NEW APPROACHES FOR UTILIZING PLANAR INDUCTIVE SENSORS FOR
GAP MEASUREMENT PROXIMITY AND LUBRICANT OIL WEAR DEBRIS
MONITORING
A Dissertation
Presented to
The Graduate Faculty of the University of Akron
In Partial Fulfillment
Of the Requirements for the Degree of
Doctor of Philosophy
Dian Jiao
May, 2021
i NEW APPROACHES FOR UTILIZING PLANAR INDUCTIVE SENSORS FOR
GAP MEASUREMENT PROXIMITY AND LUBRICANT OIL WEAR DEBRIS
MONITORING
Dian Jiao
Dissertation
Approved: Accepted:
Advisor Department Chair Dr. Jiang Zhe Dr. Sergio Felicelli
Committee Member Interim Dean of the College Dr. Jae-Won Choi Dr. Craig Menzemer
Committee Member Dean of the Graduate School Dr. Shengyong Wang Dr. Marnie Saunders
Committee Member Date Dr. Hongbo Cong
Committee Member Dr. Yi Pang
ii ABSTRACT
Planar inductive sensors have been widely used in non-contact displacement measurement applications. Due to their advantages such as low cost, easy installation, high accuracy, and stability in harsh environments, planar inductive sensors are typically used to measure turbine blade tip clearance, the displacement of metal parts in belts, and the movement of robots/manipulators. However, the planar inductive sensors has a lot of limitations. First, when the material, size, or shape of the target is changed, the calibration curve needs to be rebuilt since the eddy current varies in different materials. Second, the inductive sensor which has a high sensitivity always needs a high frequency excitation signal. This means that when using the inductive sensor in industrial applications, several high performance support instruments need to be used with the sensor, such as high sampling rate data acquisition system and multi-channel power source. All these limitations cause a lot of inconvenience while using the planar inductive sensor.
To overcome the above problems, we first presented a new method for planar inductive sensors to measure the gap between the sensor and a non-ferrite metallic target.
The eddy current on the target plate was modeled as a virtual coil. The mutual inductance between the sensing coils and the virtual coil was calculated. From our analysis, we found that when the target material is changed, the new calibration curve can be obtained by adding a constant to the base calibration curve. To verify the validity of the method, three planar inductive sensors with different dimensions were manufactured and used to measure
iii the gap from four different non-ferrite targets (Cu, Al, Zn, and Ti). Results showed that the new calibration method has a small error of 3.2% in the 500 – 5000 μm measurement range.
Second, in order to extend the new calibration method to any shape/size of the target, we presented an improved method to measure the gap from an irregular and narrow target.
The magnetic field distribution on an irregular and narrow target was numerically studied, suggesting the induced eddy current on the target can be modeled as a virtual planar coil.
The gap was calculated from the mutual influence of the sensing and virtual coils. We found that the calibration curves are parallel for targets of different materials. Therefore, for a narrow and irregular target, the calibration curves corresponding to different materials can be obtained by adding a material constant to the base curve. To validate the approach, three planar coils of different sizes were tested with four metallic turbine blade shaped targets. Results showed that the measured gaps matched well with the actual gaps, with a maximum error of about 3.703%.
Finally, a multi-sensing system using planar inductive sensors was designed to monitor the wear debris in lubrication oil, which is indicative of a machine’s health status.
Several unique features were applied to the design of the sensing system including 1) parallel sensing via multiple sensing channels in order to improve the detection throughput,
2) use of an under sampling method in order to significantly reduce the amount of data to be collected, and 3) a new multi-layer structure to increase the sensitivity of the sensing system (25 μm diameter iron particles with 1470 μm inner diameter sensing tube). Testing results indicate that the amount of data size is dramatically reduced by nearly 20 times without scarifying the sensitivity. The sensor array is suitable for online wear debris monitoring. iv TABLE OF CONTENTS
Page
LIST OF FIGURES ...... ix
LIST OF TABLES ...... xiv
CHAPTER
I. INTRODUCTION AND RESEARCH OBJECTIVES ...... 1
I.1 Introduction ...... 1
I.2 Motivation ...... 2
I.3 Research Objectives ...... 5
I.4 Summary ...... 7
II. BACKGROUND AND LITERATURE REVIEW ...... 9
II.1 Review of Non-Contact Displacement/Position Measurement Method ...... 9
II.1.1 Capacitive Method and Measurement Systems ...... 10
II.1.2 Optical Sensors and Measurement Systems ...... 11
II.1.3 Ultrasonic Method and Measurement System ...... 13
II.2 Inductive Proximity Sensors ...... 15
II.2.1 Inductive Proximity Sensor Based on a 3D Sensing Coil ...... 16
II.2.2 Working Principle of 3D Inductive Proximity Sensors ...... 17
v II.2.3 Inductive Proximity Sensor Based on a Planar Sensing Coil ...... 20
II.2.4 Working Principle of a Planar Inductive Proximity Sensor ...... 21
II.2.5 Traditional Calibration Process for Inductive Proximity Sensor ...... 23
II.3 Study of Mathematical Model of Planar Coil Induction ...... 25
II.4 The Displacement Measurement Requirements from Narrow and Irregular Target ...... 29
II.5 Study of Wear Debris Monitoring Sensor...... 31
II.5.1 Study of Wear Debris Sensors Based on Gill Sensor ...... 33
II.5.2 Study of Wear Debris Sensors Based on Inductive Sensing ...... 35
III. NEW CALIBRATION METHOD FOR PLANAR INDUCTIVE SENSORS BASED ON CALCULATING MUTUAL INDUCTANCE ...... 40
III.1 Calculation Method Based on Mathematical Model ...... 43
III.2 Method to Solve the Gap from Mutual Inductance ...... 53
III.3 Experimental Setup and Preparation ...... 54
III.4 Measurement and Calculation Results ...... 57
III.5 Validation of the Gap Measurements with the 푁1/푁2- 푑 Curves ...... 63
III.6 Discussion ...... 69
III.7 Summary ...... 71
IV. A NEW APPROACH FOR GAP MEASUREMENT FROM NARROW AND IRREGULAR TARGETS ...... 74
IV.1 Mathematical Model Analysis ...... 76
vi IV.1.1 FEA Method ...... 76
IV.1.2 Working Principle ...... 82
IV.2 Experimental Setup ...... 87
IV.3 Results and Discussions ...... 90
IV.3.1 Calibration ...... 90
IV.3.2 Error Analysis ...... 97
IV.4 Summary ...... 102
V. AN ADVANCED SENSOR ARRAY FOR WEAR DEBRIS MONITORING IN LUBRICANT OIL ...... 104
V.1 Design Concept for Single-Sensing Channel ...... 107
V.1.1 Design of Multi-layers Planar Inductive Sensing Coil ...... 107
V.1.2 Measurement Circuit ...... 111
V.1.3 Under-sampling Signal Processing Method ...... 116
V.2 Device Design ...... 119
V.3 Device Calibration and Validation ...... 122
V.3.1 Calibration Process ...... 122
V.3.2 Device Validation ...... 126
V.4 Conclusion ...... 134
VI. CONCLUSIONS AND FUTURE WORK ...... 136
VI.1 Conclusions ...... 136
vii VI.2 Future Works ...... 140
REFERENCE ...... 142
viii LIST OF FIGURES
Figure ...... Page
II.1. (a) The design and (b) working principle of capacitive proximity sensors...... 11
II.2. The working principle of an optical proximity sensor...... 12
II.3. The working principle of an ultrasonic proximity sensor...... 14
II.4. Illustrations of (a) Blade tip clearance monitoring and (b) milling tool displacement measurement using a inductive proximity sensor [43]...... 16
II.5. Typical structure of an inductive proximity sensor using a 3D sensing coil...... 17
II.6. Working principle of a 3D inductive proximity sensor...... 18
II.7. 3D inductive proximity sensor with a ferromagnetic coil [44]...... 19
II.8. The improved design of 3D inductive proximity sensors[44]...... 20
II.9. (a) Mathematical model and (b) the impedance of a planar inductive sensing coil. . 21
II.10. (a) The magnetic flux line of the planar sensing coil [67], and (b) the eddy current on the target near the sensing coil...... 23
II.11. (a) Examples of calibration curve for a planar inductive sensor and (b) linearization for a polynomial [64]...... 25
II.12. (a) The magnetic flux of a planar sensing coil [67]. (b) The eddy current distributions in an infinite plate target...... 26
II.13. The equivalent circuit of mutual influence between the sensing and virtual coils. 26
II.14. Monitoring the blade tip clearance using planar inductive sensor. The target has a narrow and irregular shape...... 30
II.15. Relationships of wear debris size, concentration, and machine conditions [71]..... 32
ix II.16. Metal wear debris in lubricant oil [72]...... 32
II.17.Gill sensor and the design of the inductive sensor...... 34
II.18. Working principle of the 3D solenoid inductive sensor [11]...... 36
II.19. Schematic of the 2-layer coil inductive sensor [79]...... 37
II.20. (a) Wear debris monitoring system with (b) multiplexing method [79]...... 39
III.1. (a) Working principle of gap measurement. Eddy current is generated in the target metal plate and causes an inductance change of the sensing coil. (b) The eddy current effect can be modeled as a virtual planar coil on the target plate. (c) Equivalent circuit model of the measurement system. (d) Mathematical model in Neumann’s formula [84] to calculate mutual inductance between the two coils. 44
III.2. Illustration of a 3D coil with multiple layer...... 45
III.3. Illustration of a planar disk coil...... 45
III.4. (a) Equivalent circuit model of the measurement system. (b) Mathematical model in Neumann’s formula to calculate mutual inductance between the two coils...... 48
III.5. Illustration of the experiment setup and a picture of one coil made of copper wire. A 500 µm thick ceramic layer was applied on top of the coil surface to protect the sensing coil and keep the shape of the coil so that the coil’s base inductance remains ...... 55
III.6. (a) Measured inductance of sensing coil 1 as a function of the gap d between the sensing coil and the target metal plate. (b) Calculated number of turns of the virtual coil as a function of the gap ...... 57
III.7. (a) Calculated N1/N2 as a function of the gap (d) between the sensing coil and the target metal plate. The N1/N2 - d curve shifts with a parallel distance C when target material is changed. (b) The constant C for zinc, aluminum and copper ...... 59
III.8. (a) Calculated N1/N2 as a function of d for sensing coils 2. (b) The constant C for zinc, aluminum and copper targets...... 61
III.9. (a) Calculated N1/N2 as a function of d for sensing coil 3. Figure III.7, III.8, and III.9 showing that N1/N2 – d curves for different materials are in parallel. There is a constant parallel distance between the two curves for different materials. (b) The constant C for zinc, aluminum and copper targets...... 62
x III.10. Comparisons of the calculated gaps (from equation 27) to the actual gaps. (a) Gap between sensing coil 1 and the zinc target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.0669. (b) Gap between sensing coil 1 and the aluminum target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.1009. (c) Gap between sensing coil 1 and the copper target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.1333...... 66
III.11. Comparisons of the calculated gaps to the actual gaps. (a) Gap between sensing coil 2 and the zinc target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.0413. (b) Gap between sensing coil 2 and the aluminum target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.0601. (c) Gap between sensing coil 2 and the copper target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.0749...... 67
III.12. Comparisons of the calculated gaps to the actual gaps. (a) Gap between sensing coil 3 and the zinc target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.0729. (b) Gap between sensing coil 3 and the aluminum target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.1096. (c) Gap between sensing coil 3 and the copper target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.1443...... 68
IV.1. Comparison in the inductance variation of the sensing coil as a function of the gap, by LCR measurement and FEM simulation...... 77
IV.2.Eddy current distribution on the target (unfolded vision), with the tip clearance as 1 mm...... 78
IV.3. Eddy current distribution on the target (unfolded vision), with the tip clearance as 1.5 mm...... 79
IV.4.Side view and isometric view of the turbine blade used in the simulations and the experiments...... 80
IV.5. Eddy current distribution on the blade target, with the tip clearance as 1 mm...... 81
IV.6. Working principle and simulations of the gap measurement for a narrow target: (a) Schematic sketch of working principle of the gap measurement for a narrow target. (b) Simulated magnetic flux density distribution when flipping the side surface to the top surface by finite element analysis. (c) Gap/displacement measurement can
xi be modeled as a configuration of two coaxial planar coils, namely, sensing coil (top) and virtual coil (bottom). (d) Equivalent circuit of coil to coil system...... 84
IV.7. Experiment setup of the gap measurement for a narrow and irregular target...... 86
IV.8. Working principle of blade target gap measurement and the design of the narrow and irregular shaped blade target: (a) Schematic sketch of gap measurement configuration between a sensing coil and a narrow and irregular shaped blade target. (b) Side view and isometric view of the blade target...... 88
IV. 9. Measured inductance and calculated 푁2 of sensing coil 1 (14.20 mm) as a function of the gap 푑 for four targets made of different materials (titanium, zinc, aluminum, and copper)...... 91
IV.10. 푁1/푁2 curves and constant C of four different target materials for coil 1: (a) 푁1/푁2 curves obtained from sensing coil 1 for four different target materials. (b) Constant C for the four target materials with sensing coil 1...... 92
IV.11. 푁1/푁2curves and constant C of four different target materials for coil 2: (a) 푁1/푁2 curves obtained from sensing coil 2 for four different target materials (b) Constant C for the four target materials with sensing coil 2...... 94
IV.12. 푁1/푁2 curves and constant C of four different target materials for coil 2: (a) 푁1/푁2 curves obtained from sensing coil 3 for four different target materials (b) Constant C for the four target materials with sensing coil 3...... 97
IV.13. Ratios of the calculated 푑 over the actual 푑 between sensing coil 1 and the irregular blade targets made of: (a) Zinc, (b) Aluminum, and (c) Copper. The maximum errors for the zinc, aluminum, and copper targets were 3.681%, 3.108%, and 3.148%, respectively...... 100
IV.14. Ratios of the calculated 푑 over the actual 푑 between sensing coil 2 and the irregular blade targets made of: (a) Zinc, (b) Aluminum, and (c) Copper. The maximum errors for the zinc, aluminum, and copper targets were 3.395%, 3.703%, and 2.535%, respectively...... 101
IV.15. Ratios of the calculated 푑 over the actual 푑 between sensing coil 3 and the irregular blade targets made of: (a) Zinc, (b) Aluminum, and (c) Copper. The maximum errors for the zinc, aluminum, and copper targets were 2.916%, 3.269%, and 2.584%, respectively...... 102
V.1. The design of the multi-layers inductive sensing coil...... 108
xii V.2. The analysis of sensitivity of the coil with different number of layers and turns. .. 109
V.3. Regular circuit (a) and LC circuit (b) for measurement...... 113
V.4. The change of total impedance with regular circuit and LC circuit when the sensing coil has a inductance and resistance of (a) 900 nH and 3 Ω, and (b) 1000 nH and 2 Ω...... 114
V.5. Signal re-construction using the cubic spline method...... 118
V.6. The details of construction and parts of the sensing device...... 120
V.7. The surface area of the particles measured from digital microscope (VHX-7000, Keyence Co., Osaka, Japan)...... 123
V.8. Illustration of the experiment setup which includes a linear stage, a single sensing tube, a measurement circuit, a power source, and a DAQ device...... 123
V.9. Relative output voltage pulses for 25.1 μm, 35.7 μm, 45.2 μm, 56.4 μm, 65.1 μm, and 75 μm diameter iron particles...... 124
V.10. The calibration curve of relative voltage for iron particles ranging from 25.1 μm to 75 μm in diameter...... 125
V.11. Measured relative voltage change caused by iron particles with size of 70±5 μm diameter...... 127
V.12. Measured relative voltage change caused by iron particles with size of 50±5 μm diameter...... 128
V.13. Measured relative voltage change caused by iron particles with size of 30±5 μm diameter...... 129
V.14. The TP value of debris monitoring devices from the past 10 years [78,105,113–117]...... 131
V.15. Results of 30 ppm (a) and 20 ppm (b) concentration test. Three different sizes of iron particles, 50±5 μm, 60±5 μm, and 70±5 μm were used for each test...... 133
xiii LIST OF TABLES
Table Page
III.1 The dimensions and parameters of the three sensing coils used in the experiments. 60
IV.1 Mesh setup (cubic target)...... 76
IV.2 Mesh setup (cubic target)...... 78
IV.3 Mesh setup (blade target)...... 80
IV.4 The geometries and the excitation voltage/frequency of the three coils employed .. 88
IV.5 The value of 퐶 of three coils for the blade target...... 97
xiv CHAPTER I
INTRODUCTION AND RESEARCH OBJECTIVES
I.1 INTRODUCTION
Inductive sensing systems have been widely used to detect the thickness, displacement and position of objects by using the electro-magnetic induction principle [1].
Since 1831 and 1832, when Michael Faraday and Joseph Henry discovered the magnetic induction phenomenon, people have realized that electromagnetic induction has huge potential in noncontact measurement applications [2]. However, the early devices, limited by fabrication, low signal processing speed and huge amount of data collection, only included electric generators, current clamps, and transformers [3]. With the advancement of fabrication and signal processing technologies, inductive sensing systems have been rapidly developed in recent years and are widely used in a variety of applications. For example, inductive proximity sensors are commonly used to calibrate the position of machine parts instead of using a contact sensor [4]. In addition, inductive sensors are used to measure the thickness of metal films without contact [5]. There is no doubt that inductive sensing systems will be applied to more and more applications in the future.
1 Among all the types of inductive sensors, planar inductive sensors have been utilized in a variety of applications such as measurements of gap/displacement, thickness, and surface treatment [6,7]. Benefiting from their working principle, inductive proximity sensors exhibit excellent performance in wet, dirty, and high-temperature environments
[8], and also provide reliable and non-contact measurement in displacement with micro and nano meter resolutions. For example, planar inductive proximity sensors are suitable for measuring gaps from large objects that can be considered as infinite plates, such as the displacement of the metal table in CNC machines, the thickness and position of the metal plate in casting processes, and the movement of large industrial manipulators [9].
Additionally, inductive proximity sensors with ceramic packages were designed to detect the tip clearance of turbine blades in high temperature environments [10]. The sensor is required to measure the blade target without any contact and survive in a high temperature environment (generally around 1300K).
I.2 MOTIVATION
Although planar inductive sensors have many advantages and are widely used in displacement and position measurement, the limitations are also obvious and formidable.
