CN102527736B - Method for confirming reeling radius of cold-rolled steel strip - Google Patents

Abstract

The invention provides a method for confirming a reeling radius of a cold-rolled steel strip. The method comprises an off-line optimizing calculating stage and an online applying stage, wherein the off-line optimizing calculating stage comprises the following steps of: adjusting a solving sequence of all physical quantities of a reeling coupling model of the steel strip, introducing a grain group optimizing algorithm and solving a coupling calculating problem, thereby avoiding the local optimized point subjected by the calculating process and the generation of diffuse phenomenon. During an executing process of the online applying stage, a reeling radius data of the steel strip obtained in the off-line optimizing calculating stage is stored into a board computer database, and a high-precision instant reeling radius data of the steel strip is supplied to a sequential steel strip reeling compensating module in real time according to a database querying method after a board control system is in an online running process, so that the important reeling compensating function in the board control system is finished. According to the method, the calculating process is prevented from falling into the local optimized point or the generation of diffuse phenomenon is avoided, the increasing of the board control precision of the cold-rolled steel strip is ensured and the significant economic benefit is brought.

Description

Determine the method for reeling radius of cold-rolled steel strip

Technical field

The present invention relates to cold-strip steel field, relate in particular to a kind of method of definite reeling radius of cold-rolled steel strip.

Background technology

Strip shape quality is one of the key technical indexes of weighing cold-rolled steel strip products, through the overall process of producing with steel.Quality and the precision controlled in order to improve plate shape; advanced cold rolled strip steel production line conventionally can be equipped with plate profile instrument and carry out the on-line measurement of belt plate shape in milling train exit; then measurement feedback is arrived to plat control system, complete the plate shape closed loop control function of whole system.In actual production, because belt steel product after cold rolling is conventionally with certain convexity, after causing strip coiling, form volume convexity, cause roll coil of strip outer radius along band steel laterally not etc., finally cause being with steel tightness to change, produce additional stress and make to be with steel tensile stress cross direction profiles to change, and then affect the authenticity that plate profile instrument detects plate shape, indirectly caused plate shape to control the variation of effect.Therefore,, in order further to improve the control accuracy of plat control system, just must give effective compensation to this scroll disturbing factor that causes plate shape measurement data error.

From domestic and international pertinent literature, can the key that plat control system carries out the compensation of scroll disturbing factor to plate shape measurement data be accurately and timely obtain strip coiling outer radius values.When strip coiling, be subject to external tension effect, directly have layer by layer the interaction of compression, and have complicated coupled relation between roll coil of strip outer radius and compression.Domestic professors Lian Jiachuan of University On The Mountain Of Swallows etc. are by considering the coil of strip characteristic that radially tightening coefficient radially changes, set up a kind of strip coiling model for coupling, in this Mathematical Modeling, between strip coiling outer radius, interlayer radial pressure, exist the complex mathematical relation intercoupling, this also makes accurately solving of this model become quite difficulty." the iteration of layer by layer calculates coiler mandrel unit pressure to document, " heavy-duty machinery ", connect family's wound etc., 2001, (6): 30-33 " successively iterative calculation method of one has been proposed: first batch inner each relative storey displacement by hypothesis and change in displacement increment is zero, then calculate corresponding interlayer radial compressive stress P1, recycling interlayer radial pressure is calculated and is batched inner each relative storey displacement and change in displacement increment, utilize interlayer radial pressure to calculate and batch inner each relative storey displacement and change in displacement increment recalculates interlayer radial compressive stress P2, deviation between interlayer radial compressive stress P1 and the P2 calculating for twice using above-mentioned computational process front and back is as measurement index function, if measurement index function is less than a certain setting value and thinks and solve convergence, otherwise make P1=P2, recalculate according to above-mentioned steps, until obtain satisfied result of calculation.

It should be noted that above-mentioned traditional the iteration of layer by layer has very large dependence for the initial value of separating, in the time solving coupling model problem, can run into the thorny problem that result of calculation does not restrain, this also greatly reduces using value and the realistic meaning of the method.On the other hand, intelligent optimization method, having obtained significant progress in the more than ten years recently, is widely used in field of engineering technology.Different from traditional computational methods, intelligent optimization method is by simulating and learn artificial intelligence, effectively overcome complicated calculations problem solving result and do not restrained or be easily absorbed in the problems such as local best points, become the effective tool that solves traditional engineering technology problem.

In the time calculating reeling radius of cold-rolled steel strip, can run into the technical barrier that result of calculation does not restrain in order to solve traditional successively alternative manner, the present invention is by adjusting the Structure matrix between the each physical quantity of strip coiling coupling model, introduce population (PSO) optimized algorithm the solving of computational problem that be coupled, successfully avoided computational process to be absorbed in the generation of local best points or Divergent Phenomenon; In addition, the coil of strip that offline optimization is calculated batches radius data and deposits in plate shape Computer Database, can be by the method for data base querying in real time for follow-up band coil of strip shape compensating module provides high-precision instantaneity coil of strip radius data after plat control system drops into on-line operation, complete scroll compensate function comparatively crucial in plat control system, improve guarantee for improving cold-rolled steel strip products strip shape quality.

