耦合结构对音叉式陀螺振动特性的影响

耦合结构对MEMS音叉式陀螺振动特性具有重要影响。针对一种典型结构的音叉式陀螺及其耦合结构,在分析其工作原理的基础上,建立了其驱动模态的振动模型。基于该模型,计算了在陀螺刚度不对称、驱动力幅值不对称及质量不对称三种情况下,该耦合结构对陀螺振动特性的影响。利用有限元仿真软件,对该耦合结构在三种情况下对陀螺振动特性的影响进行了仿真比较。计算与仿真结果表明,通过改变耦合结构尺寸,能够调整陀螺固有频率,进而对振动特性产生影响。根据结果,提出了音叉式陀螺耦合结构的设计准则。     

Modeling of gold microbeams as strain and pressure sensors for characterizing MEMS packages

This work presents the modeling of gold microbeams for characterizing Micro-electro-mechanical systems (MEMS) packages in terms of both strains induced to the MEMS devices and hermetic sealing capability. The proposed test structures are based on arrays of rectangular-shaped clamped-free and clamped–clamped beams, to be realized with a film of electroplated gold by surface micromachining technology. The resonant frequency of the microbeams is modeled by FEM simulations as a function of substrate deformations, which could be induced by the package. Clamped–clamped bridges show a linear change of the square of the resonant frequency in case of in-plane deformations, in fairly good agreement with an approximate analytical model. Cantilever beams are modeled as variable capacitors to detect out-of-plane deformations. Finally, an analytical model to study cantilever beams as resonators for detecting pressure changes is discussed and compared with preliminary experimental results, showing an impact on the quality factor in a range from 10^?2 mbar to 1?bar.     

Acceleration sensitivity of tuning fork gyroscopes: theoretical model,simulation and experimental verification

A two degrees of freedom (DOF) coupled model is investigated in this paper to analyze the acceleration sensitivity of MEMS tuning fork gyroscopes (TFG) and approaches of decreasing the acceleration sensitivity are presented. Since two tines of TFGs are asymmetric in the mass, stiffness and damping caused by the technological defects, there exists the coupled effect between two tines leading to the invalidity of a single DOF model. Therefore, a two DOFs model is established and the matrix perturbation technique is used to calculate the dynamic responses of the two tines by applying the common-mode acceleration. Our quantitative analysis reveals that the displacement difference is large in the in- and anti-phase modal frequencies between two tines, arising from the unsynchronized motion of two tines due to stiffness imbalance. The FEM simulations coincide with our theoretical calculations. Meanwhile, we take advantage of the experimental data from the other researches to verify our theoretical model and analytical expressions. Our results demonstrate that the acceleration sensitivity of TFGs can be reduced by increasing the coupled stiffness ratio, modal frequency and sense beams widths which are insensitive to technological dispersions.     

Fabrication uncertainties and yield optimization in MEMS tunable capacitors

Intrinsic uncertainties of MEMS fabrication processes can severely affect the performance of devices because the tolerance ranges of these processes are relatively large and improvement of process accuracy is very expensive. Therefore, the analysis of fabrication uncertainties and their outcome on a device performance is a vital task before finalizing the design. In this paper, the effects of process inaccuracy on the performance of MEMS tunable capacitors are studied. Design parameters such as dimensions of electrodes and the initial gap between them and the stiffness of supporting beams are considered as random variables. The variation of these parameters within tolerance ranges drastically alters the capacitor's actual response from the desired one and results in low yield. Hence, design optimization with the objective of maximizing yield in early steps becomes very important. An effective method for yield optimization of MEMS capacitors under given fabrication uncertainties is introduced. The method utilizes aspects of the advanced first-order second-moment (AFOSM) reliability method to find a linearized feasible region to estimate the yield. The yield is calculated directly using the joint cumulative distribution function (CDF) over the tolerance box requiring no numerical integration and avoiding computational complexity. The optimal design verified by Monte-Carlo (M-C) simulation exhibits a significant increase in the yield. The main advantage of this method comparing to other design optimization methods is that the proposed method does not change the design topology or fabrication accuracy. It increases the yield by finding the optimum design variables as demonstrated in this paper.     

