Nonresonant micromachined gyroscopes with structural mode-decoupling

This paper reports a novel four-degrees-of-freedom (DOF) nonresonant micromachined gyroscope design concept that addresses two major MEMS gyroscope design challenges: eliminating the mode-matching requirement and minimizing instability and drift due to mechanical coupling between the drive and sense modes. The proposed approach is based on utilizing dynamical amplification both in the 2-DOF drive-direction oscillator and the 2-DOF sense-direction oscillator, which are structurally decoupled, to achieve large oscillation amplitudes without resonance. The overall 4-DOF dynamical system is composed of three proof masses, where second and third masses form the 2-DOF sense-direction oscillator, and the first mass and the combination of the second and third masses form the 2-DOF drive-direction oscillator. The frequency responses of the drive and sense direction oscillators have two resonant peaks and a flat region between the peaks. The device is nominally operated in the flat regions of the response curves belonging to the drive and sense direction oscillators, where the gain is less sensitive to frequency fluctuations. This is achieved by designing the drive and sense anti-resonance frequencies to match. Consequently, by utilizing dynamical amplification in the decoupled 2-DOF oscillators, increased bandwidth and reduced sensitivity to structural and thermal parameter fluctuations and damping changes are achieved, leading to improved robustness and long-term stability over the operating time of the device.     

一种全对称微机械陀螺的双级解耦机构特性

为了实现微机械陀螺的频率匹配和双级解耦,提出了一种全对称双级解耦结构体硅微机械陀螺.该陀螺结构完全对称,容易实现驱动和检测模态谐振频率的匹配,提高系统灵敏度.驱动和检测方向的主要阻尼均为滑膜阻尼,在常压下工作也可以获得较高的品质因子,避免了器件的真空封装.利用4组十字折梁,实现了结构的双级解耦.仿真结果表明,模态之间的耦合系数小于0.17%.采用体硅微机械加工技术制作了样品,关键工艺有硅-玻璃阳极键合和DRIE技术.基于计算机图像技术对微机械陀螺进行了测试,验证了陀螺的解耦功能,在常压条件下测得该陀螺的品质因子为195,灵敏度为8.031 mV/（（°）.s^-1）.     

Novel concept of a single-mass adaptively controlled triaxial angular rate sensor

This paper presents a novel concept for an adaptively controlled triaxial angular rate (AR) sensor device that is able to detect rotation in three orthogonal axes, using a single vibrating mass. Pedestrian navigation is presented as an example demonstrating the suitability of the proposed device to the requirements of emerging applications. The adaptive controller performs various functions. It updates estimates of all stiffness error, damping and input rotation parameters in real time, removing the need for any offline calibration stages. The parameter estimates are used in feedforward control to cancel out their otherwise erroneous effects, including zero-rate output. The controller also drives the mass along a controlled oscillation trajectory, removing the need for additional drive control. Finally, the output of the device is simply an estimate of input rotation, removing the need for additional demodulation normally used for vibratory AR sensors. To enable all unknown parameter estimates to converge to their true values, the necessary model trajectory is shown to be a three-dimensional Lissajous pattern. A modified trajectory algorithm is presented that aims to reduce errors due to discretization of the continuous time system. Simulation results are presented to verify the operation of the adaptive controller. A finite-element modal analysis of a preliminary structural design is presented. It shows a micro electro mechanical systems realizable design having modal shapes and frequencies suitable for implementing the presented adaptive controller.     

单片三轴硅微机械振动陀螺仪研究

设计、制造了一种单片集成三轴硅微机械振动陀螺仪.该器件由两个结构完全相同的单轴水平陀螺仪和一个单轴垂直陀螺仪组合而成,三只单轴陀螺仪均采用静电驱动、电容检测的结构形式.采用体硅溶解薄片法制造了该三轴陀螺仪芯片,并对其在空气中的驱动性能进行了初步测试.测试结果表明,该单片三轴硅微机械振动陀螺仪驱动模态的实际谐振频率与理论值之间的最大误差小于5%,满足设计要求.     

Design and characterization of in-plane MEMS yaw rate sensor

In this paper, we present the design and characterization of a vibratory yaw rate MEMS sensor that uses in-plane motion for both actuation and sensing. The design criterion for the rate sensor is based on a high sensitivity and low bandwidth. The required sensitivity of the yawrate sensor is attained by using the inplane motion in which the dominant damping mechanism is the fluid loss due to slide film damping i.e. two–three orders of magnitude less than the squeeze-film damping in other rate sensors with out-of-plane motion. The low bandwidth is achieved by matching the drive and the sense mode frequencies. Based on these factors, the yaw rate sensor is designed and finally realized using surface micromachining. The inplane motion of the sensor is experimentally characterized to determine the sense and the drive mode frequencies, and corresponding damping ratios. It is found that the experimental results match well with the numerical and the analytical models with less than 5% error in frequencies measurements. The measured quality factor of the sensor is approximately 467, which is two orders of magnitude higher than that for a similar rate sensor with out-of-plane sense direction.     

