CN100357953C - Automatic flattening process parameter optimization of metal plate band - Google Patents

Abstract

The present invention belongs to the technical field of straightening metal plate belts, more specifically to an optimization method for automatic straightening process parameters of metal plate belts, which aims for the problem that because the straightening course of plate belts are complex, and the straightening course of plate belts are easily influenced by the bounce, the abrasion, the bearing clearances, etc. of a straightener in the prior art, the flatness of products can not meet requirements due to the great deviation generated between the setting value of the theoretical calculation technology and practical operation. The optimization method processes the difference value of the theory calculated value and the measured value of straightening force in a minimal optimization mode, namely that the theory calculated value of the straightening force approaches to the measured value to the utmost extent by correcting undetermined variables which are regression coefficients a0, a1, a2, a3, a4, a5, a6, a7 in the theoretical calculation formula of straightening force. The method of the present invention can automatically set technology parameters to improve straightening quality and improve straightening efficiency. An on-line system based on the present invention is successfully applied to a straightener for medium-thick plates of 3500mm. The difference between the average value and the calculated value of measured straightening force is less than +/-5%, and the residual curvature of the product is less than 1.5 mm/m.

Description

Metal plate and belt automatic flattening parameter optimizing method

Technical field

The invention belongs to the technical field of metal plate and belt aligning, specifically is a kind of metal plate and belt automatic flattening parameter optimizing method.

Background technology

Metal plate and belt aligning purpose is the finished product that obtains high straightness.Plate shape for obtaining to conform to quality requirements will accurately be set its technological parameter.But because the complicacy of strip aligning process, and be subject to the factor affecting such as spring, wearing and tearing, bearing clearance of leveller equipment itself, Theoretical Calculation technique initialization value and practical operation generation cause the product flatness not meet the demands than large deviation.

Summary of the invention

The present invention is directed to the complicacy that exists in the prior art owing to strip aligning process, and be subject to the factor affecting such as spring, wearing and tearing, bearing clearance of leveller equipment itself, Theoretical Calculation technique initialization value and practical operation produce than large deviation, the problem that causes the product flatness not meet the demands provides a kind of and can be used for deformation resistance model, and the metal plate and belt automatic flattening parameter optimizing method of 3 parts such as on-line system that straightener improves the quality of products and realizes comprising of the production automation of advanced straightening theory model, self study.Straightener is set technological parameter and is mainly contained drafts (entrance and exit roll gap), straightening force, motor load etc., and this method is by optimizing the coefficient of resistance of deformation computing formula, and indirect optimization straightener is set technological parameter.Calculate gained material deformation drag by this method database coefficient and may difference be arranged with the real material resistance of deformation; But, the resistance of deformation of using this method database coefficient to calculate, and use this resistance of deformation to obtain drafts (entrance and exit roll gap), straightening force, motor load equivalence, adopt these process value to set the straightening quality that straightener can obtain.

The present invention realizes that by following scheme metal plate and belt automatic flattening parameter optimizing method comprises following aspect: straightening theory model, deformation resistance model, the on-line system of employing straightening theory model, deformation resistance model.The straightening theory model adopts " Bauschinger effect ", " neutral line skew ", " tension force between roller " technology.

Resistance of deformation computing formula model adopts " self-adaptation ", " pattern-recognition ", " optimization " technology.Deformation resistance model is based on temperature, deformation velocity, deformation extent multiple index, and its expression formula is:

σ _s＝a ₀+exp(a ₁+a ₂t+a ₃t ²+a ₄t ⁴+a ₅t ⁴+a ₆v+a ₇n)(1)

In the formula: t---straightening temperature (℃);

V---aligning speed;

N---crooked passage;

a ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇Be regression coefficient, depend on steel grade.

Adaptive technique of the present invention comprises process data actual measurement sampling, and theoretical straightening force is calculated, and theoretical straightening force and actual measurement straightening force are relatively.

Mode identification technology comprises delimit different feature modes, reasonably to measuring and the image data denoising.