Characterization of selective polysilicon deposition for MEMS resonator tuning

Variations in micromachining processes cause submicron differences in the size of MEMS devices, which leads to frequency scatter in resonators. A new method of compensating for fabrication process variations is to add material to MEMS structures by the selective deposition of polysilicon. It is performed by electrically heating the MEMS in a 25/spl deg/C silane environment to activate the local decomposition of the gas. On a (1.0/spl times/1.5/spl times/100) /spl mu/m/sup 3/, clamped-clamped, polysilicon beam, at a power dissipation of 2.38 mW (peak temperature of 699/spl deg/C), a new layer of polysilicon (up to 1 /spl mu/m thick) was deposited in 10 min. The deposition rate was three times faster than conventional LPCVD rates for polysilicon. When selective polysilicon deposition (SPD) was applied to the frequency tuning of specially-designed, comb-drive resonators, a correlation was found between the change in resonant frequency and the length of the newly deposited material (the hotspot) on the resonator's suspension beams. A second correlation linked the length of the hotspot to the magnitude of the power fluctuation during the deposition trial. The mechanisms for changing resonant frequency by the SPD process include increasing mass and stiffness and altering residual stress. The effects of localized heating are presented. The experiments and simulations in this work yield guidelines for tuning resonators to a target frequency.     

Topology optimization of frame structures with flexible joints

A method for structural topology optimization of frame structures with flexible joints is presented. A typical frame structure is a set of beams and joints assembled to carry an applied load. The problem considered in this paper is to find the stiffest frame for a given mass. By introducing design variables for beams and joints, a mass distribution for optimal structural stiffness can be found. Each beam can have several design variables connected to its cross section. One of these is an area-type design variable which is used to represent the global size of the beam. The other design variables are of length ratio type, controlling the cross section of the beam. Joints are flexible elements connecting the beams in the structure. Each joint has stiffness properties and a mass. A framework for modelling these stiffnesses is presented and design variables for joints are introduced. We prove a theorem which can be interpreted as the fact that the removal of structural elements, e.g. joints or beams, can be modelled by a small strictly positive material amount assigned to the element. This is needed for the computations of sensitivities used in the applied gradient based iterative method. Both two and three dimensional problems, as well as multiple load cases and multiple mass constraints, are treated.     

A novel MEMS tunable antenna with wide tuning range of frequency

In this paper a novel MEMS tunable CPW antenna with wide tuning range of frequency is presented. The antenna’s frequency tuning range increment is achieved by loading three novel large tuning range capacitors at radiation edge of antenna patch. Two techniques are employed for increasing the capacitors tuning range. First, dual gap technique is used to overcome the pull-in limitation and then two lateral beams are added in order to parallel movement of capacitive plate which increases the capacitance value. The simulation result shows that the resonance frequency tuning range of antenna increased from 1.96 GHz loaded by traditional capacitor to 6.89 GHz using the new capacitor structure. Also in resonance frequency, the antenna has a good impedance matching with transmission line even in high capacitance values.     

RF MEMS压控振荡器的研制及相位噪声特性研究

利用RF MEMS可变电容作为频率调节元件,制备了中心频率为2 GHz的MEMS VCO器件.RF MEMS可变电容采用凹型结构,其控制极板与电容极板分离,并采用表面微机械工艺制造,在2 GHz时的Q值最高约为38.462.MEMS VCO的测试结果表明,偏离2.007 GHz的载波频率100kHz处的单边带相位噪声为-107 dBc/Hz,此相位噪声性能优于他们与90年代末国外同频率器件.并与采用GaAs超突变结变容二极管的VCO器件进行了比较,说明由于集成了RF MEMS可变电容,使得在RF MEMS可变电容的机械谐振频率近端时,MEMS VCO的相位噪声特性发生了改变.     

