Journal of Materials Processing Technology 113 (2001) 141±147

The forming characteristics of radial±backward extrusion

Ho-Joon Choi*, Jin-Hwa Choi, Beong-Bok Hwang
Department of Industrial Automation Engineering, Inha University, 253 Yonghyundong, Nam-ku, Inchon 402-751, South Korea

Abstract

The rigid±plastic ®nite element method is employed for the quantitative analysis of the radial extrusion process combined with backward
extrusion. Various variables such as gap size, die corner radius and frictional conditions are adopted as design or process parameters for analysis.
The emphasis is focused on the analysis of metal ¯ow into a can and ¯ange. Due to various die geometry and process conditions, the metal ¯ow
into a can and ¯ange shows different patterns and its characteristics are well summarized quantitatively in this paper. Experimental data are com-
pared with the simulation results in terms of forming load and the volume ratio of ¯ange to can to verify the usefulness of simulation work. The
comparison between experiment and simulation gives good agreement. Extensive simulation work leads to the quantitative relationships between
the process conditions, volume ratio of the ¯ange to can, and the size of the ¯ange or can. As expected, the volume ratio of the ¯ange to can
increases as the gap size and/or die corner radius increase. However, it is found that the friction condition has little in¯uence on the forming load
and the deformation pattern. Under a certain condition of die geometry, can size turns out to be smaller than that of the initial billet. The work pre-
sented in this paper could be a good reference for process design in radial±backward extrusion. # 2001 Elsevier Science B.V. All rights reserved.

Keywords: Radial extrusion; Backward extrusion; Design parameters; Metal ¯ow

1. Introduction geometry such as die corner radius, gap size, etc. Radial±
backward extrusion is commonly applied as a manufactur-
The basic or primary operations of cold extrusion are ing process as well as a process in the metallurgical industry.
upsetting, forward extrusion, backward extrusion, and radial It provides economical advantages such as high productivity,
extrusion. It is commonly accepted practice to classify the retrenchment of manpower, and strength improvement of
extrusion operation according to the direction relationships the product [3±5].
between the material ¯ow and the punch movement. More- However, it is noted that backward can extrusion of steel
over, some quali®ers based on the shape of the parts to be is one of the most critical cold forging operations due to the
produced are also added. Thus, basic extrusion operations very high normal pressure on the punch and the extremely
can be usually called backward-can-extrusion, forward- severe tribological conditions at the contact between the
tube-extrusion, forward-rod-extrusion, etc. [1]. punch land and the inner can wall. Thus recommendations
There are combined simultaneous extrusion processes in for tool design in order to perform successful backward can
which a billet is extruded simultaneously in the forward, extrusion have been proposed [6].
backward and/or lateral directions through plural ori®ces in The present paper investigates the effects of die geometry
the tool assembly. Some basic operations are sometimes and process condition such as friction on the material ¯ow.
combined at a single station to reduce the number of stations The deformation patterns are summarized in terms of punch
required for forming relatively complex shaped parts. load, volume ratio of ¯ange to can and workpiece height
Furthermore, the combined processes offer the potentiality during the forging process. So, the aim of this paper is to
of producing a variety of precise components and the analyze quantitatively the forming characteristics of radial±
versatility of the cold forging process [1,2]. backward extrusion.
Radial±backward extrusion is a forging process in which
one or two punches move axially causing radial ¯ow into a
die cavity and backward ¯ow between the punch and die by 2. Analysis of radial±backward extrusion
means of which a ¯ange and can are formed. It is possible to
restrict the metal ¯ow into the ¯ange and/or can by die 2.1. FEM analysis

*
Corresponding author. Tel.: ‡82-32-860-7387; fax: ‡82-32-867-7741. Several methods can be applied to the ®nite-element
E-mail address: g20013722@inhavision.inha.ac.kr (H.-J. Choi). analysis of metal forming processes, such as the elastic±

0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 7 0 3 - 8
142 H.-J. Choi et al. / Journal of Materials Processing Technology 113 (2001) 141±147

Fig. 1. Left: the initial billet; right: the formed part.

plastic method [7±9] and the rigid±plastic method [10,11].

