sensors
Article
Design of Diaphragm and Coil for Stable
Performance of an Eddy Current Type Pressure Sensor
Hyo Ryeol Lee 1 , Gil Seung Lee 2 , Hwa Young Kim 3 and Jung Hwan Ahn 1, *
1
2
3
*
School of Mechanical Engineering, Pusan National University, 2, Busandaehak-ro 63 beon gil,
Geumjeong-gu, Busan 46241, Korea; hong30140@pusan.ac.kr
NOVASEN Co., LTD, 25, Bansong-ro 525 beon gil, Haeundae-gu, Busan 48002, Korea; novasen@naver.com
Research Institute of Mechanical Technology, Pusan National University, 2, Busandaehak-ro 63 beon gil,
Geumjeong-gu, Busan 46241, Korea; hyokim@pusan.ac.kr
Correspondence: jhwahn@pusan.ac.kr; Tel.: +82-51-510-3087
Academic Editor: Vittorio M. N. Passaro
Received: 7 April 2016; Accepted: 22 June 2016; Published: 1 July 2016
Abstract: The aim of this work was to develop an eddy current type pressure sensor and investigate
its fundamental characteristics affected by the mechanical and electrical design parameters of sensor.
The sensor has two key components, i.e., diaphragm and coil. On the condition that the outer
diameter of sensor is 10 mm, two key parts should be designed so as to keep a good linearity and
sensitivity. Experiments showed that aluminum is the best target material for eddy current detection.
A round-grooved diaphragm is suggested in order to measure more precisely its deflection caused by
applied pressures. The design parameters of a round-grooved diaphragm can be selected depending
on the measuring requirements. A developed pressure sensor with diaphragm of t = 0.2 mm and
w = 1.05 mm was verified to measure pressure up to 10 MPa with very good linearity and errors of
less than 0.16%.
Keywords: eddy current; pressure sensor; round-groove; impedance change
1. Introduction
Pressure sensors have been widely used in such areas as chemical plants, automobile/ship,
aviation, air conditioning, biomedical, and hydraulics industries, etc., where pressure is an important
monitored parameter. In chemical plants, pressure sensors are used to monitor partial pressures
of gases in industrial units so that large chemical reactions take place under precisely controlled
environmental conditions. In automobile and ship engines where it forms an integral part of the engine
and its safety, the dynamic cylinder pressure in the combustion chamber is monitored to regulate the
power that the engine must deliver to achieve suitable speeds. Engine combustion pressure analysis
is a fundamental measurement technique applied universally in the research and development of
reciprocating combustion engines [1,2].
The three types of pressure sensors—metal thin-film, ceramic thick-film and piezoresistive—have
been most commonly used so far. Among them, silicon piezoresistive MEMS pressure sensors as
micromachined devices, are widely used in various systems because of their high accuracy, high
sensitivity, and excellent linearity over a wide range of pressures in addition to their low cost and
small size [3–7]. Pressure sensors are often exposed to harsh environments with contaminants—such
as dust, dirt, and oil—and severe temperature changes, which cause the silicon based sensors to have
poorer accuracy, sensitivity, and linearity.
In an effort to develop a robust pressure sensor that can endure such harsh environments, an eddy
current type pressure sensor is proposed in this research, due to the high resolution, high frequency
response, and robustness against contaminants of an eddy current sensor (ECS). ECS are known to
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known
to be very competitive
for displacement
measurement
harsh environments
under dynamic
be
very competitive
for displacement
measurement
in harshin
environments
under dynamic
and static
and staticFurthermore,
pressures. Furthermore,
active compensation
temperature compensation
reduce theeffect
temperature
pressures.
active temperature
to reduce the to
temperature
on ECS has
effectproved
on ECSpossible
has beenthrough
proved previous
possible through
been
researchprevious
[8,9]. research [8,9].
An
eddy
current
type
pressure
sensor
should
be composed
two transducer
An eddy current type pressure sensor should be composed
of twoof
transducer
parts—aparts—a
diaphragm
to convert
pressure into
diaphragm and
displacement
and andetector
eddy current
detector
to
todiaphragm
convert pressure
into diaphragm
displacement
an eddy current
to convert
diaphragm
convert
diaphragm
displacement
into
eddy
current
voltage.
In
this
paper,
particularly,
it
is
displacement into eddy current voltage. In this paper, particularly, it is described how the design
described
how
the
design
parameters
of
these
two
key
components
affect
the
pressure
sensor
parameters of these two key components affect the pressure sensor performance—i.e., pressure range
performance—i.e., pressure range and sensitivity—and what type of diaphragm measure the eddy
and sensitivity—and what type of diaphragm measure the eddy current sensor displacement most
current sensor displacement most stably and precisely. Finally, the characteristic of an assembled
stably and precisely. Finally, the characteristic of an assembled sensor of diaphragm and eddy current
sensor of diaphragm and eddy current probe was tested in the real pressure chamber and the
probe was tested in the real pressure chamber and the feasibility for practical use was checked.
feasibility for practical use was checked.
2. Principle and Structure of Eddy Current Type Pressure Sensor
2. Principle and Structure of Eddy Current Type Pressure Sensor
2.1. Working Principle of a Typical Pressure Sensor
2.1. Working Principle of a Typical Pressure Sensor
A typical—generally a force collector type—pressure sensor is composed of a diaphragm
A typical—generally a force collector type—pressure sensor is composed of a diaphragm and a
and a probe, where a pressurized gas from a high pressure chamber causes the diaphragm to be
probe, where a pressurized gas from a high pressure chamber causes the diaphragm to be elastically
elastically deflected. And the probe then detects the diaphragm deflection. According to detection
deflected. And the probe then detects the diaphragm deflection. According to detection principles,
principles, there are several kinds of pressure sensors such as strain gauge type, piezoresistive
there are several kinds of pressure sensors such as strain gauge type, piezoresistive type,
type,
piezoelectric
capacitive
electromagnetic
optical
In strain
gauge,
piezoelectric
type, type,
capacitive
type,type,
electromagnetic
type, type,
and and
optical
type.type.
