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A planar vibratory gyroscope using electromagnetic force
ACTUATORS A
ELSEVIER
Sensors and Actuators A 65 (1998) 101-108
PHYSICAL
A planar vibratory gyroscope using electromagnetic force Sang-Hun Lee a,., Seung-Wan Hong b, Yong-Kweon Kim a, Seung-Ki Lee ° a School of Electrical Engineering, Seoul National Universi~, San 56-1, Shinrim-dong, Kwanak-ku, Seoul 151-742, South Korea b Samsung Electronics, San 24, Nongseo-Ri, Kiheung-Eup, gongin-City, Kyungki-Do 449-900, South Korea Department of Electrical Engineering, Dankook University, Han Nam-dong, Yongsan-ku, Seoul 140-714, South Korea Received 3 February 1997; revised 25 July I997; accepted 22 August 1997
Abstract
A planar vibratory gyroscope using electromagnetic force is proposed and tested. Such a gyroscope has the advantages of simple fabrication and large output characteristics compared with an electrostatic gyroscope. The fabricated gyroscope comprises a gyroscopic element with two gimbals, driving and sensing coils. The driving coils, which are under the outer gimbaI, vibrate the gyroscopic element. Vibration of the inner gimbaI due to an applied angular rate is detected by sensing coils underneath it. Maximum output is obtained when the output gimbal is driven at a resonance frequency of the inner gimbal. Measured sensitivities are from 4.2 to 26 mV (° s - ~) - ~. Sensitivities are measured at several exciting voltages and several values of the air gap of the sensing parts. © i998 Elsevier Science S.A. Ke)words: Planar vibratory gyroscopes; Electromagnetic force; Resonance frequency; Sensitivity; Magnetic coupling
1. Introduction
The constant emergence of new automotive and consumer applications has led to an increased need for small and inexpensive gyroscopes. Conventional gyroscopes are widely used in military applications and are based on conservation of angular momentum of a spinning rotor. They are expensive, bulky, have a short working life and also have many components that require high precision in fabrication and assembly [ 1,2]. These disadvantages also apply to fibre-optic and laser gyroscopes [3], although their performance is excellent. Recently, there have been many studies on planar vibratory gyroscopes, which rely not on the conservation of angular momentum of a rotating structure but on the conservation of linear momentum of a vibrating structure. Most planar vibratory gyroscopes have been fabricated by a micromachining technology. Micromachined structures can withstand harsh environments for long periods of time, implying a lifetime not limited by the sensor element itself. They also have the additional advantages of small size, low price and low electric power consumption. A number of possible designs have been proposed, typical examples being based on a tuning fork [ 4 7], a vibrating shell [8], a vibrating beam [9] and a quasivibrating plate [10]. Electrostatic [4,10], electromagnetic * Corresponding author. Tel.: +822 888 50 17. Fax: +822 873 99 53.
[11,12], or piezoelectric [5,13] methods are used to drive the gyroscope, while capacitive [6,7,10,11,14], or piezoelectric [5,12,15 ] methods are used to sense the vibrations caused by the Coriolis force on the vibrating structure. The capacitive sensing method is well suited for micromachined batch fabrication, but it requires a high-resolution electric circuit to detect a capacitive change in the attofarad range [ 10]. Piezoelectric sensing methods are more accurate but have highly temperature-dependent output characteristics except for crystalline piezoelectric materials such as quartz. On the other hand, electromagnetic detection methods can obtain relatively large output voltage compared with the other methods. While several researchers have fabricated micromagnetic circuits by micromachining technology, it is not so easy to make a fully micromachined magnetic circuit. In order to demonstrate the feasibility of electromagnetic detection in a vibrating gyroscope, for this paper we use a gyroscope manufactured by conventional machining technology, with a gyroscopic element measuring 74 mm × 50 ram. We propose here a method to obtain high output characteristics for a planar vibratory gyroscope using electromagnetic force. The gyroscope equations are derived, and the gyroscope is designed so that the vibration of the outer gimbal coincides with the resonance frequency of the inner one. The magnetic system equations are also derived, and imply that the sensitivity of the proposed electromagnetic gyroscope can
be controlledeasily by changingthe exciting voltageand the 0924-4247/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved P//S0924-4247(97)01670-1
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$.-H. Lee et at./Sensors and ActuatorsA 65 (1998) 10t-108
102
air gap. The experimental results show that the proper determination of applied voltage and air gap is necessary for high sensitivity and linearity of the proposed gyroscope. The conventionally machined electromagnetic gyroscope shows the feasibility of electromagnetic detection.
/ , .... inertial mass
-- -,,---,.
fixed frame ....
, inner gimbal
outer gimbal fixed frame
inner flexure
I h , , . ~ ~ ; ' ~ - -
2. Structure and principle
sensing coil sensing E-core-
The proposed electromagnetic gyroscope (Fig. 1) comprises a gyroscopic element with two gimbals, driving coils and sensing coils. The gyroscopic element is composed of inner and outer gimbals, flexures and an inertial mass with linear momentum located in the inner gimbal. The driving coils, which are under the outer gimbal, vibrate the gyroscopic elements using electromagnetic force. The vibration of the inner gimbal is detected by the measurement of the induced voltage of the sensing coils underneath it. In order to minimize the magnetic coupling between the driving and the sensing coils, magnetic materials that form separated magnetic paths are attached to the paramagnetic gyroscopic elements. By magnetic coupling we mean the flux linkage of the sensing coils flowing from the flux of the driving coils. To vibrate the outer gimbal, a square-wave signal is applied to the driving coils of both sides under the outer gimbal, 180 ° out of phase with each other. Each driving coil consists of three ferrite E-cores. When an angular rate is applied, normal to the plane of the device, the Coriolis force causes vibration of the inner gimbal at the same frequency as the outer gimbal, resulting in fluctuation of the air gap between the inner gimbal and the sensing E-core. The change of air gap induces different voltages at each sensing coil, where the voltage difference is proportional to the angular rate.
z
magnetic material r~
-.~.y
driving coil driving E-core
Fig. 1. The exploded structure of the planar vibrating electromagnetic gyroscope.
sensing axis
(a)
driving axis
Z
Z
X< x ~'~
~
y
y
Co)
Fig. 2. The coordinate systems: (a) the stationary coordinate system (OXYZ) ; (b) the rotating coordinate system (Oxyz).
3. Gyroscope equation Two coordinate systems are used to express the equation of relative motion of the inner and outer gimbals. The first coordinate system (OXYZ) is attached to and concentric with the stationary frame. The second coordinate system (Oxyz) is attached to the outer gimbal, and centred at the same point as the first. Thus, we assume that point O is fixed. Fig. 2 shows the relationship between the stationary coordinate system (OXYZ) and the rotating coordinate system (Oxyz), expressed as
-= 0 _0,
1 0
(t)
The differential equation of motion of the gyroscope relative to the origin O can be written in vector form as [ 16] =
+
x
where, ~Mo is the sum of moments relative to the origin O; /)o is the angular momentum relative to the rotating coordinate system (Oxyz): ~Io= [ IxOx IyOy IzOz] T
(I?Io) oxrz is the derivative of angular momentum with respect to the stationary coordinate system; (Ho) O~.zis the derivative of angular momentum with respect to the rotating coordinate system; 0x is the deflection angle of the inner gimbal; 0v is the deflection angle of the outer gimbat; and g2 is the angular velocity of the rotating coordinate system with respect to the stationary coordinate system:
1 ]L z j
Here it is assumed that the deflection angle of the outer gimbal (Oy) is small.
