Application of the Finite-Element Analysis to the Pass Rolling Process

1

Applicationof the Finite-Element Analysis

to the Pass Rolling Process

General Director KOMMEK Ltd.

[email protected]

Moscow State Instituteof Electronics and Mathematics

(Technical University),Dep. Mathematical Simulation

[email protected]

KOMMEK

Professor, D.Sc. Chumachenko E.N.

IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

2

Introduction

The basic ratios and results of pass rolling process simulation using the SPLEN computing system developed based on the finite-element method (FEM) are discussed.The computing system allows setting any configuration of a roll profile, and presently it is used for studying isothermal and non-isothermal rolling processes with two symmetric rolls. In this model a rigid-ductile statement of the problem and special system of friction implementation are used.The computer system simulating the process of metal deformation in passes allows avoiding labor-consuming and expensive industrial experiments and reduces the time of developing technological solutions. Besides, at the design stage already, one can reveal defects of the rolled product form and working degree of the metal and thereby maximally approach a technological draft to the working one.To increase a solution algorithm speed, the half-analytical finite-elements method was used.

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3

(2)

(3)

Then and condition entry (4)

Boundary conditions

on the

on the (1)

on the

Mathematical model of form changing hot materials

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injnij iiPl

v

v

jjiiVV

iu

ijije

eijij 3

2

]P25.1

exp1[f58.0,VV

VV,0n)VV(

ee

L

roll

rollLroll

- velocity of particles of continuum; - mill roller speed; - normal pressure;

- normal to mill roller; - tangent stress; - directional cosines;

- orthonormal frames; - constant of friction.

;3

1;~

ijijijijij ;3

1

3

1;

~ijijijijij

;2

3~~~eijij eeijij 3

~2~ ;

3

2~~~eijij

.0j,ij

V rollV P

n inl

iL


4

The heat exchange of the strip with rolls and with environment is described by the following variational equation :

(5)

where - is heat conductance coefficient;

- is thermal capacity and density of the strip material;

- is a generalized parameter dependent on the temperature difference of the strip

and environment, Stephen-Boltsman constant, blackness coefficient of the body and on relative

position of the surfaces when radiating;

- is linear expansion coefficient for environment and rolls;;

- is relative speed module of the movement with friction;

- is a coefficient taking into account the part of released heat energy.

Heat exchange

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rdS]T)QTt

Tc()

z

T

z

T

r

T

r

T([

Spl

rdLT)}TT(])273T()273T[({ airairL

4roll

4

air

0dLrT]qTT[rollL

frrollroll

airroll LLS

,c

airroll ,

Lrollfr VV5.0q uuplpl kQ

rollVV

plk


5

n

n

d z z n

z+ dz

d z C o s

Z

Y

For an arbitrary element of the strain focal point of a little enough thickness, the value

characterizing relative elongation speed of the fibers in an element of the thickness dz, is

constant: . In this case constant C in each section has its own value. Speed

components of particles movement in any fixed element relative to the rolls surfaces look

like:

(6)

a)

b)

A diagram of a focal point of strain at a longitudinal rolling (a) and stresses (b) applying to a layer of an infinitesimal thickness.

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z

z

Cz~zz z~z

z

]zz,z[z;zCv);y,x(vv);y,x(vv zyyxx


6

Half-analytical of finite-elements method

Thus, the three-dimensional speed field of an element is divided into two components. The

speed field of in the section perpendicular to the rolling direction is determined from a

finite-element approximation. The speed component

along the rolling direction is calculated using an iterative procedure with a search of the

constant C. So an initial volume problem for an element was reformed into a "generalized"

two-dimensional problem which can be solved using the finite-element method.

For a spatial stress-deformed state to be constructed, the length focal point of strain is divided into

m parts by means of cross sections, and the value in each section at

is determined.

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z

}v,v{ yx

zv

z

kzz

kzz C:

k

constzz k


7

A spatial problem solution algorithm for each individual element is based on a

minimization of the functional:

(7)

Finally the longitudinal movement speed of the particles in an arbitrary section

can be determined by the ratio: , (8)

where

;

is the movement speed of an element at the focal point of

strain input .

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kz

Sdl)tg(2dxdy)C( Hzn

Szk

z~z )z(fz~Cv kkkz

kzz~

)z(fk

00 v)l(f

kz


8

Experimental verification

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For model verification the experimental data obtained in expertises on study of a tension at rolling in smooth rolls, obtained earlier by professor Tarnovskiy I.J. utilized.

Н0 , W0 - initial height and width of a strip;WF - averaged finite width of a strip.


