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 |  موضوع: رسالة دكتوراه بعنوان Vibration Isolation and Shock Protection for MEMS الخميس 21 يونيو 2012, 9:50 pm | |
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أحضرت لكم
رسالة دكتوراه بعنوان
Vibration Isolation and Shock Protection for MEMS
by Sang Won Yoon
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy (Electrical Engineering) in The University of Michigan
Doctoral Committee:
Professor Khalil Najafi, Co-Chair
Professor Noel C. Perkins, Co-Chair
Professor Karl Grosh
Professor Kensall D. Wise
Associate Professor Euisik Yoon
Research Scientist Sangwoo Lee
ويتناول الموضوعات الأتية :
TABLE OF CONTENTS
DEDICATION .ii
ACKNOWLEDGEMETNS iii
LIST OF FIGURES . viii
LIST OF TABLES xiv
LIST OF APPENDICES .xv
ABSTRACT .xvi
CHAPTER
1. INTRODUCTION .1
1.1. Shock Protection for MEMS .3
1.1.1. Shock from Environment .3
1.1.2. Shock Effects on MEMS 4
1.1.3. Shock Protection for MEMS 7
1.1.4. New Shock Protection Technologies for MEMS 11
1.2. Vibration Isolation for MEMS .13
1.2.1. Characterizing Vibration Environment 13
1.2.2. Vibration Effects on MEMS .14
1.2.3. Vibration Suppression for MEMS .15
1.2.3.1. Optimized Device Structure .16
1.2.3.2. Addition of Vibration Isolator .18
1.3. Principle Contributions 21
1.4. Organization of Dissertation 22
References . 23
2. VIBRATION EFFECTS ON MEMS .30
2.1. Vibration Effects on MEMS Devices and Selection of Gyroscope .30
2.2. Classification of MEMS Gyroscopes by Vibration Phenomena 31
2.3. Vibration Effects on Non-Degenerate Gyroscopes I
– Non-Tuning Fork Gyroscopes 36
2.4. Vibration Effects on Non-Degenerate Gyroscopes II
– Tuning Fork Gyroscopes 38
2.4.1. Modeling… .39
2.4.1.1. Equations of Motions… .40
2.4.1.2. Model Parameters… .42
2.4.2. Simulation Results… 43
2.4.3. Vibration-induced Error Sources in Tuning Fork Gyroscopes… .45
2.4.3.1. Error Source I – Capacitive nonlinearity at Sense Electrodes… 45
2.4.3.2. Error Source II – Capacitive nonlinearity at Drive Electrodes 1:
Asymmetric Electrostatic Force along Sense Direction at Drive
Electrodes… 49
2.4.3.3. Error Source III – Capacitive nonlinearity at Drive Electrodes 2:vi
Asymmetric Change of Comb-Drive Capacitance at Drive Electrodes… 50
2.4.3.4. Summary of Error Sources in the Three TFG Designs… .51
2.4.4. Dominant Error Source in Each Tuning Fork Gyroscope Design… 51
2.4.4.1. Dominant Error Source in Type-DD Gyroscopes… .51
2.4.4.2. Dominant Error Source in Type-CP and Type-DS Gyroscopes .51
2.5. Vibration Effects on Degenerate Gyroscopes – Ring Gyroscopes .53
2.5.1. Normal Mode Method 55
2.5.2. Mode Shapes .57
2.5.3. Assumptions 59
2.5.4. Kinetic Energy 60
2.5.5. Potential Energy I – Ring Structure .63
2.5.6. Potential Energy II – Support Beam Structure 65
2.5.7. Potential Energy III – Electrical Energy 67
2.5.8. Energy Lost by Viscous Damping .70
2.5.9. Lagrange Equation 70
2.5.10. Vibration-induced Error Sources at Sense Electrodes .73
2.6. Vibration Effects on MEMS Gyroscopes –Summary .75
References . 76
3. VIBRATION ISOLATION for MEMS 81
3.1. Benefits of Mechanical Low Pass Filter 81
3.2. Operation and Design of Low Pass Filter .83
3.3. Modeling and Design Guidance 85
3.4. Integration. .91
3.5. Design of Gyroscopes and Vibration Isolators by Applications 92
3.6. Summary 92
References . 93
4. NEW SHOCK PROTECTION CONCEPTS: THEORY and DESIGN .94
4.1. Underlying Principles 95
4.2. Design and Analysis I – Nonlinear Spring Shock Stops .98