In strain
gauge,
piezoresistive,
types,the
theunit
unitthat
thatdetects
detects
the
diaphragm
deflection
is connected
piezoresistive,and
and piezoelectric
piezoelectric types,
the
diaphragm
deflection
is connected
to to
ororbuilt
into
the
diaphragm
as
a
thin
layer-bonded,
and
sputtered
etc.,
while
the
others
are
separately
built into the diaphragm as a thin layer-bonded, and sputtered etc., while the others are
located
nearlocated
the diaphragm
detect its deflection
in deflection
non-contact
Piezoresistive
sensors—based
separately
near the to
diaphragm
to detect its
in mode.
non-contact
mode. Piezoresistive
on
measurementon
of measurement
the diaphragm
a good feature aingood
that feature
the resistance
sensors—based
of displacement—have
the diaphragm displacement—have
in that change
the
for
a
given
amount
of
pressure
is
much
greater
than
in
metal
strain
gauges.
resistance change for a given amount of pressure is much greater than in metal strain gauges.
The
type pressure
pressuresensor
sensorwhich
whichisistotobebe
developed
research
is one
of the
Theeddy
eddy current
current type
developed
in in
thisthis
research
is one
of the
electromagnetic type
type with the diaphragm
byby
a sensor
coil.
electromagnetic
diaphragmdeflection
deflectionbeing
beingdetected
detected
a sensor
coil.
2.2.
PressureSensor
Sensor
2.2.Structure
Structure of
of Eddy
Eddy Current Type Pressure
Thestructure
structure of an
pressure
sensor
to be
in this
is shown
in
The
aneddy
eddycurrent
currenttype
type
pressure
sensor
todeveloped
be developed
instudy
this study
is shown
is is
composed
of of
housing,
diaphragm,
insulator,
target
plate
andand
sensor
coil coil
inFigure
Figure1a.
1a.The
Thesensor
sensor
composed
housing,
diaphragm,
insulator,
target
plate
sensor
(eddycurrent
currentprobe).
probe). The diaphragm
C22
to to
prevent
sensors
from
being
rusted
(eddy
diaphragmisismade
madeofofHastelloy
Hastelloy
C22
prevent
sensors
from
being
rusted
even
under
harsh
conditions.
When
pressurized
gas
from
a
high
pressure
chamber
is
applied
to
the
even under harsh conditions. When pressurized gas from a high pressure chamber is applied to the
sensor,as
asshown
shown in
in Figure
Figure 1b,
moves
thethe
insulator
andand
the the
target
sensor,
1b, the
the diaphragm
diaphragmisisdeflected,
deflected,which
which
moves
insulator
target
plate;
the
resulting
displacement
of
the
target
plate
is
then
detected
by
the
coil.
plate; the resulting displacement of the target plate is then detected by the coil.
(a)
(b)
Figure 1.
1. Eddy
structure;
(b)(b)
on on
sitesite
application.
Figure
Eddy current
currenttype
typepressure
pressuresensor:
sensor:(a)(a)
structure;
application.
Therefore, the two key parts of an eddy current type pressure sensor—diaphragm and
Therefore,
the two key electrically
parts of an
currenttotype
pressure
sensor—diaphragm
coil—should
be well-matched
andeddy
mechanically
enhance
its sensitivity
and linearity inand
coil—should
well-matched
mechanically
to enhance
its sensitivity
andislinearity
the aspect ofbe
tiny
displacementelectrically
acquisitionand
on the
condition that
the diaphragm
deflection
within in
the aspect of tiny displacement acquisition on the condition that the diaphragm deflection is within
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the elastic limit. For compatible use with other types of commercialized pressure sensors, the
the elastic limit. For compatible use with other types of commercialized pressure sensors, the
diameter
the sensor
is fixed at
10with
mm.other types of commercialized pressure sensors, the diameter
the
elastic of
limit.
For compatible
use
diameter of the sensor is fixed at 10 mm.
of the sensor is fixed at 10 mm.
3. Design of Sensor Coil
3.
3. Design
Designof
ofSensor
SensorCoil
Coil
3.1. Design Parameters
3.1.
3.1. Design
Design Parameters
Parameters
Figure 2 shows a schematic diagram of the sensor coil unit—eddy current probe.
Figure
schematic diagram
diagram of
of the
the sensor
sensor coil
coil unit—eddy
unit—eddy current
current probe.
probe.
Figure 22 shows
shows aa schematic
Figure 2.
2. Geometry
Geometry of
of coil
coil against
against target
target plate.
plate.
Figure
Figure
2. Geometry
of coil
against target
plate.
Many design parameters are geometric ones, such as: outer diameter (a); inner diameter (b);
Many design parameters
parameters are geometric ones, such as: outer
outer diameter
diameter (a);
(a); inner
inner diameter
diameter (b);
(b);
and height (c) of the coil unit; coil diameter and gap (d) between coil and target plate. Other design
and height (c) of the coil unit; coil diameter and gap (d) between coil and target plate. Other design
parameters include magneto-electrical ones such as conductivity, temperature resistance and
parameters
includemagneto-electrical
magneto-electrical
ones
as conductivity,
temperature
resistance
and
parameters include
ones
suchsuch
as conductivity,
temperature
resistance
and magnetic
magnetic permeability. It is known that self-inductance and mutual-inductance of the sensor coil are
magnetic
permeability.
is known
that self-inductance
and mutual-inductance
of coil
the sensor
coil are
permeability.
It is knownIt that
self-inductance
and mutual-inductance
of the sensor
are dependent
dependent only on geometrical parameters [10]. Copper is used as coil material to get sensitivity and
dependent
only on geometrical
Copper
is used
as coil
to getand
sensitivity
and
only on geometrical
parameters parameters
[10]. Copper[10].
is used
as coil
material
to material
get sensitivity
linearity
of
linearity of detection as high as possible because of its high conductivity and low temperature resistance.
linearity
as high asbecause
possibleofbecause
its high conductivity
low temperature
resistance.
detectionofasdetection
high as possible
its highofconductivity
and low and
temperature
resistance.
From the viewpoint of sensor performance referring to the past works, the inner and outer
From the viewpoint of sensor performance referring
referring to the past works, the inner and outer
diameter should be minimized and maximized, respectively, and the height should be minimized as
diameter should
height
should
bebe
minimized
as
should be
beminimized
minimizedand
andmaximized,
maximized,respectively,
respectively,and
andthe
the
height
should
minimized
much as geometrically possible [10,11]. Since the coil should detect the diaphragm deflection
much
as as
geometrically
possible
as much
geometrically
possible[10,11].
