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Utilising Electromagnetic Inductance to Find the Thickness of Materials:

Abstract: Inductance is used commonly throughout everyday appliances; however, it may also be used in order to measure the thickness of materials. This provides many advantages such as accuracy and reliability throughout experiments. In order to measure certain materials however, experiments were conducted to find the ideal variables one may use. Overall, coils with a higher number of turns and a shorter distance between them proved to be more accurate. Furthermore, an ideal frequency range for materials of approx. thickness 0.513mm would be 150kHz, whilst materials of 0.001mm thickness would be 60kHz. These experiments were paired with the materials of aluminum, steel and foil being measured with varying degrees of thickness, resulting in the plot of these graphs being able to be utilized as a scale for future use. This technology is highly practical and useful, however, requires industry grade testing with a wider range of variables, allowing it to have a higher overall accuracy.

Introduction: Magnetic fields have been utilised since the early 19th century, where Nikola Tesla transferred energy without wires over an air gap between to axially aligned coils using magnetic fields (Vinge, 2015). Thus, the use of wireless energy was born, which can be seen in a plethora of devices throughout modern-day electronics. These vary from medical implants, mobile devices and computers. How do these loops conduct any sort of energy across a medium, such as air? When an AC current is passed through a coil, a varying magnetic field is produced (Knight, Randall, 2008). Due to the fact that AC stands for alternating current, meaning it is constantly changing, a changing magnetic field is induced in a coil, which is known as the transmitting coil. This magnetic field that is being produced can be further detected by a second coil which may be placed nearby. This coil is known as the pick-up coil.

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This phenomenon is known mutual induction and it is the basic operating principals of numerous devices, which include motors, generators and transformers. It is defined as the linking of two coils together through magnetic flux and as the current flows through one coil, it induces a voltage in an adjacent coil (Koizumi et al., 2012). Due to the ease of access of electronics in modern day society, using two coils to create magnetic flux and induce a current is not particularly difficult and rather inexpensive. Furthermore, the demand for this type of technology is on the rise. Throughout numerous scientific and engineering endeavors, being able to know the thickness of certain materials without having to physically come in contact with them would be a highly accurate and useful. Due to the fact that one may not have to disrupt the experiment or it may be too dangerous to come in contact with the material, such as measuring ice in the Artic. Furthermore, this method may be developed in a way in which a specific scale may be available for specific materials, making measurements highly reliable and accurate. However, in order to do this, experiments need to be conducted on what the ideal standards may be. Throughout this paper, two distinct experiments are conducted to find the ideal standards to measure sheets of aluminum, steel and foil. The first experiments consist of finding the ideal variables in terms of the number of coils required, the distance between them and the best frequency. The results from the first experiment are then narrowed even further down to the specific materials. The thickness of each material is measured against the frequency, to find which range may be ideal for its use and a range of thicknesses are plotted. These plots act as graphical scales, allowing one to be able to conduct their own tests in order to find peak to peak voltage and utilize these graphs to find the approximate thickness of their material. Furthermore, each test is done in hopes of furthering the research into this field and plotting extremely accurate graphs which may measure certain materials with very little error.

Method: Experiment 1: A spool of copper wire was wrapped around a plastic tube with a diameter of approximately 25 mm. The copper wire was secured firmly at the base of the tube and wrapped tightly around 80 times. Once the turns had been completed, the copper wire was cut with wire-cutters and carefully removed from the tube, ensuring it did not unravel. It was then bound in masking tape, keeping it secure, regardless of any overlapping wire. The end of the coil was then sandpapered to remove the pre-existing insulation and to ensure sufficient conduction. The above was repeated for coils with turns of 35, 60 and 50 respectively. Once each coil had been assembled, the 80-turn coil was used as the transmitting coil and connected into Channel 1 of the signal generator. The wires were attached to the transmitting coil, with alligator clips. These were taped down with masking tape, ensuring the coil did not pg. 2

move throughout the experiment as even slight movements could cause discrepancies. Furthermore, the output wires of the signal generator were attached to Channel 1 of the oscilloscope, as shown below in Figure 1. A 35-turn coil was used as the pick-up coil. It was attached in a similar fashion to Channel 2 of oscilloscope, as shown below. The signal generator was switched on and set to a sine wave and the frequency was set to 10kHz. The Channel 1 output was switched on. The oscilloscope was switched on and selected AUTO. A sine wave appeared on the screen and the scale was adjusted accordingly throughout the experiment for accuracy and ease of use.

