Copyright Ⓒ 2013 JSPE㪬㪈㪏Effect of Traveling Voltage Wavelength on Electrostatic Induction Actuators Driving Performance

The University of Tokyo○Tommy Tram, Atsuhiro Maeda, and Akio Yamamoto

This paper investigates the effect of voltage traveling wavelength on the driving performance of a six-phase linear electrostaticinduction motor designed for handling of plain paper copier (PPC) paper sheet. In the search for a stable and reliable thin sheet
induction actuation, there is an interest improving driving performance through stator design. For this purpose, four different
actuator designs were prototyped to generate different wavelengths, by changing the pitch between electrodes. Experimental
results showed that the highest performance is achieved with shortest traveling potential wavelengths, with the maximum speedof the paper slider decreasing linearly with increasing traveling wavelength and the optimal traveling wave speed decreasing.
The maximum speed of the slider reached 230 mm/s at a frequency of 300 Hz for the actuator with 7.2 mm wavelength, 309
mm/s at a frequency of 500 Hz for 4.8 mm traveling wave length, 344 mm/s at a frequency of 700 Hz and 383 mm/s at afrequency of 1300 Hz for 2.4 mm traveling wavelength. The maximum thrust force was measured to 13.7 mN for 2.4 mm
traveling wavelength.

1. Introduction
Electrostatic induction actuators have been known for a long time,
but new applications are being proposed until this day. Recent studies[1] described its application for sheet handling and demonstrated
handling of, e.g., plain paper copier (PPC) sheet. The actuation
technology can realize thin and flexible design for paper handling in
information devices, and thus can create new applications that were
not possible with the conventional paper handling mechanism. For
example, the technology was applied for human computer interactionin [2], where a thin and transparent electrostatic induction actuator
was integrated onto a surface of a flat-panel display in order tointegrate computer generated animations and actuation of physicalobjects for better interaction.
The actuation was realized by utilizing parallel poly-phaseelectrodes. Applying poly-phase sinusoidal wave of the same numberof phases to the electrodes creates traveling potential waveform on
the electrodes. This traveling wave induces charge wave of the same
wave length on the slider surface, which gives rise to thrust force.
Many different design parameters affect the actuation performance,some of which can be estimated through theoretical discussions given
by some previous papers [3-5]. However, theoretical discussions
often assume simplified electrode structure and thus do not always
predict the correct performance of the real actuators. Hence,experimental evaluation is still quite important in practical design.
This paper experimentally investigates how the performance ofpaper sheet actuation changes with different wavelengths of thetraveling potential wave. Four actuators were designed, with different
electrode pitches, to generate four different traveling wavelengths.
The maximum velocity and static thrust force were measured toreveal the performance tendency.
2. Actuation Principle
The basic structure of the electrostatic actuator is shown in Fig. 1.
The stator consists of six-phase parallel electrodes and the slider is athin sheet made out of dielectric material, in this case normal PPC
paper. The signal synthesizer generates a six-phase sinusoidal wavethat is thousand-fold amplified by high-voltage amplifiers before
being fed to the electrodes. This creates a traveling potential wavethat induces a charge on the slider by surface current and dielectric
polarization. The induced charge wave has the same wavelength andthe same traveling speed as the excitation potential wave, but has aspatial phase lag due to the surface resistance and/or dielectricrelaxation. The phase lag gives rise to the lateral electrostatic force
and drive the slider in the same direction as the waves travel (see Fig.
2).
3. Experimental Setup
A regular Japanese B5 size (182 mm by 257 mm) PPC paper, with asurface resistance of 1013 Ω, was used as a slider. The sketch in Fig. 1
also illustrates the measurement setup. The slider displacement wasmeasured using a laser displacement sensor (Omron ZX-100). To
facilitate the measurement, a round object with 35 mm diameter andFig. 1Sketch of the thin sheet paper actuator with displacement
laser and force sensor.

Fig. 2Driving principle with sinusoidal traveling waveTable 1 Actuator Design Parameters
Wavelength (mm)Pitch (mm)Electrode Width (mm)
7.2
1.20
0.50
4.8
0.90
0.38
3.6
0.60
0.25
2.4
0.45
0.19

Fig. 3Cross sectional view of the stator electrodes
20 mm height was placed at the center of the slider as a target point
for the laser. The velocity of the slider was calculated by numericaldifferentiation from the displacement data. For static thrust force
measurement, a load cell (Kyowa, LVS-50GA) was placed above theactuator to measure the force at the center of the round object
attached on the slider sheet.
Four different stator electrodes were tested to evaluate the effect ofthe different wavelengths. The stator electrodes were fabricated using
typical printed circuit board technology and have electrode pitches of
1.2 mm, 0.9 mm, 0.6 mm, and 0.45 mm (see table 1). The electrodes
were configured in six-phase, which resulted in wavelengths of 7.2

ISUPEN 2013
International Symposium on Ultraprecision Engineering and Nanotechnology, Tokyo, Japan, March 13, 2013.

