C1-1

PROCEEDINGS OF THE 20TH SENSOR SYMPOSIUM,2003.pp.123〜126

Development of 3-axis Gyro-Sensor Using Piezoelectric ElementKazuhiro Okada, Yosiyuki Matsu*, Nobumitsu Taniguchi, Hiromiti ItanoWacoh Corporation
4-244-1 sakuragi-cho oomiya-ku Saitama-shi Saitama, 330-0854, JapanAbstract
Operation of objects in 3-dimensional space can be expressed by acceleration and angular rate. Sensors to detect them are made byusing micromachining technology and ceramic technology. In the field of acceleration sensors, 3-axis acceleration sensors that detectacceleration in 3-dimensional space have already been commercialized, and also in the field of gyro-sensors, piezoelectric type 2-axisgyro-sensors have been developed. By applying such piezoelectric type 2-axis gyro-sensors, 3-axis angular rate can be detected withvelocity components of an oscillator in the directions of two axes, and the detection components of Coriolis’ force produced by angularrate in the directions of two axes. By using this principle, we have succeeded in developing a 3-axis gyro-sensor that detects 3-axis
angular rate with one detecting element. This report details the construction, detection principle, and detection circuit, as well as theperformance, such as sensitivity, cross-axis sensitivity, and linearity.
Keywords: 3-axis gyro-sensor, angular rate, piezoelectric, Coriolis’force.
1 INTRODUCTION

acceleration sensors. We have conducted research of 3-axisgyro-sensors(4),(5) to meet such demands. We wish to report on
the piezoelectric type 3-axis gyro-sensor we have developed
recently, superior in sensitivity, cross-axis sensitivity, andlinearity.

Operation of objects in 3-dimensional space can be expressedby parallel motion and rotational motion. Parallel motion canbe expressed by physical quantities, such as distance, velocity,and acceleration, while rotational motion can be expressed by
the physical quantities of an angle, angular rate, and angularacceleration. These physical quantities can be expressed by themathematical relationship of differential or integration function.
Thus far, for detection of the six physical quantities of distance,velocity and acceleration, which represent parallel motion, andangle, angular rate and angular acceleration, which represent
rotational motion, only acceleration sensors and gyro-sensors
have been operational in use of micromachining technology
and ceramic technology. As a matter of course, acceleration andangular rate are important physical quantities in detecting themotion of objects in 3-dimensional space. In the field ofacceleration sensors, 3-axis acceleration sensors(1)-(3) of thepiezoresistance type, capacitance type, and piezoelectric typehave already been developed, and marketed by manycompanies. However, in the field of gyro-sensors, 1-axisgyro-sensors are predominant, though only a few 2-axisgyro-sensors have been marketed.
Angular rate is also a vector quantity like force and acceleration,and 3-axis gyro-sensors are indispensable to detect the angularrate accurately. Recently, on the market, needs for multi-axisgyro-sensors are increasing gradually as is the case with

2 Detection principle of the 3-axis gyro-sensor
When an object having a mass moves at a certain velocity,
angular rate operates on the object with the result that apparent
force (Coriolis’ force) acts on it. It is the so-called Coriolis’force. The 3-axis gyro-sensor also uses the Coriolis’ force. In
the case of 3-axis gyro-sensors, the oscillator having a mass isbrought into rotational motion on the X-Y plane as shown inFig. 1.

