Measurement 124 (2018) 575–581
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A clearance measurement system based on on-component multilayer triaxial capacitive probe
T
⁎
Tommaso Addabboa, Francesco Bertoccia, Ada Forta, , Marco Mugnainia, Enza Panzardia, Valerio Vignolia, Chiara Cinellib a b
Department of Information Engineering and Mathematical Science, University of Siena, via Roma 56, 53100 Siena, Italy BHGE, via Felice Matteucci 2, 50127 Firenze, Italy
A R T I C L E I N F O
A B S T R A C T
Keywords: Capacitive sensor On-component sensor Conditioning electronics Clearance measurement Sensor modeling
In this paper the authors propose the design of a complete measurement system of clearance based on an ‘oncomponent’ triaxial capacitive probe for static and dynamic measurement of distance. The capacitive probe is designed to be deposited onto machinery components or complex structures and is aimed at reducing the impact of probe mounting on the monitored component. The problem is discussed from a theoretical point of view and then supported by the realization of a sensor prototype in screen printed technology and of two possible and alternative conditioning systems. The results prove the feasibility of this innovative measurement system.
1. Introduction ‘On-component’ sensors, printed or deposited onto machine components have many obvious advantages: a negligible mass, accurate placement, applicability to a variety of materials including ceramics, capability for operation to very high temperatures (> 1000 °C), minimal structural disturbance (minimal machining) and finally an intimate sensor to substrate contact. The use of such sensors, instead of traditional ‘bulk’ devices, allows for preserving the integrity of the components, not perturbing the operating conditions and the operation of the whole system, and accordingly permitting to ensure a greater reliability. Some solutions based on the deposition of thin films have been since a long time the subject of studies in the field of avionics. In this context, NASA has produced prototypes of sensing films for the measurement of temperature, and flow sensors based on thermocouples and resistive strain gauges [1–6]. In different studies reported in the literature, materials and deposition techniques suitable for particularly hostile operating conditions have been identified, especially in terms of temperature (up to 1100 °C). Both conductive and insulator ceramic materials for this application have been identified: the latter are able to maintain high insulation at temperatures up to 700 °C with a film thickness even less than 10 μm, and can be deposited on either steel or similar alloys. The feasibility of multi-layer structures was also proven. These results constitute a solid basis for the study and the realization of capacitive sensors deposited directly onto turbomachinery components. In particular, in this paper we explore the possibility of
⁎
realizing triaxial capacitive probes for clearance measurement (static and dynamic measurements of distances). The structure to be achieved is quite complex, since it requires the construction of sensors consisting of a large number of layers of different materials. The problem is discussed from a theoretical point of view and then supported by the development of a prototype of a film-based triaxial capacitive sensor in screen printed technology. The proposed structure is designed, studied through electric field simulations and finally realized and tested. The measurement of clearance based on capacitive sensing is a complex problem due to the presence of parasitic capacitances. The sensor capacitance is grounded and has a small value (at most some pF): in order to grant a sufficient sensitivity the parallel of this capacitance with the large capacitance of the cable, which in industrial environment can be many meters long, has to be avoided [7–9]. It is well known that the guarded structure provided by a triaxial capacitive probe wired with a triaxial cable is the only possible solution to this problem, provided that a suitable driving system for the internal shield (guard) is designed. The driving system for the guard must ensure a very low voltage across the terminals of the parasitic capacitance, usually granted inserting the capacitance in a feedback loop exploiting a large gain amplifier. Since in dynamic measurements of clearance the signal bandwidth can be very large (up to 50 kHz) the read out electronics has to operate at a frequency much higher than 100 kHz, requiring large bandwidth amplifiers. The design of the conditioning system is a complex task that requires a careful dimensioning of the circuit parameters to ensure sufficient bandwidth and accuracy, as it generally
Corresponding author. E-mail addresses:
[email protected] (A. Fort),
[email protected] (C. Cinelli).
https://doi.org/10.1016/j.measurement.2018.01.015 Received 6 October 2017; Received in revised form 2 January 2018; Accepted 9 January 2018 Available online 17 January 2018 0263-2241/ © 2018 Elsevier Ltd. All rights reserved.
