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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: IEEE Press Series on Sensors
- Sprache: Englisch
Presents the mathematical framework, technical language, and control systems know-how needed to design, develop, and instrument micro-scale whole-angle gyroscopes This comprehensive reference covers the technical fundamentals, mathematical framework, and common control strategies for degenerate mode gyroscopes, which are used in high-precision navigation applications. It explores various energy loss mechanisms and the effect of structural imperfections, along with requirements for continuous rate integrating gyroscope operation. It also provides information on the fabrication of MEMS whole-angle gyroscopes and the best methods of sustaining oscillations. Whole-Angle Gyroscopes: Challenges and Opportunities begins with a brief overview of the two main types of Coriolis Vibratory Gyroscopes (CVGs): non-degenerate mode gyroscopes and degenerate mode gyroscopes. It then introduces readers to the Foucault Pendulum analogy and a review of MEMS whole angle mode gyroscope development. Chapters cover: dynamics of whole-angle coriolis vibratory gyroscopes; fabrication of whole-angle coriolis vibratory gyroscopes; energy loss mechanisms of coriolis vibratory gyroscopes; and control strategies for whole-angle coriolis vibratory gyro- scopes. The book finishes with a chapter on conventionally machined micro-machined gyroscopes, followed by one on micro-wineglass gyroscopes. In addition, the book: * Lowers barrier to entry for aspiring scientists and engineers by providing a solid understanding of the fundamentals and control strategies of degenerate mode gyroscopes * Organizes mode-matched mechanical gyroscopes based on three classifications: wine-glass, ring/disk, and mass spring mechanical elements * Includes case studies on conventionally micro-machined and 3-D micro-machined gyroscopes Whole-Angle Gyroscopes is an ideal book for researchers, scientists, engineers, and college/graduate students involved in the technology. It will also be of great benefit to engineers in control systems, MEMS production, electronics, and semi-conductors who work with inertial sensors.
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Veröffentlichungsjahr: 2020
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Table of Contents
Cover
List of Abbreviations
Preface
About the Authors
Part I: Fundamentals of Whole‐Angle Gyroscopes
1 Introduction
1.1 Types of Coriolis Vibratory Gyroscopes
1.2 Generalized CVG Errors
1.3 Overview
2 Dynamics
2.1 Introduction to Whole‐Angle Gyroscopes
2.2 Foucault Pendulum Analogy
2.3 Canonical Variables
2.4 Effect of Structural Imperfections
2.5 Challenges of Whole‐Angle Gyroscopes
3 Control Strategies
3.1 Quadrature and Coriolis Duality
3.2 Rate Gyroscope Mechanization
3.3 Whole‐Angle Mechanization
3.4 Conclusions
Part II: 2‐D Micro‐Machined Whole‐Angle Gyroscope Architectures
4 Overview of 2‐D Micro‐Machined Whole‐Angle Gyroscopes
4.1 2‐D Micro‐Machined Whole‐Angle Gyroscope Architectures
4.2 2‐D Micro‐Machining Processes
5 Example 2‐D Micro‐Machined Whole‐Angle Gyroscopes
5.1 A Distributed Mass MEMS Gyroscope – Toroidal Ring Gyroscope
5.2 A Lumped Mass MEMS Gyroscope – Dual Foucault Pendulum Gyroscope
Part III: 3‐D Micro‐Machined Whole‐Angle Gyroscope Architectures
6 Overview of 3‐D Shell Implementations
6.1 Macro‐scale Hemispherical Resonator Gyroscopes
6.2 3‐D Micro‐Shell Fabrication Processes
6.3 Transduction of 3‐D Micro‐Shell Resonators
7 Design and Fabrication of Micro‐glassblown Wineglass Resonators
7.1 Design of Micro‐Glassblown Wineglass Resonators
7.2 An Example Fabrication Process for Micro‐glassblown Wineglass Resonators
7.3 Characterization of Micro‐Glassblown Shells
8 Transduction of Micro‐Glassblown Wineglass Resonators
8.1 Assembled Electrodes
8.2 In‐plane Electrodes
8.3 Fabrication
8.4 Experimental Characterization
8.5 Out‐of‐plane Electrodes
8.6 Design
8.7 Fabrication
8.8 Experimental Characterization
9 Conclusions and Future Trends
9.1 Mechanical Trimming of Structural Imperfections
9.2 Self‐calibration
9.3 Integration and Packaging
References
Index
IEEE Press Series on Sensors
End User License Agreement
List of Tables
List of Abbreviations
Table 1 Control system abbreviations.
