PRODUCTION SECTION

PHOTOELASTIC INVESTIGATION OF STRESSES

A MODEL BILLET UNDER DIAGONAL ROLLING

CONDITIONS WITH CONSIDERATION OF THE

GUIDE TOOL

l~. S. U m a n s k i i a n d Y u . L . K a n t e r

OF

UDC 539.319

In the production of seamless tubes the main and most cr i t ical operation is the production of a hollow shell by piercing a heated solid billet in the helical rolling mill. The p rocess is based on forming an ex- pansion in the center and its surroundings which the mandrel helps to t ransform into a hole. In the case of diagonal roll ing of var ious s t ructural components the indicated phenomenon is undesirable, since it leads to reject ion of the par t s .

An analysis of known works [1-4] showed that the formation of the axial cavity in the billet during diagonal roil ing does not present ly have its own mechanical interpretat ion and consequently calculation. The s t r e s s - s t r a i n state of the workpiece has been evaluated quite approximately on a disk compressed by paral le l plates [3-5], i .e . , without consideration of three-dimensionali ty, c ross -sec t iona l form, and cha r - ac te r of the loads being applied.

A pai r of paral le l rol ls rotating toward the same side serves as the basis of the helical rolling mill. Idle rol ls or ro l le rs , s tat ionary guides, and driving disks can serve as the guide tool. Along with the rol ls they form the groove of the mill and are intended not only for res t r ic t ing and keeping the workpiece in a certain position relative to the roils, but also for confining the flow of metal tangentially [6].

Unlike the idle rol ls , the stat ionary guides produce a more closed groove, which promotes bet ter l imitation of the d iameter of the billet and more intense flow of the metal axially. They absorb cons ider - able p r e s s u r e f rom the workpiece, which will apparently be maximum in the middle of the seat of defor- mation during roll ing of various s t ructura l components: roi ls , forging blanks, etc. During piercing the p r e s s u r e of the billet on the guides is insignificant in the piercing cone and in the reeling cone can reach 0.4 of the roll p r e s s u r e [11. If we assume that the work rolls have a cylindrical form, then intense s l ip- ping of the metal with the rol ls and twisting of the billet in the seat of deformation are the resul ts of the effect of the workpiece on the guide tool.

The average reductions on the piercing cone are within 0.5-1.2% [3]. Therefore, it is quite impor- tant to investigate s t r e s se s of the billet both in an elastic and in an elastoplastic formulation. In the present investigation we attempted to study in a three-dimensional formulation the state of s t r e ss of the billet during diagonal and c ross rolling under conditions of small reductions.

The solution of the problem stated under dynamic conditions presents considerable difficulties. In selecting the design model we direct the radius of the rolls to infinity. Then in the f i rs t approximation the given p rocesses of metalworking by p ressu re can be likened to c ross forging of a cylinder with respec t to the generatr ix , when after each blow it is turned through a certain small angle ot 1.

With an increase of the number of reductions the c ross section of the workpiece approaches a round body, but of smal le r diameter . It is obvious that the round, turned, section differs maximally f rom the regular . Therefore , it is of interest to investigate a model under conditions of the second reduction

(Fig. I).

Institute of Strength of Materials, Academy of Sciences of the Ukrainian SSR, Kiev. Translated f rom Prob lemy Prochuost i , No. 7, pp. 74-78, July, 1974. Original ar t ic le submitted February 2, 1974.

�9 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part o f this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by an}, means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A cop), o f this article is available from the publisher/or $15.00.

859

p

F i g . 1. G e n e r a l s c h e m e of l oa d ing the m o d e l .

The s t a t e of s t r e s s of the body was e v a l u a t e d e x p e r i m e n t a l l y by the p h o t o e l a s t i c ( f rozen s t r e s s ) m e t h o d . In f o r m u l a t i n g the t h r e e - d i m e n s i o n a l p r o b l e m i t was a s s u m e d tha t the cond i t ions of hot d e f o r m a - t ion a r e r e a l i z e d , i . e . , s t r e n g t h e n i n g and weaken ing p r o c e s s e s a r e m u t u a l l y b a l a n c e d . Consequen t ly , s t r e s s e s o c c u r only as a r e s u l t of the e f fec t of the tool on the b i l l e t be ing w o r k e d .

The i m p a c t a c t i on of the p a r a l l e l p l a t e s was r e p l a c e d by s t a t i c r e d u c t i o n . On l oa d ing the m o d e l i t s

r o t a r y mo t ion was e l i m i n a t e d by s i m u l a t i n g the ac t i on of the s t a t i o n a r y gu ide s . The f i r s t r e d u c t i o n of the s p e c i m e n , a c c o r d i n g to the me thod in [7], was m o d e l e d by s awing off two d i a m e t r i c a l l y o p p o s i t e f i a t s u r - f a c e s .