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Rext
Rg Rc
Fig. 2. Definition of the equivalent capacitances for the triaxial probe.
presence of the gap does not affect in any way the behavior of the sensor, but by increasing its sensitivity. According to this model there will be no error if the measurement system uses the approximation of parallel plate to determine the distance. It is apparent that in this approximation the effect of a variable distance between the electrode and the target is not accounted for, but this dependency definitely exists. Nevertheless, it was shown in [12] that this simple model describes satisfactorily the behavior of the sensor if the ratio of the outer radius of the guard and the maximum distance to the target is large (2d ≤ RC + g). The layout of the proposed printed sensor is shown in Fig. 3 and consists of:
Fig. 1. Structure of the traditional ‘bulk’ triaxial capacitive sensor.
happens when dealing with capacitive sensors [10–11]. In this paper, the design of a complete system for the measurement of clearance is described, the design of each component of the system is based on a theoretical discussion and related to the most important measurement system performance. The paper is organized as follows. In Section 2 the design of the sensor is discussed on the base of its electrical behavior. In Section 3 the realization and experimental characterization of a prototype sensor is described. In Section 4 two possible front-end architectures are presented and studied. Finally, in Section 5 some results obtained with the complete system are presented and commented. The conclusions are drawn in Section 6.
(a) the measurement electrode or central conductor; (b) the insulating layer between the measurement electrode and a guard shield (insulator gap); (c) the guard shield; (d) the insulating layer between the guard and the external shield (insulator gap); (e) the external shield.
2. Sensor design and study of the electrical behavior The proposed ‘on-component’ sensor has to operate as a bulk triaxial capacitive probe, whose structure is reported for sake of clarity in Fig. 1. The design of the sensor was based on the results obtained in previous studies concerning the traditional triaxial probes [12]. In particular, taking into account that the measurement electrode and the guard shield are maintained at the same voltage by the external frontend circuit, and referring to the symbols defined in Figs. 1 and 2, the sensing capacitance CS is given by the capacitance between the central conductor and ground:
CS = Cct + Ccs ,
The measurement electrode (and the signal wire) consists of the conductive layer (a). The electrode size is decided according to the required sensitivity. Note that the realization of printed devices allows the use of larger electrodes with respect to the traditional probes because the mounting of a probe with a large area does not affect the
(1)
where Ccs is the capacitance between the central conductor and the outer shield which is connected to ground whereas Cct is the capacitance between the central conductor and the target. In the literature there are several approximations for this capacitance depending, of course, on the distance from the target (that is the quantity of interest) but also on the insulating material thickness. In particular if Ccs is negligible, (i.e. when the guard conductor has a large area), CS can be approximated with the capacitance CSO, which takes into account the boundary effects due to the gap (g) between the guard and the central conductor, using the following equation [12,13]:
CS ≈ CSO =
g 2 εr ε0 π ⎛RC + ⎞ 2⎠ d ⎝
(2) Fig. 3. Structure of the proposed printed sensor and the reference system for the following figures.
In Eq. (2) the relationship between capacitance and distance is described by the parallel plate capacitance approximation, therefore the 576
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1.2
1 0.8 0.8
z (mm)
0.6
0.2
8
8.5
9
9.5
10
0
ρ (mm) Fig. 5. Electrical field FEA. The figure shows the voltage in false color, the equipotential lines are also shown. The voltage target-sensor is equal to 1 V, the distance from the guard to the target is d = 0.9 mm. The guard radius is 2RC. The insulating layer has a dielectric constant equal to 11 and has a radius equal to RC + 2 mm, tDIE = tc = 50 μm.