Optimization technique of the present invention minimize optimization process for setting up the optimization aim function expression with the calculated value of straightening force and the difference of measured value, promptly by revising the variable regression coefficient a undetermined in the metal deformation resistance computing formula ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇, make the calculated value of straightening force and measured value the most approaching, its optimization aim function expression is:

$\mathrm{\ΔF}(B,h,{\mathrm{\σ}}_s)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{[P_i^{\′}-P_i(B,h,{\mathrm{\σ}}_s)]}^2---\left(2\right)$

In the formula, Δ F (B, h, σ _s)---the quadratic sum of the difference of actual measurement straightening force and Theoretical Calculation straightening force;

P ' _i---the actual measurement straightening force;

p _i(B, h, σ _s)---the Theoretical Calculation straightening force.

The straightening theory model that the present invention includes, deformation resistance model, and on-line system partly specifically describe as follows.

(1) straightening theory model

The main process of model: set up each crooked geometric relationship, the moment of flexure of calculating single bending and power energy parameter, calculate whole moment of flexure and power energy parameter.In this process, it is more accurate that the present invention adopts three new technology that straightening force is calculated.

(1) first technology is for adding the resistance of deformation computation model of Bauschinger effect, and Bauschinger effect is meant original through distortion, then the phenomenon that limit of elasticity or yield strength reduce when oppositely loading.Because the aligning process is the process that an alternating bending loads, so the Bauschinger effect influence is bigger.Model is set up each crooked resistance of deformation σ that the Bauschinger effect mathematical model of simplifying is more accurately determined the aligning process on the basis of experiment _nMathematical model synoptic diagram such as Fig. 1.

${\mathrm{\σ}}_n=(1+\mathrm{n\ξ})({\mathrm{\σ}}_s-k\frac{{\mathrm{\σ}}_s}{E})+\mathrm{kx}---\left(3\right)$

σ _n---n crooked resistance of deformation;

N---crooked passage;

ξ---passage hardening coefficient;

σ _s---relevant with material, be unstrained material yield intensity, promptly original resistance of deformation;

K---sclerosis slope;

E---elastic modulus;

X---strain, odd-numbered pass are for just, and even-numbered pass is for negative.

As shown in Figure 1, distortion of materials drag and original strain regime ε _N0Relevant, method is calculated n crooked original strain regime ε earlier _N0(be the strain remnants of previous bending; Can ask by the geometric condition of last crooked remnant curvature,

First crooked strain remnants are zero); Ask by point (ε _N0, 0) and slope is the straight line of elastic modulus E

σ _n＝Ex-Eε _n0 (4)

Ask the intersection point (ε of formula (4) and formula (3) at last _i, σ _i), σ wherein _iBe exactly the resistance of deformation value of this bending strain, ε _iBe this bending strain.

(2) second technology are the neutral line skew, find to have the neutral line shift phenomenon at aligning process sheet material according to theoretical research and test, in the neutral line skew of cut deal the straightening force computing formula are had very big influence.

Model adopts the straightening force computing formula based on the neutral line skew.Sheet material is aligned the bent plate internal stress distribution as shown in Figure 2, because the sheet material upper surface is a tension, lower surface is a compressive stress, and lower surface is in the three-dimensional compressive stress state, and sheet material bottom internal force is greater than top.Because the inner internal force balance of sheet material, so produce the neutral line skew.

(interior moment of flexure) M=M _Draw+ _MPress (5)

(internal force) $N={{\∫}_0^{\frac{h}{2}+e}\mathrm{\σ}}_z+{{\∫}_{-(\frac{h}{2}-e)}^0\mathrm{\σ}}_z=0---\left(8\right)$

(straightening force) $p=\frac{4M}{T}---\left(9\right)$

Wherein: σ _zBe piecewise function,

0～Z _t ${\mathrm{\σ}}_z=\frac{{\mathrm{\σ}}_i}{Z_t}Z$

Z _t～(h/2+e) σ _z=k _SclerosisZ+ (σ _i-k _SclerosisZ _t)

0～-Z _t ${\mathrm{\σ}}_z=\frac{\mathrm{\μ}{\mathrm{\σ}}_i}{Z_t}Z$

-Z _tThe σ of～-(h/2-e) _z=k _SclerosisZ+ (μ σ _i-k _SclerosisZ _t) (10)