Parametric study to identify the cause of high torsional vibration of the propulsion shaft in the ship

Since torsional vibration can lead to fatigue failure of the propulsion shaft in a ship, it should be restricted from the first step of the design through calculation and verified at the sea trial test step through measurement. Considering that the torsional vibration of the shaft is a system characteristic, it is strongly related to the vibration modes at the natural frequencies of the shaft. Therefore, the actual torsional vibration problem can occur due to the variation of parameters such as those of the vibration system, including mass of inertia, damping, and stiffness, which differ from the design.In this research, the root cause analysis of the high torsional vibration which occurred in the actual ship is described through a parametric study performed using numerical analysis. Parameters that can increase the torsional vibration of the propulsion shaft are selected, including coupling stiffness, shaft stiffness, coupling damping, and shaft damping. Through the torsional vibration calculations with variations of these parameters, the extent of the effect of these parameters on the torsional vibration of the propulsion shaft is investigated and the cause of the increased torsional vibration is identified.     

Evaluation of the increased stiffness for the elastic coupling under the dynamic loading conditions in a ship

Torsional vibration is restricted during design because it can cause fatigue fractures of the shaft due to repetitive vibratory torque and should be verified by analytical calculations as well as experiments. Torsional vibration is a characteristic of propulsion systems and is strongly related to their natural frequency; differences between measured and analytically predicted torsional vibration could be caused by variation of parameters related to natural frequency such as stiffness, damping, and components' inertial masses. In this investigation, extreme torsional vibration caused by increased coupling stiffness is expected to be the main root cause of fracture. The variation of coupling stiffness is investigated in a laboratory excitation test in order to determine the root cause of increased stiffness. Torsional vibration analysis error is identified as the main cause, where calculated values are quite different from measured results. It is shown that this difference is caused by torsional stiffness differences between the cases of the analytic model and the real ship.     

盾构刀盘驱动三级行星齿轮系统固有特性及灵敏度分析

建立了三级行星齿轮传动系统的平移-扭转耦合动力学模型,模型考虑了时变啮合刚度、各级中行星轮位置相角的时变性、啮合综合误差、阻尼等影响因素。基于特征值问题求解了系统结构的固有频率和振型,并将其系统振动模式归为三类：扭转耦合振动模式、平移耦合振动模式、行星轮振动模式。研究了不同振动模式下固有频率对系统参数的灵敏度。研究结果表明,在一些系统参数敏感点处,参数的微小变化不仅导致固有频率灵敏度、模态能量的大幅变化,也将引起能量在各级间发生转移,使得振动特性剧烈变化。     

On Control System Design for the Conventional Mode of Operation of Vibrational Gyroscopes

This paper presents a novel control circuitry design for both vibrating axes (drive and sense) of vibrational gyroscopes, and a new sensing method for time-varying rotation rates. The control design is motivated to address the challenges posed by manufacturing imperfection and environment vibrations that are particularly pronounced in microelectromechanical systems (MEMS) gyroscopes. The method of choice is Active Disturbance Rejection Control that, unlike most existing control design methods, does not depend on an accurate model of the plant. The task of control design is simplified when the internal dynamics, such as mechanical cross coupling between the drive and sense axes, and external vibrating forces are estimated and cancelled in real time. In both simulation and hardware tests on a vibrational piezoelectric beam gyroscope, the proposed controller proves to be robust against structural uncertainties; it also facilitates accurate sensing of time-varying rotation rates. The results demonstrate a simple, economic, control solution for compensating the manufacturing imperfections and improving sensing performance of the MEMS gyroscopes.      

Mechanical-thermal noise in MEMS gyroscopes

We derive expressions for the effect of mechanical thermal noise on a vibrational microelectromechanical system gyroscope, including the angle of random walk, the noise equivalent rotation rate, and the spectral density of the noise component of the rate measurement. We explicitly calculate and compare the output signal due to rotation and the output due to noise. We avoid several ambiguities in the literature concerning bandwidth and correctly observe a factor of two reduction in noise power due to synchronous demodulation. We use stochastic averaging to obtain an approximate "slow" system that clarifies the effect of thermal noise and shows the effect of frequency mismatch between the drive and sense axes. We compute the noise equivalent rate for both open-loop and force-to-rebalance operation of the gyroscope.     

