Novel Escapement Mechanism using a Compliant Mechanism and a Piezoelectric Actuator

120 Pages·2007·2.58 MB·English

Novel Escapement Mechanism using a Compliant Mechanism and a
Piezoelectric Actuator
A Thesis
Submitted to the Faculty of the
WORCESTER POLYTECHNIC INSTITUTE
in partial requirement for the
Degree of Master of Science
in
Mechanical Engineering
by:
__________________________________
Girish S. Mali

April 27, 2007
Approved:

_______________________________________________
Professor Robert L. Norton, Advisor

_______________________________________________
Professor Yong-Mo Moon, Thesis Committee Member

_______________________________________________
Professor Mikhail Dimentberg, Thesis Committee Member

___________________________________________________
Professor Cosme Furlong, Graduate Committee Representative
ABSTRACT

Escapement mechanisms hold back a stream of parts driven either by mechanical or
pneumatic means for a length of time and release a single part as required to an assembly
station. They are used in most automatic multi-component assembly equipment. They
occupy a significant design space and have dynamic characteristics of their own. This
research aimed to develop a novel high speed mechanism for parts escapement that
occupies less design space and contributes less to the dynamic activity of the structure.
Several conceptual mechanisms were generated and evaluated. A compliant mechanism
that amplifies the very small displacement of a piezo actuator was selected for detailed
design. A proof of concept prototype was fabricated and tested. A piezo stack was used to
bend a thin, spring steel, compliant beam. Its deflection was further amplified by
attaching a comparatively rigid beam extension at the end of the compliant section. The
mechanism escapes parts at 16 Hz using constrained layer damping on the beam to
reduce vibrations. The concept is feasible to use on production machinery and provides
advantages in terms of higher operating speeds and compactness. The concept could also
be used where there is a requirement of high speed gating.
i
ACKNOWLEDGEMENTS

I would like to thank Professor Robert L. Norton and Professor Yong-Mo Moon for
providing me with motivation and guidance through out the progress of the research.
Both of them helped me unravel a lot many territories in my ignorance. Thanks to Tim
Sweet for providing with a novel idea to work on and The Gillette Company for
sponsoring the research.

Thanks to people and friends at WPI who helped in manufacture and testing of
mechanism. I would also like to thank my family and friends for providing an
unwavering support in all my endeavors.

