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Development of a technique for measuring static electricity distribution using focused ultrasound waves and an induced electric field
Journal of Electrostatics 73 (2015) 6e11
Contents lists available at ScienceDirect
Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat
Development of a technique for measuring static electricity distribution using focused ultrasound waves and an induced electric field K. Kikunaga a, *, T. Hoshi b, H. Yamashita a, M. Egashira a, K. Nonaka a a b
National Institute of Advanced Industrial Science and Technology, 807-1, Shuku-machi, Tosu, Saga 841-0052, Japan Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 May 2014 Accepted 30 October 2014 Available online 11 November 2014
A novel method is proposed for non-contact measurement of static electricity distribution on a surface using focused ultrasound to excite movement of the charge. The focused ultrasound is generated by controlling individually the phases of 285 airborne ultrasound transducers, and it was demonstrated local excitation could be measured. An electric field is induced by local excitation of a charged object. The electric field intensity and phase are related to the surface potential and electrical polarity of the object, respectively. It is possible to measure static electricity distribution over an entire object surface by scanning the position of the focused ultrasound. © 2014 Elsevier B.V. All rights reserved.
Keywords: Static electricity Electric field Focused ultrasound Measuring technology Distribution
Introduction In order to measure static electric charge on the surface of various materials, it is desirable to consider the charge distribution in terms of areas, rather than points. When electrostatic charge builds up on an insulating material, the charge is distributed unevenly over the surface. This is because electrical charges built up on the surface by localized frictions or detachments are not evenly distributed over the surface due to its insulating properties. Various types of surface potential sensors have been developed in the past as electrostatic meters for measuring charge at points, targeting the electrostatic field and electrostatic capacity [1e8]. It was necessary to bring such surface potential sensors to the proximity of a targeted sample objects and physically scan them in order to measure the electrostatic distribution accurately because readings from these sensors depend on their measurement ranges and the distance from the sensor to the target, and they are easily affected by electrostatic fields and grounding in the vicinity of the sensor [9]. A large amount of time was therefore required to take measurements of electrostatic distributions, which has been cited as a problem in
* Corresponding author. E-mail address: [email protected] (K. Kikunaga). http://dx.doi.org/10.1016/j.elstat.2014.10.016 0304-3886/© 2014 Elsevier B.V. All rights reserved.
terms of reproducibility in evaluating static electricity because such conditions change over time. We intended to develop a technology for measuring static electricity that can be used to measure electrostatic distributions without moving the sensor and without applying stimulus to the electrostatically charged targets that will affect their electrostatic charge distributions so that changes in signals can be captured as readings. Acoustic waves were chosen as stimulus to be applied to the target to induce physical oscillations of the targets thus triggering electric charge oscillations and allowing quantitative evaluation of the static charge distribution by measuring the induced oscillations of the electric field [10]. Measurements of onedimensional electrostatic charge distributions with the sensor fixed in place can be made by using pulsating excitation made possible by focused ultrasound [11]. In order to achieve our objective, however, we needed a two-dimensional scanning technology for localized oscillations and the ability to evaluate such two-dimensional oscillations in combination with corresponding low-frequency electric field measurements. In order to measure two-dimensional distributions of static electricity, the relationship between the acoustic pressure distribution of focused ultrasound using the phased array method and the localized surface oscillation had to be clarified in order to realize our scanning technology for inducing localized oscillations so that we could examine the method for detecting low-frequency electric field oscillations using plate electrodes.
K. Kikunaga et al. / Journal of Electrostatics 73 (2015) 6e11
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Experimental method Electric field induction by electric charge oscillation A conceptual diagram of electric field induction by electric charge oscillation for the purpose of electrostatic measurements is shown in Fig. 1. When an electrostatically charged sample object targeted for a measurement is physically oscillated, the electrostatic charge undergoes a spatial oscillation along with the sample object. This results in the spatial displacement of the electric charge with respect to time, and an electric field is induced in its surroundings. It is then possible to apply the theory of dipole radiation in order to derive the dominant term for the generated electric field using the equation below [12] for the cases where the electric field E [V/m] has a frequency of up to 1 kHz and an observation distance of up to 1 wavelength (300 km) when a charged particle with electric charge q [C] moves in the z direction:
E¼
1 ql ð2 cos qEr þ sin qEq Þejkr ; 4pε0 r 3
(1)
where l [m] is the displacement of the charged particle, r [m] is the distance from the charged particle to the observation point, k [m1] is the wavenumber, j is the imaginary unit, q [rad] is the inclination from the z axis, while er and eq are unit vectors in the r and q directions, respectively. The electric charge can be derived by measuring this electric field. The surface potential, which is proportional to the electric charge, was used in our research to represent the magnitude of the static charge. Focused ultrasound by phased arrays Acoustic radiation pressure was used in our research to trigger localized oscillation of our sample objects in air and without being in close proximity [13e15]. Furthermore, ultrasound generated by using the phased array method can be focused to a single focal point in air by appropriately controlling the phases of the respective oscillators that are arranged in a plane. This method allows for moving the focal point by manipulating the phase making it possible to generate an oscillating force at an arbitrary position in space from a remote location. As shown in Fig. 2, when a rectangular oscillator array is used with a focal length of R [m], and the length of a side of the square array is D [m], the diameter of focal point w [m] is given by [16]:
w¼
2lR ; D
Fig. 2. Relationship between device array size and the diameter of the focal point.
