CN104275368B - A kind of hot-strip uncoiling tension complex optimum computational methods - Google Patents

Abstract

A kind of hot-strip uncoiling tension complex optimum computational methods, it mainly comprises the following step that can be performed by computer: the technical parameter 1, collecting uncoiler; 2, the description of collecting belt steel and technological parameter; 3, collection process parameter; 4, the Optimal Step Size of given tension force and optimizing process; The radius r of any i-th layer s article in coil of strip when 5, asking uncoiling kth layer successively _si, s article i-th layer and the i-th-1 interlayer coil of strip inner radial stress p _si, circumferential stress q _si, interfacial friction τ _si, the Controlling object function of uncoiling loose winding and interlayer slip 6, the optimum tension value finally determined is exported.The present invention can forecast the uncoiling circumferential stress after tension force complex optimum, uncoiling radial stress, uncoiling interfacial friction stress distribution situation, and loose winding, interlayer slip scratch the generation of band steel phenomenon effectively to prevent being with steel to occur in uncoiling process.

Description

A kind of hot-strip uncoiling tension complex optimum computational methods

Technical field

The invention belongs to hot rolling field, particularly a kind of coils of hot-rolled steel uncoiling tension complex optimum computational methods.

Background technology

In recent years, along with the continuous expansion of strip industrial expansion and user's request, also more and more higher to the quality requirement of hot-strip.The on-the-spot research for course of hot rolling aided process in the past mainly concentrated on the field of batching, volume is unloaded to band steel, cool and the defect of downstream uncoiling process and technical study then less, have impact on the raising of hot-rolled finished product strip quality.In actual production process, hot rolling belt steel roll also often can run into some phenomenons when uncoiling, affects strip surface quality, mainly concentrates on uncoiling loose winding, uncoiling interlayer slip etc.The angular speed that uncoiling loose winding refers in particular to coil of strip core band steel in uncoiling process is greater than the phenomenon of one or more layers band steel angular speed of outermost layer, uncoiling tension will be caused sharply to decline, force uncoiling process to stop, affecting production efficiency time serious.The angular speed that uncoiling interlayer slip refers in particular to coil of strip core band steel in uncoiling process is less than the phenomenon of one or more layers band steel angular speed of outermost layer, and belt steel surface will be caused time serious to scratch.Main task in uncoiling operation is exactly choose suitable constant uncoiling tension, it is the core of uncoiling section operation, the setting of uncoiling tension is as the important step in uncoiling operation, and the quality that it realizes is directly connected to height and the quality of the production efficiency of product.In recent years, the further raising required product quality along with people, the optimization of uncoiling tension more and more attracts much attention, but in hot-strip uncoiling process, the research of Chinese scholars mainly concentrates on uncoiling constant tensile control aspect ^[1-6], seldom focus on the change of some boundary conditions of coil of strip self and the change of internal stress in uncoiling process, most of scholar ignores these changes may produce quality control on the surface impact on band steel, and this directly results in the disappearance of correlation theory research.

(bibliography: [1] Yu Xianchao, Yang Xiaoming, Huang Qingxue. hot-strip production status is analyzed and prediction of the development trend [J]. mechanical engineering and automation, 2006. [2] Jiang Shiping, the burnt time, Zhang Na. coiling machine main machine structure and motion, kinetic parameter analyzes [J]. Machine Design, 2007. [3] Xiong Shengtao, Chen Zhipeng, Xia Yue. the application [J] of uncoiler coil diameter calculation optimized algorithm in band steel splitting production line. automatic technology and application, 2009. [4] Fu Yanpeng, Jin Xiaohong. the acquisition [J] of coil of strip diameter during uncoiling tension controls. Wuhan University Of Technology's journal: natural science edition, 2005. [5] Bai Zhenhuas. coil of strip batches and unloads the research [J] licking internal stress distribution in journey. China Mechanical Engineering, 2004. [6] Bai Zhenhuas, connect family's wound, Wu Bin etc. the research [J] of cold-rolled steel coils coiling process internal stress distributed in three dimensions. iron and steel, 2001.)

Summary of the invention

The problems such as the coil of strip loose winding easily occurred for scene and interlayer slip, the present invention is to realize preventing coil of strip loose winding, to greatest extent between reduction layer for the purpose of glide band steel layer number, establishing a kind of hot-strip uncoiling tension complex optimum computational methods.

Technical scheme of the present invention is as follows:

A kind of hot-strip uncoiling tension complex optimum computational methods, comprise the following step performed by computer:

A () collects the technical parameter of uncoiler, mainly comprise: uncoiling maximum line velocity v _max, maximum uncoiling tension T _max, minimum uncoiling tension T _min, reel inside radius r _a, reel outer radius r _b, reel rises sharply footpath r most _max, the minimum footpath r that rises of reel _min, reel width B _jt, allow coil of strip maximum weight G _max, reel elastic modulus E ₁, reel Poisson's ratio ν ₁;

B the description scope of () collecting belt steel and technological parameter, mainly comprise: band steel steel grade, band steel average thickness h, belt steel thickness distribution h _s, strip width B, the heavy G of steel coil, belt steel surface roughness Ra, band steel coefficientoffrictionμ, band steel Poisson's ratio v ₂, band steel elastic modulus E ₂, the band density p of steel, coil of strip outer radius and inside radius R ₁, R ₂, the circular elasticity modulus E of band, the radial elastic modulus E of band _r, band steel strip crown Δ h, the temperature t of supplied materials coil of strip, the number of plies C of supplied materials coil of strip;

C () collection process parameter, mainly comprises: the maximum δ of strip surface unevenness _max, consider that theory and practice exists the correction factor k of difference ₀, weight coefficient α, band steel Cross slat unit number m, coil of strip number of plies n;

The Optimal Step Size Δ T of (d) given tension force, tension optimization procedure parameter j ₁, j ₂, j _1y, the Controlling object function initial value of uncoiling loose winding and interlayer slip the limit of convergence ε of computational process;

E () makes j ₁=0, uncoiling tension T=T _min+ j ₁Δ T;

F during () definition uncoiling, the coil of strip outermost layer number of plies is k;

