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A magnetic sensor to measure wear in centrifugal pumps Khoie, Ramin 2016

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A Magnetic Sensor to Measure Wear in CentrifugalPumpsbyRamin KhoieBASc, The University of British Columbia, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Mechanical Engineering)The University of British Columbia(Vancouver)April 2016© Ramin Khoie, 2016AbstractOn average, centrifugal pumps consume between 25% and 60% of the total con-sumed electrical energy inside process plants. Erosion inside open-impeller cen-trifugal pumps leads to a reduction in pump efficiency and occasional plant down-time. This work demonstrates a new concept for an online instrument capable ofmonitoring wear with the objective of improving the maintenance scheduling ofcentrifugal pumps and the prevention of unexpected failure through a predictivemaintenance system. A magnetic wear sensor is designed and fabricated that al-lows for wear measurement while the pump is in operation. This sensor can beinstalled on existing centrifugal pumps and does not require any pump modifica-tions. Wear mostly occurs on the tip of the impeller blades reducing the thicknessof the impeller which in turn increases the gap width between the impeller and theside plate inside the pump housing, from 0.65 mm (no wear) to 2.50 mm for maxi-mum allowable wear on the pump used for prototyping. By using a magnetic circuitwith the pump and its components, wear is estimated by measuring the change inthe width of the varying gap between the impeller and the side plate. To assemblethe magnetic circuit, a high-permeability clamping mechanism with a relative per-meability of 10,000 is designed and fabricated along with a magnetic coil excitedusing a 1.0 V AC voltage signal at 70 Hz to drive flux through the circuit. As wearoccurs, the total reluctance of the magnetic circuit increases causing the inductanceof the coil to drop. The coil’s inductance is also a function of the impeller’s angularposition. To estimate wear, data is collected at a sampling frequency of 500 kHzand then assessed in the frequency domain after fast Fourier transform (FFT). Theamplitude of the FFT signal at the frequency correlated with the pump’s rotationalspeed is then considered to estimate wear. For a data sampling time of one sec-ond the sensor has a signal to noise ratio of 17.8 dB with an average sensitivity of0.022 mV/mm and a resolution of 0.38 mm.iiPrefaceThe work in Chapter 2 has been presented at the IEEE Sensors 2015 conferencein Busan, South Korea and the conference paper has been published in the IEEEXplore database. (R. Khoie, B. Gopaluni, J. A. Olson, and B. Stoeber, A magneticsensor to measure wear in centrifugal pumps, in SENSORS, 2015 IEEE, Nov 2015,pp. 14. [1])All of the experimental work presented in Chapter 3 are conducted in a pi-lot plant test facility at the Pulp and Paper Center at the University of BritishColumbia.This work was performed under the supervision of Dr. Boris Stoeber and Dr.Bhushan Gopaluni. The project is a part of Energy Reduction in Mechanical Pulp-ing research program led by Dr. James Olson that is a collaboration project betweenmechanical pulp producers, associated supplier industries, research institutes, uni-versities, utilities and governmental bodies.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xixDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Sensor Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1 Sensor Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Sensing Method Variation & Comparison . . . . . . . . . . . . . 152.2.1 Permanent Magnet Model . . . . . . . . . . . . . . . . . 152.2.2 Electromagnet Model . . . . . . . . . . . . . . . . . . . . 21iv2.2.3 Coil Inductance Model . . . . . . . . . . . . . . . . . . . 252.2.4 Method Selection . . . . . . . . . . . . . . . . . . . . . . 272.3 Flux Guide Design . . . . . . . . . . . . . . . . . . . . . . . . . 302.3.1 Material Selection . . . . . . . . . . . . . . . . . . . . . 302.3.2 Sensor Geometry . . . . . . . . . . . . . . . . . . . . . . 332.3.3 Numerical Validation . . . . . . . . . . . . . . . . . . . . 372.4 Sensor Instrumentation . . . . . . . . . . . . . . . . . . . . . . . 392.4.1 Coil Design . . . . . . . . . . . . . . . . . . . . . . . . . 402.4.2 Inductance Measurement . . . . . . . . . . . . . . . . . . 442.4.3 Circuit Design . . . . . . . . . . . . . . . . . . . . . . . 482.5 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492.5.1 Expected Sensor Response . . . . . . . . . . . . . . . . . 502.5.2 Data Analysis Method . . . . . . . . . . . . . . . . . . . 533 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . 543.1 Sensor Prototype . . . . . . . . . . . . . . . . . . . . . . . . . . 543.1.1 Flux Guide Assembly . . . . . . . . . . . . . . . . . . . 543.1.2 Magnetic Coil . . . . . . . . . . . . . . . . . . . . . . . 563.1.3 Instrumentation Box . . . . . . . . . . . . . . . . . . . . 573.2 Sensor Characterization . . . . . . . . . . . . . . . . . . . . . . . 593.2.1 Coil Inductance and Parasitic Capacitance . . . . . . . . . 603.2.2 Circuit Optimization . . . . . . . . . . . . . . . . . . . . 633.2.3 Benchtop Experiments . . . . . . . . . . . . . . . . . . . 643.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 663.3.1 Pump Loop . . . . . . . . . . . . . . . . . . . . . . . . . 663.3.2 Pump Adjustments . . . . . . . . . . . . . . . . . . . . . 673.3.3 Sensor Installation . . . . . . . . . . . . . . . . . . . . . 683.3.4 Sensor Calibration . . . . . . . . . . . . . . . . . . . . . 693.4 Experimental Results & Analysis . . . . . . . . . . . . . . . . . . 713.4.1 Sensor Output . . . . . . . . . . . . . . . . . . . . . . . 713.4.2 Pump Rotational Speed Variation . . . . . . . . . . . . . 723.4.3 Signal to Noise Ratio (SNR) . . . . . . . . . . . . . . . . 733.4.4 Sampling Optimization . . . . . . . . . . . . . . . . . . . 74v3.4.5 Data Collection . . . . . . . . . . . . . . . . . . . . . . . 753.4.6 Wear Detection . . . . . . . . . . . . . . . . . . . . . . . 794 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . 834.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Appendix A Computer Simulations . . . . . . . . . . . . . . . . . . . . 90A.1 Simplified Model . . . . . . . . . . . . . . . . . . . . . . . . . . 90A.2 Advanced Model . . . . . . . . . . . . . . . . . . . . . . . . . . 92Appendix B MATLAB Code . . . . . . . . . . . . . . . . . . . . . . . . 94B.1 FFT Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . 94B.2 Signal Denoising and SNR Calculation . . . . . . . . . . . . . . . 98B.3 Scatter Plot Generation and Calibration Curve . . . . . . . . . . . 101Appendix C Sensor Optimization . . . . . . . . . . . . . . . . . . . . . 105C.1 Permanent Magnet Geometry Optimization . . . . . . . . . . . . 105C.2 Signal Quality Improvement . . . . . . . . . . . . . . . . . . . . 106viList of TablesTable 2.1 Physical dimensions of the pump components. . . . . . . . . . 13Table 2.2 Effective cross-sectional areas of the pump components. . . . . 13Table 2.3 Magnet’s physical parameters. . . . . . . . . . . . . . . . . . . 19Table 2.4 Magnetic coil’s physical parameters. . . . . . . . . . . . . . . 23Table 2.5 The comparison of the three sensing methods. . . . . . . . . . 30Table 2.6 High-permeability magnetic materials for the fabrication of theflux guide assembly. . . . . . . . . . . . . . . . . . . . . . . . 32Table 2.7 Properties of the American Wire Gape AWG30. . . . . . . . . 41Table 2.8 Parameters for the parasitic capacitance analytical equation. . . 43Table 3.1 Cost of the material and the components used for the fabricationof the physical prototype. . . . . . . . . . . . . . . . . . . . . 59viiList of FiguresFigure 1.1 Cross-sectional diagram of a typical two blade open-impellercentrifugal pump. . . . . . . . . . . . . . . . . . . . . . . . . 3Figure 1.2 Two-blade pump impeller. The typical location of wear on theimpeller is labeled on the figure. . . . . . . . . . . . . . . . . 3Figure 1.3 Top view of a two blade open impeller made from cast iron.The suitable location for wear measurement is labeled on thefigure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Figure 1.4 Westcan 40-Hp two blade open impeller centrifugal pump in-stalled in the Pulp and Paper Center pilot plant at The Univer-sity of British Columbia. The motor connected to the pump isalso shown in this picture. . . . . . . . . . . . . . . . . . . . 7Figure 2.1 The diagram of a simple magnetic circuit with a single gap. . 10Figure 2.2 The schematic drawing of the magnetic circuit created with thepump and the flux guide assembly. The dotted line representsthe path of the magnetic flux inside the circuit. The location ofthe wear on the tip of the impeller is indicated on the drawing. 12Figure 2.3 Simplified model of the pump and the sensor’s flux guide witheach component labeled on the diagram. . . . . . . . . . . . . 14Figure 2.4 Magnetic hysteresis loop. . . . . . . . . . . . . . . . . . . . . 16Figure 2.5 Demagnetization curve of a typical rare-earth magnet superim-posed on the magnet’s loadline. . . . . . . . . . . . . . . . . 17viiiFigure 2.6 Plot of the operating magnetic flux density Bm as a functionof the varying gap width lvg as it increases from the no-wearstate (0.65 mm) to the maximum-wear state (2.50 mm) for theanalytical calculation using the permanent magnet model. . . 19Figure 2.7 Magnitude of flux density [T] inside the sensor and the sim-plified pump for the analysis of the permanent magnet sensormodel generated using Comsol Multiphysics. . . . . . . . . . 20Figure 2.8 Plot of the magnetic flux density Bm as a function of the vary-ing gap width lvg for the case of the permanent magnet modelderived from Comsol Simulation. . . . . . . . . . . . . . . . 21Figure 2.9 Plot of the operating magnetic flux density Bm as a functionof the varying gap width lvg as it increases from the no-wearstate (0.65 mm) to the maximum-wear state (2.50 mm) for theanalytical calculation using the electromagnet model. . . . . . 23Figure 2.10 Plot of the magnetic flux density Bm as a function of the vary-ing gap width lvg for the case of the electromagnet model de-rived from Comsol Simulation. . . . . . . . . . . . . . . . . . 24Figure 2.11 Coil inductance as a function of the varying gap width calcu-lated using the analytical model of the coil inductance. . . . . 26Figure 2.12 The inductance of the magnetic coil as a function of the vary-ing gap width for the case of the inductance model derivedusing Comsol simulation. . . . . . . . . . . . . . . . . . . . . 27Figure 2.13 The percentage change in the measuring parameter as a func-tion of the varying gap width for the permanent magnet model,electromagnet model, and the inductance model derived fromComsol simulations. . . . . . . . . . . . . . . . . . . . . . . 29Figure 2.14 The percentage change in the inductance of the coil (outputsignal) using various magnetic permeability values for the fluxguide assembly derived from the analytical model. . . . . . . 31Figure 2.15 Sensitivity comparison of alternative material compositions forthe flux guide assembly using carbon steel and high-permeabilityM100 material derived from Comsol simulations. . . . . . . . 33ixFigure 2.16 Percentage change in the output signal as a function of thevarying gap width using different lengths for the flux guideassembly derived from the analytical model. . . . . . . . . . . 34Figure 2.17 Percentage change in the output signal as a function of thevarying gap width using various cross-sectional areas for theflux guide assembly derived from the analytical model. . . . . 35Figure 2.18 A ’C’ Clamp design for the geometry of the flux guide assem-bly with the five legs numbered on the drawing. . . . . . . . . 36Figure 2.19 The isometric drawing of the flux guide clamping mechanism. 37Figure 2.20 The dimensions of the flux guide assembly in [mm]. . . . . . 38Figure 2.21 Exploded view of the more realistic pump model and the sen-sor created in Comsol Multiphysics. All the components of thepump and the sensor are labeled on the figure. . . . . . . . . . 39Figure 2.22 Path of magnetic flux inside the sensor and the flux guide as-sembly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 2.23 Comsol simulation results yielding the magnetic coil induc-tance as a function of the varying gap width for the more re-alistic model of the sensor and the pump. The coil is excitedusing a constant current source of 10 mA at 100 Hz. . . . . . . 41Figure 2.24 The design of the bobbin for the magnetic coil to be placed onthe flux guide assembly with the dimensions in [mm]. . . . . . 44Figure 2.25 Simple RL circuit to measure the inductance of the magneticcoil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 2.26 More realistic RLC circuit representing the coil connected inseries with a resistor. . . . . . . . . . . . . . . . . . . . . . . 46Figure 2.27 The change in the frequency response of the sensor as the mag-nitude of the varying gap increases from 0.65 mm to 2.50 mmderived from the analytical model of the sensor. . . . . . . . . 47Figure 2.28 The change in the frequency response of the sensor as the mag-nitude of the varying gap increases from 0.65 mm to 2.50 mmwith the addition of the external capacitance Cext to the circuit.The plot is generated from the analytical model of the sensor. . 49xFigure 2.29 The complete drawing of the sensor’s circuit including the volt-age follower circuit. . . . . . . . . . . . . . . . . . . . . . . 50Figure 2.30 Inductance of the magnetic coil as a function of the impeller’sangular position for both the no-wear and the maximum-wearcases derived from Comsol simulations. . . . . . . . . . . . . 51Figure 2.31 Expected FFT response of the generic time signal from thesensor while the pump is operating at 900 RPM. . . . . . . . . 53Figure 3.1 The epoxy used to attach the flux guide components with thesintered M100 particles acquired from National Magnetics Group. 56Figure 3.2 The fabricated flux guide assembly with the magnetic coil. . . 57Figure 3.3 The flux guide assembly with the cushioning foam. . . . . . . 58Figure 3.4 The design of the coil bobbin in SolidWorks. . . . . . . . . . 58Figure 3.5 Prototype of the magnetic coil. . . . . . . . . . . . . . . . . . 59Figure 3.6 The instrumentation box with the electrical circuit and the DAQunit. The box also includes a pivoting door (not shown in thepicture) to protect the instruments inside. . . . . . . . . . . . 60Figure 3.7 Picture of the complete sensor prototype including the fluxguide assembly, the coil, and the instrumentation box. . . . . 61Figure 3.8 Frequency response of the sensor: experimental measurementsand the least square estimation. . . . . . . . . . . . . . . . . . 62Figure 3.9 Maximizing the change in the output signal as a function of theresistance value of R. . . . . . . . . . . . . . . . . . . . . . . 63Figure 3.10 Maximizing the change in the output signal as a function of theexcitation frequency f . . . . . . . . . . . . . . . . . . . . . . 64Figure 3.11 The benchtop experimental apparatus with the sensor placedperpendicularly to the two parallel cast iron plates. . . . . . . 65Figure 3.12 The frequency response of the sensor as the gap between thetwo parallel cast iron plates vary from 0.0 mm to 2.0 mm. . . . 65Figure 3.13 Westcan Centrifugal pump installed in the PPC Pilot Plant. Di-rection of the flow is labeled on the figure. . . . . . . . . . . . 66Figure 3.14 Schematic diagram of the pump loop in the Pulp and PaperCenter at UBC. . . . . . . . . . . . . . . . . . . . . . . . . . 67xiFigure 3.15 The magnetic polymer mixture poured on the pump’s side plate. 68Figure 3.16 The sensor assembly installed on the pump. . . . . . . . . . . 69Figure 3.17 The location of the ring gaskets on the schematic cross-sectionalview of the pump. . . . . . . . . . . . . . . . . . . . . . . . . 70Figure 3.18 The location of the ring gaskets on the centrifugal pump. . . . 70Figure 3.19 The output voltage signal from the sensor as a function of timefor a) the pump rotational speed of 0 RPM, and b) the pumprotational speed of 900 RPM. . . . . . . . . . . . . . . . . . . 71Figure 3.20 The FFT plot of the sensor output while the pump is operatingat 900 RPM. . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Figure 3.21 The amplitude spectral density of the sensor output for variouspump rotational speeds. . . . . . . . . . . . . . . . . . . . . . 73Figure 3.22 The plot of the output signal and the noise signal at the impellerrotational speed of 900 RPM. Signal is sampled at a samplingfrequency of 50 Hz for a duration of 1 second. . . . . . . . . . 75Figure 3.23 Sensor output collected at different sampling frequencies of20 kHz, 50 kHz, 100 kHz, and 500 kHz. The SNR value ofeach data is labeled on the plot. All measurements were takenduring 1 second with a pump rotational speed of 900 RPM. . . 76Figure 3.24 Signal to noise ratio in [dB] as a function of the sampling fre-quency for a one-second measurement on the pump running at900 RPM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Figure 3.25 Signal to noise ratio in [dB] as a function of the sampling fre-quency for 1M data points. . . . . . . . . . . . . . . . . . . . 77Figure 3.26 Signal to noise ratio in [dB] as a function of the total numberof samples with a fixed sampling frequency of 50 kHz. . . . . 78Figure 3.27 Scatter plot of the sensor output signal at 30 Hz versus the out-put signal 15 Hz for various gap widths. Each data point refersto 1 second of measurement collected at 500 kHz sampling fre-quency. There are 36 data points for each gap width. . . . . . 79xiiFigure 3.28 Mean and the standard deviation of the scatter plot for the sen-sor output signal at 30 Hz versus the output signal 15 Hz atvarious gap widths. The sampling frequency is set to 500 kHzand measurements are taken for a duration of 36 seconds. . . . 80Figure 3.29 The mean amplitude of the sensor’s output signal at 15 Hz ver-sus the magnitude of the varying gap width. The error bar andthe uncertainty of the gap width for each data point is shownon the plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Figure 3.30 Comparison between the experimental results and the simu-lation results. The plot shows the percentage change in theoutput of the sensor as a function of the varying gap width asit increases from 0.4 mm to 2.65 mm. . . . . . . . . . . . . . 82Figure A.1 Magnitude of flux density [T] inside the sensor and the simpli-fied pump for the analysis of the electromagnet sensor modelgenerated using Comsol Multiphysics. . . . . . . . . . . . . . 91Figure A.2 Magnitude of flux density [T] inside the sensor and the sim-plified pump for the analysis of the inductance sensor modelgenerated using Comsol Multiphysics. . . . . . . . . . . . . . 92Figure A.3 Magnitude of the flux density [T] inside the flux guide assem-bly. The saturation flux density for M100 material is 0.42 T . . 93Figure C.1 Scatter plot of the ratio of signal at 30 Hz over 70 Hz versusthe signal ratio of 15 Hz over 70 Hz at various gap widths. . . 107Figure C.2 Scatter plot of the ratio of signal at 30 Hz and 15 Hz over theRMS value of noise. . . . . . . . . . . . . . . . . . . . . . . 