Development of Linear Actuators Using Piezoelectric Elements

Yasuhiro Okamoto and Ryuichi Yoshida

Production Engineering Division, Image Information Products Manufacturing H.Q., Minolta Co., Ltd., Sakai, Japan 590

SUMMARY

We propose a new type of linear actuator that is based

on the rapid expansion of a piezoelectric element and the

inertia and friction of a mobile body. The proposed actuator,

small and capable of being driven with high precision, may

find applications in positioning devices and other precision

products. This paper presents the theory of operation, the

results of tests performed on the experimental unit built on

this principle, and a theoretical analysis of these test results.

© 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(11):

11�17, 1998

Key words: Piezoelectric element; inertia; friction;

actuator; linear; positioning.

1. Introduction

Piezoelectric elements, while offering high response

and high resolution, suffer from too small a displacement

range. Because of this very small displacement range, pie-

zoelectric elements used as actuators have only limited use.

The following methods to obtain larger displacement have

been reported:

a) Impact drive mechanism utilizing rapid strain of

piezoelectric elements.

b) Ultrasonic motors utilizing resonance of piezo-

electric elements.

But we have developed a driving system that uses the

friction of the drive rod to transmit the movement of the

piezoelectric element to a mobile body utilizing the rapid

strain of piezoelectric element. This driving system is re-

ferred to as smooth impact drive mechanism (SIDM).

In actual operation, it is capable of driving at high

frequencies beyond the range audible to humans in the

rough drive mode, while it utilizes the displacement of the

piezoelectric element itself to provide high resolution in the

fine drive mode.

Its configuration will be discussed in detail elsewhere

when we discuss the experimental unit.

This actuator may find applications in driving SPM

or precision positioning stages, and in driving optical com-

ponents in precision equipment.

2. Theory of Operation

Figure 1 is a diagram of the SIDM. One end of the

flexible piezoelectric element is secured to the fixed mem-

ber and the drive rod is attached to the other end. The mobile

body is placed on the drive rod, where a friction force is

created between it and the drive rod. Under this condition,

a sawtooth voltage waveform as shown in Fig. 2 will be

CCC1042-0967/98/110011-07

© 1998 Scripta Technica

Electronics and Communications in Japan, Part 3, Vol. 81, No. 11, 1998Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J80-A, No. 10, October 1997, pp. 1751�1756

Fig. 1. Block diagram.

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applied to the piezoelectric element. If this voltage wave-

form is applied at low frequencies, the waveform of the

displacement of the piezoelectric element will be quite

close to that of the voltage applied, so that the motion of the

drive rod follows the waveform of the voltage applied. As

will be discussed later, the mobile body will behave as

shown in Fig. 3. On the other hand, if the voltage waveform

is applied at higher frequencies, the mobile body will

behave differently from the way it does at lower frequen-

cies. Thus, we will separately discuss the cases of low-fre-

quency operation and high-frequency operation. Let us

consider the case in which the mobile body is driven to the

right as shown in Fig. 1. Also to be discussed is the fine

drive mode for a high-precision drive in addition to the

rough drive mode in which a sawtooth drive waveform is

applied.

2.1. Low frequency

When the piezoelectric element expands slowly with

a slow rise of the applied voltage (2) from the initial state

(1), thus causing the drive rod to move, the static friction

force between the mobile body and the drive rod will cause

the mobile body to move together with the drive rod. When

the applied voltage drops abruptly, causing the piezoelectric

element to contract rapidly (3), slippage will occur between

the mobile body and the drive rod, displacing them with

respect to each other by an amount determined by the

dynamic friction force between them. For slippage to occur,

the following condition must be met:

where xd is the displacement of the drive rod, mm is the mass

of mobile body, and Fs is the static frictional force.

Figure 4 is a schematic representation of this behav-

ior. The average of the mobile body reaches a quite constant

level immediately after it starts, and is determined by the

displacement of the piezoelectric element due to one pulse

and the frequency of the voltage waveform.

2.2. High frequency

A voltage waveform applied at high frequency causes

the acceleration of the drive rod to increase, so that Eq. (1)

applies even when it is moving slowly, resulting in slippage.

This gives rise to a dynamic friction force between the

mobile body and the drive rod, the direction of which is

determined by the difference in duration of the dynamic

friction force. Figure 5 is a schematic representation of this

behavior. Note that the time scale used in Fig. 4 is different

from that used in Fig. 5. The mobile body, experiencing

repeated cycles of acceleration and deceleration, will be

accelerated to eventually reach a stationary velocity. The

acceleration of the mobile body is given by

Fig. 2. Supplied voltage wave.

Fig. 3. Drive principle.

(1)

Fig. 4. Low frequency.

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where xm is the displacement of the mobile body and Fd is

the dynamic friction force. The stationary velocity of the

mobile body and the time taken to reach it are determined

by the waveform of the drive rod velocity and the accelera-

tion of the mobile body expressed by Eq. (2).

