Monitoring of Resin Transfer Molding Processes with ...
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Monitoring of Resin Transfer Molding Processes with Distributed Dielectric Sensors Michael Campbell Hegg A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering University of Washington 2004 Program Authorized to Offer Degree: Department of Electrical Engineering
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Monitoring of Resin Transfer Molding Processes with Distributed Dielectric Sensors
Michael Campbell Hegg
A thesis submitted in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering
University of Washington 2004
Program Authorized to Offer Degree: Department of Electrical Engineering
University of Washington
Graduate School
This is to certify that I have examined this copy of a master’s thesis by
Michael Campbell Hegg
and have found it complete and satisfactory in all respects,
and that any and all revisions required by the final
examining committee have been made.
Committee Members:
_________________________________________
Alexander V. Mamishev
_________________________________________
Karl Böhringer
_________________________________________
Mark Tuttle
Date: _________________
In presenting this thesis in partial fulfillment of the requirements for a master’s degree at
the University of Washington, I agree that the Library shall make its copies freely
available for inspection. I further agree that extensive copying of this thesis is allowable
only for scholarly purposes, consistent with "fair use" as prescribed in the U.S. Copyright
Law. Any other reproduction for any purposes or by any means shall not be allowed
without my written permission.
Signature_______________________________
Date___________________________________
University of Washington
Abstract
Monitoring of Resin Transfer Molding Processes with Distributed Dielectric Sensors
Michael Campbell Hegg
Chair of the Supervisory Committee Assistant Professor Alexander Mamishev
Department of Electrical Engineering
A distributed array of dielectric sensors for remote in-situ sensing in resin transfer
molding (RTM) and vacuum-assisted resin transfer molding (VARTM) is designed. The
system is composed of three dielectric sensors and a custom-designed three-channel
amplification circuit. A multiplexing circuit was designed and fabricated to accommodate
the use of a novel multi-pixel transparent sensor for future work. The sensors react to
changes in capacitance and conductance as liquid impregnates the mold. Capacitance and
conductance are inferred from raw gain and phase measurements made by the
amplification circuit. Numerical simulations of the sensors provide a means to correlate
measured capacitance values to flow-front position along the mold. Results of visual and
sensor fill-front position for RTM and VARTM are presented and are in good agreement.
Calibration-based sensing is demonstrated as a means of monitoring degree of cure for
fiberglass and carbon fiber performs during VARTM. These preliminary results suggest
the feasibility of such a method as a comprehensive adaptive control technique.
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Table of Contents
List of Figures................................................................................................................... iii
List of Tables .................................................................................................................... vi
Chapter 1. Introduction.................................................................................................... 1 1.1 Background......................................................................................................... 1 1.2 Problem Statement .............................................................................................. 2
1.2.1 Fill Front Monitoring .................................................................................. 3 1.2.2 Cure Monitoring.......................................................................................... 4
1.3 State of the Art .................................................................................................... 5 1.3.1 Fringing Electric Field Sensor Arrays ........................................................ 5 1.3.2 Alternative Technologies ............................................................................ 7 1.3.3 Vacuum-Assisted Resin Transfer Molding (VARTM)............................... 7
1.4 Outline of Thesis............................................................................................... 12
Chapter 2. Background .................................................................................................. 14 2.1 Principles of FEF Sensors................................................................................. 14
2.1.1 Imposed Frequency-Wavenumber (ω-k) Sensing..................................... 15 2.1.2 Advantages of FEF Sensors ...................................................................... 17
2.2 Dielectric Spectroscopy of Polymeric Materials .............................................. 18 2.2.1 Dielectric Permittivity............................................................................... 19 2.2.2 Polarization, Relaxation, and Resonance.................................................. 22 2.2.3 Modeling Dielectric Dispersion: Relaxation Functions............................ 24
Chapter 3. Data Acquisition System ............................................................................. 28 3.1 Sensors .............................................................................................................. 28
3.1.1 Parallel-Plate Sensor Design and Fabrication........................................... 28 3.1.2 FEF Sensor Design and Fabrication ......................................................... 31 3.1.3 Novel Transparent Multi-Pixel Sensor Design and Fabrication ............... 31 3.1.4 Design Constraints for Parallel-Plate and FEF Sensors............................ 33
3.2 Measurement Circuitry ..................................................................................... 34 3.2.1 Three-Channel Board and LabView Software.......................................... 35 3.2.2 Multiplexing Board for Multi-Pixel Sensor.............................................. 38
Chapter 4. Experimental Setup ..................................................................................... 39 4.1 RTM Mold and Materials ................................................................................. 39
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4.2 VARTM Mold and Materials............................................................................ 43 4.3 Filling Scenarios ............................................................................................... 45
Chapter 5. Experimental Results for RTM .................................................................. 47 5.1 Predicted Fill-Front Position............................................................................. 47 5.2 Predicted Sensor Performance .......................................................................... 50 5.3 Experimental Capacitance and Phase Data....................................................... 53 5.4 Data Analysis .................................................................................................... 56 5.5 Flow-Front Position .......................................................................................... 58
Chapter 6. Experimental Results for VARTM ............................................................ 60 6.1 Experimental Procedure (Fiberglass)................................................................ 60 6.2 Experimental Results for Fill-Front (Fiberglass).............................................. 60 6.3 Data Analysis .................................................................................................... 62 6.4 Experimental Results for Cure Monitoring (Fiberglass) .................................. 65 6.5 Experimental Procedure (Carbon Fiber)........................................................... 66 6.6 Experimental Results for Fill-Front (Carbon Fiber) ......................................... 67 6.7 Experimental Results for Cure Monitoring (Carbon Fiber).............................. 69 6.8 Discussion of Cure Monitoring for Carbon Fiber............................................. 74
Chapter 7. Disturbance Factors..................................................................................... 76
Chapter 8. Future Work and Conclusions ................................................................... 78 8.1 Carbon Nanotubes............................................................................................. 78 8.2 Parameter Estimation Algorithms..................................................................... 79 8.3 Conclusions....................................................................................................... 80
References........................................................................................................................ 81
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List of Figures
Figure 1.1 Photograph of closed mold cavity for RTM experimental setup with distributed dielectric sensors 1
Figure 1.2 Photograph of open mold cavity for VARTM experimental setup with distributed dielectric sensors. 2
Figure 1.3 Next generation sensor prototype design 11 Figure 2.1 A fringing field dielectrometry sensor can be visualized as a
parallel plate capacitor whose electrodes open up to provide a one-sided access to material under test. 14
Figure 2.2 A single-wavelength generic design. 17 Figure 2.3 Multiple penetration depths. Electric field lines extend into
space beyond the distributed sensor. 17 Figure 2.4 Conceptual view of the total current in a leaky capacitor. 20 Figure 2.5 Leaky capacitor: a) dielectric material sandwiched between
two perfectly conducting parallel plates. b) the equivalent circuit representation. 21
Figure 2.6 Graphical representation of the Debye function. 26 Figure 2.7 Graphical representation of the HN function. 27 Figure 3.1 General operating principle of the sensor including edge
effects. Fluid flows into the mold cavity and position is inferred from changes in capacitance. 30
Figure 3.2 Photographs of FEF sensor designed for VARTM experiments. 31
Figure 3.3 Transparent sensor fabricated by sputtering Indium Tin Oxide onto a thin polyester sheet. 32
Figure 3.4 Drawing of design pattern for multi-pixel transparent sensors. 33 Figure 3.5 Circuit schematic for three-channel board. 36 Figure 3.6 Photograph of three-channel circuit and breakout box. 37 Figure 3.7 Photograph of multiplexing board and transparent sensor. 38 Figure 4.1 RTM mold and video camera that allows for independent
measurements of fill-front position. 41 Figure 4.2 Experimental setup with distributed dielectric sensors. Fill
front position is inferred as the glycerin/water solution passes under the sensor. 42
Figure 4.3 General schematic of the experimental system with data acquisition. 42
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Figure 4.4 Photograph of VARTM experimental setup with FEF sensors. 44
Figure 4.5 Drawing of cross-section for VARTM experimental setup. 45 Figure 4.6 Illustrations of 1-D and 2-D filling scenarios for RTM and
VARTM experiments. 46 Figure 5.1 Comparison between experimental (visual) and predicted
data for varying reservoir pressures (10, 13, 16 psi). 50 Figure 5.2 Equipotential lines and distribution of the electric field in and
around the dielectric cell. The size of the arrows is logarithmically proportional to the intensity of the electric field. 51
Figure 5.3 Numerical results for sensor 2. The geometry and position of the sensor on the mold determines the characteristic curve. 52
Figure 5.4 Experimental capacitance data shows gradual increase in capacitance over time. 55
Figure 5.5 Experimental phase data shows gradual positive increase in phase over time, indicating that the material under test is weakly conductive. 56
Figure 5.6 Graphical representation of the mapping algorithm used in the data analysis. 58
Figure 5.7 Visual and experimental comparison of measured fill-front position at the centerline. 59
Figure 6.1 Measurements of 1-D fill-front position in VARTM for fiberglass preforms. 62
Figure 6.2 Plot of change in capacitance versus flow distance. 63 Figure 6.3 Plot of change in capacitance versus flow distance. 65 Figure 6.4 Measurement of parameters during cure of polyester resin for
VARTM with fiberglass. 66 Figure 6.5 Measurements of 1-D fill-front position in VARTM for
carbon fiber preforms. 68 Figure 6.6 Plot of visual and sensor predicted fill front location. 69 Figure 6.7 Measurement of parameters in the time domain during cure
of polyester resin for VARTM with carbon fiber preforms. 70 Figure 6.8 Measurement of parameters in the frequency domain during
cure of polyester resin for VARTM with carbon fiber preforms. 71
Figure 6.9 Sensor 1 measurement of parameters in the frequency domain during cure of polyester resin for VARTM with carbon fiber preforms. 72
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Figure 6.10 Sensor 2 measurement of cure cycle of polyester resin for VARTM with carbon fiber preforms at frequencies from 100 Hz to 30 kHz.. 73
Figure 6.11 Sensor 3 measurement of cure cycle of polyester resin for VARTM with carbon fiber preforms at frequencies from 100 Hz to 30 kHz. 74
Figure 8.1 Two cases of nanotube orientation: nearly aligned (left) and randomly oriented (right). 79
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List of Tables
Table 1.1 RTM manufacturing example: types of sensors converting electrical properties to other physical properties. 8
Table 2.1 Polarization phenomena in materials. 23 Table 2.2 Relaxation functions for experimental dielectric data 25
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ACKNOWLEDGEMENTS
I would like to thank my advisor, Prof. Alexander Mamishev, for supervising my
research, providing guidance when needed, and for his technical, financial, and emotional
support.