thickness of the electrode itself, and d is the distance between target and guard. Using a fixed value for the thicknesses of the dielectric and the central electrode, as can be seen in Figs. 4 and 5, the edge effect can be minimized if the insulation is realized by a material with a large dielectric constant and if the insulating layer area is increased. In fact, with reference to Fig. 5, using the approximation of infinite parallel plates to describe the field and the electric potential over the guard ring, far from the sensor central electrode, it is possible to write:
Vg (z ) = V − t Vg (z ) =
V DIE + εr (d − tDIE )
z
0 < z ≤ tDIE
V ε V V − t + ε (d − t ) tDIE− t + ε r(d − t ) (z−tDIE) DIE r DIE DIE r DIE
tDIE < z < d (3)
Therefore realizing the insulating layer between the central electrode and the guard with a radius larger than Rc and choosing a material which has a large dielectric constant, it is possible to reduce the discontinuity between the electric field above the measurement electrode (Ec) and the one above the guard (Eg). Indeed if εr > > 1 then Vg(tDIE) ≈ V and, for z > tDIE, Vg(z) ≈ V-V (z-tDIE)/(d-tDIE). In this case, therefore, you switch from a field Eg ≈ V/ (d-tDIE) above the guard electrode to the field Ec ≈ V/(d-tDIE-tc) above the measurement electrode. Compared to the case in which the dielectric is located just under the central electrode, the geometry shown in Fig. 3 reduces the fringe effect related to the thickness of the insulating layer. Note that this thickness can’t be too small, in order to grant a sufficient insulation between the conductive layers. On the other hand, the metallic layer thicknesses can be very small without affecting the sensor operation, not being critical the perfect continuity. The geometry shown in Fig. 3 allows for treating the printed probe as a ‘traditional’ bulk triaxial probe with the same size, with a measurement capacitance given by Eq. (2), being g = 0. From now on the prototype sensor capacitance is taken as a reference for the successive discussion.
0.8
z (mm)
0.4
-0.2
0.8 0.6
0.4 0.4
0
0.4
0
1
0.2
0.6
0.2
1 (V)
0.6
1 (V)
1.2
functionality and the integrity of the machine. The insulating layer between the central electrode and the guard shield must completely cover the signal wire and is therefore realized with two depositions of ceramic or glass (b). Even the guard shield must completely cover the signal wire, and must therefore be realized through the two metal or conductive depositions indicated by (c) in Fig. 3. The two layers indicated with (d) insulate the guard from the external shield. Note that in the prototype an alumina support acts as the outer insulating layer. The external shield (e) must constitute a closed conductive structure realized by two further outer conductive layers. In the final device, the metal component that supports the sensor acts as the lower part of the external shield. Note that electrodes with different geometry (e.g. rectangles) can be realized without drawbacks. The geometry chosen and realized by a prototype (Fig. 3) is similar to that of the traditional probe. This choice has been made to facilitate the comparison of performance with traditional probes. Obviously, the printed probe has the advantage, compared to traditional probes, not to have a gap between the central and the guard electrode. The proposed probe was studied by finite element analysis (FEA) of the electric field. To perform these simulations, we referred to the application of interest, in which the measurement range is centered at 500 μm, and the required accuracy is of the order of 10 μm (at 500 μm). In the general case, the results of the FEA simulations show that a sensor with the geometry shown in Fig. 3 generates an electric field disturbed if compared to the ideal situation of a uniform field generated by a capacitor with infinite parallel plane plates. The disturb is firstly due to the presence of a height difference between the central electrode and the guard, whereas the fringe effect, due to the finite area of the guard, is completely irrelevant if the guard is sufficiently large (compared to the maximum distance to be measured). Fig. 4 highlights the effect of the guard-central electrode difference in height. In the figure, the results are obtained considering an overall height difference between measurement electrode and guard surfaces of 100 μm. The simulation concerns a sensor in which the central electrode (a) and the insulation layer (b) have the same radius. As expected, in this case the edge effect is rather large and its influence is linked to the distance to be measured. The fringe effect can be described roughly by the transition from the electrical field Eg ≈ V/d (above the center of the guard ring far from the electrode edge) to the one given by Ec ≈ V/(d-tDIE-tc) (above the center of the measurement electrode), where tDIE is the thickness of the layer insulating the guard from the central electrode whereas tc is the
0.2
3. Sensor prototype realization and experimenatal characterization
-0.2 8
8.5
9
9.5
0
A prototype with the structure shown in Fig. 3 was developed on an alumina substrate in screen printing technique. The measurement electrode radius is 4.5 mm, whereas its thickness is 12 μm. The insulating layer (Resistivity > 100 GΩ cm @25 °C) between the guard and the measurement electrode has a radius of 6.5 mm and thickness of 50 μm (Fig. 6).
