Nosing of thin-walled tubes by circular curved dies

Journal of Mechanical Working Technology, 10 (1984) 287--298

287

Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

NOSING OF THIN-WALLED TUBES BY CIRCULAR CURVED DIES

KEN-ICHI MANABE and HISASHI NISHIMURA

Department of Mechanical Engineering, Faculty of Technology, Tokyo Metropolitan University, Tokyo (Japan) (Received December 2, 1983; accepted in revised form May 25, 1984)

Industrial Summary Experiments into the nosing of thin-walled aluminum tubes have been carried out in order to clarify the characteristics of nosing by a circular curved die. Comparing the results with those for a conical die, the advantages of a circular curved die are discussed in detail. It is established that a circular curved die is effective in reducing the nosing load, restraining unfavourable deformation, and improving the nosing limit for tubular materials, which buckle at the cylindrical part in conical nosing. It is suggested that it is of advantage to introduce a circular curved part into the inlet of a conical die. Further to the above, numerical analysis is performed on the optimum die radius and die contact pressure, upon which the effect of the die profile is examined.

Introduction The nosing of tubular materials is one of the most popular and simplest processes in the forming of tubes. In the conical nosing of tubes by axial compression, the region of the tube near the die inlet is subjected to local bending. Thus, for a large die semi-angle ~, the nosing load [1,2] and the die contact pressure [3] are strongly affected by the bending deformation. Furthermore, unfavourable deformation also takes place for large values of [1]. To solve these problems, it is necessary to restrain the concentration of bending deformation near the die inlet: for this purpose, a circular curved die would seem to be more effective than a conical die. Some research has been done on the nosing of tubes by a circular curved die. Nadai [4] has carried out theoretical research on the stress states and the forming loads in the nosing of a circular curved profile, and Carlson [5] has done experimental work on these aspects. Expressions for the nosing load of a conical die and a circular curved die have been presented by Averknev [6]. Recently, finite element methods have also been developed to study the nosing of tubes by a circular curved die by Tang and Kobayashi [7]. However, the effectiveness o f a circular curved die has n o t been discussed in any of these studies.

0378-3804/84/$03.00

© 1984 Elsevier Science Publishers B.V.

288 T h e p u r p o s e o f t h i s p a p e r is t o c l a r i f y t h e c h a r a c t e r i s t i c s o r f e a t u r e s o f nosing by a circular curved die. Experiments into the nosing of thin-walled aluminum tubes are carried out and the advantages of a circular curved die are established by comparing the results with those for a conical die. N u m e r i c a l a n a l y s i s is a l s o p e r f o r m e d o n t h e o p t i m u m d i e r a d i u s a n d t h e d i e contact pressure, examining the effects of die profile on these quantities. TABLE 1 Material properties Material

Direc.

Hv

oB (MPa)

r

F (MPa)

n

Feq (MPa)

neq

A1050, to = 1,5 As received

~ 0

41.3

127 136

0.42 1.08

134 145

0.008 0.009

133

0.009

A1050, to = 1,5 Annealed (400°C)

~ 0

20.2

69 74

0.61 2.01

119 132

0.181 0.207

123

0.194

A1070, to = 1.0 As received

~ 0

41.8

129 134

0.42 0.86

136 142

0.008 0.009

132

0.009

A1070, to = 1.0 Annealed (400°C)

~ 0

20.5

66 72

0.53 3.14

122 124

0.200 0.201

120

0.201

~: axial direction; 0: circumferential direction; to is in mm.

