deformation heat produced because of resistance to deformation in the operation of rolling
the frictional heat produced owing to being with the relative sliding of steel and roll
Subsequently, in step 12, with the coefficientoffrictionμ of the 1st frame
_{1}=0.0717, the deformation heat produced because of resistance to deformation in the operation of rolling
the frictional heat produced owing to being with the relative sliding of steel and roll
for primary condition, call band steel temperature rise computation model, calculate the temperature of the ith frame band steel in deformed area
Subsequently, in step 13, according to the twodimentional heat conduction equation of roll, the difference expression can listing work roll thermal equilibrium equation is:
In formula
be the ith frame working roll m, the radius corresponding to n unit;
Subsequently, at step 14, the finite difference equations of body of roll rolling section, the nonrolling section of the body of roll, connection corner point boundary condition is provided, and the boundary condition on symmetrical border, namely
Subsequently, in step 15, simultaneous step 11step 14, determines the thermo parameters method of the 1st frame working roll t+ Δ t
Subsequently, in step 16, inequality is judged
set up? obvious inequality is false, then make j=j+1, proceeds to step 10;
Subsequently, in step 17, use correlation technique described in elastic plastic theory, solve the roll thermal crown distribution of the 1st frame working roll under stable state
$\mathrm{\Δ}{D}_{m}^{i}=4(1+v)\frac{{\mathrm{\β}}_{t}}{{D}_{\mathrm{iw}}}{\∫}_{0}^{{D}_{\mathrm{iw}}/2}({T}_{m,n}^{i}{T}_{B}){r}_{m,n}^{i}{\mathrm{dr}}_{i};$
Subsequently, in step 18 do you, judge that inequality i=1<6 sets up? obvious inequality is set up, then make i=i+1=2, proceed to step 8, calculates the roll thermal crown distribution of next frame;
Subsequently, in step 19, in conjunction with roll thermal crown distribution and the spring equation of milling train, the elastic deformation model of milling train of the original roller type of roll, each breast roller, under solving current intermesh determination situation, the exit thickness distribution h of last frame band steel
_{in}with plate shape distribution σ
_{5n}(n is bar unit number);
Subsequently in step 20, object function is solved
$F={\mathrm{\α}}_{1}\left[\frac{\frac{1}{n}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{h}_{5j}{h}_{5}}{\mathrm{\Δh}}\right]+(1{\mathrm{\α}}_{1})\left[\frac{\frac{1}{n}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\σ}}_{5j}{\mathrm{\σ}}_{5}}{\mathrm{\Δ\σ}}\right],$ Wherein α
_{1}=0.45;
Do you subsequently, in step 21, judge that Powell condition is set up (namely judging that whether objective function F minimum)? if Powell condition is set up, then make best fixed value of roller slit
proceed to step 22, otherwise again original roll gap is set, proceed to step 6;
Subsequently, in step 22, under output current working, the roll thermal crown of each frame working roll distributes
and the best original fixed value of roller slit of each frame
${H}_{i}^{y}=(0.194,1.592,0.718,0.241,0.595)\mathrm{mm},$ Complete the original intermesh determination in the 3+2 type five Stands Cold Tandem Mill group strip in razorthin operation of rolling.
Finally, in order to effect of the present invention is better described, in the operation of rolling of this specification band, the working roll changed is measured immediately, and the actual roll thermal crown recorded is deducted the actual roll thermal crown that the cold roll shape after roll rolipass design can obtain in the operation of rolling, and compare with result of calculation, as shown in Fig. 5Fig. 9, as can be seen from the figure, the present invention is adopted to forecast that the deviation of roll thermal crown value and the measured value obtained is substantially within 10%, can be good at the requirement meeting produced onsite.And after providing employing correlation technique described herein, the strip flatness and gauge distribution of finished strip, as shown in Figure 10 and Figure 11, as can be seen from the figure, the plate shape of finished strip drops to 7.31I from the 10.35I before optimization, and have dropped 29.37%, strip crown drops to 1.9um from 2.7um, have dropped 29.63%, effectively raise the strip shape quality of finished product band.
From abovementioned example: compared with prior art, the present invention considers the roll thermal crown of institute's organic frame, realize the accurate setting of the original roll gap of milling train, the scene in the past that changes only considers that the roll thermal crown of singlerack carries out intermesh determination, is unfavorable for the problem of the control of strip flatness and gauge in the paperthin strip operation of rolling.After correlation technique is adopted by Baosteel 1420 sour rolling mill, plate Shape closed rate drops to 0.68% from 1.32% before application, simultaneously, strip crown is qualified reaches more than 98.5%, reduce the probability that substandard product occurs, improve the quality of unit finished strip, bring larger economic benefit to scene.