G () makes j ₂=0;

H () makes k=n-j ₂;

The radius r of any i-th layer s article in coil of strip when () asks uncoiling kth layer successively i _si, s article i-th layer and the i-th-1 interlayer coil of strip inner radial stress p _si, circumferential stress q _si, interfacial friction τ _si, the Controlling object function of uncoiling loose winding and interlayer slip mainly comprise the following steps:

The coil of strip radius r of any i-th layer s article in coil of strip when i1) calculating uncoiling kth layer _si=r _b+ ih _s;

Be with steel at s article, i-th layer and the i-th-1 interlayer coil of strip inner radial stress p when i2) calculating uncoiling kth layer _si, wherein there is relevant relational expression:

$p_{\mathrm{si}}[(1-\frac{{\mathrm{\ν}}_2}{2})\·r_{\mathrm{si}}+\frac{{\mathrm{\ν}}_2}{2}{r}_{\mathrm{si}+1}]-p_{\mathrm{si}+1}[(1-\frac{{\mathrm{\ν}}_2}{2})\·r_{\mathrm{si}+1}+\frac{{\mathrm{\ν}}_2}{2}{r}_{\mathrm{si}}]=E_2(r_{\mathrm{si}+1}-r_{\mathrm{si}})\left(\frac{r_{\mathrm{si}}-r_{01\mathrm{si}}}{r_{01\mathrm{si}}}\right),$ In formula: r _si+1the inside radius of the i-th+1 layer band steel at s article of place during uncoiling current layer, p _si+1be with steel at s article, the i-th+1 layer and the i-th interlayer coil of strip inner radial stress during uncoiling current layer, r _01sithe inside radius of i-th layer of band steel at s article of place during front one deck of uncoiling current layer;

I3) reel displacement during uncoiling kth layer is calculated

I4) the coil of strip radius of when uncoiling kth layer considers stratified deformation any i-th layer s article is calculated ${r_{\mathrm{si}}}^{\′}=\left\{\begin{array}{cc}\frac{[E_2{h}_s+\frac{{\mathrm{\ν}}_2{p}_{\mathrm{si}}{r}_{\mathrm{si}+1}}{2}+(\frac{{\mathrm{\ν}}_2}{2}-1)p_{\mathrm{si}+1}{r}_{\mathrm{si}+1}-0.5\mathrm{\ρg}{h}_s\sin \mathrm{\θ}]}{[\frac{E_2{h}_s}{r_{01\mathrm{si}}}+\frac{{\mathrm{\ν}}_2{p}_{\mathrm{si}+1}}{2}+(\frac{{\mathrm{\ν}}_2}{2}-1)p_{\mathrm{si}}+0.5\mathrm{\ρg}{h}_s\sin \mathrm{\θ}]}& i>1\\ r_b-u_s& i=1\end{array}\right.,$ θ is polar angle, and g is gravity constant;

I5) inequality is judged || r _si-r' _si|| whether≤ε sets up, if inequality is false, makes r _si=r' _si, proceed to step I 2), if inequality is set up, then directly proceed to step I 6);

Be with steel at s article, i-th layer and the i-th-1 interlayer coil of strip circumferential stress q when i6) calculating uncoiling kth layer _si=q _si+1-π (r _siτ _si-r _si+1τ _si+1)/(r _si+1-r _si), in formula: q _si+1be with steel s article, the i-th+1 layer and the i-th interlayer coil of strip circumferential stress during uncoiling kth layer, τ _si+1during uncoiling current layer the i-th+1 layer band steel and i-th layer be with the friction stree of steel at s article of place;

I7) calculate uncoiling kth layer time i-th layer band steel and the i-th-1 layer be with the tightening coefficient of steel at s article of place $m_{\mathrm{si}}=1+1.27k_0\frac{{\mathrm{\δ}}_{\max }}{h_s}{\left(\frac{E_2}{p_{\mathrm{si}}}\right)}^{0.8};$

When i8) calculating uncoiling kth layer, band steel is at s article, i-th layer τ with the i-th-1 interlayer coil of strip interior layer and interfacial friction stress _si=r _si+1τ _si+1/ r _si+ (q _si+1-q _si) (r _si+1-r _si)/π r _si;

I9) minimized friction balance allowance K during uncoiling kth layer is solved _l=min{ μ p _si-τ _si;

Uncoiling loose winding when i10) solving uncoiling kth layer and the Controlling object function of interlayer slip

J () judges inequality set up? if inequality is set up, make j _1y=j ₁, proceed to step (k); If inequality is false, then directly proceed to step (k);

Does k () judge that inequality k < 2 sets up? if inequality is set up, make j ₁=j ₁+ 1, T=T _min+ j ₁Δ T, proceeds to step (l); If inequality is false, make j ₂=j ₂+ 1, proceed to step (h);

L () judges inequality T≤T _maxset up? if inequality is set up, proceed to step (f); If inequality is false, proceed to step (m);

M () exports optimum uncoiling tension value T _y=T _min+ j _1yΔ T.

The present invention compared with prior art tool has the following advantages:

Fully in conjunction with technique and the equipment characteristic of hot rolling uncoiler, and consider the real-time change situation of the radius distribution in coils of hot-rolled steel uncoiling process, the uncoiling circumferential stress before tension force complex optimum can not only be forecast, uncoiling radial stress, uncoiling interfacial friction stress distribution situation, but also the uncoiling circumferential stress after tension force complex optimum can be forecast, uncoiling radial stress, uncoiling interfacial friction stress distribution situation, and calculated by tension force complex optimum, the final optimization pass tension force drawn, uncoiler carries out uncoiling according to this tension force, effectively prevent band steel from uncoiling process, occurring loose winding, interlayer slip scratches the generation of band steel phenomenon, greatly improve the qualification rate of product, improve product quality.