2.3. Fine mode operation

The mobile body can be fine-driven with the high

resolution of the piezoelectric element when it is displaced

by an amount equal to the expansion or contraction of the

piezoelectric element, where the acceleration of the drive

rod from the initial state (1) as shown in Fig. 3 meets the

following condition:

3. Comparison with IDM (Impact Drive

Mechanism)

Figure 6 is a diagram of an IDM. In the IDM, one end

of the piezoelectric element is secured to the mobile body

and the inertial body is attached to the other end, and they

are driven together as one. The inertial body here must be

of relatively large mass for effective transmission to the

mobile body of the impact energy produced from the rapid

expansion of the piezoelectric element. But a larger mass

of the inertial body that moves the piezoelectric element

would result in a reduced resonance frequency of the pie-

zoelectric element in the unit, making high-frequency drive

impossible. Nor would it be possible to utilize the displace-

ment of the piezoelectric element itself to move the mobile

body with the IDM configured as shown. In the SIDM that

we propose, the mass to be attached to the piezoelectric

element is provided by the drive rod as shown in Fig. 1,

making the mass of the mobile body independent of the

resonant frequency of the piezoelectric element in the unit.

This allows the lightest available material to be used for the

drive rod in order to increase the resonant frequency of the

piezoelectric element in the unit, thus making high-fre-

quency drive with sawtooth waveforms achievable.

4. Experimental Unit Configuration

Figure 7 is an oblique view of the experimental unit.

One end of the piezoelectric element is attached to

the fixed member by bonding, and the other end is attached

to the drive rod by bonding. The fixed member is provided

with a hole for the drive rod bearing that supports the

expansion or contraction of the piezoelectric element. The

mobile body consists of a slider, a friction member, and a

compression spring, so the required friction force can be

generated by having the drive rod clamped between the

slider and the friction member by the strength of the spring

action. The drive rod acts as a guide as well for the mobile

body. The bonding is provided also to ensure that the force

generated by the piezoelectric element will be transmitted

to the drive rod and to provide sufficiently large strength

and stability against the repeated stresses. The drive rod is

also expected to exhibit rigidity high enough to transmit

fine small high-speed oscillations with minimum attenu-

ation, a mass small enough to act as a load on the piezoelec-

tric element, and sliding ability and friction resistance high

enough for transmission of friction.

This actuator is configured as a very simple system

as shown by the experimental unit here, which is an obvious

(3)

(2)

Fig. 5. High frequency.

Fig. 6. Impact drive.

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advantage so that it may be built smaller and is suitable for

applications.

The physical and performance characteristics of the

piezoelectric element and components used are as follows:

Piezoelectric element

Type: Laminated-type piezoelectric element

Dimensions: 2 ´ 2 ´ 9 mm

Displacement: 7 mm/150 V

Output force: 180 N/150 V

Resonance frequency: 140 kHz

Capacitance: 80 nF

Fixed member

Material: SUS430

Dimensions: f 6 ´ 45 mm

Drive rod

Material: Carbon fiber

Dimensions: f 2 ´ 30 mm

Mobile body, friction member

Material: Phosphor bronze

Unit

Mass: 5.5 g

Resonance frequency: 55 kHz

5. Performance Test Results

The test was conducted for friction forces of 1.5, 3,

and 4 N with 30 V applied to the piezoelectric element at

the driving frequency of 25 kHz. Figure 8 is the load versus

velocity characteristic obtained from the test. Note that the

measurement is the mean velocity within the stroke when

the mobile body with a weight attached to it was driven

against gravity.

Figure 9 shows the efficiency obtained from the data

in Fig. 8 for a friction force of 3 N.

The efficiency e is given by

(4)e = (g ´ Vm ´ L)

(f ´ C ´ V2)

where g is the gravitational acceleration, Vm the mobile

body velocity, L the load, f the driving frequency, C the

piezoelectric element capacitance, and V the driving volt-

age.

Fig. 7. Oblique view of fabricated unit.

Fig. 8. Effects of load.

Fig. 9. Efficiency.

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6. Analysis

Figure 10(a) is a mechanical model of the actuator.

The electronic circuit model shown in (b), which is equiva-

lent to this mechanical model, was analyzed with an elec-

tronic circuit simulator (P-SPICE). In this model, a

distribution constant circuit was used as equivalent to the

drive rod. Two ideal zener diodes placed end to end were

used as an equivalent to friction. It is for this reason that the

model has only the dynamic friction force represented. The

analysis parameters are listed in Fig. 10. Of these parame-

ters, such piezoelectric element parameters as A, Cp, rp, and

Lp were obtained from the impedance analyzer test results.

