Design of threhold accelerometer based on multisable mechanism doctor of philosophy major multistable mechanism

Design of Threshold Accelerometer Based on Multistable Mechanism Dung-An Wang Ngoc Dang Khoa Tran... Graduate Institute of Precision Engineering, National Chung Hsing University Doctor

Design of Threshold Accelerometer Based on

Multistable Mechanism

Dung-An Wang Ngoc Dang Khoa Tran

ACKNOWLEDGEMENTS

First and foremost, I would like to send my deeply gratitude to National Chung Hsing University, Taiwan for providing me this valuable scholarship for Ph.D degree and Ho Chi Minh University of Technology and Education, Vietnam for supporting me

in the researches

I would like to thank my advisor Prof Dung-An Wang for his guidance, support and encouragement He has mentored, taught and inspired me in my academic as well as personal life I express my gratitude for the education that I have received from him I

am grateful to Professor Thien Ngon Dang Their comments and suggestions were very useful

I would like to acknowledge the help of my fellow Vietnamese and Taiwanese lab mates for their feedback, cooperation and of course friendship In addition, I would like

to express my gratitude to the staff of Graduate Institute of Precision Engineering for the last minute favor

Finally, I would like to thank my friends for accepting nothing less than excellent from me Last but not the least; I am very grateful to my parents, my sister and my girlfriend for their love, for supporting me spiritually throughout writing this thesis and encouragement of my academic pursuits, and for always expressing confidence in my abilities

Graduate Institute of Precision Engineering, National Chung Hsing University

Doctor of Philosophy Design of Threshold Accelerometer Based on Multistable Mechanism

ABSTRACT

A compliant multistable mechanism has been applied to develop a threshold accelerometer The accelerometer senses two distinct inertial signals when acceleration thresholds are exceeded along one axis This function allows the flexibility to detect two consecutive events with the expected threshold values of the stimuli or two level quasi-static acceleration thresholds The multistable mechanism is a series connection

of two bistable mechanisms (BMs) A chained beam constraint model (CBCM) is applied to build an analytical model of multistable mechanism Experiments are implemented to demonstrate the feasibility of the device The developed analytical model for the multistable mechanism is proved by finite element analyses and experiments Snap through behavior of the multistable mechanism caused by threshold values is used to evaluated the detection accuracy and fault tolerance

Keywords: Multistable; Threshold accelerometer; bistable

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TABLE OF CONTENTS

ACKNOWLEDGEMENTS i

ABSTRACT ii

TABLE OF CONTENTS iii

LIST OF FIGURES vi

LIST OF TABLES ix

LIST OF ABBREVIATION AND SYMBOLS x

CHAPTER 1 INTRODUCTION 1

1.1 Motivation 1

1.2 Contribution 2

1.3 Organization 3

CHAPTER 2 LITERATURE REVIEW 4

2.1 Threshold accelerometer 4

2.1.1 Cantilever beam thershold accelerometer 4

2.1.2 Latching mechanism threshold accelerometer 5

2.1.3 Racheting mechanism threshold accelerometer 6

2.1.4 Bistable mechanism threshold accelerometer 6

2.1.5 Multi-threshold accelerometer 7

2.2 Multistable mechanism 8

2.2.1 Tristable mechanism 8

2.2.2 Quadristable and multistable 8

CHAPTER 3 THEORITICAL MODELING 10

3.1 Conceptual design 10

3.2 Theoretical background 11

3.2.1 Beam constraint method 11

3.2.2 Chain beam constraint method 14

3.3 Modeling 15

CHAPTER 4 DESIGNS AND SIMULATIONS 30

4.1 Designs 30

4.1.1 Straight beam tristable mechanism (SBMM) 30

4.1.2 Crab-like beam tristable mechanism (CBMM) 30

4.2 Finite element model 31

4.3 Simulation 31

4.3.1 Force-displacement curves 31

4.3.2 Stress analysis 33

4.3.3 Backward motion analysis 33

4.3.4 3D simulation 34

4.3.5 Threshold values 34

CHAPTER 5 FABRICATION AND EXPERIMENTS 46

5.1 Fabrication 46

5.1.1 Manufacturing processes 46

5.1.2 Assembly 46

5.2 Experiments 47

5.2.1 Force-displacement experiment 47

5.2.2 Centrifuge experiment 47

5.2.3 Frequency sweep experiment 48

CHAPTER 6 RESULTS AND DISCUSSIONS 65

6.1 Force-deflection characteristics 65

6.2 Threshold accelerations 66

6.3 Frequency response 67

6.4 Time response 67

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6.5 Anti-jamming performance 67