In the present study, extrusion is the main process and the
elastic deformation is negligible comparing to the plastic
deformation. Thus the rigid±plastic model in the ®nite Fig. 2. Die geometry of radial±backward extrusion (d0: billet diameter; dB:
element method is employed for ef®ciency of simulation. ¯ange diameter; dst: punch diameter; h0: billet height; h1: workpiece
The material used for the simulation is AISI 1006 steel. height; hst: punch stroke; s: gap height; r1 ˆ r2 : die radius).
Usually, the ¯ow stress is in¯uenced signi®cantly by the
strain-rate in a hot forging operation, but in cold forging the
¯ow stress depends mainly on the strain. Thus the work-
hardening characteristics can be expressed by [12] (s), die corner radii (r) and friction factors (m). The other
0:31 2 parameters such as initial billet diameter (d0), punch dia-
 ˆ 62:9e
s kgf=mm (1)
meter (dst), billet height (h0) and punch stroke (hst) are used
Phosphate-soap is employed as a lubricant between the with constant values. The relative deformation (hst/d0)
workpiece and the die for the process. Therefore, the friction represents the volume of material extruded into the can
factor m at the die±workpiece interface in the simulation is and ¯ange.
assumed to be 0.05±0.15 [13]. The design parameters used for the analysis of the form-
ing characteristics are summarized in Table 1. As seen in the
2.2. The process parameters table, friction factor (m) is added for the analysis of the
in¯uence of the frictional conditions on the material ¯ow.
The left and right sides of Fig. 1 show the initial billet and Pre-simulation is conducted to see how closely the simula-
the formed shape, respectively. The geometry investigated tion could match with experiment. In the pre-simulation,
has a punch diameter of 24 mm, a billet height of 50 mm, a experimental data and simulation results for load capacity
billet diameter of 32 mm, and a maximum punch stroke of and volume ratio are compared to each other.
20 mm per side. Also, extensive simulations are carried out by varying the
Fig. 2 illustrates the initial and ®nal die position and die corner radius r ˆ r1 ˆ r2 †, the gap height (s) and the
geometrical parameters utilized in the process. Gap height friction factor (m). A total of 36 extensive simulations was
(s), die corner radius r ˆ r1 ˆ r2 † and friction factor (m) preformed for different values of r, s and m. The value of the
are considered as the major process parameters for the relative deformation (hst/d0) is constant in each case because
analysis. To investigate the deformation patterns and char- the material volume extruded is constant.
acteristics of material ¯ow into the can and ¯ange, the FEM The ¯ange volume (VB) and the can volume (VN) are
simulation was performed for selecting different gap heights de®ned in Fig. 3. The reference line ab† from the center of

Table 1
Design parameters used in the process analysis

Process parameter Pre-simulation Extensive simulation

Load capacity Volume ratio

Initial billet height (h0, mm) 50.0 50.0 50.0

Initial billet diameter (d0, mm) 32.0 32.0 32.0
Punch stroke (hst, mm) 40.0 20.0 20.0
Relative deformation (hst/d0, %) 125 62.5 62.5
Die corner radius (r, mm) 5.0 1.0, 5.0 1.0, 3.0, 5.0
Gap height (s, mm) 8.0 4.0, 8.0, 12.0, 24.0 4.0, 8.0, 12.0, 24.0
Friction factor (m) 0.05 0.05 0.05, 0.1, 0.15
 H.-J. Choi et al. / Journal of Materials Processing Technology 113 (2001) 141±147 143

Fig. 4. Comparison of the load±stroke relationship.

Fig. 3. Method for the determination of VB and VN.