108Figure C.3 Scatter plot of the denoised amplitude at 30 Hz versus the de-noised amplitude at 15 Hz at various gap widths. . . . . . . . 109xiiiNomenclatureε0 Absolute permittivityεr Relative permittivity of wire insulation (enamel)Vˆnoise Signal noise in frequency domainVˆsignal Denoised output signal in frequency domainµ Magnetic permeabilityµp Relative permeability of pump componentsµ0 Magnetic permeability of free spaceµr Relative permeabilityω Angular frequencyωpump Rotational speed of pump impellerℜ Reluctanceℜconst Constant reluctanceℜ f g Reluctance of the flux guide assemblyℜgap Reluctance of the air gapℜvar Varying reluctanceSNR Signal to noise ratioxivSNRdB Signal to noise ratio in decibels~B Magnetic flux density~H Magnetic field strengthA AreaAs Cross-sectional area of the secondary gapAcg Effective area of the constant gap widthAcoil Cross-sectional area of the magnetic coilAc Cross-sectional area of the flux guide assemblyAgap Cross-sectional area of the air gapAim Effective area of the pump impellerAmagnet Cross-sectional area of the permanent magnetAsp Effective area of the side plateAtb Effective area of the stuffing boxAvg Effective area of the varying gap widthBm Operating flux density of the permanent magnetBr Remanent flux densityCext External capacitanceCpar Parasitic capacitanceCtot Total capacitanceCtt Turn to turn capacitanceDc Wire core diameterDo Wire outer diameterxvDt Coil diameterfexc Excitation frequencyfres Resonating frequencyg Geometric ratio between the length and the cross-sectional area of the per-manent magnetHc Coercive forceHm Operating field strength of the permanent magnetHci Intrinsic coercive forceHsource Coercivity of the permanent magneti Currenticoil Current passing through the magnetic coilJ Total current densityj Imaginary numberl Lengthlh Thickness of the pump housingls Secondary air gap to accommodate the Hall-effect sensorlt Length of one wire turn on coillcg Constant gap width between the impeller and the stuffing boxLcoil Inductance of the magnetic coillcoil Length of the magnetic coillc Total length of the flux guide assemblylgap Width of the air gapxvilim Thickness of the pump impellerlmagnet Length of the permanent magnetlprobe Width of the sensor probelsp Thickness of the side plateltb Thickness of the stuffing boxlvg Varying gap width between the impeller and the side plateml Slope of the permanent magnet’s load-line equationN Total number of coil windingsPnoise Power of noisePsignal Power of output signalR ResistorRcoil Resistance of the coil wirerimp Radius of the pump impellerSnoise Power spectral density of the signal noiseSsignal Power spectral density of the denoised signaltpassing Impeller blade passing timeV VoltageVf g Peak-to-peak voltage output of function generator.Vin Input voltageVout Output voltagexviiAcknowledgmentsAbove all, I would like to express my sincere gratitude to my supervisor Dr. BorisStoeber for his invaluable insight, guidance, encouragement and most importantlyfor believing in me through out the course of this project especially the times whereI was left helpless and lost. The product, is the greatest accomplishment of my lifeand for this I’m forever thankful.I am also deeply grateful to my co-supervisor Dr. Bhushan Gopaluni for hishelp and support in this project. His one of a kind problem solving skills has helpedme become a better engineer at work and a better person in life. I would like tothank Meaghan Miller, our research engineer, for all the help she has provided inthis project. I also appreciate the help of Glenn Jolly and Sean Buxton in the in-strumentation shop for their technical assistance and for scaring away the electronsto go where they were supposed to.I extend a most genuine thank to my dear lab mates. It was for their encour-agement and support that I was able to reach this milestone. To Maziyar Jalaalin particular, for his unconditional help and support every time I asked. I sharedwith him the happiest and the toughest moments of this journey. I also owe a bigthank you to my dear friends, the Seyeds, my roommate Sina, and my girlfriendAlexandra for being there when I needed them the most and for bearing with meon the days that my experiments would all fail.And last but not least, a very special thank you to my family, for everythingand anything that I have.xviiiDedicationThis thesis is dedicated to my only sister Taraneh who with her endless heart taughtme how to live and how to love. I dedicate this to her for reasons beyond what Ican ever articulate here.xixChapter 1IntroductionThere was a door to which I found no keyThere was a veil past which I could not seeSome little talk awhile of me and theeThere seemed... and then no more of thee and me.— Omar Khayyam, Rubaiyat1.1 MotivationOn average, centrifugal pumps consume between 25% and 60% of the total con-sumed electrical energy inside process plants depending on the industry[2]. Run-ning pumps in an inefficient way is associated to high energy costs and thereforemaintaining a high pump efficiency is becoming more and more vital for the eco-nomic viability of the industrial processes [3]. Improperly operated pumps are verycommon in the industry and are costing the companies excess amount of money tomaintain[4]. Thus, any improvements to the operation of pumping systems willsignificantly reduce the total energy cost for plants.Centrifugal pumps are the most common type of process pumps used in almostevery industry[5]. One of the main factors that significantly affects the operatingefficiency of a centrifugal pump is the presence of volumetric losses [6]. A ma-jor source of volumetric loss in an open-impeller centrifugal pump is the impeller1clearance. The impeller inside a centrifugal pump is positioned between the sideplate (or the housing depending on the type of the centrifugal pump) and the stuff-ing box as shown in Figure 1.1. The impeller clearance, hereinafter referred to asthe varying gap, is identified as the gap width between the impeller and the sideplate. When the impeller is moved away from the side plate, the varying gap in-creases leading to a significant drop in the pump’s efficiency[7]. The main cause ofthis occurrence is wear being accumulated on the surface of the impeller over time.Wear typically occurs on the tip of the impeller blades[8] as shown in Figure 1.2.To estimate the magnitude of wear, measurements must be taken from the edges ofthe impeller blade as shown in Figure 1.3.Depending on the material properties of the impeller and the consistency ofthe fluid being transported through the pump, impeller blades are considered fullyworn within one to five years of operation. Subject to the severity of wear, impellersare either repaired or fully replaced during an overhaul of the equipment. The mag-nitude of the maximum allowable wear on the impeller blades ranges widely basedon the size of the pump and its significance inside the plant. For a two blade open-impeller 14-inch diameter centrifugal pump made from cast iron, the magnitude ofthe maximum allowable wear is roughly 1.85 mm.To verify the working condition of an operating centrifugal pump inside a plant,wear accumulated on the tip of the impeller blade needs to be monitored while thepump is running. This will considerably improve the maintenance scheduling ofthe pump and prevent any unexpected erosion-related failure that may occur.1.2 BackgroundThus far there is no method for monitoring erosion inside industrial sized centrifu-gal pumps while the pump is in operation. Most of the studies that aim to measureand characterize wear have focused on wear on the surface of work tools and ex-posed rotating equipment. As such, a previous study has assessed the magnitudeof wear on metallic surfaces through the deposition of a thin resistive film. As2HousingStuffing BoxImpellerSide-plateInletDischargeFigure 1.1: Cross-sectional diagram of a typical two blade open-impellercentrifugal pump.Figure 1.2: Two-blade pump impeller. The typical location of wear on theimpeller is labeled on the figure.3Figure 1.3: Top view of a two blade open impeller made from cast iron. Thesuitable location for wear measurement is labeled on the figure.wear occurs, the resistance of the film increases, allowing for accurate wear mea-surement [9]. As one application of the film sensor, the study shows successfulresults for measuring tool wear on the surface of a cutting machine. This method,however, is not suitable for the aqueous environment of a pump. Also, the depo-sition of the thin resistive film on the surface of the material requires specializedtools which increases the cost of implementation. In another study related to toolwear, an automatic tool-wear sensor is proposed for a lathe machine application[10]. In this study, wear is measured through the use of a camera and the postprocessing of the captured images are used to characterize wear with an accuracyof 0.010 mm. Since this method requires images to be taken from the surface ofthe tool, wear measurement on the blades of an operating pump impeller is notachievable through this technique. In another study, a more complex approach formeasuring tool wear during a CNC milling process has been proposed [11]. In this4study a neural network-based sensor fusion has been implemented to measure thecutting forces, vibration, spindle current, sound, and pressure during a milling pro-cess. This method has also been validated by an industrial implementation. Thissensor network, however, is specifically designed for a CNC machine and its effec-tiveness for a centrifugal pump is not validated.Another area of study related to this topic is a gap measuring tool. A methodfor measuring the gap width between two rotating plates can be used to estimatewear inside the equipment. One proposed approach for gap measurement insiderotating equipment is through the use of a capacitive or an inductive proximitysensor fixed inside the equipment [12], [13]. The patents for these two types ofsensors claim a sensing gap range of 0.127 mm to 5.08 mm. This method is beingwidely used in the industry for measuring the gap size between refiner plates insidea pulp refiner. Although this method can produce very accurate results, it requiresthe modification of the equipment to house the sensor which is an expensive pro-cess and is likely to alter the performance of the equipment. This is very critical inthe case of a centrifugal pump. In a much smaller scale, a fiber-optic gap sensoris proposed to be used on a rotary undulation pump. Undulation pumps are foruse inside artificial hearts. This study proposes the use of two parallel plastic corefibers for measuring the location of the rotor with respect to the stator plate for itsdynamic positioning inside the pump [14].Lastly, wear inside rotating equipment has also been correlated to the acousticnoise generated while the equipment is in operation. This field of study is referredto as the acoustic emission (AE) and is being widely studied for equipment thatneed continuous monitoring while in operation. A study has performed a time se-ries analysis of acoustic emission signals generated from a cutting tool through theuse of an autoregressive time-series to model the acoustics generated during thecutting process [15]. This method is highly application specific and a completeanalysis of the acoustic noise is required for every equipment. Also, the viabilityof this method on other rotating equipment such as a centrifugal pump is yet to bevalidated. In regards to the application of acoustic emission in centrifugal pumps,a study has shown the use of AE to detect cavitation inside centrifugal pumps and5to identify their best efficiency point [16].1.3 ObjectivesThe main objective of this project is to develop a wear measurement sensor tobe used on centrifugal pumps inside process plants. The sensor shall detect thedegradation of the pump impeller enabling the use of a predictive maintenancescheduling system to prevent catastrophic failure of the equipment.The manufacturing cost of the mentioned sensor needs to be considerably lowerthan the periodic overhaul expenses that could be prevented through its use. Thesensor should also provide a simple installation procedure on an operating centrifu-gal pump without further pump modification. Ideally the sensor would be installedon every critical pump inside a process plant and the readings are transferred di-rectly to the control room. The displayed data from the sensor will indicate achange in the thickness of the impeller blade due to erosion to notify the operatorof the status of the pump. The required accuracy and the resolution of the measure-ments vary depending on the dimensions and the operating conditions of the pumpand its components. For the 14-inch diameter two blade open-impeller centrifugalpump, as mentioned in Section 1.1, it can be safely assumed that resolving the fullrange of wear by 20% is sufficient to develop a predictive maintenance scheduleand prevent costly breakdowns. Given that the pump has a maximum allowablewear of 1.85 mm, the sensor needs to achieve an accuracy and a resolution betterthan 0.37 mm. Since wear occurs very slowly during a period of several months,the response time of the sensor is not an important factor.For the purpose of this project, the sensor is designed and tested on the 2-bladeopen impeller 40-Hp Westcan centrifugal pump currently installed at the UBC’sPulp and Paper pilot plant as shown in Figure 1.4.6Figure 1.4: Westcan 40-Hp two blade open impeller centrifugal pump in-stalled in the Pulp and Paper Center pilot plant at The University ofBritish Columbia. The motor connected to the pump is also shown inthis picture.7Chapter 2Sensor DesignTo measure wear inside centrifugal pumps, a magnetic wear sensor is proposed.This chapter will start by summarizing the relevant background in magnetism thatcovers the principles of the magnetic circuit that is used to measure the varyinggap width described in Section 1.1. The rest of the chapter will explain differentconcept variations of the sensor, the sensing method used, the analytical validation,the finite element analysis of the sensor assembly, and finally the method for theassessment of the sensor output.2.1 Sensor PrincipleThe proposed sensor uses the principles of a simple magnetic circuit to measurewear inside centrifugal pumps. A magnetic circuit is a closed path that allowsmagnetic flux to travel through. The main component of the circuit’s body is typi-cally made from highly permeable material to guide the flux and minimize the fluxleakage. Here, the pump is placed inside the path of the circuit with the varying gapinside the pump between the impeller and the side plate being part of the circuit. Asimple analytical model of the magnetic circuit is created to evaluate the behaviourof the sensor with respect to a change in the size of the varying gap width.The flux traveling inside a magnetic circuit is typically generated by the use8of a permanent magnet or an electromagnet such as a magnetic coil. The magni-tude of the flux carried inside the circuit can be derived from two of Maxwell’sequations[17]. According to Ampe`re’s Law∮~H ·dl =∫J ·dA = i (2.1)the closed line integral of the magnetic field strength ~H over the length of themagnetic circuit l equals the total electrical current i through the area defined bythe closed line integral. The second fundamental equation∮~B ·dA = 0, (2.2)describes the conservation of magnetic flux. This implies that the integral of themagnetic flux density over the surface area A of any enclosed volume must beequal to zero. The magnetic field strength inside the circuit and the flux density arerelated through the permeability µ~B = µ~H. (2.3)The magnetic permeability µ represents the magnetization of the material usedinside the circuit in response to an applied magnetic field. The magnitude of per-meabilityµ = µ0µr (2.4)can be written as the permeability of free space µ0 = 4pi ∗10−7 H/m, multiplied bythe relative permeability of the desired medium µr.In the case of a simple magnetic circuit, there is a single flux source driving themagnetic flux through the circuit. There is also a medium that provides a path forthe magnetic flux, referred to as the flux guide throughout this document. Since thepumps considered in this project are generally used to transport water or water withpulp suspension, and given that the relative permeability of water and potential pulpconsistency is very close to that of the air (µr,water ∼= µr,wood ∼= µr,air ∼= 1), the gapinside the pump is replaced by a gap in the simplified magnetic circuit as shown in9Magnetic flux line Flux source Gap length lgap Gap cross-sectional area Agap Gap permeability  µ0 Fluxguide permeability  µc Fluxguide length lc Fluxguide cross-sectional area Ac Figure 2.1: The diagram of a simple magnetic circuit with a single gap.Figure 2.1. Therefor the line integral of the magnetic field strength, as representedin Equation 2.1, over the length of the circuit∑H ·∆l ={0, for permanent magnet (2.5)N · icoil, for magnetic coil (2.6)is equal to zero for the case or the permanent magnet as a flux source, and N · icoil forthe magnetic coil, where icoil represents the current passing through the windings ofthe coil with N number of turns. The magnitude of the flux density inside the fluxguide is also dependent on the source of the magnetic flux. By solving Equations2.1 through 2.6, the magnetic flux densityBsource =−lmagnetAmagnetlgapµ0Agap +lcµ0µcAcHsource, magnet (2.7)NAcoillgapµ0Agap +lcµ0µcAcicoil, coil (2.8)can be written as a function of the flux guide parameters with a relative permeabil-ity of µc, cross-sectional area of Ac and a length of lc, and the parameters of thegap with a relative permeability of µr = 1, cross-sectional area of Agap and a length10of lgap. For the case of the permanent magnet, the equation also depends on thegeometry and material properties of the permanent magnet used. In this case themagnet’s length lmagnet , cross-sectional area Amagnet , and the magnet’s coercivityHsource. Similarly for the case of the magnetic coil, the equation depends on thecoil’s number of windings N, cross-sectional area Acoil and current icoil . It can beobserved that in both cases the generated flux density Bsource is inversely propor-tional to the width of the air gap lgap. This equation can also be written in terms ofthe circuit’s reluctance valueℜ=lµA. (2.9)Reluctance is an indicator of the capacity for storage of magnetic energy. Itis both a function of geometry and material properties for each element inside thecircuit. Equation 2.9 can be used to further simplify Equations 2.7 and 2.8 so thatthe magnetic flux densityBsource =−lmagnetAmagnetℜgap+ℜ f gHsource, Magnet (2.10)NAcoilℜgap+ℜ f gicoil, Coil (2.11)can be written in terms of the reluctance of the flux guideℜ f g and the reluctance ofthe gapℜgap. An increase in the width of the gap inside the circuit, increases the re-luctance of the gap which results in an increase in the total reluctance of the circuit.This situation is the same for the more realistic model of the pump. Figure 2.2shows the schematic diagram of the centrifugal pump positioned axially in the pathof the magnetic circuit with its components inside the path of the magnetic flux.As it can be seen from the drawing, the varying gap width