The m o d e l s w e r e m a d e f r o m 50 m m c y l i n d r i c a l b l o c k s . T h e i r c o m p o s i t i o n was : 100 u n i t s of I~D-6 r e s i n and 30 un i t s of m a l e i c a n h y d r i d e . A f t e r p o u r i n g into c a r d b o a r d m o l d s they w e r e s u b j e c t e d to long (8 days ) hea t t r e a t m e n t to r e m o v e r e s i d u a l s t r e s s e s .

The f r e e z i n g t e m p e r a t u r e and o p t i c a l c o n s t a n t s w e r e d e t e r m i n e d on a 40 m m d i a m e t e r , 4 m m th ick , d i s k cut f r o m one of the b l o c k s . A f t e r th is the m o d e l s w e r e m a d e with a r a t i o H / b = 0.9 and l eng th l l = do, 1.5 d o , and 2.5 d o , w h e r e d o = 2b.

t.s

42

-z/~-t~-t~-t~4-02 0 02 t14 tt6 0$zeb a

g

o E U

A

Y~ b

yl

C ~---~---'cxl ; Iz D ~-'-~---~ D

e d

F ig . 2. D i s t r i b u t i o n of s t r e s s e s a long the z ax i s (a) and s e c t i o n A - A (b) fo r l = 0. D i a g r a m of cu t t ing the c y l i n d e r with a round , t u r n e d s e c t i o n into l ong i t ud ina l (e) and t r a n s v e r s e (d) s l i c e s .

860

iii I L

\ ~ 1,2

2

o

o,,#

I ,/ r/

/ / , "

1,6 ] L - ~ o I ' ' I I : I ~ a

,-. 1,2 : ' 1

E I E o ' ~ " E 0,8 ,

/L/I/ / \ - \ ~ !L

b b

Fig. 3 Fig. 4

I

Fig. 3. Distribution of s t r e s se s along the x axis (a) and section B-B (b) for l = 0 (the solid lines denote Cry/a 0 and the dashed ax/~0).

Fig. 4. Distribution of s t r e s se s along section C-C (a) and D-D (b) for l = 0 (the solid lines denote Cry/a0, the dashed Txy/Cr0, and the dot-dashed

ax/~y).

D

I

0,2 --" ~ * ' - - - = - J

0 -- - = -

-zlb -~6 -O,2 0 ~2 0,8 z l b

Fig. 5. Distr ibut ion of stresses along the z axis for l = 0.2 d o (the solid lines denote ay/a0, the dashed lines Txy/a0, and the dot- dashed lines az/g0).

The specimens were loaded in a specially made loading device (see Fig. I) consisting of a lower 1 and upper 2 plate "and guide props

3. The pressure of the billet 5 on the stationary guides was simulated by clamp 4. On the basis of the design characteristics of the station- ary guides of the diagonal rolling mill the length of the clamp was selected equal to 30 ram.

The models were held under a static load of 10 kg in a thermo-

stat at the freezing point Tf = 130~ After reducing it to room tem- perature at 3-5 deg/h the models were cut into longitudinal and trans- verse slices.

An insufficient number of bands was revealed on transilluminat-

ing the slices on the "MEOPTA" optical device. Therefore, the slices were investigated on the KSP-5 coordinate-synchronous polarimeter by the compensation method [8].

The principle of measur ing the path difference 5 i by the given method consists in that a path dif fer- ence equal in magnitude to the unknown but opposite in sign is added to the path difference created at the investigated point of the slice by a Krasnov compensator . The position of the principal axes of the s t r e s s tensor (pseudoisocliue ~) was determined f rom the dial of the compensator . The data obtained were used for solving the three-dimensional problems according to the method presented in [9].

Compress ion and twisting of the bil lets occur at the seat of deformation of the diagonal roll ing mill [10]. On the basis of the experimental data [11] and pre l iminary calculations it is concluded that twisting

861

I, d

I,o

O,2

t,75 / \

L25 z,',qo, ,..-.-., ~ / r,

O,75

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a

,-., 1,2

.o

E o

0,a

B ~

0,4

i t - ~ - , . .o~ r .

~.#o I" -x/~ -05-0~-0,4-02 0 02 t{4 0~ 0,8 x/b

b Fig . 6. Dis t r ibu t ion of s t r e s s e s along the x axis (b) and sect ion B-B (a) for l = 0.1 d o (the s o l i d l i n e s de - note ay/a o, the dashed l ines ax /a o, and the do t -dashed l ines "rxy/a 0 . _

of the workpiece , the c h a r a c t e r of which, gene ra l ly speaking, i s cons t ra ined , s c a r c e l y causes s t r e s s e s at points of the cen t r a l ax is . The re fo re , a s e r i e s of expe r imen t s were c a r r i e d out a l so in the absence of eccen t r i c i t y of the ex te rna l f o r c e s . The p r e s - su re of the c lamp on the model was se l ec t ed equal to 0.3-0.4 P on the b a s i s of the expe r imen ta l data [1]. Some r e s u l t s of the invest igat ion in the absence of eccen t r i c i t y of the ex te rna l fo rces a r e given in F igs . 2-4. We note that the values of the s t r e s s e s in the d i a g r a m s a re r e f e r r e d to the magnitude of the opt ical con- s lan t of the m a t e r i a l of the models (r 0 = 0.004 k g / m m 2. In Fig . 2 the sol id l ines denote ay/a0, the dashed l ines az/ao, and the dot - dashed l ines r y z / a 0.

