Fini e Elemen Analysis o Tube D awing P ocess wi h Diame e ExpansionS. Kajikawa, H. Kawaguchi, T. Kuboki, I. Akasaka, Y. Te ashi a and M. Akiyama
XIV In e na ional Con e ence on Compu a ional Plas ici y. Fundamen als and Applica ions
COMPLAS 2019
E. Oña e, D.R.J. Owen, D. Pe ic , M. Chiumen i, and Edua do de Souza Ne o (Eds)
FINITE ELEMENT ANALYSIS OF TUBE DRAWING PROCESS
WITH DIAMETER EXPANSION
SHOHEI KAJIKAWA*, HIKARU KAWAGUCHI*, TAKASHI KUBOKI*,
ISAMU AKASAKA†, YUZO TERASHITA† AND MASAYOSHI AKIYAMA††
*
Depa men o Mechanical Enginee ing & In elligen Sys ems
The Uni e si y o Elec o-Communica ions
1-5-1 Cho u Gaoka, Cho u-shi, Tokyo, 182-8585, Japan
e-mail: [email protected], www.uec.ac.jp/eng/
† Miyazaki Machine y Sys ems Co., L d.
1 Nii, Kaizuka-shi, Osaka, 597-8588, Japan
www.miyazakijp.com
†† Akiyama Mechanical Enginee ing Consul ing
2-7-306 Tanaka Sekiden-cho, Sakyo-ku, Kyo o-shi, Kyo o, 606-8203, Japan
Key wo ds:
D awing, Fla ing, Tube expansion, Thickness educ ion, FEM.
Abs ac . This pape p esen s a ube d awing p ocess wi h diame e expansion o p oducing a
hin-walled ube e ec i ely. In his p oposed p ocess, he ube was la ed by a plug pushing
in o he ube, and hen he ube was expanded by d awing he plug in he ube axial di ec ion
wi h chucking he la ed ube edge. Op imum plug shape, such as he plug hal angle and he
co ne adius, was in es iga ed by a se ies o analyses using he ini e elemen me hod (FEM)
o imp o ing he o ming limi and he dimension accu acy. A i s , a ic ion coe icien was
de e mined o 0.3 by a compa ison o he la ing limi be ween he analysis and he expe imen
o he ube la ing. As a esul o he analyses in he d awing wi h he diame e expansion, he
o ming limi was high when he plug hal angle was se o 18~30°. The hickness educ ion
a io inc eased wi h an inc ease in he expansion a io and he plug hal angle. In addi ion, he
o e shoo , which is a di e ence be ween he plug diame e and he ube inne diame e a e
he d awing, was p e en ed by using he plug wi h he co ne adius o 20 mm.
1 INTRODUCTION
D awing p ocess is con en ionally applied o manu ac u ing ubes o educing hickness
and imp o ing dimensional accu acy and s eng h. The ubes, which is manu ac u ed by he
d awing, is used o a ious machine and cons uc ion componen s, such as plumbing
equipmen , cons uc ional ma e ial and so on. The e a e many esea ch wo ks o he ube
d awing. Fo example, Kuboki e al. p oposed me hods o le elling esidual s ess, and
educing hickness a ia ion in he ube d awing [1, 2].
In ecen yea s, hin-walled ubes, which con ibu e o educ ion in size and weigh o a ious
machine componen s, a e equi ed o en i onmen al p o ec ion. Howe e , ypical hickness
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S. Kajikawa, H. Kawaguchi, T. Kuboki, I. Akasaka, Y. Te ashi a and M. Akiyama
2
educ ion is abou 20 % in 1 pass d awing [3]. The e o e, many d awing passes a e equi ed o
manu ac u ing hin-walled ubes om a he hick-walled aw ubes, and he p oduc ion cos
inc eases wi h he inc ease o he numbe o he d awing passes. Ano he me hod o
manu ac u ing hin-walled ube is pilge ing [4]. A ea educ ion is o e 80 %, bu p oduc i i y
and dimensional accu acy is low compa ed o he d awing, because he pilge ing is an
inc emen al p ocessing. Fu ushima e al. p oposed dieless d awing, which con ibu es o he
la ge a ea educ ion in 1 d awing pass [5]. Howe e , he ubes, which a e manu ac u ed by he
dieless d awing, a e unsui able o machine componen which equi es he dimensional
accu acy. The e o e, e ec i e p ocessing me hod should be de eloped o manu ac u ing he
hin-walled ube.
