Stray Capacitances of an Air-Cored Eddy Current Sensor by ProQuest


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									                   Sensors & Transducers Journal, Vol. 111, Issue 12, December 2009, pp. 25-37

                                                       Sensors & Transducers
                                                                                           ISSN 1726-5479
                                                                                            © 2009 by IFSA

     Stray Capacitances of an Air-Cored Eddy Current Sensor
           Yi Jia, 2Henning Heuer, 2Susanne Hillmann, 2Norbert Meyendorf
                                 Department of Mechanical Engineering
                         University of Puerto Rico, Mayaguez, PR 00680, USA
                             Fraunhofer Institute for Non-Destructive Testing
                          Maria-Reiche Strasse 2, 01109 Dresden, Germany
                            Tel.: 787-832-4040 ext 3482, fax: 787-265-3817

   Received: 10 September 2009 /Accepted: 22 December 2009 /Published: 30 December 2009

Abstract: Stray capacitance of an air-cored eddy current sensor is one of the most crucial issues for
successful development of an eddy current based residual stress assessment technology at frequency
above 50 MHz. A two dimensional finite element model and an equivalent lumped capacitance network
have been developed to accurately quantify overall stray capacitances of an air-cored eddy current
sensor with specimen being tested. A baseline model was used to evaluate sensor design parameters,
including the effects of pitch distance, trace width, trace thickness, number of turns, inner diameter,
substrate thickness, lift-off distance, and dielectric constant of shim on the stray capacitances of the
sensor. The results clearly indicate that an appropriate sensor design parameters could reduce the stray
capacitance and improve the sensor performance. This research opens up a new design space to
minimize stray capacitance effect and improve the sensor sensitivity and its lift-off uncertainty at
elevated high frequencies. Copyright © 2009 IFSA.

Keywords: Stray capacitance, Eddy current sensor, Finite element, Residual stress assessment

1. Introduction
Surface enhancement treatment, such as shot peening, laser shock peening, low plasticity burnishing,
has been widely applied in industrial applications, especially for aircraft engine components. In the
components with surface enhancement treatment near-surface compressive residual stresses can
counterbalance applied tensile loads and significantly prolong component service life. The studies have
shown that high levels of system reliability can be gained by maintaining the compressive residual stress

                   Sensors & Transducers Journal, Vol. 111, Issue 12, December 2009, pp. 25-37

state [1]. To monitor the remaining residual stress profile or to reliably assess remaining life of the
components, an in-service non-destructive method is needed to capture the residual stress state of parts
during scheduled inspection periods.

X-ray diffraction (XRD), neutron diffraction, surface acoustic waves, thermoelectric power and eddy
current measurements have been employed to assess the residual stress. In the past few years, high
frequency eddy current conductivity spectroscopy technology was found to offer a great potential for
near-surface residual stress assessment due to its frequency-dependent penetration depth and stress
dependence of electric conductivity [2]. However, most practical problems in eddy current
non-destructive evaluation require inspection frequencies below 10 MHz. Due to the penetration depth
of the compressive layer after surface enhancement treatment is very small in a shallow depth of about
50–200 μm below the surface, the inspection frequency range for residual stress assessment has to be
extended far beyond 10MHz, where the effective inspection depth is only about 100 μm. It is expected
that inspection frequency range can be extended to at least 50 – 80 MHz in order to capture the important
part of the near-surface residual stress profile [3].

To implement the eddy current measurement technology, an air-cored eddy current sensor is typically
adopted. However, stray capacitance of an eddy current sensor becomes one of the most crucial issues
for successful development of the eddy current based measurement system at elevated frequencies. The
sensor could be constructed either single or separate excitation/receive coils. The separate two-coil
design can significantly improve the thermal stability of the measurements because the measured
transfer impedance depends only on the mutual inductance of the coils, but not on their
temperature-dependent resistance in each individual coil. Meanwhile, the behavior of the air-core eddy
current sensor at elevated high inspection frequencies is completely different from that at low
frequencies. Skin and proximity effects cause the winding resistance to increase, the inductance to
decrease slightly at high frequency, and stary capacitances significantly affect the sensor performance,
such as sensor sensitivity and lift-off uncertainty. Bassam. A. Abu-Nabah and Peter B. Nagy showed that
the spurious self- and stray capacitance effects render the complex eddy current coil impedance variation
with highly nonlinear lift-off curve, which makes it difficult to achieve accurate conductivity
measurements beyond 25MHz in the presence of even the slightest lift-off uncertainties [3].

The stray capacitances of an air-cored eddy current sensor consist of turn-to-turn capacitances between
both adjacent and nonadjacent turns and turn-to-specimen (ground) capacitances between coil turns and
material under test. At high frequencies this capacitance across the sensor carry time-varying current in
the sensor and allows signal to flow directly from the input to output port without passing through the
spiral coil. The magnitude of the stray capacitance is strongly dependent on the winding geometry and
the proximity of any conducting surfaces. Since the parasitic capacitances are distributed parameters,
determining stray capacitance of the sensor is a difficult task. Parallel plate based capacitance
computational method
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