Summary of the invention

Technical problem to be solved by this invention is: a kind of method of definite reeling radius of cold-rolled steel strip is provided, often runs into solve traditional successively iterative calculation method the technical problem that result of calculation does not restrain.

The technical scheme that the present invention solves its technical problem employing is: comprise that offline optimization calculates link and two parts of online application link.Wherein: it is by adjusting the Structure matrix between strip coiling coupling model each physical quantity that offline optimization calculates link, introduce particle swarm optimization algorithm the solving of computational problem that be coupled, to avoid computational process to be absorbed in the generation of local best points or Divergent Phenomenon; In the implementation process of online application link, be by offline optimization calculate link gained to coil of strip batch radius data and deposit in plate shape Computer Database, can be by the method for data base querying in real time for follow-up band coil of strip shape compensating module provides high-precision instantaneity coil of strip radius data after plat control system drops into on-line operation, complete scroll compensate function comparatively crucial in plat control system.

Described offline optimization calculates link and can comprise the following steps:

(1) collect the related process parameter that reeling radius of cold-rolled steel strip calculates:

This related process parameter comprises: the elasticity modulus of materials of cold-strip steel, cold-strip steel Poisson's ratio, cold-strip steel contacting surface asperity maximum, cold-strip steel width, each measuring section size of plate profile instrument measuring roller, cold-strip steel transverse gage distribute, cold rolled band steel coiling tension distribution;

(2) determine bar unit number:

Determine shaping unit number according to each measuring section size of strip width and plate profile instrument measuring roller, specifically: will be with steel center line to align with plate profile instrument measuring roller center line, the plate profile instrument measuring section that each is covered completely with steel is one and calculates bar unit, the measuring section that both sides are not completely covered is is accepted or rejected according to coverage rate size, if when choice rule is greater than critical coverage rate for coverage rate, this measuring section calculates bar unit as one, otherwise casts out this measuring section;

(3) obtain reeling radius of cold-rolled steel strip data:

Complete offline optimization and calculate link, calculate the reeling radius of cold-rolled steel strip data that produce in dynamic successively coiling process.

In above-mentioned steps (2), should set critical coverage rate by operating personnel, this critical coverage rate is >=50%.

In above-mentioned steps (2), distribute and tensile stress distributes all when being with steel center line symmetry at belt steel thickness, only choose with the calculating bar unit of steel center line one side and calculate, now the result of calculation of an other side and this side result of calculation are symmetry equivalent relation.

In above-mentioned steps (3), can adopt following methods to obtain reeling radius of cold-rolled steel strip data:

Step 1: make j=1, batch ground floor since i article unit and carry out dynamically successively calculating of reeling radius.

Step 2: according to roll coil of strip interlayer radial compressive stress roughly the regularity of distribution generate at random n group roll coil of strip interlayer radial compressive stress p _{i, k, j}, the wherein p of each group _{i, k, j}create-rule be:

p _i,k,j＝p _i,k,j-1+c×rand

In formula: p _{i, j, j-1}=0; If have when j=1, k=1,2, Λ, j; C is random number penalty coefficient; Rand is that the one-dimensional random on [0,1] interval is counted generating function.

Step 3: according to the n group p obtaining _{i, k, j}, utilize respectively following mathematical formulae to calculate n group Δ u _{i, k, j}and r _{i, k, j}:

$m_i=1+k\frac{{\mathrm{\δ}}_{\max }}{h_i}{\left(\frac{E}{p_{i,k,j}}\right)}^{0.8},$

In formula: m _iit is the coil of strip tightening coefficient of i article unit; K has considered a correction factor theoretical and that actual value exists deviation to do, k=1,2, Λ, j; δ _maxfor band steel contacting surface asperity maximum, it comprises microcosmic surface unevenness and meso-and mega-relief; h _ibe thickness before i article of unit's strip coiling; E is the elastic modelling quantity of belt steel material; p _{i, k, j}it is the interlayer radial compressive stress of i article unit k layer inner side in the time batching j layer;

${\mathrm{\ϵ}}_{\mathrm{ri},k,j-1}=\frac{m_i}{E}[(1-\frac{v}{m_i})p_{i,k,j-1}-\frac{v}{m_i}({\mathrm{\σ}}_{\mathrm{Ti},j-1}+r_{i,k,j-1}\frac{p_{i,k+1,j-1}-p_{i,k,j-1}}{h_{i,k,j-1}})],$

${\mathrm{\ϵ}}_{\mathrm{ri},k,j}=\frac{m_i}{E}[(1-\frac{v}{m_i})p_{i,k,j}-\frac{v}{m_i}({\mathrm{\σ}}_{\mathrm{Ti},j}+r_{i,k,j}\frac{p_{i,k+1,j}-p_{i,k,j}}{h_{i,k,j}})],$