///,.:/l////.///.j//...,/

r~ = (eO/et)

I aO =

0;

r0 =

(e~/er) l ~ = 0;

X t" Rcc~,l'd~'r

Fig. 1. Schematic view of the nosing apparatus. Experimental procedure The materials used are two kinds of drawn seamless aluminum tubes (outside diameter: 40 mm; wall thickness: 1.0 and 1.5 mm), the material p r o p e r t i e s o f w h i c h a r e g i v e n in T a b l e 1. T h e s p e c i m e n s a r e o f 1 0 0 m m

289

length. The circular curved dies used in the experiment are of three different die radii Pw (nominal 20, 50 and 100 mm). Figure 1 presents a schematic view of the nosing apparatus set up in an Instron-type tensile-testing machine. Nosing is conducted at a crosshead speed of 3 mm/min. During the nosing process, the load--displacement curves are recorded on an X - - Y recorder and the reduction of the end of the nosing zone is measured using a trial manufactured clip-gage and recorded on an X - - T recorder. Molybdenum disulphide (MoS2) is used as a lubricant and is coated on both the die and the specimens. The wall thickness of the specimens is measured by means of a point micrometer. Nosing by conical dies with semi-cone angle ~ = 1 0 °, 20 °, 30 ° and 45 ° is performed, as well as circular nosing, in order to examine the effect of die profile quantitatively. The nosing ratio K which expresses the degree of reduction shown in Fig. A1 (appendix) is defined by K = (Ro

-

Ro)IRo

(1)

Experimental results and discussion

Nosing load--displacement curve (W--L curve) The effects of die profile are shown in the nosing load--displacement curve. Figure 2 affords a comparison of the W--L curves for circular curved dies and conical dies. In the case of the conical dies -- broken curves -a peak load appears at an early stage in the nosing, the value of the peak load increasing with increasing die semi-angle ~. The variation of the W--L curves is particularly conspicuous for ~ = 45°: this is because the profile of the tube changes most markedly near the die inlet, the bending deformation T LiRo 0

0.5

1.0

i

Coni cal.~--..-

2c

~ 45°`

/

_

~ ;ending / ~process /

.~ lo,

/

rl

/

/

6

.z

/0.4,,'"/

/71.O/~y...//R,,/fl,,

0.2

~

/ ."/' / / t~7!t I ,1/ s~ ~,~ I .###l ..ji"

1/

/____~C~r~.la,-

I~

2

5 Octll'Ve

.

OXtl e As ree iv d .

0

:~

'

,"

.... ,

I

/

it

~,' 30y .,

2.0

i

,' 20J

;

'~

1.5

i

10

,

l

20

.

.

.

.

I

,

30 Displacement LCmrn)

Fig. 2. C o m p a r i s o n o f t h e

W--L

,

,

•

I

40

,

0

c u r v e s f o r c i r c u l a r c u r v e d dies a n d c o n i c a l dies.

290

localizing at this portion. In the case o f circular curved dies -- solid curves -the peak load at the early stage in t he nosing disappears and the increment of load W increases s m oot hl y with increasing displacement L for any die radius pw. The W--L curves f or circular curved dies are steeper t h a n those for conical dies: this is due to t he increase in the die semi-angle at the end of t h e nosing zone in the progress of the nosing operation, and is one of the features of circular curved dies.

Relationships between nosing load and die radius An o p t i m u m die semi-angle ~m at which the nosing load is a minimum exists in th e case of conical dies [1,6] : for a circular curved die it is therefore relevant to discuss t he o p t i m u m die radius Pwm corresponding to the o p t i m u m die semi-angle ~ for conical dies. Figure 3 shows the effects of dimensionless die radius Rw/pw on the nosing load for circular curved dies. F r o m this figure, it is seen that the nosing load decreases as R~/p~ increases, and t hat t he o p t i m u m die radius P,~m is n o t present within the range of these experiments: this can obviously be ascribed to the small bending effect t ha t exists when nosing by circular curved dies. 2.5-

60

¢40×t1.0 Annealed

2.0-

l.ar~~1 1.O-

40 ~

0.24

2O

0.13

0.5-

o.o8

"vO-

0

~

0.03

02

0.4 0.6 0.8 10 R,,/p,,, Fig. 3. Effect of dimensionless die radius Rw/pw on the nosing load for circular curved dies. Dash(') indicates the tube surface. Quantitative comparison of conical dies with circular curved dies with regard to the nosing load can now be made for t he following two cases. Figure 4(a) shows t ype 1, where the die semi-angle ~, at t he end of the nosing zone of a circular curved die is equal to that of a conical die, and Fig. 4(b) shows t y p e 2, where ~, is equal to twice the die semi-angle ~2 of the conical die, which latter consists of chords connecting the tube end a

291

(a) Tubular ~ specimen ]

/:!