inside the pump is also acomponent of the sensor and therefore a change in its reluctance will alter the totalreluctance of the circuit. The geometry and the material properties of all the othercomponents of the pump placed inside the path of the flux also affect the behaviourof the circuit.11Stuffing BoxImpellerWearMagnetic FluxFluxguideHousingSide-plateVarying GapFlux Guide Figure 2.2: The schematic drawing of the magnetic circuit created with thepump and the flux guide assembly. The dotted line represents the pathof the magnetic flux inside the circuit. The location of the wear on thetip of the impeller is indicated on the drawing.As mentioned in Section 1.3, a two-blade 14-inch open impeller 40-HP cen-trifugal pump by Westcan is used for this study. All of the components of the pumpare made from cast iron with a relative permeability of µp = 500. This is commonfor the majority of centrifugal pumps used inside process plants. To evaluate theperformance of the sensor, the thickness of the pump housing lh, the stuffing boxltb, the side-plate lsp, and also the constant gap width between the stuffing box andthe impeller lcg are physically measured. The thickness of the impeller lim and alsothe varying gap width lvg vary as wear occurs on the blades of the impeller. Thechange in the magnitude of the varying gap between no-wear and maximum-wearstates is identified by the pump manufacturer. For the purpose of validating thewear sensor concept, a simplified version of the pump is considered as shown inFigure 2.3. All the physical dimensions of the pump are presented in Table 2.1.Since the permeability of the impeller is much greater than the permeability of the12Table 2.1: Physical dimensions of the pump components.Parameter Symbol ValueVarying gap (no wear - maximum wear) lvg 0.65 mm-2.50 mmHousing thickness lh 10 mmStuffing box thickness ltb 15 mmConstant gap width lcg 0.762 mmSide plate thickness lsp 11 mmImpeller thickness lim 38 mmTable 2.2: Effective cross-sectional areasof the pump components.Effective area Symbol Value1Variable gap Avg 400 mm2Housing Ah 10000 mm2Stuffing box Atb 10000 mm2Constant gap Acg 10000 mm2Side plate Asp 10000 mm2Impeller Aim 400 mm2flux guide Ac 2000 mm21 The presented values are estimatesbased on the 3D simulation model.gap (1:500), the change in the total reluctance of the sensor due to a change inthe thickness of the impeller can be neglected. The flux guide assembly is alsoassumed to have a high relative permeability of µc = 10,000 and a length of lc. Thereasoning behind this selection will be explained in Section 2.3. To analyticallymodel the behaviour of the magnetic circuit, the effective cross-sectional areas ofall the components of the circuit are also taken into consideration. For this reason,the cross-sectional areas have been estimated by fitting a simple parametric modelwith the more realistic 3D model of the circuit in Comsol Multiphysics. The re-sulting estimated areas are shown in Table 2.2.13Flux Φ lvg lh lsp lcg lim ltb Flux guide Pump Housing Side plate Impeller Stuffing box Figure 2.3: Simplified model of the pump and the sensor’s flux guide witheach component labeled on the diagram.To measure the width of the varying gap inside the pump, the change in the totalreluctance of the circuit is measured. The total reluctance of the circuit created withthe pumpℜtotal =ℜvar +ℜconst (2.12)is composed of a varying reluctance referring to the varying gap width between theimpeller and the side plateℜvar =lvgµ0Avg(2.13)and a constant reluctance for the remaining components of the pumpℜconst =lhµ0µpAh+ltbµ0µpAtb+lcgµ0Acg+lspµ0µpAsp+limµ0µpAim+lcµ0µcAc.(2.14)14As wear occurs at the tip of the impeller blades, the magnitude of the vary-ing reluctance is increased, leading to an increase in the total reluctance of thecircuit. To monitor the circuit’s total reluctance in real time, three methods havebeen proposed: (1) a permanent magnet model, (2) an electromagnet model, and(3) an inductance model. The characteristics of these methods are discussed andcompared in the following section.2.2 Sensing Method Variation & Comparison2.2.1 Permanent Magnet ModelIn this approach, a rare-earth permanent magnet is used to drive magnetic fluxthrough the circuit. Wear is estimated by monitoring the change in the magnitudeof the flux density as the total reluctance of the circuit increases. The operation ofthis method is described in this section.Permanent MagnetsPermanent magnets are commonly characterized by their magnetization curve asa function of an applied magnetic field. The resulting hysteresis curve is referredto as the BH curve and it represents the total energy that can be delivered by thepermanent magnet [17]. To determine the characteristics of a magnet, both thenormal curve and the intrinsic curve on the BH plot is considered as represented inFigure 2.4. The intrinsic BH curve is obtained by subtracting the flux density of theapplied field H in vacuum from the normal BH curve. As the applied field varies,so does the operating flux density of the magnet. The field required to reduce theflux density B to 0 is called the coercive force or coercivity Hc. When this valueis smaller than the intrinsic coercivity Hci, the BH curve becomes entirely linear inthe second quadrant of the BH curve with a slope of µ0. The value of B when theapplied field is reduced to zero is called the remanent flux density Br and is anotherfundamental property of the permanent magnet. For the design of the sensor, arare-earth magnet is selected with a composition of neodymium-iron-boron (Ne-15Intrinsic B H Normal Br -Br Hc Hci Figure 2.4: Magnetic hysteresis loop.FeB) also referred to as N42 with a remanent flux density of 1.3 Tesla. The use ofthis permanent magnet provides a linear relation between the flux density and thefield strength of the magnet in the second quadrant of the BH curve also referredto as the demagnetization curve which helps further simplify the analytical modelof the sensor.Analytical ModelingThe operating point of a permanent magnet when placed inside a magnetic circuitcan be determined by a combination of the circuit’s load line equation and themagnet’s demagnetization curve. The intersection of the two lines in the secondquadrant of the BH curve will define the magnet’s operating point as shown inFigure 2.5. Assuming the selected permanent magnet has a linear demagnetizationcurve in the second quadrant, as in the case of the N42 magnet, the demagnetizationcurve can be represented by the line equationB(H) = µ0H +Br. (2.15)and the equation of the load line for the proposed sensor design16Operating point B H Bm Hc Hm Br Loadline BH Curve Figure 2.5: Demagnetization curve of a typical rare-earth magnet superim-posed on the magnet’s loadline.B(H) =−lmagnetAmagnetlvgµ0Avg +ℜconstH. (2.16)is derived from Equation 2.10. By solving Equation 2.15 and Equation 2.16, themagnet’s operating flux densityBm(lvg) =Br1+( lvgµ0Avg +ℜconst)µ0Amagnetlmagnet(2.17)can be calculated as a function of the varying gap lvg. It is observed that the op-erating point of the magnet varies as the varying gap width increases and this re-lationship can be used to measure wear. The most suitable method to measure theflux density inside the circuit is through the use of a Hall-effect sensor placed insidethe path of the magnetic flux. Hall-effect sensors use the fundamental laws of mag-netism to convert the magnitude of flux density to a voltage signal. For this project,an analog Hall-effect sensor was selected from Analog Devices (AD22151) witha sensitivity of 4 V/T when excited using a 6 mA current. The full scale range of17the sensor is 1.25 T with an adjustable offset and a non linearity error of 0.1% FS.Since the sensor needs to be positioned inside the path of the flux, a secondary airgap must be created in the flux guide assembly to accommodate the sensor. Forthis reason, Equation 2.17 is revised intoBm(lvg) =Br1+( lvgµ0Avg +lsµ0As +ℜconst)µ0Amagnetlmagnet(2.18)where ls = 2 mm is the gap width required to fit the sensor and As = 4 mm2 is thecross-sectional area of the secondary gap that is determined from the working areaof the sensor to ensure the sensor captures all the flux traveling through the circuit.The response of the sensor can then be observed by solving Equation 2.18 forBm as a function of the varying the gap width lvg . The geometric parameters of thepermanent magnet used in this equation have been optimized to capture the highestsensitivity possible. The relevant equations for the geometry optimization of themagnet are presented in Appendix C. According to the geometric optimization, theideal ratio between the magnet’s length lmagnet and the cross-sectional area Amagnetg =lmagnetAmagnet= µ√ℜiℜ f (2.19)is calculated as a function of the total reluctance of the circuit where ℜi refersto the reluctance of the circuit before wear and ℜ f refers to the reluctance whenmaximum wear is observed. For this case, the ratio g was calculated to be 9 m−1.The magnet’s physical parameters used in the analytical model are shown in Ta-ble 2.3. Figure 2.6 shows the the magnet’s operating flux density as a functionof the varying gap width. As the gap width increases from 0.65 mm(no wear)to 2.50 mm(maximum wear), the magnetic flux density drops from 1.178 T to0.9324 T.Finite Element Simulation ResultsTo derive the analytical equation for the behaviour of the sensor, many simplifyingassumptions are made. To validate these assumptions, a 3D model of the simplified18Table 2.3: Magnet’s physical parameters.Parameter Symbol ValueLength lmagnet 0.018 mCross-sectional Area Amagnet 0.002 m2Remanent flux density Br 1.3 TVarying Gap Width [mm]MagneticFluxDensity[T]0.5 1 1.5 2 2.50.90.9511.051.11.151.2Figure 2.6: Plot of the operating magnetic flux density Bm as a function of thevarying gap width lvg as it increases from the no-wear state (0.65 mm) tothe maximum-wear state (2.50 mm) for the analytical calculation usingthe permanent magnet model.pump and the sensor is developed using Comsol Multiphysics shown in Figure 2.7and the behaviour of the sensor is determined using this model. For the purpose ofthis investigation and to simplify the simulation results, the pump impeller is as-sumed to be stationary and positioned such that one impeller tip is in the magneticflux path while the thickness of the impeller is reduced incrementally to accountfor wear inside the pump. The numerical analysis yields the magnetic flux density19Bm passing through the sensor as wear increases from no wear to maximum wearas shown in Figure 2.8.Hall-effect sensor Flux guide Side plate Stuffing box Housing Impeller Permanent magnet Figure 2.7: Magnitude of flux density [T] inside the sensor and the simplifiedpump for the analysis of the permanent magnet sensor model generatedusing Comsol Multiphysics.The resulting transfer behaviour from the analytical calculation (Figure 2.6)and the finite element simulation in Comsol (Figure 2.8) are fairly similar in bothmagnitude and shape. The minor difference between the two models are primar-ily due to material saturation and flux leakage that exist in the simulation but areignored in the analytical calculation. According to the simulation results, the fluxdensity changes 0.51% as the varying gap inside the pump increases from 0.65 mmto 2.50 mm. This indicates that the sensitivity achievable with the permanent mag-net sensor model is 2.4 mT/mm. By using the specified Hall-effect sensor with asensitivity of 4 V/T, the sensitivity can be translated into 9.6 mV/mm.20Varying Gap Width [mm]MagneticFluxDensity[T]0.5 1 1.5 2 2.50.8540.85450.8550.85550.8560.85650.8570.85750.8580.8585Figure 2.8: Plot of the magnetic flux density Bm as a function of the varyinggap width lvg for the case of the permanent magnet model derived fromComsol Simulation.2.2.2 Electromagnet ModelSimilar to the permanent magnet model, the electromagnet model also uses thechange in the flux density to measure the width of the varying gap inside the pumpcaused by wear. However, instead of using a permanent magnet as a source of flux,an electromagnet is produced through the means of a magnetic coil placed on theflux guide assembly. The coil is connected to an AC voltage source to generate analternating magnetic flux inside the flux guide. This allows for the fine tuning ofthe intensity of the magnetic flux to prevent saturation inside the flux guide materialas observed in the case of the permanent magnet model. Also by applying an ACmagnetic flux at a specific frequency, a large portion of the AC and DC noise canbe filtered from the output of the Hall-effect sensor. On the down side, this modelrequires a more complex circuitry for data collection and analysis which makes thedesign less desirable. The rest of this section will go into the details of the ana-21lytical modeling of the sensor and the numerical validation of the analytical results.Analytical ModelingAs described in the beginning of this chapter, wear can be estimated by correlatingthe change in the varying gap width to the change in the reluctance of the magneticcircuit created with the pump. If a magnetic coil is used as the source of flux insidethe circuit, then Equation 2.11 can be used to derive the magnitude of the fluxdensityBsource(lvg) =NAsourcelvgµ0Avg +ℜconsticoil (2.20)as a function of the varying gap width lvg, and the coil parameters such as thecross sectional area Acoil , number of turns N and the current passing through thecoil windings icoil . To measure the change in the total reluctance of the circuit inreal time, the same Hall-effect sensor can be used as in the case of the permanentmagnet model. Therefore, there needs to be an addition of a secondary air gapin the equation of magnetic flux to account for the sensor. This will change therelation for the magnetic flux densityBsource(lvg) =NAcoillvgµ0Avg +ℜconst +lsµ0Asicoil (2.21)passing through the sensor to include the reluctance caused by the secondary airgap with the same dimensions as in the case of the permanent magnet. For the ana-lytical calculations, the dimensions of the coil are selected so that the sensitivity ofthe sensor is maximized. The values used in the analytical model are representedin Table 2.4.For the analytical modeling of the sensor, MATLAB software is used to cal-culate the change in the magnitude of the flux density as wear causes an increasein the gap width inside the centrifugal pump. The result yields the magnitude ofthe flux density passing through the Hall-effect sensor as a function of the varying22Table 2.4: Magnetic coil’s physical parameters.Parameter Symbol ValueNumber of coil windings N 1000Cross-sectional area Acoil 0.002 m2Excitation current icoil 10 mAExcitation frequency fexc 100 Hzgap width as shown in Figure 2.9. It can be seen that the response of the sensoris very similar to the permanent magnet model as expected based on the analyticalequations. In this case, the magnitude of flux density varies from 15 mT to 12 mTas the gap increases from no-wear state to the maximum-wear state.Varying Gap Width [mm]MagneticFluxDensity[T]0.5 1 1.5 2 2.50.0120.01250.0130.01350.0140.01450.015Figure 2.9: Plot of the operating magnetic flux density Bm as a function of thevarying gap width lvg as it increases from the no-wear state (0.65 mm) tothe maximum-wear state (2.50 mm) for the analytical calculation usingthe electromagnet model.23Finite Element Simulation ResultsTo validate the analytical results, a 3D model of the sensor is developed using theAC/DC module of Comsol Multiphysics software, represented in Appendix A, andthe magnetic coil on the sensor is excited at 100 Hz with a current source of 10 mA.Similar to the permanent magnet model, the impeller blades are assumed to be sta-tionary to further simplify the simulation results. The numerical simulation yieldsthe change in the flux density as a function of the varying gap width shown in Fig-ure 2.10. The results yield a sensitivity of 2.8 mT/mm that can be converted into11 mV/mm using the same Hall-effect sensor as mentioned previously.Varying Gap Width [mm]MagneticFluxDensity[T]0.5 1 1.5 2 2.50.017060.017080.01710.017120.017140.017160.01718Figure 2.10: Plot of the magnetic flux density Bm as a function of the varyinggap width lvg for the case of the electromagnet model derived fromComsol Simulation.242.2.3 Coil Inductance ModelThis method also requires the use of a magnetic coil to drive magnetic flux throughthe flux guide. The reluctance, however, is calculated by measuring the inductanceof the coil as opposed to the magnitude of the flux density. This eliminates theneed for a Hall-effect sensor to be placed inside the path of the magnetic flux andtherefore eliminating the need for a secondary air-gap inside the flux guide. As aresult, the total reluctance of the circuit is significantly reduced.The inductance of a magnetic coil is a function of its core’s reluctance value.Therefore, when a coil is placed on the flux guide assembly, the inductance of thecoilLcoil =N2ℜtotal(2.22)can be written as a function of the number of coil windings N, divided by the totalreluctance of the magnetic circuit [18]. This implies that as the total reluctance ofthe circuit increases due to wear, the inductance of the magnetic coil drops and thisrelation could be used to monitor wear while the pump is in operation. The restof this section will go into the details of the analytical model of the sensor and thesimulation results to validate the analytical calculations.Analytical ModelingThe relationship between the coil’s Inductance value and the circuit’s total reluc-tance is used to analytically model the output of the sensor as wear occurs on thetip of the impeller blades inside the pump. By combining Equation 2.12, Equa-tion 2.13, Equation 2.14, and Equation 2.22, the inductance of the coilLcoil(lvg) =N2lvgµ0Avg +ℜconst(2.23)can be written as a function of the gap width lvg. The analytical calculation yieldsthe change in the inductance of the magnetic coil as the gap width increases from250.65 mm to 2.50 mm. The result of this analysis is shown in Figure 2.11. It can beobserved that the inductance changes from 12.3 mH to 9.55 mH as a result of thechange in the varying gap size.Varying Gap Width [mm]CoilInductance[mH]0.5 1 1.5 2 2.59.51010.51111.51212.5Figure 2.11: Coil inductance as a function of the varying gap width calcu-lated using the analytical model of the coil inductance.Finite Element Simulation ResultsTo further validate the analytical results of the inductance model, the pump and thesensor are modeled in a more realistic 3D geometry using Comsol Multiphysics asshown in Appendix A. Once again the AC/DC module of the Comsol Multiphysicsis used to monitor the change in the inductance of the coil as the varying gap widthinside the pump increases. Similar to the previous two models, the impeller bladesof the pump are assumed to be stationary to further simplify the problem. The re-sult of the simulation yields the inductance of the magnetic coil as a function of thevarying gap width as shown in Figure 2.12. As the plot indicates, the inductance26varies from 9.72 mH to 8.96mH as the gap increases from 0.65 mm to 2.50 mm.Varying Gap Width [mm]CoilInductance[mH]0.5 1 1.5 2 2.58.999.19.29.39.49.59.69.79.8Figure 2.12: The inductance of the magnetic coil as