In formula: v is material Poisson's ratio; σ _{ti, j}be the coiling tension of i article unit while batching j layer, unit is MPa; r _{i, k, j}it is the radius of i article unit k layer correspondence in the time batching j layer; h _{i, k, j}be thickness after i article unit k layer in the time batching j layer batches; ε _{ri, k, j}be i article unit k layer radial deformation with steel in the time batching j layer;

Δε _ri,k,j＝ε _ri,k,j-ε _ri,k,j-1，

In formula: Δ ε _{ri, k, j}be that the k layer of i article unit is with steel radially deformation variable quantity when batching j-1 layer in the time batching j layer;

Δh _i,k,j＝h _iΔε _ri,k,j，

In formula: Δ h _{i, k, j}be that the k layer of i article unit is with steel amounts of thickness variation when batching j-1 layer in the time batching j layer;

$u_{0i}=\frac{r_{0i}}{E_c}[\frac{r_{0i}^2+r_{\mathrm{ci}}^2}{r_{0i}^2-r_{\mathrm{ci}}^2}-v_c](p_{i,1,j}-p_{i,1,j-1}),$

In formula: u _0ibe i article of displacement that the corresponding reel outer surface of unit occurs when batching j-1 layer in the time of strip coiling j layer, r _0ibe i article of reel outer radius that unit is corresponding, r _cibe i article of reel inside radius that unit is corresponding, E _cfor the elasticity modulus of materials of reel, v _cfor the material Poisson's ratio of reel;

Δu _i,1,j＝u _0i+Δh _i,1,j，

In formula: Δ u _{i, 1, j}the displacement that to be i article of unit's ground floor band steel batching j layer and occur afterwards;

Δu _i,k,j＝Δu _i,k-1,j+Δh _i,k,j，

In formula: Δ u _{i, k, j}the displacement that to be i article of unit's k layer batching j layer and occur afterwards with steel;

r _i,k,j＝r _i,k-1,j+h _i,k,j-Δu _i,k,j，

In formula: r _{i, k, j}be i article of unit's k layer with steel at the reeling radius batching after j layer.

Step 4: by the n group Δ u obtaining in step 3 _{i, k, j}and r _{i, k, j}the following strip coiling radial stress of substitution computing formula is asked for n group respectively

$p_{i,k,m}^{*}=\frac{1}{(1-v)\frac{r_{i,k,j}}{E}-\frac{r_{i,k,j}^2}{{\mathrm{Eh}}_{i,k,j}}}[{\mathrm{\Δu}}_{i,k,j}+u_{i,k,j-1}-\frac{r_{i,k,j}}{E}({\mathrm{\σ}}_i+r_{i,k,j}\frac{p_{i,k+1,j}}{h_{i,k,j}})],$

In formula: σ _ibe that the coiling tension that outermost layer is corresponding batches in i article unit, unit is MPa.

Step 5: with for measurement index function judges each group of p _{i, k, j}with between error size; If there is one group of p _{i, k, j}with j≤ε is set up, go to step 6, ε is error calculated metrics-thresholds here; Produce new n group p according to PSO algorithm particle create-rule if be false _{i, k, j}, each organizes new p _{i, k, j}create-rule as follows:

V _i,k,j＝V _i,k,j+c ₁×rand×(pb _i,k,j-p _i,k,j)+c ₂×rand×(gb _i,k,j-p _i,k,j)，

p _i,k,j＝p _i,k,j+V _i,k,j

In formula: V _{i, k, j}for PSO algorithm calculates p _{i, k, j}velocity component, initial velocity component is random number, k=1,2, Λ, a j of generating; c ₁and c ₂for the acceleration weight of algorithm; Pb _{i, k, j}corresponding p while obtaining minimum J value for this group particle when this cycle calculations _{i, k, j}; Gb _{i, k, j}corresponding p while obtaining minimum J value for n group particle when this cycle calculations _{i, k, j},

Generating new n group p _{i, k, j}after, go to step 3;

Step 6: if j=N calculates and finishes, N batches the number of plies according to the definite roll coil of strip maximum of practical condition here.If J is not equal to N, makes j=j+1, and forward step 2 continuation calculating to.

The present invention compared with prior art, has following main beneficial effect:

1. offline optimization calculates link by adjusting the Structure matrix between the each physical quantity of strip coiling coupling model, introduce population (PSO) optimized algorithm the solving of computational problem that be coupled, successfully avoided computational process to be absorbed in the generation of local best points or Divergent Phenomenon;

2. online application link is calculated by offline optimization coil of strip that link obtains and is batched radius data and deposit in plate shape Computer Database, can be by the method for data base querying in real time for follow-up band coil of strip shape compensating module provides high-precision instantaneity coil of strip radius data after plat control system drops into on-line operation, complete scroll compensate function comparatively crucial in plat control system.

3. improve guarantee for improving cold-rolled strip steel shape control accuracy, can bring considerable economic benefit.

Brief description of the drawings

Fig. 1 is the strip coiling radius calculation flow chart of the inventive method offline optimization calculating section.

Fig. 2 is cold-strip steel transverse gage distribution map in this example.

Fig. 3 is cold rolled band steel coiling tension distribution figure in this example.

