Experimental Investigation of High Temperature-Resistant ... - MDPI

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Experimental Investigation of High Temperature-Resistant Inductive Sensor for Blade Tip Clearance Measurement Ziyu Zhao , Zhenxia Liu, Yaguo Lyu * and Yajun Gao School of Power and Energy, Northwestern Polytechnical University, Youyi West Road 127#, Xi’an 710054, China; [email protected] (Z.Z.); [email protected] (Z.L.); [email protected] (Y.G.) * Correspondence: [email protected]; Tel.: +86-029-8840-3456 Received: 19 November 2018; Accepted: 20 December 2018; Published: 24 December 2018

Abstract: Turbine tip clearance of aero-engine is important to engine performance. Proper control of rotor tip clearance contributes to engine efficiency improvement and fuel consumption reduction. Therefore, accurate tip clearance measurement is essential. The inductive measurement method is one of the non-contact distance measurement methods, which has the characteristics of high sensitivity, fast response speed and strong anti-interference ability. Based on the principle of inductive sensor measuring tip clearance, the ambient temperature change will cause the material electromagnetic performance change for the conductivity and permeability varies with temperature. The calibration experiment was conducted to obtain the sensor resolution and sensing range. The effect of temperature on sensor parameters was extracted from high temperature experiment data. Results show the resolution of planar coil made of platinum wire can be 10 µm and the maximum sensing range can reach 5 mm. At temperature from 500 °C to 1100 °C, coil inductance almost does not change with temperature while coil resistance varies exponentially with temperature, that means the coil inductance variation can reflect the tip clearance change and resistance can indicate the measuring temperature. Keywords: inductive sensor; tip clearance; turbine blade; temperature influence

1. Introduction The blade tip clearance of gas turbine is significant for its performance and efficiency. Therefore, precise measurement of tip clearance is the premise of accurate design and optimization the tip clearance [1–3]. The study of sensor with high precision and high resolution for tip clearance is necessary and crucial. Numerous non-contact measurement technologies are developed, including microwave, optical, capacitive, and inductive. Mark R.W. et al. [4–6] from NASA Glenn Research Center started effort on microwave method applying to tip clearance measurement since 2003. The microwave sensor probe is able to operate at extremely high temperature and is unaffected by contaminants in turbine engines. While the sensing range is limited by the frequency and the probe can only operate at 900 ◦ C without cooling. As early as 1982, NASA and GE published their cooperative research results of an optical sensor for measuring tip clearance, including test results on the compressor disk [7]. Since 2013, García I. and Zubia J. et al. from University of the Basque Country had been continuously published the results of optical method application in tip clearance measurement [8–12]. While, the study of Andreas K. et.al. [13] proved the optical sensor still have some problems to be solved such as optical fiber heat-resistance, lens cleanness, and the Doppler effect. Capacitive method is the most mature technology so far. Early as 1953, Mossop I.A. et al. [14] published a set of capacitive measurement system for turbine tip Sensors 2019, 19, 61; doi:10.3390/s19010061

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2 of 13 turbine tip clearance. Muller D. et al [15] conducted the dynamic tip clearance measurement experiment on the compressor and turbine and validated the system uncertainty and stabilization. While the Muller sensor may by permittivity change of medium and has zero drift problems. clearance. D. etbe al.influenced [15] conducted the dynamic tip clearance measurement experiment on the Sridhar V. and Chana K.S. et al [16–19] anuncertainty eddy current on the gas turbine engine to compressor and turbine and validated the used system andprobe stabilization. While the sensor may obtain tip clearance values in the high pressure turbine stage. The results showed the sensor was be influenced by permittivity change of medium and has zero drift problems. Sridhar V. and Chana ableettoal. perform these environments without losingengine accuracy. Du L.tip and Zhu X.L. et al K.S. [16–19] at used an extreme eddy current probe on the gas turbine to obtain clearance values [20,21] verified theturbine eddy current method laboratory withwas 3000 rpm revolution and extreme 1300 K in the high pressure stage. The results in showed the sensor able to perform at these temperature. environments without losing accuracy. Du L. and Zhu X.L. et al. [20,21] verified the eddy current Based on above,with eddy3000 current method is and a potential way to monitor the dynamic blade tip method in laboratory rpm revolution 1300 K temperature. clearance in above, turbine. Unfortunately, of the inductive inevitably Based on eddy current methodthe is ameasurement potential way tosignal monitor dynamicsensor blade tipisclearance in affected by temperature variation due to its working principle and unavoidable temperature drift turbine. Unfortunately, the measurement signal of inductive sensor is inevitably affected by temperature problems.due Lyu et al [22] used temperature-compensation circuit toproblems. eliminate Lyu temperature variation toY.T. its working principle and unavoidable temperature drift Y.T. et al.drift [22] ◦ of inductive sensor from 20 ℃ to 500 ℃. Wang H.B. et al [23] reported their experimental finding used temperature-compensation circuit to eliminate temperature drift of inductive sensor from 20 C to that◦resistance has et a larger withexperimental temperaturefinding changethat compared to that inductance, and 500 C. Wang H.B. al. [23]coefficient reported their resistance has of a larger coefficient resistance variation compensates for of temperature on inductance variation. This with temperature change compared tothe thatinfluence of inductance, and resistance variation compensates forselfthe temperature compensation method for ECS is simple and low cost, and has competitive advantages influence of temperature on inductance variation. This self-temperature compensation method for ECS is in mostand applications. simple low cost, and has competitive advantages in most applications. Hence, this paper paper focused focused on on validating validating the the high-resolution high-resolution inductive inductive sensor sensor performance performance and and Hence, this aimed at finding the temperature influence law and using it in the actual turbine measurement at aimed at finding the temperature influence law and using it in the actual turbine measurement at ◦ extremely high high temperature temperature such such as as 1000 1000 ℃. Furthermore, instead instead of of the the complex complex signal signal processing processing extremely C. Furthermore, circuits [23], a simpler voltage division circuit was used to calculate the coil resistance and coil coil circuits [23], a simpler voltage division circuit was used to calculate the coil resistance and inductance based on the phasor analysis. The sensor resolution and range were verified by inductance based on the phasor analysis. The sensor resolution and range were verified by calibration calibration thenheat-resistance the sensor heat-resistance tested thermal test the bench. Finally, and then theand sensor was tested on was thermal teston bench. Finally, influence lawthe of influence law of temperature on sensor parameters was explored experimentally. temperature on sensor parameters was explored experimentally.