ρ (mm) Fig. 4. Electrical field FEA. The figure shows the voltage in false color, the equipotential lines are also shown. The voltage target-sensor is equal to 1 V, the distance from the guard to the target is d = 0.9 mm. The guard radius is 2RC. The insulating layer has a relative dielectric constant equal to 11 and a radius equal to RC, tDIE = tc = 50 μm.
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16
x 10
-3
14
dmeasured (m)
12 Fig. 6. Sensor prototype after the deposition of the first three layers.
To test the device in a large frequency range, an automatic measurement system was developed. The system provides an accurate capacitance-voltage conversion in the bandwidth 10 Hz–10 kHz. The measurement system allows both to analyze the frequency behavior of the device (influence of parasitic components), and to calibrate the sensor with respect to distance. The sensor under test is placed at a known distance d (accuracy 0.3 mm) from a metallic plate, which is driven by a waveform generator (Agilent AG33220A), at the known voltage Vin(t) with respect to the ground. The charge, Q(t), induced on the measurement electrode is converted into a voltage by a charge amplifier (Bruel and Kjaer Nexus 2692-A). The guard and the shield are connected to the voltage reference of the charge amplifier. The expected charge is given by the following:
Q (f ) = Vin (f ) Cs =
Vin (f ) επRC2 , d
4 2 2
|Vin (f0 )| |Vout (f0 )|
6
8
10
12
14
16 x 10
-3
Fig. 8. Sensor characterization results: measured distance (Eq. (6)) vs. ‘true’ distance.
4. Front end design and charcterization As mentioned in the introduction the printed sensor is connected to the measurement system via a triaxial cable, with the internal shield acting as the needed guard. In this paper a measurement electronics driving the guard and providing, as an output, an AM modulated signal is considered. With this solution the variable capacitance of the sensor determines the amplitude of a sine signal (at a fixed frequency) generated by an oscillator circuit. In this context the output of the system, VO, can be written as follows:
(4)
(5)
επRC2 |H (f0 )|
4
d (m)
where H(f) is the transfer function of the charge amplifier (bandwidth10% 1 Hz to 30 kHz). At the frequency f0 in the center of the frequency band the distance (see Fig. 7) d can be assessed exploiting the above equations:
dmeasured =
8 6
where RC, for the prototype, is 4.5 mm. The output of the charge amplifier, Vout (t), is given by:
Vout (f ) = Q (f ) H (f ),
10
VO = h (Cs (d )))sin(2πf0 t + ϕ),
(7)
where f0 is the oscillator frequency, ϕ is a phase shift, and h(Cs) is a function of the sensor capacitance determined by the front-end architecture. Fig. 9 shows the structure of the measurement system: the front end circuit outputs the AM signal and drives the shield, an envelope detector recovers the measurement information. The design of the system takes into account the requirements typical for clearance measurement systems in turbo-machines, i.e. resolution of about 10 μm in a measurement range of 1 mm centered around 500 μm, and bandwidth (fmax) for dynamic clearance measurements in the order of tens of kHz. In this paper we propose two possible front-end circuits for the measurement system (operating with f0 higher than 500 kHz). The first one provides ideally a linear conversion of the sensor capacitance, whereas the other gives an output voltage signal amplitude proportional to the target distance. In the following subsections the two proposed front-end circuits are described, and their operating principle is analyzed taking into account the main parasitic effects.