[10,11].Since
Sincethe
thecoil
coilshould
shoulddetect
detect the
the diaphragm
diaphragm deflection
appropriately, it is desirable that the diameter of the probe is limited to a maximum of 5 mm. The
appropriately, itit isis desirable
of of
thethe
probe
is limited
to atomaximum
of 5 of
mm.
The
desirablethat
thatthe
thediameter
diameter
probe
is limited
a maximum
5 mm.
inner diameter and height should be at least 2 mm and 1 mm respectively for convenience of coil
inner
diameter
and height
should
be at be
least
mm2and
mm 1respectively
for convenience
of coil
The inner
diameter
and height
should
at 2least
mm1 and
mm respectively
for convenience
manufacturing. The copper wire diameter is at most 0.1 mm, as anything larger reduces the
manufacturing.
The copper
wire wire
diameter
is atismost
0.1 0.1
mm,
asasanything
of coil manufacturing.
The copper
diameter
at most
mm,
anythinglarger
larger reduces
reduces the
sensitivity and the anything smaller is too sensitive to disturbance. The gap is fixed at 0.3 mm to
sensitivity and
andthe
theanything
anythingsmaller
smaller
sensitive
to disturbance.
is fixed
0.3tomm
to
is is
tootoo
sensitive
to disturbance.
TheThe
gap gap
is fixed
at 0.3at
mm
avoid
avoid the effect of parasitic capacitance largely generated in ranges less than 0.2 mm.
avoid
the of
effect
of parasitic
capacitance
generated
in ranges
less0.2
than
0.2 mm.
the effect
parasitic
capacitance
largelylargely
generated
in ranges
less than
mm.
3.2. Signal Processing for Eddy Current Detection
3.2. Signal Processing for Eddy Current Detection
The principle of eddy current detection is to detect a variation of coil impedance caused by a
The principle of eddy current detection is to detect a variation of coil impedance caused by a
change of the gap between coil and target plate. Figure 3 shows a signal processing block for
between
coilcoil
andand
target
plate.plate.
Figure
3 shows
a signalaprocessing
block for block
detecting
change of
ofthe
thegap
gap
between
target
Figure
3 shows
signal processing
for
detecting a change of coil impedance and removing disturbances from the acquired R and L impedances.
a
change
of
coil
impedance
and
removing
disturbances
from
the
acquired
R
and
L
impedances.
detecting a change of coil impedance and removing disturbances from the acquired R and L impedances.
Figure
Figure 3.
3. Functional
Functional block
block diagram
diagram for
for signal
signal processing
processing of
of eddy
eddy current
current acquisition.
acquisition.
Figure 3. Functional block diagram for signal processing of eddy current acquisition.
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Given
kHz)
Given the
the optimal
optimal frequency
frequency (250
(250 kHz)
kHz) and
and amplitude
amplitude of
of the
the coil
coil excitation
excitation current
current (25
(25 mA)
mA) by
by
Given
the
optimal
frequency
(250
and
amplitude
of
the
coil
excitation
current
(25
mA)
by
DSP
(Digital
Signal
Processor),
DDS
(Direct
Digital
Synthesizer)
circuit
transmits
corresponding
DSP (Digital
(Digital Signal
Signal Processor),
Processor),aaaDDS
DDS(Direct
(DirectDigital
DigitalSynthesizer)
Synthesizer)circuit
circuittransmits
transmits aaacorresponding
corresponding
DSP
voltage
signal
to
current
pump
which
supplies
corresponding
current
to
the
coil.
Eddy
current
voltage signal
signal to
to aaa current
current pump
pumpwhich
whichsupplies
supplies aaacorresponding
corresponding current
current to
tothe
thecoil.
coil. Eddy
Eddy current
current
voltage
electromagnetically
induced
in
the
target
plate
placed
close
to
the
sensor
coil
causes
a
change
of
electromagneticallyinduced
inducedinin
target
plate
placed
the sensor
coil causes
a of
change
of
electromagnetically
thethe
target
plate
placed
closeclose
to thetosensor
coil causes
a change
voltage
voltage
in
sensor
coil,
which
is
by
detector
is
to
of
the
voltage
in the
thecoil,
sensor
coil,is
which
is detected
detected
by aa voltage
voltage
detector
and
is converted
converted
to aa change
change
ofcoil
the
in
the sensor
which
detected
by a voltage
detector
and isand
converted
to a change
of the
coil
aa demodulator
circuit.
coil impedance
impedance
by
demodulator
circuit.
impedance
by aby
demodulator
circuit.
3.3.
3.3. Experiment
Experiment Evaluation
Evaluation of
of Sensor
Sensor Coil
Coil
The
characteristics
of the
the sensor
coilare
areexamined
examinedalong
alongwith
withthe
thegap
gapprecisely
preciselycontrolled
controlledon
onaa
The characteristics
characteristics of
sensor coil
coil
are
examined
along
with
the
gap
precisely
controlled
on
measurement
a
measurementsystem,
system,as
shownin
Figure4,
whichis
is composed
composed of
measurement
system,
asasshown
shown
ininFigure
Figure
4,4,which
which
is
composed
of aa precision
precision positioning
positioning unit
unit
the
gap
and
an
LCR
(inductance
(L),
capacitance
(C),
and
resistance
(R))
meter
controlling
the
gap
and
an
LCR
(inductance
(L),
capacitance
(C),
and
resistance
(R))
meter
measuring
controlling the gap and an LCR (inductance (L), capacitance (C), and resistance (R)) meter
measuring
coil
coil
impedance.
measuring
coil impedance.
impedance.
Figure
with
gap
controlled.
Figure 4.
4. Coil
Coil impedance
impedance measurement
measurement system
system with
with gap
gapcontrolled.
controlled.
Figure
4.