Experiment method In the present study, it was necessary to use low-frequency sound waves in order to focus ultrasonic waves with sufficient amplitude to trigger localized oscillation due to the relationship between Eqs. (1) and (2). In order to achieve such conditions, the compact ultrasound device fabricated for the study in Ref. [17] was used. The size of the array was D ¼ 170 mm, with 285 individual ultrasonic oscillators arranged within a rectangular region, with a maximum generated force at the focal point of 16 mN. This device can be modulated at DC e 1 kHz by turning the 40 kHz ultrasonic signal on and off. It is therefore possible to trigger oscillations at low frequencies while maintaining the degree of focus and without deteriorating the essential qualities of the ultrasonic waves. The experimental system used for evaluating the focused ultrasonic waves is shown in Fig. 3. First, a hole of 10 mm diameter was drilled in a plate, which was then mounted on the front of a speaker. The speaker was then placed at a distance of 170 mm from and facing the ultrasound device in order to evaluate the characteristics of the focused ultrasonic waves (Fig. 3(a)). This speaker was moved using an xey stage (range: 40 40 mm2; 2 mm pitch) to evaluate the degree of focus of the focused ultrasonic waves. In order to evaluate the oscillation due to the radiation of the focused ultrasonic waves on the sample object surface, the ultrasound device was installed 170 mm from and facing the sample object (Fig. 3(b)). A vinyl chloride sheet (thickness 10 mm; size 250 250 mm2) was used as our sample object, which was irradiated by the focused ultrasonic waves. The displacement distribution (measurement range: 50 mm) in the vicinity of the focal point of the ultrasonic waves was measured using a line laser displacement sensor (LJ-G200, Keyence Corp.).
(2)
where l [m] is the wavelength of the ultrasonic wave. A trade-off relationship between the array size and spatial resolution is evident from Eq. (2).
Fig. 1. Concept and coordinate system for an electric field induced by charge oscillation.
Fig. 3. Experimental setup for (a) characterizing a focused ultrasound wave and (b) evaluating the induced excitation.
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K. Kikunaga et al. / Journal of Electrostatics 73 (2015) 6e11
ultrasound device, the results of which are shown in Fig. 5(a), and the line profile of the acoustic distribution with respect to x and y axes thereof, is shown in Fig. 5(b). A focused acoustic pressure with the focal diameter of 20 mm was achieved in this manner. Furthermore, the acoustic pressure of the focused ultrasonic array maintained good spatial symmetry. The wavelength was l ¼ 8.5 mm for an ultrasonic wave of 40 kHz, and w ¼ 17 mm was calculated from the relationship described by Eq. (2) for D ¼ 170 mm and R ¼ 170 mm. The experimental results provided values that were slightly broader than the theoretical values, but it was possible to generate ultrasonic waves by focusing the acoustic pressure of the phased array. Localized oscillation using focused ultrasonic waves
Fig. 4. Experimental system comprising equipment to generate focused ultrasound and to measure electric fields.