2 TUBE DRAWING PROCESS WITH DIAMETER EXPANSION
This pape p oposed a ube d awing p ocess wi h a diame e expansion as shown in Figu e
1. The p oposed me hod is composed o wo s eps. In he i s s ep which is ube la ing, he
ube edge is expanded by pushing he plug in o he ube as shown in Fig. 1 (a). In second s ep
which is he plug d awing, he ube is expanded h ough he whole ube leng h by d awing he
plug while he la ed po ion is chucked as shown in Fig. 1 (b).
The ad an age o he p oposed me hod is he e ec i e p oduc ion o he hin-walled ube.
Figu e 2 shows he compa ison o s ess s a e be ween he con en ional and he p oposed
me hod. In he case o he p oposed me hod, he ube wall is s e ched in bo h o he axial and
he hoop di ec ions, hen a nega i e de ia o ic s ess is la ge in he hickness di ec ion, wi h
Figu e 1: Schema ic diag am o ube d awing p ocess wi h diame e expansion
Figu e 2: Compa ison o s ess s a e be ween d awing wi h sh ink and expansion
49
S. Kajikawa, H. Kawaguchi, T. Kuboki, I. Akasaka, Y. Te ashi a and M. Akiyama
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compa ed o ha o he con en ional ube d awing wi h diame e sh inkage. Thus, he p oposed
me hod is conside ed o be e ec i e o educing he hickness o he ube.
In his s udy, op imum plug shape, such as he plug hal angle and he co ne adius, was
in es iga ed o imp o ing he o ming limi and he dimension accu acy. A i s , he ube
la ing, which is 1s s ep, was ca ied ou in he expe imen and he analysis by ini e elemen
me hod (FEM), and he ic ion coe icien μ was es ima ed by compa ison o he la ing limi
be ween he expe imen and he FEM. In d awing p ocess, which is 2nd s ep, a se ies o he
analyses we e ca ied ou o iden i ying he op imum plug shape.
3 INVESTIGATION IN FLARING PROCESS
3.1 Fla ing me hod and condi ions
An elas ic-plas ic analysis by he FEM was ca ied ou by using he comme cial code
“ELFEN” which was de eloped by Rock ield So wa e Limi ed, Swansea. Figu e 3 shows he
schema ic diag am o he model o he ube la ing. The model is wo dimensional wi h
axisymme y. The on Mises yield c i e ion was adop ed, and no mali y p inciple was applied
o he low ule. The cons ain s we e de e mined by he penal y unc ion me hod, and an
implici scheme was adop ed. Fou -node ec angula elemen s we e adop ed. The F-ba me hod
was applied o he elemen o o e coming olume ic locking [6].
In he analysis o he ube la ing, one ube edge was la ed by he plug pushing, while he
o he edge was ixed in he axial di ec ion and he ou e su ace was held by he holde . The
Figu e 3: Schema ic diag am o FEA model o ube la ing
Figu e 4: Appea ance o expe imen al se -up and la ed ube
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S. Kajikawa, H. Kawaguchi, T. Kuboki, I. Akasaka, Y. Te ashi a and M. Akiyama
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Table 1: Wo king condi ions in la ing p ocess
Tube
Tube ma e ial SUS304
Swi ’s equa ion o SUS304
(FEM) σ=1275(εp+0.01)0.39
Ini ial diame e d0 [mm] 30
Ini ial hickness 0 [mm] 1, 2, 3, 4
Ini ial leng h l 0 [mm] 200
Ini ial la ed leng h l [mm] 100
Elemen size (FEM) Axial 1 mm/di ision
Radial 8 di isions
Plug Hal angle φ [°] 12, 24, 36, 48
F ic ion coe icien μ (FEM) 0.1, 0.2, 0.3, 0.4
Lub ica ion (Expe imen ) Wi h lub ican
la ing a io E
was de ined as he ollowing equa ion.
E
=
di
−
di0
di0
(1)
whe e d
i
is he inne diame e a he la ed edge, and d
i0
is he ini ial inne diame e . The
buckling occu ed as a de ec by he plug pushing as shown in Fig. 3 (b). The buckling amoun
B was de ined as he ollowing equa ion.
B
=
db
−
d0
d0
(2)
whe e d
b
was he ou e diame e o he buckling po ion, and d
0
was he ini ial ou e diame e .
Maximum la ing a io E
_max
, which means la ing limi , was de ined as he maximum alue
o E
be o e B eaching 0.05. The expe imen s we e ca ied ou in a simila way o FEM as
shown in Figu e 4. d
i
and d
b
we e measu ed e e y 2 mm o he plug pushing in he axial
di ec ion.
Table 1 shows he wo king condi ions o he ube la ing in he FEM and he expe imen .