An inductive proximity sensor relies on the sensor’s calibration process [11]. To measure the gap or displacement between a sensing coil and a target metal plate, an AC signal is applied to the sensing coil and a magnetic field is generated. When a metal plate is present near the sensing coil, an eddy current is induced in the metal plate, which generates a magnetic field opposite to that generated by the sensing coil. In turn it causes an inductance
2 decrease of the sensing coil, which can be measured in terms of output voltage. The smaller the gap, the larger the decrease in the inductance. Traditionally inductive sensors rely on calibrating the relations between the coil inductance and the gap [12]. From the calibration curves, unknown gaps can be back calculated from the measured coil inductance without calculating the complex mutual inductance between the sensing coil and a target plate.
However, there are two limitations of the tradition calibration methods. First, if a target material is changed, the calibration curve needs to be rebuilt since the eddy current will vary in a different material [12]. This is also true for measuring the gap from a metallic target at various temperatures [10]. This means that the tedious calibrations have to be conducted in order to obtain a family of calibration curves for each material or at each measured temperature. Second, because of the complex relationship between the inductance and the gap, in order to provide good accuracy and simplify the calculations the calibration curves are typically divided into discrete sections; each section covers a small gap range which can be approximated as a straight line. While using separate sections of calibration curves can provide accurate measurements [12], calibration needs to be done at many gaps with fine incremental steps, making the calibration very time consuming. In addition, if one does not know the exact range of the gap to be measured, choosing an incorrect section of the calibration curve may cause a large measurement error.
Traditional gap measurement relies on establishing a calibration curve between the inductance variation of the planar coil and the displacement, which is usually established with an infinite target plate[13,14]. One limitation of planar inductive proximity sensors is that they always require the measured area of the target to be at least twice as much as that of the sensing coil [15] so that the target can be considered as an infinite plate. When the 3 target is narrower than the sensing coil, one has to either use a smaller sensor or recalibrate the sensor with the narrow object since the eddy current will be different in the narrow object. Further, if the target material is changed, the calibration curve also needs to be rebuilt to reflect the conductivity change. Therefore, a set of calibration curves corresponding to various materials needs to be established for an inductive sensor, which is undoubtedly a tedious and complex process.
To address the above calibration problems, efforts have been made to evaluate the gap based upon studying the mutual inductance between the sensing coil and the target plate. Several new calibration methods or algorithms were attempted by different researchers [5,10,16]. Because the calculation of the mutual inductance is complex and contains many unknowns, most of these prior methods were used to qualitatively evaluate the influence of one parameter/condition on the gap measurement, but cannot be used to calculate the gap from the inductance change mathematically [6]. More importantly, all these methods are only applicable for gap measurements from infinite plate targets, and cannot be used for gap measurements from narrow and irregular objects. Therefore, simplifying the calibration process of planar inductive proximity sensors for measuring gaps from objects with arbitrary sizes and shapes is of utmost importance for many applications.
The calibration process in gap measurement is not the only limitation that planar inductive sensors face. When applied to other non-contact measurement applications, they also have other problems such as the big data that cannot be ignored. On example is using planar inductive sensors to monitor the wear debris in lubricant oils. The size and
4 concentration of metallic wear debris are representative of a machine’s health status. To detect small wear debris (e.g. in the range of 20 microns to 500 microns, the sensing coil needs an AC excitation frequency of ~ 2 MHz [17]. With such a high frequency excitation signal, the sampling rate of the data acquisition board needs to be ~ 50 MHz or higher so that the inductive pulse induced by the debris signal can be fully captured. However, such a high sampling frequency will ultimately result in a large volume of data. Since an inductive pulse sensing array is typically used to process a large-volume oil sample, the size of the data will be increased even further. As an example, with a 50MHz sampling frequency, 10.8 Terabytes of data would be generated within one hour when using a 10- channel sensor. It is a significant challenge to process such a large volume of data in real time. However, this is critical for online machine condition monitoring. An oil debris sensing array with real time data processing capability that significantly reduces the amount of data while keeping decent sensitivities and doesn’t lose any useful debris information is highly desired. Finally while wear debris could be come from different metallic coatings (e.g. iron, copper, zinc, etc), the calibration process could be potentially applied to wear debris detection to simplify size measurement of wear debris.
I.3 RESEARCH OBJECTIVES
This thesis aims to address the above mentioned technical challenges. The specific research objects are:
Part I Research a new calibration method for using planar inductive sensors to measure gaps from infinite plate targets based on calculating the mutual influence.
5 Analyze the relations between the planar sensing coil and a metal target based
on the Maxwell induction magnetic model.
Establish a new mathematical transfer model based on coil-to-coil theory and
analyze the parameters in a mathematical model.
Propose a reasonable assumption to reduce the parameters and solve the
governing equation of the coil-to-coil system based on the assumption.
Use the new method to calibrate the planar inductive sensor, and then measure
the gap from plate targets made of different materials.
Demonstrate that planar inductive sensors with this new calibration method can
precisely measure the displacement of the targets made of different materials.
Part II Research a new calibration method development for planar inductive sensors to measure the gaps from an irregular and narrow target.
Analyze the magnetic flux distribution on a target that is smaller than the planar
sensing coil.
Develop a new assumption based on FEM so that the coil-to-coil model can be
applied to a narrow and irregular target.
Establish a mathematical transfer model for the gap measurement from a narrow
target and analyze the parameters in a mathematical model.
Design a new calibration method for using planar inductive sensor for gap
measurement from narrow and irregular objects.
6 Test the new calibration method by measuring the narrow and irregular targets
made of different materials, and demonstrate the new calibration method only
contains small errors.
Part III Develop a new planar inductive sensor array for wear debris monitoring in lubricant oil with high speed and high sensitivity.
Design a new multi-layers planar inductive sensor based on transfer function of
sensitivity of the planar sensing coil.
Study the under-sampling method in combination with an LC resonant circuit
to increase the sensor’s sensitivity and reduce the sampling frequency.
Demonstrate the single-sensing channel has high sensitivity and establish the
calibration curve with known size of the wear debris in static conditions.
Test the multi-channel sensing system in continuous oil flow with wear debris.
Demonstrate the accuracy of the multi-channel sensing system in wear debris
concentration measurement.
I.4 SUMMARY
The rest of the dissertation thesis will be arranged as the following. The displacement measurement methods will be reviewed in Chapter II. The working principle and traditional calibration methods of inductive sensors will also be reviewed in the same chapter. In Chapter III, the mathematical transfer model of an inductive planar coil sensor for displacement measurement will be presented and analyzed. The details of the
7 assumptions and the algorithm of the new calibration method will be explained in Chapter
III as well. At the end of Chapter III, a set of experimental results will be provided to validate the new calibration method. Chapter IV presents the new assumption, new mathematical model, and algorithm that can be used to measure the displacement from a narrow and irregular target. A set of experimental results are presented to demonstrate the feasibility and accuracy of the new method. Chapter V focuses on developing a new wear debris sensor array based on planar inductive sensing. A set of experimental results will be provided to demonstrate the new wear debris sensor array has a higher sensitivity and less collected data. Chapter VI summarizes the work that has been done and the future research directions.
8 CHAPTER II
BACKGROUND AND LITERATURE REVIEW
II.1 REVIEW OF NON-CONTACT DISPLACEMENT/POSITION MEASUREMENT
METHOD
Non-contact displacement sensors are used for many applications where the measurement of untouchable metal targets movement/position are required [18,19]. They are commonly used in machine automation, the aerospace industry, and hydraulics
[20][21]. The benefits of non-contact displacement sensors include accurate measurements, easy installation, low cost, and fast response times [22]. There are several types of non-contact sensors for gap measurements including capacitive, inductive, optical, and ultrasonic sensors. Each of them has its advantages and disadvantages, and is suitable for specific applications and environments. The details of each type of non-contact measurement sensor, such as its working principles, limitations, and applications, are all introduced in the next section.
9 II.1.1 Capacitive method and measurement systems
Capacitive sensors are widely used for noncontact measurement of displacement, position, and thickness of metallic objects. They have high resolutions and stabilized output signals [23]. The working principle of a capacitive sensor is simple (Shown in Figure II.1)
[24]. A sensing metal plate is installed at the head of the sensor and connected with a measurement circuit which contains an oscillator, a trigger circuit, and an output switching device. When an AC excitation is applied, an electrostatic field will be generated between the sensing plate and the target plate. When the gap between the sensing plate and the target plate is changed, the capacitance between them is changed and can be estimated by equation II.1 [25]:
퐴 퐶 = 휀 II.1 푑
Where 푑 is the gap between the sensing plate and the target, 퐴 is the overlap area of the two conductive plates, 휀 is the dielectric complex permittivity between two plates which can be expressed as 휀0 × 휀푟. 휀0 is the base level of permittivity in free space and is always equal to 1. 휀푟 is the relative permittivity. In equation II.1, 퐶 increases as there is a decreasing of 푑. When the capacitor (formed by sensing plate and target plate) affects the output signal of the oscillating circuit, the variance of the gap can be determined from that output signal.
10
Figure II.1. (a) The design and (b) working principle of capacitive proximity sensors.
Although the capacitive sensor has high resolution, long detecting range, and enables noncontact measurement, its drawback is also fatal. The variance of the capacitance is affected by relative permittivity 휀 [26]. Any variation in medium between the two plates caused by temperature, particle concentration, or moisture will change the 휀 value. Measurement error could also be induced by parasitic capacitance in the measurement, in particular when the base capacitance is small [27].
II.1.2 Optical sensors and measurement systems
Although there are several of types of optical displacement sensors such as position-sensitive diodes (PSD) sensors, charge coupled device (CCD) sensors, and complementary metal oxide semiconductor image (CMOS) sensors [28], the working 11 principles of them are similar: they are all based on measuring the angle of reflecting light
[29]. As shown in Figure II.2, when the position of the light source is fixed at the head of sensor, different gaps between the target and the sensor will induce a different angle of reflected light. By measuring the reflecting angle using a receiver, the position of the target can be determined.
Figure II.2. The working principle of an optical proximity sensor.
With the highest resolution and fastest process speeds, optical proximity sensors are always used to measure static targets in industrial applications [30]. However, they are easily affected by external conditions [31]. For example, the sensing range is affected by the color and reflectivity of the target [32]. In addition, because of lens contamination over the course of time, the optical sensor needs frequent services and cannot work in harsh environments [33].
12 II.1.3 Ultrasonic method and measurement system
The ultrasonic proximity sensors in early years were limited by their high cost and large size [34]. Recently, following the development of integrated chip technology, fabricating an ultrasonic wave source in a small chip has become easier and cheaper [35].
Therefore, the ultrasonic proximity sensor is becoming another choice for noncontact displacement measurement applications. Similar to the optical proximity sensor, an ultrasonic wave is emitted by an ultrasonic wave generator installed at the head of the sensor, and a receiver is used to receive the waves reflected from the target [36]. As shown in Figure II.3, the gap between the sensor’s head and the target is L, the time from the ultrasonic source to target is T, and the speed of the wave is C. The relationship between those parameters can be expressed as:
1 퐿 = ∙ 퐶 ∙ 푇 II.2 2
If the wave speed is a constant, and the time 푇 is precisely measured, then the distance L between the sensor and the target can be calculated easily.
13 Figure II.3. The working principle of an ultrasonic proximity sensor.
Even though ultrasonic proximity sensors can provide precise displacement measurements, the use of ultrasonic sensors is not yet common because of their disadvantages. First, it is very sensitive to temperature variation as a temperature variation will change the sound waves travelling speed [37]. Second, it is very difficult to receive the desired reflections from soft, narrow, irregular, or thin targets [38] due to refraction effect from these targets.
14 II.2 INDUCTIVE PROXIMITY SENSORS
Inductive proximity sensors, as one type of non-contact displacement/position measurement devices, are widely used in advanced industrial applications including the measurement of the position of metal parts on a belt, the movement of manipulators, and the thickness of metal plates during casting [39]. Compared to other types of non-contact displacement measurement sensors such as optical, capacitance, and ultrasonic, inductive proximity sensors have obvious advantages. Because the direction and magnitude of the magnetic field can always stay steady even if the transmitters between the sensor and target is changed, inductive proximity sensors are suitable for measurement tasks in harsh environments with high temperature, or environments containing large amounts of dust or liquid [40][41]. Also, because of their simple fabrication and relatively small size, inductive proximity sensors have low cost and can be installed in a narrow space [2].
Benefitting from their fast response time, an inductive proximity sensors can also be used to not only measure the static gap, but also monitor the dynamic positions of a target in motion [42]. Figure II.4 (a) illustrates how the inductive proximity sensor can be used to monitor the dynamic tip clearance of turbine blades [43]. The sensor probe is installed parallel to the inner surface of the casing and can detect tip clearances in the range of 0 to
3mm with a resolution under 10 microns, at a ~20000 rpm rotation speed. Figure II.4 (b) shows the inductive proximity sensor installed at a milling machine being used for detecting the position of the milling tools. In the upper left corner of II.4(b), the calibration curve between the sensor’s inductance and target’s position is also illustrated. Users can recognize if the target/tool is at the correct position from the sensor output in terms of the
15 calibration curve. In addition, several types of sensing coils, such as the 2D planar coil, 3D coil, moving coil, and Rogowski coil were all developed for different proposes [44].
Among them, the 3D coil is the most commonly used sensing coil used in inductive proximity sensors. The details of the 3D coil structure will be introduced in next section.
Figure II.4. Illustrations of (a) Blade tip clearance monitoring and (b) milling tool displacement measurement using a inductive proximity sensor [43].
II.2.1 Inductive proximity sensor based on a 3D sensing coil
The 3D Inductive proximity sensor was first developed by Kohler, H. as a metal detector [45]. Now, it has assisted mankind in analyzing and controlling thousands of functions for many decades. The details of the 3D coil inductive proximity sensor are shown in Figure II.5, which consists of a 3D sensing coil, a control and amplification circuit, and a data acquisition system [46]. The fabrication process is simple, and the winding materials such as copper, aluminum, gold and silver are also commonly available
[47][48]. With these advantages, 3D inductive sensors occupy a large portion of the market.
16
Figure II.5. Typical structure of an inductive proximity sensor using a 3D sensing coil.
II.2.2 Working principle of 3D inductive proximity sensors
The working principle of 3D inductive proximity sensor is straightforward. In short, when applying an AC signal, a magnetic field will be generated from the sensing coil [49].
When a nonferrous metal target is present in the magnetic field, an eddy current will be induced on the target with a penetration depth, and generates another magnetic field which has an opposite direction to the magnetic field from the sensing coil. Therefore, the total magnetic flux in the sensing coil is reduced due to the offsetting effect from the opposite magnetic field. The closer the target, the larges the eddy current effect (Shown in Figure
II.6) [50].
17 Figure II.6. Working principle of a 3D inductive proximity sensor.
The voltage output of a 3D sensing coil can be estimated from Faraday’s law of induction [44]:
푑∅ 푑퐵 푉 = −푁 ∙ = −푁 ∙ 퐴 ∙ II.3 푑푡 푑푡
Where ∅ is the magnetic flux passing through the coil, A is the area of the sensing coil which can be approximated as 퐴 = 휋푟2, 푟 is the radius of the sensing coil, N is the
푑퐵 number of turns of the coil, and is the magnetic flux density changing rate. The output 푑푡 signal of the sensor is the voltage V. From equation II.3, an increase in the number of coil turns and the active area A of the sensing coil will improve the sensitivity of the sensing coil. However, in many cases, an increase in the number of coil turns will increase the sensor volume of the sensor, making it unsuitable for being used in limited space.
In the early 1970s, a new design of inductive proximity sensors with a ferromagnetic core was introduced to improve the sensitivity (Shown in Figure II.7) [44].
The ferromagnetic core, made by soft magnetic materials, has a permeability larger-than
105. Compared to the air coil, the sensing coil with ferromagnetic core has a more concentrated magnetic flux, therefore, it has a higher sensitivity [51]. With a fixed geometry (turns, length, and inner and outer diameters) of the sensing coil, the higher the permeability of the ferromagnetic core the higher the sensitivity of the sensor.
18
Figure II.7. 3D inductive proximity sensor with a ferromagnetic coil [44].
Changing the geometry is also one of the methods to improve the sensitivity of the sensing coil. Several designs have been developed over the years. One of the most efficient designs is the multi-layer air-coil [44]. As shown in Figure II.8, the total sensing cross section has a diameter D, and the inner air cross section has a diameter of Di. In this design, the calculation of the resultant area of the multi-layer air-coil can be written as [44]:
휋 퐷3 − 퐷2 퐴 = ∙ 푖 II.4 12 퐷 − 퐷푖
Compared to the traditional air sensing coil, it has the same length but a larger cross section A so that the output voltage can be amplified according to equation II.3.
19
Figure II.8. The improved design of 3D inductive proximity sensors[44].
Although many researchers showed their effort to improve the performance of the
3D inductive proximity sensor, they have a major drawback [52]. The high sensitivity proximity sensor based on a 3D sensing coil usually has a larger size compared to other types of sensors such as capacitance and optical [2], making it harder to use in order to identify single small targets such as wear debris in lubricant oil [17]. To overcome these shortcomings, inductive proximity sensors based on planar sensing coils were developed.
The details of planar inductive proximity sensors are introduced in next section.
II.2.3 Inductive proximity sensor based on a planar sensing coil
An inductive proximity sensor with a planar sensing coil was first introduced by
Soohoo et al and was used for integrated circuit application [53]. Planar sensing coils have 20 small sizes so that they requires less installation space [54]. In an oscillation circuit, they also have lower resonant frequencies that minimize the requirement of the power source
[55]. In addition, a good setting of hollowness parameter, which is defined as the ratio between the inner radius of the sensing coil and the outer radius of the sensing coil, can reduce the induction loss under a high frequency AC excitation [56]. These benefits are the reasons that planar sensing coils are rapidly being adopted by researchers.
II.2.4 Working principle of a planar inductive proximity sensor
Generally, a planar inductive proximity sensing system includes a planar inductive sensor, a data acquisition board, an AC power source, and a digital signal processor [57].
Previous studies show that an inductor can be treated as a series of an inductor and a resistor
(Shown in Figure II.9(a)) [58]. For a well fabricated planar sensing coil, the inductance usually holds dominance over the impedance. Generally, the phase angle of a planar sensing coil is between 70 to 88 degree (Shown in Figure II.9(b)).