a function of the varyinggap width for the case of the inductance model derived using Comsolsimulation.2.2.4 Method SelectionIn this chapter three different methods have been proposed for measuring the vary-ing gap inside the pump, namely, the permanent magnet model, the electromagnetmodel, and the inductance model. To choose the most suitable approach, thesemethods are evaluated and compared based on the three most important designattributes as listed below in the order of importance:a. Sensitivityb. Signal to noise ratioc. Sensor complexity27a. SensitivityThe sensitivity of the sensor is the most important parameter that needs to be takeninto consideration. To compare the sensitivity of the three different models, thepercentage change in the magnitude of the measuring parameter is calculated usingthe Comsol simulation results presented earlier. The plot of the percentage changeversus the varying gap width is shown in Figure 2.13. As it can be seen fromthe generated plots, the responsiveness of the inductance model to a change in thevarying gap width is much larger than the other two methods. This is primarilydue to the absence of the Hall-effect sensor in the assembly and thus eliminatingthe need for a secondary air gap. It can also be observed that the electromagnetmodel operates slightly better than the permanent magnet model. This is due tomaterial saturation at the sharp corners of the flux guide assembly in the case ofthe permanent magnet for the high magnetic flux density exerted by the permanentmagnet.b. Signal to noise ratioThe noise level inside a plant environment with the presence of motors and pumpsoperating in close vicinity is expected to be relatively high. The difference betweenthe designs is in the effect of the existent noise on the output of the sensor. Themain advantage of the electromagnet model and the inductance model over the per-manent magnet model with regards to noise is in the use of an alternating magneticfield. Since an AC voltage signal is being used to operate the magnetic coil at afixed frequency, the output signal can also be collected at the same excitation fre-quency to reduce the effect of any DC or AC noise apparent in the environment.Another potential source of noise inside a plant is the magnetic field from nearbypermanent magnets that could exist in various coupling systems and motors. Sincethe permanent magnet model and the electromagnet model use a Hall-effect sensorto measure the change in the magnitude of the flux density, any neighboring mag-netic field will add additional noise to the output of the sensor.28Varying Gap Width [mm]0.5 1 1.5 2 2.5OutputSignal[%]012345678Permanent magnet modelElectromagnet modelInductance modelFigure 2.13: The percentage change in the measuring parameter as a func-tion of the varying gap width for the permanent magnet model, elec-tromagnet model, and the inductance model derived from Comsol sim-ulations.C. Sensor complexityThe complexity of the design of the sensor is also an important factor when it comesto selecting the most optimum design. The complexity could be in the physical fab-rication of the flux guide assembly, or in the electrical circuitry required to operatethe sensor. For the permanent magnet model and the magnetic coil model, the useof a Hall-effect sensor adds to the complexity of both the design of the flux guideassembly and to the circuitry required to operate the Hall-effect sensor.ConclusionIn summary, the coil inductance model is the most suitable method for measuringthe change in the varying gap width inside a centrifugal pump. Table 2.5 shows the29comparison of the three different models based on the mentioned design attributes.Through the use of a magnetic coil, the flux generated inside the path of the circuitcan be fine tuned to prevent any material saturation and the same coil can be usedto monitor the change in the reluctance of the circuit. By using a single coil in thesensor, the design of the assembly and the circuitry is considerably simplified.Table 2.5: The comparison of the three sensing methods.Design AttributesPermanent magnetmodelElectromagnetmodelInductancemodelSensitivity - - +Signal to noise ratio - + +Sensor complexity + - +2.3 Flux Guide DesignThe flux guide assembly is one of the key components of the sensor and its designwill significantly affect the sensor’s performance. The two most important param-eters for the design of the flux guide assembly are the material properties and thephysical geometry. The rest of this section will further explain the design processof the flux guide for an optimized performance.2.3.1 Material SelectionThe material used for the fabrication of the flux guide assembly plays an importantrole in the performance of the sensor. The most critical parameters that need to beconsidered when selecting the right material are the magnetic permeability, cost,and in some cases the saturation flux density.For identifying the magnetic permeability required for the flux guide assembly,the effect of permeability is analyzed on the output of the sensor. The analyticalmodel of the sensor is used to calculate the percentage change in the output signalusing various material permeability values. As shown in Figure 2.14, when the30magnetic permeability of the flux guide material increases, the sensitivity of thesensor is significantly improved. The improved sensitivity due to an increase in thematerial permeability saturates at just below µr = 10,000. This indicates that thereis no significant improvement to the sensor once the permeability of the materialexceeds this limit.Varying Gap Width [mm]OutputSignal[%]0.5 1 1.5 2 2.5012345678µr  = 10 µr  = 100 µr  = 1,000  µ r  = 2,000  µ r  = 5,000  µ r  = 100,000  µr  = 10,000 µr  = 7,000 Figure 2.14: The percentage change in the inductance of the coil (output sig-nal) using various magnetic permeability values for the flux guide as-sembly derived from the analytical model.To select the most suitable material for the fabrication of the flux guide as-sembly, several alternatives are considered and compared based on their magneticpermeability, saturation flux density and cost as shown in Table 2.6. It is importantto mention that the materials considered are also shortlisted based on their avail-ability and delivery time. Based on the characteristics of the materials selected andthe design parameters required to operate the sensor, the high-permeability VimVarmaterial and the M100 material are the most suitable options for the fabrication ofthe flux guide assembly. Since the M100 material has an initial permeability also31equal to its highest permeability of µr = 10,000, it does not require a biased fieldto be applied to the material to reach the highest possible permeability as in thecase for the VimVar material. This further simplifies the fabrication process ofthe sensor and the instrumentation required. The M100 is a brand name for theManganese Zinc Iron Ferrite material manufactured by National Magnetics GroupIncorporation in the United States.Table 2.6: High-permeability magnetic materials for the fabrication of the fluxguide assembly.Material Relative permeability1 Saturation flux density Cost per mass2M100 10,000 0.42 T $67.24/kgVimVar 10,000 2.15 T $65.17/kgHiperco 50 15,000 2.42 T $251.33/kgHy-Mu 80 230,000 0.87 T $81.35/kg1 Relative permeability refers to the maximum permeability achievable fromthe material. For the case of the M100 material, this value is referring to theinitial permeability which is also the maximum achievable.2 The total weight of the flux guide assembly is roughly 30 kg and the densitiesfor the selected materials are very similar.Since the M100 material is very expensive compared to the cost of other com-ponents of the sensor, a study is done to analyze the behaviour of the sensor whenthe usage of this material is reduced by creating a composition of high-permeabilityM100 material and a cheaper alternative such as Carbon Steel with a relative per-meability of 100 [19]. The purpose of this study is to identify a potential alternativeassembly with a similar sensitivity except by using the M100 material on only spe-cific parts of the assembly. However, as Figure 2.15 implies, the sensitivity ofthe sensor is only maximized when the entire assembly is made from the high-permeability M100 material.32Varying Gap Width [mm]0.5 1 1.5 2 2.5OutputSignal[%]012345678Model 1: All carbon steelModel 2: Pump endModel 3: Coil coreModel 4: Fuxguide sidesModel 5: All M100Magnetic Flux Φ Magnetic Flux Φ Magnetic Flux Φ 1 2 3 4 Carbon Steel M100 Magnetic Flux Φ 5 Magnetic Flux Φ Figure 2.15: Sensitivity comparison of alternative material compositions forthe flux guide assembly using carbon steel and high-permeabilityM100 material derived from Comsol simulations.2.3.2 Sensor GeometryThe design of the flux guide geometry is vital for the operation of the magneticwear sensor. Since the flux guide assembly constitutes the body of the sensor, itsdesign should be easy to fabricate, easy to install, durable, rigid, and most impor-tantly it should maximize the sensitivity of the sensor. The design should also takeinto account the cost of the material and the machining requirement in order tominimize the total cost of the sensor.Parameter OptimizationThe performance of the sensor is highly dependent on the geometry of the fluxguide assembly. The geometry must provide the most ideal path for the flux fieldto pass through while creating a clamping mechanism for the sensor to be installedon any centrifugal pump inside a plant. The two most important design parametersfor the geometry are the length and the cross-sectional area of the flux guide. Sinceboth of these parameters exist in the equation of the circuit’s total reluctance and33given that by lowering the reluctance the sensitivity of the sensor can be improved,it can be expected that a shorter length and a larger cross-sectional area may referto a higher sensitivity. To find the most optimum design, the analytical model of thesensor is used to calculate the change in the output signal as the design parametersare varied. The sensitivity is compared against varying the length of the assemblyas shown in Figure 2.16, and the cross-sectional area as shown in Figure 2.17. Asexpected, the most ideal design is the one with the shortest length and the largestcross-sectional areal. However, since the assembly needs to be wrapped around acentrifugal pump, there is a minimum length requirement that limits the sensitivityimprovement. Also, given that the material is valued at a cost per weight, the largercross-sectional area refers to a higher cost and thus there is a trade-off between thesensitivity and the cost.Varying Gap Width [mm]OutputSignal[%]2.3 2.35 2.4 2.45 2.56.46.66.877.27.47.67.88Increasing fluxguide length 100mm to 1,000mm   Figure 2.16: Percentage change in the output signal as a function of the vary-ing gap width using different lengths for the flux guide assembly de-rived from the analytical model.34Varying Gap Width [mm]OutputSignal[%]0.5 1 1.5 2 2.5012345678Increasing fluxguide cross-sectional area 50mm2 to 10,000mm2   Figure 2.17: Percentage change in the output signal as a function of the vary-ing gap width using various cross-sectional areas for the flux guideassembly derived from the analytical model.Geometry SelectionThe high-permeability M100 material used for the fabrication of the flux guide as-sembly is a highly brittle material and not easily machinable. For this reason, thedesign of the sensor should minimize any machining required to be done on thematerial to ensure the integrity of the material remains intact during the fabricationprocess. After going through different iterations for a clamping mechanism, a ’C’shaped geometry is selected with five legs to affix the sensor to the pump as shownin Figure 2.18. Each leg of the flux guide assembly can be a circular rod or a squareblock. Although the round edges of a cylindrical rod reduces material saturationat the sharp edges of the material, it is harder to machine and this makes the as-sembling process more complex. The square bars, on the other hand, can simplyfit together in a form they are shipped and be bonded together without the need forany additional attaching mechanism.351 2 3 4 5 Figure 2.18: A ’C’ Clamp design for the geometry of the flux guide assemblywith the five legs numbered on the drawing.For creating an adjustable clamping mechanism, there needs to be at least onedegree of freedom in the flux guide design. Several design alternatives are testedboth on paper and in the form of physical prototypes made from inexpensive lowpermeability material to test the feasibility and rigidity of the clamping mecha-nism once placed on the pump. The most ideal design based on the performanceand machining minimization is a 5 legged ’C’ clamp with legs 1 through 3 beingsquare blocks bonded together, for example using epoxy, and legs 4 and 5 beingcircular rods passing through the legs 2 and 3 as shown in Figure 2.19. This designallows for adjustable clamping of the sensor on to the pump while minimizing thereluctance in the path of the magnetic flux going through the sensor.To select the most ideal dimensions for the flux guide assembly, the sensitiv-ity of the sensor was compared against the cost and material dimensions availablefrom the vendor. Final dimensions of the flux guide assembly are shown in Fig-ure 2.20.36Figure 2.19: The isometric drawing of the flux guide clamping mechanism.2.3.3 Numerical ValidationTo numerically validate the effect of geometry on the output of the sensor, a morerealistic model of the pump is developed using Comsol Multiphysics. The modelincludes all the components of the pump to scale with an exception of the impellerin which it assumes a straight impeller vane as opposed to the real curved impellerto simplify the geometry. The exploded view of the pump is shown in Figure 2.21.One of the parameters of the design that needs to be tested is the material satu-ration. Although the use of the square block material is a more suitable option forthe assembling of the flux guide, the sharp corners on the blocks will amplify themagnitude of the flux density that could cause flux saturation inside the material.Comsol Multiphysics is used to measure the intensity of the magnetic flux densityat the sharp edges of the flux guide as shown in Appendix A. As the simulationresult illustrates, there is no saturation occurring inside the material due to the lowmagnitude of flux flowing through the material. The maximum concentration offlux density detected inside the flux guide material is roughly 5 mT and the satu-ration flux density of the M100 material is 420 mT. To further observe the flowof the flux inside the sensor, a 2D drawing of the sensor is plotted as shown in37 24.638  254  50.800  254  177.800  50.800  25.400  25.400  25.400  355.600  50.800 DO NOT SCALE DRAWINGAssem1SHEET 1 OF 1UNLESS OTHERWISE SPECIFIED:SCALE: 1:4 WEIGHT: REVDWG.  NO.ASIZETITLE:NAME DATECOMMENTS:Q.A.MFG APPR.ENG APPR.CHECKEDDRAWNFINISHMATERIALINTERPRET GEOMETRICTOLERANCING PER:DIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH      BEND TWO PLACE DECIMAL    THREE PLACE DECIMAL  APPLICATIONUSED ONNEXT ASSYPROPRIETARY AND CONFIDENTIALTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>.  ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS PROHIBITED.5 4 3 2 1Figure 2.20: The dimensions of the flux guide assembly in [mm].Figure 2.22, with the arrows indicating the direction of the magnetic flux densitypassing through the senor and the pump. It can be noticed from the plot that themajority of the flux field passes through the varying gap inside the pump and onlya small portion of the field leaks through the housing and the pump’s shaft.After finalizing the geometry of the sensor, the more realistic Comsol model ofthe pump and the sensor assembly is used to estimate the change in the inductanceof the magnetic coil as a function of the varying gap width. The simulation resultsare shown in Figure 2.23. As the figure indicates, the inductance of the coil drops3.6% as the varying gap increases from 0.65 mm to 2.50 mm. The difference in theresults compared to the simple model of the sensor and the pump (Figure 2.12) isprimarily due to the simplifying assumptions made in the flux guide geometry andalso the flux leakage to the surrounding air and the pump housing that is increasedin the more realistic model.38FluxguideSide-plateHousingWearStuffing boxMagnetic coilImpellerExploded viewGap widthFigure 2.21: Exploded view of the more realistic pump model and the sensorcreated in Comsol Multiphysics. All the components of the pump andthe sensor are labeled on the figure.2.4 Sensor InstrumentationAnother important element of the wear sensor is the instrumentation and circuitryrequired to operate the sensor. The main component of the instrumentation is themagnetic coil placed on the flux guide assembly to drive flux through the pump andto evaluate the total reluctance of the magnetic circuit. To collect measurements,the sensor requires a portable instrumentation box that connects to the magneticcoil for continuous data logging while the pump is in operation. The instrumen-tation box includes a circuit for measuring the coil’s inductance value, and a dataacquisition unit to collect the readings and to transfer them to a computer for theuser to analyze the data. This section will go through the design stages of the mag-netic coil and the instrumentation box used in the magnetic wear sensor.39Figure 2.22: Path of magnetic flux inside the sensor and the flux guide as-sembly.2.4.1 Coil DesignThe use of a magnetic coil in the magnetic wear sensor has two purposes: to gen-erate and drive magnetic flux through the sensor, and to monitor the reluctancechange inside the path of the magnetic circuit. For this reason, the design of themagnetic coil plays a critical role in the performance of the sensor. The most im-portant design parameters for the magnetic coil are its wire rating, number of turns,winding layers, coil dimensions, and bobbin geometry.Wiring MaterialThe selection of the coil wire depends on the operating conditions of the sensor. Toensure that the wire is capable of carrying the current required to operate the sensorat a given frequency, the extreme operating conditions are identified to be 100 mAat a maximum 200 kHz frequency. Based on these parameters, an American Wire40Varying Gap Width [mm]CoilInductance[mH]0.5 1 1.5 2 2.599.059.19.159.29.259.39.359.4Figure 2.23: Comsol simulation results yielding the magnetic coil inductanceas a function of the varying gap width for the more realistic model ofthe sensor and the pump. The coil is excited using a constant currentsource of 10 mA at 100 Hz.Gage 30 (AWG30) magnetic wire with enamel coating from EIS Incorporation, At-lanta, USA, is selected for the design of the magnetic coil. The parameter ratingsof this wire are represented in Table 2.7.Table 2.7: Properties of the American Wire Gape AWG30.Property Value [20]Diameter 0.254 mmResistivity 338.5Ω/kmMaximum amperage 0.142 AMaximum frequency 270 kHz41Coil LayoutTo find the most appropriate coil layout for the operation of the sensor, the changein the inductance of the coil is analyzed as a function of the varying gap widthwhile