$Z_t=\frac{h}{2}\frac{1/{\mathrm{\ρ}}_t}{\frac{1}{\mathrm{\ρ}}+\frac{1}{{\mathrm{\ρ}}_t}}---\left(11\right)$

ρ _tSheet material spring-go limit curvature, ${\mathrm{\ρ}}_t=\frac{2{\mathrm{\σ}}_i}{\mathrm{hE}};---\left(12\right)$

ρ is this unit bending curvature, $\mathrm{\ρ}=\frac{T^2}{12s};---\left(13\right)$

μ＝(σ _j+σ _i)/σ _i (14)

Contact stress σ _jAdopt contact stress-hertz formula to obtain by straightening force P; In the formula:

E is the neutral line side-play amount;

μ is a lower surface stress and the ratio of upper surface;

k _SclerosisBe hardening coefficient;

σ _zBe stress;

Z _tBe the ductile bed height;

S is a drafts;

T is roll spacing;

The width of B sheet material;

H is the thickness of sheet material.

Promptly know the elastic layer thickness Z under the crooked geometric relationship knowing _t(formula 11) separates according to above-mentioned formula (5) (8) (9) connection, calculates moment M, and the relation according to M and straightening force P calculates straightening force P.Neutral line side-play amount e value influences M, and the M value influences P, and the P value influences e.Because the calculated relationship of M and P, the calculated relationship of P and μ, e is calculated as a loop iteration process.Computation process is as follows, e ₀=0, → M ₀→ P ₀→ μ ₁μ ₁→ e ₁→ M ₁→ P ₁→ μ ₂So P is worked as in circulation _iAnd P _I-1When differing from, calculate and finish, P less than definite value _iBy being asked straightening force.

(3) three technologies are tension force between roller, because straightener roller speed is different, between each bending unit, there is tension force in reasons such as sheet material transverse plate shape in the sheet material in the aligning process.Because the existence of tension force, thereby the value of moment of resistance M changes to some extent, causes the change of straightening force P.Model calculates the tension force of each bending unit from geometric relationship, and result of calculation is added the calculation expression of M.Tension force is mainly friction force.

F=f _{Friction force}(15)

f _{Friction force}=p * μ (16)

σ _{Friction force}=f _{Friction force}/ (Bh) (17)

In the formula: p is the straightening force of the smoothing roll of bending unit correspondence;

μ is a friction factor;

B is the sheet material width;

H is the sheet material height;

Because the existence of tension force, thereby the value of moment of resistance M changes to some extent, causes the change of straightening force P.Be calculated as a loop iteration process, from M ₀(not considering tension force between roller) → P ₀→ f _{Friction force 0}Again by f _{Friction force 0}→ M ₁→ P ₁→ f _{Friction force 1}So P is worked as in circulation _iAnd P _I-1When differing from, calculate and finish, P less than definite value _iBy being asked straightening force.This process and neutral line skew circulation are carried out simultaneously, and detailed process is as follows: the stress σ that friction force produces _{Friction force}Be evenly to distribute in the sheet material cross section, be superimposed upon the σ described in the formula (10) _ZIn the stress distribution, consider that friction force influences stress distribution:

σ _{Z_new}=σ _Z+ σ _{Friction force}(definite value) (18)

σ in wushu during calculating (5) (6) (7) (8) _{Z_new}Replace σ _ZObtain interior moment of flexure together.Because the cycle calculations of tension force influences each other between neutral line skew and roller, its cyclic process can turn to a cyclic process, e ₀=0, f _{Friction force 0}=0 → M ₀→ P ₀→ μ ₁, f _{Friction force 1}e ₁, f _{Friction force 1}→ M ₁→ P ₁→ μ ₂, f _{Friction force 2}So P is worked as in circulation _iAnd P _I-1When differing from, calculate and finish, P less than definite value _iBy being asked straightening force.