Rw (-Ro)

.

C~rcular curve (type 1)

(b)

hi

]

Rw (-Ro)

Tubular specimen"-~ Conical (Chord)

] .4 I//// Die !

9~ //:'

" q92 a Conical £ / ~ a ( tangent at the ~"//['<,,~.

i

I I

o n c e

Circu (type2)_

~

"~_~

Ra~

Fig. 4. Schematic illustration of a circular curved die and a conical die: (a) type 1; (b) type 2. to the die inlet b. In the former type, ~1 is given geometrically by ~1 = cos -1 [1 - (RoK/pw)]

(2)

and in the latter type, ~2 is represented by ~

= ~1/2

(3)

Figure 5 compares the nosing loads for circular curved dies and conical dies by transforming the results for circular curved dies into those of conical dies using eqns. (2) and (3). Firstly, in comparison with those for a circular curved die such as type 1 in Fig. 4(a), the results for conical dies are higher in the range where ~ is large, since the bending effect near the die inlet is considerable and, conversely, t h e y are lower in the range where ~ is small, since the contact length between the die and the tube is shorter, i.e. the frictional resistance is less than that of circular curved dies. Secondly, in comparison with those for a circular curved die such as type 2 in Fig. 4 (b), all results for circular curved dies are smaller than those for conical dies. From these results, therefore, changing a conical die into a circular curved die is effective in reducing the nosing load. In particular, the effect is great in the case of conical dies where q is large. Moreover, a circular curve such as t y p e 2 in Fig. 4(b) is favourable. From eqn. (2) the associated die radius is given by Pw = RoK/(1 - cos 2~)

(4)

292

where ~ indicates t h e semi-angle of the conical die. For a conical die where is large, a circular curve o f t y p e 1 as s h o w n in Fig. 4 (a) also has a significant effect. In addition, these results suggest that it is better to introduce a circular curved part into the inlet o f conical die. 2.0¢40" tl.0 Annealed ~' 0.18

40

30

~ i FCUI~II" CUI'VO ! tangent ) \ I

~'x "~ R,, P,, 0.2 0.2 0 ~ " " "

~1.o-

0.4

Cm~

~= 20] I

lol I

i Chord

/

• '

~ A' B

I

ol

0 -

1

10

,a

20

cp,,

I

I

30

40

50

Fig. 5. C o m p a r i s o n o f t h e nosing loads for circular curved dies and conical dies. A indicates a region w h e r e t h e e f f e c t s o f f r i c t i o n are greater for circular curved dies t h a n for conical dies, whilst B indicates a region w h e r e t h e e f f e c t s o f b e n d i n g are greater for conical dies t h a n for circular curved dies. ~0m indicates t h e o p t i m u m die semi-angle in conical nosing ( e x p e r i m e n t a l results). Narrow wrinkle

C on i e a I

.:~-g~-:.

~ (a)

(b)

Tubular specimen

(e)

Fig. 6. M o d e s o f buckling observed at t h e nosing z o n e o f a circular curved die and a conical die: (a) n a r r o w c i r c u m f e r e n t i a l wrinkle for a circular curved die, R w / p w = 1.0, × t = 40 × 1.0 m m (as-received t u b e ) ; (b) w r i n k l e a t t h e end o f t h e nosing z o n e for a conical die, ~ = 45 °, 0 × t = 40 x l . 0 m m (as-received t u b e ) ; (e) waving along t h e die surface for a conical die, ~0 = 45 °, ~ × t = 40 × 1.5 m m (annealed tube).