4.2.1. Design of Nonlinear Spring Shock Stops 98
4.2.2. Definition of Parameters .100
4.2.3. Stiffness and Restoring Force of Shock Spring Structures .100
4.2.3.1. Stiffness and Restoring Force of Beam Cascade Structures .100
4.2.3.2. Stiffness of Single Beam with Nonlinear Hardening Effects .103
4.2.3.2.1. Linear and Nonlinear Stiffness of a Cantilever Beam 104
4.2.3.2.2. Linear and Nonlinear Stiffness of a Bridge Beam 105
4.2.3.2.3. Comparison of Nonlinearity in a Cantilever Beam and a
Bridge Beam .106
4.2.4. Design Considerations for Nonlinear Spring Shock Stops 107
4.2.4.1. Beam Cascade Structure 108
4.2.4.2. Single Beam with Nonlinear Hardening Effects .109
4.3. Simulation Results I – Nonlinear Spring Shock Stops .110
4.3.1. Nonlinear Spring I - Beam Cascade .111
4.3.2. Nonlinear Spring II - Single Nonlinear Bridge 112
4.3.2.1. Single Nonlinear Bridge .112
4.3.2.2. Single Nonlinear Cantilever .114
4.4. Design and Analysis II – Soft Coating Shock Stops .115
4.4.1. Design of Soft Coating Shock Stops 115vii
4.4.2. Damping in Soft Coating 116
4.4.3. Elasticity in Soft Coating 117
4.5. Simulation Results II – Soft Coating Shock Stops 118
4.5.1. Simulation Results of Damping Properties 118
4.5.2. Simulation Results of Elastic Properties 119
4.6. Limits of Proposed Approaches .121
4.7. Summary 122
References . 123
5. NEW SHOCK PROTECTION CONCEPTS: EXPERIMENTS and
DISCUSSIONS 124
5.1. Design of Shock Test Setup .124
5.1.1. Shock Test Methods .125
5.1.1.1. Shaker Table .125
5.1.1.2. Impact Hammer 126
5.1.1.3. Hopkinson Bar 126
5.1.1.4. Ballistic Test .127
5.1.1.5. Drop Machine (Drop Test) .127
5.1.2. Design of Shock Test Machine 128
5.1.3. Manufactured Drop Test Machine .129
5.1.4. Average and Peak Shock Load .131
5.2. Design of Shock-Test Devices .132
5.2.1. Fracture Stress of Silicon-based Microstructures 132
5.2.2. Design of Test Devices .135
5.2.3. Design of Nonlinear Spring Shock Stops 136
5.2.4. Design of Soft Coating Shock Stops 137
5.3. Test Device Fabrication .137
5.3.1. Devices with Nonlinear Spring Shock Stops .138
5.3.2. Devices with Soft Coating Shock Stops 139
5.4. Shock Test Results .142
5.4.1. Shock Test Process .142
5.4.2. Shock Test I – Comparison of Nonlinear-Spring-Stop Devices to HardStop Devices .142
5.4.3. Shock Test II – Comparison of Soft-Coating-Stop Devices to Hard-Stop
Devices 143
5.4.4. Summary of Shock Tests Comparison with Hard Shock Stops 144
5.4.5. Shock Test III – Tailor-Made Nonlinear Spring Shock Stops 145
5.5. Fracture Mechanism by Impact Force .148
5.5.1. Impact-Force-Induced Fracture in Our Test Devices 148
5.5.2. Impact-Force-Induced Fracture in Clamped-Clamped Beam Structure .150
5.6. Summary 150
References . 152
6. CONCLUSION 155
6.1. Conclusion 155
6.2. Suggestions For Future Work 157
6.2.1. Advanced Vibration Suppression Methods .157
6.2.2. Shock-Induced Device Fracture .158
APPENDICES 159viii
LIST OF FIGURES
Figure 1.1. MEMS damage by brittle fracture [23] .5
Figure 1.2. (a) Complex microengine used in shock tests [4] and (b) shock-induced
damage in simple comb-drive actuator (top) and an array of micro-cantilever
beams (bottom) [13] .6
Figure 1.3. Computed bending stress as a the function of the resonant frequency (or
stiffness of support beams) and shock amplitude 9
Figure 1.4. Conceptual design of hard shock stops .10
Figure 1.5. Conceptual views of our two novel shock protection technologies.