This thesis would not have been possible but for the hard work of several
undergraduate researchers in the Sensors, Energy, and Automation Laboratory (SEAL),
namely, Gio Hwang, Patrick Aubin, Annika Lee, and Cindy Huang.
I would like to acknowledge Prof. David Sukow at Washington and Lee
University for his continued encouragement and support and for giving me my first
opportunity to conduct academic research at a professional level.
I would like to thank all those who have given me technical, financial, and
emotional support during my two years at the University of Washington. Some of those
people are: Kishore Sundara-Rajan, Nels Jewell-Larsen, Xiaobei Li, Alexei Zyuzin, Dinh
Bowman, Adam Bily, Min Wang, Bing Jiang, Gabe Rowe, Sam Larson, and Sidhartha
Goyal.
Finally, this thesis would not have been possible but for the guidance and support
of my family and friends. On a personal level, I would like to thank Valerie for all of her
love and support.
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Chapter 1. Introduction
1.1 Background
Resin Transfer Molding (RTM) and Vacuum-Assisted Resin Transfer Molding
(VARTM) are widely used composite material manufacturing processes that produce
high-strength and lightweight parts for various industrial applications. Such parts are used
extensively during the manufacturing of aircraft, such as the F-22 Raptor, Joint Strike
Fighter, and Boeing 7E7, as well as missiles for the U.S. Air Force. Traditional RTM
uses a closed mold cavity where the part is typically incased in a metallic mold that is
tightly sealed and under pressure. Resin is injected into the mold through several inlet
ports. Figure 1.1 shows an example of an RTM setup for a 1-D filling process with one
injection port on the right-hand side of the figure.
Figure 1.1. Photograph of closed mold cavity for RTM experimental setup
with distributed dielectric sensors
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VARTM uses an open mold cavity with one side of the mold covered by an air-
impervious vacuum bag. Resin is then pulled into the part by vacuuming the air out of the
mold cavity. High-permeable plies or grooves are often used to assist the filling. Figure
1.2 shows an example of an open mold VARTM setup with one injection port.
Figure 1.2. Photograph of open mold cavity for VARTM experimental
setup with distributed dielectric sensors.
1.2 Problem Statement
Current lack of a comprehensive and integrated sensor-based adaptive control
system for filling and curing results in costly and time-consuming trial-and-error
procedures to manufacture defect-free parts with consistent material properties. An
adaptive control system can minimize production engineering iterations by accounting for
variations in process parameters such as changes in permeability of the preform/fiber
mat, resin kinetics, temperature-dependent viscosity, relative position of inlets, etc. A
comprehensive and integrated adaptive process control strategy will substantially reduce
the manufacturing cost and time for lightweight and high-strength polymer composite
parts used in industry. A sensor system capable of monitoring important process
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parameters like fill-front position and degree of cure in situ is an important element of
this adaptive control strategy. Dielectric spectroscopy is one of the most powerful
instrumentation tools for manufacturing of polymer composite parts; however, its use has
not been fully explored due to relatively young age of high-tech applications in this field
and insufficient speed of embedded electronics of earlier generations.
1.2.1 Fill Front Monitoring
Dry spot formation is a phenomenon that can seriously jeopardize the mechanical
integrity of the part [1,2]. Any part in which a dry spot has formed is a defective part that
is scrapped. Dry spots form when the resin reaches the exit vent before the part is
completely filled, resulting in “dry spot” regions not filled by resin. Dry spot formation is
strongly dependent on processing parameters such as temperature, viscosity, pressure,
fill-front location, and permeability of the part. In theory, the use of simulation codes
such as [1] may allow for selection of the appropriate exit port location if parameters
such as permeability and resin kinetics do not change within the same batch or from one
batch to another. In practice however, the parameters which affect dry spot formation do
change from cycle to cycle, and accurate distribution of the permeability of the part
within the mold is rarely known. In particular, fill-front position has been identified as a
crucial parameter in determining last-point-to-fill (LPF) and thus dry spot formation [3].
In order to manufacture defect-free parts with consistent material properties it is
important to monitor and control the fill-front through an adaptive control system.
Information on the location of the fill-front can then be fed back into an adaptive control
algorithm designed to optimize the process [4,5]. Such a comprehensive and integrated
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sensor-based adaptive control system does not exist and previous attempts to regulate
parameters such as fill-front location have shown limited controllability [6-8].
1.2.2 Cure Monitoring
The temperature and curing history of the resin are also parameters that strongly
affect the final material properties of the polymer composite part. An uneven temperature
distribution and curing pattern will result in inconsistent material properties within a part
or from part to part.
During the filling stage in RTM or VARTM, the mold is maintained at a
temperature (~80-120 oC) that is usually higher than the resin inlet temperature (~25 oC).
This practice results in an uneven temperature distribution in the resin since the resin
injected at the early stage of filling is in contact with the hot mold wall for a longer
period of time. Excessively high resin temperatures may lead to premature curing. An
uneven temperature field results in non-uniform viscosity, which affects the filling
pattern, thereby leading to formation of dry spots. Resin properties may also vary due to
different resin formulations and degradation during shelf life. Curing of resin in RTM and
VARTM releases reaction heat. Due to the high reaction heat and low thermal
conductivity of the resin, temperature gradients within the mold can become significant.
For example, during RTM, the temperature gradient along the in-plane direction can be
as high as 15 oC/cm and the temperature gradient across the thickness of the part can be
as high as 40 oC/cm. These temperature gradients along with uneven curing introduce
thermal stresses in the part and can cause fracture during future application. In addition,
experiments have shown that, during manufacturing of a thick (~2.5 cm) RTM part, the
temperature at the mid-point of the part thickness can be as high as 200 oC, leading to
some degree of polymer degradation. Material delaminations (cracks) at the center of the
part have been observed using typical mold processing temperatures (~80-120 oC) [99].
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Crack formation in RTM parts intended for aerospace or any other application is a serious
problem. To overcome this, the mold processing temperature was reduced to 55 oC.
However, this reduction in mold temperature resulted in a significantly lower degree of
curing during the usual processing period. All of these factors contribute additional
uncertainties during curing and illustrate the need for a sensor system that can accurately
measure temperature distribution and curing pattern.
The above discussion illustrates industry’s need to monitor fill-front position and
curing pattern during RTM and VARTM. This thesis attempts to address this need by
designing a comprehensive and integrated sensor system to monitor filling pattern,
temperature, and curing pattern.
1.3 State of the Art
A sensor system that is suitable for monitoring process parameters for both RTM
and VARTM needs to be built as large-area flexible units, suitable for accurate
measurements of curved surface objects for complex RTM mold geometries, material
samples with dynamically varying dimensions for specific VARTM applications, and
porous or transparent substrates for flow front verification. What follows is a general
overview of non-destructive sensing techniques starting with the concept for this thesis,
fringing electric field sensors, followed by a discussion of the implementation and
effectiveness of many of these techniques in RTM and VARTM processes.
1.3.1 Fringing Electric Field Sensor Arrays
The modern technology of fringing electric field sensing can be loosely broken into
five categories, in order of increasing complexity. The boundaries between the individual
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categories are not sharply defined. This classification serves as some guidance in
determining what future advances are possible in each domain.
(i) capacitive sensors for position measurement, proximity control, and similar
applications [9];
(ii) single-wavelength single-frequency sensors for detection of chemicals and humidity
sensing [10,11] ;
(iii) single-wavelength spectroscopic impedance or dielectric sensors [12];
(iv) electrical impedance tomography sensor arrays for industrial and biomedical 3D
imaging [13-15];
(v) multiple penetration depth dielectric spectroscopy sensors, for study of physical
phenomena [16,17].
Research work on reconstruction algorithms for impedance-based imaging is very
active. Possible significant advances in the manufacturing applications of fringing field
array sensing come from ever-increasing speed of electronics and from invention of new
materials applicable to sensor and electronics design. The point of engineering trade-off
between the number of pixels in the imaging system that displays several properties at
once is shifting from several electrodes to high-resolution arrays with many electrodes
without sacrificing the accuracy and dimensionality of parameter estimation algorithms.
The main drive for such superior sensing systems comes from increasing quality, product
complexity, desired accuracy, and manufacturing volume output requirements.
There are currently very few sensors with multiple penetration depths and
multiple property estimation capabilities on the market or in the research stage. Existing
systems are very far from their fundamental limits and their presence in manufacturing
plants is orders of magnitude lower than comparable techniques, such as acoustic sensing.
Generally speaking, the evaluation of material properties with fringing electric fields is a
much less developed area than comparable techniques that involve eddy currents,
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acoustic sensing, or x-rays. This field holds a tremendous potential due to the inherent
accuracy of capacitance and conductance measurements (as high as to the 7th significant
digit) and due to imaging capabilities combined with noninvasive measurement principles
and model-based signal analysis.
1.3.2 Alternative Technologies
The proposed technology has the highest potential for successful measurement of
fill-front location, cure state, viscosity, and temperature among all non-destructive testing
technologies, which include ultrasonic, infrared, CCD, optical, and microwave
measurements. Unlike ultrasound, FEF (fringing electric field) sensors can be built non-
contact. Unlike infrared, CCD, optical, and other variations of ultra-high frequency
spectrum measurements, low frequency (LF) FEF sensors penetrate into the bulk of
material instead of measuring only near-surface layers. Unlike microwave range sensors,
LF FEF sensors measure distinctively different dielectric signatures that reflect a
multitude of mechanisms of response to oscillating electric fields. Unlike most high-end
laboratory approaches, such as NMR and x-ray backscattering, these sensors involve
rugged, compact, and relatively inexpensive instrumentation. Dielectric spectroscopy
analysis allows efficient discrimination of output signal components due to simultaneous
change of several physical variables. At the same time, acquiring simultaneous signals
from infrared, optical, or acoustic sensors will provide a desirable source of additional
information about the material.
