A method for the evaluation of lubrication using injection upsetting

Journal of

Materials Processing

ELSEVIER

Journal of Materials Processing Technology 53 (1995) 712 725

Technology

A method for the evaluation of lubrication using injection upsetting T. Nishimura*, T. Sato, Kyin Hoke, Y. Tada Department of Mechanical Engineering, The University of Tokushima, 2-1 Minamijosanfima-cho, Tokushima 770, Japan

Received 5 April 1994

Industrial Summary A simple test method based on injection upsetting is proposed to evaluate the frictional shear factor under near industrial forging conditions. The injection upsetting is combined with backward extrusion to enable the determination of the frictional shear factor without measuring the flow stress of the work material and/or the forging load. The relationship between the flange diameter after injection upsetting and the frictional shear factor is determined using the upper-bound method. When a parallel flange is used, necking or failure sometimes occurs at the rim, and so the forged flange does not extend to a circular shape. Thus a test with a sloped flange is suitable for industrial experiments to prevent undesirable irregular deformation. The surface extension ratio of the lower-flange surface increases with increase in the diameter of the flange. During the testing, however, the lubricated side surface of the billet flows mainly to the upper surface of the flange, so that new surface generation is slight at the upper-flange surface. When the non-dimensional residual length of the billet is less than 0.6, the analysis can not be adopted, since the plastic zones of upsetting and backward extrusion meet each other. Except for this, other upsetting parameters, i.e. the billet length, the flange thickness, the slope angle have little effect on the frictional shear factor. Keywords: Injection upsetting; Backward extrusion; Tribology; Friction; Forging; Upper-

bound method

Nomenclature

OF l Pinj Pbe

flange d i a m e t e r residual billet length injection u p s e t t i n g pressure b a c k w a r d e x t r u s i o n pressure m e a n flow stress of the w o r k m a t e r i a l

* Corresponding author. 0924-0136/95/$9.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0 9 2 4 - 0 1 3 6 ( 9 4 ) 0 1 7 6 0 - X

T. Nishimura et al./ Journal o f Materials Processing Technology 53 (1995) 712-725 O~ a

b P 1£

2 m ml

R

wd

Ws

713

die semi-angle slope angle of the flange billet radius flange thickness non-dimensional flange thickness, b/a non-dimensional residual billet length, l/a geometrical parameter frictional shear factor frictional shear factor between the backward-extrusion die and the work material backward extrusion ratio internal power due to deformation shear power at surfaces of velocity discontinuity frictional power at the contact surfaces of the deforming billet

1. Introduction The ring-compression test is an effective test method because it enables the frictional factors of lubricants to be determined easily under various test temperatures and strain rates [1-3]. However, little new surface is created in this test, so that the results of this test cannot be applied immediately to an industrial forging in which the shape of the product is complicated and the surface extension ratio is different from point-to-point. Though many industrial experiments have been carried out [4-6], it is not easy to assess the frictional factors for practical forging conditions. In general, the forging loads in a working process are often compared in order to evaluate the frictional conditions. In evaluating the frictional factor from the forging load, the flow stress of a work material must be determined, an appropriate measurement of the flow stress under industrial forging conditions not being easy since this value changes with the working temperature and/or the strain rate. When the flow stresses obtained are only slightly different, the frictional factors become very different. It would be very useful if the frictional conditions in forging could be known by making use of a simple test method which dose not need any measurement of the flow stress of the work material. The aim of this study is to propose a new simple method of evaluation of the frictional shear factor under near industrial forging condition. Injection upsetting, which has a relatively large new-surface generation, is chosen as the experimental method. Injection upsetting makes the diameter of a part of a cylindrical billet increase locally by forcing the metal to flow into an annular space of fixed clearance. Experimental and analytical studies of this process have been performed by earlier investigators [7-9]. If the injection-upsetting pressure applied is constant, it is known that the diameter of the formed flange depends on the lubrication conditions at the interface between the flange and the platen. If the forging loads are equal, the flange diameter with poor lubrication is smaller. In the present study, injection upsetting is combined with backward extrusion to estimate the frictional shear factor without

714

7". Nishimura et al. /Journal of Materials Processing Technology 53 (1995) 712 725

measuring the flow stress of the work material and/or the forging load. The characteristics of various lubricants were investigated using the present method. In addition, the effects of the upsetting parameters on the frictional shear factor were examined for this evaluation method.