Next, the two-dimensional distribution evaluation system for detecting the oscillations caused by the focused ultrasonic waves and the induced electric field (220 220 mm2; height 230 mm) is shown in Fig. 4. The focused ultrasonic wave was directed downwards, and the sample object was installed on top of a sponge cushion (thickness 5 mm) and positioned 170 mm away from and facing the ultrasound device. An elastic sheet (Teflon; thickness 50 mm; 10 10 mm2), electrostatically charged to a surface potential of 100 V by coronal discharge, was used as our sample object. A plate electrode (thickness 0.3 mm; size 150 150 mm2) was placed under the sponge to detect the electric field and was connected to a lock-in amplifier. The output voltage of the lock-in amplifier was used to indicate the electric field intensity for our purpose due to the relationship between the electric field and the antenna output voltage. Results and discussion Evaluation of acoustic pressure distribution of focused ultrasonic waves An evaluation of the spatial distribution of acoustic pressure was conducted to verify the focused ultrasonic waves. The evaluation system displayed in Fig. 3(a) was used to measure the spatial distribution of focused ultrasonic acoustic pressure generated by the
An experiment for measuring the localized displacements was conducted next to validate the localized oscillation of the sample object caused by irradiating focused ultrasonic waves onto its surface as shown in Fig. 3(b). Focused ultrasonic waves were irradiated onto the vinyl chloride sheet, and the location of the focal point was displaced in 10 mm increments every 100 ms. The displacement distribution in the vicinity of the ultrasonic wave focal point was measured for a width of 50 mm along the x axis with a line laser displacement sensor. Fig. 6(a) shows a one-dimensional distribution of the displacements along a line passing through the center of the ultrasonic wave focal point. Furthermore, the overlapping of the displacement distribution at 200 ms as shown in Fig. 6(a) and the acoustic distributions (x axis) from Fig. 5(b), with the line profile at the center, is shown in Fig. 6(b). These indicate that a portion on the vinyl chloride sheet is being moved due to the force of the focused ultrasonic waves. Fig. 6(a) and (b) shows that the displacement at the center of the ultrasonic wave focal point was a maximum of ~1.1 mm with a full width at half maximum of FWHM z 30 mm. This indicates that the oscillation is occurring over a wider range than the degree of focus of the focused ultrasonic waves, which is believed to be due to the Young's Modulus of the sample object. At any rate, localized oscillation on the sample object by focused ultrasonic waves was confirmed. The frequencies of such focused acoustic waves can be modulated at the focal point, and localized oscillations can be scanned in a short time by moving the focal point of the ultrasonic waves. Frequency dependence of electric field intensity by focused ultrasonic wave modulations The size of the electric field generated by such oscillation is proportional to the amplitude of the physical oscillation of the sample object. In order to raise the occurrence rate of the electric
Fig. 5. (a) Image of radiation pressure distribution in the xey plane and (b) one-dimensional distributions of measured radiation pressure (z ¼ 170 mm).
K. Kikunaga et al. / Journal of Electrostatics 73 (2015) 6e11
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Fig. 6. (a) Series of one-dimensional distributions around the moving center of the focused ultrasound with each shift, and (b) comparisons with spatial distributions measured radiation pressure and measured displacement of sample.
field, therefore, it is necessary to acoustically oscillate the sample object with a resonance frequency. The frequency dependence of electric field intensity as the sample object is irradiated with focused ultrasonic waves modulated in the range of 1e200 Hz, with the aforementioned rubber sheet electrostatically charged to 100 V using the experimental system depicted in Fig. 4 as the target, is shown in Fig. 7. The peaks in the vicinity of 60 Hz, 120 Hz, and 180 Hz in Fig. 7 are from the noise of the commercial electric supply frequency (60 Hz). Once this signal is eliminated, the maximum electric field intensity lies around 72 Hz. With this method, the spatial oscillation of the electrostatic charge induces an electric field at the same frequency as the oscillation frequency. 72 Hz is the oscillation frequency at which the amplitude is greatest for the resonance frequency of the sample object. It is for this reason that 72 Hz was adopted as the frequency for oscillating the sample object. Relationship between the electric field intensity and phase with surface potential It is possible to investigate the magnitude of static charge and the electrical polarity by using the intensity and phase of the
detected electric field with this method [12], but as the electric field occurrence rate varies depending on the sample object, and the accuracy of electrostatic measurements also differs. In order to clarify this, the electric field intensity and phase were measured using the plate electrode and lock-in amplifier, while the experimental system shown in Fig. 4 was used to oscillate the rubber sheet at 72 Hz while the electrostatic voltage of the sample object was varied between 0 and ±100 V for our purpose. Fig. 8(a) shows the relationship of electrical field intensity and phase within the electrostatic voltage range of 100 to 0 V, while Fig. 8(b) shows the relationship between the electric field intensity and phase within the electrostatic voltage range of 0e100 V. The difference between the reference signal of the modulation signal of the ultrasound device and the measured electric field signal was used for the phase in this instance. Fig. 8(a) and (b) indicates that the absolute value of electrostatic voltage was linearly proportional to the electric field intensity and that the phase was nearly constant (170 degrees and 10 ) at or above the absolute value for the electrostatic voltage of 20 V. This led to the revelation that the electrostatic potential and polarity can be evaluated for an electrical potential of at least 20 V with an accuracy of ~10% by using this sample object and system. Electrostatic distribution measurements by focused ultrasonic wave scanning
Fig. 7. Frequency dependence of electric field intensity induced by exciting a charged rubber sheet.