In sum, patent of the present invention is on the basis of a large amount of field trials and theoretical research, fully in conjunction with the equipment and technology feature of 3+2 type five Stands Cold Tandem Mill group paperthin strip rolling, a kind of original intermesh determination technology be suitable for based on roll thermal crown in the 3+2 type five Stands Cold Tandem Mill group strip in razorthin operation of rolling is provided, by returning out the Dynamic Thermal convexity of roll accurately, realize the accurate setting of original roll gap, improve the gage and shape control precision of unit, thus effectively improve product quality and production efficiency, for enterprise creates economic benefit, and can further genralrlization to various cold mill complex, popularizing application prospect is more wide.
Should be understood that those skilled in the art can make various changes or modifications the present invention, and these equivalent form of values fall within the application's appended claims limited range equally after having read abovementioned instruction content of the present invention.
Claims (10)
1. in the rolling of tandem mills strip in razorthin based on an original intermesh determination method for roll thermal crown, it is characterized in that, comprising: first adopt finite difference calculus set up roll twodimensional temperature field computation model; The method of recycling plastoelasticity solves the dynamic change of roller heat convex degree learning; Finally realize the setting of original roll gap.
2. in tandem mills strip in razorthin according to claim 1 rolling based on the original intermesh determination method of roll thermal crown, it is characterized in that, set up roll twodimensional temperature field computation model comprise obtain relevant parameter, parameter initialize.
3. in tandem mills strip in razorthin according to claim 2 rolling based on the original intermesh determination method of roll thermal crown, it is characterized in that, parameter initialize is the setting value H to the original roll gap of each frame
_{i}initialize.
4. in tandem mills strip in razorthin according to claim 1 rolling based on the original intermesh determination method of roll thermal crown, it is characterized in that, the dynamic change solving roller heat convex degree learning comprises determines each frame work roll thermal crown.
5. in tandem mills strip in razorthin according to claim 1 rolling based on the original intermesh determination method of roll thermal crown, it is characterized in that, wherein, obtain relevant parameter to comprise: collect capital equipment and the technological parameter of 3+2 type five Stands Cold Tandem Mill group, define relevant process parameters involved in roll thermal crown computational process.
6. in tandem mills strip in razorthin according to claim 5 rolling based on the original intermesh determination method of roll thermal crown, it is characterized in that, wherein, the capital equipment collecting 3+2 type five Stands Cold Tandem Mill group comprises to technological parameter: collect relevant roller system parameter, given band steel to be produced specification feature and technological parameter, collect main technique lubricating regime parameter, collect the relevant parameter related in heat transfer computational process.
7. in tandem mills strip in razorthin according to claim 5 rolling based on the original intermesh determination method of roll thermal crown, it is characterized in that, in definition roll thermal crown computational process, involved relevant process parameters comprises: belt steel rolling time t, roll are along body of roll direction segments M, roll along direction, roller footpath segments N, process variable m=1,2, M, n=1,2 ... roll thermal crown distribution when N, the ith frame working roll temperature rolling
ith frame working roll Temperature Distribution initial value
t ith frame working roll Temperature Distribution
ith frame working roll reaches Temperature Distribution during stable state
the coefficientoffrictionμ of time search step delta t, process variable j, the ith frame
_{i}, the ith frame deformation heat
the frictional heat of the ith frame
the temperature of the ith frame band steel in deformed area
thermal expansion of the working roll factor beta
_{t}, the Poisson's ratio ν of working roll material, the original fixed value of roller slit H of each frame
_{i}, the best original fixed value of roller slit of each frame
8. in tandem mills strip in razorthin according to claim 4 rolling based on the original intermesh determination method of roll thermal crown, it is characterized in that, determine that each frame work roll thermal crown comprises:
D () order represents the process variable i=1 of shelf number;
E () gets each frame working roll
model carries out dividing elements, sets up twodimensional cell model that is radial and axis, each equal segments width along body of roll direction
along each equal segments width in direction, roller footpath
(f) preset time stepsize in search Δ t, roll initial temperature
process variable j=0, wherein should meet inequality according to the restrictive condition time search step delta t of two dimensions and unstable heat conduction
$\mathrm{\Δt}\≤\frac{1}{2\mathrm{\α}(\frac{1}{\mathrm{\Δ}{L}_{i}^{2}}+\frac{1}{\mathrm{\Δ}{r}_{i}^{2}})};$
G () uses finite difference calculus to calculate the ith frame working roll Temperature Distribution