1.3.3 Vacuum-Assisted Resin Transfer Molding (VARTM)
Many techniques have been used to monitor the resin transfer molding process,
such as optics [18-20], ultrasound [21,22], fluorescence [23], calorimetry [24], and DC
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resistance measurements [3,25-27] These techniques are similar in that they all require
either embedded parts or partial contact with the resin itself. Among these techniques,
DC resistance measurement arrays, such as SMARTweave, have the ability to monitor
fill-front position and degree of cure simultaneously. However, this technique relies on
point sensing where resolution of important parameters such as fill-front location is
limited by the number of sensors (pixels) the system can handle. A system capable of
continuously sensing fill-front progression will more accurately determine the velocity
and therefore position of the fill-front. Table 1.1 summarizes the capability and
limitations of main sensor types.
Table 1.1 RTM manufacturing example: types of sensors converting electrical properties to other physical properties.
Sensor Sensing
technique What can be
sensed? Senses
points or distributed
field?
Requires direct
contact?
Embedded in the part?
SMARTweave [28]
DC Filling, Curing
Points Yes Yes
Lineal [29] DC Filling Distributed Field
Yes No
FDEMS [30,31]
AC Filling, Curing
Points Yes Yes
On-chip Dielectrometry
[32]
AC Filling, Curing, &
Temperature
Points Yes Yes
FEF Array System
Distributed fringing field
AC
Filling, Curing, &
Temperature
Distributed Field
& Points
No No
9
A promising candidate technology to base an adaptive control system on is AC
dielectrometry. This technique is capable of sensing fill-front location, curing,
temperature, and viscosity simultaneously. Among the commercially available AC
dielectrometry systems is FDEMS [30,31,33-35]. However, this system relies on point
sensing and requires direct contact and embedded parts. It has been shown in [36,37] that
AC dielectric sensors are capable of accurately measuring fill-front position and degree
of cure. In [37], a linear dependence of the admittance signal upon the fill-front position
is established. This particular type of sensor relies on fringing electric field technology
and its relative position underneath the mold allows for continual sensing of fill-front
progression. However, a single sensor is inherently one-dimensional and its resolution is
limited. The system described in [36] is a three-channel system capable of converting
capacitance to voltage and correlating this to flow-front position. Though [36]
demonstrates a simple capacitive system capable of sensing fill-front location, it does not
pursue phase shift measurements which are important with conductive material and also
with spectroscopy measurements. The system presented in this thesis is designed to
perform spectroscopy measurements (i.e., measurements at multiple frequencies) and
combine point sensing with continuous sensing.
In order to measure viscosity, temperature, and degree of cure in 3D, a sensor
needs to be designed that can perform spectroscopy at different points along the mold.
Although these measurements are inherently discrete measurements in space and time,
increasing the number of pixel elements will make the measurements more useful.
Additionally, fill-front location should be sensed continuously for most accurate results.
For this type of measurement, spectroscopy is not necessary. Thus, a sensor capable of
measuring multiple parameters of interest will have multiple sensing elements within the
array that are capable of measuring their respective parameter of interest. This paper
discusses the design and testing of the multi-pixel elements intended for the sensor array.
The first type of element is capable of continuously sensing the fill-front location of a
liquid material as it flows through the mold. The second type of element is capable of
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performing dielectric spectroscopy at discrete points in space and time as the material
flows through the mold. Both elements will be duplicated several times and will comprise
a larger array of pixels. The conceptual design for this array is shown in Figure 1.3.
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Figure 1.3. Next generation sensor prototype design
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1.4 Outline of Thesis
This thesis describes the design and preliminary testing of fill front and curing
elements of a multi-pixel sensor system with continuous dielectric sensing capabilities for
remote and in-situ monitoring of fill-front position, viscosity, temperature, and degree of
cure during resin transfer molding. The design and fabrication of novel transparent
sensors is described, as well as the design and fabrication of lineal FEF sensors on FR4
substrates. Furthermore, a novel multiplexing multi-channel circuit is described that
increases the resolution of the existing data acquisition system by a factor of four. The
calibration of the system is described and it is demonstrated that the fill front element can
accurately monitor fill front location of a glycerin/water solution as it is injected into an
RTM mold with a foam preform. It is further demonstrated that this element is capable of
monitoring the fill front of an epoxy resin as it is injected into a VARTM mold with both
fiberglass and carbon fiber preforms. The cure element of the multi-pixel system is
demonstrated to monitor the degree of cure of an epoxy resin during the filling and curing
stages for VARTM using both fiberglass and carbon fiber preforms. Unlike previous
techniques, these sensors are capable of continuous and simultaneous measurements of
transadmittance over a wide range of frequencies.
In Chapter 2, theoretical background on the principles of FEF sensors, and
dielectric spectroscopy of polymers is presented. Chapter 3 describes the data acquisition
system including the design and fabrication of the sensors and measurement circuitry.
Chapter 4 describes the experimental setup for VARTM and RTM molds. In Chapter 5,
the experimental work and raw data is described for fill front monitoring in RTM with
water/glycerin solution and foam preforms. Chapter 6 describes the data and results for
fill front and cure monitoring in VARTM with fiber glass and carbon fiber performs.
Chapter 7 discusses disturbance factors present in the experiments. Chapter 8 discusses
future work, including the development of parameter estimation algorithms in
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dielectrometry measurements and the potential of the sensing technique for carbon
nanotube characterization. Finally, Chapter 9 presents the conclusions of the work.
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Chapter 2. Background
2.1 Principles of FEF Sensors
The operating principle of a fringing electric field (FEF) sensor can be understood
in terms of the more conventional parallel plate capacitor (PPC), which is commonly
used to measure dielectric properties of materials. Figure 2.1 shows a gradual transition
from the parallel plate capacitor to a fringing field capacitor. In all cases, electric field
lines pass through the material under test; therefore the capacitance between the two
electrodes depends on the material dielectric properties as well as on the electrode and
material geometry. The central sensing mechanism in FEF sensors is the attenuation of
the electric field due to the presence of the material under test (MUT). For PPC
geometries, transconductance and transcapacitance are linearly related to the conductivity
and permittivity of the material under test. For FEF geometries, no closed form analytical
solution exists and the relationship between terminal measurements and material
properties must be arrived at numerically.
Figure 2.1. A fringing field dielectrometry sensor can be visualized as a
parallel plate capacitor whose electrodes open up to provide a one-sided
access to material under test.
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The capacitance between two co-planar strips, as shown in Figure 2.1(c), is typically
comparable to the stray capacitance of the leads (conductors that connect the electrodes
with the electrical excitation source). Therefore, in order to increase the capacitance, and
hence the signal to noise ratio of the sensor, the coplanar pattern may be repeated several
times.
A variety of interdigital sensors are used for research and commercial applications
to measure material properties [38,39], control manufacturing processes [40,41], monitor
chemical and physical changes of fluid and solid dielectrics [42,43], etc. In many cases,
the interpretation of the sensor response depends on simple calibration procedures, yet, in
other cases, it requires sophisticated signal processing algorithms [44] and deep
understanding of the physics and chemistry of the dynamic processes that are being
monitored [45].
2.1.1 Imposed Frequency-Wavenumber (ω-k) Sensing
Overviews of important concepts related to interdigital frequency-wavenumber (ω-
k) dielectrometry are available in [16,39,46-48]. For a more thorough discussion of FEF
sensors in general, the reader is referred to [49] One of the most attractive features of
multi-wavelength dielectrometry is the ability to measure from one side the complex
spatially inhomogeneous distributions of properties. The types of spatial distributions
include, but are not limited to, homogeneous materials, multiple layer materials, local
discontinuities (such as cracks and electrical trees), global discontinuities of
microstructure (such as grains or fibers forming the material), and smoothly varying
properties. On the electrical properties side, materials under test (MUT) may be purely
insulating or weakly conductive. Various phenomena may affect sensor response,
including frequency dispersion, electrode polarization due to an electrochemical double
layer, quality of interfacial contact, and many others.
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A conceptual schematic of ω-k dielectrometry is presented in Figure 2.2. For a
homogeneous medium of semi-infinite extent, periodic variation of electric potential
along the surface in the x direction produces an exponentially decaying pattern of electric
fields penetrating into the medium in the z direction. The penetration depth of the
fringing electric fields above the interdigital electrodes is proportional to the spacing λ/3
between the centerlines of the sensing and the driven fingers. The variation of the
material properties across the thickness of the material in the z direction can be found by
simultaneously solving complex integral equations, which represent a functional
dependence of the terminal characteristics on material properties and cannot be solved
analytically for most cases.
The complex Laplace's equation within the fringing field volume is:
( ) 0j∇ ⋅ σ − ωε ∇Φ = (2.1)
where Φ is the electric potential, ω is the angular frequency of excitation, σ is
conductivity, and ε is dielectric permittivity of the material under test. The boundary
conditions at the sensor electrodes for voltage measurement mode are
0DV⎡ ⎤
Φ = ⎢ ⎥⎣ ⎦
(2.2)
where VD is driving excitation voltage, and the BC's for current measurement mode
ˆ( )0J
j n−⎡ ⎤
σ − ωε ⋅∇Φ = ⎢ ⎥⎣ ⎦
(2.3)
where – J represents current into the electrodes.
Figure 2.3 illustrates the idea of multiple penetration depths in the same space.
The penetration depth of the fields is proportional to the spacing between the centerlines
of the sensing and the driven fingers. The information from excitation pattern can be used
to detect boundaries of discontinuities and property distributions in materials.
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Figure 2.2. A single-wavelength generic design.
Figure 2.3. Multiple penetration depths. Electric field lines extend into
space beyond the distributed sensor.
2.1.2 Advantages of FEF Sensors
Sensors for non-destructive measurements with fringing electric fields (FEF) can
provide extensive information about geometrical, structural, physical, and chemical
properties of materials. Their advantages include:
• Physical contact between the sensor and the material under test is not
required, which is highly desirable for high-speed scanning in manufacturing
applications.
• Measurements are perfectly safe, in contrast to, for example, x-ray based
techniques.
• The signal dependence on ionic conductivity is comparable to the
dependence on the real part of complex dielectric permittivity. Therefore, it is easier to
18
separate simultaneously acting effects of temperature, moisture, concentration of
chemicals, curing status, etc. through wideband dielectric spectroscopy.
• FEF sensors are economical, as long as accuracy of raw signals can be on the
order of 1%. The more accurate circuits require additional shielding and bridges, but still
remain reasonably low-cost.
• Fringing fields penetrate through non-conducting materials; thus, plastic
walls can separate the material under test without significantly affecting the measurement
sensitivity (this is highly valuable for RTM and VARTM applications).