Fig. 4 is the inventive method offline optimization internal compressive stress three-dimensional distribution map when calculating the coil of strip that obtains of link and batching.

Fig. 5 is that the inventive method offline optimization calculates each first reeling radius distribution map of coil of strip that link is got.

Fig. 6 is the error of calculation tendency chart that the inventive method offline optimization calculates link.

Fig. 7 is that the inventive method drops into application front and rear panel shape control effect comparison diagram.

Detailed description of the invention

The core calculations part of the inventive method is divided into offline optimization and calculates link and two parts of online application link, wherein offline optimization calculates link by adjusting the Structure matrix between the each physical quantity of strip coiling coupling model, introduce population (PSO) optimized algorithm the solving of computational problem that be coupled, avoided computational process to be absorbed in the generation of local best points or Divergent Phenomenon; The Main Function of online application link be by offline optimization calculate link gained to coil of strip batch radius data and deposit in plate shape Computer Database, can be by the method for data base querying in real time for follow-up band coil of strip shape compensating module provides high-precision instantaneity coil of strip radius data after plat control system drops into on-line operation, complete scroll compensate function comparatively crucial in plat control system.Simultaneously the inventive method simple and feasible, meets the requirement of real-time of existing cold-rolled strip steel shape control system completely, provides strong guarantee for further improving cold-rolled steel strip products strip shape quality.

Below in conjunction with embodiment and accompanying drawing, the invention will be further described, but do not limit the present invention.

Method based on definite reeling radius of cold-rolled steel strip of the present invention can be used for four rollers, six roller single chassis or multi-frame tandem mills.The present embodiment is disclosed is the method for the definite reeling radius of cold-rolled steel strip in certain single chassis six roller reversable cold-rolling machine plat control system.This six-high cluster mill can rolling product comprise common plate, high-strength steel, part stainless steel and silicon steel etc.The present embodiment rolling be middle high grade silicon steel, type is UCM milling train, plate shape control device comprises that roller declination, the positive and negative roller of working roll, the positive roller of intermediate calender rolls, intermediate roll shifting and emulsion section are cooling etc.Basic mechanical design feature index and the device parameter of this unit are:

Mill speed: Max900m/min, draught pressure: Max18000KN, maximum rolling force square: 140.3KN × m, coiling tension: Max220KN, main motor current: 5500KW;

Supplied materials thickness range: 1.8～2.5mm, supplied materials width range: 850～1280mm, outgoing gauge scope: 0.3mm～1.0mm;

Work roll diameter: 290～340mm, working roll height: 1400mm, intermediate calender rolls diameter: 440～500mm, intermediate calender rolls height: 1640mm, backing roll diameter: 1150～1250mm, backing roll height: 1400mm;

Every side work roll bending power :-280～350KN, every side intermediate calender rolls bending roller force: 0～500KN, the axial traversing amount of intermediate calender rolls :-120～120mm, auxiliary hydraulic system pressure: 14MPa, balance bending system pressure: 28MPa, press down system pressure: 28MPa;

Plate Profile Measuring System adopts the ABB plate shape roller of Sweden, this plate shape roller roller footpath 313mm, formed by solid steel axle, broad ways is divided into a measured zone every 52mm, in each measured zone, the surrounding at measuring roller is uniform-distribution with four grooves to place magnetoelasticity power sensor vertically, and the outside of sensor is wrapped up by steel loop.Product specification (thickness × width): 0.80mm × 840mm.Reel outer radius initial value is 300mm, and reel inside radius initial value is 100mm, and the elasticity modulus of materials of reel is taken as E _c=2.06 × 10 ⁵.

Because the band steel finished product after rolling is conventionally with certain convexity, after causing strip coiling, form volume convexity, cause roll coil of strip outer radius along band steel laterally not etc., finally cause being with steel tightness to change, produce additional stress and make to be with steel tensile stress cross direction profiles to change, and then affect the authenticity that plate profile instrument detects plate shape, finally cause plate shape to control the variation of effect.Production practices show, if do not give effective compensation to this scroll disturbing factor that causes plate shape measurement data error, will greatly increase the defect rate of product, have a strong impact on the economic benefit of enterprise.From control technology angle, can the key that plat control system carries out the compensation of scroll disturbing factor to plate shape measurement data be accurately and timely obtain strip coiling outer radius values; But because strip coiling outer radius is calculated design operation of rolling factors, and between each factor, there is the complexity contact intercoupling, utilize routine techniques method to be difficult to obtain satisfied result, this also becomes a technical barrier that hinders cold-rolled strip steel shape control system and realize effective scroll compensate function.

Definite reeling radius of cold-rolled steel strip method that the present embodiment provides adopts and comprises the following steps:

1. collect the related process parameter that reeling radius of cold-rolled steel strip calculates:

The related process coefficient that reeling radius of cold-rolled steel strip calculates is the reference frame of calculating strip coiling radius, and the collected technological parameter of this example mainly contains: elasticity modulus of materials E=2.06 × 10 of cold-strip steel ⁵, cold-strip steel Poisson's ratio v=0.3, cold-strip steel contacting surface asperity maximum δ _max=1.52 × 10 ^-5m, cold-strip steel width B=840mm, the each measuring section width dimensions of plate profile instrument measuring roller are 52mm; In addition the distribution of cold-strip steel transverse gage and coiling tension distribute respectively as shown in Figures 2 and 3.