alternating the total number of turns on the coil. After detail analysis of theresults, it can be concluded that the total number of windings has no effect on thesensitivity of the sensor. The higher number of turns will only lead to a larger fluxdensity value which if exceeds the material saturation flux density can lower thesensitivity of the sensor. One important parameter that should be considered is theparasitic capacitance of the coil. If the parasitic capacitance causes a resonancein the circuit at a resonating frequency below the operating point, the sensor cancompletely loose its sensitivity to the reluctance change. To estimate the maximumparasitic capacitance allowable in the coil, the equation of the resonating frequencyis used. The resonating frequency in this casefres =12pi√LcoilCpar(2.24)can be written as a function of the coil inductance Lcoil and the parasitic capaci-tance between the coil windings Cpar. The excitation frequency of the coil for theproposed sensor is 70 Hz and the reasoning behind this selection will be describedin Chapter 3. If the maximum inductance of the coil is assumed to be 9.375 mHbased on the simulation results, by using Equation 2.24 the maximum allowableparasitic capacitance is calculated to be 551 µF.To estimate the parasitic capacitance based on the number of windings andwinding layers, an analytical model of the parasitic capacitance is used [21]. Ac-cording to the analytical model, the total parasitic capacitance of a coilCpar ∼= 1.366Ctt Single layer (2.25)Cpar ∼= 1.618Ctt Twolayer (2.26)Cpar ∼= 1.830Ctt T hree layer (2.27)42depends on the number of coil layers and is written as a function of the turn-to-turn capacitance of the coil wires for any number of turns N greater than 10. Theturn-to-turn capacitanceCtt = ε0lt[εrθ ∗ln DoDc+ cot(θ ∗2)− cot( pi12)](2.28)is a function of the wire parameters, coil geometry and θ ∗ , where θ ∗ is given byθ ∗ = arccos(1− lnDoDcεr)(2.29)and all of the parameters required to solve the above equations are labeled in Ta-ble 2.8. By solving Equation 2.25, Equation 2.26, Equation 2.27, Equation 2.28,and Equation 2.29, the parasitic capacitance of the coil is estimated to be 26.3 pF,31.1 pF, and 35.2 pF, for the single layer, two layer and the three layer coils re-spectively. Since the values of the paracitic capacitance between the coil windingsare very small, it can be concluded that the parasitic capacitance inside the coil canbe neglected. Considering the number of turns on the coil also has a minor effecton the sensitivity of the sensor, a single layer 150-turn coil is selected to furthersimplify the fabrication process.Table 2.8: Parameters for the parasitic capacitance analytical equation.Parameter Definition Valueε0 Absolute permittivity 8.85×10−12 F/mεr Relative permittivity of wire insulation (enamel) 3.68Do Wire outer diameter 0.280 mmDc Wire core diameter (no insulation) 0.254 mmDt Coil diameter 50.8 mmlt Length of one turn (piDt) 160 mm43Coil & Bobbin GeometryAs seen from the many simulation models performed, the geometry of the coil hasvery little effect on the sensitivity of the sensor as long as the geometry is functionaland the bobbin can be fitted on the sensor’s flux guide legs. Since the flux guideis decided to have a square shaped cross-section, the coil’s bobbin should also besquare shaped to prevent any flux leakage. The length of the bobbin should bedesigned to fit the 150 turn coil in one layer. The design of the bobbin is presentedin Figure 2.24 with the dimensions labeled on the drawing. 68  52  R5  68  52 4 3 2DO NOT SCALE DRAWINGBobbin - SquareSHEET 1 OF 1UNLESS OTHERWISE SPECIFIED:SCALE: 1:2 WEIGHT: REVDWG.  NO.ASIZETITLE:NAME DATECOMMENTS:Q.A.MFG APPR.ENG APPR.CHECKEDDRAWN5FINISHPROHIBITED.PROPRIETARY AND CONFIDENTIALTWO PLACE DECIMAL    MATERIALTHREE PLACE DECIMAL  NEXT ASSYINTERPRET GEOMETRICUSED ON     BEND TOLERANCING PER:APPLICATIONDIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACHTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>.  ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS 1 57  51 Figure 2.24: The design of the bobbin for the magnetic coil to be placed onthe flux guide assembly with the dimensions in [mm].2.4.2 Inductance MeasurementFor the operation of the wear sensor, the designed magnetic coil is used to driveflux through the sensor. More importantly, the same coil is used to measure thechange in the reluctance of the sensor caused by wear on the impeller blades of acentrifugal pump. As discussed in Section 2.2, the inductance of a magnetic coil isinversely proportional to the reluctance of its core material. To monitor wear, theinductance of the coil needs to be measured while the pump is in operation.44To achieve this, several different methods are considered that allow for liveinductance measurement. The most simple yet completely functional method forthis sensor is through the use of an RL circuit created by connecting a resistor inseries with the coil as shown in Figure 2.25. When an AC input voltage Vin isapplied across the circuit, the output voltageVout =RR+ jωLcoilVin (2.30)Vin Lcoil(lvg) Vout R Figure 2.25: Simple RL circuit to measure the inductance of the magneticcoil.measured across the resistor will be a function of the resistance R, the angular ex-citation frequency ω , and most importantly the inductance of the coil Lcoil . Tofurther improve the analytical model of the electrical circuit, the parasitic capaci-tance of the coil Cpar and also the resistance of the coil wire Rcoil are also added tothe simple RL circuit as shown in Figure 2.26. The equation for the output voltageVout =RR+(Rcoil + jωLcoil)|| 1jωCparVin (2.31)now includes all the circuit elements. To monitor the change in the magnitude of45Cpar Vin Lcoil(lvg) Vout R Rcoil Figure 2.26: More realistic RLC circuit representing the coil connected inseries with a resistor.the output voltage as a function of the coil inductance, the magnitude of the ratiobetween the output voltage over the input voltage∣∣∣∣VoutVin∣∣∣∣=√[R(1−ω2LcoilCpar)]2+ω2R2R2coilC2par[Rcoil +R−ω2RLcoilCpar]2+[ωL+RRcoilωCpar]2 (2.32)is derived by solving Equation 2.31 where the angular frequency, ω = 2pi f , canbe written as a function of the excitation frequency f . The magnitude of the para-sitic capacitance in this equation is known to be 26.3 pF from the analytical modelshown in Equation 2.25. The resistance of the coil wire can also be calculated byestimating the length of the wire and multiplying that value by the unit length re-sistivity of the AWG30 wire as noted in Table 2.7. Thus, the total resistance of thecoilRcoil = 150 turn · 4edgesturn · 0.0508medge· 0.3385Ωm(2.33)is calculated to be 10.32Ω. The only flexible design parameter in the circuit isthe resistance value of the resistor R that can be selected to maximize the change46in the output signal as the inductance value varies from 9.375 mH to 9.035 mH at100 Hz as predicted from the simulation results. This will result in the resistancebeing equal to 6Ω. Next chapter will go into the details of optimizing all the circuitelements to maximize the sensitivity of the wear sensor. To observe the change inthe output voltage as the inductance varies from no-wear to maximum-wear stages,the frequency response of the sensor is derived from the analytical model of thecircuit and the resulting plots at the two extreme cases are shown in Figure 2.27.As it can be seen from the figure, if the sensor is excited using a 1.0 V AC signal at100 Hz, the output voltage changes from 647.1 mV to 661.0 mV as the gap variesfrom 0.65 mm to 2.50 mm. This leads to a sensitivity of 7.51 mV/mm.Frequency [Hz]|Vout/Vin|50 100 1500.450.50.550.60.650.70.750.80.850.9No-wear (Lcoil = 9.375 mH)Max-wear (Lcoil = 9.035 mH)Figure 2.27: The change in the frequency response of the sensor as the mag-nitude of the varying gap increases from 0.65 mm to 2.50 mm derivedfrom the analytical model of the sensor.472.4.3 Circuit DesignThe sensitivity of the sensor can be enhanced by optimizing all the circuit elementsused to measure the inductance of the coil. One of the parameters that can signif-icantly improve the sensitivity of the sensor is the circuit’s resonating frequency.As discussed in the beginning of this section, the presence of the parasitic capac-itance inside the circuit creates resonance within the circuit that is undesirable ifthe operating frequency is selected to be above the resonating frequency. How-ever, if the resonating frequency is manually tuned so that the sensor is operatingjust below the resonating frequency, the sensitivity of the sensor can be greatlyimproved. To accomplish this, an external capacitor Cext is added in parallel withthe coil and in combination with the parasitic capacitance Cpar a total capacitanceof Ctot = Cext +Cpar is created. The magnitude of the external capacitance is se-lected so that the resonating frequency fres falls at 105 Hz just above the 100 Hzoperating frequency. For this, Equation 2.24 is used to calculate the total requiredcapacitanceCtot =14pi2 f 2resLcoil(2.34)where the lowest magnitude of inductance is used to calculate for the resonatingfrequency. The equation yields the required external capacitance of 254 µF. Byapplying this value to the analytical model of the circuit, the frequency response ofthe sensor changes as shown in Figure 2.28. To evaluate the response of the sensor,the optimized resistance value R used is calculated to be 54Ω. As it can be seenfrom the modified sensor response, the magnitude of the output voltage changesfrom 481.5 mV to 666.6 mV with an input voltage signal of 1.0 V at 100 Hz. Thisshows a sensitivity of 100.1 mV/mm which is more than 12× improvement overthe previous model.To excite the magnetic coil, a function generator with a constant power out-put is to be used with a sinusoidal voltage signal Vf g. To prevent the amplitudeof the voltage to be dependent on the input impedance of the sensor, there needsto be a voltage buffer in place. For this reason, a voltage follower apparatus isdesigned and placed at the input terminal of the circuit. This ensures that the sen-48Frequency [Hz]|Vout/Vin|80 85 90 95 100 105 110 115 12000.20.40.60.81No-wear (Lcoil = 9.375 mH)Max-wear (Lcoil = 9.035 mH)Figure 2.28: The change in the frequency response of the sensor as the mag-nitude of the varying gap increases from 0.65 mm to 2.50 mm withthe addition of the external capacitance Cext to the circuit. The plot isgenerated from the analytical model of the sensor.sitivity of the sensor is unchanged when the impedance of the circuit is varied dueto the change in the inductance of the coil. The voltage follower circuit uses anOp-Amp (TL084CN) selected from STMicroelectronics Corporation in Geneva,Switzerland. The Op-Amp is powered using a DC voltage supply of ± 15 V. Thecomplete drawing of the circuit including the voltage follower is shown in Fig-ure 2.29.2.5 Data AnalysisUp to now, the analysis of the wear sensor and its components are covered as-suming the impeller blade is held stationary in between the probes of the sensor.The designed sensor, however, is expected to acquire and interpret sensor readings49Cpar Vin Lcoil(lvg) Vout R Rcoil + _ +V -V Vfg Cext TL084CN Coil Figure 2.29: The complete drawing of the sensor’s circuit including the volt-age follower circuit.while the impeller is moving. In this section, the output of the sensor is analyzedwith the pump in operation and a data analysis method is proposed to accuratelymeasure the gap width between the impeller and the side plate.2.5.1 Expected Sensor ResponseThe output of the sensor is proportional to the change in the inductance of the mag-netic coil placed on the flux guide assembly. The inductance can then be correlatedto wear due to the increase in the varying gap between the impeller and the sideplate. To observe the change in the inductance of the coil as the impeller does afull rotation, Comsol Multiphysics is used to numerically simulate the inductanceas a function of the impeller’s angular position for the two extreme cases of no-wear and maximum-wear gap sizes. The resulting plots are shown in Figure 2.30.The peak inductance in these plots refer to the angular position when the impelleris crossing the probes of the sensor and therefore minimizing the gap inside the50path of the magnetic circuit. The two peaks seen on the plot correspond to the twoblades of the pump impeller. To correlate wear to the change in the inductancevalue of the magnetic coil, only the peak inductance value is taken into considera-tion.Impeller Angular Position [deg]Inductance[mH]0 90 180 270 3608.78.88.999.19.29.39.49.5 No-wear (lvg = 0.65mm)Maximum-wear (lvg = 2.50mm)Figure 2.30: Inductance of the magnetic coil as a function of the impeller’sangular position for both the no-wear and the maximum-wear casesderived from Comsol simulations.To detect the impeller blades as they cross the probes of the sensor, the mag-netic coil needs to be excited at a minimum frequency of 10 kHz. The issue withhigh excitation frequency is the presence of eddy currents. Since the housingof the pump is made from cast iron with an electrical conductivity of roughly1×106 S/m, high frequency magnetic field will induce eddy currents to form in-side the pump material, completely diminishing the sensitivity of the sensor. Forthis reason, Comsol Multiphysics is used to estimate the maximum excitation fre-quency possible without inducing strong eddy currents inside the pump’s hous-ing. The finite element simulation results suggest the ideal frequency to be below51100 Hz. Although by operating at 100 Hz the effect of eddy current on the outputof the sensor is negligible, the excitation frequency will not be fast enough to ac-quire useful readings while the pump is in operation. To overcome this problem,the signal can be over sampled and the effect of wear is determined on the shape ofthe output signal.To ensure that there are sufficient readings while the impeller is crossing theprobes of the sensor, the sampling frequency is calculated with respect to the an-gular speed of the impeller blades. The maximum typical rotational speed of anopen impeller centrifugal pump inside a plant environment is around 3600 RPM.To analytically calculate the time it takes the impeller blade to cross the probes ofthe sensor, the equations of the arc length and the tip velocity of the impeller areused to derive an equation for the sensor passing timetpassing =lprobeωpump rimp(2.35)as a function of the sensor probe length lprobe, pump rotational speed ωpump, andthe radius of the pump’s impeller rimp. The probe length is known to be roughly0.030 m, and the impeller’s maximum rotational speed is converted into 376.99 rad/swith a radius of 0.1778 m. By using these values, the sensor’s passing time is cal-culated to be 0.4476 ms for each impeller blade. To acquire accurate measurementwhile the impeller is passing the probes of the sensor, it is safe to assume that thesampling frequency needs to be such that there are at least twenty readings whilethe impeller is positioned inside the path of the sensor. This indicates that the sam-pling period needs to be limited to 0.02238 ms which translates into a minimumsampling frequency of 44 kHz. To achieve the best performance from the sensor, asampling frequency of 500 kHz is used to acquire wear measurements. The selec-tion of this sampling frequency is further explained in the following chapter of thisthesis.522.5.2 Data Analysis MethodTo measure the width of the varying gap while the impeller blade is passing theprobes of the sensor, the coil is excited at 70 Hz and the reasoning behind theselection of this frequency is explained in Chapter 3. The data is then sampled at500 Hz and the output time signal is transformed into the frequency domain usingthe fast Fourier transform algorithm (FFT) in MATLAB. Assuming the impelleris rotating at 900 RPM, which is the typical average speed of centrifugal pumpsinside a plant, a generic time signal is created and transformed into the frequencydomain as shown in Figure 2.31. As indicated on the drawing, there are three peaksexpected on the FFT plot. The first peak is detected at 15 Hz and it corresponds tothe impeller rotational speed of 900 RPM. The second peak is at 30 Hz referring tothe impeller blade passing frequency. Since there are two blades of the impeller ofthe pump, the passing frequency is double the frequency of the impeller’s rotationalspeed. The last peak is at 70 Hz that is the excitation frequency of the coil. Tomeasure the change in the inductance of the coil due to the change in the varyinggap width between the impeller and the side plate, the amplitude of the FFT plot at15 Hz and 30 Hz are monitored. A scatter plot of the amplitude at 15 Hz versus theamplitude at 30 Hz can be used to indicate the change in the varying gap width.Frequency [Hz]Amplitude[V]0 10 20 30 40 50 60 70 8000.20.40.60.811.215 Hz  Impeller rotation 30 Hz  Blade crossing 70 Hz  Excitation frequency Figure 2.31: Expected FFT response of the generic time signal from the sen-sor while the pump is operating at 900 RPM.53Chapter 3Experimental ValidationThis chapter will start by explaining the design and fabrication process of the sen-sor prototype as described in Chapter 2. The rest of the chapter will focus onsensor characterization, calibration process, experimental setup, and finally the ex-perimental results and analysis.3.1 Sensor PrototypeTo experimentally validate the functionality of the sensor, a physical prototypeneeds to be built and tested while installed on a centrifugal pump inside a plantenvironment. The sensor prototype includes three individual components, namely,the flux guide, the magnetic coil, and the portable instrumentation box for collect-ing sensor readings.3.1.1 Flux Guide AssemblyMaterial AcquisitionThe flux guide assembly is made from the high-permeability M100 material as de-scribed in Section 2.3. For the assembling of the flux guide geometry, three squareblocks with a length of 254 mm and a side width of 50.8 mm, and two cylindricalrods with a diameter of 24.6 mm and a length of 177.8 mm are purchased from the54National Magnetics Group Incorporation. The tolerance of the materials purchasedare ±0.5mm rated by the manufacturer. Since the selected material is highly brit-tle, the machining done on the material needs to be minimized. for this reason,the three square blocks are to be bonded together while the two cylindrical rodsneed to go through the square blocks to complete the magnetic circuit as shown inFigure 2.19.Machining of the Flux Guide AssemblyTo accommodate for the two cylindrical rods inside the square blocks, two throughholes with a diameter of 25.40 mm are punctured inside the blocks. For the ma-chining of the holes, a water jet cutter is used with extra-low pressure settings de-sirable for the highly-brittle materials. The water jet cutter uses pressurized watermixed with an abrasive substance such as sand to puncture the two holes throughthe M100 blocks. To dampen the impact of the water mixture on the surface of thematerial so to avoid the chipping of the surface, two thin aluminum plates with athickness of 1.6 mm are attached on both sides of the blocks.Magnetic EpoxyTo assemble the three square blocks together without performing additional