High-Performance Micromachined Vibratory Rate- and Rate-Integrating Gyroscopes.

We aim to reduce vibration sensitivity by developing gyros that operate in the balanced mode. The balanced mode creates zero net momentum and reduces energy loss through an anchor. The gyro can differentially cancel measurement errors from external vibration along both sensor axes. The vibration sensitivity of the balanced-mode gyroscope including structural imbalance from microfabrication reduces as the absolute difference between in-phase parasitic mode and operating mode frequencies increases. The parasitic sensing mode frequency is designed larger than the operating mode frequency to achieve both improved vibration insensitivity and shock resistivity. A single anchor is used to minimize thermoresidual stress change. We developed two gyroscope based on these design principles. The Balanced Oscillating Gyro (BOG) is a quad-mass tuning-fork rate gyroscope. The relationship between gyro design and modal characteristics is studied extensively using finite element method (FEM). The gyro is fabricated using the planar Si-on-glass (SOG) process with a device thickness of 100 micrometers. The BOG is evaluated using the first-generation analog interface circuitry. Under a frequency mismatch of 5Hz between driving and sense modes, the angle random walk (ARW) is measured to be 0.44deg/sec/sqrt(Hz). The Cylindrical Rate-Integrating Gyroscope (CING) operates in whole-angle mode. The gyro is completely axisymmetric and self-aligned to maximize mechanical isotropy. The gyro offers a large frequency ratio of ~1.7 between parasitic and the wineglass modes. The CING is fabricated using the 3D Si-on-glass (SOG) process with a device thickness of 300 micrometers. The 1st and 2nd generation CINGs operate at 18kHz and 3kHz, respectively and demonstrate a frequency mismatch of <1% and a large Q (~20,000 at 18kHz and ~100,000 at 3kHz under exact mode matching). In the rate-sensing mode, the first-generation CING (18kHz) demonstrates an Ag of 0.05, an angle random walk (ARW) of 7deg/sqrt(hr), and a bias stability of 72deg/hr without temperature compensation. In the rate-sensing mode, the second-generation CING measures an Ag of 0.0065, an ARW of 0.09deg/sqrt(hr), and a bias stability of 129deg/hr without temperature compensation. In the rate-integration mode, the second-generation CING demonstrates precession with an Ag of 0.011±0.001 under a frequency mismatch of 20~80mHz during several hours of operation.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91440/1/jycho_1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/91440/2/jycho_2.pd

Development and experimental analysis of a micromachined Resonant Gyrocope

This thesis is concerned with the development and experimental analysis of a resonant gyroscope. Initially, this involved the development of a fabrication process suitable for the construction of metallic microstructures, employing a combination of nickel electroforming and sacrificial layer techniques to realise free-standing and self-supporting mechanical elements. This was undertaken and achieved. Simple beam elements of typically 2.7mm x 1mm x 40µm dimensions have been constructed and subject to analysis using laser doppler interferometry. This analysis tool was used to implement a fill modal analysis in order to experimentally derive dynamic parameters. The characteristic resonance frequencies of these cantilevers have been measured, with 3.14kHz, 23.79kHz, 37.94kHz and 71.22kHz being the typical frequencies of the first four resonant modes. Q-factors of 912, 532, 1490 and 752 have been measured for these modes respectively at 0.01mbar ambient pressure. Additionally the mode shapes of each resonance was derived experimentally and found to be in excellent agreement with finite element predictions. A 4mm nickel ring gyroscope structure has been constructed and analysed using both optical analysis tools and electrical techniques. Using laser doppler interferometry the first four out-of-plane modes of the ring structure were found to be typically 9.893 kHz, 11.349 kHz, 11.418 kHz and 13.904 kHz with respective Q-factors of 1151, 1659, 1573 and 1407 at 0.01 mbar ambient pressure. Although electrical measurements were found to be obscured through cross coupling between drive and detection circuitry, the in-plane operational modes of the gyroscope were sucessfully determined. The Cos2Ө and Sin2Ө operational modes were measured at 36.141 kHz and 36.346 kHz, highlighting a frequency split of 205kHz. Again all experimentally derived modal parameters were in good agreement with finite element predictions. Furthermore, using the analysis model, the angular resolution of the gyroscope has been predicted to be approximately 4.75º/s