29

Copyright Ⓒ 2013 JSPE㪬㪈㪏

Fig. 6Maximum velocity of slider and corresponding travelingwave speed for each traveling wavelength

Fig. 4Experiment setup with a displacement laser andmeasuring object.

Fig. 7Measured static thrust force for different appliedfrequencies

Fig. 5Maximum velocity obtained for different appliedfrequencies and difference wavelengths
mm, 4.8 mm, 3.6 mm and 2.4 mm, respectively.
The specific design parameters are shown in table 1 and thedefinition is illustrated in figure 4. The electrode width was designed
to keep a constant ratio against electrode pitch (see Fig. 3). Electrodeheight was designed the same for all the electrodes and was about
0.04 mm. An epoxy insulation layer of 0.254 mm thickness covers theelectrodes. Glass beads of 100 µm diameter were scattered on thesurface of the stator electrodes to lower the friction and create an air
gap between the stator and slider. All the experiments were conducted
inside a sealed volume with silica gel to keep a stable low-humidity
condition.
4. Results and Discussions
Figure 4 shows a displacement data and calculated speed from one
measurement. The measurement was repeated three times for eachfrequency. The maximum velocity was calculated for eachmeasurement and averaged for the final results.
Figure 5 shows the measured maximum speed of the slider for
applied frequencies from 0 to 1500 Hz with 0.7 kV0-p applied voltage.
The maximum value displayed in figure 5 is the mean value of thethree repeated measurements. The maximum speed of the slider
reached 230 mm/s at a frequency of 300 Hz for the actuator with 7.2mm wavelength, 309 mm/s at a frequency of 500 Hz for 4.8 mm
traveling wave length, 344 mm/s at a frequency of 700 Hz for 3.6 mmand 383 mm/s at a frequency of 1300 Hz for 2.4 mm travelingwavelength. The optimum wave speed, which is calculated as a
product of optimum frequency and wavelength, was found increasing
as the wavelength decreases (see Fig. 6). In an ideal system, themaximum possible velocity should be the same throughout the boards,
but achieved at a different frequency. From this data, the performanceof the electrostatic actuator is higher with lower traveling voltage
wavelength. However, it should be noted that the minimum pitch
distance between electrodes is limited by physical constraints, as theshorter pitch distances gives higher chance of discharge.
The static force was measured for frequencies between 0 and 50 Hz.
The steady state thrust force of the slider for all four travelingwavelengths is shown in figure 7. The maximum thrust force of 12.7mN was generated by 2.4 mm traveling wavelength with a 12 Hz

30

applied frequency. While 3.6 mm traveling wavelength generated
12.5 mN with at 8 Hz, 4.8 mm traveling wavelength generated 11.2mN at 6 Hz and 7.2 mm traveling wavelength generated 7.5 mN at
5.5 Hz. The results almost follow the known performance curve forinduction motors.
4. Conclusion
The experiment results showed that shortest traveling potential
wave of 2.4 mm gave the best driving performance for PPC sheet
actuation and the maximum velocity of the slider did not reach acommon value between the different wavelengths. These results arevalid only for stators with constant gap, constant electrode height of
0.04 mm and a constant 0.47 ratio between pitch and electrode width.
Different designs should be investigated in the future.
Acknowledgements
This work was supported in part by Funding Program for Next
Generation World-Leading Researchers and the research grant from
Yazaki Memorial Foundation for Science and Technology.
References[1] B. Bollee, “Electrostatic motors”, Philips tech. Rev, Vol. 30, pp.
178-194, 1969.
[2] E. Mognaschi and J. Calderwood, “Asyncronous dielectric inductionmotor,” IEE proceedings Part A. Physical science, Measurements andinstrumentation, Management and education, Reviews, vol. 137, no.
6, pp. 331-338, 1990.
[3] S. Nagle, C.Livermore, L. Frechette, R. Ghodssi, and J. Lang, “Anelectric induction micromotor,” Microelectromechanical Systems
Journal of, vol. 14, no. 5, pp. 1127-1143, oct. 2005.
[4] A. Yamamoto, S. Tsuruta, and T. Higuchi, “Planar 3-DOF paper sheet
manipulation using electrostatic Induction,” Industrial Electronics(ISIE), 2010 IEEE International Symposium on , vol., no.,pp.493-498, July 2010[5] K. Amano and A. Yamamoto. “An interaction on flat panel display
using a planar 1-dof electrostatic actuator”, in Proceedings of theACM International Conference on Interactive Tabletops and Surfaces,
ser. ITS ’11. New York, NY, USA: ACM, 2011, pp. 258-259.

ISUPEN 2013
International Symposium on Ultraprecision Engineering and Nanotechnology, Tokyo, Japan, March 13, 2013.