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mm LIBRARY
Michigan State

2 0 0 Z . .
University

This is to certify that the
dissertation entitled

DEVELOPMENT OF A WIRELESS INSTRUMENTED
PROJECTILE FOR IMPACT TESTING BASED ON
ELASTIC WAVE REDUCTION

presented by

Guojing Li

has been accepted towards fulfillment
of the requirements for the

Doctoral degree in Engineering Mechanics

 

 

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W”; 95A,

 

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7/30 /0 9

Date

 

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5/08 K:IProyAcc8Pres/ClRC/DateDueindd

DEVELOPMENT OF A WIRELESS INSTRUMENTED
PROJECTILE FOR IMPACT TESTING BASED ON
ELASTIC WAVE REDUCTION

By

Guojing Li

A DISSERTATION

Submitted to
Michigan State University
In partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Mechanical Engineering

2008

ABSTRACT
DEVELOPMENT OF A WIRELESS INSTRUMENTED
PROJECTILE FOR IMPACT TESTING BASED ON
ELASTIC WAVE REDUCTION
By

Guojing Li

Dynamic loadings, such as impact, crash and blast loadings, are commonly
encountered in the real world. Multiple dynamic testing techniques and devices,
instrumented as well as non-instrumented, have been developed for material
Characterizations and laboratory simulations. The objective of this thesis
research is to develop a wireless instrumented projectile for low-velocity impact.
The research is divided into three sections. The first section addressed the
fundamental difference between horizontal impact and vertical impact. Sensors
based on strain gages and accelerometers were also compared. It was found
that a horizontal impactor equipped with strain gages could be used for
investigations on impact loading if the wave propagation associated with the
dynamic loading could be reduced or eliminated. In the second section, wave
reflection and wave superposition induced by impact loading in short projectiles
were studied. Both mechanical and numerical methods were proposed for
reducing the effect due to wave reflection so the initial wave associated with the
impact could be identified. Parabola-like surfaces at the free end of projectiles
were found to be able to reduce the effect of wave reflection and were
incorporated into the design of the projectile. Issues concerning the damage of

lead wires during impact testing were important to the success of the

instrumented projectile. The third section presented the detailed construction of a
wireless instrumented projectile, including the selection of the geometry, the
manufacturing procedures, the circuit design of the microprocessor, and the
assembly of the projectile. Calibrations on projectile body and electronic
components were carefully performed. Testing results seemed to validate the
feasibility of using the wireless instrumented projectile for impact events with a
velocity up to 20m/s and bandwidth of 170 kHz. Both the impact velocity and the

bandwidth are much higher than what are available commercially.

ACKNOWLEDGEMENTS

I would like to thank my professor, mentor, and good friend Dr. Dahsin Liu
for his insight and directions; he directed my thesis research step by step from
the very beginning and helped me to review the thesis. I am very grateful to Dr.
Gary Cloud, Dr. Brian Feeny, Dr. Andre Y. Lee and Dr. Alfred Loos for serving on
my committee. I would like to thank Dr. Hanqing Zhao and Mr. Brian Wright for
their help and directions on the circuit designs. I would like to thank Dr. Chun-
Ying Lee and Mr. Shawn Klann for reviewing my thesis. I would also like to thank
my wife Sen Li, and my daughter Xinui Li for all of their love and understanding,

though they probably don’t know it. Thank you, I appreciate everything you have

done for me.

iv

TABLE OF CONTENTS

LIST OF TABLES ............................................................................... ix
LIST OF FIGURES ............................................................................... x
CHAPTER ONE
INTRODUCTION
1. BACKGROUND .......................................................................... 1
2. STATEMENT OF PROBLEM .......................................................... 4
3. ORGANIZATION OF THE THESIS .................................................. 6
REFERENCES ........................................................................... 9
CHAPTER TWO

SENSOR EFFECTS AND SIGNAL
ANALYSIS IN DYNAMIC MEASUREMENTS

ABSTRACT ............................................................................... 13

1. INTRODUCTION ....................................................................... 14
2. EXPERIMENTAL TECHNIQUES ................................................... 17
2.1 Sensors and Data Acquisition ................................................... 17
2.2 Experimental Setup and Procedure .......................................... 18

A. Vertical Impact Systems ..................................................... 19

a. Load-cell type ......................................................... 19

b. Striker-bar type ........................................................ 20

B. Horizontal Impact Tests ...................................................... 21

a. Type I .................................................................... 21

b. Type II ................................................................... 21

c. Type III .................................................................. 22

3. EXPERIMENTAL RESULTS ........................................................ 23
3.1 Vertical Impact Test Systems .................................................. 23

A. Load Cell Type ................................................................. 23

B. Striker-Bar Type ................................................................ 27

3.2 Horizontal Impact Systems ..................................................... 29
A. TypeI ............................................................................. 29

B. Type II ............................................................................. 31

C. Type III ........................................................................... 32

3.3 Structures’ spectrum tests and signals’ spectral analysis ............... 32

4. DISCUSSION ............................................................................ 33
4.1 Load Cell vs. Stricker Bar ....................................................... 33
4.2 Quartz Accelerometers vs. Piezoresistive Accelerometer .............. 34
4.3 Strain Gages vs. Accelerometers ............................................. 34

4.4 Vertical Impact vs. Horizontal Impact ....................................... 36

5. ANALYSIS ................................................................................ 37
5.1 Effects of Masses ................................................................. 37
5.2 Effect of Wave Propagation .................................................... 40

A. Basic Wave Equation ......................................................... 40
B. Simulation ........................................................................ 42

6. CONCLUSIONS ......................................................................... 46
ACKNOWLEDGMENTS .............................................................. 46
REFEFENCES .......................................................................... 47

CHAPTER THREE
WAVE PROPAGATION IN LOAD TRANSDUCERS
ABSTRACT .............................................................................. 49

1. INTRODUCTION ....................................................................... 50

2. FORCE TRANSDUCERS ............................................................ 52

3. WAVE PROPAGATION IN RODS ................................................. 54
3.1 Experiments on Effect of Rod Length ....................................... 55
3.2 Experiments on Contact Duration ............................................ 57
3.3 Experiments Based on Three Sets of Gages .............................. 60
3.4 Experiments on Wave Dissipation ........................................... 62

4. MECHANICAL METHODS FOR WAVE REDUCTION ....................... 64
4.1 Rod with Cone-Ball End ......................................................... 64
4.2 Bar with Double Parabolic-Lines and Double Tails ........................ 67

5. NUMERICAL METHODS FOR WAVE REDUCTION ......................... 72
5.1 Technique Based on Assuming an Initial Wave ........................... 72
5.2 Two-Position Technique ......................................................... 75

6. CONCLUSIONS ........................................................................ 79
REFERENCES ......................................................................... 81

CHAPTER FOUR
DESIGN AND CALIBRATION OF AN INSTRUMENTED PROJECTILE
ABSTRACT .............................................................................. 84

1. INTRODUCTION ...................................................................... 85

2. SIGNAL TRANSFER .................................................................. 87
2.1 Wired Method ...................................................................... 87
2.2 Wireless Technique ............................................................... 90

A. Conductive Technique ....................................................... 90
B. Radio Signal Transfer Technique ......................................... 91
C. Wireless Technique .......................................................... 91

3. DESIGN OF AN INSTRUMENTED PROJECTILE ............................ 91
3.1 Cutting Tools ....................................................................... 93
3.2 Projectile Body ..................................................................... 95
3.3 Wave Transferring Section ..................................................... 95
3.4 Instrumentation and Assembly ................................................ 97

vi

4. TESTING OF SIGNAL MEASUREMENTS ..................................... 99
4.1 Accuracy Test .................................................................... 100
4.2 Dynamic Signal Test ............................................................ 101
5. TESTING WAVE REDUCTION ................................................... 103
6. CALIBRATION OF THE INSTRUMENTED PROJECTILE ................ 106
7. CASE STUDY OF THE INSTRUMENTED PROJECTILE ................. 109
8. DISCUSSIONS ....................................................................... 112
8.1 Longer Gun Barrel ............................................................... 112
8.2 Wave Transfer Section ......................................................... 112
8.3 The Sampling Rate .............................................................. 112
8.4 Trigger Mechanism .............................................................. 113
8.5 The Connectors .................................................................. 113
8.6 Assembly Issues ................................................................. 114
9. CONCLUSIONS ...................................................................... 114
REFERENCES ....................................................................... 115
CHAPTER FIVE
CONCLUSIONS AND RECOMMENDATIONS
1. CONCLUSIONS ....................................................................... 117
2. RECOMMENDATIONS ............................................................. 118
APPENDIX A

DESIGN A PENNY-SIZE SIGNAL PROCESSING
AND DATA ACQUISITION SYSTEM

1. INTRODUCTION ..................................................................... 121
2. DESIGN OVERVIEW ................................................................ 121
2.1 Strain Gages and Wheatstone Bridge ..................................... 123
2.2 Amplifier ........................................................................... 124
2.3 Data Acquisition and Saving ................................................. 125
2.4 Trigger ............................................................................. 126
3. DESIGN AND MANUFACTURING .............................................. 127
3.1 Strain Gages ..................................................................... 127
3.2 Trigger ............................................................................. 127
3.3 Signal Processing, Data Acquisition and Saving Unit ................. 128
3.4 Microprocessor .................................................................. 130
3.5 Amplifiers .......................................................................... 131
3.6 Resistors for the Wheatstone Bridge ....................................... 132
3.7 Print Board and Soldering ..................................................... 132
3.8 Battery ............................................................................. 134
3.9 Wiring .............................................................................. 135
3.10 Connectors ...................................................................... 136
3.11 Protection of the Battery and SP&DAQ unit ............................ 136
4. SUPPORTING SYSTEMS ......................................................... 137

vii

4.1 The Control Programs ......................................................... 137

4.2 Data Transferring Circuit and Software .................................... 138
4.3 Program for Data Processing ................................................ 141
4.4 Velocity Measurement ......................................................... 142
REFERENCES ........................................................................ 144

APPENDIX B

THE MICROPROCESSOR’S CONTROL PROGRAM FOR DATA

SAMPLING AND SAVING - IN ASSEMBLY LANGUAGE ........................ 145

APPENDIX C

THE MATLAB PROGRAM FOR CHANGING DATA FORMAT

FROM HEXADECIMAL TO DECIMAL .................................................. 152

APPENDIX D

MATLAB PROGRAM FOR THE NUMERICAL METHOD

-- INITIAL WAVE ASSUMPTION ......................................................... 154

APPENDIX E

LABVIEW PROGRAM FOR THE NUMERICAL METHOD

- TWO POSITION ............................................................................ 161

viii

LIST OF TABLES

Table 2.1 Parameters of sensors and their data acquisition system ................ 18
Table 2.2 Spectrum testing results ........................................................... 33
Table 2.3 Spectrum analysis of the signals in

figure 2.3(b), 2.4(b), 2.5(b) and 2.7 ............................................ 33
Table A1 Electrical current consumption of each component ....................... 135

ix

LIST OF FIGURES

Figure 2.1(a) Vertical impact tests: the load-cell type .................................. 19
Figure 2.1(b) Vertical impact tests: the striker-bar type ............................... 20
Figure 2.2 Horizontal impact systems (a) type I, (b) type II, and (c) type llI......23
Figure 2.3(a) Aluminum with thick vinyl under vertical impact, load cell type....25
Figure 2.3(b) Aluminum with thin vinyl under vertical impact, load cell type......26

Figure 2.4(a) Aluminum with thick vinyl under vertical impact,
striker-bar type .................................................................. 28

Figure 2.4(b) Aluminum with thin vinyl under vertical impact, striker-bar type....28

Figure 2.5(a) Steel with rubber under horizontal impact, type I ....................... 30
Figure 2.5(b) Glass/epoxy under horizontal impact, type I ............................. 30
Figure 2.6 Striker bar and load cell under horizontal impact, type II ................ 31
Figure 2.7 Force histories from type III horizontal impact .............................. 32

Figure 2.8 Schematic diagrams of (a) impactor
and (b) individual components ................................................. 38

Figure 2.9 Wave patterns based on measurement and simulations ................. 44

Figure 2.10 Simulation of apparent dent in force history due to blunt impact.....45

Figure 3.1 Testing setup for the impact rod ................................................ 56
Figure 3.2 Strain histories from the impact rods with various lengths .............. 56
Figure 3.3 Experimental setup for impact duration and strain history ............. 59
Figure 3.4 Impact duration (upper) and the strain history (lower) ................... 59
Figure 3.5(a) Experimental setup of the three sets of strain gages ................. 60
Figure 3.5(b) Experimental results of the three sets of strain gages ................ 61

Figure 3.6 The signal in frequency domain obtained from the pair

of strain gages located 38 mm from the impact end ...................... 62

Figure 3.7(a) Experimental setup for wave dissipation ................................. 63
Figure 3.7(b) Experimental result of wave dissipation .................................. 63
Figure 3.8(a) Schematic of a rod with a cone-ball end ................................. 65
Figure 3.8(b) Detailed drawings of a rod with a cone-ball end ....................... 65
Figure 3.8(c) Image of a cylindrical rod and a rod with a cone-ball end............66

Figure 3.9 Force histories in the rod with a flat end (top)

and a rod with a cone-ball end (bottom) ...................................... 67
Figure 3.10(a) Bar with double parabolic—lines and double tails.......................68
Figure 3.10(b) Drawing of the bar with double parabolic-lines

and double tails .................................................................... 68
Figure 3.10(c) Image of bar with double parabolic-lines and double tails ......... 69

Figure 3.11 Impact response of the flat bar with double
parabolic-lines and double tails ............................................... 71

Figure 3.12 Impact response of the bar with double-lines

and double tails ................................................................... 71
Figure 3.13 The assumed input wave, superimposed wave

and experimental curve ......................................................... 74
Figure 3.14 Experimental setup of the two-position technique ...................... 77

Figure 3.15(a) Experimental curves from two-position of a short bar

and from a long bar ............................................................ 78

Figure 3.15(b) Results based on the two-position technique ......................... 78

Figure 4.1 Assembly of the wired projectile ................................................ 89
Figure 4.2 Result measured by an instrumented rod with

the protected wound-lead wire ................................................ 90

Figure 4.3 Layout of the instrumented projectile ......................................... 93

Figure 4.4 Images of endmill (left) and round-corner cutting tool (right) ........... 94

xi

Figure 4.5(a) Overall geometry and dimensions of the projectile body ............. 96

Figure 4.5(b) Schematic of the wave transfer mechanism ............................. 96
Figure 4.6(a) Schematic layout of the instrumented projectile ........................ 98
Figure 4.6(b) Parts of the instrumented projectile ....................................... 99
Figure 4.6(c) Assembled instrumented projectile ........................................ 99
Figure 4.7 Input and output of a constant voltage test ................................ 101
Figure 4.8 Square wave testing result ..................................................... 103
Figure 4.9 Setup of the wave reduction test experiment .............................. 104

Figure 4.10 Comparison between the results from the long bar

and the projectile body .......................................................... 106
Figure 4.11 Setup for the calibration of the instrumented projectile ................ 107
Figure 4.12 Impact result measured by the instrumented projectile ............... 108

Figure 4.13 Comparison between the result from the long bar and that from
the instrumented projectile when they impact with each other ...... 109

Figure 4.14(a) Setup for impact test based on instrumented projectile .......... 110
Figure 4.14(b) Force history measured by instrumented projectile ................ 111

Figure 4.14(c) Force history measured by a low-velocity
drop-weight impact tester .................................................... 111

Figure A1 Schematic layout of the measurement system of the

instrumented projectile .......................................................... 122
Figure A2 Schematic of the Wheatstone bridge ........................................ 123
Figure A3 Schematic of the amplifier Circuit .............................................. 125
Figure A4 The schematic triggering circuits .............................................. 127

Figure A5 The circuit drawing of the signal processing,
data acquisition and saving .................................................... 129

xii

Figure A6 Both sides of the print board ................................................... 133

Figure A7 Pictures of the soldered signal processing

and data acquisition unit ......................................................... 134
Figure A8 Circuit drawings of the data transferring and its power supply ........ 140
Figure A9 Picture of the data transferring box ........................................... 141
Figure A10 Schematic of the velocity measurement ................................... 143

xiii

CHAPTER ONE

INTRODUCTION

1. BACKGROUND

Impact loading is commonly found in the real world. For example, two ground
vehicles crash into each other, an air vehicle is struck by a bird, and a marine
structure collides with icebergs. The crash, strike, and collision can cause
damage to vehicles. Injury to occupants is the primary concern in the study of
vehicle survivability and occupant safety. Many impact testing techniques and
devices have been developed in laboratories for material characterizations and
loading simulations. In Characterizing the behavior of materials and structures
subjected to impact loading, measurements of stress and strain histories are
required for establishing the constitutive models. In simulating the impact loading,
measurements of displacement, velocity, acceleration, and force histories during
impact events are necessary [1-4]. With the measured histories, impact
characteristics such as the maximum deflection and the energy absorption of the
materials and structures, and the peak force and the contact duration between
them and the impactor can be subsequently identified.

Among the various impact characteristics, energy absorption capability plays
the most important role in the study of vehicle survivability and occupant safety.
In order to Characterize the energy absorption capabilities of materials and
structures subjected to impact loading, several experimental techniques have

been developed and used by researchers. Among them, the simplest one is

perhaps to measure the velocities of the impactor before and after it contacts the
specimen [5, 6]. The energy absorbed by the specimen can be taken as the
difference of the kinetic energies of the impactor before and after the impact
event. This technique requires a relatively simple setup for velocity
measurements and works in both perforation and non-perforation (rebounding
from the Specimen) cases. However, this technique does not give detailed
information during the impact event, such as the deformation of the Specimen
and the change of impact force.

To better understand the energy absorption capability of a specimen and
even its mechanism of energy absorption, it is necessary to identify the
interaction between the impactor and the specimen through the entire impact
event. Several experimental techniques for measuring the histories of
displacement, velocity, acceleration, and force during impact events have been
developed and are commercially available.

High-speed cameras can provide detailed images of what exactly happens
during an impact event [5-9]. With sufficient photographs, the displacement
history, the velocity history, and even the acceleration history can be identified.
Since most impact events last only a very short period, such as no more than 1
millisecond, high-speed cameras with a very high frame rate and a capability of
recording sufficient frames within the short time period are required for extracting
accurate displacement, velocity, and acceleration histories. However, high-speed

photography is expected to be high cost.

With the advancement in laser diodes, high-speed photo-detectors and fiber
optics, researchers are able to build velocity measurement devices based on
integrating these components together to measure the velocity of impactors [10,
11]. The devices are able to sense very small Changes in velocity and give the
velocity history with high accuracy. However, the complexities of testing
environment and impactor geometry should not be underestimated because they
can further complicate the testing setup and affect the measurement.

Accelerometers of various designs and data acquisition systems with high-
speed capability have been developed for measuring acceleration history in
impact tests [12,13,33,34]. They have been found to be useful for investigating
relatively soft materials and structures, although their low natural frequencies
may hinder their uses in high-speed impact events.

Some force transducers are commercially available for measuring impact
force histories [14,15]. They measure the dynamic forces by sensing the motion
of piezoelectric elements inside them during impacts although they are usually
not calibrated dynamically. The application bandwidth of the force transducers is
often only around a few kHz and may limit their uses in high-precision
applications.

Strain-gage based load cells are also commonly used in impact tests [16-18].
The load cells measure the force history based on the deformation of specially
designed and machined components involved in the construction of the load cells.
The force history obtained from the load cells and the acceleration history

obtained from the accelerometers are commonly assumed to be interchangeable

with each other based on the corresponding mass of the impactor. However, due

to the difference in the nature of the individual sensors, care must be exercised.

2. STATEMENT OF PROBLEM

Multiple dynamic testing techniques have been developed for laboratory uses
ranging from material characterization to loading simulation. Examples are the
split Hopkinson’s pressure bar (SHPB) for characterizing dynamic stress-strain
relations [19-24], Taylor’s impact test [25] for finding dynamic yielding stress,
instrumented weight-drop impact test for obtaining material response under low-
velocity impacts, and gas gun for simulating ballistic impacts. Among the four
techniques mentioned, the SHPB and weight-drop impact test are instrumented
tests while Taylor’s impact and gas gun tests are non-instrumented.

Non-instrumented tests are much simpler than instrumented tests in
construction. They are usually built for Simulating loading conditions that occur in
the real world. Instrumented tests, however, are equipped with sensors to detect
physical quantities and require sophisticated data acquisition and signal
processing systems for further understanding the physics of the tests. Since
dynamic loadings usually last a very short instant and involve many physical
parameters during the events, instrumented tests are preferred over non-
instrumented tests in studying dynamic loading events.

There are many candidates for dynamic measurements. Optical methods,
such as fiber Fabry—Perot interferometer (EFPI) strain sensors and fiber Bragg

grating (FBG) strain sensors [26], are suitable for sensing dynamic strain

histories [27]. Magnetic methods, such as linear variable differential transformers
(LVDT) [28,29], are normally used for measuring dynamic displacements [30].
Electrical methods are more commonly used in dynamic measurements.
Capacitances based device can be used for sensing minimal distances [31].
Resistances based gages can be attached to an elastic element for sensing
strains. Piezoelectric effect based sensors [32] are used for sensing forces and
accelerations. The dynamic signals measured by these methods can be
converted into dynamic force histories under certain conditions.

Strain gages have been commonly used for measuring strain history [35—37].
Owing to their technology maturity, low sensitivity to environmental impact,
accessibility, and low cost, strain gages may be the most commonly used
techniques for measuring parameters involved in impact events [16-24,38]. The
measured strain history can then be converted into stress history and even force
history.

For Characterizing materials and structures under impact loading, the
instrumented projectiles will be accelerated to certain speeds before impacting
on the specimens. Fumes and fragments can occur in most cases. Therefore, the
methods concern delicate sensors, such as optical methods and the magnetic
methods, are not very suitable for use in the impact environment.

A major issue in measuring the signals in impact events is the understanding
of wave propagation [39-41]. When a rod is impacted on a specimen, the
compressive strain wave generated at the impact-contact surface would

propagate to the opposite end of the rod. The wave is then reflected back from

the free end of the rod as a tensile strain wave. This process could repeat many
times until the strain wave was completely attenuated. If the rod was long, the
strain wave would propagate in the rod back and forth without superposition. A
good example could be found in a split Hopkinson’s pressure bar. On the
contrary, if the rod was relatively short and the length of the strain wave was
relatively long, superposition of the transmitted portion and the reflected portion
of the strain wave would take place. The superposed wave pattern could become
very complex and be recorded in the measurements.

This thesis research is aimed at developing an instrumented free projectile for
Simulating and Characterizing impact events. Selecting a suitable sensor for
detecting the wave propagation in the projectile, converting the signal into
loading history, and solving the manufacturing issues are the primary goals of the

research.

3. ORGANIZATION OF THE THESIS

This thesis contains five chapters. Chapter 1 gives a general introduction.
Chapter 2 discusses the impact techniques and the effects of the types of sensor
on dynamic measurements. Chapter 3 addresses the elastic wave reduction
techniques and their applications in instrumented cylinders. Chapter 4 presents
the detailed procedures for designing and constructing a wireless instrumented
projectile for low-velocity impact tests. Chapter 5 summarizes the conclusions

and suggests recommendations for future studies.

Chapters 2, 3 and 4 are the core contents of this thesis research. They are
essentially arranged following the order of research progress but presented as
three independent documents with the latter ones closely referencing to the
former ones for clarity, continuity and completeness. For example, some
materials presented in Chapter 2 are repeated in Chapters 3 and 4. Similarly,
some materials given in Chapter 3 are also duplicated in Chapter 4. Hence, the
thesis may be considered as a collection of research works grouped into three
main subjects.