(6)
The expected accuracy due to the accuracy of the voltage measurements and to the tolerance given by the printing process is of 5%. The results of such estimation, reported in Fig. 8 confirm that the behavior of the printed probe is the one expected. Finally, the behavior of the proposed probe was compared to the one of a traditional triaxial probe with the same size, showing similar performance also in term of noise.
4.1. Front-end design: Linear distance-voltage converter Fig. 10 shows the schematics of the first front-end circuit. A wideFront-end C-V converter/ d-V converter Sensor
Oscillator f0
VO
Envelope detector
Guard driver Fig. 7. Magnitude of the charge amplifier output, Vout(f), obtained at a fixed distance of the sensor from the metallic plate as a function of frequency.
Fig. 9. Block diagram of the measurement system.
578
Amplifier Filters
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Rf +
Cs + Csp
A
Cf
Vguard
LM6172
C
Ccg
G
Cgs
S
R1 C1c
Vi
Ra +
A
Ca
VO
LM6172
Fig. 10. Schematic of the front-end: distance-voltage converter topology.
band operational amplifier was used to drive the guard. The impedance given by the parallel Rf and Cf was put in the feedback path to avoid self-oscillation and compensate the effect of the stray capacitance from the inverting input to ground, and will not be taken into account in what follows. The sensor was put in a voltage divider with R1 and C1c. An amplifier was used to buffer the voltage divider output signal. Considering the output buffer ideal, and considering the distance to ground of the sensor d a slowly varying quantity with respect to the circuit excitation signal (f0 > > fmax), the circuit transfer function can be written as follows:
V0 = Vi
1 Z1 1 Z1
+
1 Zs
where Z1 =
+
1 Zpar
R1 1 + jωR1 Cp
1
1
+ ( A + 1 )·( Z ) +
parallel parasitic capacitance can’t be neglected. So in Eq. (10) the rightmost inequality becomes meaningless, and the leftmost one has to be considered. Hence what matters is the ratio Z1/Zs, which is limited by the parasitic capacitance. Note that when described by Eq. (11) the circuit behaves as a linear converter of distance into voltage, but this behavior is expected when all the parasitic effects can be neglected. The circuit was both simulated, taking into account the parasitic effects, and experimentally characterized. A prototype circuit was realized using a large bandwidth amplifier (100 MHz GBW) based on a transconductance architecture (LM6172). This IC behaves as an operational amplifier. Three different values of the resistance R1 were considered (1 MΩ, 5 MΩ, 10 MΩ) obtaining similar results. The experimental data shown in the following figures are obtained connecting the prototype printed sensor to the front end with a 1.6 m long tri-axial cable (Ccg = 120 pF/m, Cgs = 350 pF/m). As can it be seen in Fig. 11, where simulation results are shown, and in Fig. 12, where simulated data are compared to the experimental
, (8)
cg
1 jωC1c
Fig. 11. Output voltage amplitude of the front-end circuit in Fig. 10 as a function of distance, assuming R1 = 1 MΩ, C1c = 330 F, Cp = 1 pF, Csp = 2 pF. Different colors refer to different frequencies f0 (as per legend) Different line styles refer to different cable lengths as per legend.