Coil
impedance
measurement
system
In
In order
order to
to find
find out
out the
the best
best target
target material
material in
in the
the magneto
magneto electrical
electrical aspect,
aspect, five
five materials—copper,
materials—copper,
In order to find out the best target material in the magneto electrical aspect, five materials—copper,
aluminum,
brass,
bronze
and
stainless
steel—are
considered
as
alternatives.
aluminum, brass, bronze and stainless steel—are considered as alternatives. The
The results
results of
of
aluminum, brass, bronze and stainless steel—are considered as alternatives. The results of impedance
impedance
impedance measurements
measurements for
for the
the five
five target
target materials
materials are
are displayed
displayed in
in the
the R-L
R-L impedance
impedance plane,
plane,
measurements for the five target materials are displayed in the R-L impedance plane, which is specially
which
which is
is specially
specially adopted
adopted to
to improve
improve the
the typical
typical measurement
measurement method
method based
based on
on amplitude
amplitude data
data
adopted to improve the typical measurement method based on amplitude data acquired from an LCR
acquired
from
an
LCR
meter,
as
shown
in
Figure
5.
acquired from an LCR meter, as shown in Figure 5.
meter, as shown in Figure 5.
Figure
Figure 5.
5. Coil
Coil impedance
impedance measurement
measurement system
system with
with gap
gapcontrolled.
controlled.
Both
impedance
changes
against
gap—ΔL/Δd,
Both impedance
impedancechanges
changesagainst
againstgap—∆L/∆d,
gap—ΔL/Δd, ΔR/Δd—are
ΔR/Δd—are almost
almost linear
linear in
range less
less than
than
Both
∆R/∆d—are
in aa range
range
less
than
500
μm,
although
they
become
nonlinear
as
the
gap
increases
beyond
that.
As
R
is
actually
affected
500
μm,
although
they
become
nonlinear
as
the
gap
increases
beyond
that.
As
R
is
actually
affected
500 µm, although they become nonlinear as the gap increases beyond that. As R is actually affected
more
aluminum
is
over
the
other
materials
as
more than
than LL by
by temperature
temperature
change,
copper
oror
aluminum
is preferred
preferred
over
thethe
other
materials
as the
the
more
than
temperaturechange,
change,copper
copperor
aluminum
is
preferred
over
other
materials
as
target
material,
because
of
higher
conductivity
and
lower
temperature
sensitivity
in
addition
to
target
material,
because
of
higher
conductivity
and
lower
temperature
sensitivity
in
addition
to
the target material, because of higher conductivity and lower temperature sensitivity in
to
nonmagnetic
nonmagnetic metals
metals property.
property. Furthermore,
Furthermore, in
in terms
terms of
of corrosion-resistance,
corrosion-resistance, aluminum
aluminum is
is much
much
better
better than
than copper.
copper. Therefore,
Therefore, Al6061
Al6061 is
is chosen
chosen as
as the
the target
target material.
material.
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nonmagnetic
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2016, 16, 1025metals
property. Furthermore, in terms of corrosion-resistance, aluminum is much
5 of better
11
than copper. Therefore, Al6061 is chosen as the target material.
4. Design of Round-Grooved Diaphragm
4. Design of Round-Grooved Diaphragm
4.1. Shape of Diaphragm for Stably Measurable Deflection
4.1. Shape of Diaphragm for Stably Measurable Deflection
The diaphragm plays an important role in the elastic deflection in response to an applied
The diaphragm plays an important role in the elastic deflection in response to an applied pressure.
pressure. The shape and geometrical dimensions of a diaphragm should be well-chosen so that its
The shape and geometrical dimensions of a diaphragm should be well-chosen so that its deflection
deflection matches the performance of the sensor coil designed in Section 3. A small sensor diameter
matches the performance of the sensor coil designed in Section 3. A small sensor diameter of 10 mm
of 10 mm limits the diaphragm diameter up to 8.6 mm at most. Furthermore, its deflection being
limits the diaphragm diameter up to 8.6 mm at most. Furthermore, its deflection being measured more
measured more accurately by the sensor coil, the diaphragm should be designed so that some area of
accurately by the sensor coil, the diaphragm should be designed so that some area of its central part
its central part goes up and down near flatly as the acting pressure goes up or down.
goes up and down near flatly as the acting pressure goes up or down.
What shape of the diaphragm is needed to meet such restricted requirements? Wang et al.
What shape of the diaphragm is needed to meet such restricted requirements? Wang et al.
revealed that the center-embossed diaphragm is superior in optical characteristics to the flat one
revealed that the center-embossed diaphragm is superior in optical characteristics to the flat one which
which is seriously deteriorated by the central area being wrapped under high hydrostatic pressure [12].
is seriously deteriorated by the central area being wrapped under high hydrostatic pressure [12].
In this study, a round-grooved, square-grooved diaphragm—like a center-embossed one—shown in
In this study, a round-grooved, square-grooved diaphragm—like a center-embossed one—shown in
Figure 6a,b, are considered for rather flatter deflection of the central part, which helps the eddy
Figure 6a,b, are considered for rather flatter deflection of the central part, which helps the eddy current
current probe measure a gap more stably and precisely. The design parameters, as depicted in
probe measure a gap more stably and precisely. The design parameters, as depicted in Figure 6a,b,
Figure 6a,b, are the width and thickness of the groove while the thickness of the diaphragm and the
are the width and thickness of the groove while the thickness of the diaphragm and the distance of the
distance of the groove from the wall are set as 1 mm and 1.5 mm, respectively. For deflection
groove from the wall are set as 1 mm and 1.5 mm, respectively. For deflection comparison a flat type,
comparison a flat type, shown in Figure 6c, is used as a reference.
shown in Figure 6c, is used as a reference.
(a)
(b)
(c)
Figure
6. Shape
and and
design
parameter
of three
types
of diaphragm:
(a) round-grooved;
(b) square
Figure
6. Shape
design
parameter
of three
types
of diaphragm:
(a) round-grooved;
(b) square
grooved;
(c)
flat.
grooved; (c) flat.
4.2. 4.2.
Analysis
of Diaphragm
Deflection
Analysis
of Diaphragm
Deflection
Structural
analyses
were
carried
out out
to investigate
the the
effects
of design
parameters
on on
the the
Structural
analyses
were
carried
to investigate
effects
of design
parameters
maximum
deflection
andand
stress
of the
diaphragm
by increasing
pressure
in 0.25
MPa
increments
maximum
deflection
stress
of the
diaphragm
by increasing
pressure
in 0.25
MPa
increments
until
yielding
occurs
using
ANSYS
Workbench
V15.
The
material
properties
of
Hastelloy
C22
are are
until yielding occurs using ANSYS Workbench V15. The material properties of Hastelloy C22
elastic
modulus
206
GPa,
yield
strength
438
MPa,
and
Poisson
ratio
0.3.
elastic modulus 206 GPa, yield strength 438 MPa, and Poisson ratio 0.3.
