micromachines
Article
Ultrasonic-Assisted Incremental Microforming of
Thin Shell Pyramids of Metallic Foil
Toshiyuki Obikawa *,† and Mamoru Hayashi ‡
Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan; [email protected]
* Correspondence: [email protected]; Tel.: +81-3-5284-5902
† Current address: Center for Manufacturing Science and Technology, Tokyo Denki University,
Tokyo 120-8551, Japan.
‡ Current address: Nidec Center for Industrial Science, Nidec Corporation, Kawasaki 212-0032, Japan.
Academic Editor: Guido Tosello
Received: 28 February 2017; Accepted: 25 April 2017; Published: 3 May 2017
Abstract: Single point incremental forming is used for rapid prototyping of sheet metal parts. This
forming technology was applied to the fabrication of thin shell micropyramids of aluminum, stainless
steel, and titanium foils. A single point tool used had a tip radius of 0.1 mm or 0.01 mm. An ultrasonic
spindle with axial vibration was implemented for improving the shape accuracy of micropyramids
formed on 5–12 micrometers-thick aluminum, stainless steel, and titanium foils. The formability
was also investigated by comparing the forming limits of micropyramids of aluminum foil formed
with and without ultrasonic vibration. The shapes of pyramids incrementally formed were truncated
pyramids, twisted pyramids, stepwise pyramids, and star pyramids about 1 mm in size. A much
smaller truncated pyramid was formed only for titanium foil for qualitative investigation of the
size reduction on forming accuracy. It was found that the ultrasonic vibration improved the shape
accuracy of the formed pyramids. In addition, laser heating increased the forming limit of aluminum
foil and it is more effective when both the ultrasonic vibration and laser heating are applied.
Keywords: incremental microforming; ultrasonic spindle; shin shell micropyramid; metallic foil;
forming limit; shape accuracy
1. Introduction
Functional miniaturized structures of various materials will be widely applied to sensors,
filters, biotesters, bioscaffold, etc. in the near future. For this purpose, efficient microprocessing
technologies with high accuracy and high surface quality are required to meet the demand for their
production. Microcutting [1], micro-laser-machining [2], micro-electric discharge machining [3,4], and
microforming [5] have been intensively studied, and recently, micro-additive-manufacturing combined
with other microprocessing [6] is more and more important in tailor-made manufacturing or high-mix
low-volume production of complex parts.
Incremental forming with a single point tool is regarded as a rapid prototyping process for
sheet metal forming because no die is needed and parts of free-form surfaces can be fabricated
incrementally [7]. The forming limit is much larger for this technology than for other forming
methods [8]. Therefore, this technology can be applied to the fabrication of various shapes of sheet
metal parts [9]. It also can be applied to microforming of the miniature shell structures of aluminium,
gold, and stainless steel foils [10–14]. The preparation of backing plates of various shapes, which are
used as a support in ordinary incremental forming, is not easy for incremental forming of microparts.
For this reason, no backing plate is needed for the developed microforming technologies. However,
the accuracy of microshell structures formed without using a backing plate is not so high, and thus, it
should be improved without reducing the forming limit.
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microshell structures formed without using a backing plate is not so high, and thus, it should be
improved without reducing the forming limit.
thispaper,
paper,ultrasonic
ultrasonic
assisted
incremental
microforming
technology
has developed
been developed
In this
assisted
incremental
microforming
technology
has been
using
using
an ultrasonic
spindle
for improving
theofaccuracy
ofstructures
microshell
aluminium,
an
ultrasonic
spindle for
improving
the accuracy
microshell
of structures
aluminium,ofstainless
steel,
stainless
steel,
and
titanium
foils.
Laser
heating
was
also
applied
to
the
ultrasonic
assisted
and titanium foils. Laser heating was also applied to the ultrasonic assisted incremental microforming
incremental
microforming
for softening
and increasing
formability
of aluminum
under
for
softening and
increasing formability
of aluminum
foil under
deformation.
The formingfoil
limit
and
deformation.
The forming
limit and forming
accuracy of micropyramids
were investigated
the
forming
accuracy
of micropyramids
were investigated
under the conditions
of with andunder
without
conditions
of
with
and
without
ultrasonic
vibration
and
laser
heating.
Only
for
a
foil
of
titanium—a
ultrasonic vibration and laser heating. Only for a foil of titanium—a difficult-to-work material—a
difficult-to-work
in a sizeunder
of 283 the
μm conditions
was also formed
under the
conditions
micropyramid
inmaterial—a
a size of 283micropyramid
µm was also formed
of ultrasonic
vibration
for
of
ultrasonic
vibration
for
qualitatively
investigating
the
size
reduction
on
forming
accuracy.
qualitatively investigating the size reduction on forming accuracy.
2. Materials and Methods
An incremental microforming machine with an ultrasonic spindle is shown in Figure
Figure 1.
1. It is
placed on a vibration-free
vibration-free table
table for
for insulating
insulatingexternal
externaldisturbances.
disturbances.ItItisiscomposed
composedofofanan
x-y
table,
x-y
table,
z
zstage,
stage,ultrasonic
ultrasonicspindle
spindlewith
witha aLangevin
Langevinultrasonic
ultrasonictransducer,
transducer,forming
formingtool,
tool, blank
blank holder,
holder, base,
base,
column, and laser source and its optical system. An ordinary motor spindle used in the original and
improved forming machines [10–13] has been replaced with an ultrasonic spindle and laser source
and its optical system has been newly
newly installed.
installed. The ultrasonic spindle causes vibration in the axial
direction of the
the spindle.
spindle.The
Thevibration
vibrationfrequency
frequencyis is
42.5
kHz
and
amplitude
is set
to 0.5
be μm,
0.5 µm,
42.5
kHz
and
its its
amplitude
is set
to be
the
the
minimum
amplitude
the spindle.
x-y
table
and are
z-stage
are controlled
with acomputer
personal
minimum
amplitude
of theofspindle.
The x-yThe
table
and
z-stage
controlled
with a personal
computer
numerically.
Their resolutions
motion
µm, is
which
small enough
to fabricate
a
numerically.
Their resolutions
of motionofare
0.01 are
μm,0.01
which
smallisenough
to fabricate
a shell
shell
structure
the order
ofmillimeter.
one millimeter.
structure
of theoforder
of one
Figure 1.
1. Desktop
machine.
Figure
Desktop microforming
microforming machine.
Aluminum foil of type 8021 used for the experiments is 6.5 and 12 μm-thick, while stainless steel
Aluminum
of type 8021
for the
is The
6.5 and
µm-thick,
while stainless
steel
foil of type 304 isfoil
8 μm-thick
and used
titanium
foilexperiments
is 5 μm-thick.
