Indian Joumal of Pure & Applied Physics Vol. 42, June 2004, pp. 452-458

Vibrating single crystal piezoelectric disc gyroscope

A K Singh & Vrushali DCD

Institute of Armament Technology, Girinagar, Pune 4 11025

Received 3 Fehrttary 2003; revised 3 March 2004; accepled 18 March 2004

This paper deals with a single crystal piezoelectric disc gyro sensor. The principle of basic operation and the pract ical struct ure of the disc vibrating gyro has been described along with the experimental results for a protutype of the gyro sensor. The resulls obtained show that the proposed disc resonator operates as a gyro sen. or, ,. aving sensiti vity of about 0.9 mVI "Is, and behaves almost linear in the range of upto 180 ·"ls .

IPC Code: G OIC 19/00

I Keywords: Piezoelectric, Gyroscope, Cori olis force, Vibrat ing mode, Resonance frequency 1

I Introduction

Recently, vibratory gyroscopes are be ing used in many industrial applications I · ] i.e. image stabilizing syste ms of camcorders, direction sensors of car navigation systems, etc., however, early efforts were moti vated by military app lications4

.s where space had

been the main restriction , including guidance and stabi li zat ion of mi ssiles, stabilization of gun, camera and antenna platforms, smart munitions including gun­fired munitions and GPS augmented navigation, stab ilization and navigation of underwater vehicle. These gyroscopes offer important advantages over the traditional gyroscopes .

Vibrating gyroscope,> work on the principle of the Coriol is acce lerat ion. This acceleration is experienced by a particle undergoing linear motion , in a fra me of refe re nce rotating about an axis perpendicular to that of the linear motion. The resulting acceleration is directly proportional to the rate of tum , occurs in the third ax is, which is perpendicu lar to the plane contai ning the other two axes. In these sensors, vibration motion is coupled from a primary vibrating mode in to a secondary mode, when the sensor experiences angular rate. ]n recent years, several different types of vibratory gyroscopes have been proposed3NJ and developed. These can be subdivided into three groups as follows: (i) s imple oscillator i.e. mass on a string, beam(" (ii) balanced oscillators i.e. tuning forks lO and (iii ) shell resonators i.e. ring,1 1 cylinderl}, disc7. J3 . By correct design of a shell resonator,

it is possible to overcome problems assoc iated with resonator mount sensitivity, experienced by simple osci llators and balanced osc illators, and thus improve bias performance and reduce sensiti vi ty to shock and vibration. Also, the layout of the sensor is very important, as it dec ides the rotation ax is of the equipment. Almost, a ll vibrating gyro sensors, which are being used practically and are bei ng studied at present, are long in the same direction as the detecti on ax is. Hence, these gyroscopes cannot be used in the case of thinly packed equipment and inadequate space in the direction of detection axi s. T herefore, a flat structured gyro sensor for detection axis , is in demand . The purpose of this study is to develop a flatl y equipped gyro sensor. Besides this, vibrating disc structure has certain added advantages over ot her types of vibratory gyroscopes- (a) T he inherent symmetry of the st ructure makes it less sensiti ve to spurious vibrations. (b) As two identical flex ural modes of the structure, with equal resonant frequencies, are used to sense the rotation, the sensitivity of the sensor is amplified by the quality facto r of the structure, resulting in higher sensitivity. (c) The vibrati ng di sc is less sensitive to temperature, since both the vibration modes are equall y affected by the temperature .

The theory of piezoelectric gyroscopes is wel l established and discussed elsewhe re7. ~. !.> and , in particular by Tamura et aF. and Burdess and Wren !'> deals with disc gyroscopes. The developed gyro is made of th in piezoelectric disc, axially po larized PZT,

SINGH & DEO : PI EZOELECf RIC DISC GYROSCOPE 453

on which, are deposited drive and pickoff electrodes to give the monolithic arrangement. This is achieved by making the disc out of piezoelectric material and providing the drive and detection mechanism via simple electrodes deposited on the surface of the disc . Disc gyroscopes are based on in-plane vibration of thin piezoelectric disc, which is rotated about its polar axis.

2 Experimental Details

Figure I shows the basic design of the disc gyroscope sensor. The disc is made of PZT (SP - 5H trade name of manufacturer) material and has a diameter of 10 mm and thickness I mm. Eight equispaced identical posi tive electrodes numbered I to 8 are deposi ted on the upper surface of the disc, covering outer diameter of 5 mm as shown in the figure. A si ngle negative e lectrode covers the whole of the lower surface of the disc. The piezoe lectric disc of this required electrode design has been manufactured by MIs Sparkler Ceramics, Pune, as per the given drawing and spec ifications. The centerline of electrode I is defined by the axis OX. Electrodes I and 5 are paired to drive the disc at resonance. A sinusoidal voltage, at the mechanical resonance frequency, is applied to the excitation electrodes (I and 5) .