2. Method and Sensor Sensor 2. 2.1. 2.1. Inductive Inductive Tip Tip Clearance Clearance Measurement Measurement The of inductive sensor is based on Faraday’s law of electromagnetic induction The working workingprinciple principle of inductive sensor is based on Faraday's law of electromagnetic and Lenz’s and law. Lenz’s The main component the sensor isofanthe inductive can becoil, threewhich dimensional induction law. The mainofcomponent sensor coil, is anwhich inductive can be spiral or two dimensional The coil generates a magnetic when excited by a high three coil dimensional spiral coil planar or twocoil. dimensional planar coil. The coilfield generates a magnetic field frequency AC signal, and then eddy current is induced in the metallic target when it passing through when excited by a high frequency AC signal, and then eddy current is induced in the metallic target the magnetic field through and thus the a reverse magnetic eddy current declines inductance of when it passing magnetic fieldflux andcaused thus abyreverse magnetic flux the caused by eddy sensor coil. Figure 1 shows the working principle of the inductive sensor (encapsulated planar coil). current declines the inductance of sensor coil. Figure 1 shows the working principle of the inductive Figure is the measurement sensor 2(encapsulated planar equivalent coil). Figurecircuit. 2 is the measurement equivalent circuit.

Figure Figure 1. 1. Schematic diagram diagram of of measuring measuring principle. principle.

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Figure Figure 2. 2. Equivalent circuit circuit of of measurement. measurement.

The The relation relation between between equivalent equivalent circuit circuit parameters parameters and and output output signal signal can can be be derived derived from from the the Kirchhoff and (2)). Kirchhoff Voltage VoltageLaw Law(Equations (Equations(1) (1)–(2)). j·ωMI =V 𝑅𝑐 𝐼1 R +c 𝑗I1∙ + 𝜔𝐿j·𝑐ωL 𝐼1 c I1𝑗 − ∙ 𝜔𝑀𝐼 2 =2 𝑉𝑜𝑢𝑡 out

(1)

(1)

R I + j·ωL I − j·ωMI = 0 (2) 𝑅𝑡 𝐼2 +t 𝑗2∙ 𝜔𝐿𝑡 𝐼2 t 2𝑗 ∙ 𝜔𝑀𝐼1 =1 0 (2) The equivalent resistance R, inductance L and impedance Z of sensor coil can be derived from Equations (1) and (2), as in Equation (3)–(5): The equivalent resistance R, inductance L and impedance Z of sensor coil can be derived from 2 M2 Equation (1) and Equation (2), as in Equation ω (3)–(5): R = Rc + Rt = Rc + Re (3) Rt 2 + (ωLt )2

𝜔 𝑀 𝑅 =𝑅 +𝑅 ω 2 M)2 (𝜔𝐿 𝑅 + L = Lc − Le L = Lc − 2 t 2

𝑅=𝑅 +

Rt + (ωLt )

(3) (4)

𝜔 𝑀 +𝐿 jω [ Lc 𝐿 − Le ] 𝐿 = Z𝐿 = R + jωL = [ Rc + 𝐿Re ]= 𝑅 + (𝜔𝐿 )

(5) (4) Therefore, the equivalent impedance of coil Z is related to the target and the distance between target and sensor coil under the certain excitation signal. The change of equivalent impedance is 𝑍 = 𝑅 R+and 𝑗𝜔Lequivalent = 𝑅 +𝑅 𝐿 + 𝑗𝜔 𝐿L variation caused by equivalent resistance inductance while R(5) and L are determined by the clearance between coil and target (M), exciting voltage frequency (f, f = 2πω), coil inductance (Lc), and coil resistance (Rc) as Equations (3) and (4) show. Rt is the equivalent resistance of induced Therefore, the equivalent impedance of coil 𝑍 is related to the target and the distance between eddy and Ltcoil is equivalent of induced eddy current. Under the certain condition, is f, targetcurrent and sensor under the inductance certain excitation signal. The change of equivalent impedance Lc and Rc are constants so the equivalent impedance becomes the univalent function of distance (d). caused by equivalent resistance R and equivalent inductance L variation while R and L are