(4) the concrete computation process of aligning process is as follows:

I, carry out geometric analysis, determine the drafts of roller system

In the straightener of current trend, because type difference, it is different that each smoothing roll is depressed method for determination of amount, there are following two kinds substantially: the one, top roll is an one-piece construction, this straightener is the drafts according to housing screw, determine second and the drafts of penult smoothing roll (drafts that it is generally acknowledged housing screw with second and the drafts of penult smoothing roll equate substantially), be linear distribution according to drafts in the one-piece construction again, by second and the intermediate interpolated of the drafts of penult smoothing roll, obtain the drafts of each smoothing roll.The 2nd, top roll is that each smoothing roll is adjustable separately, the drafts of each smoothing roll of top roll system all is (present this structure straightener all has the online in real time measuring equipment) that can survey in this straightener, and the drafts linear interpolation that the drafts of lower roll system can be a smoothing roll by two adjacent top rolls is obtained.

The general technology setting is, determined roller is that to make the first bending unit bending curvature be (3～5) ρ to drafts _t(sheet material spring-go limit curvature); The first bending unit bending curvature of seizing back confiscated property is (1～1.5) ρ _tObtain second and the drafts of penult smoothing roll according to formula (13).Then, determine the drafts of each smoothing roll in the whole roller system according to said method.

II, determine the degree of crook of each bending unit of aligning process

According to the drafts and the formula (13) of each bending unit of determining among the I, can obtain the degree of crook of each bending unit.

III, from the self study deformation resistance model, obtain original resistance of deformation

The original resistance of deformation ρ of material _sBe by the self study deformation resistance model mentioned herein by calculating, the computation process deformation resistance model introduction that sees below.

IV, add Bauschinger effect in resistance of deformation

Because the aligning process is the process of alternating bending, the Bauschinger effect influence of material is very big.The resistance of deformation σ of each bending unit _iCan be by the original resistance of deformation σ among the III _sAnd formula (3) (4) obtains.

V, with flexural deformation drag σ _iBe the basis, under the influencing each other of tension force, set up the interior moment of flexure and the straightening force of each bending unit between property layer skew under consideration and roller

Set up the interior bending moment (5) (6) (7) (18) of bending unit according to formula (10～14) by the ρ bending radius.Because the cycle calculations of tension force influences each other between neutral line skew and roller, its cyclic process can turn to a cyclic process, e ₀, f _{Friction force 0}→ M ₀→ P ₀→ μ ₁, f _{Friction force 1}e ₁, f _{Friction force 1}→ M ₁→ P ₁→ μ ₂, f _{Friction force 2}So P is worked as in circulation _iAnd P _I-1When differing from, calculate and finish, P less than definite value _iBy being asked straightening force.

VI, straightening force, aligning load, remnant curvature with interior each bending unit of calculation of Bending Moment

According to straightening force, aligning load, the remnant curvature of interior each bending unit of calculation of Bending Moment, a lot of books all have introduction.

VII, according to the straightening force of each bending unit data computation integral body, aligning load, the whole straightening force of final residual curvature, aligning load, final residual curvature equal each bending unit and.

(2) deformation resistance model

The main process of model: the parametric measurement of strip straightening process and collection; Optimize strip material resistance of deformation computing formula model database coefficient by self-adaptation, pattern-recognition, optimization technique; Use resistance of deformation computing formula model gained resistance of deformation σ _s, calculate the calculated value and the setting value of various technological parameters.As shown in Figure 3.

At first: set up distortion of materials drag computing formula database, every kind of material coefficient of correspondence a ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇Value, primary data manually are provided with (according to the resistance of deformation curve of material experiment gained, to be determined or is provided with the definite value of regression coefficient, thereby set up above-mentioned database.Determining of regression coefficient is that the foundation of database is as well known to those skilled in the art and easy realization), in the production run by deformation resistance model optimization and renewal.

The second, set up metal straightening deformation drag computing formula model,, set up the multiple index resistance of deformation computing formula mould of innovation with temperature, deformation velocity, deformation extent basis to a certain steel grade.

Resistance of deformation computing formula model tormulation formula:

σ _s＝a ₀+exp(a ₁+a ₂t+a ₃t ²+a ₄t ⁴+a ₅t ⁴+a ₆v+a ₇n)(19)

In the formula: the t-straightening temperature (℃);

V-aligns speed;

The crooked passage of n-;

a ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇, be regression coefficient, depend on steel grade.