Figure II.9. (a) Mathematical model and (b) the impedance of a planar inductive sensing coil.
21 When a sensing coil is excited by a high frequency AC excitation, say from 1 MHz up to 25 MHz, a magnetic flux will be generated [59], which concentrates into a nearly uniform field in the center of the planar coil (Shown in Figure II.10(a)) [60]. The magnetic flux reduces progressively with the distance from the center. The further away from the center, the weaker the magnetic field will be. When a metal plate approaches the sensing coil, the changing magnetic flux in the sensing coil will induce an eddy current on the plate surface (Shown in Figure II.10 (b)). The eddy current flowing in the metal plate forms a closed loop. From Lenz’s law, the magnetic field generated by eddy current that is induced by the changing magnetic field always opposes the initial changing magnetic field [61]. If the position/displacement of the metal target is changed, the magnetic flux from the sensing coil in the operating area will be also changed. This change can be determined by monitoring the inductance variance of the sensing coil. In addition, because the induced magnetic field is always opposite to the original magnetic field, the inductance variance of the sensing coil is always monotonically increasing along with the distance between the sensing coil and the target. The larger the distance from the target, the larger the inductance observed from the sensing coil [62].
22
Figure II.10. (a) The magnetic flux line of the planar sensing coil [67], and (b) the eddy current on the target near the sensing coil.
II.2.5 Traditional calibration process for inductive proximity sensor
As mentioned in previous section, the inductance of the sensing coil as a function of gap will always be a monotone curve. Thus, the traditional calibration method for planar inductive sensors is developed based on relating the inductance variance and the distance between the sensing coil and the target [15]. As the first step of the calibration process, several points with known displacements from the sensing coil are selected. Each point has an appropriate interval with others in the measurement range. With a fixed high frequency
AC excitation, the inductance of the sensing coil at each point is measured. After collecting enough data points, the calibration curve can be obtained by using the polynomial regression method [63]. The orders of the polynomial can be adjusted based on the accuracy requirement. Note that even after a calibration curve is established, it is for a specific geometry of sensing coil, and for a given target. When using the sensing coil with
23 different geometry or measuring the displacement/position for a target made by different materials, one needs to redo the calibration process. Therefore, an inductive proximity sensor calibration process always contains the building of a set of calibration curves which correspond to different metallic targets [50]. Figure II.11(a) shows the calibration curves for a planar inductive proximity sensor which includes 3 different materials [50]. In addition, because of the complex relationship between the inductance and the gap, to provide good accuracy and simplify the calculations the calibration curves are typically divided into discrete sections with each section covering a small gap range that can be approximated as a straight line. While using separate sections of calibration curves can provide accurate measurements [15], calibration needs to be done at many gaps with fine incremental steps, making the calibration very time consuming.
24 Figure II.11. (a) Examples of calibration curve for a planar inductive sensor and (b) linearization for a polynomial [64].
II.3 STUDY OF MATHEMATICAL MODEL OF PLANAR COIL INDUCTION
In order to analyze the relations between the planar sensing coil and the target, many efforts were made by researchers. Previous study by Vyroubal indicate that an eddy current in a metal plate can be treated as a virtual planar coil [65]. In addition, several finite element analyses also showed that the eddy current on the surface of a plate metal target is almost contained within a coil footprint [66]. Figure II.12(a) shows the magnetic flux of a planar sensing coil, and Figure II.12(b) shows the footprint of the eddy current on the target while the target is very close to the sensing coil [67]. Thus, the eddy current can be approximately modeled as a virtual coil, and the gap sensing model with a planar coil can be transferred into a coil to coil model.
25
Figure II.12. (a) The magnetic flux of a planar sensing coil [67]. (b) The eddy current distributions in an infinite plate target.
Figure II.13. The equivalent circuit of mutual influence between the sensing and virtual coils.
The top coil in Figure II.12 (b) is the sensing coil and the bottom coil is the virtual coil which is based on the generated magnetic flux by the eddy current. In addition, an inductor in the circuit is always treated as a series of a pure inductor and a pure resistor.
26 Therefore, the equivalent circuit for mutual influence between two coils can be obtained
(Shown in Figure II.13), and derived from Kirchhoff’s Law [68]:
푅1퐼1 + 푗2휋푓퐿1퐼1 − 푗2휋푓푀퐼2 = 푈1 II.5
푅2퐼2 + 푗2휋푓퐿2퐼2 − 푗2휋푓푀퐼1 = 푈2 II.6
Where 퐿1 and 푅1 are the values of the inductance and resistance of the sensing coil without any influence from the eddy current, M is the mutual inductance between the sensing coil and the virtual coil, 퐿2 and 푅2 are the self-relative inductance and resistance of the virtual coil generated by the eddy current (or equivalent inductance and resistance of the virtual coil), 퐿 and 푅 are the equivalent inductance and resistance of the sensing coil while effected by mutual inductance. 푓 is the excitation frequency. The value of 푈2 is 0 in this case because there is no voltage applied to the virtual coil. The current 퐼1 can be solved from equation II.5 and II.6, and expressed as:
푈1 퐼1 = 2 2 2 2 2 2 4휋 푓 푀 푅2 4휋 푓 푀 퐿2 II.7 [푅1 + 2 2] + 푗2휋푓[퐿1 − 2 2] 푅2 + (2휋푓퐿2) 푅2 + (2휋푓퐿2)
The impedance of the sensing coil can be expressed as:
4휋2푓2푀2푅 4휋2푓2푀2퐿 2 2 II.8 푧(푠푒푛푠푖푛푔 푐표푖푙) = [푅1 + 2 2] + 푗2휋푓[퐿1 − 2 2] 푅2 + (2휋푓퐿2) 푅2 + (2휋푓퐿2)
Once the impedance of the sensing coil is determined, the equivalent inductance and resistance of the sensing coil can be calculated using equation II.9 and II.10:
4휋2푓2푀2푅 2 II.9 푅 = [푅1 + 2 2] 푅2 + (2휋푓퐿2)
27 4휋2푓2푀2퐿 2 II.10 퐿 = [퐿1 − 2 2] 푅2 + (2휋푓퐿2)
Let 휔 = 2휋푓, equation II.9 and II.10 can be simplified as:
휔2푀2푅 2 II.11 푅 = [푅1 + 2 2] 푅2 + (2휋푓퐿2)
휔2푀2퐿 2 II.12 퐿 = [퐿1 − 2 2] 푅2 + (2휋푓퐿2)
28 II.4 THE DISPLACEMENT MEASUREMENT REQUIREMENTS FROM NARROW
AND IRREGULAR TARGET
In some industrial applications, the shape of the targets are not always an infinite plate. For example, while using the inductive proximity sensor to monitor the tip clearance of a turbine blade, the target is much smaller than the area of the sensing head of the sensor
(Shown in Figure II.14) [69]. Another example is detecting the displacement of a tooth in a gear [70]. In both examples, the shape of target is narrow and irregular, and the diameter of the sensing coil is larger than the widest part of the target. Because the eddy current distribution on narrow and irregular target is significantly different from the plate shape target, the output (voltage/inductance) of planar inductive sensor would change and the calibration curve for infinite plate target would fail to work while the target changes from an infinite plate to a narrow and irregular target. Most planar inductive sensors need the target to be at least 2 times larger than the sensing coil. When the target has a narrow or irregular shape, such as a gear tooth or turbine blade, one needs to either use a smaller sensing coil or conduct tedious calibration. In addition, if the target material is changed, the relation between the inductance variance and gap will be also changed. Therefore the inductive proximity sensor for narrow and irregular target displacement measurement is specially customized based on the target’s geometry and materials. The calibration curve for such a sensor is completely different from that for gap measurement from an infinite plate, and can only be used to measure the specific targets. Therefore, a gap measurement method for narrow and irregular targets that uses any size face of the inductive sensor needs to be developed, with simple calibration and sufficient measurement accuracy.
29
Figure II.14. Monitoring the blade tip clearance using planar inductive sensor. The target has a narrow and irregular shape.
30 II.5 STUDY OF WEAR DEBRIS MONITORING SENSOR
One effective alternative approach is to detect signs of potential machine failure by examining the life blood of a rotating or reciprocating machine, its lubricant oil [5, 6], similar to a blood test in human health assessment. The main function of the lubricant oil is to reduce the heat, wear, and friction between the contact metal parts inside of the machine [17]. Wear debris is generated during a machine’s operation. This debris will disperse through the lubricant oil and reduce the performance of the lubrication. Studies have shown there exists a direct relationship between the size and concentration of wear debris in the lubricant oil and the level of wear in the machinery components. The concentration and size of wear debris increases gradually with time, even after the working fluid is changed, until the machine fails, as shown in Figure II.15.
31 Figure II.15. Relationships of wear debris size, concentration, and machine conditions
[71].
It is clear that accurate measurement of size and concentration of wear debris is critical to evaluate a machine’s wear condition and health status. Figure II.16 shows a set of pictures of the used lubricant oil from a cylinder-piston machine; the black particles are the wear debris [72]. The size and concentration of debris in oil are not only representative of machine’ health status, but also indicative of whether or not the lubricant will lose its lubricating functionality.
Figure II.16. Metal wear debris in lubricant oil [72][73].
The size of metal debris in lubricant oil has been always used as a criterion for judging a machine’s health status. Related analysis showed that during normal machine operation the concentration of wear debris is low, and usually the sizes of wear debris are 32 in the range of 1 to 20µm. When abnormal/severe wear begins, larger wear debris is seen in the range of 20 to 100µm [5, 7].
The debris in this range is produced by a normal friction between the contact parts and would not cause any machine failure. If the machine operates with heavier loads, a larger size of debris will be produced. When the debris in lubricant oil has diameter ranging from 50-100 microns, it should draw the user’s attention and they should plan to schedule a service for the machine as soon as possible. Debris with a diameter over 100 - 200 microns is probably produced in the late stage of the mechanical useful life. Once debris within or over this range is detected, machine failure may happen at any time [74]. Due to the important relationship between wear debris size/concentration and machine health status, many studies have been conducted on measuring the size, concentration and presence debris in oil lubricant at real time.
II.5.1 Study of wear debris sensors based on Gill sensor
The Gill oil contamination sensor was developed to assist users in improving the reliability of their equipment [17]. As shown in Figure II.17, a container is used to collect the lubricant oil. Four inductive sensors are installed at the bottom of the container, and the positions of the sensors are fixed. The structure of the sensor is shown in Figure II.17, which contains a sensing tip, inductive coil, and a set of support circuits. The sensing tip is made by magnetic materials so that it can generate a strong permanent magnetic field around the sensing tip. The magnetic field will attract surrounded ferrous debris. The inductive sensing coil (Shown in Figure II.17) is excited by an AC excitation. While there
33 are many metal debris particles around the head of the sensor, the magnetic field generated by the sensing coil will be increased [75]. By monitoring the inductance variance of the sensing coil, the total volume of the metal debris in container can be approximately obtained.
Figure II.17.Gill sensor and the design of the inductive sensor.
The Gill sensor has a simple structure and can detect the debris in a large volume of lubricant oil each time. However, this method has a few problems. First, it cannot detect non-ferrous particles, which will not be attracted by the sensing tip [17]. Second, this sensor can only detect a large amount of aggregated ferrous debris and is unable to identify the size of individual debris particles in lubricant oil. When detecting the variance of inductance through the sensing coil, the sensor only reports the total volume or density of debris attracted by the sensing tip. In addition, because metal debris will be at different positions of the sensing tip, they will generate a different effect on the magnetic field of the sensing coil, and the final report from the sensor will typically have conflicting information which is difficult to explain. Finally, the Gill sensor cannot detect non-ferrous particles in lubricant oil since the sensing tip can only attract ferrous metallic debris. Based 34 on the disadvantages mentioned above, research focuses are rapidly moved towards other types of sensors that can be applied to monitor the debris in lubricant oil. Several new sensors using different methods are mentioned in next section.
II.5.2 Study of wear debris sensors based on inductive sensing
Unique advantages such as high throughput, the ability to distinguish between ferrous and non-ferrous metal debris, and insensitivity to oil quality pipes would greatly benefit online debris monitoring. Researchers have put more attention towards using inductive sensors to monitor the size, concentration and presence of metallic wear debris in lubricant oil over the past thirty years [76]. The earlier inductive wear debris sensors were developed based on the 3D coil structure. The design of the wear debris sensor based on 3D coil is shown in Figure II.18 [77]. While a nonferrous metallic debris is present in the magnetic field, an eddy current will be induced on the debris and the direction of the magnetic field generated by the eddy current will be opposite to the original magnetic field.
Therefore, the total magnetic flux from sensing coil will be reduced due to eddy current offsetting effects. The larger the debris, the more offsetting the effect is. This effect can be also observed by measuring the reduction of the inductance of the sensing coil. Once the nonferrous metal debris is changed to ferrous metal debris, a high permeability will increase the magnetic flux, and the eddy current will cause a decrease of the magnetic flux.
While the induced eddy current is small in a low frequency excitation, the variance of magnetic flux in sensing coil is dominated by the debris’ magnetic permeability so that the inductance of the sensing coil will increase. Intuitively, with a relatively low frequency
35 excitation, the nonferrous and ferrous metal debris can be identified by observing the increasing or decreasing inductance of the sensing coil and the size of the debris can be determined by measuring the magnitude of the inductance variance.
Figure II.18. Working principle of the 3D solenoid inductive sensor [11].
Although the inductive method can effectively distinguish the ferrous and nonferrous metal debris in flowing lubricant oil, it still has obvious disadvantages. Due to its large sensing zone [78], the sensitivity is typically lower. As a result, the 3D inductive pulse sensors are unable to measure the debris smaller than 100 microns in diameter.
Furthermore, based on its 3D coil structure, the length of the 3D coil’s sensing zone is too long to detect individual debris at higher concentration. Two or more small debris may pass through the sensing zone, causing the sensor to mistakenly judge them as one large debris passing through the 3D coil. This will result in incorrect size and concentration measurements of wear debris.
In order to improve the sensitivity of the sensor and overcome the single debris detecting limitation, an inductive sensor based on a 2D planar coil is developed by Du et 36 al. [79]. The structure of the 2D planar inductive sensor is shown in Figure II.18. With the
2D coil structure, the magnetic flux generated from the sensing coil is concentrated in a narrower and smaller sensing cone. In fabrication, a 2-layer sensing coil was wound around a glass tube. The glass tube has 0.5mm inner radius and 0.6mm outer radius. On two glass slides, a 1.3mm hole was drilled to insert the 1.2mm glass tube and the space between two glass slides was adjusted with seven layers of cellophane tape (Shown in Figure II.18). The thickness of tape was around 175 microns. The sensing coil was made of 80 microns diameter copper wire. It was reported the sensor can detect debris as small as 50 microns.
In addition, the 2D planar coil sensor was capable of measuring single debris detection [17] and the debris concentration.
Figure II.19. Schematic of the 2-layer coil inductive sensor [80].
One limitation of the above single channel 2D planar coil sensor is its low throughput, i.e, it can only process a very limited flowrate of oil. Another limitation is that
37 the sensitivity is insufficient in monitoring the early stage of wear debris in the range of 20 to 50 microns [74]. Zhu et al. made efforts to increase the throughput (the maximum flow rate the sensor can process) with the use of parallel sensing channels [81]. Coupled with a time multiplexing method applied to the parallel wear debris sensors, the flow rate of the oil that can be processed was able to reach up to 200 ml/min. The sensor system is shown in Figure II.20 (a). The sensor system has a 120mm (length) x 110 mm (width) x 60 mm
(height) compact size and was integrated along an acrylic sheet. Eight channels were used to detect wear debris in parallel which require only one combined excitation signal. The equivalent measurement circuit for the wear debris sensor is shown in Figure II.20 (b).
However, for a 2MHz excitation frequency, the sensing system used a 100MHz sampling rate to capture the highly dynamic inductive pulses induced by individual wear debris.
With 8 parallel channels, there was a huge amount of data. The sensor had to collect the data for 30 seconds, and then stopped data collection for signal processing that lasted 3 minutes or more due to the large amount of the data. This limitation limits its ability of continuous wear debris monitoring. In summary, there are two major limitations of the 2-
D planar inductive sensors for oil debris monitoring: 1) the inability to process the big data generated from the sensor in real time, and 2) the insufficient sensitivity for the detection of smaller debris particles. I attempted to address these problems in Chapter V.
38
Figure II.20. (a) Wear debris monitoring system with [80] (b) multiplexing method.
39 CHAPTER III
NEW CALIBRATION METHOD FOR PLANAR INDUCTIVE SENSORS BASED ON
CALCULATING MUTUAL INDUCTANCE
As mentioned in chapter II, Traditional inductive gap measurement relies on establishing a calibration curve between the inductance variation of the planar coil and the displacement, which is usually established with an infinite target plate[13,14]. When the object shape or material is changed, a new set of calibration curves should be re-established for the measurement, a process that is tedious and time consuming. To address this problem, Tian et al. proposed that the effect of different target materials on the calibration can be reduced by increasing the excitation frequency of the inductive sensor [82].
However, using a high excitation frequency (e.g. 5 MHz or higher) significantly increases the amount of data and hence the processing time, yet the material effect still cannot be completely eliminated. Yu et al. developed a new eddy current displacement measuring instrument which is independent of a sample’s electromagnetic properties [83]. Although the influence of changes in a target material can be somewhat eliminated by using a coil impedance vector projection approach, a roughly 13% error in the 0.1-0.2 mm gap measurement range was found when using an aluminum and copper plate target. Recently
Wang et al. developed a method with where the displacement measurement is made 40 independent from the target conductivity by shifting the calibration curve for different materials with an offset value [84]. While the method is based on calculating the geometry of the superconductor image plane, the conductivity of each material needs to be measured precisely. Developing new calibration methods for planar inductive sensors will always be a topic that researchers will put effort into.
Alternatively Vyroubal et al presented the coil to coil theory and indicated that it could be used as a mathematical transfer model for gap sensing using planar coils. Several new methods or algorithms were attempted by many different researchers [5,12,85].
However, because most of parameters in equation II.5 and II.6 are complex and contain too many unknowns, most methods were used only to qualitatively evaluate the influence of one parameter/condition on the gap measurement, but cannot be used to calculate the gap from the inductance change mathematically. Some researchers [5] tended to use finite element analysis (FEA) to analyze the equivalent resistance and inductance of the virtual coil and distribution of the eddy current with a known gap. However, it is impractical to use the FEA to back calculate the unknown gap from the measured coil inductance for gap measurement applications.