determined by the clearance between coil and target (M), exciting voltage frequency (f, f = 2π𝜔), coil 2.2. Sensor Structure and Manufacture inductance (Lc), and coil resistance (Rc) as Equation (3) and Equation (4) show. Rt is the equivalent The magnetic fieldeddy intensity of circular is higherinductance than that ofofsquare coil. The current. magnetic field resistance of induced current and Lt iscoil equivalent induced eddy Under intensity B generated by circular coil is calculated by Equation (6). When the material permeability µ the certain condition, f, Lc and Rc are constants so the equivalent impedance becomes the univalent is determined by material function of distance (d). property and current I is determined by exciting circuit, it can be seen that coil turns (N) and coil thickness (h) can both influence the magnetic field intensity. 2.2. Sensor Structure and Manufacture N∗I B=µ (6) The magnetic field intensity of circular coil ishhigher than that of square coil. The magnetic field intensity B generated by circular coil is calculated by Equation (6). When the material Harold Wheeler [24] had published the research results of eddy current coil in 1928 and Equation (7) permeability 𝜇 is determined by material property and current I is determined by exciting circuit, it is the planar coil inductance formula. It indicates the coil inductance also has positive correlation with can be seen that coil turns (N) and coil thickness (h) can both influence the magnetic field intensity. coil turns (N), radial dimension (r), and inverse correlation with thickness (h). ∗ B =𝜇 (6) r2 × N 2 L(µH ) = (7) Harold Wheeler [24] had published the research results of eddy current coil in 1928 and (8r + 279.4h ) Equation (7) is the planar coil inductance formula. It indicates the coil inductance also has positive correlation with coil turns (N), radial dimension (r), and inverse correlation with thickness (h).

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𝐿(𝜇𝐻) = 𝐿(𝜇𝐻) = ( (

× × . ) . )

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(7) (7) From the above, above, the magnetic field From the the magnetic field intensity intensity and and coil coil inductance inductance are are proportional proportional to to N N and and From the above, thetomagnetic field intensity and coil inductance are circuit. proportional to Nsay and inversely proportional h when the sensor coil is connected to a certain That is to inversely proportional to h when the sensor coil is connected to a certain circuit. That is to say the the inversely proportional to h thinner when the sensor coil isgenerate connected to a magnetic certain circuit. That is to thus say the coil with more turns and thickness can higher field intensity, coil coil with more turns and thinner thickness can generate higher magnetic field intensity, thus coil has coil with more turns and thinner thickness can generate higher magnetic field intensity, thus coil has higher sensitivity wider measuring range. higher sensitivity and and wider measuring range. has higher sensitivity range. The study resultand of wider Du L. L. measuring et al. al [20] intensive The study result of Du et [20] indicated indicated the the planar planar coil coil had had simple simple geometry, geometry, intensive The study result of Du L. et al [20] indicated the planar coil satisfied had simple geometry, intensive magnetic field and fast response speed, its sensitivity and range the turbine tip clearance magnetic field and fast response speed, its sensitivity and range satisfied the turbine tip clearance magnetic field and fast response speed, its sensitivity and range satisfied the without turbine iron tip clearance measurement requirement. Thus, the sensor sensor inthis thispaper paper alsoplanar planarcoil coil core, that measurement requirement. Thus, the in isisalso without iron core, that is measurement requirement. Thus, the sensor in this paper is also planar coil without iron core, that is to say the minimum h equals to the wire diameter and the compact method is adopted to wrap to say the minimum h equals to the wire diameter and the compact method is adopted to wrap coils to iscoils to say the minimum h equals to given the wire diameter and the compact method flux is adopted to wrap to more permit more for the and generate higher magnetic permit turns forturns the given coil sizecoil andsize generate higher magnetic flux density. density. coils toThe permit more turns for given coildesigned size and generate magnetic density. thisthe paper was Figure higher 3 shows, shows, mainly flux included The sensor sensor probe probe in in this paper was designed as as Figure 3 mainly included aa planar planar coil coil The sensor probe in this paper was designed as Figure 3 shows, mainly included a planar coil and its sealed ceramic package. According to the study results in [25,26], the planar coil was made and its sealed ceramic package. According to the study results in [25,26], the planar coil was made and its sealed ceramicwire package. According to the study results [25,26], the 1mm planar coil washoles made of 0.2 mm platinum platinum which melting point over 2000 2000 K.in First, drilled of 0.2 mm wire which melting point is is over K. First, drilled 1mm diameter diameter holes in in ofthe 0.2center mm platinum wire which melting point is overand 2000 K. First, drilled 1mm diameter holes in of two two separate separate cm×4 the center of 33 cm × 4cm cmacrylic acrylicplates plates andfixed fixedthem them in in parallel parallel and and kept kept the the distance distance the centerover of two separate 3 cm×4 cm acrylic plates andwas fixed them in parallelthe and keptand the distance slightly 0.2mm. mm.Then, Then, 0.8mm mm diameter tube inserted through The slightly over 0.2 a a0.8 diameter tube was inserted through the holesholes and held.held. The wire slightly over 0.2 mm.around Then, athe 0.8tube mm between diameterthe tube was inserted through the holes and coil. held.When The wire was wrapped two plates to form the planar hollow was wrapped around the tube between the two plates to form the planar hollow coil. When the planar wire was wrapped around thecarefully tube between thethe twocentral platestube to form the planar hollowand coil. When the coil was formed, and theand upper then thin coil planar was formed, carefully removed theremoved central tube and the upper plate, thenplate, thin coil was glued the planar coil was formed, carefully removed the central tube and the upper plate, and then thin coil was glued off the bottom plate by adhesive tape. Finally, a high temperature ceramic adhesive off the bottom plate by adhesive tape. Finally, a high temperature ceramic adhesive gel was used to coil was glued offseal the bottom plate byitadhesive tape. Finally, a highenvironment. temperature The ceramic adhesivein gel usedtoto coil to avoid corroded at corrosive sealwas the coil avoid the it being corroded atbeing corrosive environment. The sensor used in thesensor paperused was an gel was used to seal the coil to avoid it being corroded at corrosive environment. The sensor used in the paper was an encapsulated 10-turns coil as Figure 4 shows. encapsulated 10-turns coil as Figure 4 shows. the paper was an encapsulated 10-turns coil as Figure 4 shows.

