Download Fiber Bragg Grating sensors to measure the coefficient of

Sensors and Actuators A 189 (2013) 195–203
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Sensors and Actuators A: Physical
journal homepage: www.elsevier.com/locate/sna
Fiber Bragg Grating sensors to measure the coefficient of thermal expansion of
polymers at cryogenic temperatures
Marco Esposito a,h , Salvatore Buontempo a,f , Angelo Petriccione b , Mauro Zarrelli b , Giovanni Breglio c,f ,
Andrea Saccomanno c , Zoltan Szillasi d,f , Alajos Makovec e,f , Andrea Cusano g,f , Antonella Chiuchiolo g,f ,
Marta Bajko h,f , Michele Giordano b,f,∗
a
INFN – National Institute of Nuclear Physics, Sez.NA, Italy
CNR-IMCB – Institute for Composites and Biomedical Materials, National Research Council, Italy
c
DIBET – University of Napoli Federico II, Italy
d
ATOMKI – Institute of Nuclear Research of the Hungarian Academy of Science, Hungary
e
University of Debrecen, Hungary
f
CERN – European Organization for Nuclear Research, Switzerland
g
Engineering Department – University of Sannio-Benevento, Italy
h
DSF – Physical Sciences Department, University of Naples Federico II, Italy
b
a r t i c l e
i n f o
Article history:
Received 3 May 2012
Received in revised form 3 September 2012
Accepted 14 September 2012
Available online 25 September 2012
Keywords:
Thermal expansion
Cryogenic temperature
Fiber optic sensor
FBG
Epoxy
PMMA
a b s t r a c t
One of the fundamental advantages in the employment of the Fiber Bragg Grating (FBG) sensors lies
in their capability to allow measurements in extreme environmental conditions with also very high
immunity toward external electromagnetic interference factors.
The behavior of a polymer-coated FBG sensor, tested in cryogenic conditions at the laboratories of
the European Organization for the Nuclear Research (CERN) in Geneva, has been analyzed and will be
discussed in this paper. Magnets used in the Large Hadron Collider (LHC) for the High Energy Physics
Researches at CERN need in fact extreme cooling conditions to preserve the internal superconductivity
highly crucial for their performances. The magnets, built with NbTi based superconductors, are cooled
with liquid helium and they operate at 1.9 K. The aim of the present work is to estimate the thermal
expansion coefficient of two polymers based on epoxy and methacrylate (PMMA) used as coating of
FBGs, in the temperature range from 4 K to 300 K and to check their suitability for the use in temperature
monitoring of the superconducting magnets. A standard numerical derivative method has been employed
to estimate thermal expansion coefficients; moreover the correlated fluctuation analysis (CFA) based
procedure is proposed, as a reliable alternative, to overcome numerical derivative drawbacks at very low
temperatures within the range of 4–20 K. The calculated values of thermal expansion coefficient for both
systems are in agreement with literature data on similar material.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
The measure of the linear thermal expansion coefficient (CTE) of
a material is generally obtained by the experimental data relative
to the strain or length changes due to the temperature variations.
In fact, it is well known that this material property is defined as
the derivative of the free thermal strain in respect to the temperature. There are many different kinds of sensors which can be
used to measure thermal strain or equivalently material elongation, such as resistive strain gauges sensors, capacitive strain gauges
sensors, laser interferometers, optical sensors, linear variable
∗ Corresponding author at: CNR-IMCB – Institute for Composites and Biomedical
Materials, National Research Council, Italy.
E-mail address: [email protected] (M. Giordano).
0924-4247/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.sna.2012.09.016
differential transformers (LVDT). Many of these sensors have found
applications also in cryogenic conditions, as the resistive strain
gauges [1–4], the LVDT [5] or the capacitance dilatometers, this
latter based on the capacitance changes due to the distance variations between armatures. For example, Escher [6], by using an
highly sensitive capacitance dilatometer, has obtained CTE values from 0.12·10−6 K−1 (at 9.8 K) to 71.9, 68.4 and 61.9·10−6 K−1
at 278 K, depending on the cross-link densities of the examined
epoxy system. Schwarz [7], by an inductive dilatometer, has found
the CTE in cryogenic conditions for both an epoxy (2.9·10−6 K−1 at
16.6 K, 90.6·10−6 K−1 at 289 K) and a PMMA (2.0·10−6 K−1 at 12.2 K,
61.4·10−6 K−1 at 276.9 K); other studies on the CTE of epoxies with
different ZrW2 O8 filler content were also performed by Chu et al.
[1], employing resistive strain gauge sensors.
