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Research on the effect of relative movement on the output characteristic of inductive sensors
Accepted Manuscript Title: Research on the Effect of Relative Movement on the Output Characteristic of Inductive Sensors Authors: Yu Wu, Hongpeng Zhang PII: DOI: Reference:
S0924-4247(16)31079-2 https://doi.org/10.1016/j.sna.2017.10.004 SNA 10370
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
7-12-2016 4-6-2017 1-10-2017
Please cite this article as: Yu Wu, Hongpeng Zhang, Research on the Effect of Relative Movement on the Output Characteristic of Inductive Sensors, Sensors and Actuators: A Physical https://doi.org/10.1016/j.sna.2017.10.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Research on the Effect of Relative Movement on the Output Characteristic of Inductive Sensors Yu Wu, Hongpeng Zhang* Marine Engineering College, Dalian Maritime University, Dalian 116026, China
Highlights
Inductive sensors have achieved considerable success because of their low manufacturing cost, high reliability, robustness, resistance to fouling and contact-free operation. The operating conditions of inductive sensors are less strongly affected than those of other types of sensors by environmental factors, including humidity, temperature, dust, contamination and mechanical offsets; therefore, they can be applied in certain harsh working environments.
Relative movement typically occurs in an inductive sensor between a fixed coil and a metal target or another coil, and inductive sensors are often used to measure moving, rotating and reciprocating targets. For example, for the detection of metal wear particles in lubrication oil, the sensor coil is fixed, and oil mixed with metal particles is passed through the coil. In tip clearance detection, a fixed planar spiral coil is used to detect the passage of rotor blades. In position measurement, the position of a moving object is detected. In displacement measurement, each displacement sensor usually consists of a pair of coils. In each pair, one of the coils is fixed and the other is movable. However, the effect of this relative movement (or velocity) on the detection capabilities of inductive sensors has not previously been investigated. Therefore, the influence of velocity on the sensitivity of inductive sensors for metal particle detection should be addressed to improve the performance of inductive sensors in terms of their sensitivity for metal particle detection and in other areas of application.
In previous work, it has been found that identical particles traveling at different velocities induce different signals in inductive sensors. In other words, the particle velocity can be adjusted to enhance the sensitivity of an inductive sensor. This paper presents a theoretical analysis and experimental validation of the effect of particle velocity on the sensitivity of inductive sensors.
Abstract: The metallic objects are commonly detected in the inductive sensors with relative movement including reciprocation and rotation. However the effect of the relative movement on the inductive sensors was not in consideration. In order to improve the sensitivity of inductive sensors in metal particle detection and other areas of application, the effect of particle movement on inductive sensor is studied. A theoretical analysis is presented, in accordance with the experimental validation depending on the velocity of copper particles. It results that the absolute value of the inductance variation of the copper particle is up to 0.1005 nH at the velocity 2.9×10-2 m/s, in comparing with 0.0593 nH at the velocity 5.8×10-3
m/s, with a 69.48% improvement on the sensitivity, which is indicated that the sensitivity of the inductive sensor is improved by the velocity of copper particle. Keywords: inductive sensor; oil detection; microfluidic chip; movement 1. Introduction There are exactly defined requirements for industrial sensors, accuracy, reliability, hardness, resistance to fouling, water tightness, etc. Contactless inductive sensors are prime candidates meeting these requirements, especially in harsh environments [1-4]. These sensors can eliminate the need for costly machine shutdowns for inspection
[5]
. The structure of
inductive sensor is simple enough to achieve the performance of long lifetime, easy installation，low manufacturing costs and compactness
[6-7]
. Also, the excellent precision
performances and virtually infinite resolution can be achieved with proper reading algorithm [8]
. Thus it can be applied in many areas of industry, such as detecting metal wear particles in
oil [9-10], detecting tip clearances of rotor blades [11], detecting defects [12], measuring normal force and shear force [13], measuring linear or angular displacement [14-15], measuring linear or angular positions of objects [16-17], and tracking automatic weld seam [18]. In these devices, the movement of a mechanical element changes the inductance of a coil or a mutual inductance between coils. For example, for the detection of metal wear particles in lubrication oil, the sensor coil is fixed, and oil mixed with metal particles passes through the coil
[19]
. In tip
clearance detection, a fixed planar spiral coil is used to detect the passage of rotor blades [11]. In position measurement, the position of a moving object is detected [20-21]. In displacement measurement, each displacement sensor usually consists of a pair of coils. In each pair, one of the coils is fixed and the other is movable
[22-24]
. However, the effect of the relative
movement on the detection of inductive sensors is not taken in consideration so far. In this paper, theoretical analysis and experiment validation are implemented to study the sensitivity of inductive sensor affected by the velocity of particle, which is expecting to improve the sensitivity of the inductive sensor in metal particle detection and other areas of application. 2. Model establishment The schematic of the microfluidic chip for metal particle detection in oil is shown in Figure 1. When an AC voltage is applied across the coil, a magnetic field can be induced around the coil. Eddy currents are generated in a metallic particle as it passes through the channel, and the magnetic field of these eddy currents, which oppose the magnetic field of the coil, are detected by the coil, causing a change in the inductance.