Promptly further theoretic straightening force is expressed as a ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇, function:

P＝P(a ₀，a ₁，a ₂，a ₃，a ₄，a ₅，a ₆，a ₇)。

The the 3rd: the aligning process is carried out on-line measurement (force transducer and position transducer), measurement data retrieval system.

The the 4th: the data that measurement is returned are carried out pattern-recognition, comprise established standards (, adjustable), remove invalid bad point, data qualification according to the actual conditions established standards.This process comprises two aspects, and the one, behind aligning, it is qualified and defective that plate shape situation is divided into; The 2nd, according to straightening force and aligning load and calculated value deviation, be divided into little big of deviation with deviation; Wherein plate shape is qualified was used for for the 4th step with the little data of deviation.

The 5th: go out relevant straightening force energy parameter with the straightening force Model Calculation, handle the back data relatively with the online actual measurement in scene, error is less, has successfully realized the accurate Calculation to straightening force energy parameter.Concrete grammar:

(1) set up the optimization aim function expression: purpose is that the difference of the calculated value of straightening force and measured value is carried out minimum optimization process, promptly by revising variable (the regression coefficient a undetermined in the straightening force theoretical calculation formula ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇), make the calculated value of straightening force and measured value the most approaching.So the optimization aim function expression is:

$\mathrm{\ΔF}(B,h,{\mathrm{\σ}}_s)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{[P_i^{\′}-P_i(B,h,{\mathrm{\σ}}_s)]}^2---\left(20\right)$

In the formula, Δ F (B, h, σ _s)---the quadratic sum of the difference of actual measurement straightening force and Theoretical Calculation straightening force;

P _i'---the actual measurement straightening force;

p _i(B, h, σ _s)---the Theoretical Calculation straightening force.

(2) according to aligning mechanical model and the deformation resistance model set up, we can be expressed as following formula following form:

$\mathrm{\ΔF}(B,h,{\mathrm{\σ}}_s)=\mathrm{\ΔF}(a_0{a}_1,a_2,a_3,a_4,a_5,a_6{a}_7,B,h)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{[P_i^{\′}-P_i(t,a_0,a_1,a_2,a_3,a_4,a_5,a_6,a_7,B,h)]}^2$

(21)

In the formula: i is the piece number of the sheet metal of same specification;

Δ F (V, h, σ _sThe quadratic sum of the difference of)-actual measurement straightening force and Theoretical Calculation straightening force;

P _i'---the actual measurement straightening force;

p _i(V, h, σ _s)---the Theoretical Calculation straightening force;

B---steel plate width;

H---steel plate thickness;

T---steel billet temperature;

a ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇---the variation coefficient in the resistance of deformation computing formula model.

(3) optimization process is determined resistance of deformation computing formula model: get optimization method-simplex of choosing and replace method, optimization process objective function

$\mathrm{\ΔF}(a_0{a}_1,a_2,a_3,a_4,a_5,a_6{a}_7,B,h)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{[P_i^{\′}-P_i(t,a_0,a_1,a_2,a_3,a_4,a_5,a_6,a_7,B,h)]}^2---\left(22\right)$

A has been determined in calculating ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇Value, a of this kind material correspondence in the new database more ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇Value.

(3) on-line system

On-line system is the robotization straightening system that adopts (one) (twos') theoretical model, in the on-line system, and the original resistance of deformation σ of material in (one) straightening theory model _sFor (two) deformation resistance model result calculated (by a in formula 19 and the database ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇Value calculate); (2) the theoretical straightening force p (B, h, the σ that use in the deformation resistance model _s) for adopting (one) straightening theory Model Calculation gained.On-line system can be provided with and adapt to the distinctive straightening process parameter of this TV station straightener fully, and the technological parameter of its setting can guarantee the straightening quality of high aligning.

The present invention compared with prior art has the following advantages and effect: method of the present invention can be provided with technological parameter automatically, improve straightening quality, improve aligning efficient, based on the application of on the 3500mm plate leveler, having succeeded of the present invention's on-line system, measure straightening force mean value and calculated value and differ less than ± 5%, product flatness (remnant curvature) is less than 1.5mm/m.