The Resonating Star Gyroscope: A Novel Multiple-Shell Silicon Gyroscope With Sub-5 deg/hr Allan Deviation Bias Instability

We report on the design, fabrication and characterization of a novel multiple-shell silicon vibratory microgyroscope. The resonating star gyroscope (RSG) is formed as a merged superposition of two square shells, yielding in-plane flexural modes that are utilized to sense rotation along the normal axis. The first prototypes of the single-shell RSG were implemented with 65 $mu$m thick trench-refilled polysilicon structural material using the HARPSS process. These devices exhibited open-loop rate sensitivity of approximately 800 $mu$V/deg/s. Despite high-aspect ratio sensing gaps, the device yielded poor sensitivity caused by low resonant-mode quality factors. To alleviate the ${Q}_{rm TED}$ losses caused by the inevitable formation of voids in trench-refilled structural material, the RSG was implemented in (111) single crystalline silicon. A 2.5-mm multiple-shell RSG was fabricated in 40 $mu$m-thick SOI device layer using a simple two-mask process. Multiple-shells enable a higher operating frequency and larger resonant mass, essential components for reducing the mechanical noise floor of the sensor. Experimental data of a high-Q (111) multiple-shell prototype indicates sub-5 deg/hr Brownian noise floor, with a measured Allan deviation bias drift of 3.5 deg/hr. The gyroscope exhibits an open-loop rate sensitivity of approximately 16.7 mV/deg/s in vacuum.      

Optimizing ultrasonic transducers based on piezoelectric composites using a finite-element method

A novel approach to understanding the vibratory behavior of composite piezoelectric materials is proposed. Elementary ceramic rods, and the effects of their width-to-thickness (W/T) ratio are studied. A model based on the finite-element methods is used. Some experimental results that agree well with the computed data are presented. Plots of resonant frequencies and coupling coefficients versus W/T are given that can be used in transducer design.     

三自由度水平轴硅微机械陀螺结构设计与仿真

为了兼顾测量带宽和灵敏度的要求，提出了一种三自由度水平轴硅微陀螺系统，此系统由3个质量块组成。质量块2与质量块3组合后与质量块1构成了一个二自由度驱动方向的谐振器，再利用该谐振器进行动力学放大，得到非谐振状态下的大驱动振幅．陀螺驱动频率响应曲线有两个谐振尖峰，在两峰值之间存在一个较平坦的区域，当陀螺驱动工作在频率响应曲线的平坦区域时，机械增益虽然比工作在谐振尖峰处小，但机械增益受频率变化的影响减小，驱动频率的工作带宽增加，使得对驱动的控制要求相对宽松．文中给出了动力学放大原理及所设计的陀螺结构的理论计算和仿真值．     

法向接触刚度对装配体振动模态影响的研究

在对装配体进行模态分析时,装配体接触面间的法向接触刚度对计算结果具有很大影响,但在实际中由于处理困难却往往被省略。基于有限元建模方法分析了装配体接触面法向接触刚度对装配体振动模态的影响。首先,根据接触力学理论推导了法向接触刚度与接触表面粗糙度和接触应力之间的关系;然后,探讨了通过改变层单元弹性模量来模拟法向接触刚度的有限元建模方法;最后,通过算例分析了考虑与不考虑接触刚度时振动模态的差异。研究结果表明,考虑法向接触刚度的有限元等效模型计算结果与解析解非常接近,不考虑接触刚度的整体模型计算结果与解析解异较大,一般超过了10%以上,且频率越低差异越大,另外振型也有明显差异。本文建立的有限元建模方法可用于研究法向接触刚度对装配体振动模态的影响。     

Prediction of material coupling effect on structural damping of composite beams and blades

The present paper investigates the effect of material coupling on static and modal characteristics of composite structures. Incorporation of stiffness and damping coupling terms into a beam formulation yields equivalent section stiffness and damping properties. Building upon the damping mechanics, an extended beam finite element is developed capable of providing the stiffness and damping matrices of the structure. Validation cases on beams and blades demonstrate the importance of all stiffness and damping terms. Numerical results validate the predicted effect of material coupling on static characteristics of composite box-section beams. The effect of the full coupling damping matrices on modal frequencies and structural modal damping of composite beams is investigated. Box-section beams and small blade models with various ply angle laminations at the girder segments are considered. Finally, the developed finite element is applied to the prediction of the modal characteristics of a 19 m realistic wind-turbine model blade.     