Chapter 2 is entitled “Sensor Effects and Signal Analysis in Impact
Measurements.” It compares the differences between vertical impact and
horizontal impact and evaluates the advantages and disadvantages of strain-
gage based load cells and piezoelectric/ piezoresistive accelerometers in
measuring low-velocity impact events. Horizontal impact with strain-gage based
load cell is found to be a better choice for studying the wave propagation
involved in dynamic impacts.

Chapter 3 is entitled “Wave Propagation in Force Transducers.” Although
strain wave reflection and superposition have been identified in Chapter 2, this
chapter presents two techniques for isolating the primary strain wave in cylinders
subject to impact loading, namely mechanical method and numerical method.
The former is based on geometrical effect to remove unnecessary wave
components reflecting from boundaries while the latter is essentially based on a
numerical process. Both methods are found to be efficient for identifying the

primary strain waves.

Chapter 4 is entitled “Design and Calibration of an Instrumented Projectile.” It
is also the ultimate goal of this thesis research. Many details involving the
manufacturing of the projectile body, the instrumentation of the sensor and the
calibration of the projectile are included in the study.

The design of a microprocessor is also the critical part to achieve a wireless,

high-bandwidth free projectile, which is presented in Appendix A.

REFERENCES

[1] Jan Hjelmgren, “Dynamic Measurement of Force-A literature Survey”, SP
Swedish National Testing and Research Institute, SP Measurement
Technology. SP REPORT 2002:27

[2] S. P. Virostek, J. Dual and W. Goldsmith, “Direct Force Measurement in
Normal and Oblique Impact of Plates by Projectiles”, Int. J. Impact Engng.
Vol. 6, No. 4, p247-269, 1987

[3] Ralph Burton, “Vibration and Impact”, Dover Publications, Inc. New York
10014,1968

[4] Jonas A. Zukas, Theodore Nicholas and Hallock. F. Swift, “Impact Dynamics”,
John Wiley & sons Inc. 287-308, 1982.

[5] Guoqi Zhu, Werner Goldsmith and C. K. H. Dharan, “Penetration of
Laminated Kevlar by Projectiles—I. Experimental Investigation”, Int. J. Solids
Structures, Vol. 29, No 4, pp.399-420, 1992

[6] Werner Goldsmith, Eric Tam, David Tomer, “Yawing Impact on Thin Plates by
Blunt Projectiles”, Int. J. Impact Engng, Vol. 16, No. 3, pp.479-498, 1995

[7] S. J. Bless, D. R. Hartman, “Ballistic Penetration of S-2 Glass Laminates”, 21St
International SAMPE Technical Conference, Sept. 25-28, 1989

[8] Stephan J. Bless, Moshe Benyami, David Hartman, “Penetration Through
Glass-Reinforced Phenolic”, 22nd International SAMPE Technical Conference,
Nov. 6-8, 1990. pp.293-303

[9] J.H. Choi, C. H. Lee, S.N. Chang and SK. Moon, “Long-Rod Impact
Phenomena: Role of Wave Interaction on Crack Propagation”, Int. J. Impact
Engng. Vol. 17, pp.195-204, 1995

[10] Jun Lu, Subra Suresh, Guruswami Ravichandran, “Dynamic indentation for
determining the strain rate sensitivity of metals”, Journal of the Mechanics
and Physics of Solids, 51 (2003), pp.1923 — 1938

[11] Jun Lu, “Mechanical Behavior of 3 Bulk Metallic Glass and its Composite
over a Wide Range of Strain Rates and Temperatures”, Thesis for the
Degree of Doctor of Philosophy, California Institute of Technology,
California, March, 2002

[12] Eirik Svinsas, Cathy O’Carroll, Cyril M. Wentzel, and Anders Carlberg,
“Benchmark Trial Designed to Provide Validation Data for Modelling”

[13] Michael A. Christopher, Tim S. Edwards, “Instrumented Projectile”, NDIA
48th Annual Fuze Conference, NSWC / Dahlgren Division

[14] www.0mega.com
[15] www.instron.com

[16] Michael J. Dixon, “Development of a Load-cell compensation System”,
Experimental Mechanics (31 ), p21-24, 1991

[17] Michael J. Dixon, “A Traceable Dynamic Force Transducer”, Experimental
Mechanics (30), p152-157, 1990

[18] D. R. Ambur, C. B. Prasad and W. A. Waters, Jr., “A Dropped-weight
Apparatus for Low-speed Impact Testing of Composite Structures”,
Experimental Mechanics 35(1), p77-82, 1995

[19] C. Bacon, “Numerical prediction of the propagation of elastic waves in
longitudinally impacted rods: application to Hopkinson testing”, International
Journal of Impact Engineering, 13 (4), 527-539, 1993.

[20] Jonas A. Zukas, Theodore Nicholas and Hallock. F. Swift, “Impact
Dynamics”, John Wiley 8. sons Inc. 287-308, 1982.

[21] D. J. Frew, M. J. Forrestal and W. Chen. “Pulse shaping techniques for
testing brittle materials with a split Hopkinson pressure bar", Experimental
Mechanics, 42 (1), 93-106, 2002.

[22] Michael Adam Kaiser, “Advancements in the split Hopkinson bar test”,
Master’s thesis, Blacksburg, Virginia, 1998.

[23] Frank E. Hauser, “Techniques for measuring stress-strain relations at high
strain rates”, Experimental Mechanics, 395-402, 1966.

[24] J. F. Bell, “An experimental diffraction grating study of the quasi-static
hypothesis of the split Hopkinson bar experiment”, J. Mech. Phys. Solids, 14,
309-327,1 966.

[25] Gong, Song, “The Analysis of dynamic stress and plastic wave propagation
in the Taylor impact test”, PhD thesis, Michigan State University, Dept. of
Mechanical Engineering, 2006

[26] Liu, J-G., Schmidt—Hattenberger, C. and Borm, 6., “Dynamic strain
Measurement with a fiber Bragg Garting Sensor System”, Measurement,

10

Vol. 32, 2002, pp. 151-161

[27] Jin, W. L., Venuvinod, PK. and Wang, X., “An Optical Fiber Sensor based
Cutting Force Measuring Device”, International Journal of Machining and
Tools Manufacturing, Vol. 35, No. 6, 1995, pp. 877-883

[28] www.rdpe.com
[29] www.sensotec.com

[30] L. E. Malvern, “The Propagation of Longitudinal Waves of Plastic
Deformation in a Bar of Material Exhibiting a Strain-rate Effect”, Journal of
applied mechanics, Trans. ASME, 18, p203-208, 1951

[31] www.synaptics.com
[32] www.pcb.com

[33] Robert W. Lally, PCB Piezotronics, Inc. Buffalo, N. Y. “Testing the Behavior
of structures”, Reprinted from TEST, Aug/September 1978

[34] William G. Halvorsen, David L. Brown, “Impulse Technique for Structural
Frequency Response Testing, Sound and Vibration”, November 1977, p8-
21, 1977

[35] Sia Nemat-nasser; Jon B. lsaacs; John E. Starrett, “Hopkinson Techniques
for Dynamic Recovery Experiments”, Proc. Roy. Soc. London 435 (A), p371-
391, 1991

[36] M. Vural and D. Rittel, “An Educational Visualization Technique for Kolsky
(split Hopkinson) Bar’, Experimental Techniques, Nov-Dec 2003, p35-39.
2003

[37] Daniel J. lnman, “Engineering Vibration”, Prentice Hall, Englewood Cliffs,
New Jersey 07632, 1994

[38] S. Venzi, A. H. Priest, and M. J. May, “Influence of Inertial Load in
Instrumented Impact Tests”, Impact Testing of Metals, ASTM STP 466,
American Society for Testing and Materials, 1970, pp.165-180

[39] J Reed, “Energy losses due to elastic wave propagation during an elastic
impact”, J. Phys. D: Appl, Phys. 18(1985) pp. 2329-2337, Printed in Great
Britain

[40] Karl F. Graff, “Wave Motion in Elastic Solids”, Unabridged Dover (1991)

[41] M. T. Martin and J. F. Doyle, “Impact force identification from wave
propagation responses”, International Journal of Impact Engineering
Vol. 18, Issue 1, January 1996, pp. 65-77

12

CHAPTER TWO
SENSOR EFFECTS AND SIGNAL ANALYSIS

IN IMPACT MEASUREMENTS

ABSTRACT

Comparison between vertical impact and horizontal impact was of primary
interest in this study. Both accelerometers and strain gages were used in the
impact measurements. These two types of sensors gave comparable
measurements of acceleration/force histories for relatively soft materials
subjected to relatively low-velocity impacts. However, as impacted materials
become harder and impact velocities became higher, the dynamic
measurements from these two types of sensors become more Significantly
different. During impact events, reflected waves and transmitted waves
superimposed with one another and resulted in a mountain-shaped strain history.
In order to investigate the details of wave propagation in the impact events in a
more analytical manner so that experimental results could be compared with the

numerical simulation, some instrumented rods were built.

13

1. INTRODUCTION

In studying the behavior of materials subjected to impact loading, the
measurement of force or acceleration history during the impact events is
necessary [1, 2]. With the measured history, some mechanical Characteristics
such as the peak force, the maximum deflection, and the energy absorption of
the materials [3, 4] can be subsequently identified.

There are many methods suitable for the measurement. Optical [5] and
magnetic [6] methods had been used for particle velocity history measurement;
strain gages [7-9] were widely used for strain history as well as wave traveling
measurement; and accelerometers [10,11] were used for measuring acceleration
history. The measured particle velocity history or strain history can then be
transferred into force history or acceleration history under certain conditions.
Since the impact sensors have to endure a harsh environment due to the impact
events, the optical and magnetic methods are not suitable for general purpose
impact sensor designs.

Sensors such as load cells and accelerometers are commonly used in the
impact tests [12-14]. Load cells measure the force history, while accelerometers
measure the acceleration history. The force history and the acceleration history
are commonly assumed to be interchangeable with each other if the
corresponding mass of the impactor can be taken as a rigid body. However, due
to the difference in the nature of the individual sensors, care must be exercised.

A calibration is required before the use of a sensor [15]. Load cells based on

electrical resistance strain gages are usually calibrated with static loading, as

they are sensitive to deformation. For example, several deadweights can be
added to a load cell to establish the relationship between the loads and the
corresponding electronic outputs to identify the calibration factor. The calibration
factor obtained from the static loading, however, may pose errors when used in
dynamic measurements as static loading involves deformation while dynamic
loading comes with wave propagation.

Being different from load cells, accelerometers are sensitive to motions but not
deformations. When an accelerometer is subject to a motion, it can cause
relative movements in the internal mass blocks and result in a corresponding
reading associated with the acceleration it experiences. Accordingly,
accelerometers are frequency dependent and require extra care in obtaining
constant calibration factors.

The installation of sensors is not a trivial task. To avoid being damaged, the
sensors should not be mounted on the impact surfaces. Often times, they are
also encapsulated by a cover component for protection [16]. The dislocation and
the additional mass in front of the sensors can introduce additional errors to the
measurements [17].

The distance between the contact surfaces to the sensor’s positions exists for
most measurements. The impact forces generate when the impact occurs, but
the sensors can not measure the forces immediately because of the time
required for the impact force to transfer from the contact end to the sensors’
positions. The transferring dynamic force/acceleration Shows as the strain wave

propagates along the whole sensor structure at the sound speed of its material

15

[18-20]. The strain waves will rebound and superimpose with each other, making
the measured values complex.

Stainless steel 347 is a well-known material for elastic wave propagation from
the former research about split Hopkinson pressure bar. If a one-dimensional bar
is deformed in elastic stage and just the elastic wave stays in the bar, the strain
could be proportional to the stress. Therefore, the stress will be proportional to
the impact force. Hence, a stainless steel 347 bar with 19mm diameter was cut
into several pieces to work together with a load cell and accelerometers. Strain
gages were installed on the surface of the bar along the axis direction to
measure the dynamic strain during impacts. The bars are called “strikers” in the
following chapters when strain gages have been installed.

The impact devices could be roughly divided into two groups: vertical impact
devices and horizontal impact devices. The vertical impact devices usually raise
a weight to a certain height and then release it to achieve the impact velocities.
Sometimes an extra power source such as pressure gas or a spring is used to
achieve a higher-impact velocity. Extra-weight blocks could be added to the
weight to increase the impact energy [21]. Horizontal impact devices usually use
a gas gun as a power source to push bullets to impact the specimen. Some
researchers use a gas gun and a spring together. The bullet could be
accelerated to very high velocities to impact the specimens. These two impact
methods are both used in this research.

In order to compare the differences among the different measurement

methods, several impact tests were designed and carried out. There are two

16

groups of tests in vertical impact tests: one is the load cell, a striker, and an
accelerometer together for several different specimens; another is the load cell
and two accelerometers that work together for different specimens. There are
three groups of tests in horizontal tests: the first has a striker and an
accelerometer working together for different specimens, the second is a striker
impacts on the load cell directly, and the third one involves three pairs of gages
on the different positions of a striker for different specimens. A simulation for the

wave superposition is also presented.

2. EXPERIMENTAL TECHNIQUES
2.1 Sensors and Data Acquisition

Two accelerometers and one load cell were used in the experiments. One
accelerometer was of piezoelectric type and had a mass of 10.5 gm (gram). It
had high precision for measurements of acceleration up to 500 g (gravitational
acceleration) and frequency up to 10 kHz. The other accelerometer weighed only
1 gram and was of a piezoresistive type. It is useful for applications that require
accelerometers with small mass. lts capability was up to 2,000 g for acceleration
and up to 7 kHz for frequency. The load cell was based on electrical resistance
strain gages and had a maximum capacity of 22.5 kN.

Three cylindrical striker bars with a diameter of 19 mm were also prepared.
They were made of stainless steel 347 because of its low-sensitivity to strain
rate. Several sets of strain gages were mounted on the striker bars. Each set

contained two gages located on two opposite sides of a striker bar. They were

I7

then connected to the opposite arms of a Wheatstone bridge Circuit to allow the

measurements of axial deformation while eliminating the bending effect. Power

supplies and amplifiers were required to enhance the output signals from the

accelerometers and the Wheatstone bridge circuits.

Table 2.1 summarized the sensors and their signal amplifying and data

acquisition systems.

Table 2.1 Parameters of sensors and data acquisition system

 

 

 

 

 

 

 

 

 

 

 

Piezoelectric Piezoresistive Strain gage Strain Gage
accelerometer accelerometer based load Based
cell Striker bars
Measurement :I: 500 g :t 2000 g 22.5 kN 58 kN
range
Frequency 0.7Hz-10 kHz 0.7Hz-7 kHz 4 kHz To be
range determined
Resonance 38 kHz 25 kHz To be To be
frequency determined determined
Amplifier’s 100 kHz 150 kHz 4 kHz 150 kHz
bandwidth
Sampling 5MS/s 5MS/s 5MS/s 5MS/s
rate

 

2.2 Experimental Setup and Procedure

Both vertical impact and horizontal impact tests were investigated. One

objective of the studies was to identify the effects of gravitational acceleration on

the dynamic force measurements.

 

A. Vertical Impact Systems
In the vertical impact system, a drop-weight impact testing machine was used.

Two types of tests were performed.

a. Load-cell type

In the first type, as shown in Figure 2.1(a), the load cell was located between
the drop-weight and the impactor tup. The impactor tup was made of hardened
steel and had a diameter of 12.7 mm and length of 55 mm. The piezoelectric
accelerometer was attached to the drop-weight, while the piezoresistive
accelerometer was mounted between the load cell and the impactor tup. In this
type of test, the load cell was the primary impactor, hence, this type of vertical

impact system was called the load-cell type.

,_____i3,-'-_~__ - - Piezoelectric acc.

 

 

 

 

 

 

 

 

If»
I \
3 --------- Load cell
[1 I:
x T ........ Piezoresistive acc.
\\‘\“‘ < ...... ~ ~’::,
"""" Impactor tup

 

 

 

 

Figure 2.1 (a) Vertical impact tests: the load-cell type

I9

uuuuuu

' Piezoelectric acc.

 

 

 

 

Striker bar &
strain gages

 

[l

Load cell

 

 

 

 

 

 

Figure 2.1(b) Vertical impact tests: the striker-bar type

b. Striker-bar type

In the second type, as shown in Figure 2.1(b), a 200 mm-Iong striker bar was
added to the impact testing machine. It was attached to the drop-weight and was
used as the impactor with a set of strain gages 32 mm from the free end. Hence,
this type of vertical impact was called the striker-bar type. Similar to the load-cell
type, the piezoelectric accelerometer was attached to the drop-weight. The load
cell was located underneath the specimen.

A triggering device based on an infrared photocell was used to start the
recording of the outputs from the striker bar, the load cell, and the
accelerometers. The recorded data points were stored in a computer for
processing. The purpose of performing these two types of test was to compare

the measurements from the strain gages and the accelerometers.

20

B. Horizontal Impact Systems

In horizontal impact systems, a gas gun was used to accelerate striker bars. A
connector was designed as a transition unit between the gun barrel and the
striker bars, because the former had an inner diameter of 12.7 mm while the
latter had an outer diameter of 19mm. In each impact system, half of the striker
bar was inserted into the transition unit and accelerated by a high-pressure
nitrogen gas. Three types of setup were carried out in the horizontal impact tests.
The comparison of the measurements based on strain gages and
accelerometers could be made, as could the effect of sensor location on the

measurements.

a. Typel

The setup of type I included a 200 mm-long striker bar. The bar was
instrumented with the piezoresistive accelerometer and a set of strain gages.
They were located 15 mm from the impacting end as shown in Figure 2.2(a).

Several kinds of material were tested with this type of horizontal impact system.

b. Type II

The setup of type II included a striker bar and the load cell, as shown in Figure
2.2(b). The striker bar was 250 mm long, a set of strain gages were located 37.5
mm from the impacting end. The load cell was held horizontally to a solid wall.

The horizontal axes of the load cell and the striker bar were carefully aligned.

21

The data acquisition system for the striker bars was triggered by the
electromagnetic valve of the gas gun. The triggering device for the load cell, as
mentioned earlier, was based on an infrared photocell. A triggering device was

designed to synchronize the readings of the striker bar and the load cell.

c. Type III

The setup of type III was similar to that of type I, as Shown in Figure 2.2(c).
However, it used a 250 mm striker bar and three sets of strain gages. The sets of
strain gages were located 37.5 mm, 75 mm, and 112.5 mm from the impact end.

Several types of material were tested.

strain gages

 

///

 

4»

(a) f §;____j <---- specimen

#-

 

 

 

 

 

I

striker bar piezoresistive acc.

strain gages

 

 

 

 

 

 

V
, [2 p
(b) .4 2- 1 m 5
A A “/
' ' /
striker bar load cell

22

strain gages

 

 

v I // /
(C) E a. .a._..j:-,,,,,_,J 4: ------ Specimen

 

 

striker bar

Figure 2.2 Horizontal impact systems (a) type I, (b) type II and (C) type III

3. EXPERIMENTAL RESULTS

In impacting tests, the output of a load cell was force history, while that of an
accelerometer was acceleration history. In order to compare the different
measurements from the different types of sensors, all dynamic measurements
were converted into the same unit, either force or acceleration. Based on careful
alignment, the striker bars in all these systems were assumed to be under one-
dimensional, elastic deformation during impacting. The strain histories recorded
by the sets of strain gages could be multiplied by the Young’s modulus and
cross-sectional areas of the striker bars to determine the correspond impacting
forces. The corresponding accelerations were calculated by dividing the impact

forces by the mass of the bars.

3.1 Vertical Impact Test Systems

A. Load Cell Type

23

In this type of impacting testing, two kinds of specimen were used in the
investigations: one was a 19mm-thick aluminum plate covered by a 13 mm-thick
vinyl layer, while the other was covered by a 3 mm-thick vinyl layer.

For the specimen covered with the thicker-vinyl layer, all three sensors had
very similar acceleration histories through the entire impact event if the maximum
acceleration was around 50 g. If the maximum acceleration was increased to 140
g, the similarity of the acceleration histories maintained very well except at the
very end of the impact event, as shown in Figure 2.3(a). It was also noted that
the curve obtained from the load cell was quite smooth. The curves obtained
from the piezoelectric and piezoresistive accelerometers, however, had very
large oscillations. If the maximum acceleration was raised to 250 g, the
oscillation in the accelerometers became very significant. In Figure 2.3(a), the
oscillation frequency in the curves from the accelerometers, after 8 ms, matches
well with one of the natural frequencies of the drop weight (710 Hz), and the
oscillation frequency in the curve from the piezoresistive accelerometer,
especially from 3 ms to 7 ms, is close to the first bending frequency of the impact

tup (~32 kHz).

24

1601

— Piezoresistive acc.
Piezoelectric acc.
— Load cell

*

 

 

120 - ” t
I” ‘ —-
80 - I \.
a. x
40] “'1 7
V8.
0 _ JIJIITI I I '.
_40 _2 4 6 8 k/ 1
t(ms)

Figure 2.3(a). Aluminum with thick vinyl under vertical impact, load cell type

For the specimen covered with the thinner-vinyl layer, the acceleration curves

obtained from the two accelerometers were very

the piezoelectric accelerometer was slightly

piezoresistive accelerometer. However, the result obtained from the load cell was
quite different from those obtained from the accelerometers. As shown in Figure

2.3(b), all three curves are very similar up to the peak acceleration. Beyond it,

however, huge oscillations are seen in the curves

that obtained from the load cell remains to be very smooth. The major oscillation

frequency in the curves from the accelerometers matches well with one of the

natural frequencies of the drop weight (710 Hz).

25

, s

12

similar, though the curve from

higher than that from the

from the accelerometers, while

—— Piezoresistive acc.
300 - —— Piezoelectric acc.
—— Load cell

j \

   
 

 

-100 - t (ms)

 

 

-200 -

Figure 2.3(b) Aluminum with thin vinyl under vertical impact, load cell type

The results from the foregoing experiments seemed to indicate that the
measurements from the two types of accelerometers agreed with each other
quite well in all tests. However, the measurements from the load cell and the
accelerometers agreed well only when the maximum acceleration was relatively
low and the impacted specimen was relatively soft. When the maximum
acceleration became higher and the impacted specimens became harder, the

results between them deviated greatly.

26

B. Striker-Bar Type

In these vertical impact tests, the specimens were identical to those used in
the vertical impact tests based on the load-cell type. The specimens were placed
on the specimen holder supported by the load cell.

When the maximum acceleration was relatively low and the impact specimen
was relatively soft, the acceleration histories from the striker bar, the load cell,
and the piezoelectric accelerometer were very similar although minor oscillation
was found in the result obtained from the striker bar. Figure 2.4(a) Shows the
results for the aluminum plate covered with the thick vinyl when the maximum
acceleration was up to 70 Q.

When the maximum acceleration became higher and the impact specimen
became harder, the acceleration histories from the striker bar and the load cell
remained to be consistent. However, that obtained from the piezoelectric
accelerometer had major oscillation and deviated significantly from those
obtained from the strain-gage based sensors. Figure 2.4(b) shows the results for
the aluminum plate covered with the thin vinyl when the maximum acceleration
was up to 250 9. Once again, the curve from the accelerometer shows the

natural frequency of the drop weight — 710 Hz.