The system depicted in Fig. 4 was used to take measurements of the location where a rubber sheet electrostatically charged to 100 V was irradiated by focused ultrasonic waves and then horizontally scanned to derive the electric field distribution. The photograph of the sample object set for the measurement and the measurement results are shown in Fig. 9. The parameters set as experimental conditions were a scanning range for focused ultrasonic waves of 100 100 mm2, modulation frequency for ultrasonic waves of 72 Hz, pitch width for scanning of 5 mm, as well as excitation time and electric field detection elapsed time of 200 ms. Since the rubber sheet was positively charged, no phase detection was performed and only the electric field intensity was measured, with the intensity of the electric field represented by grayscale level. It is evident from Fig. 9 that an electric field was detected only at the locations of charged objects. The spatial resolution, determined by the oscillation of the focused ultrasonic waves, was about 30 mm diameter, but the spatial resolution could be increased to some extent by narrowing the scanning pitch. It is however important to note that in so, doing the information with a 30 mm a beam diameter was being averaged. The reason why the electric field
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K. Kikunaga et al. / Journal of Electrostatics 73 (2015) 6e11
Fig. 8. Relationship between surface potential and electric field properties, induced electric field intensity, and phase in (a) negatively charged and (b) positively charged rubber sheet.
Fig. 9. A sample setting photo and a measured electric field distribution by scanning focused ultrasound.
intensity differed within the sample object surface is believed to have been due to the non-uniformity of electrostatic charging by coronal discharge. These results, however, should make it possible to perform evaluations using this system to obtain rough estimates of electrostatic distributions. The coupling coefficient for the sample object and the antenna in relation to the electric field measurement, however, is determined by the amplitude of the oscillations of the sample object, measurement distance, length of antenna, and the like [10]. It is therefore necessary to calibrate this system using standard samples. Scanning with focused ultrasonic waves in this research is theoretically possible at 1 ms, but due to the low detection sensitivity of the plate electrode used as the electric field sensor, it required about 200 ms for the lock-in amplifier to stabilize. Therefore, the measurement time per point was 200 ms, and it required 80 s to measure the entire 100 100 mm2 area. Methods such as oscillating with high-frequency acoustic waves or detecting the induced electric field with higher sensitivity can be considered as methods for shortening this time.
electrode with a lock-in amplifier. It was also possible in this research to take measurements of electrostatic distribution with a surface potential of 20 V or more with an accuracy of 10% and a spatial resolution of 30 mm diameter over an area of 100 100 mm2 with a scanning time per point of 200 ms or less. A measurement time of 80 s was required to scan a surface of 100 100 mm2 at the time this report was written, but it would be possible to shorten that time by shortening the time for electric field measurements. The use of even higher frequencies is also considered an effective means to increase the spatial resolution of electrostatic distributions studied by this research. We believe this electrostatic distribution measurement system can contribute to the electronics industry by making it possible to evaluate materials with electrostatic and electrical properties that are triggered by friction or contact. In the future, we intend to shorten the electrostatic distribution measurement time by improving the performance of focused ultrasonic wave generation and by raising the sensitivity of the electric field sensors at low frequencies, as well as by improving the spatial resolution through inverse problem solving using obtained measured values.
Conclusions Acknowledgments A technology for measuring electrostatic distribution was developed by this research by using scanning technology to induce localized oscillations using focused ultrasonic waves and lowfrequency electric field measurement technology using a plane
This study was supported by an Industrial Technology Research Grant Program in 2011 from the New Energy and Industrial Technology Development Organization (NEDO) of Japan.
K. Kikunaga et al. / Journal of Electrostatics 73 (2015) 6e11
References [1] P.E. Secker, J. Electrostat. 1 (1975) 27. [2] E. Eisenmenger, M. Haardt, Solid State Commun. 41 (1982) 917. [3] R.E. Vosteen, in: International Conference on Charged ParticlesdManagement of Electrostatic Hazards and Problems, Oyez, 1982. [4] R.A. Anderson, S.R. Kurtz, J. Appl. Phys. 56 (1984) 2856. [5] M. Matsui, J. Inst. Electrostat. Jpn. 10 (1986) 217e224. [6] H. Yamada, T. Kobayashi, J. Inst. Electrostat. Jpn. 10 (1986) 213e216. [7] D.M. Taylor, P.E. Secker, Industrial Electrostatics: Fundamentals and Measurements, Research Studies Press, John Wiley, 1994. [8] A. Sowinski, F. Salama, P. Mehrani, J. Electrostat. 67 (2009) 568. [9] T. Takuma, M. Yashima, T. Kawamoto, IEEE Trans. Dielectr. Electr. Insul. 5 (1998) 497.