The aim of this work is the evaluation of the thermal expansion coefficient within the temperature range from 4 K to 300 K,
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for two polymeric materials (i.e. an epoxy and a PMMA) by using
coated FBG sensors. In this way, the suitability of the epoxy and
the PMMA for use in cryogenic sensors has been also checked. The
FBG sensors have several and well-known advantages: compactness, intrinsic multiplexing, lower cost of the devices for the data
acquisition, noise immunity (especially with respect to the electromagnetic fields), low attenuation of the optic signal; but free FBG
sensors also present very low sensitivity to the temperature in cryo
temperature conditions. Epoxy and PMMA have been chosen and
preferred to other coating materials not only for their large thermal expansion coefficients but mainly for their excellent adhesion
to the surface of the fiber which can assure an optimal stress distribution at the fiber-coating interface. Many authors have studied
the FBG sensor behavior in cryogenic condition, mainly for strain,
temperature and structural health monitoring. Rajinikumar et al.
[8] have evaluated the physical properties influencing the Bragg
response (thermo-optic coefficient, photo-elastic coefficient, glass
thermal expansion coefficient) as function of temperature in the
wide range 4–300 K. In his work FBGs were tested at cryogenic
conditions and coated with metal materials to enhance the sensor sensitivity at low temperature. The calculated values of the
sensitivity resulted anyway lower than the sensitivity achievable
through polymer coating due the difference between the CTE of the
tested metals and the CTE of an epoxy or PMMA. Mizunami et al. [9]
measured at low temperature the temperature sensitivity of FBG
sensors fixed on a Teflon substrate, which have showed a higher
sensitivity compared to other substrate materials. It was found that
the temperature sensitivity was even higher than the sensitivity
achievable by using a PMMA substrate; however the main inconvenience relies on the epoxy adhesive layer required to fix the FBG
to the Teflon substrate. James et al. [10] evaluated the temperature sensitivity of the nude FBGs down to 2.2 K. Habisreuther et al.
[11] analyzed instead the response at cryogenic temperatures of
Ormocer (an hybrid polymer material synthesized by a sol–gel process) coated FBG sensors: at 10 K, the thermal expansion coefficient
for the Ormocer coated fiber resulted 1.5·10−6 K−1 . Tanaka et al.
[12] tested FGB sensors at cryogenic conditions under high magnetic fields confirming the magnetic field immunity. Latka et al.
[13] showed the negligibility of the thermo-optic and magnetooptic effects in cryogenic environments for FBG strain sensors
employed for the structural health monitoring of superconductors
when subjected to significant forces generated by strong magnetic
fields.
The present paper has been organized as follows. The onedimensional thermo-mechanical model of coated FBG has been
illustrated in Section 2 to present the governing equations. The
samples manufacturing and the experimental set up have been
detailed in Sections 3 and 4. Raw data from thermal cycling have
been presented in Section 5. The CFA method has been introduced
in Section 6, evaluating the thermal expansion coefficients within
the range 4–300 K. Main results regarding the effectiveness of the
coated FBG as a sensor for the evaluation of the thermal expansion coefficient of the coating material have been presented in
Section 7.
2. Coated Fiber Bragg Grating (FBG)
The structure of the FBG is formed by a periodic refractive
index modulation within the fiber core, which results in a series
of grating planes formed along the fiber axis. If the Bragg condition is met, light signal is coupled into the device and reflected
by each of the grating planes to form a reflected signal substantially characterized by a wavelength commonly known as the Bragg
wavelength (). The Bragg wavelength of a FBG is dependent on
the effective refractive index of the fiber core (n) and the period
of the grating plane () and can be expressed by the well-known
equation [8]:
= 2n
(1)
Any strain variation, dε = d/ or temperature perturbation, dT,
experienced by the FBG results in a shift in Bragg wavelength, which
is given by [9]:
d
= (1 − pe )dε + dT
(2)
In Eq. (2) the photo elastic constant is pe = −(∂n/n∂ε) ≈ 0.23 [8]
and the thermo optic coefficient is = ∂n/n∂T ≈ 8 ppm/K for silica at room temperature [8]. Detailing the mechanical constraints
acting on the fiber optic, it is possible to evaluate the effective deformation experienced by the FBG sensor. As an example, in the case
of free FBG subjected to a temperature variation dT the deformation
of the fiber is determined by the thermal expansion coefficient of
the optical fiber constituent material, ˛glass :
dε = ˛glass dT
(3)
and the shift is obtained from Eq. (2):
d
= [(1 − pe )˛glass + ]dT
(4)
In the case of a temperature variation dT applied to the coating
(having radius R, Young modulus Ec and coefficient of thermal
expansion ˛c ), a difference in tension with respect to the fiber
(having radius r, Young modulus Eglass and coefficient of thermal
expansion ˛glass ) is generated due to the thermal expansion coefficient mismatch between the different materials. The balancing of
the resulting thermal forces along the fiber axis allows the determination of the common deformation of the coating and the fiber,
i.e. dεFBG = dεcoating = dε and, thus, the evaluation of the effective
thermal expansion coefficient of the coated fiber system:
dε
= ˛coated
dT
FBG
=
˛c Hc + ˛glass Hglass
(5)
Hc + Hglass
where H is the longitudinal stiffness, respectively of the coating,
Hc = (R2 − r2 )Ecoating , and glass, Hglass = r2 Eglass . The model of the
coated FBG subjected to the only thermal variation dT is then
derived:
d
=
(1 − pe )
˛c Hc + ˛glass Hglass
Hc + Hglass
+
dT
(6)
The approximation of considering constant the properties of
different materials with temperature leads to a description of the
coated FBG behavior with respect to the temperature starting from
a reference status, i.e. (T0 , 0 ), according to the following expression:
ln
0
=
(1 − pe )
˛c Hc + ˛glass Hglass
Hc + Hglass
+
(T − T0 )
(7)
3. Samples preparation
Fiber Bragg Gratings have been provided by Welltech Instrument Company Limited (Hong Kong) with the following specifications: grating length 10 mm; Bragg wavelength tolerance ±0.5 nm;
reflectivity >90%; FWHM (full width at half maximum of the spectrum) <0.3 nm.
