Sensors and Materials, Vol. 14, No. 6 (2002) 347-351
MYUTokyoLETTER

S &M0494

Force Sensing in a Multilayered Ceramic Actuator
Using a Piezoelectric Ceramic Plate
Hideto Tanaka, Yuuta Matsuse 1 and Tatsuo Fukami 1
Suzuki Co. Ltd., Department ofDevelopment,2150-1 Ogawara, Suzaka-shi, Nagano, Japan
1Faculty of Engineering, Shinshu University,4-1 7-1 Wakasato, Nagano-shi, Nagano, Japan(Received May 17, 2002; accepted July 25 , 2002)

Key words:

piezoelectric effect, nonlinear characteristics, load detection, actuator, pressure sensor

A method of sensing the force of a multilayered ceramic actuator using a piezoelectric
ceramic plate is described. The newly developed system consists of a mutually bonded
piezoelectric actuator and a piezoelectric ceramic plate, which are interposed between
nonlinear elastic elements. The graphical analysis suggested that a small signal superim­
posed on the driving voltage of the actuator makes it possible to detect the force and asubsequent experiment confirmed thus.

1.

Introduction

In recent years, multilayered piezoelectric ceramic actuators driven by a small voltage,
which have a fast response without electromagnetic noise, have been proposed,0·2l thus
receiving increasing attention as a fundamental element in precision mechanical engineer­ing. However, they have some puzzling problems in terms of nonlinear and hysteresis
displacement response due to creeping movement of domain walls in ferroelectric materi­als.(3.4) In order to overcome such disadvantages, the actuators usually have to be used
together with a rather complicated negative feedback system.<5·6l
The multilayered ceramic actuators are often used with the application of a pre-stress.
In such cases, the pressure sensor is an appropriate element for detecting how the system
works. Although the piezoelectric ceramics have an excellent sensitivity for pressure, they
only respond to the rate of pressure change, in other words, they work in a differentialmode, making it difficult to apply them to the sensor for the quasi-static pressure. We havetherefore developed a new sensing system which consists of a piezoelectric ceramic platecombined with a nonlinear elastic spring.

347348

Sensors and Materials, Vol. 14, No. 6 (2002)

In the following, we first describe the operation of the system by analyzing it graphi­
cally and then report the experimental results of the newly devised system.

2.

Operation of the Sensor System

The model under consideration consists of a multilayered ceramic actuator adhered to apiezoelectric ceramic plate and this composite system, which we call an intelligent
actuator, was uniaxially bound with a nonlinear elastic spring (Fig. 1). A hard sphere anda strain-gauge-type load cell were inserted for realizing the nonlinear characteristic and forcalibration, respectively. According to Hertz's theory on elastic contact, the relationshipbetween the displacement X and the applied mechanical force F is

X=kF213,(1)

where k is the coefficient determined from both the sphere's dimension and its materialconstant.
The multilayered ceramic actuator deforms as the sum of each elemental layer with anapplied driving voltage V but without an external force, as(2)
where X0 is the displacement of the actuator, d33 is the piezoelectric strain constant in thethickness direction and n is the number of stacked layers. Based on the elastic property ofthe actuator, we obtain its displacement X1 against the external force F,

X=a·F
E
a= S33.A,(3)where a is a constant, sf:, is the elastic compliance in the length direction, l is the length and
A is the cross section of the actuator. Then the total displacement of the actuator under theoperating conditions isHard Sphere
Metal Plate�--Load CellIntelligent

i ..::.---Multilayered Ceramic ActuatorActuator�-��.;:,;t,;i�,..,.,.,.,

Piezoelectric Ceramic Plate for Sensor

ll l������������!!IIII l IIII!�����������
Fig. 1.

Construction of the actuator system.

Sensors and Materials, Vol. 14, No. 6 (2002)

349

X=-X1+Xo=-a·F+d33·n·V.

(4)

If one superimposes this actuator characteristic on the elastic property of the nonlinear
binding system, one obtains Fig. 2. The operating point is designated by the intersection of
the nonlinear binder curve with the actuator line and at this point the following relationshipshould be maintained.
(5)This relationship gives the variation of the force M with a small fluctuation of the applied
voltage to the actuator Ll V.