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[10] K. Kikunaga, H. Yamashita, Y. Fujii, K. Nonaka, Jpn. J. Appl. Phys. 52 (2013), 05DB16-1. [11] K. Kikunaga, T. Hoshi, H. Yamashita, Y. Fujii, K. Nonaka, J. Electrostat. 71 (2012) 554. [12] K. Kikunaga, H. Yamashita, Y. Fujii, K. Nonaka, in: Proc. Int. Symp. Electromagn. Compat., 2014, p. 41. [13] J. Awatani, J. Acoust. Soc. Am. 27 (1955) 278. [14] T. Hasegawa, T. Kido, T. Iizuka, C. Matsuoka, Acoust. Sci. Technol. 21 (2000) 145. [15] B.T. Chu, R.E. Apfel, J. Acoust. Soc. Am. 72 (1982) 1673. [16] T. Hoshi, M. Takahashi, T. Iwamoto, H. Shinoda, IEEE Trans. Haptics 3 (2010) 155. [17] T. Hoshi, in: Proc. JSME Conf. on Robotics and Mechatronics, 2012, 1A1A03(1e2).
Contents lists available at ScienceDirect
Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat
Development of a technique for measuring static electricity distribution using focused ultrasound waves and an induced electric field K. Kikunaga a, *, T. Hoshi b, H. Yamashita a, M. Egashira a, K. Nonaka a a b
National Institute of Advanced Industrial Science and Technology, 807-1, Shuku-machi, Tosu, Saga 841-0052, Japan Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 May 2014 Accepted 30 October 2014 Available online 11 November 2014
A novel method is proposed for non-contact measurement of static electricity distribution on a surface using focused ultrasound to excite movement of the charge. The focused ultrasound is generated by controlling individually the phases of 285 airborne ultrasound transducers, and it was demonstrated local excitation could be measured. An electric field is induced by local excitation of a charged object. The electric field intensity and phase are related to the surface potential and electrical polarity of the object, respectively. It is possible to measure static electricity distribution over an entire object surface by scanning the position of the focused ultrasound. © 2014 Elsevier B.V. All rights reserved.
Keywords: Static electricity Electric field Focused ultrasound Measuring technology Distribution
Introduction In order to measure static electric charge on the surface of various materials, it is desirable to consider the charge distribution in terms of areas, rather than points. When electrostatic charge builds up on an insulating material, the charge is distributed unevenly over the surface. This is because electrical charges built up on the surface by localized frictions or detachments are not evenly distributed over the surface due to its insulating properties. Various types of surface potential sensors have been developed in the past as electrostatic meters for measuring charge at points, targeting the electrostatic field and electrostatic capacity [1e8]. It was necessary to bring such surface potential sensors to the proximity of a targeted sample objects and physically scan them in order to measure the electrostatic distribution accurately because readings from these sensors depend on their measurement ranges and the distance from the sensor to the target, and they are easily affected by electrostatic fields and grounding in the vicinity of the sensor [9]. A large amount of time was therefore required to take measurements of electrostatic distributions, which has been cited as a problem in
* Corresponding author. E-mail address: [email protected] (K. Kikunaga). http://dx.doi.org/10.1016/j.elstat.2014.10.016 0304-3886/© 2014 Elsevier B.V. All rights reserved.
terms of reproducibility in evaluating static electricity because such conditions change over time. We intended to develop a technology for measuring static electricity that can be used to measure electrostatic distributions without moving the sensor and without applying stimulus to the electrostatically charged targets that will affect their electrostatic charge distributions so that changes in signals can be captured as readings. Acoustic waves were chosen as stimulus to be applied to the target to induce physical oscillations of the targets thus triggering electric charge oscillations and allowing quantitative evaluation of the static charge distribution by measuring the induced oscillations of the electric field [10]. Measurements of onedimensional electrostatic charge distributions with the sensor fixed in place can be made by using pulsating excitation made possible by focused ultrasound [11]. In order to achieve our objective, however, we needed a two-dimensional scanning technology for localized oscillations and the ability to evaluate such two-dimensional oscillations in combination with corresponding low-frequency electric field measurements. In order to measure two-dimensional distributions of static electricity, the relationship between the acoustic pressure distribution of focused ultrasound using the phased array method and the localized surface oscillation had to be clarified in order to realize our scanning technology for inducing localized oscillations so that we could examine the method for detecting low-frequency electric field oscillations using plate electrodes.