Table 2 Mechanical parameters of the resonator.
Chapter 5
Table 5.1 Summary of design parameters.
Table 5.2 As‐fabricated frequency symmetry of four devices.
Table 5.3 Summary of design parameters.
Chapter 7
Table 7.1 Comparison of wineglass dimensions obtained from analytical solutio...
Table 7.2 Anchor loss analysis shows a large change in
for different stem di...
Table 7.3 Sample design parameters for micro‐glassblown mushroom structure.
Table 7.4 Sample design parameters for micro‐glassblown hemisphere.
Chapter 8
Table 8.1 Table summarizing frequency splits and center frequency of five dif...
Table 8.2 Summary of device parameters for a 7 mm fused silica wineglass reso...
List of Illustrations
Chapter 1
Figure 1.1 Coriolis Vibratory Gyroscopes, in their simplest form, consist of...
Figure 1.2 Micro‐rate integrating gyroscope (MRIG) architectures.
Figure 1.3 Sample Allan variance analysis of gyroscope output, showing error...
Chapter 2
Figure 2.1 Foucault Pendulum is a proof mass suspended from a long string th...
Figure 2.2 Misalignment in principal axes of (a) elasticity and (b) damping ...
Figure 2.3 Elliptical orbit of a CVG and the canonical variables.
Chapter 3
Figure 3.1 Quadrature signal can be separated from Coriolis signal via synch...
Figure 3.2 Open‐loop mechanization utilizes no feedback loop in the sense mo...
Figure 3.3 Force‐to‐rebalance utilizes feedback loops in both the drive (
) ...
Figure 3.4 Whole‐angle gyroscope control with (optional) parametric drive.
Chapter 4
Figure 4.1 Traditional silicon MEMS encapsulation process consists of: (a) f...
Figure 4.2 Integrated MEMS/CMOS fabrication process consists of: (a) pre‐etc...
Figure 4.3 Epitaxial Silicon Encapsulation (EpiSeal) process consists of: (a...
Chapter 5
Figure 5.1 Ring/disk gyroscopes can be anchored (a) at the outer perimeter o...
Figure 5.2 A 100k
‐factor, epitaxial silicon encapsulated Toroidal Ring Gyr...
Figure 5.3 In this implementation, the central electrode assembly consists o...
Figure 5.4 Due to the distributed suspension system vibrational energy is tr...
Figure 5.5 Frequency sweep showing the
wineglass modes with
‐factor above...
Figure 5.6 Electrostatic tuning with 3.26 and 0.5 V resulted in
(
at
)....
Figure 5.7 Scale factor of Toroidal Ring Gyroscope in force‐to‐rebalance mod...
Figure 5.8 Allan Variance of gyroscope in the force‐to‐rebalance mechanizati...
Figure 5.9 Experimental demonstration of rate integrating operation under pa...
Figure 5.10 Comparison of residual errors of conventional drive and parametr...
Figure 5.11 Wineglass modes of axisymmetric architectures, such as ring/disk...
Figure 5.12 Dual Foucault Pendulum (DFP) gyroscope consists of two mechanica...
Figure 5.13 Vibration immunity and anchor loss mitigation are provided by an...
Figure 5.14 FEA showing
–
symmetric anti‐phase operation. Device is anchor...
Figure 5.15 Image of fabricated gyroscope with closeups of the shuttle assem...
Figure 5.16 High‐vacuum test‐bed with nonevaporable getter pump provided
To...
Figure 5.17 Ring‐down experiment showing energy decay time constant (
) of 3...
Figure 5.18 Rate characterization with
s step input showed a FRB scale fact...
Figure 5.19 Allan Variance of the gyroscope's zero rate output, showing ARW ...
Figure 5.20 Polar plots showing the pattern angle dependence of four main cl...