(6)

Equation (6) represents the principle of the present sensing system. When the driving
voltage fluctuates, the instantaneous force varies about the operating point; if the applied
voltage moves from V1 to V2 , the resultant force upon the same voltage variation Ll V
changes from M1 to '1F2 , reflecting the difference of the operating point. It goes without
saying that the sensor's output signal is proportional to this force variation.

3.

Experimental Results and Discussion

By using a commercially available piezoelectric ceramic actuator (Tokin Ceramics Co.
Ltd., AE1424D16), an experiment for the confirmation of the preceding analysis wasFig. 2. Elastic characteristics of the actuator system where a multilayered ceramic actuator is boundwith a nonlinear elastic spring.

350

Sensors and Materials, Vol. 14, No. 6 (2002)

carried out. Figure 3 shows the displacement vs. force characteristics for various driving
voltages. As can be seen from the figure, a significant hysteresis phenomenon is observed.
A piezoelectric ceramic plate for the force sensor, 14x14x0.l mm3, was adhered to theactuator. It was then inserted in the binding system with a cp3 mm hard sphere together witha load cell for monitoring 01ALCOM,VLC-10KNE159).
An example of the voltage wavef orm applied to the actuator and resultant output signal
is shown in Fig. 4. In this figure, a small square wave voltage of 1 V for sensing is
superimposed on the driving voltage of 59 V. The cycle period and duty ratio of the squarewave are 0.5 s and 50%, respectively. The output signal gives an exponential responsewith a small variation of the driving voltage, whose peak value corresponds to theoperating force.
Figure 5 shows the output signal voltage vs the force to which the actuator is subjected.

615
L..-J

E

10 '\::._,::-.._s
8 5�°"-�·-.::.,.

., ...

Q)

Cl O

2.0

Fig. 3.

>

000:>

'•:t,

q"

4.0

Force

6.0

[kN]

Displacement vs f orce characteristics.

4060

Applied voltage

L..-Jtl)--��---...�...

20Sensor output

400-�-a 20"Cl>Q)

00!:l0:>'5fr;::l-20 0....
0<!'.

Cl.

-40 Cl)
Q)

00.1

0.2

0.3

Time[s]0.4

0.5

Fig. 4. Output signal of the sensor piezoelectric plate in case a small square voltage of 1 V issuperimposed on the driving voltage of 59 V under the initial binding force of 0.75 kN.

351Sensors and Materials, Vol. 14, No. 6 (2002)

> 60
�V40

::i20

V.59vLllv

::i0

0.2

0.4

Force

0.6
[kN]

0.8

Fig. 5. Output signal vs force characteristics.

It should be said, at least in principle, that we can detect the force of the actuator using thepiezoelectric ceramic plate. The saturation tendency in the figure may be caused by thedeviation from the assumed nonlinear elastic property of eq. (1). The minimum detectable
force, of course, should be limited by the signal/noise ratio.

4.

Conclusions

The newly devised force sensing system for the multilayered ceramic actuator was
shown to work well using a piezoelectric ceramic plate. Further efforts of our group will bedirected at developing an automatic pressure controller for high-pressure gasses.

Acknowledgements
The authors thank Professors, M. Tanaka and N. Henmi for useful discussions onnonlinear elastic elements.

References
23456S. Yamashita: Jpn. J. Appl. Phys., Supplement 20-4 (1981) 93.
S. Takahashi: Jpn. J. Appl. Phys., Supplement 24-2 (1985) 41.
C. Newcomb and I. Flinn: Electron. Lett. 18 (1982) 442.
X. Yanjiang, B. Huppe and T. Fukami: Ferroelectrics 160 (1994) 331.
T. Niimi, T. Fujimoto and K. Wada: J. Jpn. Soc. Mech. Eng. C57 (1991) 3347.
K. Furutani and M. Urushibata: Nanotechnology 9 (1998) 93.