293

Buckling modes T h e p r o g r e s s o f nosing is h a m p e r e d b y b u c k l i n g in t h e n o s e - f o r m i n g p o r t i o n a n d in t h e cylindrical p o r t i o n [1]. Figure 6 p r e s e n t s t h e d i f f e r e n c e s in t h e m o d e s o f b u c k l i n g o b s e r v e d at t h e nosing z o n e o f a c o n i c a l die a n d a circular curved die. T h e waviness a n d t h e wrinkles at t h e end o f nosing z o n e w h i c h are o b s e r v e d in conical nosing are n o t p r e s e n t , a n d o n l y n a r r o w c i r c u m f e r e n t i a l w r i n k l e s o c c u r in nosing b y circular c u r v e d dies. T h e die semi-angle a t t h e end o f t h e nosing z o n e in a circular c u r v e g r a d u a l l y increases f r o m zero d u r i n g t h e progress o f nosing, as given b y eqn. (2): thus, edge w r i n k l e s a n d waviness w h i c h a l w a y s o c c u r f o r t h e conical nosing at a large value o f ¢ do n o t o c c u r in t h e case o f a circular c u r v e d die.

Improvement of nosing limit As m e n t i o n e d a b o v e , a circular c u r v e d die is e f f e c t i v e in r e d u c i n g t h e nosing load, w h i c h suggests t h a t t h e nosing limit will be i m p r o v e d f o r t h o s e t u b u l a r m a t e r i a l s w h i c h b u c k l e at t h e cylindrical p a r t in c o n i c a l nosing. Figure 7 a f f o r d s a c o m p a r i s o n o f t h e m a x i m u m nosing r a t i o Km (nosing limit} f o r conical d i e s a n d - - in t h e case o f a circular c u r v e d die - - f o r t h e m a t e r i a l w h i c h b u c k l e s a t t h e cylindrical p a r t in c o n i c a l nosing. As is e x p e c t e d , circular c u r v e d dies o f t y p e 2 a n d t y p e 1 in Fig. 4 are f o u n d t o b e e f f e c t i v e in i m p r o v i n g t h e n o s i n g limit f o r large values o f t h e die semi-angle ~.

0.5

0.4 ':

j Circular curve (chord) t--l.O~

02

04

3

Circular curve , (tangent).

Rw/p

"~

:l.o "cal

0.2 ~40× tl.5 AnneaLed 0.1

0

I

20

:

I

~o (o)

I

40

,

60

Fig. 7. Comparison of the maximum nosing ratio Km in the case of conical dies and circular curved dies, for materials which buckle at the cylindrical part in conical nosing. The solid curve relates to experimental results for conical dies.

Wall thickness distribution F i g u r e 8 s h o w s t h e strain d i s t r i b u t i o n s in t h e case o f a circular c u r v e d die. It is seen t h a t a m a x i m u m "thickness strain a p p e a r s in circular nosing as well as in conical nosing [ 8 ] . This p h e n o m e n o n also t a k e s p l a c e in t h e case o f a circular c u r v e d die a t t h e s a m e c o m b i n a t i o n o f t h e nosing r a t i o K a n d t h e die semi-angle a t t h e e n d o f t h e n o s i n g z o n e as t h a t f o r t h e o c c u r r e n c e o f t h e m a x i m u m wall t h i c k n e s s in c o n i c a l nosing [8].

294

I

SO Gnd

L

1.0

0 End of nosing

,

2.0

L

SO= SolRo zone

Fig. 8. Strain distributions in the case of a circular curved die. et) : circumferential strain; 66: meridional strain; et: thickness strain; S, : original axial distance from tube end.