Figure 5.21 Spooling of the whole‐angle gyro output over 2 h of continuous r...
Chapter 6
Figure 6.1 Northrop Grumman HRG uses a double‐stemmed fused silica wineglass...
Figure 6.2 SAGEM HRG uses a mushroom/bell type fused silica resonator [88]....
Figure 6.3 Cross‐sectional view of various micro‐shell resonator geometries:...
Figure 6.4 Micro‐shell fabrication processes can be categorized into two mai...
Figure 6.5 Arrays of spherical shells were created by bonding borosilicate g...
Figure 6.6 3‐D metal traces can be fabricated on the surface of glass shells...
Figure 6.7 Bulk metallic glass shell structures are inherently conductive, e...
Figure 6.8 Blow‐torch molded birdbath shell resonator [103].
Figure 6.9 Fused silica spheres were micro‐machined into 3‐D shell structure...
Figure 6.10 Silicon dioxide shells were formed by isotropic etching of silic...
Figure 6.11 Hemispherical shell structures were fabricated by isotropically ...
Figure 6.12 SEM image of arrays of 1 mm diameter released polycrystalline di...
Figure 6.13 Cylindrical polycrystalline diamond shells can be created if the...
Figure 6.14 SEM image of an all‐dielectric cylindrical shell [116].
Figure 6.15 Diamond hemisphere deposited into a pre‐etched glass cavity and ...
Figure 6.16 Thin film sputtered ULE (Ultra Low Expansion Glass) shells were ...
Figure 6.17 Hemitoroidal polycrystalline diamond shell structure [123].
Figure 6.18 SEM image of extremely small (200 μm diameter) cenosphere‐derive...
Figure 6.19 Highly doped silicon electrodes adjacent to a
micro‐shell, fri...
Figure 6.20 Blow‐torch molded fused silica micro‐shell resonator with silico...
Figure 6.21 Polydiamond micro‐shell resonator with integrated electrodes [11...
Figure 6.22 Bulk Metallic Glass (BMG) micro‐shell resonator with integrated ...
Figure 6.23 Micro‐shell resonator with polysilicon electrodes [111]. The ele...
Figure 6.24 Silicon electrodes for “Poached Egg” micro‐shell resonators [118...
Chapter 7
Figure 7.1 ULE TSG/fused silica micro‐glassblowing process, consists of: (a)...
Figure 7.2 Small central post diameters create solid stem structures (left),...
Figure 7.3 Geometric parameters of an inverted‐wineglass structure: Minor ra...
Figure 7.4 Analytical solution of etch depth (
), wineglass diameter (
) ver...
Figure 7.5 Boundary conditions for finite element analysis: (a) before glass...
Figure 7.6 Transient FEA of micro‐glassblowing process showing the formation...
Figure 7.7 Finite element predictions and cross‐sectional SEM shots of fabri...
Figure 7.8 Wineglass structures with (a) 1.2 mm outer diameter and 600 μm st...
Figure 7.9 Mode shapes and minimal electrode configuration required for
(a...
Figure 7.10 Polar plots showing the first four harmonics of thickness imperf...
Figure 7.11 Sketch of an ideal wineglass (perfectly spherical), showing
as...
Figure 7.12 Plot showing wineglass thickness versus thickness imperfections ...
Figure 7.13 The effect of thickness variation of the fourth harmonic on freq...
Figure 7.14 Surface tension‐induced pressure differential depends on geometr...
Figure 7.15 Custom‐built micro‐glassblowing furnace with process capability ...
Figure 7.16 Optical photograph of glassblown fused silica inverted‐wineglass...
Figure 7.17 Optical photograph of fused silica spherical shell structures, g...
Figure 7.18 Optical photograph of inverted‐wineglass, released along the per...
Figure 7.19 AFM surface profiles of TSG, (a) before and (b) after glassblowi...
Figure 7.20 Slow cooling of TSG (
8 h) causes recrystallization [13].
Figure 7.21 Glassblowing with rapid cooling of TSG (
1 min) prevents recrys...
Figure 7.22 EDS spectral analysis of TSG and fused silica reveals that compo...
Chapter 8
Figure 8.1 Electrodes are fabricated separately on an SOI stack, bonded to t...