The experimental setup of the piezoelectric disc

z

~5mm

~10mm

Fig. I- Single crystal piezoelectric disc gyroscope sensor element

x

gyroscope is shown in Fig. 2. The disc is rigidly fixed at its inner radius to a turntable, the stepper motor stem and is excited through a Systronics function generator. The output of this disc is taken through a bunch of wires containing nine flexible wires. Eight wires are connected to eight equispaced identical positive electrodes I to 8, and the ninth wire is connected to the negative electrode. The disc output is fed to the signal conditioner circuit and the output is displayed on the Keithley 6 Y2 digital multi meter and on digital storage oscilloscope. The stepper motor is operated through a microprocessor based controlled driver card. The 8085 microprocessor has been interfaced with the stepper motor driver card . The stepper motor used is 611 2V permanent magnet, 2 phase, 1.80 ± 5 % full step, 200 steps/rev, 0.5 Nphase, holding torque is 2 kg cm1 with single phase energized, 2.8 kg cm1 with both phases energised, rotor inertia 0.1 kg cm1

.

3 Piezoelectric Gyro Operation Since the disc is thin, a voltage applied to terminals

I and 5 will produce an axial electric field in that region of the disc , which is defined by the shape of the electrodes I and 5. This periodic field can be used to drive the disc into resonant vibration due to piezoelectric action and can excite a combined radial and torsional mode of vibration with radial displacement. The nodal lines of this mode will occur at ±4S" with respect to axis OX. A large o/p signal is obtained if large drive amplitude is used, which is obtained by utilizing one of the drive resonance frequencies. The o/p signal can be further increased by letting the resonance frequencies of the sense vibration to be same as the drive frequency. The resonant frequency of the disc has been determined experimentally. At the natural frequency, the disc wi ll have maximum vibrating amplitude and hence maximum strain on the piezoelectric disc and as a result of inverse piezoelectric effect, output will be maximum. This disc is excited with 20-volt ac signal, generated from the Systronics function generator. The output from electrode 3 is taken through the current to voltage converter and displayed on the oscilloscope. Now, as the input frequency to the disc from the function genemtor is varied manually, the output keeps changing. This output will touch a maximum value at the resonant frequency of the disc which has been measured and found to be 148 kHz. The disc is excited with 148 kHz ac signal of 20 V for gyroscopic operation.

When this disc is rotated through the stepper motor at excited condition, the secondary mode of

454 INDIAN J PURE & APPL PHYS, VOL 42, JUNE 2004

r . - - . - - - - - . - . - - . - . - .. .. . - - . - - - . - . . - - . . - - . .. . • -

Function Generator IOscillator

10 Ko

Converter

6.6Ko

Differential Amplifier

~ . . ...... . . . .. . .. . ..... ·t······ · ·· ··· · · ··· · · · ~ Shaft

Signal Conditioning Circuit

--~ Digital Muittmeter

Digital Storage Osci~loscope

- - . . - - . - - - - - - . .. .. . . ... . - .. - - - - - - . - . . - . . . . . . - . . .... - . -- . -- . . . - ... . . - ,

Stepper Motor

Tum table

Stepper Motor Driver Circuit

Microprocessm~ w--~8085

L-______________ ~ ~ ________ _

Fig. 2- Schematic block di agram of experimental

vibration is generated as a result of the Coriolis Force. Using the inverse piezoelectric effect, the modal response produced by this excitation can be measured directly by taking the current produced by electrode 4 through a high input impedance current to voltage converter A I as shown in Fig. 2. A second measurement electrode 8 is provided by connecting the terminal to a second high input impedance current to voltage converter A~ . Since these electrodes are centered precisely on the 45"" nodal lines of the foregoing mode, they will register no output current as a result of the oscillator vi bration . If the disc is now rotated about OZ, Corioli s inertia forces will excite a secondary motion . This motion will cause an output to be generated by A I and A~. The voltages are applied to a high gain di fferential amplifier A) as shown in Fig. 2. The value of the differential voltage is taken as the measure of the applied rate of tum .