(2)
Also, the angular momentum relative to the origin O is
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S.-H. Lee et aL / Sensors and Actuators A 65 (1998) 101-108
(#o) o ~ = [I] [ #] o~=
O~ 0 0]i ° -oyo,1[1 0i.
=
z,o
0
o
I=
1
(3)
0y o
F Ox-O,o:)l
=/
/
inner gimbal and the sensing E-core. Figs. 3 and 4 show the equivalent circuit of the sensing part. In the system of Fig. 3, if the air gap is varied, then the flux linkage will also be varied and by Faraday's law an electromotive force will be induced in each sensing coil. This electromotive force will be dha
gsa= - - -dt
(10a)
where, Ix, Iy, I z are the moments of inertia of mass along each axis. Then
dab V~b= - - - dt
(lOb)
bX#o= ~ x//,,o.:./=/(z~-/~o~0.2/
where, h a, hb are the flux linkages of the sensing coils defined by
LZz(0A + 0~)j
(4)
kZ=0~J k(Z,,-IOo, oy] From Eqs. (3) and (4), the gyroscope equation is obtained as follows:
(5)
- K y O y - D y O y + Ty - K=Oz - DzOz
where, 0z=W~ is the angular rate (constant), 0z= dL.=0; K~ is the torsional spring constant along each axis (i = x,y,z); D~ is the damping factor along each axis ( i = x , y , z ) ; T~,e is the applied torque along the Y axis. The motion equation along the Y axis is IyOy + DyOy + KyOy= Ty +
( Iz- Ix) O~coz= Ty
(6)
and the motion equation along the X axis is IxO~+ DxOx+ KxOx= (I~+ I y - I ~ ) Oywz
(lla)
ha= --Lcia+Lbib
(llb)
where X~=N( 49~+ @2), ~b =N(
.. Zy4. .. |+ (Ix-L)0=0. / Lh(OxOy+O:&+Oz)J (I:-£)o~g,J -K&-nA =
Aa=Laia-Lcib
(/)3"1-(/)4)
L~ = N z L~=N 2
~c~1~2~3+~C~I~2~4@~¢~1~3~4+~C~2~3~4+~i~2~3~4
where La is the self inductance of the sensing part S~; Lb is the self inductance of the sensing part Sb; Lo is the mutual inductance between the sensing part S~ and the sensing part Sb; N; is the reluctance of the equivalent magnetic circuit (i= 1,2,3,4,c); and N is the number of turns of the sensing coil.
(7)
From the above equations, the deflection angle of the inner gimbal becomes
~1~
~2!
~cI
~3~
~4I
s(Zx+z~-~)o,, Ox----g(XZ + 2~conS_t_co2)co z
(8)
To obtain the maximum sensitivity, the driving frequency of the outer gimbal was adjusted to the resonance frequency of the inner gimbal. Setting the transform variable s equal to jw and assuming the vibratory frequency is equal to the resonance frequency of the inner gimbal, the sensitivity is expressed as Ox=(Ix-k-Iy-Iz) OyO
coz
Nia@
Nib,~,
Fig. 3. The equivalentmagnenccircuitof the sensingpart. inertial mass i
""&
"" I
(9)
/xCOn
innergimbal
. ~ l ~ m a g n e t i c material
where the Q-factor is Q-- 1/2~. sensingc ° i l ( ~
~
~"sensing
4. Magnetic system equation As described above, the angular rate normal to the plane ~{ the de'dee leacis to fmctuation of the air gap between the
v~ v~: Fig. 4. The electriccircuitof the ~engingpart.
c°il(Sb)
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S.-H. Lee et aL / Sensors and Actuators A 65 (1998) 101-108
It is assumed that the permeability of the magnetic material is infinite and the leakage flux is negligible. Thus, the magnetic system equation is dL~
L dia
Ri~+--~-ti~+
dLc. dib dt lb--L¢-~-t = Vd.o.
~-~t
dLc
dia dLb.
(12a)
dib
Rib -- --~-ti~-- Lo-~t + --~-ttb + Lb-~- = Va.c.
(12b)
When the inertial mass vibrates along the inner flexure, the air gap between the inner gimbal and the sensing coils changes. This change of air gap causes the inductance to vary. From Eqs. (12), induced voltages in the sensing coils are detected by the change of the current flowing through the sensing coil: V.~a=Vd.c.-Ri.~
(13a)
V~b = Vd.c.-Riu
(13b)
The induced voltages V~a, Vsbhave a sinusoidal waveform with d.c. offset. Each voltage has the same amplitude but they are 180° out of phase. The vibration of the inner gimbal is measured from the difference in voltage (V~,-V~b). Fig. 5 shows the simulation of the output voltage produced by changing the deflection angle of the inner gimbal; as the air gap varied from 1.4 to 2.2 mm, the deflection angle of the inner gimbal is changed from 1 to 3 °. As in Fig. 4, the applied d.c. voltage (Vd.o.) is 5 V, the resistance (R) is 300 f~ and the gain is 80.6. As shown in Fig. 5, the output voltage increases as the deflection angle of the inner gimbal increases and the air gap is reduced. Thus, the output voltage can be expressed as a function of the air gap and a deflection of the inner gimbal: 1
Vout(3(- -
z-Az
=
where z is the air gap and Az is the deflection of the inner gimbal. More specifically, the output voltage is proportional to the deflection of the inner gimbal (Az) and inversely proportional to the square of the air gap (z) when the ratio of the deflection of the inner gimbal and air gap is very small. To obtain a high output voltage, we therefore need a high deflection angle of the inner gimbal and a small air gap. However, as the deflection angle of the inner gimbal increases or the air gap is reduced, the linearity decreases becausethe assumption that the ratio of the deflection of the inner gimbal and the air gap is very small is not valid. To obtain both high output voltage and good linearity involves a compromise; determination of the appropriate values of deflection angle and air gap is necessary. 5. Simulation a n d e x p e r i m e n t a l r e s u l t s o f r e s o n a n c e frequency The gyroscopic element is designed to give a match between the resonance frequencies of the outer and the inner gimbals. The proposed geometry of the gyroscope element is given in Table 1. Resonance frequencies are calculated by analytical methods. Fig. 6 shows the mode shape of the gyro-
(a)
1
z+Az
1--7
j
-7
y~
cZ~(-~), if A---~Z< az
(14) (b)
1.6
1.4 ~' 1.2 o.8 0,6 =5
01=1 ,
0.4 0.2
1.4
1,6
1.8
2
2.2
air gap [mm] Fig. 5. Simulationresults of output voltagevs. air gap of the sensingparts.
Fig. 6. Modeshapes simulatedby ABAQUS: (a) outergimbaI (37.1 Hz); (b) innergimbal (37.7 Hz).