Figure 8.2 SEM image of an adjustable electrode with 400 μm maximum displace...
Figure 8.3 Ratchet mechanism acting on the electrode structure, the electrod...
Figure 8.4 Released wineglass structure with 4.2 mm diameter, 50 μm thicknes...
Figure 8.5 Electrode structures assembled onto a micro‐glassblown wineglass ...
Figure 8.6 Electrostatic frequency sweep using adjustable electrode assembly...
Figure 8.7 A glassblown spherical resonator with assembled electrodes. Diame...
Figure 8.8 Process flow for fabrication of micro‐glassblown wineglass resona...
Figure 8.9 SEM image of a stand‐alone micro‐wineglass structure after releas...
Figure 8.10 Metallized micro‐wineglass structure with integrated electrodes....
Figure 8.11 Packaged and wirebonded micro‐wineglass resonator. Diameter 4.4 ...
Figure 8.12 Laser Doppler Vibrometer was used to scan along the perimeter of...
Figure 8.13 Measured velocity amplitude distribution (mm/s) identifying (a)
Figure 8.14 Experimental frequency sweeps of
and
wineglass modes, showin...
Figure 8.15 Frequency split versus DC bias, showing that the frequency split...
Figure 8.16 Frequency sweeps of
mode of four additional wineglass resonato...
Figure 8.17 Micro‐glassblowing process can create arrays of inverted‐winegla...
Figure 8.18 Out‐of‐plane electrode architecture consists of a micro‐glassblo...
Figure 8.19 Out‐of‐plane transduction scheme utilizes out‐of‐plane component...
Figure 8.20 Electrode configuration: four electrodes are designated as force...
Figure 8.21 Out‐of‐plane to in‐plane displacement ratio for mushroom‐shaped ...
Figure 8.22 A packaged one million
‐factor fused silica wineglass structure...
Figure 8.23 Wafer‐level fabrication process for fused silica micro‐wineglass...
Figure 8.24 Uniform 10 μm capacitive gaps have been demonstrated on 7 mm she...
Figure 8.25 Frequency sweep revealed a
‐factor of 1.14 million and as fabri...
Figure 8.26 Ring‐down experiment at
shows
, giving 1.05 million
‐factor ...
Figure 8.27
‐factor versus pressure level experiment.
‐factors above 1 mil...
Chapter 9
Figure 9.1 Fabrication process consists of (a) bonding of pre‐etched cap and...
Guide
Cover
Table of Contents
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IEEE Press445 Hoes LanePiscataway, NJ 08854
IEEE Press Editorial BoardEkram Hossain, Editor in Chief
Jón Atli Benediktsson
David Alan Grier
Elya B. Joffe
Xiaoou Li
Peter Lian
Andreas Molisch
Saeid Nahavandi
Jeffrey Reed
Diomidis Spinellis
Sarah Spurgeon
Ahmet Murat Tekalp
Whole-Angle MEMS Gyroscopes
Challenges and Opportunities
Doruk Senkal
Andrei M. Shkel
Copyright © 2020 by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data is applied for
ISBN 9781119441885
Cover Design: WileyCover Image: Courtesy of Doruk Senkal
List of Abbreviations
Table 1 Control system abbreviations.
Symbol
Description
Quadrature
Unwanted component of oscillation that interferes with estimation of the pattern angle, manifests as a result of structural imperfections
AGC
Amplitude Gain Control, closed‐loop control of drive amplitude
PLL
Phase Locked Loop, closed‐loop control system that generates an AC signal with a predetermined phase offset from the resonator
FTR
Force‐to‐rebalance, closed‐loop control system that actively drives the pattern angle to a setpoint
Quadrature null
Closed‐loop control system that actively suppresses the effects of structural imperfections within the gyroscope
Table 2 Mechanical parameters of the resonator.