ii
CONTENTS

LIST OF FIGURES……………………………………...………………………………..v
LIST OF TABLES………………………………………………...…………………......vii
1. Introduction................................................................................................................1
2. Project Scope.............................................................................................................3
2.1. Goal Statement........................................................................................................3
2.2. Project Objective.....................................................................................................3
2.3. Proposed Approach.................................................................................................3
3. Background Study......................................................................................................5
3.1. Compliant Mechanisms..........................................................................................5
3.1.1. Advantages of Compliant Mechanisms.........................................................5
3.2. Piezoelectricity........................................................................................................6
3.2.1. Poling.............................................................................................................6
3.2.2. Piezoelectric Properties..................................................................................7
3.2.3. Piezoelectric Forces and Stiffness Characteristics.........................................7
3.2.4. Driving conditions of PZT-elements.............................................................9
3.2.5. Piezoelectric Actuators................................................................................12
3.3. Damping Techniques............................................................................................15
3.3.1. Free Layer or Extension Damping...............................................................16
3.3.2. Constrained Layer Damping........................................................................17
3.4. Literature review...................................................................................................17
4. Design Concepts......................................................................................................21
4.1. Concept 1..............................................................................................................21
4.2. Concept 2..............................................................................................................22
4.3. Concept 3..............................................................................................................24
4.4. Concept 4..............................................................................................................25
4.5. Concept 5..............................................................................................................27
4.6. Concept 6..............................................................................................................28
4.7. Concept Selection.................................................................................................28
5. Detailed Design........................................................................................................30
5.1. Design Specifications............................................................................................30
5.2. Motion Analysis....................................................................................................30
5.3. Vibration Analysis................................................................................................33
5.4. Parameter Effects..................................................................................................34
5.4.1. Thickness of the Cantilever Beam...............................................................35
5.4.2. Width of the Cantilever Beam.....................................................................36
5.4.3. Lengths of the compliant and rigid section:.................................................37
iii
5.4.4. Material for Rigid Part of the Cantilever Beam...........................................37
5.5. Design Parameters Selected..................................................................................39
5.6. Test Bed Requirements.........................................................................................42
5.6.1. Set-up Requirements....................................................................................43
5.7. Test Bed Description.............................................................................................43
5.8. Testing Procedure.................................................................................................49
6. Experimentation.......................................................................................................51
6.1. Experiment Setup..................................................................................................51
6.1.1. Function Generator......................................................................................51
6.1.2. Dynamic Signal Analyzer............................................................................52
6.1.3. Feeding System............................................................................................52
6.1.4. High Speed Camera.....................................................................................52
6.2. Dynamic Characteristic of the Cantilever Beam..................................................53
6.3. Escapement Experiments with Square Waveform................................................54
6.4. Escapement experiments with modified square wave..........................................56
6.5. Escapement Experiments with Cam Profiled Waveform.....................................61
6.6. Escapement Experiments with Holding Back Device..........................................64
6.7. Experiments with Damping..................................................................................65
6.7.1. Constrained Layer Damping Study..............................................................66
6.7.2. Escapement Experiment with Constrained Layer Damping........................68
7. Results......................................................................................................................71
8. Conclusions..............................................................................................................73
9. Recommendations....................................................................................................75
REFERENCES.................................................................................................................77
BIBLIOGRAPHY AND REFERENCES.........................................................................79
Appendix 1........................................................................................................................80
Appendix 2........................................................................................................................83
Appendix 3........................................................................................................................86
Appendix 4........................................................................................................................96
Appendix 5......................................................................................................................107
Appendix 6......................................................................................................................112
iv
LIST OF FIGURES
Figure 3-1: Force generation vs. displacement of a piezo actuator. Stiffness at various
operating voltages.......................................................................................................8
Figure 3-2: Quasi-static characteristic mechanical stress/strain curves for piezo ceramic
actuators and the derived stiffness values...................................................................9
Figure 3-3: Driving Conditions of PZT elements.............................................................10
Source:..............................................................................................................................10
Figure 3-4: Piezo Stack Actuator......................................................................................13
Figure 3-5: Unimorph Design...........................................................................................14
Figure 3-6: Energy is dissipated as result of extension and compression of the material
under flexural stress from the base structure............................................................16
Figure 3-7: Constrained-layer damping. Energy is dissipated as a result of shear
deformation of the damping layer.............................................................................17
Figure 4-1: Layout of Concept 1.......................................................................................21
Figure 4-2: Schematic of Concept 2.................................................................................23
Figure 4-3: Fourbar Linkage Concepts.............................................................................24
Figure 4-4: Schematic of Concept 4.................................................................................25
Figure 4-5: Schematic of Concept 5.................................................................................27
Figure 4-6: Schematic of Concept 6.................................................................................28
Figure 5-1: The Selected Concept.....................................................................................31
Figure 5-2: Variables used in analysis of selected concept.............................................32
Figure 5-3: Variables used in analysis of selected concept.............................................32
Figure 5-4: Variation of natural frequency and tip displacement of mechanism with
change in thickness of the compliant section............................................................35
Figure 5-5: Variation of natural frequency and tip displacement of mechanism with
change in width of the compliant section.................................................................36
Figure 5-6: Variation of tip displacement with lengths of compliant and rigid sections of
the cantilever.............................................................................................................37
Figure 5-7: Piezo Stack Actuator used for the research(P-885.90)..................................41
Figure 5-8: Piezo Amplifier used for the Research E-663................................................42
Figure 5-9: Schematic of the test setup............................................................................44
Figure 5-10: Escapement Mechanism...............................................................................44
Figure 5-11: Capsule.........................................................................................................45
Figure 5-12: Modified Gate used to block capsules........................................................47
Figure 5-13: Front View of the Test Bed..........................................................................47
Figure 5-14: Components used in mechanism..................................................................48
Figure 5-15: PVDF tubing fitted to the Nozzle on the Test Bed.....................................49
Figure 5-16: Way to fill the capsules in the tube.............................................................49
Figure 5-17: Connection with the air outlet.....................................................................50
Figure 6-1: A Periodic Chirp Signal used to excite Piezo Actuator.................................53
Figure 6-2: Coherence for the measurement data.............................................................53
Figure 6-3: Frequency Domain response of the mechanism............................................53
Figure 6-4: Square Wave with 50 % symmetry................................................................54
Figure 6-5: Square Wave 90% asymmetry.......................................................................55
Figure 6-6: Gate of the mechanism and the nozzle...........................................................56
v
Figure 6-7: Modified square wave....................................................................................57
Figure 6-8: Capsule slipping over the gate (Video 6.01)..................................................58
Figure 6-9: Two Capsules escaping in a single stroke (Video 6.03)................................58
Figure 6-10: Mechanism in closed state...........................................................................59
Video (6.04)......................................................................................................................59
Figure 6-11: Mechanism in open state Video (6.04)........................................................59
Figure 6-12: Mechanism in closed state Video (6.05)......................................................59
Figure 6-13: Mechanism in open state..............................................................................59
Video (6.05)......................................................................................................................59
Figure 6-14: Capsule slipping over the gate. Gate in up or closed position (Video 6.06) 60
Figure 6-15: Synthesized waveform using Dynacam.......................................................61
Figure 6-16: Capsule held back by gate in up position (Video 6.09)...............................62
Figure 6-17: A single capsule released by mechanism. The next capsule properly held
back by the mechanism (Video 6.09).......................................................................62
Figure 6-18: Extreme up position of the cantilever at 16 Hz. (Video 6.10).....................63
Figure 6-19: Extreme down position of the cantilever at 16 Hz. (Video 6.10)................63
Figure 6-20: Capsule slowly dragging out of nozzle (Video 6.12)...................................65
Figure 6-21: Hold-Back Device stuck over the capsule causing the total tip displacement
to be drastically reduced (Video 6.13)......................................................................65
Figure 6-22: Gate in up position causing the capsule to be held back (Video 6.14)........68
Figure 6-23: Gate moving down, allowing capsule to escape the nozzle (Video 6.14)...68
Figure 6-24: Gate in up position before next capsule tries to escape the nozzle (Video
6.14)..........................................................................................................................68
Figure 7-1: Fabricated Prototype......................................................................................72