Stochastic Stability and Uncertainty Quantification of Ring-based Vibratory Gyroscopes

Effect of stochastic fluctuations in angular velocity on the stability of two DOF ring-type MEMS gyroscopes is investigated. The governing Stochastic Differential Equations are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of Largest Lyapunov Exponents are employed for validation purposes due to lack of similar analytical or experimental data. The stability investigation predicts that the threshold fluctuation intensity increases nonlinearly with damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability. Furthermore, construction, electrical improvements, testing and troubleshooting of a macro-scale ring-type gyroscope prototype is completed. Experiments have been conducted in order to investigate the linearity of system response, system behavior when subjected to environmental fluctuation in angular rate as well as the effects of angular rate and mass mismatch on system natural frequency. It is shown that the system natural frequency decreases with input angular rate and mass mismatch. It is also revealed that the system exhibits a more efficient damping behavior when subjected to stochastic speed fluctuations with fixed intensity at higher input angular rates

Thin-Film AlN-on-Silicon Resonant Gyroscopes: Design, Fabrication, and Eigenmode Operation

Resonant MEMS gyroscopes have been rapidly adopted in various consumer, industrial, and automotive applications thanks to the significant improvements in their performance over the past decade. The current efforts in enhancing the performance of high-precision resonant gyroscopes are mainly focused on two seemingly contradictory metrics, larger bandwidth and lower noise level, to push the technology towards navigation applications. The key enabling factor for the realization of low-noise high-bandwidth resonant gyroscopes is the utilization of a strong electromechanical transducer at high frequencies. Thin-film piezoelectric-on-silicon technology provides a very efficient transduction mechanism suitable for implementation of bulk-mode resonant gyroscopes without the need for submicron capacitive gaps or large DC polarization voltages. More importantly, in-air operation of piezoelectric devices at moderate Q values allows for the cointegration of mode-matched gyroscopes and accelerometers on a common substrate for inertial measurement units. This work presents the design, fabrication, characterization, and method of mode matching of piezoelectric-on-silicon resonant gyroscopes. The degenerate in-plane flexural vibration mode shapes of the resonating structure are demonstrated to have a strong gyroscopic coupling as well as a large piezoelectric transduction coefficient. Eigenmode operation of resonant gyroscopes is introduced as the modal alignment technique for the piezoelectric devices independently of the transduction mechanism. Controlled displacement feedback is also employed as the frequency matching technique to accomplish complete mode matching of the piezoelectric gyroscopes.Ph.D