ma-chining on the material, the blocks can be bonded together in a form of a ’C’ shapebracket using epoxy. The downside of using an epoxy is that it will induce an in-evitable gap inside the flux guide where the epoxy solution is applied. Since thisgap will have a relatively high reluctance value, it will significantly reduce the sen-sitivity of the sensor. To minimize the reluctance of the gaps created, the epoxy ismixed with the high-permeability M100 sintered particles, acquired from the Na-tional Magnetics Group Incorporation, with a relative permeability of µr = 10,000through a 50% weight ratio to create a magnetic epoxy with a relatively higher per-meability. The epoxy itself is selected based on the strength test results of severaldifferent brands when applied on magnetic core materials [22]. The selected epoxyis Loctite Adhesive Cartridge, E-00NS Epoxy manufactured by Henkel Corpora-55tion from Dusseldorf, Germany, purchased from McMaster Carr. The picture of theepoxy and the sintered particles is shown in Figure 3.1. The mixture is then appliedto the blocks and the final assembly is left at room temperature for 24 hours to cure.The final geometry is shown in Figure 3.2 To protect the flux guide assembly fromfracturing, a water-resistant super-cushioning polyurethane foam with a thicknessof 6.35 mm is bonded to the sensor as shown in Figure 3.3.Figure 3.1: The epoxy used to attach the flux guide components with the sin-tered M100 particles acquired from National Magnetics Group.3.1.2 Magnetic CoilFor the fabrication of the magnetic coil and the bobbin, the design parametersobtained in Section 2.4 are used. The bobbin is 3D printed with the geometrymodeled in SolidWorks as shown in Figure 3.4. Since the current flowing throughthe wire is no more than 1 mA and the sensor takes merely few seconds to acquireeach reading, the effect of temperature on the bobbin material is neglected. TheAWG30 magnetic wire used for the magnetic coil is purchased from McMasterCarr. To wind the wire around the bobbin, a manual coil winding apparatus is usedthat creates a rotating mechanism for the bobbin to be placed on and counts thetotal number of revolutions as the bobbin is turned. The winding apparatus wasused from the research lab supervised by Dr. Martin Ordonez and with the help of56Figure 3.2: The fabricated flux guide assembly with the magnetic coil.his PhD student Navid Shafiei. To protect the windings of the coil, a thin sheet oftransparent adhesive tape is applied to the coil as shown in Figure 3.5.3.1.3 Instrumentation BoxThe portable instrumentation box is meant to connect the sensor to a computerdevice for data logging. The box is connected via a plug-in connection to the mag-netic coil and it includes all the circuit components of the sensor including a dataacquisition system to sample the data. For the exterior of the box, a sheet metalinstrument case (LB-1525) is selected and purchased from Lee’s Electronics inVancouver, Canada. The connection from the box to the coil is made by using atwo-wire shielded cable that is soldered on one end to the coil and a heat shrinkis used to protect the connection. On the other end of the cable, a male circu-lar DIN connector is attached that fits onto a female DIN connector mounted onthe instrumentation box. The inductance measuring RLC circuit as represented inFigure 2.29 is made using a breadboard like circuit panel to allow for easy replace-ment of the circuit elements. The DAQ unit used for the sensor is an NI USB-6212unit manufactured by National Instruments Corporation. The DAQ selected has amaximum sampling frequency of 500 kS/s that is sufficient for the operation of thesensor. The final design of the instrumentation box is shown in Figure 3.6.57Figure 3.3: The flux guide assembly with the cushioning foam.Figure 3.4: The design of the coil bobbin in SolidWorks.The complete sensor prototype includes the flux guide assembly, the magneticcoil installed onto the upper leg of the flux guide, and the instrumentation boxthat connects the sensor to a computer running LabVIEW software as shown inFigure 3.7. The cost of the material and the components used for the fabricationof the sensor prototype are shown in Table 3.1. The cost of components that are58Figure 3.5: Prototype of the magnetic coil.Table 3.1: Cost of the material and the components used for the fabricationof the physical prototype.Part Quantity Cost per unit (CAD)M100 square block 3 $650.00M100 cylindrical rod 2 $165.00NI Daq USB-6212 1 $1,530.00E-00NS Epoxy 1 $14.47Cushioning foam (24” by 24”) 1 $35.23Instrument box 1 $32.00DIN connector 2 $17.74Shielded cable (1 m) 2 $19.38below $10.00 are excluded from the list.3.2 Sensor CharacterizationOnce the physical prototype of the sensor is built, the performance of the sensorand its components need to be characterized and verified with the analytical modelprior to running experiments on the pump.59Figure 3.6: The instrumentation box with the electrical circuit and the DAQunit. The box also includes a pivoting door (not shown in the picture) toprotect the instruments inside.3.2.1 Coil Inductance and Parasitic CapacitanceWithout attaching the external capacitor to the measurement circuit, the frequencyresponse of the sensor is acquired to calculate the coil’s inductance value and theparasitic capacitance between the windings of the coil. To acquire the frequencyresponse, a function generator is connected to the input terminals of the sensorand the peak-to-peak amplitude is set to 1.0 V while the frequency is varied from500 Hz to 200 kHz. To measure both the inductance Lcoil and the parasitic capaci-tance Cext of the coil assembly from the frequency response of the sensor, initiallyonly the lower frequency readings of the output signal are taken into considerationwhere the effect of the parasitic capacitance of the magnetic coil can be neglected.By assuming no parasitic capacitance, the magnitude of the output voltage over theinput voltage60Figure 3.7: Picture of the complete sensor prototype including the flux guideassembly, the coil, and the instrumentation box.∣∣∣∣VoutVin∣∣∣∣= R√R2+(2pi f Lcoil)2 (3.1)is written merely as a function of the known resistance R and the coil’s inductanceLcoil . The analytical model of the simplified sensor can be used to derive an equa-tion for the inductance of the coilLcoil =R2pi f√(VinVout)2−1 (3.2)as a function of the input voltage Vin, output voltage Vout , frequency f , and theresistance R. Through the means of a least square estimation, the inductance of themagnetic coil placed on the flux guide is estimated to be 33.1 mH. The value ofthe measured inductance is in the same order of magnitude as the inductance valuepredicted from the analytical results (Lcoil = 9.375 mH) as shown in Section 2.3.The higher inductance value observed in the physical measurement is primarilydue to the circuit being fully closed while the measurements are taken with theprobes of the sensor in contact with each other. The magnitude of the inductance61is also verified through the use of an RLC-meter (BK-Precision 875B) to ensurethe analytical model matches the physical prototype. The plot of the experimentalmeasurements and the least-square estimation is shown in Figure 3.8.Frequency [kHz]|Vout/Vin|0 2 4 6 8 100.40.50.60.70.80.91Experimental DataLeast Square Estimation: Lcoil = 33.1 mHFigure 3.8: Frequency response of the sensor: experimental measurementsand the least square estimation.The resonating frequency of the circuit is estimated to be roughly 160 kHz. Byusing the equation for the resonance frequency as stated in Equation 2.24, the para-sitic capacitance of the coil is calculated to be 29.8 pF. This is very close to the ana-lytical prediction (Cpar = 26.3 pF) as noted in Section 2.4. To ensure that neglectingthe capacitance did not alter the inductance calculation shown in Equation 3.2, theimpedance of the inductor, ZL = jωLcoil , is compared against the impedance of theparasitic capacitor, ZC = 1jωCext , at the cutoff frequency. The cut-off frequency isincreased incrementally at each iteration to bring the impedance of the inductor atleast 100 times higher than the impedance of the capacitor Lcoil×100≤ 1ω2Cext forthe inductance measurement. This brings the cutoff frequency to 10 kHz.623.2.2 Circuit OptimizationOnce the physical parameters of the coil are identified, all the external circuit ele-ments such as the resistance R, the external capacitance Cext and also the excitationfrequency f need to be optimized. Based on the simulation results, the excitationfrequency of the coil needs to be kept below 100 Hz to avoid eddy currents beingformed inside the pump material. To adjust the resonating frequency of the circuitto 100 Hz, a capacitor with a capacitance of Cext = 100µF is selected. To optimizethe rest of the circuit parameters, the output voltage of the sensor is modeled withthe new capacitance value using the analytical model shown in Equation 2.32. Bycomparing the value of R with the change in the output voltage obtained from theanalytical model, the optimum resistance value is estimated to be 7.5Ω as shown inFigure 3.9. The same analytical model is used to compare the change in the outputvoltage as a function of the excitation frequency. Based on the analytical resultsshown in Figure 3.10, the ideal operating frequency is estimated to be 70 Hz.Resistance [Ohm]ChangeinOutputVoltage[V]R = 7.5 Ohm5 10 15 20 25 300.0050.010.0150.020.0250.030.0350.04Figure 3.9: Maximizing the change in the output signal as a function of theresistance value of R.63Frequency [Hz]ChangeinOutputVoltage[V]f = 70 Hz50 100 150 200 250 30000.0050.010.0150.020.0250.030.0350.04Figure 3.10: Maximizing the change in the output signal as a function of theexcitation frequency f .3.2.3 Benchtop ExperimentsPrior to performing experiments on a physical pump, a benchtop experimentalsetup is created to test the behaviour of the sensor in a more controlled environ-ment. By using a simpler setup, many of the uncontrollable parameters during theexperiment can be prevented which could in turn help improve the result of anyfuture experiments done on a physical pump. The benchtop experimental setupincludes two parallel cast iron plates separated by thin plastic gaskets at knownthicknesses. The gap between the two plates is increased incrementally while thesensor is placed perpendicular to the surface of the plates as shown in Figure 3.11.The frequency response of the sensor is collected at each gap width to observe thechange in the output of the sensor as shown in Figure 3.12. As it can be observed,the frequency response of the sensor shifts to the right as the gap width betweenthe two parallel plates increases. This is very compatible with the expected sen-sor response as shown in Figure 2.28. With these results, the experiments can bemoved toward a real pump inside a plant.64Figure 3.11: The benchtop experimental apparatus with the sensor placedperpendicularly to the two parallel cast iron plates.Frequency [Hz]|Vout/Vin|40 50 60 70 80 900.220.230.240.250.260.270.280.290.30.31gap = 0.0mmgap = 0.5mmgap = 1.0mmgap = 2.0mmFigure 3.12: The frequency response of the sensor as the gap between the twoparallel cast iron plates vary from 0.0 mm to 2.0 mm.653.3 Experimental Setup3.3.1 Pump LoopAfter validating the analytical model of the sensor and testing its performance inthe benchtop experiment, the sensor is to be tested on a physical pump. The pumpused to perform the experiments in this project is a 40-hp two blade open impellercentrifugal pump manufactured by Westcan installed at the UBC’s Pulp and Pa-per Center pilot plant. The pump is built entirely from cast iron with a relativemagnetic permeability of µr = 500. The picture of the pump with the directionof the flow is shown in Figure 3.13 and the schematic diagram of the pump loopinside the facility is shown in Figure 3.14. The setup is used to pump water withpulp suspension through a double tank mixing loop. Since the water and the pulpconsistency both have a magnetic permeability close to that of the vacuum, theirpresence has no effect on the output of the sensor.Figure 3.13: Westcan Centrifugal pump installed in the PPC Pilot Plant. Di-rection of the flow is labeled on the figure.66Tank 1 Tank 2 Flow Pump Figure 3.14: Schematic diagram of the pump loop in the Pulp and Paper Cen-ter at UBC.3.3.2 Pump AdjustmentsThrough observing the manufacturer’s data sheet of the pump and the pump’scross-sectional drawing, it is identified that there is a large void in between theside plate and the housing of the pump. The geometry and the dimensions of thevoid is acquired by placing a piece of clay material behind the pump’s side plate atthe location where the sensor is to be installed. After the clay material is removed,the void is verified to have a width close to 2 cm which is a large enough gap insidethe path of the magnetic flux to completely diminish the functionality of the sen-sor on the pump. To fully close the path of the magnetic circuit inside the pump,the void needs to be filled with a material that has a relative permeability close tothat of the pump material. To achieve this, a high permeability polymer is formedby mixing a two-part polyurethane kit by Smooth-Cast Onyx with the M100 sin-tered particles in a 50% weight ratio. To further increase the permeability of the67polymer, thin plates of the M100 material are cut and placed inside the mixture asshown in Figure 3.15. The magnetic polymer is then poured in the void and left atroom temperature to cure. This problem is expected for all the pumps that utilizea side plate. For the majority of the centrifugal pumps, however, the sensor can beinstalled without any additional modifications.Figure 3.15: The magnetic polymer mixture poured on the pump’s side plate.3.3.3 Sensor InstallationAfter adjusting the pump to accommodate the sensor, the sensor is installed on theedge of the pump for data collection. To keep the sensor affixed to the pump andto protect the sensor from tipping over, the assembly is also supported from anabove fixture by the means of two wire cables. The probes of the sensor are thenclamped on the sides of the pump to close the magnetic circuit. The picture of thesensor installed on the pump is shown in Figure 3.16. The instrumentation boxconnected to the coil is placed on a table beside the pump and the box is connectedto a computer for data acquisition. To power the op-amp in the circuit, a DC power68supply is also attached to the instrumentation box and a function generator is usedto excite the coil.Figure 3.16: The sensor assembly installed on the pump.3.3.4 Sensor CalibrationTo calibrate the magnetic wear sensor and to observe the change in the output ofthe sensor as wear accumulates on the tip of the impeller blades of the centrifugalpump, the sensor needs to take measurements at various stages of the impeller’s lifewhile it is being eroded. Since wear occurs very slowly over a period of monthsor even years, an alternative method for calibrating the sensor is proposed. Inthis method, the gap between the impeller and the side plate is manually varied toreproduce the effect of wear on the varying gap width inside the pump. To manuallyvary the gap, thin ring gaskets with a thickness of 0.8 mm are inserted behind thepump housing to shift the stuffing box along with the impeller outwards. Sincethe gaskets are slightly compressed when placed inside the pump, the thickness ofeach gasket is estimated to be 0.75 mm± 0.05 mm through measuring the physical69change in the location of the stuffing box with respect to the housing of the pump.The initial clearance inside the pump between the impeller and the side plate isset to 0.40 mm ± 0.05 mm. Gaskets are then placed one at a time and the processis repeated three times to increase the gap from an initial width of 0.40 mm ±0.05 mm to a width of 2.65 mm ± 0.20 mm. Each time a gasket is inserted, thesensor is installed on the pump and measurements are collected while the pumpis running. The location of the gaskets on the schematic drawing of the pump isshown in Figure 3.17. The location is also labeled on the physical pump as shownin Figure 3.18.HousingStuffing BoxImpellerSide-plateInletDischargeGasket Stuffing box I ell r Housing Figure 3.17: The location of the ring gaskets on the schematic cross-sectionalview of the pump.Figure 3.18: The location of the ring gaskets on the centrifugal pump.703.4 Experimental Results & Analysis3.4.1 Sensor OutputOnce the sensor is installed, data is collected while the pump is held stationary toanalyze the output voltage signal generated from the circuit. To obtain the mea-surements, the coil is excited at 70 Hz and data is collected at 50 kHz samplingfrequency for a duration of one second. The rotational speed of the pump is thenincreased to 900 RPM using a variable frequency drive (VFD) connected to themotor that runs the pump. Data is again collected with the same sampling con-ditions and the output of the sensor is plotted against time to observe the changein the behaviour of the sensor. The output voltage signal for both pump rotationalspeeds of 0 RPM and 900 RPM are presented in Figure 3.19.Time [ms]OutputVoltage[V]0 10 20 30 40 50 60−0.15−0.1−0.0500.050.10.15Time [ms]OutputVoltage[V]0 10 20 30 40 50 60−0.15−0.1−0.0500.050.10.15a) b) Figure 3.19: The output voltage signal from the sensor as a function of timefor a) the pump rotational speed of 0 RPM, and b) the pump rotationalspeed of 900 RPM.As described in Section 2.5, to analyze the change in the behaviour of the cir-cuit as a function of the varying gap width inside the pump, the time domain signalVout(t) is then transformed into its frequency domain equivalent Vˆout( f ) using thefast Fourier transform algorithm. The resulting FFT plot of the sensor’s outputsignal at the pump rotational speed of 900 RPM is shown in Figure 3.20. The twopeaks identified on the FFT plot correlate directly to the impeller’s rotation speed.The first peak at 15 Hz is referring to the impellers rotational frequency and the71second peak at 30 Hz refers to the blade passing frequency. Since there are twoblades on the impeller of the pump, the blade’s passing frequency is double the fre-quency of the impeller’s rotational speed. To measure wear on the impeller blades,only the peak amplitudes are considered.Frequency [Hz]Amplitude[V]0 10 20 30 40 50×10−400.511.522.53Figure 3.20: The FFT plot of the sensor output while the pump is operatingat 900 RPM.3.4.2 Pump Rotational Speed VariationTo ensure that the peaks identified on the FFT plot generated at the pump rota-tional speed of 900 RPM is consistent at various pump rotational speeds, measure-ments are taken while the rotational speed of the pump is varied from 450 RPMto 900 RPM. For these measurements the excitation frequency of the coil is set to70 Hz while the signal is sampled at 50 kHz sampling frequency for a duration ofone second. The output signal is then transformed into the frequency domain asshown in Figure 3.21. The peaks visible on the plot are consistent with the rota-tional speed of the pump.72Frequency [Hz]Amplitude[V]5 10 15 20 25 30 35 40 45 50 55×10−40.511.522.5450RPM - 7.5/15Hz600RPM - 10/20Hz750RPM - 12.5/25Hz900RPM - 15/30HzFigure 3.21: The amplitude spectral density of the