CN101038606A - Twinning four-high rolling mill self-adaptive roll shape design method - Google Patents

Abstract

The invention relates to a roll shape design method for the twinning four high mill. Dividing a working roll 2, a support roll 3 into n units along the half roll length direction, adopting the reverse method for calculate the roll shape, firstly fixing the width level, conducting the rolling pressure weighting to the convexity vector Mj of the half roll length of the working roll 2 and the supporting roll under different rolling pressure Pj, the convexity of the half roll length is the Mi in the formula (2), then conducting the plate width weighting to the convexity vector Mi with the different plate widths Bi, the convexity of the half roll length is the MB in the formula (3), then using the non-linear regression simplex method to enable the discrete MB to be continued, the roll shape curve of the half roll length is twinned: M=a*xb. By using the roll shape designed by the invention, the rolled product has small convexity, favorable shape and accurate size.

Description

A kind of twin four-high mill self-adaptation roll design method

Technical field

The invention belongs to the four-high mill technical field.Be specifically related to a kind of method for designing of twin four-high mill self-adaptation roll shape.

Background technology

For making the wide little good with plate shape to thick difference of rolled products, for four-high mill, main roller rest type system is controlled.Traditional general backing roll of roll shape system mostly is plain-barreled roll, working roll or be plain-barreled roll or with certain convexity.Obviously for given specification product scope, different roll shape systems need be arranged.Because the description that milling train is produced is more, causes roll shape system more complicated, strip shape quality is not ideal.For this reason, some scholars carried out some researchs in this respect both at home and abroad, and had also obtained certain application aborning.But their work all is to be centered around in the research of backing roll roll shape.For working roller is that the ascending principle of employing compensates the abrasion gradually in the backing roll military service cycle, so roller management is still complicated.In addition, when the roll shape computation optimization was programmed, they were the thought that adopts multiple iterative computation.

Summary of the invention

Task of the present invention provides a kind ofly can improve plate shape, improve rolled products lateral dimension precision, keep contacting between working roll and backing roll roller that stress is equal, the uniform twin four-high mill of abrasion is adaptive to the roll design method.

For realizing above-mentioned task, the technical solution used in the present invention is: working roll, backing roll are divided into n unit along half body of roll length direction, employing is retrodicted and is calculated the method for roll shape, calculates the convexity vector of the wide and roll shape outer profile curve correspondence that edge half body of roll of draught pressure under certain level is long of ejecting plate respectively:

${\stackrel{\→}{M}}_{\mathrm{ij}}=a\·X{n}^b---\left(1\right)$

In the formula: X _nThe unit sequence number that-half body of roll direction is divided, value is X ₁, X ₂X _n

The span of a-working roll is: 5.2E-19～4.0E-10, and the span of backing roll is: 1.9E-13～7.2E-12;

The span of b-working roll is: 2.2～5.6, and the span of backing roll is: 3.15～4.3;

The certain level that the i-plate is wide;

The certain level of j-draught pressure.

When calculating, earlier fixing a certain width levels is calculated different draught pressure P respectively _jUnder the long convexity vector M of working roll, backing roll half body of roll _j, with the long convexity vector of half body of roll of these convexity vectors after the draught pressure weighted be:

${\stackrel{\→}{M}}_i=\mathrm{\Σ}\frac{P_j}{\mathrm{\Σ}{P}_j}{\stackrel{\→}{M}}_j---\left(2\right)$

Calculate the wide B of different operating mode lower plates respectively by formula (2) again _iThe long convexity vector M of half body of roll of working roll, backing roll _i, with the long convexity vector of half body of roll of these convexity vectors after the wide weighted of plate be:

${\stackrel{\→}{M}}_B=\mathrm{\Σ}\frac{B_i}{\mathrm{\Σ}{B}_i}{\stackrel{\→}{M}}_i---\left(3\right)$

In formula (2), (3):

P _jThe draught pressure an of-Di j level;

B _iThe plate an of-Di i level is wide;

∑ B _iWide each the horizontal sum of-plate;

∑ P _jEach horizontal sum of-draught pressure.

And then the simplicial method of utilizing non-linear regression makes discrete

Serialization, the then twin long roll shape outer profile curve of half body of roll that goes out working roll, backing roll:

M＝a·x ^b (4)

In the formula: x-half body of roll direction length, mm;

The span of a-working roll is: 5.2E-19～4.0E-10;

The span of backing roll is: 1.9E-13～7.2E-12;

The span of b-working roll is: 2.2～5;

The span of backing roll is: 3.15～4.3.