27

80 - Piezoelectric acc.
— Striker bar
— Load cell

   
  

 

 

40 -
a)
20 -
U l I I l
O 2 4 6 8
-20 _
t (ms)

Figure 2.4(a) Aluminum with thick vinyl under vertical impact, striker-bar type

- Piezoelectric acc.
— Striker bar
— Load cell

 

 

 

t (ms)

Figure 2.4(b) Aluminum with thin vinyl under vertical impact, striker-bar type

It was also noted that the results from the striker bar and the load cell agreed
with each other very well in all cases. These agreements were believed to be

attributed to the fact that both the striker bar and the load cell were based on

28

deformation. The different characteristics between the strain-gage-based
sensors, e.g. the striker bar and the load cell, and the accelerometers, either

piezoelectric type or piezoresistive type, were once again verified.

3.2 Horizontal Impact Systems

A. Typel

Two kinds of specimen were investigated. One was a 25.4 mm steel plate
covered with a layer of rubber of 12.7 mm and the other was a 3.2 mm thick
glass/epoxy plate. The two sensors gave similar acceleration histories for both
kinds of specimen. Figure 25(3) and 2.5(b) show the results. The striker bar
seems to oscillate more than the piezoresistive accelerometer in the impact test
for the steel plate covered with rubber. However, the piezoresistive
accelerometer seems to oscillate more than the striker bar in the impact test for
the glass/epoxy plate. In Figure 2.5(b), the oscillation frequency in the curve from
the piezoresistive accelerometer is very Close to the striker’s first bending

frequency — 2020 Hz.

29

550 -
450 -
350 -
250 -
150 -

50- ..

-50 *

 

-150 -

[AI — Striker bar

r Piezoresistive acc.

 

t (ms)

Figure 2.5(a) Steel with rubber under horizontal impact, type I

650 -
550 -
450 -
350 -
U) 250 -
150 -

 

-150 -

_ Striker bar

/ \ Piezoresistive acc.

 

t (ms)

Figure 2.5(b) Glass/epoxy under horizontal impact, type I

30

B. Type II

In this test, the load cell was impacted by a striker bar horizontally. The
spherical nose of the tup of the load cell used in the vertical impact test (the load
cell type) was replaced by a flat nose with a diameter slightly smaller than that of
the striker bar. The impact duration was very short due to the high rigidities of the
tup of the load cell and the striker bar. The force histories are shown in Figure
2.6. The force history from the striker bar has double peaks while that from the
load cell has only one single peak. The slow increasing / decreasing shapes of
the curve from the load cell are probably due to its low frequency range (4 kHz).
The oscillation frequency in the curve from the striker bar (~20 kHz) matches well

with the inverse of the elastic wave traveling time in the 250 mm striker bar.

 

 

 

10 w
8 J
— Strikerbar
2 5 - Loadcell
'3‘,
a) 4-
8
0 K
LL. 2.. _
0 ,/ f I Iii-Iriifi
0 0.05 0.1 0.15 v 0.2
-2 -

t (ms)

Figure 2.6 Striker bar and load cell under horizontal impact, type II

31

C. Type III

In this test, the striker bar impacted perpendicularly on a 25 mm thick steel
plate covered with a layer of rubber of 1 mm. There were three sets of strain
gages on the striker bar. Their force histories are shown in Figure 2.7. They have
similar oscillation patterns. Each major oscillation seems to include three to four
minor oscillations. AS shown in the diagram, the maximum force decreased as

the gages were located farther away from the impact end.

 

3 0 -
2 5 d \rI:1—-—-— 38 mm
20 - 3' '2‘; —— 76 mm
3 15 - ,5: [I ------ 114 mm
. I
ll 1‘ ,_ n
E; 1 0 T I : 0‘ v In ?
3-1 I I ’ TI} I 7,:
L3 5 q l . '1‘.
1'! '1 , . '1: '
0 _ f.“ . . ‘ - 'v‘. ‘1' l-V,«"'fll'(l [fix
_ 5 _ ll"~._,r"‘;'. It .' Liv“; I'l‘__,l'1w.£
10.5 0.6 0.7 0.8 0.9 1
-1 0
t (ms)

Figure 2.7 Force histories from type III horizontal impact

3.3 Structures’ spectrum tests and signals’ spectral analysis
Spectral testing results for the drop weight system and the striker bar with

piezoresistive accelerometers are presented in Table 2.2.

32

Table 2.2 Spectrum testing results

 

 

 

 

 

 

 

 

The whole system 84 Hz
The cover plate on drogweight 240 Hz
Drop weight Drop weight, vibrate horizontally 420 Hz
impact device Drop weight, knock on top beam 528 Hz
Drop weight, knock on lower 710 Hz
beam
Striker with First bending mode 2020 Hz
piezoresistive Second bending mode 5360 Hz
accelerometer

 

 

 

 

The spectral analysis of the signals in Figure 2.3(b), Figure 2.4(b), Figure
2.5(b), and Figure 2.7 are listed in Table 2.3.

Table 2.3 Spectrum analysis of the signals in Figure 2.3(b), 2.4(b), 2.5(b) and 2.7

 

 

 

 

 

 

 

 

 

Major frequencies of the signals
in frequency domain
Piezo- Piezo- Load Striker Comments
electric resistive Cell -
Acc. Acc.
Figure 100 Hz, 100 Hz, 100 Hz N/A Drop weight natural
3 2.3(b) 700 Hz 700 Hz, frequency: 710 Hz;
.2 26500 Hz Piezoresistive
E Figure 200 Hz, N/A 200 Hz 200 Hz Accelerometer’s
> 2.4(b) 710 Hz resonance frequency:
25000 Hz
_ Figure N/A 170 Hz, N/A 170 Hz First natural frequency
:3 2.5(b) 1920 Hz of the striker: 2020 Hz
5 Figure N/A N/A N/A 10 kHz, They are the
E 2.7 20 kHz longitudinal natural
2 frequencies of the
striker

 

 

 

 

 

 

4. DISCUSSIONS

4.1 Load Cell vs. Striker Bar

33

The striker bars were built based on strain gages. When the striker bars
deformed, they caused the strain gages attached to them to undergo the same
deformations. The deformation histories were then converted into force histories
with a calibration factor. The load cell was constructed based on the same
principle. Experimental results based on Figures 2.4 clearly indicated that the
load cell and the striker bars, both based on strain gages, gave similar
measurements. Their differences in Figure 2.6 are due to the low frequency
range of the load cell and the wave superposition effect in the striker bar. The

wave superposition effect will be discussed later.

4.2 Piezoelectric Accelerometer vs. Piezoresistive Accelerometer

The two accelerometers used in this research were quite different in their
constructions and measurement principles. When subjected to excitation, the
piezoelectric accelerometer produced Charges while the piezoresistive
accelerometer experienced resistance Change. The application ranges of
acceleration and frequency were different for the accelerometers, as was the
error percentage. However, the results obtained from the experiments, as shown
in Figures 2.3, were very similar. The small differences between their results are

probably due to the different locations at which they were mounted.

4.3 Strain Gages vs. Accelerometers

The difference between the measurements from the strain gage based

sensors and the accelerometers were very significant. The strain gage based

34

sensors measured the impact forces based on the deformation of the strain
gages, which was also the deformation of the impactor. The accelerometer
measured the accelerations based on the relative motions between the inside
mass of the accelerometer and its base, which is also the impactor on which the
accelerometers attached. When an impactor is subjected to contact-impact, it
experiences both deformation and rigid body motion. If a strain gage is carefully
mounted on the impactor, it should deform with the impactor, and its
measurement should be almost the same as the deformation of the impactor.
The strain gages, however, can not sense the rigid body motion. On the contrary,
accelerometers measure the rigid body motion of its base, and the motion is from
both the deformation and the whole impacter’s motion. Hence, the sensitivities of
the strain gage and the accelerometer are strongly dependent on the rigidity (or
flexibility) of the impactor. An impactor with adequate flexibility is required for
strain measurements, while high rigidity is desired for high accuracy of
acceleration measurements. The strain rate dependency and viscoelastic
property of the impactor are also important to the responding time and the
measurement accuracy of the sensors. Rigid materials tend to respond instantly,
while flexible materials have a time delay. Hence, time lagging and response
overshooting can occur. They usually are not significant, except that the impact
period is very short.

Experimental results seemed to support the aforementioned statements. In the
vertical impacts, as shown in Figures 2.3(a) and 2.4(a), the strain gage based

sensors and the accelerometers gave similar acceleration curves when the

35

specimen was relatively soft and the impact velocity was relatively low. However,
as the specimen became harder and the impact velocity became higher, the
measurements from the accelerometers showed significant oscillations, as
shown in Figure 2.3(b) and 2.4(b). This resulted in much larger discrepancies
with those from the strain gage based sensors. The source of the oscillations
was believed to be tied to the vibrations of the impactor, the specimen, and the
impact test system. The discrepancies between the two types of sensors,

however, were not Significant, as Shown in Figures 2.5.

4.4 Vertical Impact vs. Horizontal Impact

The vertical impact systems used gravitational force to perform low-velocity
impacts, up to 4m/s. A pneumatic system could be added to double the impact
velocity. The horizontal impact systems, however, were able to achieve higher
impact velocities with the use of a high compressed gas. The experimental
results of the vertical impacts, shown in Figures 2.3 and 2.4, revealed that the
difference of acceleration histories between the two types of sensors became
very Significant at high acceleration levels. However, the difference of
acceleration histories between the two types of sensors from the horizontal
impacts, shown in Figures 2.5, was not affected significantly at high acceleration
levels. This is because the lower natural frequencies of the vertical impact

systems played a key role in the vertical impacts.

36

5. ANALYSIS
5.1 Effects of Masses

The impact-contact forces occurred between the impactors and the test
specimens were of primary interest in the impact tests. However, both strain
gages and accelerometers could not be installed exactly at the contact surfaces.
There was always a fore-mass, such as the tup of the impactor, located in front
of the sensoring component. An aft-mass was also frequently added behind the
sensoring component for various impact simulations. Both the fore-mass and the
aft-mass were usually made of rigid materials and firmly connected to the
sensoring component. These masses, however, had a significant effect on the
measurements.

Figure 2.8(a) shows the organization of an impactor, while Figure 2.8(b)

shows the free-body diagrams of individual components. Based on Newton’s
second law, the following equation of motions for the aft-mass component,

sensoring component, and fore-mass component can be established.

37

aft-mass rna

 

 

 

sensoring rnS

 

 

Fma
fore-mass mf

 

 

 

 

 

 

 

 

 

 

 

I ”c

Figure 2.8 Schematic diagrams of (a) impactor and (b) individual components

End _mag : maama (13)
E —m,g "‘17,... =msams (1b)
FL—mfg—FS =mfamf (1c)

Rewriting the equations, they become

Fma = ma (g + an...) (2a)
E =5... +7". (g +0....) =ma (g +ama) +7". (g +4....) (2b)
E :E +”?f(g+amf) :niz(g+ama) +17%: (g+ams) +%@+%f) (26)

If the mass of the sensor mS is negligible, the foregoing equations can be

simplified as follows.

38

Fma =ma(g+ama) (33)

E9 =Fma+ms(g+ams):ma(g+ama) (3b)

1;;=13;+mf(g+amf):ma(g+ama)+mf(g+amf) (3C)
Apparently, there is always a difference between the force measured by the

sensor FS and the real contact force Fc. The difference between them is

associated with the inertia force of the fore-mass, i.e. m f (g + amf) . Hence, in

order to reduce the measurement error, it is necessary to reduce the fore-mass.
Similarly, in order to compare the measurements from different sensors, it is
imperative that the sensors must be installed in the same locations. Results
given in Figure 2.7 seem to support this analysis.

Once the fore-mass becomes negligible, all three force measurements

become the same and are equal to the inertia force of the aft-mass, i.e.
Fma=E=E=ma(8+ama) (4)

Besides, it is interesting to point out that the gravitational acceleration will vanish

if the vertical impact system is changed to a horizontal impact system, i.e.

Fma = maama (53)
P; :- Fma + msams : maama (5b)
Fc = Fs + mfamf = maama + mfamf (5C)

Moreover, in static loading, the following equilibrium equations hold.

39

F =F=F m

5.2 Effect of Wave Propagation

When a striker bar was impacted on a specimen, the compressive strain wave
generated at the impact-contact surface would propagate to the opposite end of
the striker bar. The wave then was reflected back from the free end of the bar as
a tensile strain wave. This process could repeat many times until the strain wave
was completely attenuated. If the striker bar was long, the strain wave would
propagate in the striker bar back and forth without superposition. A good
example could be found in a split Hopkinson’s pressure bar. On the contrary, if
the striker bar was relatively short and the length of the strain wave was relatively
long, superposition of the transmitted portion and the reflected portion of the
strain wave would take place. The superposed wave pattern could become very
complex and be recorded in the measurements.

The striker bars used in the foregoing horizontal impact tests had a cylindrical
shape. The wave patterns in them, hence, could be analyzed with ease even if
complex superposition were involved. On the contrary, the wave patterns in the

load cell could not be simple because of the complex geometry of the load cell.
A. Basic Wave Equation

Consider a slender bar under uniaxial stress and neglect the Poisson’s effect.

For a small segment of the bar, the equation of motion can be expressed as, [22]

40

 

6 Cu 8211 au
— EA— = A + A——
6xI ax] p at2 77 6t q (7)

where E is Young’s modulus, p is density, A is the cross-sectional area, 27 is
damping coefficient per unit volume, q is the external force per unit length, I is

time, and u is displacement along the axial direction x. Assuming that both the
modulus and the cross-sectional area do not vary with position and the solution
of Eqn. (7) can be expressed in spectral representation, it yields

A

dzu

2

EA

 

+ ((0sz — iamA)u = 0 (8)

where a) is the angular frequency. The solution of the foregoing equation is

A —'kx 'k.
u(x) = Cle ’ + C26+1 "

 

 

k _ \/(o2pA —ia)77/l
= (9)
EA

where C, and C2 are undetermined amplitudes. With the inclusion of time

variation, this solution corresponds to two waves: a fonivard wave and a

backward wave.

u (x,t) : Z Cle—i(kx—a)t) + Z Cze+i(kx+wt) (10)

If a force history P(t) is applied to a bar end, then at x=0 (the bar end)

EA 6u(x,t) = —p(t)
6x

 

41

Let all functions of time have the spectral representation; the boundary

condition becomes, in expanded form

d A iwt A iwt
EA Egun(x)e " =—Zn pne "

This has to be true for all time, hence the equality must be true on a term by

term basis giving

dun _ _ A
—dx .0"

At x=0, there is only a forward moving wave, so the condition becomes

EA

A

EA {—lkCl} = —P or

A

C P
1 — ikEA

 

The displacement of the forward wave becomes

/\

1 P e—i(kx—a)t)

W"): EA— .1. <11

and the corresponding force is

F()C,t) : —ikEAu : _Z Pe—i(ICX—a)t) (12)
B. Simulation

42

As mentioned earlier, a compression wave occurred in a striker bar when it
collided with a solid. The wave propagated into the free end and reflected back
with a tensile magnitude. It was believed that this tension wave caused the
separation effect of the striker bar from the solid when it reached the contact-
impact surface. The wave would again rebound from this surface as compression
wave and continue to propagate between the two free ends until the strain
energy dissipated.

In simulating the wave propagation in the striker bar, a sinusoidal wave was
input into the striker bar, as shown In Figure 2.9. The following material

properties and wave parameters were used in the simulation: E: 192 GPa, p =

7,560 kg/m3, a): 2717‘, T: 1/f = 2UC; where the length of the striker bar L: 250
mm and the elastic wave velocity C= /% = 5,040 Me. With six rebounds, the

overlapped wave pattern is shown in the diagram along with the experimental
measurement. They seem to agree with each other reasonably. This result
indicated the nature of wave propagation in the cylindrical striker bar and the

difference between the input Signal and what was experienced in the bar.

43

 

DJ
0

  
   

M
(It

 

Simulated

N
O

' input

p—n
LII

Experimental

Force (kN)
3

LII

 

 

 

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9
Time (ms)

Figure 2.9 Wave patterns based on measurement and simulation.

A similar analysis was also applied to the horizontal impact of type II, as
shown in Figure 2.6. Apparently, there was a dent in the force history measured
by the striker bar. Figure'2.10 also shows the apparent dent in the simulation.
The “square” input was based on a 30-term Fourier series to represent the blunt
impact between the striker bar and the load cell. This result further confirmed the

nature of wave propagation in the striker bar.

44

 

p-‘
I

.O
00
I

 

Force (Unit)
0 O
4:. bx

P
N
I

 

O
‘l

 

 

I

-0.2

 

 

_O.4 I I 1 1 I J 1
0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0.72

 

Time (ms)

Figure 2.10 Simulation of apparent dent in force history due to blunt impact.

Since the compression wave generated at the impact end of the striker will
reflect from the free end as a tension wave, and this tension wave will reflect
from the impact end again as compression wave, they may cancel each other at
the sensor position if the tension wave does not lose much at the impact end.
This explains the phenomena that the striker gave the same results with the load
cell in soft impacts, which had relatively longer impact durations and the wave
superposition made minor oscillation around the true impact curve. For the hard
impacts, such as type II and III of the horizontal impact, the impact duration was
close to the wave traveling period, and the wave superposition effect shows up

and can not be neglected.

45

6. CONCLUSIONS

The vertical impact systems are Simpler and less costly than the horizontal
impact systems. However, the latter are free of gravitational effect and can
achieve higher impact velocity. In measuring the contact-impact forces, the
strain-gage based sensors are not sensitive to oscillation as much as the
accelerometers because the former are based on deformation while the latter,
the motion. This is especially true in vertical impact tests. Among the strain-gage
based sensors, the load cell seems to be more effective for relatively soft
specimens, while the striker is more suitable for recording hard impact if the
wave superposition effects can be eliminated. Accordingly, a horizontal impact
system using a strain-gage-based force transducer seems to be an ideal system

for contact-impact testing.

ACKNOWLEDGMENTS
The author thanks to the US. Army TARDEC, Warren, Michigan, for financial

support.

46

REFERENCES

[1] S. P. Virostek, J. Dual and W. Goldsmith, Direct Force Measurement in
Normal and Oblique Impact of Plates by Projectiles, Int. J. Impact Engng.
Vol. 6, No.4, p247-269, 1987

[2] Ralph Burton, Vibration and Impact, Dover Publications, Inc. New York
10014, 1968

[3] Liu, D., Lee, C. Y., and Lu, X., “Reparability of Impact-induced Damage in
SML Composites”, J. Composite Materials, 27(13), 1257-1271,1993

[4] Liu, D., and Dang, X., “Testing and Simulation of Laminated Composites
Subjected to Impact Loading”, ASTM STP 1330, R. B. Bucinell , Ed.
273-284, 1998

[5] Jun Lu, Mechanical Behavior of 3 Bulk Metallic Glass and its Composite over
a Wide Range of Strain Rates and Temperatures, Thesis for the Degree of
Doctor of Philosophy, California Institute of Technology, Pasadena, California,
2002

[6] L. E. Malvern, The Propagation of Longitudinal Waves of Plastic Deformation
in a Bar of Material Exhibiting a Strain-rate Effect, Journal of applied
mechanics, Trans. ASME, 18, p203-208, 1951

[7] Sia Nemat-nasser; Jon B. lsaacs; John E. Starrett, Hopkinson Techniques
for Dynamic Recovery Experiments, Proc. Roy. Soc. London 435 (A), p371-
391, 1991

[8] M. Vural and D. Rittel, An Educational Visualization Technique for Kolsky
(split Hopkinson) Bar, Experimental Techniques, Nov-Dec 2003, p35-39.
2003

[9] Daniel J. lnman, Engineering Vibration, Prentice Hall, Englewood Cliffs, New
Jersey 07632, 1994

[10] Robert W. Lally, PCB Piezotronics, Inc. Buffalo, N. Y. Testing the Behavior
of structures, Reprinted from TEST, Aug/September 1978

[11] William G. Halvorsen, David L. Brown, Impulse Technique for Structural
requency Response Testing, Sound and Vibration, November 1977, p8-21,
1977

[12] Michael J. Dixon, Development of a Load-cell compensation System,

47

Experimental Mechanics (31), p21-24, 1991

[13] Michael J. Dixon, A Traceable Dynamic Force Transducer, Experimental
Mechanics (30), p152-157, 1990

[14] Jan Hjelmgren, Dynamic Measurement of Force-A literature Survey, SP
Swedish National Testing and Research Institute, SP Measurement
Technology, SP REPORT 2002:27

[15] Mark Sheplak, Aravind Padmanabhan, Martin A. Schmidt, and Kenneth S.
Breuer, Dynamic Calibration of a Shear-stress Sensor Using Stokers-layer

Excitation, Massachusetts Institute of Technology. Cambridge,
Massachusetts 02139 AIAA Journal, Vol. 39, No. 5, May 2001

[16] Jurg Dual, Application of a Transducer Embedded in a Projectile for
Penetration Force Measurement, Master’s thesis, University of California,
Berkeley, 1984

[17] S. Venzi, A. H. Priest and M. J. May, Influence of Inertial Load in
Instrumented Impact Tests. Impact Testing of Metals, ASTM STP 466,
American Society for Testing and Materials, p165—180, 1970

[18] D. J. Frew, M. J. Forrestal, W. Chen, Pulse Shaping Techniques for Testing
Brittle Materials with a Split Hopkinson Pressure Bar, Experimental
Mechanics (42), No. 1, p93-106, 2002

[19] W. Chen, F. Lu, D. J. Frew, M. J. Forrestal, Dynamic Compression Testing
of Soft Materials, Journal of Applied Mechanics (69), p214-223, 2002

[20] D. J. Frew, M. J. Forrestal, W. Chen, A Split Hopkinson Pressure Bar
Technique to Determine Compressive Stress-strain Data for Rock Materials,
Experimental Mechanics (41), No. 1, p40-67, 2001

[21] D. R. Ambur, C. B. Prasad and W. A. Waters, Jr., A Dropped-weight
Apparatus for Low-speed Impact Testing of Composite Structures,
Experimental Mechanics 35(1), p77-82, 1995

[22] James F. Doyle, Waves Propagation in Structures, Spectral Analysis Using

Fast Discrete Fourier Transforms, Second Edition, Mechanical Engineering
Series, 1997

48

CHAPTER TH REE

WAVE PROPAGATION IN FORCE TRANSDUCERS

ABSTRACT

Instrumented projectiles for impact testing have great advantages over non-
instrumented projectiles. Because of the length restriction on the impact
projectiles, wave reflection and wave superposition can take place in the
projectiles and result in distorted wave signals. In order to recover the initial
impact wave, several techniques based on both mechanical and numerical
methods are proposed. Experimental results based on instrumented short rods
showed the feasibility of the proposed techniques for reducing the wave
reflection and reconstructing the initial impact wave to some extent. The
techniques were used for designing an instrumented projectile for ballistic

impacts.

49

1. INTRODUCTION

The capability of energy absorption plays an important role in the design of
vehicle survivability and occupant safety. In order to characterize the energy
absorption capability of a material or a structure subjected to impact loading,
several experimental techniques have been developed and used. Among them,
the simplest one is perhaps the method to measure the velocities of the impactor
before and after it contacts a specimen [1,2]. The energy absorbed by the
specimen can be taken as the difference of the kinetic energy of the impactor
before and after the impact event. This technique requires a relatively simple
setup for velocity measurements and works for both perforation and non-
perforation (rebounding from the specimen) cases. However, this technique does
not give detailed information during the impact event, such as the deformation of
the specimen and the change of the impact force.