2. Lubrication-testing method The method of evaluation of the frictional condition proposed in this study is illustrated schematically in Fig. 1. The lubricant is applied on all surfaces in contact with the deforming billet during the experiment, i.e., the platen surface, the lower surface of the container and the container wall. In this test, the hollow punch is forced downwards extruded until the billet is extruded backwards, and then the diameter of the flange radially into the cavity, Dr, and the residual billet length, l, are measured. The flange diameter Dv is defined by the actual contact diameter with the platen, the bulged rim being neglected in this measurement. If the forging pressures and residual billet lengths in all cases are constant, the diameter of the flange, flange depends mainly on the lubrication conditions. A flange with good lubrication expands widely because the frictional force on the boundary surface is small; contrarily it does not expand for poor lubrication. If the flange diameters for various lubricants are compared under the same upsetting conditions, it is possible to judge their relative performance. In order to secure constant forging pressure in the experiment, injection upsetting is combined with backward extrusion, in which the die surface is roughened to keep the frictional conditions constant (the frictional shear factor is unity in this case). Until the plastic zones of the two processes meet each other, the diameter of the

before

after __pressure

111

Hollowpunch Backward extrusion~

I

B I I I ~

Spacerring [

Q~.t

T

Platen~ ~[~ ~

I t~

Fig. 1. Showing the test apparatus, based on combined radial and backward extrusions.

T. Nishimura et al./Journal of Materials Processing Technology 53 (1995) 712 725

715

flange can be determined analytically from the equilibrium condition of the injection upsetting pressure, Pi,j, and backward extrusion pressure, Pbe- The effect of the flow stress on the frictional shear factor is removed by equating non-dimensional pressures P i n j / f f and Pbe/6, which are the ratios of the pressures to the mean flow stress, 6". Therefore, measurement of the flow stress of the work material is unnecessary in this test. If the relationship between the flange diameter and the frictional shear factor is established analytically, the frictional shear factor of the lubricant can be evaluated from the experimentally-obtained flange diameter.

3. Upper-bound analysis In this analysis, the work material is assumed to be isotropic, rigid-plastic and to obey the von Mises yield criterion. Both pressures, i.e., that for injection upsetting and that for backward extrusion, are calculated by the upper-bound method as an axi-symmetric problem. Based on the analytical results of Parsons et al. [7], a kinematically admissible velocity field can be divided into five distinct regions, as shown in Fig. 2. Region 1 is the backward-extrusion region in which the material is extruded backwards through the conical die. From region 2 to region 5 are the injectionupsetting regions. In region 2, the material is rigid and is moving axially downwards. Regions 3 and 5 are deformation zones and region 4 is a dead-metal zone. The non-dimensional injection-upsetting pressure Pi.Fr is calculated by summing the power terms for deformation, shear and friction. For region 3, the internal power due to deformation is calculated as follows: 2rtaff 2)A3 rdr Jo ~a'b/aN/ z2 + 2A2 22a2(1 _+ 2)2A~ A2 + A2 dz, I~,3 =------~-j ° x / 3 F" (1 2-bA-~lwhere A1 = 2a + r(1 - 2),

A2 =

(1)

22a + r(1 - 2), A3 = 32a + r(1 - 2).

Fig. 2. A kinematically-admissiblevelocity field for injection upsetting combined with backward extrusion.

716

T. Nishimura et al./Journal of Materials Processing Technology 53 (1995) 712-725

The slope angle of the upper surface of flange is set at/3. The flange is assumed to be expanding in the radial direction whilst always in contact with the surfaces of both the container and the platen. The internal power for deformation in region 5 is as follows: when/3 > 0

l/Vas_rtaZ~tanfl fo.,2 B3 f~x / 2B~ i~2 x/3 Jo rB~ rd o Z2+ B~nfl,l~l+r2tan2fl+B2)dz, where B l = b - ( r - - a ) /3 = 0, from [83

tanfl, B 2 = b - ( 2 r - - a )

tan/3, B 3 = b - - ( 3 r - a )

(2)

tan/3, for

[£Va5- 2Tca26m In Dv

(3)

The shear powers at the velocity discontinuity surfaces, i.e., the 1-3, 2-4 and 3-4 boundaries, are given by I~13 =

7raZe{1 + p2(1 ~ -- 2)2} {~ ~-/3o (i ~ y

1~24 -

•

1 ~;[

( ~22 +

~} In

,

rta2ff ){1 ~p(l/t 2

2 1~

22 + ( ~1 - 2 )

ln~}

(5) '

7~a2 rY .