Considerations of numerical analyses Recently, a nosing process predictions of circular curved the Appendix.

finite-difference method has been developed to simulate the for a conical die [Z]. Using the same method, analytical optimum die radius and die contact pressure in nosing by a die are made here: details of the basic equations are given in

Optimum die radius Figure 9 shows the calculated relationships between the nosing load and the dimensionless die radius R,/p,. * these curves are similar to the experimental curves of Fig. 3. Although theoretically there is an optimum die radius, the nosing load is almost independent of R,/p, at all nosing stages for values of Rw/pw greater than 0.5. Die con tat t pressure

In the case of a conical die, it was found that the die contact pressure was extremely high near the die inlet [ 31. A circular curved die seems to have a significant effect in making the die contact pressure more uniform because of the small bending effect at the die inlet. Figure 10 affords a comparison of the calculated die contact pressure for a conical die and for a circular curved die. From this figure, it is suggested that the die contact pressure could become more uniform in the case of the

295

6.0 ,u = O. in=0.2

5.C

'

Ir~=r~:l.O F __

i

4.£ ~ _ _

--. 3.0

0.4

....

o.3

1

II I~ 2.0

I

t

'I I

1.0

---- ~

die r a d i u s . ,

0.5

1.0

1.5

2.1b 5

R,,/G Fig. 9. Calculated relationships b e t w e e n the nosing load and the dimensionless die radius

Rw/pw. Frictional coefficient ~ = 0.1, plastic planar anisotropy r e = r~ = 1.0 and the work-hardening e x p o n e n t n = 0.2.

S (ram) 10

0

i

....

I

20 [

I

Conical (~o: 20 ° ) C i r c u l a r curve(Rw/p,,=l.O)

r'-. L

~, o.1 ""%,

n

l '~ "-.,, I~ x = u . 4

0.2

r~=ru

^.

1.0

¢a

1.0 1

'~

%%%

I

0 End of nosing zone

i

0.4

I

I

S

S/Ro

I

0.8

I

I |

1.2

Fig. 10. C o m p a r i s o n o f the calculated die c o n t a c t pressure for a conical die and a circular curved die. S : distance along die surface f r o m t u b e end; ~ = 0.1; r e = r~b = 1.0; n = 0.2.

296 circular curved die t h a n in the case o f a conical die, such effect b e c o m i n g greater at later stages in t h e nosing process. Conclusions To c o n f i r m the a d v a n t a g e s o f using a circular curved die as o p p o s e d to using a conical die, nosing b y circular curved dies has been carried o u t e x p e r i m e n t a l l y o n thin-walled a l u m i n u m tubes. N u m e r i c a l analysis has also b e e n m a d e t o enable p r e d i c t i o n s o f o p t i m u m die radius and die c o n t a c t pressure. T h e f o l l o w i n g c o n c l u s i o n s are o b t a i n e d : (i) A circular curved die is effective in r e d u c i n g the nosing load a n d p r e v e n t i n g the p e a k load t h a t arises in the early stages o f conical nosing because o f restraint d u e to the c o n c e n t r a t i o n of b e n d i n g d e f o r m a t i o n near t h e inlet of t h e conical die for large values o f ~. T h e nosing load f o r a circular curved die is, relative to t h a t f o r a conical die, a l m o s t i n d e p e n d e n t o f R~,/Pw. (ii) O c c u r r e n c e o f t h e waviness and the edge wrinkles w h i c h are o b s e r v e d in conical nosing is restrained, a n d o n l y n a r r o w c i r c u m f e r e n t i a l wrinkles o c c u r in t h e case o f circular curved dies. (iii) T h e die c o n t a c t pressure f o r a circular-curve die profile is p r e d i c t e d as being quite u n i f o r m , relative to t h a t f o r a conical die profile. (iv) F o r t u b u l a r materials w h i c h b u c k l e at t h e cylindrical p a r t in conical nosing, t h e m a x i m u m nosing ratio Km (nosing limit) i m p r o v e s with the use o f circular curved dies: t h e e f f e c t b e c o m e s greater in the a p p l i c a t i o n of circular curves as s h o w n in Fig. 4 to a conical die w i t h a large value o f ~. It is suggested t h a t it is p r e f e r a b l e f o r a circular curved p a r t to be i n t r o d u c e d into t h e inlet o f t h e conical die. Acknowledgements T h e a u t h o r s w o u l d like to e x p r e s s t h e i r a p p r e c i a t i o n to Prof. M. M i y a g a w a o f t h e T e c h n o l o g i c a l University o f N a g a o k a for valuable advice. T h e y also wish to e x p r e s s their t h a n k s to H. K o i k e w h o carried o u t m u c h o f t h e experimental work.