To characterize the energy absorption capability of a specimen and even to
understand the mechanism of energy absorption of it, it is necessary to identify
the interaction between the impactor and the specimen through the entire impact
event. Several experimental techniques for measuring the histories of
displacement, velocity, acceleration, and force during impact events have been
developed and are commercially available. For example, accelerometers of
various designs and data acquisition systems with high-speed capability have
been developed for measuring acceleration history in crash tests [3,4]. They

have been found to be useful for investigating relatively soft materials and

50

structures. However, their low natural frequencies may hinder their uses in high-
speed impact events.

With the advancement in laser diode technology, high-speed photo-detectors,
and fiber optics, researchers have been able to build velocity measurement
devices of various kinds to measure the velocity of impactors [5,6]. Most of them
are able to sense very small changes in velocity and give velocity history with
high accuracy. However, the complexity of the testing environment and impactor
geometry should not be underestimated because they can complicate the testing
setup and affect the measurement.

High-speed photography can provide detailed images of what exactly
happens during impact events [1 ,2,7,8,9]. With sufficient photographs, the
displacement history, the velocity history, and even the acceleration history can
be identified. Since most impact events last only a very short time period, such
as less than 1 millisecond, high-speed cameras with the capability of recording
sufficient frames are required for obtaining accurate displacement, velocity, and
acceleration histories. It Should be noted that high-speed cameras capable of
recording 1 million frames per second are very costly.

Strain gages have been commonly used for measuring strain history. Owing
to their technology maturity, low sensitivity to environmental impact, accessibility,
and low cost, strain gages have been used in device designs more frequently
than many modern sensors such as laser and fiber-optic based sensors. In fact,
strain-gage techniques are the most common methods used for measuring

mechanical parameters involved in impact events [10]. The measured strain

51

history can then be converted into stress history and force history for further
applications.

Based on the advantages of strain gages mentioned above, the objective of
this study is to investigate the feasibility of using strain gages for measuring
dynamic forces during impact events. High speed, high acceleration, large force,
and short duration are expected to be involved in these events. Issues
concerning the wave propagation are expected to be the dominant subjects in

the study.

2. FORCE TRANSDUCERS

Many force transducers are commercially available. Although they have
various geometries and use different types of sensors, many of them are based
on a common design fundamental — measuring force history from deformation
history. Accordingly, each deformation based force transducer has a precisely
designed body to sense the deformation during loading while the remaining
components of the transducer are considered to be rigid bodies.

The sensors for measuring deformation can be based on electrical,
mechanical, acoustical, or optical fundamentals. Once a deformation history is
identified, it can be converted into a force history with the use of physical laws. A
coefficient called the calibration factor is usually established for direct conversion
from a measured signal to an output reading. The procedures required for

obtaining a calibration factor are called calibration procedures.

52

Deformation-based force transducers work adequately for static and dynamic
force measurements involving long contact duration and low skew rate (small
force ramping). If the force duration is very short or the magnitude of force
changes very rapidly (high skew rate), the deformation-based force transducer
may not sense the force Signals accurately. This is because the deformation
signals at different instants may superimpose one another or some components
of the transducers may not be taken as rigid bodies.

When a force transducer is loaded, the loaded area of the transducer
undergoes an immediate deformation. However, the portion where the sensor is
located, usually a short distance away from the loaded area, does not experience
the deformation immediately. A short time period is necessary for the
deformation to take place at the position where the sensor located. The traveling
of the deformation from one location to another resembles wave propagation,
and the wave is called elastic if the deformation is within the elastic range of the
transducer body.

The elastic wave travels through the entire force transducer and rebounds
from boundaries, such as material interfaces and free ends. The sensor does not
only sense the initial deformation signal corresponding to the loading but also the
signals reflected from the boundaries subsequently. Besides, because the elastic
wave travels quickly along hard materials commonly used for the force
transducer, the signals should be of high frequency. The shape of the elastic
wave may be very complex if the geometry of the transducer is of highly irregular

shape. Many transducer designers choose to eliminate high-frequency signals

53

during signal processing. However, filtering out high-frequency signals may result
in the loss of useful signals, especially for the force history with a high skew rate.
In order to design a force transducer for high-speed loading, such as impact
loading, the superposition of initial deformation wave and rebounded waves

reflected from boundaries must be investigated.

3. WAVE PROPAGATION IN RODS

In understanding the fundamentals of wave propagation due to dynamic
loading and its effect on signal acquisition and processing, some experiments
were performed. To begin with, a cylindrical rod made of stainless steel 347 and
having a diameter of 19 mm and a length of 254 mm was prepared as an
impacting rod. A pair of strain gages with a gage length of 1.575 mm was
mounted on the opposite surfaces, 38 mm from the impacting end. The two
gages were then connected to the opposite arms of a Wheatstone bridge Circuit
for measuring the axial deformation while eliminating any bending effect due to
impact loading. The signal from the Wheatstone bridge Circuit was then
transferred to a differential amplifier with a bandwidth of 10 MHz and then an
oscilloscope with a sampling rate up to 100 S/S.

In impact testing, an aluminum plate with dimensions of 150 mm x 150 mm
and a thickness of 13 mm was used as a target specimen. The specimen was
held by two steel square plates with dimensions of 150 mm x 150 mm, a central
opening of 125 mm x 125 mm, and a thickness of 13 mm. The impacting rod was

launched from a gas gun with a low speed up to 20 m/S. The resultant strain

54

Signal combining the initial strain wave signal and reflected strain wave signals

was recorded by the strain gages.

3.1 Experiments on Effect of Rod Length

In understanding the effect of rod length on wave propagation, the 254 mm
rod was trimmed by removing a section of 41 mm from the non-impacting end
after the impact test, leaving the remaining length of the rod to be 203 mm for a
second impact test. Similar removals were repeated. Accordingly, impacting rods
with lengths of 254 mm, 203 mm, 152 mm, 127 mm, 102 mm and 76 mm were
formed and used for tests.

A strain gage measures the strain at the location where the gage is mounted.
If a rod undergoes elastic deformation due to static loading, the multiplication of
the strain with the Young’s modulus of the rod Should equal the stress in the rod.
Subsequently, the multiplication of the stress with the cross-sectional area of the
rod should equal the force exerted on the rod. When the rod undergoes dynamic
loading, the calculation of the stress, however, should be based on a dynamic
Young’s modulus. The stainless steel 347 mentioned earlier has an almost
identical static Young’s modulus and dynamic Young’s modulus [11]. Hence, it is
suitable for use as the body of force transducers.

Figure 3.1 shows the overall setup for the impact testing while Figure 3.2
gives the measured strain histories from the rods with various lengths. The
results are Significantly different, and it is believed that the differences are

attributed to the difference of the length. In comparing the wave propagation in

55

the rods, the Shape of the strain curves bears more important fundamentals than
the magnitude, since the former is depended on the length of the rods while the

latter is subjected to the individual impact forces.

 

 

Wheatstone Differential
Bridge Amplifier

\:>

Gun Barrel Rod Strain Gages 13mm Al Plate

~> Oscilloscope

 

 

 

 

 

 

 

 

 

 

Figure 3.1 Testing setup for impacting rod.

 

 

 

- —254mm'" :-_
WWII-[UM — 203 mm : F. “7 ;:
.W V/\/\, tin/\VNVMMK —- 152mm ”'7'"

_M _ " :Jn’VI'fi; fl/fir’vyx m. .vfif‘VI 4 127mm"?
“—1...“

‘ II -- 102 mm """""""
‘ — 76 mm ,__;___
0 0.2 0.4 0.6 0.8 1

time (ms)

 

Voltage (1 V/div)

 

Figure 3.2 Strain histories from the impact rods with various lengths.

56

Some conclusions can be drawn from comparing the strain curves.

a. The steady oscillation seems to begin around 0.5 ms for each case.

b. As the rod becomes shorter, the oscillation frequency becomes higher.
The oscillation frequency is proportional to the inverse of the period of the
elastic wave traveling between the ends of a rod.

c. The longer the rod, the longer the flat portion of the very beginning

oscillation. It indicates that a longer rod is less influenced by oscillation.

3.2 Experiments on Contact Duration

In order to gain insight into the strain wave propagation in the rods, a second
type of experiment was performed on the rod of 76 mm length. The setup is
shown in Figure 3.3 and the impact testing procedures were similar to the first
type of experiments. The second type of experiment was aimed at measuring the
impact duration. The fundamental design concept of the second type of
experiment was to take advantage of the contact and separation between the
metallic rod and a metallic specimen as a power switch. More specifically, one
terminal of a DC power supply was connected to the specimen and the other
terminal was connected to the rod through two resistors in series. An
oscilloscope was used to measure the voltage of one resistor. Before impact, the
circuit was open due to the separation between the rod and the specimen; hence,
there was no reading in voltage. During the impact, however, the circuit was

closed due to the contact between the rod and the specimen; hence, there was a

57

reading in voltage. The duration of the voltage measured by the oscilloscope
should be the impact duration.

Figure 3.4 shows the measured curves. The upper one is the contact duration
history while the lower one is the output of strain signal. When the rod impacts
with the specimen, the duration curve shows a jump in reading. About 0.024 ms
later, the strain curve shows a significant change in compressive strain. This time
delay is attributed to the distance between the impact end and the gage location.
During the impact, the contact between the rod and the specimen continues. The
voltage remains high while the compressive strain reduces. It should be noted
that the strain gages experience oscillation with tensile and compressive strains.
Since an impact event should only result in compressive strains, the measured
tension-compression signals may indicate an involvement of complicated wave

propagation during the impact event and require more careful examination.

58

 

Wheatstone _> Differential
Bridge Amplifier

—v

* Oscilloscope

 

 

 

 

 

 

 

WWW \ <——l3mm AL Plate
W ‘ _- é ______.___....
.3

 

 

 

 

Oscilloscope

 

 

 

Figure 3.3 Experimental setup for impact duration and strain history.

First Impact Second Impact

1 \
‘ I

 

 

/\
V
cub——

 

 

 

 

 

 

 

 

 

 

 

 

E /”’\\ 'l/NI‘“ IH‘V.‘ ‘ (”It Latx'fi”! \‘."/'\ /‘\/ ”'~\¢/fly\\
3 l“ l 0 32 ms \‘w .
E 4 ' ‘ 1 _ Duration Signal
2 xxx-w T we UV
.3.
o
._1
.
E
Z
.. 42mV .f.
5' (Gain=20) 0-32 ms Straln Signal
3’ 4
on
o
> * :
Time (0.06 ms/divl

Figure 3.4 Impact duration (upper) and strain history (lower).

59

3.3 Experiments Based on Three Sets of Gages

To further understand the wave propagation and superposition in the rods,
another cylindrical rod made of stainless steel 347 and having a diameter of 19
mm and a length of 254 mm was prepared. It was then installed with three sets of
strain gages at 38 mm, 76 mm and 114 mm from the impact end as shown in
Figure 3.5(a). Each set of strain gages consisted of two gage elements mounted
on opposite surfaces of the rod. The experimental setup and the Wheatstone
bridge circuit were similar to previous experiments. The rod was then launched
from a gas gun and impacted onto a specimen. The three sets of strain gages
measured the impact signals individually. Figure 3.5(b) shows experimental

results in all three sets of strain gages.

 

Wheatstone _, Differential Oscilloscopes

Bridges Amplifiers

 

 

 

 

 

 

 

 

 

 

 

69 38mm ‘—— 25mm

 

 

 

76mm . ‘ "7" ’ Thickness
é " ' 9 Steel Plate
114mm

 

Figure 3.5(a) Experimental setup of the three sets of strain gages.

6O

Force (kN)

 

0.5 0.6 0.7 0.8 0.9 l

 

Time (ms)

Figure 3.5(b) Experimental results of the three sets of strain gages.

As shown in Figure 3.5(b), the elastic wave was generated at the impact end
and traveled along the rod. It reached the first set of strain gages located at 38
mm from the impact end, then the second set located at 76 mm from the impact
end, and finally the third set located at 114 mm from the impact end. The
reflected wave reached the strain gages in a reverse way, i.e. the third set of
strain gages was the first to sense, followed by the second set, and the first set
was the last to sense the reflected wave. The study based on comparing the
magnitudes of the forces shown in Figure 3.5(b) clearly indicates the order of the
wave propagation along the rod.

The wave length of the strains is also of interest. Figure 3.6 shows the signals
of the strain gages located 38 mm from the impact end in the freqUency domain.
Two major peaks appear around 10 kHz and 20 kHz. Since the wave speed in
the stainless steel 347 is around 4,934 m/s and the rod has a length of 254 mm,

it takes about 0.05 ms for the wave to travel between the impact end and the free

61

end. Hence, the total traveling time of 0.1 ms back and forth between the two
ends seems to match well with the fundamental frequency of 10 kHz and the
higher order frequency of 20 kHz. It then can be concluded that superposition of

the elastic wave can take place and cause the change of wave shape.

 

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0.*‘3'3"3'=" - - -" 4AA ""'""
D 1 2 3 4 5 6
Frequency (10 kHz)
Figure 3.6 The signal in frequency domain obtained from the pair of
strain gages located 38mm from the impact end.
3.4 Experiments on Wave Dissipation
The wave traveling inside rods will dissipate finally. To understand the
dissipative rate, a cylindrical rod made of stainless steel 347 and having a
diameter of 19 mm and a length of 840 mm was prepared. A pair of strain gages
was installed at the middle as usual. The rod was then hanged up with fishing

thread as shown in Figure 3.7(a). A hammer was used to apply the impact force

to the rod.

62

////

 

L I: n- _L ]

Figure 3.7(a) Experimental setup for wave dissipation.

 

The first 10 cycles;
20 reflections;
traveling distance:

 

 

 

 

 

 

    

 

 

~17m
l U l l I l
it I ’7 , _ _ z
E
E
>
E I . . ,, , , a,
O i . .
:9 l l 3 . l I l g
8, The first 10 cycles ‘ l 1000 cycles; 2000 reflections,
Lg l l _ § Traveling distance: ~1670m
> 1 l l L E ' j i I I

 

 

time (50 ms/div)
Figure 3.7(b) Experimental result of wave dissipation.

Figure 3.7(b) shows one of the experimental results of the wave dissipation in
the stainless steel rod. The wave traveled roughly half second before dissipated
totally. There is no obvious difference in the magnitudes of the first ten cycles, in

which the wave reflected 20 times from ends, traveled about 17 m totally.

63

4. MECHANICAL METHOD FOR WAVE REDUCTION

The wave propagation in a cylindrical rod can be considered as one-
dimensional phenomenon. However, the wave formed in the rod can be very
complex due to the superposition of the impact-induced wave with reflected
waves resulting from finite boundary or inhomogeneous material of the rod. The
superimposed wave may not be useful, or at least not easy, for applications. The
initial impact-induced wave should hold the fundamental information of the
impact mechanism and needs to be identified. The identification requires a
technique to remove, or even eliminate, the reflected waves. A mechanical

method for wave reduction, or even wave elimination, was proposed.

4.1 Rod with Cone-Ball End

A cylindrical rod with a short cone section followed by a ball section is shown
in Figure 3.8(a). The design concept of the cone-ball end was aimed at trapping
the impact-induced wave inside the ball end without rebounding back to the
cylindrical section. When the axial wave reached the cone section, it would be
reflected from the conic surface according to the wave reflection law. The cone
was carefully machined such that the reflected wave was guided into the ball
section. Once the wave got into the ball section, the majority of it would move
around continuously and get trapped inside the ball. Figure 3.8(b) and 3.8(c)

show the dimensions and image of the rod with a cone-ball end.

64

 

 

 

 

 

 

 

 

 

Figure 3.8(b) Detailed drawings of a rod with a cone-ball end.

65

 

Figure 3.8(c) Image of a cylindrical rod and a rod with a cone-ball end.

The rod was installed with a set of strain gages at a distance of 51 mm from
the impact end. The testing setup and the testing procedures were identical to
the previous experiments. Figure 3.9 shows the measured force histories for a
rod with a flat end and a rod with a cone-ball end. It is obvious that the wave
travels and reflects in the rod with a flat end many times. However, the wave
travels and reflects in the rod with a cone-ball end fades more quickly. The
difference is apparently due to the reduction of the wave in the rod with the cone-

ball end.

66

 

Force (kN)

time (ms)

 

-2-

 

-5.

Force (kN)
is

time (ms)

I
U3
1

 

-10 a

Figure 3.9 Force histories in the rod with a flat end (top) and
a rod with a cone-ball end (bottom).

4.2 Bar with Double Parabolic-Lines and Double Tails

A concave mirror with a parabolic surface can converge all incoming rays
onto a focal point. This phenomenon can be used to manipulate the wave
propagation at the end of a cylindrical rod. However, due to the difficulty involved

in machining a three-dimensional cylindrical rod with a parabolic-surface end, a

67

two-dimensional flat bar with a parabolic-line end was used to demonstrate the
fundamental concept. Figure 3.10(a) shows the schematic while Figures 3.10(b)
and 3.10(c) are detailed drawings and image of the bar with a double parabolic-

line end and double tails.

 

 

 

 

—-—-—.—I-.—.—._-—._I—I I—I

 

 

 

Figure 3.10(a) Bar with double parabolic-lines and double tails.

“\

- -E117°38'
17.53:::::"':\.::

IIIIIIIIIIIIIIIIIIIIIII

 

 

 

 

 

   

 

curve

 

 

IIIIIIIIIIIIIIIIIIIIIIIIIII

 

 

455.9

'ff-~"‘~W°H:H':H': .......... ....... :...:...:...:

 

 

 

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

 

 

 

Unit: mm
Aluminum
606 1 -T6

 

 

 

 

IIIIIIIIIIIII

 

 

 

 

Figure 3.10(b) Drawing of the bar with double parabolic-lines
and double tails.

68

 

Figure 3.10 (c) Image of bars with double parabolic-lines
and double tails.

Because the two-dimensional flat bar could not be launched by the gas gun, it
was hung up with wires at two positions close to the bar ends and impacted by a
cylindrical rod launched from the gas gun. When impact takes place, the elastic
wave generated at the flat bar end can be viewed as a combination of numerous
wave fronts traveling together along the axis of the bar. As they reach the
parabolic line, they will be redirected to the individual focal points. Shown in
Figure 3.10(a) is a flat bar with double parabolic-lines and double tails. The wave
fronts on the upper half will be converged to a focal point located at the lower half
while those on the lower half will be converged to a focal point located at the
upper half. The two focused waves at the two focal points will then be redirected
to the two tails and propagate along the tails until they fade out at the very ends
of the tails. In order to realize this design, an aluminum plate with a thickness of 5
mm was machined according to the drawing in Figure 3.10(b). The flat bar was

chosen over a cylindrical rod because it was much simpler to machine a two-

69

dimensional flat bar than a three-dimensional circular rod while retaining similar
wave propagation phenomena.

Two pairs of strain gages were installed in the flat bar. Each pair had two
strain gages. All gages were aligned along the axial direction and had the same
location from the impact end, i.e. 200 mm. One pair of the strain gages was
installed on the opposite surfaces of the bar while the other pair on the opposite
edges of the bar as shown in Figure 3.10(c). The associated Wheatstone bridge
circuits were identical to those used in previous experiments; so were the
amplifiers and oscilloscope.

Since the flat bar was very light, a low-speed impact was performed, resulting
in low magnitude of strain signals. In order to distinguish the difference,
Wheatstone bridge circuits for the two pairs of strain gages were set to have
opposite outputs, as shown in Figure 3.11. The upper curve was obtained from
the gages on the edges while the lower one was obtained from the gages on the
surfaces. The oscillations in both curves are very smaller, implying a good
reduction of the reflected wave back to the bar section by the double parabolic-
lines and the double tails.

Figure 3.12 shows the strain signal and contact duration from the gages on
the edges. The contact duration is longer than the strain signal. The contact
duration before the strain signal is due to the distance between the impact end
and the position of the gages while the contact duration after the strain signal is
likely due to the simultaneous travel of the flat bar and the cylindrical rod with no

contact between them.

70

 

 

 

Voltage (20 mV/div)

 

 

I 12 mV Signal from gages on edges
(gain= 0 .
‘1‘" YTA‘AJ 7"er ELL“
AL- I Signal from gages on surfaces
0.05 ms
D
Time (0.08ms/div)

Figure 3.11 Impact response of the flat bar with double
parabolic-lines and double tails.

  
   
  

l 0.05 ms
AI I Strain srgnal from gages on edges
. I: A $1» ‘!“f"‘.hofiv‘" y." k .'. It left). A If“ “(h ,Mgwmfl daw‘b ‘IY'K‘N‘ITJ‘M )1u1'd Km»-
30 mV ‘
(Gain=20)

Contact duration

Voltage (Strain signal ZOmV/div)
(Contact duration lV/div)

 

k; _ 4
vv—— 7 ——v‘

 

~<—>
0.09 ms

 

 

 

Time (0.15ms/div)

Figure 3.12 Impact response of the bar with double parabolic-lines
and double tails.

71

5. NUMERICAL METHODS FOR WAVE REDUCTION

Besides the mechanical method for reducing wave reflection, numerical
methods can also be used to achieve the goal. Details of wave propagation
equations and the physical fundamentals can be found in the references [12-16].
The primary concept to be used in this thesis research is that a compressive
wave reflects as a compressive wave after hitting a rigid boundary while a tensile
wave reflects as a tensile wave after hitting a rigid boundary. On the contrary, a
compressive wave reflects as a tensile wave after hitting a free boundary while a
tensile wave reflects as a compressive wave after hitting a free boundary [14,15].

In impact events, the impacted end of a rod or a bar undergoes compression
while the non-impacted end is free. Hence, a compressive wave will occur at the
impacted end and propagates toward the free end. The compressive wave
reflects from the free end with a tensile wave and propagates back to the
impacted end. When the rod or the bar separates from the impacted specimen,
the impacted end will become a free end. If this separation occurs before the
tensile wave reaches the end, the tensile wave will be reflected to be a
compressive one. The wave will then travel between the ends back and forth in

compression and tension alternatively.

5.1 Technique Based on Assuming an Initial Wave

When an impact-induced wave propagates inside a rod or a bar, a reflected
wave from part of the initial wave may interfere with the remaining part of the
initial wave around the boundaries. The shape of the superimposed wave usually

becomes very complex and does not bear the shape of the initial wave. For

72

impact events lasting a longer contact time or involving a softer specimen, the
interference of the waves results in fine zigzags along the impact curves. For
impact events lasting a shorter duration, the interference distorts the impact
signals seriously.

The measured wave signals are results from superimposing the initial wave
and the reflected waves. In order to recover the initial impact wave signals, an
unwrapping technique is required. As a demonstration, an artificial initial wave is
assumed. The wave is allowed to bounce between two ends. The initial wave
and the reflected waves are superimposed to form a complex resultant wave. By
comparing the artificially superimposed curve with the measured curve at the
gage position, the assumed initial wave is then modified and the superposition
procedures are performed again. The iterative modification and superposition are
continued until the superimposed curve matches well with the measured wave.
The assumed wave is then considered as the initial wave.

In the simulation of wave superposition, the commercial computer program
MATLAB was used to formulate the required computational scheme for
simulations. Figure 3.13 shows two examples; each contains an assumed initial
wave, a superimposed wave, and the associated measured wave. The
superimposed waves seem to agree with the measured waves up to some extent.
The assumed initial wave seems to be reasonable, and the numerical method for
identifying the superimposed wave seems to be feasible.

There is an apparent limit on the numerical method presented above. The

method is only meant for elastic wave propagation. Any plastic deformation and

73

associated plastic wave will have to be handled with a more advanced method
involving plastic wave propagation. Besides, if a boundary is not completely free,
partial transmission and partial reflection may take place. The ratio of reflection to
transmission is dependent on the interfacial condition of impact and the

properties of the involved materials, and can further complicate the numerical

 

method.
Measured curve Input curve Simulated curve
30 /

 
 

20”

Force (RN)
8

O

 

 

I .- .. q
". ." -'. -i
2.: X __ .: 1. 4
' *5. .' -.
I A L

I
_10 i . i 4
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

Time (ms)

 

Measured curve Input curve Simulated curve
25

 

Force (kN)
3

CM

 

 

 

l
M

 

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

Time (ms)

Figure 3.13 The assumed initial wave, superimposed wave
and measured wave.