sensor output for variouspump rotational speeds.3.4.3 Signal to Noise Ratio (SNR)To analyze the quality of the output signal collected while the pump is in operation,the ratio of the signal with respect to the background noise or the signal to noiseratioSNR =PsignalPnoise(3.3)is calculated as a function of the signal power Psignal and the power of the noisePnoise. To calculate the SNR value of the sensor, only the signal collected at900 RPM is taken into consideration as shown in Figure 3.20. To separate thenoise from the raw signal, an interval-dependent haar wavelet denoising functionis used in MATLAB. Figure 3.22 shows the plot of the denoised signal Vˆsignal( f )and the noise Vˆnoise( f ). The amplitudes at the 15 Hz and 30 Hz frequencies arecorrelated to the absolute magnitude of the gap width and therefore the signal tonoise ratio is calculated in the vicinity of these two frequencies and the total SNR73is estimated by taking the average between the two resulting values. The SNR at15 HzSNR15 =17Hz∫f=13HzS( f )signal ·d f17Hz∫f=13HzS( f )noise ·d f(3.4)is measured by integrating the power spectral density of the denoised signal Ssignal( f )=∣∣Vˆsignal∣∣2 divided by the power spectral density of the noise signal Snoise( f ) =∣∣Vˆnoise∣∣2 between 13 Hz to 17 Hz. The SNR value at the 15 Hz peak is calculated tobe 14.30. Similarly, the SNR at 30 HzSNR30 =32Hz∫f=28HzSsignal( f ) ·d f32Hz∫f=28HzSnoise( f ) ·d f(3.5)is also calculated to be 14.30 by integrating the signals from 28 Hz to 32 Hz. Thiswill produce an average SNR value of 14.30. The SNR can also be expressed indecibelsSNRdB = 10 · log10(PsignalPnoise)(3.6)and the calculated magnitude of the SNRdB is 11.6 dB.3.4.4 Sampling OptimizationTo further improve the quality of the output signal and to increase the SNR of thesensor, the sampling frequency is varied and its effect on the noise level is observedas shown in Figure 3.23. By increasing the sampling frequency of the sensor whilekeeping the measurement duration constant at 1 second, the SNR increases leading74Frequency [Hz]Amplitude[V]0 10 20 30 40 50×10−4012Denoised signal∣∣∣Vˆsignal∣∣∣Noise∣∣∣Vˆnoise∣∣∣Figure 3.22: The plot of the output signal and the noise signal at the impellerrotational speed of 900 RPM. Signal is sampled at a sampling fre-quency of 50 Hz for a duration of 1 second.to an improved output signal. This effect, however, declines as the sampling fre-quency is increased as shown in Figure 3.24. To ensure that the improvement in thesensor output is due to the sampling frequency and not the number of samples, theSNR is also calculated as a function of the sampling frequency for a constant num-ber of samples at 1M data points as shown in Figure 3.25. In this study, the highestSNR is reached at 500 kHz and the value of the SNRdB is 17.8 dB for one secondof measurement. To observe the effect of measurement duration on the output ofthe sensor, the SNR is also plotted against the total number of samples used. Asshown in Figure 3.26, the SNR is greatly improved with a higher sample numberthat is derived from a longer measurement duration.3.4.5 Data CollectionTo evaluate the functionality of the sensor and to validate the analytical and simu-lation results obtained earlier in this thesis, the change in the sensor’s output signal75Frequency [Hz]Amplitude[V]SNRdB = 5.02 dB0 20 40×10−40123Sampling frequency fs = 20 kHzFrequency [Hz]Amplitude[V]SNRdB = 11.6 dB0 20 40×10−40123Sampling frequency fs = 50 kHzFrequency [Hz]Amplitude[V]SNRdB = 14.6 dB0 20 40×10−40123Sampling frequency fs = 100 kHzFrequency [Hz]Amplitude[V]SNRdB = 17.8 dB0 20 40×10−40123Sampling frequency fs = 500 kHzFigure 3.23: Sensor output collected at different sampling frequencies of20 kHz, 50 kHz, 100 kHz, and 500 kHz. The SNR value of each datais labeled on the plot. All measurements were taken during 1 secondwith a pump rotational speed of 900 RPM.is examined as a function of the varying gap width inside the pump. As explainedin Section 3.3 the sensor is calibrated by incrementally increasing the varying gapinside the pump at 0.75 mm ± 0.05 mm increments from 0.40 mm ± 0.05 mm to2.65 mm ± 0.20 mm and measurements are taken at each gap width. To correlatethe output of the sensor with the width of the varying gap, the amplitude of theFFT signal at 30 Hz is plotted against the amplitude at 15 Hz for each 1 second ofmeasurement. The resulting scatter plot is shown in Figure 3.27 and the mean andstandard deviations of the scatter plot are shown in Figure 3.28. The amplitude atthe 15 Hz frequency is clearly correlated to the varying gap width inside the pump,whereas the amplitude at the 30 Hz frequency has no evident relation with the gap.This behaviour in the sensor indicates that the two blades on the impeller are dif-ferent in thickness and this could have been caused by the accumulation of unevenwear on the blades. Figure 3.29 shows the amplitude of the output signal at 15 Hz76Sampling Frequency [kHz]SNR[dB]50040030020010004681012141618Figure 3.24: Signal to noise ratio in [dB] as a function of the samplingfrequency for a one-second measurement on the pump running at900 RPM.Sampling Frequency [kHz]SNR[dB]5004003002001000131415161718192021Figure 3.25: Signal to noise ratio in [dB] as a function of the sampling fre-quency for 1M data points.versus the magnitude of the varying gap, with the error bars and the uncertaintyin the gap width identified at each data point. The average size of the error bar isalso compared against the duration of the measurement and it is observed that asthe sampling time increases, the size of the error bar decreases leading to a higheraccuracy and resolution of the output signal.77Number of Samples [Millions]SNR[dB]0 0.5 1 1.5 2024681012Figure 3.26: Signal to noise ratio in [dB] as a function of the total number ofsamples with a fixed sampling frequency of 50 kHz.It is noteworthy to mention that many other alternative methods for measuringthe peak amplitude are also considered such as the ratio between the peak am-plitude at both frequencies with respect to the amplitude at 70 Hz (the excitationfrequency), the ratio between the peak amplitude to the RMS value of the noise,and also the difference between the amplitude of the signal and the noise level. Theresulting plots, however, did not improve in neither of these scenarios. The plotsare presented in Appendix C.To compare the experimental data with the simulation results generated as de-scribed in Chapter 2, the calibration curve of the sensor (Figure 3.29) is plottedagainst the simulation results as shown in Figure 3.30. In this comparison, thesimulation results are multiplied by a gain of 12 to account for the amplificationcreated using the external capacitor in the sensor’s circuit. As expected, the simu-lation results yield a considerably higher sensitivity primarily due to the inevitablegaps created inside the flux guide assembly during the fabrication process and inthe contacts between the sensor and the pump that were not included in the simu-lation model.78Amplitude @ f = 15 Hz [V]Amplitude@f=30Hz[V]×10−30.08 0.1 0.12 0.14 0.16 0.18 0.2×10−40.40.60.811.21.41.61.822.22.4lvg= 0.40mm ± 0.05mmlvg= 1.15mm ± 0.10mmlvg= 1.90mm ± 0.15mmlvg= 2.65mm ± 0.20mmFigure 3.27: Scatter plot of the sensor output signal at 30 Hz versus the outputsignal 15 Hz for various gap widths. Each data point refers to 1 secondof measurement collected at 500 kHz sampling frequency. There are36 data points for each gap width.3.4.6 Wear DetectionOnce the sensor is calibrated, the magnetic wear sensor can be used to estimatethe magnitude of wear inside the centrifugal pump while the pump is in operation.To do this, data will be collected every few days for a duration of no more thanone minute and the resulting data is used to estimate the change in the width of theimpeller blade. To measure the magnitude of wear based on the sensor’s output sig-nal, the collected data is transformed into the frequency domain and the amplitudeof the resulting signals at 15 Hz is compared against the acquired calibration curveshown in Figure 3.29. Based on the calibration curve, the sensor has an averagesensitivity of S = ∆V∆l = 0.022 mV/mm. With an average error bar size of δV =0.0082 mV, the resolution achieved by the sensor is δ l = δVS= 0.38 mm. Sincewear measurements are taken with reference to the initial clearance between theimpeller and the side plate, the accuracy of the sensor is limited by the accuracy ofthe initial gap measurement and the resolution of the sensor.79Amplitude @ f = 15 Hz [V]Amplitude@f=30Hz[V]×10−30.08 0.1 0.12 0.14 0.16 0.18 0.2×10−40.40.60.811.21.41.61.822.22.4lvg= 0.40mm ± 0.05mmlvg= 1.15mm ± 0.10mmlvg= 1.90mm ± 0.15mmlvg= 2.65mm ± 0.20mmFigure 3.28: Mean and the standard deviation of the scatter plot for the sensoroutput signal at 30 Hz versus the output signal 15 Hz at various gapwidths. The sampling frequency is set to 500 kHz and measurementsare taken for a duration of 36 seconds.The reproducibility and the repeatability of the data collected from the sensorare also very crucial when assessing the performance of the wear sensor. To test thereproducibility of the sensor output, the assembly is completely removed from thepump and placed back again three times while measurements are taken each timethe sensor is affixed to the pump. The samples are collected at 500 kHz samplingfrequency for a duration of one second while the pump is running at 900 RPM. Toquantify the reproducibility of the sensor output, the voltage amplitude at 15 Hzfrequency in the FFT plot for each data set is obtained and the standard deviationbetween the resulting values is calculated. In this case, the standard deviation iscalculated to be 6.60 µV. Similarly, to quantify the repeatability of the sensor out-put, 10 sets of one-second measurements are taken from the pump with the samesampling conditions while the sensor is kept affixed to the pump. Using the sameprocedure as in the case of the reproducibility check, the standard deviation be-tween the resulting values is calculated to be 10.86 µV. As it can be observed, bothmagnitudes are in the same order of magnitude but more experiments are required80Varying Gap Width [mm]SinglalAmplitude@f=15Hz[V]0 0.5 1 1.5 2 2.5 3×10−411.11.21.31.41.51.61.71.8Figure 3.29: The mean amplitude of the sensor’s output signal at 15 Hz ver-sus the magnitude of the varying gap width. The error bar and theuncertainty of the gap width for each data point is shown on the plot.to derive a more accurate estimation of the error. In comparison to the resolutionand the sensitivity of the sensor output, both the reproducibility and the repeatabil-ity of the sensor are well within the acceptable range.81Varying Gap Width [mm]PercentageChangeinOutput[%]0.5 1 1.5 2 2.501020304050607080Simulation Results (with G = 12X)Experimental ResultsFigure 3.30: Comparison between the experimental results and the simula-tion results. The plot shows the percentage change in the output ofthe sensor as a function of the varying gap width as it increases from0.4 mm to 2.65 mm.82Chapter 4Conclusions and Future Work4.1 ConclusionsIn this study, a live magnetic wear sensor is designed and tested that allows forwear measurement inside centrifugal pumps. The sensor is in a form of a clampingmechanism attached to a portable instrumentation box allowing it to be installed onany operational centrifugal pump. The sensor designed has a signal to noise ratio of17.8 dB with an average sensitivity of 0.022 mV/mm and a resolution of 0.38 mm.The sensitivity and the resolution achieved by this sensor make it suitable for wearmeasurements of industrial pumps inside a plant. The standard deviation valuesreferring to the reproducibility and the repeatability of the sensor are 6.60 µV and10.86 µV respectively.The main limitation of this sensor is that it requires recalibration for everypump it is placed on which could be a time consuming process. Also, the sensor isonly functional for open-impeller centrifugal pumps. This class of pumps are mostcommonly used inside process plants for transporting slurry fluids or fluids withsolid inconsistencies.This sensor, however, introduces many other opportunities for similar wear orgap measurements. Wear measurement inside rotating machinery, for instance,where there are two parallel plates such as a pulp refiner could be achieved by this83sensor. Clearance or gap measurement inside machinery is also achievable by thissensor in cases where access to the inside of the component is limited.4.2 Future WorkThe sensor developed in this project is proven to be functional while testing itsperformance on a single centrifugal pump in a pilot plant. To further improve theperformance of the sensor and to make it into a final product, there are several im-provements that can be done.Flux Guide MaterialBecause of the time and cost limitations of this project, there was only one pro-totype of the sensor fabricated and this limited the potentials achievable with thesensor concept. The material used in the flux guide assembly was selected based onextreme design parameters to ensure the functionality of the sensor. Since the costof the flux guide material is the main part of the total cost of the sensor as shown inTable 3.1, to lower the cost of fabrication, cheaper materials can be used withoutsacrificing a large fraction of the sensitivity. As it could be seen from the analyticaland simulation results, a material with a relative permeability of µr = 5,000 is suf-ficient for the operation of the sensor. Also, since the sensor needs to be installedinside a plant for a duration of several years, the body of the sensor needs to berigid and durable. The material used for the flux guide assembly in this project ishighly brittle and can easily break once placed on a pump. The design of the fluxguide assembly can also be further improved to minimize the air gaps inside thebody. Currently the two moving cylindrical rods inside the sensor are not tightlyconnected to the rest of the assembly and this creates an air gap inside the fluxguide.84Sensor ProbesOne of the most important components of the flux guide assembly that was notstudies thoroughly in this project is the tip of the sensor probes that connect thesensor to the pump. To make the wear measurements repeatable with a higher sen-sitivity, a firm and a more rigid sensor probe needs to be designed and implementedto first, minimize the contact gap between the probe and the pump, and second, tostay in contact with the pump with the presence of vibrations and external distur-bances from the surroundings. As a recommendation to overcome this problem,the designed magnetic polymer as described in Section 3.3 can be used to create anadapter on the pump for the sensor probes. The polymer can form the shape of thepump on one end to minimize any air gaps between the pump and the sensor, andon the other end, it can embody a mouth piece the same size as the sensor probes.The adapter can be bonded to the pump housing by using the magnetic epoxy asdescribed in Section 3.1.Clamping MechanismSince the body of the sensor is relatively heavy, a proper clamping mechanismneeds to be designed to hold the sensor on the pump. For this study, the sensor wasaffixed to the pump by a hanging mechanism that supported the sensor from anabove fixture. Although this method worked very well for this project, if the sensoris to be installed on every pump inside a plant, this method needs to be improved.As an example of a potential clamping mechanism, an additional C-clamp can beused over the sensor to hold the sensor on the pump. Since the size of the sensoris rather large, the additional C-clamp might need to be fabricated specifically forthis purpose.Data CollectionIt is believed that the sampling frequency plays an important role in reducing thenoise level in the output signal. As Figure 3.23 shows, the SNR is significantlyimproved when the sampling frequency is increased from 20 kHz to 500 kHz. The85sampling frequency in this project was limited to 500 kHz due to hardware limi-tations. To potentially improve the signal quality, higher sampling rates must betested and their effect on the performance of the sensor needs to be verified.Sensor CalibrationBecause of time constraints in this project, the gap inside the pump is manuallyincreased to simulate a wear effect inside the pump. To further validate the func-tionality of the sensor, the assembly needs to be installed on a pump for a longerduration to observe the effect of erosion on the output of the sensor. As an alter-native approach, the impeller can also be replaced with used impellers each havinga different depth of wear on the blades that are physically measured prior to beingplaced inside the pump.Pump EfficiencyTo monitor the effect of wear on the efficiency of centrifugal pumps and to quan-tify the energy losses associated with wear, pump efficiency needs to be monitoredalong with the impeller wear while the pump is in operation.Field TestTo make this sensor operable inside a process plant with little to no supervision,there are several additional steps that needs to be taken both on the hardware sideand the software. In regards to the physical assembly of the sensor, a more rigidand stable clamping mechanism is to be designed to ensure the sensor stays in con-tact with the pump given the potential disturbances inside an operating plant. Asfor the software, a simple program needs to be written that enables the sensor toautomatically collect data every few days and interpret the data so that the operatorcan assess the integrity of the pump without any additional work.86Bibliography[1] R. Khoie, B. Gopaluni, J. A. Olson, and B. Stoeber, “A magnetic sensor tomeasure wear in centrifugal pumps,” in SENSORS, 2015 IEEE, Nov 2015,pp. 1–4. → pages iv[2] T. Sahoo and A. Guharoy, “Energy cost savings with centrifugal pumps,”World Pumps, vol. 2009, no. 510, pp. 35–37, 2009. → pages 1[3] M. Pemberton, “Strategies for optimizing pump efficiency and lccperformance,” 2003. → pages 1[4] L. Frenning, Pump life cycle costs: A guide to LCC analysis for pumpingsystems. Hydraulic Institite & Europum, 2001. → pages 1[5] M. Holloway, C. Nwaoha, and O. Onyewuenyi, Process Plant Equipment:Operation, Control, and Reliability, ser. EngineeringPro collection. Wiley,2012. → pages 1[6] C. Lei, Z. Yiyang, W. Zhengwei, X. Yexiang, and L. Ruixiang, “Effect ofaxial clearance on the efficiency of a shrouded centrifugal pump,” Journal ofFluids Engineering, vol. 137, no. 7, p. 071101, 2015. → pages 1[7] G. Wood, H. Welna, and R. Lamers, “Tip-clearance effects in centrifugalpumps,” Journal of Fluids Engineering, vol. 87, no. 4, pp. 932–939, 1965.