vi
LIST OF TABLES
Table 4-1: Concept Selection Matrix................................................................................29
Table 5-1: Natural Frequency variation with material of Rigid Section..........................38
Table 5-2: Specifications of the piezo actuator selected for the research.........................41
Table 5-3: Specifications of capsule in inches..................................................................46
Table 6-1: Various combinations used to evaluate the damping introduced. Damping
quantified for two peaks. Table sorted by area under the Frequency response
between 40 Hz and 160 Hz.......................................................................................69
Table 6-2: Various combinations used to evaluate the damping introduced. Damping
quantified for first peak using i) V for the time response, and ii) Damping
rms
Coefficient using DSA..............................................................................................70

vii
1.
INTRODUCTION

Assembly lines for consumer products were studied as a potential application for this
improved escapement mechanism. Such assembly lines are composed of various stations
at which the assembly of multi component parts takes place. The product travels on a
nest while it goes through a series of assembly procedures. The assembly starts with a
single base part mounted on a nest onto which various components are added as the nest
moves forward along the line. The motion of the nest along the line is traditionally
intermittent while recently developed assembly lines are designed with continuous nest
motion resulting in much higher assembly speeds. In intermittent assembly lines,
assembly of the components occurs during the dwell period of nest travel. The assembly
machines are fully automated and use cam driven linkage mechanisms. These
mechanisms in turn are driven by an input from a single motor for synchronization
purposes. This motor is also used to drive auxiliary mechanisms for parts escapement and
indexing.

Automated manufacturing of multi-component products requires that the parts be fed to
the assembly station at a particular rate. Escapement mechanisms are often used to
achieve this objective. The mechanisms can be driven by various methods. Cam follower
systems, solenoids synchronized with the assembly line, fourbar crank-rockers, or slider
cranks are some of the options that can be used. The main purpose of an escapement
mechanism is to control the parts’ feed rate by holding back a stream of parts driven
either by mechanical or pneumatic means for a length of time, and releasing a single part
as required.
1
The sponsor’s manufacturing facility uses cam driven linkage mechanisms to provide
escapement in its assembly machines. The assembly lines, and thus the escapement
mechanism, are designed for a certain operating speed. The mechanism is driven by a
main camshaft which also controls the cams in other systems. The camshaft allows
synchronizing all the stations in the line to meet the required production rate.

When operating at speeds higher than the design intent, one of the problems associated
with cam driven and fourbar linkage mechanisms is undesired dynamic response of the
mechanism to the driving frequencies. As operating speeds increase, they may excite the
resonant frequencies of the whole assembly. This causes undesired vibrations and noise
in the system.

2