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S.-H. Lee et al. / Sensors and Actuators A 65 (1998) 101-108
TabIe 1 The dimensions of the gyroscope Element
Size
Gyroscopic element Inertial mass Outer flexure Inner flexure
74 mm x 50 mm × 0.5 mm 15 r a m × 5 r a m × 3 4 mm 0.5 m m x 3 m m x 0.7 mm 0.5 mm x 4.5 mm × 0.7 mm
Table 2 Comparison of resonance frequencies and Q-values Q-value
Resonance frequency (Hz)
Inner gimbal Outer gimbal
Analytical method
ABAQUS
38.9 38.6
37.7 37.1
Experiment Fig. 7. The assembled planar vibrating gyroscope. 34.1 29.0
40 18
scope simulated by the FEM (finite-element method) package ABAQUS. The resonance frequencies are measured using a laser displacement meter (KEYENCE 2510, resolution 0.05 ~m, sampling frequency 400 kHz). The resonance frequencies of the outer and inner gimbals are given in Table 2. From Table 2, we see that there are differences between the results of the analytical methods and the experiment; the resonance frequencies seen in the experiment are lower than those predicted. This is due to a damping effect present in the experimental set-up, which is ignored in the analytical calculation because the resonance frequencies are obtained by detecting the frequency of the maximum displacement. This frequency is obtained as ~r = o J n ~
2~ 2
(Is)
where, wr is the amplitude resonance frequency, wn is the frequency of the freely running undamped oscillator and ~:is the damping ratio. Therefore, the amplitude resonance frequency differs by only a small amount from the resonance frequency given by analytical methods.
driving coils, 180° out of phase with each other. 5 V d.c. is applied to each sensing coil, and the sensing air gap is varied to measure its effect on output voltage.
6.1. The effect of resonance frequency and magnetic coupling The effect of driving frequency on the output characteristics was investigated experimentally. Fig. 8 shows the waveform of the output voltages obtained when the driving frequency is equal to the resonance frequency and when it is not. When the driving frequency is the same as the resonance frequency of the inner gimbal, a sinusoidal wavefonn is detected. In the other case, a sinusoidaI waveform is not detected. Also, as shown in Eq. (8) and Fig. 8, the maximum output voltage is obtained when the driving frequency is equal to the resonance frequency of the inner gimbal. Thus, to obtain a larger output voltage, the exciting frequency should be the same as the resonance frequency of the inner gimbal. In Fig. 8(a) and (b), not only a sinusoidal waveform but also a sharp decreasing waveform (A in Fig. 8) is detected [v] 0.4
0.2 ,/J'
\.
f
0
,/
-0.2
6. Experiments and discussion The electromagnetic gyroscope was fabricated using conventional mechanical machining technology. The driving and sensing parts consist of ferrite E-core and coils. Each driving part is composed of three driving coils, and the sensing parts are composed of two sensing coils. The driving coils and sensing coils have 500 and 1000 turns, respectively. Fig. 7 shows the assembled planar vibrating electromagnetic gyroscope. The driving coils and gyroscopic element are fixed, and the XYZ stage is used to move the sensing coils in three axes by increments of 10 txm. To vibrate the outer gimbai, a square-wave signal with d.c. offset is applied to the
-0.4
(a)
10
20
"\ 30
40
50 [msecl
4o
5o [msec]
[v] 0.4 A 0.2 0
t
b
-0.2
-O.4 (b)
10
2o
30
Fig. 8. Output voltages of the sensing parts influenced by the driving frequencies: (a) driving frequency is equal to resonance frequency; (b) driving
frequencyis not equal to resonancefrequency.
106
S.-H. Lee et at./Sensors and Actuators A 65 (1998) 101-108 z
in the output voltage [17]. This waveform is induced by magnetic coupling. In the ideal case on which the analytical calculations are based, no such waveform should be detected since the magnetic flux generated by the driving coils flows successively through the driving E-core, air gap, magnetic material, air gap and the other driving E-core (Fig. 9 ( a ) ) . But in actuality, there is also leakage of magnetic flux through the sensing E-core and air gap (Fig. 9 ( b ) ), and the magnetic coupling waveform detected in the sensing coils is caused l~y flux leakage from the driving E-core when angular rate is applied. The sharp decreasing waveform reflects that of the driving rectangular voltage with d.c. offset. Hence, the exact dependence of output voltages on the variation of the angular rate must be obtained through calibration of the magnetic coupling. In these experiments, the exact output voltages are obtained by subtracting from the output voltages the sharp decreasing waveform detected in 0 ° S- l .
T inertial mass
~
|
driving E-core
sensingE-core
(a)
yl.
,X
magneticmaterial
i 1
driving E-core
driving E-core
(b)
.2 ~
,,.~,..-<.j
6.2. A n g u l a r rate tests a n d discussion
sensing E-core Fig. 9. Magnetic flux path: (a) ideal case, no flux leakage; (b) reai case, flux leakage.
The dependence of the gyroscope output on angular rate was also measured. The measuring circuits were placed on a
1 0.8 0.6
air gap ...... : -*- 1.4mm
0.4 >~ 0.2 = 0
--,-1.6mm
-0.2
~ 2.0ram
-0.4 -0.6
-4-2,2mini
O
--,-1.8mm
-0.8
-51.6
-34.4
(a)
-17.2
0
17.2
34.4
51.6
angular rate [dog/see] 0.8 0.6
Vp.p ...........
0.4
--- 5V
0.2 >
~4V -0.2
-,,.-3V
-0.4 -0.6 -0.8 -51.6
(b)
-34.4
- 17.2
0
17.2
34.4
51.6
angular rate ldeg/sec]
Fig. 10. Output voltage vs. angular rate: (a) the air gap is varied from 1.4 to 2.2 mm when the applied voltage is fixed to 4 V; (b) the applied voltage is varied from 3 to 5 V when the air gap is fixed to 1.8 mm.