With
thickness
(t) 0.2
mmmm
andand
pressure
2.5 2.5
MPa,
Figure
7 shows
a typical
deflection
behavior
With
thickness
(t) 0.2
pressure
MPa,
Figure
7 shows
a typical
deflection
behavior
along
the
radial
axis
of
the
round-grooved,
square-grooved,
and
flat
diaphragms,
respectively.
along the radial axis of the round-grooved, square-grooved, and flat diaphragms, respectively.
TheThe
point
0 indicates
the diaphragm.
diaphragm.The
Thedeflection
deflection
whole
diaphragm
point
0 indicatesthe
thecenter
center of
of the
of of
thethe
whole
diaphragm
surface
surface
under
2.5
MPa
is
displayed
on
the
axis
of
−4.3~4.3
mm.
While
a
much
larger
deflection
with
under 2.5 MPa is displayed on the axis of ´4.3~4.3 mm. While a much larger deflection with no flat
no flat
central
is seen
the
flat the
type,
the grooved
type deflects
much
with
quite
a flat in
central
part part
is seen
in theinflat
type,
grooved
type deflects
much less
withless
quite
a flat
deflection
deflection
in
the
center
part
compared
to
the
flat
type,
which
makes
the
eddy
current
probe
measure
the center part compared to the flat type, which makes the eddy current probe measure the diaphragm
the deflection
diaphragmwith
deflection
with more
and precision.
more stability
andstability
precision.
Figure
8
shows
comparisons
of
the
simulated
results
in terms
of maximum
deflection
andand
Figure 8 shows comparisons of the simulated
results
in terms
of maximum
deflection
maximum
stress
at each
pressure
between
flat,flat,
square-grooved,
andand
round-grooved
types
with
maximum
stress
at each
pressure
between
square-grooved,
round-grooved
types
with
increasing
pressure
at
the
same
thickness.
increasing pressure at the same thickness.
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(a)
(a) (a)
(b)
(b) (b)
(c)
(c) (c)
Figure 7.
7. Deflection
Deflection behavior
behavior along
along the
the diaphragm
diaphragm axis
axis with
with tt == 0.2
0.2 mm,
mm, w
w == 1.05
1.05 mm,
mm, P
P = 2.5
2.5 MPa:
MPa:
Figure
Figure
7. Deflection
behavior
along
thethe
diaphragm
axisaxis
withwith
t = 0.2
w =w
1.05
mm,mm,
P = 2.5
Figure
7. Deflection
behavior
along
diaphragm
t = mm,
0.2 mm,
= 1.05
P ==MPa:
2.5 MPa:
(a)
round-grooved;
(b)
square-grooved;
(c)
flat.
(a)
round-grooved;
(b)
square-grooved;
(c)flat.
flat.
(a)(a)
round-grooved;
(b)(b)
square-grooved;
(c) (c)
flat.
round-grooved;
square-grooved;
(a)
(a) (a)
(b)
(b) (b)
Figure
8.Comparison
Comparison
ofmaximum
maximum
deflection/stress
against
pressure
among
flat,
square-grooved,
Figure
deflection/stress
against
pressure
among
flat, flat,
and
Figure
8. 8.
Comparison
ofofmaximum
deflection/stress
against
pressure
among
flat,
square-grooved,
Figure
8.
Comparison
of
maximum
deflection/stress
against
pressure
among
square-grooved,
and
round-grooved
types
with
w
=
1.05
mm:
(a)
maximum
deflection,
(b)
maximum
stress.
round-grooved
types
with
w
=
1.05
mm:
(a)
maximum
deflection;
(b)
maximum
stress.
and
round-grooved
types
with
w
=
1.05
mm:
(a)
maximum
deflection,
(b)
maximum
stress.
and round-grooved types with w = 1.05 mm: (a) maximum deflection, (b) maximum stress.
(b) (b)
(b)
(a) (a)
(a)
Figure
9. Analysis
results
at t at
= 0.2= mm,
w0.2
=w
1.05
mm,
P==1.05
12.5
MPa:
(a)
stress
distribution;
yield
points.
Figure
9. Analysis
Analysis
results
0.2
mm,
1.05
mm,
P == 12.5
12.5
MPa:
(a)
stress
distribution;
(b)distribution;
yield
points.
Figure
Analysis
results
t =
wmm,
mm,MPa:
P =
12.5
MPa:
(a) (b)
stress
Figure
9.
results
at tt =at
0.2
mm,
wmm,
== 1.05
P
(a)
stress
distribution;
(b)
yield
points.
(b) yield points.
ForFor
t = 0.20.2
mm,
thethe
flatflat
type
hashas
a yielding
pressure
around
at 3.55
MPa,
which
is much
lower
mm,
type
yielding
pressure
around
at 3.55
3.55
MPa,
which
is much
much
lower
For tt == 0.2
mm,
the flat
type
has aa yielding
pressure
around
at
MPa,
which
is
lower
than
the
round-grooved
type
at
13.75
MPa
or
the
square-grooved
type
at
5.87
MPa.
For
t
=
0.3
mm,
than
the
round-grooved
type
at
13.75
MPa
or
the
square-grooved
type
at
5.87
MPa.
For
t
=
0.3
mm,
than the round-grooved type at 13.75 MPa or the square-grooved type at 5.87 MPa. For t = 0.3 mm,
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the flat type has a yielding pressure around 8.15 MPa, which is much lower than the round-grooved
For20.88
t = 0.2MPa
mm,orthe
flat type has a yielding
around
at 3.55
MPa, which
is much lower
than
type at
square-grooved
type at pressure
12.87 MPa.
Figure
9 shows
the numerical
analytical
the
round-grooved
type
at
13.75
MPa
or
the
square-grooved
type
at
5.87
MPa.
For
t
=
0.3
mm,
the
flat
results of how the stress is distributed on the round-grooved diaphragm and how the yielding stress
type has
a yielding
around
MPa,ofwhich
is much lower
than
type at
occurs
at points
1, 2,pressure
3, and 4 on
both 8.15
surfaces
the round-groove
with
t =the
0.2round-grooved
mm at 12.5 MPa.