802112foil
has a chemical
composition
foil
of
type
304
is
8
µm-thick
and
titanium
foil
is
5
µm-thick.
The
8021
foil
has
a
chemical
composition
listed in Table 1 and a crystal grain size of 5–10 μm [15]. The elongation of metallic foils decreases
listed
in Table 1 and
a crystalIt grain
sizefive
of 5–10
µm [15].
The
elongation
of metallic
decreases
with
with decreasing
thickness.
is about
percent
for the
aluminum
foils
[15] andfoils
about
one percent
decreasing
It blank
is about
fiveispercent
the side
aluminum
foils [15]
aboutand
oneO-ring,
percentand
for
for stainlessthickness.
foil [16]. A
sheet
put on for
matte
up between
the and
tensioner
stainless
foil
[16].
A
blank
sheet
is
put
on
matte
side
up
between
the
tensioner
and
O-ring,
and
then,
then, it was clamped in a blank holder as shown in Figure 2. The holder can apply an appropriate size
it
clamped
in a blank
holderthe
as shown
Figure 2. and
The O-ring
holder[10–12].
can apply
anmethod
appropriate
size of
ofwas
tension
to a blank
by adjusting
sizes ofin
a tensioner
This
for applying
tension
to
a
blank
by
adjusting
the
sizes
of
a
tensioner
and
O-ring
[10–12].
This
method
for
applying
tension to a blank was also adopted in reference [14]. As described elsewhere [10–12] in details, no
tension
a blank
was also
adopted
in reference
[14]. As described
[10–12]
details, no
backing to
plate
supporting
a blank
is used
because miniaturization
of a elsewhere
backing plate
is notineasy.
backing plate supporting a blank is used because miniaturization of a backing plate is not easy.
Table 1. Chemical composition of 8021 aluminum foil [wt %].
Si
<0.15
Fe
>1.2, <1.7
Cu
<0.05
Mn
<0.05
Mg
<0.05
Zn
<0.05
Others
<0.05
Al
Remainder
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Table 1. Chemical composition of 8021 aluminum foil [wt %].
Si
Fe
Micromachines
8, 142
Micromachines2017,
2017,
<0.158, 142 >1.2, <1.7
Cu
Mn
Mg
Zn
Others
Al
<0.05
<0.05
<0.05
<0.05
<0.05
Remainder
33ofof10
10
AAsingle
singlepoint
pointforming
formingtool
toolof
ofultra-fine
ultra-finegrain
graincemented
cementedcarbide
carbidewith
withaatip
tipradius
radiusof
ofRR==100
100μm
μm
A
single
point
forming
tool
of
ultra-fine
grain
cemented
carbide
with
a
tip
radius
of
R
=
100
µm
or
10
μm
is
used
in
this
study
(Figure
3).
Before
starting
microforming,
z-position
of
the
top
surface
or 10 μm is used in this study (Figure 3). Before starting microforming, z-position of the top surface
or
µm is
used
in this study
(Figureby
3).
Before
starting
microforming,
z-position
ofblank.
the top
surface
of
blank
was
determined
accurately
the
between
tool
n-propyl
ofaa10
blank
was
determined
accurately
bydetecting
detecting
thecontact
contact
betweenthe
the
tooland
and
blank.
n-propyl
of
a blank
wasas
determined
byadhesion
detecting
the abrasion
contact
between
and blank.
n-propyl
alcohol
isisused
for
between
the
forming
tool
blank.
alcohol
used
asaalubricant
lubricantaccurately
foravoiding
avoiding
adhesionand
and
abrasion
betweenthe
thetool
forming
tooland
and
blank.
alcohol
is
used
as
a
lubricant
for
avoiding
adhesion
and
abrasion
between
the
forming
tool
and
blank.
High
speed
rotation
of
the
tool
generates
the
hydrodynamic
pressure
between
the
rotating
tool
and
High speed rotation of the tool generates the hydrodynamic pressure between the rotating tool
and
High
speed
rotation
of
the
tool
generates
the
hydrodynamic
pressure
between
the
rotating
tool
and
blank
blankbeing
beingformed.
formed.Under
Underthis
thiscondition,
condition,the
thealcohol
alcoholmay
maypenetrate
penetrateinto
intothe
theinterface
interfacebetween
betweenthem
them
being formed.
ifblank
stress
low.
ifthe
thecontact
contact
stressisisUnder
low. this condition, the alcohol may penetrate into the interface between them
if the contact stress is low.
ddt t
Figure2.2.
2.Blank
Blankholder
holderand
andtensioner.
tensioner.
Figure
Figure
Blank
holder
and
tensioner.
200
200μm
μm
(a)
(a)
(b)
(b)
Figure
μm.
Figure3.
3.Microtool
Microtoolfor
forincremental
incrementalmicroforming:
microforming:(a)
(a)RR
R===100
100μm;
μm;(b)
(b)RR
R==
=10
10
Figure
3.
Microtool
for
incremental
microforming:
(a)
100
µm;
(b)
10 μm.
µm.
Incremental
Incrementalmicroforming
microformingprocess
processof
ofaatriangular
triangularpyramid,
pyramid,for
forexample,
example,isisshown
shownin
inFigure
Figure4,4,
Incremental
microforming
process ofcircle
a triangular
pyramid,
for example,
isapex
shown
in Figure
4,
where
D
is
the
diameter
of
a
circumscribed
of
a
base
of
a
pyramid,
α
is
a
half
angle
where D is the diameter of a circumscribed circle of a base of a pyramid, α is a half apex angledefined
defined
where
D is the diameter
of a circumscribed
circle of a through
base of a pyramid,
α is a halfapex
apex angledefined
defined
as
asan
anangle
anglebetween
betweenaalateral
lateraledge
edgeand
andaavertical
verticalline
line throughan
anapex,
apex,θθisisaahalf
half apexangle
angle defined
as
an
angle
between
a
lateral
edge
and
a
vertical
line
through
an
apex,
θ
is
a
half
apex
angle
defined
as
as
asan
anangle
anglebetween
betweenaatriangular
triangularlateral
lateralface
faceand
andthe
thevertical
verticalline,
line,ttisisthe
thethickness
thicknessof
ofaablank,
blank,ωωisisthe
the
an
angle
between
a
triangular
lateral
face
and
the
vertical
line,
t
is
the
thickness
of
a
blank,
ω
is
the
tool
toolrotational
rotationalspeed,
speed,and
andΔz
Δzisisthe
theaxial
axialfeed
feedper
peraaplanar
planartool
toolpath.
path.The
Theside
sidelength
lengthof
ofaatriangular
triangular
tool
rotational
speed,
and
∆z
is
the
axial
feed
per
a
planar
tool
path.