2 2

3 3 1 1

Figure 3. Design sketch of sensor, wherein 1 is leading line, 2 is sealing package, 3 is platinum coil Figure Figure3.3.Design Designsketch sketchofofsensor, sensor,wherein wherein1 1isisleading leadingline, line,22isissealing sealingpackage, package,33isisplatinum platinumcoil coil.

(a) (a)

(b) (b)

Figure 4. (a) Sensor coil before encapsulation; (b) sensor after encapsulation. Figure 4. (a) Sensor coil before encapsulation; (b) sensor after Figure 4. (a) Sensor coil before encapsulation; (b) sensor after encapsulation. encapsulation.

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In order to evaluate the coil quality, quality factor (Q) is used to indicate the quality of In order to evaluate the coil quality, quality factor (Q) is used to indicate the quality of inductive inductive elements. The higher Q value means the coil is more inductive and effective in the nonelements. The higher Q value means the coil is more inductive and effective in the non-contact contact measuring. The Q is calculated by Equation (8): measuring. The Q is calculated by Equation (8):

𝑄=

∗

= 𝑡𝑎𝑛(𝑝ℎ𝑎𝑠𝑒𝑎𝑛𝑔𝑙𝑒)

(8)

ω ∗ Lc Q= = tan( phaseangle) (8) Rc frequency and 𝜔 = 2*pi*f, 𝐿 is the coil equivalent where 𝜔 is the excitation signal angular inductance andexcitation 𝑅 is the coil equivalent resistance.and ω = 2∗pi∗f, L is the coil equivalent inductance where ω is the signal angular frequency c The parameters of coil (Lc, Rc) adopted in the research were measured by LCR meter (HIOKI and Rc is the coil equivalent resistance. IM3536). The inductance Lc (Lc, and Rc) resistance Rcinare μHwere and 1.1262 Ω under 4MHz excitation The parameters of coil adopted the0.6399 research measured by LCR meter (HIOKI signal. Then coil Q value is calculated and phase angle is 86.2° (the 4MHz phase excitation angles of IM3536). Thethe inductance Lc and resistance as Rc 14.27 are 0.6399 µH and 1.1262 Ω under inductance elements which means thephase coil is angle a goodisinductance element. signal. Then the coilare Q usually value is45°~90°) calculated as 14.27 and 86.2◦ (the phase angles of inductance elements are usually 45◦ ~90◦ ) which means the coil is a good inductance element. 3. Sensor Performance 3. Sensor Performance 3.1. Characteristics Calibration 3.1. Characteristics Calibration In order to verify the sensitivity and measuring range of designed platinum coil, the calibration experiment was conducted room temperature to obtain the sensor characteristic In order to verify the sensitivity and at measuring range of designed platinum coil, the calibration curve. The characteristic curve of the tip clearance sensor refers to the relationship curve of sensor experiment was conducted at room temperature to obtain the sensor characteristic curve. The characteristic characteristic and the clearance. The relativecurve variation of voltage was used as measuring curve of the tipparameter clearance sensor refers to the relationship of sensor characteristic parameter and the quantity therelative study.variation Data processing is as shown in Figure 5. The signal was collected by clearance.in The of voltageprocess was used measuring quantity in the study. Data processing DAQ (Data Acquisition) then input into Matlab.byInDAQ order(Data to increase the signal-to-noise process is shown in Figureand 5. The signal was collected Acquisition) and then inputratio into (SNR), method was the used to remove ratio the high noise wavelet Matlab. FFT In order to increase signal-to-noise (SNR),frequency FFT method wasand usedstationary to remove the high decomposition method wavelet was used to smooth the(SWD) voltage signal.was Figure is smooth the comparison of frequency noise(SWD) and stationary decomposition method used6to the voltage the signal sequence time domain before andsequence after SWD. It isdomain provedbefore that SWD can SWD. efficiently signal. Figure 6 is theincomparison of the signal in time and after It is suppress high frequency noise and increase SNR of voltage signal. proved that SWD can efficiently suppress highthe frequency noise and increase the SNR of voltage signal.

Figure 5. Data processing process. SWD: stationary wavelet decomposition. DAQ: data acquisition.

Figure 5. Data processing process. SWD: stationary wavelet decomposition. DAQ: data acquisition.

The calibration system includes sensor probe, calibration target, position controller, function generator, and DAQ system. The calibration target is a 10 mm width and 1.5 mm thickness plate, and the target material is Inconel 718 which is one of the turbine blade materials. The precision of position controller is 1 µm and its control range is 13 mm. The excitation signal in the calibration experiment was 4 MHz and 3 Vpp sinusoidal AC signal generated by Agilent Keysight 33600A (Agilent Technologies Inc., Santa Clara, CA, USA).


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(a)

(b)

Figure 6. SWD effect comparison; (a) signal sequence before SWD; (b) signal sequence after SWD.