The ube ma e ial was SUS304, and hickness
0
was om 1 o 4 mm. Plugs wi h a ious hal
angle φ, which we e om 12 o 48°, we e p epa ed. The expe imen al esul s we e compa ed
o he FEM esul s wi h a ious ic ion coe icien μ.
3.2 Maximum la ing a io
Figu e 5 shows he e ec o he ube ini ial hickness
0
on he maximum la ing a io E
_max
when he plug hal angle
φ
was 12°. E
_max
inc eased wi h an inc ease in
0
. In addi ion, E
_max
was highe unde he condi ion o he low ic ion coe icien µ in FEM esul s. This is because
he axial load, which causes buckling occu ence, dec eases wi h he dec ease in he ic ional
o ce. The expe imen al esul s almos ag eed wi h he FEM esul o µ=0.3.
Figu e 6 shows he e ec o he plug hal angle φ on he maximum la ing a io E
_max
when
he ube ini ial hickness
0
was 2 mm. E
_max
was low unde he condi ion o low φ because he
ic ional o ce was high due o he la ge con ac a ea a he plug ape po ion. On he o he
hand, E
_max
was also low when φ was oo la ge, because he axial load was high due o he la ge
bending/unbending de o ma ion o he ube wall. The e o e, he op imum φ was anged om
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S. Kajikawa, H. Kawaguchi, T. Kuboki, I. Akasaka, Y. Te ashi a and M. Akiyama
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Figu e 5: E ec o ube ini ial hickness 0 on
maximum la ing a io E _max (Plug hal angle φ=12°)
Figu e 6: E ec o plug hal angle φ on maximum
la ing a io E _max (Tube ini ial hickness 0=2 mm)
24 o 36°.
The expe imen al esul s ag eed wi h he FEM esul o he ic ion coe icien µ=0.3 when
he plug hal angle φ was 12~24°, bu he expe imen al esul s we e anged om 0.1 o 0.2 o
μ in FEM esul s when φ was 36~48°. I was conside ed ha he lub ica ion s a e changed by
φ in he expe imen . Oil ilm, which is be ween he ube wall and he plug, is easy o be los
when he sliding leng h is long wi h he low φ in he expe imen . In addi ion, he ube wall
wa ed a he ape po ion unde he condi ion o high φ [7]. The wa ed ube wall did no
con ac o he plug and held he lub ican in he expe imen . The e o e, i was conside ed
ha µ which he expe imen al esul s ag eed wi h he FEM esul s dec eased wi h he
inc ease in φ. Base on he esul s as shown in Fig. 5 and 6, µ was se o 0.3 o he analysis
o he d awing p ocess, which is desc ibed in he nex sec ion, in o de o es ima e he
o ming limi in sa e y.
4 INVESTIGATION IN DRAWING PROCESS
4.1 D awing me hod and condi ions
Figu e 7 shows he schema ic diag am o he FEM model o he d awing p ocess. The plug
was d awn in o he ube, while one ube edge was ixed in he axial di ec ion. Expansion a io
E
d
, hickness educ ion a io γ and dimensional accu acy we e e alua ed. E
d
was de ined as he
ollowing equa ion.
Ed
=
di
−
di0
di0
(3)
whe e d
i
is he ube inne diame e a e he plug d awing, and d
i0
is he ini ial ube inne
diame e . γ was de ined as he ollowing equa ion.
γ
=
−
0
0
(4)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 10 20 30 40 50
Maximum la ing a io E _max
Hal angle o plug φ[°]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
012345
Maximum la ing a io E _max
Ini ial hickness
0
[mm]
μ=0.1 (FEM) μ=0.2 (FEM)
μ=0.3 (FEM)
μ=0.4 (FEM)
Expe imen
μ=0.1 (FEM)
μ=0.2 (FEM)
μ=0.3 (FEM) μ=0.4 (FEM)
Expe imen
φ=12°
0
=2mm
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S. Kajikawa, H. Kawaguchi, T. Kuboki, I. Akasaka, Y. Te ashi a and M. Akiyama
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Figu e 7: Schema ic diag am o FEM model o
d awing p ocess
Figu e 8: Appea ance o local hinning (Tube ini ial
hickness 0=2 mm, plug hal angle φ=18°, Plug
diame e dp=45 mm, plug co ne adius p=0 mm)
Table 2: Wo king condi ions in d awing p ocess
Tube
Tube ma e ial SUS304
Swi ’s equa ion o SUS304 σ=1275(εp+0.01)0.39
Ini ial diame e d0 [mm] 30
Ini ial hickness 0 [mm] 1, 2, 3, 4
Ini ial leng h l 0 [mm] 200
Elemen size Axial 1 mm/di ision
Radial 8 di isions
Plug
S aigh leng h lp [mm] 15
Hal angle φ [°] 6, 12, 18, 24, 30, 36
Diame e dp [mm] 30~47.5
Co ne adius p [mm] 0, 10, 20, 30
F ic ion coe icien μ 0.3
whe e is he hickness a e he plug d awing, and
0
is he ini ial hickness. The dimensional
accu acy was e alua ed by o e shoo δ, which means he di e ence be ween d
i
and d
p
. δ was
de ined as he ollowing equa ion.