Thermomechanical and mechanical characterization of a 3-axial MEMS gyroscope

Työn tavoitteena oli automaattisten, tehokkaiden ja edullisten testauslaitteistojen ja -menetelmien kehittäminen kolmiakselisten mikroelektromekaanisten (MEMS) gyroskooppien mekaaniseen ja termomekaaniseen karakterisointiin. Työn painotuksena oli testausmenetelmien ja -laitteistojen kehittäminen ja gyroskooppien vaurioanalyysit jäävät tämän työn ulkopuolelle. Gyroskooppi on kulmanopeuden mittaamiseen ja asennon aistimiseen käytettävä anturi. Mekaaninen karakteristointi kattaa gyroskooppien korkean G-arvon iskumaiset kuormitukset ja tärinäkuormitukset. Lämpömekaaninen karakterisointi kattaa gyroskooppien ympäristöolojen kontrolloimista lämpö-, kosteus- tai monikaasu -kaapissa. Tässä työssä kehitettiin menetelmä kolmiakselisten MEMS-gyroskooppien karakterisointiin lämpö- ja kosteuskaapissa. Menetelmä koostuu yksiakselisesta servomoottorista, servo-ohjaimesta ja ohjaussovelluksesta, jonka avulla voidaan samanaikaisesti mitata ja tallentaa gyroskooppien kulmanopeus kaikilta kolmelta (X, Y ja Z) akselilta sekä mitata ympäristön lämpötilaa. Korkean G-arvon iskumaisiin kuormituksiin tarkoitettu laitteisto koostuu pneumaattisesta iskutestauslaitteesta, jossa käytetään mekaanista iskua korkean G-arvon saavuttamiseen. Olemassa olevaa laitteistoa muutettiin siten että sillä voidaan saavuttaa suurempia G-arvoja (aina 80 000G:hen asti) ja mahdollistaa gyroskooppien tutkiminen eri asennoissa. Tärinäkuormituslaittesto koostuu signaaligeneraattorista ja täristinmoottorista, joka soveltuu gyroskooppien tärinätestaukseen. Signaaligeneraattoria käytetään eri taajuisten signaalimuotojen syöttämiseen täristinmoottorille, joka tärisee annetun syötteen mukaisesti. Pyörityslaitteen toiminnallisuutta testattiin yhdellä gyroskoopilla huoneenlämmössä. Gyroskoopin X, Y ja Z-akselien kulmanopeuksien keskiarvot sekä -hajonta mitattiin. Korkean g-arvon iskutestauslaitteistoa testattiin kuudella mittauksella, jossa gyroskoopit rikkoutuivat ensimmäisellä iskulla. Tärinätestauslaitteistoa testattiin yhdellä gyroskooppi-piirilevyllä. Gyroskooppi-piirilevyn päälle asetettiin kiihtyvyysanturi, jolla mitattiin tärinästä aiheutuvan kiihtyvyyden RMS-arvo, huippuarvo ja kokonaisenergia. Tulevat jatkotutkimukset keskittyvät pyöritys-, isku- ja tärinälaitteistoilla testattujen MEMS-gyroskooppien vaurioanalyysiin.The purpose of this thesis was to develop automated, efficient and economical methods for the mechanical and thermomechanical characterization of a digital 3-axial microelectromechanical systems (MEMS) gyroscope. The development of the test equipment and methods was the emphasis of this thesis, but the failure analyses of MEMS gyroscopes are beyond the scope of this work. A gyroscope is a device for measuring angular velocity and sensing change in orientation around its X, Y and Z-axis. The experimental part is divided into two sections, of which the first one is focused on high-G shock impact and vibration loading and the second on thermomechanical characterization. A rotation device was developed for the characterization of the MEMS gyroscopes in a temperature and humidity chamber. The rotation device consists of a oneaxial servo-motor, a servo-drive and a control program for the readout of angular velocity. The device is capable of simultaneously recording the angular velocities of the gyroscopes from all three axes while rotating the gyroscopes around a single axis. The device also records the temperature of the environment. The high-G shock impact equipment consists of a pneumatically assisted shock tester that relies on mechanical impact to generate the high-G shock pulse. An existing mechanical shock impact system was modified to gain higher G-values (up to 80 000G) and to enable the inspection of gyroscopes in different orientations. The vibration test equipment consists of a waveform generator and a vibration shaker, for the vibration testing of gyroscopes. The waveform generator is capable of outputting different waveforms with different frequencies to the shaker that vibrates with the given output. The functionality of the rotation device was tested with rotating one gyroscope board at room temperature. Respective averages and standard deviations of angular velocities were measured in the direction of X, Y and Z axes. The functionality of the high-G shock impact test equipment was verified with six measurements where all of the gyroscopes failed on first impact. The vibration test equipment was tested with one gyroscope board. Root mean square (RMS), peak value and total energy of acceleration were measured with an accelerometer placed on top of the vibrating gyroscope board

Design and implementation of a control scheme for a MEMS rate integrating gyroscope