Figure 1 Schematic of the microfluidic chip for metal particle detection in oil
Ein is the electric field intensity induced in metal particle, according to the Faraday law of electromagnetic induction, the induced electromotive force ε in particle can be obtained:
C
E dl in
d dt
(1)
B is the magnetic field intensity of the coil, the induced electromotive force ε in Equation 1 can be expressed as
d B B dS dS B dS dt S t t S
(2)
The first term on the right-hand side is the induced electromotive force produced by the time varying magnetic field B alone, if the particle was assumed stationary, εt; and the second term is the induced electromotive force produced by the movement of the particle, if B was assumed time-independent, εm. Then, the induced electromotive force ε can be divided into the following equations: t
dt B dS dt t S
m
(3)
dm B dS dt t S
(4)
The movement of the closed loop forming the eddy current is illustrated in Figure 2(a).
(a)
(b)
Figure 2 Schematic diagrams of (a) the movement of the closed loop in three dimensions and (b) the movement of
the closed loop inside the particle
It is assumed that the closed loop C moves from C(t) to C(t+dt) at velocity v in dt. There are two different areas surrounded by C(t): S1 and S2+S3. Thus, dΦm in Equation 4 can be expressed as
dm S2 S1 S2 (S2 S3 ) S3
(5)
The magnetic flux affected by the movement can be expressed as dm S3 B dl v dt
(6)
C
Figure 2(a) is the movement of the closed loop in general. However, for the planar coil, the eddy current loop is located in the particle and its area is perpendicular to the applied magnetic field B according to Lenz's law; therefore, the schematic diagram of the model considered in this paper is as shown in Figure 2(b). The induced electromotive force εm can be obtained:
m
dm dt
C
B dl v
v B dl
(7)
C
Thus, according to the Stokes formula, Equation 2 can be expressed as B v B t
Ein
(8)
For the first term on the right-hand side of Equation 8, a time-varying magnetic field will always accompany a spatially-varying (Maxwell–Faraday equation): E B t
(9)
In addition, according to Equation 2 d dt
C
E dl , in consideration of the definition in
of the inductance: dL
d I
(10)
Thus, the inductance variation of coil affected by the velocity can be expressed as L
c
(v Β) dldt I
(11)
As a result, the inductance of the coil decreases with an increasing particle velocity. In fact, as the velocity increases, more magnetic induction lines are cut by the coil in dt; consequently, dΦ/dt increases with increasing velocity, therefore, the induced electromotive force also increases as ε=-dΦ/dt. Based on Lenz's law, the direction of the induced electromotive force ε drives a current density that results in a magnetic field that is opposite
to that of the magnetic field of the coil. Thus, the inductance of the coil decreases with an increasing particle velocity. 3. Experimental validation The principle of detection system is shown in Figure 3. A 2 V 2 MHz AC voltage is applied, which induces a harmonic magnetic field around the inductor. The AC is supplied by an LCR meter (Agilent E4980A, Santa Clara, CA). In the experiment, when a particle passes through the channel, the voltage is changed. The change is amplified by an AD797 (Analog Devices, USA) and converted to DC by an AD637 (Analog Devices, USA).Then it is fed to the digital data acquisition system (NI USB 6259) to measure the inductance change of the inductor. The microfluidic chip is shown in Figure 1 and Figure 3, a one-layer planar coil was fabricated with 33 turns of copper wire with a diameter of 50 μm, and the diameter of microchannel is 270 μm.