1~s34 - ~

(4)

- -

{p(1 + 2) - tan//},

(6)

where p the non-dimensional flange thickness, b/a. Similarly, the frictional powers at the 3-5 and 4~6 boundaries are given as follows, respectively, when/3/> 0

¢¢f35 =

~ta2(1 + tan 2 ~3)mr ~oF.,2 1 x/~ 0. {b - (r - a)tan/3} dr,

W f 4 6 -- ~a2mrYm ~oF/2

x/~

~,

(7)

1

{b-(r-a)

tan/3}dr"

(8)

The frictional power at the interface of the container and the work material, i.e. the 3-7 boundary, is given by

2ha 2mftc VIZf37 --

,

(9)

where K is the non-dimensional residual length of the billet, l/a, and m is the frictional shear factor in the injection-upsetting region. Therefore, the non-dimensional upsetting pressure is expressed as follows: Pinj __ 1 (ldga3-}- Wd5 -~- VgZsl3 -[- Vl'Ys24 q'- l/~fs34 -]- Vg~f35 Jr- [/Vf46 -}- VI/'f37)rY 7ta 2 6

(10)

Z Nishimura et al./Journal of Materials Processing Technology 53 (1995) 712-725

717

For region 1, it is assumed that dead metal does not occur at the interface between the die and extruded material. It is considered that the total power of backward extrusion in region 1 is equal to that of the axi-symmetric forward extrusion in which no friction acts at the container wall. Consequently, the non-dimensional backwardextrusion pressure is expressed as the following equation [10]: Pbe_ 2 [ r ( ~ ) l n x / ~ + ~~/31 2 { ( ~s~n2~

cot~)-t-mlcot~lnw/R}]

#

(11)

where F(ct) = ~

1 [11

+ - -

cos~t ~ 1 -]~slnll. 2 In

1+

a/ll/12 -] x/~-i 1/12) cos£ +- ~----- (11/12) sin 2

J

and R is the backward-extrusion ratio, i.e. R = a 2~ R e2, ~x is the die semi-angle and mt is the frictional shear factor between the die and extruded material. Finally, the relationship between the diameter of the flange formed and the frictional shear factor is calculated by equating Eqs. (10) and (11) for equilibrium condition of power.

4. Results of the analysis The relationship between the non-dimensional flange diameter and the frictional factor in the injection-upsetting region is shown in Fig. 3. The calculation conditions

"7

"E 3o

I

a

i

I

I

1

i

I

i

E 2.5 ._~ "

2.0

t-

.o 1.5 ¢--

E "o 1.0 o 0 z

~~'--0.4 1.0

i

I 0.2

I

I

-0.60.E

1 2

I

I

'

~'--~

'~z'"

0.4 0.6 0.8 Frictional shear factor rn

Fig. 3. R e l a t i o n s h i p b e t w e e n f l a n g e d i a m e t e r a n d f r i c t i o n a l s h e a r f a c t o r (R = 4; c~ = 45°; p = 0.8; x = 0.8).

718

T. Nishimura et al. /Journal of Materials Processing Technology 53 (1995) 712- 725 "7

6_ 3 . 0 £3

'

I

'

I

~

I

t

I 0.2

I

I 0.4

I

I 0.6

,

"1o

~ 2.0 '~ 1.5 0

._E 1.0 o

Z

0

Frictional

shear

factor

I

I 0.8

I

1.0

m

Fig. 4. Influence of slope angle on flange diamete~frictional shear factor curves (R - 4; ~ - 45; p - 0.8; = 0.8). are R = 4, e = 45 °, p = 0.8 and/~ = 15 ~, the non-dimensional residual length ~c being changed. The frictional shear factors at the frictional surfaces, i.e. at the upper and lower surfaces of the flange and the container wall, are assumed to be equal. In addition, it is assumed also that the frictional shear factor m, at the interface between the die and the extruding material is equal to unity. The non-dimensional flange diameter increases with increasing •. W h e n the frictional shear factor approaches zero, the influence of K on the flange diameter becomes insignificant. F o r a parallel flange (/~ = 0), it was found experimentally that there was no contact between the flange and the lower surface of the container. Therefore, the n o m o g r a m is calculated by assuming no friction at the upper flange. T h o u g h the flange diameter is a little smaller than the sloped flange, the results show a similar tendency to those of Fig. 3. The influence of the slope angle on the flange diameter friction curves is shown in Fig. 4. W h e n the slope angle increases, the flange diameter reduces suddenly for low frictional shear factor because the ratio of the power for deformation to the total power increases, i.e. the restraint for deformation becomes strong. However, the flange diameters are approximately equal for a high frictional shear factor because the ratio of the frictional power to the total power becomes relatively larger.