Accompanying drawing explanation

Fig. 1 is the total calculation flow chart of the present invention;

Calculation flow chart when Fig. 2 is uncoiling kth layer of the present invention;

Fig. 3 is uncoiling radial stress curve distribution figure in the embodiment of the present invention 1;

Fig. 4 is uncoiling circumferential stress curve distribution figure in the embodiment of the present invention 1;

Fig. 5 is uncoiling friction stree curve distribution figure in the embodiment of the present invention 1;

Fig. 6 is optimal control object function in the embodiment of the present invention 1 curve map;

Fig. 7 is uncoiling tension distribution map after complex optimum in the embodiment of the present invention 1;

Fig. 8 is uncoiling radial stress curve distribution figure in the embodiment of the present invention 2;

Fig. 9 is uncoiling circumferential stress curve distribution figure in the embodiment of the present invention 2;

Figure 10 is uncoiling friction stree curve distribution figure in the embodiment of the present invention 2;

Figure 11 is optimal control object function in the embodiment of the present invention 2 curve map;

Figure 12 is uncoiling tension distribution map after complex optimum in the embodiment of the present invention 2;

Detailed description of the invention

Embodiment 1

Now describe the concrete computational process of hot-strip uncoiling tension complex optimum for common straightcarbon steel, its calculation process as shown in Figure 1.

First, in step 1, collect the technical parameter of uncoiler, mainly comprise: uncoiling maximum line velocity v _max=30m/min, maximum uncoiling tension T _max=15MPa, minimum uncoiling tension T _min=5MPa, reel inside radius r _a=300mm, reel outer radius r _b=375mm, reel rise sharply footpath r most _maxthe minimum footpath r that rises of=50mm, reel _min=20mm, reel width B _jt=1800mm, permission coil of strip maximum weight G _maxthe elastic modulus E of=30t, reel ₁=2 × 10 ¹¹the Poisson's ratio ν of Pa, reel ₁=0.3;

Subsequently, in step 2, the description scope of collecting belt steel and technological parameter, mainly comprise: band steel steel grade is common straightcarbon steel, band steel average thickness h=8mm, belt steel thickness distribution h _s={ 7.9829,7.9883,7.9931,7.9973,8.0009,8.0039,8.0063,8.0081,8.0093,8.0099,8.0099, band steel wide by 8.0093,8.0081,8.0063,8.0039,8.0009,7.9973,7.9931,7.9883,7.9829} degree B=1500mm, the heavy G=25t of steel coil, belt steel surface roughness Ra=2, band steel coefficientoffrictionμ=0.25, the Poisson's ratio v of band steel ₂=0.3, the elastic modulus E of steel is with ₂=2.1 × 10 ¹¹density p=7.85 × 10 of Pa, band steel ³kg/m ³, coil of strip outer radius and inside radius R ₁=928mm, R ₂circular elasticity modulus E=2.1 × 10 of=375mm, band ¹¹the radial elastic modulus E of Pa, band _r=2.1 × 10 ¹¹pa, the strip crown Δ h=30um of band steel, temperature t=50 DEG C of supplied materials coil of strip, the number of plies C=66 of supplied materials coil of strip;

Subsequently, in step 3, collection process parameter, mainly comprises: the maximum δ of strip surface unevenness _max, be taken as δ at this _max=0.02h=0.16mm, considers that theory and practice exists the correction factor k of difference ₀, be generally taken as 0.3 ~ 0.6, be taken as k at this ₀=0.45, weight coefficient α=0.3, band steel Cross slat unit number m=20, coil of strip number of plies n=66;

Subsequently, in step 4, the Optimal Step Size Δ T=0.1MPa of given tension force, tension optimization procedure parameter j ₁, j ₂, j _1y, the Controlling object function initial value of uncoiling loose winding and interlayer slip limit of convergence ε=0.03 of computational process;

Subsequently, in steps of 5, j is made ₁=0, T=T _min+ j ₁Δ T=5MPa;

Subsequently, in step 6, during definition uncoiling, the coil of strip outermost layer number of plies is k=66;

Subsequently, in step 7, j is made ₂=0;

Subsequently, in step 8, k=n-j is made ₂=66;

Subsequently, as shown in Figure 2, in step 9, the radius r of any i-th layer s article in coil of strip when asking uncoiling kth layer successively _si, s article i-th layer and the i-th-1 interlayer coil of strip inner radial stress p _si, circumferential stress q _si, interfacial friction τ _si, the Controlling object function of uncoiling loose winding and interlayer slip the coil of strip radius r of any i-th layer s article in coil of strip when calculating uncoiling kth layer _si=r _b+ ih _s, substitute into related data and try to achieve:

r ₀₁₆₆＝r ₂₀₆₆＝901.8714mm、r ₀₂₆₆＝r ₁₉₆₆＝902.2278mm、r ₀₃₆₆＝r ₁₈₆₆＝902.5446mm、

r ₀₄₆₆＝r ₁₇₆₆＝902.8218mm、r ₀₅₆₆＝r ₁₆₆₆＝903.0594mm、r ₀₆₆₆＝r ₁₅₆₆＝903.2574mm、

r ₀₇₆₆＝r ₁₄₆₆＝903.4158mm、r ₀₈₆₆＝r ₁₃₆₆＝903.5346mm、r ₀₉₆₆＝r ₁₂₆₆＝903.6138mm、

r ₁₀₆₆＝r ₁₁₆₆＝903.6534mm；

Subsequently, in step 10, be with steel at s article, i-th layer and the i-th-1 interlayer coil of strip inner radial stress p when calculating uncoiling kth layer _si, wherein there is relevant relational expression:

$p_{\mathrm{si}}[(1-\frac{{\mathrm{\&nu;}}_2}{2})\&CenterDot;r_{\mathrm{si}}+\frac{{\mathrm{\&nu;}}_2}{2}{r}_{\mathrm{si}+1}]-p_{\mathrm{si}+1}[(1-\frac{{\mathrm{\&nu;}}_2}{2})\&CenterDot;r_{\mathrm{si}+1}+\frac{{\mathrm{\&nu;}}_2}{2}{r}_{\mathrm{si}}]=E_2(r_{\mathrm{si}+1}-r_{\mathrm{si}})\left(\frac{r_{\mathrm{si}}-r_{01\mathrm{si}}}{r_{01\mathrm{si}}}\right),$ In formula: r _si+1the inside radius of the i-th+1 layer band steel at s article of place during uncoiling current layer, p _si+1be with steel at s article, the i-th+1 layer and the i-th interlayer coil of strip inner radial stress during uncoiling current layer, r _01siduring front one deck of uncoiling current layer, the inside radius of i-th layer of band steel at s article of place, substitutes into related data and tries to achieve: p ₀₁₆₆=p ₂₀₆₆=2.5232MPa, p ₀₂₆₆=p ₁₉₆₆=2.8108MPa,

p ₀₃₆₆＝p ₁₈₆₆＝3.0681MPa、p ₀₄₆₆＝p ₁₇₆₆＝3.2951MPa、p ₀₅₆₆＝p ₁₆₆₆＝3.4918MPa、

p ₀₆₆₆＝p ₁₅₆₆＝3.6583MPa、p ₀₇₆₆＝p ₁₄₆₆＝3.7945MPa、p ₀₈₆₆＝p ₁₃₆₆＝3.9004MPa、

P ₀₉₆₆=p ₁₂₆₆=3.9761MPa, p ₁₀₆₆=p ₁₁₆₆=4.0215MPa (the uncoiling radial stress curve after continuous loop optimization is shown in accompanying drawing 3);

Subsequently, in a step 11, reel displacement equation u during uncoiling kth layer is solved _s, wherein there is relevant relational expression: substitution related data is tried to achieve: u ₀₁₆₆=u ₂₀₆₆=1.716 × 10 ^-5,

u ₀₂₆₆＝u ₁₉₆₆＝1.910×10 ^-5，u ₀₃₆₆＝u ₁₈₆₆＝2.082×10 ^-5，u ₀₄₆₆＝u ₁₇₆₆＝2.234×10 ^-5，

u ₀₅₆₆＝u ₁₆₆₆＝2.366×10 ^-5，u ₀₆₆₆＝u ₁₅₆₆＝2.477×10 ^-5，u ₀₇₆₆＝u ₁₄₆₆＝2.568×10 ^-5，

u ₀₈₆₆＝u ₁₃₆₆＝2.639×10 ^-5，u ₀₉₆₆＝u ₁₂₆₆＝2.689×10 ^-5，u ₁₀₆₆＝u ₁₁₆₆＝2.719×10 ^-5；

Subsequently, in step 12, the coil of strip radius of when uncoiling kth layer considers stratified deformation any i-th layer s article is calculated ${r_{\mathrm{si}}}^{\&prime;}=\left\{\begin{array}{cc}\frac{[E_2{h}_s+\frac{{\mathrm{\&nu;}}_2{p}_{\mathrm{si}}{r}_{\mathrm{si}+1}}{2}+(\frac{{\mathrm{\&nu;}}_2}{2}-1)p_{\mathrm{si}+1}{r}_{\mathrm{si}+1}-0.5\mathrm{\&rho;g}{h}_s\sin \mathrm{\&theta;}]}{[\frac{E_2{h}_s}{r_{01\mathrm{si}}}+\frac{{\mathrm{\&nu;}}_2{p}_{\mathrm{si}+1}}{2}+(\frac{{\mathrm{\&nu;}}_2}{2}-1)p_{\mathrm{si}}+0.5\mathrm{\&rho;g}{h}_s\sin \mathrm{\&theta;}]}& i>1\\ r_b-u_s& i=1\end{array}\right.,$ θ is polar angle, and g is gravity constant, substitutes into related data and tries to achieve: r' ₀₁₆₆=r' ₂₀₆₆=901.8535mm, r' ₀₂₆₆=r' ₁₉₆₆=902.2099mm,

r′ ₀₃₆₆＝r′ ₁₈₆₆＝902.5267mm、r′ ₀₄₆₆＝r′ ₁₇₆₆＝902.8038mm、r′ ₀₅₆₆＝r′ ₁₆₆₆＝903.0414mm、

r′ ₀₆₆₆＝r′ ₁₅₆₆＝903.2394mm、r′ ₀₇₆₆＝r′ ₁₄₆₆＝903.3978mm、r′ ₀₈₆₆＝r′ ₁₃₆₆＝903.5167mm、

r' ₀₉₆₆＝r' ₁₂₆₆＝903.5959mm、r' ₁₀₆₆＝r' ₁₁₆₆＝903.6355mm；

Subsequently, in step 13, judge inequality || r _si-r' _si|| whether≤ε sets up, and empirical tests is all set up, therefore goes to step 14;

Subsequently, at step 14, be with steel at s article, i-th layer and the i-th-1 interlayer coil of strip circumferential stress q when calculating uncoiling kth layer _si, wherein have dependency relation formula: q _si=q _si+1-π (r _siτ _si-r _si+1τ _si+1)/(r _si+1-r _si), in formula: q _si+1be with steel s article, the i-th+1 layer and the i-th interlayer coil of strip circumferential stress during uncoiling kth layer, τ _si+1during uncoiling current layer the i-th+1 layer band steel with i-th layer be with the friction stree of steel at s article of place, substitution related data try to achieve:

q ₀₁₆₆＝q ₂₀₆₆＝2.015×10 ^-5MPa、q ₀₂₆₆＝q ₁₉₆₆＝2.245×10 ^-5MPa、q ₀₃₆₆＝q ₁₈₆₆＝2.451×10 ^-5MPa、

q ₀₄₆₆＝q ₁₇₆₆＝2.632×10 ^-5MPa、q ₀₅₆₆＝q ₁₆₆₆＝2.789×10 ^-5MPa、q ₀₆₆₆＝q ₁₅₆₆＝2.922×10 ^-5MPa、

q ₀₇₆₆＝q ₁₄₆₆＝3.031×10 ^-5MPa、q ₀₈₆₆＝q ₁₃₆₆＝3.116×10 ^-5MPa、q ₀₉₆₆＝q ₁₂₆₆＝3.176×10 ^-5MPa、

Q ₁₀₆₆=q ₁₁₆₆=3.212 × 10 ^-5mPa (the uncoiling circumferential stress curve after continuous loop optimization is shown in accompanying drawing 4);