An a n a l y s i s of the s ta te of s t r e s s showed that volume of the spec imens is ac ted on by c o m p r e s s i v e s t r e s s e s ay and az that a r e maximum along the cen t ra l ax is at point z = 0. In the core of the b i l l e t in the region of the ends there a r e ten- s i le s t r e s s e s ax, which in the zone of act ion of the guides a r e c o m p r e s s i v e . Along the z ax is the tangential s t r e s s e s a r e equal to ze ro .

F u r t h e r expe r imen t s were c a r r i e d out accord ing to the scheme shown in F ig . 1. The eccen t r i c i ty of the ex te rna l f o r ce s was se lec ted equal to 0.2 d 0. Some r e s u l t s of the inves t iga t ion a r e p r e sen t ed in F igs . 5 and 6. As we see , the d i a g r a m s of the d i s t r ibu t ion of no rma l s t r e s s e s a x, ay, and a z with r e s p e c t to the volume of the model have the c h a r a c t e r d e s c r i b e d above. In addit ion, tangent ia l s t r e s s e s rxy that a r e max imum along the z axis in the region of maximum cons t ra in t appea r .

C O N C L U S I O N S

1. The c h a r a c t e r of appl ica t ion of c o m p r e s s i v e fo rces to the workpiece f rom the working tool during diagonal ro l l ing c r ea t e s condit ions under which the p l a s t i c i t y of the b i l l e t me ta l i n c r e a s e s in the zone of act ion of the guides.

2. The r eac t ive p r e s s u r e of the s t a t iona ry guides on the b i l l e t during c r o s s ro i l ing causes twist ing of the workpiece , the c h a r a c t e r of which is cons t ra ined .

3. Three main p a r a m e t e r s of deformat ion of the b i l l e t act at the sea t of deformat ion of the diagonal and c r o s s ro l l ing mi l l : compre s s ion , cons t ra ined twist ing, and shear . Consequently, d i s in teg ra t ion of the me ta l occurs owing to the r epea ted a l t e rna t ing change of no rma l and tangential s t r e s s e s in the cen t r a l region of the b i l l e t during c r o s s ro i l ing caused by c o m p r e s s i o n and s h e a r of the workpiece . The tangent ia l s t r e s s e s causing p la s t i c shea r and fa i lu re by shear ing have a dec i s ive effect on the fo rmat ion and deve lop- ment of c r acks in the middle of the sea t of deformat ion . The format ion of an ax ia l cavi ty in the indicated zone dur ing diagonal ro i l ing wil l be a c c e l e r a t e d due to the accumula t ion of r e s i d u a l tens i le and s h e a r s t r a i n s in the cen te r .

4. With an i n c r e a s e of the length of the workpiece (ll > 1.5-2 do) the s t a r t of fa i lu re during c r o s s ro l I ing should be expected along the z ax is in the reg ion of the ends as a r e su l t of the effect of tangent ia l and tens i le s t r e s s e s .

L I T E R A T U R E C I T E D

1. R . M . Golubchik et a l . , Invest igat ion of the Tube Product ion P r o c e s s [in Russ ian] , Meta l lu rg iya , Moscow (1970).

2. Z. Z ibe l ' , Metalworking in a P l a s t i c s ta te [in Russ ian] , Meta l lu rg izda t , Moscow (1934). 3. V . S . Smirnov, Theory of Metalworking by P r e s s u r e [in Russ ian] , Meta t lurg iya , Moscow (1973). 4. I. Ya. Ta rnovsk i i e t at . , Theory of Metalworking by P r e s s u r e [in Russ ian] , Meta l lu rg izda t , Moscow

(1963). 5. K . N . Shevcheuko, "Plane e l a s top la s t i c deformat ion of a cy l inder loaded by a ba lanced s y s t e m of two

concent ra ted fo rces , " P r ik l . Matem. i Mekhau., 16, No. 1 (1952).

862

6. E . S . Bokotyan (editor), The Boiling Industry. Handbook [in Bussian], Voh-1, GNTIL po Chernoi i Tsvetnoi Metallurgii , Moscow (1962).

7. E . P . Unksov, Engineering Methods of CaIculating F o rce s in Metalworking by P r e s s u r e [in B u s - sian], GNTIML, Moscow (1955).

8. V . F . Trumbachev and G. A. Katkov, Measurement of ~ t resses and Strains by the Method of Photo- elast ic Coatings [in Bussian], Nauka, Moscow (1966).

9. D . V . Vainberg et ah, Use of Computers for Solving Elast ic Static Problems by the Photoetast ic Method [ia Russian], Tekhnika, Kiev (1971).

10. A . P . Chekmarev, Intensification of Helical Boiling [in Bussian], Metallurgiya, Moscow (1970). 11. P . K . Teter in , Theory of Helical Bolli~Ig [in Russian], Metallurgiya, Moscow (1969).

863