The
side
length
of
a triangular
tool
toolpath
pathon
onaaplane
planeshrinks
shrinksstep
stepby
bystep.
step.The
Thetool
toolrotational
rotationalspeed
speedωωand
andtable
tablespeed
speedvvt twere
wereset
setto
to
tool
path
on−1−1aand
plane
shrinks
step by step. except
The tool
rotational
speed
ω
and table
speed
vtfor
were
set to be
−1−1and
be
5000
min
200
μm/s,
respectively,
that
ω
=
10,000
min
v
t
=
150
μm/s
a
titanium
be 5000 min and 200 μm/s, respectively, except that ω = 10,000 min
and vt = 150 μm/s for a titanium
5000 min−1 and
200 µm/s,μm.
respectively,
except
that ω5=and
10,000 μm
min−1 and
vt = 12
150 µm/s foraluminum
a titanium
micropyramid
micropyramidof
ofDD==283
283 μm.The
Theaxial
axialfeed
feedΔz
Δzwas
was 5 and12
12 μmfor
for6.5
6.5and
and 12μm-thick
μm-thick aluminum
micropyramid
of D = 283
µm. The axial
feed ∆z wasfoil,
5 and 122µm
for 6.5 for
and 12 µm-thick
aluminum
foils,
foils,respectively,
respectively,55μm
μmfor
for88μm-thick
μm-thickstainless
stainlesssteel
steel foil,and
and 2and
and11μm
μm fortitanium
titaniumpyramids
pyramidsof
ofDD
foils,
respectively,
5
µm
for
8
µm-thick
stainless
steel
foil,
and
2
and
1
µm
for
titanium
pyramids
of
==1.41
mm
and
D
=
283
μm,
respectively.
When
the
forming
was
conducted
under
the
condition
1.41 mm and D = 283 μm, respectively. When the forming was conducted under the conditionof
of
D = 1.41
mm and forming
D = 283 µm, respectively.
When the forming
wastop
conducted
under the condition
of
laser
laserheating,
heating,the
the formingarea
areaof
ofthe
thefoil
foilwas
wasirradiated
irradiatedfrom
fromthe
the topof
ofaapyramid
pyramid(from
(fromthe
thebelow
below
laser
heating, the forming
area of the foil was
irradiated
fromlaser
the top of awas
pyramid (from
the below of
of
ofaapyramid)
pyramid)using
usingaasemiconductor
semiconductorlaser
laserof
of130
130mW;
mW;the
the laserbeam
beam wasreflected
reflectedusing
usingaaprism
prism
a
pyramid)
using
a
semiconductor
laser
of
130
mW;
the
laser
beam
was
reflected
using
a
prism
under
under
the
blank
holder.
under the blank holder.
the blank holder.
Micromachines 2017, 8, 142
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Y
Y X
Δy
X
Δy
Δz
Z
D
Δz
Zh
D
ω
h
ω
θ
θ
t
α
t
Figure 4. Schematic diagram of tool path and α
foil deformation during forming of a triangular pyramid.
Figure 4. Schematic diagram of tool path and foil deformation during forming of a triangular pyramid.
Figure 4. Schematic
diagram
tool
pathpyramid
and foil deformation
during
of a triangular
pyramid.
The
faces
ofofa of
square
elongates
from
h0 forming
to
h1 by
incremental
The triangular
triangularlateral
lateral
faces
a square
pyramid
elongates
from
h0single
to h1point
by single
point
forming
as
shown
in
Figure
5.
Its
elongation
e
in
percent
is
given
by
incremental forming as shown in Figure 5. Its elongation e in percent is given by
The triangular lateral faces of a square pyramid elongates from h0 to h1 by single point
=Figure
100(h
15.
/h00Its
− 1)
== 100(cosec
−−1)1) is given by
(1)
incremental forming as showne in
elongation
e inθθpercent
=e 100(h
−
1)
100(cosec
(1)
1 /h
while the logarithmic strain ε corresponding
to0 −the
e = 100(h1/h
1) elongation
= 100(coseceθis− 1)
(1)
while the logarithmic strain ε corresponding to the elongation e is
ε = ln(h1/h
= ln(cosec
θ) e is
(2)
while the logarithmic strain ε corresponding
to0)the
elongation
ε = ln(h1 /h0 ) = ln(cosec θ)
(2)
Both the elongation and strain increase
with
ε = ln(h
1/h0decreasing
) = ln(cosec half
θ) apex angle. Equations (1) and (2)
(2)
are applied
truncatedand
pyramids
with thewith
same
half apex half
angle
θ. angle. Equations (1) and (2) are
Both
thefor
elongation
strain
increase
decreasing
apex
Both
the
elongation and
strain
increase with
decreasing half
apex angle. Equations (1) and (2)
applied
for
truncated
pyramids
with
the
same
half
apex
angle
θ.
are applied for truncated pyramids with the same half apex angle θ.
(a)
(b)
(c)
(d)
Figure
(c) formed
(a) 5. Forming of a square
(b) pyramid: (a) square blank
(c)to be formed; (b) tool path; (d)
pyramid; (d) development view of a square pyramid.
Figure
Formingofofa square
a square
pyramid:(a)(a)square
squareblank
blanktoto
formed;
tool
path;
formed
Figure
5. 5.Forming
pyramid:
bebe
formed;
(b)(b)
tool
path;
(c)(c)
formed
pyramid;
(d)
development
view
a square
pyramid.
pyramid;
development
view
of of
a square
pyramid.
3. Results
and(d)Discussion
The influence
of ultrasonic vibration on the forming limit of a truncated pyramid of 6.5 μm-thick
Results
and
Discussion
3. 3.
Results
and
Discussion
aluminum foil is shown in Figure 6, whereas, those of ultrasonic vibration and laser heating on the
The
influence
ultrasonic
vibration
forming
limit
a truncated
pyramid of
μm-thick
The
influence
ofof
ultrasonic
vibration
onon
thethe
forming
limit
ofof
a truncated
6.56.5
µm-thick
forming
limit
is shown
in Figure
7. The diameter
of a circumscribed
circle ofpyramid
a squareofpyramid
base
aluminum
foil
is
shown
in
Figure
6,
whereas,
those
of
ultrasonic
vibration
and
laser
heating
on
the
aluminum
foil
is
shown
in
Figure
6,
whereas,
those
of
ultrasonic
vibration
and
laser
heating
on
the
D was 1.41 mm. Forming conditions of with and without ultrasonic vibration are denoted as V and
forming
limit
shown
Figure
7.
