Motion Estimation of a Levitation Mechanisms Using Piezoelectric Element

Shori Sone, Akihiro Torii, Kae Doki Department of Electrical and Electronics Engineering, Aichi Institute of Technology

1247 Yachigusa, Yakusa, Toyota, Aichi Japan

Abstract: We are studying a friction force control mechanism using levitation mechanism. We usually measure levitation height of the levitation mechanisms by the use of a displacement sensor. An inchworm using the levitation mechanisms was proposed, and realized micron order precise displacement over large horizontal working range. An optical fiber displacement sensor used in this research can measure the vertical levitation height but cannot follow the horizontal displacement. Therefore, it is difficult for the displacement sensor to measure the levitation height since the levitation mechanism moves horizontally even though the levitation height is in the vertical direction. We estimate the levitation height by measuring the capacitance between the levitation mechanism and the substrate, which realizes sensorless levitation estimation. The circuit which detects the electric capacitance is a series RC circuit. We apply sine wave AC voltage to the series RC circuit and measure the terminal voltage of the resistance. The estimation method proposed can extend the working range. This paper describes the comparison of the levitation height estimated by the method proposed and one measured by the optical fiber displacement sensor.

1. INTRODUCTION

In recent years, the demand for micro-mechanical components is increasing according to the miniaturization of products. The micro mechanical components are produced by using a large machine. However, large machine required large energy and space. Therefore, small production apparatuses using a piezoelectric element capable of realizing a minute displacement are studied. The small production apparatus has the advantages of space saving and energy saving by using microrobots(1)(2)(3).

Micro robot described in this paper has a structure combining a levitation mechanism shown in Figure 1. We are researching the levitation mechanism using a piezoelectric element that generates small displacement and has good response. By applying the high-frequency voltage in the vertical direction to the piezoelectric element of the levitation mechanism, the squeeze effect is generated between the ground plane and operating substrate. And, the levitation mechanisms levitate by squeeze effect. In order to

confirm the motion of the levitation mechanism, we measure the levitation height of the levitation mechanisms by the use of a displacement sensor or camera. However, the measurement method using an optical fiber displacement sensor uses measurement mirrors. The weight of mirror affects the motion of the microrobot. In addition, an inchworm using the levitation mechanisms was proposed, and realized micron order precise displacement over large horizontal working range. An optical fiber displacement sensor used in this research can measure the vertical levitation height but cannot follow the horizontal displacement. Therefore, the development of the levitation measurement method in wide range is required.

In this research, it is noted that the plate and substrate of the levitation mechanism were metal. We consider them as a capacitor when the levitation mechanism levitated. We estimate levitation height by the capacitance between the ground plane and the operating substrate of levitation mechanism. This paper describes the comparison of the levitation height estimated by the method proposed and one measured by the optical fiber displacement sensor.

Fig. 1 Levitation mechanism

Weight

Piezo Operating substrate

Mirror Ground plane

Fig. 2 Inchworm type microrobot

2. Structure

The levitation mechanisms are shown in Figure 1. The levitation mechanism is composed of an operating substrate (a metal plate), a weight, and a stacked type piezoelectric element. The size of the levitation mechanisms is 35.0 mm in height and 47.0 g in weight. The metal plate is 30.0 mm in diameter, and 1.05 mm in thick. The stacked type piezo (NEC-tokin) is 20 mm in length. Expansion and contraction of levitation mechanism depend on the frequency. This study uses the operation frequency from 9 kHz to 13 kHz. The levitation mechanisms levitate by applying high frequency voltage to the piezoelectric element. The levitation mechanisms reduce the friction force. Figure 2 shows the proposed microrobot developed in our laboratory. The microrobot is composed of three levitation mechanisms and two horizontal piezos. These microrobot moves by the principle of an inchworm.

3. Measurement

Model of the levitation mechanism is shown in Figure 3. When we considered the parallel plate between the ground plane and the operating substrate as a capacitor, the capacitance C is expressed by C = εS/d (1)

where S is the area of operating substrate, ε is dielectric constant, and d is distance between the ground plane and the operating substrate. The levitation height d is inversely proportional to the capacitance C from equation (1).

Equivalent circuit of the capacitance detection circuit is

shown in Figure 4. The circuit which detects the electric capacitance C is a series RC circuit. We apply sine wave AC voltage Vi to the series RC circuit and measure the terminal voltage Vo of the resistance R. The magnitude of the impedance Z of the circuit is obtained by Z = R + {1/ωC} . (2) Input voltage Vi is expressed by Vi = ZVo/R. (3) From equations (2) and (3), the capacitance C is obtained by the following equation using the terminal voltage Vo and the input voltage Vi. C = 1/{ωR (Vi/Vo) − 1} (4) From equations (1) and (4), distance d is expressed by d = ωεSR (Vi/Vo) − 1. (5) By detecting the terminal voltage Vo of the resistor R, the capacitance C is calculated from equation (4). The levitation height d is calculated from equation (5).