K. Kikunaga et al. / Journal of Electrostatics 73 (2015) 6e11
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Experimental method Electric field induction by electric charge oscillation A conceptual diagram of electric field induction by electric charge oscillation for the purpose of electrostatic measurements is shown in Fig. 1. When an electrostatically charged sample object targeted for a measurement is physically oscillated, the electrostatic charge undergoes a spatial oscillation along with the sample object. This results in the spatial displacement of the electric charge with respect to time, and an electric field is induced in its surroundings. It is then possible to apply the theory of dipole radiation in order to derive the dominant term for the generated electric field using the equation below [12] for the cases where the electric field E [V/m] has a frequency of up to 1 kHz and an observation distance of up to 1 wavelength (300 km) when a charged particle with electric charge q [C] moves in the z direction:
E¼
1 ql ð2 cos qEr þ sin qEq Þejkr ; 4pε0 r 3
(1)
where l [m] is the displacement of the charged particle, r [m] is the distance from the charged particle to the observation point, k [m1] is the wavenumber, j is the imaginary unit, q [rad] is the inclination from the z axis, while er and eq are unit vectors in the r and q directions, respectively. The electric charge can be derived by measuring this electric field. The surface potential, which is proportional to the electric charge, was used in our research to represent the magnitude of the static charge. Focused ultrasound by phased arrays Acoustic radiation pressure was used in our research to trigger localized oscillation of our sample objects in air and without being in close proximity [13e15]. Furthermore, ultrasound generated by using the phased array method can be focused to a single focal point in air by appropriately controlling the phases of the respective oscillators that are arranged in a plane. This method allows for moving the focal point by manipulating the phase making it possible to generate an oscillating force at an arbitrary position in space from a remote location. As shown in Fig. 2, when a rectangular oscillator array is used with a focal length of R [m], and the length of a side of the square array is D [m], the diameter of focal point w [m] is given by [16]:
w¼
2lR ; D
Fig. 2. Relationship between device array size and the diameter of the focal point.
Experiment method In the present study, it was necessary to use low-frequency sound waves in order to focus ultrasonic waves with sufficient amplitude to trigger localized oscillation due to the relationship between Eqs. (1) and (2). In order to achieve such conditions, the compact ultrasound device fabricated for the study in Ref. [17] was used. The size of the array was D ¼ 170 mm, with 285 individual ultrasonic oscillators arranged within a rectangular region, with a maximum generated force at the focal point of 16 mN. This device can be modulated at DC e 1 kHz by turning the 40 kHz ultrasonic signal on and off. It is therefore possible to trigger oscillations at low frequencies while maintaining the degree of focus and without deteriorating the essential qualities of the ultrasonic waves. The experimental system used for evaluating the focused ultrasonic waves is shown in Fig. 3. First, a hole of 10 mm diameter was drilled in a plate, which was then mounted on the front of a speaker. The speaker was then placed at a distance of 170 mm from and facing the ultrasound device in order to evaluate the characteristics of the focused ultrasonic waves (Fig. 3(a)). This speaker was moved using an xey stage (range: 40 40 mm2; 2 mm pitch) to evaluate the degree of focus of the focused ultrasonic waves. In order to evaluate the oscillation due to the radiation of the focused ultrasonic waves on the sample object surface, the ultrasound device was installed 170 mm from and facing the sample object (Fig. 3(b)). A vinyl chloride sheet (thickness 10 mm; size 250 250 mm2) was used as our sample object, which was irradiated by the focused ultrasonic waves. The displacement distribution (measurement range: 50 mm) in the vicinity of the focal point of the ultrasonic waves was measured using a line laser displacement sensor (LJ-G200, Keyence Corp.).
(2)
where l [m] is the wavelength of the ultrasonic wave. A trade-off relationship between the array size and spatial resolution is evident from Eq. (2).
Fig. 1. Concept and coordinate system for an electric field induced by charge oscillation.
Fig. 3. Experimental setup for (a) characterizing a focused ultrasound wave and (b) evaluating the induced excitation.
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K. Kikunaga et al. / Journal of Electrostatics 73 (2015) 6e11
ultrasound device, the results of which are shown in Fig. 5(a), and the line profile of the acoustic distribution with respect to x and y axes thereof, is shown in Fig. 5(b). A focused acoustic pressure with the focal diameter of 20 mm was achieved in this manner. Furthermore, the acoustic pressure of the focused ultrasonic array maintained good spatial symmetry. The wavelength was l ¼ 8.5 mm for an ultrasonic wave of 40 kHz, and w ¼ 17 mm was calculated from the relationship described by Eq. (2) for D ¼ 170 mm and R ¼ 170 mm. The experimental results provided values that were slightly broader than the theoretical values, but it was possible to generate ultrasonic waves by focusing the acoustic pressure of the phased array. Localized oscillation using focused ultrasonic waves
Fig. 4. Experimental system comprising equipment to generate focused ultrasound and to measure electric fields.