The
diameter
a circumscribed
circle
of square
a square
pyramid
base
forming
limit
is is
shown
inin
Figure
7. and
The
diameter
ofof
aheating
circumscribed
circle
base
NV, respectively
and those
of with
without
laser
are denoted
asofHaand
NH,pyramid
respectively.
D
was
1.41
mm.
Forming
conditions
of
with
and
without
ultrasonic
vibration
are
denoted
as
V
and
D
mm. the
Forming
of angle
with and
without
ultrasonic
vibration
are denoted
as V
and
Inwas
these1.41
figures,
valuesconditions
of half apex
θ and
corresponding
strain
ε are written
in rows
above
NV,
respectively
and
those
of
with
and
without
laser
heating
are
denoted
as
H
and
NH,
respectively.
NV,
respectively
andtop
those
of with
and without
laser
heating
as Hstep
andby
NH,
respectively.
micrographs
of the
views
of formed
pyramids.
The
value are
of θdenoted
is changed
step
so that the
In
these
figures,
the
values
of
half
apex
angle
θ
and
corresponding
strain
ε
are
written
in
rows
above
In
these
the values
of 0.05.
half apex angle θ and corresponding strain ε are written in rows
above
value
of figures,
ε increases
by about
micrographs of the top views of formed pyramids. The value of θ is changed step by step so that the
value of ε increases by about 0.05.
Micromachines 2017, 8, 142
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It is seen in Figure 6 that square pyramids of θ = 39.5° were formed without cracks under the
It is seen in Figure 6 that square pyramids of θ = 39.5° were formed without cracks under the
conditions of with and without ultrasonic vibration, but cracks grew especially along the lateral edges
conditions of with and without ultrasonic vibration, but cracks grew especially along the lateral edges
of pyramids of θ = 37.4° formed under both the conditions. Thus, the forming limit εc was 0.45 for the
of pyramids of θ = 37.4° formed under both the conditions. Thus, the forming limit εc was 0.45 for the
condition
of without
heating and the ultrasonic vibration increased the forming limit marginally.
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condition of2017,
without
laser heating and the ultrasonic vibration increased the forming limit marginally.
The fact that the forming limit obtained above is less than those obtained in the previous research
The fact that the forming limit obtained above is less than those obtained in the previous research
works [11,12] is partly because n-propyl alcohol is a poor lubricant compared with pure water used
works [11,12]of
is the
partly
alcohol is aThe
poor
lubricant
withbypure
water
used
micrographs
top because
views
ofn-propyl
formed
pyramids.
value
of θ is compared
changed
step
stepfrom
so that
the
in
the previous research
and partly
because
the thickness
of aluminium
foil was
reduced
12 μm
in
the
previous
research
and
partly
because
the
thickness
of
aluminium
foil
was
reduced
from
12
μm
value
of
ε
increases
by
about
0.05.
to 6.5 μm.
to 6.5 μm.
θ
θ
ε
ε
NV & NH
NV & NH
39.5°
39.5°
0.45
0.45
37.4°
37.4°
0.50
0.50
V & NH
V & NH
1.0 mm
1.0 mm
Figure
6. Forming
limits
pyramids
Figure
limits for
for truncated
truncated
pyramids with
with and
and without
without ultrasonic
ultrasonic vibration
vibration (V
(V and
and NV)
NV)
Figure 6.
6. Forming
Forming limits
for
truncated pyramids
with
and
without
ultrasonic
vibration
(V
and
NV)
and
without
laser
heating
(NH).
and
without
laser
heating
(NH).
and without laser heating (NH).
θ
θ
ε
ε
NV & H
NV & H
37.4°
37.4°
0.50
0.50
35.2°
35.2°
0.55
0.55
32.9°
32.9°
0.61
0.61
30.0°
30.0°
0.69
0.69
V&H
V&H
θ
θ
ε
ε
V&H
V&H
Pin hole
Pin hole
1.0 mm
1.0 mm
Figure 7. Forming limits for truncated pyramids with and without ultrasonic vibration (V and NV)
and with laser heating (H).
Micromachines 2017, 8, 142
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It is seen in Figure 6 that square pyramids of θ = 39.5◦ were formed without cracks under the
conditions of with and without ultrasonic vibration, but cracks grew especially along the lateral edges
Micromachines 2017, 8, 142
6 of 10
of pyramids of θ = 37.4◦ formed under both the conditions. Thus, the forming limit εc was 0.45 for the
condition
of without laser heating and the ultrasonic vibration increased the forming limit marginally.
Figure 7. Forming limits for truncated pyramids with and without ultrasonic vibration (V and NV)
The fact
that
limit obtained above is less than those obtained in the previous research
and with the
laserforming
heating (H).
works [11,12] is partly because n-propyl alcohol is a poor lubricant compared with pure water used in
the previous
research
and
partly itbecause
thefrom
thickness
from
12 µm to
In the case
of laser
heating,
is found
Figureof7 aluminium
that εc was foil
0.55was
andreduced
0.50 for the
conditions
6.5
µm. and without ultrasonic vibration, respectively. This indicates that the laser heating can
of with
In the
of laser
heating,
is found from
Figure
that εceffective
was 0.55when
and 0.50
the conditions
of
increase
thecase
forming
limit
of theitaluminum
foil and
it is7 more
the for
ultrasonic
vibration
with
and
without
ultrasonic
vibration,
respectively.
This
indicates
that
the
laser
heating
can
increase
is applied. Because only a pinhole was found on a pyramid of θ = 32.9° under the conditions of with
the
limitvibration
of the aluminum
foilheating,
and it isoptimization
more effective
the ultrasonic
vibration
is applied.
bothforming
ultrasonic
and laser
ofwhen
forming
parameters
may increase
the
◦ under the conditions of with both
Because
only
a
pinhole
was
found
on
a
pyramid
of
θ
=
32.9
forming limit under these conditions. It should be noted that elongation for θ = 35.2°, which is
ultrasonic
and
laser
heating,(1),
optimization
of forming
mayof
increase
theobtained
forming
calculated vibration
to be 73.4%
from
Equation
is more than
10 times parameters
as large as that
about 5%
◦
limit
undertest.
these conditions. It should be noted that elongation for θ = 35.2 , which is calculated to be
for tensile
73.4%Infrom
Equation
is more than
10confirmed
times as large
that of
5% obtained
foron
tensile
test.
addition
to the(1),
formability,
it is
that as
almost
allabout
the cracks
appeared
the lateral
the formability,
it is
that almost
all the
cracks appeared
on[13],
the lateral
edgesInofaddition
formed to
pyramids.