Figure 3 Schematic diagram
Copper particles (Shahong Electromechanical Technology Company, Hefei, China) with diameters ranging from 120 to 125 μm were used in the test. 10 mg particles were weighed by the precision balance (XS225A, precision: 0.1mg), then they were mixed with Hyspin AWS10 hydraulic oil to test the device. The movement of particles was controlled by a syringe pump (Harvard Apparatus, 70-2212), and the volume flows were set from 0.02 mL/min to 0.10 mL/min, thus the velocities of copper particles can be calculated according to the diameter of microchannel (270 μm), which are shown in Table 2. The experiment data and the inductive pulses of the coil at the velocity of particles 5.8×10-3 m/s are recorded in Figure 4 and Table 1. As shown in Table 1, 4 groups of tests were recorded at each velocity.
Figure 4 Inductive pulses in the coil at a copper particle velocity of 5.8×10-3 m/s in test 1
Table 1 Experimental data recorded at a copper particle velocity of 5.8×10-3 m/s Test number
1
2
3
4
Base inductance (μH)
1.25917
1.25917
1.25917
1.25917
Minimum inductance (μH)
1.2591084
1.2591112
1.259108
1.259115
Inductance variation (nH) Average inductance variation (nH) Standard deviation of inductance variation (nH)
-0.0616 -0.0588 -0.0593 0.003230583
-0.062
-0.055
According to Table 1, it is concluded that the average inductance variation of coil is 0.0593 nH at a particle velocity 5.8×10-3 m/s. The similar inductive pulses of the coil at different velocities of particles are shown in Figure 5, and the experiment data are summarized in Table 2.
(a) 1.16×10-2 m/s
(b) 1.74×10-2 m/s
(c) 2.32×10-2 m/s
(d) 2.9×10-2 m/s Figure 5 Inductive pulses in the coil recorded at different copper particle velocities
In the table 2, the average inductance variation of the coil at a particle velocity of 5.8×103
m/s is treated as the reference, the rates of inductance variation of the coil for the different
velocities are calculated. Table 2 Summary of the experimental data Velocity of copper particles (m/s)
5.8×10-3
1.16×10-2
1.74×10-2
2.32×10-2
2.9×10-2
Inductance variation (nH)
-0.0593
-0.0728
-0.0848
-0.0903
-0.1005
Rate of inductance variation Standard deviation of inductance variation (nH)
0% 0.0032306
22.77% 0.0031064
43% 0.0025134
52.28% 0.0018394
69.48% 0.0016536
As shown in Table 2, when the velocity of the copper particles was increased from 5.8×10-3 m/s to 2.9×10-2 m/s, the inductance variation of the coil increased from 0.0593 nH to 0.1005 nH. Which means the enhancement of sensitivity is up to 69.48%, and the standard deviation of the inductance variation decreased from 0.0032306 nH to 0.0016536 nH. The data therefore show that as the particle velocity increases, the absolute value and standard deviation of the inductance variation of the coil increase and decrease, respectively, and the rate of inductance variation also increases. 4. Discussion Figure 6 illustrates the sensing mechanism for ferrous and nonferrous metallic particles. When an AC voltage is applied across the coil, a magnetic field is induced around the coil. When metallic particles pass through the channel, two factors (magnetic permeability and eddy currents) cause competing changes in the coil’s inductance. Eddy currents in opposition to the original magnetic field are generated in a nonferrous metallic particle. As a result, the coil’s inductance decreases, as shown in Figure 6 (b). By contrast, in a ferrous metallic particle, the coil’s inductance is enhanced because of the higher permeability (μr>1), as shown in Figure 6 (c).