is expected, the simulation loads are quite consistent with

the experimental loads, the greatest difference between them
the punch nose to the inner wall of the die along the face being less than about 10%. The punch load is almost
angle of the punch nose is drawn to calculate the can volume constant in the middle of the operation. However, when
(VN). For the ¯ange volume (VB), the reference line bc† is part of the can is ®lled up completely, the forming load
drawn from the inner side of the die to the centerline along sharply increases. According to Ref. [14], the load required
the extension line perpendicular to the horizontal center for this radial extrusion combined with simultaneous back-
line. The volume ratio, VB/VN, is employed for the analysis ward can extrusion becomes lower than that of the radial
of the effect of gap height (s) and die corner radius on extrusion combined with subsequent backward can extru-
material ¯ow. This ratio represents the relative material sion. The material ¯ow into the annular gap between the
¯ow into the ¯ange compared with that into the can. Thus punch and die provides a relief so that the material ¯ow
if the ratio is high, it is assumed that the material ¯ow into is in the path of least resistance, thus lowering the punch
the ¯ange is relatively favorable compared with that into the loads.
can. The comparison of the gap height±volume ratio is pre-
sented in Fig. 5. Also, this ®gure illustrates the effect of the
die corner radius (r) and gap height (s) on the material ¯ow.
3. Results As is de®ned, VB is the ®nal volume of the material in the
¯ange, and VN the ®nal volume of the can. The volume ratio,
The results of the FEM simulation are given and discussed VB/VN, is investigated at the punch stroke of hst ˆ 20 mm
in terms of the punch load and the volume ratio of the with different gap height for s ˆ 4, 8, 12 and 24 mm and die
¯ange to the can and the change of workpiece height in corner radii, r ˆ 1 and 5 mm, as seen in Table 1.
this section. Furthermore, the in¯uence of the major para- As can be seen in the ®gure, there is only a sight difference
meters as stated above on the deformation pattern and between experimental data and simulation results. The graph
characteristics of material ¯ow are considered. Firstly, the
validation of simulation results is investigated, and then
the forming characteristics are analyzed in extensive
simulations.

3.1. The comparison with experiment

To verify good agreement between experimental data [14]

and simulation results, the load±stroke relationship is inves-
tigated between them. Under the same process conditions as
those of experiment such as punch stroke hst ˆ 40 mm,
friction factor m ˆ 0:05, gap height s ˆ 8 mm and die corner
radius r ˆ 5 mm, simulation is preformed for AISI 1006
steel.
Fig. 4 shows a comparison of the load±stroke relationship
between the experimental data and the simulation results. As Fig. 5. Comparison of the gap height±volume ratio relationship.
144 H.-J. Choi et al. / Journal of Materials Processing Technology 113 (2001) 141±147

Table 2
Results in extensive simulation for friction factor m ˆ 0:1 at punch stroke,
hst ˆ 20 mm

r (mm) s (mm) Load (kN) h1 (mm)

1.0 12 596.96 50.34

24 445.70 44.76
3.0 12 572.04 48.25
24 425.68 43.83
5.0 12 548.11 46.23
24 405.97 43.10

shows that a larger gap height and die radius help the
material to ¯ow easily into the ¯ange. Thus, it is obvious
from the ®gure that the gap height and die radius are
important parameters in¯uencing the material ¯ow.
Based on the previous comparison between analytical and
experimental results for punch load and volume ratio in
Figs. 4 and 5, respectively, it can be concluded that there is
good agreement between them. Therefore the FEM simula-
tion applied in this paper is valid.

3.2. Analysis of extensive simulation

Due to the various die geometry and process conditions,

different patterns and characteristics of material ¯ow are
expressed in terms of forming load, volume ratio and change
of workpiece height. Emphasis is focused on these in this
section. Extensive simulation is preformed at the punch
stroke of hst ˆ 20 mm with different values of the para-
meters, as can be seen in Table 1.