PhD ThesisMEMS gyroscopes are found across a large range of applications, from low precision low cost applications through to high budget projects that require almost perfect accuracy. MEMS gyroscopes fall into two categories – ‘rate’ and ‘rate integrating’, with the latter offering superior performance. The key advantage that the rate integrating type possesses is that it directly measures angle, eliminating the need for any integration step. This reduces the potential for errors, particularly at high rates. However, the manufacturing precision required is far tighter than that of the rate gyroscope, and this has thus far limited the development of rate integrating gyroscopes. This thesis proposes a method for reducing the effect of structural imperfections on the performance of a rate integrating gyroscope. By taking a conventional rate gyroscope and adjusting its control scheme to operate in rate integrating mode, the thesis shows that it is possible to artificially eliminate the effect of some structural imperfections on the accuracy of angular measurement through the combined use of electrostatic tuning and capacitive forcing. Further, it demonstrates that it is viable to base the designs for rate integrating gyroscopes on existing rate gyroscope architectures, albeit with some modifications. Initially, the control scheme is derived through the method of multiple scales and its potential efficacy demonstrated through computational modelling using Simulink. The control scheme is then implemented onto an existing rate gyroscope architecture, with a series of tests conducted that benchmark the gyroscope performance in comparison to standard performance measures. Experimental work demonstrates the angle measurement capability of the rate integrating control scheme, with the gyroscope shown to be able to measure angle, although not to the precision necessary for commercial implementation. However, the scheme is shown to be viable with some modifications to the gyroscope architecture, and initial tests on an alternative architecture based on these results are presented.United Technologies and System

High-Q Fused Silica Micro-Shell Resonators for Navigation-Grade MEMS Gyroscopes

This research aims to develop the resonator for a navigation-grade microelectromechanical system (MEMS) Coriolis vibratory gyroscope (CVG) that will bring inertial navigation capabilities to a wider range of applications by reducing gyroscope size and cost. To achieve the desired gyroscope performance, the gyroscope resonator must have low energy dissipation and a highly symmetric structure. Several challenges arise at the micro-scale due to the increased sensitivity to imperfections and increased susceptibility to energy loss mechanisms. This work investigates the lower limit on energy dissipation in a micro-shell resonator known as the birdbath (BB) resonator. The BB resonator is designed to mitigate the energy loss mechanisms that commonly limit MEMS resonators, including anchor loss and thermoelastic dissipation, through a unique shape and fabrication process and through the use of fused silica as the structural material. A blowtorch molding process is used to form high aspect ratio fused silica shells with a range of wall profiles, providing a high level of control in three dimensions that is not possible with conventional micromachining techniques. Prototype BB resonators were developed prior to this dissertation work but they achieved low quality factors (Q) and low ring-down time constants (T) on the order of 100 thousand and 1 s, respectively. The goal of this work is to drastically increase performance above these initial results. Each relevant energy loss mechanism is considered in order to identify the dominant loss mechanism for a given device. Process improvements are implemented to mitigate each loss mechanism, including improved thermal management during blowtorch molding, cleaner lapping and polishing, reduced upfront surface contamination, and methods to remove contaminants after fabrication. Following optimization, Qs up to 10 million and Ts up to 500 s are measured, representing a marked improvement over the prototype resonators. It is found that BB resonators are now limited by surface loss, as indicated by the observed inverse relationship between Q and surface-to-volume ratio. The surface-loss-limited regime results in a high sensitivity to added surface layers. The addition of a conductive layer to enable electrostatic transduction is found to have a large impact, decreasing Q by 50% with the addition of only 30 angstroms of metal. It is suggested that the origin of this loss may be interfacial slippage due to a large increase in stress that occurs at the interface during oscillation. Experimental investigation into the dependence of Q on conductive layer composition, thickness, deposition conditions, and post-deposition treatments is carried out. Following treatments to removed adsorbed contaminants from the surface, resonators with a 15/50 angstrom Ti/Pt layer are found to maintain 60% of their initial Qs. Indium tin oxide (ITO) is identified as a promising conductive layer candidate, with initial experiments producing shells that maintain 70% of their initial Q. The values of Q and T produced in this work are unprecedented for MEMS resonators. Even accounting for the losses that accompany conductive layer deposition, birdbath resonator gyroscopes are expected to achieve navigation-grade performance.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146096/1/taln_1.pd