(a)
(b)
(c)
Figure 6. Schematic diagrams of the sensing mechanism: (a) in the absence of a particle, (b) for a nonferrous particle, and (c) for a ferrous particle
Copper particles were used in the experimental validation. From the discussion above, it is evident that the experimental results agree with the theoretical analysis: the inductance of the coil will decrease as the particle velocity increases. Because the value of the inductance variation is less than zero (ΔL<0), the sensitivity can be improved by increasing the velocity of copper particles. For ferrous metallic particles, the coil’s inductance is enhanced because of the higher permeability (μr>1). The electromotive force ε induced in such a particle will increase with an increasing particle velocity. However, because the direction of the magnetic field of the induced electromotive force is opposite to that of the particle magnetization, the inductance of the coil will decrease as the velocity of the ferrous particle increases. The quantitative analysis of the influence of particle velocity on the sensitivity of inductive sensors presented here was implemented for nonferrous copper particles, rather than for metallic particles consisting of ferrous materials such as iron. The eddy currents and the effect of particle magnetization will be considered in future work. It should be noted that according to Ampere's Rule, a magnetic field will be induced around the coil not only under AC excitation but also under direct current (DC) excitation. DC excitation is simpler to consider both theoretically and experimentally. However, the experimental signals obtained under DC excitation are too weak to be detected compared with the results of AC excitation, and therefore, this approach is unsuitable for metallic particle detection. Nevertheless, the DC excitation of inductive sensors is expected to be applicable for other purposes. 5. Conclusion In this paper, the effect of relative movement on the inductive sensors is studied, which is expected to improve the sensitivity of inductive sensors in metal particle detection and other areas of application. A theoretical analysis is studied, and copper particles with different velocities were investigated in the experiment. The absolute value of the inductance variation
of the copper particle is up to 0.1005 nH at the velocity 2.9×10-2 m/s, in comparing with 0.0593 nH at the velocity of 5.8×10-3 m/s, which means the enhancement of sensitivity is up to 69.48%. These results indicate that the sensitivity can be significantly improved by increasing the velocity of copper particles. The different influence of the particle velocity on the sensitivity of inductive sensors for ferrous and nonferrous particles are also discussed to provide a foundation for improving the performance of inductive sensors. Acknowledgments
Yu Wu received her Master’s Degree from Dalian Maritime University in 2011. Now she is a PhD candidate in Dalian Maritime University, China. Her research interests include marine engineering, mechatronics and microfluidics.
Hongpeng Zhang received his Ph.D. degree of Marine Engineering from the Dalian Maritime University in 2005. Currently he is a professor in Marine Engineering College in Dalian Maritime University. His main area of interest is microfluidics in marine engineering. The authors wish to thank the financial support of the Natural Science Foundation of China (51679022) and the Fundamental Research Funds for the Central Universities (3132016326).
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[7] P. Kejik, C. Kluser, R. Bischofberger, R.S. Popovic, A low-cost inductive proximity sensor for industrial applications , Sensors and Actuators A-physical. 110 (1) (2004) 93-97. [8] M. Norhisam, A. Norrimah, R.Wagiran, R.M. Sidek, N. Mariun, H. Wakiwaka, Consideration of theoretical equation for output voltage of linear displacement sensor using meander coil and pattern guide, Sensors and Actuators A-physical. 147 (2) (2008) 28-34. [9] Y.J. Cha, B. Nam, J. Kim, K.H. Kim, Evaluation of the planar inductive magnetic field sensors for metallic crack detections, Sensors and Actuators A-physical. 162 (1) (2010) 13-19. [10] L. Du, X.L. Zhu, Y. Han, J. Zhe, High throughput wear debris detection in lubricants using a resonance frequency division multiplexed sensor, Tribology Letters. 51 (3) (2013) 453-460. [11] Y.H. Kim, S. Hashi, K. Ishiyama, K.I. Arai, M. Inoue, Remote temperature sensing system using reverberated magnetic flux, IEEE Transactions on Magnetics. 36 (5) (2000) 3643-3645. [12] Y.J. Cha, B. Nam, J. Kim, K.H. Kim, Evaluation of the planar inductive magnetic field sensors for metallic crack detections, Sensors and Actuators A-physical. 