107
S.-H. Lee et al. / Sensors and Actuators A 65 (1998) 101-I08
30
Vlyp
25 -.-5V 20
-,-4V
> &
IS
-~
............ i r
~-Z I0 5
---,,-3V
0
1.2
1.4
1.6
1.8
2
2.2
2.4
air gap [mm] Fig. 11. Sensitivity vs. air gap of the sensing parts. rate table with slip rings for feeding the sensor output and electric power to the circuit. The gain of the amplifier circuit is 80.6. Measurements were performed over a range of angular rate from - 5 1 . 6 to + 5 1 . 6 ° s-~, the procedure being to accelerate from 0 to 51.6 ° s - 1, to 0 ° s - ~, to - 51.6 ° s - ~, and so on for a few cycles. The rate table was accelerated smoothly from speed to speed so as not to overshoot a reading [ 1]. Fig. 10 shows the output voltage measured with the variation of the exciting voltage and the sensing air gap. A squarewave signal with d.c. offset is applied to the driving coils. The applied peak-to-peak voltage (Vp_p) is 3, 4, 5 V, and the d.c. offset is 1.5, 2, 2.5 V, respectively. The air gap between the inner gimbal and the sensing coils is varied from 1.4 to 2.2 ram. The measured sensitivities vary from 4.2 to 26 mV (o s - 1) - ~depending on the exciting voltage and the sensing air gap. The sensitivities are improved with an increase of the exciting voltage of the driving coils; as the exciting voltage increased, the deflection angle of the outer gimbal increased because of the higher torque generated. As shown in Eq. (9), the sensitivity is proportional to the deflection angle of the outer gimbal. Also, the sensitivities are improved with the decrease of the air gap of the sensing parts. Because a small air gap increases the flux linkage of the sensing coils, the induced output voltage increased as the air gap of the sensing parts decreased. However, as mentioned in Section 4 and shown in Fig. 11, the linearity decreases if the exciting voltage is higher or the air gap is smaller. To determine the performance of the gyroscope, high sensitivity as well as good linearity are needed, requiring the choice of appropriate values for the exciting voltage and the air gap. From the above results, the electromagnetic gyroscope gives various output characteristics by changing the exciting voltage and the air gap of the sensing parts. Although the proposed gyroscope is not as small as other vibratory gyroscope based on micromachining technology, its sensitivity can be controlled easily by adjusting its sensing part. 7. Conclusions A planar vibratory gyroscope using electromagnetic force
was vo9osed, buitt and tested. This gyroscope is driven by
electromagnetic force and detection is performed by the inductive method. Maximum output voltage is obtained when the driving frequency equals to the resonance frequency of the inner gimbal. The measured sensitivities were varied from 4.2 to 26 mV (° s - i) - 1 by changing the exciting voltage and the air gap of the sensing parts. While the dynamic range of the proposed gyroscope is not very wide, a high sensitivity is obtained compared with electrostatic devices, which have sensitivities from several p~V (° s - I ) -1 to several mV (° s - ~) - 1 [ 6,7,9-11,14]. Also, the sensitivity can be controlled easily by changing the number of turns of the driving and sensing coils, the exciting voltage and the air gap of the sensing parts. In conclusion, the proposed planar vibratory gyroscope using electromagnetic force, which has advantages of simple fabrication and large output characteristics, can be applied practically.
Acknowledgements
This work has been supported in part by Electrical Engineering and Science Research Institute, grant no. 94-043, which is funded by Korea Electric Power Co.
References
[ 1] A. Lawrence,ModemInertial Technology:Navigation,Guidance, and Control, Springer-Verlag,New York, 1993, pp. 148-162. [ 2] P.H. Savet, Gyroscopes:Theoryand Design,McGraw-Hill,New York, 1961, pp. 204-211. [3] G.M. Siouris, Aerospace Avionics Systems, Academic Press, New York, 1993, pp. 83-133. [4] R.A. Buser and N.F. de Rooij, Tuning forks in silicon, IEEE Micro Electro MechanicalSystemsWorkshop,Salt Lake City, UT, USA,2022 Feb., 1989, pp. 94-95. [5] J. S6derkvist, Piezoelectric beams and vibrating angular rate sensors, IEEE Trans. Ultrasonics, Ferroelectr. Freq. Control, 38 (1991) 271280. [6] J. Bernstein, S. Cho, A.T. King, A. Kourepenis, P. Maciel and M. Weinberg, A micromachinedcomb-drivetuning fork rate gyroscope, MEMS Proc., Fort Lauderdale, FL, USA, 7-10 Feb., 1993, pp. I43148.
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[7] K. Tanaka, Y. Mochida, M. Sugimoto, K. Moriya, T. FIasegawa,K. Atsuchi and K. Ohwada, A micromachined vibrating gyroscope, Sensors and ActuatorsA, 50 (1995) 111-115. [ 8] M.W. Putty and K. Najafi, A micromachinedvibratingring gyroscope, Solid State Sensor and Actuator Workshop, Hilton Head Island. SC, USA. t3-16 June, 1994, pp. 213-220. [ 9] K. Maenaka and T. Shiozawa, A study of silicon angular rate sensors using anisotropic etching technology,Sensors and Actuators A, 4143 (1994) 72-77. [ 10] B. Boxenhornand P. Greiff, A vibratorymicromechanicalgyroscope, AIAA Guidance and Controls Conf., Minneapolis, MN, USA, 15-17 August, 1988,pp. 1033-1040. [ i 1] M. Hashimoto. C. Cabuz, K. Minami and M. Esashi. Silicon resonant angular rate sensor using electromagnetic excitation and capacitive detection, Tech. Digest, 12thSensorSyrup.,Japan, 1994,pp. 163-166. [ 12] F. Paoletti, M.A. Gretillat and N.F. de Rooij, A silicon micrornachined vibrating gyroscopewith piezoresistivedetection and electromagnetic excitation, MEMS Prec., San Diego,CA, USA, 11-15 Feb., 1996,pp. 162-167. [ 13] J. SOderkvist, Micromachinedgyroscopes,Sensors and ActuatorsA, 41-43 (1994) 65-71. [ 14] M. Yamashita, K. Minami and M, Esashi, A silicon micromachined resonant angular rate sensor using electrostatic excitation and capacitive detection, Tech. Digest, 14th Sensor Syrup., Japan, 1996, pp. 39--42. [ 15] J.S. Burdessand T. Wren,The theoryof a piezoelectricdiscgyroscope, IEEE Trans. AerospaceElectronic Syst., AEA-22 (1986) 410--4t8. [16] F.P. Beer and E.R. Johnston, Jr., Vector-Dynamics,McGraw-Hill, New York, 1992, pp. 448-453. [ 17] Seung-WanHong, A study on the planar vibratory gyroscopeusing the electromagnetic detection, Master's Thesis, Seoul National University, Korea, 1996.
Biographies Sang-Hun Lee received the B.S. and M.S. degrees in electrical engineering from Seoul National University, Korea, in 1991 and 1993, respectively. He is currently studying for his Ph.D. degree at the Laboratory for Micro Sensors and Actuators, School of Electrical Engineering, Seoul National University, Korea. His current research interests are modelling,
design, fabrication and testing of accelerometers and vibratory gyroscopes. Seung-Wan Hong received the B.S. and M.S. degrees in electrical engineering from Seoul National University, Korea, in 1994 and 1996, respectively. He is currently with Samsung Electronics, Co., Ltd. His research is on microelectromechanical systems and semiconductor devices. Yong-Kweon Kim received the B.S. and M.S. degrees in electrical engineering from Seoul National University, Korea, in 1983 and 1985, respectively, and the Dr.Eng. degree from the University of Tokyo in 1990. His doctoral dissertation was on modelling, design, fabrication and testing of micro linear actuators in magnetic levitation using high-criticaltemperature superconductors. In 1990, he joined the Central Research Laboratory of Hitachi Ltd. in Tokyo as a researcher and worked on actuators of hard disk drives. In 1992, he joined Seoul National University, where he is currently an associate professor in the School of Electrical Engineeringl His current research interests are modelling, design, fabrication and testing of electric machines, especially microelectro mechanical systems. Seung-Ki Lee graduated from the Department of Electrical Engineering, Seoul National University, in 1986. In 1988 and 1992, respectively, he received his M.S. and Ph.D. degrees from the Department of Electrical Engineering of Seoul National University. His Ph.D. work dealt with studies on InSb Hall devices and silicon magnetotransistors. From 1992 to 1993, he was at Tohoku University, Japan, as a guest researcher with a JSPS fellowship, where he conducted research on micro actuators. In 1994, he joined the Department of Electrical Engineering, Dankook University, where he is now an assistant professor. He is a member of the IEEE and the KIEE. His current research interest includes silicon magnetic sensors and micro actuators.