20.88The
MPa
or square-grooved
type
at 12.87
MPa. Figure
shows measurable
the numerical
analytical
results
of
round-grooved
type has
a wider
pressure
range 9linearly
prior
to yielding
than
how
the
stress
is
distributed
on
the
round-grooved
diaphragm
and
how
the
yielding
stress
occurs
at
the square-grooved and the flat types. Thus, only the round-grooved type is considered for further
points 1, 2, 3, of
and
on bothofsurfaces
of the
round-groove with t = 0.2 mm at 12.5 MPa.
investigation
the4 effects
the design
parameters.
The
round-grooved
type
has
a
wider
pressure
range
to yielding
Table 1 summarizes the 16 analysis cases with the
twolinearly
designmeasurable
parameters prior
properly
selectedthan
for
the round-grooved
square-grooved diaphragm
and the flat and
types.
Thus,
only theanalytical
round-grooved
is considered
for further
the
their
numerical
resultstype
of maximum
pressure
and
investigation
of the effects
of the design
parameters.
deflection.
In addition,
the sensitivity
is calculated
as maximum deflection/maximum pressure.
Table 1 summarizes the 16 analysis cases with the two design parameters properly selected for the
Table 1. 16 diaphragm
cases of properly
selected
design
parameters
withofanalytical
of maximum
round-grooved
and their
numerical
analytical
results
maximumresults
pressure
and deflection.
pressure,the
maximum
deflection
and sensitivity.
In addition,
sensitivity
is calculated
as maximum deflection/maximum pressure.
Max.
Pressurewith Max.
Deflection
Sensitivity
Table 1. 16 Thichness
cases of properlyWidth
selected design
parameters
analytical
results of maximum
pressure,
(mm)
(mm)
(MPa)
(μm)
(μm/MPa)
maximum deflection and sensitivity.
Case 1
0.20
1.05
13.75
6.65
0.48
Case 2
0.20Thichness 1.30 Width
9.68Pressure
7.15
0.74
Max.
Max. Deflection
Sensitivity
Case 3
0.20 (mm)
1.55 (mm)
7.38
8.38
1.14
(MPa)
(µm)
(µm/MPa)
Case 4 Case 1 0.20 0.20
1.80 1.05
6.38
10.74
13.75
6.65
0.48 1.68
Case 5 Case 2 0.25 0.20
1.05 1.30
16.88
7.14
9.68
7.15
0.74 0.42
7.38
8.38
1.14 0.58
Case 6 Case 3 0.25 0.20
1.30 1.55
12.88
7.49
Case 4
0.20
1.80
6.38
10.74
1.68
Case 7
0.25
1.55
10.25
8.41
0.82
Case 5
0.25
1.05
16.88
7.14
0.42
Case 8 Case 6 0.25 0.25
1.80 1.30
8.88
10.11
12.88
7.49
0.58 1.14
Case 9 Case 7 0.30 0.25
1.05 1.55
20.88
8.03
10.25
8.41
0.82 0.38
8.88
10.11
1.14 0.49
Case 10 Case 8 0.30 0.25
1.30 1.80
16.38
8.06
20.88
8.03
0.38 0.65
Case 11 Case 9 0.30 0.30
1.55 1.05
12.88
8.35
Case 10
0.30
1.30
16.38
8.06
0.49
Case 12 Case 11 0.30 0.30
1.80 1.55
11.88
10.13
0.82
12.88
8.35
0.65
Case 13 Case 12 0.35 0.30
1.05 1.80
25.00
9.05
11.88
10.13
0.82 0.36
25.00
9.05
0.36 0.44
Case 14 Case 13 0.35 0.35
1.30 1.05
18.88
8.29
18.88
8.29
0.44 0.55
Case 15 Case 14 0.35 0.35
1.55 1.30
15.88
8.69
Case 15
0.35
1.55
15.88
8.69
0.55
Case 16
0.35
1.80
14.38
9.90
0.69
Case 16
0.35
1.80
(a)
14.38
9.90
0.69
(b)
Figure
10. Maximum
pressurepressure
(a) and maximum
deflection (b)deflection
with design
of round-groove
Figure
10. Maximum
(a) and maximum
(b)parameters
with design
parameterstype.
of
round-groove type.
Figure 10 shows the maximum pressure and deflection at varied thickness and width. Figure 10a
indicates that as the round-groove thickness increases and width decreases, the maximum pressure
Figure 10 shows the maximum pressure and deflection at varied thickness and width. Figure 10a
prior to yielding becomes larger. The change rates affected by both parameters are almost equal.
indicates that as the round-groove thickness increases and width decreases, the maximum pressure
Figure 10b shows that the round-groove width affects the deflection much more than the
prior to yielding becomes larger. The change rates affected by both parameters are almost equal.
round-groove thickness but does not show a consistent trend when thickness increased. So it would
Figure 10b shows that the round-groove width affects the deflection much more than the round-groove
be better to use the sensitivity calculated in Table 1 as an indicator to compare how sensitive the
thickness but does not show a consistent trend when thickness increased. So it would be better to
diaphragm is to pressure. The thinner and wider one is more sensitive to pressure change. The larger
use the sensitivity calculated in Table 1 as an indicator to compare how sensitive the diaphragm is to
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pressure. The thinner and wider one is more sensitive to pressure change. The larger width increases
width increases the sensitivity much more than the thickness but lowers the measurable maximum
the sensitivity much more than the thickness but lowers the measurable maximum pressure too much,
pressure too much, as shown in Figure 10a.
as shown in Figure 10a.
Based on the measurement requirements of pressure and sensitivity, the design parameters of
Based on the measurement requirements of pressure and sensitivity, the design parameters of
diaphragm can be selected. In this study the round-groove diaphragm with a groove 0.2 mm thick
diaphragm can be selected. In this study the round-groove diaphragm with a groove 0.2 mm thick and
and 1.05 mm wide is chosen to investigate its performances throughout the experiment.
1.05 mm wide is chosen to investigate its performances throughout the experiment.
5. Sensor
5.
SensorPerformance
PerformanceEvaluation
Evaluationthrough
throughPressure
PressureMeasurement
MeasurementTest
Test
Applied Pressure
Pressure
5.1. Measurements of Diaphragm Deflection According to Applied
It is necessary to examine how well the diaphragm deflection
deflection relates
relates to the applied
applied pressure.
pressure.