162 (1) (2010) 13-19. [13] L. Du, X.L. Zhu, Y. Han, J. Zhe, An inductive sensor for real-time measurement of plantar normal and shear forces distribution, IEEE Transactions on Biomedical Engineering. 62 (5) (2015) 1316-1323. [14] S.C. Bera, R. Sarkar, M. Bhowmick, Study of a modified differential inductance measurement circuit as position transducer of a power cylinder, Transactions on Instrumentation and Measurement. 61(2) (2012) 530-538. [15] Q.F. Tang, D.L. Peng, L. Wu, X.H. Chen, An inductive angular displacement sensor based on planar coil and contrate rotor, IEEE Sensors Journal. 15 (7) (2015) 3947-3954. [16] Z.J. Zhang, F.L. Ni, Y.Y. Dong, M.H. Jin, H. Liu, A novel absolute angular position sensor based on electromagnetism, Sensors and Actuators A-physical.194 (2013) 196-203. [17] B. Aschenbrenner, B.G. Zagar, Analysis and validation of a planar high-frequency contactless absolute inductive position sensor, Transactions on Instrumentation and Measurement. 64 (3) (2015) 768-775. [18] K.Y. Bae, J.H. Park, A study on development of inductive sensor for automatic weld seam tracking, Journal of Materials Processing Technology. 176 (2006) 111-116. [19] L. Du, J.A. Zhe, J. Carletta, R. Veillette, F. Choy, Real-time monitoring of wear debris in lubrication oil using a microfluidic inductive Coulter counting device, Microfluidics and Nanofluidics. 9 (6) (2010) 1241-1245. [20] J. Figueiredo, Resolver models for manufacturing, IEEE Transactions on Industrial Electronics. 58 (8) (2010) 3693-3700. [21] A. Masi, A. Danisi, R. Losito, Y. Perriard, Ironless position sensor with intrinsic immunity to external magnetic fields, 10th IEEE Conference on Sensors, Limerick, Ireland, Oct. 2011, pp. 2018-2021. [22] M.B. Coskun, K. Thotahewa, Y.S. Ying, M. Yuce, A. Neild, T. Alan, Nanoscale displacement sensing using microfabricated variable-inductance planar coils, Applied Physics Letters. 103 (14) (2013) 143501–143504. [23] S.M. Djuric, Performance analysis of a planar displacement sensor with inductive spiral coils, IEEE Transactions on Magnetics. 50 (4) (2014) 4004104. [24] N. Philip, B. George, Design and analysis of a dual-slope inductance-to-digital converter for differential reluctance sensors, Transactions on Instrumentation and Measurement. 63 (5) (2014) 1364-1371.
S0924-4247(16)31079-2 https://doi.org/10.1016/j.sna.2017.10.004 SNA 10370
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
7-12-2016 4-6-2017 1-10-2017
Please cite this article as: Yu Wu, Hongpeng Zhang, Research on the Effect of Relative Movement on the Output Characteristic of Inductive Sensors, Sensors and Actuators: A Physical https://doi.org/10.1016/j.sna.2017.10.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Research on the Effect of Relative Movement on the Output Characteristic of Inductive Sensors Yu Wu, Hongpeng Zhang* Marine Engineering College, Dalian Maritime University, Dalian 116026, China
Highlights
Inductive sensors have achieved considerable success because of their low manufacturing cost, high reliability, robustness, resistance to fouling and contact-free operation. The operating conditions of inductive sensors are less strongly affected than those of other types of sensors by environmental factors, including humidity, temperature, dust, contamination and mechanical offsets; therefore, they can be applied in certain harsh working environments.
Relative movement typically occurs in an inductive sensor between a fixed coil and a metal target or another coil, and inductive sensors are often used to measure moving, rotating and reciprocating targets. For example, for the detection of metal wear particles in lubrication oil, the sensor coil is fixed, and oil mixed with metal particles is passed through the coil. In tip clearance detection, a fixed planar spiral coil is used to detect the passage of rotor blades. In position measurement, the position of a moving object is detected. In displacement measurement, each displacement sensor usually consists of a pair of coils. In each pair, one of the coils is fixed and the other is movable. However, the effect of this relative movement (or velocity) on the detection capabilities of inductive sensors has not previously been investigated. Therefore, the influence of velocity on the sensitivity of inductive sensors for metal particle detection should be addressed to improve the performance of inductive sensors in terms of their sensitivity for metal particle detection and in other areas of application.
In previous work, it has been found that identical particles traveling at different velocities induce different signals in inductive sensors. In other words, the particle velocity can be adjusted to enhance the sensitivity of an inductive sensor. This paper presents a theoretical analysis and experimental validation of the effect of particle velocity on the sensitivity of inductive sensors.