ELSEVIER
Sensors and Actuators A 65 (1998) 101-108
PHYSICAL
A planar vibratory gyroscope using electromagnetic force Sang-Hun Lee a,., Seung-Wan Hong b, Yong-Kweon Kim a, Seung-Ki Lee ° a School of Electrical Engineering, Seoul National Universi~, San 56-1, Shinrim-dong, Kwanak-ku, Seoul 151-742, South Korea b Samsung Electronics, San 24, Nongseo-Ri, Kiheung-Eup, gongin-City, Kyungki-Do 449-900, South Korea Department of Electrical Engineering, Dankook University, Han Nam-dong, Yongsan-ku, Seoul 140-714, South Korea Received 3 February 1997; revised 25 July I997; accepted 22 August 1997
Abstract
A planar vibratory gyroscope using electromagnetic force is proposed and tested. Such a gyroscope has the advantages of simple fabrication and large output characteristics compared with an electrostatic gyroscope. The fabricated gyroscope comprises a gyroscopic element with two gimbals, driving and sensing coils. The driving coils, which are under the outer gimbaI, vibrate the gyroscopic element. Vibration of the inner gimbaI due to an applied angular rate is detected by sensing coils underneath it. Maximum output is obtained when the output gimbal is driven at a resonance frequency of the inner gimbal. Measured sensitivities are from 4.2 to 26 mV (° s - ~) - ~. Sensitivities are measured at several exciting voltages and several values of the air gap of the sensing parts. © i998 Elsevier Science S.A. Ke)words: Planar vibratory gyroscopes; Electromagnetic force; Resonance frequency; Sensitivity; Magnetic coupling
1. Introduction
The constant emergence of new automotive and consumer applications has led to an increased need for small and inexpensive gyroscopes. Conventional gyroscopes are widely used in military applications and are based on conservation of angular momentum of a spinning rotor. They are expensive, bulky, have a short working life and also have many components that require high precision in fabrication and assembly [ 1,2]. These disadvantages also apply to fibre-optic and laser gyroscopes [3], although their performance is excellent. Recently, there have been many studies on planar vibratory gyroscopes, which rely not on the conservation of angular momentum of a rotating structure but on the conservation of linear momentum of a vibrating structure. Most planar vibratory gyroscopes have been fabricated by a micromachining technology. Micromachined structures can withstand harsh environments for long periods of time, implying a lifetime not limited by the sensor element itself. They also have the additional advantages of small size, low price and low electric power consumption. A number of possible designs have been proposed, typical examples being based on a tuning fork [ 4 7], a vibrating shell [8], a vibrating beam [9] and a quasivibrating plate [10]. Electrostatic [4,10], electromagnetic * Corresponding author. Tel.: +822 888 50 17. Fax: +822 873 99 53.
[11,12], or piezoelectric [5,13] methods are used to drive the gyroscope, while capacitive [6,7,10,11,14], or piezoelectric [5,12,15 ] methods are used to sense the vibrations caused by the Coriolis force on the vibrating structure. The capacitive sensing method is well suited for micromachined batch fabrication, but it requires a high-resolution electric circuit to detect a capacitive change in the attofarad range [ 10]. Piezoelectric sensing methods are more accurate but have highly temperature-dependent output characteristics except for crystalline piezoelectric materials such as quartz. On the other hand, electromagnetic detection methods can obtain relatively large output voltage compared with the other methods. While several researchers have fabricated micromagnetic circuits by micromachining technology, it is not so easy to make a fully micromachined magnetic circuit. In order to demonstrate the feasibility of electromagnetic detection in a vibrating gyroscope, for this paper we use a gyroscope manufactured by conventional machining technology, with a gyroscopic element measuring 74 mm × 50 ram. We propose here a method to obtain high output characteristics for a planar vibratory gyroscope using electromagnetic force. The gyroscope equations are derived, and the gyroscope is designed so that the vibration of the outer gimbal coincides with the resonance frequency of the inner one. The magnetic system equations are also derived, and imply that the sensitivity of the proposed electromagnetic gyroscope can
be controlledeasily by changingthe exciting voltageand the 0924-4247/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved P//S0924-4247(97)01670-1
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$.-H. Lee et at./Sensors and ActuatorsA 65 (1998) 10t-108
102
air gap. The experimental results show that the proper determination of applied voltage and air gap is necessary for high sensitivity and linearity of the proposed gyroscope. The conventionally machined electromagnetic gyroscope shows the feasibility of electromagnetic detection.
/ , .... inertial mass
-- -,,---,.
fixed frame ....
, inner gimbal
outer gimbal fixed frame
inner flexure
I h , , . ~ ~ ; ' ~ - -
2. Structure and principle
sensing coil sensing E-core-
The proposed electromagnetic gyroscope (Fig. 1) comprises a gyroscopic element with two gimbals, driving coils and sensing coils. The gyroscopic element is composed of inner and outer gimbals, flexures and an inertial mass with linear momentum located in the inner gimbal. The driving coils, which are under the outer gimbal, vibrate the gyroscopic elements using electromagnetic force. The vibration of the inner gimbal is detected by the measurement of the induced voltage of the sensing coils underneath it. In order to minimize the magnetic coupling between the driving and the sensing coils, magnetic materials that form separated magnetic paths are attached to the paramagnetic gyroscopic elements. By magnetic coupling we mean the flux linkage of the sensing coils flowing from the flux of the driving coils. To vibrate the outer gimbal, a square-wave signal is applied to the driving coils of both sides under the outer gimbal, 180 ° out of phase with each other. Each driving coil consists of three ferrite E-cores. When an angular rate is applied, normal to the plane of the device, the Coriolis force causes vibration of the inner gimbal at the same frequency as the outer gimbal, resulting in fluctuation of the air gap between the inner gimbal and the sensing E-core. The change of air gap induces different voltages at each sensing coil, where the voltage difference is proportional to the angular rate.
z
magnetic material r~
-.~.y
driving coil driving E-core
Fig. 1. The exploded structure of the planar vibrating electromagnetic gyroscope.
sensing axis
(a)
driving axis
Z
Z
X< x ~'~
~
y
y
Co)
Fig. 2. The coordinate systems: (a) the stationary coordinate system (OXYZ) ; (b) the rotating coordinate system (Oxyz).
3. Gyroscope equation Two coordinate systems are used to express the equation of relative motion of the inner and outer gimbals. The first coordinate system (OXYZ) is attached to and concentric with the stationary frame. The second coordinate system (Oxyz) is attached to the outer gimbal, and centred at the same point as the first. Thus, we assume that point O is fixed. Fig. 2 shows the relationship between the stationary coordinate system (OXYZ) and the rotating coordinate system (Oxyz), expressed as
-= 0 _0,
1 0
(t)
The differential equation of motion of the gyroscope relative to the origin O can be written in vector form as [ 16] =
+
x
where, ~Mo is the sum of moments relative to the origin O; /)o is the angular momentum relative to the rotating coordinate system (Oxyz): ~Io= [ IxOx IyOy IzOz] T
(I?Io) oxrz is the derivative of angular momentum with respect to the stationary coordinate system; (Ho) O~.zis the derivative of angular momentum with respect to the rotating coordinate system; 0x is the deflection angle of the inner gimbal; 0v is the deflection angle of the outer gimbat; and g2 is the angular velocity of the rotating coordinate system with respect to the stationary coordinate system:
1 ]L z j
Here it is assumed that the deflection angle of the outer gimbal (Oy) is small.