Figure
11
shows
a
setup
of
an
apparatus
composed
of
a
pressure
chamber,
dead
weight
tester
and
Figure 11 shows a setup of an apparatus composed of a pressure chamber, dead weight tester and half
half bridge
transformer
(HBT)
forexperiment.
the experiment.
bridge
transformer
(HBT)
for the
Figure
equipment with
with pressure
pressure varied
varied by
by dead
dead weights.
weights.
Figure 11.
11. Diaphragm
Diaphragm deflection
deflection measurement
measurement equipment
The deflection is measured by a HBT with pressure increased by 2.5 MPa increments up to 20
The deflection is measured by a HBT with pressure increased by 2.5 MPa increments up to
MPa. To evaluate the repeatability of diaphragm deflection in response to changes in pressure, the
20 MPa. To evaluate the repeatability of diaphragm deflection in response to changes in pressure,
measurement experiments were performed six times with a single specimen. The measurement
the measurement experiments were performed six times with a single specimen. The measurement
results are listed in Table 2 and displayed in Figure 12, which shows almost the same behavior.
results are listed in Table 2 and displayed in Figure 12, which shows almost the same behavior.
Table 2. 6 times measured results of diaphragm deflection according to varied pressure
Table 2. 6 times measured results of diaphragm deflection according to varied pressure
Pressure Test 1 Test 2
Test 3
Test 4
1
Test 2(μm)
Test 3 (μm)
Test 4
(MPa) Pressure
(μm) Test(μm)
(MPa)
0.0
0.00
(µm)
0.26
12.5
0.0
0.5 0.57
2.5
2.85
5.0
7.5 5.70
10.0
12.58.60
15.011.55
17.5
20.014.27
0.00
0.570.82
2.85
3.14
5.70
8.606.05
11.55
14.278.90
16.14
11.81
17.69
18.9414.4
15.0
16.14
16.22
0.5
2.5
5.0
7.5
10.0
(µm)
0.26
0.82
3.14
6.05
8.90
11.81
14.4
16.22
17.71
18.94
(µm)
0.00
0.00
0.56 0.56
2.82
2.82 5.72
5.72 8.59
11.47
8.5914.15
11.4716.01
17.50
14.1518.80
16.01
(µm)
0.09
0.09
0.68
0.68
3.00
3.00
5.94
8.82
5.94
11.7
8.82
14.3
16.11
11.7
17.58
14.3
18.8
16.11
Test 5
Test
5
(μm)
(µm)
0.00
Test 6
Standard
Average
Test(μm)
6
Standard
Deviation
Average
(µm)
Deviation
0.02
0.00
0.59
0.59
2.85
2.85
5.70
8.58
5.70
11.48
8.58
14.16
16.00
11.48
17.47
14.16
18.76
0.02
0.61 0.61
2.93
2.93
5.85
8.72 5.85
11.63
14.218.72
16.0211.63
17.50
18.7614.21
16.00
16.02
0.06
0.64
2.93
5.83
8.70
11.61
14.25
16.08
17.57
18.83
0.06
0.10
0.64 0.10
0.12
2.93 0.15
5.83 0.14
0.13
8.70 0.10
11.61 0.09
0.11
14.25 0.09
16.08
0.10
0.10
0.12
0.15
0.14
0.13
0.10
0.09
17.5
17.69
17.71 curve
17.50
17.58 up to17.47
17.50
17.57
0.11
The deflection-pressure
appears linear
about 12.5
MPa lower
than the simulated
yielding
MPa and
to remain
even up18.83
to 20 MPa, 0.09
although
20.0 pressure
18.94of 13.75
18.94
18.80the elasticity
18.8 seems
18.76
18.76
the deflection rate against pressure becomes lower. This would be due to work hardening of
the round-groove
of the diaphragm.
Through
regression
analysis
linear
relationship
between
The deflection-pressure
curve appears
linear
up to about
12.5the
MPa
lower
than the simulated
yielding pressure of 13.75 MPa and the elasticity seems to remain even up to 20 MPa, although the
deflection rate against pressure becomes lower. This would be due to work hardening of the
round-groove of the diaphragm. Through regression analysis the linear relationship between
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diaphragm deflection (δ) and pressure (P), δ (μm) = 1.142P (MPa) + 0.087, is of such good fitness that
(δ) andof
pressure
δ (μm) = 1.142P (MPa) + 0.087, is of such good fitness that
adiaphragm
coefficient deflection
of determination
0.999 is(P),
obtained.
diaphragm
deflection
(δ) and pressure
δ (µm) = 1.142P (MPa) + 0.087, is of such good fitness that a
a coefficient
of determination
of 0.999(P),
is obtained.
coefficient of determination of 0.999 is obtained.
Figure 12. Plot of measured diaphragm deflection with pressure.
Figure 12. Plot of measured diaphragm deflection with pressure.
Figure 12. Plot of measured diaphragm deflection with pressure.
5.2. Assembled Pressure Sensor
5.2.
5.2.Assembled
AssembledPressure
PressureSensor
Sensor
Figure 13 shows a cross section view of an assembled pressure sensor developed for this research.
Figure
of an
an assembled
assembledpressure
pressuresensor
sensordeveloped
developedfor
forthis
thisresearch.
research.
Figure13
13shows
showsaa cross
cross section
section view
view of
Figure 13.
13. Cross
Cross section
section view
view of
of an
an assembled
assembled pressure
pressure sensor.
Figure
sensor.
Figure 13. Cross section view of an assembled pressure sensor.
Its round-groove
a round-grooved
diaphragm
was
welded
on
round-groovemachined
machinedininboth
bothfaces
facesbybyturning,
turning,
a round-grooved
diaphragm
was
welded
Itsone
round-groove
machined
in both
faces
by
turning,
a round-grooved
diaphragm
was
welded
the
one
end
of housing.
An An
insulator
waswas
placed
between
diaphragm
and and
target
plateplate
to prevent
heat
on the
end
of housing.
insulator
placed
between
diaphragm
target
to prevent
on the
one
end
housing.
An
insulator
was
between
diaphragm
and target plate to prevent
transfer
from
theofdiaphragm
since
the coil
impedance
is affected
by temperature.
heat
transfer
from
the
diaphragm
since
the
coilplaced
impedance
is affected
by temperature.
heat transfer from the diaphragm since the coil impedance is affected by temperature.