Here I introduce a mathematical model to model the mutual inductance between a sensing coil and a target plate. We then simplify the model and propose a new calibration method based on the model. Compared to the traditional calibration methods, the new calibration method allows us to obtain the calibration curve for a different material in a single step without recalibrating the curve.
41 This chapter is reused and modified from Dian, J., Liwei, N., Xiaoliang, Z., Jiang,
Z., Ziyu, Z., Yaguo, L., Zhenxia, L., and Zhe, J., 2019. Measuring gaps using planar inductive sensors based on calculating mutual inductance. Sensors and Actuators, Volume
295, Pages 59-69. Copyright © 2019 Elsevier B.V.
42 III.1 CALCULATION METHOD BASED ON MATHEMATICAL MODEL
Figure III.1(a) illustrates the working principle of the inductive planar coil sensor for gap/displacement measurement from a large metallic plate. The sensing coil has an inner and outer radii of r1 and r2. When the sensing coil is excited by a high frequency AC signal, a magnetic field is generated, which induces an eddy current in the metal plate. Prior work by Vyroubal [65] indicates that eddy current in a metal plate can be regarded as a planar coil. Thus, here we modeled the eddy current as a virtual coil with inner and outer radiuses of r3 and r4 [65,86].
43 Figure III.1. (a) Working principle of gap measurement. Eddy current is generated in the target metal plate and causes an inductance change of the sensing coil. (b) The eddy current effect can be modeled as a virtual planar coil on the target plate. (c) Equivalent circuit model of the measurement system. (d) Mathematical model in Neumann’s formula [85] to calculate mutual inductance between the two coils.
With a fixed excitation frequency, if the gap d between the sensing coil and the target is varied, the equivalent inductance and resistance of the sensing coil is changed due to the mutual induction change between the coil and the target metal plate. The gap measurement can be considered as the mutual inductance problem of the two coils: the sensing coil and the virtual coil (Shown in Figure III.1(b)). Assuming the planar sensing coil and the target are parallel (Shown in Figure III.1(b)), the directions of two magnetic fields are opposite. Thus the magnetic flux of the sensing coil is reduced with the presence of the eddy current. The smaller the distance, the larger the reduction in the magnetic flux of the sensing coil, which is reflected as the change of the equivalent inductance of the sensing coil.
The relationship between the equivalent inductance (L) and the equivalent resistance R of sensing coil and the target is derived from Kirchhoff’s Law [82,87]:
휔2푀2퐿 푡 III.1 퐿 = 퐿퐶 − 2 2 2 푅푡 + 휔 퐿푡
휔2푀2푅 푡 III.2 푅 = 푅퐶 + 2 2 2 푅푡 + 휔 퐿푡
44 \
where Lc and Rc are the values of the inductance and resistance of the sensing coil without any influence from the eddy current, M is the mutual inductance between the sensing coil and the virtual coil, Lt and Rt are the self-relative inductance and resistance of the target generated by the eddy current (or equivalent inductance and resistance of the virtual coil, 휔 is excitation frequency in rad/s (휔=2 휋 푓).
Figure III.2. Illustration of a 3D coil with multiple layer.
Figure III.3. Illustration of a planar disk coil.
45 The formula of the equivalent inductance of the virtual coil can be found from D.Yu and K.S. Han’s work in 1987. The self-inductance of a coil using the Bio-Savart law can be expressed as [88]:
2 휋 푅2 푅2 푎 푎 푐표푠휃푟1푟2푑푟1푑푟2푑푧1푑푧2푑휃 휇0푁 ∫ ∫ ∫ ∫ ∫ 0 푅1 푅1 −푎 −푎 푟푄푁 III.3 퐿 = 2 2 4(푅2 − 푅1) 푎
Where loop 1 is at (푟1, 푧1) and loop 2 is at (푟2, 푧2) Shown in Figure III.2, which carrying the current 푖1 and 푖2, 푅1 and 푅2 are the inner radii and outer radii of the coil, 푎 is the distance from the 0 point in y axis to the end of the coil. 휇0 is the vacuum permeability,
푁 is the number of turns of the coil, 푟푄푁 can be expressed as;
2 2 2 푟푄푁 = √(푍2 − 푍1) + 푟1 + 푟2 − 2푟1푟2푐표푠휃 III.4
When considering a single disk coil (Shown in Figure III.3), Slobodan Baic simplified equation III.1 and the self-inductance of a single disk coil can be written as [89]:
휇 푁2푅 퐿 = 0 1 1 푆(푘) III.5 푑푐 3(훼 − 1)2
푅 Where the first shape factor of the coil 훼 is defined as 1, and 푆(푘) can be written 푅2 as:
46 푟 3 β = [( 2) + 1] [0.832 − 퐸(푎)] 푟1 휋 − log(2) 2
푟2 ( ) + 1 4 3 푟1 푟2 푟2 푟2 2 + 푟 {[( ) + 4 ( ) + 4 ( ) + 1] 푎 2 ( 2) 푎2 푟1 푟1 푟1 푟1 III.6 푟 푟 2 − 4 ( 2) [( 2) + 1] ∙ 퐸(푎) 푟1 푟1
푟 4 푟 3 푟 푟 3 + [(− ( 2) − 2 ( 2) − 2 ( 2) − 1) 푎2 + 4 ( 2) + 4] 퐾(푎)} 푟1 푟1 푟1 푟1
3 푟2 (푟 ) 푟 푟 − 1 퐻 ( 2) − 퐿 ( 2) 2 푟1 푟1 푟 4 ( 4) 2 푟3 푎 = 푟 III.7 [1 + ( 4)]2 푟3
푟 2 푟 푟 휋 √1 + ( 2) + 2 ( 2) cos 푥 + 1 + ( 2) cos 푥 푟 2 푟 푟 푟 퐻 ( 4) = ∫ log 1 1 1 푑푥 III.8 푟3 푟 2 푟 푟 0 √1 + ( 2) − 2 ( 2) sin 푥 + ( 2) sin 푥 − 1 푟1 푟1 푟1
휋 푟 2 푟 2 푟 푟 퐿 ( 2) = ∫ log [√1 + ( 2) + 2 ( 2) cos 2푥 + ( 2) + cos 2푥] 푑푥 III.9 푟1 0 푟1 푟1 푟1
푟1 and 푟2 in above equation is the inner radii and outer radii of the coil. The E and
K in above equation are the first and second kind of complete elliptic integrals. 푁1 is the number of turns of the coil. Notice that the self-inductance of a coil is only affected by several physical factors which contain the inner and outer radii of the coil, the number of
47 turns of the coil, the length of the winding wire, and the cross sections of the coil. Equation
III.3–III.9 shows that the inductance of a coil is a function of 푟1, 푟2 and 푁1.
The equivalent resistance of a coil can be obtained by integrating the resistance of the loops with infinitesimal cross section. Hongbo et al. reports that the formula for the equivalent resistance can be written as [5]:
2휋 푅푡 = 푟 III.10 ℎ휎 ln 2 푟1
Where ℎ is the depth of the penetration. In this analysis, we assume that the target has full penetration depth. From this assumption, the penetration depth can be expressed by:
1 ℎ ≈ III.11 √휋휇푓휎
Figure III.4. (a) Equivalent circuit model of the measurement system. (b) Mathematical model in Neumann’s formula to calculate mutual inductance between the two coils.
48 When considering a coil to coil system, the magnetic field produced from one coil will affect the magnetic field from another coil. Therefore, the mutual inductance between the coils needs to be considered. From Faraday’s law, if two coils are parallel and with the same center, it indicates that the two magnetic fields are always opposite. The equation of mutual inductance between two coils are expressed as:
휇 푑푠⃗⃗⃗⃗⃗⃗ ∙ 푑푠⃗⃗⃗⃗⃗⃗ 푀 = 0 ∬ 1 2 III.12 4휋 푑
Where 푑푠⃑1 and 푑푠⃑2 are incremental sections of the filaments (Shown in Figure
III.4(a)). While two coils are parallel the mutual inductance of two disk coils is deduced by Sobodan Babic and simplified as [89,90]:
퐴1 − 퐴2 + 퐴3 − 퐴4 푀 = (휇0푁1푁2) III.13 (3푟2 − 3푟1)(푟4 − 푟3)
Where:
49 2푙푛휌푛√푙푛휌푛 4푙푛휌푛 퐴푛 = − ∙ 퐸 (√ 2 2) 4푙푛휌푛 (푙푛 + 휌푛) + 푑 √ 2 2 (푙푛 + 휌푛) + 푑
4 2 2 2 + 푙푛휌푛√ 2 2 (푑 − 푙푛 − 휌푛 (푙푛 + 휌푛) + 푑
2 2 2 2 + 휌푛√휌푛 + 푑 + 푙푛√푙푛 + 푑 )
2 2 4푙푛휌푛 휌푛√휌푛 + 푑 ∙ 퐾 (√ 2 2) − 휋|푑| [1 (푙푛 + 휌푛) + 푑 2
4푙푛휌푛 − 훬 (휃1,푛,√ 2 2) (푙푛 + 휌푛) + 푑
2 2 − signum (√휌푛 + 푑 − 푙푛)
4푙푛휌푛 ∙ (1 − 훬 (휃2,푛,√ 2 2))] (푙푛 + 휌푛) + 푑
푙 √푙2 + 푑2 − 휋|푑| 푛 푛 [1 2
4푙푛휌푛 − 훬 (휃3,푛,√ 2 2) (푙푛 + 휌푛) + 푑
2 2 − signum (√푙푛 + 푑 − 휌푛)
3 4푙푛휌푛 푑 ∙ (1 − 훬 (휃4,푛,√ 2 2))] − 퐽1푛 (푙푛 + 휌푛) + 푑 2
3 3 + 휌푛퐽2푛 + 푙푛 n= 1, 2, 3, 4. III.14
50 휋 2 퐽1푛 = ∫ 푓(훽) 푑훽 0
휋 2 1 푑2 푐표푠(훽) + 푙 휌 푠푖푛2(훽) = ∫ [arctan 푛 푛 푠푖푛 (훽) 2 2 2 0 푑푠푖푛 (훽)√푙푛 + 휌푛 + 푑 − 2푙푛휌푛 푐표푠(훽)
푑2 푐표푠(훽) − 푙 휌 푠푖푛2(훽) − arctan 푛 푛 ] 푑훽 2 2 2 푑푠푖푛 (훽)√푙푛 + 휌푛 + 푑 + 2푙푛휌푛 푐표푠(훽) n= 1, 2, 3, 4. III.15
휋 2 푙푛 + 휌푛 푐표푠(2훽) 퐽2푛 = ∫ arcsinh ( ) 푑훽 n= 1, 2, 3, 4. III.16 2 2 2 0 √휌푛 푠푖푛 (2훽) + 푑
휋 2 휌푛 + 푙푛 푐표푠(2훽) 퐽3푛 = ∫ arcsinh ( ) 푑훽 n= 1, 2, 3, 4. III.17 2 2 2 0 √푙푛 푠푖푛 (2훽) + 푑
√푙2 + 휌2 + 푑2 + 2푙 휌 − √푙2 + 휌2 + 푑2 − 2푙 휌 푓(0) = 푛 푛 푛 푛 푛 푛 푛 푛 n= 1, 2, 3, 4. III.18 푑
휋 푙푛휌푛 푓 ( ) = 2arctan n= 1, 2, 3, 4. III.19 2 2 2 2 푑√푙푛 + 휌푛 + 푑
|푑| 휃1,푛 = arcsin ( ) n= 1, 2, 3, 4. III.20 2 2 √휌푛 + 푑 + 휌푛
2 4휌푛 − 2 + 1 2 2 √ (√휌푛 + 푑 + 휌푛) 휃2,푛 = arcsin n= 1, 2, 3, 4. III.21 4푙푛휌푛 − 2 2 + 1 (푙푛 + 휌푛) + 푑 ( )
|푑| 휃3,푛 = arcsin ( ) n= 1, 2, 3, 4. III.22 2 2 √푙푛 + 푑 + 푙푛
2 4푙푛 − 2 + 1 2 2 √ (√푙푛 + 푑 + 휌푛) 휃4,푛 = arcsin n= 1, 2, 3, 4. III.23 4푙푛휌푛 − 2 2 + 1 (푙푛 + 휌푛) + 푑 ( )
51 푟1 = 휌1 = 휌2 III.24
푟2 = 휌3 = 휌4 III.25
푟3 = 푙1 = 푙4 III.26
푟4 = 푙2 = 푙3 III.27
훬 is Heuman’s Lambda function . The E and K in the above equation are the first and second kind of complete elliptic integrals. 푟1, 푟2, 푟3 and 푟4 corresponds to the inner and outer radii of the first 2D disk coil and virtual disk coil. 푁1 and 푁2 are number of turns of the coil 1 and coil 2 (Shown in Figure III.4(b)). Equation III.13–III.27 shows that the mutual inductance is a function of 푟1, 푟2, 푟3, 푟4, 푁1 and 푁2.
Therefore, by plugging equations III.14-III.27 into equation II.13, let Lc and Rc be the values of the inductance and resistance of the sensing coil without any influence from the eddy current, Lt and Rt are the self-relative inductance and resistance of the target generated by the eddy current, the equation II.13 can be written as follows:
휔2푀(푑, 푟 , 푟 , 푟 , 푟 , 푁 , 푁 ) 2퐿 (푟 , 푟 , 푁 ) 1 2 3 4 1 2 푡 3 4 2 III.28 퐿 = 퐿퐶 − 2 2 2 푅푡(푟3, 푟4) + 휔 퐿푡(푟3, 푟4, 푁2)
52 III.2 METHOD TO SOLVE THE GAP FROM MUTUAL INDUCTANCE
In equation III.28, the unknowns are r3 and r4 (the inner and outer radius of the virtual coil), d (the gap between the center of the two coils), and N2 (the number of turns of the virtual coil). Next, we present a method to solve 푑 from equation III.28 with a measured L.
At a fixed gap between the sensing coil and the virtual coil, the eddy current generated on the target plate (and thus the Lt and Rt) is determined by r3, r4 and N2. From equation III.3, the equivalent inductance of the virtual coil (Lt) is determined by N2 (the coil turns of the virtual coil), r3 and r4. The Lt change caused by the variations in r3 and r4 can be achieved by changing N2. In addition, prior finite element study indicated that when the gap is small, the change in the inner and outer radius of the virtual coil (r3 and r4) is less than 10% when the gap d varies, implying that r3 and r4 can be assumed to be nearly constant when the gap changes. From the above, we assume that r1 is equal to r3, and r2 is equal to r4. If the gap changes, the Lt variation can be attributed to the change of N2. The wire radius of the virtual coil can be considered as a variable, such that r3 and r4 can remain the same when the coil turns of the virtual coil varies. With this assumption, in equation
III.28 there are only two unknowns left, the gap d and the number of turns of the virtual coil (N2).
By taking a number of measurements of equivalent inductances (L) of the sensing coil at a number of gaps (say 6-7 gaps), we can build a calibration curve between d and N2.
53 After the d - N2 relationship curve is built, an unknown gap can be calculated from a measured coil inductance by coupling this relationship with equation III.28.
III.3 EXPERIMENTAL SETUP AND PREPARATION
To validate the proposed calculation method, a set of experiments were designed.
First, a planar sensing coil was fabricated by using 0.45mm inner diameter copper wires.
To fabricate the planar coil, two 15 mm × 40 mm polymethylmethacrylate (PMMA) slides were prepared and drilled with a 1.5 mm diameter hole at the center of the slides. Then, the two PMMA slides were adjusted with 18 layers cellulose tape so that the gap between two slides is around 450 μm. The planar coil was wound around a 1.4mm steel tube. Next, the fabricated sensing coil is packaged using a ceramic layer (made of ceramic 645-N). As shown in Figure 3.4, each sensing coil has a 500 μm thick ceramic layer on top to protect the coil and preserve its shape (such that the base inductance of each coil remains unchanged in all experiments). The experimental setup is showed in Figure III.5. The fabricated sensor was attached on a precision X-Y-Z stage. The X-Y-Z stage was positioned above a metal plate. The metal plate has a cubic shape with 5 cm height, 5cm width and 5cm thickness. The X-Y-Z stage can regulate the gap between the sensing coil and the metal plate in the X axis with 10 µm resolution.
54
Figure III.5. Illustration of the experiment setup and a picture of one coil made of copper wire. A 500 µm thick ceramic layer was applied on top of the coil surface to protect the sensing coil and keep the shape of the coil so that the coil’s base inductance remains
To validate the calibration method for various planar coils regardless of their sizes, three different coils were fabricated with the same material but different geometries. The turns of sensing coil 1, 2, and 3 are 6, 8, and 10. The dimensions and parameters of the sensing coils are listed in Table III.1. The targets were four metal plates made of titanium, zin, copper, and aluminum and were used to study the mutual influence of the material change. The conductivity of the target ranged from 4.032 to 59.95 × 106 S/m which covers the range of most commonly used metallic materials. In all experiments, an LCR meter
(E4980A1-030, Keysight Technologies) was used to record the equivalent inductance of the planar coils at various gaps. Considering that most of the planar inductive sensors in industrial applications have a working frequency from 10 kHz to 10 MHz. A 1 MHz
55 frequency, and 1V peak to peak AC excitation signal was chosen, coming from a signal generator (N9310A RF Signal Generator, 9kHz to 3GHz). Before the experiment, the phase angles of the three sensing coils were measured using the LCR meter to demonstrate that the LR mathematical model for planar inductive sensors and the electrical equivalent circuit model (Shown in Figure II.13) for coil to coil systems can be safely used to calculate the mutual influence between the sensing and virtual coil. Three different excitation frequencies, 0.5 MHz, 1MHz, and 2MHz, were applied to the sensing coil. The phase angle varied from 87.2 to 88.0 degrees, indicating that the inductance was dominant in the impedance of the sensing coil. In addition, the impedances of the sensing coils were nearly doubled when the frequencies of the AC excitation increased from 0.5 MHz to 2 MHz, also demonstrating that the impedance of the coil mostly came from the coil inductance (2πfL).
The above experiments demonstrate that the mathematical equivalent model for sensing coils and electrical circuits for sensing systems can be applied to analyze the mutual influence without worry.