is the reference impedance in the voltage
divider. R1 and C1c are defined in Fig. 10, whereas Cp is the parasitic parallel resistance of R1. C1c is a coupling capacitor with a large value, whose effect can be neglected at the frequency of interest, so in the following simplified discussion it will be neglected. 1 Zs = jω (C + C ) is the impedance of the sensor (comprising the fixed s
sp
parasitic capacitance Csp), whereas Zpar represents the parasitic impedance between node C (central conductor) and ground, and A is the open loop gain of the amplifier. Finally Zcg is the impedance of the capacitance Ccg between the central conductor and the guard (nodes C and G). 1 1 Obviously in the ideal case the term ( A + 1 )( Z ) is small, C1c and all cg
the parasitic capacitances (Csp and Cp) are negligible, and Cs ≪ C1c, therefore we have the simple result:
V0 1 = Vi 1+
Z1 Zs
≈
1 1 + jωR1 Cs
0.65
(9) 0.6
Eq. (9) shows that the circuit behaves as low pass filter. Obviously, to obtain a good sensitivity of the output voltage to the variation of Cs the R1 value has to be chosen to satisfy the following condition:
Z1 1 ≫ 1 → f0 ≫ Zs 2πR1 Cs
f=1 MHz experimental f=1 MHz predicted
0.55
0.5
(10)
Under the assumption in Eq. (10) it is possible to write: 0.45
V0 1 d ≈ = , Vi 2πf0 R1 Cs 2π 2f0 R1 εr ε0 RC2
(11)
0.4
where RC is the sensor radius defined in Section 2. As shown in its derivation, the ideal behavior described by Eq. (11) is followed by the circuit only if working at a frequency higher than the cut-off frequency, i.e. the limit frequency set by Eq. (10). Note that this limit tends to be very high due to the small value of the sensor capacitance and to the fact that, in practice, there is an upper bound to the value of R1, since in the frequency range of interest, for large values of this resistance, the
0.35 0
0.2
0.4
0.6
0.8
1
1.2
d (mm) Fig. 12. Output voltage of the circuit in Fig. 10. The measurement data (markers) are compared to simulated data (dashed line).
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Fig. 13. Circuit transfer function as a function of frequency for different sensor capacitance values. Circuit parameters are listed in the caption of Fig. 11.
Cs+Csp Ccg Cgs
Rf C
-
G
+
S
A
vO
Fig. 16. Upper plots: frequency response assuming different cable lengths at fixed value of Cs. Lower plots: |V0/Vi | at different frequencies f0 and different cable lengths as a function of distance d. Different colors indicate different frequencies. Different line styles indicate different cable lengths. The obtained results refer to Rf = 1M Ω and
Vi
Ccg = 100pF/m . For experimental data L = 1.6 m.
measured distance (mm)
Fig. 14. Schematic of the front-end: capacitance-voltage converter topology.
-0.2 -0.4 -0.6 -0.8 0
0.01
0.02
0.03
0.04
0.05
0.03
0.04
0.05
measured distance (mm)
Time (s) -0.2 -0.4 -0.6 -0.8 0
0.01
0.02
Time (s) Fig. 15. Circuit transfer function as a function of frequency for different sensor capacitance values. Simulated data are solid lines without markers, black lines with markers show measurement values. The red lines are obtained with Rf = 1 MΩ while magenta lines with Rf = 10 MΩ. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
Fig. 17. Dynamic clearance measurements obtained with a rotating toothed wheel. Upper Plot: output of the measurement system based on the linear distance-voltage converter. Lower plot: output of the measurement system based on the linear capacitance-voltage converter.
4.2. Front-end design: Linear capacitance-voltage converter
data, the voltage response of the proposed front-end circuit deviates from linearity at large distance values due to parasitic effects. In particular, in Fig. 11, it is shown how the effect of the capacitance of the guard is effectively cancelled only for short cables (shorter than 10 m, corresponding to a capacitance close to 1 nF) in the whole considered measurement range. For a cable longer than 10 m the measurement range results insufficient for the considered application. In Fig. 13 the circuit transfer functions obtained with different sensor capacitance values are shown. In this figure the simulated data are compared with measurement data.
