A three-dimensional rigid±plastic FEM analysis of rotary forgingdeformation of a ring workpiece

Wang Guangchun*, Zhao Guoqun

Mold and Die Engineering Center, Shandong University of Technology, Jinan, Shandong 250061, China

Received 12 April 1998

Abstract

The deformation of a ring workpiece by the rotary forging process is analyzed using a three-dimensional rigid±plastic ®nite element

method. Velocity ®elds and stress±strain ®elds of the ring workpiece in the rotary forging deformation are obtained. The new metal ¯ow

demarcation model obtained in this paper is different from that ever provided before. The deformation mechanism of the rotary forging of

the ring workpiece is revealed thoroughly. # 1999 Elsevier Science S.A. All rights reserved.

Keywords: Ring workpiece; Rotary forging; Deformation analysis; FEM

1. Introduction

Rotary forging is a new rotaform process which deforms

only a small portion of a workpiece at a time using a conical

rocking die whose axis is tilted at an angle with respect to the

axis of the other die or the workpiece. To date, this technol-

ogy has been applied widely in practice, but many problems

involved in this technology have not yet been solved. The

majority of current researchers have not exploited the the-

oretical aspect. Most of their work still remains experimen-

tal due to the eccentric load of the process and the

complicated contact contour and shape between the conical

upper die and the workpiece. Especially for a ring work-

piece, there still exist many unsolvable problems in manu-

facturing. The related technical problems have to be solved

by the trial-and-error method. The ®nite element analysis

method has been proved a good method, which can obtain

more detailed information in analyzing metal working and

applied for almost types of metal forming processes. How-

ever, so far, from the present survey of the literature, this

method has hardly been used to analyze the rotary forging

process.

2. Fundamental principle of the rigid±plastic FEM

The rigid±plastic FEM solution equations usually satisfy:

the equilibrium equation; the geometrical equation; volume

constancy; the assumption of not considering volume force;

neglecting the elastic deformation of the material; and the

material con®rming to the Mises Yield criterion. Using the

penalty function method to handle the condition of volume

constancy, the energy function is expressed as follows:

� �Z� _�" dV � �

2

Z� _"V�2 dV ÿ

ZST

Fiui dS; (1)

where �� is the equivalent stress, _�" the equivalent strain rate,

� the penalty factor, _"V the volume strain rate, V the volume

of the deformating body, Fi the external force, ui the velocity

at the surface ST and ST is the area of the surface acted upon

by the external force.

3. Finite-element model of the rotary forging processof a ring workpiece

In rotary forging, the relative motion between the work-

piece and the conical upper die is a spiral penetration. The

contact surface is a portion of an Archimedes spiral surface,

as shown in Fig. 1. The eight-node hexahedron isopara-*Corresponding author. Tel.: +86-0531-6041359; fax: +86-0531-2953-

623.

Journal of Materials Processing Technology 95 (1999) 112±115

0924-0136/99/$ ± see front matter # 1999 Elsevier Science S.A. All rights reserved.

PII: S 0 9 2 4 - 0 1 3 6 ( 9 9 ) 0 0 2 6 8 - X

metric element was used and the workpiece was divided into

900 elements and 1200 nodes, as shown in Fig. 2.

The contour and shape of the contact zone can be calcu-

lated according to the rotary forging parameters and the

geometrical dimensions of the workpiece. The zone sur-

rounded by points A, B, C and D can be adjusted according

to the actual situation under analysis. All nodes at the bottom

surface of the workpiece are ®xed in both the axial and

tangential directions. The velocity boundary condition of the

contact surface is exerted automatically by the normal

direction cosine of the contact surface according to the

rotary forging parameters. The frictional model proposed

by Chen and Kobayashi is used here [1]. The other deforma-

tion conditions are: rocking angle �38; feed S�1.34 mm/

rev; friction factor m�0.2; outside diameter of the work-

piece D0�70 mm; inside diameter of the workpiece

d0�40 mm; height of the workpiece H0�40 mm.

4. Metal flow patterns of a ring workpiece in rotaryforging

On the basis of the principle of rigid±plastic FEM and

according to the established mechanical model, a set of

three-dimensional FEM programs was developed and used

to analyze the rotary forging deformation of the ring work-

piece [2,3]. Fig. 3 shows the metal ¯ow ®elds of the axial

section and the cross section, respectively. The metal in the

contact layer ¯ows mainly along the radial direction. Fig. 4

gives a new metal ¯ow demarcation pattern in the contact

surface layer obtained by FEM analysis results. The metal

near to the exit ¯ows along the same tangential direction as

that of the rotation of the upper die whilst the metal at the

entrance ¯ows along the reverse direction of the rotation the

upper die. R� indicates that the metal ¯ows outside along the

radial direction, and Rÿ inside along the radial direction. T�

indicates that the metal ¯ows along the tangential direction,

which is the same as that of rotation of the upper die. Tÿ is

the reverse direction of rotation of the upper die. From

Fig. 3(b), it can be seen clearly that the metal at the contact

surface layer ¯ows both inside and outside along the radial

direction when it is compressed in the axial direction. The

metal ¯ow demarcation line locates near the inside wall of

the ring workpiece.