74

5.2 Two-Position Technique

Suppose that two pairs of strain gages are mounted on two different positions
(position one and position two) along the axial direction of a rod. When the rod
impacts onto a specimen, a compressive wave will be generated and propagate
to gages on position one first and then gages on position two. The signal
measured at position one will be measured at position two after a certain time
interval. When the compressive wave reaches the free end of the rod, it will
reflect as a tensile wave and propagates back to gages at position two first and
then gages at position one. The reflected signals measured at the two positions
will also have the same time interval. If the impacted end is still in contact with
the specimen when the tensile wave reaches it, the tensile wave will be reflected
with a fractional compressive wave, depending on the materials of the rod and
the specimen, and propagates back to the strain gages. Othen~ise, the tensile
wave will be reflected completely as a compressive wave. The reflected wave will
be measured at position one and then at position two.

For gages at position one, the first signal the gages detect should be the
impact signal. In the second time, they should detect a signal combining the
impact signal and the reflected signal from the free end. In the third time, the
gages should detect a combined signal superimposing the impact signal, the first
reflected signal from the free end, and the first reflected signal from the impacted
end. Gages at position two should have similar detections but at different time

instants due to their different location from position one.

75

Based on the wave propagation and wave superposition at position one and
position two, a technique for identifying the initial impact signal can be
established. To start with, assume a signal X is measured at position one at time
To. After a time period T1, it is measured at position two. If a reflected signal Y
also reaches position two at time T0+T1, then position two will measure (X+Y).
Since the two positions will measure the same ongoing signal with a time interval
T1, the reflected signal can be calculated by (X+Y)—X=Y. The reflected signal Y
will also reach position one after another T1 since the wave speed in the rod is a
fixed value. So, at time To+2T1, position one will measure X’+Y. Eliminating Y
from the (X’+Y), the ongoing wave X’ at the time To+2T1 can be identified.
Increasing To for other sampling data points and repeating the procedures, one
can find the complete initial impact signal from the impact end that is not
interfered by any reflected one. As a summary, the signal at position one can be
used to identify the signal at position two which in turn can be used to identify the
signal at position one with its reflected wave portion. A computer program based
on this method was written with the use of LabVIEW.

In order to demonstrate this method, a rod made of stainless steel 347 with a
diameter of 19 mm and a length of 203 mm was prepared. Two pairs of strain
gages similar to the ones used earlier were installed at locations 19 mm and 95
mm from the impact end. All the gages were mounted along the axial direction.
Each pair of gages consisted of two gages and was mounted on opposite
surfaces of the rod. They were then connected to the opposite arms of a

Wheatstone bridge circuit in order to eliminate any bending effect.

76

An 840 mm-Iong rod made of the same stainless steel and having the same
diameter was used as an impacting target. It was also mounted with the same
type of strain gages. Figure 3.14 shows the experimental setup. Three differential
amplifiers with a bandwidth of 10 MHz and an input impendence of 1M!) were
used while the gain was set to 50. Two double-channel digital oscilloscopes with
a bandwidth of 100 MHz and a sampling rate of 100 MS/s (Samples per second)
were used for data acquisition. The longer rod was expected to receive impact-

induced signals with less distortion than the shorter one [17-28].

Gas Gun Strain Long Cylindrical Rod Stopper
Barrel Gages with Strain Gages l

 

4*... I... __._.__L_‘

- ll

 

[ZZZ

 

 

 

Shorter Rod

 

 

 

Wheatstone L’ Amplifiers Oscilloscopes
Bridges : 3MHz * 10 MS/s

 

 

 

 

 

 

 

 

 

 

i

 

Figure 3.14 Experimental setup of the two-position technique.

77

0.12 - ‘ ‘ ‘ _ ‘ ‘ , . .
0'1-...__.._..;. ‘ ' ' I LongRod
0.08 ‘ f I , j ‘
006--~~£~-4
0.04 WWW ‘ I I 0
0.02 ' . , ‘ T
0 $4- 95mm from End
-002 .... -' 3 ~ .
I - . v I

-0.04 'I I I l I l I I I I I l I
61.5 61.56 61.58 61.6 61.62 61.64 61.66

Time (ms)

l

   

 

1

19mm from End

   
 

  

Voltage (V)

       
  

    

l
61.68 61.7

  
    

Figure 3.15(a) Experimental curves from two-position of a shorter rod
and from a long rod.

  
 
 
     

0.12 - ‘
0.1 - Long Rod
A 0‘08 ' 7 ' Compensated ‘19
a 0-06 ' - mm’ gages curve
300.04» ii
N ..I
=5 0.02 - :nr 3.
> 0 _ . . Compensated ‘95 ~ 7 7 . ,1? 11 ,
mm’ gages curve 1" 0' "r”, ,
-0'02 - . . . . . . . . . . . 1. .-: - ”-1 . .
-004 'I I l I I I I I I I l I l r ‘I l I
61.54 61.56 61.58 61.6 61.62 61.64 61.66 61.68 61.7

Time (ms)

Figure 3.15(b) Results based on the two-position technique.

One set of experimental results can be seen in Figure 3.15(a). The enhanced
dark curve represents signals obtained from the long rod. The other two curves
are from gages located at position one and position two of the short rod. Results
from both rods had identical sampling time and sampling rate since they were
simultaneously sampled from three channels of the two oscilloscopes. The curve

from the long rod was shifted along the time axis to match with the other two

78

curves. The three curves are quite different in period. The curve from the long
rod has the longest period, it records the real impact signal [17-28]. The curves
from the short rod have shorter periods which decrease as the gages located
further away from the impact end.

Figure 3.15(b) shows the curves processed by the LabVlEW-based program
with the use of signals from the two positions of the short rod. The curve from the
long rod is also presented for comparison. Figure 3.15(b) shows that the
processed signals of the short rod are almost the same as the initial impact
signal measured from the long rod. With this two-position method, the initial
impact signal can be recovered from the short rod and may be used for wide-

band load cell design.

6. CONCLUSIONS

Experimental results showed that reflected waves and their superposition
with the initial impact wave can complicate the impact force measurements. The
complication increases as the impact duration becomes shorter. Based on a
mechanical technique to redirect the reflected waves, a wave reduction method
was proposed and verified. The initial wave associated with the impact force
could be identified.

Besides the mechanical technique, two numerical techniques, the so-called
Initial Wave Assumption technique and the Two-Point technique, were also

proposed and verified to be able to recover the initial impact force wave.

79

The success of the wave reduction techniques to recover the initial impact

force wave shed light on designing an instrumented projectile with a short rod.

80

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[12] Karl F. Graft, “Wave Motion in Elastic Solids”, Ohio State University, pp.75-

81

134, 1975.

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[16] Ralph Burton, office of naval research, London, “Vibration and Impact”,
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[17] Michael Adam Kaiser, “Advancements in the split Hopkinson bar test”,
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technique to determine compressive stress-strain data for rock materials”,
Experimental Mechanics, 41 (1), pp.44—46, 2001.

[20] W. Chen and F. Lu, “Dynamic compression testing of soft materials”, ASME
Journal of Applied Mechanics, 69, pp.214—223, 2002.

[21] H. M. Hsiao, I. M. Daniel and R. D. Cordes, “Dynamic compressive behavior
of thick composite materials”, Experimental Mechanics, 38. pp.172-180,
1998.

[22] O. Sawas, N. S. Brar and R. A. Brockman, “Dynamic characterization of
compliant materials using an All-polymeric split Hopkinson bar",
Experimental Mechanics, 38, pp.204-210, 1998.

[23] Frank E. Hauser, “Techniques for measuring stress-strain relations at high
strain rates”, Experimental Mechanics, pp.395-402, 1966.

[24] J. F. Bell, “An experimental diffraction grating study of the quasi-static
hypothesis of the split Hopkinson bar experiment”, J. Mech. Phys. Solids, 14,
pp.309—327,1966.

[25] Robert L. Sierakowski and Shive K. Chaturvedi, “Dynamic loading and

82

characterization of fiber-reinforced composites”, John wiley&sons, inc. New
York, pp.41-77, 1997.

[26] Jonas A. Zukas, Theodore Nicholas and Hallock. F. Swift, “Impact
Dynamics”, John Wiley & sons Inc. pp.287-308, 1982.

[27] David E. Lambert and C. Allen Ross, “Strain rate effects on dynamic fracture
and strength”, International Journal of Impact Engineering, 24, pp.985-998,
2000.

[28] Weinong Chen, “Dynamic Failure Behavior of Ceramics under Multiaxial

Compression”, Thesis for the Degree of Doctor of Philosophy, California
Institute of Technology, 1995

83

CHAPTER FOUR

DESIGN AND CALIBRATION OF AN INSTRUMENTED PROJECTILE

ABSTRACT

Almost all free projectile impacts are of non-instrumented tests. They are
simply based on the difference of kinetic energies of free projectiles before and
after impacts. Accordingly, valuable information leading to the understanding of
impact mechanism may be lost. Issues concerning wired and wireless projectiles
are discussed. A preliminary design is also presented. Based on a mechanical
wave reduction technique, this study presents the detailed construction of a
wireless instrumented projectile, including the selection of the geometry, the
manufacturing procedures, the circuit design of the microprocessor, and the
assembly of the projectile. Calibrations on projectile body and electronic
components were carefully performed. Testing results seemed to validate the
feasibility of using the instrumented wireless projectile which has a bandwidth of
170 kHz for impact events with velocities up to 20m/s. Both the maximum impact
velocity and the bandwidth are much higher than those commonly used in the

instrumented drop-weight impactor.

84

1. INTRODUCTION

Dynamic loadings such as impact, crash and blast loadings are commonly
found in the real world. Many dynamic testing techniques have been developed
for laboratory uses ranging from material characterizations to testing simulations.
Examples are the split Hopkinson’s pressure bar (SHPB) for characterizing
dynamic stress-strain relations, Taylor’s impact test for finding dynamic yielding
stress, instrumented drop-weight impact test for finding material response under
low-velocity impacts, and gas gun for simulating ballistic impacts. Among the four
techniques mentioned, SHPB and drop-weight impact test are instrumented tests
while Taylor’s impact and gas gun tests are non-instrumented.

Non-instrumented tests are much simpler than instrumented tests in terms of
construction. They are usually built in the laboratory for simulating the loading
conditions occurring in the real world. Instrumented tests, however, are equipped
with sensors to detect physical quantities and require sophisticated data
acquisition and signal processing systems for understanding the parameters
involved in the loadings. Since dynamic loadings usually last a very short time
period and involve many physical parameters during the events, instrumented
tests are preferred over non-instrumented tests in studying dynamic loading
events. This thesis research is aimed at developing an instrumented free
projectile for simulating low-velocity ballistic impact tests. Detecting the wave
propagation in the small projectile and converting the signal into loading history

are the primary studies of this research.

85

Both numerical and mechanical methods have been proposed for elastic
wave reductions in a previous study [chapter 3]. A numerical technique, the so-
called two-position technique, requires acquiring a significant amount of data
points during a short time interval while the wave travels between two positions
of a short projectile. To meet this demand, a data acquisition unit must have a
very high sampling rate, which usually comes with a large memory. Hence, the
size of the data acquisition unit is also likely to be large. Such a data acquisition
unit, however, cannot be attached to the small projectile economically. On the
contrary, if the data points are to be transferred to a data acquisition unit located
outside the projectile during operations, the lead wires will have to join the
projectile and the data acquisition unit correctly. Otherwise, entanglement or
even damage to the lead wires can take place during high-speed operations
[chapter 3].

The mechanical method for wave reduction is essentially based on
geometrical effects and does not require a high-performance data acquisition and
signal processing unit for wave reduction as the numerical method. The data
acquisition and signal processing unit can be relatively simple and possibly
integrated with the body of the projectile. With no lead wires, such as a wireless
design, the projectile can then be operated freely. Hence, the mechanical method
should bear more advantages over the numerical method and is suitable for
designing an instrumented free projectile for use in impact events. The objective
of this study is focused on the feasibility of building such an instrumented free

projectile.

86

2. SIGNAL TRANSFER

For the demonstration on instrumented rods mentioned earlier, only the rear
sections of the rods were inserted into the gas gun barrel. The front sections with
strain gages were left outside the gun barrel so the lead wires for the strain
gages could be easily connected to the Wheatstone bridge circuits without being
interfered by the gun barrel. In order to achieve higher impact velocities, the rods
should be accelerated with either a higher gas pressure and/or with a longer
acceleration time. This section is aimed at the techniques of signal transfer for

designing an instrumented projectile for higher impacting velocities.

2.1 Wired Method

Signal transfer with lead wires was a primary concern in constructing
instrumented projectiles [1,2]. As a first approach, the lead wire was wound
around a projectile before it was inserted into a gun barrel. In the circuit design,
one end of the lead wire should be connected to strain gages on the projectile,
while the other to a Wheatstone bridge circuit located outside the gun barrel. As
the projectile was accelerated, it would carry the lead wire with it along the gun
barrel.

The design leaving lead wire inside the gun barrel seemed to be
straightfonrvard. However, it failed quite often. There were two major failure
modes. One was related to the breakage of the lead wire. The other was related
to the entanglement of the lead wire inside the gun barrel, resulting in

unsuccessful launch of the projectile. Some studies were performed to identify

87

the cause of the failures and to explore the solutions. It was confirmed that the
over-stretch of the lead wire around the joining point with the projectile could take
place right after the sudden rise of the high-pressure gas, resulting in the
breakage of the joining of the lead wire. The high-pressure gas rebounded from
the projectile end could entangle the wound lead wire.

The high-pressure gas pushed the projectile forward which in turn pulled the
lead wire with it. In order to overcome the failures of the lead wire, the lead wire
should be enclosed inside a tube to avoid its direct contact with the high-pressure
gas. The tube was made of copper and had an outside diameter of 9.5 mm. Its
length is 980 mm, roughly two-fifths of the total length of the gun barrel. In
assembly, the lead wire was inserted into the copper tube which was then
inserted into the 13 mm diameter gun barrel and fixed to the gun barrel at one
end, a closed end. One end of the lead wire was connected to the projectile
through the other end, an open end of the copper tube while the other was pulled

out of a hole at the closed end of the tube and then the gun barrel.

88

Barrier Fixing Bar Copper Tube

 
 

 
 
     

High Pressure Gas Lead Wires Gun Barrel Projectile

Figure 4.1 Assembly of the wired projectile.

The wound lead wire should be finer and stronger and have at least four
conducting lines for connecting the two strain gages to a Wheatstone bridge
circuit. A telephone cord was used for this purpose. This wired technique worked
well for signal transfer. The telephone cord was used more than ten times without
any damage. Figure 4.2 shows an experimental result of an instrumented
stainless steel 347 rod with diameter 12.5 mm and length 38 mm impacting on a
fixed 100 mm x 100 mm x 25 mm aluminum plate. The signal measured by the
strain gages on the rod was transferred with the protected wound lead wires. The
impact velocity was 51 m/s. The rod was accelerated a distance of 1 m inside the
gun barrel before impacting on the specimen, so the lead wires were stretched
and extended to the same distance too. Figure 4.2 does not show large
oscillation in the section of the curve before the impact signal section. This
indicates that the cord wire did not introduce any significant resistance change

during the operations.

89

30 - Signal Impact
25 j before signal

. impact section
20 ; happens

A

15 I ‘

Force (kN)

 

   

0 0.05 0.1

time (ms)

Figure 4.2 Result measured by an instrumented rod
with the protected wound-lead wire

2.2 Wireless Technique
A wireless technique is perhaps the ultimate solution to solve the problems
related to the lead wire failures. However, some potential difficulty should not be

underestimated.

A. Conductive Technique

An instrumented projectile can be made in close contact with the gun barrel
[3,4]. Hence, the gas gun barrel, the projectile, and a conductive specimen can
be integrated to form a closed circuit for signal transfer. This technique, however,
limits the sensor to be piezoelectric or similar types and requires the specimens

to be conductive.

90

B. Radio Signal Transfer Technique

A radio signal transmitter can be built up with the projectile to transfer the
measured signals with a certain frequency. A corresponding signal receiver can
be used to accept the measured signals within a certain distance. Such a
technique requires a high data transfer rate for the transmitter and receiver.
Since the transmitter will need to be built together with the projectile, it should be
battery powered and small enough, especially in diameter to fit inside the gun
barrel. A built-in differential amplifier may also be needed. However, it was
difficult to find a signal transmitter with a suitable size and a high signal transfer

rate for the instrumented projectile.

C. Wireless Technique

The measured signals can be saved to a built-in memory chip attached to the
projectile. The fundamental idea is to amplify the signals detected by strain
gages or other sensors attached to the projectile with a small amplifier chip and
then sample and save them to a memory chip. All the chips and the associated
battery should be integrated with the projectile body together. After each impact
test, the instrumental projectile will then be unsealed to remove the chips for

further data processing.

3. DESIGN OF AN INSTRUMENTED PROJECTILE

91

In order to launch the instrumented free projectile from a circular gun barrel,
the projectile must be of a cylindrical shape. Since the data acquisition and signal
processing unit is to be attached to the cylindrical body and subjected to harsh
impact environments, it should be enclosed inside the projectile to avoid being
damaged by the high-pressure gas and the large impact force involved in the
impact events. As discussed in a previous study [chapter 3], a parabolic surface
at the end of a rod can help in reducing wave reflections in the rod. A
demonstration based on a flat bar, however, was presented in the previous
study. The use of the two-dimensional bar, instead of a three-dimensional rod,
was because the former was much easier to machine than the latter. However, it
should be noted that only the three-dimensional rod can accommodate the data
acquisition and signal processing unit and be launched by the gas gun.

In the previous study, a two-dimensional double parabolic-line end was
machined for a flat bar such that one half of the wave fronts generated from
impacts was redirected to one focal point, while the other half of the wave fronts
was redirected to the other focal point. In the present study, two three-
dimensional curved surfaces were prepared for the circular end of the projectile
body because of the difficulty in machining two three-dimensional parabolic
surfaces. Figure 4.3 shows the schematic of the three-dimensional cylindrical
projectile. The two curved lines in the middle section of the cylindrical body are
actually two axially symmetric curved surfaces. Each of the two focal points
(actually a focal ring) is located at the root of a tail that is able to redirect each set

of the wave fronts reaching the focal point to the tip end of the tail. This

92

eventually reduces the intensity of the wave fronts to an insignificant level. To
machine the two three-dimensional parabolic surfaces, 3 special cutting tool was
required. Since no such a cutting tool was available to the author during the
period of this research, two three-dimensional curved surfaces closely

resembling the two parabolic surfaces were used as a substitute.

Strain Gages Body of the Projectile Protection Tube

.. I,
\

—--—---------- -_‘

 

 

   

System

\. \ - - -1'::':'.':'::'::':<:;_

.1

Body of the ProjEctile in Projected View

 

 

 

 

 

 

 

 

 

 

 

 

/ 7 \L 7 Y i x i
L
— » — Wave Fronts _ -
Front Middle Rear
Section Section Section
F ’|‘ 1‘

Figure 4.3 Layout of the instrumented projectile.

3.1 Cutting Tools

93

A (D16 mm cylindrical rounding endmill with a radius of 6.35 mm cutting arc
was selected for machining the major portion of the wave-reduction geometry,
i.e. the double three-dimensional curved surfaces of the projectile body. There
were two reasons for choosing this cutting tool. One reason was due to its
capability of machining an arc with a radius of 6.35 mm that was very similar to
the ideal parabolic surface for redirecting the wave fronts to a small zone.
Another reason was because the diameter of the endmill was close to the size of
a desired data acquisition and signal processing unit [Appendix A] that had a
width of 15 mm and played the primary role in the determination of the inner
diameter of the projectile body. Beyond the double curved section, a tail section
was required to further reduce the wave intensity. A round-corner cutting tool with
a radius of 2.38 mm cutting edge was used.

Figure 4.4 shows the images of the cutting tools.

I3

[1

   

<§D5=15.875mm

 

Figure 4.4 Images of endmill (left) and round-corner cutting tool (right).

94

3.2 Projectile Body

Shown in Figure 4.3, the body of the projectile can be divided into three
sections. The front section is a cylinder for impact, the middle section has a
curved shape for wave redirection, while the rear section is a hollow cylinder for
wave divergence. Figure 4.5(a) shows the drawing of the overall geometry of the
body of the projectile. The length of the front section is selected based on the
theory of one-dimensional wave propagation [5-11] and the convenience for
installation of strain gages. The shape of the middle section is determined by the
availability of cutting tools, instead of an optimal shape for wave transfer. The
length of the rear section is based on the need for wave divergence and the
volume of the rear section for holding the data acquisition and signal processing

unit, i.e. the SP&DAQ board, the battery, and shock absorption cushions.

3.3 Wave Transfer Section

The key to achieve wave reduction was to eliminate wave reflection at the
end of the projectile body as much as possible. A special geometry may help to
achieve such a goal. Figure 4.5(b) shows the details of the middle curved section
and associated nomenclature for dimensions. The dash-dot line at the bottom of
Figure 4.5(b) stands for the centerline of the body. The lower right arc is formed
with a center at point B and a radius R1. The parallel lines on the left-hand side
between LINE 1 (outer radius R3) and LINE 2 (inner radius R4) represent one-

dimensional wave fronts traveling along the projectile body after impact.

95

[GE45-RAD3] P 0.019"

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

@045" oo.2' R3f32' l ‘l oo.745 15.
P [TL\ \ 3' \ \ \ \_ 3 \ \ \ y m
I “ a r @0525- Rounding Endmill
\ \_\ s \ \ I . (0.25-m...)
\ \+\\ \\\ ' [GE45-CRE625250]
I " l
‘ J \ \ x \ 3 \ \‘T X \ \ \ Lw
J .- . -.--fi. ..... .,
1.5“ 0.09" 25"
Middle
Front Section Section Rear Section
’I‘ ’I‘ '

Figure 4.5(a) Overall geometry and dimensions of the projectile body.

 

 

 

 

 

 

 

r
1K j Y
\\ '
38 l
LINE r l
..-. - I — l
. -. . . -- I
j i
I " *3 V" '
:..............__. .IL—r” --:— .:__g [801'
_ . ‘. .. Ll!!!"
m-~ * u; o
—— i I
l a m
N); <r'
CC l on
- I _ t - - ' l ‘

 

 

 

Figure 4.5(b) Schematic of the wave transfer mechanism.

96

When the wave fronts reach the lower right arc, they are redirected to a small
zone on the upper left arc governed by the law of wave reflection in solids [12-
19]. For wave reduction purpose, the wave fronts need to be further transferred
into a rear section, i.e. the tail section, for wave divergence. The arc formed by
the center C and the radius R2 in Figure 4.5(b) can help to achieve this goal. The
rear section is essentially a hollow section with R5 as the inner radius and R6 as
the outer radius. The upper left arc could be machined by a round-corner cutting
tool. However, the lower right arc was the most difficult part to machine. For
convenience of machining, the front section of the projectile body was made
hollow with an inner radius R4. Hence, there was no end surface like the one

given in Figure 4.3.