The calibration system includes sensor probe, calibration target, position controller, function generator, and DAQ system. The calibration target is a 10 mm width and 1.5 mm thickness plate, (a) (b) and the target material is Inconel 718 which is one of the turbine blade materials. The precision of position controller iseffect 1 comparison; μm and its control range is 13before mm. SWD; The excitation signal inafter the calibration Figure 6. SWD effect (a) sequence before SWD; (b) signal sequence after SWD. Figure 6. SWD comparison; (a)signal signal sequence (b) signal sequence SWD. experiment was 4 MHz and 3 Vpp sinusoidal AC signal generated by Agilent Keysight 33600A connecting theSanta measuring circuit (function generator, target, sensor probe andcontroller, DAQ card)function and (Agilent Technologies Inc., Clara, sensor California, USA).calibration TheAfter calibration system includes probe, position fixingAfter the target position, collected the voltage V0 on the coil. Then, adjusted thecard) distance connecting the measuring circuit (function probe and DAQ and generator, and DAQ system. The calibration target is generator, a 10sensor mm sensor width and 1.5 mm thickness plate, between sensor surface and target surface from 0mm to 5 mm with 50 µm step, and collected voltage the target position, collected voltage V0 on the sensor Then, adjustedThe the precision distance of andfixing the target material is Inconel 718the which is one of the turbinecoil. blade materials. signals onsensor the sensor coil at each position. Voltage variation waswith denoted as sensor characteristic between surface surface from is 0mm to 5dV mm 50 μm step,inand position controller is 1 μmand andtarget its control range 13 mm. The excitation signal thecollected calibration parameter and calculated in Matlab. voltage signals on the sensor coil at each position. Voltage variation dV was denoted as sensor experiment was 4 MHz and 3 Vpp sinusoidal AC signal generated by Agilent Keysight 33600A The calibration resultand is shown in Figure 7. Equation (9) is five order fitting formula and its fitting characteristic parameter calculated in Matlab. (Agilent Technologies Inc., Santa Clara, California, 2 degree R calibration is 0.9992. The signal data near 5mm isUSA). in Table The result is shown in Figure 7.listed Equation (9)1.is five order fitting formula and its After connecting the measuring circuit (function generator, sensor probe and DAQ card) and fitting degree R² is 0.9992. The signal 5data near4 5mm is listed in Table 1. fixing the target position, collected ond3the dV/V d +voltage a4 ×d +Va03 × + a2sensor ×d2 + acoil. + a0 adjusted the distance (9) 0 = a5 × the 1 × dThen, dV/V 0 = a5 × d5 + a4 × d4 + a3 × d3 + a2 × d2 + a1 × d + a0 (9) between sensor surface and target surface from 0mm to 5 mm with 50 μm step, and collected wherein, a0 = on 10.1, a1 =sensor 10.7, a = −at 5.86, a3 =position. 1.73, a4 = Voltage −0.259, a5variation = 0.0155. dV was denoted as sensor voltage signals wherein, a0 = 10.1,the a1 = 10.7, a2 2=coil −5.86, aeach 3 = 1.73, a4 = −0.259, a5 = 0.0155.

characteristic parameter and calculated in Matlab. The calibration result is shown in Figure 7. Equation (9) is five order fitting formula and its fitting degree R² is 0.9992. The signal data near 5mm is listed in Table 1. dV/V0 = a5 × d5 + a4 × d4 + a3 × d3 + a2 × d2 + a1 × d + a0 wherein, a0 = 10.1, a1 = 10.7, a2 = −5.86, a3 = 1.73, a4 = −0.259, a5 = 0.0155.

Figure 7. 7. Calibration temperature. Figure Calibration curve curve at at room room temperature. Table 1. Table 1. Calibration Calibration data data at at near near full full range range area. area. Clearance(mm)

Clearance(mm)

dV/V0 (−%)

dV/V0(-%)

4.95 0.465 4.96 0.457 4.95 0.465 4.97 0.450 4.98 0.442 4.96 0.457 Figure 7. Calibration curve at room 4.99 0.434temperature. 4.97 0.450 5.00 0.427

Table 1. Calibration data at near full range area.

Clearance(mm)

dV/V0(-%)

4.95

0.465

4.96

0.457

(9)

4.99

0.434

5.00

0.427

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According to the calibration curve in Figure 7, the sensor has good sensitivity (4%/mm) within to the curve in 7, the sensor has good (4%/mm) within 2 mm. TheAccording sensitivity andcalibration the resolution ofFigure the sensor decrease with sensitivity the distance as Figure 7 shows 2 mm. The sensitivity and the resolution of the sensor decrease with the distance as Figure 7 shows and the data precision of measurement system is 0.001%, data listed in Table.1 proves the and the data precision of measurement system is 0.001%, data listed in Table 1 proves the measuring measuring range of the sensor is over 5 mm and the resolution reaches 10 μm for the data still has range of the sensor is over 5 mm and the resolution reaches 10 µm for the data still has 0.07% variation 0.07% at variation 5 mm. at 5 mm. In order to verify the accuracy of of calibration repeatabilityofof measuring signal In order to verify the accuracy calibrationresults, results, the the repeatability measuring signal of of 11 11 position points within 0–5 mm range was calculated with with 95.56% confidence interval. Ten sets of sets of position points within 0–5 mm range was calculated 95.56% confidence interval. Ten data were collected each position position point andand the measurement results inresults the whole are plotted data were collected at ateach point the measurement in range the whole range are in Figure 8. The relative standard deviation can be calculated by Equation (10): plotted in Figure 8. The relative standard deviation can be calculated by Equation (10): RSD =

∗ 2 ∗ SX 𝑅𝑆𝐷 = ¯ × 100% X

× 100%

(10)

¯

(10)

X is meanmean of theof sample. where SX is standard deviation based thesample sample population, is standard deviation based ononthe population, 𝑋 arithmetic is arithmetic the sample. 𝑤ℎ𝑒𝑟𝑒𝑆

Figure 8. Repeatability different position. Figure 8. Repeatabilitymeasurement measurement atat different position. From the data in Table 2,Table the measuring repeatability at different positions is almost within 0.05% 2. Repeatability measurement data. which means the coil had good repeatability within measuring range.