Thus, the primary and secondary modes of the piezoelectric disc can be excited electrically by pairs of surface e lectrodes. A rate of tum produces a dynamic couplin g between these modes of the piezoelectric disc and thereby, because of piezoelectric action, causes a voltage to be generated at another

electrode pair, which can be taken as a measure of the applied rate of turn . 4 Results and Analysis

The overall performance of the gyroscope and electronics has been tested using programmable stepper motor turntable which has been calibrated for different speeds to suit rotation of the g yroscope . The microprocessor program corresponding to the speed is changed serially and different speeds corresponding to the program are being measured with the he lp of a tachometer. Under rotation output of the sensor has been measured and it is observed that olp of gyro sensor consi sts of ac and dc signal which changes with rotation of turntable. The output waveforms of the ae and dc components of signal are shown , respecti ve ly, in Fig. 3 (without rotation) and Fig. 4 (after rotation), and in Fig. 5 (without rotation) and Fig. 6 (after rotation). The results for different speeds of counter clockwise rotation of the gyroscope are tabulated in Table I for ac component of signal and in Tabl e 2 for dc. The variation of output(average of three readings for ac and dc component) with rotati on speed is shown in Fig. 7 and Fig. 8. From the resu lL, it is observed that for counter clockwise rotation, the increased vo ltage remains unchanged until it is rotated clockwise to

SING H & DEO : PI EZOELECTRIC DISC GYROSCOPE 455

18-Hov-92 19:51: 19

2 IlS

2 V AC

I

IA " I

'V

" 1.

I I

.\ . \

pkpk (2) mean (2) sdev (2) rms (2) ampl (2)

II

rv

II " I 7

1\ 1\ IV 'V

800mV 260.7 mV 249.7 mV 361 .8 mV

761 mV

.\ 1 ~ 'V 'V

2 .2 V AC 2 DC 0.136 V 100 MS/s

Fig. 3-011 tPlit ac signal waveform withou t rotati on

18-Ho~-92 19: 39: ~3

r~ U

I VS 1 2 V AC

2 .5 V AC

1./ 1\ I r\ .1 II ,\11 \l!

pkpk (2) mean (2) sdev (2) rms (2) ampl (2)

S 2 DC 2.44 V

t\ I ~ / "\ ''\, .~

781 mV 2.1325 V

227.6 mV 2.1446 V

781 mV

100 MS/s

Fi g. 5- 0 utput signal dc waveform wi thout rotati on

p

2

18-Nov-82 19: 41 :57

r~ U

2 IlS

1 1 2 V AC

IA /I

\ V

3 2 .2 V AC S

\ V

A

II I r

\ \

pkpk (2) mean (2) sdev (2) rms (2) ampl (2)

1

2 DC 0.120 V

1 1

1\

W IV rv

831 mV -24.5 mV

254.9 mV 256.0 mV

798 mV

r

\

V

100 MS/s

Fi g. 4-01ltput ac signal waveform aft er coun ter c lockwise ro tatio n

18-tbJ-82 19: ~2 : 32

[~ L:J

I IlS

1 2 V AC

2 .5 V AC

r.

I\. V V

1\ / \ '\.

pkpk (2) mean (2) sdev (2) rms (2) ampl (2 )

/ ;7

2 DC 1.80 V

~ I ......

\ J \ 'V

812 mV 1.9980 V

252.3 mV 2.0139 V

797 mV

V

100 Ms/s

Fig. 6-0utPllt de signal wa veform :1fter counte r clockwi se rotation

~

~

Z

456

o 50

•• •

INDIAN J PURE & APPL PHYS. YOL 42, JUNE 2004

100 150 250

•

• • •

Speed in degs

o 100 200 300 > c: 0.00 +--__ ----L ____ .L-. ___ -'

Q) ••• • ..... Cl -0.20 +------~h ................ -,. - .. ----­c: ~ -0.40 +-----------+- .----­(,)

~ -0.60 +---------.--.. ----

oS -0.80 +-____________ + ___ _ "0 > ~

-1.00 +---------.------.~.---

-1.20

Fig. 7-Yariation of ou tput (ac signal) wi th rotation sJ1ced Speed in c1egis

RPM

8

II

16

IX

20

22

24

26

30

" .'-

34

36

·w

.. 13

Fig. 8-Yari ation of ou tput (de signal) with rotation speed

Table I - Output volt<:ge(ac) for gyroscope withoLit and w ith counter clockwise rotation for different speeds

