طراحی و تجزیه و تحلیل عملکرد از یک نانو ژیروسکوپ بر اساس تحریک الکترواستاتیکی و سنجش خازنی

In this paper, a vibrating beam gyroscope with high operational frequencies at mode-matched condition is proposed. The model comprises a micro-cantilever with attached tip mass operating in the flextural–flextural mode. The drive mode is actuated via the electrostatic force, and due to the angular rotation of the base about the longitudinal axis. The secondary sub-nanometric vibration is induced in the sense direction which causes a capacitive change in the sense electrodes. The coupled electro-mechanical equation of motion is derived using the extended Hamilton's principle, and it is solved by direct numerical integration method. The gyroscope performance is investigated through the simulation results, where the device dynamic response, rate sensitivity, resolution, bandwidth, dynamic range, gg sensitivity and shock resistance are studied. The obtained results show that the proposed device may have better performance compared to commercial micro electromechanical gyroscope characteristics.

Gyroscopes as angular rate sensors find broad range of applications from automotive to aerospace and consumer electronics industries. Optical and mechanical gyroscopes in comparison with micro-machined vibratory gyroscopes are more accurate and have better scale factor stability [1]. However, they are too expensive and too bulky. The micro-machined gyroscopes due to their small size, light weight, low power consumption and low cost find application in automotive and electronic consumer and makes them ideal for use in handheld applications. Today, common silicon micro-machined vibratory gyroscopes operate in low frequency range (3–30 kHz) which suffer from the low bandwidth and bias stability and low reliability due to low shock resistance [2]. To increase the scale factor, resolution, and bias stability a high quality factor is desirable which is accomplished by device packaging in high vacuum. It may be further noted that, even in high vacuum, the effective quality factor is restricted by thermoelastic damping [3] and [4]. In some applications such as automotive, a very fast response time is required. Consequently, higher bandwidth is desired which could be achieved by increasing the resonant frequency or decreasing the quality factor of the gyroscope. Although, the later, decreases the scale factor, and the performance of the device. Micro/nano cantilevers have fined various applications such as mass sensor [5] and [6], resonators [7], atomic force microscopes [8] and vibrating beam gyroscopes. Electrostatic actuation as a versatile and applicable method is employed to design and develop various micro/nano electromechanical systems (MEMS/NEMS) [9], [10], [11], [12] and [13]. Recently vibrating beam gyroscopes as an interesting issue has obtained more attention. The optimal size and the level of thermal noise of a vibrating beam gyroscope have been investigated and it is shown the longer the beam the lower the thermal noise [14]. Rotating beams with piezoelectric films as an angular rate sensor has been investigated [15]. The Finite element modeling of a rotational motion sensor which uses tuning fork to sense the angular rate has been performed and dynamic properties of the sensor has been investigated [16]. Dynamic characteristics of a gyroscope based on beam structure have been investigated in which the bandwidth and sensitivity analysis have been performed [17]. Vibrating beam microgyroscope under general base motion has been studied and comprehensive dynamic model has been presented [18]. Silicon angular rate sensor for automotive applications has been designed and simulated; the sensor was based on a tuning fork principle and piezoelectric excitation [19]. Piezoelectrically actuated vibrating beam gyroscope operated in flexural/torsional mode has been proposed and a dynamic model has been presented. It has been shown the device performance is adversely affected by the cross-axis effects [20]. Dynamic stability of vibrating beam gyroscope subjected to rate fluctuations has been analyzed using the method of averaging, and closed-form stability conditions have been presented [21]. Several companies provide microgyroscopes as standard components. The first of these was an integrated z -axis gyroscope announced in 2002 by Analog Devices Inc. (ADI), offering a very high resolution of 0.05°/s/View the MathML sourceHz [22]. Robert Bosch presented a z -axis gyroscope with 1.5°/s/View the MathML sourceHz resolution and 30 Hz frequency bandwidth [23]. In 2006, a high resolution gyroscope (SiRRS01) was introduced by Silicon Sensing, with noise density of 0.35°/s/View the MathML sourceHz and 50 Hz bandwidth [24]. Northrop Grumman Corporation introduced a MAG-16 MEMS gyroscope with 0.03°/s/View the MathML sourceHz resolution and operational range of 150°/s [25]. Later on, in 2007, InvenSense Inc. offered the first commercialized dual-axis integrated gyroscope (IDG-300). Its resolution was claimed of 0.014°/s/View the MathML sourceHz in operational range of 50°/s [26]. All the aforementioned researches and products are related to low frequency gyroscopes which suffer from Brownian noise and low quality factor due to the high level of thermoelastic damping. To overcome these deficiencies, high frequency MEMS gyroscopes have been proposed. The novel capacitive bulk acoustic wave gyroscopes have been established with a very high quality factor and broader bandwidth in comparing to the common low frequency MEMS gyroscopes [27] and [28]. In this paper, modeling and simulation of a vibrating beam gyroscope with high resonance frequency (in order of MHz) working at matched mode condition are performed and it is shown that the proposed device can overcome the deficiency of the common micro-machined gyroscopes. By increasing the resonant frequency, the device finds a stiffer structure, which improves its shock survivability and acceleration sensitivity. Another virtue of the high frequency gyro is the reduction of the Brownian noise which consequently improves the device resolution while having a broader bandwidth. Due to considering the coupled electro-mechanical equation, by dynamic simulations, the device rate sensitivity, resolution, bandwidth, dynamic range, g sensitivity and shock resistance are studied.

Dynamic behavior of a vibrating beam angular rate sensor with high operational frequency is studied and the dynamic characteristics of the device are investigated. The device equations of motion are derived using the extended Hamilton principle. The drive mode is actuated through the electrostatic force, and capacitive sensing is employed to convert the sub nanometric Coriolis induced vibrations to electrical charges which are also converted to output voltage signals via the transimpedance amplifier. The key parameters of the sensor are summarized in Table 6. The beam length is considered 50 μm and the sense and drive electrode gaps are assumed 100 nm and 2 μm, respectively. The rate sensitivity of 0.28 mV/deg/s in a linear operational range of 400°/s is obtained. The device resolution under atmospheric pressure and effective quality factor of 13,200 is calculated as 0.0073°/s/View the MathML sourceHz and the device bandwidth is obtained near to 40 Hz. It is shown that the device survives the 3000g shock. The obtained results show that the proposed device may have better performance compared to commercial MEMS gyroscope characteristics. Table 6. Performance summary for the sensor in atmospheric pressure condition. Parameter Value Unit Operational frequency 1.01×6101.01×106 Hz Effective quality factor 13,20013,200 – Theoretical mechanical resolution 0.00730.0073 deg/s/View the MathML sourceHz Turn-on time <0.1<0.1 s Mechanical scale factor 25 pm/deg/s Sensor sensitivity 4.42 aF/deg/s Rate sensitivity 0.288 mV/deg/s Bandwidth 40 Hz Response time <0.025<0.025 s Linear full scale range ±400±400 deg/s Dynamic range 100 dB g Sensitivity 0.011 deg/s/g