Next, the two-dimensional distribution evaluation system for detecting the oscillations caused by the focused ultrasonic waves and the induced electric field (220 220 mm2; height 230 mm) is shown in Fig. 4. The focused ultrasonic wave was directed downwards, and the sample object was installed on top of a sponge cushion (thickness 5 mm) and positioned 170 mm away from and facing the ultrasound device. An elastic sheet (Teflon; thickness 50 mm; 10 10 mm2), electrostatically charged to a surface potential of 100 V by coronal discharge, was used as our sample object. A plate electrode (thickness 0.3 mm; size 150 150 mm2) was placed under the sponge to detect the electric field and was connected to a lock-in amplifier. The output voltage of the lock-in amplifier was used to indicate the electric field intensity for our purpose due to the relationship between the electric field and the antenna output voltage. Results and discussion Evaluation of acoustic pressure distribution of focused ultrasonic waves An evaluation of the spatial distribution of acoustic pressure was conducted to verify the focused ultrasonic waves. The evaluation system displayed in Fig. 3(a) was used to measure the spatial distribution of focused ultrasonic acoustic pressure generated by the
An experiment for measuring the localized displacements was conducted next to validate the localized oscillation of the sample object caused by irradiating focused ultrasonic waves onto its surface as shown in Fig. 3(b). Focused ultrasonic waves were irradiated onto the vinyl chloride sheet, and the location of the focal point was displaced in 10 mm increments every 100 ms. The displacement distribution in the vicinity of the ultrasonic wave focal point was measured for a width of 50 mm along the x axis with a line laser displacement sensor. Fig. 6(a) shows a one-dimensional distribution of the displacements along a line passing through the center of the ultrasonic wave focal point. Furthermore, the overlapping of the displacement distribution at 200 ms as shown in Fig. 6(a) and the acoustic distributions (x axis) from Fig. 5(b), with the line profile at the center, is shown in Fig. 6(b). These indicate that a portion on the vinyl chloride sheet is being moved due to the force of the focused ultrasonic waves. Fig. 6(a) and (b) shows that the displacement at the center of the ultrasonic wave focal point was a maximum of ~1.1 mm with a full width at half maximum of FWHM z 30 mm. This indicates that the oscillation is occurring over a wider range than the degree of focus of the focused ultrasonic waves, which is believed to be due to the Young's Modulus of the sample object. At any rate, localized oscillation on the sample object by focused ultrasonic waves was confirmed. The frequencies of such focused acoustic waves can be modulated at the focal point, and localized oscillations can be scanned in a short time by moving the focal point of the ultrasonic waves. Frequency dependence of electric field intensity by focused ultrasonic wave modulations The size of the electric field generated by such oscillation is proportional to the amplitude of the physical oscillation of the sample object. In order to raise the occurrence rate of the electric
Fig. 5. (a) Image of radiation pressure distribution in the xey plane and (b) one-dimensional distributions of measured radiation pressure (z ¼ 170 mm).
K. Kikunaga et al. / Journal of Electrostatics 73 (2015) 6e11
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Fig. 6. (a) Series of one-dimensional distributions around the moving center of the focused ultrasound with each shift, and (b) comparisons with spatial distributions measured radiation pressure and measured displacement of sample.
field, therefore, it is necessary to acoustically oscillate the sample object with a resonance frequency. The frequency dependence of electric field intensity as the sample object is irradiated with focused ultrasonic waves modulated in the range of 1e200 Hz, with the aforementioned rubber sheet electrostatically charged to 100 V using the experimental system depicted in Fig. 4 as the target, is shown in Fig. 7. The peaks in the vicinity of 60 Hz, 120 Hz, and 180 Hz in Fig. 7 are from the noise of the commercial electric supply frequency (60 Hz). Once this signal is eliminated, the maximum electric field intensity lies around 72 Hz. With this method, the spatial oscillation of the electrostatic charge induces an electric field at the same frequency as the oscillation frequency. 72 Hz is the oscillation frequency at which the amplitude is greatest for the resonance frequency of the sample object. It is for this reason that 72 Hz was adopted as the frequency for oscillating the sample object. Relationship between the electric field intensity and phase with surface potential It is possible to investigate the magnitude of static charge and the electrical polarity by using the intensity and phase of the
detected electric field with this method [12], but as the electric field occurrence rate varies depending on the sample object, and the accuracy of electrostatic measurements also differs. In order to clarify this, the electric field intensity and phase were measured using the plate electrode and lock-in amplifier, while the experimental system shown in Fig. 4 was used to oscillate the rubber sheet at 72 Hz while the electrostatic voltage of the sample object was varied between 0 and ±100 V for our purpose. Fig. 8(a) shows the relationship of electrical field intensity and phase within the electrostatic voltage range of 100 to 0 V, while Fig. 8(b) shows the relationship between the electric field intensity and phase within the electrostatic voltage range of 0e100 V. The difference between the reference signal of the modulation signal of the ultrasound device and the measured electric field signal was used for the phase in this instance. Fig. 8(a) and (b) indicates that the absolute value of electrostatic voltage was linearly proportional to the electric field intensity and that the phase was nearly constant (170 degrees and 10 ) at or above the absolute value for the electrostatic voltage of 20 V. This led to the revelation that the electrostatic potential and polarity can be evaluated for an electrical potential of at least 20 V with an accuracy of ~10% by using this sample object and system. Electrostatic distribution measurements by focused ultrasonic wave scanning
Fig. 7. Frequency dependence of electric field intensity induced by exciting a charged rubber sheet.