Subsequently, in step 15, calculate uncoiling kth layer time i-th layer band steel and the i-th-1 layer be with the tightening coefficient of steel at s article of place substitution related data is tried to achieve: m ₀₁₆₆=m ₂₀₆₆=0.372483,

m ₀₂₆₆＝m ₁₉₆₆＝0.372481，m ₀₃₆₆＝m ₁₈₆₆＝0.372480，m ₀₄₆₆＝m ₁₇₆₆＝0.372478，

m ₀₅₆₆＝m ₁₆₆₆＝0.372476，m ₀₆₆₆＝m ₁₅₆₆＝0.372475，m ₀₇₆₆＝m ₁₄₆₆＝0.372474，

m ₀₈₆₆＝m ₁₃₆₆＝0.372473，m ₀₉₆₆＝m ₁₂₆₆＝0.372473，m ₁₀₆₆＝m ₁₁₆₆＝0.372483；

Subsequently, in step 16, be with steel at s article, i-th layer and the i-th-1 interlayer coil of strip interior layer and interfacial friction stress τ when calculating uncoiling kth layer _si, wherein there is dependency relation formula:

τ _si=r _si+1τ _si+1/ r _si+ (q _si+1-q _si) (r _si+1-r _si)/π r _si, substitute into related data and try to achieve: τ ₀₁₆₆=τ ₂₀₆₆=0.0233MPa,

τ ₀₂₆₆＝τ ₁₉₆₆＝0.0259MPa、τ ₀₃₆₆＝τ ₁₈₆₆＝0.0283MPa、τ ₀₄₆₆＝τ ₁₇₆₆＝0.0304MPa、

τ ₀₅₆₆＝τ ₁₆₆₆＝0.0322MPa、τ ₀₆₆₆＝τ ₁₅₆₆＝0.0338MPa、τ ₀₇₆₆＝τ ₁₄₆₆＝0.0350MPa、

τ ₀₈₆₆=τ ₁₃₆₆=0.0360MPa, τ ₀₉₆₆=τ ₁₂₆₆=0.0367MPa, τ ₁₀₆₆=τ ₁₁₆₆=0.0371MPa (the uncoiling friction stree curve after continuous loop optimization is shown in accompanying drawing 5);

Subsequently, in step 17, minimized friction balance allowance K during uncoiling kth layer is solved _l, K _l=min{ μ p _si-τ _si, substitute into related data and try to achieve: K _l=0.06075;

Subsequently, in step 18, uncoiling loose winding when solving uncoiling kth layer and the Controlling object function of interlayer slip substitution related data is tried to achieve: (through the optimal control object function of constantly circulation curve is shown in accompanying drawing 6);

Subsequently, in step 19, judge inequality whether set up, obvious establishment then makes j _1y=j ₁=0, go to step 20;

Subsequently, in step 20, judge whether inequality k=66 < 2 sets up, and is obviously false, then makes j ₂=j ₂+ 1=1, proceeds to step 8;

Subsequently, in step 21, j ₁=j ₁+ 1=1, T=T _min+ j ₁Δ T=5.1MPa, judges inequality T=5.1MPa < T _maxwhether=15MPa sets up, and obviously sets up, then skip to step 6;

Subsequently, in step 22, optimum uncoiling tension value T is exported _y=T _min+ j _1yΔ T=8.5MPa (as shown in Figure 7).

Embodiment 2

First, in step 1, collect the technical parameter of uncoiler, mainly comprise: uncoiling maximum line velocity v _max=30m/min, maximum uncoiling tension T _max=15MPa, minimum uncoiling tension T _min=5MPa, reel inside radius r _a=300mm, reel outer radius r _b=375mm, reel rises sharply footpath r most _max=50mm, the minimum footpath r that rises of reel _min=20mm, reel width B _jt=1800mm, allows coil of strip maximum weight G _max=30t, the elastic modulus E of reel ₁=2 × 10 ¹¹pa, the Poisson's ratio ν of reel ₁=0.3;

Subsequently, in step 2, the description scope of collecting belt steel and technological parameter, mainly comprise: band steel steel grade is common straightcarbon steel, band steel average thickness h=6mm, belt steel thickness distribution h _s={ 5.9886,5.9922,5.9954,5.9982,6.0006,6.0026,6.0042,6.0054,6.0062,6.0066,6.0066, band steel is wide by 6.0062,6.0054,6.0042,6.0026,6.0006,5.9982,5.9954,5.9922,5.9886} degree B=1200mm, the heavy G=15t of steel coil, belt steel surface roughness Ra=1, band steel coefficientoffrictionμ=0.2, the Poisson's ratio v of band steel ₂=0.3, the elastic modulus E of band steel ₂=2.1 × 10 ¹¹pa, density p=7.85 × 10 of band steel ³kg/m ³, coil of strip outer radius and inside radius R ₁=768mm, R ₂=375mm, circumferential springform E=2.1 × 10 of band ¹¹pa; The radial elastic modulus E of band _r=2.1 × 10 ¹¹pa, the strip crown Δ h=20um of band steel, the temperature t=40 DEG C of supplied materials coil of strip, the number of plies C=66 of supplied materials coil of strip;

Subsequently, in step 3, collection process parameter, mainly comprises: the maximum δ of strip surface unevenness _max, be taken as δ at this _max=0.02h=0.12mm, considers that theory and practice exists the correction factor k of difference ₀, be generally taken as 0.3 ~ 0.6, be taken as k at this ₀=0.45, weight coefficient α=0.3, band steel Cross slat unit number m=20, coil of strip number of plies n=66;

Subsequently, in step 4, the Optimal Step Size Δ T=0.1MPa of given tension force, tension optimization procedure parameter j ₁, j ₂, j _1y, the Controlling object function initial value of uncoiling loose winding and interlayer slip limit of convergence ε=0.03 of computational process;

Subsequently, in steps of 5, j is made ₁=0, T=T _min+ j ₁Δ T=5MPa;

Subsequently, in step 6, during definition uncoiling, the coil of strip outermost layer number of plies is k=66;

Subsequently, in step 7, j is made ₂=0;

Subsequently, in step 8, k=n-j is made ₂=66;