The Inhomogeneous Waves in a Rotating Piezoelectric Body

This paper presents the analysis and numerical results of rotation, propagation angle, and attenuation angle upon the waves propagating in the piezoelectric body. Via considering the centripetal and Coriolis accelerations in the piezoelectric equations with respect to a rotating frame of reference, wave velocities and attenuations are derived and plotted graphically. It is demonstrated that rotation speed vector can affect wave velocities and make the piezoelectric body behaves as if it was damping. Besides, the effects of propagation angle and attenuation angle are presented. Critical point is found when rotation speed is equal to wave frequency, around which wave characteristics change drastically

Design and Analysis of Extremely Low-Noise MEMS Gyroscopes for Navigation

Inertial measurement sensors that include three gyroscopes and three accelerometers are key elements of inertial navigation systems. Miniaturization of these sensors is desirable to achieve low manufacturing cost, high durability, low weight, small size, and low energy consumption. However, there is a tradeoff between miniaturization of inertial sensors and their performance. Developing all the necessary components for navigation using inertial sensors in a small volume requires major redesign and innovation in these sensors. The main goal of this research is to identify, analyze and optimize parameters that limit the performance of miniaturized inertial gyroscopes and provide comprehensive design guidelines for achieving multi-axis navigation-grade MEMS gyroscopes. It is shown that the fundamental performance limit of inertial gyroscopes is angle random walk (ARW) due to thermo-mechanical and electronic noises. Theoretical models show that resonant frequency, frequency mismatch between sensing and driving modes, effective mass, quality factor (Q), driving amplitude, sensing gap, sensing area and angular gain are the most important parameters that need to be optimized for best noise and most practical device design. In this research, two different structures are considered for low-noise MEMS gyroscopes: 1) shell gyroscopes in yaw direction, and 2) a novel super sensitive stacked (S3) gyroscope for pitch/roll directions. Extensive analytical and FEM numerical modeling was conducted throughout this research to investigate the mechanisms that affect Q and noise in shell resonators used in yaw-rate gyroscopes. These models provided insight into ways to significantly improve resonator design, structure, fabrication, and assembly and helped fabricate fused silica shells with Qs as high as 10 million (at least an order of magnitude larger than other similar shells). Noise performance of these fused silica shell gyroscopes with 5 mm dimeter improved by about two orders of magnitude (< 5×10-3 °/√hr), representing one of the best noise performances reported for a MEMS gyroscope. To build a high-performance MEMS-based planar vibratory pitch/roll gyroscope, it is critical to have a resonator with high Q in the out-of-plane resonant mode. Existing out-of-plane resonators suffer from low Q due to anchor loss or/and thermoelastic dissipation (TED). Increasing the thickness of the out-of-plane resonator reduces TED, but this increases the anchor loss. To reduce anchor loss significantly, a novel structure called S3 is designed. In this structure, two similar resonators are stacked on top of each other and move in opposite directions, thus providing a balanced stacked resonator with reduced anchor loss. The reduction of anchor loss allows larger thickness of silicon S3 gyroscopes, leading to a very low TED. A large-scale model of a stacked balanced resonator is fabricated and tested. The initial results show more than 50 times improvement in Q (measured in air) when resonators are stacked. It is expected that by testing this device in vacuum, Q would improve by more than three orders of magnitude. The S3 design also has an extremely large effective mass, a very large angular gain, a large driving amplitude, a very small sensing gap, and a large sensing area. It is estimated that a 500 µm thick silicon S3 gyroscope provides ARW of about 1.5×10-5 °/√hr (more than two orders of magnitude better performance than a navigation-grade gyroscope). This extraordinary small value can be improved for 1mm thick fused silica to 7.6×10-7 °/√hr if the technology for etching fused silica could be developed in the future.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147701/1/darvishi_1.pd