This fact
is confirmed
consistent with
the results
obtained
in reference
that a
edges
of
formed
pyramids.
This
fact
is
consistent
with
the
results
obtained
in
reference
[13],
that
crack nucleated on a pyramid edge in the microforming of aluminum foil, whereas it nucleated on aa
crack
nucleated
on aface
pyramid
in the microforming
aluminum
foil, whereas it nucleated on a
triangular
pyramid
in the edge
microforming
of stainless of
steel
foil.
triangular
pyramid
face in the
microforming
of stainless
steel foil.
The effect
of ultrasonic
vibration
assistance
on the shape
accuracy in incremental microforming
The
effect
of
ultrasonic
vibration
assistance
on
the
shape
accuracy
in incremental
microforming
was investigated by forming a twisted pyramid of 6.5 μm-thick aluminum
foil and a star
pyramid of
was
investigated
by forming
a twisted
pyramid
of 6.5 µm-thick
aluminum
and1.41
a star
pyramid
12 μm-thick
aluminum
foil with
and without
ultrasonic
vibration.
Diameter foil
D was
mm
for the
of
12 µm-thick
aluminum
andstar
without
ultrasonic
D was
for
twisted
pyramid
and 1.60 foil
mmwith
for the
pyramid.
Figurevibration.
8 shows Diameter
the top views
of1.41
the mm
twisted
the
twisted
pyramid
and
1.60
mm
for
the
star
pyramid.
Figure
8
shows
the
top
views
of
the
twisted
pyramids incrementally formed. The surfaces and edges of the pyramid made by ultrasonic assisted
pyramids
incrementally
Theand
surfaces
and edges
the pyramid
mademicroforming
by ultrasonic without
assisted
microforming
are muchformed.
smoother
not wavier
thanofthose
by ordinary
microforming
are
much
smoother
and
not
wavier
than
those
by
ordinary
microforming
without
ultrasonic vibration. The top and bottom views of star pyramids formed with and without ultrasonic
ultrasonic
vibration.
The
top and
bottom
views of starItpyramids
formed
with
and
without
ultrasonic
vibration are
shown in
Figures
9 and
10, respectively.
is seen that
not only
the
convex
parts
but also
vibration
areparts
shown
Figureswell,
9 and
10, respectively.
It is seen According
that not only
the top
convex
parts
butdoes
also
the concave
areinformed
much
better than expected.
to the
views,
there
the
concave
parts
are
formed
well,
much
better
than
expected.
According
to
the
top
views,
there
does
not seem to be a significant difference in the shape accuracy between the two pyramids formed with
not
to be
a significant
difference
in the shape
accuracyfrom
between
the twoviews
pyramids
with
andseem
without
ultrasonic
vibration.
However,
it is confirmed
the bottom
and formed
more clearly
and
ultrasonic
vibration.
it is confirmed
from of
thethe
bottom
viewsnear
and the
more
clearly
fromwithout
the magnified
center
of the However,
bottom views
that the traces
tool path
center
of
from
the
magnified
center
of
the
bottom
views
that
the
traces
of
the
tool
path
near
the
center
of
pyramid
pyramid on the bottom surface is a nearly regular pentagon for ultrasonic assisted microforming,
on
the bottom
surface
is a nearly
regular
pentagon
for ultrasonic
assisted
microforming,
whilst
is
whilst
it is heavily
distorted
for the
ordinary
microforming.
Results
in Figures
8–10 prove
that itthe
heavily
distorted
for
the
ordinary
microforming.
Results
in
Figures
8–10
prove
that
the
ultrasonic
ultrasonic vibration can improve the shape accuracy of the formed pyramids. Other pyramids formed
vibration
can improve
the shapefoil
accuracy
of the formedsunflower
pyramids.ofOther
pyramids
formed
in this
in this study
using aluminum
are a pyramid-like
D = 1.72
mm and
a stepwise
study
using
aluminum
foilshown
are a pyramid-like
D = 1.72
mm
and ultrasonic
a stepwiseincremental
pyramid of
pyramid
of D
= 1.41 mm
in Figure 11. sunflower
They wereofformed
well
using
D
=
1.41
mm
shown
in
Figure
11.
They
were
formed
well
using
ultrasonic
incremental
microforming.
microforming.
(a)
(b)
Figure 8.
views
of twisted
pyramids
formed:
(a) with(a)ultrasonic
vibration;vibration;
(b) without
Figure
8.Top
Top
views
of twisted
pyramids
formed:
with ultrasonic
(b)ultrasonic
without
vibration.
ultrasonic vibration.
Micromachines 2017, 8, 142
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7 of 10
(a)
(a)
(a)
(b)
(b)
(b)
(c)
(c)
(c)
Figure 9. Top and bottom views of a star pyramid formed with ultrasonic vibration: (a) top view;
Figure 9. Top and bottom views of a star pyramid formed with ultrasonic vibration: (a) top view;
Figure
9.
and
bottom
views
ofofa astar
formed
ultrasonic vibration: (a) top view;
(b)
bottom
view;
(c)
magnified
center
part
of
bottom
view. with
Figure
9. Top
Top
and
views
starpyramid
pyramid
(b) bottom
view;
(c)bottom
magnified
center
part
of
bottom formed
view. with ultrasonic vibration: (a) top view;
(b)
bottom
view;
(c)
magnified
center
part
of
bottom
view.
(b) bottom view; (c) magnified center part of bottom view.
(a)
(a)
(a)
(b)
(b)
(b)
(c)
(c)
(c)
Figure 10. Top and bottom views of a star pyramid formed without ultrasonic vibration: (a) top view;
Figure 10.
10. Top and
and bottom views
views of
formed without
ultrasonic vibration: (a) top
view;
Figure
of aa star
star pyramid
pyramid
top view;
view;
(b)
bottom Top
view; (c)bottom
magnified center
part
of bottomformed
view. without ultrasonic vibration: (a) top
(b) bottom
bottom view;
view; (c)
(c) magnified
magnified center
center part
part of
of bottom
bottom view.
view.
(b)
magnified center part of bottom view.
(a)
(a)
(a)
(b)
(b)
(b)
Figure
11.Other
Otherpyramids
pyramids
formed
by ultrasonic
incremental
microforming:
(a) like
pyramid
like
Figure
formed
by ultrasonic
incremental
microforming:
(a) pyramid
sunflower;
Figure 11.
11. Other
pyramids
formed
by ultrasonic
incremental
microforming:
(a) pyramid
like
Figure 11. (b)
Other
pyramids
formed by ultrasonic incremental microforming: (a) pyramid like
sunflower;
stepwise
pyramid.