2. determine and calculate bar unit number according to each measuring section size of strip width and plate profile instrument measuring roller:

The main application that reeling radius of cold-rolled steel strip calculates is the instant outside dimension that the horizontal zones of different of coil of strip is provided for scroll compensating module comparatively crucial in plat control system, therefore calculating bar unit number really establishes rules and is: will be with steel center line to align with plate profile instrument measuring roller center line, the plate profile instrument measuring section that each is covered completely with steel is one and calculates bar unit, the measuring section that both sides are not completely covered is is accepted or rejected according to coverage rate size, if this measuring section calculates bar unit as one when choice rule is greater than critical coverage rate for coverage rate, otherwise cast out this measuring section.Here critical coverage rate can manually be set according to technological requirement, is conventionally not less than 50%.In particular cases, as belt steel thickness distributes and tensile stress distributes all when being with steel center line symmetry, can only choose with the calculating bar unit of steel center line one side and calculate, now the result of calculation of an other side and this side result of calculation broad ways center line are symmetry equivalent relation.

Because strip width in this example is 840mm, the each measuring section width dimensions of plate profile instrument measuring roller is 52mm, therefore be with steel altogether to cover 840/52=16.1538 measuring section, due to two measuring section coverage rates very little (less than 8%) of milling train fore side and transmission side outermost end, therefore can cast out two measuring sections of milling train fore side and transmission side outermost end, that is to say and only need to calculate 16 bar units; In addition, from Fig. 2 and Fig. 3, belt steel thickness distributes and tensile stress distributes all along band steel center line symmetry, calculate so now can only choose with 8 bar units of steel center line one side, the result of calculation of 8 bar units of opposite side and this side result of calculation broad ways center line are symmetry equivalent relation.

3. complete offline optimization and calculate link, calculate the reeling radius of cold-rolled steel strip data that produce in dynamic successively coiling process.

Fig. 1 has provided the reeling radius calculation flow chart of i article unit (amounting to 8 articles of units) of this example offline optimization calculating link, and the calculation procedure of this part is divided into:

Step 1: make j=1, batch ground floor since i article unit and carry out dynamically successively calculating of reeling radius;

Step 2: according to roll coil of strip interlayer radial compressive stress roughly the regularity of distribution generate at random n group roll coil of strip interlayer radial compressive stress p _{i, k, j}(k=1,2, Λ, j), wherein each group roll coil of strip interlayer radial compressive stress p _{i, k, j}the create-rule of (k=1,2, Λ, j) is:

p _i,k,j＝p _i,k,j-1+c×rand，

Wherein there is p _{i, j, j-1}=0; If there is p when j=1 _{i, k, j-1}=0; C is random number penalty coefficient; Rand is that the one-dimensional random on [0,1] interval is counted generating function.

Step 3: according to the n group p obtaining _{i, k, j}(k=1,2, Λ, j), utilization is calculated n as next group cold rolled band steel coiling Mathematical Modeling and is organized Δ u respectively _{i, k, j}and r _{i, k, j}:

$m_i=1+k\frac{{\mathrm{\δ}}_{\max }}{h_i}{\left(\frac{E}{p_{i,k,j}}\right)}^{0.8},$

In formula: m _iit is the coil of strip tightening coefficient of i article unit; K has considered a correction factor theoretical and that actual value exists deviation to do, and in this example, value is k=0.45; δ _maxfor band steel contacting surface asperity maximum, it comprises microcosmic surface unevenness and meso-and mega-relief, is δ according to correlation technique data value _max=1.52 × 10 ^-5; h _ibe thickness before i article of unit's strip coiling, its value as shown in Figure 2; E=2.06 × 10 ⁵for the elastic modelling quantity of belt steel material; p _{i, k, j}it is the interlayer radial compressive stress of i article unit k layer inner side in the time batching j layer;

${\mathrm{\ϵ}}_{\mathrm{ri},k,j-1}=\frac{m_i}{E}[(1-\frac{v}{m_i})p_{i,k,j-1}-\frac{v}{m_i}({\mathrm{\σ}}_{\mathrm{Ti},j-1}+r_{i,k,j-1}\frac{p_{i,k+1,j-1}-p_{i,k,j-1}}{h_{i,k,j-1}})],$

${\mathrm{\ϵ}}_{\mathrm{ri},k,j}=\frac{m_i}{E}[(1-\frac{v}{m_i})p_{i,k,j}-\frac{v}{m_i}({\mathrm{\σ}}_{\mathrm{Ti},j}+r_{i,k,j}\frac{p_{i,k+1,j}-p_{i,k,j}}{h_{i,k,j}})],$