9

Experimental verification

0,00

50,00

100,00

150,00

200,00

250,00

300,00

350,00

400,00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Experim enta l

C alculate

Reduction Roughing tra in

I betw eening tra in II betw eening tra in

Finish ing tra in

38

70

R1 5

10R15

R126 28

78

6R60

47,334

44,8

4

58

17,8 5

R54,2

4

27

30R16,7

40,3

24,5

144 14’

3,42,3

17,8

23,6

24,5

R34

32

9,0

3,3 2,2

R8,7

16,215

14 5’

2,6

22,2

9,6

1,8

10,6

14,5

13,6

21,5

2,46,0

R26

11,0

11,9

4,5

1,6

12,5

7,0

1,7

6,9

6,9

2,0

5,0

17

R18

2

8,4

8,5

R4,2

Calibration of ro lls of continuous ro lling m ill 260 factory "K rasniy O ctiabr"

M atching of the experim ental and ca lculated size of tem plates

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10

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A comparison of the considered model with a three-dimensional pass rolling version of J.J.Park and S.I.Oh accomplished in the SHPROL program based on the finite-elements method was carried out.

SHPROL

▲ Distribution of strain intensities on the surface of a rolled square section strip into oval at a stable mode.

◄ Diagrams of normal stresses at a focal point of strain when rolling a square section strip into oval..

SPLEN

Compare 3D and 2.5D simulators


11

An experimental test of the calculation results showed a high enough accuracy of forecasts for

passes fillability at a profile rolling. The maximum error of the values characterizing geometrical

parameters of a strip at a focal point of strain output in laboratory and industrial conditions did

not exceed 6.4 per cent.

Axial section of rolls when rolling a strip of square section in oval pass:

- initial section of the strip; - section of the deformed strip.

System SPLEN allows:

- to model the rolling in groove;

- to analyze the groove for optimal the ultimate article

with respect to of process productivity filling the groove,

the friction, the drawing, influence of roller temperature.

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F I L L I N G O F T H E G R O O V E

P a r a me t e r s o f P r o c e s s

I n i t i a l D i me n s i o n F i n a l D i me n s i o n

SPLEN-RK

H = 12.10

B = 15 .37

S = 14 9.88

max

max

вх

R = 183.50 мм

= 12.40 1/сLg = 42.71 мм

= 13.46 град

D r a w I n g 1.55F i l l I n g 97%

H = 19.35

B = 7.59

S = 96.91

max

max

вых

Lg

R

Lg

Lg


12

When developing a new industrial calibration of rolls at the profiled rolling mill 320/250 ("Serp&Molot“ Works) for rolling strip steel of the 18x36 mm size of Steel 35, they decided to carry out a preliminary analysis based on imitating simulation using the SPLEN computing system.In conformity with the algorithm of numerical calibration test, of search and correction of the intermediate passes form, we accomplished a sequential change of initial calibration and solved problems of imitating simulation.

Technological diagram of check and change of calibration

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C rea tin g ca lib ra tio n b y a ca lib ra to r

S e t o f th e p ass fo rm

S e t o f th e ex p ec ted fo rm fo r a s trip sec tio n ad v an ced to th e ro lls ,an d o f co n d itio n s (m o d e) o f th e ro llin g

C a lcu la tio n u sin g S P L E N

If th e fo rm o f a m an u fac tu red s tripco rre sp o n d s to th e req u ired o n e ?

C h ecko f req u ired co n d itio n s ?

W h e th e rth e p ass is th e f irs t o n e in a ca lib ra tio n ?

A d ju stm en t o f sp eed s. C h an g e o f ro llsro ta tio n sp eed w ith d u e reg a rd fo rth e ra tio o f th e a reas rece iv ed u s in gca lcu la tio n s (d raw in g co e ffic ien ts)

S eq u en tia l ca lcu la tio n s o n a llca lib ra tio n fro m th e s ta rt till th e en d

G o o d co n fo rm ityo f th e fin a l sec tio n o f a ro lled p ro d u c t b y th e fo rm ?

И зм ен ен и е тем п ер ату р н о - ско р о стн ы х у сл о в и й

R eco m m en d a tio n s o n test o r in d u str ia l im p lem en ta tio n o f th e ca lib ra tio n

C h an g e o f th e fo rm o f a s tripsec tio n ad v an ced to th e in p u to r ad ju stm en t o f th e p rev io u s s tan d

И зм ен ен и е ф о рм ы с еч ен и яп од аваем о й н а в ход п ол о сы и л ин аст р о й к и п р ед ы д у щ ей к л ети

R etu rn to a fin ish in g s tan d an dv aria tio n o f e lem en ts o f p assesin o rd e r to in c rease (d ecrease ) th e a rea o f an in itia l s trip

R ev is io n o f n u m b er an d seq u en ce o f p asses

At t

he c

alib

rato

r

dis

cret

ion

Is it p o ss ib le to se lec t a su itab lefo rm an d size o f th e sh ee t fro m av a ilab le o n es?