δ
=
di
−
dp (5)
Table 2 shows he wo king condi ions in d awing p ocess. The ube ini ial hickness
0
, he
plug diame e d
p
, hal angle φ and co ne adius
p
we e changed a iously. When d
p
was oo
high in each
0
and φ, a local hinning occu ed a he ube edge, which is ixed in he axial
di ec ion, as shown in Figu e 8. Maximum expansion a io E
d_max
was de ined as he maximum
alue o he expansion a io E
d
when he plug was d awn wi hou he local hinning. E
d_max
was
sea ched by inc easing d
p
in he s ep o 0.5 mm un il he local hinning occu ed.
4.2 E ec o plug hal angle on expansion a io and hickness educ ion
Figu e 9 shows he e ec o he plug hal angle φ and he ube ini ial hickness
0
on
maximum expansion a io E
d_max
. E
d_max
inc eased wi h an inc ease in φ, and E
d_max
was highe
when φ was 18~30 °. Howe e , E
d_max
dec eased when φ was o e 30°. Fo ming limi was
conside ed o be de e mined by he d awing load P. Figu e 10 shows he e ec o φ on he
53
S. Kajikawa, H. Kawaguchi, T. Kuboki, I. Akasaka, Y. Te ashi a and M. Akiyama
7
d awing load P in each d
p
. P was highe unde he condi ion ha φ was oo low o high. In he
case ha φ was oo low, P became high due o he la ge ic ional o ce, which is de i ed om
he la ge con ac a ea a he plug ape po ion. In he case ha φ was oo high, P was highe
because bending/unbending de o ma ion became la ge by inc easing φ. Op imum φ, which
dec eases P, inc eased wi h he inc ease in d
p
, and he op imum φ was 24° when d
p
was 42 mm,
which was nea he o ming limi . This alue o φ was same as φ when E
d_max
was he highes
in Fig. 9. This esul sugges ed ha P should be dec eased by con olling φ app op ia ely o
imp o ing he o ming limi .
Figu e 11 shows he e ec o he plug hal angle φ and ube ini ial hickness
0
on maximum
hickness educ ion a io γ
max
. γ
max
is he hickness educ ion a io γ when he expansion a io
E
d
was he maximum E
d_max
. γ
max
inc eased d as ically wi h he inc ease in φ when φ was 6~18°,
Figu e 9: E ec o plug hal angle φ and ube ini ial
hickness 0 on maximum expansion a io Ed_max (Plug
co ne adius p=0 mm)
Figu e 10: E ec o plug hal angle φ and plug
diame e dp on d awing load P (Tube ini ial hickness
0=2 mm, plug co ne adius p=0 mm)
Figu e 11: E ec o plug hal angle φ and ube ini ial
hickness 0 on maximum hickness educ ion a io γmax
(Plug co ne adius
p
=0 mm)
Figu e 12: E ec o plug hal angle φ and plug
diame e dp on hickness educ ion a io γ (Tube ini ial
hickness
0
=2 mm, plug co ne adius
p
=0 mm)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50
Maximum expansion a io E
d_max
Hal angle o plug φ[°]
0
50
100
150
200
0 10 20 30 40 50
Load P[kN]
Hal angle o plug φ[°]
d
p
=42 mm
d
p
=38 mm
d
p
=34 mm
d
p
=30 mm
0
=1 mm
0
=2 mm
0
=3 mm
0
=4 mm
p
=0 mm
p
=0 mm
0
= 2 mm
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50
Maximum expansion a io E
d_max
Hal angle o plug φ[°]
0
50
100
150
200
0 10 20 30 40 50
Load P[kN]
Hal angle o plug φ[°]
d
p
=42 mm
d
p
=38 mm
d
p
=34 mm
d
p
=30 mm
0
=1 mm
0
=2 mm
0
=3 mm
0
=4 mm
p
=0 mm
p
=0 mm
0
= 2 mm
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S. Kajikawa, H. Kawaguchi, T. Kuboki, I. Akasaka, Y. Te ashi a and M. Akiyama
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Figu e 13: E ec o plug hal angle φ on dis ibu ion
o hickness educ ion a io γ (Tube ini ial hickness
0=2 mm, plug diame e dp=42 mm, plug co ne
adius p=0 mm)
Figu e 14: Dis ibu ion o s ess in logi udinal
di ec ion σφ (Tube ini ial hickness 0=2 mm, plug
diame e dp=42 mm, plug co ne adius p=0 mm)
and γ
max
inc eased g adually wi h he inc ease in φ when φ was o e 18°, al hough E
d_max
dec eased wi h he inc ease in φ when φ was o e 24°. This is because γ inc eased by inc easing
φ in each plug diame e d
p
, as shown in Figu e 12.