Figure 11 is the result of transient analysis of the

mobile body and drive rod velocities. While the drive rod

is changing in velocity with large acceleration, the mobile

body is subjected to repeated cycles of acceleration and

deceleration at a constant acceleration determined by the

dynamic friction force and the mobile body mass. The time

difference between acceleration and deceleration causes the

velocity to eventually become equal to the lower velocity

of the drive rod, thus effecting the transition to the station-

ary state.

The result of this analysis agreed qualitatively with

the observed behavior of the drive rod and the mobile body,

although the details are not presented here.

7. Comparison and Discussion of

Measurement Data and Analyzed Data

Next, the measurement data and analyzed data will

be compared. The analyzed velocity data are those at the

stationary state, obtained as a result of transient analysis.

Figure 12 is a comparison of the measurement and analysis

data with respect to the load versus velocity characteristic,

as shown before. The comparison reveals that the analysis

Fig. 10. Mechanical model and electrical model of actuator.

Fig. 11. Transient analysis of velocity.

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data plot is strongly curved for higher values of the load,

whereas the measurement plot is linear enough to be ap-

proximated by a straight line.

Figure 13 shows the measurement data and analysis

data with respect to voltage versus velocity characteristic.

Notice the threshold voltage at which the velocity starts to

rise from zero. The velocity rises quite linearly after the

threshold voltage.

Figure 14 plots the measurement data and analyzed

data with respect to the driving frequency versus velocity

characteristic. The analyzed data show that the velocity

increases in proportion to the driving frequency and peaks

at around 30 kHz, with some dips here and there, and starts

decreasing after 30 kHz. The result of analysis shows that

the velocity peaks at around half the resonance frequency,

since the resonance frequency of the piezoelectric element

in the unit is 55 kHz. On the other hand, the measurement

data show that the velocity rises in quite the same manner

as the analyzed data for lower frequencies, but it behaves

differently as the driving frequency increases. The compari-

son of the measurement data and analyzed data for the three

characteristics has revealed some understandable tenden-

cies. The discrepancies between the measurement data and

the analyzed data may be attributed to the following.

· The driving conditions may not have been opti-

mized for measurement.

· The model used for analysis was too simplified,

with only dynamic friction force used as the fric-

tion force.

· The analysis mode was only in the d33 direction

(horizontal oscillation was ignored).

· No allowance was made for the geometric sizes

and materials of the unit.

These problems should be dealt with in the future for

more accurate measurement and analysis, to demonstrate

the performance of SIDM.

8. Conclusions

This paper has described the theory of operation of

the SIDM, its performance test results, and the results of

examination of initial analysis. The features of this driving

system can be summarized as follows:

Fig. 12. Effects of load.

Fig. 13. Effects of drive voltage.

Fig. 14. Effects of drive frequency.

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1. It is configured so simply that it can be made more

compact.

2. It can be driven at frequencies higher than the

audible range without using resonance in the rough drive

mode. This provides noiseless drive such as can be achieved

by an ultrasonic motor.

3. High resolution of the piezoelectric element itself

can be used in the fine drive mode.

4. The self-retarding force provided by friction en-

sures stable stopping.

Taking full advantage of these features may well

allow applications in fields unsuitable for existing linear

actuators.

Our challenges now are:

· to improve efficiency, and especially to work to-

ward lower driving voltages, and

· to improve reliability, and especially to work to-

ward higher durability.

These are goals for wider application of our actuator.

Acknowledgments. We express our heart-felt ap-

preciation for the cooperative efforts, assistance, and advice

extended to us by Professor Higuchi, Assistant Professor

Kurosawa of the University of Tokyo, and Research Fellow

Mr. Yamagata of the Institute of Physical and Chemical

Research.

REFERENCES

1. R. Yoshida, Y. Okamoto, and H. Katuragi. Proceeding

of the spring annual meeting of the Japan Society of

Precision Engineering, p. 27 (March 1995).

2. Y. Okamoto, R. Yoshida, and H. Katuragi. Proceeding

of the autumn annual meeting of the Japan Society of

Precision Engineering, p. 942 (Oct. 1994).

3. T. Higuchi, M. Watanabe, and K. Kudou. Journal of

the Japan Society of Precision Engineering, 54, No.

1, pp. 2107�2112 (Nov. 1988).

4. T. Higachi and Y. Yamagata. Proceeding of the

autumn annual meeting of the Japan Society of Pre-

cision Engineering, p. 421 (Oct. 1992).

5. K. Uchino. Piezoelectric/Electric Strain Actuator.

Morikita (1986).

AUTHORS (from left to right)

Yasuhiro Okamoto received his B.S. degree in mechanical engineering from Tokushima University in 1983. He then

joined Minolta Co. and currently is with the Production Engineering Division.

Ryuichi Yoshida received his B.S. degree in chemical engineering from Osaka University in 1989. He then joined Minolta

Co. and currently is with the Production Engineering Division.

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