56 III.4 MEASUREMENT AND CALCULATION RESULTS
The experiments were conducted as the following: First, we measured the base inductance of the sensing coil (Lc) without the presence of any metallic object. Next, we measured the inductance of the coil (L) when a 5 cm × 5 cm × 5 cm titanium plate was placed below the sensing coil. Using the precision X–Y stage, the gap between the sensing coil and the target was regulated from 500 μm to 5000 μm. The relation between the gap and inductance are shown in Figure III.6(a). Four metal plate targets made of Ti, Al, Zn, and Cu were employed for the test. The inductance of the sensing coil 퐿 increases as the gap 푑 increases because of the increased mutual inductance M.
Figure III.6. (a) Measured inductance of sensing coil 1 as a function of the gap d between the sensing coil and the target metal plate. (b) Calculated number of turns of the virtual coil as a function of the gap
Since 퐿 was measured, , 푁2 can be solved with the bisection method by applying all knowns (Rt, r1, r2, r3, r4, N1, etc) in equation III.28. With a set of measured inductances at
57 known gaps, we built a relationship curve between 푁2 and d. For metal plates made of different materials (zinc, copper and aluminum), N2 - d relationships were obtained by repeating the same process. The results of the N2-d curves are shown in Figure III.6(b).
Each curve was established with 8-9 measured data points. Figure III.6(b) also shows that as the gap increases, 푁2 decreases due to decreased eddy current. Similarly, at the same gap, a material with higher conductivity has higher value of 푁2, indicating that the eddy current/mutual inductance between two coils is increased with increased target conductivity. Each non-ferrite materials has its own 푁2- 푑 curve.
Next, the vertical axis 푁1/푁2 for different materials was converted from 푁2, where
푁1 is the number of turns of the sensing coil. Figure III.7 shows the 푁1/푁2- 푑 curve for plate target made of titanium, zinc, aluminum, and copper. We found that the 푁1/푁2- 푑 curve moves in parallel when the target material is changed. In other words, there is a parallel distance C of 푁1/푁2 regardless of the gap d when the material of the target plate is changed:
푁1 푁1 퐶 = ( )푟푒푓푒푟푒푛푐푒 − ( )푡푎푟푔푒푡 III.29 푁2 푁2
The subscription reference and target in equation III.29 represent the base material and target material. Here, titanium was selected as the base material, and C was calculated at different gaps. Figure III.8 and III.9 also shows the results indicating that C is a constant with small variations for different geometries of sensing coils. While this is not mathematically proven due to complex relation between N1/N2 and d, this finding significantly simplifies the calibration process for different materials. Only one calibration
58 curve for a base material is needed; the calibration curves for other materials can be determined by adding a constant C to the base curve.
Figure III.7. (a) Calculated N1/N2 as a function of the gap (d) between the sensing coil and the target metal plate. The N1/N2 - d curve shifts with a parallel distance C when target material is changed. (b) The constant C for zinc, aluminum and copper
To validate that this method can be applied to all planar sensing coils with different geometries, the experiments mentioned above were repeated using sensing coils 2 and 3.
Table III.1 lists the geometries and excitation signals for all sensing coils. When defined inductor’s Q factor as ωL/R, the Q factor for the fabricated sensing coil 1 is 12.14, 7.07 for sensing coil 2, and 14.71 for sensing coil 3 while applied 1 MHz excitation frequency. Four plate targets made of four materials: titanium, zinc, aluminum and copper, were employed for each experiment. The conductivities of the four selected targets range from 4.032 to
59.95×106 S/m, which covers the most common conductivity range of used metallic materials. The results are shown in Figures III.7, III.8, and III.9, and they indicate that the parallel relation of 푁1 /푁2 - 푑 curves for different materials still exist even when the
59 geometries of the sensing coils are quite different. For coil 2, the C is -0.0413±0.0016 for zinc, -0.0601±0.0038 for aluminum and -0.0749±0.0009 for copper targets. For coil 3, the
C is -0.0729±0.0057 for zinc, -0.1096±0.0047 for aluminum and -0.1443±0.0082 for copper targets. When one calibration curve for one material and the constant C is determined, the calibration curves for a different material can be obtained. Note that the parallel distance C can be determined at one gap, avoiding generating a complete new curve with many calibration data points. Next, to validate this method, we will evaluate the accuracy of the gap measurements using the obtained 푁1/푁2- 푑 curves.
Table III.1 The dimensions and parameters of the three sensing coils used in the
experiments.
Coil 1 Coil 2 Coil 3
Inner Dia 1.4 mm 1.4 mm 1.4 mm
Outer Dia 12.92 mm 9.02 mm 14.20 mm
Turns 8 6 10
Voltage 1 V 1 V 1 V
Frequency 1 MHz 1 MHz 1 MHz
Gap range 500-5000 μm 500-5000 μm 500-5000 μm
60
Figure III.8. (a) Calculated N1/N2 as a function of d for sensing coils 2. (b) The constant C for zinc, aluminum and copper targets.
61
Figure III.9. (a) Calculated N1/N2 as a function of d for sensing coil 3. Figure III.7, III.8, and III.9 showing that N1/N2 – d curves for different materials are in parallel. There is a constant parallel distance between the two curves for different materials. (b) The constant
C for zinc, aluminum and copper targets.
62 III.5 VALIDATION OF THE GAP MEASUREMENTS WITH THE 푁1/푁2- 푑 CURVES
The orders of polynomials for 푁1 /푁2 - 푑 curve can be selected based on the accuracy requirements of measurement. The more precision required, the higher the order
th of polynomial needed. Here, 6 -order polynomials were used to correlate the 푁1/푁2- 푑 curves as shown below:
Coil 1 (12.9 mm in diameter):
푁1 −22 6 −18 5 −14 4 ( )푇푖 = 1.631 × 10 푑 − 2.588 × 10 푑 + 1.507 × 10 푑 푁2
− 2.707 × 10−11푑3 + 2.911 × 10−8푑2 − 1.303 × 10−5푑
+ 1.3262 III.30
푁1 푁1 ( )퐶푢 = ( )푇푖 − 0.1333 III.31 푁2 푁2
푁1 푁1 ( )퐴푙 = ( )푇푖 − 0.1009 III.32 푁2 푁2
푁1 푁1 ( )푍푛 = ( )푇푖 − 0.0669 III.33 푁2 푁2
Coil 2 (9.02 mm in diameter):
푁1 −21 6 −17 5 −14 4 ( )푇푖 = 1.156 × 10 푥 − 1.4028 × 10 푥 + 5.931 × 10 푥 푁2
− 0.754 × 10−10푥3 + 0.466 × 10−8푥2 − 0.0000372푥
+ 0.919 III.34
푁1 푁1 ( )퐶푢 = ( )푇푖 − 0.0749 III.35 푁2 푁2
63 푁1 푁1 ( )퐴푙 = ( )푇푖 − 0.0601 III.36 푁2 푁2
푁1 푁1 ( )푍푛 = ( )푇푖 − 0.0413 III.37 푁2 푁2
Coil 3 (14.2 mm in diameter):
푁1 −23 6 −18 5 −14 4 ( )푇푖 = 8.862 × 10 푥 − 1.836 × 10 푥 + 1.441 × 10 푥 − 3.901 푁2
× 10−11푥3 + 0.776 × 10−7푥2 − 0.867 × 10−5푥 + 1.951 III.38
푁1 푁1 ( )퐶푢 = ( )푇푖 − 0.1443 III.39 푁2 푁2
푁1 푁1 ( )퐴푙 = ( )푇푖 − 0.1096 III.40 푁2 푁2
푁1 푁1 ( )푍푛 = ( )푇푖 − 0.0729 III.41 푁2 푁2
Note that with a fixed sensing coil, while changing the material, the 푁1/푁2- 푑 curve will shift up or down with a parallel distance C, and the value of C can be determined at a single measured gap, which significantly simplifies the calibration process. Next, we prove the 푁1/푁2- 푑 curves can be used to calculate the gap accurately from the measured coil inductance. The procedures were as follows: we 1) took measurements of the inductance of the sensing coil at many positions, ranging from 500µm to 5000µm, 2) applied the inductance L, the base inductance Lc, all known parameters (r1, r2, r3, r4 and N1), and coupled the N1/N2 - d relationship with equation (III.28), and 3) used the bi-section method to calculate the gap d.
The comparisons between the calculated gaps and the actual gaps for various materials and sensing coils are given in Figure III.10, III.11, and III.12. Figure III.10(a)
64 shows the gap comparison between sensing coil 1 and the zinc target. The 푁1 /푁2 - 푑 relation was obtained from the 푁1/푁2- 푑 relation of Titanium by adding a constant -0.0669.
The calculated gaps are in good agreement with the actual gaps: the maximum error,
2.50%, occurred at an actual gap of 840 µm for the zinc target (Figure. III.10(a)). When the target material was changed to aluminum, using the proposed calculation method, the maximum error was 2.43% at an actual gap of 4040 µm (Fig. III.10(b)). When the target material was changed to copper, the maximum error was 3.19% at an actual gap of 690 µm
(Fig. III.10(c)). Figures III.11(a), 11(b), and 11(c) show the calculated gap compared to the actual gap for coil 2. The maximum error was 2.69% occurring at an actual gap of 520 µm displacement for zinc target (Figure. III.11(a)). A maximum error 3.07% for aluminum target occurred at an actual gap of 1240 µm (Figure. III.11(b)). When the target material was changed to copper, the maximum error was 2.45% at an actual gap of 940 µm (Figure.
III.11(c)). The maximum error for coil 3 was 2.60% occurring at a 4040 micron displacement for the zinc target (Figure. III.12(a)). As the target material was changed to aluminum, using the proposed calculation method, the maximum error was 2.53% at an actual gap of 3240 microns (Figure. III.12(b)). A maximum error 2.49% occurred at an actual gap of 4440 µm for a copper target (Figure. III.12(c)).
All results show that the calculated gaps have small errors when compared to the actual gap. This indicates that although there exist small variations of C, when C is considered as a constant to back calculate the gap d, the prediction in d matches well with the actual d. Thus C can be taken as a constant to simplify the calibration without sacrificing the measurement accuracy.
65
Figure III.10. Comparisons of the calculated gaps (from equation III.30) to the actual gaps.
(a) Gap between sensing coil 1 and the zinc target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.0669. (b) Gap between sensing coil 1 and the aluminum target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.1009. (c) Gap between sensing coil 1 and the copper target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.1333.
66
Figure III.11. Comparisons of the calculated gaps to the actual gaps. (a) Gap between sensing coil 2 and the zinc target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.0413. (b) Gap between sensing coil 2 and the aluminum target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.0601. (c) Gap between sensing coil 2 and the copper target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.0749.
67
Figure III.12. Comparisons of the calculated gaps to the actual gaps. (a) Gap between sensing coil 3 and the zinc target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.0729. (b) Gap between sensing coil 3 and the aluminum target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.1096. (c) Gap between sensing coil 3 and the copper target; N1/N2 - d relation was obtained from the N1/N2 - d relation of titanium by adding a constant -0.1443.
68 III.6 DISCUSSION
The result proves the feasibility of the method/algorithm presented in previous sections to calculate the gap with simplified calibration. The error in the calculated gap comes from 3 parts. 1) The amount of measured data used to establish the base calibration curve, 2) the number of polynomial orders using to correlate the 푁1/푁2- 푑 curve, and 3) the bisection method. The error can be further reduced by 1) adding a few more data points in the L vs d measurements, and 2) increasing the amount of iterations when calculating N2 from L in equation III.28 to obtain a more accurate 푁1/푁2- 푑 base curve, and calculating d by coupling the N1/N2 - d curve with equation III.28. The results also indicate that the parallel distance C is dependent on both the target material and the geometry of the coil.
From the data showed in Figures III.7, III.8, and III.9, coil 3 with the largest outer diameter has the largest value of C for the same target material. In addition, it seems that the smaller the conductivity, the larger the value of C for the same coil.
For a coil with fixed geometry, only one base calibration curve for one material is needed. When the coil is used for measuring the gap from a different target material, we only need to take one measurement at one known gap to obtain C for this material, instead of obtaining a new calibration curve by taking many measurements at different gaps. This significantly simplifies the calibration. Only if the sensing coil is changed, a new calibration curve will be needed for this coil. Compared to the traditional method which relies on calibrating an inductance-gap curve for each material, the calibration process is significantly simplified and can back calculate the gap using only one base calibration curve for various materials. 69 One limitation for this work is that the assumption for the new calibration method is based on the idea that the magnetic field from the sensing coil has full penetration to the target. In other words, the thickness of the plate target t needs to be larger than the full penetration depth h in equation III.10. From equation III.10, the penetration depth of each material will change if the excitation frequency is varied. Therefore, while measuring the gap from a thick target, the excitation frequency for the planar inductive sensor needs to be guaranteed in a suitable range.
70 III.7 SUMMARY
We developed a new method to calculate the gap between the non-ferrite materials plate target and planar proximity sensor. Different from traditional calibration methods that relied on the relation between the target displacement and inductance of the sensing coil, the new method relies on calculating the mutual influence between the planar sensing coil and the eddy current on the target. The method referred to the model analysis from
Vyroubal so that the sensing system (sensing coil to target) can be transferred to a researchable mathematical model (sensing coil to virtual coil). Next, an assumption of coil geometry was applied to the coil to coil mathematical model in order to reduce the unknown parameters. Once we had a solvable transfer model, the gap of the target could be obtained by calculating the mutual induction between a planar sensing coil and the eddy current on a metal plate. While establishing the 푁1/푁2- 푑 curve, we found that the curve for different materials are in parallel with a constant parallel distances, where 푁1 and 푁2 are the coil turns of the sensing coil and the virtual coil. Hence the 푁1/푁2- 푑 curve for a new material can be obtained by adding a constant C to an existing curve, where C can be calibrated at a single gap. A planar inductive sensor using this new calibration method has a simpler calibration process when the target material is changed.
We also demonstrated that the new calibration method for a planar inductive sensor has small error with a long measurement range, and it is valid regardless of the dimension of the sensing coil. In experiments, we tested three sensing coils with different geometries from 500 µm-5000 µm. Each sensing coil was measured with four plate targets made of different materials. Our gap measurement results showed to be within the 500 µm-5000 71 µm range, and the measurement error of the gap can be smaller than 3.2%. We expect that it can be used gap measurement and metal detecting applications in machines and automation equipment made of various materials.
In short, the contributions of objective 1 can be summarized to:
We developed a new calibration method to measure the target gap from a plate shape
target using a planar inductive sensor based on studying the mutual inductance between
the planar sensing coil and the target.
The new calibration method significantly simplifies the calibration process when the
target material is changed, without sacrificing the accuracy. The calibration curve for
a new material can be obtained by simply adding a material constant to an existing
curve, and the material constant can be determined by measuring a single gap. In
comparison, existing gap sensors requires a complete calibration if target material is
changed.
The new calibration method has small error in the 500 μm – 5000 μm measurement
range.
While the new method can simplify the calibration process for using planar inductive sensors, one obvious limitation is that the uses of the new approach requires that the targets be considered as an infinite plate so that the eddy current can fully spread out along the target. If the target is switched to a narrow or irregular object the eddy current distribution on the target is very different from that with an infinite plate target. Hence the above approach cannot be directly used. In the next chapter, I will develop an improved
72 method in order to overcome the problem. The details of the improved method will be presented in CHAPTER IV.
73 CHAPTER IV
A NEW APPROACH FOR GAP MEASUREMENT FROM NARROW AND
IRREGULAR TARGETS
In CHAPTER III, an improved calibration method for planar inductive sensors based on calculating the mutual influence between the sensing coil and the eddy current on the target was presented. However, this method requires that the area of the target is at least twice as large as the sensing coil so that it can be considered as an infinite plate.
Nevertheless in many industrial applications, it is always required that planar inductive sensors can precisely measure the gaps from narrow and irregular targets. For example, in
3D printing, when a task requires the changing of printing material, the build platform (i.e. thin metallic plates where the material is printed) needs to be replaced because printing various materials requires different adherence and thermal conductivities [91]. For instance, a titanium platform is used for high-temperature printing, while a copper platform is used for uniform heat dissipation when a large object is printed [92]. To guarantee the printing process starts and ends at the designed locations, there is a critical need to monitor
X, Y, and Z positions with high accuracy before and after the replacement of the build platforms [93]. Currently there is no low-cost sensor to detect the accurate position of the thin build platform made of different materials [94]. Similarly, precise position monitoring 74 is necessary for bandsaw blade deviation when bandsaw blades made of different materials are used for cutting different materials [95,96]. In fan blade tip clearance monitoring, dynamic tip clearance needs to be measured in real time with a resolution of ~10 µm to ensure safe operation [11]. Fan blade width could be narrower than the sensing coil and usually cannot be considered as an infinite plate. When there is a need to increase the thrust or power in a harsh environment, the most common way is to change the blade material from aluminum alloy to titanium alloy, which has higher strength and corrosion/creep resistance [97,98]. The above applications all need monitoring of gaps or locations of narrow or irregular shaped targets with high resolution (e.g. 10 µm to 20 µm). Planar inductive sensors could play an indispensable role in these applications because of their simplicity, low cost, and robustness. Thus, it is necessary to develop a gap measurement method for narrow and irregular targets using any size of the planar inductive gap sensor, with simple calibration and sufficient measurement accuracy.
In CHAPTER IV, I will present a new approach to measure the gap from irregular and narrow targets using a planar inductive sensor of any size. This approach expands the measurement capabilities of inductive sensors for narrow and irregular objects made of various materials, without tedious calibrations. The approach is based on calculating the mutual inductance of the sensor and irregular/narrow targets. Finite element method (FEM) simulation was conducted to prove an assumption used in the model. Multiple sensing coils of different sizes were tested to demonstrate the generality of the method. Each sensing coil was tested with four irregular and narrow targets made of four materials. The test results have validated the new approach’s ability to measure the gap from various narrow, irregularly shaped targets with concise calibration and high accuracy.
75 IV.1 MATHEMATICAL MODEL ANALYSIS
IV.1.1 FEA Method
We validated the simulation with a planar coil consisting of 6 turns of copper wire.
The outer diameter and the inner diameters are 8.8 mm and 1.8 mm. The copper wire is
0.45 mm in diameter, with 5.995 × 107 S/m conductivity. The excitation frequency and peak to peak voltage for the sensing coil are 1 MHz and 1 V.