Vy

VxFigure 1. Detection principle of the 3-axis gyro-sensor
In this motion, the oscillator has velocity component Vx in theX-axis direction at a certain instant, and has velocity

123component Vy in the Y-axis direction at the next instant. As
shown in Fig. 2, when the oscillator moves having velocity
component Vy in the Y-axis direction, if angular rate ωz in theZ-axis direction acts, Coriolis’ force Fx in the X-axis direction
is produced, and if angular rate ωx in the X-axis direction acts,
Coriolis’ force Fz in the Z-axis direction is produced.
FzElectrode
Elinvar

Piezoelectricelement

Oscilator

Fz

Figure3. Cross-sectionof the 3-axis gyro-sensor

ωzωx

Vx

Fx

ωyVy

Figure2. Detection of ωx, ωy and ωz
Also, when the oscillator moves having velocity component
Vx in the X-axis direction, if angular rate ωy in Y-axis direction
acts, Coriolis’force Fz in the Z-axis direction is produced.
The relationship is shown by the following expression (1).
Fx=2mVy ×ωz
Fz=2mVy ×ωx(1)
Fz=2mVx×ωyThis expression shows that the angular rate components (ωx,ωy, ωz) of three axes can be detected by detecting Coriolis’force (Fy, Fz) in the directions of two axes while giving
velocity components (Vx, Vy) in the directions of two axes bybringing the oscillator into rotational motion on the X-Y plane.
The 3-axis gyro-sensor we have developed this time uses theso-called piezoelectric effect of piezoelectric ceramic;“principle on which distortion occurs if voltage is applied, andcharge occurs if distortion is given.” The piezoelectric effectof the piezoelectric element is used for both circular motion
within the X-Y plane, and detection of Coriolis’ force in theY-axis direction and Z-axis direction. Since drive and detection
are essential to gyro-sensors, it can be said that the piezoelectricelement is one of the suitable materials for gyro-sensors.

Figure4. Surface of the piezoelectric ceramic substrate
The node point of the diaphragm is supported, and fixed to thepackage. The surface of the piezoelectric ceramic substrate isshown in Fig. 4. Nine divided electrodes are formed on thesurface. Coriolis’ force is detected by the four sector electrodes(x+, x-, y+, y-) placed at the center. Coriolis’ force in the X-axis
direction is detected from the difference in charge produced
between the two electrodes (x+, x-) placed on the X-axis, andCoriolis’ force in the Y-axis direction is detected from thedifference in charge produced between the two electrodes (y+,y-) placed on the Y-axis also. The four electrodes (X+, X-, Y+,Y-) placed outside the detecting electrodes are used for bringing
the oscillator into rotational motion, and the oscillator makes
rotational motion on the X-Y plane when AC signals with a 90°
phase shift are applied. Ring electrode placed outermost is tomonitor the motion in the Z-axis direction, which is used forsynchronous detection. The placement of the nine electrodes
shown here is determined by FEM analysis. Especially,
positions of electrodes (x+, x-, y+, y-) detecting Coriolis’ force
are important, which must be placed in the stress concentration
area. The results of FEM analysis of stress and displacement inthis construction are shown in Fig. 5 and Fig. 6. From theseresults, it can be seen that stress concentrates around theoscillator joining part. If the Coriolis’ force detecting electrodes(x+, x-, y+, y-) are placed in this area, Coriolis’ force canefficiently be detected. It is efficient to bring the oscillator into

3. Construction of the 3-axis gyro-sensor
For the piezoelectric effect, the cross-sectional view of the3-axis gyro-sensor is shown in Fig. 3. The piezoelectric element
substrate is bonded to the top face of the diaphragm made of
elinvar, and the oscillator is joined to the back.

124

rotational motion by the surrounding four electrodes (X+, X-,Y+, Y-).

motion as shown in Fig. 1, the velocity components areconstant. In this research, the oscillator was brought into
rotational motion on the X-Z plane in consideration of thedetection sensitivity and noise resistance. When passing on theX-axis, it has a velocity component in the Z-axis direction, andwhen passing on the Z-axis, it has a velocity component in theX-axis direction. If Coriolis’ force is measured in the X-axis
direction and Y-axis direction the instant when it passes on theX-axis (velocity component Vz), angular rate ωx and angularrate ωy can be detected. Furthermore, if Coriolis’ force ismeasured in the Y-axis direction the instant when it passes on
the Z-axis (velocity component Vx), angular rate ωz can bedetected. Rotational motion on the X-Z plane is made byapplying signals with a phase difference of 0°,90°,180°,270°
from the corresponding phase of the electrodes (X+ and X-) on
the X-axis alternately, and Coriolis’ force in the X-axis direction
and Y-axis direction is detected from the charge produced
between the central four detecting electrodes (x+, x-, y+, y-).
The circuit block diagram used for detecting 3-axis angular rateis shown in Fig.7. Synchronous detection of the signals fromthe detecting electrodes (x+, x-, y+, y-) with the drive signal of
the oscillator can be seen.