5.3.
Performance Evaluation
Evaluation of
of an
an Assembled
5.3. Performance
Assembled Pressure
Pressure Sensor
Sensor According
According to
to Applied
Applied Pressure
Pressure
5.3. Performance
Evaluation
of
an
Assembled
Pressure
Sensor
According
to
Applied
Pressure
The
performance of
assembled sensor
same equipment
equipment
as
in Figure
Figure 11
11 with
with
The performance
of an
an assembled
sensor was
was tested
tested on
on the
the same
as in
aa HBT
probe
replaced
by
a
multi-meter
to
measure
the
pressure
output
(voltage)
depicted
in
Figure
3.
performance
of aanmulti-meter
assembled to
sensor
was the
tested
on theoutput
same equipment
as in Figure
11 with
HBTThe
probe
replaced by
measure
pressure
(voltage) depicted
in Figure
3.
The
measurement
results
are
summarized
in
Table 33the
andpressure
the
output
is displayed
displayed
in Figure
Figure
14a.
a HBT
probe replaced
byare
a multi-meter
toin
measure
output
(voltage)
depicted
in Figure
3.
The
measurement
results
summarized
Table
and
the sensor
sensor
output
is
in
14a.
The
sensor
output
is
linearly
well
related
with
input
pressure
up
to
10
MPa
and
has
maximum
linearity
The sensor
measurement
are summarized
Tableinput
3 andpressure
the sensor
is displayed
in maximum
Figure 14a.
The
output results
is linearly
well relatedinwith
upoutput
to 10 MPa
and has
errors
lesserrors
than
0.16%,
seen0.16%,
in well
Figure
14b,
is
much
smaller
than
commercialized
sensors.
The sensor
output
linearly
related
with
input
pressure
up is
toother
10
MPa
and hasthan
maximum
linearity
lessisas
than
as
seenwhich
in Figure
14b,
which
much
smaller
other
linearity
errors
less
than
0.16%,
as
seen
in
Figure
14b,
which
is
much
smaller
than
other
commercialized sensors.
commercialized sensors.
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Sensors 2016, 16, 1025
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(a)
(b)
Figure
14. 14.
Pressure
sensor
error(b)
(b)
along
with
applied
pressure
Figure
Pressure
sensoroutput
output(a)
(a) and
and linearity
linearity error
along
with
applied
pressure
Table
3. Measurement
sensoraccording
according
to varied
pressure.
Table
3. Measurementresults
resultsof
ofthe
the assembled
assembled sensor
to varied
pressure.
Pressure Pressure
(MPa) (MPa)
Impedance
Change
Impedance
Change (mΩ)
(mΩ)
0
1
2
3
4
5
6
7
8
9
10
6. Conclusions
Sensor
Output
(V)
Sensor
Output
(V)
Error (%)
0.000.00
0
0.00 0.00
1
11.66
0.98 0.98
11.66
2
23.45
1.99
23.45
1.99
3
35.29
2.99
35.29
4
47.14
3.99 2.99
5
58.96
4.99 3.99
47.14
6
70.75
5.99
58.96
4.99
7
82.52
6.99
70.75
8
94.30
7.99 5.99
9
106.14
8.99 6.99
82.52
10
118.10
10.00
94.30
7.99
* Error (%) = (Sensor output (V)—Expected value(V))/(10V) ˆ 100.
106.14
8.99
118.10
10.00
0.00
0.13
0.15
0.12
0.09
0.08
0.10
0.13
0.16
0.13
0.00
Error (%)
0.00
0.13
0.15
0.12
0.09
0.08
0.10
0.13
0.16
0.13
0.00
* Error (%) = (Sensor output (V)—Expected value(V))/(10V) × 100.
An eddy current type pressure sensor with an outer diameter of 10 mm was developed and its
characteristic was investigated so as to get appropriate values of the design parameters of the sensor’s
6. Conclusions
two key components, i.e., diaphragm and coil. Some important findings are summarized as follows.
An eddy current type pressure sensor with an outer diameter of 10 mm was developed and its
(1) The coil
designed
in this research
hasget
a good
linear relationship
between
the impedance
change
characteristic
was
investigated
so as to
appropriate
values of
the design
parameters
of the
and the
to targeti.e.,
platediaphragm
up to 500 µm.
sensor’s two
keydistance
components,
and coil. Some important findings are summarized
(2) A round-grooved diaphragm is much better for stable measurement of deflection even with much
as follows.
less deflection compared to a flat type one.
(1) (3)
The Depending
coil designed
in this
research
has aand
good
linear relationship
between
theparameters
impedanceofchange
on the
required
pressure
sensitivity
measurement,
the design
a
and round-grooved
the distance todiaphragm
target plate
up
to
500
μm.
can be selected.
(2) (4)
A round-grooved
betterlinearity
for stable
measurement
deflection
even
The developed diaphragm
sensor showsisamuch
very good
up to
10 MPa withof
linearity
errors
less with
much
less
deflection
compared
to
a
flat
type
one.
than 0.16%.
(3) Depending on the required pressure and sensitivity measurement, the design parameters of a
Acknowledgments: This work was supported by the Human Resource Training Program for Regional
round-grooved diaphragm can be selected.
Innovation and Creativity through the Ministry of Education and National Research Foundation of
(4) Korea
The developed
sensor shows a very good linearity up to 10 MPa with linearity errors less than
(2013H1B8A2032233).
0.16%.
Author Contributions: H.R. Lee and G.S. Lee designed and performed the experiments; H.R. Lee and J.H. Ahn
analyzed the data and wrote the paper; G.S. Lee and H.Y. Kim built up the research project.
Acknowledgments:
This
was
supported
byofthe
Human Resource Training Program for Regional
Conflicts of Interest:
Thework
authors
declare
no conflict
interest.
Innovation and Creativity through the Ministry of Education and National Research Foundation of Korea
(2013H1B8A2032233).
Author Contributions: H.R. Lee and G.S. Lee designed and performed the experiments; H.R. Lee and J.H. Ahn
analyzed the data and wrote the paper; G.S. Lee and H.Y. Kim built up the research project.
Conflicts of Interest: The authors declare no conflict of interest.
Sensors 2016, 16, 1025
11 of 11
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