CHAPTER 7 CONCLUSIONS AND FUTURE WORKS 76

7.1 Conclusions 76

7.2 Future works 76

References 78

Publications during Ph.D studies 85

LIST OF FIGURES

Fig 3.1 Illustration of threshold acceleration sensing by a MM Acceleration impulse

and the equilibrium positions are the input and the output, respectively 20

Fig 3.2 (a) A typical f-d curve of a MM (b) MM at the first stable equilibrium position (c) MM at the second stable equilibrium position (d) MM at the third stable equilibrium position 21

Fig 3.3 (a) A schematic of the MM (b) A schematic of the inner BM (c) A schematic of the outer BM 22

Fig 3.4 A simple beam with a generalized end load 23

Fig 3.5 Discretization of a simple beam 24

Fig 3.6 A quarter model of a MM 25

Fig 3.7 Original configuration and deformed configuration of a MM are represented by solid lines and dashed lines 26

Fig 3.8 Free-body diagrams of the inner BM 27

Fig 3.9 Free-body diagrams of the outer BM 28

Fig 3.10 Free-body diagram of the half shuttle mass 29

Fig 4.1 The profile of straight beam divided into 5 segments 37

Fig 4.2 F-d curves based on the analytical CBCM model for SBMM 37

Fig 4.3 The profile of crab-leg beam with 5 segments 38

Fig 4.4 F-d curves based on the analytical CBCM model for CBMM 38

Fig 4.5 A mesh of SBMM for FEA 39

Fig 4.6 A mesh of CBMM for FEA 39

Fig 4.7 (a) F-d curves of a MM for SBMM based on the CBCM and the FEA (b) Strain energy curve of a MM for SBMM based on the FEA 40

Fig 4.8 (a) F-d curves of a MM for CBMM based on the CBCM and the FEA (b) Strain energy curve of a MM for CBMM based on the FEA 41

Fig 4.9 (a) A f-d curve of a MM for CBMM (b) MM at the first stable equilibrium position (c) MM at the second stable equilibrium position (d) Snap shots of shuttle mass moving (e) MM at the third stable equilibrium position 42

Fig 4.10 A stress-displacement curve of the CBMM 43

Fig 4.11 Location of the peak value of the maximum stress in the CBMM 43

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Fig 4.12 F-d curve for backward motion of the CBMM 44

Fig 4.13 F-d curves of inner beam, outer beam bistable mechanism and MM based on CBMM model 44

Fig 4.14 Two-dimensional f-d curves and three-dimensional f-d curves of FEA and the CBCM model of design model 45

Fig 5.1 (a) Dimension of the MM, (b) Dimesion of anchor 51

Fig 5.2 Dimension of spacer 52

Fig 5.3 Dimension of base 53

Fig 5.4 MM with linkage components 54

Fig 5.5 Assembly prototype 55

Fig 5.6 The fabricated prototype in its (a) first; (b) second and (c) third stable equilibrium position 56

Fig 5.7 (a) An experimental setup for measurement the f-d curves of the fabricated prototype (b) An illustration of the fillet radius of the fabricated prototype 57 Fig 5.8 (a) An experimental setup for testing the acceleration thresholds of the device (b) A block diagram of the position sensing of the device and the feedback loop for rotational speed control of the centrifuge 58

Fig 5.9 Flowchart control system of centrifuge experiment 59

Fig 5.10 Labview for control centrifuge experiments 60

Fig 5.11 Experimental setup for frequency sweep test 61

Fig 5.12 A block diagram of the position sensing of the device and the feedback loop for frequency sweep of shaker 62

Fig 5.13 Flowchart control system of frequency sweep experiment 63

Fig 5.14 Labview for control frequency sweep experiments 64

Fig 6.1 F-d curves of the MM based on the experiments and the finite element analyses The material of the MM and (b) 2.20 GPa 69

Fig 6.2 F-d curves of the MM based on the reverse experiments and the finite element analyses 70