3.1. Coating materials
Polymeric coatings around FBGs were produced using two
classes of polymeric precursors: epoxy and acrylic. For the epoxy
based polymer, precursors are DGEBA high purity liquids with
M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203
197
which facilitates the casting process but, conversely, it allows air
inclusions during premixing operation. To overcome this inconvenience, mixing stage was performed by using a planetary mixer
under vacuum (10 kPa abs) at room temperature.
For the epoxy based system, all components were premixed
in the right proportion (100:14, according to supplier data sheet)
to obtain a reactive mixture and, then, degassed to prevent gas
entrapment in the final product. After degassing the casting was
performed very quickly. The curing profile was then divided in two
steps: a preliminary curing stage at room temperature for 12 h and
a post-curing stage at 100 ◦ C for 4 h.
For the acrylic systems, the premixing stage was slightly different, due to both the presence of the solid component to dissolve
in the liquid one and the long lasting degassing stage not suitable
for such a quick reactive system. For these reasons, the component mixing was a very critical operation; however, by adding the
solid component into the liquid and mixing very carefully it was
found that air entrapment sensibly reduce allowing to abbreviate
the degassing stage. For the acrylic system the first polymerization
stage was very fast, as gelation occurred in a few minutes and solidification in less than 1 h. Post curing stage was the same as for epoxy
system.
Fig. 1. Mould set up for manufacturing of polymer coating on FBG fiber.
an EEW of 170–175, multi-functional aliphatic amine as hardener
and a tertiary amine as catalyst. The employed epoxy system was
supplied by Elantas Camattini (Italy) under the label, EC-170 + IG
824-K24.
PMMA precursors were arranged in a two-component system:
a very fine PMMA powder mixed with a peroxide catalyst and a liquid mixture, characterized by the presence of methylmethacrylate
monomers, crosslinking agent and initiator. The acrylic system was
supplied by Heraeus (Paladur). The powder and the liquid mixture
were premixed in the right proportion and then quickly used due
to its rapid reaction time (within a few minutes).
3.2. Coating methods
Epoxy based and acrylic polymers were obtained starting from
its liquid precursors by in situ polymerization, and then reactive
casting was employed as most suitable manufacturing process to
realize the coated FBG samples. This solution allows producing an
interface between polymeric material and fiber cladding, which
ensures an efficient strain transfer from the polymer system to
fiber. Polymer precursors are liquid and highly compatible with
silica, which represents the main constituent of the fiber cladding,
and thus a good surface wetting could be achieved before polymerization.
After the fiber was cleaned with isopropylic alcohol, the polymeric material was casted around the cladding section near the
Bragg grating. The final nominal dimensions of coating of the fiber
containing the Bragg grating were 2.5 mm height, 5.0 mm width,
and 25.0 mm length.
To carry out the manufacturing process by reactive casting, an
optimized mould was realized (the inferior half mould is reported
in Fig. 1). In the manufacturing setup, a constrain system was accurately designed in order to induce pre-alignment and pre-stress
to the FBG sensor and at the same time to control the chemical
shrinkage due to the polymerization reaction during the first curing
stage. An extra post-curing stage was considered for both reactive
systems by using a constrain-free configuration; this was to allow
the natural rearrangement of the system and to reduce the local
interfacial stresses between polymer coating and cladding near the
FBG grating. For each polymeric coating, four different specimens
were prepared at once, in order to obtain fully comparable items.
Both systems exhibit a very low viscosity at room temperature,
4. Experimental set up
The samples were positioned in a dedicated sample holder and
then inserted into the cryostat as shown in Fig. 2(a). The FBG sensor
holder consists in a small copper box assuring a good thermal stability among the FBG fibers and the reference temperature sensors.
Two temperature sensors, one of a type CERNOXTM and another
thermo resistive Platinum thermocouple (PT100), previously calibrated, where used to monitor the ambient temperature. The
cooling down of the system was performed by using liquid helium
pumped into the cryostat until the final temperature reached 4.2 K.
Due to this pumping operation, the cool-down turned to be too
rapid and later analysis proved that the thermal equilibrium could
not be reached within the sample holder. In contrary, the warmup could take sufficiently long time, since the liquid helium was
allowed to boil away in the cryostat.