2.2 Dielectric Spectroscopy of Polymeric Materials
Dielectric spectroscopy of material properties was first investigated by Von Hippel
in the 1940’s [50]. More advanced techniques for investigating dielectric properties in
polymer composites, including the advent of interdigital dielectrometry, were developed
by Matis in the 1960’s [51]. Microdielectrometry as a means of measuring dielectric
properties in polymers was developed and used by Senturia in the early 1980’s
[40,52,53], and subsequently by other groups during the last ten years [54-56]. The recent
trend has been an attempt to integrate dielectric spectroscopy into a self-contained system
capable of measuring multiple parameters of interest for material manufacturing
processes.
Dielectric spectroscopy is defined as the measurement of the dielectric permittivity
of a material over a range of frequencies. In order to understand why this information is
useful, it is first necessary to understand the nature of the dielectric permittivity and its
frequency response. A brief derivation of the complex permittivity, following the
example found in [57], is given here; more thorough derivations can be found in
[50,58,59].
19
2.2.1 Dielectric Permittivity
Consider a PPC with a capacitance in vacuum given by
00
ACd
ε= (2.4)
where A is the surface area of the electrodes, d is the electrode spacing, and 0ε is the
permittivity of free space. When an a.c. voltage
0j tV V e ω= (2.5)
is applied to the PPC, a charge 0Q C V= appears on the electrodes. This charge is in phase
with the applied voltage. The current is given by
0ddQI j C Vdt
= = ω (2.6)
where the subscript d denotes the fact that this is the non-dissipative displacement
current, also referred to as the induction current, and is 90° out of phase with the applied
voltage. When the volume between the electrodes is filled with a non-polar, perfect
insulator, the new capacitance is given by 0rC C= ε where εr is the relative permittivity
of the material given by0
rε
ε =ε
. For perfect insulators, ε is real. The displacement
current is increased by the same factor εr but is still 90° out of phase with the applied
voltage.
20
Now consider the case when the material is conductive. This can be due to free
charges, or permanent dipoles if the material contains polar molecules. The current is not
exactly 90° out of phase with the applied voltage due to a small component of conduction
current GV that is in phase with the voltage. Figure 2.4 shows a conceptual picture of the
total current in the non-ideal capacitor.
Figure 2.4. Conceptual view of the total current in a leaky capacitor.
The total current in the capacitor is given by
( )totalI j CV GV j C G V= ω + = ω +
ur ur ur (2.7)
From a circuit perspective, j C Gω + represents the complex admittance of the capacitor
where the lumped circuit representation of the material filling the capacitor is a parallel
RC network. Figure 2.5 illustrates this concept.
21
ε,σ Rs (ω) Cs (ω) d
+ σs
− σs
V V
(a) (b)
Figure 2.5. Leaky capacitor: a) dielectric material sandwiched between
two perfectly conducting parallel plates. b) the equivalent circuit
representation.
The conductance is given by G A d= σ for free charges, and since C A d= ε , the current
density can be found by substituting these values into (2.7) to get
( )totalJ j E= ωε + σ
ur ur (2.8)
Here, j Eωεur
is the displacement current density and Eσur
is the conduction current
density. (2.8) can be simplified by introducing a complex dielectric permittivity
j∗ σε = ε −
ω (2.9)
and the total current density becomes totalJ j E∗= ωεur ur
. The loss angle, shown in Figure
2.4, is a parameter used to quantify the pure conductance in the system and is given by
22
tan σδ =
ωε (2.10)
When the conduction current is not due exclusively to free charges, but is also due to
permanent dipoles, the conductivity σ is a complex quantity that is frequency dependent
and the real part of ∗ε is not ε and the imaginary part is not σ ω . Thus, the most general
expression for the complex dielectric permittivity is
( ) ( ) ( )∗ ′ ′′ε ω = ε ω − ε ω (2.11)
where the real and imaginary parts are frequency dependent.
2.2.2 Polarization, Relaxation, and Resonance
All matter is comprised of charges of one type or another. When subjected to an
externally applied electric field, these charges respond in such a way as to produce their
own local electric field within the material. When a material produces its own electric
field in response to an external electric field, the material is said to be polarized. Material
responds only when the frequency of the applied field is below the resonant frequency of
the charge system. Table 2.1 lists the types of charges and their responses to an applied
electric field.
23
Table 2.1. Polarization phenomena in materials.
A resonance response is analogous to a mechanical vibration of the charge about its
equilibrium position. The charge exhibits a restoring force and resonates about this
equilibrium; resonance occurs when the frequency of the applied electric field is equal to
the natural frequency of the system. The resonance response exhibited by bound electrons
is called atomic polarization.
A second type of response exhibited by matter in an externally applied electric
field is called relaxation. Dielectric relaxation is defined as the exponential decay with
time of the polarization in a dielectric when an externally applied field is removed. The
relaxation time is characterized by a time constant τ and is equal to the time in which the
polarization is reduced to 1 e times its original value [59]. Unlike resonance phenomena
that are associated with bound electrons, relaxation phenomena are associated with
permanent dipoles in the material. These dipoles can exist because of the asymmetric
nature of the molecules, or space charge separation within the material. These permanent
dipoles do not resonate with the applied field, but instead align themselves anti-parallel to
the direction of the applied field, a process known as orientation polarization. When the
applied field is removed, the dipoles “relax” and reorient themselves in random
directions. This relaxation process is viscous in character and is dependent on the
medium containing the dipoles, and the finite moment of inertia of the dipoles. Space
Inner electrons
Outer electrons
Free electrons
Bound ions
Free ions
Multipoles
Response Resonance Resonance Relaxation Relaxation Relaxation Relaxation
Type Atomic polarization
Atomic polarization
Space charge
polarization
Orientation polarization
Space charge
polarization
Orientation polarization
Resonance Frequency
~1019 Hz
~1014 Hz
~10-1 Hz
~108 Hz
~10-1 Hz
~108 Hz
24
charge polarization is also a relaxation phenomenon and occurs when free electrons or
ions in the material behave as macroscopic dipoles, which reverse their direction in
accordance with the frequency of the field. In general, the relaxation response can yield
important information about the viscosity, temperature, and molecular dynamics of the
material and, as a consequence, is the response that is most relevant to this thesis.
2.2.3 Modeling Dielectric Dispersion: Relaxation Functions
All polarization phenomena contribute to raising the relative dielectric
permittivity above unity. The most important type of polarization for studying
macroscopic and microscopic dynamics of polymer resins is polarization that causes a
relaxation effect in the material once the applied field is removed. This type of
polarization involves the interactions of permanent dipoles with the applied field. The
polarization and therefore the permittivity is frequency dependent and its frequency
response can be modeled with relaxation functions. Rather than deriving these relaxation
functions explicitly, Table 2.2 lists the types of functions and their applications. Several
of these will be discussed in detail.
25
Table 2.2 Relaxation functions for experimental dielectric data
Function
Debye
( )
0
220
022
0
( )1
( )1
( )1
s
s
s
j∗ ∞
∞
∞∞
∞
ε − εε ω = ε +
+ ωτ
ε − ε′ε ω = ε ++ ω τ
ωτ′′ε ω = ε − ε+ ω τ
Cole-Cole ( )0
( )1
s
j∗ ∞
∞ α
ε − εε ω = ε +
+ ωτ
Davidson-Cole ( )0
( )1
s
j∗ ∞
∞ β
ε − εε ω = ε +
+ ωτ
Havriliak-Negami
(HN) ( ) 0
( )1
s
j∗ ∞
∞ βα
ε − εε ω = ε +
+ ωτ
Fuoss-Kirkwood
(FK) ( )0
max
( ) sec lnh m′′ε ω
= ωτ⎡ ⎤⎣ ⎦′′ε
Jonscher ( ) ( )
max1
0 0
( ) m n− −
′′ε′′ε ω =ω ω + ω ω
Kohlrausch-
Williams-Watts
(KWW)
( )0( ) 1k
t
n t e⎡ ⎤−⎢ ⎥τ⎢ ⎥⎣ ⎦ε = −
26
The Debye relaxation function [60] is the classic relaxation function from which all other
relaxation functions are derived. Several assumptions limit the use of the Debye function
to a narrow range of cases. These assumptions are as follows:
1. The local field within the material is not different from the applied field.
2. The conductivity σ of the material is negligible.
3. All dipoles have the same relation time τ0.
For most materials, these assumptions are false and the Debye equation can no longer be
used. Other models such as Cole-Cole and Davidson-Cole modify the Debye equation to
account for these assumptions. A graphical representation that is particularly useful for
visualizing relaxation functions is the Cole-Cole plot. This involves plotting ′ε versus ′′ε ;
Figure 2.6 shows a Cole-Cole plot for the Debye function.
Figure 2.6. Graphical representation of the Debye function.
The Havriliak-Negami (HN) function is a combination of the Cole-Cole, Davidson-Cole,
and Debye functions and represents the best function to date for fitting relaxation data.
Figure 2.7 shows a graphical representation of the HN function.
27
Figure 2.7. Graphical representation of the HN function.
Other functions, such as the Jonscher and Fuoss-Kirkwood functions, present a modified
fit for the dielectric loss ′′ε , while the Kohlrausch-Williams-Watts (KWW) function
attempts to fit data in the time domain. When fitting dielectric data, all of these functions
should be considered before choosing the function with the best fit.
28
Chapter 3. Data Acquisition System
3.1 Sensors
Both parallel-plate and FEF sensors can be used to non-invasively monitor RTM
and VARTM processes. RTM molds are typically conductive and this aspect can be
exploited. By using the bottom of the RTM mold as a driving electrode, parallel-plate
sensors can be easily integrated into the setup. VARTM molds are non-conductive and
FEF sensors are a more practical choice for these configurations because VARTM
requires one-sided access to the mold. Both parallel-plate and FEF sensors were designed
and fabricated for experiments with RTM and VARTM molds. The general operating
principle and design for parallel-plate sensors in RTM molds is outlined next.
3.1.1 Parallel-Plate Sensor Design and Fabrication
Two parallel conducting plates with equal but opposite surface charge densities σs
have a potential difference given by
1 2V φ φ= − (3.1)
Since the potential difference is equal to the work required to move charge from one plate
to the other, we can write
V Ed= (3.2)
29
where d is the distance between the plates. From Gauss’ law, the electric field between
the plates is
sE σε
= (3.3)
It follows that
s dV d QA
σε ε
= = (3.4)
The total charge, Q, on both plates is proportional to the potential difference between the
plates. The constant of proportionality is the capacitance and is given by
ACd
ε= (3.5)
and the conductance is given by
AGd
σ= (3.6)
where σ is the conductivity of the material.