(b)
stepwise
pyramid.
sunflower; (b) stepwise pyramid.
sunflower; (b) stepwise pyramid.
As described above, the ultrasonic vibration was effective in improving the shape accuracy of
As described
described above,
above, the
the ultrasonic
ultrasonic vibration
vibration was
was
effective in
in improving
improving the
the shape
shape accuracy
accuracy of
of
As
vibration
was effective
effective
in
described
above,
the
ultrasonic
improving
shape
of
ratherAscomplicated
pyramids
such as a twisted pyramid
and a star
pyramid,the
whilst
theaccuracy
ultrasonic
rather complicated
complicated pyramids
pyramids
such
as
a twisted
twisted pyramid
pyramid and
and aaa star
star pyramid,
pyramid, whilst
whilst the
the ultrasonic
ultrasonic
rather
pyramids such
such as
as a
rather
complicated
twisted
pyramid
and
star
pyramid,
whilst
the
ultrasonic
vibration
and laser heating were
not soaeffective
for truncated
pyramids.
In contrast,
they
were able
vibration
and
laser
heating
were
not
so
effective
for
truncated
pyramids.
In
contrast,
they
were
able
vibration
and laser
heating
were
not sosoeffective
for
pyramids.
InIn
contrast,
they were
able
to
vibration
heating
were
effective
fortruncated
truncated
pyramids.
contrast,
were
able
to
improveand
thelaser
shape
accuracy
of anot
truncated
pyramid
of 8 μm-thick
stainless
steel
foil, they
which
is much
to
improve
the
shape
accuracy
of
a
truncated
pyramid
of
8
μm-thick
stainless
steel
foil,
which
is
much
improve
the
shape
accuracy
of
a
truncated
pyramid
of
8
µm-thick
stainless
steel
foil,
which
is
much
to improve
accuracy
of a truncated
of of
8 μm-thick
which
is much
stiffer
than the
6.5 shape
μm-thick
aluminum
foil. Twopyramid
pyramids
stainless stainless
steel foilsteel
of Dfoil,
= 1.0
mm and
θ =◦
stiffer than
than 6.5
6.5µm-thick
μm-thickaluminum
aluminumfoil.
foil.Two
Twopyramids
pyramids
of
stainless
steel
foil
of=D
D1.0
= 1.0
1.0
mm
and
θ ==
stiffer
of of
stainless
steel
foilfoil
of D
mmmm
andand
θ = 45
stiffer
than
6.5
μm-thick
aluminum
foil.
Two
pyramids
stainless
steel
of
=
θ
45° were formed under NV and NH conditions and under V and H conditions. Their profiles
45°
were
formed
under
NV
and
NH
conditions
and
under
V
and
H
conditions.
Their
profiles
were
formed
underunder
NV and
NH conditions
and under
V and HVconditions.
Their profiles
measured
45° were
formed
NV
NH conditions
and
conditions.
profiles
measured
with a confocal
laserand
displacement
meter and
alongunder
line AB of
an H
attached
figureTheir
are shown
in
measured
with
a
confocal
laser
displacement
meter
along
line
AB
of
an
attached
figure
are
shown
in
with
a
confocal
laser
displacement
meter
along
line
AB
of
an
attached
figure
are
shown
in
Figure
12b,c.
measured
with
a
confocal
laser
displacement
meter
along
line
AB
of
an
attached
figure
are
shown
in
Figure 12b,c. It is seen that the line of lateral face is connected with the base line via a curved line
Figure
12b,c.
It
is
seen
that
the
line
of
lateral
face
is
connected
with
the
base
line
via
a
curved
line
It
is
seen
that
the
line
of
lateral
face
is
connected
with
the
base
line
via
a
curved
line
with
a
small
radius
Figure
12b,c.radius
It is seen
thatV the
of lateral face is connected with the base line via a curved line
with
a small
under
andline
H conditions.
with
a
small
radius
under
V
and
H
conditions.
under
V
and
H
conditions.
with a small radius under V and H conditions.
Micromachines 2017, 8, 142
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8 of 10
8 of 10
Figure
12. Profiles
of pyramids
of stainless
steel foil
under different
conditions: (a)
top view
of aa
Figure
Figure12.
12. Profiles
Profiles of
of pyramids
pyramids of
of stainless
stainless steel
steel foil
foilunder
underdifferent
differentconditions:
conditions: (a)
(a) top
top view
view of
of a
pyramid
formed
without
ultrasonic
vibration
and
heating;
(b)
surface
profile
along
AB
in
the
case
of
pyramid
pyramidformed
formedwithout
withoutultrasonic
ultrasonicvibration
vibrationand
andheating;
heating;(b)
(b)surface
surfaceprofile
profilealong
alongAB
ABin
inthe
thecase
caseof
of
NV
and
NH;
(c)
surface
profile
along
AB
in
the
case
of
V
and
H.
NV
NVand
andNH;
NH;(c)
(c)surface
surfaceprofile
profilealong
alongAB
ABininthe
thecase
caseofofVVand
andH.
H.
The forming accuracy was evaluated based on distance δ from point C to the pyramid profile as
The
Theforming
formingaccuracy
accuracywas
wasevaluated
evaluatedbased
basedon
ondistance
distanceδδfrom
frompoint
pointCCto
tothe
thepyramid
pyramidprofile
profileas
as
shown in Figure 13. The value of δ was 43 μm and 26 μm for NV and NH conditions and V and H
shown
shownin
inFigure
Figure13.
13. The
The value
value of
of δδwas
was43
43µm
μmand
and26
26µm
μmfor
forNV
NVand
andNH
NHconditions
conditionsand
andVVand
andH
H
conditions, respectively. The theoretical value of the distance δth for perfect forming is given by
conditions,
conditions,respectively.
respectively.The
Thetheoretical
theoreticalvalue
valueofofthe
thedistance
distanceδth
δthfor
forperfect
perfectforming
formingisisgiven
givenby
by
"s
 π − 2θ  #
δ th = R   1 + tan 22 2θ − 1
2 ππ−−2θ
δ th==RR  11++tan
tan   4  −−11 
δth



44
  
(3)
(3)
(3)
and hence, the forming error can be defined by δ − δth. Because the value of δth is calculated to be 8.2
and
defined by
by δδ −−δδthth
. Because
the
value
is calculated
to be
th calculated
andhence,
hence, the
the forming
forming error
error can
can be
be defined
. Because
the
value
ofof
δthδis
to be
8.2
μm for R = 100 μm and θ = 45°, the
ultrasonic vibration and laser heating reduced the forming error
8.2
= 100
and
45◦the
, theultrasonic
ultrasonicvibration
vibrationand
andlaser
laserheating
heating reduced
reduced the
μmµm
forfor
R =R100
μmµm
and
θ =θ =
45°,
the forming
forming error
error
by half. However, neither the ultrasonic vibration nor the laser heating increased the forming limit
by
byhalf.