3.2.1. Load comparison

Fig. 6(a)±(c) shows the variation of punch load with punch
stroke for varying corner radius for r ˆ 1:0, 3.0 and 5.0 mm,
respectively. The maximum punch load is checked for each
operation. There are four patterns of forming load with
different gap heights, s ˆ 4, 8, 12 and 24 mm for each
die corner radius. Also, with constant gap height, the effect
of a friction factor (m) from 0.05, 0.1±0.15 is analyzed.
Some results are summarized in Table 2. Fig. 6. Effect of the die corner radius on the forming load.
As a result, forming load increases as the gap height
decreases. As can be seen in the table, the punch load
decreases by 25.3% when the gap height (s) increases
from 12 to 24 mm. This means a 100% increase of the 3.2.2. Analysis of volume ratio
gap height for friction factor m ˆ 0:1 and die corner The volume ratio of the ¯ange to the can for different
radius, r ˆ 1:0 mm. It is evident from the ®gure that the friction factors such as m ˆ 0:05, 0.1 and 0.15 is shown in
gap height has more in¯uence on the material ¯ow than Fig. 7(a)±(c), respectively. As can be seen in the ®gures, the
the die corner radius. The forming load increases as the effect of die corner radius and gap height on the material
friction factor increases when the gap height is small. ¯ow is represented. As de®ned, VB is the ®nal ¯ange volume
However, the friction factor has little effect on the forming and VN the ®nal can volume. It is also found from the ®gure
load as the die corner radius and/or the gap height increase. that the friction condition has little in¯uence on the volume
Therefore, the friction factor has only a slight effect on ratio.
the material ¯ow relative to that of the die corner radius The ratio increases as the die corner radius increases.
and gap height. Hence, provided that the die corner radius increases, the
 H.-J. Choi et al. / Journal of Materials Processing Technology 113 (2001) 141±147 145

Fig. 7. Effect of the gap height on the volume ratio for various values of
die corner radius and friction.

Fig. 8. Effect of friction factor. Fig. 9. Material ¯ow into the can.
146 H.-J. Choi et al. / Journal of Materials Processing Technology 113 (2001) 141±147

material ¯ow into the ¯ange becomes relatively more favor- has a substantial in¯uence on the material ¯ow, whilst
able than that into the can. As expected, the ratio increases as the friction factor has little.
gap height increases. As a result, a larger die corner radius 2. The forming load increases as the gap height decreases.
and gap height are more favorable for material ¯ow into the 3. The forming load decreases as the die corner radius
¯ange, compared with that into can. Furthermore, as stated increases because a larger die corner radius favors the
above, it is found that the gap height has more in¯uence on material ¯ow.
the volume ratio, i.e. on the relative material ¯ow into ¯ange, 4. The gap height has more in¯uence on the load or
than the die corner radius as seen in Fig. 7. material ¯ow than the die corner radius.
Fig. 8 shows in detail the effect of friction between the die 5. The friction factor has little in¯uence on the load as the
and the workpiece on the material ¯ow. The volume ratio die corner radius and/or gap height increases.
increases as the die corner radius and gap height increase. 6. The friction factor has little in¯uence on the volume
The can volume is larger than the ¯ange volume when the ratio.
gap height is small, i.e. the ratio has a value of less than 1. 7. The volume ratio increases as the die corner radius
However, a larger gap height favors the material ¯ow into increases: a larger die corner radius results in a more
the ¯ange as the gap height increases. As was stated earlier, favorable material ¯ow into the ¯ange.
the friction factor has only a slight in¯uence on the volume 8. The volume ratio increases as the gap height increases.
ratio or the material ¯ow, in spite of the increase in gap 9. The gap height has more in¯uence on the volume ratio
height. It is evident from the ®gure that the material ¯ow is or the relative material ¯ow into ¯ange than the die
affected very much by the gap height for constant the die corner radius.
corner radius. 10. The workpiece height decreases in most cases as the
gap height increases.
3.2.3. Material ¯ow into can 11. The height of formed part for some gap heights is
The punch stroke±workpiece height relationship is plotted smaller than that of the initial billet.
in Fig. 9 under the condition of constant friction factor,
The work presented in this paper could be a good refer-
m ˆ 0:1. Also, the results are summarized in Table 2. Fig. 9
ence for process design in radial±backward extrusion.
shows the change of workpiece height with different gap
heights for s ˆ 4, 8, 12 and 24 mm to represent the defor-
mation pattern into the can. As can be seen in the ®gure, the
Acknowledgements
height of some workpieces increases or decreases as the
stroke proceeds for varying die corner radius from r ˆ 1:0,
This work was supported by the development program for
3.0 to 5.0 mm. The workpiece height decreases as the
the exemplary schools in information and communication
gap height increases. Also, the workpiece height decreases
from the Ministry of Information and Communication
as the die corner radius increases. When the gap height is
(MIC) and an R.A. research grant from Inha University.
12 mm, the workpiece height remains constant during the
process (see Fig. 9(a)). This means that material ¯ow into
can rarely occurs. The case is the same when the gap height
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