ELSEVIER Jourv, al of Materials Processing Technology 69 (1997) 273-276

Jcutm~ c[

Matc als Frocess g Technology

The extremum parameters in ring rolling

Hua Lin *, Zhao Zhong Zhi Department of Mechanical Engineering, Wuhan Institute of Technology, No. 75 Luoshi Road. Wuhan 430070, People'~ Republic o./ China

Received 18 November 1995

Abstract

A mechanical model for ring rolling is established, the extremum parameters in ring rolling being derived based on the model, and predicted results compared with experimental results. ~ 1997 Published by Elsevier Science S.A.

Keywords: Ring rolling; Extremum rolling parameters

1. Introduction

Ring rolling, shown as Fig. 1, is a special rolling process in which a ring work-piece is drawn into the gap between the driven roll and the pressure roll by the driven roll, and caused to expand in diameter and reduce in ihickness. Because of the feeding of the pressure roll, the workpiece is rolled repeatedly through the gap, one rotation following another, with its thickness reducing gradually, similar to multi-pass rolling. Moreover, there is only one driven roll in ring rolling, the pressure roll being freely mounted and undriven. Research into ring rolling theory started in the 1960s [1], the research work being mainly on the rolling force and power. Research into ring-rolling conditions is much more scarce, this situation not matching the technological development of ring rolling. Because fast and slow feeding of the pressure roll in ring rolling may cause the ring workpiece to stop rotating and stop expanding, respectively, these situations represent two extremum conditions. In this paper these two extremum conditions are analyzed and the extremum parameters corresponding to the extremum conditions are derived.

* Corresponding author.

2. Mechanical model of ring rolling and the extremum draft

2.1. Mechanical model of ring rolling

Compared to the rolling force, the force of the guide roll acting on the ring workpiece is much smaller, so that it can be neglected. In the deforma- tion zone, there are the normal force P~ and the fric- tion force T~ acting on the outer surface of the ring workpiece by the driven roll, there being only the normal force P2 acting on the inner surface of the ring workpiece by the pressure roll, the latter being freely mounted. Assuming that the point of action of each force is situated at the central point of the corre- sponding contact arc between the roll and the work

Fig. 1. Ring rolling diagram.

driven roll J J

j ring

~ g u i d e rull

pressure rull

0924-0136/97/$17.00 © 1997 Published by Elsevier Science S.A. All rights reserved.

PII S0924-0136(97)00029-0

pi~e, then the mechanical model for ring rolling as shown in Fig. 2 is obtained. The ring workpiece is drawn into the gap and deformed continuously by the driven roll forces P~ and T~ and the pressure roll force /2. Assuming that Ho and H are the ring workpiece thickness at the entry and the exit of the deformation zone respectively, then the thickness reduction, i.e. the draft in one rotation, is Ah = Ho-H. If the elastic defor- mation of the mill and the rolls is neglected, then the draft is equal to the feed of the pressure roll in one rotation.

2.2, The minimum draft

o

The plastic deformation zone of the ring workpiece in rolling is related directly to the draft Ah, see Fig. 2. If the draft Ah is too small, then the plastic zones that are located in the outer and inner surfaces of the workpiece can not penetrate through the whole thick- ness. As a result, there is a rigid zone located in the central part of the thickness and the ring workpiece can not expand in diameter. In order to cause the ri:',g workpiece to expand in rolling, the draft Ah must exceed the minimum draft Ahmin needed to penetrate through the whole thickness. From Ref. [2], ring rolling as shown in Fig. 2 is similar to indentation by opposed flat indentors, so that its penetrating condition [3] based on slip-line theory is as follows:

L 1 ~mm = 8.74 (1)

where L is the length of the contract arc of the defor- mation zone and Hm is the average thickness of the workpiece in the deformation zone (see Fig. 2), i.e. Hm=(H0 + H)/2 ~ H. From [4], the length L of the contact arc is as follows:

2Ah L = l l 1 l (2)

where R, and R2 are the radii of the driven roll and the pressure roll respectively, and R and r are the radii of the outer and inner surfaces of the ring workpiece. Substituting Eq. (2) and H m - H = R - r into Eq. (1) and re-arranging, the minimum draft Ahmi, is obtained, as follows:

Ah > Ahmi n = 6.55

x 1O-3R, ( ~ RI RI RI ) Y(I+ + R , / \ R

(3)

2.3. Tile maximum draft

In ring rolling, the workpiece must be drawn into the

274 H. Lin, Z, Zhong Zhi /Journal of Materials Process#zg Technology 69 (1997) 273-276

Fig. 2. Mechanical model of ring rolling.

gap continuously, so that the drawing force must be greater than the pushing force, i.e. Y~ F, > 0 (see Fig. 2) in the drawing direction. However, there is force equi- librium in the feeding direction, i.e. ~ F,, > 0, therefore:

F, = Th + Pl:~ + P2..

51 51 51 = T, cos -~-- Pi sin -~-- Pz sin ~ > 0

5j 0~ ! Fj. = T,y + Pt, + P2y = - Tt sin ~ - P~ cos

51 - P2 cos ~ = 0

where 51 and 52 are the contact angles of the driven and the pressure roll, respectively. Assuming that the Cou- lomb friction condition is satisfied at the contact sur- face between the driven roll and the ring workpiece and taking/t as the friction coefficient, then T ! - - l t P j . Sub- stituting Tj =/tP~ into the above expressions above and re-arranging:

51 + 52 (4) 2

where fl is the friction angle and fl = tg-~/ t . Eq. (4) represents the biting-in condition in ring

rolling. Because the friction coefficient/L or the friction angle fl is finite, the contact angles ~ and 5 2 corre- sponding to draft Ah are finite also. If draft Ah in- creases to exceed the maximum draft Ahm,x corresponding to the extremum biting-in condition, then the ring workpiece will not be drawn into the gap, so the draft Ah can not exceed the maximum draft Ahm..,x. From the geometrical relationships of Fig. 2,

L L 5, g-S' 5,

H. LOt, Z. Zhong Zhi / Journal of Materials Pr,,cessing Tecknoh,gy 69 (I997) 273-276 275

Table 1 Experimental and theoretical feeding speeds in ring rolling

No. R {mm) H (mm) s (r rain- ~) r (mm s - ' ) %,,,-, (ram s ') r~,, {ram s ')

1 49.2 9.5 160 0.88 O. 13 2.98 2 55.6 15.9 30 0.24 0.06 0.49 3 61.9 15.9 30 0.24 0.05 0.45 4 61.9 22.2 160 1.22 0.55 2.36 5 63.5 25.4 30 0.20 0.13 0.43 6 69.8 31.8 30 0.38 0.19 0.39

Substituting these values and Eq. (2) into Eq. (4) and re-arranging, the maximum draft Ahm~,x is obtained:

2f12R~ ( R ~ R ~ R ~ ) (5) A h < A h m , ~ = ( l + R , / R 2 ) 2 1 + ~ - ~ 2 + ~ - - ,--T

3. Extremum feeding speed

Assuming that the feeding speed is v, and the rolling time for one rotation is At, then the feed in one rotation pass, i.e. the draft is:

Ah = v At (6)

If the slip between the driven roll and the ring workpiece is neglected [3], then the circumference of the outer surface of the ring workpiece in one rotation is equal to the perimeter of the driven roll, i.e.

