This paper reports a novel kind of solid-state microgyroscope, which is called piezoelectric micromachined modal gyroscope (PMMG). PMMG has large stiffness and robust resistance to shake and strike because there is no evident mass-spring component in its structure. This work focused on quantitative optimization of the gyroscope, which is still blank for such gyroscope. The modal analysis by the finite element method (FEM) was firstly conducted. A set of quantitative indicators were developed to optimize the operation mode. By FEM, the harmonic analysis was conducted to find the way to efficiently actuate the operational mode needed. The optimal configuration of driving electrodes was obtained. At last, the Coriolis analysis was conducted to show the relation between angular velocity and differential output voltage by the Coriolis force under working condition. The results obtained in this paper provide theoretical basis for realizing this novel kind of micromachined gyroscope.
Different from the micromachined vibratory gyroscope, which has the structure of suspending springs and proof masses, some kinds of solid-state gyroscopes have no part which moves as a whole. According to their working principle, these kinds of gyroscopes can be classified into two categories: one that has no vibration unit at all such as optical gyroscopes [
Piezoelectric gyroscopes make use of two vibration modes of a vibratory piezoelectric body in which material particles move in two perpendicular directions, respectively. When a piezoelectric gyroscope is excited into vibration in one of the two modes (the primary mode) by an applied alternating voltage and attached to a rotating body, Coriolis force will excite the other mode (the secondary mode) through which the rotation rate of the body can be detected. These piezoelectric gyroscopes include flexural vibrations in two perpendicular directions of beams and tuning forks [
In January of 2006, Japanese researchers Maenaka et al. proposed a novel piezoelectric solid-state microgyroscope [
In this paper, quantitative indicators were introduced to evaluate the modes and thus determine the best operational mode. Besides, the same indicators were used to determine the size and configuration of the driving electrodes with which the operational mode can be efficiently actuated. At last, the Coriolis analysis was conducted to show the relation between angular velocity and differential output voltage by the Coriolis force under working condition.
The basic operation principle of the device we applied is shown in Figure
Operation principle of the gyroscope.
The detail structure of the piezoelectric solid-state microgyroscope is introduced as shown in Figure
Detail structure of the piezoelectric solid-state microgyroscope.
Piezoelectric material is commonly used for electromechanical transducers, and the requirements for the performance of piezoelectric ceramic vary for different regions of applications. As for the solid-state microgyroscope we used, the piezoelectric material serves as the excitation source and sensing element simultaneously, so the piezoelectric material should have larger piezoelectric constant
In this section, the finite element analysis of the piezoelectric body of the PMMG was first conducted to find the operation mode, and then quantitative indicators were introduced to evaluate these modes and at last the best operation mode and the corresponding size of the device was given.
From the operation principle of the PMMG, it can be concluded that the working resonance mode should have the following characteristics.
Particular mode shapes meeting our needs.
Size* (mm) | Mode shape ( | Size* (mm) | Mode shape ( | Size* (mm) | Mode shape ( |
---|---|---|---|---|---|
(*The first number of the size refers to the size in the polarization direction).
As can be seen from Table
Before we introduce these quantitative indicators, it is necessary to clarify that the device was meshed before simulation was conducted; therefore, it is reasonable to think the device was composed of many small units and nodes.
The quantitative indicators are shown as follows:
To calculate
Through derivation, we can calculate velocity of element
Using Kinetic Energy Theory, we got the kinetic energy of element
In the same way, we got
Using (
Table
Calculating results of quantitative indicators.
Size* | F(Hz) | |||||
---|---|---|---|---|---|---|
388045 | 0.1940 | 0.3021 | ||||
348154 | 0.1546 | 0.2527 | ||||
372396 | 0.0884 | 0.1326 | ||||
428269 | 0.3043 | 0.6798 | ||||
370765 | 0.8983 | 0.7870 | ||||
427822 | 0.7185 | 1.9623 | ||||
389186 | 0.6045 | 1.0323 |
(*The first number of the size refers to the size in the polarization direction).
In order to get the best performance, we hope the value of
In real applications, we need to apply a driving voltage to actuate the device. To make sure the mode shape we activate is the same as the one we get in modal analysis, we used ANSYS to perform harmonic analysis. The configuration of the driving electrodes is shown in Figure
The configuration of the driving electrodes.
Harmonic excitation analysis result of the PMMG.
Then, we need to optimize the size and configuration of the driving electrode to actuate the device more efficiently. Similar to modal analysis, we used
The original configuration and optimizing variables of the driving electrodes.
We changed one variable at a time and keet the other two variables unchanged; Table
Relation between the quantitative indicators and the optimizing variables.
Variable | Value (mm) | |||||
---|---|---|---|---|---|---|
0.5 | 0.5602 | 0.2789 | ||||
1 | 0.6017 | 0.3016 | ||||
0.6815 | 0.3341 | |||||
0.45 | 0.6125 | 0.2966 | ||||
0.75 | 0.5602 | 0.2789 | ||||
1.05 | 0.6030 | 0.3027 | ||||
0.6837 | 0.3384 | |||||
0.5 | 0.5804 | 0.2861 | ||||
1 | 0.5602 | 0.2789 | ||||
1.5 | 0.5800 | 0.2890 | ||||
0.6334 | 0.3129 |
From Table
The new configuration and optimizing variables of the driving electrodes.
We changed one variable at a time and keep the other two variables unchanged; Table
Relation between the quantitative indicators and the optimizing variables.
Variable | Value | |||||
---|---|---|---|---|---|---|
0.5 | 0.7126 | 0.3366 | ||||
1 | 0.7174 | 0.3282 | ||||
1.5 | 0.7215 | 0.3163 | ||||
2 | 0.7204 | 0.3028 | ||||
0.4 | 0.7205 | 0.3272 | ||||
1 | 0.7218 | 0.3232 | ||||
1.6 | 0.7215 | 0.3163 | ||||
2 | 0.7212 | 0.3130 | ||||
0.5 | ||||||
1 | ||||||
1.5 | ||||||
2 |
It can be concluded from Table
As mentioned before, when the angular velocity along
With excitation at operation mode, we changed the angular velocity applied to the device, and surface potential at the detecting electrodes was calculated by ANSYS taking account of the Coriolis force. Because the raw result of the output voltage for the applied angular velocity is differential with respect to
The configuration of the driving electrodes at Coriolis analysis.
Relation between
As we can see from Figure
The structure of the PMMG has larger stiffness, so it is resistant to shake and strike. In this paper, modal analysis was firstly conducted to determine the best operation mode for PMMG, and we developed a set of quantitative indicators to evaluate various operation modes. It can be concluded from that the device with the size
The work in this paper provides a theoretical basis for realizing this novel kind of micromachined gyroscope.
The main purpose of this paper is to provide a method to optimize the size of the device as well as the way to efficiently actuate the operation mode we needed. At present, it is almost impossible for us to simulate the device with any size because it is too time-consuming. Our subsequent research will further improve the optimizing results and put more focus on the theoretical derivation of the optimizing process.
Financial supports from the National Natural Science Foundation of China (50805096/E051202) and Defense Key Laboratory Foundation (2009–2011) are gratefully acknowledged.