Figure 1.

Exp. 1: Part A (Varying Distance): The 35-turn pick-up coil begun touching the transmitting coil, with the frequency set to 10kHz and the peak to peak voltage was measured. The pick-up coil was then placed exactly 5mm away and taped in place, where the peak to peak voltage was measured. The pick-up coil was then increased by 5mm from 10mm to 30mm respectively. With the peak to peak voltage being measured and recorded at each instance. Exp. 1: Part B (Varying Frequency): The 35-turn pick-up coil was placed at exactly 1cm away from the 80-turn transmitting coil. The frequency was initially set to 5kHz and the peak to peak voltage was measured. This was

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increased by 5 from 10kHz to 30KHz respectively. With the peak to peak voltage being measured and recorded at each instance. Exp. 1: Part C (Varying Number of Turns): The 35-turn pick-up coil was placed at exactly 1cm away from the 80-turn transmitting coil, with the frequency set to 10kHz and the peak to peak voltage was measured. The pick-up coil was then replaced with a 50-turn coil and the peak to peak was measured. The 50-turn coil was then replaced with a 65-turn pick-up coil and the peak to peak was measured and recorded.

Experiment 2: A transmitting coil of 80 turns was connected to the signal generator and placed at an exact distance of 20mm away from a pick-up coil of 65 turns, which was connected to the oscilloscope (refer to Figure 1). Both coils were fastened onto the table with masking tape to ensure no movement. Exp 2.: Part A (Varying Thickness): Three different materials were used: aluminum, steel and foil. One sheet of aluminum had a thickness of 0.512mm, a sheet of steel had a thickness of 0.514 and a sheet of foil had a thickness of 0.01mm. A sheet of aluminum was placed between the coils, as shown below (Figure 2), and the peak to peak voltage was measured. This was repeated, except with 6 sheets of aluminum and continued until a total of 6 sheets of aluminum were used, the thickness increasing by 0.512mm each time. The above was repeated for steel, where its thickness increased by 0.514mm and for foil, where its thickness increased by 0.01mm. The peak to peak voltage was measured and recorded.

Figure 2.

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Exp. 2: Part B (Varying Frequency): A single sheet of aluminum was placed between the two coils. The frequency was initially set to 30kHz and peak to peak voltage was measured and recorded. The frequency was then increased to by 30 from 60kHz to 150kHz respectively, with the peak to peak being measured and recorded at each instance. The above was repeated for both a single sheet of steel and foil.

Results: Experiment 1: Part A: Figure 3: Changing distance between the coils

Varying Distance 180

Peak to Peak Voltage (mV)

160 140 120 100 80 60 40 20 0

0

5

10

15

20

25

30

35

Distance (mm)

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Part B: Figure 4: Changing the frequency

Varying Frequency Peak to Peak Voltage (mV)

70 60 50 40 30 20 10 0

0

5

10

15

20

25

30

35

Frequency (mV)

Part C: Figure 5: Changing the number of turns

Varying Number of Turns Peak to Peak Voltage (mv)

250 200 150 100 50 0 25

30

35

40

45

50

55

60

65

70

Pick-up Turns

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Experiment 2: Part A: Figure 6: Aluminum changing thickness

Aluminium (vPP vs Thickness) Peak to Peak Voltage (mV)

40 35 R² = 0.85

30 25 20 15 10 5 0

0

0.5

1

1.5

2

2.5

3

3.5

Thickness (mm)

Figure 7: Steel changing thickness

Steel (vPP vs Thickness) Peak to Peak Voltage (mV)

30 25

R² = 0.93

20 15 10 5 0

0

0.5

1

1.5

2

2.5

3

3.5

Thickness (mm)

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Figure 8: Foil changing thickness

Foil (vPP vs Thickness) Peak to Peak Voltage (mV)

70 60 R² = 0.93

50 40 30 20 10 0

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Thickness (mm)

Part B: Figure 9: Aluminum with changing frequency

Aluminium (vPP vs Frequency) Peak to Peak Voltage (mV)

70 60 50 40 30 20 10 0 20

40

60

80

100

120

140

160

Frequency (kHz)

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Figure 10: Steel with changing frequency