(a) Nonlinear spring shock stops and (b) soft coating shock stops 12
Figure 1.6. Concepts for vibration suppression in MEMS 16
Figure 1.7. Conceptual views of a passive vibration isolator (left) and an active
vibration isolator (right) .19
Figure 1.8. Conceptual views of (a) a mechanical low-pass-filter (LPF) and (b) a
mechanical notch filter (NF, i.e. a vibration absorber) 20
Figure 2.1. Genealogical tree of reported MEMS vibratory gyroscopes .32
Figure 2.2. Classification of non-degenerate gyroscopes. (a) a design that has coupled
sense and drive masses (CP type), (b) a design that has decoupled sense and drive
masses with an anchored sense mass (DS type), (c) a design that has decoupled
sense and drive masses with an anchored drive mass (DD type), and (d) a doubly
decoupled design that has completely decoupled sense and drive masses with one
coupling (or connecting) mass .33
Figure 2.3. Detailed view of the three major designs of tuning fork gyroscopes. (a) CP
design, (b) DS design, (c) DD design 35
Figure 2.4. Block diagram of the simulation model built using MATLAB and
SIMULINK 40
Figure 2.5. Impact-shaped vibration observed in a real vibration testing of gyroscopes
[42] (top) and impact-shaped vibration used in our simulations (bottom) 43
Figure 2.6. Simulated outputs for Type-CP, Type-DS, and Type-DD gyroscopes after
subjected to a impact-shaped vibration shown in Figure 2.5. The impact has
100g amplitude and 3 ms duration .44ix
Figure 2.7. Vibration-angle dependency of the errors induced by the asymmetric
electrostatic force at drive electrodes .50
Figure 2.8. Simulated output of Type-DD gyroscopes. During rotation (a), vibrationinduced errors occur and increase with larger vibration amplitude (100, 300,
500g). However, when no rotation exists (b), no error is observed. Moreover,
the errors are proportional to rotation speed (c) .52
Figure 2.9. Simulated output of Type-DS gyroscopes. The dominant vibrationinduced errors in Type-DS are almost independent of rotation speed (a). The
vibration-induced errors depend on the vibration amplitude (b). The simulated
outputs of Type-CP gyroscopes are almost identical .53
Figure 2.10. Conceptual view of a ring gyroscope 54
Figure 2.11. Four fundamental vibration modes of a ring gyroscope. (a) mode from
drive operation, (b) mode from sense operation, (c) mode from x-axis external
vibration, (d) mode from y-axis external vibration 56
Figure 2.12. Ring structure and coordinates at point P (XP, Yp). (a) Cartesian
coordinate with x and y axes and (b) cylindrical coordinate with radial (r) and
tangential (?) axes 59
Figure 2.13. Coordinate system used to calculate kinetic energy. (a) the overview of
the inertial and translating/rotating coordinate systems, (b) the detailed top view of
the translating/rotating coordinate system and the deformed ring structure 61
Figure 2.14. Deflection of support springs (a) in translation modes and (b) in flexural
modes… .66
Figure 2.15. Stiffness of a semicircular spring into three directions. (a) Horizontal
stiffness (KHA), (b) vertical stiffness (KVA), (c) stiffness to 450 direction (K45) 67
Figure 2.16. Symmetric set of drive electrodes. Two drive electrodes are located at
?n=00 and 1800 and actuated in-phase 68
Figure 2.17. Single-ended sensing mechanism in a ring gyroscope 74
Figure 3.1. Conceptual view of a LPF integrated with a device and the frequency
spectrum of the LPF .82
Figure 3.2. Multiple vibration-isolation platforms. (a) Two platforms and (b) multiple
platforms with N platforms 83
Figure 3.3. Operation of a mechanical low pass filter integrated with a MEMS
gyroscope .84x
Figure 3.4. Modeling of multiple vibration-isolation platforms. (a) Conceptual view of
the multiple platforms, (b) forces involved with the device mass and each platform
(J=1,2,…, N-1) .86
Figure 3.5. Change of resonance frequency of the gyroscope due to the integration of
vibration-isolation platforms 87
Figure 3.6. Q and ?f0 calculation after integrating with a platform .89
Figure 3.7. The resonant frequency and Q-factor of a gyroscope integrated with a
vibration-isolation platform .89
Figure 4.1. Three different shock stops: (a) conventional hard, (b) nonlinear spring,
(c) soft thin-film coating 96
Figure 4.2. Simulated device mass displacement during first impact with
(a) conventional hard (silicon) shock stop, (b) nonlinear spring shock stop, (c) soft
thin-film coated shock stop 97
Figure 4.3. Schematic of nonlinear spring shock stop designs. Beam cascade (left) and