In order to control the warm-up, resistors were placed at the
bottom of the sample holder; however, since no further helium
was pumped into the holder, this setup did not allowed a suitable
temperature stabilization and thus only a slow and poor controlled
warming-up stage could be achieved.
The two temperature sensors were connected electrically in
series and powered by a Keithley 2400 source meter operating in
a constant current source mode. Voltage readouts were performed
by a Keithley 2000 and a Keithley 2001 precision DMM devices. In
order to reduce the bias on the measured temperature associated
to the Seebeck-effect, voltage drops on both temperature sensors
were read out at different polarities and the voltage drop readouts
were averaged to compute temperature values. This temperature
value then served as an input for the proportional warm-up control. The resistors were connected to a TTi TSX3510 power supply.
All three Keithleys and the TTi devices were connected to a GPIB
bus that controlled by customized software through a Prologix
GPIB-ethernet controller. A schematic diagram showing all the
instruments used in the experimental set up for the data acquisition is reported in Fig. 2(b), where the optical measurement (a),
the readout of the reference temperature sensors (b) and the heater
with the PR 4116 Universal transmitter – DSS (c) are drawn.
Four different FBG sensors were located in the sample holder.
In order to increase the reliability of the sensors, two epoxy coated
FBGs were spliced together and both ends were brought out from
the cryostat. The same setup was built for the PMMA coated sensors.
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Fig. 2. (a) Experimental setup. (b) Schematic drawing of the DAQ: the optical measurement (a), the readout of the reference temperature sensors (b) and the heater with the
PR 4116 Universal transmitter – DSS (c).
This configuration, allowed the readout on all sensors from both
sides, so data were assured to be recorded even in case of optic
fiber break. One end of the epoxy sensors array and one end of
the PMMA sensors array were connected to a Micronoptics sm125
interrogator. Fig. 3 shows the reflected spectra of the sensors at
room temperature.
5. Experimental results
Data acquisition has been performed for several cooling down
and warm up cycles. The experimental dataset consists of two types
of signal: voltage from the thermal resistive sensors (PT100 and
CERNOXTM ) and central reflected wavelength signals from FBG sensors. The experimental data from the cryogenic test-bench was
stored in a Network-attached Storage unit (NAS) situate at CERN
and off-line processed. Fig. 4(a) shows the temporal evolution of the
Bragg wavelength for all the FBG sensors. The letter A represents
the epoxy-coated sensor while the letter B represents the PMMAcoated sensor. The two digits indicate the sensors reference Bragg
wavelength in nanometers at room temperature (e.g. 62 stands for
1562 nm). Fig. 4(b) shows the time evolution of the temperature,
as measured by the CERNOXTM sensor. In total 16 different warmup and 16 cool-down steps were performed. Raw data related to
the Bragg wavelength and temperature evolution, as reported in
Fig. 4, were computed according to Eq. (7) normalizing the sensor responses to the room temperature and to the reference Bragg
wavelength.
Fig. 5 reports the normalized sensors output as a function of the
temperature (only warm up test were analyzed).
Epoxy-coated sensors present in general a smaller change of the
Bragg wavelength compared to the PMMA-coated sensors within
the range 4–300 K.
Fig. 6 shows the normalized sensors outputs in the low temperature range. Fig. 6(a) and (b) reports the normalized sensors outputs,
relative to the epoxy and PMMA coated sensors, respectively. All
the thermal cycles are reported. Fig. 6(c) and (d) shows the values
averaged among all the warming up cycles. The sensitivity of the
FBG sensors decreases at low temperatures for both the polymers.
6. Evaluation of the thermal expansion coefficient
6.1. Methodology
The thermal expansion coefficient of the coating system,
˛coating (T), can be easily found starting from Eq. (6):
˛coating (T ) =
Hglass + Hc
1 d
Hc (1 − pe )
dT
−
−
Hglass
Hc
˛glass
(8)
Fig. 3. Spectral distribution of the reflected light from the FBG sensors on room temperature. Blue line refers to epoxy coated FBGs array. Black line refers to PMMA coated
FBGs array. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203
199
Fig. 4. (a) Bragg wavelength of the FBG sensors vs. time. The blue and the red lines represent the epoxy-coated FBGs (A55 and A65), the green and the black line represents
the PMMA-coated FBGs (B52 and B62). (b) Reference sensor temperature vs. time. (For interpretation of the references to color in this figure legend, the reader is referred to
the web version of the article.)
The thermal expansion coefficient of the coating material is not
only dependent on the thermo and elasto optical properties of the
FBG sensor but also on thermo-mechanical properties of the fiber
itself and its coating material. Therefore the more accurate analysis
of the terms in Eq. (8) is needed.