Description of drawings

Fig. 1 Bauschinger mathematical model synoptic diagram;

Fig. 2 sheet material is aligned crooked internal stress distribution synoptic diagram;

The main process synoptic diagram of Fig. 3 deformation resistance model

Embodiment

Present embodiment is to be used for illustrating of the present invention, rather than the present invention is done any restriction.

Method of the present invention has been successfully applied to plate straightener among the 3500mm of Shoudu Iron and Steel Co medium plate mill.Measure straightening force mean value and calculated value and differ less than ± 5%, the product remnant curvature is less than the regulation requirement.

Selecting steel grade 345D for use is example, thickness 60mm, width 2350mm, 681 ℃ of processing temperatures.Straightener theory setting value: inlet roll gap 59.01mm (sheet metal thickness deducts the drafts of second smoothing roll), outlet roll gap 59.21mm (sheet metal thickness deducts smoothing roll second from the bottom), theoretical straightening force is calculated P=7336KN, the straightening force P survey=7638kN that measures by force transducer, the actual measurement aligning after flatness less than 1.5mm/m, motor load 235KW.It is 4% that measurement straightening force mean value and calculated value differ, less than ± 5%.

Process is as follows:

One), sets up the database of resistance of deformation computing formula model, every kind of corresponding a of material according to material category ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇Different values.

Two) for every block of aligning sheet material:

1) according to the specifications parameter of product, by the various technological parameters of (one) straightening theory Model Calculation, the wherein original resistance of deformation σ of material _sBe that (two) deformation resistance model calculates and gets.

2) calculate technological parameter control straightener and finish the aligning process, and the aligning process is surveyed.

3) adopt measured data to optimize a of this material by deformation resistance model ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇Value.

4) these data are judged, removed bad point, and classify, main according to being the aligning strip shape quality; The difference of measured value and theoretical value; Plate shape is poor, the removal that difference is big.

Three) a of this kind material correspondence in the renewal deformation resistance model database ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇Value, be used for next piece sheet material aligning.

Claims (1)

1, a kind of metal plate and belt automatic flattening parameter optimizing method is characterized by: comprise the steps:

One), sets up the database of resistance of deformation computing formula model, every kind of corresponding a of material according to material category ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇Different values;

Two) for every block of aligning sheet material:

1) according to the specifications parameter of product, by the various technological parameters of straightening theory Model Calculation, the straightening theory model adopts " Bauschinger effect ", " neutral line skew ", " tension force between roller " technology;

Concrete computation process is as follows:

I, carry out geometric analysis, determine the drafts s of roller system

II, determine degree of crook---the bending curvature ρ of each bending unit of aligning process according to drafts

III, from following deformation resistance model, obtain original resistance of deformation

σ _s＝a ₀+exp(a ₁+a ₂t+a ₃t ²+a ₄t ⁴+a ₅t ⁴+a ₆v+a ₇n)

In the formula: t-straightening temperature ℃;

V-aligns speed;

The crooked passage of n-;

a ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇, be regression coefficient, depend on steel grade, its primary data manually is provided with;

IV, add Bauschinger effect in resistance of deformation

Set up the Bauschinger effect mathematical model of simplifying and more accurately determine each crooked resistance of deformation σ of aligning process _n:

${\mathrm{\σ}}_n=(1+\mathrm{n\ξ})({\mathrm{\σ}}_s-k\frac{{\mathrm{\σ}}_s}{E})+\mathrm{kx}---\left(3\right)$

σ _n---n crooked resistance of deformation;

N---crooked passage;

ξ---passage hardening coefficient;

σ _s---relevant with material, be unstrained material yield intensity, promptly original resistance of deformation;

K---sclerosis slope;

E---elastic modulus;

X---strain, odd-numbered pass are for just, and even-numbered pass is for negative

Distortion of materials drag and original strain regime ε _N0Relevant, n crooked original strain regime ε _N0Strain remnants for previous bending; First crooked strain remnants are zero; Ask by point (ε _N0, 0) and slope is the straight line of elastic modulus E,

σ _n＝Ex-Eε _n0 (4)