The system depicted in Fig. 4 was used to take measurements of the location where a rubber sheet electrostatically charged to 100 V was irradiated by focused ultrasonic waves and then horizontally scanned to derive the electric field distribution. The photograph of the sample object set for the measurement and the measurement results are shown in Fig. 9. The parameters set as experimental conditions were a scanning range for focused ultrasonic waves of 100 100 mm2, modulation frequency for ultrasonic waves of 72 Hz, pitch width for scanning of 5 mm, as well as excitation time and electric field detection elapsed time of 200 ms. Since the rubber sheet was positively charged, no phase detection was performed and only the electric field intensity was measured, with the intensity of the electric field represented by grayscale level. It is evident from Fig. 9 that an electric field was detected only at the locations of charged objects. The spatial resolution, determined by the oscillation of the focused ultrasonic waves, was about 30 mm diameter, but the spatial resolution could be increased to some extent by narrowing the scanning pitch. It is however important to note that in so, doing the information with a 30 mm a beam diameter was being averaged. The reason why the electric field
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Fig. 8. Relationship between surface potential and electric field properties, induced electric field intensity, and phase in (a) negatively charged and (b) positively charged rubber sheet.
Fig. 9. A sample setting photo and a measured electric field distribution by scanning focused ultrasound.
intensity differed within the sample object surface is believed to have been due to the non-uniformity of electrostatic charging by coronal discharge. These results, however, should make it possible to perform evaluations using this system to obtain rough estimates of electrostatic distributions. The coupling coefficient for the sample object and the antenna in relation to the electric field measurement, however, is determined by the amplitude of the oscillations of the sample object, measurement distance, length of antenna, and the like [10]. It is therefore necessary to calibrate this system using standard samples. Scanning with focused ultrasonic waves in this research is theoretically possible at 1 ms, but due to the low detection sensitivity of the plate electrode used as the electric field sensor, it required about 200 ms for the lock-in amplifier to stabilize. Therefore, the measurement time per point was 200 ms, and it required 80 s to measure the entire 100 100 mm2 area. Methods such as oscillating with high-frequency acoustic waves or detecting the induced electric field with higher sensitivity can be considered as methods for shortening this time.
electrode with a lock-in amplifier. It was also possible in this research to take measurements of electrostatic distribution with a surface potential of 20 V or more with an accuracy of 10% and a spatial resolution of 30 mm diameter over an area of 100 100 mm2 with a scanning time per point of 200 ms or less. A measurement time of 80 s was required to scan a surface of 100 100 mm2 at the time this report was written, but it would be possible to shorten that time by shortening the time for electric field measurements. The use of even higher frequencies is also considered an effective means to increase the spatial resolution of electrostatic distributions studied by this research. We believe this electrostatic distribution measurement system can contribute to the electronics industry by making it possible to evaluate materials with electrostatic and electrical properties that are triggered by friction or contact. In the future, we intend to shorten the electrostatic distribution measurement time by improving the performance of focused ultrasonic wave generation and by raising the sensitivity of the electric field sensors at low frequencies, as well as by improving the spatial resolution through inverse problem solving using obtained measured values.
Conclusions Acknowledgments A technology for measuring electrostatic distribution was developed by this research by using scanning technology to induce localized oscillations using focused ultrasonic waves and lowfrequency electric field measurement technology using a plane
This study was supported by an Industrial Technology Research Grant Program in 2011 from the New Energy and Industrial Technology Development Organization (NEDO) of Japan.
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