At room temperature (RT), 300 K, the Young modulus of the glass
and the polymers, are Eglass = 77 GPa and Ecoating = 3 GPa, respectively, according to Takeda [14]. These values lead to the following
relative stiffness for the tested sensors: Hglass /Hc = 0.015 @ RT. On
the other hand, at very low temperature the polymers Young modulus, Ecoating , increases more than the Young modulus of the silica,
Eglass , with a further arising of the relative stiffness of coating.
In particular, at cryo temperature (CT), 4 K, the Young modulus of the glass and the polymers are respectively Eglass = 83 GPa,
Ecoating = 9 GPa [14] and thus relative stiffness is Hglass /Hc = 0.005 @
CT.
Furthermore at RT, according to Rajinikumar et al. [8], James
et al. [10] and Habisreuther et al. [11], the physical properties of the
FBG silica are: ˛glass = 2.6 ppm/K, = 8.59 ppm/K, pe ∼
= 0.23, while at
low temperatures (4 K), the physical properties of the FBG silica
are: ˛glass = 1.0 ppm/K, = 1.02 ppm/K, pe ∼
= 0.23 [8,10,11].
Table 1 summarizes all the properties at cryo and room temperature of the fiber and the coating. Based on these values, the
following engineering assumptions have been set: Hglass /Hc ∼
= 0 and
pe (T) ∼
= 0.23 independently of the temperature. Substituting in Eqs.
(5) and (6), these assumptions give back:
k(T ) ≡
d ln(/u )
= ˛coating (T )(1 − pe ) + (T )
dT
(9)
(with u = 1 nm), or equivalently:
˛coating (T ) =
1
(k(T ) − (T ))
1 − pe
(10)
Fig. 5. Normalization to room temperature and reference Bragg wavelength of FBG sensors outputs vs. temperature (only warm-ups). Solid lines are averaged over different
warm ups, dotted lines are individual warm-ups outputs.
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M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203
Fig. 6. Zoom plot for normalized sensor outputs from 4 K to 15 K. (a) Epoxy-coated sensors. All the warm-ups. (b) PMMA-coated sensors. All the warm-ups. (c) Epoxy-coated
sensors. Average sensitivity curves. (d) PMMA-coated sensors. Average sensitivity curves.
Table 1
List of all the properties at cryo and room temperature of fiber and coating.
Temperature (K)
Eglass (GPa)
Ecoating (GPa)
˛glass (ppm/K)
(ppm/K)
pe
4
300
83
77
9
3
1.0
2.6
1.02
8.59
0.23
0.2
The evaluation of the thermal expansion coefficient of the coating material can be obtained by the estimation of the temperature
derivative of the logarithm of sensor outputs, (T). A standard
procedure to perform numerical temperature derivative has been
applied to the outputs of FBG and temperature sensors. The numerical derivative method needs a continuous monotonic temperature
variation to reconstruct the function and thereof its temperature
derivative. Due to the poor temperature control in very low temperature range, the numerical derivative algorithm inevitably fails.
An alternative method should be implemented to overcome such
drawback.
6.2. Correlated fluctuation analysis (CFA)
u
(t) = ki · T (t) + c
(11)
where i indicates the i-th interval and ki is provided by Eq. (9). Under
this hypothesis, for the i-th set of points, for the expected value E{}
and variance Var{}, it results:
E ln
u
i
= ki E{T }i + c
u
i
= ki2 · Var{T }i
(13)
or, equivalently:
ki =
ln(/u )i
Ti
(14)
where ln(/u ) and T are, respectively, the logarithm of Bragg
wavelength shift and temperature standard deviations relative to
the i-th interval. The time duration of each sub interval i, was chosen such as the corresponding temperature variation within the
sub-interval was less than 0.3 K.
7. Results and discussion
Hereafter, an alternative methodology is proposed to evaluate
the CTE based on correlated fluctuation analysis (CFA) of the two
time signals, namely the Bragg wavelength shift, ln(), and temperature, T. The fluctuation analysis has been performed by dividing
the temperature history in short temporal intervals, I, in which the
temperature is almost constant. In these conditions the relationship between temperature T and ln(/u ) can be considered linear,
thus it can be written:
ln
Var ln
(12)
The thermal expansion coefficients of coating polymers were
obtained by computing both methods, i.e. by evaluating the temperature derivative and by performing the CFA based procedure.
Fig. 7 shows the estimated CTE values (averaged over the all
warm-ups) accounting the sensor raw data (different for coating
material employed and reference Bragg wavelength) according to
the numerical temperature derivative method without considering the thermo-optic effect. Analysis performed on different FBG
sensors coated by the same material gives CTE values substantially
identical. Similar results have been obtained with the fluctuation
analysis procedure.
Fig. 8(a) and (b) reports respectively, for each of the indicated
material and employed algorithm, the mean and the standard deviation. These latter values were computed by taking into account all
curves (one for each warm-up step from 4 to 300 K) of the thermal expansion coefficient as function of the temperature achieved
M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203
201
Fig. 7. Thermal expansion coefficient obtained through numeric derivative from
sensors with different reference Bragg wavelength data averaged on all the warmups.