5. Experimental procedure Commercially-pure aluminium was selected as the billet material and was annealed for two hours at 673 K. Cylindrical billets were machined in order to remove surface scratches and were finished from 1 6 m m diameter bars to a diameter of 15.5 4- 0.3 mm. According to the lubrication conditions, the range of the billet lengths is varied from 25 to 60 mm. T w o types of containers, parallel and sloped flange (/~ = 0 °, 15 °), were employed. The container, with a bore diameter of 16 ram, and the

72 Nishimura et al./Journal of Materials Processing Technology 53 (1995) 712-725

719

platen were made from heat-treated SKD62 alloy tool steel. The backward-extrusion die, having an extrusion ratio of 4 and a semi-cone angle of 45 °, was made from SKD61. In order to obtain sticking friction, i.e. ml = 1, grooves were provided on the conical surface of the die (see Fig. 1). The flange thickness can be adjusted by changing the height of the die (see Fig. 1). The flange thickness can be adjusted by changing the height of the spacer ring. Five lubrication conditions were employed in the experiments, using Oildag, JF, Dag, MoSz and 'dry'. The upper surface of the platen, the lower surface of the container and the billet surface were lubricated. Oildag and Dag are oil-based graphite lubricants, whilst JF is a water-based BN lubricant. These latter lubricants were applied by brushing, whilst MoS2 was applied by spraying. Before applying the lubricant, the container and platen were ground with emery paper of # 800 grade and cleaned with acetone. The experiments for the sloped flange and parallel flange were carried out at room temperature. The experimentally-obtained non-dimensional flange diameters were plotted on the nomogram calculated by the upper-bound analysis, enabling the frictional shear factor of the lubricant to be obtained.

6. Results and discussion

6.1. Comparison of the parallel flange and the sloped flange In the case of a parallel flange, the results of various lubrication conditions are shown in Fig. 5, the curves representing the results of the upper-bound analysis and the symbols presenting the experimental results. In the tests, the billets were upset up to a non-dimensional residual length of about 0.7. The flange expanded easily in the

~-~ 3.0 6_ 13

~

I

I

'

I

i

I

I

I

i

2.5

._~ "0

~e.0 ~ 1.5 ¢-

E ~ 1.0 o 0 z

0.2 0.4 0.6 0.8 Frictional shear factor rn

1.0

Fig. 5. Results for different lubricants in injection upsetting with a parallel flange (R = 4; ~ = 45°;/~ = 0°; p = 0.8; • dry; V Oildag; ~ JF; O Dag; • MoSe).

720

T. Nishimura et al. /Journal of Materials Processing Technology 53 (1995) 712 725

radial direction because the upper flange surface was out of contact with the lower surface of the container. A number of flanges formed with Oildag, Dag and JF lubricants extended to an irregular shape and necking or failure occurred at the rim of the flange. The cause of the irregular shape is the breakdown of the lubricant layer at the interface of the flange where the extension of the flange in the radial direction is partially constrained: in this case, the results of the experiment were eliminated. When the lubrication condition was uniform under the same test conditions, almost equal flange diameters were obtained, as shown in Fig. 5: this test method has good reproducibility. Moreover, according to the lubricant used, obvious differences appear in the flange diameters. In order to prevent necking or failure, the same experiments were performed with the sloped flange, then extension of which in the radial direction was controlled by the container. When fl = 15 ° is employed, the flange extended to a circular shape, and necking or failure at the rim did not occur at all. The results for the sloped flange are shown in Fig. 6, from which it is noted that the difference in the frictional shear factors for Oildag, Dag and JF are not so large when compared with those in Fig. 5. In the upper-bound calculation, the flange is assumed to be always in contact with the lower surface of the container during the deformation. In the experiment, the actual flange deformation becomes "mushroom shaped" when the flange diameter is relatively small, but it expands as per the assumption when it being larger. The frictional shear factor for the dry condition is under-estimated because of the very small contact area between the flange and the lower surface of the container. The sloped flange is more suitable than the parallel flange in industrial testing, because the measurement of the diameter is easy to perform after the experiment and any lubricating condition rarely produces an irregular shape.

v_. t~ ¢Xl

"~" 3.0 D

i

I

l

I

I

I

i

|

I

~ 2.5 "0

~ 2.0 ~ r = 0 . 4

E

.o 1.5 E

E E

o z

1.0

0

0.2

0.4

0.6

0.8

1.0

Frictional shear factor m

Fig. 6. As for Fig. 5, but for a sloped flange (fl = 15).