In formula: v=0.3 is material Poisson's ratio; σ _{ti, j}be the coiling tension (unit be MPa) of i article unit while batching j layer, its value as shown in Figure 3; r _{i, k, j}be the radius of i article unit k layer correspondence in the time batching j layer, h _{i, k, j}be thickness after i article unit k layer in the time batching j layer batches, ε _{ri, k, j}be i article unit k layer radial deformation with steel in the time batching j layer;

Δε _ri,k,j＝ε _ri,k,j-ε _ri,k,j-1，

In formula: Δ ε _{ri, k, j}be that the k layer of i article unit is with steel radially deformation variable quantity when batching j-1 layer in the time batching j layer;

Δh _i,k,j＝h _iΔε _ri,k,j，

In formula: Δ h _{i, k, j}be that the k layer of i article unit is with steel amounts of thickness variation when batching j-1 layer in the time batching j layer;

$u_{0i}=\frac{r_{0i}}{E_c}[\frac{r_{0i}^2+r_{\mathrm{ci}}^2}{r_{0i}^2-r_{\mathrm{ci}}^2}-v_c](p_{i,1,j}-p_{i,1,j-1}),$

In formula: u _0ibe i article of displacement that the corresponding reel outer surface of unit occurs when batching j-1 layer in the time of strip coiling j layer, r _0ibe i article of reel outer radius that unit is corresponding, r _cibe i article of reel inside radius that unit is corresponding, E _cfor the elasticity modulus of materials of reel;

Δu _i,1,j＝u _0i+Δh _i,1,j，

In formula: Δ u _{i, 1, j}the displacement that to be i article of unit's ground floor band steel batching j layer and occur afterwards;

Δu _i,k,j＝Δu _i,k-1,j+Δh _i,k,j，

In formula, Δ u _{i, k, j}the displacement that to be i article of unit's k layer batching j layer and occur afterwards with steel;

r _i,k,j＝r _i,k-1,j+h _i,k,j-Δu _i,k,j，

In formula, r _{i, k, j}be i article of unit's k layer with steel at the reeling radius batching after j layer.

Step 4: by the n group Δ u obtaining in step 3 _{i, k, j}and r _{i, k, j}the following strip coiling radial stress of substitution computing formula is asked for n group respectively

$p_{i,k,m}^{*}=\frac{1}{(1-v)\frac{r_{i,k,j}}{E}-\frac{r_{i,k,j}^2}{{\mathrm{Eh}}_{i,k,j}}}[{\mathrm{\Δu}}_{i,k,j}+u_{i,k,j-1}-\frac{r_{i,k,j}}{E}({\mathrm{\σ}}_i+r_{i,k,j}\frac{p_{i,k+1,j}}{h_{i,k,j}})].$

Step 5: with for measurement index function judges each group of p _{i, k, j}with between error size.If there is one group of p _{i, k, j}with j≤ε is set up, go to step six; Produce new n group p according to PSO algorithm particle create-rule if be false _{i, k, j}(k=1,2, Λ, j), each organizes new p _{i, k, j}the create-rule of (k=1,2, Λ, j) is as follows:

V _i,k,j＝V _i,k,j+c ₁×rand×(pb _i,k,j-p _i,k,j)+c ₂×rand×(gb _i,k,j-p _i,k,j)

p _i,k,j＝p _i,k,j+V _i,k,j

Wherein V _{i, k, j}for PSO algorithm calculates p _{i, k, j}velocity component, initial velocity component is random number, a c of generating ₁and c ₂for the acceleration weight of algorithm, pb _{i, k, j}corresponding p while obtaining minimum J value for this group particle when the cycle calculations _{i, k, j}, gb _{i, k, j}corresponding p while obtaining minimum J value for n group particle when the cycle calculations _{i, k, j}.

Generating new n group p _{i, k, j}after (k=1,2, Λ, j), go to step three.

Step 6: if j=N (N batches the number of plies according to the definite roll coil of strip maximum of practical condition here) calculates and finishes, otherwise makes j=j+1, forward step 2 to and continue to calculate.

For this example, it is N=60 that setting maximum is batched the number of plies, if now adopt traditional successively iterative calculation method, the result obtaining is dispersed, and that is to say that conventional method can not be used for the calculating of this example.We adopt the offline optimization computational methods that the present invention proposes in this example, set error calculated index need to be less than ε (here ε value be meet commercial Application 0.01), the method can obtain satisfied result of calculation.Internal compressive stress three-dimensional distribution map when Fig. 4 has provided the inventive method offline optimization and calculates coil of strip that link obtains and batch, Fig. 5 has provided the inventive method offline optimization and has calculated each first reeling radius distribution map of coil of strip that link is got, result of calculation and field data are substantially identical, have larger using value.Fig. 6 has provided the error of calculation tendency chart of the inventive method offline optimization calculating link, and as can be seen from Figure 6, the error criterion function J of gained is all less than 0.01, meets computational accuracy requirement.In sum, calculated off-line link of the present invention has successfully avoided computational process to be absorbed in the generation of local best points or Divergent Phenomenon, provides guarantee for obtaining high-precision strip coiling radius data.