The roll shape outer profile curve of working roll, backing roll and the counterpart of rolled piece width B are curve, and being positioned at the rolled piece width B is smooth junction curve with exterior domain, and the outer profile curve of roll shape is centrosymmetric along the barrel length direction.

In formula (2),

Convexity vector for working roll, backing roll

General name, its calculating formula is:

(1) relation equation between distortion and the power

Working roll elastic bending equation:

${\stackrel{\→}{Y}}_w={\stackrel{\→}{\stackrel{\→}{G}}}_w(\stackrel{\→}{Q}-\stackrel{\→}{P})---\left(5\right)$

Backing roll elastic bending equation:

${\stackrel{\→}{Y}}_b={\stackrel{\→}{\stackrel{\→}{G}}}_b\stackrel{\→}{Q}---\left(6\right)$

The working roll that draught pressure causes flattens equation:

${\stackrel{\→}{Y}}_{\mathrm{ws}}={\stackrel{\→}{\stackrel{\→}{G}}}_{\mathrm{ws}}\stackrel{\→}{P}---\left(7\right)$

Flatten equation between roller:

${\stackrel{\→}{Y}}_{\mathrm{wb}}={\stackrel{\→}{\stackrel{\→}{G}}}_{\mathrm{wb}}\stackrel{\→}{Q}---\left(8\right)$

(2) dynamic balance relation equation

$\stackrel{\→}{P^T}\·\stackrel{\→}{I}=\stackrel{\→}{Q^T}\·\stackrel{\→}{I}---\left(9\right)$

In the formula:

-working roll, backing roll elastic bending vector;

-working roll, backing roll elastic bending influence function vector;

Contact pressure vector between-roller;

-draught pressure vector;

Elastic flattening distortion vector between-roller;

Elastic flattening deformation effect functional vector between-working roll and rolled piece;

Elastic flattening deformation effect functional vector between-roller;

-unit column vector.

During with formula (5), (6), (8), (9) calculating, equate with the wide B of plate with contact length L between roller, and make each unit contact pressure keep equating being constraint condition, consider compatibility of deformation and the relation of the compatibility of deformation between working roll and rolled piece between working roll and backing roll again, that is:

Compatibility of deformation relation equation between working roll and the backing roll:

${\stackrel{\→}{Y}}_{\mathrm{wb}}={\stackrel{\→}{Y}}_{\mathrm{wbo}}+{\stackrel{\→}{Y}}_b-{\stackrel{\→}{Y}}_w-{\stackrel{\→}{M}}_b-{\stackrel{\→}{M}}_w---\left(10\right)$

Compatibility of deformation relation equation between rolled piece and the working roll:

$\stackrel{\→}{H}={\stackrel{\→}{H}}_0+2({\stackrel{\→}{Y}}_{\mathrm{ws}}-{\stackrel{\→}{Y}}_{\mathrm{wso}})+2({\stackrel{\→}{M}}_w-{\stackrel{\→}{Y}}_w)---\left(11\right)$

In the formula:

-constant vector, i.e. the flattening amount of roll surface center;

-constant vector, i.e. the flattening amount of plate center;

-backing roll convexity vector;

-work roll crown vector;

-part outgoing gauge vector;

-constant vector, the i.e. outgoing gauge of plate center;

Then, according to formula (5)～(11) establishment operation program.The main flow chart of operation program is: earlier with raw data input, division unit.After given strip crown expectation value, carry out the outgoing gauge vector Calculate hot convexity vector Calculate the draught pressure vector

Calculating.After given working roll, backing roll press the power expectation regularity of distribution indirectly, carry out working roll, backing roll and press force vector indirectly then

Calculating, crooked influence function vector

Calculating, the flexural deformation vector

Calculating, flatten the influence function vector Calculating, the flattening deformation vector

Calculating, constant vector

Calculating, working roll, backing roll convexity vector

Calculating.

Owing to adopt technique scheme, the working roll that is drawn, backing roll roller curve have that draught pressure in the self-adaptation field working conditions changes and the function of the wide variation of plate, and the upper and lower working roll bus that keeps constituting in rolling roll gap shape is parallel, so guaranteed to roll the plate shape and the dimensional accuracy of product good.

Four, description of drawings

Fig. 1 is a kind of synoptic diagram of the present invention;

Fig. 2 is the side view of Fig. 1;

Fig. 3 is the main flow block diagram of roll shape convexity vector calculation program of the present invention.