When a dielectric material such as resin is passed between the plates of the mold,
the capacitance changes. In this way, the system is able to detect the presence of
dielectric materials. Guard electrodes are included in the parallel-plate configuration to
ensure a uniform electric field within the sensing area. Figure 3.1 shows the general
operating principle of the parallel-plate sensor. In order to test the sensitivity of the
30
system, independent measurements of fill-front position can be made with a video
camera.
Figure 3.1. General operating principle of the sensor including edge
effects. Fluid flows into the mold cavity and position is inferred from
changes in capacitance.
A six volt amplitude sinusoidal input signal is applied to the bottom half of the
RTM mold. Each sensor outputs to a channel on an impedance divider circuit which is
designed to infer the impedance of the material under test (MUT) from the measured
intermediate node voltage and reference impedance. The complex voltage signal is fed
into a PC via a DAQ card operating at 96 ks/s. An extensive data acquisition program
was developed in LabView to convert the measured gain and phase to capacitance and
conductance and display these values in real time. The sensor was fabricated on FR4
substrates by etching a guard plane around the sensing electrode with copper sulfate
solution. Figure 12 shows the parallel-plate sensors implemented in a RTM setup.
Electric Field
Sensing Electrode
Edge Effects
Guard Electrode
Air and fiberglass preform
Dielectric Liquid
d
hA
hL
Polycarbonate Plate
Bottom Plate of Mold
31
3.1.2 FEF Sensor Design and Fabrication
FEF sensors were fabricated on FR4 substrates by etching with copper sulfate.
These sensors are 23 x 2 inches with a 5 mm penetration depth and 15 mm spatial
wavelength. Figure 3.2 shows the FEF sensors and implementation in VARTM setups.
Figure 3.2. Photographs of FEF sensor designed for VARTM
experiments.
3.1.3 Novel Transparent Multi-Pixel Sensor Design and Fabrication
Transparent multi-pixel FEF sensors were fabricated for use with multiplexing
circuitry to be discussed in the next section. The fabrication process for the transparent
sensors is as follows: The chemical compound indium tin oxide (ITO) is evenly sputtered
onto a thin polymer film such as polyester. The indium oxide is doped with tin oxide to
increase the ratio of electrons to holes, making the film electrically conductive. The guard
plane and sensing electrode are electrically isolated using a wet etching technique. An
32
acid is used to remove the ITO coating where necessary. Ultraviolet-activated optical
glue is then used to attach both sides of the film. SMA cables are attached to the sensors
using highly conductive epoxy. The transparency of the sensors allows for complete
visual confirmation of flow front position and offers the possibility of enhancing the
system with an infrared sensor. Figure 3.3 shows a complete ITO sensor. Figure 3.4
shows a drawing of the design that is patterned onto the sensors. The pattern involves one
fill-front pixel and three spectroscopy pixels.
Figure 3.3. Transparent sensor fabricated by sputtering Indium Tin Oxide
onto a thin polyester sheet.
33
FEF Spectroscopy Pixels
Fill-Front Pixel
Figure 3.4. Drawing of design pattern for multi-pixel transparent sensors.
3.1.4 Design Constraints for Parallel-Plate and FEF Sensors
The uniformity of the electric field is strongly dependent on the geometry of the
sensor, and therefore the design of the sensor is an inherent constraint on the system. The
uniformity of the electric field does not depend on material between the sensing electrode
and driving electrode. For a parallel-plate configuration, the parameters of the setup that
affect the uniformity of the electric field are the distance between the plates and the
degree to which the plates are parallel. If the material between the plates is non-
homogeneous, the capacitance measured is then based on an average value of the
dielectric permittivity over the sensing area. However, as long as the plates are parallel
and the distance between the plates is relatively small, the electric field will be uniform.
If the distance between the plates varies considerably over the sensing area, the electric
field will not be uniform. It may be possible to quantify the shape of the electric field for
a given part geometry; however a more practical solution would be to utilize a fringing
electric field (FEF) setup where the electric field fringes into the part and only one-sided
34
access is needed. This would allow for point sensing within the part and allow for
complex part geometries where parallel-plate setups become impractical.
The shape of the sensor can be designed to accommodate different mold
geometries and for optimal adaptive control needs. Sensing area is the most important
design criteria for parallel-plate sensors, and therefore long strips are commonly used.
For FEF sensors, the spacing between electrodes determines the penetration depth.
Longer and thinner sensor geometries will not accommodate as many electrodes as a
wider design. However, for our purposes one fringing electric field is adequate and
therefore a longer and thinner sensor is realizable.
As demonstrated in [61], FEF sensors can be bent (i.e., wrapped around objects
with complex geometries) with no perceivable effect on their performance. This is of
importance in composite material manufacturing processes where the mold geometry is
complex. In addition, it may be possible to line the walls of the mold with complex
sensor shapes in order to achieve more uniform sensing of the part.
3.2 Measurement Circuitry
Deduction of material properties from electrical parameter measurements is defined
as an inverse problem of impedance spectroscopy. In the case of this study, viscosity,
temperature, and degree of cure must be inferred from measurements of capacitance and
conductance between sensor array electrodes. For homogenous materials, such as water,
the solution is relatively straight-forward. However, for non-homogenous media, the
problem becomes more difficult to solve: ideally, electrical properties would be obtained
at an infinite number of locations within the media. Realistically however, the number of
pixel elements in the sensor array determines the resolution of the measurements.
Furthermore, the number of pixel elements is limited by the measurement circuitry. An
35
existing three-channel board was used for measurements reported in this thesis, while a
novel multiplexing board was designed and fabricated for use in later experiments.
3.2.1 Three-Channel Board and LabView Software
For every operating frequency, when a dielectric material is placed between two
parallel conducting plates, the resultant circuit can be modeled as an RC parallel
combination. For sensor impedance measurements, the custom designed three-channel
circuit utilizes a floating-voltage measurement technique. Figure 3.5 shows that for a
single channel, the voltage divider is formed by the sensor and the additional reference
impedance. The voltage is sensed in the middle of the divider pole by an ultra-high input
impedance op-amp in a voltage follower configuration. The reference impedance is
chosen such that the value is close to the expected measurement impedance. Since the
MUT is weakly conductive, the lumped circuit approximation can be reduced to a single
capacitor. The reference capacitance value used in these experiments is 7 pF for all three
channels.
The coaxial cable connecting a sensor to the measurement circuit is 5 ft long. To
eliminate the effect of stray capacitance in the cable, the output of the voltage follower is
fed back to the cable’s shielding conductor. The technique ensures that there is no
potential difference between the inner conductor carrying the weak sense signal and the
shielding conductor around it. The signal from the shield is also used to keep the guard
electrode at the same potential as the sensing electrode.
For the specified sensor geometry, the capacitances in the voltage divider pole are
usually very small. The leakage current from the op-amp input causes static charge to
accumulate on the sensor plates as well as on the reference capacitor. To discharge both
capacitances, a reed relay is connected between the middle of the voltage divider and
36
ground terminal. The switch is automatically closed for a short period of time before each
measurement.
The outputs of the three-channel circuit and the function generator signal are
connected to a NI-DAQ 6035E data acquisition card operating at 96 kS/s. The card
simultaneously samples all four voltage signals. In addition, it provides the digital signal
for controlling the discharge relays. It should be noted that the input impedance of the NI
card when connected to the output of the op-amp can greatly decrease the phase margin
of the circuit, causing high-frequency instability. To prevent possible oscillatory
behavior, a 1 kΩ resistance can be added between each of the circuit’s outputs and the
positive power supply rail.
_
+
Rref Cref
Sensor
Rsense Csense
Sensor Reed Relay
Figure 3.5. Circuit schematic for three-channel board.
37
The LabView software is programmed to acquire a complex voltage signal from
each channel on the circuit and reduce this signal to its gain and phase components. The
corresponding conductance and capacitance can be inferred from (3.7) and (3.8),
respectively, where V is the gain, θ is the phase, ω is the angular frequency, Cr is the
reference capacitance, and Gr is the reference conductance.
2
(sin( ) cos( ) )2 cos( ) 1
r r rsense
V C G V GGV V
θ ω θθ
⋅ ⋅ ⋅ − ⋅ + ⋅= −
− ⋅ ⋅ + (3.7)
2
( cos( ) sin( ) )( 2 cos( ) 1)
r r rsense
V C V C GCV V
ω θ ω θω θ
⋅ − ⋅ ⋅ + ⋅ ⋅ − ⋅= −
⋅ − ⋅ ⋅ + (3.8)
Figure 3.6 shows a photograph of the three-channel circuit and the custom-designed
breakout box.
Figure 3.6. Photograph of three-channel circuit and breakout box.
38
3.2.2 Multiplexing Board for Multi-Pixel Sensor
The three-channel board inherently limits the resolution of the sensing system
because it can only accommodate three sensing inputs. A novel multiplexing circuit was
designed to accommodate more pixels on each individual sensor head so that the
resolution might be increased from three pixels to twelve pixels total. This represents a 4-
fold increase in resolution of the sensing system and will significantly improve the
resolution. Current sensing methods were pursued for this circuit design to enhance the
sensitivity of the system. By multiplexing the drive channels instead of the sensing
channels, the circuit bypasses much of the parasitic capacitance in the circuit leads and
elements. Figure 3.7 shows the fabricated PCB with transparent sensor.
Figure 3.7. Photograph of multiplexing board and transparent sensor.
39
Chapter 4. Experimental Setup
Several molds were designed and fabricated to simulate both industrial RTM and
VARTM processes. For RTM, a reusable mold constructed from aluminum was
fabricated to simulate industrial standard molds and to facilitate a high volume of
experiments. For VARTM, the mold cannot be reusable and several vacuum bag molds
were prepared for experiments. Parallel-plate sensors were used in conjunction with the
RTM mold, while FEF sensors were used with VARTM molds with both fiberglass and
carbon fiber preforms. The goal of the RTM experiments was to demonstrate the
feasibility of dielectric sensors for remote monitoring of fill front position. Once this was
established, the dielectric sensors were extended to VARTM processes in an attempt to
monitor fill front position and degree of cure.