half. However,
However,neither
neitherthe
theultrasonic
ultrasonicvibration
vibrationnor
northe
thelaser
laserheating
heatingincreased
increasedthe
theforming
forminglimit
limit
of a square pyramid of stainless steel foil: εc was 0.38 for (NV & NH) and (V & NH); it was slightly
of
ofaasquare
squarepyramid
pyramidof
ofstainless
stainlesssteel
steelfoil:
foil: εεcc was
was 0.38
0.38 for
for (NV
(NV &
&NH)
NH)and
and(V
(V&
&NH);
NH);ititwas
wasslightly
slightly
reduced to 0.35 for (NV & H) and (V & H). This is probably because it is difficult to heat the forming
reduced
reducedto
to0.35
0.35for
for(NV
(NV&&H)
H)and
and(V
(V&&H).
H).This
Thisisisprobably
probablybecause
becauseititisisdifficult
difficultto
toheat
heatthe
theforming
forming
area uniformly due to very low heat conductivity of stainless steel.
area
uniformly
due
to
very
low
heat
conductivity
of
stainless
steel.
area uniformly due to very low heat conductivity of stainless steel.
Figure 13. The forming accuracy based on distance δ from point C to the pyramid profile.
Figure
Figure13.
13. The
Theforming
formingaccuracy
accuracybased
basedon
ondistance
distanceδδfrom
frompoint
pointCCto
tothe
thepyramid
pyramidprofile.
profile.
Thin shell pyramids of titanium foil of D = 1.41 mm and θ = 50° formed with and without
◦ formed with
Thin shell
shell pyramids
pyramids of
of titanium
titanium foil
foil of
of DD == 1.41
1.41 mm
mm and
and θθ==50
50°
with and
and without
without
Thin
ultrasonic
vibration
are shown
in Figures 14
and 15, respectively.
It wasformed
seen that wrinkles
were
ultrasonic vibration
vibration are
are shown
shown in
in Figures
Figures 14
14and
and15,
15,respectively.
respectively. ItIt was
was seen
seen that
that wrinkles
wrinkles were
were
ultrasonic
caused
on the lateral faces
by incremental
microforming
when ultrasonic vibration
was not applied.
caused
on
the
lateral
faces
by
incremental
microforming
when
ultrasonic
vibration
was
not
applied.
caused
on the
lateral
faces
by incremental
microforming
was
noton
applied.
In
In
contrast,
they
almost
disappeared
and feed
marks of awhen
singleultrasonic
point toolvibration
were seen
only
the back
In contrast,
they
almost
disappeared
and
feed
marks
of
a singlepoint
pointtool
toolwere
wereseen
seenonly
onlyon
onthe
theback
back
contrast,
they
almost
disappeared
and
feed
marks
of
a
single
surface of a pyramid when ultrasonic vibration was applied. It should be noted that the ultrasonic
surfaceof
ofaapyramid
pyramidwhen
whenultrasonic
ultrasonicvibration
vibrationwas
wasapplied.
applied. ItItshould
should be notedthat
thatthe
theultrasonic
ultrasonic
surface
vibration
effectively removed
the wrinkles in a difficult
forming processbeofnoted
the twisted
pyramid in
vibration
effectively
removed
the
wrinkles
in
a
difficult
forming
process
of
the
twisted
pyramid
in
vibration
Figure
8 aseffectively
described removed
above. the wrinkles in a difficult forming process of the twisted pyramid in
Figure88as
asdescribed
describedabove.
above.
Figure
A truncated
micropyramid of D = 283 μm formed with ultrasonic vibration is shown in Figure
A truncated micropyramid of D = 283 μm formed with ultrasonic vibration is shown in Figure
16. Although the tool rotational speed ω was increased and table speed vt and axial feed Δz were
16. Although the tool rotational speed ω was increased and table speed vt and axial feed Δz were
decreased for forming a smaller pyramid, its shape accuracy was not good, and partially distorted. It
decreased for forming a smaller pyramid, its shape accuracy was not good, and partially distorted. It
Micromachines 2017, 8, 142
9 of 10
Micromachines 2017, 8, 142
Micromachines
2017, 8,micropyramid
142
A truncated
Micromachines 2017, 8, 142
9 of 10
9 of16.
10
of D = 283 µm formed with ultrasonic vibration is shown in Figure
9 of 10
Although
the
tool
rotational
speed
ω
was
increased
and
table
speed
v
and
axial
feed
∆z
were
decreased
is seen that the radius of lateral edges was much larger than that tof the forming tool and the feed
is seen
that athe
radiuspyramid,
of lateral
edges
was
muchwas
larger
than
that
the forming
tool It
and
the feed
for
forming
smaller
its
shapeof
accuracy
not
good,
andof
partially
distorted.
is seen
that
is
seen
that
radius
of back
lateral
edges
was
larger
than
that
of
theThe
forming
tool
and
the feed
marks
of
thethe
tool
on the
surface
themuch
pyramid
were
disturbed.
size of
a pyramid
was
marks
of
the
tool
on
the
back
surface
of
the
pyramid
were
disturbed.
The
size
of
a
pyramid
was
the
radius
of
lateral
edges
was
much
larger
than
that
of
the
forming
tool
and
the
feed
marks
of
the
tool
marks
of by
thea tool
on of
thefive,
back
surface
of thickness
the pyramid
disturbed.Hence,
The size
a pyramid
was
reduced
factor
but
the foil
waswere
not reduced.
theofbending
stiffness
reduced
by surface
a factorofofthe
five,
but the
foildisturbed.
thickness The
wassize
notof
reduced.
Hence,
the bending
stiffness
on
the
back
pyramid
were
a
pyramid
was
reduced
by
a
factor
of
reduced
a factor This
of five,
thereason
foil thickness
wasdifficult
not reduced.
Hence,
the bending
stiffness
relativelyby
increased.
is abut
main
that it was
to form
a smaller
micropyramid
of
relatively
increased.
This
is
a
main
reason
that
it
was
difficult
to
form
a
smaller
micropyramid
five,
but the
foil thickness
reduced.
This isof
relatively
increased.