Subsequently, in step 9, the radius r of any i-th layer s article in coil of strip when asking uncoiling kth layer successively _si, s article i-th layer and the i-th-1 interlayer coil of strip inner radial stress p _si, circumferential stress q _si, interfacial friction τ _si, the Controlling object function of uncoiling loose winding and interlayer slip the coil of strip radius r of any i-th layer s article in coil of strip when calculating uncoiling kth layer _si=r _b+ ih _s, substitute into related data and try to achieve: r ₀₁₆₆=r ₂₀₆₆=769.4927mm,

r ₀₂₆₆＝r ₁₉₆₆＝769.5017mm、r ₀₃₆₆＝r ₁₈₆₆＝769.5107mm、r ₀₄₆₆＝r ₁₇₆₆＝769.5197mm、

r ₀₅₆₆＝r ₁₆₆₆＝769.5287mm、r ₀₆₆₆＝r ₁₅₆₆＝769.5377mm、r ₀₇₆₆＝r ₁₄₆₆＝769.5466mm、

r ₀₈₆₆＝r ₁₃₆₆＝769.5556mm、r ₀₉₆₆＝r ₁₂₆₆＝769.5646mm、r ₁₀₆₆＝r ₁₁₆₆＝769.5736mm；

Subsequently, in step 10, be with steel at s article, i-th layer and the i-th-1 interlayer coil of strip inner radial stress p when calculating uncoiling kth layer _si, wherein there is relevant relational expression:

$p_{\mathrm{si}}[(1-\frac{{\mathrm{\&nu;}}_2}{2})\&CenterDot;r_{\mathrm{si}}+\frac{{\mathrm{\&nu;}}_2}{2}{r}_{\mathrm{si}+1}]-p_{\mathrm{si}+1}[(1-\frac{{\mathrm{\&nu;}}_2}{2})\&CenterDot;r_{\mathrm{si}+1}+\frac{{\mathrm{\&nu;}}_2}{2}{r}_{\mathrm{si}}]=E_2(r_{\mathrm{si}+1}-r_{\mathrm{si}})\left(\frac{r_{\mathrm{si}}-r_{01\mathrm{si}}}{r_{01\mathrm{si}}}\right),$ In formula: r _si+1the inside radius of the i-th+1 layer band steel at s article of place during uncoiling current layer, p _si+1be with steel at s article, the i-th+1 layer and the i-th interlayer coil of strip inner radial stress during uncoiling current layer, r _01siduring front one deck of uncoiling current layer, the inside radius of i-th layer of band steel at s article of place, substitutes into related data and tries to achieve: p ₀₁₆₆=p ₂₀₆₆=2.6759MPa, p ₀₂₆₆=p ₁₉₆₆=2.9809MPa,

p ₀₃₆₆＝p ₁₈₆₆＝3.2538MPa、p ₀₄₆₆＝p ₁₇₆₆＝3.4945MPa、p ₀₅₆₆＝p ₁₆₆₆＝3.7032MPa、

p ₀₆₆₆＝p ₁₅₆₆＝3.8797MPa、p ₀₇₆₆＝p ₁₄₆₆＝4.0241MPa、p ₀₈₆₆＝p ₁₃₆₆＝4.1365MPa、

P ₀₉₆₆=p ₁₂₆₆=4.2167MPa, p ₁₀₆₆=p ₁₁₆₆=4.2649MPa (the uncoiling radial stress curve after continuous loop optimization is shown in accompanying drawing 8);

Subsequently, in a step 11, reel displacement equation u during uncoiling kth layer is solved _s, wherein there is relevant relational expression: substitution related data is tried to achieve: u ₀₁₆₆=u ₂₀₆₆=1.715 × 10 ^-5,

u ₀₂₆₆＝u ₁₉₆₆＝1.911×10 ^-5，u ₀₃₆₆＝u ₁₈₆₆＝2.082×10 ^-5，u ₀₄₆₆＝u ₁₇₆₆＝2.240×10 ^-5，

u ₀₅₆₆＝u ₁₆₆₆＝2.374×10 ^-5，u ₀₆₆₆＝u ₁₅₆₆＝2.488×10 ^-5，u ₀₇₆₆＝u ₁₄₆₆＝2.580×10 ^-5，

u ₀₈₆₆＝u ₁₃₆₆＝2.653×10 ^-5，u ₀₉₆₆＝u ₁₂₆₆＝2.704×10 ^-5，u ₁₀₆₆＝u ₁₁₆₆＝2.735×10 ^-5；

Subsequently, in step 12, the coil of strip radius of when uncoiling kth layer considers stratified deformation any i-th layer s article is calculated ${r_{\mathrm{si}}}^{\&prime;}=\left\{\begin{array}{cc}\frac{[E_2{h}_s+\frac{{\mathrm{\&nu;}}_2{p}_{\mathrm{si}}{r}_{\mathrm{si}+1}}{2}+(\frac{{\mathrm{\&nu;}}_2}{2}-1)p_{\mathrm{si}+1}{r}_{\mathrm{si}+1}-0.5\mathrm{\&rho;g}{h}_s\sin \mathrm{\&theta;}]}{[\frac{E_2{h}_s}{r_{01\mathrm{si}}}+\frac{{\mathrm{\&nu;}}_2{p}_{\mathrm{si}+1}}{2}+(\frac{{\mathrm{\&nu;}}_2}{2}-1)p_{\mathrm{si}}+0.5\mathrm{\&rho;g}{h}_s\sin \mathrm{\&theta;}]}& i>1\\ r_b-u_s& i=1\end{array}\right.,$ θ is polar angle, and g is gravity constant, substitutes into related data and tries to achieve: r' ₀₁₆₆=r' ₂₀₆₆=769.4748mm, r' ₀₂₆₆=r' ₁₉₆₆=769.4837mm, r' ₀₃₆₆=r' ₁₈₆₆=769.4927mm,

r′ ₀₄₆₆＝r′ ₁₇₆₆＝769.5017mm、r′ ₀₅₆₆＝r′ ₁₆₆₆＝769.5107mm、r′ ₀₆₆₆＝r′ ₁₅₆₆＝769.5197mm、r′ ₀₇₆₆＝r′ ₁₄₆₆＝769.5287mm、

r′ ₀₈₆₆＝r′ ₁₃₆₆＝769.5377mm、r′ ₀₉₆₆＝r′ ₁₂₆₆＝769.5467mm、r′ ₁₀₆₆＝r′ ₁₁₆₆＝769.5556mm；