Fig. 9. Thermal expansion coefficient (zoom at low temperatures).
without considering the thermo-optic effect. On the same graph,
literature data for similar material systems were reported as dotted
points [15].
Good agreement was found between the two methods for the
estimation of the thermal expansion coefficient in the temperature
range between 50 and 300 K, while remarkable discrepancies were
found in the very low temperature range between 4 and 50 K.
Estimated values of the thermal expansion coefficients for epoxy
and PMMA systems used in this study have been compared with
literature data regarding similar material systems [15] showing an
excellent agreement. Very interestingly, the numerical derivative
method provides a worse estimation of the CTE values within the
low temperature range. In the range 4–20 K the standard deviations
are of the same order of magnitude of the estimated CTE values. This
effect is probably due to the fact that numerical derivative method
needs a continuous monotonically temperature variation to reconstruct the function and thereof its temperature derivative, while
fluctuation analysis do not require this constrained conditions. In
particular, correlated fluctuation analysis method has been proposed, in this work, to overcome limitations arising from a not
“ideal” temperature and Bragg wavelength signal synchronicity
(from diffusive time lags and analog signals synchronization) and
a “not monotonic” temperature variations (due to the not perfectly
controlled temperature ramping). It is worth noting that correlated fluctuation analysis is well performing also in the temperature
range where a numerical derivative method results ineffective.
Fig. 9 shows a close up of the thermal expansion coefficients
in the low temperature range 4–50 K. In this range the two
methods provide significant difference in the thermal expansion
coefficients estimates. Most relevant is the concavity of the function ˛coating (T). CFA analysis registers a level off of the thermal
expansion coefficients just below 10 K, while numerical derivative method suggests a sharp decrease of the thermal expansion
coefficient within the same range.
In particular, CFA analysis suggests a strong non linearity within
the range 4–10 K. In this range, defined as Debye temperature
range, maxima of the thermal expansion coefficient have been
already reported [15]. The 4–10 K range will be matter of further and dedicated experimental investigations. Finally, Fig. 10
shows thermal expansion coefficient predictions obtained by using
Rajinikumar et al. [8] measurements of the temperature dependent
thermo-optic coefficient. As a matter of fact, neglecting the thermo
optic coefficient will introduce a maximum 20% overestimation
of the CTE values, as showed in Fig. 10 by the ratio between the
Fig. 8. (a) Thermal expansion coefficients of epoxy and PMMA (averaged on all the warm-ups) without considering thermo-optic coefficient. (b) Standard deviation of the
thermal expansion coefficient for the epoxy and the PMMA thermo-optic coefficient without considering thermo-optic coefficient.
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M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203
correlated analysis of the FBGs outputs and the temperature sensors to evaluate the thermal expansion coefficient extending the
data interpretation in the Debye temperature range (4–10 K) and
(c) the suitability of the epoxy and PMMA coatings to be employed
for cryogenic temperature monitoring, since they can guarantee
adequate level of the sensitivity to the sensor as assured by their
thermal expansion coefficient values in the wide range 4–300 K.
References
Fig. 10. Ratio between the thermal expansion coefficients obtained considering and
not the thermo-optic effect.
CTE values obtained considering thermo optic effect and those
achieved without taking into account this effect.
8. Conclusions
FBGs have been used to evaluate the thermal expansion
coefficients of two coating polymeric materials: namely, an epoxy
and a PMMA resin. In general, the response to a temperature change
of a coated FBG depends on the physical properties of the fiber
(thermo-mechanical, thermo-optical and elasto-optic properties),
on the thermo-mechanical properties of the coating material and
on the geometry of the assembly, i.e. fiber radius and the coating
thickness. Such a complex interplay between these factors makes
very complex the response of the coated FBG sensor to the temperature variations. The potential application of this sensor system for
the evaluation of the thermal expansion coefficient of the coating
material requires an appropriate design. In particular, the thickness of the coating could be chosen in order to set the stiffness of
the coating in respect to that of the sensor. In fact, when Hc Hglass ,
the temperature response of the coated FBG is dominated by the
thermal expansion coefficient of the coating. Based on this engineering approximation, the thermal expansion coefficients of an
epoxy resin and a PMMA have been evaluated accounting for both
the elasto-optic coefficient and thermo-optic coefficient of the optical fiber in a wide range of temperature, i.e. 4–300 K. Results for the
two polymers have been compared with literature data for similar
polymeric systems resulting in an excellent agreement.
Thermal expansion coefficient requires the evaluation of sensor
output variation due to the temperature variation. The standard
numerical temperature derivative method suffers of serious drawbacks due to the phase mismatch between the two experimental
signals, mostly in the very low temperature range where temperature control is difficult. To overcome such problems a method based
on the analysis of the fluctuations of the two signals has been proposed such as a correlated fluctuation analysis based procedure.
Comparison between the direct calculation from the sensors output
of the numerical temperature derivative and the CFA method have
showed that thermal expansion coefficients evaluation are consistent and in the very low temperature range, the so-called Debye
temperature range (4–10 K), the CFA produces better estimates.