(2)
Also, the angular momentum relative to the origin O is
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S.-H. Lee et aL / Sensors and Actuators A 65 (1998) 101-108
(#o) o ~ = [I] [ #] o~=
O~ 0 0]i ° -oyo,1[1 0i.
=
z,o
0
o
I=
1
(3)
0y o
F Ox-O,o:)l
=/
/
inner gimbal and the sensing E-core. Figs. 3 and 4 show the equivalent circuit of the sensing part. In the system of Fig. 3, if the air gap is varied, then the flux linkage will also be varied and by Faraday's law an electromotive force will be induced in each sensing coil. This electromotive force will be dha
gsa= - - -dt
(10a)
where, Ix, Iy, I z are the moments of inertia of mass along each axis. Then
dab V~b= - - - dt
(lOb)
bX#o= ~ x//,,o.:./=/(z~-/~o~0.2/
where, h a, hb are the flux linkages of the sensing coils defined by
LZz(0A + 0~)j
(4)
kZ=0~J k(Z,,-IOo, oy] From Eqs. (3) and (4), the gyroscope equation is obtained as follows:
(5)
- K y O y - D y O y + Ty - K=Oz - DzOz
where, 0z=W~ is the angular rate (constant), 0z= dL.=0; K~ is the torsional spring constant along each axis (i = x,y,z); D~ is the damping factor along each axis ( i = x , y , z ) ; T~,e is the applied torque along the Y axis. The motion equation along the Y axis is IyOy + DyOy + KyOy= Ty +
( Iz- Ix) O~coz= Ty
(6)
and the motion equation along the X axis is IxO~+ DxOx+ KxOx= (I~+ I y - I ~ ) Oywz
(lla)
ha= --Lcia+Lbib
(llb)
where X~=N( 49~+ @2), ~b =N(
.. Zy4. .. |+ (Ix-L)0=0. / Lh(OxOy+O:&+Oz)J (I:-£)o~g,J -K&-nA =
Aa=Laia-Lcib
(/)3"1-(/)4)
L~ = N z L~=N 2
~c~1~2~3+~C~I~2~4@~¢~1~3~4+~C~2~3~4+~i~2~3~4
where La is the self inductance of the sensing part S~; Lb is the self inductance of the sensing part Sb; Lo is the mutual inductance between the sensing part S~ and the sensing part Sb; N; is the reluctance of the equivalent magnetic circuit (i= 1,2,3,4,c); and N is the number of turns of the sensing coil.
(7)
From the above equations, the deflection angle of the inner gimbal becomes
~1~
~2!
~cI
~3~
~4I
s(Zx+z~-~)o,, Ox----g(XZ + 2~conS_t_co2)co z
(8)
To obtain the maximum sensitivity, the driving frequency of the outer gimbal was adjusted to the resonance frequency of the inner gimbal. Setting the transform variable s equal to jw and assuming the vibratory frequency is equal to the resonance frequency of the inner gimbal, the sensitivity is expressed as Ox=(Ix-k-Iy-Iz) OyO
coz
Nia@
Nib,~,
Fig. 3. The equivalentmagnenccircuitof the sensingpart. inertial mass i
""&
"" I
(9)
/xCOn
innergimbal
. ~ l ~ m a g n e t i c material
where the Q-factor is Q-- 1/2~. sensingc ° i l ( ~
~
~"sensing
4. Magnetic system equation As described above, the angular rate normal to the plane ~{ the de'dee leacis to fmctuation of the air gap between the
v~ v~: Fig. 4. The electriccircuitof the ~engingpart.
c°il(Sb)
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S.-H. Lee et aL / Sensors and Actuators A 65 (1998) 101-108
It is assumed that the permeability of the magnetic material is infinite and the leakage flux is negligible. Thus, the magnetic system equation is dL~
L dia
Ri~+--~-ti~+
dLc. dib dt lb--L¢-~-t = Vd.o.
~-~t
dLc
dia dLb.
(12a)
dib
Rib -- --~-ti~-- Lo-~t + --~-ttb + Lb-~- = Va.c.
(12b)
When the inertial mass vibrates along the inner flexure, the air gap between the inner gimbal and the sensing coils changes. This change of air gap causes the inductance to vary. From Eqs. (12), induced voltages in the sensing coils are detected by the change of the current flowing through the sensing coil: V.~a=Vd.c.-Ri.~
(13a)
V~b = Vd.c.-Riu
(13b)
The induced voltages V~a, Vsbhave a sinusoidal waveform with d.c. offset. Each voltage has the same amplitude but they are 180° out of phase. The vibration of the inner gimbal is measured from the difference in voltage (V~,-V~b). Fig. 5 shows the simulation of the output voltage produced by changing the deflection angle of the inner gimbal; as the air gap varied from 1.4 to 2.2 mm, the deflection angle of the inner gimbal is changed from 1 to 3 °. As in Fig. 4, the applied d.c. voltage (Vd.o.) is 5 V, the resistance (R) is 300 f~ and the gain is 80.6. As shown in Fig. 5, the output voltage increases as the deflection angle of the inner gimbal increases and the air gap is reduced. Thus, the output voltage can be expressed as a function of the air gap and a deflection of the inner gimbal: 1
Vout(3(- -
z-Az
=
where z is the air gap and Az is the deflection of the inner gimbal. More specifically, the output voltage is proportional to the deflection of the inner gimbal (Az) and inversely proportional to the square of the air gap (z) when the ratio of the deflection of the inner gimbal and air gap is very small. To obtain a high output voltage, we therefore need a high deflection angle of the inner gimbal and a small air gap. However, as the deflection angle of the inner gimbal increases or the air gap is reduced, the linearity decreases becausethe assumption that the ratio of the deflection of the inner gimbal and the air gap is very small is not valid. To obtain both high output voltage and good linearity involves a compromise; determination of the appropriate values of deflection angle and air gap is necessary. 5. Simulation a n d e x p e r i m e n t a l r e s u l t s o f r e s o n a n c e frequency The gyroscopic element is designed to give a match between the resonance frequencies of the outer and the inner gimbals. The proposed geometry of the gyroscope element is given in Table 1. Resonance frequencies are calculated by analytical methods. Fig. 6 shows the mode shape of the gyro-
(a)
1
z+Az
1--7
j
-7
y~
cZ~(-~), if A---~Z< az
(14) (b)
1.6
1.4 ~' 1.2 o.8 0,6 =5
01=1 ,
0.4 0.2
1.4
1,6
1.8
2
2.2
air gap [mm] Fig. 5. Simulationresults of output voltagevs. air gap of the sensingparts.
Fig. 6. Modeshapes simulatedby ABAQUS: (a) outergimbaI (37.1 Hz); (b) innergimbal (37.7 Hz).