4.1 RTM Mold and Materials
Figure 4.1 shows the experimental system consisting of a resin transfer mold and
a fluid delivery system. The mold is rectangular with a transparent upper plate for
visualization of the fill front. The working fluid is delivered to the mold using a
pressurized reservoir. A video camera is mounted above the mold in a steel frame.
Dielectric sensors are used to monitor the fill front. The preform is simulated using an
open-celled polyurethane foam (MA70) having a uniform permeability throughout the
material. The permeability of the medium is determined from Darcy’s law using
measured fill front velocities and pressure gradients. The foam has a solid fraction of
3.8%. The fill front velocity is calculated using change in fill front position over a known
interval of time. The pressure gradient is obtained from pressure measurements within the
40
mold cavity. A mixture of 80% glycerin and 20% water is used as the working fluid. The
viscosity of glycerin solution is similar to resins used and it also does not wick into the
foam. This allows for easy cleaning and fast repeatability of the experiments. An
aluminum mold of dimensions 350 x 250 x 10 mm with one inlet port and one outlet port
is used as the mold cavity. A 38 mm thick Lexan plate serves as the upper assembly of
the mold. A digital video camera is mounted 1 m from the top of the mold to
independently record the fill-front position. The mold is assembled by clamping the two
aluminum plates together with bolts. Glycerin water solution is delivered to the mold
from the pressure pot using flexible tubing. The preform used is 3/4ths inch shorter than
the mold cavity to allow for pressure equalization on the leading edge to ensure a one
dimensional fill front. Multiple trials were performed to ensure repeatability of the
system. Experiments were conducted for varying reservoir pressures ranging from 10psi
to 16.5psi. All trials were conducted at room temperature.
Figure 4.2 shows the geometrical distribution of sensors on top of the Lexan plate.
This geometry allows for comprehensive and continuous sensing of the fill-front. The
sensors are aligned parallel to the expected direction of the glycerin flow front
movement. A BNC cable was used to connect the function generator to the top plate of
the aluminum mold. For all experiments reported here, the function generator supplied a
constant 6 V sinusoidal signal at 1 kHz driving frequency. An electric field is generated
between the sensors and the mold due to the applied signal. Progression of the fill-front is
detected by continuously sensing a change in the complex gain of the input signal.
Changes in capacitance and conductance are then inferred from changes in complex gain
using a simple impedance divider circuit. Figure 4.3 shows the general schematic of the
experimental system with data acquisition.
41
InputOutput
Pressure Pot
Camera
InputOutput
Camera
Pressure Reservoir
Mold Cavity
Drain
SensorsUpper plate (Lexan)
Bottom plate (aluminum)
Figure 4.1. RTM mold and video camera that allows for independent
measurements of fill-front position.
42
Figure 4.2. Experimental setup with distributed dielectric sensors. Fill
front position is inferred as the glycerin/water solution passes under the
sensor.
Channel 1
Channel 2
Channel 3
Gain Capacitance
Phase Conductance
RTM Mold 3-Channel DAQ Circuit
Function Generator DAQ Card / Computer
Input Output
Figure 4.3. General schematic of the experimental system with data
acquisition.
43
4.2 VARTM Mold and Materials
Figure 4.4 shows the experimental system consisting of a VARTM mold and a
fluid delivery system. The mold is rectangular and consists of either fiberglass or carbon
fiber preforms. Epoxy resin is delivered to the mold by evacuating the mold with a
vacuum pump and drawing the resin in from a reservoir. A video camera is mounted
above the mold on a tripod. FEF dielectric sensors are used to monitor the fill front and
the degree of cure. Figure 4.4 shows the geometrical distribution of sensors on top of the
vacuum bag. This geometry allows for comprehensive and continuous sensing of the fill-
front. The sensors are aligned parallel to the expected direction of the resin flow front
movement. SMA cables was used to connect the function generator to the driving
channels of the sensors. For all fill front experiments with the VARTM setup, the
function generator supplied a constant 6 V sinusoidal signal at 1 kHz driving frequency.
Progression of the fill-front is detected by continuously sensing a change in the complex
gain of the input signal. Changes in capacitance and conductance are then inferred from
changes in complex gain using a simple impedance divider circuit.
44
Figure 4.4. Photograph of VARTM experimental setup with FEF sensors.
Figure 4.5 shows a cross-sectional view of the mold. The preform consists of
several layers of fiberglass or carbon fiber mats and the total thickness can vary from 5 –
20 mm. A 0.6 mm layer of peel ply is placed over the part, follow by a 1.2 mm layer of
distribution media. The entire structure is placed inside a sealed vacuum bag that is 0.3
mm thick. The bag is transparent and allows for visualization of the fill front. The FEF
sensors are designed to penetrate to the mid-point of the preform.
45
1.2 mm
0.6 mm
5.0 mm
12.7 mm
0.3 mm
0.3 mm
Drive DriveSense
Distribution Media Peel Ply Part Polycarbonate
Vacuum Bag Electrode Substrate
Figure 4.5. Drawing of cross-section for VARTM experimental setup.
An industrial standard, room-temperature curing epoxy resin is used as the
working fluid. This allows for easy cleaning and fast repeatability of the experiments.
Multiple trials were performed to ensure repeatability of the system. Experiments were
conducted for vacuum pressures of 27 Hg. All trials were conducted at room temperature.
4.3 Filling Scenarios
Figure 4.6 illustrates the two important filling scenarios for RTM and VARTM
experiments. For both RTM and VARTM filling experiments, only the 1-D filling case is
46
considered. For 2-D filling cases, sensors of different dimensions will need to be
fabricated in order to sense along the spine lines.
Element dimensions2 in x 23 in
Element dimensions2 in x 10.5 in
1ft Vent0.5 in
2 ftVent
0.5 in
Figure 4.6. Illustrations of 1-D and 2-D filling scenarios for RTM and VARTM
experiments.
47
Chapter 5. Experimental Results for RTM
5.1 Predicted Fill-Front Position
The average fluid velocity through the porous preform is given by
mold
frac
QVA
= (5.1)
where Qmold is the volumetric flow rate in the mold and Afrac is the cross sectional area of
the mold perpendicular to the direction of the flow not occupied by the porous medium.
Also from Darcy’s law, the flow from the leading edge of the porous medium to the fill
front is given by
k PVxµ
∂= −
∂ (5.2)
where V is the average velocity of the fluid, k is the permeability of the porous medium,
µ is the viscosity of the fluid and Px
∂∂
is the pressure gradient in the x direction. The
pressure change for a one-dimensional flow through an isotropic porous medium is
linear. Therefore the average velocity can be written as
xPPkV fillfrontin −
= µ (5.3)
48
where x is the distance from the leading edge of the porous medium to the fill front and
Pin is a function of x. Expressing the pressures as gauge pressures, (5.1) and (5.3) can be
combined to give
xPk
dtdxV in
µ = =
(5.4)
where
( )2 4
032
16
frres
rein
AA B A B CD P g h x
AP C
ρ
π
⎡ ⎤⎛ ⎞+ ± + − − +⎢ ⎥⎜ ⎟
⎝ ⎠⎣ ⎦= (5.5)
where
128 freq
kAl
xA = (5.6)
4B Dπ= (5.7)
2
frkAx
Cµ
ρ⎛ ⎞⎜ ⎟⎝ ⎠
= (5.8)
49
x is the flow front location, Pin is the inlet pressure recorded, leq is the equivalent length of
tubing, k is the permeability of porous medium, Afr is the cross sectional area of the mold
perpendicular to the direction of the fluid flow not occupied by the porous material, Are is the
cross sectional area of the reservoir, µ is the viscosity of the fluid, D is the inside diameter of the
tube, Pres is the pressure in the pressure pot, h0 is the initial height difference between the fluid
level in pot and the inlet port when the fill front is at the leading edge of porous medium and ρ is
the density of the fluid. (5.4) can be rearranged as follows to give the fill front position as a
function of time
''
00∫∫ =x
in
t
dxPxdtk
µ (5.9)
''
0∫=x
in
dxPxtk
µ (5.10)
The above equation expresses the fill front position at any time as a function of the
reservoir pressure alone. It is numerically solved for x after substituting for Pin from (5.5).
Figure 5.1 shows comparisons between experimental data obtained visually and
predicted data for varying reservoir pressures. As the pressure was increased, a
corresponding fall in the fill time was observed. It was also noted that there was a slight
deviation of predicted values from the experimental results. This can be attributed to a
rounding error in the inlet pressure readings.
50
Figure 5.1. Comparison between experimental (visual) and predicted data
for varying reservoir pressures (10, 13, 16 psi).
The good agreement between visually recorded flow front position and
theoretically predicted position suggests that the system is sufficient for simulating
industrial resin transfer molding processes. It follows that a sensor technique capable of
monitoring flow front position on this system will also measure position accurately on an
industrial setup.
5.2 Predicted Sensor Performance
The numerical simulations were performed with Maxwell software by Ansoft
Corp. Each transparent sensor was modeled as a cross-section of infinite depth on a per-
meter length basis. A parametric simulation of each sensor was run in order to find the
predicted capacitance as a function of flow-position along the mold. Figure 5.2 shows the
51
distribution of equipotential lines and electric field in and around the dielectric cell.
Figure 5.2 also shows the uniformity of the field between the sensing and driving
electrodes, while the field begins to fringe between the guard and drive electrodes. Figure
5.3 shows the results of a numerical simulation for sensor 2. The results show a gradual
increase in the capacitance as the fluid flows through the mold. Ideally, the sensors will
record a change in capacitance only when the liquid is directly between the parallel-plate
setup. However, this gradual rise in capacitance indicates the Maxwell capacitor is
sensing the glycerin well before the fluid moves between the plates. This is due to edge
effects in the Maxwell capacitor setup. These effects give inaccurate results for flow-
front position and must be taken into account. The numerical simulations are designed to
show what the capacitance values should be when the fluid is directly underneath the
sensor. Using these results, the experimental capacitance can effectively be mapped to a
distance along the sensor.
Figure 5.2. Equipotential lines and distribution of the electric field in and
around the dielectric cell. The size of the arrows is logarithmically
proportional to the intensity of the electric field.
52
Figure 5.3. Numerical results for sensor 2. The geometry and position of
the sensor on the mold determines the characteristic curve.