Abstract: The metallic objects are commonly detected in the inductive sensors with relative movement including reciprocation and rotation. However the effect of the relative movement on the inductive sensors was not in consideration. In order to improve the sensitivity of inductive sensors in metal particle detection and other areas of application, the effect of particle movement on inductive sensor is studied. A theoretical analysis is presented, in accordance with the experimental validation depending on the velocity of copper particles. It results that the absolute value of the inductance variation of the copper particle is up to 0.1005 nH at the velocity 2.9×10-2 m/s, in comparing with 0.0593 nH at the velocity 5.8×10-3
m/s, with a 69.48% improvement on the sensitivity, which is indicated that the sensitivity of the inductive sensor is improved by the velocity of copper particle. Keywords: inductive sensor; oil detection; microfluidic chip; movement 1. Introduction There are exactly defined requirements for industrial sensors, accuracy, reliability, hardness, resistance to fouling, water tightness, etc. Contactless inductive sensors are prime candidates meeting these requirements, especially in harsh environments [1-4]. These sensors can eliminate the need for costly machine shutdowns for inspection
[5]
. The structure of
inductive sensor is simple enough to achieve the performance of long lifetime, easy installation，low manufacturing costs and compactness
[6-7]
. Also, the excellent precision
performances and virtually infinite resolution can be achieved with proper reading algorithm [8]
. Thus it can be applied in many areas of industry, such as detecting metal wear particles in
oil [9-10], detecting tip clearances of rotor blades [11], detecting defects [12], measuring normal force and shear force [13], measuring linear or angular displacement [14-15], measuring linear or angular positions of objects [16-17], and tracking automatic weld seam [18]. In these devices, the movement of a mechanical element changes the inductance of a coil or a mutual inductance between coils. For example, for the detection of metal wear particles in lubrication oil, the sensor coil is fixed, and oil mixed with metal particles passes through the coil
[19]
. In tip
clearance detection, a fixed planar spiral coil is used to detect the passage of rotor blades [11]. In position measurement, the position of a moving object is detected [20-21]. In displacement measurement, each displacement sensor usually consists of a pair of coils. In each pair, one of the coils is fixed and the other is movable
[22-24]
. However, the effect of the relative
movement on the detection of inductive sensors is not taken in consideration so far. In this paper, theoretical analysis and experiment validation are implemented to study the sensitivity of inductive sensor affected by the velocity of particle, which is expecting to improve the sensitivity of the inductive sensor in metal particle detection and other areas of application. 2. Model establishment The schematic of the microfluidic chip for metal particle detection in oil is shown in Figure 1. When an AC voltage is applied across the coil, a magnetic field can be induced around the coil. Eddy currents are generated in a metallic particle as it passes through the channel, and the magnetic field of these eddy currents, which oppose the magnetic field of the coil, are detected by the coil, causing a change in the inductance.
Figure 1 Schematic of the microfluidic chip for metal particle detection in oil
Ein is the electric field intensity induced in metal particle, according to the Faraday law of electromagnetic induction, the induced electromotive force ε in particle can be obtained:
C
E dl in
d dt
(1)
B is the magnetic field intensity of the coil, the induced electromotive force ε in Equation 1 can be expressed as
d B B dS dS B dS dt S t t S
(2)
The first term on the right-hand side is the induced electromotive force produced by the time varying magnetic field B alone, if the particle was assumed stationary, εt; and the second term is the induced electromotive force produced by the movement of the particle, if B was assumed time-independent, εm. Then, the induced electromotive force ε can be divided into the following equations: t
dt B dS dt t S
m
(3)
dm B dS dt t S
(4)
The movement of the closed loop forming the eddy current is illustrated in Figure 2(a).