Clearance(mm)

Voltage(V)

Repeatibility(%)

Table 2. Repeatability measurement data.

0.0 (mm) Clearance

0.41332 Voltage (V)

0.0

0.43260 0.43260

2.0

0.45032

1.52.5

0.45314 0.44786

3.0 2.03.5 4.0 4.5 2.55.0

0.45352 0.45458 0.45032 0.45614 0.45706 0.45314 0.45781

0.0327 0.0300 0.0300 0.0171 0.0171 0.0288 0.0179 0.0055 0.0288 0.0311 0.0593 0.0179 0.0483 0.0378 0.0055 0.0327

3.0

0.45352

0.0311

0.50.5 1.0

1.01.5

3.2. Heat Resistance Test

0.41332

0.0327(%) Repeatibility

0.44202

0.44202 0.44786

3.5 test is validating 0.45458the sensor can 0.0593 The purpose of heat resistance withstand the actual operating ◦ environment temperature over 1000 C. The heat resistance of the sensor was verified according to

From the data in Table 2, the measuring repeatability at different positions is almost within 3.2. Heat Resistance Test 0.05% which means the coil had good repeatability within measuring range. The purpose of heat resistance test is validating the sensor can withstand the actual operating 3.2. Heat Resistance Test environment temperature over 1000 ℃. The heat resistance of the sensor was verified according to the stability and repeatability of the output signal during the multiple thermal cycles. The thermal Sensors 2019, 19, 61 8 of 13 The purpose of heat resistance test is validating the sensor can withstand the actual operating cycling test was conducted on the static test rig as Figure 9 shows, it is actually a tubular heater environment temperature over 1000 ℃. The heat resistance of the sensor was verified according to with an accurate temperature controller, which control precision is ±1 ℃. Figure 10 shows the test the stability stability and and repeatability repeatability of of the theoutput outputsignal signalduring duringthe themultiple multiplethermal thermalcycles. cycles. The The thermal thermal the rig at 1100 ℃. cycling test testwas wasconducted conductedononthe the static as Figure 9 shows, it is actually a tubular cycling static testtest rigrig as Figure 9 shows, it is actually a tubular heaterheater with ◦ with an accurate temperature controller, which control precision is ±1 . Figure 10 shows the an accurate temperature controller, which control precision is ±1 C Figure 10 shows the test rigtest at rig at◦ C. 1100 . 1100

Figure 9. Static thermal test rig scheme (1—sensor，2—heating rod, 3—insulating layer, 4— thermocouple). Figure 9. Static9.thermal test rig test scheme (1—sensor, 2—heating rod, 3—insulating layer, 4—thermocouple). Figure Static thermal rig scheme (1—sensor，2—heating rod, 3—insulating layer, 4—

thermocouple).

(a)

(b)

Figure 10. Test rig at 1100 ◦ C; (a) sensor position; (b) inside the heater. Figure 10. Test rig at 1100 ℃; (a) sensor position; (b) inside the heater.


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(a) (b) In the process of thermal cycle, temperature increased from 300 ◦ C to 1100 ◦ C (~1373K) after reliable at least 2 hours in 1100 ℃ environment and the sensor voltage changed with temperature 60 minInand maintained at 1100 ◦cycle, C for 2temperature h, then cooled down to 300 ◦300 C afterto401100 min, and repeated this the process thermal increased Figure 10. Test rigcooling at 1100 ℃; (a) sensor position;from (b) inside ℃ the heater. ℃(~1373K) after 60 similarly during theofheating and processes. cycle for five times as the operating condition curve shown in Figure 11. minutes and maintained at 1100 ℃ for 2 hours, then cooled down to 300 ℃ after 40 minutes, and repeated this cycle for five times as the operating condition curve shown in Figure 11. In the process of thermal cycle, temperature increased from 300 ℃ to 1100 ℃(~1373K) after 60 The measuring result of voltage on sensor is demonstrated in Figure 12. The result indicates minutes and maintained at 1100 ℃ for 2 hours, then cooled down to 300 ℃ after 40 minutes, and the sensor voltage remained stable in high temperature duration which proves the sensor can keep repeated this cycle for five times as the operating condition curve shown in Figure 11. The measuring result of voltage on sensor is demonstrated in Figure 12. The result indicates the sensor voltage remained stable in high temperature duration which proves the sensor can keep

Figure 11. Temperature cycling curve. Figure 11. Temperature cycling curve.

The measuring result of voltage on sensor is demonstrated in Figure 12. The result indicates the sensor voltage remained stable in high temperature duration which proves the sensor can keep reliable at least 2 h in 1100 ◦ C environment and the sensor voltage changed with temperature similarly during the heating and cooling processes.