Towards a biomimetic gyroscope inspired by the fly's haltere using microelectromechanical systems technology

Flies use so-called halteres to sense body rotation based on Coriolis forces for supporting equilibrium reflexes. Inspired by these halteres, a biomimetic gimbal-suspended gyroscope has been developed using microelectromechanical systems (MEMS) technology. Design rules for this type of gyroscope are derived, in which the haltere-inspired MEMS gyroscope is geared towards a large measurement bandwidth and a fast response, rather than towards a high responsivity. Measurements for the biomimetic gyroscope indicate a (drive mode) resonance frequency of about 550 Hz and a damping ratio of 0.9. Further, the theoretical performance of the fly''s gyroscopic system and the developed MEMS haltere-based gyroscope is assessed and the potential of this MEMS gyroscope is discussed.     

Nonlinear Dynamic Analysis of Electrostatically Actuated Resonant MEMS Sensors Under Parametric Excitation

Electrostatically actuated resonant microelectromechanical systems (MEMS) sensors have gotten significant attention due to their geometric simplicity and broad applicability. In this paper, nonlinear responses and dynamics of the electrostatically actuated MEMS resonant sensors under two-frequency parametric and external excitations are presented. The presented model and methodology enable simulation of the steady-state dynamics of electrostatic MEMS undergoing small motions. Response and dynamics of the MEMS resonator to a combination resonance are studied. The responses of the system at steady-state conditions and their stability are investigated using the method of multiple scales. The results showing the effect of varying the dc bias, the squeeze film damping, cubic stiffness, and ac excitation amplitude on the frequency response curves, resonant frequencies and nonlinear dynamic characteristics are given in detail. Frequency response, resonant frequency and peak amplitude are examined for variation of the dynamic parameters involved. This investigation provides an understanding of the nonlinear dynamic characteristics of microbeam-based resonant sensors in MEMS     

Oscillations of Charged Helium II Drops

We report on an experimental study of the shape oscillations of charged helium drops levitated with a magnetic field. Shape oscillations are excited with an AC electric field. Many different modes of oscillation of the drop are observable. The resonant frequencies of the drops are found to be a function of amplitude. Quantitative measurements of the damping of shape oscillations are made by using a laser beam focused through the drop. The observed damping of shape oscillations is found to be greater than the damping due to the viscosities of the liquid and the surrounding vapor. Other mechanisms possibly responsible for this damping are discussed. We also report experiments on drops with angular momentum.     

Carbon nanotube-reinforced composites: frequency analysis theories based on the matrix stiffness

Strong and versatile carbon nanotubes are finding new applications in improving conventional polymer-based fibers and films. This paper studies the influence of matrix stiffness and the intertube radial displacements on free vibration of an individual double-walled carbon nanotube (DWNT). For this, a double elastic beam model is presented for frequency analysis in a DWNT embedded in an elastic matrix. The analysis is based on both Euler–Bernoulli and Timoshenko beam theories which considers shear deformation and rotary inertia and for both concentric and non-concentric assumptions considering intertube radial displacements and the related internal degrees of freedom. New intertube resonant frequencies and the associated non-coaxial vibrational modes are calculated. Detailed results are demonstrated for the dependence of resonant frequencies and mode shapes on the matrix stiffness. The results indicate that internal radial displacement and surrounding matrix stiffness could substantially affect resonant frequencies especially for longer double-walled carbon nanotubes of larger innermost radius at higher resonant frequencies, and thus the latter does not keep the otherwise concentric structure at ultrahigh frequencies. Therefore, depending on the matrix stiffness, for carbon nanotubes reinforced composites, different analysis techniques should be used while the aspect ratio of carbon nanotubes has a little effect on the analysis theory which should be selected.     

Damping function estimation based on modal receptance models and neural nets

 A method for the estimation of an isotropic material damping based on the isotropic, augmented Hooke's law (AHL) and the concept of isotropic, modal and material damping functions is proposed. The method is a straightforward application of standard neural net (NN) back propagation techniques combined with back propagation of simulation errors using “response-to-damping parameter” mapping based on an analytical, modal receptance model incorporating AHL damping. Damping parameters are estimated by fitting the receptance model iteratively, using NN technique, to measured receptance data. Owing to the response model used, the proposed estimation technique provides new possibilities to completely separate pure damping properties from geometry, elastic (static) data and undamped modal data. The method is applicable to homogeneous materials and cases where cross coupling, due to damping, between the modes can be neglected. Even though in this sense restricted, the technique may be applied to a wide class of cases, including cases with very high damping and highly overlapping damped modes. Necessary background theory, including a suitable NN structure, for application of the method is presented. The estimation procedure is demonstrated for a plexiglas (PMMA) plate (modal loss factors ≈ 0.1 at room temperature) used as experimental test case. Very good agreement between measured receptances and responses predicted using the estimated damping function parameters is obtained. Validation was done using both modal and direct finite element (FE) computations.