R eferences 1 K. Manabe and H. Nishimura, Jour. Japan Soc. Tech. Plasticity (in Japanese), 23 (1982) 335. 2 Ibid., 650. 3 H. Nishimura and K. Manabe, Report of JSTP Research Committee, Pressforming of stainless steel sheets (in Japanese), No. 49, 1981, p. 2. 4 A. Nadai, ASME Symposium on Forging of Steel Shells, 1943. ASME, 1944, p. 31. 5 R.K. Carlson, ibid., p. 45. 6 Y.A. Averknev, Knigor, 42 (1957) 167. 7 M.C. Tang and S. Kobayashi, Trans. ASME, J. Engrg. Industry, 104 (1982) 305 and 312. 8 K. Manabe and H. Nishimura, Jour. Japan Soc. Tech. Plasticity (in Japanese), (1982) 878.

297 Appendix

1. Basic equations T h e equilibrium e q u a t i o n o f an e l e m e n t o f t h e nosing z o n e is o b t a i n e d as

d ( R a , t ) / ~ + (sin~ + pcos~)pwtO o + p R t a ~ = 0

(A1)

w h e r e t is the wall thickness o f t h e t u b e , ao is the c i r c u m f e r e n t i a l stress, and a¢ is t h e m e r i d i o n a l stress. (o)

W R' /tO

Ro(- R,:

(b)

Original ring element R.i+l

~::i::i::i::!::! b

I' t~ t_

x--

p~

"Deformed ring element "7

Fig. A1. Schematic illustration of notations. Dash (') indicates the surface of the tube. Subscript a indicates the tube-end and b indicates the die inlet. F r o m t h e g e o m e t r y in Fig. A - l , t h e following e q u a t i o n is o b t a i n e d b y a p p r o x i m a t i n g t h e profile t o t h e f r u s t u m o f a cone. Ri+I 2 =

Ri 2 + 4RoAS0 ~ t °

ti+ti+l

sin( ~i-b~i+l- ) \

2

(A2)

Based o n Hill's t h e o r y o f plastic a n i s o t r o p y u n d e r plane stress conditions, the following e q u a t i o n s can be o b t a i n e d :

a¢' =

_ 1 . [ r~

XLro

e°+(

r,+

r0)] rV

et

'

(A3)

and 1

oo = -~ (eo - r¢et)

(A4)

where = 3r~[1 + (1/ro + rv/ro)] ee__qq 211 + (r~/ro) + r~]

Oeq

298 The expressions for Oeq and eeq are given by

1 ~ [r°(l +rc')°~+rc'(l +r°)°~ eeq = I -~23 r~+ro+ror eeq

=

_ 2r°r~°~e°] I ~:2

t 2 r°+r~+r°r~ [r_fo ] I ~/2 3 r~{1 + ro + r~) (eo + et): + e$ + r~e~

,

(A5)

(A6)

The work-hardening characteristics of the material are assumed to follow the form Oeq ---- Feeq

n

(A7)

Taking into account the bending effect, the nosing load W for a circular curved die is written as

W = 2~rRot~ (o~b + F [ ( t a + tb)/4p,~]l÷n/2 }

(AS)

and the die contact pressure p is obtained according to

p = -t(o~/pw + oocos~/R)

(A9)

and for a conical die,

p = -teocos~/R

(A10)

2. Calculation procedure The difference equations of eqn. (A1) and eqn. (A2} are solved by using a successive approximation method. The calculation starts at the end of the nosing zone a -- at which the boundary condition is given as a~a = 0 -- along the die profile in a number of steps to the die inlet b.