I. INTRODUCTION

Advancements in microelectromechanical systems (MEMS) technology have made inexpensive vibrating structure MEMS gyroscopes widely available ^(1-3). Multiple-axis gyroscopes and accelerometers with six or nine full degrees of freedom (DOF) have been incorporated in devices to determine the locations and orientations of these devices. In a MEMS gyroscope, the actuator converts an electrical signal, either voltage or current, into a force that sustains the resonant modes. The amplitude readout of both resonant modes requires converting the position of the vibrating mass into a physical quantity which can be measured by an electronic circuit ⁽⁴⁾.

Generally, a MEMS gyroscope consists of a micro-resonator with two resonant modes, i.e., the primary mode and the secondary mode. The resonator can vibrate at its primary resonant mode with a constant frequency and amplitude under driving by electrostatic, electromagnetic, piezoelectric or other forces ^(1-3). A vibrating structure gyroscope uses a vibrating structure to determine the rate of rotation ^(5-7). Vibrating structure gyroscopes can be implemented with various resonating structures. Examples include cylindrical resonator gyroscopes ⁽⁸⁾, piezoelectric gyroscopes ⁽⁹⁾, tuning fork gyroscopes ⁽¹⁰⁾, wine-glass resonators ⁽¹¹⁾, and vibrating wheel gyroscopes ⁽¹²⁾. In vibratory gyroscopes, the excitation and detection of vibrations can be achieved electrostatically or piezoelectrically, or by other ways ^(13,14). In particular, piezoelectric gyroscopes have received much attention because of their rugged construction, good frequency response, and negligible phase shift.

Piezoelectric gyroscopes make use of two vibration modes, the primary mode and the secondary mode, of a piezoelectric body. The piezoelectric material moves in perpendicular directions in the two modes. The modes are hence coupled by the Coriolis force when the gyroscope is rotating ^(9,13,14).

The operation of a piezoelectric gyroscope involves a suspended proof mass moving in two-dimensional space inside a rigid frame which is attached to an object in motion and rotated along with the object ⁽⁹⁾. When the proof mass is actuated by an applied alternating electric voltage in a designated direction (called the ‘Drive’ axis, or the primary mode) and the object is rotating with an angular rate as observed from the frame, the Coriolis force would actuate the proof mass in a direction perpendicular to the driven direction (called the ‘Sense’ axis, or the secondary mode). The angular rate can then be detected from electrical signals (voltage or current) accompanying the secondary motion ^(9,13,14).

However, the expansion of the operating bandwidth in piezoelectric gyroscopes is limited by the time-sharing between the horizontal and vertical resonance modes. Okada et al. proposed a 3-axis gyroscope which can be continuously operated without time-sharing ^(15-18). They showed that the gyroscope must be driven sequentially by X1 ${\rightarrow}$ Y1 ${\rightarrow}$ X2 ${\rightarrow}$ Y2 ${\rightarrow}$ X1 ... in the orbital driving mode.

This paper aims to develop a multi-axial inertial sensor that operates at atmospheric pressure by fabricating a piezoelectric gyroscope sensor with orbital drive. Orbital drive is a frequency component that uses the gyroscopic precession to implement a rotational angular velocity sensor, so that the input rotational angular velocity and the force acting on the output are the same. In order to achieve orbital drive, we propose a method with a square wave signal having a phase difference of π / 2 by utilizing the gyroscope resonance characteristics. We experimentally verify the method.

II. STRUCTURE SCHEMATIC AND SIMULATION

Fig. 1. Structure of piezoelectric gyroscope

The gyroscope is designed to have a high Q-factor without vacuum packaging with a single proof mass under 3-axis acceleration and 3-axis angular rotation. The driving and sensing methods are based on the piezoelectric effect ⁽¹⁹⁾. Figure 1 shows the structure of the piezoelectric gyroscope, consisting of a lead zirconate titanate (PZT) film and metal electrodes for driving and sensing, and a suspended bulk silicon acting as a single proof mass ⁽¹⁹⁾. The proof mass is designed with a diameter of 350 ${\mathrm{\mu}}$m. The inner circle has a diameter of 300 ${\mathrm{\mu}}$m whereas the outermost circle has a diameter of 600 ${\mathrm{\mu}}$m. The driving and sensing electrodes are both 100 ${\mathrm{\mu}}$m with a 50 ${\mathrm{\mu}}$m gap. Figure 2 shows the simulation results of the gyroscope⁽¹⁹⁾. The piezoelectric material is deformed by a driving voltage. Therefore, the gyroscope can detect the rotation of the proof mass by converting the deformation to voltage. The rotation and z-translation of the proof mass are simulated for acceleration in the x(y)-direction (Fig. 2(a) left) and z-direction (Fig. 2(a) right), xz(yz) ⁽¹⁹⁾. The simulation results show an angular rate response of 1 deg/s in the x- and y-directions, and a measurement sensitivity of 17.2 ${\mathrm{\mu}}$V/(deg/s) as shown in Fig. 3 ⁽¹⁹⁾. Under a sensing electrode potential of 10.2 ${\mathrm{\mu}}$V and driving electrode potential of 7 ${\mathrm{\mu}}$V, the differential output is 17.2 ${\mathrm{\mu}}$V/(deg/s), and the displacement in the z-direction is 3.59 x 10$^{-4}$ nm. All the designed systems have been verified through simulations and experiments.