(a)
(b)
Figure 2 Schematic diagrams of (a) the movement of the closed loop in three dimensions and (b) the movement of
the closed loop inside the particle
It is assumed that the closed loop C moves from C(t) to C(t+dt) at velocity v in dt. There are two different areas surrounded by C(t): S1 and S2+S3. Thus, dΦm in Equation 4 can be expressed as
dm S2 S1 S2 (S2 S3 ) S3
(5)
The magnetic flux affected by the movement can be expressed as dm S3 B dl v dt
(6)
C
Figure 2(a) is the movement of the closed loop in general. However, for the planar coil, the eddy current loop is located in the particle and its area is perpendicular to the applied magnetic field B according to Lenz's law; therefore, the schematic diagram of the model considered in this paper is as shown in Figure 2(b). The induced electromotive force εm can be obtained:
m
dm dt
C
B dl v
v B dl
(7)
C
Thus, according to the Stokes formula, Equation 2 can be expressed as B v B t
Ein
(8)
For the first term on the right-hand side of Equation 8, a time-varying magnetic field will always accompany a spatially-varying (Maxwell–Faraday equation): E B t
(9)
In addition, according to Equation 2 d dt
C
E dl , in consideration of the definition in
of the inductance: dL
d I
(10)
Thus, the inductance variation of coil affected by the velocity can be expressed as L
c
(v Β) dldt I
(11)
As a result, the inductance of the coil decreases with an increasing particle velocity. In fact, as the velocity increases, more magnetic induction lines are cut by the coil in dt; consequently, dΦ/dt increases with increasing velocity, therefore, the induced electromotive force also increases as ε=-dΦ/dt. Based on Lenz's law, the direction of the induced electromotive force ε drives a current density that results in a magnetic field that is opposite
to that of the magnetic field of the coil. Thus, the inductance of the coil decreases with an increasing particle velocity. 3. Experimental validation The principle of detection system is shown in Figure 3. A 2 V 2 MHz AC voltage is applied, which induces a harmonic magnetic field around the inductor. The AC is supplied by an LCR meter (Agilent E4980A, Santa Clara, CA). In the experiment, when a particle passes through the channel, the voltage is changed. The change is amplified by an AD797 (Analog Devices, USA) and converted to DC by an AD637 (Analog Devices, USA).Then it is fed to the digital data acquisition system (NI USB 6259) to measure the inductance change of the inductor. The microfluidic chip is shown in Figure 1 and Figure 3, a one-layer planar coil was fabricated with 33 turns of copper wire with a diameter of 50 μm, and the diameter of microchannel is 270 μm.
Figure 3 Schematic diagram
Copper particles (Shahong Electromechanical Technology Company, Hefei, China) with diameters ranging from 120 to 125 μm were used in the test. 10 mg particles were weighed by the precision balance (XS225A, precision: 0.1mg), then they were mixed with Hyspin AWS10 hydraulic oil to test the device. The movement of particles was controlled by a syringe pump (Harvard Apparatus, 70-2212), and the volume flows were set from 0.02 mL/min to 0.10 mL/min, thus the velocities of copper particles can be calculated according to the diameter of microchannel (270 μm), which are shown in Table 2. The experiment data and the inductive pulses of the coil at the velocity of particles 5.8×10-3 m/s are recorded in Figure 4 and Table 1. As shown in Table 1, 4 groups of tests were recorded at each velocity.
Figure 4 Inductive pulses in the coil at a copper particle velocity of 5.8×10-3 m/s in test 1
Table 1 Experimental data recorded at a copper particle velocity of 5.8×10-3 m/s Test number
1
2
3
4
Base inductance (μH)
1.25917
1.25917
1.25917
1.25917
Minimum inductance (μH)
1.2591084
1.2591112
1.259108
1.259115
Inductance variation (nH) Average inductance variation (nH) Standard deviation of inductance variation (nH)
-0.0616 -0.0588 -0.0593 0.003230583
-0.062
-0.055
According to Table 1, it is concluded that the average inductance variation of coil is 0.0593 nH at a particle velocity 5.8×10-3 m/s. The similar inductive pulses of the coil at different velocities of particles are shown in Figure 5, and the experiment data are summarized in Table 2.