T. Nishimura et al. / Journal of Materials Processing Technology 53 (1995) 712 725

721

6.2. Surface extension ratio In order to be adopted under industrial forging conditions, the present injectionupsetting method must show sufficient new-surface generation. Thus, the surface areas before and after the experiment are compared for various lubrication conditions. A billet inscribed with 2 × 5 mm rectangles on its side surface, as shown in Fig. 7(a), is used for the test, the flange of slant line after experiment being illustrated schematically in Fig. 7b. The area hatched with slanted lines was used for calculation of the surface extension ratio, the area before the experiment that contributed to the extension being As and the lower or upper surface area on the formed flange being A: the extension ratio of the surface area is defined as Rs = A/As. In the calculation, the a r e a Arim on the rim and the area Ares on the residual side surface of the billet are excepted because the shape of the rim does not influence the friction and the latter has no relationship to any new-surface generation. The surface extension ratio is shown in Fig. 8, the surface extension ratio of the lower surface of the flange being completely different from that of the upper surface: it increases linearly at the lower surface with increase in the diameter, whilst it decreases slightly at the upper surface. Under

2mm

A

A

Adm

(a)

(b)

Fig. 7. Schematic illustration of the m e a s u r e m e n t of surface extension: (a) before; and (b) after; testing.

15 .o

10

lz 0

Y I

I

O

1.0 1.5 2.0 2.5 3.0 Nondimensional flange diameter DF.(2a)1 Fig. 8. Variation of the surface extension ratio as a function of the flange diameter (R = 4; c~ = 45°; fl = 15°; p = 0.8; K = 0.8; • lower surface; O u p p e r surface).

722

T. Nishimura et al. /Journal of Materials Processing Technology 53 (1995) 712 725

conditions of good lubricantion, the side surface of a billet flows mainly to the upper surface of the flange without restraint at the container wall. Therefore, the ratio Rs of the upper surface does not increase because not only the area A, but also the area As, becomes larger with an increase in the flange diameter. Thus the new-surface generation is slight at the upper surface. On the other hand, most of the lower surface is new due to the expansion of a part of the billet in the radial direction. The surface extension ratio in this test is adequately large when compared with that for the ring-comperssion test. It is considered, therefore, that this test method is suitable for assessing the lubrication for near-industrial forging conditions. The frictional shear factors obtained suggest the use of the mean value for this forging system.

6. 3. Effects o f injection-upsetting parameters

In order to use this evaluation method, the effects of injection-upsetting parameters such as residual billet length and the flange thickness on the lubrication characteristic must necessarily be investigated. The relationship between the frictional shear factor and the non-dimensional billet length with a sloped flange for various lubricants is shown in Fig. 9. The billet length is normalized by dividing it by the container radius, a. It is possible to neglect the initial billet length in this test because the curves are approximately flat for all of the lubricants used. The effect of the flange thickness on the frictional shear factor with a sloped flange is shown in Fig. 10. The curves are obtained from the upper-bound analysis whilst the symbols in the figure indicate the experimental results. Nearly equal values of the frictional shear factors are obtained for the each lubrication condition. Contact of the flange with the lower surface of the container did not occur for p >~ 1.0 and the billet could not be upset for p < 0.6 due to the slope angle. Therefore, experiments were performed only for the two conditions of p = 0.6 and 0.8. The variation of the flange diameter for different slope angles is shown in Fig. 11. Although the spread of the frictional shear factor for Dag lubricant is greater in comparison with those for the other lubricants, its value is able to be surmised. It is considered that the slope angle slightly affects the experimental results.

E 0.6

i

-

i

•

i

,

i

"E 0.4

0.z 0

u_ 0.0

i

3

l

i

t

4 5 6 7 8 Nondimensional billet length L

Fig. 9. Relationshipbetween the frictional shear factor and the initial billet length (O dry; • MoS2;C) Dag).

T. Nishimura et al. /Journal of Materials Processing Technology 53 (1995) 712 725

723

"7 v

3.0

n

"6

=

I

=

1

I

l

I

I

=

2.5

e,}

2.0 ~1.2

E

.o 1.5 E

E

"O tO

-

1.0

0.2 0.4 0.6 0.8 Frictional shear factor m

0

z

Fig. 10. Influence of the flange thickness on the flange diameter in injection upsetting with a sloped flange (R = 4; c~ = 45~';/3 = 15c'; ~c = 0.8; • dry; • MoS2; O Dag).