Design sensitivity analysis with isoparametric shell elements

This paper deals with design sensitivity calculation by the direct differentiation method for isoparametric curved shell elements. Sensitivity parameters include geometric variables which influence the size and the shape of a structure, as well as the shell thickness. The influence of design variables, therefore, may be separated into two distinct contributions. The parametric mapping within an element, as well as the influence of geometric variables on the orientation of an element in space, is accounted for by the sensitivity calculation of geometric variables, and efficient formulations of sensitivity calculation are derived for the element stiffness, the geometric stiffness and the mass matrices. The methods presented here are applied to the sensitivity calculations of displacement, stress, buckling stress and natural frequency of typical basic examples such as a square plate and a cylindrical shell. The numerical results are compared with the theoretical solutions and finite difference values.     

GaAs-based tuning fork microresonators: A first step towards a GaAs-based coriolis 3-axis Micro-Vibrating Rate Gyro (GaAs 3-axis μCVG)

This paper presents the design of a piezoelectric MEMS Coriolis Vibrating Gyroscope (CVG) based on a single gallium arsenide vibrating structure allowing the measurement of rotation rate along 3 orthogonal sensitive axes. Based on a theoretical and FEM study, we demonstrate that the achieved sensitivities reached for each axis is about 1.6 × 10⁻¹⁶ C/(°/s). We then demonstrate the feasibility of the realization of simple MEMS structures from C-doped Gallium Arsenide (GaAs) using standard micromachining processes. Finally, we show the fabrication and characterization of GaAs-based tuning fork microresonators as a first step towards a complete 3-axis GaAs MEMS CVG. These resonators show a resonance frequency of 42 350 Hz, a quality factor of 122 000 and a frequency temperature coefficient of 24 ppm/°K, validating the high potential of GaAs as a structural material for 3-axis MEMS CVGs.     

A novel high tuning ratio MEMS cantilever variable capacitor

This paper presents a novel cantilever-type MEMS variable capacitor with high tuning ratio. In previous works, the cantilever is used as a switch but in our design, it is applied as a variable capacitor. For increasing the maximum achievable capacitance of the cantilever, the suspended capacitive plate should be moved as parallel with fixed plate. The parallel movement can be obtained using the novel structure which utilized two additional lateral beams. Also to overcome the pull-in phenomenon in new structure, the different membrane thickness technique is used. The novelty of our design is adding the lateral beams to make parallel movement of the suspended plate to increase the variable capacitor of the cantilever. The new device is designed on a thick silicon substrate with a thin poly silicon membrane. The results show the tuning range of tunable capacitor with initial capacitance of 560.1 fF can be improved from 6:1 for conventional cantilever to 22.5:1 for the new cantilever. In other words the capacitance tuning range increased three times.     

Frequency response of in-plane coupled resonators for investigating the acceleration sensitivity of MEMS tuning fork gyroscopes

The frequency response of in-plane coupled resonators is used for investigating the acceleration sensitivity of a MEMS tuning fork gyroscope (TFG) and a new method of suppressing the acceleration output is presented. The unbalancing of two sense resonators in the TFG caused by fabrication errors converted an external vibration into anti-phase mode excitation. To reduce the acceleration output, decoupling between in- and anti-phase modal frequencies [decoupling ratio (DR)] is crucial, since coupled resonators may cause large anti-phase vibrations from the acceleration. The acceleration output model was verified using two coupled resonators with 1 and 5?% stiffness unbalance. FEM simulation results showed a 25?% reduction in the anti-phase vibration by increasing the decoupling ratio from 0.09 to 0.29, irrespective of the coupled resonators designs. Quantitative analysis of a TFG based on coupled resonators with 1?% stiffness unbalance showed the acceleration output decreased from 5.65 to 1.43?deg/s/g.     