Subsequently, in step 13, judge inequality || r _si-r' _si|| whether≤ε sets up, and empirical tests is all set up, therefore skips to step 14;

Subsequently, at step 14, be with steel at s article, i-th layer and the i-th-1 interlayer coil of strip circumferential stress q when calculating uncoiling kth layer _si, wherein have dependency relation formula: q _si=q _si+1-π (r _siτ _si-r _si+1τ _si+1)/(r _si+1-r _si), in formula: q _si+1be with steel s article, the i-th+1 layer and the i-th interlayer coil of strip circumferential stress during uncoiling kth layer, τ _si+1during uncoiling current layer the i-th+1 layer band steel with i-th layer be with the friction stree of steel at s article of place, substitution related data try to achieve:

q ₀₁₆₆＝q ₂₀₆₆＝2.137×10 ^-5MPa、q ₀₂₆₆＝q ₁₉₆₆＝2.381×10 ^-5MPa、q ₀₃₆₆＝q ₁₈₆₆＝2.599×10 ^-5MPa、

q ₀₄₆₆＝q ₁₇₆₆＝2.791×10 ^-5MPa、q ₀₅₆₆＝q ₁₆₆₆＝2.958×10 ^-5MPa、q ₀₆₆₆＝q ₁₅₆₆＝3.099×10 ^-5MPa、

q ₀₇₆₆＝q ₁₄₆₆＝3.214×10 ^-5MPa、q ₀₈₆₆＝q ₁₃₆₆＝3.304×10 ^-5MPa、q ₀₉₆₆＝q ₁₂₆₆＝3.368×10 ^-5MPa、

Q ₁₀₆₆=q ₁₁₆₆=3.407 × 10 ^-5mPa (the uncoiling circumferential stress curve after continuous loop optimization is shown in accompanying drawing 9);

Subsequently, in step 15, calculate uncoiling kth layer time i-th layer band steel and the i-th-1 layer be with the tightening coefficient of steel at s article of place substitution related data is tried to achieve: m ₀₁₆₆=m ₂₀₆₆=0.381470,

m ₀₂₆₆＝m ₁₉₆₆＝0.381468，m ₀₃₆₆＝m ₁₈₆₆＝0.381466，m ₀₄₆₆＝m ₁₇₆₆＝0.381464，

m ₀₅₆₆＝m ₁₆₆₆＝0.381462，m ₀₆₆₆＝m ₁₅₆₆＝0.381461，m ₀₇₆₆＝m ₁₄₆₆＝0.381460，

m ₀₈₆₆＝m ₁₃₆₆＝0.381459，m ₀₉₆₆＝m ₁₂₆₆＝0.381459，m ₁₀₆₆＝m ₁₁₆₆＝0.381458；

Subsequently, in step 16, be with steel at s article, i-th layer and the i-th-1 interlayer coil of strip interior layer and interfacial friction stress τ when calculating uncoiling kth layer _si, wherein there is dependency relation formula:

τ _si=r _si+1τ _si+1/ r _si+ (q _si+1-q _si) (r _si+1-r _si)/π r _si, substitute into related data and try to achieve: τ ₀₁₆₆=τ ₂₀₆₆=0.0247MPa,

τ ₀₂₆₆＝τ ₁₉₆₆＝0.0275MPa、τ ₀₃₆₆＝τ ₁₈₆₆＝0.0300MPa、τ ₀₄₆₆＝τ ₁₇₆₆＝0.0323MPa、

τ ₀₅₆₆＝τ ₁₆₆₆＝0.0342MPa、τ ₀₆₆₆＝τ ₁₅₆₆＝0.0358MPa、τ ₀₇₆₆＝τ ₁₄₆₆＝0.0371MPa、

τ ₀₈₆₆=τ ₁₃₆₆=0.0382MPa, τ ₀₉₆₆=τ ₁₂₆₆=0.0390MPa, τ ₁₀₆₆=τ ₁₁₆₆=0.0394MPa (the uncoiling friction stree curve after continuous loop optimization is shown in accompanying drawing 10);

Subsequently, in step 17, minimized friction balance allowance K during uncoiling kth layer is solved _l, K _l=min{ μ p _si-τ _si, substitute into related data and try to achieve: K _l=0.05077;

Subsequently, in step 18, uncoiling loose winding when solving uncoiling kth layer and the Controlling object function of interlayer slip substitution related data is tried to achieve: (through the optimal control object function of constantly circulation curve is shown in accompanying drawing 11);

Subsequently, in step 19, judge inequality whether set up, obvious establishment then makes j _1y=j ₁=0, skip to step 20;

Subsequently, in step 20, judge whether inequality k=66 < 2 sets up, and is obviously false, then makes j ₂=j ₂+ 1=1, proceeds to step 8;

Subsequently, in step 21, j ₁=j ₁+ 1=1, T=T _min+ j ₁Δ T=5.1MPa, judges inequality T=5.1MPa < T _maxwhether=15MPa sets up, and obviously sets up, then skip to step 6;

Subsequently, in step 22, optimum uncoiling tension value T is exported _y=T _min+ j _1yΔ T=8.9MPa (as shown in figure 12).