It is important to compare the numerical results to theoretically predicted values
for a guarded parallel plate capacitor in order to ensure the accuracy of the simulation.
The theoretical capacitance for an empty mold can be calculated by assuming a series
combination of capacitances from the Lexan plate and air. Likewise, for a mold filled
with glycerin/water solution, the capacitance is calculated by assuming series
capacitances from Lexan and glycerin/water solution. Theoretical capacitance is given by
01 2
1 2
1C Ad d
ε
ε ε
⎡ ⎤⎢ ⎥⎢ ⎥= ⋅ ⋅⎢ ⎥⎛ ⎞ ⎛ ⎞
+⎢ ⎥⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦
(5.11)
53
where A is the area of the sensing electrode, d1 is the thickness of the Lexan plate, d2 is
the air gap thickness, and ε1 and ε2 are the permitivities of Lexan and air, respectively.
For this study ε1 ≈ 3.1 and ε2 ≈ 1. Theory predicts an empty-mold capacitance of 0.8257
pF while the numerical simulations predict a value of 0.887 pF. The discrepancy suggests
that the numerical simulations take into account the secondary edge effects described
previously. The material properties of the glycerin/water solution were measured using a
simple dielectric cell and compared favorably with values taken from the data sheet
provided by the manufacturer. The dielectric constant of the solution was ε2* ≈ 46. This
value was used in the theoretical calculations as well as the Maxwell simulations. When
the mold is filled with glycerin/water solution, theory predicts a capacitance of 1.532 pF
while numerical simulations predict a value of 1.500 pF. For this study, the
glycerin/water solution was assumed to be weakly conductive.
5.3 Experimental Capacitance and Phase Data
Terminal admittance values were acquired using the dielectric sensor array
system. Gain and phase measurements were measured by the three-channel board and
converted to capacitance and conductance values. Some cross-talk between parallel plate
sensors was observed during experiments. However, the effects on the measured
capacitance were deemed negligible considering that measured capacitance values from
one sensor, driven alone and driven simultaneously with two other sensors, differed by
less than 1 percent.
Figure 5.4 shows experimental results for a run at 13 psi. The capacitance is
plotted as a function of time and the characteristic curve is shown to be similar to the
numerical simulation. The data exhibits a gradual increase in capacitance as the fluid
flows through the mold. This gradual increase is predicted by numerical simulations and
is due to edge-effects of the Maxwell capacitor setup. The glycerin/water solution is
54
detected by the sensors before the liquid is actually between the plates. This effect can be
accounted for using numerical simulation results. Figure 5.5 shows the phase as a
function of time. There is a small but distinct positive increase in the phase as the
glycerin/water solution passes between the plates. This indicates that the material under
test is weakly conductive and is important to consider when measuring other parameters
such as viscosity, temperature, and degree of cure.
55
Figure 5.4. Experimental capacitance data shows gradual increase in
capacitance over time.
56
Figure 5.5. Experimental phase data shows gradual positive increase in
phase over time, indicating that the material under test is weakly
conductive.
5.4 Data Analysis
A mapping algorithm was developed to convert measured capacitance values to flow
front position as a function of time for each sensor. The following algorithm includes a
normalization procedure and curve fitting routine using MATLAB:
(1) Normalize experimental and numerical data. For this normalization procedure,
assume only errors of the form ax+b. Zero the data by subtracting the lowest
value (‘b’) from each data point. Then divide each new data point by the highest
value data point, eliminating ‘a’.
57
(2) Use the spline-fitting tool in MATLAB to fit a curve to the normalized numerical
data. The spline-fitting tool will draw straight lines between consecutive data
points and will find the equation for each line. Thus, there is an equation
describing any region on the graph containing to consecutive points, instead of
one equation describing the region encapsulated by all points. A better fit to the
data is achieved in this manner.
(3) Substitute in each experimental capacitance value (with its corresponding time) to
this equation and find the distance at which this capacitance was measured.
(4) Plot distance as a function of time for each sensor.
This method of analysis is preferred because it can easily be developed into a fast real-
time algorithm once the respective look-up tables are generated for each sensor. For
example, if the sensor geometry and relative position on the mold is kept constant, only
one numerical simulation is needed to correlate a measured capacitance with a distance
along the mold. Figure 5.6 shows this mapping algorithm graphically. It should be noted
that when the sensor geometry or position on the mold changes, additional numerical
simulations will be needed in order to develop a mapping routine. However, extensive
studies are underway to determine if and what the functional dependencies are between
the mapping algorithm and sensor geometry.
58
Figure 5.6. Graphical representation of the mapping algorithm used in the
data analysis.
5.5 Flow-Front Position
Figure 5.7 shows the converted experimental capacitance data to position versus
time. The fill-front location as detected by the sensors in comparison with the visually
obtained data for different reservoir pressures is in good agreement. The small
discrepancies seen during the early and middle stages of the run can be explained by the
59
sensor edge effects. The discrepancies suggest that second-order fringing electric field
effects are contributing to a small non-linear change in capacitance with fill-front
position. As can be seen from the data, this non-linear effect quickly dissipates and the
sensor data is in good agreement with the visual measurements. It is interesting to note
that these second-order edge effects still exist even after implementation of the mapping
algorithm. More detailed numerical simulations will be needed to completely eliminate
these effects.
Figure 5.7. Visual and experimental comparison of measured fill-front
position at the centerline.
60
Chapter 6. Experimental Results for VARTM
Experiments were conducted to characterize the response of the sensor to the
variation in fill front position and degree of cure. Both fiberglass and carbon fiber
preforms were used to simulate industrial needs. Carbon fiber preforms are especially
important in the manufacturing of aircraft and armor.
6.1 Experimental Procedure (Fiberglass)
Industry-standard polyester resin is combined with methyl ethyl ketone peroxide
in a ratio of 100 parts resin to 1 part catalyst and the mixture is injected into the VARTM
mold using vacuum. It is important that the mold be completely sealed with no tears or
holes in the vacuum bag. In order to reduce outside electromagnetic interference and
increase the signal to noise ratio, the entire mold was placed in a cardboard box that was
lined with aluminum foil. The new chassis was grounded by attaching a wire from the
power supply ground terminal to the aluminum foil. Fill-front position versus time is
recorded with a digital camcorder. Capacitance, conductance, phase and gain versus time
are all recorded with the FEF sensors, where the driving frequency is held constant at 1
kHz. Once the mold is completely filled, the sensors perform spectroscopic cure analysis
from 100 Hz to 30 kHz until the resin has solidified so that it is hard to the touch.
6.2 Experimental Results for Fill-Front (Fiberglass)
Figure 6.1 (a) shows the dependence of the phase on the time of the experiment. It
can be seen that the magnitude of the phase change is small, indicating that even a small
61
amount of noise in the phase measurement will give an erroneous fill-front position.
Thus, phase is not a good parameter to use for fill-front estimation for this particular case.
Figure 6.1 (b-d) show the dependence of the gain, capacitance, and conductance on the
time of the experiment. These parameters exhibit a significant change is magnitude over
time, indicating they can be used for estimating fill-front position.
62
0 200 400 600 800 1000 1200 1400-2
-1
0
1
2
3
4
5
6
Sensor 1Sensor 2Sensor 3
0 200 400 600 800 1000 1200-5
0
5
10
15
20 x 10-9
Sensor 1Sensor 2Sensor 3
0 200 400 600 800 1000 1200-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Sensor 1Sensor 2Sensor 3
(a) (b)
(c) (d)
Figure 6.1. Measurements of 1-D fill-front position in VARTM for
fiberglass preforms.
6.3 Data Analysis
Figure 6.1 indicates that capacitance, conductance, and gain are acceptable
parameters to use for prediction of fill-front position. All of these parameters exhibit
63
similar dependences on experiment time and hence on fill-front position. Here,
capacitance is chosen to model the dependence of sensor response to fill front position.
Figure 6.2 shows a plot of change in capacitance versus fill front distance. The fill front
distance at discreet times was obtained from a digital camcorder during the experiment
and this distance was matched with normalized capacitance values.
Figure 6.2. Plot of change in capacitance versus flow distance.
Figure 6.3 shows a regression analysis for flow distance as a function of
capacitance. A cubic fit to the data was obtained with an R2 value of 0.9928, indicating a
good fit to the data. This analysis was conducted for each sensor head, and the resulting
equations are given here:
3 21 1 1 10.4316 3.3235 11.1693 1.7149sensorD C C C= ⋅∆ − ⋅∆ + ⋅∆ + (6.1)
64
3 22 2 2 20.3082 2.0331 9.1215 1.4223sensorD C C C= ⋅∆ − ⋅∆ + ⋅∆ + (6.2)
3 23 3 3 30.4738 3.2959 11.4769 1.9375sensorD C C C= ⋅∆ − ⋅∆ + ⋅∆ + (6.3)
These equations characterize the sensor response as a function of flow distance
and allow for real-time fill front monitoring. The next section will address the
implementation of these algorithms for carbon fiber preforms.
65
2 0.9928R =
∆C1
2 0.9928R =
∆C1 Figure 6.3. Plot of change in capacitance versus flow distance.
6.4 Experimental Results for Cure Monitoring (Fiberglass)
Figure 6.4 (a) shows phase as a function of time for the curing cycle of polyester
resin after it has completely filled the VARTM mold. The phase decreases with time, and
hence degree of cure, indicating the potential of this parameter to monitor the curing
during VARTM. Figure 6.4 (b-d) all show slight decreases with time, and hence degree
of cure, indicating these parameters are also candidates to monitor degree of cure.
66
(a) (b)
(c) (d)
Figure 6.4. Measurement of parameters during cure of polyester resin for
VARTM with fiberglass.
6.5 Experimental Procedure (Carbon Fiber)
Industry-standard polyester resin is combined with methyl ethyl ketone peroxide
in a ratio of 100 parts resin to 1 part catalyst and the mixture is injected into the VARTM
67
mold using vacuum. It is important that the mold be completely sealed with no tears or
holes in the vacuum bag. In order to reduce outside electromagnetic interference and
increase the signal to noise ratio, the entire mold was placed in a cardboard box that was
lined with aluminum foil. The new chassis was grounded by attaching a wire from the
power supply ground terminal to the aluminum foil. Fill-front position versus time is
recorded with a digital camcorder. Capacitance, conductance, phase and gain versus time
are all recorded with the FEF sensors, where the driving frequency is held constant at 1
kHz. Once the mold is completely filled, the sensors perform spectroscopic cure analysis
from 100 Hz to 30 kHz until the resin has solidified so that it is hard to the touch.