The simulation was conducted with COMSOL, and the mesh size was conducted. The inductance of the planar coil was simulated and compared with the experimental results measured by an LCR meter (E4980A1-030, Keysight technologies). The results in Figure
IV.1 show that the simulation results are in good agreement with the experiments. The difference between the simulation and the experiments is caused by the connection wires between the coil and the LCR meter, which behave as a small inductor at 1 MHz. In addition, mesh independence was also confirmed when using denser and coarser meshes.
Table IV.1 Mesh setup (cubic target)
Max Min Narrow element element Max element Curvature regions size size growth rate resolution resolution (mm) (mm) Target 0.8 0.008 1.3 0.2 1 Coil 3.2 0.4 1.45 0.3 0.85 Domain 3.2 0.4 1.45 0.5 0.6
76
Figure IV.1. Comparison in the inductance variation of the sensing coil as a function of the gap, by LCR measurement and FEM simulation.
First, we simulated the inductance change of a planar coil when a narrow rectangle cubic target made of titanium is placed below the sensing coil. The coil consists of 10 turns of copper wire with an outer diameter of 12.8 mm and an inner diameter of 2 mm. The copper wire is 0.45 mm in diameter, with 5.995 × 107 S/m conductivity. The narrow target is 9 mm in width, 30 mm in length, and 12 mm in height. The gap between the target and coil is 1 mm and 1.5 mm. The excitation frequency and peak to peak voltage for sensing coil are 1 MHz and 1 V.
77 Figure IV.2 and IV.3 demonstrate the unfolded eddy current distribution of the narrow rectangular target when the clearance is 1 mm and 1.5 mm, respectively. It is noted that we flipped the side wall eddy current to the top surface. The FEM simulation shows that the magnetic field distribution on the target is close to a circular footprint for both different gaps. Therefore, the magnetic field induced by the sensing coil on the target can approximately be modeled as a virtual circular coil.
Table IV.2 Mesh setup (cubic target)
Max Min Narrow element element Max element Curvature regions size size growth rate resolution resolution (mm) (mm) Target 0.8 0.008 1.3 0.2 1 Coil 3.2 0.4 1.45 0.3 0.85 Domain 3.2 0.4 1.45 0.5 0.6
Figure IV.2.Eddy current distribution on the target (unfolded vision), with the tip clearance as 1 mm.
78
Figure IV.3. Eddy current distribution on the target (unfolded vision), with the tip clearance as
1.5 mm.
It is noted that the eddy current distribution of the target at different gaps (0.5 mm and
2 mm), different materials (zinc, aluminum, and copper), and a different sensing coil (8 coil turns with inner and outer diameters of 2 mm and 10.4 mm) were also simulated. The simulation suggests that the magnetic field on the rectangular target can be approximated as a circular coil.
Next, we simulated the interaction of the 10-turns copper planar coil (the same as the one used before) and a turbine blade target (titanium). The geometry of the turbine blade is given in Figure IV. The gap between the target and the coil was set to be 1 mm. The excitation frequency and peak to peak voltage for the sensing coil are also 1 MHz and 1 V.
The mesh information of the simulation provided in Table IV.3.
79
Figure IV.4.Side view and isometric view of the turbine blade used in the simulations and the experiments.
Table IV.3 Mesh setup (blade target)
Max Min Narrow element element Max element Curvature regions size size growth rate resolution resolution (mm) (mm) Target 0.8 0.008 1.3 0.2 1 Coil 3.2 0.4 1.45 0.3 0.85 Domain 3.2 0.4 1.45 0.5 0.6
Figure IV.5 shows the view of magnetic field distribution of the blade shape target.
The FEA results show that the magnetic field in the blade target can be still modeled as a circular virtual coil. Note that that we also modeled the magnetic flux distribution on the blade made of other materials (zinc, aluminum, and copper), at other gaps (0.5 mm, 1.5 mm, and 2 mm), and with a smaller coil (8 coil turns with inner and outer diameters of 2 mm and 10.4 mm). With similar eddy current distributions, the magnetic field can be modeled as a virtual circular coil.
80
Figure IV.5. Eddy current distribution on the blade target, with the tip clearance as 1 mm.
81 IV.1.2 Working Principle
Different from the infinite plate target, the foot print of the eddy current distribution on a narrow and irregular target does not concentrate in a horizontal plane. To analyze the distribution of eddy current on a narrow and irregular target, finite element analysis (FEA) was first conducted on a narrow, rectangular target. The details of validation and eddy current distribution in a narrow and irregular target are shown in the previous section. The working principle of the gap measurement from a narrow target using a planar sensing coil is shown in Figure IV.6. While there is an AC excitation with fixed frequency applied to the sensing coil, a magnetic field is induced and causes an eddy current on the target surface
(Shown in Figure IV.6(a)). Finite element analysis (FEA) shows that the magnetic flux density mapping on the target surface shows eddy current being distributed on the surface, and extending along two side walls of the target (see details of the FEM simulation in the previous section). The magnetic flux density mapping on a more complex target was also simulated. The same results are obtained when the target changes to a blade-shape target
(narrow and irregular target). The details can be found from the previous section. From the simulation results, we found that the magnetic flux on the edge of the target’s front area has almost the same magnitude when compared to the magnetic flux on the edge of the target side area (Shown in Figure IV.6(b)). Both the cubic target and the blade shape target showed the same results (See Appendix A). In addition, after flipping the magnetic flux on the side surface to the top surface, it showed that the boundaries of the two surfaces are continuous and can form a circle-like shape. Figure IV.6(b) shows the top view of a typical magnetic flux density distribution once the side surface is flipped to the top surface.
82 Therefore, the eddy current in an irregular and narrow target can be approximately modeled as a virtual planar circular coil. More details of the FEM simulations are provided in previous section. Thus, the coil to coil model can be established to analyze the mutual inductance between the sensing and virtual coils, as shown in Figure IV.6(c). In the mathematical the model, 푟1, 푟2, 푟3, and 푟4 are the inner and outer radii, 푑 is the gap between the sensing and virtual coils, and 푁1 and 푁2 are the turn numbers of the two planar coils
[65]. The sensing coil has the resistance 푅퐶 and the inductance 퐿퐶. Similarly, the virtual coil is modeled as a self-relative inductance 퐿푡 in series with a resistance 푅푡 (as shown in
Figure IV.6(d)). The equivalent circuit of the coil to coil system is shown in Figure IV.6(d)
[5].
83
Figure IV.6. Working principle and simulations of the gap measurement for a narrow target: (a) Schematic sketch of working principle of the gap measurement for a narrow target. (b) Simulated magnetic flux density distribution when flipping the side surface to the top surface by finite element analysis. (c) Gap/displacement measurement can be modeled as a configuration of two coaxial planar coils, namely, sensing coil (top) and virtual coil (bottom). (d) Equivalent circuit of coil to coil system.
The equivalent inductance (L) of the sensing coil can be expressed as the equation
[99]:
휔2푀2퐿 푡 IV.1 퐿 = 퐿퐶 − 2 2 2 푅푡 + 휔 퐿푡
84 Where M represents the mutual inductance between the two coils, and ω refers to the angular frequency of the excitation signal. The M, 퐿푡, and 푅푡 in equation IV.1 can be expressed as the functions of the gap 푑, inner and outer radii, and turn numbers of the two coils [90,100,101]:
푀 = 푓(푟1, 푟2, 푟3, 푟4, 푑, 푁1, 푁2) IV.2
퐿푡 = 푓(푟3, 푟4, 푑, 푁2) IV.3
푅푡 = 푓(푟3, 푟4, 푑, 푁2) IV.4
The details of equations IV.2, IV.3 and IV.4 are described in [50,89,90]. 퐿푡 refers to the function of 푁2 (virtual planar coil turn numbers), 푟3 and 푟4, and 푑 (gap distance), and changing 푁2 can generate the same variations of 퐿푡 as changing 푟3 and 푟4 . Hence, we assume 푟3 equals 푟1 , and 푟4 equals 푟2 . Note that the FEA simulation on a narrow rectangular object and a turbine blade confirmed the reasonability of this assumption (see section IV.1). Further FEA simulation showed that the eddy current distribution remains nearly unchanged when the gap 푑 varies within a small range (푑 from 0.05 to 0.5 times of the sensing coil size 푟2), indicating that the geometry of the virtual coil (푟3, 푟4) can be treated as a constant in calculations [5]. Thus, equation IV.2 can be simplified as [89,102]:
퐿 = 퐿퐶 − 푓(푟1, 푟2, 푑, 푁1, 푁2) IV.5
In equation IV.5, 푟1, 푟2 and 푁1 (the geometry of the sensing coil) are known while the gap 푑 and 푁2 in equation are unknown. 푑 and 푁1/푁2 relations can be established by measuring the sensing coil inductance (L) at 5-6 different gaps [50]. Once the 푁1/푁2- 푑 relation is established, gap 푑 can be calculated based on equation IV.5 with the measured sensing coil inductance L.
85
Figure IV.7. Experiment setup of the gap measurement for a narrow and irregular target.
86 IV.2 EXPERIMENTAL SETUP
The experiment setup is illustrated in Figure IV.7, consisting of a sensing coil, a target, an X-Y-Z manual travel translation stage (10 μm resolution, Thorlabs Inc.) and an LCR-
Meter (E4980A1-030, Keysight technologies). To verify that the method is valid for targets with complex and irregular shapes, a target mimicking a turbine blade shape was selected.
To validate that the algorithm and calibration method can be applied to sensing coils of different sizes, three planar coils with different geometries were fabricated using copper wires with insulation coating (18 Gauge, Solid Round Copper, Essex), with the size of the coils listed in Table IV.4. Each sensing coil was packaged with a ceramic protection layer
(645-N, Ceramacast). The thickness of the ceramic layer is approximately 500 μm, protecting the sensing coil. Four targets with the same geometry, made of different materials, titanium, zinc, aluminum, and copper, were tested to analyze the effect of the materials/conductivity variations. The conductivities of these four materials vary from 0.75
× 106 S/m to 59.95 × 106 S/m, covering all the conductivities of the commonly-used metallic materials. The narrow and irregular shaped targets employed in the tests (Figure
IV.8(a)) mimic a gas turbine blade, whose geometry and dimension are given in Figure
IV.8(b) [103]. The targets were manufactured by a CNC machine (VF-1, Haas Automation
Inc.). The thickness of the target is 13.03 mm, which is much larger than the full penetration depth of the four materials [5].
87
Figure IV.8. Working principle of blade target gap measurement and the design of the
narrow and irregular shaped blade target: (a) Schematic sketch of gap measurement
configuration between a sensing coil and a narrow and irregular shaped blade target. (b)
Side view and isometric view of the blade target.
The gap was adjusted by the X-Y-Z stage. The inductance of the sensing coil was
measured using the LCR meter at various gaps.
Table IV.4 The geometries and the excitation voltage/frequency of the three coils employed
Inner Outer Excitation # of Turns Diameter Diameter Voltage/Frequency Coil 1 2.0 mm 14.20 mm 10 1V / 1MHz Coil 2 2.0 mm 12.92 mm 8 1V / 1MHz Coil 3 2.0 mm 9.02 mm 6 1V / 1MHz
Before the gap measurement tests, the phase angles of the three coils were measured
under three different excitation frequencies (0.5, 1, and 2 MHz). Results showed that the
phase angles of the three coils were all larger than 85 degrees, implying that the coil
88 inductance dominates the impedance of each coil. Thus, the serial R-L mathematical model can be applied within the working frequencies (0.5-2 MHz). The base inductances, 퐿퐶, were also measured to be 1.601 μH, 1.248 μH, and 0.923 μH at 1 MHz. When defined inductor’s Q factor as ωL/R, the Q factor for the fabricated sensing coil 1 is 14.71, 12.14 for sensing coil 2, and 7.07 for sensing coil 3 while applied 1 MHz excitation frequency.
89 IV.3 RESULTS AND DISCUSSIONS
IV.3.1 Calibration
The equivalent inductance of each sensing coil was measured when the target was moved closer to or away from the sensing coil. Seven 푑 values (as shown in Figure IV.9) ranging from 500 μm to 3600 μm were used to establish the relation between the inductance change and 푑. All three coils were measured with four targets (with the same geometry) made of titanium, zinc, aluminum, and copper. Figure IV.9 (top) demonstrates the inductance variations of the sensing coil 1, suggesting that the inductance increased with the increase of the gap because of the decrease of the mutual inductance between the sensor and the target. Then, all the knowns 푑, 푟1, 푟2, 푁1, and 퐿푐 were applied to equation IV.5 to solve 푁2 with the bi-section method for measureing the inductance 퐿. A relation between
푁2 and 푑 of sensing coil 1 (14.20 mm diameter) was established for the four targets, as shown in Figure IV.9 (bottom). With the increasing gap 푑, 푁2 is decreased, reflecting the decease in mutual inductance (or eddy current). In addition, the higher the conductivity of the material, the larger the value of 푁2, because the eddy current increases with the increase of the conductivity.
90
Figure IV. 9. Measured inductance and calculated 푁2 of sensing coil 1 (14.20 mm) as a function of the gap 푑 for four targets made of different materials (titanium, zinc, aluminum, and copper).
91
Figure IV.10. 푁1/푁2 curves and constant C of four different target materials for coil 1:
(a) 푁1/푁2 curves obtained from sensing coil 1 for four different target materials. (b)
Constant C for the four target materials with sensing coil 1.
Subsequently, 푁2 -푑 curves were then converted to 푁1/푁2 -푑 curves, where 푁1 represents the turn number of the sensing coil (푁1 = 10 for sensing coil 1). 푁2-푑 curves for sensing coil 2 and 3 can be obtained by repeating the same procedure, which can be converted to 푁1/푁2-푑 curves (푁1 values of sensing coil 2 and 3 are 6 and 8). Each sensing coil was tested with four targets made of different materials. Figures IV.10(a), 11(a) and
12(a) show the 푁1/푁2-푑 curves of the three sensing coils of different sizes. For irregular
92 and narrow targets, the 푁1/푁2-푑 curves are parallel when changing the materials. Thus, a base calibration curve can be established for a reference material, and the 푁1/푁2-푑 curves for targets made of different materials can be calculated by adding a constant C to the base curve. Here, titanium is used as the base material. The constant C is the 푁1/푁2 differences between the base material and another target material.
푁1 푁1 퐶 = ( ) − ( ) IV.6 푁2 푇푎푟푔푒푡 푁2 퐵푎푠푒
The C values and standard variations for the three coils are shown in Figures IV.10(b),
11(b), and 12(b) and listed in Table IV.5. The variations in C are relatively small. The larger the sensing coil, the larger C is. A small sensing coil has a small value of C. The trend is in agreement with that for large plate targets.
93
Figure IV.11. 푁1/푁2 curves and constant C of four different target materials for coil 2:
(a) 푁1/푁2 curves obtained from sensing coil 2 for four different target materials (b)
Constant C for the four target materials with sensing coil 2.
th Next, we used 6 -order polynomials to represent the 푁1/푁푇-푑 relation for the base material, and obtain the curves for other materials. The calibration curves for each coil are given below:
For coil 1 calibration curves:
94 푁1 = 푓푇 + 2.459 + 퐶 IV.7 푁2
Where:
−22 6 −18 5 −14 4 푓푇 = −5.831 × 10 푑 + 5.601 × 10 푑 − 1.882 × 10 푑 + 5.276 IV.8 × 10−11푑3 − 6.408 × 10−8푑2 + 2.333 × 10−4푑
For coil 2 calibration curves:
푁1 = 푔푇 + 2.247 + 퐶 IV.9 푁2
Where:
−21 6 −17 5 −13 4 푔푇 = 3.446 × 10 푑 − 4.621 × 10 푑 + 2.469 × 10 푑 − 6.458 IV.10 × 10−10푑3 + 9.305 × 10−7푑2 − 6.607 × 10−4푑
For coil 3 calibration curves:
푁1 = 푦푇 + 1.150 + 퐶 IV. 11 푁2
Where:
−20 6 −16 5 −13 4 푦푇 = 1.706 × 10 푑 + 2.018 × 10 푑 − 9.282 × 10 푑 IV. 12 + 2.153 × 10−9푑3 − 2.505 × 10−6푑2 + 1.343 × 10−3푑
All values of C for different materials and sensing coil combinations can be found in Table
IV.5.
Next, we evaluated the gap measurement accuracy using the calibration method. We selected the 푁1/푁2-푑 curve for titanium as the base calibration curve, and obtained the
95 푁1/푁2-푑 curve for the zinc, aluminum, and copper targets by adding constants C listed in
Table IV.5.
96 Table IV.5. The value of 퐶 of three coils for the blade target.
Coil 1 (14.20 mm) Coil 2 (12.92 mm) Coil 3 (9.02 mm) 퐶 (Zinc) -0.1550±0.0142 -0.1149±0.0065 -0.0711±0.0049 퐶 (Aluminum) -0.2776±0.0084 -0.2001±0.0103 -0.1310±0.0093 퐶 (Copper) -0.4034±0.0071 -0.2862±0.0070 -0.1931±0.0069
Figure IV.12. 푁1/푁2 curves and constant C of four different target materials for coil 2:
(a) 푁1/푁2 curves obtained from sensing coil 3 for four different target materials (b)
Constant C for the four target materials with sensing coil 3.
IV.3.2 Error analysis
97 To estimate the accuracy of the calibration method, approximately 20 gap values ranging from 500 μm to 3600 μm were tested for each blade target. From the calibration curves listed above, the gap 푑 can be determined from the measured inductance. The ratios of the calculated 푑 over the actual 푑 were also calculated, and plotted in Figures IV.13, 14 and 15.
For sensing coil 1, the maximum error of the zinc blade was 3.681% when 푑 = 1440
μm (Figure IV.13(a)). For the aluminum blade (Figure IV.13(b)), the maximum error was
3.108% at 푑 = 740 μm. When switching to a copper blade (Figure IV.13(c)), the maximum error was 3.148% when 푑 = 540 μm. Figures IV.14(a), 9(b) and 9(c) show the accuracy test results of the sensing coil 2. The maximum error was 3.703% when 푑 = 540 μm with an aluminum blade (Figure IV.14(b)). The accuracy test results for coil 3 are shown in
Figures IV.15(a), 15(b) and 15(c). The maximum error was 3.269% at 푑 = 520 μm for an aluminum blade (Figure IV.15(b)). Three factors are responsible for the errors: 1) the 10
µm resolution of the XYZ stage when setting the gap; 2) the truncating error when calculating 푁2 with the bisection method; and 3) limited data points when establishing the calibration curves for base materials [104].
