MEMS Vibrating Ring Gyroscope with Worm-Shaped Support Springs for Space Applications ^†

Abstract

Microelectromechanical system (MEMS) devices have gained tremendous attention in the field of smart electronics applications. A MEMS vibrating gyroscope is a rotational inertial sensor that is exhaustively used in many applications, from GPS, household, smart appliances, and space applications. The reliability of MEMS devices for space applications is a big concern. The devices need to be robust in harsh environments. This paper reports a double-ring MEMS vibrating ring gyroscope with sixteen worm-shaped support springs. The inclusion of the two rings with sixteen worm-shaped springs enhances the sensitivity of the gyroscope. The design symmetry and the worm-shaped springs increase the robustness, mode matching, and gyroscopic sensitivity against harsh environments. The design modeling of the gyroscope is investigated using the ANSYSTM software. The design of the vibrating ring gyroscope incorporates two 10 µm thick rings with an outer ring radius of 1000 µm and an inner ring radius of 750 µm. Both rings are attached with sixteen worm-shaped springs, and a centrally placed anchor supports the whole structure with a radius of 260 µm. The proposed gyroscope operates in two identical wine glass modes. The first targeted resonant mode was recorded at 29.07 kHz, and the second mode of the same shape was recorded at 29.35 kHz. There is a low-mode mismatch of 0.38 kHz observed between the two resonant frequencies, which can be resolved with tuning electrodes. The initial modeling results show a good prospect for the design of a vibrating gyroscope for space applications.

1. Introduction

The usage of smart devices in human life has risen enormously throughout the last decade. These smart devices need advanced and efficient sensors for working operations [1]. A gyroscope is one of those inertial sensors that is being used for sensing and controlling the rotational motion of these devices [2,3], and it is being extensively used in smartphones, digital cameras, military, biomedical, household, space applications, and so on. The timeline history of the MEMS vibrating gyroscopes is presented [4].

Microelectromechanical systems (MEMS) with vibrating gyroscopes [5,6] are widely used inertial sensors. The MEMS vibrating ring gyroscope’s usage is increased because of its best mode matching, symmetrical design features, higher sensitivity, and robust design for space applications [7,8]. There are various MEMS vibrating ring gyroscopes discussed by Jia et al. [9]. Cao et al. developed a double U-beam-shaped vibratory ring gyroscope with twenty-four control and tuning electrodes [10].

We present a double-ring MEMS vibrating gyroscope comprising sixteen worm-shaped springs with higher sensitivity for space applications. The paper discusses the modeling results obtained using ANSYS software. The modal and harmonic analysis have been discussed, as well as the effectiveness of the worm-shaped support springs. The worm-shaped support springs provide robust characteristics for the gyroscope design.

2. MEMS Vibrating Ring Gyroscope

MEMS vibrating gyroscopes have vibratory systems that need to oscillate continuously at the given resonant frequency. The working principle of the gyroscope is comprised of two vibrational modes. One vibration mode is used for driving the vibrating structure, and the second vibration mode is used for sensing the rotational movement of that vibrating structure.

The basic MEMS vibrating ring gyroscope has comprised a vibrating proof mass “m” with eight support springs having two degrees of freedom. The vibrating ring gyroscope vibrates along the driving direction with an elliptical shape of the ring. The schematic diagram of the vibrating ring mass system is shown in Figure 1.

The general equations of motion for vibrating gyroscopes are shown below. The driving motion equation is written as Equation (1), the equation of motion detection along the sensing direction is written as Equation (2), and the Coriolis motion equation is presented as Equation (3). The “m” represents the proof of mass, the “c” is the damping coefficient, the “k” represents the spring constant, the “x” represents motion along the driving direction, the “y” represents the motion along the sensing direction, and the “$\mathsf{\Omega }$” represents the external rotation applied to the gyroscope. There $F_d$, $F_s$, and $F_c$ are driving, sensing, and Coriolis forces applied to the gyroscope motion equations.