This was
is a not
main
reason Hence,
that it the
wasbending
difficultstiffness
to formrelatively
a smallerincreased.
micropyramid
ofa
titanium.
titanium.
main
reason that it was difficult to form a smaller micropyramid of titanium.
titanium.
(a)
(a)
(a)
(b)
(b)
(b)
(a)
(a)
(a)
(b)
(b)
(b)
1000μm
1000μm
1000μm
(c)
(c)
(c)
Figure 14. Titanium pyramids of D = 1.41 mm formed with ultrasonic vibration: (a) top view; (b)
Figure 14. Titanium pyramids of D = 1.41 mm formed with ultrasonic vibration: (a) top view; (b)
Figure
14.
Titanium
pyramids
= 1.41
formed
ultrasonic
vibration:
top(b)
view;
(b)
bottom14.
view;
(c) high
angle view.
Figure
Titanium
pyramids
ofof
D =D1.41
mmmm
formed
withwith
ultrasonic
vibration:
(a) top(a)
view;
bottom
bottom view; (c) high angle view.
bottom
high
angle view.
view;
(c)view;
high (c)
angle
view.
1000μm
1000μm
1000μm
(c)
(c)
(c)
Figure 15. Titanium pyramids of D = 1.41 mm formed without ultrasonic vibration: (a) top view; (b)
Figure
15.
Titanium
pyramids
ofofDD= =1.41
mm
formed
without
ultrasonic
vibration:
(a) top
view;
(b)
Figure
15.
Titanium
pyramids
1.41
mm
formed
without
ultrasonic
vibration:
(a) top
view;
Figure
Titanium
of D = 1.41
mm
formed
without
ultrasonic
vibration:
(a) top
view;
(b)
bottom 15.
view;
(c) highpyramids
angle view.
bottom
view;
(c)
high
angle
view.
(b)
bottom
view;
(c) high
angle
view.
bottom
view;
(c) high
angle
view.
(a)
(a)
(a)
(b)
(b)
(b)
200μm
200μm
(c)
200μm
(c)
(c)
Figure 16.
Titanium
pyramids
of D =
= 283
μm
formed
with
ultrasonic
vibration:
(a)
top
view;
(b)
bottom
Figure
16. Titanium
Titanium pyramids
pyramids of
283 μm
µm formed
formed with
with ultrasonic
ultrasonic vibration:
vibration: (a)
(a) top
top view;
view; (b)
(b) bottom
bottom
Figure
16.
of D
D = 283
Figure
16.
Titanium
pyramids
of
D
=
283
μm
formed
with
ultrasonic
vibration:
(a)
top
view;
(b)
bottom
view; (c)
(c) high
high angle
angle view.
view.
view;
view; (c) high angle view.
view; (c) high angle view.
4. Conclusions
4. Conclusions
4. Conclusions
Single point incremental microforming of thin shell pyramids of aluminum, stainless steel, and
Single point incremental microforming of thin shell pyramids of aluminum, stainless steel, and
Single
point
microforming
of thinofshell
of aluminum,
stainless steel,
and
titanium
foils
wasincremental
conducted under
the conditions
withpyramids
and without
ultrasonic vibration
and with
titanium foils was conducted under the conditions of with and without ultrasonic vibration and with
titanium
foils
was
conducted
under
the
conditions
of
with
and
without
ultrasonic
vibration
and
with
and without laser heating. It was
found
that
the
laser
heating
can improve the forming limit of a
and without laser heating. ItIt was
was found
found that
that the
the laser
laser heating
heating can improve the forming limit of a
and
without
laser
It was
found that
laser
heating
improve
theultrasonic
forming limit
of a
square
pyramid
of heating.
6.5 μm-thick
aluminum
foilthe
and
it was
morecan
effective
when
vibration
square pyramid of 6.5 µm-thick
μm-thick aluminum foil and it was more effective when ultrasonic vibration
square
pyramid
of 6.5 μm-thick
foil
and it was
more effective
when
ultrasonic
vibration
was applied
in addition
to laser aluminum
heating. The
elongation
obtained
under the
assistance
of ultrasonic
was applied in addition to laser heating.
heating. The elongation obtained under the assistance of ultrasonic
was
applied
in
addition
to
laser
heating.
The
elongation
obtained
under
the
assistance
of
ultrasonic
vibration and laser heating was 73.4%, more than 10 times as large as that obtained by tensile test. It
vibration
obtained
byby
tensile
test.
It is
vibration and
and laser
laser heating
heatingwas
was73.4%,
73.4%,more
morethan
than1010times
timesasaslarge
largeasasthat
that
obtained
tensile
test.
It
vibration
and laser
was 73.4%,
than 10
times as can
largeimprove
as that obtained
by tensile
It
is confirmed
that heating
the assistance
of more
ultrasonic
vibration
the accuracy
of test.
rather
confirmed
thatthat
the assistance
of ultrasonic
vibration
can improve
accuracy
rather complicated
is confirmed
the assistance
of ultrasonic
vibration
can the
improve
theofaccuracy
of rather
is
confirmedshape
that of
thepyramids
assistance
ofasultrasonic
vibrationand
cana improve
the It
accuracy
of rather
complicated
such
a twisted pyramid
star pyramid.
is also found
that
complicated shape of pyramids such as a twisted pyramid and a star pyramid. It is also found that
complicated
shape
of
pyramids
such
as
a
twisted
pyramid
and
a
star
pyramid.
It
is
also
found
that
ultrasonic vibration improves the forming accuracy of stiff materials or difficult-to-work materials
ultrasonic vibration improves the forming accuracy of stiff materials or difficult-to-work materials
ultrasonic
the forming
accuracy of stiff materials or difficult-to-work materials
even if the vibration
shapes of improves
micropyramids
are simple.
even if the shapes of micropyramids are simple.
even if the shapes of micropyramids are simple.
Micromachines 2017, 8, 142
10 of 10
shape of pyramids such as a twisted pyramid and a star pyramid. It is also found that ultrasonic
vibration improves the forming accuracy of stiff materials or difficult-to-work materials even if the
shapes of micropyramids are simple.
Acknowledgments: The authors would like to extend their thanks to cutting tool manufacturers, OSG Corporation
and NS Tool Co., Ltd. for the fabrication of microforming tools used in this study. This study is partly based
on projects supported by Amada Foundation (AF-2014023) and JSPS Grant-in-Aids for Challenging Exploratory
Research (24656097, 2012), Japan. These contributions are gratefully acknowledged.
Author Contributions: T.O. conceived and designed the experiments; M.H. completed the experimental
apparatus, its controlling software, and forming experiments.
Conflicts of Interest: The authors declare no conflict of interest.
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