single nonlinear beam (right) .99
Figure 4.4. Piecewise linear system formed by a cascade of beams. (a) Structure
showing three beams separated by a gap of D. Cantilever (left, smaller kS) and
bridge structure (right, larger kS); (b) restoring force as a function of deflection;
(c) simple model of a device and the beam cascade 102
Figure 4.5. Piecewise linear system before (left) and after (right) compression of
entire beam cascade .102
Figure 4.6. Schematic of two nonlinear single beam designs. Single clamped
cantilever (left) and double clamped bridge beam (right). Note that in the
cantilever case, the length of a beam L is defined as the position where the mass
contacts the shock stop, where the overall length of the beam L0 is larger than L 103
Figure 4.7. Restoring force as a function of deflection in a single beam with nonlinear
hardening effects 104
Figure 4.8. Dimensions defining a single clamped cantilever beam (above) and a
clamped-clamped bridge beam (below) .105
Figure 4.9. Range of shock protection offered by a device with a single nonlinear
beam…… .108
Figure 4.10. Impact force reduction and maximum displacement due to beam cascade
as functions of beam stiffness (kS) and spacing (D=5 or 10 ?m). Two shock-stop
beams are considered. 112xi
Figure 4.11. Maximum allowable shock as a function of the width and length of
shock-stop beams made of both polysilicon and aluminum 113
Figure 4.12. Impact force reduction and maximum deflection for a single nonlinear
beam (w=20 ?m) as functions of the linear beam stiffness kL. Results for a beam
cascade (N=2, D=10 ?m, w=20 ?m) from Figure 4.10 are shown as a reference .114
Figure 4.13. Impact force reduction and maximum deflection for a single nonlinear
bridge and cantilever (w=20 ?m, t=50 ?m) as functions of the shock-beam length
(L). Used beam lengths are selected to make similar linear stiffness (kL), which
is used in Figure 4.12 .115
Figure 4.14. A thin film layer on a semi-infinite substrate indented by (a) a rigid flatended indenter, (b) a conical indenter, or (c) a spherical indenter [7] .118
Figure 4.15. Impulse reduction and impact number reduction as function of COR –
Results shown for three coatings: glass /oxide, silicon and gold/copper .119
Figure 4.16. Elastic energy vs. deflection of a Parylene film (?i is assumed to be 20
GPa) for a device mass that has one bumper of different shapes. The energy
produced by a 1000-g shock applied to a device mass is shown as the solid line,
which is labeled as threshold. 120
Figure 4.17. The time record of (a) the displacement of a device mass and (b) the
involved impact force during this movement 121
Figure 5.1. Conceptual view of a Hopkinson bar [7] .127
Figure 5.2. Conceptual view of ballistic tests [12] 127
Figure 5.3. IMPAC66 HVA drop test machine .128
Figure 5.4. Our drop test machine (left: conceptual view, right: manufactured
machine)… .130
Figure 5.5. Time record of the contact time (?T) between the steel plate and the steel
rail in our drop test machine in Figure 5.4 .131
Figure 5.6. Conceptual illustration of (a) shock generated in a real environment and its
peak value (FPK) and (b) average shock (FAV) .131
Figure 5.7. Schematic of fracture planes at the anchor of a micro-beam [24] .133
Figure 5.8. Fracture plane at the anchor of a micro-cantilever beam [9] .133
Figure 5.9. Three point test to measure bending stress [25] 134
Figure 5.10. Test devices damaged by static loading in the vertical direction, where no
shock stops exist. As expected, both SOG and piezoresistive (Piezo) devices
were damaged at their anchors (highlighted) .136xii
Figure 5.11. Fabrication process flow of (a) Silicon-On-Glass (SOG) capacitive and
(b) high-doped polysilicon piezoresistive devices .138
Figure 5.12. Fabricated capacitive accelerometer integrated with nonlinear spring
shock stops using SOG process .139
Figure 5.13. Fabricated piezoresistive accelerometer integrated with nonlinear spring
shock stops using highly doped polysilicon .139
Figure 5.14. Fabrication process flow of soft-coating test devices and Parylene coated
shock stops .140
Figure 5.15. Top views of the fabricated hard (silicon) and soft coated (Parylene)
devices. Each sample has three wall and two nonlinear spring devices .141
Figure 5.16. SEM of the top view of suspended micro-beams after Parylene
deposition. It shows excellent step coverage. 141
Figure 5.17. Nonlinear spring stops and hard stops after several impacts. Only a