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S.-H. Lee et al. / Sensors and Actuators A 65 (1998) 101-108
TabIe 1 The dimensions of the gyroscope Element
Size
Gyroscopic element Inertial mass Outer flexure Inner flexure
74 mm x 50 mm × 0.5 mm 15 r a m × 5 r a m × 3 4 mm 0.5 m m x 3 m m x 0.7 mm 0.5 mm x 4.5 mm × 0.7 mm
Table 2 Comparison of resonance frequencies and Q-values Q-value
Resonance frequency (Hz)
Inner gimbal Outer gimbal
Analytical method
ABAQUS
38.9 38.6
37.7 37.1
Experiment Fig. 7. The assembled planar vibrating gyroscope. 34.1 29.0
40 18
scope simulated by the FEM (finite-element method) package ABAQUS. The resonance frequencies are measured using a laser displacement meter (KEYENCE 2510, resolution 0.05 ~m, sampling frequency 400 kHz). The resonance frequencies of the outer and inner gimbals are given in Table 2. From Table 2, we see that there are differences between the results of the analytical methods and the experiment; the resonance frequencies seen in the experiment are lower than those predicted. This is due to a damping effect present in the experimental set-up, which is ignored in the analytical calculation because the resonance frequencies are obtained by detecting the frequency of the maximum displacement. This frequency is obtained as ~r = o J n ~
2~ 2
(Is)
where, wr is the amplitude resonance frequency, wn is the frequency of the freely running undamped oscillator and ~:is the damping ratio. Therefore, the amplitude resonance frequency differs by only a small amount from the resonance frequency given by analytical methods.
driving coils, 180° out of phase with each other. 5 V d.c. is applied to each sensing coil, and the sensing air gap is varied to measure its effect on output voltage.
6.1. The effect of resonance frequency and magnetic coupling The effect of driving frequency on the output characteristics was investigated experimentally. Fig. 8 shows the waveform of the output voltages obtained when the driving frequency is equal to the resonance frequency and when it is not. When the driving frequency is the same as the resonance frequency of the inner gimbal, a sinusoidal wavefonn is detected. In the other case, a sinusoidaI waveform is not detected. Also, as shown in Eq. (8) and Fig. 8, the maximum output voltage is obtained when the driving frequency is equal to the resonance frequency of the inner gimbal. Thus, to obtain a larger output voltage, the exciting frequency should be the same as the resonance frequency of the inner gimbal. In Fig. 8(a) and (b), not only a sinusoidal waveform but also a sharp decreasing waveform (A in Fig. 8) is detected [v] 0.4
0.2 ,/J'
\.
f
0
,/
-0.2
6. Experiments and discussion The electromagnetic gyroscope was fabricated using conventional mechanical machining technology. The driving and sensing parts consist of ferrite E-core and coils. Each driving part is composed of three driving coils, and the sensing parts are composed of two sensing coils. The driving coils and sensing coils have 500 and 1000 turns, respectively. Fig. 7 shows the assembled planar vibrating electromagnetic gyroscope. The driving coils and gyroscopic element are fixed, and the XYZ stage is used to move the sensing coils in three axes by increments of 10 txm. To vibrate the outer gimbai, a square-wave signal with d.c. offset is applied to the
-0.4
(a)
10
20
"\ 30
40
50 [msecl
4o
5o [msec]
[v] 0.4 A 0.2 0
t
b
-0.2
-O.4 (b)
10
2o
30
Fig. 8. Output voltages of the sensing parts influenced by the driving frequencies: (a) driving frequency is equal to resonance frequency; (b) driving
frequencyis not equal to resonancefrequency.
106
S.-H. Lee et at./Sensors and Actuators A 65 (1998) 101-108 z
in the output voltage [17]. This waveform is induced by magnetic coupling. In the ideal case on which the analytical calculations are based, no such waveform should be detected since the magnetic flux generated by the driving coils flows successively through the driving E-core, air gap, magnetic material, air gap and the other driving E-core (Fig. 9 ( a ) ) . But in actuality, there is also leakage of magnetic flux through the sensing E-core and air gap (Fig. 9 ( b ) ), and the magnetic coupling waveform detected in the sensing coils is caused l~y flux leakage from the driving E-core when angular rate is applied. The sharp decreasing waveform reflects that of the driving rectangular voltage with d.c. offset. Hence, the exact dependence of output voltages on the variation of the angular rate must be obtained through calibration of the magnetic coupling. In these experiments, the exact output voltages are obtained by subtracting from the output voltages the sharp decreasing waveform detected in 0 ° S- l .
T inertial mass
~
|
driving E-core
sensingE-core
(a)
yl.
,X
magneticmaterial
i 1
driving E-core
driving E-core
(b)
.2 ~
,,.~,..-<.j
6.2. A n g u l a r rate tests a n d discussion
sensing E-core Fig. 9. Magnetic flux path: (a) ideal case, no flux leakage; (b) reai case, flux leakage.
The dependence of the gyroscope output on angular rate was also measured. The measuring circuits were placed on a
1 0.8 0.6
air gap ...... : -*- 1.4mm
0.4 >~ 0.2 = 0
--,-1.6mm
-0.2
~ 2.0ram
-0.4 -0.6
-4-2,2mini
O
--,-1.8mm
-0.8
-51.6
-34.4
(a)
-17.2
0
17.2
34.4
51.6
angular rate [dog/see] 0.8 0.6
Vp.p ...........
0.4
--- 5V
0.2 >
~4V -0.2
-,,.-3V
-0.4 -0.6 -0.8 -51.6
(b)
-34.4
- 17.2
0
17.2
34.4
51.6
angular rate ldeg/sec]
Fig. 10. Output voltage vs. angular rate: (a) the air gap is varied from 1.4 to 2.2 mm when the applied voltage is fixed to 4 V; (b) the applied voltage is varied from 3 to 5 V when the air gap is fixed to 1.8 mm.