Five, embodiment

The invention will be further described below in conjunction with the drawings and specific embodiments:

As shown in Figure 1 and Figure 2, four-high mill comprises working roll 2, backing roll 3, memorial archway 4, bearing shell 5, bearing seat 6, breading cap 7, depress spiro rod 8, rolling disc 9, pull bar 10, and whole rolling is fixed on the basis by foot bolt 11.

When rolled piece 1 was rolled, working roll 2 produced flexural deformation under roll-force P effect.Working roll 2 is in contact with one another as shown in Figure 2 with rolled piece 1 in the wide B scope of plate, can make working roll 2 produce flattening deformation simultaneously.The stack of two classes distortion can make rolled piece 1 look as Fig. 2 direction and produce thick middle, the thin phenomenon in two limits, that is: strip crown is bigger, and dimensional accuracy is also poor.For strip crown being reduced even leveling off to zero, working roll 2 is designed to certain convexity, promptly working roll 2 has roll shape; In addition, because working roll 2 is in contact with one another with backing roll 3, backing roll 3 can produce flexural deformation when producing flattening deformation, the superposition of this two classes distortion and working roll 2 convexitys, and the contact stress that makes working roll 2 and backing roll 3 look as Fig. 2 direction does not wait.Contact stress equates that backing roll 3 also is designed to have the roll shape of certain outer profile curve between roller in order to make.

This embodiment is an example with 2800mm four roller jobbing sheet-rolling mills, and the rolled piece width is that 2200mm, draught pressure are 25000KN.When working roll 2 materials are cast steel, backing roll 3 materials are 70Cr3Mo.

Calculate at first, respectively by

The working roll 2 of general name, the convexity vector of backing roll 3

Its calculating formula is:

(1) relation equation between distortion and the power:

Working roll elastic bending equation:

${\stackrel{\→}{Y}}_w={\stackrel{\→}{\stackrel{\→}{G}}}_w(\stackrel{\→}{Q}-\stackrel{\→}{P})---\left(5\right)$

Backing roll elastic bending equation:

${\stackrel{\→}{Y}}_b={\stackrel{\→}{\stackrel{\→}{G}}}_b\stackrel{\→}{Q}---\left(6\right)$

The working roll that draught pressure causes flattens equation:

${\stackrel{\→}{Y}}_{\mathrm{ws}}={\stackrel{\→}{\stackrel{\→}{G}}}_{\mathrm{ws}}\stackrel{\→}{P}---\left(7\right)$

Flatten equation between roller:

${\stackrel{\→}{\stackrel{\→}{Y}}}_{\mathrm{wb}}{=\stackrel{\→}{\stackrel{\→}{G}}}_{\mathrm{wb}}\stackrel{\→}{Q}---\left(8\right)$

(2) dynamic balance relation equation:

$\stackrel{\→}{P^T}\·\stackrel{\→}{I}=\stackrel{\→}{Q^T}\·\stackrel{\→}{I}---\left(9\right)$

In the formula:

-working roll 2, backing roll 3 elastic bending vectors:

-working roll 2, backing roll 3 elastic bending influence function vectors;

Contact pressure vector between-roller;

-draught pressure vector;

Elastic flattening distortion vector between-roller;

-working roll 2 and 1 elastic flattening deformation effect of rolled piece functional vector;

Elastic flattening deformation effect functional vector between-roller;

-unit column vector.

During with formula (5), (6), (8), (9) calculating, equate with the wide B of plate, as shown in Figure 1, and make each unit contact pressure keep equating to be constraint condition with contact length L between roller.Consider the compatibility of deformation relation of 1 in the compatibility of deformation of 3 of working roll 2 and backing rolls and working roll 2 and rolled piece again, that is:

Compatibility of deformation relation equation between working roll 2 and the backing roll 3:

${\stackrel{\→}{Y}}_{\mathrm{wb}}={\stackrel{\→}{Y}}_{\mathrm{wbo}}+{\stackrel{\→}{Y}}_b-{\stackrel{\→}{Y}}_w-{\stackrel{\→}{M}}_b-{\stackrel{\→}{M}}_w---\left(10\right)$

Compatibility of deformation relation equation between rolled piece 1 and the working roll 2:

$\stackrel{\→}{H}={\stackrel{\→}{H}}_0+2({\stackrel{\→}{Y}}_{\mathrm{ws}}-{\stackrel{\→}{Y}}_{\mathrm{wso}})+2({\stackrel{\→}{M}}_w-{\stackrel{\→}{Y}}_w)---\left(11\right)$