For all measurements, the calculated 푑 is in good agreement with the actual 푑, with relatively small measurement errors. The results indicate that there is no need to switch to a small sensing coil to measure the gaps from narrow or irregular targets. In the calibration process, only one base curve needs to be established for a given irregular and narrow shape of the target; calibration curves for targets made by other materials can be obtained by adding constants to the base curve. The value of constant C can be determined by measuring once at a known gap. This approach significantly simplifies the calibration when 98 using planar inductive sensors to measure the gaps from narrow and irregular targets while the target materials are changed.
99
Figure IV.13. Ratios of the calculated 푑 over the actual 푑 between sensing coil 1 and the irregular blade targets made of: (a) Zinc, (b) Aluminum, and (c) Copper. The maximum errors for the zinc, aluminum, and copper targets were 3.681%, 3.108%, and 3.148%, respectively.
100
Figure IV.14. Ratios of the calculated 푑 over the actual 푑 between sensing coil 2 and the irregular blade targets made of: (a) Zinc, (b) Aluminum, and (c) Copper. The maximum errors for the zinc, aluminum, and copper targets were 3.395%, 3.703%, and 2.535%, respectively.
101
Figure IV.15. Ratios of the calculated 푑 over the actual 푑 between sensing coil 3 and the irregular blade targets made of: (a) Zinc, (b) Aluminum, and (c) Copper. The maximum errors for the zinc, aluminum, and copper targets were 2.916%, 3.269%, and 2.584%, respectively.
IV.4 SUMMARY
In this chapter, I developed a new calibration method for planar inductive sensors.
With this method, the gap from a narrow and/or irregular object can be accurately measured without tedious calibration while materials of the targets are changed. In our experiments, four targets made of four different materials, with a narrow width and an irregular shape,
102 were used for the demonstration. Three planar coils of different sizes were fabricated for testing. The inductance variation of each coil was measured for gaps ranging from 500 μm to 3600 μm with four blade-like targets made of multiple materials. The established 푁1/푁2-
푑 curve for each coil shows that the 푁1/푁2-푑 curves are in parallel even when the target is an irregular and narrow object. Hence, the calibration curves for a different material can be obtained by adding a constant C to the base curve. The value of the constant C can be determined by measuring the coil inductance only one time and at one known gap. The accuracy tests show that the measurement error in the gap is within 3.703% with this new calibration methods. It is expected that this method can significantly reduce the calibration work to monitor the gap/displacement of irregular/narrow targets in advanced industrial applications including: 3D printer build platform calibration, bandsaw blade deviation detection, and blade tip clearance monitoring.
In short, the contributions of objective 2 can be summarized that we expanded the application range of the calibration method from objective 1 so that the calibration method can be applied to:
Measure the gaps from any narrow and irregular objects made of various materials
without tedious calibrations. It can be used for a wide variety applications, including
dynamic tip clearance measurement, CNC machine platform calibration, and bandsaw
blade deviation detection. These applications would otherwise need tedious calibration
if the target material is changed.
The new method does not require the planar coil sensor to be larger than the target.
This provides great flexibilities in using planar inductive sensors of any size to measure
the gaps from narrow and irregular objects. 103 CHAPTER V
AN ADVANCED SENSOR ARRAY FOR WEAR DEBRIS MONITORING IN
LUBRICANT OIL
In addition to the calibration process limiting the use of planar inductive sensors for displacement measurement, there are a number of other limitations that restrict the use of planar inductive sensors in other non-contact measurement applications. One typical example is the monitoring of wear debris in lubricant oil.
Machine parts normally suffer from increasing levels of wear as a machine operates. The wear debris generated by operating the machine can be roughly classified into four stages based on the degree of damage that they could cause the machine. 1) The diameter of wear debris is less than 10 µm diameter. The wear debris at this range is always found as the normal benign wear in sliding surfaces. 2) The diameter of wear debris is from
10 to 100 µm. It usually occurs as abnormal abrasive wear due to the interpenetration of sliding wear. 3) The diameter of wear debris is larger than 100 but smaller than 500 µm.
The wear debris at this range is generated from the onset of severe wear. 4) The diameter of wear debris is larger than 500 µm. This happens due to extra excessive load and high speed. Normally, most of the wear debris generated by friction between the parts can be
104 carried by the lubricant oil inside of the machine [105]. Thus, monitoring the wear debris in lubricant oil can help to estimate the working condition of the machine.
As mentioned in Chapter II, monitoring the wear debris in lubricant oil using planar inductive sensors has several obvious unique advantages. In short, they can be summarized as 1) Based on the working principle of the planar inductive sensor, the monitored results will not be effected by different properties of the lubricant oil, such as viscosity, density, and moisture. 2) Because of their large measurement range, they can identify the wear debris in widely varying sizes (from 50-300 µm) [106]. 3) Since the planar inductive sensor has fast response time and high sensitivity, it can monitor the concentration of the wear debris in lubricant oil.
However, the limitations of the planar inductive sensors for oil debris monitoring are also conspicuous. First, they have an inability to process the large amount of data generated from the sensor in real time. Second, the sensitivity is insufficient in detecting smaller debris which fit the latest requirements from industrial applications [107].
Detection of the smaller (20-100µm) debris allows for the monitoring of the entire wear progression from the start of the severe wear, and provides early warning of pending failure well ahead of catastrophic failure. Until now, monitoring sensing systems cannot reduce the amount of data from the sensor without sacrificing the sensitivity that allows for real time detection of wear debris (during severe and advanced machine wear). Third, the monitoring speed of the planar inductive sensor cannot reach the required speed which is
200-500 ml/min for normal machine [108]. All of these factors are critical for avoiding catastrophic machine failure and enabling predictive maintenance.
105 In this chapter, a new sensor for monitoring the wear debris in lubricant oil is presented in order to overcome the inconveniences and limitations of using planar inductive sensors in real applications. The new sensor will utilize an under sampling method to significantly reduce the amount of data that is collected from the parallel sensing channels. Furthermore, the new design of the sensing coil further increases the sensitivity of the sensing system. In addition, with the parallel sensing system, the measurement speed of the sensing system can be easily adjusted without re-designing the system or requiring the extra supply equipment, and also has a high speed upper limit. All these advantages make the sensor suitable for onsite oil condition monitoring which is required by many industries.
106 V.1 DESIGN CONCEPT FOR SINGLE-SENSING CHANNEL
V.1.1 Design of multi-layers planar inductive sensing coil
A single sensing tube in the sensing system includes a sensing planar coil which is made of a planar coil wound around a 1.56 mm outer diameter tubing (Shown in Figure
V.1a). While applying a high AC excitation frequency to the sensing coil, a magnetic field is generated. When a ferrous debris in lubricant oil passes through the sensing channel, the magnetic permeability effect dominates the main change of the inductance variance of the sensing coil so that the inductance of the sensing coil is increased. Section II.5.2 illustrated the working principle of the planar inductive sensor for monitoring the wear debris in lubricant oil. While a nonferrous debris passes through the sensing channel, the eddy current effect dominates the main change of the inductance variance of the sensing coil and causes a decrease of the inductance of the sensing coil. The variance of magnitude depends on the geometric design and the excitation frequency of the sensing coil.
107
Figure V.1. The design of the multi-layers inductive sensing coil.
The transfer function of the sensitivity of the multi-layers planar inductive coil can be expressed as equation V.1 [44]:
108 10−7 휋3 ∙ 푓 ∙ 푙 푆 = ∙ ∙ (퐷 − 퐷 ) ∙ (퐷 + 퐷 )2 V.1 4 푘푑2 푖 푖
Where 퐷푖 and 퐷 is the inner and outer diameter of the coil, 푙 is the length of the coil, 푑 is the diameter of the wire, 푘 is the packing factor which is a constant of 0.85, and
푓 is the excitation frequency (Shown in Figure V.1c). When designing a multi-layer inductive planar sensing coil to monitor the debris in lubricant oil, in order to identify the single debris, the length of the coil 푙 in equation V.1 needs to be controlled and limited.
Previous research by Zhu, et al indicated that the maximum length of the sensing coil needs to be smaller than 150 μm for identifying less than 50 μm diameter debris [79]. Thus, the maximum number of sensing coil’s layers can be calculated once the diameter of the wire is known.
Figure V.2. The analysis of sensitivity of the coil with different number of layers and turns.
109 Figure V.2 shows the analysis results of the coil’s sensitivity from equation V.1 based on different geometries. It indicates that the higher number of turns and length brings the higher sensitivity. From the analysis above, the three-layer planar sensing coil is designed by using 44 AWG (50 µm diameter) copper wire. Considering the difficulties during fabrication, each layer has 8 turns (Shown in Figure V.1b). In order to fabricate the three-layer planar sensing coil, two small flangeless ferrules (1.60 mm inner diameter) were slipped at the mid of the transfer tube with opposite direction (Shown in Figure V.1b), the gap between two flangeless ferrules is about 150 µm. Then, the hot-melt glue was used to fix the position of the ferrules. Next, the copper wires are winded with 8 turns for the each layer.
After fabricating the three-layer planar coil, a small amount of the super glue was applied at gap between two ferrules so that the position of the sensing coil can be fixed.
Afterwards, the two ferrules can be taken away by melting the hot-melt glue. Finally, an
LCR (E4980A1-030, Keysight Technologies) is used to measure the impedance of the sensing coil which has 952 nH inductance and 1.81 Ω resistance. When defining the inductor’s Q factor as ωL/R, the Q factor for the fabricated sensing coil is 6.61 when a 2
MHz excitation frequency is applied.
Note that we selected the 1.47 mm inner diameter and 1.56 mm outer diameter polyimide tubing as the transfer tubing. It has a good resistance to abrasion and has wear properties rivalling even those of PPEK. Furthermore, the polyimide tubing also shows a good resistance to acids, hydrocarbons, and common solvents. All of these characteristics mean that the sensing channel can have a long life and stable flow rate.
110 V.1.2 Measurement Circuit
Although the designed planar sensing coil in previous section has a high sensitivity, it still may not be enough to identify the wear debris that has a diameter of less than 50 µm.
In order to further increase the sensitivity, an LC circuit is designed and used to amplify the relative change of output signal from the sensing coil. The equivalent circuit is shown in Figure V.3b, the sensing coil connects in parallel with an external capacitor 퐶푖 so that the LC circuit has a unique resonant frequency. The resonant frequency 푓푅 of the LC circuit can be calculated using equation V.2-V.5:
1 푓푅 = V.2 2휋√퐿푖퐶푖
At the resonant frequency, the circuit has the largest impedance. In addition, when the debris passes through the sensing coil, the small inductance change of the sensing coil causes a large impedance change of the LC circuit. Thus, the sensitivity can be improved.
In order to study the magnitude of sensitivity improvement, two circuits were simulated and studied (Shown in Figure V.3). The first circuit (Shown in Figure V.3a) is without the
LC resonance circuit and the second is with the LC resonance circuit. When there is an inductance change ∆퐿 caused by passing the debris, the relative change of the impedance of the sensing coil in circuit 1 and circuit 2 can be expanded as equation V.3 and V.4:
∆푍 [푅 + 푗휔(퐿 + ∆퐿)] − [푅 + 푗휔퐿 ] ( ) = | 1 1 1 1 | V.3 푍 1 푅1 + 푗휔퐿1
111 ∆푍 ( ) 푍 2
푅 + 푗휔(퐿 + ∆퐿) 푅 + 푗휔퐿 V.4 [ 2 2 ] − [ 2 2 ] (1 − 휔2(퐿 + ∆퐿)퐶 ) + 푗휔푅 퐶 (1 − 휔2퐿 퐶 ) + 푗휔푅 퐶 = | 2 2 2 2 2 2 2 2 | 푅2 + 푗휔퐿2 2 (1 − 휔 퐿2퐶2) + 푗휔퐶2
Where the 퐿1 and 퐿2 are the inductance of the sensing coil in circuit 1 and circuit
2, 푅1 and 푅2 are the resistance of the sensing coil in circuit 1 and circuit 2, 퐶2 is the capacitance of the external capacitor in circuit 2, 휔 is the excitation frequency which is equal to 2πf. Since the measured phase angle of an inductive sensing coil is always from
70 to 90 degrees, the inductance dominates the impedance. Thus, the resistance of the sensing coil 푅1 and 푅2 in both circuits can be approximately ignored, and the equation V.3 and V.4 can be roughly simplified as:
∆푍 ∆퐿 ( ) ≈ | | V.5 푍 1 퐿1
∆퐿 | | ∆푍 퐿2 V.6 ( ) ≈ 2 푍 2 |1 − 휔 퐿2퐶2|
When the selected excitation frequency is closest to the resonant frequency, the
2 |1 − 휔 퐿2퐶2| in equal V.4 is smaller than 1. Thus, with the same inductance variance of the sensing coil ∆퐿, the change of impedance in equation V.6 is larger than the change of impedance in equation V.5. The precisely calculated results using equation V.3 and V.4 are shown in next paragraph.
112
Figure V.3. Regular circuit (a) and LC circuit (b) for measurement.
We assume that for each circuit, the inductance of the sensing coil is changed about
0.5% when there is a debris particle passing through the sensing coil. The relative change of impedance in equation V.3 and V.4 were calculated with two different sensing coils, the first sensing coil has an inductance and resistance of 900 nH and 3 Ω, which has a 76.4 degree phase angle, and the second sensing coil has a 1000 nH inductance and 2 Ω resistance with 81.7574 degree phase angle. When plugging the first sensing coil in both circuit 1 and circuit 2 (퐿1 is equal to 퐿2), selecting 퐶2 to be 6.8 nF, the relative change of the impedance of the sensing part in circuit 1 and circuit 2 while changing the excitation frequency is shown in Figure V.4a. Figure V.4b shows the calculation result when switched to the second sensing coil in both circuit.
113
Figure V.4. The change of total impedance with regular circuit and LC circuit when the sensing coil has a inductance and resistance of (a) 900 nH and 3 Ω, and (b) 1000 nH and 2
Ω.
114 From Figure V.4, it is easy to find that the change of total impedance at the highest point with the LC circuit (circuit 2) is much larger than the circuit 1. The relative change of the total impedance with the LC circuit reaches the peak when the excitation frequency reaches the resonant frequency. The resonant frequency for the first sensing coil is about
2.03 MHz, and 1.93 MHz for the second sensing coil, which matches the calculation results from equation V.2. In addition, the results also indicates that the sensing coil which has higher phase angle has the lower resonant frequency.
In our case, the fabricated sensing coil has the 952 nH inductance and 1.81 Ω resistance. When connected in parallel with a 6.8 nF external capacitor, the resonant frequency occurs at 1.98 MHz. Therefore, the excitation signal applied to the fabricated sensing coil was set to be a 2 MHz frequency and 10 V peak to peak signal.
115 V.1.3 Under-sampling signal processing method
Generally, in order to re-construct the full excitation signal, an appropriate sampling rate needs to be selected based on the Nyquist sampling theorem [109], which the sampling rate is at least 2 times than the excitation frequency [110]. For example, while using 2 MHz as the excitation frequency, the minimum required sampling rate is about 4
MHz. However, the range of sampling rate of a common portable compact data acquisition system is always less than 3.2 MHz [111]. Thus, when designing a monitoring device, the signal processing method needs to consider the limitations of the data acquisition system.
Obviously, a maximum sampling rate of 3.2 MHz is too low to re-construct a 2 MHz excitation frequency. Thus, the under-sampling signal processing method is introduced.
Under-sampling is a method which allows people to analyze and re-construct a signal by using a much lower sampling rate than the Nyquist rate. In short, the re-constructed signal from using under-sampling method can still reflect the signal peak from original signal, and the frequency of the original signal can be still determined. Pharr M, et al provides the concept and the method of the under-sampling [112]. In addition, Du L, et al proves that the under-sampling at the appropriate range can be used to capture the peak from the excitation signal even if there is a time lag between the start of the sample process and excitation signal. The selection range of the under-sampling rate can be calculated using equation V.7 [113]:
푇 푛 ∙ 푇 < 푇 < 푒푥푐푖푡푎푡푖표푛 + 푛 ∙ 푇 V.7 푒푥푐푖푡푎푡푖표푛 푠푎푚푝푙푖푛푔 4 푒푥푐푖푡푎푡푖표푛
116 Where 푛 is an integer which is larger than 0, 푇푠푎푚푝푙푖푛푔 is the period of sampling rate, and 푇푒푥푐푖푡푎푡푖표푛 is the period of excitation signal. The period of peak frequency (Tpeak) can be determined by using equation V.8:
푇푒푥푐푖푡푎푡푖표푛 ∙ 푇푠푎푚푝푙푖푛푔 푇푝푒푎푘 = V.8 푇푠푎푚푝푙푖푛푔 − 푛푇푒푥푐푖푡푎푡푖표푛
When using NI-DAQ-6124 S Series as the data acquisition system, the maximum total sampling rate for all 8 channels is 2 MHz. In multi-channel measurement, the maximum sampling rate for each single channel is limited to less than 150k Hz. Thus, from equation V.7, when using 2 MHz as the excitation frequency, the range of 푛 needs to be larger than 14. We select the sampling rate from 80k Hz and increase 10k Hz for each time.
While increasing from 80k Hz to 150k Hz, since 푛 needs to be an integer, only a sampling rate of 110k Hz (푛 = 18) satisfied the relation from equation V.7. Next, in order to prove that the under-sampling method can satisfy our requirement, a ±10V peak to peak with 2
MHz frequency excitation signal was captured using a 110k Hz sampling rate. Figure V.5
(black points and blue line) shows the results of collection. After using the cubic spline in
Matlab to re-construct the signal, the result (red line) is shown in Figure V.5, which indicates that the 110k Hz sampling rate can capture the peaks of the excitation signal well.
In addition, based on the equation V.8, the period between two peaks while using a 110k
Hz sampling rate to record the 2 MHz excitation frequency is 0.00005s.
117
Figure V.5. Signal re-construction using the cubic spline method.