Steel (vPP vs Frequency) Peak to Peak Voltage (mV)

60 50 40 30 20 10 0 20

40

60

80

100

120

140

160

Frequency (kHz)

Figure 11: Foil with changing frequency

Foil (vPP vs Frequency) Peak to Peak Voltage (mV)

120 100 80 60 40 20 0 20

40

60

80

100

120

140

160

Frequency (kHz)

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Discussion: The desire for accurately measuring the thickness of materials throughout scientific and engineering endeavours without having the need to physically be in contact with them has continuously risen over the years (G.G. Liversidge, K.C. Cundy, J.F. Bishop, 1980). Thus, electrical inductance has become even more so incorporated throughout industry. As the employer desired to deduce an accurate and reliable method in which one may measure the thickness of aluminum, steel and foil plates and each experiment conducted above illustrates that. As Figure 3 states, an increasing distance between a pair of coils resulted in an exponential decrease in the peak to peak voltage. Thus, it can be said that the closer the coils are when attempting to find the thickness, the better. Furthermore, Figure 5 depicts that a higher number of turns in a coil will result in a higher peak to peak voltage. Therefore, coils with a higher number of turns should be utilized as they will produce more responsive and accurate results. Hence, for experiment two coils with 65 turns and 80 turns were used. On the other hand, a changing frequency did not have an impact on the peak to peak voltage throughout experiment 1, as shown in Figure 4. However, it is to be noted that the frequency had an impact on the period of the sine waves, as the waves appeared to become “tighter” as the frequency increased. Nonetheless, peak to peak voltage did vary with changing frequency when a material of certain thickness was placed in between the coils. According to Figures 9 and 10 a changing frequency resulted in an exponential rise of peak to peak voltage. Thus, an ideal frequency for that thickness range can be denoted. Due to the fact that aluminum and steel had a similar thickness with a difference of ±0.002mm, the ideal frequency for that range of thickness according the graphs would be approximately 150kHz. However, due to the drastic size difference of foil, an ideal frequency for a thickness of 0.01mm would be approximately 60kHz, according to Figure 11. The overall graphs of steel and foil (Figures 7 and 8), showed a steady linear trend, with both the R2 values being above 0.9. Thus, these graphs can be deemed as accurate and can either be utilised by an employer to find the thickness of similar material or to be further developed. On the other hand, the graph of thickness for aluminium (Figure 6) has an R2 value in the range of 0.8, resulting in it not being entirely accurate. Overall, it is certainly probable to utilise inductance in measuring the thickness of various materials. The methods which were illustrated throughout this paper can most certainly be developed further to ensure accuracy reliability and to cover an even wider range of materials. For example, a larger range of frequencies could cover a more minute range of thickness in material, resulting in a highly accurate graph for a very specific range of thickness.

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Conclusion: In conclusion, the use of inductance to measure the thickness of sheets of aluminum, steel and foil is a probable and practical procedure. As found throughout the series of testing, a higher number of coils results in a more accurate peak to peak voltage. Furthermore, keeping the coils as close together as possible will result in more accurate peak to peak. The ideal frequencies which were found throughout the experiments can be used in future experiments to provide more valid results. This also applies for the linear scales of materials which can be used as a reference. Although the trend lines of steel and foil were accurate, aluminum was not highly reliable. This may be proven further in the future using industry grade equipment, resulting in more accurate results with less human error. Overall, this method is certainly promising and the data above will provide an adequate reference for a prospective employer wishing to use such a method. However, it can be certainly improved, with more accurate equipment and a larger range of data.

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References: G.G. Liversidge, K.C. Cundy, J.F. Bishop, D. A. C. (1980) ‘United States Patent (19) 54’, 96(19), pp. 62–66. doi: US005485919A. Knight, Randall D. Physics for Scientists and Engineers,”Magnetic Forces on Current-Carrying Wires” 2nd ed, Calfornia: Pearson Addison-Wesley, 2008. pg 1024-1026. Koizumi, M. et al. (2012) ‘Wireless Power Feeding with Strongly Coupled Magnetic Resonance for a Flying Object’, Wireless Engineering and Technology, 03(02), pp. 86–89. doi: 10.4236/wet.2012.32014. Vinge, R. (2015) ‘Wireless Energy Transfer by Resonant Inductive Coupling’, p. 83.

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