9. in tandem mills strip in razorthin according to claim 8 rolling based on the original intermesh determination method of roll thermal crown, it is characterized in that, use finite difference calculus calculate the ith frame working roll Temperature Distribution
comprise the following step performed by computer:
G1) belt steel rolling time t=j Δ t is made;
G2) with the initial strength σ of band
_{s0}, strain hardening coefficient k
_{s}, the width B of band, inlet thickness be h
_{i1}, exit thickness is h
_{i}, entrance tension force is T
_{i1}, outlet tension force is T
_{i}, muzzle velocity is v
_{i}, concentration of emulsion used C, emulsion initial temperature setting value T
_{b}, the ith frame emulsion flow setting value W
_{i}for primary condition, under calculating current working, the coefficientoffrictionμ of the ith frame
_{i}, the deformation heat that produces because of resistance to deformation in the operation of rolling
the frictional heat produced owing to being with the relative sliding of steel and roll
G3) with the coefficientoffrictionμ of the ith frame
_{i}, the deformation heat that produces because of resistance to deformation in the operation of rolling
the frictional heat produced owing to being with the relative sliding of steel and roll
for primary condition, call band steel temperature rise computation model, determine the temperature of the ith frame band steel in deformed area
G4) ignore the circumferential heat conduction of roll, and deformation heat and frictional heat are passed to the heat that the part of working roll and cooling fluid take away and regard boundary condition as, according to the twodimentional heat conduction equation of roll, the difference expression can listing work roll thermal equilibrium equation is:
$[\frac{{T}_{m,n+1}^{i,t}2{T}_{m,n}^{i,t}+{T}_{m,n1}^{i,t}}{{\left(\mathrm{\Δ}{r}_{i}\right)}^{2}}+\frac{{T}_{m,n+1}^{i,t}{T}_{m,n1}^{i,t}}{2{r}_{m,n}^{i}\mathrm{\Δ}{r}_{i}}+\frac{{T}_{m+1,n}^{i,t}2{T}_{m,n}^{i,t}+{T}_{m1,n}^{i,t}}{{\left(\mathrm{\Δ}{L}_{i}\right)}^{2}}]=\left(\frac{{T}_{m,n}^{i,t+\mathrm{\Δt}}{T}_{m,n}^{i,t}}{\mathrm{\α\Δt}}\right),$ In formula
${r}_{m,n}^{i}=n\×\mathrm{\Δ}{r}_{i}$ Be the ith frame working roll m, the radius corresponding to n unit;
G5) according to principle of energy balance, with Newton's law of cooling obtain roll each several part boundary condition difference equation, by the cell node (m on the surface of roll for body of roll rolling section, n+1) heat transfer between internal node is no longer regarded as, but replaced by Newton's law of cooling, for the nonrolling section of the body of roll, heat transfer not with steel and roll shop building, for roller shoulder portion, cell node (the m+1 of roller shoulder portion, n) no longer as being heat transfer between internal node, but replaced by Newton's law of cooling; For symmetrical border, its thermograde should be zero, namely
G6) according to g2)g5), determine the thermo parameters method of the ith frame working roll t+ Δ t
G7) inequality is judged
set up? if inequality is set up, illustrate that the thermo parameters method of now working roll reaches stable state, order
proceed to step (h); If inequality is false, then make j=j+1, proceed to step g 1).
10. in tandem mills strip in razorthin according to claim 9 rolling based on the original intermesh determination method of roll thermal crown, it is characterized in that, comprise step (h) further and use correlation technique described in elastic plastic theory, solve the roll thermal crown distribution of the ith frame working roll under stable state
$\mathrm{\Δ}{D}_{m}^{i}=4(1+v)\frac{{\mathrm{\β}}_{t}}{{D}_{\mathrm{iw}}}{\∫}_{0}^{{D}_{\mathrm{iw}}/2}({T}_{m,n}^{i}{T}_{B}){r}_{m,n}^{i}{\mathrm{dr}}_{i};$
Does i () judge that inequality i<6 sets up? if inequality is set up, then make i=i+1, proceed to step (d), calculate the roll thermal crown distribution of next frame; If inequality is false, then proceed to step (j);
Wherein, the setting realizing original roll gap comprises:
J () distributes and the spring equation of milling train, the elastic deformation model of milling train in conjunction with the roll thermal crown of the original roller type of roll, each breast roller, under solving current intermesh determination situation, and the exit thickness distribution h of last frame band steel
_{in}with plate shape distribution σ
_{5n}(n is bar unit number);
K () solves the object function of intermesh determination
$F={\mathrm{\α}}_{1}\left[\frac{\frac{1}{n}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{h}_{5j}{h}_{5}}{\mathrm{\Δh}}\right]+(1{\mathrm{\α}}_{1})\left[\frac{\frac{1}{n}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\σ}}_{5j}{\mathrm{\σ}}_{5}}{\mathrm{\Δ\σ}}\right],$ Wherein
strip crown relative deviation surplus, Target Board convexity relative deviation surplus is less, and strip crown is better;
be plate shape relative deviation surplus, target flatness relative deviation surplus is less, and plate shape is better; α
_{1}for the weight coefficient of merit plate shape and plate convexity, general α
_{1}=0.30.7;
Does l () judge that Powell condition is set up (namely judging that whether objective function F minimum)? if Powell condition is set up, then make best fixed value of roller slit
proceed to step (m), otherwise again original roll gap is set, proceed to step (c);
The roll thermal crown distribution of each frame working roll under (m) output current working
and the best original fixed value of roller slit of each frame
complete the original intermesh determination in the 3+2 type five Stands Cold Tandem Mill group strip in razorthin operation of rolling.
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