3.4 Instrumentation and Assembly

Two strain gages were installed on the surface of the front section of the
projectile body. They were oriented along the axial direction and opposite to each
other. They were then connected to the two opposite arms of a Wheatstone
bridge circuit. The output strain signal from the Wheatstone bridge was amplified
by an amplifier circuit and then sampled and stored in a microprocessor. The
amplifier circuit, the microprocessor, and the resistors in the Wheatstone bridge
circuit were built together in a data acquisition and signal processing (SP&DAQ)
board [Appendix A].

For protecting the strain gages during the operation of the projectile, a

protection gear was necessary. Besides, the lead wires connecting the gages

97

and the data acquisition and signal processing unit also required protection. An
aluminum tube with a length of 100 mm, an inner diameter of 19 mm, and an
outer diameter of 21 mm was chosen as a protection jacket.

In assembly, the projectile body was inserted into the aluminum tube. Two
circular rings and one conic ring were used to hold the projectile body tightly to
the aluminum tube. Weld glue was also applied between the rear section of the
projectile body and the aluminum tube. An aluminum lid was installed in the rear
end of the tube after the battery and the SP&DAQ board were installed inside the
rear section of the projectile body. Figure 4.6(a) shows a schematic of the overall
assembly of the instrumented projectile while Figure 4.6(b) and 4.6(c) are the
photographs of all individual parts of the instrumented projectile and the
assembled instrumented projectile. For a signal triggering purpose, an infrared

phototransistor was installed in the front end of the aluminum tube.

Cone Trigger Ullit Ring Aluminum Tube Cushion Ring
Ring 5 l, - E
‘, __:______ V i i

     

 

/////////////// ////

/////////////////////////

 
  

    

 

 

 

 

 

 

Body of the Strain Gages Battery SP&DAQ Board Lid
Projectile

Figure 4.6 (a) Schematic layout of the instrumented projectile

98

 

Figure 4.6(c) Assembled instrumented projectile.

4. TESTING SIGNAL MEASUREMENTS
The penny-thin SP&DAQ board was used in the instrumented projectile rather
than a high-performance amplifier and oscilloscope. It was designed compact

enough so that it can be integrated with the instrumented projectile body

99

[Appendix A]. This system should be well tested in both measurement accuracy
and dynamic performance before any applications. For all required tests on the

SP&DAQ board, signals were input to the amplifier circuits.

4.1 Accuracy Test

The impact signals measured by the strain gages were amplified first and
then sampled. Even though the gain of the amplifier can be calculated based on
the selected resistors, it should be verified. The linearity of the gain within the
working range of the amplifier also needs to be checked.

A high-accuracy DC power supply with an output display was used as the
signal source. In the test, a DC micro-voltage was given to the input terminal of
the amplifier circuit. The board was then triggered for data sampling and storing.
The stored data was then transferred to a computer. During the data processing,
the measured data points were expressed in voltage and presented against the
corresponding input voltage. Figure 4.7 shows the results of seven tests for the
SP&DAQ board. The measured gain for this board is 155, a little smaller than
156, which is the theoretical gain calculated from the nominal resistance of the

resistors.

IOO

 

3000

2500 _

N
O
O
O
1

1500 r

I

l 000

Measured Voltage (mV)

 

500 —

 

 

0 1 1 1 1 L 1 1 1

2 4 6 8 10 12 14 16 18 20
Input Voltage (mV)

 

Figure 4.7 Input and output of a constant voltage test.

4.2 Dynamic Signal Test

The SP&DAQ board was designed to measure dynamic signals. For later
applications, it is necessary to identify the dynamic performance of the board,
e.g. the sampling rate and the bandwidth of the whole system. The identification
process was based on a dynamical signal test.

A signal generator was used as a signal source for the required dynamic test.
Since the amplifier circuit required two inputs, one was always greater than the
other, othenrvise the output of the amplifier circuit would be zero [Appendix A, 20,
21, 22]. A continuous square wave with a micro-voltage and a proper positive
offset was generated and forwarded to the ‘always larger’ input terminal of the

amplifier circuit, while the other input terminal was connected to the ground. The

101

board was triggered by providing a required voltage to the trigger terminal, and
then a part of the square wave series was amplified and sampled. Figure 4.8
shows the sampled result of an input square wave of 1075 Hz and 15 mV with an
offset of 7.5 mV. In order to ensure the accuracy of the input square wave signal,
the frequency was double checked by an oscilloscope. Based on the results
shown in Figure 4.8, the sampling rate of the microprocessor was calculated by
counting the sampled data points within a unit time. Using only the interior
oscillator of the microprocessor and setting it to work at its highest frequency, the
board was able to acquire 115 k samples per second (S/s). With the help of an
extra 8 MHz oscillator for the microprocessor in the board, the microprocessor
achieved 171 kS/s. The op-amps used in the SP&DAQ board have a bandwidth
of 50 MHz, but the available microprocessors during this thesis research can only
achieve roughly 200 kS/s. Due to the low sampling rate, the bandwidth of the

whole SP&DAQ system is about 170 kHz.

102

5?)???
j.
i
i

Voltage (V)

 

 

1.0 ’
O 5 i W m M O
0 1 1 L .L J
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Time (ms)

Figure 4.8 Square wave testing result.

5. TESTING WAVE REDUCTION

The wave reduction capability of the projectile needed to be identified before
being used for any application. To begin with, the projectile body was half
inserted into a gas gun barrel, leaving the front section outside the gun barrel,
and was then launched onto a long instrumented rod aligned coaxially with the
instrumented projectile. The long rod was made of stainless steel 347 and had a
diameter of 12.7 mm and a length of 730 mm. A pair of strain gages was installed
on the opposite surfaces about 334 mm from the impact end. Signals from both
the projectile and the long rod were recorded simultaneously. Because the front
section of the projectile body (where the strain gages were installed) was left
outside of the gas gun barrel, there was no lead wire damage during testing.
Therefore, the high-performance differential amplifier and the oscilloscope can be

used for signal amplification and data acquisition. Identical Wheatstone bridge

103

circuits, amplifiers, and computer based oscilloscopes were used for both the

instrumented projectile and the long rod.

Gun Barrel Strain Long Cylindrical Rod

   
   

 

 

 

 

 

 

 

 

Sto er
Sleeve Gages with Strain Gages pp

M i [All

C - I" ’ T _ “T.-- * T P I
7 7 7 7 7 7 7 7

Instrumented i i
Projectile Wheatstone " Amplifiers " Oscilloscope
Bridges 3MHz IO MS/s
“F *H

 

 

 

 

 

 

 

 

Figure 4.9 Setup of the wave reduction test experiment.

The impact-induced signal was amplified by a differential amplifier with a
bandwidth of 3 MHz and acquired by a computer based oscilloscope with a
sampling rate of 5 MS/s. Based on the setup of using a gun barrel sleeve, as
shown in Figure 4.9, without manufacturing a new gun barrel, the wave reduction
capability of the projectile body could be assessed for impact speeds up to 20
m/s. To avoid wave superposition in the location where strain gages were
mounted, the impact duration should be equal or less than twice the time the
wave travels from the gages to the nearest end of the rod [5-11]. When a long
rod impacts with a short one, the impact duration is very much decided by the
short one. So it is often required to have impact durations shorter than the time
the wave travels between the two ends of the long rod. However, for the long rod

to be completely exempted from wave superposition, the gage position is

104

essentially important. If the gage is located in the middle of the long rod, the
chance for the wave to reflect from both ends and be superimposed at the gage
position will be equal. If the gage is close to one end, even though the duration of
a wave is shorter than the time the wave travels between the two ends, wave
superposition at the gage position may still happen.

Both the wave propagations in the long rod and the short projectile were
assumed to be one-dimensional. If the cross-section of the front section of the
projectile body was identical to that of the long rod and they collided with each
other coaxially, one-dimensional wave theory should satisfactorily predict the
same impact force from both of them. Due to the limited selection of the cutting
tools available as mentioned earlier, the front section of the projectile body was
made hollow with an inner diameter of 5 mm and an outer diameter of 11.4 mm,
which was not the same as the solid long rod with a diameter of 12.7 mm. The
difference in cross-section might cause the imperfect use of one-dimensional
wave propagation theory. Hence, similar but not identical results from both of
them were expected.

Figure 4.10 shows the impact results from both the short projectile and the
long rod. As expected, the two curves are not identical though they resemble
each other up to some extent, implying the feasibility of using the short projectile.
The result from the long rod shows that the initial waves and the reflected wave
do not superimpose with each other. The result from the short projectile also
does not show any obvious reflected waves except a little oscillation right after

the impact wave, likely due to imperfection from the machining of the projectile

105

body. It then is concluded that the short projectile works well against wave

reflection and superposition.

 

 

 

 

:3
2 7(S)ing:illslg ‘ 1 ‘7 Long rod
gn I: 3, . ‘ — Short projectile
1 ._
‘8’ o 0.05 0.1 0.15 10.2 , 0.25 ,
1—1 —1 r
if, Vibrating Reflected
_2 _ Signals Signals
-3

 

 

Time (ms)

Figure 4.10 Comparison between the results from
the long bar and the projectile body.

6. CALIBRATION OF THE INSTRUMENTED PROJECTILE

The instrumented projectile needs to be calibrated before being used for
impact testing. The setup for calibration was similar to future real applications
except that the testing specimen was substituted by a long instrumented rod. The
velocity of the instrumented projectile was measured by a speed measurement
device [Appendix A], and the infrared emitting diodes on it were used to trigger
the data acquisition for the instrumented projectile. Once a test was completed,
the projectile was unsealed and the recorded data on the SP&DAQ board was

downloaded onto a computer for analysis.

106

As mentioned above, the only difference between the calibration and a real
application is the target for impact. In the calibration, a long instrumented rod was
used as the target instead of a real specimen. The long instrumented rod was
very similar to the rod used for dynamic testing used earlier except the rod length
and the positions of the strain gages. The rod used for calibration had a length of
1790 mm and the gages were installed at a location 430 mm from the impact
end. The reason for using this longer rod than the one used before (730 mm)
was aimed at increasing the impact duration between the instrumented projectile
and the longer instrumented rod.

Figure 4.11 shows the setup of the calibration for the instrumented projectile.
A calibration test based on a projectile speed of 15 m/s was performed. Figure
4.12 shows the result measured by the instrumented projectile, while Figure 4.13

shows the same result in force domain from the longer instrumented rod.

Gun Barrel .Infrared Emitting Longer Cylindrical Rod S
Sleeve DIOdeS for Triggerlng with Strain Gages topper

l I l l

\\\\\\\\\\\\\\\\\:

 
   

  
 

Add
.\\\\\\\\\\ s\\\\\\ ifmfii 7777 I 7777

Instrumented Velocity Wheatstone _, Amplifier _, Oscilloscope
Projectile Measurement Bridge 3M Bandwidth 10 MS/s

 

 

 

 

 

 

 

 

Figure 4.11 Setup for the calibration of the instrumented projectile.

107

Value (Voltage related)

Value (Voltage related)

 

 

4200 ,—. " ‘
“ Voltage = Value*Vref/2912 = data*2.5 /4096

 

‘, Time=l' L "‘ " Rate=Number/115k

 

3000 ~ W W 4
0 500 1000 1500 2000 2500
Number (time related)
4200 __, 7&6‘* ‘r‘ 7 I
. .09 l
4000 , ,3, 9 ,5:
3800 ‘ I l I? l
I o 9 0508
3600 , 3 ¢ ‘ogl l P 3 f
. (6W? 0’ ‘ I 69 19131295 8 .
w wiw. a m .1 1 Wm
; ‘ « 3‘ 6“ is ‘6 I a
3200 , o W I
3000 77-7 7.,7 fiffi * %_,7%_0
200 220 240 260 280 300

Number (time related)

Figure 4.12 Impact result measured by the instrumented projectile.

108

 

 

 

12 me ~ — ~ - —
10 ,2 Longer Rod
8 ’ . . —+-lnstrumented
E 6 ' ' ? Projectile
v 4 ’
CD 2 N ‘ m . - 'j- .... ...-V ‘
g 0 , .- ”. _,____1_‘-‘r\; ' '_" 111.111 Lug _
O l y (; k __-
LL - p 2
2 0 0. 2 0. 4 0. 6 .8 1

 

-4
-6 L
_8 _ “A,“ ._ _.___-- ____

Time (ms)

Figure 4.13 Comparison between the result from the longer rod and that
from the instrumented projectile when they impact with each other.

7. CASE STUDY OF THE INSTRUMENTED PROJECTILE

Figure 4.14(a) shows a setup for the application of the instrumented projectile
and Figure 4.14(b) shows the impact force history measured by the instrumented
projectile impacting onto a 114 mm x 76 mm x 25.4 mm aluminum plate having
fixed edges. The impact speed of the instrumented projectile was 14 m/s. A ring-
shaped indentation was found on the aluminum plate with a depth of about 0.1
mm. The ring-shape indentation was caused by the hollow cylindrical head of the
instrumented projectile.

Figure 4.14(c) shows the impact force history measured by a load cell in a
low-velocity drop-weight impact tester for the same type of aluminum plate

mentioned above. The plate had a fixed boundary condition around four edges,

109

as well. The impact speed was 4 m/s. A semi-sphere indentation with roughly 5
mm in diameter and 0.5 mm in depth was found on the aluminum plate. The
semi-spherical indentation was caused by the solid semi-spherical head of the

low-velocity impact tester.

Aluminum

Gun Barrel Infrared Emitting S .
pecmen

Sleeve Diodes for Triggering

[that] #7/

 

 

 

 

///'/

 

Instrumented Velocity
Projectile Measurement

Figure 4.14(a) Setup for impact test based on instrumented projectile.

110

 

Force (kN)

 

- 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

 

Time (ms)

Figure 4.14(b) Force history measured by instrumented projectile.

Force (kN)
N DJ 4} M 0\

fl

 

 

Time (ms)

Figure 4.14(c) Force history measured by a low-velocity
drop-weight impact tester.

lll

8. DISCUSSIONS
The calibration test shows that the prototype instrumented projectile meets
the requirements for a wireless high-bandwidth force transducer. The following

issues may be addressed for future improvements.

8.1 Longer Gun Barrel

The current setup allows the instrumented projectile be accelerated up to
20m/s. It provides enough power for the instrumented projectile to reach a high
impact force when impacting on a ‘hard specimen’, such as a stainless steel rod.
However, it is not powerful enough for real applications such as ballistic impact.

A longer gun barrel is needed for high-speed ballistic impacts.

8.2 Wave Transfer Section

The current wave reduction mechanism was achieved by using the cutting
tools available. The cutting tools unfortunately do not have the ideal geometry to
machine double parabolic surfaces for focusing wave fronts onto a ring for wave
transfer and eventually divergence. In order to machine the double curved
surfaces of the middle transfer section, the inner portion of the front section of the
projectile body needed to be removed, resulting in a hollow tube instead of a

desired solid circular rod.

8.3 The Sampling Rate

112

For the microprocessor used in the SP&DAQ board, the maximum sampling
rate was 200 kS/s (Samplings per second). With its own oscillator and the battery
used, the sampling rate is 115 kS/s; with the help of an extra 8 MHz oscillator,
the sampling rate is 171 kS/s. To increase the sampling rate to the maximum of
the microprocessor, 200 kS/s, an extra oscillator with a higher frequency should

be used, and the power voltage of the microprocessor should also be increased.

8.4 Triggering Mechanism

A 940nm infrared phototransistor was used for the measurement of projectile
speed as well as the triggering of the data acquisition system. The trigger
terminal of the microprocessor was connected to the positive terminal (+3 VDC)
of the power supply through a 1 k0 resistor that was also connected to the
ground of the system through the infrared phototransistor. The voltage at the
trigger terminal would be kept with a high voltage by this setup, and the control
program used a low voltage (0 - 0.4 VDC) as a trigger signal. When the
phototransistor received an infrared light from the emitting diode, it lowered the
voltage of the trigger terminal to trigger the data acquisition system. This action
required an infrared light with a high intensity and long duration. When the speed
of the projectile increases, more infrared emitting diodes along the path of the
projectile would be required to ensure the phototransistor has more time to

receive the infrared light.

8.5 The Connectors

”3

Some connectors were used for the power and data transferring interfaces of
the SP&DAQ board. Due to the limited space, relatively smaller connectors were
used. Some unsuccessful tests during the course of the study were traced down
to the failure of the connectors. Small and reliable connectors are needed for

future improvement.

8.6 Assembly Issues

Two rings were attached to the inside of the aluminum tube to hold the rear
section of the projectile body and weld glue was also applied between the tube
and the rear section of the projectile body. However, these were still not sufficient
for impacts involving large forces. A new assembling technique is highly

necessary.

9. CONCLUSIONS

An instrumented projectile was designed and constructed. The wave
reduction section of the instrumented projectile was not optimal due to the
limitation of the available cutting tools. Based on a series of calibration tests on
the instrumented projectile itself, as well as its components, the ability of the
instrumented projectile to be used as a low-velocity (up to 20 m/s) and a high-

bandwidth (170 kHz) dynamic force transducer was validated.

114

REFERENCES

[1] Jurg Dual, “Application of a Transducer Embedded in a Projectile for
Penetration Force Measurement”, Thesis for Master Degree, University of
California, Berkeley, July 10, 1984

[2] S. P. Virostek, J. Dual and W. Goldsmith, “Direct Force Measurement in
Normal and Oblique Impact of Plates by Projectiles”, Int. J. Impact Engng
Vol. 6, No.4, pp.247-269, 1987

[3] Joshua Liss, Werner Goldsmith, “Plate Perforation Phenomena due to
Normal Impact by Blunt Cylinders”, Int. J. Impact Engng, Vol. 2, No. 1,
pp.37-64, 1984

[4] S. Venzi, A. H. Priest, and M. J. May, “Influence of Inertial Load in
Instrumented Impact Tests”, Impact Testing of Metals, ASTM STP 466,
American Society for Testing and Materials, 1970, pp.165-180

[5] James F. Doyle, “Waves Propagation in Structures, Spectral Analysis Using
Fast Discrete Fourier Transforms”, Second Edition, Mechanical Engineering
Series, 1997

[6] C. Bacon, “Numerical prediction of the propagation of elastic waves in
longitudinally impacted rods: application to Hopkinson testing”, lntemational
Journal of Impact Engineering, 13 (4), 527-539, 1993.

[7] Jonas A. Zukas, Theodore Nicholas and Hallock. F. Swift, Impact Dynamics,
John Wiley & sons Inc. 287-308, 1982.

[8] D. J. Frew, M. J. Forrestal and W. Chen. “Pulse shaping techniques for testing
brittle materials with a split Hopkinson pressure bar", Experimental
Mechanics, 42 (1), 93-106, 2002.

[9] Michael Adam Kaiser, Advancements in the split Hopkinson bar test, Master’s
thesis, Blacksburg, Virginia, 1998.

[10] Frank E. Hauser, “Techniques for measuring stress-strain relations at high
strain rates”, Experimental Mechanics, 395-402, 1966.

[11] J. F. Bell, “An experimental diffraction grating study of the quasi-static
hypothesis of the split Hopkinson bar experiment”, J. Mech. Phys. Solids, 14,
309-327, 1 966.

[12] Gerald L. Jones and Edmund G. Henneke, ll, “Reflection of Stress Waves at

115

a Free Boundary in Quartz Single Crystals”, IEEE Transactions on Sonics
and Ultrasonics, Vol, Su-20, No. 3, July 1973

[13] Kasaburo Harumi, Tetsuo Saito, “Educational Films for Ultrasonic
Engineers”, IEEE Ultrasonics Symposium, 1982, pp. 1074-1078

[14] M. D. Sharma, “3-D wave propagation in a general anisotropic poroelastic
medium: reflection and refraction at an interface with fluid”, Geophys. J. Int.
(2004) 157, pp. 947-958

[15] Baljeet Singh, “Reflection of P and SV waves from free surface of an elastic
solid with generalized thermodiffusion”, Earth Syst. Sci. 114, No. 2, April
2005, pp. 159-168

[16] Baljeet, Singh, “Reflection of homogeneous elastic waves from free surface
of nematic elastormer half-space”, J. Phys. D: Appl. Phys. 40 (2007), pp.
584-592

[17] Zhi-Jun Dai, Zhen-Bang Kuang, She-Xu Zhao, “Reflection and transmission
of elastic waves at the interface between an elastic solid and a double
porosity medium”, International Journal of Rock Mechanics and Mining
Sciences 43 (2006) pp. 961-971

[18] Kunyu Wu, Qiang Xue, and Laszlo Adler, “Reflection and transmission of
elastic waves from a fluid-saturated porous solid boundary”, J. Acoust. Soc.
Am. 87(6), June 1990

[19] Jose M. Carcione, “Reflection and transmission of qP-qS plane waves at a
plane boundary between viscoelastic transversely isotropic media”,
Geophys. J. Int. (1997) 129, PP. 669-680

[20] Texas Instruments, “2.2V, 50MHz, Low-Noise, Single-Supply Rail-to-Rail
Operational Amplifiers”, SBOS365B, June, 2006, Revised Sep. 2006

[21] Bonnie Baker, “Single-Supply, Low-Power Measurements of Bridge
Networks”, Burr-Brown Application Bulletin, April, 1993

[22] James Karki, “Signal Conditioning Wheatstone Resistive Bridge Sensors”,
Application Report, Texas Instruments, SLOA034, Sept, 1999

116

CHAPTER FIVE

CONCLUSIONS AND RECOMMENDATIONS

1. CONCLUSIONS

The vertical impact systems are simpler and less costly than the horizontal
impact systems. However, the latter are free of gravitational effect and can
achieve higher impact velocity. In measuring the contact-impact forces, strain-
gage based sensors are not sensitive to oscillation as much as accelerometers.
This is because the former are based on deformation while the latter, the motion.
This is especially true in vertical impact tests. Among the strain-gage based
sensors, the load cell seems to be more effective for relatively soft specimens,
while the striker is more suitable for recording hard impact if the wave
superposition effects can be eliminated. Accordingly, a horizontal impact system
using a strain-gage-based force transducer seems to be an ideal system for
contact-impact testing.

Experimental results showed that reflected waves and their superposition
with the initial impact wave can complicate the impact force measurements. The
complication increases as the impact duration becomes shorter. Based on a
mechanical technique to redirect the reflected waves, a wave reduction method
was proposed and verified. The initial wave associated with the impact force

could be identified.

117

Besides the mechanical technique, two numerical techniques, the so-called
Initial Wave Assumption technique and the Two-Point technique, were also
proposed and verified to be able to recover the initial impact force wave.

The success of the wave reduction techniques to recover the initial impact
force wave shed light on designing an instrumented projectile with a short rod.
Preliminary studies for both wired and wireless instrumented projectiles were
explored.

An instrumented projectile was designed and constructed. The wave
reduction section of the instrumented projectile was not optimal due to the
limitation of the available cutting tools. Based on a series of calibration tests on
the instrumented projectile itself, as well as its components, the ability of the
instrumented projectile to be used as a low-velocity (up to 20 m/s) and a high-

bandwidth (170 kHz) dynamic force transducer was validated.

2. RECOMMENDATIONS

The calibration test shows that the prototype instrumented projectile meets
the requirements for a wireless high-bandwidth force transducer. The following
issues may be addressed for future improvements.

The current setup allows the instrumented projectile to be accelerated up to
20m/s. It provides enough power for the instrumented projectile to reach a high
impact force when impacting on a ‘hard specimen’, such as a stainless steel rod.
However, it is not powerful enough for real applications such as ballistic impact.

A longer gun barrel is needed for high-speed ballistic impacts.

118

The current wave reduction mechanism was achieved by using the cutting
tools available. The cutting tools unfortunately do not have the ideal geometry to
machine double parabolic surfaces for focusing wave fronts onto a ring for wave
transfer and eventually divergence. In order to machine the double curved
surfaces of the middle transfer section, the inner portion of the front section of the
projectile body needed to be removed, resulting in a hollow tube instead of a
desired solid circular rod.