107
S.-H. Lee et al. / Sensors and Actuators A 65 (1998) 101-I08
30
Vlyp
25 -.-5V 20
-,-4V
> &
IS
-~
............ i r
~-Z I0 5
---,,-3V
0
1.2
1.4
1.6
1.8
2
2.2
2.4
air gap [mm] Fig. 11. Sensitivity vs. air gap of the sensing parts. rate table with slip rings for feeding the sensor output and electric power to the circuit. The gain of the amplifier circuit is 80.6. Measurements were performed over a range of angular rate from - 5 1 . 6 to + 5 1 . 6 ° s-~, the procedure being to accelerate from 0 to 51.6 ° s - 1, to 0 ° s - ~, to - 51.6 ° s - ~, and so on for a few cycles. The rate table was accelerated smoothly from speed to speed so as not to overshoot a reading [ 1]. Fig. 10 shows the output voltage measured with the variation of the exciting voltage and the sensing air gap. A squarewave signal with d.c. offset is applied to the driving coils. The applied peak-to-peak voltage (Vp_p) is 3, 4, 5 V, and the d.c. offset is 1.5, 2, 2.5 V, respectively. The air gap between the inner gimbal and the sensing coils is varied from 1.4 to 2.2 ram. The measured sensitivities vary from 4.2 to 26 mV (o s - 1) - ~depending on the exciting voltage and the sensing air gap. The sensitivities are improved with an increase of the exciting voltage of the driving coils; as the exciting voltage increased, the deflection angle of the outer gimbal increased because of the higher torque generated. As shown in Eq. (9), the sensitivity is proportional to the deflection angle of the outer gimbal. Also, the sensitivities are improved with the decrease of the air gap of the sensing parts. Because a small air gap increases the flux linkage of the sensing coils, the induced output voltage increased as the air gap of the sensing parts decreased. However, as mentioned in Section 4 and shown in Fig. 11, the linearity decreases if the exciting voltage is higher or the air gap is smaller. To determine the performance of the gyroscope, high sensitivity as well as good linearity are needed, requiring the choice of appropriate values for the exciting voltage and the air gap. From the above results, the electromagnetic gyroscope gives various output characteristics by changing the exciting voltage and the air gap of the sensing parts. Although the proposed gyroscope is not as small as other vibratory gyroscope based on micromachining technology, its sensitivity can be controlled easily by adjusting its sensing part. 7. Conclusions A planar vibratory gyroscope using electromagnetic force
was vo9osed, buitt and tested. This gyroscope is driven by
electromagnetic force and detection is performed by the inductive method. Maximum output voltage is obtained when the driving frequency equals to the resonance frequency of the inner gimbal. The measured sensitivities were varied from 4.2 to 26 mV (° s - i) - 1 by changing the exciting voltage and the air gap of the sensing parts. While the dynamic range of the proposed gyroscope is not very wide, a high sensitivity is obtained compared with electrostatic devices, which have sensitivities from several p~V (° s - I ) -1 to several mV (° s - ~) - 1 [ 6,7,9-11,14]. Also, the sensitivity can be controlled easily by changing the number of turns of the driving and sensing coils, the exciting voltage and the air gap of the sensing parts. In conclusion, the proposed planar vibratory gyroscope using electromagnetic force, which has advantages of simple fabrication and large output characteristics, can be applied practically.
Acknowledgements
This work has been supported in part by Electrical Engineering and Science Research Institute, grant no. 94-043, which is funded by Korea Electric Power Co.
References
[ 1] A. Lawrence,ModemInertial Technology:Navigation,Guidance, and Control, Springer-Verlag,New York, 1993, pp. 148-162. [ 2] P.H. Savet, Gyroscopes:Theoryand Design,McGraw-Hill,New York, 1961, pp. 204-211. [3] G.M. Siouris, Aerospace Avionics Systems, Academic Press, New York, 1993, pp. 83-133. [4] R.A. Buser and N.F. de Rooij, Tuning forks in silicon, IEEE Micro Electro MechanicalSystemsWorkshop,Salt Lake City, UT, USA,2022 Feb., 1989, pp. 94-95. [5] J. S6derkvist, Piezoelectric beams and vibrating angular rate sensors, IEEE Trans. Ultrasonics, Ferroelectr. Freq. Control, 38 (1991) 271280. [6] J. Bernstein, S. Cho, A.T. King, A. Kourepenis, P. Maciel and M. Weinberg, A micromachinedcomb-drivetuning fork rate gyroscope, MEMS Proc., Fort Lauderdale, FL, USA, 7-10 Feb., 1993, pp. I43148.
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[7] K. Tanaka, Y. Mochida, M. Sugimoto, K. Moriya, T. FIasegawa,K. Atsuchi and K. Ohwada, A micromachined vibrating gyroscope, Sensors and ActuatorsA, 50 (1995) 111-115. [ 8] M.W. Putty and K. Najafi, A micromachinedvibratingring gyroscope, Solid State Sensor and Actuator Workshop, Hilton Head Island. SC, USA. t3-16 June, 1994, pp. 213-220. [ 9] K. Maenaka and T. Shiozawa, A study of silicon angular rate sensors using anisotropic etching technology,Sensors and Actuators A, 4143 (1994) 72-77. [ 10] B. Boxenhornand P. Greiff, A vibratorymicromechanicalgyroscope, AIAA Guidance and Controls Conf., Minneapolis, MN, USA, 15-17 August, 1988,pp. 1033-1040. [ i 1] M. Hashimoto. C. Cabuz, K. Minami and M. Esashi. Silicon resonant angular rate sensor using electromagnetic excitation and capacitive detection, Tech. Digest, 12thSensorSyrup.,Japan, 1994,pp. 163-166. [ 12] F. Paoletti, M.A. Gretillat and N.F. de Rooij, A silicon micrornachined vibrating gyroscopewith piezoresistivedetection and electromagnetic excitation, MEMS Prec., San Diego,CA, USA, 11-15 Feb., 1996,pp. 162-167. [ 13] J. SOderkvist, Micromachinedgyroscopes,Sensors and ActuatorsA, 41-43 (1994) 65-71. [ 14] M. Yamashita, K. Minami and M, Esashi, A silicon micromachined resonant angular rate sensor using electrostatic excitation and capacitive detection, Tech. Digest, 14th Sensor Syrup., Japan, 1996, pp. 39--42. [ 15] J.S. Burdessand T. Wren,The theoryof a piezoelectricdiscgyroscope, IEEE Trans. AerospaceElectronic Syst., AEA-22 (1986) 410--4t8. [16] F.P. Beer and E.R. Johnston, Jr., Vector-Dynamics,McGraw-Hill, New York, 1992, pp. 448-453. [ 17] Seung-WanHong, A study on the planar vibratory gyroscopeusing the electromagnetic detection, Master's Thesis, Seoul National University, Korea, 1996.
Biographies Sang-Hun Lee received the B.S. and M.S. degrees in electrical engineering from Seoul National University, Korea, in 1991 and 1993, respectively. He is currently studying for his Ph.D. degree at the Laboratory for Micro Sensors and Actuators, School of Electrical Engineering, Seoul National University, Korea. His current research interests are modelling,
design, fabrication and testing of accelerometers and vibratory gyroscopes. Seung-Wan Hong received the B.S. and M.S. degrees in electrical engineering from Seoul National University, Korea, in 1994 and 1996, respectively. He is currently with Samsung Electronics, Co., Ltd. His research is on microelectromechanical systems and semiconductor devices. Yong-Kweon Kim received the B.S. and M.S. degrees in electrical engineering from Seoul National University, Korea, in 1983 and 1985, respectively, and the Dr.Eng. degree from the University of Tokyo in 1990. His doctoral dissertation was on modelling, design, fabrication and testing of micro linear actuators in magnetic levitation using high-criticaltemperature superconductors. In 1990, he joined the Central Research Laboratory of Hitachi Ltd. in Tokyo as a researcher and worked on actuators of hard disk drives. In 1992, he joined Seoul National University, where he is currently an associate professor in the School of Electrical Engineeringl His current research interests are modelling, design, fabrication and testing of electric machines, especially microelectro mechanical systems. Seung-Ki Lee graduated from the Department of Electrical Engineering, Seoul National University, in 1986. In 1988 and 1992, respectively, he received his M.S. and Ph.D. degrees from the Department of Electrical Engineering of Seoul National University. His Ph.D. work dealt with studies on InSb Hall devices and silicon magnetotransistors. From 1992 to 1993, he was at Tohoku University, Japan, as a guest researcher with a JSPS fellowship, where he conducted research on micro actuators. In 1994, he joined the Department of Electrical Engineering, Dankook University, where he is now an assistant professor. He is a member of the IEEE and the KIEE. His current research interest includes silicon magnetic sensors and micro actuators.