Symbol
Description
f
Mean frequency of the two primary modes of the resonator
τ
Mean energy decay time constant of the resonator
Q
‐factor
Ratio of stored energy to energy loss per vibration cycle (
Q
=
τπf
)
Δ
f
Frequency split between primary modes in Hz (Δ
f
=
f
x
−
f
y
)
Δ
ω
Frequency split between primary modes in rad/s (Δ
ω
=
ω
x
−
ω
y
)
Δ
τ
−1
Measure of anisodamping within the gyroscope (
)
θ
ω
Angle defining the orientation of actual versus intended axes of elasticity
θ
τ
Angle defining the orientation of actual versus intended axes of damping
(
x
,
y
,
z
)
Coordinate frame oriented along intended axes of symmetry
x
and
y
n
= 2 mode
A 4‐node degenerate mode pair of a wineglass or ring/disk system
n
= 3 mode
A 6‐node degenerate mode pair of a wineglass or ring/disk system
Precession pattern
Vibration pattern formed by superposition of
x
and
y
vibratory modes, which is capable of changing its orientation (precesses) when subjected to Coriolis forces or an external forcing function
Pattern angle (
θ
)
Orientation of the precession pattern in degrees, which is a measure of angular rotation in a Rate Integrating Gyroscope
Preface
Coriolis Vibratory Gyroscopes (CVGs) can be divided into two broad categories based on the gyroscope's mechanical element: degenerate mode gyroscopes (type 1), which have x–y symmetry, and nondegenerate mode gyroscopes (type 2), which are designed intentionally to be asymmetric in x and y modes.
Currently, nondegenerate mode gyroscopes fulfill the needs of a variety of commercial applications, such as tilt detection, activity tracking, and gaming. However, when it comes to inertial navigation, where sensitivity and stability of the sensors are very important, commercially available MEMS sensors fall short by three orders of magnitude. Degenerate mode gyroscopes, on the other hand, offer a number of unique advantages compared to nondegenerate vibratory rate gyroscopes, including higher rate sensitivity, ability to implement whole‐angle mechanization with mechanically unlimited dynamic range, exceptional scale factor stability, and a potential for self‐calibration. For this reason, as the MEMS gyroscope development is reaching maturity, the Research and Development focus is shifting from high‐volume production of low‐cost nondegenerate mode gyroscopes to high performance degenerate mode gyroscopes. This paradigm shift in MEMS gyroscope research and development creates a need for a reference book to serve both as a guide and an entry point to the field of degenerate mode gyroscopes.
Despite the growing interest in this field, the available information is scattered across a disparate group of conference proceedings and journal papers. For the aspiring scientist/engineer, the scarcity of information forms a large barrier to entry into the field of degenerate mode gyroscopes. This book aims to lower the barrier to entry by providing the reader with a solid understanding of the fundamentals of degenerate mode gyroscopes and its control strategies, as well as providing the necessary know‐how and technical jargon needed to interpret future publications in the field.
The book is intended to be a reference material for researchers, scientists, engineers, and college/graduate students who are interested in inertial sensors. The book may also be of interest to control systems engineers, electrical and electronics engineers, as well as semiconductor engineers who work with inertial sensors. Finally, materials scientists and MEMS production engineers may find the section regarding various fabrication technologies and fabrication defects/energy loss mechanisms interesting.
Doruk Senkal
Andrei M. Shkel
About the Authors
Doruk Senkal
Dr. Senkal has been working on the development of Inertial Navigation Technologies for Augmented and Virtual Reality applications at Facebook since 2018. Before joining Facebook, he was working as a MEMS designer at TDK Invensense, developing MEMS Inertial Sensors for mobile devices.
He received his PhD degree (2015) in Mechanical and Aerospace Engineering from the University of California, Irvine, with a focus on MEMS Coriolis Vibratory Gyroscopes, received his MSc degree (2009) in Mechanical Engineering from Washington State University with a focus on robotics, and received his BSc degree (2007) in Mechanical Engineering from Middle East Technical University.
His research interests, represented in over 20 international conference papers, 9 peer‐reviewed journal papers, and 16 patent applications, encompass all aspects of MEMS inertial sensor development, including sensor design, device fabrication, algorithms, and control.