4. the online application link of this method: first deposit plate shape Computer Database in by calculate the reeling radius of cold-rolled steel strip data that link obtains at offline optimization; After plat control system puts into operation, cold-strip steel has often batched one deck, control system by the query manipulation of database immediately for providing each unit in the reeling radius value of batching after this layer with coil of strip shape compensating module, complete quickly and easily the scroll compensate function in plat control system.

Fig. 7 has provided the plate shape control effect comparison diagram that drops into application front and back two volume same size belt steel products in this example in the inventive method.Can find out that the inventive method can improve cold-rolled strip steel shape control accuracy, significantly reduce the flatness defect of cold-rolled steel strip products, improve quality and the class of product, can bring considerable economic benefit for enterprise.

Above embodiment is only for illustrating calculating thought of the present invention and feature; its object is to make those skilled in the art can understand content of the present invention and implement according to this; protection scope of the present invention is not limited to above-described embodiment; the disclosed principle of all foundations, equivalent variations or the modification that mentality of designing is done, all within protection scope of the present invention.

Claims (5)

1. the method for a definite reeling radius of cold-rolled steel strip, it is characterized in that comprising that offline optimization calculates link and two parts of online application link, wherein: it is by adjusting the Structure matrix between the each physical quantity of strip coiling coupling model that offline optimization calculates link, introduce particle swarm optimization algorithm the solving of computational problem that be coupled, to avoid computational process to be absorbed in the generation of local best points or Divergent Phenomenon; In the implementation process of online application link, be by offline optimization calculate link gained to coil of strip batch radius data and deposit in plate shape Computer Database, when plat control system drops into after on-line operation method by data base querying in real time for follow-up band coil of strip shape compensating module provides high-precision instantaneity coil of strip radius data, complete scroll compensate function comparatively crucial in plat control system;

Described offline optimization calculates link and comprises the following steps:

(1) collect the related process parameter that reeling radius of cold-rolled steel strip calculates:

This related process parameter comprises: the elasticity modulus of materials of cold-strip steel, cold-strip steel Poisson's ratio, cold-strip steel contacting surface asperity maximum, cold-strip steel width, each measuring section size of plate profile instrument measuring roller, cold-strip steel transverse gage distribute, cold rolled band steel coiling tension distribution;

(2) determine bar unit number:

Determine shaping unit number according to each measuring section size of strip width and plate profile instrument measuring roller, specifically: will be with steel center line to align with plate profile instrument measuring roller center line, the plate profile instrument measuring section that each is covered completely with steel is one and calculates bar unit, the measuring section that both sides are not completely covered is is accepted or rejected according to coverage rate size, if when choice rule is greater than critical coverage rate for coverage rate, this measuring section calculates bar unit as one, otherwise casts out this measuring section;

(3) obtain reeling radius of cold-rolled steel strip data:

Complete offline optimization and calculate link, calculate the reeling radius of cold-rolled steel strip data that produce in dynamic successively coiling process.

2. the method for definite reeling radius of cold-rolled steel strip according to claim 1, is characterized in that, in step (2), should setting critical coverage rate by operating personnel, and this critical coverage rate is >=50%.

3. the method for definite reeling radius of cold-rolled steel strip according to claim 1, it is characterized in that in step (2), distribute and tensile stress distributes all when being with steel center line symmetry at belt steel thickness, only choose with the calculating bar unit of steel center line one side and calculate, now the result of calculation of an other side and this side result of calculation are symmetry equivalent relation.

4. the method for definite reeling radius of cold-rolled steel strip according to claim 1, is characterized in that in step (3), adopts following methods to obtain reeling radius of cold-rolled steel strip data:

Step 1: make j=1, batch ground floor since i article unit and carry out dynamically successively calculating of reeling radius;

Step 2: according to roll coil of strip interlayer radial compressive stress roughly the regularity of distribution generate at random n group roll coil of strip interlayer radial compressive stress p _{i, k, j}, the wherein p of each group _{i, k, j}create-rule be:

p _i,k,j＝p _i,k,j-1+c×rand

In formula: p _{i, j, j-1}=0; If have when j=1, k=1,2, Λ, j; C is random number penalty coefficient; Rand is that the one-dimensional random on [0,1] interval is counted generating function;

Step 3: according to the n group p obtaining _{i, k, j}, utilize respectively following mathematical formulae to calculate n group Δ u _{i, k, j}and r _{i, k, j}:

$m_i=1+k\frac{{\mathrm{\δ}}_{\max }}{h_i}{\left(\frac{E}{p_{i,k,j}}\right)}^{0.8},$

In formula: m _iit is the coil of strip tightening coefficient of i article unit; K has considered a correction factor theoretical and that actual value exists deviation to do, k=1,2, Λ, j; δ _maxfor band steel contacting surface asperity maximum, it comprises microcosmic surface unevenness and meso-and mega-relief; h _ibe thickness before i article of unit's strip coiling; E is the elastic modelling quantity of belt steel material; p _{i, k, j}it is the interlayer radial compressive stress of i article unit k layer inner side in the time batching j layer;