RTN Deg/s

36

48

66

108

120

132

144

156

168

180

192

204

216

228

240

25S

First Reading in illY

WIO Rtn

215

218

222

215

221

230

218

228

235

240

270

306

318

324

285

254

AI'tr Rtn

200

205

210

200

207

216

203

210

220

220

255

249

239

233

235

240

220

Dill

.. 15

.. 13

.. 12

- I S

.. 14

-14

.. 15

.. I S

.. IS

.. 20

-23

.. 21

-67

.. 85

.. 89

-45

-34

Second Read ing in illY

WIO Rtn

22 1

223

220

220

219

223

215

230

228

228

279

275

307

320

338

282

248

AftI' Rtn

210

208

206

205

202

212

198

215

210

210

260

253

243

235

240

239

202

Dill

- II

.. IS

-14

-15

.. 17

.. II

-17

.. 15

.. 18

.. J 8

-19

-22

.. 64

-85

.. 98

.. 43

.. 46

Third Read ing

in mY

WIO Rtn

214

220

216

214

223

22 1

224

235

227

225

265

272

309

315

340

285

244

AftI' Rtll

202

209

202

202

210

200

210

218

209

209

250

257

238

239

242

239

205

Dill Av eh ill illY

.. 12 .. 12.67

··11 .. J3.0

-14 .. 3.33

.. 12 A .OO

.. i 3 .. 4.67

.. 21 .. 5.33

.. 14 .. 5.33

.. 17 .. 6.6

.. 18 .. 7.00

.. 16 -8 .00

.. I S .. 9.00

.. 15 .. 9.33

.. 71 .. 7.33

.. 76 -2.00

-98 .. 5.00

-46 .. 4.67

-39 .. 9. 67

SINGH & DEO : PI EZOELECTRIC DI SC GYROSCOPE 457

Tahlc 2-0utput vo ltagc( ac) for gyrosco pe without and with counter cloc kwisc ro tati on ror differe nt specds

Firs t Read ing in mV

Second Rcadi ng in mV

T hi rd Readi ng in mV

RPM

6

II

16

18

20

2'2

24

26

28

30

'') .'-

36

40

4-'

RTN Deg/s

36

48

66

96

108

120

1-'2

144

156

168

180

192

204

2 16

228

240

258

W/O Rln

3.55

3.7 1

3.66

3.85

3.73

3.63

3.88

4.05

4. 15

3.8 1

3.88

3.9 1

5.27

5.2'J

5.2 1

5.82

Aftr Rln

3.46

3.6 1

3.55

3.73

3.6 1

3.45

3.65

3.58

3.82

3.85

3.57

3.52

3.54

4.62

4.58

4.37

4.84

Dill

-0.09

-0. 1

-0. 11

-0. 12

-0. 12

-0. 18

-0.23

-0.22

-0.23

-0.3

-0.24

-0.36

-0.37

-0.65

-0.7 1

-0.84

-0.98

WIO Rtn

3.62

3.65

3.72

3.81

3.65

3.75

-'.7'J

4.08

3.93

4. 1

3.75

3.84

385

5.2'J

5.31

5.24

5.82

decrease it to the same reference voltage. Hence, the developed gyroscope is able to detect the directi on of rotati on also. For consecuti ve rotati ons III the same directi on, the voltage increases or decreases as per the direc tion.

From the results and the corresponding graphs, it can be seen that the gy roscope operates linearl y up Lo a rotati on rate of approx imately 180"/s, after whi ch it

shows non linear behav iour. In the linear range, the

dc out put sensiti vity of gy roscope IS about 0.9

mY I Is and ac output sensiti vity is about 0.06 mY I Is.

For vanous applicat ions, the max Imum range for

rotati on required IS about 50-60'/s and the des igned

Aftr Rln

3.55

3.53

3.59

3.49

3.53

3.6 1

.185

-'.74

3.8'J

3.53

-'55

.\.56

4.6 1

4.55

4. 19

4.77

Dill

-0.07

-0. 12

-0. 13

-0. 12

-0. 16

-0.22

-0. 18

-0.23

-0. 19

-0.2 1

-0.21

-0.29

-0.29

-0.68

-0.77

- I .05

- 1.05

W /O Rt n

3.68

3. 61

3.82

3.75

3.69

3.75

3.73

3.95

4. 1

3.98

-'.86

3.85

5.17

5.3 5

5. 17

5.7'J

Alh Rtn

3.5X

-,A'J

.U I

3.65

355

3.6

3.55

3.711

3.6

3. 54

3.12

4 .62

4.65

4.2 5

4.82

Dill AI' Ch in mY

-0. 1 -0087

-0. 12 -0. 113

-0. 11 -0. 117

-0.1 -0. 113

-0. 14 -0. 140

-0. 15 -0. 183

-0. 18 -0.197

-0. 17 -0.207

-0. 22 -0.21 3

-0. 18 -0 .2-'0

-0.26 -0.240

-0.3 1 -0.320

-0.66 -OA40

-0.65 -0.660

-0.7 -0.727

-0.92 -0.937

-0.97 -1.000

gy roscope, which can be u ~cd upLO a max imum rotat ion

speed of 180'/s, suits most of the applicati ons. Acknowledgement

Authors are thankful to Prof G C Pant, Chairman. Guided Miss iles Faculty, fo r the encouragement and Director & Dean, institute of Armament Techn ology, G irinagar, Pune (MS) for granting permi ssion to publ ish thi s work .

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