“ D irec t m o v e”

y es

n o

y es

y es

n o

y es

n o

n o

n o

y es

W h e th e rth e p ass is th e f irs t o n e in a ca lib ra tio n ?


13

Changes made Calculated section of a strip

Parameters form changing

Initial calibration

Hmax/2= 9.00 Bmax/2=18.57 S1/4= 162.7

elongation ratio 1.23 fillability 99.1 %

Reduction of a pass width by the bottom

Hmax/2= 9.00 Bmax/2= 18.07 S1/4= 159.2


The general width of a pass is reduced

Hmax/2= 9.00 Bmax/2= 17.71 S1/4= 156.9


0.0. 2. 4. 6. 8. 10. 12. 14. 16. 18.0.0.

2.

4.

6.

8.

0.0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.0.0.

1.

2.

3.

4.

5.

6.

7.

8.

9.

0.0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.0.0.

1.

2.

3.

4.

5.

6.

7.

8.

9.

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Change of a leader pass to product the most qualitative profile


14

Changes made Calculated section of a strip

Parameters form changing

The groove is deepened

Hmax/2= 9.00 Bmax/2=17.16 S1/4= 152.2


The clearance is increased, the width is reduced

Hmax/2= 9.00 Bmax/2= 17.69 S1/4= 157.8


The height of a final strip is reduced down to 17.5 mm

Hmax/2= 8.75 Bmax/2= 17.93 S1/4= 155.5


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0.0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.0.0.

1.

2.

3.

4.

5.

6.

7.

8.

9.

0.0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.0.0.

1.

2.

3.

4.

5.

6.

7.

8.

9.

0.0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.0.0.

1.

2.

3.

4.

5.

6.

7.

8.

Change of a leader pass to product the most qualitative profile


15

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Physical simulation as result the mathematical simulation

According to the changed calibration, a rolling was carried out, as a result of which a strip

satisfying all preset requirements was manufactured. The deviation of the calculated results

from the contour of a real template at the same mill adjustment did not exceed 1.5 per cent.

The templates of a finish strip manufactured when rolling according

to an initial (a) and changed (b)

calibrations, and also according to a new

calibration when rolling strips with cross sections

of 18 x 36 (c), 20 x 32 (d) and 16 x 36 mm

(e)

a) b) c) d) e)


16

A trial test of the SPLEN

system during real calibrations

of the profile mills 500,

300-2, 250-1 and the wire

mill 250-2 is accomplished

in the Calibration Bureau

of the Magnitogorsky

Metallurgical Works.

Specialists of the Works

made the conclusion that

the received results had

a high degree of reliability,

and graphic possibilities

of the calculation results presentation are convenient to operate with.

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17

Resume

The mathematical model and algorithms define a

simulation of steadied calibrating process is

designed.

On the basis of the above-stated method of application the operations on

creation of a service system of simulation and optimization of manufacturing

processes of rolling calibrating process are carried on.

The response rate of designed systems on the degrees exceeds response rate of existing algorithms of spatial simulation calibrating process that is the important advantage at problem solving of optimization.

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18

• National Institute of Aviation Technology (NIAT), Moscow, Russia• Research Institute of Metallurgical Machinery (VNIIMetmash), Moscow, Russia• Moscow Institute of Heat Technic (MIT), Russia• Harkov's Plant of Malushev, Ukraine• Joint Stock Corporation "Technomash", Moscow, Russia• Miass's Design Department of Machinery, Russia• Zlatoust's Machinery plant of V.I.Lenin, Russia

AIRBUS INDUSTRYAerospatiale Societe Nationale Industrielle, FranceDaimler-Benz Aerospace Airbus GmbH, GermanyConstrucciones Aeronauticas S.A., SpainBritish Aerospace (Operations) Ltd., England

• Research and Industrial Company "Igsteel", Igevsk, Russia• Research and Industrial Aviation Company, Kazan, Russia• Bearing plants (Vologda, Kursk, Volgskiy), Russia• REINZ Dichtungs GmbH, Germany• Rolling plant “Serp&Molot”, Moscow, Russia• Magnitogorsky Metallurgical Works, Russia

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We employ the positive scientific results which came aboutdue to our extensive cooperation with:


Application of the Finite-Element Analysis to the Pass Rolling Process

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