Figu e 13 shows he e ec o he plug hal angle φ on he dis ibu ion o he hickness
educ ion a io γ in he case ha he plug diame e d
p
was 42 mm. γ inc eased g adually wi h
he ube expanding a he plug ape po ion, and γ inc eased d as ically a he po ion nea he
plug co ne . This d as ic hickness educ ion occu ed due o he axial s e ching wi h he
bending a he plug co ne as shown in Figu e 14. The s ess in he longi udinal di ec ion σ
φ
is
la ge a he plug co ne . The e o e, he hickness d as ically dec eased by s e ching he ube
wall in he hoop and he axial di ec ion. In addi ion, γ inc eased by inc easing φ, because σ
φ
inc eased wi h he inc ease in φ as shown in Fig. 14 (a) and (b). This esul means ha he
hickness could be con olled by se ing φ app op ia ely.
4.3 E ec o plug co ne adius on dimensional accu acy
Figu e 15 shows he e ec o he plug hal angle φ and he expansion a io E
d
on he
o e shoo δ in he case ha he ube ini ial hickness
0
was 2 mm, and he plug co ne adius
p
was ze o. δ dec eased wi h he inc ease in E
d
, bu δ inc eased wi h he inc ease in φ. Figu e 16
shows he ypical appea ances o he ube du ing he plug d awing. When φ and E
d
we e small,
δ was small as shown in Fig. 16 (a). When φ was la ge wi h small E
d
, δ became la ge because
he bending angle was la ge as shown in Fig. 16 (b). When φ was la ge wi h la ge E
d
, δ became
small because he ube wall was s e ched s ongly in he axial di ec ion due o he la ge d awing
load P, and i o he plug su ace as shown in Fig. 16 (c).
I was conside ed o be e ec i e o apply he plug wi h co ne adius
p
o imp o ing he
dimensional accu acy by p e en ing he o e shoo δ. Figu e 17 shows he ube shape du ing he
d awing in he cases ha he plug wi h and wi hou
p
we e used. The ube wall was ben wi h
la ge bending adius, and i o he plug su ace by using he plug wi h
p
as shown in Fig. 17
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S. Kajikawa, H. Kawaguchi, T. Kuboki, I. Akasaka, Y. Te ashi a and M. Akiyama
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Figu e 15: E ec o plug hal angle φ and expansion
a io Ed on o e shoo δ (Tube ini ial hickness 0=2
mm, plug co ne adius p=0 mm)
Figu e 16: Appea ance o ube wall du ing d awing
wi h diame e expansion (Tube ini ial hickness 0=2
mm, plug co ne adius p=0 mm)
(b). The e o e, δ dec eased by applying la ge
p
o he plug. Figu e 18 shows he e ec o
p
on
δ in he case ha he plug hal angle φ was 18°. δ dec eased wi h an inc ease in
p
, and δ was
anged a ound ze o by se ing
p
o 20 mm. Howe e , δ was nega i e alue unde he condi ion
ha E
d
was la ge, such as E
d
=0.61. This is because he ube wall sh ink in he hoop di ec ion
a e he plug passing, while he ube wall was s e ched s ongly in axial di ec ion due o he
la ge d awing load. Figu e 19 shows he e ec o
p
on δ in he case ha φ was 18, 24 and 30°,
which was he op imum φ o imp o ing he o ming limi as shown in Fig. 9. I was possible
o p e en δ by se ing
p
o 20 mm ega dless o φ.
Figu e 17: Appea ance o ube wall du ing d awing
wi h diame e expansion (Tube ini ial hickness 0=2
mm, plug hal angle φ=18°)
Figu e 18: E ec o plug co ne adius p and
expansion a io Ed on o e shoo δ (Tube ini ial
hickness 0=2 mm, plug hal angle φ=18°)
56