Andrei M. Shkel
Prof. Shkel has been on faculty at the University of California, Irvine, since 2000. From 2009 to 2013, he was on leave from academia serving as a Program Manager in the Microsystems Technology Office of DARPA, where he initiated and managed over $200M investment portfolio in technology development. His research interests are reflected in over 250 publications, 40 patents, and 3 books. Dr. Shkel has been on a number of editorial boards, most recently as Editor of IEEE JMEMS and the founding chair of the IEEE Inertial Sensors (INERTIAL). He has been awarded in 2013 the Office of the Secretary of Defense Medal for Exceptional Public Service, 2020 Innovator of the Year Award, 2009 IEEE Sensors Council Technical Achievement Award, 2008 Researcher of the Year Award, and the 2005 NSF CAREER award. He received his Diploma with excellence (1991) in Mechanics and Mathematics from Moscow State University, PhD degree (1997) in Mechanical Engineering from the University of Wisconsin at Madison, and completed his postdoc (1999) at UC Berkeley. Dr. Shkel is the 2020–2022 President of the IEEE Sensors Council and the IEEE Fellow.
Part IFundamentals of Whole‐Angle Gyroscopes
1Introduction
Coriolis Vibratory Gyroscopes (CVGs) are mechanical transducers that detect angular rotation around a particular axis. In its most fundamental form, a CVG consists of two or more mechanically coupled vibratory modes, a forcing system to induce vibratory motion and a sensing system to detect vibratory motion. Angular rotation can be detected by sensing the energy transfer from one vibratory mode to another in the presense of Coriolis forces, Figure 1.1.
Historically, first examples of CVGs can be found in the Aerospace Industry, which were primarily used for navigation and platform stabilization applications. Later, advent of Micro‐electromechanical System (MEMS) fabrication techniques brought along orders of magnitude reduction in cost, size, weight, and power (CSWaP), which made CVGs truly ubiquitous. Today CVGs are used in a wide variety of civilian applications, examples include:
Industrial applications, such as robotics and automation;
Automobile stabilization, traction control, and roll‐over detection;
Gesture recognition and localization in gaming and mobile devices;
Optical image stabilization (OIS) of cameras;
Head tracking in Augmented Reality (AR) and Virtual Reality (VR);
Autonomous vehicles, such as self‐driving cars and Unmanned Aerial Vehicles (UAVs).
1.1 Types of Coriolis Vibratory Gyroscopes
CVGs can be divided into two broad categories based on the gyroscope's mechanical element [1]: degenerate mode (i.e. ‐axis) gyroscopes, which have – symmetry ( of 0 Hz), and nondegenerate mode gyroscopes, which are designed intentionally to be asymmetric in and modes (). Degenerate mode ‐axis gyroscopes offer a number of unique advantages compared to nondegenerate vibratory rate gyroscopes, including higher rate sensitivity, ability to implement whole‐angle mechanization with mechanically unlimited dynamic range, exceptional scale factor stability, and a potential for self‐calibration.
Figure 1.1 Coriolis Vibratory Gyroscopes, in their simplest form, consist of a vibrating element with two or more mechanically coupled vibratory modes. Illustration shows a ‐axis gyroscope and its vibratory modes along ‐ and ‐axis.
1.1.1 Nondegenerate Mode Gyroscopes
Nondegenerate mode CVGs are currently being used in a variety of commercial applications due to ease of fabrication and lower cost. Most common implementations utilize two to four vibratory modes for sensing angular velocity along one to three axes. This is commonly achieved by forcing a proof mass structure into oscillation in a so‐called “drive” mode and sensing the oscillation on one or more “sense” modes. For example, the ‐axis of the gyroscope in Figure 1.1, can be instrumented as a drive mode and the ‐axis can be instrumented as a sense mode. When a nonzero angular velocity is exerted (i.e. along the ‐axis in Figure 1.1), the resultant Coriolis force causes the sense mode (i.e. the mode along the ‐axis in Figure 1.1) to oscillate at the drive frequency at an amplitude proportional to input angular velocity.
Resonance frequency of sense modes are typically designed to be several hundreds to a few thousand hertzs away from the drive frequency. The existence of this so‐called drive‐sense separation () makes nondegenerate mode gyroscopes robust to fabrication imperfections. However, a trade‐off between bandwidth and transducer sensitivity exists since smaller drive‐sense separation frequency leads to higher transducer sensitivity, while the mechanical bandwidth of the sensor is typically limited by drive‐sense separation ().