device with hard stops was damaged at the tip close to the device mass. .143
Figure 5.18. A series of photographs of the test samples containing both hard wall and
soft coating shock stops following each drop test for the device shown in Figure
5.15. All hard stops were damaged at the tip close to the device mass. .144
Figure 5.19. Fabricated shock-stops designed to have different target-shock
amplitudes. Hard stops are also fabricated as a benchmark 146
Figure 5.20. Fractured device and shock-stop beams after shocks 147
Figure 5.21. Test results of the nonlinear spring shock stops in Figure 5.19 148
Figure 5.22. Device facture mechanism by impact force (FIM) generated from the
contact between the device mass and its hard shock stops. A device with
cantilever beam is used in our shock tests. 149
Figure 5.23. Impact-force induced fracture mechanism in another device with
clamped-clamped beam structure 150
Figure A.1. Schematic of the micromachined vibration isolator integrated to a vacuum
package previously presented [2] .159
Figure A.2. FEM simulation results showing the fundamental resonant frequencies of
lateral and vertical isolator designs. The lateral design has ~0.8 kHz resonance,
whereas vertical design has ~3.6 kHz 160
Figure A.3. The fabrication process for the vibration-isolation platform. The
platform and the substrate wafer are processed separately and boned together
using TLP bonding .161xiii
Figure A.4. (a) Fabricated lateral and vertical vibration isolator, (b) Isolation platform
after TLP bonding on a substrate .162
Figure A.5. Fabricated vibration-isolation platforms (on a single wafer) and detached
vertical design showing good bonding quality and released vibration springs .163
Figure A.6. The frequency response of the lateral vibration isolator. This design
shows vibration suppression after ~2.1k Hz vibration frequency 163
Figure B.1. SIMULINK model for Type-CP and Type-DS gyroscopes .169
Figure B.2. SIMULINK model for Type-DD gyroscopes .170
Figure C.1. SIMULINK model for nonlinear spring and soft coating shock stop
simulations. (a) Nonlinear_e.mdl and SoftStop_e.mdl, (b) Nonlinear_s.mdl and
SoftStop_s.mdl .
LIST OF TABLES
Table 1.1. Shock amplitudes realized in various environments .4
Table 1.2. Dominant Vibration Frequencies in Various Frequencies in Various
Environments .14
Table 2.1. Summary of our classification of reported gyroscopes 34
Table 2.2. Model parameters .42
Table 2.3. Conditions leading to vibration-induced errors. FC denotes Coriolis force
(due to rotation), AX denotes vibration along drive direction, and AY denotes
vibration along sense direction 46
Table 2.4. Summary of vibration-induced error sources in each gyro design
(The dominant error source is highlighted.) 76
Table 3.1. Performance of a gyroscope [4] integrated with one or two vibrationisolation platform. The gyroscope has resonant frequency of 15k Hz and Q of 40k 90
Table 3.2. Performance of another gyroscope [5, 6] integrated with one or two
vibration-isolation platform. The gyroscope has resonant frequency of 8.9k Hz
and Q of 4.1k…… 91
Table 4.1. Characteristics of the three shock protection methods in Figure 4.1 97
Table 4.2. COR and Mohs hardness for candidate coating materials [4-6] (Maximum
Mohs hardness=10) 116
Table 4.3. Comparison of shock protection afforded by the three designs shown in
Figure 4.1. Cascade-beam and single-bridge designs have the same linear
stiffness 122
Table 5.1. Characteristics of shock test methods .125
Table 5.2. Shock test methods (in Table 5.1) compared with our requirements .129
Table 5.3. Designed test devices and their characteristics .135
Table 5.4. Physical dimensions of designed shock beams .137
Table 5.5. Summary of tests results comparing three shock-protection methods .145xv
LIST OF APPENDICES
APPENDICE
A. Micromachined Multi-Axis Vibration-Isolation Platform 159
B. MATLAB Codes to Generate Figures in Section 2.4 .165
C. MATLAB Codes to Generate Figures in Chapter 4 .171
D. Derivation of Kinetic Energy of Ring Gyroscopes in Section 2.5.4 .183
E. Derivation of Potential Energy from Drive Electrodes of Ring
Gyroscopes in Section 2.5.7
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Admin
مدير المنتدى
عدد المساهمات : 18717
التقييم : 34685
تاريخ التسجيل : 01/07/2009
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| | موضوع: رد: رسالة دكتوراه بعنوان Vibration Isolation and Shock Protection for MEMS الخميس 10 يناير 2013, 12:52 pm | |
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