Fig. 2. Simulation of the gyroscope. (a) Acceleration in x(y)-direction (left) and acceleration in z-direction (right), (b) xz(yz)-rotation of the proof mass, and (c) z-translation of the proof mass

Fig. 3. Electrical potential simulation of the gyroscope

Fig. 4. Orbital driving mode. (a) Concept of the orbital driving mode and (b) voltage application method for orbital drive

1. Driving mode

The orbital motion is equivalent to the continuous movement of the center of mass in the gyroscope membrane spring on the same horizontal plane to the left ${\rightarrow}$ lower ${\rightarrow}$ right ${\rightarrow}$ upper ${\rightarrow}$ left positions with vertical deviation. In order to realize this motion, a voltage is sequentially applied to the piezoelectric driving electrodes (Fx and Fy). Figure 4 shows the concept of the orbital driving mode and the voltage application method. The gyroscope is fabricated on a silicon-on-insulator (SOI) wafer with a 10 ${\mathrm{\mu}}$m silicon layer and a 2 ${\mathrm{\mu}}$m sacrificial oxide layer. After patterning the Pt electrode via a photolithography and etching process, the PZT was deposited, and the final Pt electrode was formed.

Fig. 5. Voltage application for orbital drive. (a) Fabricated gyroscope and (b) differential driving signal

Fig. 6. Block diagram for orbital drive mode gyroscope

Figure 5 shows a fabricated gyroscope and the differential driving signals for the gyroscope⁽¹⁹⁾. Although it is more efficient to apply the sequential differential voltage in Figure 5 due to the arrangement of the electrodes in the gyroscope, the same effect can be obtained with a simple square wave since the driving of the gyroscope utilizes its resonance characteristics. This is equivalent to phase shifting the x-axis drive signal used in conventional horizontal drive type gyroscopes by π / 2 to simultaneously excite the y-axis drive section.

The y-axis is thus driven in phase with the x-axis oscillation displacement, and the driving unit can be constructed as shown in Fig. 6 and Fig. 7. The two horizontal resonance modes of the gyroscope operate in resonance because the natural frequency will almost be the same if the fabrication process is well-controlled. Since the phases of the oscillation displacements obtained differ by π / 2 from each other, the Lissajous waveform of x-y will take the shape of a circle.

Fig. 7. Orbital driven Simulink block diagram

However, a Matlab (MathWorks. Inc. USA) simulation shows that the Lissajous waveform of x-y is not exactly a circle even when the natural frequencies of the x and y modes are almost the same, as shown in Fig. 8. This is because one of the two resonance modes is slightly above the resonance point, and the other mode is below the resonance point. This problem is solved by controlling the phases so that the phase difference between the two oscillation displacement signals is maintained at π / 2, instead of synchronizing the y-axis drive signal generation to the displacement in the x-axis oscillation mode. Figure 9 shows that the Lissajous waveform changes from elliptical to circular after controlling the phase.

Fig. 8. Orbital drive simulation

The self-oscillating characteristics of the orbital drive have been experimentally confirmed to be similar to the simulation. However, except for some gyroscopes, the Lissajous waveforms of x-y show large deviations from circles in most cases. This deviation is attributed to the high frequency selectivity of the high Q secondary vibration system. In other words, for the orbital drive, the two horizontal natural frequencies must be close to each other, which can be achieved during the fabrication process,

but the actual production results often do not meet this requirement. Therefore, a higher level of process control is required for applications. Figure 10 shows the frequency response as a function of the horizontal resonance (x / y) modes. The two natural frequencies on the left differ slightly while the two frequencies on the right are almost identical.

Fig. 9. Orbital drive experiment

Fig. 10. Frequency response function in horizontal resonance (x / y) mode. (a) the difference of two resonant frequencies at a frequency greater than 150 Hz and (b) at approximately 11 Hz.

IV. CONCLUSIONS

Orbital drive is a frequency component that uses the gyroscopic precession to implement a rotational angular velocity sensor, so that the input rotational angular

velocity and the force acting on the output are the same. In order for the gyroscope to be driven in orbital mode, we have developed a driving method with a square wave signal having a phase difference of π / 2 by utilizing the resonance characteristics. We experimentally verified the driving method.