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.

Table of Contents:
List of Abbreviations ix Preface xi About the Authors xiii Part I Fundamentals of Whole-Angle Gyroscopes 1 1 Introduction 3 1.1 Types of Coriolis Vibratory Gyroscopes 3 1.1.1 Nondegenerate Mode Gyroscopes 4 1.1.2 Degenerate Mode Gyroscopes 5 1.2 Generalized CVG Errors 5 1.2.1 Scale Factor Errors 7 1.2.2 Bias Errors 7 1.2.3 Noise Processes 7 1.2.3.1 Allan Variance 7 1.3 Overview 9 2 Dynamics 11 2.1 Introduction to Whole-Angle Gyroscopes 11 2.2 Foucault Pendulum Analogy 11 2.2.1 Damping and Q-factor 12 2.2.1.1 Viscous Damping 13 2.2.1.2 Anchor Losses 14 2.2.1.3 Material Losses 15 2.2.1.4 Surface Losses 16 2.2.1.5 Mode Coupling Losses 16 2.2.1.6 Additional Dissipation Mechanisms 16 2.2.2 Principal Axes of Elasticity and Damping 16 2.3 Canonical Variables 18 2.4 Effect of Structural Imperfections 18 2.5 Challenges of Whole-Angle Gyroscopes 20 3 Control Strategies 23 3.1 Quadrature and Coriolis Duality 23 3.2 Rate Gyroscope Mechanization 24 3.2.1 Open-loop Mechanization 24 3.2.1.1 Drive Mode Oscillator 24 3.2.1.2 Amplitude Gain Control 26 3.2.1.3 Phase Locked Loop/Demodulation 26 3.2.1.4 Quadrature Cancellation 26 3.2.2 Force-to-rebalance Mechanization 27 3.2.2.1 Force-to-rebalance Loop 27 3.2.2.2 Quadrature Null Loop 29 3.3 Whole-Angle Mechanization 29 3.3.1 Control System Overview 30 3.3.2 Amplitude Gain Control 32 3.3.2.1 Vector Drive 32 3.3.2.2 Parametric Drive 33 3.3.3 Quadrature Null Loop 34 3.3.3.1 AC Quadrature Null 34 3.3.3.2 DC Quadrature Null 34 3.3.4 Force-to-rebalance and Virtual Carouseling 35 3.4 Conclusions 35 Part II 2-D Micro-Machined Whole-Angle Gyroscope Architectures 37 4 Overview of 2-D Micro-Machined Whole-Angle Gyroscopes 39 4.1 2-D Micro-Machined Whole-Angle Gyroscope Architectures 39 4.1.1 Lumped Mass Systems 39 4.1.2 Ring/Disk Systems 40 4.1.2.1 Ring Gyroscopes 40 4.1.2.2 Concentric Ring Systems 41 4.1.2.3 Disk Gyroscopes 42 4.2 2-D Micro-Machining Processes 42 4.2.1 Traditional Silicon MEMS Process 43 4.2.2 Integrated MEMS/CMOS Fabrication Process 43 4.2.3 Epitaxial Silicon Encapsulation Process 44 5 Example 2-D Micro-Machined Whole-Angle Gyroscopes 47 5.1 A Distributed Mass MEMS Gyroscope – Toroidal Ring Gyroscope 47 5.1.1 Architecture 48 5.1.1.1 Electrode Architecture 49 5.1.2 Experimental Demonstration of the Concept 49 5.1.2.1 Fabrication 49 5.1.2.2 Experimental Setup 50 5.1.2.3 Mechanical Characterization 51 5.1.2.4 Rate Gyroscope Operation 52 5.1.2.5 Comparison of Vector Drive and Parametric Drive 53 5.2 A Lumped Mass MEMS Gyroscope – Dual Foucault Pendulum Gyroscope 54 5.2.1 Architecture 56 5.2.1.1 Electrode Architecture 57 5.2.2 Experimental Demonstration of the Concept 57 5.2.2.1 Fabrication 57 5.2.2.2 Experimental Setup 58 5.2.2.3 Mechanical Characterization 60 5.2.2.4 Rate Gyroscope Operation 60 5.2.2.5 Parameter Identification 60 Part III 3-D Micro-Machined Whole-Angle Gyroscope Architectures 65 6 Overview of 3-D Shell Implementations 67 6.1 Macro-scale Hemispherical Resonator Gyroscopes 67 6.2 3-D Micro-Shell Fabrication Processes 69 6.2.1 Bulk Micro-Machining Processes 69 6.2.2 Surface-Micro-Machined Micro-Shell Resonators 74 6.3 Transduction of 3-D Micro-Shell Resonators 79 6.3.1 Electromagnetic Excitation 79 6.3.2 Optomechanical Detection 80 6.3.3 Electrostatic Transduction 81 7 Design and Fabrication of Micro-glassblown Wineglass Resonators 87 7.1 Design of Micro-Glassblown Wineglass Resonators 88 7.1.1 Design of Micro-Wineglass Geometry 90 7.1.1.1 Analytical Solution 90 7.1.1.2 Finite Element Analysis 92 7.1.1.3 Effect of Stem Geometry on Anchor Loss 94 7.1.2 Design for High Frequency Symmetry 96 7.1.2.1 Frequency Symmetry Scaling Laws 97 7.1.2.2 Stability of Micro-Glassblown Structures 101 7.2 An Example Fabrication Process for Micro-glassblown Wineglass Resonators 102 7.2.1 Substrate Preparation 103 7.2.2 Wafer Bonding 103 7.2.3 Micro-Glassblowing 104 7.2.4 Wineglass Release 105 7.3 Characterization of Micro-Glassblown Shells 106 7.3.1 Surface Roughness 107 7.3.2 Material Composition 108 8 Transduction of Micro-Glassblown Wineglass Resonators 111 8.1 Assembled Electrodes 111 8.1.1 Design 111 8.1.2 Fabrication 112 8.1.2.1 Experimental Characterization 113 8.2 In-plane Electrodes 115 8.3 Fabrication 115 8.4 Experimental Characterization 118 8.5 Out-of-plane Electrodes 123 8.6 Design 123 8.7 Fabrication 126 8.8 Experimental Characterization 129 9 Conclusions and Future Trends 133 9.1 Mechanical Trimming of Structural Imperfections 133 9.2 Self-calibration 134 9.3 Integration and Packaging 135 References 137 Index 149