For the microprocessor used in the SP&DAQ board, the maximum sampling
rate was 200 kS/s (kilo-Samples per second). With its own oscillator and the
battery used, the sampling rate is 115 kS/s; with the help of an extra 8 MHz
oscillator, the sampling rate is 171 kS/s. To increase the sampling rate to the
maximum of the microprocessor, 200 kS/s, an extra oscillator with a higher
frequency should be used, and the power voltage of the microprocessor should
also be increased.

A 940nm infrared phototransistor was used for the measurement of projectile
speed, as well as the triggering of the data acquisition system. The trigger
terminal of the microprocessor was connected to the positive terminal (+3 VDC)
of the power supply through a 1 kn resistor that was also connected to the
ground of the system through the infrared phototransistor. The voltage at the
trigger terminal would be kept with a high voltage by this setup, and the control
program used a low voltage (0 - 0.4 VDC) as a trigger signal. When the
phototransistor received an infrared light from the emitting diode, it lowered the

voltage of the trigger terminal to trigger the data acquisition system. This action

119

required an infrared light with a high intensity and long duration. When the speed
of the projectile increases, more infrared emitting diodes along the path of the
projectile would be required to ensure the phototransistor has more time to
receive the infrared light.

Some connectors were used for the power and data transferring interfaces of
the SP&DAQ board. Due to the limited space, relatively smaller connectors were
used. Some unsuccessful tests during the course of the study were traced down
to the failure of the connectors. Small and reliable connectors are needed for
future improvement.

Two rings were attached to the inside of the aluminum tube to hold the rear
section of the projectile body and weld glue was also applied between the tube
and the rear section of the projectile body. However, these were still not sufficient
for impacts involving large forces. A new assembling technique is highly

necessary.

120

APPENDIX A

DESIGN A PENNY-SIZE SIGNAL PROCESSING

AND DATA ACQUISITION (SP&DAQ) SYSTEM

1. INTRODUCTION

The instrumented projectiles are designed to measure the dynamic force
history during impacts; they will be shot out from the gas gun powered by high
pressure Nitrogen gas or air. The signal measurement unit and its battery should
be put into the instrumented projectile and move with it during impact tests. The
impact information measured will be saved by the measurement unit during
impacts. The saved data is then transferred out for further data processing.

Besides the instrumented projectile unit, the whole system also includes a
gas gun unit, a speed measurement unit, a trigger unit, and a calibration unit.
The instrumented projectile, the trigger, and the speed measurement units will be

discussed in this section.

2. DESIGN OVERVIEW

When the instrumented projectile impacts the specimen, the impact force
history is measured by two strain gages installed on the projectile. The gages are
connected to the opposite arms of a Wheatstone bridge circuit, which is followed

by a signal amplifier. The data acquisition system digitizes the amplified signals

121

and saves them during impact tests. After the test, the saved digitized signals will
be transferred out.

The whole electrical measurement system includes: a Wheatstone bridge
circuit section; a signal amplifier section; a data acquisition section and a data
saving section. Because the instrumented projectile is used for dynamic force
measurement, a trigger section is also needed. After the test, a data transferring

section will be used to transfer the saved data out.

 

' High bandwidth& sampling rate
Signal Processing &

 

 

 

 

 

DAQ System
I 'I i I i v i
Trigger Strain Gages Power Amplifier DAQ Data Saving

Figure A1 Schematic layout of the measurement system of the
instrumented projectile

Because the whole system is powered by a battery, the energy consumption
should always be kept in mind. For example, using strain gages with larger
resistance, choosing low energy consuming chips, and programming the system
to low energy consuming status when waiting for trigger, etc. Since the
instrumented projectiles are designed for impact tests, the amplifiers should have
high bandwidth and the data acquisition part should have a high sampling rate.

The data saving speed should keep the same rate with the data sampling.

122

2.1 Strain Gages and Wheatstone Bridge

Strain gages are used to sense the impact force. At a cross-section of the
cylindrical projectile body, two strain gages are installed oppositely across the
diameter. They are then connected to the opposite arms of a Wheatstone bridge
circuit in order to measure the compression & tension waves and eliminate the
bending effects of the projectile. The Wheatstone bridge is chosen here because
of its differential output -- the useful signals could be amplified without any kind of
filtering. Another two arms of the Wheatstone bridge are resistors; their
resistances should be a little larger than the strain gages since the followed
amplifier circuits require this condition [1-3]. Temperature compensation is not
considered here since the whole circuit is for dynamic tests, which usually

happen in a fraction of second.

 

 

 

 

 

 

 

Figure A2 Schematic of the Wheatstone bridge

The whole instrumented projectile measurement unit is powered by a battery,
and the Wheatstone bridge circuits are the major energy consuming parts in the

whole system. 1000 ohm strain gages are used because they consume less

123

energy than the common 350 ohm and 120 ohm strain gages. The gage length

should be less than 3 mm for the elastic wave measurement [4,5].

2.2 Amplifier

It is designed that the materials of the projectiles only deformed in their
elastic stage. Therefore, the strain signals from the instrumented projectiles are
relatively small, this requires the signals to be amplified for the subsequence data
acquisition and saving.

Differential amplifiers are ideal for the signals from the Wheatstone bridge
circuits. The differential amplifier circuit containing three operational amplifiers
(op-amp) is usually used, one for amplifying, and another two for improving the
input impedance [6]. The op-amps in the differential amplifier circuit require the
dual polarity power supply. However, the single battery cannot provide these
without the help of some special circuits.

There is an amplifying circuit which has high input impedance and contains
only two op-amps. It requires one input to be always larger than the other; if it is
equal or less than another one, the output would be zero [1-3]. In this circuit, the
op-amps could be powered with normal DC power sources. For the impact tests,
the first pulse is the focus, and it always contains compression signals. The
signals after the first pulse should be constant or just have minimal vibration due
to the special geometry of the projectiles. In order to save space and reduce the

energy consumption, the amplifying circuit with two op-amps is used. To make

124

sure one output is always larger than another one, two extra resisters with small

resistance are added to the dummy arms of the Wheatstone bridge circuit.

$g+ R2 2R2
V0: Si+—S'— x l+—+—
[(g)(lg)1[R1Rg]

 

R1=R2

_ 1 _
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Sig -

 

R3
L

Figure A3 Schematic of the amplifier circuit.

2.3 Data Acquisition and Saving

The amplified impact signals are to be digitized and saved for later data
processing. Since the instrumented projectiles are designed for measuring
impact force histories with very short durations, the sampling rate of the data
acquisition should be as high as possible. For most microprocessors during this
thesis research, the maximum sampling rate is about 200 k samples per second.

The sampled data should be saved immediately. Therefore, the data saving
rate must be the same with the data sampling rate. RAM is the suitable media for
the data saving, rather than flash memory, hard disc, etc. because the high data
saving rate can be achieved easily. RAM requires continuous electrical power to

maintain the data.

125

An impact usually lasts only a few milliseconds. The high sampling rate with
limited memory cannot acquire the desired impact signals in such a short
duration without proper triggering. There are two common sampling modes with
triggering. One is, the processor keeps sampling and saving, the new data will
ovenlvrite the old one inside the memory; when the trigger comes, it will keep
sampling and saving for a certain time, then stop; The other is, the whole data
acquisition and saving system waits for the trigger, when the trigger event
happens, they wake up and begin to sample. Because the electrical system of
the instrumented projectile is powered by a battery, the energy consumption
becomes a major concern. Therefore, the second operation mode is used for the

controlling program of the microprocessor.

2.4 Trigger

With the limited memory and extra high sampling rate, an efficient trigger is a
key factor for a successful measurement.

An infrared phototransistor and several infrared emitting diodes are used
together to trigger the data acquisition and saving. The infrared phototransistor is
installed in the instrumented projectile, while the infrared emitting diodes are
installed on the outlet of the gas gun barrel. When the projectile passes by the
infrared emitting diodes, the phototransistor in the projectile will sense the
infrared radiation and cause the voltage variation on it, which can be used for

tfiggefing.

126

VDC VDC

 

Figure A4 The schematic triggering circuits with the infrared
emitting diode and infrared phototransistor.

3. DESIGN AND MANUFACTURING
3.1 Strain Gages

1.524 mm gauge length strain gages with 1000 ohm resistance from the
Vishay Company are used in the instrumented projectiles. Small length gages
are chosen because they are more suitable for sensing strain waves [7]. Larger

resistance gages are chosen since they will consume less electrical energy.

3.2 Trigger

Peak wavelength 940 nm with 19 mm diameter infrared phototransistors and
infrared emitting diodes are selected for the triggering. One infrared
phototransistor is installed in the projectile while 28 infrared emitting diodes are
installed on a sleeve, which is coaxially installed at the outlet of the gun barrel.
The infrared emitting diodes are in 4 x 7 array, four of them are installed in the
same cross section of the sleeve, roughly 20 degrees between the neighbored

ones, and there are 7 layers altogether along the axial direction. Installing 28

127

infrared emitting diodes instead of one is to avoid mis-triggering during tests. The
infrared emitting diodes are always on during tests. When the projectile passes
by, the infrared phototransistor can sense the infrared emission and trigger the
data acquisition and saving system. Since the visible Iight’s wavelengths are from
400 nm to 700 nm, choosing a phototransistor with 940 nm peak wavelength can
reduce the influences of the visible lights. Choosing small size parts is due to the

limited space for the parts in the projectile.

3.3 Signal Processing, Data Acquiring and Saving Unit (SP&DAQ unit)

The dummy resistors of the Wheatstone bridge circuits, the op-amps and the
resistors of the amplifying circuits, the microprocessors for data acquisition and
saving, and the accessory parts for the circuit are all designed to be in the same

unit. The drawing of the circuit is showed in Figure A5.

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and saving

3.4 Microprocessor

An MSP430f1611 microcontroller from TI was chosen to be the
microprocessor for the data acquisition and saving [8-12]. Its features include: an
ultra low power consumption processor with low supply voltage range, 1.8 — 3.6
V; five power-saving modes, wake-up time from standby mode is less than 6 us;
dual 12 bit A/D converters with synchronization; 48 kB flash memory, in which
the control program can be saved; 10 kB RAM, which can be used to save the
measured data.

This microprocessor can be controlled by the programs written in C language
or in the assembly language. C language is easier for programming, but the
program in C language can only control half of the total 10 kB RAM. Finally, the
assembly language is used to write the control program of the microprocessor.

The program is based on the Interrupt mode. It includes a main program and
several subroutines. The main program sets up and initializes all the interrupt
vectors and the RAM; a data acquisition and saving subroutine is programmed
for digitalizing the signals and saving them; a trigger interrupt subroutine is used
to start the data acquisition and saving subroutine; a data transferring interrupt
subroutine is designed to transfer the measured data out and reset the vectors
for next test. The data acquisition and saving subroutine used the highest
frequency clock (up to 8 MHz) for the highest sampling rate. The standby and the
data transfer subroutine used the lowest frequency clock (33 KHz) for power

saving purpose.

130

In the main program, there are several alternative variables which include a
variable to set the input channel numbers: single or dual channels; a variable to
decide the data acquisition reference voltage: 3 V or 2.5 V; a variable to decide
the data accuracy: 8 bit or 12 bit; a variable to increase the trigger delay time.
These variables can be combined, thus making it easier to obtain a suitable
program to download to the microcontrollers for different tasks.

An LED indicator is used to show the running status of the program [13]. It is
ON when the electrical power is added to the microprocessor and it is OFF after
the data acquisition and data saving. When the data is transferred out, the LED
indicator is turned on again to indicate that the system is ready for the next test.

The microcontroller is of 64-Pin Quad Flat Pack. The total dimension is 11.8
mm x 11.8 mm x 1.45 mm. It makes the total width of the electrical board not less
than 12 mm; it also makes the diameter of the projectile larger than the expected

size — half inch.

3.5 Amplifiers

An operational amplifier OPA2365 from the TI Company is used for the
amplifier circuit [2]. It can be powered by a range from +2.2 VDC to +5.5 VDC,
and has 50 MHz bandwidth and relatively low noise. There are two op-amps in
one SO-8 package. Therefore, it is easier to achieve the desired differential

amplifier circuit with one amplifier chip.

131

In the design, there are two amplifying circuits corresponding to the possible
two input channels. There are two amplifier chips installed on the electrical print

board.

3.6 Resistors for the Wheatstone Bridge

The strain gages installed on the instrumented projectile have 1000 10.3%
ohm resistance. Accordingly, originally 1000 10.1% ohm resistors are selected
for the dummy arms of the Wheatstone bridges. Even though it is not necessary
to make the bridge circuit balance for dynamic measurements, an almost zero
output at unloading status would be preferred since it makes the followed signal
amplifying and data acquisition easier.

As mentioned before, the amplifying circuit needs one input to be always
larger than the other. Therefore, an extra 6 15% ohm resistor is put into each
resistor’s arm in series (shown in Figure A5, the right-upper corner). Since the
projectile is desired to work in the elastic stage, the strain signals from the stain
gages have a fixed range. The extra resistors will make the outputs of the
Wheatstone bridge to meet the requirement of the chosen amplifying circuit —

one output is always larger than the other.

3.7 Print Board and Soldering
After the breadboard verifications, the print board is designed and some
pieces are manufactured. The print board is designed as small as possible, and

all of the electrical parts are chosen in their relatively small packages.

132

The ‘ExpressPCB’ company provides convenient service for manufacturing
customer designed print board. The drawings of the board are made with the
software provided by this company. The board is penny-sized and double-sided,
with length 26 mm and width 15 mm.

The 64 pins small chips are soldered with a normal soldering gun. The
surface mounted chips are very sensitive to moisture, they had to be kept in a dry

cabinet and their moisture rate must be monitored [14].

 

 

 

 

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Oh- am I' ”a; n 1:; ‘ LI/j‘ - o'. n n boo

CU rum... im unmw Cg

..
o...-
0!.)-
'ub-
0‘1"
r..-
ugh
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'ur
'-0-
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C1
01...!—
o_ o
03"
[o

 

Figure A7 Pictures of the soldered Signal Processing and
Data Acquisition Unit.

3.1 Battery

Even though all selected chips are so called low energy consuming ones,

their working currents are still in micro ampere levels. Table A1 shows the power

134

consumption of each components and their summation when tested under 3.3

VDC voltages.

Table A1 Electrical current consumption of each component

 

 

Voltage = . Signal _
Microcontroller . Bridge Sum
3.3V Amplifier
Current (mA) 1.15 6.24*2 8.3*2 30.23

 

 

 

 

 

 

 

The total currents are beyond the ability of the normal button batteries. A
Lithium battery—EL1CR2 from the Energizer company is selected, its feature
includes: 3.0 V nominal voltage with 800 mAh capacity; 11 grams in weight. It
has 15.1 mm in diameter and 27 mm in length. One battery can power all of
these electrical parts, and its volume, especially the diameter, meets the

requirement.

3.9 Wiring

The strain gages are installed on the surface of the front part of the projectile.
The battery and the signal processing, data acquisition and saving unit are at the
rear part, inside of the projectile. Wires have to be used to connect them.
Because the body of the projectile has strict geometrical limitations, there is no
possibility for the connecting wires to go through directly. The wires have to be
installed between the main projectile body and the protection tube. Since there is
only tiny space left between this two, the small square cross-section enamel

insulated wire, 134-AWP, from the Vishay Company is selected and glued inside

135

of the gap between the projectile body and the protection tube. Because the
projectile and the protection tube are also glued together permanently, 50% extra

wires are installed in case of wires broken during impacts.

3.10 Connectors

There are two sets of connectors used. One is between the battery and the
SP&DAQ unit, and another is for the data transferring port of the SP&DAQ unit.
The battery cannot be connected permanently, and it will be replaced after
several tests, so a connector is very necessary here. The connector for data
transferring will be used after each test, because the impact information will be
read out through it.

Since the battery and the SP&DAQ unit occupies almost all the space inside
of the projectile, the connectors have to be tiny. Because the power must remain
on for the microprocessor, especially its RAM memory, the connectors must be
very reliable. The 1 mm micro socket and header with 2 conductors and 4

conductors are chosen and carefully soldered for the connections.

3.11 Battery and SP&DAQ unit protection

The battery and the SP&DAQ unit are installed into the instrumented
projectile and run with it. They will sustain the impact force during tests. The
survivability of the battery and the SP&DAQ unit during tests is worthy of

discussion.

136

The board needs electrical power during the impact tests, and the power
should be kept on until the data is transferred out. If the power supply is
disconnected, the system will be shut down; all of the measured data will be lost.

The possible power disconnection could happen at the terminals of the
battery. The battery cannot be soldiered due to safety and performance reasons.
How to connect the wires with the terminals of the battery becomes a problem.
There is a hole at the anode terminal of the battery, which can be used to tie the
wire. For the cathode terminal, a small spring is used to keep the connection.

Two rubber pads are tightly attached to both ends of the battery; they are tied
with thin fish line. The rubber pads will work like cushions to reduce the possible
battery damage during impacts. There are two rubber pads attached to the
electrical print board, as well. The board is also wrapped with electrical tape to

ease the lateral acceleration of the chips during impacts.

4. SUPPORTING SYSTEMS
4.1 The Control Programs

The control program is written in assembly language. It is written, debugged
with specific software, and then downloaded into the microprocessor. The
software is called IAR Embedded Workbench, the program developing
environment for Tl’s MSP 430 family microprocessors. Another
MSP430f1611developing kit from the SoftBaugh company is also used. It
includes a testing board with the microprocessor and some accessories; a USBP

MSP430 Flash Programming Adapter for implanting the program into the

137

microprocessors; and an installation program for modifying the IAR environment
and for installing the driver of the USBP Programming Adapter.

The IAR software is installed first, and then the installation program from
SoftBaugh modifies the IAR for its hardware. The program for the microprocessor
is written, debugged in the modified IAR environment, and then downloaded to
the microprocessor in the testing board for verification until the program is finally
successful for the task. For any new manufactured SP&DAQ unit, the control
program is opened in the IAR software first, and then downloaded to the

microprocessor of the unit through the USBP MSP430 Programming Adapter.

4.2 Data Transferring Circuit and Software

The data saved in the RAM of the microcontroller is in binary format. They
should be transferred into a computer as hexadecimal numbers or decimal
numbers for further processing. An interface box is designed and manufactured,
and a free interface program is downloaded for this purpose.

The microcontroller has many pins for input/output, two of them are chosen
for the data transferring. In the data transfer subroutine of the program, one of
these pins is appointed to be the data transfer controller and another to be data
port. At anytime during running the program, if the microcontroller gets data from
the data transfer controller pin with specific format and value, the program will go
to the data transferring interrupt subroutine and send all the data in the RAM out

through the data port.

138

The COM port of a desktop computer is used to communicate with the
microcontroller under the R8232 interface protocol. Because the microcontroller
has a different communication protocol, a data transfer interface box is designed
and manufactured.

The data transfer interface box bases on the chip — MAX3223, which is for the
R8232 protocol communication. The drawing is shown below. From the drawing,
one can see that the board and computer will share common ground. When the
computer gives. commands through its COM port—DBQ, the MAX3223 will
translate the command to the format the board can understand and then send it.
When the board sends the data out, the MAX3223 will receive first, then transfer
the data to the computer.

The power of the MAX3223 is given by a power supply unit. The MAX3223
chip can be powered from 3 V to 5.5 V, 3.3 V is chosen as its power supply for
the safety of the board. Since the board is powered with a 3 V battery, the same

level power supplies can reduce the risks for both sides in case of malfunction.

139

~

\

(3x)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LN our

 

. 5
.' I Tothe _L10uF, I 10k I_.o
: 3 Board 13 15 T‘OV ? ' 3 0 °
5 c : r1111 R1 IN 1:: 0:
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Ic.‘ R10UT I 1.0x 0 °
\ x 1 01+ 2
' d EN 02* __10uF, DB9
14 fllguF, L 0.47uF, -—-1ov
—- 16V
FORON _ 6_T T
FOROFF __
C1 - :—
100k ll 19 4 -
V+ 3
100k 100k VCC 0 47 F
GND v- 0.47uF, 16Vu '
18 7 |16V
10uF, —— Z:
10v "' —|—
30mH Common Mode
Line Filter
N ___o+3.3voc
KQQQJ 00pF
Y2 FSK-SS
220nF —— -3R3U ?
x2 "’ _
= 2200pF
2200pF Y1

 

 

Figure A8 Circuit drawings of the data transferring (upper)
and its power supply (down)

140

 

Figure A9 Picture of the data transferring box

Software is also needed to control the COM port to communicate with the
microprocessor through the COM port and the RS232 interface box. A free COM
port control software ComMaster is downloaded and used for this purpose.

The ComMaster is free software for COM port(s) monitoring, testing,
debugging, and filtering. Its basic functions are used here to send the ‘getting
data’ command to the electrical board and receive the data and show them in

hexadecimal format. The data can then be saved for further data processing.

4.1 Program for Data Processing
The data transferred from the COM port is in hexadecimal format. They are
converted into decimal number for the followed data processing, and the

matched time series is also needed to be added to the data file.

141

A Matlab program is made for this purpose, it is used to calculate the time
series based on the sampling rate, and to transfer the hexadecimal numbers to
decimal numbers. The time series and the date series are in column style. They

can be read by Excel software.

4.4 Velocity Measurements

Force-Deflection curves are desired for the specimens under impact loading.
The force history can be measured by the instrumented projectiles. If the
projectile’s velocity before the impact can also be measured, the deflection
history can then be calculated.

As mentioned before, an infrared phototransistor can be used as an electrical
switch when working with a matched infrared emitting diode. When the infrared
phototransistor is installed into a serial circuit, the voltage between its two
terminals will change if its faced infrared is blocked. The velocity measurement
system is base on this fact. Actually, two sets of the infrared emitting diodes and
infrared phototransistors are working together. They are installed at two axial
positions of a sleeve, which is installed at the outlet end of the gas gun barrel
coaxially. At each cross-section, the infrared phototransistor and the infrared
emitting diode are installed oppositely into the sleeve’s wall. The emitting diodes
are always on during tests, so the phototransistor can get the infrared normally.
When the projectile is shot out, it will pass by the sleeve and blocks the infrared.
Therefore, the voltage on the phototransistor will change. The projectile passes

the two positions one by one. The time interval can be monitored through an

142

oscilloscope by monitoring the voltages of the two phototransistors. With a well
measured distance between the two cross-sections, the velocity of the projectile

can be calculated out.

Infrared emitting diode

Position one Position two

 

 

 

 

 

I <— Sleeve

Projectile Gun arrel
Infrared phototransistors

Figure A10 Schematic of the velocity measurement

I43

REFERENCES

[1] Bonnie Baker, “Single-Supply, Low-Power Measurements of Bridge
Networks”, Burr-Brown Application Bulletin, April, 1993

[2] Texas Instruments, “2.2V, 50MHz, Low-Noise, Single-Supply Rail-to—Rail
Operational Amplifiers”, SBOSBG5B, June, 2006, Revised Sep. 2006

[3] James Karki, “Signal Conditioning Wheatstone Resistive Bridge Sensors”,
Application Report, Texas Instruments, SLOAO34, Sept, 1999

[4] James F. Doyle, “Waves Propagation in Structures, Spectral Analysis Using
Fast Discrete Fourier Transforms”, Second Edition, Mechanical Engineering
Series, 1997

[5] Ralph Burton, office of naval research, London, ‘Vibration and Impact”, Dover
Publications, Inc. New York 10014, 1968

[6] Dennis L. Feucht, “Handbook of Analog Circuit Design”, Academic Press, Inc.,
San Diego, California, 1990

[7] Jonas A. Zukas, Theodore Nicholas and Hallock. F. Swift, “Impact Dynamics”,
John Wiley & sons Inc. 287-308, 1982.