6.6 Experimental Results for Fill-Front (Carbon Fiber)
Figure 6.5 (a-d) shows the dependence of the phase, gain, capacitance, and
conductance on the time of the experiment. It can be seen that the magnitude of the
change of these parameters is significant, indicating they can all be used for estimating
fill-front position. Furthermore, the data from all three sensors is nearly overlapping,
indicating that each sensor’s response is similar and that the fill-front is flowing
uniformly through the mold.
68
(a) (b)
(c) (d)
Figure 6.5. Measurements of 1-D fill-front position in VARTM for carbon fiber
preforms.
Figure 6.6 shows a comparison of the predicted fill front location versus the visual
verification of the flow front from the digital camcorder. The equations generated from
curve fitting the fiberglass data were used to predict the fill location as a function of the
capacitance for carbon fiber performs. The agreement between the curves indicates that
69
the sensors can successfully predict the location of the fill front during VARTM
processes with carbon fiber performs.
Figure 6.6. Plot of visual and sensor predicted fill front location.
6.7 Experimental Results for Cure Monitoring (Carbon Fiber)
Figure 6.7 (a) shows phase as a function of time for the curing cycle of polyester
resin after it has completely filled the VARTM mold. The phase decreases with time and
then reaches relative steady-state. Figure 6.7 (b-d) all show significant decreases with
time, and hence degree of cure, indicating these parameters are also candidates to monitor
degree of cure.
70
(a) (b)
(c) (d)
Figure 6.7. Measurement of parameters in the time domain during cure of
polyester resin for VARTM with carbon fiber preforms.
Figure 6.8 (a-c) show phase, gain, and capacitance as a function of frequency for
the curing cycle of polyester resin after it has completely filled the VARTM mold. Phase,
gain, and capacitance decrease with increasing frequency. Useful information on
viscosity and degree of cure can be extracted from these parameters. Figure 6.8 (d) shows
the conductance exponentially increasing with increasing frequency.
71
(a) (b)
(c) (d)
Figure 6.8. Measurement of parameters in the frequency domain during cure of
polyester resin for VARTM with carbon fiber preforms.
Figure 6.9 (a-d) shows phase, gain, capacitance, and conductance as a function of
time and frequency for sensor 1 for the curing cycle of polyester resin after it has
completely filled the VARTM mold.
72
(a) (b)
(c) (d)
Time (s)
Figure 6.9. Sensor 1 measurement of parameters in the frequency domain
during cure of polyester resin for VARTM with carbon fiber preforms.
Figure 6.10 (a-d) shows phase, gain, capacitance, conductance as a function of
time and frequency for sensor 2 for the curing cycle of polyester resin after it has
completely filled the VARTM mold.
73
(a) (b)
(c) (d)
Figure 6.10. Sensor 2 measurement of cure cycle of polyester resin for
VARTM with carbon fiber preforms at frequencies from 100 Hz to 30 kHz..
Figure 6.11 (a-d) shows phase, gain, capacitance, and conductance as a function
of time and frequency for sensor 3 for the curing cycle of polyester resin after it has
completely filled the VARTM mold.
74
(a) (b)
(c) (d)
Figure 6.11. Sensor 3 measurement of cure cycle of polyester resin for
VARTM with carbon fiber preforms at frequencies from 100 Hz to 30 kHz.
6.8 Discussion of Cure Monitoring for Carbon Fiber
All sensors show similar trends for phase, gain, capacitance, and conductance as a
function of frequency and time. This is a good indication that curing is uniform
throughout the mold. Furthermore, the capacitance as a function of time and frequency
clearly reflects some molecular dynamics of the resin. Qualitatively speaking, there will
75
be a 1-to-1 correspondence between the capacitance and the permittivity of the resin.
Thus, several qualitative observations can be made about the permittivity of the resin as it
varies with time and frequency:
1. The permittivity decreases with increasing frequency.
2. The permittivity decreases with increasing time with an inflection point at
around t = 400 sec.
Unfortunately, there is no closed form analytical solution relating the transadmittance of
the interdigital sensor to the material properties. Such a solution does exist for parallel-
plate sensors, where the transadmittance is linearly proportional to the permittivity and
conductivity of the material. Interdigital capacitance and conductance measurements can
qualitatively tell us about the permittivity and conductivity of the material. In order to
quantify the molecular dynamics of the resin, however, the sensor needs to be able to
indirectly measure these material properties. Mapping these material properties from
transadmittance measurements is defined as an inverse problem of dielectric
spectroscopy. An algorithm has been proposed in [62,63] to solve this particular inverse
problem. This algorithm involves tabulating the entire discretized permittivity-
conductivity space in terms of terminal conductance and capacitance for each operating
wavelength of the sensor (the sensor has the potential to operate at multiple wavelengths,
and thus multiple penetration depths). By storing these precomputed values in a
computer, the inverse problem can be done in real-time by interpolation. Constructing
this calibration space involves extensive numerical simulations that were not performed
for this thesis. This is, however, a direction of future work.
76
Chapter 7. Disturbance Factors
The dielectric properties of the resin vary with temperature. Though the resin used
in the experiments reported here is a room temperature curing resin, the curing reaction is
exothermic and the resin and mold were observed to increase dramatically in temperature
during the cure cycle. Temperature gradients in the mold will almost certainly affect the
curing process. Moreover, temperature gradients during the filling stage will affect the
local viscosity of the resin. Non-uniform viscosity can lead to race-tracking and non-
uniform fill front. To compensate for this disturbance factor, thermocouples will be
installed in the mold to monitor and control the temperature during filling and curing.
The transparency of the sensor may also allow for coupling with an infrared heat sensor.
The amount of catalyst added to the resin during the VARTM experiments was
carefully measured to be consistent for all experiments. Small variations in catalyst, as
well as uneven mixing, can results in non-uniform curing of the part.
The fill front position was validated by means of a digital camcorder. The values
of distance as a function of time were found by playing back the video recording and
correlating a visual distance with the machine time. This method is prone to numerous
inaccuracies and a more automated method of fill front verification is being implemented.
Sensors are being designed that self-calibrate by using the time-derivative of the output
signal to verify fill front location.
Measurement noise in the system plays an important role for this particular
application because the sensors are very sensitive to outside electromagnetic interference.
A sharp and anomalous change in the sensor response due to noise will produce
detrimental results in a feed-forward control loop. To compensate for this interference, a
shielded chassis was designed consisting of a large card board box wrapped in aluminum
foil. The entire mold and sensor system was placed inside this chassis to reduce stray
77
electric field lines. This, however, may not be a feasible implementation in industry. The
sensors must be designed to be more robust and less susceptible to outside interference.
Finally, the algorithm that is used by the sensor to predict fill front location is
created using a trial run and a fitting function. Variations from mold to mold or from
batch to batch will adversely affect this fitting function. In essence, this algorithm will
only be precise if the mold, sensors, and resin are exactly identical for different
experiments. Since this is not the case, an algorithm that is independent of the
experimental setup must be designed before the sensors can be implemented in industry.
78
Chapter 8. Future Work and Conclusions
8.1 Carbon Nanotubes
Carbon nanotubes offer the possibility of creating functionally graded material,
i.e., material reinforced by single and multi-walled carbon nanotubes. At present, carbon
nanotubes are expensive to manufacture in bulk and it would require a large amount to
reinforce a composite part such as an airplane wing. However, as production costs of
nanotubes diminish, the composite material industry will find an increasing need for
process control of nanotube dispersion in composite parts.
Fringing electric fields are a promising as well as already recognized means of
characterizing [37] and manipulating nanotubes [38,39] dispersed throughout polymer
base.
The complex dielectric permittivity of the composite material that contains
embedded nanotubes is a function of nanotube concentration, orientation, alignment, and
length-to-width ratio. This general statement is true for all types of nanotubes. The
specifics of applications are very diverse. The following examples are representative, but
not comprehensive.
The dramatic variation of the imaginary part of dielectric permittivity near the
percolation threshold is perhaps the most common subject of investigation in this area
today [40]. Figure 8.1 shows two cases of nanotube alignment, the nearly aligned case,
and the randomly distributed case. Conventional nanotechnology characterization
methods, for example, Scanning Electron Microscopy (SEM) are capable of
differentiating such cases in specially prepared samples. However, for practical
manufacturing control methods, in-situ characterization would be much more desirable.
Application of the electrodes to the sides of the specimen shown in Figure 8.1 will result
79
in a nearly insulating material on the left and a conducting material on the right
(assuming high conductivity of carbon nanotubes), when the percolation threshold is
achieved.
Figure 8.1. Two cases of nanotube orientation: nearly aligned (left) and
randomly oriented (right).
The proposed work will take this basic idea to a level practically not explored to
date. The fringing field dielectric spectroscopy will allow measurement of alignment and
concentration of nanotubes as a function of position, applicable for scanning of
manufactured products in-situ in real time.
8.2 Parameter Estimation Algorithms
Sophisticated parameter estimation algorithms will be developed to relate the
terminal measurements of the interdigital FEF sensor to material properties such as
permittivity and conductivity. This will allow for more quantitative cure monitoring than
the calibration-based sensing reported in this thesis. In order to develop such algorithms,
extensive numerical simulations will be performed using the Maxwell electrostatics
software by Ansoft. Maxwell has been used before in this thesis to model the parallel-
plate geometry to account for fringing fields due to the presence of the glycerin fill front
during RTM measurements.
80
8.3 Conclusions
A distributed dielectric sensor array is capable of measuring flow-front location
during the resin transfer molding process (RTM) and vacuum-assisted resin transfer
molding processes (VARTM). In addition, calibration sensing was demonstrated to show
correlation between terminal admittance measurements and degree of cure during the
curing phase of VARTM processes. The result was demonstrated for fiberglass and
carbon fiber performs. The technique allows for continuous sensing over the entire mold
while being completely non-invasive and not requiring embedded materials. The
technique is useful for manufacturing of composite materials where controllability of the
process is desired. In addition, the sensors can be fabricated to be completely transparent,
allowing for good visual calibration and the possibility of a coupled infrared sensor
system. The results of measurements of the flow-front position were presented. The
results were compared to visual measurements and theoretical predictions of the system.
The results suggest the feasibility of such a technique for in-situ monitoring of the resin
transfer molding process.
81
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