Main results of the present work are: (a) the demonstration
of the efficiency of FBG sensor in the measurement of the coating material thermal expansion coefficient down to cryogenic
temperatures, (b) the proposal of a methodology based on the
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Biographies
Marco Esposito got the Master degree in Mechanical Engineering in 2006 at the
University Federico II of Naples – Italy. From 2007 to 2010 he collaborated with the
Institute for Composite and Biomedical Materials of the National Research Council,
CNR – IMCB Italy, in the fields of structural and fluid dynamic analysis on components in composite materials. After the 2nd Level Master degree in Automotive
Engineering got in 2010, he started in 2011 the PhD in Fundamental and Applied
Physic. Current fields of interest: simulations/numerical analysis, optical sensors,
high energy physic.
Salvatore Buontempo got the degree in Electronic Engineering in Naples University
in 1989 with an experimental thesis at CERN. He specialized in Particle Physics
Detectors and he got a permanent position as researched in INFN Naples in 1993. In
2000 he got the level of INFN Senior Researcher and INFN Research Director in 2004.
In 2001-2002 he was CERN Scientific Associate. In 2003-2005 he was CERN Project
Associate. In 1991-1998 he participated in CHORUS experiment at CERN as Project
Manager of Electromagnetic Calorimeter. In 1998-2008 he participated in OPERA
experiment in CERN and LNGS as Technical Coordinator. Since 2008 he is Technical
Coordinator of the RPC detector in CMS Experiment at CERN and member of CMS
Central Technical Coordination Office. Fields of Interest: Construction and R&D on
Particle Physics Detectors, their Instrumentation and Technology Transfer.
Angelo Petriccione graduated in Materials Engineering and received the Ph.D.
degree in Materials and Structures Engineering from the University of Naples “Federico II”, Naples, Italy, respectively in 2006 and 2011. He is currently working as
Post-doc fellow at Institute for Composite and Biomedical Materials of the Italian
National Research Council (IMCB-CNR). His current research interests include the
study of carbon nanoparticles composites and advanced thermoplastic PMCs made
by rective processing.
M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203
Mauro Zarrelli is permanent researcher at Institute for Composite and Biomedical
Materials (IMCB) of the National Research Council (CNR). He obtained an Undergraduate Degree in Materials Engineering at University of Naples “Federico II” in 1998.
He defended his PhD at Cranfield University in 2002 working on novel polymer
composite matrix for aerospace application, receiving an AUDI Foundation grant
(2001) as young researcher. Major area of expertise are: polymer composite for
aerospace application, nano-composites, electrical mechanical and thermal property, degradation and fire behavior, delamination and residual stress, fire resistance.
He took part to several EU and National projects and he has published 25 scientific papers, 3 book contributions and more than 40 contributions to international
conferences.
Giovanni Breglio was born on 1965. He graduated in electronic engineering cum
laude at University of Naples Federico II on 1990. On 1994 he took the PhD degree.
From 1996 to 2001 he was as Permanent Researcher at Electronic Department at
University of Naples. Since 2001 he is Associate Professor at the Faculty of Engineering of Federico II. Since 2006 he is the Coordinator of the Electronic Engineering
Courses at the University of Naples Federico II. The actual scientific activities of
Giovanni Breglio are manly in the areas of Power Electronic Devices development
and characterization, and the design and optimization of optoelectronic devices and
Fiber Optic Sensor systems. On these topics he is author or coauthor of more than
150 among journal and proceedings articles. He is owner of six international patents.
He contributes as reviewer or TPC component to the most important Journals and
Conference of the cited topics.
Andrea Saccomanno was born on April 7, 1982 in Benevento, Italy. In 2009 he
received the M. S. degree in Telecommunication Engineering from University of
Sannio, Italy, defending an experimental thesis on the fabrication of photonic quasicristals. In 2010 he joined the University of Napoli “Federico II” as PhD student.
His main research interests are in monitoring system based on Fiber Bragg Grating
sensors and Photonic Crystals for sensing applications.
Zoltan Szillasi got the MSc in 1996 in Physics at the Kossuth University, Debrecen,
Hungary. Between 1999 and 2008 he was an assistant lecturer of the same University
(which in the meantime became University of Debrecen). In 2008 he obtained his
PhD in Physics. Since then he is an associate researcher of the Institute of Nuclear
Physics of the Hungarian Academy of Sciences (ATOMKI) in Debrecen. Since his MSc
he have worked on the Charged Higgs Boson search in the L3 experiment at LEP, then
he joined the CMS collaboration in 2000 where he participated in the development
of the Hardware Muon Barrel Alignment System of which he is presently the project
coordinator from the Hungarian side. In 2009 he joined the FOS4CMS collaboration.
His principal interests are the measurement development and large scale integration
of the measurement technologies.
Alajos Makovec got the MSc at the University of Debrecen in 2011 where he continued his work as a PhD student. Presently, he is working on data acquisition and
measurement automation.