→ pages 2[8] Y. Khalid and S. Sapuan, “Wear analysis of centrifugal slurry pumpimpellers,” Industrial Lubrication and Tribology, vol. 59, no. 1, pp. 18–28,2007. → pages 2[9] F. Schmaljohann, D. Hagedorn, A. Bu, R. Kumme, and F. Lo¨ffler, “Thin-filmsensors with small structure size on flat and curved surfaces,” MeasurementScience and Technology, vol. 23, no. 7, p. 074019, 2012. → pages 487[10] G. Rutelli and D. Cuppini, “Development of wear sensor for toolmanagement system,” Journal of Engineering Materials and Technology,vol. 110, pp. 59–62, 1988/01/01. → pages 4[11] N. Ghosh, Y. Ravi, A. Patra, S. Mukhopadhyay, S. Paul, A. Mohanty, andA. Chattopadhyay, “Estimation of tool wear during cnc milling using neuralnetwork-based sensor fusion,” Mechanical Systems and Signal Processing,vol. 21, no. 1, pp. 466–479, 2007. → pages 4[12] H. Guerrero, “Magnetic proximity sensor for measuring gap betweenopposed refiner plates,” Patent, Aug. 21, 1990, US Patent 4,950,986. →pages 5[13] D. Dodson-Edgars, “Gap, wear and tram measurement system and methodfor grinding machines,” Apr. 11 1989, US Patent 4,820,980. → pages 5[14] N. Mitsumune, I. Saito, S. Mochizuki, Y. Abe, T. Isoyama, H. Nakagawa,T. Ono, A. Kouno, A. Sugino, and T. Chinzei, “Fundamental study todevelop a fiber-optic gap sensor for a rotary undulation pump,” Journal ofArtificial Organs, vol. 10, no. 4, pp. 231–235, 2007. → pages 5[15] S. Liang and D. Dornfeld, “Tool wear detection using time series analysis ofacoustic emission,” Journal of Engineering for Industry, vol. 111, no. 3, pp.199–205, 1989. → pages 5[16] L. Alfayez, D. Mba, and G. Dyson, “The application of acoustic emissionfor detecting incipient cavitation and the best efficiency point of a 60kwcentrifugal pump: case study,” Ndt & E International, vol. 38, no. 5, pp.354–358, 2005. → pages 6[17] P. Campbell, Permanent Magnet Materials and Their Application.Cambridge University Press, 1996. → pages 9, 15[18] L. Matsch, Capacitors, Magnetic Circuits, and Transformers, ser.Prentice-Hall electrical engineering series. Prentice-Hall, 1964. → pages25[19] C. R. Nave. (2011) Relative permeability - hyperphysics. (retrieved on09/05/2014). [Online]. Available:http://hyperphysics.phy-astr.gsu.edu/hbase/solids/ferro.html → pages 32[20] “Astm b258 - 14, specification for nominal diameters and cross-sectionalareas of AWG sizes of solid round wires used as electrical conductors.” →pages 4188[21] A. Massarini and M. K. Kazimierczuk, “Self-capacitance of inductors,”IEEE Transactions on Power Electronics, vol. 12, no. 4, pp. 671–676, Jul1997. → pages 42[22] “Gluing of ferrite cores,” 2002, (retrieved on 03/22/2015). [Online].Available: http://www.elnamagnetics.com/wp-content/uploads/library/Elna-Magnetics/Gluing of Ferrite Cores.pdf → pages 5589Appendix AComputer SimulationsA.1 Simplified ModelFor the numerical analysis of the sensor model, Comsol Multiphysics is used tomodel the pump and the sensor. For rapid modeling and the proof of concept, ini-tially a simplified model of the pump is used to derive the change in the magnitudeof the flux density as a function of the varying gap width inside the pump. Fig-ure A.1 represents the Comsol model used to plot the change in the magnetic fluxdensity as a function of the gap width for the electromagnet sensor model. Sim-ilarly, Figure A.2 is used to derive the change in the inductance of the magneticcoil as a function of the varying gap in the case of the inductance model. It canbe noticed that the inductance model does not contain a secondary air gap insidethe flux guide assembly since there is no need for a Hall-effect sensor to be in place.90Magnetic coil Hall-effect sensor Flux guide Figure A.1: Magnitude of flux density [T] inside the sensor and the simpli-fied pump for the analysis of the electromagnet sensor model generatedusing Comsol Multiphysics.91Magnetic coil Flux guide Figure A.2: Magnitude of flux density [T] inside the sensor and the simplifiedpump for the analysis of the inductance sensor model generated usingComsol Multiphysics.A.2 Advanced ModelTo monitor the magnitude of flux inside the clamping mechanism designed inChapter 2, the sensor body and the pump are modeled in Comsol Multiphysics.For the finite element simulations, the magnetic coil is excited at 100 Hz using a1 V voltage signal. Figure A.3 represents the magnitude of flux inside the sensorand the pump. As it can be noticed from the simulation model, there is no satura-tion occurring inside the flux guide geometry as the saturation flux density for theM100 material is 0.42 T.92Figure A.3: Magnitude of the flux density [T] inside the flux guide assembly.The saturation flux density for M100 material is 0.42 T93Appendix BMATLAB CodeFor this project, MATLAB software is used to derive all the analytical results pre-sented in the thesis document. For reference, only the MATLAB codes that aremore complex have been included in the Appendix section. This chapter includesthe codes related to FFT calculations, signal denoising, scatter plots, error bar esti-mation, and calibration curves.B.1 FFT CalculationThe MATLAB code generated to calculate the FFT plots represented in Section 3.4is represented below.%FFTcalculationclc%************************************************************%Read Excel Filefilename = '900RPM 50kHz - 50kS.xlsx';samp50kat50k = xlsread(filename,'sheet1','C2:C50001');%Setup Time and Sampling FreqFs = 50000; % Sampling frequency94T = 1/Fs; % Sampling periodL = 50000; % Length of signalt = (0:L-1)*T; % Time vectorf = Fs*(0:(L/2))/L;%Convert to frequency domain%FFTf50at50 = fft(samp50kat50k);Q50at50 = abs(f50at50/L); %2sidedP50at50 = Q50at50(1:L/2+1); %1sidedP50at50(2:end-1) = 2*P50at50(2:end-1);%plot FFTplotImage = figure(1);plotName = 'Sample Freq: 50kHz - Sample Num: 50kS - FFT';plot(f,P50at50);set(0,'defaulttextinterpreter','latex')xlabel('Frequency Hz','Interpreter','latex');ylabel('Magnitude - Sample Freq: 50kHz - Sample Num: 50kS - FFT',...'Interpreter','latex');%print(plotImage,'-dpdf',plotName)%************************************************************%Read Excel Filefilename = '900RPM 50kHz - 500kS.xlsx';samp500kat50k = xlsread(filename,'sheet1','C2:C500001');%Setup Time and Sampling FreqFs = 50000; % Sampling frequencyT = 1/Fs; % Sampling periodL = 500000; % Length of signalt = (0:L-1)*T; % Time vectorf = Fs*(0:(L/2))/L;%Convert to frequency domain%FFTf500at50 = fft(samp500kat50k);Q500at50 = abs(f500at50/L); %2sided95P500at50 = Q500at50(1:L/2+1); %1sidedP500at50(2:end-1) = 2*P500at50(2:end-1);%plot FFTplotImage = figure(2);plotName = 'Sample Freq: 50kHz - Sample Num: 500kS - FFT';plot(f,P500at50);set(0,'defaulttextinterpreter','latex')xlabel('Frequency Hz','Interpreter','latex');ylabel('Magnitude - Sample Freq: 50kHz - Sample Num: 500kS - FFT',...'Interpreter','latex');%print(plotImage,'-dpdf',plotName)%************************************************************%Read Excel Filefilename = '900RPM 200kHz - 1MS.xlsx';samp1Mat200k = xlsread(filename,'sheet1','C2:C1000001');%Setup Time and Sampling FreqFs = 200000; % Sampling frequencyT = 1/Fs; % Sampling periodL = 1000000; % Length of signalt = (0:L-1)*T; % Time vectorf = Fs*(0:(L/2))/L;%Convert to frequency domain%FFTf1000at200 = fft(samp1Mat200k);Q1000at200 = abs(f1000at200/L); %2sidedP1000at200 = Q1000at200(1:L/2+1); %1sidedP1000at200(2:end-1) = 2*P1000at200(2:end-1);%plot FFTplotImage = figure(3);plotName = 'Sample Freq: 200kHz - Sample Num: 1MS - FFT';plot(f,P1000at200);set(0,'defaulttextinterpreter','latex')xlabel('Frequency Hz','Interpreter','latex');ylabel('Magnitude - Sample Freq: 200kHz - Sample Num: 1MS - FFT',...96'Interpreter','latex');%print(plotImage,'-dpdf',plotName)%************************************************************%Read Excel Filefilename = '900RPM 200kHz - 50kS.xlsx';samp50kat200k = xlsread(filename,'sheet1','C2:C50001');%Setup Time and Sampling FreqFs = 200000; % Sampling frequencyT = 1/Fs; % Sampling periodL = 50000; % Length of signalt = (0:L-1)*T; % Time vectorf = Fs*(0:(L/2))/L;%Convert to frequency domain%FFTf50at200 = fft(samp50kat200k);Q50at200 = abs(f50at200/L); %2sidedP50at200 = Q50at200(1:L/2+1); %1sidedP50at200(2:end-1) = 2*P50at200(2:end-1);%plot FFTplotImage = figure(4);plotName = 'Sample Freq: 200kHz - Sample Num: 50kS - FFT';plot(f,P50at200);set(0,'defaulttextinterpreter','latex')xlabel('Frequency Hz','Interpreter','latex');ylabel('Magnitude - Sample Freq: 200kHz - Sample Num: 50kS - FFT',...'Interpreter','latex');%print(plotImage,'-dpdf',plotName)%*************************************************************97B.2 Signal Denoising and SNR CalculationOnce the FFT plot is calculated using the original time series data, the signal isdenoised and the SNR value is estimated using the MATLAB software. The MAT-LAB code used for this purpose is represented below.%Signal Denoising and SNR Measurementclear%Setup Time and Sampling FreqFs = 50000; % Sampling frequencyT = 1/Fs; % Sampling periodL = 50000; % Length of signalt = (0:L-1)*T; % Time vectorf = Fs*(0:(L/2))/L;%Read Datafilename = 'data50kHz-2MS-2-2.lvm';data = dlmread(filename);a = 1;b = L;for i = 1:numel(data)/LF = fft(data(a:b));Q = abs(F/L);P = Q(1:L/2+1);P(2:end-1) = 2*P(2:end-1);D(i,:) = P;a = a + L;b = b + L;end%Denoise signal using HAAR wavelett functionS = cmddenoise(P,'haar',10, 'h');N = P-S;%Calculate the Power Spectral DensityPS = S.ˆ2;PN = N.ˆ2;98%Integrate area below the Power Spectral Density Plot%Integrate signal @ 15HzIS15 = trapz(PS(find(f==13):find(f==17)));IN15 = trapz(PN(find(f==13):find(f==17)));SNR15 = IS15/IN15;%Integrate signal @ 30HzIS30 = trapz(PS(find(f==28):find(f==32)));IN30 = trapz(PN(find(f==28):find(f==32)));SNR30 = IS30/IN30;%Estimate SNRSNRave = (SNR15+SNR30)/2;%plot original signalplotImage = figure(1);plotName = 'Plot of the Original Signal, Denoised Signal and Noise';set(0,'DefaultTextFontSize', 15);set(0,'DefaultAxesFontSize', 15);plot(f,P, 'k','MarkerSize', 12);hold on;plot(f,S, 'b','MarkerSize', 12);plot(f,N, 'r','MarkerSize', 12);axis([0 55 0 3e-4]);plotTickLatex2D('xlabeldy', 0.02);set(0,'defaulttextinterpreter','latex')xlabel('Frequency [Hz]','Interpreter','latex');ylabel('Amplitude [V]','Interpreter','latex');%plot smooth signalplotImage = figure(2);plotName = 'Power Spectral Density Plot of the Noise and Signal';set(0,'DefaultTextFontSize', 15);set(0,'DefaultAxesFontSize', 15);plot(f,PS, 'k','LineWidth', 1);hold on;plot(f,PN, 'r:','LineWidth', 2);axis([0 55 0 30e-9]);plotTickLatex2D('xlabeldy', 0.02);99set(0,'defaulttextinterpreter','latex')xlabel('Frequency [Hz]','Interpreter','latex');ylabel('Power [$Vˆ2$]','Interpreter','latex');h = legend('Signal Power', 'Noise Power','Interpreter','latex');set(h,'interpreter','latex')set(h,'FontSize',18);legend boxoff;%plot noiseplotImage = figure(3);plotName = 'Plot of Noise';set(0,'DefaultTextFontSize', 15);set(0,'DefaultAxesFontSize', 15);plot(f,N, 'r:','MarkerSize', 12);axis([0 55 -4e-4 4e-4]);%plotTickLatex2D('xlabeldy', 0.02);set(0,'defaulttextinterpreter','latex')xlabel('Frequency [Hz]','Interpreter','latex');ylabel('Amplitude [V]','Interpreter','latex');%plot smooth signalplotImage = figure(4);plotName = 'Plot of absolute denoised signal and absolute noise signal';set(0,'DefaultTextFontSize', 15);set(0,'DefaultAxesFontSize', 15);plot(f,abs(S), 'k','LineWidth', 1);hold on;plot(f,abs(N), 'r:','LineWidth', 2);%hline = refline([0 rms(N)]);axis([0 55 -5e-6 2.4e-4]);plotTickLatex2D('xlabeldy', 0.02);set(0,'defaulttextinterpreter','latex')xlabel('Frequency [Hz]','Interpreter','latex');ylabel('Amplitude [V]','Interpreter','latex');h = legend('Denoised signal $\left|\hat{V}_{signal}\right|$',...'Noise $\left|\hat{V}_{noise}\right|$','Interpreter','latex');set(h,'interpreter','latex')set(h,'FontSize',18);100B.3 Scatter Plot Generation and Calibration CurveThe MATLAB code to generate the scatter plot and the calibration curve is pre-sented below.%Scatter Plot Data Setsclear%Setup Time and Sampling FreqFs = 500000; % Sampling frequencyT = 1/Fs; % Sampling periodL = 500000; % Length of signalt = (0:L-1)*T; % Time vectorf = Fs*(0:(L/2))/L;%Read Excel Filej = 1;for m=1:4q = 1;for k=1:10filename=[num2str(m),'-',num2str(k),'.lvm'];data = dlmread(filename);a = 1;b = L;for i = 1:numel(data)/LF = fft(data(a:b));Q = abs(F/L);P = Q(1:L/2+1);P(2:end-1) = 2*P(2:end-1);a15(j,q) = P(15+1);a30(j,q) = P(30+1);a = a + L;b = b + L;q = q + 1;101endendj = j + 1;end%Calculate mean at 15 Hzmean15(1) = mean(a15(1,:));mean15(2) = mean(a15(2,:));mean15(3) = mean(a15(3,:));mean15(4) = mean(a15(4,:));%Calculate mean at 30 Hzmean30(1) = mean(a30(1,:));mean30(2) = mean(a30(2,:));mean30(3) = mean(a30(3,:));mean30(4) = mean(a30(4,:));%Calculate STD at 15 Hzstd15(1) = std(a15(1,:),1,2);std15(2) = std(a15(2,:),1,2);std15(3) = std(a15(3,:),1,2);std15(4) = std(a15(4,:),1,2);%Calculate STD at 30 Hzstd30(1) = std(a30(1,:),1,2);std30(2) = std(a30(2,:),1,2);std30(3) = std(a30(3,:),1,2);std30(4) = std(a30(4,:),1,2);%Calculate A15 wrt weargap = [0.4 1.15 1.9 2.65];wear = mean15;gapError = [0.05 0.1 0.15 0.2];%Calculate sensitivity and resolutionSensitivity = (wear(end)-wear(1))/(gap(end)-gap(1)) * 1000delV = mean(std15) * 1000resolution = delV/Sensitivity102%Scatter Plot of Sensor Output 30 Hz versus 15 HzplotImage = figure(1);plotName = 'Scatter Plot of Sensor Output at 30 Hz versus 15 Hz';set(0,'DefaultTextFontSize', 15)set(0,'DefaultAxesFontSize', 15)plot(a15(1,:),a30(1,:), 'rx','MarkerSize', 12);hold on;plot(a15(2,:),a30(2,:), 'kˆ','MarkerSize', 12);plot(a15(3,:),a30(3,:), 'o','MarkerSize', 12,'Color',[0,0.7,0.9]);plot(a15(4,:),a30(4,:), 'bs','MarkerSize', 12);axis([0.08e-3 0.2e-3 0.4e-4 2.4e-4]);plotTickLatex2D('xlabeldy', 0.02);set(0,'defaulttextinterpreter','latex');xlabel('Amplitude @ f = 15 Hz [V]','Interpreter','latex','FontSize',18);ylabel('Amplitude @ f = 30 Hz [V]','Interpreter','latex','FontSize',18);h = legend('$l_{vg}$= 0.40mm $\pm$ 0.05mm', '$l_{vg}$= 1.15mm $\pm$ 0.10mm'..., '$l_{vg}$= 1.90mm $\pm$ 0.15mm', '$l_{vg}$= 2.65mm $\pm$ 0.20mm',...'location', 'NorthWest');set(h,'interpreter','latex')set(h,'FontSize',16);%Mean and Standard Deviation of the Sensor Output Scatter PlotplotImage = figure(2);plotName = 'Mean and Standard Deviation of the Sensor Output Scatter Plot';set(0,'DefaultTextFontSize', 15)set(0,'DefaultAxesFontSize', 15)h = errorbar(mean15(1),mean30(1),std30(1), 'rx-','MarkerSize', 12);hold on;h = errorbar(mean15(2),mean30(2),std30(2), 'kˆ-','MarkerSize', 12);h = errorbar(mean15(3),mean30(3),std30(3), 'o-','MarkerSize', 12,...'Color',[0,0.7,0.9]);h = errorbar(mean15(4),mean30(4),std30(4), 'bs-','MarkerSize', 12);herrorbar(mean15(1),mean30(1),std15(1), 'r');herrorbar(mean15(2),mean30(2),std15(2), 'k');103herrorbar(mean15(3),mean30(3),std15(3));herrorbar(mean15(4),mean30(4),std15(4), 'b');axis([0.08e-3 0.2e-3 0.4e-4 2.4e-4]);plotTickLatex2D('xlabeldy', 0.02);set(0,'defaulttextinterpreter','latex');xlabel('Amplitude @ f = 15 Hz [V]','Interpreter','latex','FontSize',18);ylabel('Amplitude @ f = 30 Hz [V]','Interpreter','latex','FontSize',18);h = legend('$l_{vg}$= 0.40mm $\pm$ 0.05mm', '$l_{vg}$= 1.15mm $\pm$ 0.10mm',...'$l_{vg}$= 1.90mm $\pm$ 0.15mm', '$l_{vg}$= 2.65mm $\pm$ 0.20mm',...'location', 'NorthWest');set(h,'interpreter','latex')set(h,'FontSize',16);%plot C1 vs C2plotImage = figure(3);plotName = 'Combined Plots first and second experiment C1 vs C2';set(0,'DefaultTextFontSize', 15)set(0,'DefaultAxesFontSize', 15)plot(gap, wear, 'kd-','MarkerSize', 12);hold on;h = errorbar(gap,wear,std15, 'k','MarkerSize', 12, 'AlignVertexCenters', 'on');herrorbar(gap,wear,gapError, 'k');plotTickLatex2D('xlabeldy', 0.02);set(0,'defaulttextinterpreter','latex');xlabel('Varying Gap Width [mm]','Interpreter','latex','FontSize',18);ylabel('Singlal Amplitude @ f = 15 Hz [V]','Interpreter','latex','FontSize',18);104Appendix CSensor OptimizationTo improve the quality of the sensor’s output signal, several methods are used asdescribed in Chapter 3. However, many of the methods used did not significantlyaffect the signal quality. This section will go into the detail of the cases not men-tioned in the body of the thesis.C.1 Permanent Magnet Geometry OptimizationTo select the best suitable sensing technique, three different techniques were con-sidered as described in Section 2.2. To ensure that each method is optimized toderive the best performance possible in the comparison, the geometry of the perma-nent magnet in the permanent magnet model sensor needs to be optimized. Sincethis method is not used for the sensor, the derivation of the technical calculation isonly included in the Appendix section of the thesis. To optimize the geometry, theratio between the magnet’s length and cross-sectional areag =lmagnetAmagnet(C.1)is considered as a single parameter. The slope of the load-line equation of themagnet105ml =BmHm=− glvgµ0Avg +ℜconst(C.2)is also written as a ratio between the operating flux density Bm and the operatingfield intensity Hm. By combining the equation for the demagnetization curve of thepermanent magnet as shown in Equation 2.15 and the magnet’s load-line equation,the operating magnetic flux densityBm =mlHcBrmlHc−Br (C.3)can be written in terms of the slope of the load-line equation ml , magnet’s remanentflux density Br, and the magnet’s coercivity Hc. To maximize the change in theoperating flux density as the reluctance of the magnetic circuit varies from theinitial reluctance ℜi to the final reluctance ℜ f , the change in the flux density∆Bm = Bm(@lvg=0.65mm)−Bm(@lvg=2.50mm) (C.4)is calculated as the varying gap lvg increases. By solving this equation for thegeometric ratio of the permanent magnet g in the load-line equation, the ratiog = µ√ℜiℜ f (C.5)can be written in terms of the initial and final reluctance values as stated in Equa-tion 2.19.C.2 Signal Quality ImprovementAs mentioned in Section 3.4, to calculate the peak amplitudes used for the scatterplot as shown in Figure 3.27 four different techniques are used. First method is tosimply take the amplitude voltage at 15 Hz and 30 Hz and plot them against eachother. To potentially improve the quality of the scatter plot, the ratio of the peakamplitude can also be calculated with respect to the amplitude of the FFT plot at70 Hz which is the sensor’s excitation frequency. Figure C.1 shows the resultingscatter plot. As it can be seen, the resulting plot is not much improved from the106original plot.Amplitude @ f = 15 Hz [V] ×10-30.7 0.8 0.9 1 1.1 1.2 1.3 1.4Amplitude@f=30Hz[V]×10-30.40.60.811.21.41.61.82lvg= 0.40mm ± 0.05mmlvg= 1.15mm ± 0.10mmlvg= 1.90mm ± 0.15mmlvg= 2.65mm ± 0.20mmFigure C.1: Scatter plot of the ratio of signal at 30 Hz over 70 Hz versus thesignal ratio of 15 Hz over 70 Hz at various gap widths.Another method to obtain the scatter plot is to evaluate the ratio of the peakamplitude at both frequencies with the RMS value of the signal noise at each mea-surement point. Figure C.2 represents the scatter plot referenced to this technique.107Amplitude @ f = 15 Hz [V] ×10-40.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8Amplitude@f=30Hz[V]×10-40.40.60.811.21.41.61.822.22.4lvg= 0.40mm ± 0.05mmlvg= 1.15mm ± 0.10mmlvg= 1.90mm ± 0.15mmlvg= 2.65mm ± 0.20mmFigure C.2: Scatter plot of the ratio of signal at 30 Hz and 15 Hz over theRMS value of noise.Lastly, the scatter plot can also be derived form the difference between theoriginal signal and the noise calculated through the means of wavelet denoisingfunction in MATLAB. Figure C.3 represents the scatter plot of the peak ampli-tudes at 15 Hz and at 30 Hz for the denoised signal.108Amplitude @ f = 15 Hz [V] ×10-40.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8Amplitude@f=30Hz[V]×10-40.40.60.811.21.41.61.822.22.4lvg= 0.40mm ± 0.05mmlvg= 1.15mm ± 0.10mmlvg= 1.90mm ± 0.15mmlvg= 2.65mm ± 0.20mmFigure C.3: Scatter plot of the denoised amplitude at 30 Hz versus the de-noised amplitude at 15 Hz at various gap widths.109

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