Fig.3 Model of the levitation mechanism

Operating substrate

Ground plane

Fig. 4 Equivalent circuit

4. EXPERIMENT

The levitation mechanisms levitate by applying sine wave AC voltage to the piezoelectric element. The sine wave AC voltage is 10 Vp-p and 5 V offset. We apply sine wave AC voltage of the effective value 7.45 V to capacitance detection circuit, and estimating levitation height between the ground plane and the operating substrate, by measuring the terminal voltage of the resistance. Input frequency of the voltage applied to the capacitance detection circuit is 1 MHz. The resistance of the detection circuit is 500 Ω. This study compares measured value with the estimated value of levitation height by changing the frequency of the voltage applied to the piezoelectric element. The levitation height d is calculated from equation (5) by measuring the terminal voltage Vo of resistor R. We describe the comparison of the levitation height estimated by the method proposed and one measured by the optical fiber displacement sensor. The optical fiber displacement sensor (ST-3711, IWATSU) is used for the levitation height measurement. The estimation method proposed can extend the working range.

5. EXPERIMENTAL RESULTS

The input and output waveforms of the terminal voltage are shown in Figure 5. Figure 5(a) shows input and output waveforms obtained by the applied AC voltage of frequency 9 kHz. By the use of this signal, the levitation mechanism does not levitate, since the input and output signals are same.

(a) 9kHz

(b) 10.8kHz

Fig.5 Input-Output signal

Input Voltage

Input Voltage

Output Voltage

Output Voltage

Figure 5(b) shows input and output waveforms obtained by the applied AC voltage of frequency 10.8 kHz to the piezoelectric element. By the use of this frequency, the maximum levitation of the levitation mechanism is obtained. When levitation mechanism was levitation from the waveform of Figure 5(b), distance between the ground plane and the operating substrate became parallel plate and the phase of an output waveform under the influence of capacitance is advanced, and the amplitude of output voltage decrease. The output voltage is terminal voltage Vo and we can estimate the levitation height from equation (5) by the relationship between the input voltage. One benefit of using this approach can be estimated by measuring the terminal voltage. From Figure 5(b), when applying an effective value 7.45 V to the input voltage Vi, the measured value of the output voltage Vo becomes effective value 2.75 V. The levitation height can be estimated as 49.5 μm from equation (5).

Figure 6 shows the levitation height that measured by the optical fiber displacement meter and estimated by using a capacitance detection circuit. Figure 6(a), (b) and (c) shows the results of three trials. Frequency applied to the piezoelectric element was changed in increments of 0.2 kHz to 13.0 kHz from 8.0 kHz. The levitation height is changed by changing the frequency applied to the piezoelectric element. The levitation height is estimated from the terminal voltage of the resistance of the capacitance detection circuit. From Figure 6, the levitation height is increased by raising the frequency applied to the piezoelectric element. The maximum levitation height was obtained at the frequency 10.8 kHz that applied to the piezoelectric element.

The difference between the measured value and the estimated value are shown in Figure 7. From Figure 7, the average offset is 29.3μm, 30.4μm, 31.2μm respectively.

(a)First trial

(b) Second trial

(c) Third trial

Fig.6 Frequency characteristic

Estimation

Estimation

Estimation

Optical fiber

Optical fiber

Optical fiber

10.8

10.8

10.8

(a)First trial

(b)Second trial

(c)Third trial

Fig.7 Offset

Figure 8 shows the estimation of the levitation height excluded by the average offset. The measured height and the estimated levitation height show similar values by considering the proper offset. The estimated levitation heights shows the similar values of the measured levitation height by considering the estimation offset.

(a)First trial

(b)Second trial

(c)Third trial

Fig.8 Frequency characteristic using the offset

Estimation

Estimation

Estimation

Optical fiber

Optical fiber

Optical fiber

29.3μm

30.4μm

31.2μm

10.8

10.8

10.8

The experimental results shown in Figures 6, 7, 8 were obtained under the same conditions, but some errors are observed in the results. It is necessary for us to repeat the measurement and to evaluate the accuracy and error.

6. SUMMARY

In this paper, as a means of estimating the flying height, we proposed a method of estimating the levitation height by detecting the capacitance of the ground plane and operating substrate of the levitation mechanism. As a means of estimating the capacitance, we apply a sine wave AC voltage to the capacitance detection circuit and have attempted to detect the capacitance by the terminal voltage of the resistor. It is shown that there is a possibility to accurately estimate the levitation height by setting the offset.

REFERENCES 1. T.Yamada, A.Torii and A.Ueda: “Inchworm Actuator with Five Degrees of Freedom” The 23rd Symposium on Electromagnetics and Dynamics, pp. 353-354 (2011) (in Japanese) 2. Y.Itatsu, A.Torii, and A.Ueda: ”Moving speed of Inchworm type microrobot using levitation mechabisms ” Journal of the Japan Society for Precision Engineering, J67 (2011) (in Japanese) 3. M.Nishio, A.Torii, K.Doki and A.Ueda: ”Delta-Type Miniature Robot using Levitation Medhanism ” Journal of the Japan Society for Precision Engineering, B26 (2012) (in Japanese) 4. R.Kamiya, A.Torii, K.Doki and A.Ueda: ”Levitation height estimation of levitation mechanism using capacitance measurement” Journal of the Japan Society for Precision Engineering, B24 (2012) (in Japanese)