In case the electronics must be placed far from the printed circuit (most of cases in industrial applications), an alternative front-end circuit providing an AM modulated signal is proposed (Fig. 14). Considering that d varies much more slowly than the excitation voltage so that Cs is constant, it is possible to write the frequency transfer function with the following equation: 1
Vo = Vi
580
(Z + s
A Zf
1
+ (Z + s
1 )A Zf 1 Zf
+
1 ) Zcg
(12)
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In analogy to what discussed for the first circuit topology, the ideal behavior of the circuit is found when the open loop gain of the amplifier is infinite and the parasitic effects can be neglected:
Zf Vo =1+ = 1 + jωRf Cs Vi Zs
shown in Fig. 16 from the cable length and from Rf. Obviously to avoid the dependency of the output amplitude on the cable, an output amplifier with a gain proportional to the cable length has to be inserted in the measurement chain. The maximum cable length is determined essentially by the limit on the tolerable attenuation.
(13)
The circuit behaves as high pass filter. Obviously also in this case a condition analog to the one in Eq. (10) has to be satisfied in order to get a sufficient variation of the output, i.e.:
2πf0 Rf Cs ≫ 1
5. Dynamic test of the overall system The measurement system was calibrated in static conditions, with a micrometric positioning system. Finally the overall system was tested in dynamic conditions using a rotating toothed wheel, with 300 mm diameter and 60 teeth, driven by a motor. The probe was mounted at the nominal distance of 0.5 mm. A working frequency f0 of 1 MHz was used for both the front-end circuits. The demodulated output was acquired by an oscilloscope (Tektronix TDS3000), and then processed in order to obtain the clearance estimation. An example of the results obtained with the wheel rotating at about 500 rpm is shown in Fig. 17. An eccentricity of 400 µm is clearly detected using both the front-end structures.
(14)
And:
2π 2f0 Rf εr ε0 RC2 V0 = Vi d
(15)
The effect of the non-idealities can be studied in the following way. Referring to Eq. (12), we can write:
V0 = Vi
( 1 Zf
+
1 ⎛1 ⎜ ADC Zs
⎝
1 Zs
+
+ 1 Zf
1 Zf
+
)
,
1 ⎞⎛ ⎟ ⎜1 Zcg
⎠⎝
+
jω ⎞ ⎟ ωH
⎠
6. Conclusion (16) The feasibility of a clearance measurement system based on ‘oncomponent’ triaxial capacitive probes for clearance monitoring is demonstrated both from a theoretical and an experimental point of view. In particular, the test of a prototype in screen printed technology demonstrated that the behavior of such components is comparable with the one of a ‘bulk’ triaxal probe. The next step of this work will be to deposit and test a similar structure on turbomachinery components.
where we considered A = ADC/(1 + jω/ωH), being ADC the DC gain of the amplifier and ωH its dominant pole angular frequency. If ω ≫ ωH and ω ≫ 1/(CcgRf), being Cs ≪ Ccg, Eq. (16) becomes:
(jωRf Cs + 1) V0 ≈ ω2Rf Ccg Vi 1− 2πGBW
(17)
where GBW is the gain bandwidth product of the amplifier. Eq. (17) shows that the circuit behaves as a one zero-two poles band pass circuit. The poles are close to the imaginary axis if the parasitic capacitance of Rf is not considered. At frequencies much lower than the pole ones it approximately follows the ideal behavior of Eq. (13), whereas at high frequency we have:
Vo 1 Cs 2πGBW ≈− . Vi jω Ccg