The metal ¯ow laws at the contact surface layer of a ring

workpiece can be stated as follows. The metal is compressed

in the axial direction and ¯ows mainly along the radial and

tangential directions. Along the radial direction the metal

¯ows from the demarcation line to either the inside or the

outside. The demarcation line is near to the interior of the

inside wall of the ring workpiece because the resistance to

metal ¯ows to the inside is greater than that to the outside. At

the same time, the metal located at the entrance and the

exit ¯ows to the center of the contact zone along the

tangential direction due to the strong restraint by the non-

contact zone.

Fig. 1. Geometrical description of the shape of a ring workpiece in rotary

forging.

Fig. 2. Discretization meshes of a ring workpiece in rotary forging.

Fig. 3. Velocity fields of a ring workpiece at the contact layer in rotary

forging: (a) cross section; (b) axial section.

Fig. 4. New metal flow demarcation pattern in the contact surface layer in

the rotary forging of a ring workpiece.

W. Guangchun, Z. Guoqun / Journal of Materials Processing Technology 95 (1999) 112±115 113

5. Deformation mechanism of the ring workpiece inrotary forging

From the whole process of the deformation, rotary forging

process of the ring workpiece is somewhat similar to upset-

ting, but is rather different from the upsetting because both

the forging load and the geometric shape of the contact zone

are non-symmetrical. From the view of loading conditions, it

is also similar to the rolling process, but there is also quite a

difference from the rolling process because of the differ-

ences of the load and boundary conditions, the load situation

and boundary conditions of the rotary forging process all

being very complicated. Fig. 5 shows the strain rate dis-

tributions of the ring workpiece in the rotary forging, whilst

Fig. 6 shows the stress distributions of the ring workpiece.

From Fig. 5, it can be seen that the workpiece is compressed

Fig. 5. Strain-rate distributions in the surface of the ring workpiece in rotary forging: (a) _"r ; (b) _"�; (c) _"z; (d) _�".

Fig. 6. Stress distributions in the surface of the ring workpiece in the rotary forging: (a) �r (MPa); (b) �� (MPa); �z (MPa); ���MPa�.

114 W. Guangchun, Z. Guoqun / Journal of Materials Processing Technology 95 (1999) 112±115

in the axial direction and elongated along the radial direc-

tion. The deformation zone expands to a certain extent at the

contact surface layer and shrinks gradually downwards

along the height. The shape of the deformation zone is like

that of a funnel. From Fig. 6, it can be seen that the contact

deformation zone suffers three-dimensional negative stress,

where the absolute values of the axial stress and the equiva-

lent stress decrease gradually with height. From the above

analysis, the following deformation mechanism of the rotary

forging process of the ring workpiece is obtained.

(1) Because the workpiece is loaded partly and eccen-

trically by the conical upper die along the axial direction, the

metal at the local contact layer yields ®rstly and then

deforms.

(2) The absolute value of the axial stress becomes smaller

as the area of the loaded zone becomes larger downwards.

The deformation zone concentrates mainly on the upper part

of the ring workpiece and the area of the deformation zone

decreases gradually along the axial direction and shows a

funnel shape.

(3) At the contact surface layer, the metal is compressed in

the axial direction and shows strong tensile deformation in

the radial direction because of the strong tangential restraint

by the non-contact zone. This results in the inside diameter

shrinking and the outside diameter increasing.

(4) That the contact surface is loaded partly by the conical

upper die results in the strong tangential deformation along

the same direction as the rotation of the upper die. With the

ring workpiece being loaded intermittently and formed

successively, the deformation is accumulated gradually until

the required ring shape is accomplished ®nally.

6. Conclusions

(1) The mechanical model of the rotary forging process of

a ring workpiece with three-dimensional rigid±plastic ®nite

element method presented in this paper is in accordance with

the actual deformation conditions.

(2) The deformation in the rotary forging of a ring

workpiece results mainly from the yielding of the metal

at the local layer zone. Because the ring workpiece is loaded

locally and eccentrically by the conical upper die in rotary

forging, the metal at the local contact surface layer zone

yields and deforms ®rstly. The metal here is compressed in

the axial direction and elongated along the radial and

tangential directions. The absolute value of the axial stress

decreases gradually downwards and the deformed zone is

concentrated mainly on a small portion of the upper part of

the ring workpiece.

(3) Due to the restraint of the non-contact zone along the

tangential direction, the metal at the contact surface layer

¯ows mainly from the middle deformation zone to either

inside or outside along the radial direction. The demarcation

line is near to the interior of the inside wall of the ring

workpiece. Along the tangential direction, the metal at the

contact surface layer ¯ows from the entrance and exit to the

center because of the strong restraint from the non-contact

zone.

(4) That the contact surface is loaded partly by the conical

upper die results in the strong tangential deformation along

the same direction as of the rotation of the upper die.

Acknowledgements

This research work has been supported by the Shandong

Province Outstanding Young Scientists Grant 97235510

and the Shandong Province Nature Science Fund

Y98F08089.

References

[1] C.C. Chen, S. Kobayashi, Rigid plastic finite element analysis of ring

compression, Application of numerical methods to forming process,

ASME AMD 28 (1978) 107.

[2] G. Wang, A 3D rigid±plastic FEM analysis of rotary forging

deformation of ring workpieces, Ph.D. Dissertation, HIT, April

1996.

[3] G. Wang et al., Methods of dealing with some problems in analyzing

rotary forging with the FEM and initial application to a ring

workpiece, J. Mat. Proc. Tech. 71 (1997) 299±304.

W. Guangchun, Z. Guoqun / Journal of Materials Processing Technology 95 (1999) 112±115 115