Fig 6.3 Experimental acceleration thresholds of the ten test trials 71

Fig 6.4 Frequency response of the device based on the experiments 71

Fig 6.5 Mode shapes of MM (a) and (b) original and deformed shape of MM for the

first vibration mode, respectively (c) and (d) original and deformed shape of

MM for the second vibration mode, , respectively 72 Fig 6.6 Time response of MM -4 73 Fig 6.7 (a) Unit-step input of the acceleration signal of 1.30 g (b) Unit-step input of

the acceleration signal of 4.85 g (c) Transient response of the device to the step input of the acceleration signal of 1.30 g (d) Transient response of the device to the step input of the acceleration signal of 4.85 g 74 Fig 6.8 Acceleration values for the device to snap into its second and third stable

equilibrium positions when it is subjected to impulse noises 75 Fig 6.9 Acceleration values for the device to snap into its second and third stable

equilibrium positions when it is subjected to sinusoidal noises 75

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LIST OF TABLES

Table 3.1 Beam characteristic coefficients of simple beam 19

Table 4.1 Dimensions of the inner beam of the MM for SBMM 35

Table 4.2 Dimensions of the outer beam of the MM for SBMM 35

Table 4.4 Design parameters of the inner beam of the MM for CBMM 36

Table 4.5 Design parameters of the outer beam of the MM for CBMM 36

Table 5.1 Measured dimensions of the inner beam of the CBMM 50

Table 5.2 Measured dimensions of the outer beam of the CBMM 50

LIST OF ABBREVIATION AND SYMBOLS

English symbols

Linear acceleration Damping coefficient

F Transverse force

Transverse force on ith element segment

Nondimensional transverse force on ith element segment Length of shuttle mass

Apex height of inner beam

Apex height of outer beam

Moment Moment on ith element segment

Moment at the center of shuttle mass

Nondimesional moment on ith element segment

P Axial force

Axial force on ith element segment

Concentrated force at the center of shuttle mass

Nondimensional axial force on ith element segment Distance of the center of the prototype from the center of the centrifuge

Thickness of beam Width of beam Width of ith element segment

xi

Greek symbols

End slope of beam

End slope of the ith element

Axial deflection of ith element

Transverse deflection of the ith element Initial angle of the beam

Initial angle of the ith element

Frequency

First modal frequency

Abbreviations

BCM Beam constraint method

CBCM Chain beam constraint method

CBMM Crab-like beam tristable mechanism POM Polyoxymethylene

SBMM Straight beam tristable mechanism

MM Multistable mechanism

Chapter 1 INTRODUCTION

1.1 Motivation

Accelerometers are used in a wide range of applications in which force, acceleration, vibration and displacement are to be sensed Accelerometers are often implemented in laptop computers to protect hard drives in the event of a drop or jolt [1], micro switch or micro relays [2], etc Information from a shock event can be provided

by applying multiple threshold level to design accelerometers [3] They can be used for monitoring activities of daily living of patients [4], and could serve the purpose for providing triggering signals when an acceleration peaks are identified [5] Accuracy, repeatability and reliability are required for appropriate operation of the above mentioned applications Some industrial systems have utilized high precision accelerometers incorporated with high speed controller And many applications required sensors that will switch electrical states using the detection of a preset threshold acceleration level Many transportation companies are interested in tracking the delivery of packages to detect any impacts that may occur during transit In the automobile industry, many accelerometers are applied in the airbag systems and seat-belt pretensioner in order to detects an impact above a given threshold

Some applications of the threshold accelerometer require extremely high reliability For example, the accelerometers used in airbags and rockets should avoid any malfunctioning including repeated operation due to mechanical bounce Many mechanisms have been applied to develop the threshold stable mechanism Some complaint bistable mechanisms (BMs) have been applied to develop threshold accelerometer However, few mechanisms with three or more stable positions used in design of threshold accelerometer, have been reported The challenge in developing multistable mechanism is the difficulty to design their geometry, sythesizing and analyzing Although accelerometers constructed by intergrating multisensor signals can

an alternative design for threshold accelerometers Insensibility to noise are excellent candidates for design of threshold accelerometers The switching force to initiate snap through of the multistable mechanisms can be taken as the threshold value for acceleration sensing applications

The main goal of this dissertation is the development of a multistable mechanism for measuring multiple threshold accelerations The design is aimed for detecting of two level quasi-static acceleration thresholds There are two disparate threshold forces for the multistable mechanism to change the position of stable equilibrium positions This behaviors promotes the two threshold acceleration values of the accelerometer

1.2 Contribution

The main contributions of this dissertation are, listed in order of appearance:

A concise overview of threshold accelerometer, BM and multistable mechanism

A brief overview of beam flexure analytical method to research the behavior of

MM and dynamic behaviors of this mechanism

The design of complaint multistable mechanism is verified by an analytical method

A comparison of analytical methods results with finite element analysis for deflection of flexible members

The fabrication of the prototype and setup of the experiments to evaluate the performance of complaint mechanisms

The setup and design control system of centrifuge experiment to detect threshold accelerations

The development and design of the control system and testing of a real-time experiment to evaluate the behaviors of the device

The investigation of dynamic characteristics of accelerometer based onthe prototype

Chapter 7 summarizes this dissertation and gives possible directions for future works