In the formula:

-constant vector, i.e. the flattening amount of roll surface center;

-constant vector, i.e. the flattening amount of plate center;

-backing roll 3 convexity vectors;

-working roll 2 convexity vectors;

-rolled piece 1 outgoing gauge vector;

-constant vector, the i.e. outgoing gauge of plate center;

According to formula (5)～(11) establishment operation program.Present embodiment is in program composition, and employing is directly retrodicted and calculated the thought of convexity, and section distribution supposition, roller press power distribution supposition indirectly after having avoided rolling.And the flattening deformation value of the long midpoint of the working roll and the backing roll body of roll is its adjacent 3 flattening deformation to be made nonlinear smoothing handle gained, has avoided the hypothesis of this place's flattening deformation.Avoided all iterative computation fully, simplified programming greatly and made the result of calculation expectation value that more becomes.

The main flow chart of operation program is as shown in Figure 3: earlier with the raw data input, and division unit, given strip crown expectation value is carried out the outgoing gauge vector again Calculate hot convexity vector

Calculate the draught pressure vector

Calculating; After given working roll, backing roll press the power expectation regularity of distribution indirectly, carry out working roll, backing roll and press force vector indirectly then

Calculating, crooked influence function vector

Calculating, the flexural deformation vector

Calculating, flatten the influence function vector

Calculating, the flattening deformation vector Calculating, constant vector

Calculating, working roll, backing roll convexity vector

Calculating.

Again respectively according to formula

${\stackrel{\→}{M}}_i=\mathrm{\Σ}\frac{P_j}{\mathrm{\Σ}{P}_j}{\stackrel{\→}{M}}_j---\left(2\right)$

${\stackrel{\→}{M}}_B=\mathrm{\Σ}\frac{B_i}{\mathrm{\Σ}{B}_i}{\stackrel{\→}{M}}_i---\left(3\right)$

Calculate different draught pressure P _j, the wide B of different plates _iThe long convexity vector of working roll 2, backing roll 3 half body of roll after draught pressure and the wide weighted of plate

And then the simplicial method of utilizing non-linear regression makes discrete Serialization, the then twin long roll shape outer profile curve of half body of roll that goes out working roll 2, backing roll 3:

M＝a·x ^b (4)

In the formula: x-half body of roll direction length, mm;

The span of a-working roll is: 5.2E-19～4.0E-10;

The span of backing roll is: 1.9E-13～7.2E-12;

The span of b-working roll is: 2.2～5.6;

The span of backing roll is: 3.15～4.3.

According to formula (4), concerning working roll 2, the value of a, b is respectively 4.9 * 10 ^-10With 2.65, M then _wMaximal value be 0.1065mm.Concerning backing roll 3, the value of a, b is respectively 2.1 * 10 ^-13With 3.83, M then _bMaximal value be 0.2167mm.

The product convexity that roll shape shut out with the design of present embodiment method is little, and plate shape is good, the dimensional accuracy height.

Claims (3)

1, a kind of method for designing of twin four-high mill self-adaptation roll shape, it is characterized in that working roll 2, backing roll 3 are divided into n unit along half body of roll length direction, employing is retrodicted and is calculated the method for roll shape, calculates the convexity vector of the wide and roll shape outer profile curve correspondence that edge half body of roll of draught pressure under certain level is long of plate in the lump:

${\stackrel{\→}{M}}_{\mathrm{ij}}=a\·{\mathrm{Xn}}^b---\left(1\right)$

In the formula: X _nThe unit sequence number that-half body of roll direction is divided, value is X ₁, X ₂X _n,

The span of a-working roll is: 5.2E-19～4.0E-10, and the span of backing roll is: 1.9E-13～7.2E-12,

The span of b-working roll is: 2.2～5.6, and the span of backing roll is: 3.15～4.3,

The certain level that the i-plate is wide,

The certain level of j-draught pressure;

When operation was calculated, earlier fixing a certain width levels was calculated different draught pressure P respectively _jUnder the long convexity vector M of working roll 2, backing roll 3 half bodies of roll _j, with the long convexity vector of half body of roll of these convexity vectors after the draught pressure weighted be:

${\stackrel{\→}{M}}_i=\mathrm{\Σ}\frac{P_j}{\mathrm{\Σ}{P}_j}{\stackrel{\→}{M}}_i---\left(2\right)$