References [1] R.D. Meredith, J.D. Wrbanek, G.C. Fralick, L.C. Greer, G.W. Hunter, L.Y. Chen, Design and operation of a fast, thin-film thermocouple probe on a turbine engine, 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 2014. [2] A. Von Moll, A.R. Behbahani, G.C. Fralick, J.D. Wrbanek, G.W. Hunter, A Review of exhaust gas temperature sensing techniques for modern turbine engine controls, 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 2014, 18. [3] J.D. Wrbanek, G.C. Fralick, D. Zhu, Ceramic thin film thermocouples for SiC-based ceramic matrix composites, Thin Solid Films 520 (17) (2012) 5801–5806. [4] J.D. Wrbanek, G.C. Fralick, Thin film ceramic strain sensor development for harsh environments, in: Proceedings of the 53rd International Instrumentation Symposium, 2007, vol. 470, pp. 551–572. [5] O.J. Gregory, E. Busch, G.C. Fralick, Thermoelectric properties of ceramic thin film thermocouples, in: Proceedings of the 52nd International Instrumentation Symposium, 2006, vol. 467, pp. 234–248. [6] J.D. Wrbanek, G.C. Fralick, J.M. Gonzalez III, Developing multilayer thin film strain sensors with high thermal stability, in: Collection of Technical Papers - AIAA/ ASME/SAE/ASEE 42nd Joint Propulsion Conference, 2006, vol. 4, pp. 2731–2740. [7] I.D. Baikie, E. Venderbosch, J.A. Meyer, P.J.Z. Estrup, Analysis of stray capacitance in the kelvin method, Rev Sci Instrum 62 (3) (1991) 725–735. [8] S.M. Huang, A.L. Stott, R.G. Green, M.S. Beck, Electronic transducers for industrial measurement of low value capacitances, J Phys E: Sci Instrum 21 (1988) 242–250. [9] F. Reverter, X. Li, G.C.M. Meijer, Stability and accuracy of active shielding for grounded capacitive sensors, Meas Sci Technol 17 (2006) 2884–2890. [10] T. Addabbo, A. Fort, R. Garbin, M. Mugnaini, S. Rocchi, V. Vignoli, Theoretical characterization of a gas path debris detection monitoring system based on electrostatic sensors and charge amplifiers, Meas: J Int Meas Confederation 64 (2015) 138–146. [11] H. Volkers, T. Bruns, The influence of source impedance on charge amplifiers, Acta Imeko 2 (2) (2013) 56–60. [12] T. Addabbo, A. Fort, M. Mugnaini, S. Rocchi, V. Vignoli, A heuristic reliable model for guarded capacitive sensors to measure displacements, in: Proceedings of the 2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Pisa, 2015, pp. 1488–1491. [13] T. Addabbo, A. Fort, M. Mugnaini, S. Rocchi, V. Vignoli, Improved model for the capacitance estimation of guarded capacitive sensors, in: Proceedings of the 2015 XVIII AISEM Annual Conference, Trento, 2015, pp. 1–4.
(18)
Eq. (18) shows how also when accounting for the effect of long cables (large Ccg values) at high frequency the output of the circuit is directly proportional to the sensor capacitance, even if the gain depends on the cable length. This solution is viable also for long cables since, even if the output voltage level depends on the cable length, the relative variation of the output |V0 (d )|/|V0 (∞)|, due to sensor capacitance variation, does not depend on cable length. It can be seen that a large GBW of the amplifier is needed to grant a sufficient SNR at the selected frequency. Also in this case a prototype circuit was realized using the large band amplifiers LM6172. Three different value of the resistance Rf were considered (1 MΩ, 5 MΩ, 10 MΩ). The experimental data shown in the following figures are obtained connecting the prototype printed sensor to the front end with a 1.5 m long tri-axial cable. In Fig. 15 the transfer functions obtained varying Cs and Rf are shown, simulated data in solid colored lines are superimposed to measurement data plotted with black lines with markers. It can be seen from Fig. 16 that the performance of the front end are satisfactory even in presence of very long cables corresponding to parasitic capacitances up to 10 nF. Actually working with cables longer than 1 m and with frequencies f0 higher than 500 kHz the output of the circuit is given by Eq. (18) and this justify the independency of the relative response
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