Stress distribution of Z direection

Stress distribution of X direection

Figure5. FEM analysis of stress

AMPSensor
element

X+
XY+
Y-Y

LPF

ωyX
Synchronousdetectorωxωzreference signal
ZZ
Drive Circuit
oscillator

Drive signal

Displacement distribution of Z direection

Phase/Gain controller

Figure7. Circuit block diagram of 3-axis gyro-sensor
5. Performance of the 3-axis gyro-sensor
The principal axis sensitivity and cross-axis sensitivity of the3-axis gyro-sensor we have developed this time are shown in
Fig. 8. It can be seen that the cross-axis sensitivity is 5% or lesson each axis. Performance is shown in Table 1. Compared withthe piezoelectric ceramic type 1-axis gyro-sensor that iscommercially available at present, we have found that the3-axis gyro-sensor can achieve performance of the same levelin the cross axis sensitivity , non-linearity et al, and theperformance is equivalent to three 1-axis gyro-sensors.

Displacement distribution of X direection

Figure6. FEM analysis of displacement
4. Detection circuit of the 3-axis gyro-sensor
Since the oscillator of the 3-axis gyro-sensor makes rotational

1256. Acknowledgement
The authors wish to acknowledge
Dr. S.Fujiki, and
Mr. A.Nakagawa of Toyama Industrial Technology Center for
their helpful suggestion and cooperation in carrying out rotarytable measurements. This research was conducted based on theProgram for Promotion of Technology Innovation on Specified
Issues by JASMEC (Japan Small and Medium Enterprise
Corporation).

Conclusion
This report has shown that 3-axis angular rate can be detectedwith one detecting element by bringing the oscillator into
rotational motion within a 2-dimensional plane, and detecting
Coriolis’ force in the directions of two axes. In this research, thevibrator was brought into rotational motion and Coriolis’ force
was detected by using the piezoelectric effect of thepiezoelectric element, but the oscillator may be brought into
rotational motion by Coulomb force and Coriolis’ force being
detected by electrostatic capacitance. In this case, it isconsidered that compact and highly reliable 3-axis gyro-sensors
can be realized with use of micromachining technology. We
think that research in this field will advance in synchronicity
with market trends in the future.

7 References[1] K.Okada “Tri-axial piezoresistive accelerometer”
Tech.Dig. of The 11th Sensor Symposium, 1992,
pp245-248[2] Joost C.Lotters “A Highly Symmetrical Capacitive TraxialAccelerometer” ISBN 90-365-0982-3[3] K.Okada et al “Development of Maicro-machined
Three-axis Sesors in Venture Business” Transducer’01
Munich 1280-1283 2001
[4] N.Taniguchi et al “The 5-axis Motion Sensor” Tech. Dig.
of The 16th Sensor Symposium.1998, pp41-44[5] Y.Watanabe et al “Five-axis motion sensor withelectrostatic drive and capacitive detection fabricatedsilicon bulk micromaching”, Sesors and Actuators A
97-98(2002) 109-115

Figure8. Detection sensitivity and cross-axis sensitivity
Items
Detection axis
Sensitivity
Cross-axis sensitivity
Non-linearity
Response frequency

Performance
3-axis(X,Y,Z)
2.5mV/deg/sec
5%3%DC-50Hz

Table1. Performance of 3-axis gyro-sensor

126