(a) 1.16×10-2 m/s
(b) 1.74×10-2 m/s
(c) 2.32×10-2 m/s
(d) 2.9×10-2 m/s Figure 5 Inductive pulses in the coil recorded at different copper particle velocities
In the table 2, the average inductance variation of the coil at a particle velocity of 5.8×103
m/s is treated as the reference, the rates of inductance variation of the coil for the different
velocities are calculated. Table 2 Summary of the experimental data Velocity of copper particles (m/s)
5.8×10-3
1.16×10-2
1.74×10-2
2.32×10-2
2.9×10-2
Inductance variation (nH)
-0.0593
-0.0728
-0.0848
-0.0903
-0.1005
Rate of inductance variation Standard deviation of inductance variation (nH)
0% 0.0032306
22.77% 0.0031064
43% 0.0025134
52.28% 0.0018394
69.48% 0.0016536
As shown in Table 2, when the velocity of the copper particles was increased from 5.8×10-3 m/s to 2.9×10-2 m/s, the inductance variation of the coil increased from 0.0593 nH to 0.1005 nH. Which means the enhancement of sensitivity is up to 69.48%, and the standard deviation of the inductance variation decreased from 0.0032306 nH to 0.0016536 nH. The data therefore show that as the particle velocity increases, the absolute value and standard deviation of the inductance variation of the coil increase and decrease, respectively, and the rate of inductance variation also increases. 4. Discussion Figure 6 illustrates the sensing mechanism for ferrous and nonferrous metallic particles. When an AC voltage is applied across the coil, a magnetic field is induced around the coil. When metallic particles pass through the channel, two factors (magnetic permeability and eddy currents) cause competing changes in the coil’s inductance. Eddy currents in opposition to the original magnetic field are generated in a nonferrous metallic particle. As a result, the coil’s inductance decreases, as shown in Figure 6 (b). By contrast, in a ferrous metallic particle, the coil’s inductance is enhanced because of the higher permeability (μr>1), as shown in Figure 6 (c).
(a)
(b)
(c)
Figure 6. Schematic diagrams of the sensing mechanism: (a) in the absence of a particle, (b) for a nonferrous particle, and (c) for a ferrous particle
Copper particles were used in the experimental validation. From the discussion above, it is evident that the experimental results agree with the theoretical analysis: the inductance of the coil will decrease as the particle velocity increases. Because the value of the inductance variation is less than zero (ΔL<0), the sensitivity can be improved by increasing the velocity of copper particles. For ferrous metallic particles, the coil’s inductance is enhanced because of the higher permeability (μr>1). The electromotive force ε induced in such a particle will increase with an increasing particle velocity. However, because the direction of the magnetic field of the induced electromotive force is opposite to that of the particle magnetization, the inductance of the coil will decrease as the velocity of the ferrous particle increases. The quantitative analysis of the influence of particle velocity on the sensitivity of inductive sensors presented here was implemented for nonferrous copper particles, rather than for metallic particles consisting of ferrous materials such as iron. The eddy currents and the effect of particle magnetization will be considered in future work. It should be noted that according to Ampere's Rule, a magnetic field will be induced around the coil not only under AC excitation but also under direct current (DC) excitation. DC excitation is simpler to consider both theoretically and experimentally. However, the experimental signals obtained under DC excitation are too weak to be detected compared with the results of AC excitation, and therefore, this approach is unsuitable for metallic particle detection. Nevertheless, the DC excitation of inductive sensors is expected to be applicable for other purposes. 5. Conclusion In this paper, the effect of relative movement on the inductive sensors is studied, which is expected to improve the sensitivity of inductive sensors in metal particle detection and other areas of application. A theoretical analysis is studied, and copper particles with different velocities were investigated in the experiment. The absolute value of the inductance variation
of the copper particle is up to 0.1005 nH at the velocity 2.9×10-2 m/s, in comparing with 0.0593 nH at the velocity of 5.8×10-3 m/s, which means the enhancement of sensitivity is up to 69.48%. These results indicate that the sensitivity can be significantly improved by increasing the velocity of copper particles. The different influence of the particle velocity on the sensitivity of inductive sensors for ferrous and nonferrous particles are also discussed to provide a foundation for improving the performance of inductive sensors. Acknowledgments
Yu Wu received her Master’s Degree from Dalian Maritime University in 2011. Now she is a PhD candidate in Dalian Maritime University, China. Her research interests include marine engineering, mechatronics and microfluidics.
Hongpeng Zhang received his Ph.D. degree of Marine Engineering from the Dalian Maritime University in 2005. Currently he is a professor in Marine Engineering College in Dalian Maritime University. His main area of interest is microfluidics in marine engineering. The authors wish to thank the financial support of the Natural Science Foundation of China (51679022) and the Fundamental Research Funds for the Central Universities (3132016326).
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