1 R 2nR = 2rmR~At, At = - ~ (7)

nR~

where n is the rotational speed. Substituting Eq. (7) into Eq. (6):

v R A h = - ~ ( 8 )

n R~

S u b s t i t u t i n g Ahmi n of Eq. (3) and Ahma x of Eq. (5) into Eq. (8), respectively, the minimum feeding speed /)rain and the maximum feeding speed/)max are obtained:

/)rain'-" 6 .55 X I 0 - 3 1 / " ~ " /~1 I ~ t - ' ~ 2 - [ - ' ~ ' - - T

( 9 )

2f12nR21 ( RI Ri R I ) (10) Vm,,~ -- R(I + RI/R2) 2 1 + ~ + R r

4. The extremum roll radius and ring thickness

4.1. The extremum roll radius

From Eqs. (3) and (5) it is known that the minimum and the maximum drafts are related to the size of the ring workpiece and the rolls and to the friction coeffi- cient, etc. If the size of the ring workpiece and the value

of the friction coefficient are given, then the extremum drafts are dependent on the size of the rolls. In ring rolling, the minimum draft needed to penetrate the whole thickness of the ring workpiece can not exceed the maximum draft determined by the biting-in condi- tion i.e. Ahm,~x ~ Ahmi n. Substitutirlg Eqs. (3) and (5) into this expression and re-arranging:

1 l 1 7 . 5 / s ~ < ~ (11)

R~ + R 2 R - r

The radii of rolls must satisfy Eq. (11) in ring rolling, so that re-arranging, the minimum radii of driven roll R~min and pressure roll R2m~, are obtained:

R2(R - r) Rl >__ Rlmin -- 17.5flR2 - (R - r)

(12)

R l ( R - r ) R 2 ~ R2min -- (13)

17.5flRi - (R - r)

The maximum radii of the driven roll and the pres- sure roll can be determined by the mill size and tile bore of the rough ring, respectively.

4.2. The exlremum ring thickness

If the roll size and friction coefficient are given, then the extremum drafts are dependent on the ring size. In order to maintaii~ stable rolling, the minimum draft can not exceed the maximum draft, i.e. Eq. (11) must be satisfied. Considering H = R - r and re-arranging Eq. (11), the maximum ring thickness Hm~x is obtained:

17.5fiR, (14) H < Hm~x - 1 + R~/R2

There is a minimum ring thickness in ring rolling, which is dependent on the rigid condition of the ring in rolling. This, ;ninimum ring thickness, Hmin, is to be calculated in another paper.

5. Experimental results

The extremum parameters in ring rolling are derived on the basis of the extremum drafts, and the extremum drafts are determined by the extremum feeding speeds,

276 H. Lin, Z. Zhong Zhi /Journal of Materials Processing Technology 69 (1997) 273-276

therefore the experimental ring-rolling experimental re- suits o f [ 2 ] are used to verify the extremum feeding s ~ s . From [2]: the driven roll radius R~ = 104.8 mm; the pressure roll radius R2 = 34.9 mm; and the ring is made of aluminium alloy HE30WP. From [5], the friction coefficient in the rolling of aluminium alloy at room temperature is/z = 0.1. The experimental feeding speeds and theoretical extremum feeding speeds are shown in Table t, from which table it is seen that the experimental feeding speeds lie between the minimum and the maximum feeding speeds.

6. Conclusions

The plastic penetrating and biting-in conditions for ring rolling have been researched. The minimum and the maximum drafts, the minimum and the maximum

feeding speeds, the minimum radii of the rolls and the maximum thickness of the ring have been derived. Theoretical extremum feeding speeds in ring rolling have been found to compare favourably with experi- mental feeding speeds.

References

[1] W. Johnson, G. Needham, Experiments on ring rolling, Int. J. Mech. Sci. 10 (1968) 95.

[2] J.B. Hawkyard, et ai., Analyses for roll force and torque in ring rolling with some supporting experiments, Int. J. Mech. Sci. 15 (ll) (1973) 873.

[3] Qiao Duan, Engineering plasticity for Metal Forming Process, Metallurgical Industry Press, Beijing, 1988.

[4] Forging Handbook, Machinery Industry Press, Beijing, 1975. [5] Dai Zhouyuan et al., Mechanical calculating theory for steel

rolling; Chinese Industry Press, Beijing, 1965.