Effect of Die-Bonding Process on MEMS Device Performance: System-Level Modeling and Experimental Verification

This paper presents a distributed nodal method (DNM) for compact modeling of the package-device interaction of microelectromechanical systems (MEMS). MEMS devices have movable structures that are sensitive to structural stresses and easily influenced by package structures and environmental parameters. Hence, it is necessary to include the packaged behavior of MEMS into a compact simulation tool with acceptable precision. The conventional nodal method is therefore modified to achieve this purpose. A node with distributed nodal quantities is defined to describe the distributed interactions among the device, package, and environmental temperature. Based on the definition, the related processes of element partition, nodal matrix formation, and element assembly have been demonstrated. The case of a die-bonded microbridge has been used as an example, since the microbridge is not only a typical MEMS structure but also is influenced easily by structural stresses. The DNM model is validated first by a finite-element method (FEM) simulation, then by two individual experiments, including the measurement of die warpage using a digital image correlation system and the detection of shifted natural frequencies of surface-micromachined bridges using a laser Doppler vibrometer system, both after die bonding. The FEM and test results agree with those evaluated by the model with a relative error of less than 10%. Stress alleviation of the test structure has been unintentionally achieved by die bonding, leading to relative shifts of 12%-26% and 19%-26% of the first and third natural frequencies of the microbridges. The packaged behavior also exhibits an evident distributed feature along the die surface as expected. Although, at current stage, the application of the DNM is still limited to static domain, it shows potential in developing hierarchical models of MEMS devices including the package.     

Optimal electrode shaping for precise modal electromechanical filtering

This paper addresses the optimal shape design of segmented spatial sensors and actuators that isolate selected mode shapes and perform modal filtering. Electromechanical filters have reappeared with the new manufacturing capabilities of micro-electro-mechanical structures (MEMS). In such small dimensions it proves essential to treat their elastic behaviour as continuous rather than discrete systems that require suitable design methods, some of which are developed here. In MEMS filters, the input signal is converted to external electrostatic forces and in order to perform the desired filtering, the electrodes need to be shaped such that they excite only a desired part of the dynamics. An optimization scheme that shapes these electrodes to achieve optimal filtering is developed. In order to enhance the filter’s performance and minimize energy lost to the supporting structure, a special support tuning method is proposed. Several simulated examples examine the effectiveness of the proposed optimization methods.     

微型半球谐振陀螺仪谐振体振动特性研究

半球壳谐振体是微型半球谐振陀螺的敏感部件。应用有限元方法对半球谐振体进行振动特性分析,得出一种计算其质量和刚度矩阵的方法,并通过M athem atica软件计算出各阶固有频率;同时,应用ANSYS软件,分析谐振体的各阶振型和固有频率与半球壳半径、厚度及固定角之间的关系。在理论分析的基础之上,提出了对于半球壳谐振体的结构设计的合理建议。     

磁浮列车底盘梁的有限元优化减重设计

为在已有型号基础上获得更轻型有效的底盘梁结构而保持相对稳定的动力特性,首先利用ANSYS软件建立磁浮列车车体结构的有限元模型,利用Block Lanczos Method进行模态求解并得到结构一阶弹性固有频率.然后以结构一阶弹性固有频率值为约束函数,以车厢底盘梁8个截面上17个主要厚度参数为设计变量,以底盘梁总体积为目标函数,建立磁浮列车底盘梁减重优化的数学模型并进行计算.结果表明,磁浮列车一阶弹性固有模态为前后扭转的振型,在满足模态频率值不小于8.OHz的设计要求下,底盘梁减重20%的设计目标可以达到.说明以一阶弹性固有模态频率值为约束函数的优化方案可行且效果良好.     