Ask the intersection point (ε of formula (4) and formula (3) at last _i, σ _i), σ wherein _iBe exactly the resistance of deformation value of this bending strain, ε _iBe this bending strain;

V, with flexural deformation drag σ _iBe the basis, under the influencing each other of tension force, set up the interior moment of flexure and the straightening force of each bending unit between property layer skew under consideration and roller

In the neutral line skew, calculate moment M, the relation according to M and straightening force P calculates straightening force P; Neutral line side-play amount e value influences M, and the M value influences P, and the P value influences e; Because the calculated relationship of M and P, the calculated relationship of P and μ, e is calculated as a loop iteration process; Computation process is as follows, e ₀=0, → M ₀→ P ₀→ μ ₁μ ₁→ e ₁→ M ₁→ P ₁→ μ ₂So P is worked as in circulation _iAnd P _I-1When differing from, calculate and finish, P less than definite value _iBy being asked straightening force;

Tension force and neutral line skew circulation is carried out simultaneously between roller, and detailed process is as follows:

The stress σ that friction force produces _{Friction force}Be evenly to distribute in the sheet material cross section, be superimposed upon σ _ZIn the stress distribution, consider that friction force influences stress distribution:

σ _{Z_new}=σ _Z+ σ _{Friction force}

According to stress distribution σ _{Z_new}Obtain interior moment of flexure together, because the cycle calculations of tension force influences each other between neutral line skew and roller, its cyclic process can turn to a cyclic process, e ₀=0, f _{Friction force 0}=0 → M ₀→ P ₀→ μ ₁, f _{Friction force 1}e ₁, f _{Friction force 1}→ M ₁→ P ₁→ μ ₂, f _{Friction force 2}So P is worked as in circulation _iAnd P _I-1When differing from, calculate and finish, P less than definite value _iBy being asked straightening force;

VI, straightening force, aligning load, remnant curvature with interior each bending unit of calculation of Bending Moment

VII, straightening force, aligning load, final residual curvature according to each bending unit data computation integral body

2) calculate technological parameter control straightener and finish the aligning process, and the aligning process is surveyed;

3) adopt measured data to optimize a of this material by deformation resistance model ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇Value;

1. set up the optimization aim function expression:

$\mathrm{\ΔF}(B,h,{\mathrm{\σ}}_s)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left[{P_i^{\′}-P}_i(B,h,{\mathrm{\σ}}_s)\right]}^2---\left(20\right)$

In the formula, Δ F (B, h, σ _s)---the quadratic sum of the difference of actual measurement straightening force and Theoretical Calculation straightening force;

P ' _i---the actual measurement straightening force;

p _i(B, h, σ _s)---the Theoretical Calculation straightening force

2. according to aligning mechanical model and the deformation resistance model set up, following formula (20) is expressed as following form:

$\mathrm{\ΔF}(B,h,{\mathrm{\σ}}_s)=\mathrm{\ΔF}(a_0,a_1,a_2,a_3,a_4,a_5,a_6,a_7,B,h)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}[P_i^{\′}-P_i(t,a_0,a_1{,a}_2,a_3,a_4,a_5,a_6,a_7,B,h){]}^2$

In the formula: i is the piece number of the sheet metal of same specification;

B---steel plate width;

H---steel plate thickness;

T---plate temperature;

a ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇---the variation coefficient in the resistance of deformation computing formula model;

3. optimization process is determined resistance of deformation computing formula model: get optimization method-simplex of choosing and replace method, optimization process objective function

$\mathrm{\Δ}F(a_0,a_1,a_2,a_3,a_4,a_5,a_6,a_7,B,h)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}[P_i^{\′}-P_i(t,a_0,a_1{,a}_2,a_3,a_4,a_5,a_6,a_7,B,h){]}^2$

Calculate and determine a ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇Value;

4) these data are judged, removed bad point, and classify, main according to being the aligning strip shape quality; The difference of measured value and theoretical value; Plate shape is poor, the removal that difference is big;

Three) a of this kind material correspondence in the renewal deformation resistance model database ₀, a ₁, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇Value, be used for next piece sheet material aligning.

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