Calculate the wide B of different operating mode lower plates respectively by formula (2) again _iThe long convexity vector M of half body of roll of working roll 2, backing roll 3 _i, with the long convexity vector of half body of roll of these convexity vectors after the wide weighted of plate be:

${\stackrel{\→}{M}}_B=\mathrm{\Σ}\frac{B_i}{\mathrm{\Σ}{B}_i}{\stackrel{\→}{M}}_i---\left(3\right)$

In formula (2), (3):

P _jThe draught pressure an of-Di j level,

B _iThe plate an of-Di i level is wide,

∑ B _iWide each the horizontal sum of-plate,

∑ P _jEach horizontal sum of-draught pressure;

And then the simplicial method of utilizing non-linear regression makes discrete

Serialization, the then twin long roll shape outer profile curve of half body of roll that goes out working roll 2, backing roll 3:

M＝a·x ^b (4)

In the formula: x-half body of roll direction length, mm,

The span of a-working roll 2 is: 5.2E-19～4.0E-10,

The span of backing roll 3 is: 1.9E-13～7.2E-12,

The span of b-working roll 2 is: 2.2～5,

The span of backing roll 3 is: 3.15～4.3;

The counterpart of the roll shape outer profile curve of working roll 2, backing roll 3 and rolled piece 1 width is a curve, and being positioned at rolled piece 1 width is smooth junction curve with exterior domain, and the outer profile curve of roll shape is centrosymmetric along the barrel length direction.

2, twin four-high mill self-adaptation roll shape according to claim 1 is characterized in that described

Convexity vector for working roll 2, backing roll 3

General name, its calculating formula is:

(1) relation equation between distortion and the power:

Working roll elastic bending equation:

Backing roll elastic bending equation:

The working roll that draught pressure causes flattens equation:

Flatten equation between roller:

(2) dynamic balance relation equation:

$\stackrel{\→}{P^T}\·\stackrel{\→}{I}=\stackrel{\→}{Q^T}\·\stackrel{\→}{I}---\left(9\right)$

In the formula:

-working roll 2, backing roll 3 elastic bending vectors;

-working roll 2, backing roll 3 elastic bending influence function vectors;

Contact pressure vector between-roller;

-draught pressure vector;

Elastic flattening distortion vector between-roller;

-working roll 2 and 1 elastic flattening deformation effect of rolled piece functional vector;

Elastic flattening deformation effect functional vector between-roller;

-unit column vector.

When calculating, keep equating to be constraint condition, consider that again the compatibility of deformation of 1 in the compatibility of deformation of 3 of working roll 2 and backing rolls and working roll 2 and rolled piece concerns, that is: with each unit contact pressure between roller with formula (5), (6), (8), (9)

Compatibility of deformation relation equation between working roll 2 and the backing roll 3:

${\stackrel{\→}{Y}}_{\mathrm{wb}}={\stackrel{\→}{Y}}_{\mathrm{wbo}}+{\stackrel{\→}{Y}}_b-{\stackrel{\→}{Y}}_w-{\stackrel{\→}{M}}_b-{\stackrel{\→}{M}}_w---\left(10\right)$

Compatibility of deformation relation equation between rolled piece 1 and the working roll 2:

$\stackrel{\→}{H}={\stackrel{\→}{H}}_0+2({\stackrel{\→}{Y}}_{\mathrm{ws}}-{\stackrel{\→}{Y}}_{\mathrm{wso}})+2({\stackrel{\→}{M}}_w-{\stackrel{\→}{Y}}_w)---\left(11\right)$

In the formula:

-constant vector, i.e. the flattening amount of roll surface center;

-constant vector, i.e. the flattening amount of plate center;

-backing roll 3 convexity vectors;

-working roll 2 convexity vectors;

-rolled piece 1 outgoing gauge vector;

-constant vector, the i.e. outgoing gauge of plate center; Then, according to formula (5)～(11) establishment operation program.

3, twin four-high mill self-adaptation roll shape according to claim 2 is characterized in that the main flow chart of described operation program is: earlier with the raw data input, and division unit, given strip crown expectation value is carried out the outgoing gauge vector again

Calculate hot convexity vector

Calculate the draught pressure vector

Calculating; After given working roll, backing roll press the power expectation regularity of distribution indirectly, carry out working roll, backing roll and press force vector indirectly then

Calculating, crooked influence function vector

Calculating, the flexural deformation vector

Calculating, flatten the influence function vector

Calculating, the flattening deformation vector

Calculating, constant vector

Calculating, working roll, backing roll convexity vector

Calculating.

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