Claims (1)

1. hot-strip uncoiling tension complex optimum computational methods, is characterized in that: it mainly comprises the following step performed by computer:

A () collects the technical parameter of uncoiler, mainly comprise: uncoiling maximum line velocity v _max, maximum uncoiling tension T _max, minimum uncoiling tension T _min, reel inside radius r _a, reel outer radius r _b, reel rises sharply footpath r most _max, the minimum footpath r that rises of reel _min, reel width B _jt, allow coil of strip maximum weight G _max, the elastic modulus E of reel ₁, the Poisson's ratio ν of reel ₁;

B the description scope of () collecting belt steel and technological parameter, mainly comprise: band steel steel grade, band steel average thickness h, belt steel thickness distribution h _s, strip width B, the heavy G of steel coil, belt steel surface roughness Ra, band steel coefficientoffrictionμ, the Poisson's ratio v of band steel ₂, the elastic modulus E of band steel ₂, the density p of band steel, coil of strip outer radius and inside radius R ₁, R ₂, the circular elasticity modulus E of band, the radial elastic modulus E of band _r, the strip crown Δ h of band steel, the temperature t of supplied materials coil of strip, the number of plies C of supplied materials coil of strip;

C () collection process parameter, mainly comprises: the maximum δ of strip surface unevenness _max, consider that theory and practice exists the correction factor k of difference ₀, weight coefficient α, band steel Cross slat unit number m, coil of strip number of plies n;

The Optimal Step Size Δ T of (d) given tension force, tension optimization procedure parameter j ₁, j ₂, j _1y, the Controlling object function initial value of uncoiling loose winding and interlayer slip the limit of convergence ε of computational process;

E () makes j ₁=0, uncoiling tension T=T _min+ j ₁Δ T;

F during () definition uncoiling, the coil of strip outermost layer number of plies is k;

G () makes j ₂=0;

H () makes k=n-j ₂;

The radius r of any i-th layer s article in coil of strip when () asks uncoiling kth layer successively i _si, s article i-th layer and the i-th-1 interlayer coil of strip inner radial stress p _si, circumferential stress q _si, interfacial friction τ _si, the Controlling object function of uncoiling loose winding and interlayer slip mainly comprise the following steps:

The coil of strip radius r of any i-th layer s article in coil of strip when i1) calculating uncoiling kth layer _si=r _b+ ih _s;

Be with steel at s article, i-th layer and the i-th-1 interlayer coil of strip inner radial stress p when i2) calculating uncoiling kth layer _si, wherein there is relevant relational expression: $p_{\mathrm{si}}[(1-\frac{{\mathrm{\&nu;}}_2}{2})\&CenterDot;r_{\mathrm{si}}+\frac{{\mathrm{\&nu;}}_2}{2}{r}_{\mathrm{si}+1}]-p_{\mathrm{si}+1}[(1-\frac{{\mathrm{\&nu;}}_2}{2})\&CenterDot;r_{\mathrm{si}+1}+\frac{{\mathrm{\&nu;}}_2}{2}{r}_{\mathrm{si}}]=E_2(r_{\mathrm{si}+1}-r_{\mathrm{si}})\left(\frac{r_{\mathrm{si}}-r_{01\mathrm{si}}}{r_{01\mathrm{si}}}\right),$ In formula: r _si+1the inside radius of the i-th+1 layer band steel at s article of place during uncoiling current layer, p _si+1be with steel at s article, the i-th+1 layer and the i-th interlayer coil of strip inner radial stress during uncoiling current layer, r _01sithe inside radius of i-th layer of band steel at s article of place during front one deck of uncoiling current layer;

I3) reel displacement during uncoiling kth layer is calculated

I4) the coil of strip radius of when uncoiling kth layer considers stratified deformation any i-th layer s article is calculated ${r_{\mathrm{si}}}^{\&prime;}=\left\{\begin{array}{cc}\frac{[E_2{h}_s+\frac{{\mathrm{\&nu;}}_2{p}_{\mathrm{si}}{r}_{\mathrm{si}+1}}{2}+(\frac{{\mathrm{\&nu;}}_2}{2}-1)p_{\mathrm{si}+1}{r}_{\mathrm{si}+1}-0.5\mathrm{\&rho;g}{h}_s\sin \mathrm{\&theta;}]}{[\frac{E_2{h}_s}{r_{01\mathrm{si}}}+\frac{{\mathrm{\&nu;}}_2{p}_{\mathrm{si}+1}}{2}+(\frac{{\mathrm{\&nu;}}_2}{2}-1)p_{\mathrm{si}}+0.5\mathrm{\&rho;g}{h}_s\sin \mathrm{\&theta;}]}& i>1\\ r_b-u_s& i=1\end{array}\right.,$ θ is polar angle, and g is gravity constant;

I5) inequality is judged || r _si-r' _si|| whether≤ε sets up, if inequality is false, makes r _si=r' _si, proceed to step I 2), if inequality is set up, then directly proceed to step I 6);

Be with steel at s article, i-th layer and the i-th-1 interlayer coil of strip circumferential stress q when i6) calculating uncoiling kth layer _si=q _si+1-π (r _siτ _si-r _si+1τ _si+1)/(r _si+1-r _si), in formula: q _si+1be with steel s article, the i-th+1 layer and the i-th interlayer coil of strip circumferential stress during uncoiling kth layer, τ _si+1during uncoiling current layer the i-th+1 layer band steel and i-th layer be with the friction stree of steel at s article of place;

I7) calculate uncoiling kth layer time i-th layer band steel and the i-th-1 layer be with the tightening coefficient of steel at s article of place $m_{\mathrm{si}}=1+1.27k_0\frac{{\mathrm{\&delta;}}_{\max }}{h_s}{\left(\frac{E_2}{p_{\mathrm{si}}}\right)}^{0.8};$

When i8) calculating uncoiling kth layer, band steel is at s article, i-th layer τ with the i-th-1 interlayer coil of strip interior layer and interfacial friction stress _si=r _si+1τ _si+1/ r _si+ (q _si+1-q _si) (r _si+1-r _si)/π r _si;

I9) minimized friction balance allowance K during uncoiling kth layer is solved _l=min{ μ p _si-τ _si;

Uncoiling loose winding when i10) solving uncoiling kth layer and the Controlling object function of interlayer slip

J () judges inequality set up? if inequality is set up, make j _1y=j ₁, proceed to step (k); If inequality is false, then directly proceed to step (k);

Does k () judge that inequality k < 2 sets up? if inequality is set up, make j ₁=j ₁+ 1, T=T _min+ j ₁Δ T, proceeds to step (l); If inequality is false, make j ₂=j ₂+ 1, proceed to step (h);

L () judges inequality T≤T _maxset up? if inequality is set up, proceed to step (f); If inequality is false, proceed to step (m);

M () exports optimum uncoiling tension value T _y=T _min+ j _1yΔ T.