~" • 3.0

I

J

1

=

I

I

K

I

I

I

I

p=lO o

-

2.5

~5

g¢-

2.0 (

E Q

1.,5

E

E E Q

z

f.O

I

0

I

I

J

I

0.2 0.4 0.6 0.8 Frictional shear factor m

J

1.0

Fig. 11. Variation of the flange diameter with the frictional shear factor for different slope angles ( • dry; • MoS2; O Dag).

The relationships between the experimentally-obtained frictional shear factor and the residual length for three lubrication conditions are shown in Fig. 12. When the billet was upset to less than ~c = 0.6, the material was extruded backwards through the die without increase in the flange diameter: it is suggested that the analysis can not be employed for this condition. Since the influence of residual length with good lubricity is sufficiently small for any x values, the frictional shear factor with Dag lubricant is approximately constant. On the other hand, that of the 'dry' condition increases dramatically for ~c less than 0.6. Therefore, it is required that the non-dimensional residual billet length be kept at up to 0.6 times the container radius.

724

T. Nishimura et al. /Journal o f Materials Processing Technology 53 (1995) 712 725

E o

0.6 0.5 0.4

c"-

0.3

",.0 ¢.-

0.2

o---

'6 0.1 ii 0.0 0.2

i

L

i

i

i

0.4

0.6

0.8

1.0

1.2

N o n d i m e n s i o n a l residual length

1.4

~

Fig. 12. Relationship between the frictional shear factor and the non-dimensional residual length for R = 4, ~ = 45 °, fl = 15 ~', p = 0.8 (R = 4; ~ = 4 5 ° ; / / = 15~'; p = 0.8; • dry; • MoS2; (~ Dag).

7. Conclusions

In order to be able to estimate the lubrication under near industrial forging conditions, without measuring the flow stress of a work material and/or the forging load, a simple test method based on injection upsetting is proposed. This method of evaluation was investigated experimentally, the results obtained being as follows: (1) A test with the sloped flange is suitable for industrial experiments. On the other hand, necking or failure occurs at the rim of the flange for the parallel flange without slope, and the flange becomes of irregular shape. Therefore, the parallel flange is difficult to use for this test. (2) The surface extension ratio on the lower surface of the flange increases linearly with the diameter of the flange and there is new surface generated. The generation of new surface on the upper surface is very slight due to the supply of metal to the side surface of the lubricated billet. (3) The upsetting parameters, i.e. billet length, flange thickness and slope angle, do not have an influence on the evaluation of the frictional shear factor. (4) When the non-dimensional residual length of the billet is less than 0.6, the analysis can not be adopted, since work material is extruded backwards without increase in the flange diameter.

References [1] P.W. Wallace and J.A. Schey, Speed effect in forging lubrication, Trans. ASME, Ser. F, J. Lub Tech., 93-3 (1971) 317-323. [2] S.C. Jain and A.N. Bramley, Speed and frictional effects in hot forging, Proc. Inst. Mech. Engrs., 182 39 (1967 68). 783 795. [3] A.T. Male, The effect of temperature on the frictional behavior of various metal during mechanical working, J. Inst. Mets., 93 (1964-65). 4 8 9 4 9 4 .

T. Nishimura et al./ Journal o f Materials Processing Technology 53 (1995) 712-725

725

[4] S. Isogawa and A. Kimura, Proposal of an evaluating method on lubrication, Ann. CIRP.,41(1)(1992) 263-266. [5] A. Buschhausen, K. Weinmann, J.Y. Lee and T. Altan, Evaluation of lubrication and friction in cold forging using a double backward-extrusion process, J. Mat. Proc. Tech., 33 (1992). 95-108. [6] G. Ahen, A. Vedhanayagam, E. Kropp and T. Altan, A method for evaluating friction using a backward extrusion-type forging, J. Mat. Proc. Tech., 33 (1992) 109-123. [7] B. Parsons, P.R. Milner and B.N. Cole, Study of the injection upsetting of metals, J. Mech. Eng. Sci., 15(6) (1973) 410421. [8] B. Balendra, Process mechanics of injection upsetting, Int. J. Mech. Tool Des. Res., 25(1) (1985). 66-73. [9] J.M. Alexander and B. Lengyel, On the cold extrusion of flange against high hydrostatic pressure, J. Inst. Mat., 93 (1964~65) 137 145. 10] B. Avitzur, Metal Forming Processes and Analysis, McGraw-Hill, New York, 1968, p. 266.