Figure 11. Temperature cycling curve. Sensors 2019, 19, 61

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Figure high temperature. temperature. Figure 12. 12. Heat Heat resistance resistance test test results results at at high

4. Thermal Effect on Sensor

Based on the principle of eddy current sensing, temperature change will leads to the coil likepermeability permeability conductivity change. Then the measuring results will be parameters like andand conductivity change. Then the measuring results will be influenced. influenced. In order howsensor the inductive sensorbycan betemperature, affected by experiment high temperature, In order to know how to theknow inductive can be affected high method experiment was usedof totemperature get the influence of temperature on sensor. was used to method get the influence on sensor. 4.1. EXperimentmethod Method 4.1. Experiment The as as Figures 9 and 10 show create thetoadjustable The research researchadopted adoptedthe theequipment equipment Figure 9 and Figureto10 show create thetemperature adjustable environment and measureand coil measure parameters R) without(L,target under target test at under different temperature environment coil(L, parameters R) without testtemperature. at different ◦ C to 1100 ◦ C. The equivalent measurement circuit of The experiment temperature increased from 500 temperature. The experiment temperature increased from 500 ℃ to 1100 ℃. The equivalent LR is shown ascircuit Figure sensorascoil is equivalent to a series R and measurement of13. LR The is shown Figure 13. The sensor coil isresistor equivalent to aa pure seriesinductor resistor L. R The resistor Rs Ω and the excitation signal wasthe 4 MHz 3 Vppsignal AC voltage (U0 ). 3When and divider a pure inductor L. was The 7.5 divider resistor Rs was 7.5 Ω and excitation was 4 MHz Vpp the environment changes, coil inductance changes, L and coilcoil resistance R may bothcoil vary. AC voltage ). temperature When the environment temperature inductance L and resistance Sensors 2018, 18,(U x 0FOR PEER REVIEW 10 of 14

R may both vary.

Figure 13. Equivalent Equivalent measurement circuit of measure coil parameters (L, R).

The measurement areare represented by phasor as Figure 14 shows. V1 is divide measurementcircuit circuitparameters parameters represented by phasor as Figure 14 shows. V1 is voltage on the on Rs the andRs coil while is divide voltage on theoncoil. to Figures 13 and 14, divide voltage and coil V2 while V2 is divide voltage the According coil. According to Figure 13 and formulas for calculating sensor resistance and inductance were derived as Equation (11)–(15) show. Figure 14, formulas for calculating sensor resistance and inductance were derived as Equation (11)– The data (V1, V2) was(V1, processed MATLABintoMATLAB be filteredtothrough FFT through method (15) measured show. Theoriginal measured original data V2) wasinprocessed be filtered and coil inductance andinductance resistance RLwere different temperature. the FFT then method and then Lcoil and calculated resistanceunder R were calculated under Then different variation law Then of coilthe parameters temperature is obtained. temperature. variation with law of coil parameters with temperature is obtained. I1 =

V1 − V2 , Rs

(11)

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α1 = arcsin

V2·sinϕ , I1 Rs

Figure 13. Equivalent measurement of measure coil parameters (L, R). α =circuit α + ϕ, 2

1

(12) (13)

|·cosα2 The measurement circuit parameters are|V2 represented is , by phasor as Figure 14 shows. V1 (14) R= I | | 1 divide voltage on the Rs and coil while V2 is divide voltage on the coil. According to Figure 13 and Figure 14, formulas for calculating sensor resistance and2 inductance were derived as Equation (11)– |V2|·sinα L= (15) (15) show. The measured original data (V1, V2) was in MATLAB to be filtered through ω ·| I1processed | FFT method and then coil L and were V1 calculated different where I1 is the current in the LRinductance circuit, ϕ is the phaseresistance difference Rbetween and V2, αunder 1 and α2 are the temperature. Then the variation law of coil parameters with temperature is obtained. phase angle of V1 and V2 respectively.

Figure Figure 14. 14. Phasor Phasor representation representation of of measured measured signal. signal. Sensors 18, x FORResults PEER REVIEW 4.2.2018, Experiment

˙

˙

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˙

𝑉1−𝑉2

= , is plotted in Figure 15. It can be observed (11) 1temperature relationship sensorvoltage voltageand and𝐼temperature 𝑅𝑠 TheThe relationship ofof sensor is plotted in Figure 15. It can be observed that the sensor voltage and temperature has quadratic relationship so the voltage can be expressed by ˙ that the sensor voltage and temperature has quadratic relationship so the voltage can be expressed 𝑉2∙𝑠𝑖𝑛𝜑 quadratic polynomial fitting expression as Equation (16) shown and under(12) the 𝛼1 = 𝑎𝑟𝑐𝑠𝑖𝑛 , the R2 equals to 0.9999, ˙ by quadratic polynomial fitting expression◦ as Equation (16) shown and the R2 equals to 0.9999, condition that the temperature range is 500 C to 1100 ◦ C. 𝐼1 𝑅𝑠 under the condition that the temperature range is 500 ℃ to 1100 ℃. 𝛼2 = 𝛼−16 + 𝜑 , (13) −9 V(T) = 0.15791 −= 1.8905 × 10˙− 1.8905e × T + 3.3333 × T2 – 9 × T2 (16)(16) V(T) 0.15791 – 6 ××T10+ 3.3333e R=

|𝑉2|∙𝑐𝑜𝑠𝛼2 ˙

,

(14)

|𝐼1 | ˙

L=

|𝑉2|∙𝑠𝑖𝑛𝛼2 ˙

(15)

𝜔∙|𝐼1 | ˙

where 𝐼1 is the current in the LR circuit, 𝜑 is the phase difference between V1 and V2, 𝛼1 and 𝛼2 are the phase angle of V1 and V2 respectively. 4.2. Experiment Results

Figure withtemperature. temperature. Figure15. 15.Coil Coilvoltage voltage curve curve with

The coil resistance and inductance at different temperatures are compared in Figure 16. It is clearly that the coil resistance increases with temperature especially between 700 ℃ to 1100 ℃, the resistance increment is up to 11.4% from 500 ℃ to 1100 ℃. The coil inductance is almost unchanged when temperature increased from 500 ℃ to 1100 ℃.