Andrea Cusano was born on May 31, 1971, in Caserta. He received his Master degree
cum Laude in Electronic Engineering on November 27, 1998 from University of
Naples “Federico II”, Italy and his Ph.D. in “Information Engineering” from the same
University. He is actually Associate Professor at the University of Sannio in Benevento. From 1999 his activity is focused in the field of optoelectronic and photonic
devices for sensing and telecommunication applications. He was cofounder in 2005
of the spin-off company “OptoSmart S.r.l.” and in 2007 of the spin-off company
“MDTech”. He published over 120 papers on prestigious international journals and
more than 150 communications in well known international conferences worldwide; he has 4 international patents currently in charge of prestigious industrial
companies (Ansaldo STS, Alenia WASS, Optosmart and MdTEch) and more than
10 national patents. He is Editor-in-Chief of the journal Optics & Laser Technology (Elsevier), and associate editor of Sensors and Transducers Journal, Journal of
Sensors (Hindawi), The Open Optics Journal (Bentham), The Open Environmental
203
& Biological Monitoring Journal (Bentham) and the International Journal on Smart
Sensing and Intelligent Systems. He is also referee of several scientific international
journals. He is a member of the technical committee of several international conferences such as IEEE Sensors, ICST, EWSHM, EWOFS. Andrea Cusano was principal
investigator and scientific responsible of several national and international research
projects. He is coauthor of more than 10 chapters published in international books
and invited papers in prestigious scientific international journals. He is coeditor of 2
Special Issues (Special Issue on Optical Fiber Sensors, IEEE Sensors 2008, and Special
Issue on “Fiber Optic Chemical and Biochemical Sensors: Perspectives and Challenges approaching the Nano-Era”, Current Analytical Chemistry, Bentham, 2008,
and of 3 scientific international books. He is also consultant for big companies of the
Finmeccanica group such as Ansaldo STS and Alenia WASS. He has also collaborations with CERN in Geneva where he is working on the development of innovative
sensors for high energy physics applications.
Antonella Chiuchiolo was born in Benevento on April 1983. In 2006 she obtained
the first level degree in Computer Science Engineering at University of Sannio (Benevento). For her thesis about the structural monitoring with fiber optic sensors, she
has been working with the Optoelectronic Division of University of Sannio in collaboration with CIRA (The Italian Aerospace Research Centre). Then she started her
studies in Automation Engineering at University of Sannio. During her master thesis activities, from January to June 2011, she has been involved with a stage of 5
months at CERN (European Organization for Nuclear Research) in Geneva, in the
project devoted to the development of new temperature sensors based on Fiber
Bragg Gratings technology. On July 2011 she obtained the master degree with mark
110/110 cum laude and the thesis “Feasibility study of the use of Fiber Optic Sensors
in cryogenic environment for superconducting magnets at CERN”.
Marta Bajko is MS. Mechanical Engineer from the Technical University of Budapest
where she got her degree in 1994. From 1994-1996 she worked in Spain as engineer
in the Physics department of the CEDEX Laboratory on superconducting technology.
From 1996-today she is employed by CERN where she is presently leading the superconducting magnet test facility after having worked on the design and development
of the LHC superconducting magnets <correctors and main dipoles> and having followed as project engineer the production of 1/3 of the main dipoles of the LHC.
Current fields of interest: superconducting technology, cryogenics, instrumentation
at low temperature for superconductors.
Michele Giordano, born in 1968, he received his Master degree cum Laude in
Chemical Engineering at the University of Naples “Federico II” in 1992. In the same
year he started a Ph.D. course in Materials Engineering. Ph. Doctor in 1995. Up to
1998 he completed the formative track within the Institute for Composite Materials Technology ITMC of the National Research Council CNR. In 1998 he acquired
a definite time position as a Researcher at ITMC CNR where he become a Permanent Research in 2001. From 2003 to present he has been selected as a Lecturer at
the University of Naples “Federico II” giving the “Composite Materials Technology”
course. Since 2005 Senior Scientist at the Institute of Composite and Biomedical
Materials IMCB CNR. In 2005 he has also been cofounder of the research spin-off
company “OptoSmart”, focused on the development of fiber optic sensor systems.
Since 2006 he has designed as the Responsible of the Composite Technology unit of
IMCB-CNR coordinating the corporate CNR project “Polymers, composite and nanostructures technologies”. Since 2010 he is adjunct researcher at CERN. In 2007, he
has cofounded a new research spin off company, MDTech, acting in the field of optical systems for biomedical applications. In 2011, he has cofounded a new research
spin off company, Optoadvance, acting in the field of applications of optical sensors
systems in music. Research activities are within the area of engineering and materials science. In particular the main research focuses are nano and macro composite
materials, mainly polymer based, including multiscale design and processing of multifunctional composite materials, structural health management systems and thin
films engineering for sensing and optoelectronic applications. He is author of more
than 120 peer reviewed (ISI indexed) scientific papers and seven book chapters.