$$m\frac{d^{2}x}{d{t}^2}+c\frac{dx}{dt}+kx=F_d$$

(1)

$$m\frac{d^{2}y}{d{t}^2}+c\frac{dy}{dt}+ky=F_s-F_c$$

(2)

$$F_c=-2m\mathsf{\Omega }\frac{dx}{dt}$$

(3)

Basic Operating Mechanism

The basic operation of the vibrating ring gyroscope is described from steps a to d in Figure 2. There are eight driving and sensing electrodes placed around the ring structure. Continuous oscillation and excitation are provided to the ring structure by driving electrodes at the set resonant frequency. The ring structure oscillates as an elliptical shape by driving electrodes along the driving axis. At the same time, there is no displacement along the sensing axis. However, when the gyroscope is exposed to external rotation, the Coriolis force generates and repels elliptical-shaped oscillations towards the sensing axis. The sensing electrodes sense the change in displacement.

3. Design Conceptualization

The proposed gyroscope design comprises double resonator rings, sixteen worm-shaped springs, and one centrally placed anchor. The sixteen worm-shaped springs were placed in two sets. The large sizes of the eight springs were placed with the internal set and attached to the internal ring and the centrally placed anchor. The small sizes of the eight springs are placed with the external set and attached to the external and internal rings of the gyroscope. The proposed vibrating ring gyroscope is shown in Figure 3.

The concept of including two sets of sixteen worm-shaped springs enhances the gyroscope’s sensitivity and resistance to high-shock environments. The symmetric design of the proposed springs corroborates the need for high shock absorbers in harsh environments. The gyroscope design must be robust enough to operate in the space environment and provide excellent performance for space applications. The complete design features of the proposed vibrating ring gyroscope are listed in

Table 1. Design parameters of MEMS vibrating ring gyroscope with worm-shaped springs.

Design Parameters	Value (µm)
External ring radius	1000
Internal ring radius	750
Ring thickness	10
Length of internal worm-shaped spring	480
Length of external worm-shaped spring	240
Arc radius of internal worm-shaped spring	30
Arc radius of external worm-shaped spring	12.5
Internal worm-shaped spring thickness	10
External worm-shaped spring thickness	10
Radius of anchor	260
Device width	40

. We have set the radius of the external ring resonator to 1000 µm, the reason to set this radius is to achieve an operating resonant frequency within the range of double-digit kHz. If we decrease the device size, the gyroscope’s operational resonant frequency will be higher. Therefore, higher resonant frequencies provide a large split resonant frequency of up to 100 s of kHz between driving and sensing resonant frequencies. If we increase the radius of the ring, then the operating resonant frequency will be lower, which means we need to increase the device size. Most of the MEMS vibrating gyroscopes operate at double-digit kHz resonant frequencies.

4. Modelling Analysis of Worm-Shaped Springs Vibrating Ring Gyroscope

Modal Analysis

The finite element analysis of the proposed design has been conducted using the ANSYS software. The modal analysis describes the basic vibrational shapes of the selected design structure. The modal analysis provides information regarding natural frequencies, different vibrational shapes, structure displacement, and the vibration stability of the structure. The modal frequencies for mode n = 1 are shown in Figure 4. The elliptical shapes of vibrations for the vibrating ring gyroscope can be seen in Figure 4.

The driving and sensing resonant frequencies were measured at 29.07 kHz and 29.35 kHz, respectively. The frequency mismatch between driving and sensing resonant frequencies is recorded at 0.38 kHz.

5. Conclusions

This paper successfully demonstrated the initial development of the new worm-shaped spring vibrating ring gyroscope. Including two rings with sixteen worm-shaped springs enhances the performance reliability of the gyroscope for space applications. The 480 µm and 240 µm lengths of internal and external springs provide a higher compliance number, which shows a good response as a shock absorber. The vibrating ring radius is 1000 µm, with two elliptical shapes of resonant frequencies at 29.07 kHz and 29.35 kHz, respectively. The mode mismatch is recorded at 0.38 kHz. The proposed gyroscope design will be fabricated and dynamically tested for further investigation for space applications.