An Efficient Macromodeling Methodology for Lateral Air Damping Effects

In this paper, a macromodeling methodology for lateral air damping effect is presented. This methodology employs a simplified governing equation, the Quasi-3D (Q3D) Stokes equation , and an Arnoldi-based model-order-reduction algorithm. A finite-difference (FDM) solver based on the Q3D-Stokes equation is implemented, and then the Arnoldi-based algorithm is used to create macromodels from the system matrices generated by the solver. This methodology can also be realized by using commercial MEMS packages for solid-model generation, and by using commercial finite-element (FEM) thermal packages for system-matrix generation. The generated macromodels are compatible with system-level modeling simulators, such as SPICE, Saber, or Simulink for fast transient and frequency analyses. It is demonstrated that the macromodels are at least 600 times more efficient than the FDM Q3D Stokes solver, while are still capable of capturing the three-dimensional (3-D) effect that usually requires very expensive 3-D FEM Stokes-flow calculations. Experimental results of comb-drive devices show that the error of the macromodel is less than 10%, which is a significant improvement when compared with the results by widely used 1-D analytical approaches. Finally, the guidelines of using this macromodeling methodology for typical MEMS devices are also provided.hfillhbox[1262]     

Design,modeling, and mechanical characterizations of micromachined InP-based actuator for tunable MOEMS applications

A novel InP-based microactuator, which is actuated by electrostatic means, has been proposed, designed, fabricated, and characterized for tuning applications in the 1.5 μm wavelength domains. Its structural design is based on the global optimization method. The tunable device is a big square membrane, which is supported by four identical cantilever beams. The three alternating layers Si₃N₄/SiO₂ as a distributed Bragg reflector (DBR) mirror, which were previously reported, have been formed on the top of the membrane. Based on the optical interferometric measurements, the proposed Fabry–Perot filter has demonstrated a maximum deflection of ∼321 nm with an applied voltage up to 12 V, an average sensitivity of ∼27 nm/V, a pull-in voltage of 12.7 V, and a release voltage of 10.7 V. It is also observed that its natural frequency is 88.4 kHz. This measured frequency implies that the tuning speed of our device is fast for optical operations within 0.01 ms. In addition, our device’s mirror remains so flat with a good planarity of 0.07°, which is strictly required for the filter’s optical performance. This optical performance can be achieved, when the micromachined structure has a tuning displacement up to ∼38 nm with a low tuning voltage up to 5 V. When compared with the finite element models (FEM), which were generated by the commercialized software, Coventor™, our experimental results agree well in terms of the natural frequency, pull-in voltage and deflections. Thus, our tunable filter, which is based on the optimized design, enables better performances including reduced actuation voltages, large pull-in voltage, improved device reliability, and fast switching times. Our device can also quickly snap back to the original position. In addition, the undesired spring-softening effect has been reduced.     

Numerical and experimental validation of out-of-plane resonance closed formulas for MEMS suspended plates with square holes

A compact analytical model for out-of-plane resonance evaluation is proposed for large diffuse MEMS vibrating plates with squared holes. A closed form expression was developed from a structural reduced order model with equivalent concentrated mass and stiffness parameters. Results were validated through FEM models and experimental modal analysis. Numerical FEM simulations were performed by 1D, 2D and 3D FEM models; experiments on polysilicon test structures were conducted using an interferometric microscope. Specimens were designed ad hoc to highlight the sensitivity of proposed formulas to main structural dimensional parameters of vibrating plates. Experiments and models helped investigate the sensitivity of the proposed reduced linearized model when exposed to electrostatic non-linear coupling effects and fluidic damping coupling. Both numerical results and experiments are in good agreement with analytical results predicted by closed formulas.     

Theory and FEM simulation study of the double-clamped resonant beam with slit-structure

In this paper, we established the vibration model of double-clamped resonant beam with slit structure, and we theoretically analyzed the effect of rectangular slits with round corners on vibration amplitude and natural frequency of the resonant beam. The effect of rectangular slits on detection sensitivity of resonant beam is also analyzed. According to the theoretical analysis, computational studies of slit size and location influence on vibration amplitude, natural frequency and detection sensitivity of the resonant beam were carried out. Meanwhile, stress concentration of proposed slit structure with rounded corners was calculated by finite element method (FEM) and was compared with the stress concentration of slit with right corners. Finally, for resonant beams with slits of different size and location, theoretical calculation results and the FEM simulation results of natural frequency were compared. Theoretical analysis and FEM simulation are in good agreement.