${\mathrm{\ϵ}}_{\mathrm{ri},k,j-1}=\frac{m_i}{E}[(1-\frac{v}{m_i})p_{i,k,j-1}-\frac{v}{m_i}({\mathrm{\σ}}_{\mathrm{Ti},j-1}+r_{i,k,j-1}\frac{p_{i,k+1,j-1}-p_{i,k,j-1}}{h_{i,k,j-1}})],$

${\mathrm{\ϵ}}_{\mathrm{ri},k,j}=\frac{m_i}{E}[(1-\frac{v}{m_i})p_{i,k,j}-\frac{v}{m_i}({\mathrm{\σ}}_{\mathrm{Ti},j}+r_{i,k,j}\frac{p_{i,k+1,j}-p_{i,k,j}}{h_{i,k,j}})],$

In formula: v is material Poisson's ratio; σ _{ti, j}be the coiling tension of i article unit while batching j layer, unit is MPa; r _{i, k, j}it is the radius of i article unit k layer correspondence in the time batching j layer; h _{i, k, j}be thickness after i article unit k layer in the time batching j layer batches; ε _{ri, k, j}be i article unit k layer radial deformation with steel in the time batching j layer;

Δε _ri,k,j＝ε _ri,k,j-ε _ri,k,j-1，

In formula: Δ ε _{ri, k, j}be that the k layer of i article unit is with steel radially deformation variable quantity when batching j-1 layer in the time batching j layer;

Δh _i,k,j＝h _iΔε _ri,k,j，

In formula: Δ h _{i, k, j}be that the k layer of i article unit is with steel amounts of thickness variation when batching j-1 layer in the time batching j layer;

$u_{0i}=\frac{r_{0i}}{E_c}[\frac{r_{0i}^2+r_{\mathrm{ci}}^2}{r_{0i}^2-r_{\mathrm{ci}}^3}-v_c](p_{i,1,j}-p_{i,1,j-1}),$

In formula: u _0ibe i article of displacement that the corresponding reel outer surface of unit occurs when batching j-1 layer in the time of strip coiling j layer, r _0ibe i article of reel outer radius that unit is corresponding, r _cibe i article of reel inside radius that unit is corresponding, E _cfor the elasticity modulus of materials of reel, v _cfor the material Poisson's ratio of reel;

Δu _i,1,j＝u _0i+Δh _i,1,j，

In formula: Δ u _{i, 1, j}the displacement that to be i article of unit's ground floor band steel batching j layer and occur afterwards;

Δu _i,k,j＝Δu _i,k-1,j+Δh _i,k,j，

In formula: Δ u _{i, k, j}the displacement that to be i article of unit's k layer batching j layer and occur afterwards with steel;

r _i,k,j＝r _i,k-1,j+h _i,k,j-Δu _i,k,j，

In formula: r _{i, k, j}be i article of unit's k layer with steel at the reeling radius batching after j layer;

Step 4: by the n group Δ u obtaining in step 3 _{i, k, j}and r _{i, k, j}the following strip coiling radial stress of substitution computing formula is asked for n group respectively

$p_{i,k,m}^{*}=\frac{1}{(1-v)\frac{r_{i,k,j}}{E}-\frac{r_{i,k,j}^2}{{\mathrm{Eh}}_{i,k,j}}}[{\mathrm{\Δu}}_{i,k,j}+u_{i,k,j-1}-\frac{r_{i,k,j}}{E}({\mathrm{\σ}}_i+r_{i,k,j}\frac{p_{i,k+1,j}}{h_{i,k,j}})];$

In formula: σ _ibe that the coiling tension that outermost layer is corresponding batches in i article unit, unit is MPa;

Step 5: with for measurement index function judges each group of p _{i, k, j}with between error size; If there is one group of p _{i, k, j}with j≤ε is set up, go to step 6, ε is error calculated metrics-thresholds here; Produce new n group p according to PSO algorithm particle create-rule if be false _{i, k, j}, each organizes new p _{i, k, j}create-rule be:

$\begin{array}{c}{V}_{i,k,j}=V_{i,k,j}+c_1\×\mathrm{rand}\×({\mathrm{pb}}_{i,k,j}-p_{i,k,j})+c_2\×\mathrm{rand}\×({\mathrm{gb}}_{i,k,j}-p_{i,k,j})\\ p_{i,k,j}=p_{i,k,j}+V_{i,k,j}\end{array},$

In formula: V _{i, k, j}for PSO algorithm calculates p _{i, k, j}velocity component, initial velocity component is random number, k=1,2, Λ, a j of generating; c ₁and c ₂for the acceleration weight of algorithm; Pb _{i, k, j}corresponding p while obtaining minimum J value for this group particle when this cycle calculations _{i, k, j}; Gb _{i, k, j}corresponding p while obtaining minimum J value for n group particle when this cycle calculations _{i, k, j},

Generating new n group p _{i, k, j}after go to step 3;

Step 6: if j=N calculates and finishes, N batches the number of plies according to the definite roll coil of strip maximum of practical condition here.

5. the method for definite reeling radius of cold-rolled steel strip according to claim 4, is characterized in that in step 6, if J is not equal to N, makes j=j+1, and forwards the step 2 continuation calculating of claim 4 to.