118 V.2 DEVICE DESIGN
The lubricant oil monitoring device includes two flow dividers, a multi-sensing system, a data acquisition system, and a power source (Shown in Figure V.6a). First, the lubricant oil flows into the first flow divider which is used to separate the lubricant oil from the total inlet and divide to each single channel. The multi-sensing system contains several single polyimide sensing tubes. There is a 16.7 mm distance between two tubes. Each tube has a 130 mm length and connects to the flow divider through an adapter. The structure of the adapter is shown in Figure V.6b so that the different sizes of the two outlet/inlet (the outlet of flow divider and inlet of the single tubing) can be transferred. The flangeless fittings also guarantee the tightness between two joints. There is a multi-layer planar inductive sensing coil with LC measurement circuit at the middle of each sensing tubing.
A 10 volt peak to peak, 2 MHz excitation signal is applied to the sensing coil, and a multi- channel data acquisition systems (NI-6124 S) is used to collect the data from the sensing coil using the under-sampling method (110k Hz). Each single tube connects in parallel with the power source so that it requires only one power supply for the whole sensing system.
The number of the tubes is based on the number of divided channels in the flow divider.
Next, the lubricant oil passes through all the sensing tubes, and then flows into the second flow divider (the outlet of the device). In order to keep each part of the device in a horizontal position a set of supports for the adapters, flow dividers and tubes are designed.
All the supports are manufactured by using 3D printers. The supports for the flow dividers use Tango materials (Stratasys Ltd., MN, USA), and PLA materials (Ultimater Inc., USA) are used for the adapters and tubes.
119
Figure V.6. The details of construction and parts of the sensing device.
The obvious advantage of this design is that it has a high upper limit of measurement speed. Theoretically, since all of the sensing tubes have a parallel connection to the power source, increasing the measurement flow rate can be achieved by just
120 increasing the number of sensing tubes. In addition, when the total sampling rate is fixed, for larger numbers of sensing tubes, using a lower appropriate sampling rate through the under-sampling method can significantly reduce the amount of data. In summary, the measurement speed of this device only depends on the number of divided channels in the flow divider and the number of sensing channels in the data acquisition board.
121 V.3 DEVICE CALIBRATION AND VALIDATION
V.3.1 Calibration process
In order to establish the calibration curve, which represents the relations between the relative voltage change and the debris size, first, iron particles with different sizes were selected and the surface area of each iron particle was calculated. We used a digital microscope (VHX-7000, Keyence Co., Osaka, Japan) to import the 6 selected particles.
Each iron particle was considered to be a sphere shape particle. The area of each particle was calculated using a built-in algorithm from the digital microscope where the boundary of each iron particle was first described using a complicated polygon, and then the area of the polygon was calculated (Shown in Figure V.7). Since each particle was approximated as a sphere and the surface area was known, the equivalent diameter of each particle can be determined using equation V.9:
4 ∙ 퐴푝 퐷 = √ (V.9) 푝 휋
Where 퐴푝 is the calculated area of the particle. Next, each selected particle was fixed at the head of a 200 μm diameter plastic fiber (Shown in Figure V.8). One side of the plastic fiber was fixed on an X linear stage. The other side of the plastic fiber with the iron particle was inserted inside of a single sensing tubing. The geometries and information of the sensing tubing was provided in the previous section. The excitation signal for the sensing circuit was selected to be 10 V peak to peak and 2 MHz frequency. Finally, an NI-
DAQ-6124 S collected the output data using a 110k Hz sampling rate. Figure V.9 shows
122 the relative output voltage pulses when 6 different sizes of iron particle pass through sensing coil.
Figure V.7. The surface area of the particles measured from digital microscope (VHX-
7000, Keyence Co., Osaka, Japan).
Figure V. 8. Illustration of the experiment setup which includes a linear stage, a single sensing tube, a measurement circuit, a power source, and a DAQ device. 123
Figure V.9. Relative output voltage pulses for 25.1 μm, 35.7 μm, 45.2 μm, 56.4 μm, 65.1
μm, and 75 μm diameter iron particles.
124 As shown in Figure V.9, the pulse height for the smallest iron particle (25.1 μm diameter) is about 0.000526. For the largest iron particle which has 75 μm diameter, the pulse height is about 0.0034. The maximum noise level is around ±0.0002 which is much smaller than the smallest iron particle’s pulse height. Thus, a calibration curve which describe the relations between the magnitude of the relative output change and the sizes of the particles can be established (Shown in Figure V.10).
Figure V.10. The calibration curve of relative voltage for iron particles ranging from 25.1
μm to 75 μm in diameter.
125 V.3.2 Device validation
In order to validate the multi-sensing channel system, a 6 channel sensing system was used to detect the three different samples which contain different sizes of iron particles.
The range of iron particle size for each sample is about 30±5 μm, 50±5 μm, and 70±5 μm.
0.8-1.5 mg of each sample was measured and mixed with 100 ml lubricant oil. The relative output pulses for the six channels are shown in Figure V.11, V.12, and V.13.
126
Figure V.11. Measured relative voltage change caused by iron particles with size of 70±5
μm diameter.
127
Figure V.12.Measured relative voltage change caused by iron particles with size of 50±5
μm diameter.
128
Figure V.13. Measured relative voltage change caused by iron particles with size of 30±5
μm diameter.
129 As shown in Figure V.11, V.12, and V.13, for 70±5 μm diameter iron particles, the relative output pulse of most of the particles ranged from 0.001868 to 0.0034. For 50±5
μm dimeter particles, most of the pulses fell between 0.000981 and 0.00132. Finally, the range from 0.000526 to 0.00065 contains most of the pulses for the 30±5 μm diameter iron particles. The test shows that the sensing system can detect ferrous particles well and that the measured particle’s size has a good agreement with the calibration curve. Furthermore, with a three layer sensing coil, the sensor can detect down to 25 μm diameter iron particles in 1.46 mm diameter tubing. In order to compare the sensitivity to other devices, we defined a TP value for each device in equation V.10 which presents the ratios between the inner diameter (퐷푡) of the sensing tubing and the diameter of the smallest detectable particles
(퐷푃):
퐷 푇푃 = 푡 V.10 퐷푃
Figure V.14 shows the TP values for debris monitoring devices designed for monitoring iron particles under 100 μm in diameter within the past ten years. Our device has the highest 푇푃 value compared to the other 7 devices in past 10 years.
130
Figure V.14. The TP value of debris monitoring devices from the past 10 years [77,79,114–
118].
In addition, the test also proved that using a 110k Hz under-sampling rate shows no problem in collecting the data from a 2 MHz excitation signal. With the multi-channel sensing system, the monitored flow rate was improved without sacrificing the sensitivity.
Furthermore, the flow rate can be continually increased when using a flow divider and a
DAQ device with more channels. While increasing the number of sensing channels, only a lower under-sampling rate needs to be applied. However, there are a few pulses which are outside of the expected range; the reason for this may be because of different sized particles in the samples.
131 In section V.1, it is proved that the under-sampling method can capture the peak of the excitation signal. However, when re-constructing the original signal, the reconstructed sine wave signal has a lower frequency than the excitation frequency. This may cause an issue when a particle passes through the sensing coil with a high speed, it may not be able to capture the pulses caused by the particles. During machine operation, it is suggested that the lubricant oil needs to be replaced when it contains more than 20-30 ppm debris [119].
In order to demonstrate that the under-sampling method in our device can satisfy the requirement from the industrial applications, two more tests were designed. First, in order to prepare the samples with 30 ppm particles, 3 mg of 50±5 μm, 60±5 μm, and 70±5 μm size of the particles were prepared. Each group of particles was mixed well with 150 ml of
10W-30 lubricant oil (Manufactured by Warren Distribution, Inc., NE, U.S.A.). Then, the flow rate speed was set as 180 ml/min for the sensing system (0.5 ml/s for each single sensing tube). The number of particles were counted when 1 ml mixed sample passed through the single sensing tubing. Since the size of the particles have a ±5 μm variance, the number of the upper and lower limits of the particles which were expected to pass the sensing tube in 1 ml of sample were calculated. For example, when testing the 30 ppm sample which contains 70±5 μm particles, we first calculated the total weight of the particles in 150 ml lubricant oil. Then, we assumed that all the particles have 65 μm diameter so that the weight of each particle can be determined. Thus, the number of 65 μm diameter particles in 150ml lubricant oil can be calculated. After that, we repeated the steps mentioned above, but changed the particle’s diameter to be 75 μm. Finally, we transferred the results from 150 ml to 1 ml lubricant oil. From this, the lower and upper limit of the particle numbers were determined. The results in Figure V.15a indicates that our
132 measurements for all the different sizes of the particles are within the range. Figure V.15b shows the same results when the samples were switched to 20 ppm. All these results show that the under-sampling method can meet the basic measurement requirements for industrial applications.
Figure V.15. Results of 30 ppm (a) and 20 ppm (b) concentration test. Three different sizes of iron particles, 50±5 μm, 60±5 μm, and 70±5 μm were used for each test. 133 V.4 CONCLUSION
We developed a multi-sensing channel system which can be used to monitor the wear debris in lubricant oil. The new structure of the multi-layer planar inductive sensor was designed and the LC circuit was applied to improve the sensitivity (detect 25 μm iron particles by using a 1470 μm inner diameter sensing tube). It is worthy to mention that when detecting wear debris in lubricant oil, a large portion of the running lubricant of the machine needs to be analyzed to represent the machine’s working condition and health statues properly. General real time detection typically requires that the sensing system has an ability to detect wear debris at a flow rate above 180 ml/s [120]. If a small pipe is used, although the sensitivity could be higher, it can only process a very small flow rate. One goal of this research is to use a relatively large pipe to achieve wear debris detection at a higher flow rate while the sensor still has the ability to detect wear debris of ~20 μm.
In addition, the under-sampling signal processing method was applied in order to significantly reduce the amount of data that is collected from the parallel sensing channels.
Thus, most of the data acquisition systems which are used in industrial applications can meet the requirement of the sampling rate of the multi-sensing channel system. During the test, we demonstrated that the new device can detect 25 μm iron particles in a 1470 μm inner diameter sensing tube. Furthermore, the concentration test demonstrated that reducing the amount of collected data will not cause pulses to be missed when the debris is passing through the sensing tube. In addition, the parallel connection between each single sensing channel makes the monitored flow rate easily adjustable by simply changing the number of channels in the flow divider and the data acquisition board. 134 Note that the sensing device is able to differentiate nonferrous and ferrous wear particles by looking at the polarities of inductive pulses. When a nonferrous metallic particle passes through the sensing coil, it leads to a decrease in inductance of the sensing coil, because an eddy current generated inside the metallic particle tends to decrease the magnetic flux at high excitation frequency. When a ferrous metallic particle passes through the sensing coil, it leads an increase in inductance of the sensing coil, because the magnetic permeability effect is dominant at relatively low frequencies. However, currently the sensor cannot differentiate nonferrous debris. For instance, if a copper and zinc debris with the same size pass the sensing col, the sensor is unable to difference them because they all generate negative pulses. The magnitude would be different work. Future work needs to be done to identify the debris materials.
In short, the contributions of objective 2 can be summarized that we developed a new multi-channel sensing system to detect the wear debris in lubricant oil. The developed sensing system has:
A high sensitivity, which can detect 25 μm diameter size particles using a 1470 μm
diameter tubing. The TP ratios is the highest among recent research works.
By applying the under-sampling method, we greatly reduced the amount of data by
nearly 20 times. With the dramatic data reduction, the sensor array is suitable for online
wear debris monitoring.
135 CHAPTER VI
CONCLUSIONS AND FUTURE WORK
VI.1 CONCLUSIONS
Planar inductive sensors have great potential in non-contact measurement applications based on their low cost, easy installation, high accuracy, and stability in harsh environments. However, the use of the planar inductive sensors is always limited by their tedious calibration process, issues dealing with variance in a target’s materials and shape, and requirements of various support instruments used with the sensor such as a data acquisition system and a power source. Furthermore, increasing the sensitivity of inductive sensors is always an inescapable problem during the designing of the sensors. In this thesis, we are committed to solve the limitations of the planar inductive sensors mentioned above.
First, we focused on simplifying the calibration process of the planar inductive sensor. When using an inductive planar sensor in non-contact gap measurement, the traditional calibration process is complicated and tedious. Since the working principle of the planar sensing coil is based on detecting the inductance variance of the sensing coil based on the mutual influence caused by the eddy current, different materials of the targets
136 have variance conductivities so that the magnitude of the generated eddy current on the targets are different. Therefore, in a traditional calibration process, each material of the target needs one unique calibration curve. In order to simplify the calibration process, we first analyzed the mutual inductance based on the mathematical model between the target and the planar sensing coil. Since the eddy current footprint in an infinite plate shape target can be modeled as a virtual circular coil, the coil to coil theory (sensing coil to virtual coil) and algorithm was presented and developed. Then, we found that the change of the mutual inductance between the two coils, and the change of the inductance of the sensing coil based on the gap variance can be equivalently boiled down to the difference in the number of turns of the virtual coil. In other words, all the geometric changes of the virtual coil can be mathematically reconstructed by changing the number of turns. When reducing the parameters which need to be considered, we are provided with the possibility to solve the complicated transfer function of the mutual influence between the sensing coil and the target. In addition, we found that the gap versus the ratio of the turns of two coils curve shifts while remaining parallel when we changed the materials of the target. Hence, the calibration curve when switching to a new target made by a different material can be determined by adding a constant number to an existing curve. The constant number can be calibrated at a single gap. With the new calibration method, the planar inductive sensor has a simpler calibration process when the target material is changed. In addition, we validated that our new calibration method for planar inductive sensors provides a small error and will not be affected by the dimension variance of the sensing coil. Three different geometries of the sensing coils were fabricated and used to measure the gap from 500 µm-5000 µm.
Each sensing coil was tested with four different plate shape targets made of copper,
137 aluminum, zinc, and titanium. The results showed that all the errors were smaller than
3.2%, which indicates that the new calibration process fits the general standard of the industrial applications.
Next, we have further improved the new calibration method for planar inductive sensors so that they can respond with not only the variance in materials of the infinite plate shape targets, but also to the narrow and irregular shaped targets. Several finite element analyses of the eddy current distributions on the narrow and irregular targets were studied. We found that for both narrow and irregular targets, even the eddy current being distributed on the surface, and extending along two side walls of the target, the magnetic flux on the edge of the target’s front area has almost the same magnitude when compared to the magnetic flux on the edge of the target side area. Thus, a new assumption based on the finite element analysis results was proposed that the coil to coil theory can be still used with the dimensions of the virtual coil. Next, we flipped the magnetic flux from the side surface to the top surface, and we found that the boundaries of the two surfaces are continuous and can form a circle-like shape. Therefore, an assumption which models the flipped eddy current distribution as a virtual coil was developed. The calibration method from previous work can be applied. In order to demonstrate the calculated gap from the new calibration method for narrow and irregular target has a good agreement with the actual gap, four blade shape targets made of copper, aluminum, zinc, and titanium were fabricated using a CNC machine. Three sensing coils with different geometries were used in the test. From the results, while comparing the calculated gap and actual gap, we found that all the errors are within 3.703% in the 500 μm to 3600 μm measurement range with this new calibration method. Thus, we developed a new calibration method for gap 138 measurement of narrow and irregular target without tedious calibration while materials of the targets are changed. It is expected that this method can significantly reduce the calibration work to monitor the gap/displacement of irregular/narrow targets in advanced industrial applications including: 3D printer build platform calibration, bandsaw blade deviation detection, and blade tip clearance monitoring.
Finally, since we improved the calibration process of the planar inductive sensors, we turned to another aspect which focused on overcoming the limitations of planar inductive sensors while in use. The application we selected is the wear debris monitoring system for lubricant oil. By analyzing the transfer function from Faraday’s law of induction, a three layers planar inductive sensor was designed. This designed structure increases the sensitivity of sensor. Next, the multi-channel sensing system was designed so that the measurement speed required by industrial applications can be satisfied. The LC circuit was applied to the measurement circuit in order to further improve the sensitivity of the sensing system. In addition, the under-sampling signal processing method was used to reduce the total amount of data which needs to be collected. Test results demonstrated that the designed sensing device can be competent for detecting the debris as small as 25 μm, and the measurement speed can be easily adjusted and has a high upper limit based on the number of channels in the flow divider and DAQ board. In addition, the concentration of measured debris has a good agreement with the estimated actual concentration.
139
VI.2 FUTURE WORKS
When considering further improvements to the sensitivity of planar inductive sensors, it should notice that reducing the noise level is another method which can be considered. From the previous study, The transfer function of signal-to-noise (SNR) during the can be expressed as [121]:
−7 2 2 퐵 10 푓 ∙ √푙(퐷 − 퐷푖 ) ∙ (퐷 + 퐷푖) ∙ 휇0 VI.1 푆푁푅 = 휋3 2 8√∆푓 ∙ √푘 푘퐵푇휌
Where 푓 is the excitation frequency, ∆푓 is the coefficient of frequency band width,
푙 is the length of the planar sensing coil, 퐷 and 퐷푖 is the outer and inner diameter of the planar sensing coil, 퐵 is the flux density, 휇0 is the permeability of vacuum, 푇 is the
−23 -1 temperature, 푘퐵 is the Boltzmann factor which equals to 1.38 ·10 WsK , 푘 is the packing factor which equals to 0.85, and 휌 is the density of the materials of the wire. In equation VI.1, in addition to the dimensions of the sensing coil, both the temperature of the sensing coil and the magnitude of the magnetic field generated by planar sensing coil effects the noise level during measurement. Since the flux density of the magnetic field is hard to measure, solving the equation VI.1 is impossible. In order to find the best combination of those parameters, finite element analysis can be used to first establish the relation between the magnitude of the flux density at the required sensing area and the dimension of the sensing coil so that the magnitude of the flux density in the sensing area can be expressed as a function of the geometric parameters of the sensing coil. Second, the 140 relation between the temperature and geometric parameters of the sensing coil at a fixed excitation frequency can be analyzed so that the temperature of the sensing coil during measurement can be expressed as a function of the geometric parameters of the sensing coil. Therefore, at a fixed excitation frequency, the signal-to-noise of the sensing coil during measurement in a required sensing area can be transferred to an equation which includes the geometric parameters of the sensing coil. From this, the best combination of the geometric parameters of the planar inductive sensing coil can be determined and the sensitivity of the sensing coil can be further improved.
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