Figure 15. Coil voltage curve with temperature. SensorsThe 2019,coil 19, 61 resistance

11 It of 13 and inductance at different temperatures are compared in Figure 16. is clearly that the coil resistance increases with temperature especially between 700 ℃ to 1100 ℃, the resistance increment is up to 11.4% from 500 ℃ to 1100 ℃. The coil resistance and inductance at different temperatures are compared in Figure 16. It is The coil inductance is almost unchanged when temperature increased from 500 ℃ to 1100 ℃. clearly that the coil resistance increases with temperature especially between 700 ◦ C to 1100 ◦ C, the The inductance remained stably about 0.1223 μH and the maximum inductance fluctuation is resistance increment is up to 11.4% from 500 ◦ C to 1100 ◦ C. 0.343%.

Figure temperature. Figure 16. 16. Comparison Comparison of of L L and and R R under under different different temperature.

Figure (a) and (b) illustrate the variation resistance and inductance with◦ Ctemperature The coil17 inductance is almost unchanged whenoftemperature increased from 500 to 1100 ◦ C. respectively. It is also clearly that the 0.1223 resistance has the quadratic relationship with temperature. This The inductance remained stably about µH and maximum inductance fluctuation is 0.343%. relationship can illustrate be usedthetovariation indicateof operating temperature need forrespectively. additional Figure 17a,b resistance and inductancewithout with temperature thermocouple. in the application of distance measurement, coil inductance is determined It is also clearlyTherefore, that the resistance has quadratic relationship with temperature. This relationship can as measurement parameter to temperature avoid the temperature driftfor problems. be used to indicate operating without need additional thermocouple. Therefore, in Meanwhile, compared with linearcoil fitting and higher order fitting, the fitting degree of the application of distance measurement, inductance is determined as measurement parameter to quadratic fitting is good enough and in order to facilitate subsequent back-extrapolation of ambient avoid the temperature drift problems. Sensors 2018, 18, x FOR PEER REVIEW 12 of 14 temperature through resistance values, the coil resistance and inductance are expressed by quadratic fitting relation and linear fitting relation as Equation (17) and Equation (18) show. The polynomial coefficients are listed in Table 3.

(a)

(b)

Figure (a) resistance; resistance; (b) (b) inductance. inductance. Figure 17. 17. Coil Coil parameters parameters change change curve curve with with temperature; temperature; (a)

Meanwhile, compared with linear fitting and higher order fitting, the fitting degree of quadratic fitting is good enough and in order to3.facilitate subsequent of ambient temperature Table Polynomial coefficientback-extrapolation of R and L. through resistance values, the coil resistance and inductance are expressed by quadratic fitting relation and linear fitting relation as Equations (17) and (18) show. The polynomial p0 p1 p2 coefficients are listed in Table 3. R(T) 1.9779 R(T) = p0 + p1 ∗ −9.7757e−5 T + p2 ∗ T2 R2 = 0.9829 3.1143e−7 (17)

L(T)

p1 ∗ T R2 = 0.9998 0.12227L(T) = p0 + −2.8571e−9

/

(18)

Based on the above discussions, it is found by experiment that temperature has obvious influence on induction coil resistance while the coil inductance almost does not change with temperature. Hence, in the tip clearance measurement, the coil inductance value is determined as

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Table 3. Polynomial coefficient of R and L. p0 R(T) L(T)

1.9779 0.12227

p1

p2 10−5

−9.7757 × −2.8571 × 10−9

3.1143 × 10−7 /

Based on the above discussions, it is found by experiment that temperature has obvious influence on induction coil resistance while the coil inductance almost does not change with temperature. Hence, in the tip clearance measurement, the coil inductance value is determined as measurement variable for it is not affected by temperature changes, that is to say the characteristic curve of the sensor becomes the relationship curve between coil inductance and the clearance. While, the resistance value change can indicate the environment temperature change. In this way, an inductive sensor can measure tip clearance as well as measure the environment temperature through the data processing. 5. Conclusions Based on Faraday’s law of electromagnetic induction and Lenz’s law, the following conclusions are obtained by experiments: 1. 2.

3.

4.

The designed sensor with planar coil made of platinum wire is proved to be a good inductive sensor for its phase angle is up to 85◦ and quality factor is 14.27 under 4 MHz excitation frequency. The sensor performance meets the requirements of tip clearance measurement for the measuring range of sensor is proved to be at least 5 mm and the resolution is better than 10 µm within 5 mm range according to static calibration result. It is also found that the sensor coil repeatability is almost better than 0.05% within the whole sensing range. The encapsulated platinum coil can be long-term (2 h) heat-resistant at 1100 ◦ C and maintains a good stability during multiple temperature cycles. This suggests the designed sensor is capable to operate in the high temperature for a long time and that is an important basis for the sensor to be used in turbine tip clearance measurement in the future. The inductance and resistance of the sensor coil can be solved based by phasor analysis and using the series resistance circuit. This decoupled analysis of sensor parameters makes its application range wider.

Author Contributions: All authors contributed in writing, proofreading, and providing suggestions for the improvement of the paper. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

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