[8] Texas Instruments, “Mixed signal microcontroller (Rev. E)
(msp430f1611.pdf)”, SLA836BE, Texas, October 2002, Revised August 2006

[9] Texas Instruments, “MSP430F15x/16x/161x” SLAZO18B, Texas, 7/23/2007

[10] Texas Instruments, “MSP430x1xx Family User’s Guide”, Texas, SLAUO49F,
2006

[11] SoftBaugh, “Using the USBP with a Third-Party IDE”, Suwanee, Georgia,
Feb, 2006

[12] Murugavel Raju, “Digital FIR Filter Design Using the MSP430F16x”,
Application Report, Texas Instruments, SLAA228, Nov., 2004

[13] J. Honsi, “Porting of RF Blinking LED Software Example to CC2420-
MSP430”, Application Note, Chipcon Products from Texas Instruments,
ANOO33, 2004

[14] Stephen W. Hinch, “Handbook of Surface Mount Technology”, Longman
Group UK limited, England, 1988

144

APPENDIX B

THE MICROPROCESSOR’S CONTROL PROGRAM

FOR DATA SAMPLING AND SAVING

— IN ASSEMBLY LANGUAGE

#include "msp430x16x.h" ; #defme controlled include file
#defme PointerTX R9
#define PointerRX R10
AOresult EQU 1100b ; Channel A0 results
Alresult EQU 2500B ; Channel Al results
endmem EQU 3800H ; end of memory
Channel_num EQU 1 ; AD Channel number:0 for only A0, 1: A0 & Al
Delay_timel EQU 2h ;Delay timel from trigger to start ADC12
Delay_time2 EQU 2h ;Delay time2 from trigger to start ADC12
Adc_bit EQU 00h ;ADC bits: 00h for 12bits(word),02h for 8bit(byte)
sample_num EQU 2800b ;Sampling Number saved in the ram
Voltage_ref EQU 2 ;Voltage reference: 3 for VAcc, 2 for 2.5

NAME main ; module name

PUBLIC main ; make the main label vissible

; outside this module

 

; Interrupt Vectors (15) RESET

 

ORG 0FFFEh
DC 1 6 init ; set reset vector to 'init' label

 

Interrupt Vectors (l4) NMI interrupt

 

ORG OFF FCh
DW NMIPROC ;NMI interrupt process

 

; Interrupt Vectors (13)

 

ORG OFF FAh
DW int_no_l3 ;Timer_B7 interrupt process

 

; Interrupt Vectors (12)

 

ORG 0FFF8h
DW int_no_12 ;Timer_B7 interrupt process

145

 

Interrupt Vectors (l l)

 

 

 

ORG 0FFF6h

DW int_no_ll ; interrupt process
Interrupt Vectors (10)

ORG 0FFF4h

DW int_no_IO ; interrupt process

 

Interrupt Vectors (9) for UARTO receive

 

ORG OFFFZh ;
DW USARTORX_ISR ;USARTO receive

 

Interrupt Vectors (8) for UARTO transmit

 

ORG 0FFFOh ;
DW USARTOTX_ISR ;USARTO transmit

 

Interrupt Vectors (7) for ADC 12

 

ORG 0FFEEh ;ADC12 Interrupt Vector
DW ADCIZISR ;

 

Interrupt Vectors (6)

 

ORG 0FFECh
DW int_no_6 ; interrupt process

 

Interrupt Vectors (5)

 

ORG 0FFEAh
DW int_no_S ; interrupt process

 

Interrupt Vectors (4)

 

ORG 0FFE8h
DW int_no_4 ; interrupt process

 

Interrupt Vectors (3)

 

ORG OFF E6h
DW int_no_3 ; interrupt process

 

Interrupt Vectors (2)

 

ORG OFF E4h
DW int_no_2 ; interrupt process

 

Interrupt Vectors (1) for I/O Port P2

 

ORG OFFEZH ;I/O Port P2
DW IOP2

 

146

 

; Interrupt Vectors (0)

 

 

ORG 0FFEOh

DW int_no_O ; interrupt process

RSEG CSTACK ; pre-declaration of segment

RSEG CODE ; place program in 'CODE' segment
init: MOV #SFE(CSTACK), SP ; set up stack
main: NOP ; main program

MOV.W #WDTPW+WDTHOLD,&WDTCTL ; Stop watchdog timer
;+—+—1—H+I+++++++—+—H—+—+ Set high DCO frequency CLK 1++H++++I+H~+++++—+—H-H—++++1~
BIS.B #RSEL2+RSELI+RSELO,&BCSCTLI
BIS.B #DC02+DCO 1+DC00, &DCOCTL
;H‘t-H-H-l-H-H-H Clear RAM -i-l—H—l—H—i—l-I-l—H—I—+—I—I-++—+—H—I—

mov.w #2700h,R5 ;clear ram: 1 lOOh-—3800h
clrram: mov.w #0000h,A0result(R5)
decd R5
jnz clrram
mov.w #0000h,R12 ;counter for trigger number
;~I—+—I—H—H—H—H—++l—l—I—l-UARTO initializationH—F-l—F+++-l—-l—+—I—++
SetupP3 bis.b #030h,&P3SEL ; P3.4,5 = USARTO TXD/RXD
SetupUARTO bis.b #UTXEO+URXEO,&MEI ; Enable USARTO TXD/RXD
bis.b #CHAR,&UCTLO ; 8-bit characters
mov.b #SSELO,&UTCTLO ; UCLK = ACLK
mov.b #003h,&UBR00 ; 32k/9600 - 3.41
mov.b #000h,&UBR10 ;
mov.b #04Ah,&UMCTLO ; Modulation 4A
bic.b #SWRST,&UCTLO ; "Initialize USART state machine"
bis.b #URXIEO+UTXIEO,&IE1 ; Enable USARTO RX/TX interrupt
bic.b #UTXIFGO,&IFG1 ; Clear inital flag on POR

bic.b #OFIFG,&IFG1
clr.w PointerRX ,
;-l—l-+++-+—l—I-+-l—I—i-l—I—+—l—+-Portl Portz initialization-l-i—F-F-l—i—H-H-I-i-H

bis.b #01h,&PlDIR ;setPl.0 to output direction
bis.b #20h,&PlDIR ;setPl.5 to output direction
bis.b #40h,&PlDIR ;setPl.6 to output direction

mov.b #OOh,&P11FG
mov.b #00,&Pl IE

mov.b #Ofeh, &P2DIR ;set P2 to output direction

mov.b #0h,&P21FG ;CLEAR interrupt flag register
mov.b #Olh, &P21ES ;set P2.0 interrupt edge is high-to-low
mov.b #Olh, &P21E ;P2.0 interrupt is enabled

;+—l—-+—l-+-l-—I—H—l—+—l—I—l—I~I—i-ADC 1 2 initialization+—i—H-i-+-+—+—H—i—+—i+
bis.b #BITO+BIT1,&P6SEL ;EnableA/Dinputs +BIT2+BIT3
mov.b #Channel_num,R6 ;get AD sampling mode
add.b #Adc_bit,R6 ;R6=00h 2A0 12bits
;R6=Olh :AOA112bits
;R6=02h :AO 8bits
;R6=O3h :AOA18bits
bis.b #01h,&PlOUT ;turn on the LED
bic.b #20h,&PIOUT
SetupADC 12 mov #Voltage_ref, R5
cmp #02h,R5
jnz REF_VCC
mov #REFON+REF2_5V+SHTO_0+MSC+ADC120N,&ADC l 2CTLO;lntemal 2.5V reference
;Turn on ADC12, use int. osc.

147

; extend sampling time so won't

; get overflow

; Set MSC so conversions triggered
jmp goon ; automatically

REF_VCC mov #SHTO_0+MSC+ADCI20N,&ADC12CTLO;exteral VAcc reference

goon mov.b #Channel_num, R4
cmp.b #1,R4
jnz Chl
mov #SHP+CONSEQ_3,&ADC12CTL1 ;Two channel A0 and Al
; Use sampling timer, set mode

mov #BIT1,&ADC121E ; Enable ADCIZIFGJ for ADClZMEMl

mov.b #INCH_0,ADC12MCTLO ; A0 goes to MEMO

mov.b #EOS+INCH_1,ADC12MCTL1 ; A1 goes to MEMl, end of sequence

jmp Ch_end
Chl: mov.b #INCH_0+EOS,ADC12MCTLO ;one channel A0

mov #SHP+CONSEQ_2,&ADC12CTL1 ;SAMPCON: sampling timer,repeat-

;single-channel;+ADC12D1V_0

mov #BITO,&ADC121E ; Enable ADC12IFG.0 for ADCIZMEMI
Ch_end clr R5 ;Clear pointer
Mainloop mov.w #0ffffh,R4

mov.b #0h,&P21FG ;CLEAR interrupt flag register

bic.b #01h,&P21FG
bic.b #01h,&P21FG
bic.b #01h,&P21FG
bic.b #01h,&P21FG
mov.b #0h,&P21FG

 

bis #GIE,SR ;Hold in LPMO, Enable interrupts CPUOFF+
MMainloop nop ;Need only for debug

jmp MMainloop ;
delaypSms: mov.w #Delay_time2,Rl4 ;Delay time to R15
delaypSmsl : nop

dec.w R14

jnz delaypSmsl
ret

 

ADCIZISR ; Interrupt Service Routine for ADC12

9

 

cmp.b #00h,R6 ;how many bits to save
jnz adcmodel
mov &ADC]2MEMO,A0result(R5) ;AO only,12bits. Move results to RAM
cmp.w #2700h,R5
jlo incword
jmp endconv
adcmodel: cmp.b #01h,R6
jnz adcmode2
mov &ADC]2MEMO,A0result(R5) ;AO & A1,12bits. Move results to RAM
mov &ADC l 2MEM l ,A lresult( R5)
cmp.w #1300h,R5
jlo incword
jmp endconv
adcmode2: cmp.b #02h,R6
jnz adcmode3
mov &ADC]2MEMO,R8 ;AO only, 8bits
rra.w R8
rra.w R8

148

 

rra.w R8

rra.w R8

mov.b R8,A0result(R5)

cmp.w #2600h,RS

jlo incbyte

jmp endconv
adcmode3: cmp.b #O3h,R6

jnz endconv

mov &ADC]2MEMO,R8

rra.w R8

rra.w R8

rra.w R8

rra.w R8

mov.b R8,A0result(R5)

mov &ADC12MEM1,R8

rra.w R8

rra.w R8

rra.w R8

rra.w R8

mov.b R8,A1result(R5)

cmp.w #1300h,R5

jlo incbyte

jmp endconv
incbyte: inc R5

jmp ADC12_ISR__1
incword: incd R5

jmp ADC12_ISR_1
endconv: bic #ENC,&ADC12CTLO

bis.b #20h,&P10UT

mov.b #0h,&P21FG

clr R5

mov #0,&ADC121FG

jmp ADC12_ISR_1
ADC 12_ISR_I reti

;save byte to RAM

; ADC l 2 Conversion disabled

;tum off led

;CLEAR P2 interrupt flag register
;Clear point

;Clear ADC 12 interrupt flag register

 

9

; Interrupt Service Routine for ADC12

 

IOP2: mov.b #0h,&P21FG
xor.b #001h,&P10UT
mov.b #0h,&P21FG
; bic.b #01h,&P21E

cmp #Offffh,R4

jnz IOP3

mov.w #Delay_time1,R15
Delay]: call #delaypSms

dec.w R15

jnz Delayl

bis #ENC,&ADC12CTLO

bis #ADClZSC,&ADC12CTLO

inc R12
mov.w #OOOOh,R4
IOP3: reti

;CLEAR interrupt flag register
; Toggle Pl .0
;CLEAR interrupt flag register

; Delay time to R15

; Delay time to R15

; Decrement R15

; Delay over?

; Enable conversions
; Start conversions

 

USARTOTX_ISR;

 

9

cmp.w #endmem,PointerTX

; Complete string TX’ed?

149

jeq Done0 ;
mov.b @PointerTX+,&TXBUFO ;

jmp Done
DoneO bic.b #20h,&PlOUT ;tum on led
bic.b #01h,&PIOUT ;tum on led************

mov.b #00h,&P21FG

mov.w #0ffffh,R4

clr.w PointerRX
; mov.b #01h,&P21E ;enable P2.0 interrupt
Done reti ;

 

USARTORX_ISR;

9

 

mov.b &RXBUFO,AOresult(PointerRX) ; Store RX data

inc.w PointerRX ;

cmp.b #4,PointerRX ;

jne USART_Done ;

dec PointerRX

mov.b A0result(PointerRX),Rll ;

dec PointerRX

add.b A0result(PointerRX),Rl l

dec PointerRX

add.b AOresult(PointerRX),Rll

dec PointerRX

add.b A0result(PointerRX),Rl l

cmp.w #OOaah,Rll

jnz USART_a

mov.w R12,A0result

mov.b #Channel_num,&A0result+2

mov.b #Adc_bit,&AOresult+3

mov.w #AOresult,PointerTX ;

mov.b @PointerTX+,&TXBUFO ;
USART_a clr.w PointerRX
USART_Done reti ;

 

NMIPROC;

9

 

reti

 

int_no_13;

 

9

reti

 

int_no_12;

 

9

reti

 

int_no_l l;

 

9

reti

 

int_no_10;

 

9

reti

 

int_no_6;

150

 

reti

 

int_no_S;

 

reti

 

int_no_4;

 

reti

 

int_no_3;

 

reti

 

9
int_no_2;

 

reti

 

int_no_O;

 

reti

END

15]

APPENDIX C

THE MATLAB PROGRAM FOR CHANGING DATA FORMAT

FROM HEXADEIMAL TO DECIMAL

% change the data file from Hex to Dec string
% useage:
% Format: file_transfer 'source file','target file','SampIing
% Time',Paral , Para2
% source file: the data file name needed to be transfered.
% target file: the data file name want to be saved
% Sampling Time: sampling time in ms
% Paral: parameter for channel 1
% Para2: parameter for channel 2
function file_trans(strl ,str2,s_time,paral ,para2)
fid = fopen(strl ,'r');
%data format in original file:
%1 lOOh -- 3800h total data
%for one channel save
%1104h -- 3800h A0 12bit samples number is 4990
%1104h -- 3800h A0 8bit samples number = 9980
%1104--2400h A0 12bit; 2500h-3800h Al 12bit, Num_A0 = 2430; Num_Al = 2432
%l 104--2400h A0 8bit; 2500h--3800h Al 8bit, Num_A0 = 4860; Num_A1 = 4864
fidl = fopen(str2,'w');
[P N] = fscanf(fid,'%x',4);
trigger_num = P(2)*256+P( l );
if P(3) == 0 & P(4) = 0 %one channel 12 bits ADC
fprintf(fidl ,'one channel 12 bit ADC\n');
fprintf(fid1,'Sampling Time(ms)\t\t\tCh-l Force(N)\n');
for i=1 :4990
if ~feof(fid)
data = fscanf(fid,'%x',2);
sprintfi'%x\n',data);
datal = data(2)*256+data( l );
fprintf(fid l ,'\t\t %s \t\t\t
%s\n',num25tr(i*str2double(s_time),'°/o.4f‘),num23tr(datal *str2doub1e(paral ),'%.4t‘));
else
break;
end
end
elseif P(3) = O & P(4) = 1 %one channel 8 bit ADC
fprintf(fidl ,'one channel 8 bit ADC\n');
fprintf(fid 1 ,'Sampling Time(ms)\t\t\tCh-l Force(N)\n');
for i=1 :9980
if ~feof(fid)
data = fscanf(fid,'%x', 1 );
datal(i) = data;
fprintf(fidl ,'\t\t %s \t\t\t
%s\n',num25tr(i*str2double(s_time),'%.4f'),num25tr(data*str2double(para 1 ),'%.4f‘));
else

152

break;

end
end
elseif P(3) = l & P(4) = 0 %two channel 12 bit
for i=1:2430

data = fscanf(fid,'%x',2);
datal(i) = data(2)*256+data( l );
end
fseek(fid,3*5 120,-1);
for i=1 :2430
data = fscanf(fid,'%x',2);
data2(i) = data(2)*256+data( l );
end
fprintf(fid1,'two channel 12 bit ADC\n');
fprintf(fidl,’Sampling Time(ms)\t\tCh-l Force(N) \t Ch-2 Force(N)\n');
for i=1 :2430
fprintf(fid1,'\t %s \t\t\t %s \t\t
%s\n',num23tr(i*str2double(s_time),'%.4f),num25tr(datal(i)*str2double(paral ),'%.4t‘),num23tr(data2(i)*str
2double(para2),'%.4f‘));
end
elseif P(3) = l & P(4) == 1 %two channel 8 bit
for i=1 :4860
data = fscanf(fid,'%x', 1);
datal(i) = data;
end
fseek(fid,3*5 120,-1);
for i=1:4860
data = fscanf(fid,'%x', 1 );
data2(i) = data;
end
fprintf(fidl ,'two channel 8 bit ADC\n');
fprintf(fidl,'Sampling Time(ms)\t\tCh-l Force(N) \t Ch-2 Force(N)\n');
for i=1 :4860
fprintf(fid1,'\t %s \t\t\t %s \t\t
%s\n',num25tr(i*str2double(s_time),'%.4f'),num25tr(data l (i)*str2double(paral ),'%.4f‘),num2str(data2(i)*str
2doub1e(para2),'%.4f));
end
end
fclose(fid);
fclose(fidl)

153

APPENDIX D

MATLAB PROGRAM FOR THE NUMERICAL METHOD

— INITIAL WAVE ASSUMPTION

A. MAIN PROGRAM

%Wave propogation simulation. Long impact period, short bar, wave reflect
%and reinter the bar several times before the impact finish.

de=7560; %density

E=192000000000; %Young’s Modulus

dam=0.003; %damping

%Area=(0.75*0.0254/2)"2*3. 14159265; %area of the bar intersection
le=3*0.0254; %length of the bar

ws=sqrt(E/de); %wave speed in the bar

%fi=2*3.14159265/(2*le/ws); %frequency

fr=2*pi*800; %anglar frequency of input force
k1=sqrt(((f1"‘2)*de-i*fi'*dam)/E) % coefficient in the wave equation
%kl=fr/ws

%kl=sqrt(((fre"2)*de)/E);

forceperiod=pi; %period of the impact force

p00=0; %impact end
pol=1.5*0.0254; %first gages position
%p02=3.0*0.0254; %second gages position
%po3=4.5*0.0254; %third gages position

lr=1; %wave lose at the rear end--free end
lf=0.8; %wave lose at the front end--impact end

tb=2*((1e-pol )/ws); %the time constance that wave needs to travel back to the gages again
ta=2*(pol/ws); %the time constance that wave from reflect wave to input wave again

tf=3.14159265; %force period
fc=l7500; %constant for time stages to match the wave number in experimental curve
dt=1050; %drawing constant to match the time of the experimental data

da=30; %drawing constant to match the magnitude of the experimental data
ds=0.2; %drawing constant to shift the time value to match the experimental data

tO=0:tb/1002tb; %time stage before the wave go back to the gages, no vibration
[p0] = forcein(fc*0,fc*(tb)); %use the subprogram (function'forcein'), which is in the same directory

tl=tb:(ta)/100:(tb+ta); %time stage that the reflect wave overlaps with input wave
t1 a=0:(ta)/100:(ta); %time for reflect wave

[pl ]=forcein(fc*tb,fc*(tb+ta));
[p1a]=forcein(0,fc*ta);

154

t2=(tb+ta):tb/100:(tb+ta+tb); %time state that the wave pass gage again from input direction
t2a=taztb/ 100:(tb+ta);

t2b=0:tb/100:tb; %time for input wave

[p2]=forcein(fc*(tb+ta),fc*(tb+ta+tb));

[p2a]=forcein(fc*(ta),fc*(tb+ta));

[p2b]=forcein(0,fc*(tb));

t3=(tb+ta+tb):ta/l00:(tb+ta+tb+ta);
t3a=(tb+ta):ta/ 100:(tb+ta+ta);
t3b=tb:ta/100:(ta+tb);

t3c=0ztal100zta;
[p3]=forcein(fc*(tb+ta+tb),fc*(tb+ta+tb+ta));
[p3a]=forcein(fc*(tb+ta),fc*(ta+tb+ta));
[p3b]=forcein(fc*(tb),fc*(tb+ta));
[p3c]=forcein(fc*(0),fc*(ta));

t4=(tb+ta+tb+ta):tb/100:(tb+ta+tb+ta+tb);
t4a=(tb+ta+ta):tb/ 100:(tb+ta+ta+tb);
t4b=(ta+tb):tb/1 00:(ta+tb+tb);

t4c=taztb/ 100:(tb+ta);

t4d=0:tb/1002tb;
[p4]=forcein(fc*(tb+ta+tb+ta),fc*(tb+ta+tb+ta+tb));
[p4a]=forcein(fc*(tb+ta+ta),fc*(tb+ta+tb+ta));
[p4b]=forcein(fc*(tb+ta),fc*(tb+ta+tb));
[p4¢]=forcein(fc*(ta),fc*(tb+ta));
[p4d]=forcein(fc*(0),fc*(tb));

t5=(tb+ta+tb+ta+tb):ta/l00:(tb+ta+tb+ta+tb+ta);
t5a=(tb+ta+ta+tb):ta/ l 00:(tb+ta+ta+tb+ta);
t5b=(ta+tb+tb):ta/l00:(ta+tb+tb+ta);

t5c=(ta+tb):ta/ 100:(tb+ta+ta);

t5dfibzta/100:(tb+ta);

t5e=0:ta/ 100:ta;
[p5]=forcein(fc*(tb+ta+tb+ta+tb),fc*(tb+ta+tb+ta+tb+ta));
[p5a]=forcein(fc*(tb+ta+tb+ta),fc*(tb+ta+tb+ta+ta));
[p5b]=forcein(fc*(tb+ta+tb),fc*(tb+ta+tb+ta));
[p5c]=forcein(fc*(tb+ta),fc*(tb+ta+ta));
[p5d]=forcein(fc*(tb),fc*(tb+ta));
[p5e]=forcein(fc*(0),fc*(ta));

t6=(tb+ta+tb+ta+tb+ta):tb/l 00:(tb+ta+tb+ta+tb+ta+tb);
t6a=(tb+ta+ta+tb+ta):tb/ l 00:(tb+ta+ta+tb+ta+tb);
t6b=(ta+tb+tb+ta):tb/100:(ta+tb+tb+ta+tb);

t6c=(ta+tb+ta):tb/ 1 00:(tb+ta+ta+tb);

t6d=(tb+ta):tb/ 100:(tb+ta+tb);

t6e=taztb/ 1 OO:(ta+tb);

t6f=0:tb/100:tb;
[p6]=forcein(fc*(tb+ta+tb+ta+tb+ta),fc*(tb+ta+tb+ta+tb+ta+tb));
[p6a]=forcein(fc*(tb+ta+tb+ta+ta),fc*(tb+ta+tb+ta+tb+ta));
[p6b]=forcein(fc*(tb+ta+tb+ta),fc“(tb+ta+tb+ta+tb));

155

[p6c]=forcein(fc*(ta+tb+ta),fc*(tb+ta+tb+ta));
[p6d]=forcein(fc*(tb+ta),fc*(tb+ta+tb));
[p6e]=forcein(fc"‘(ta),fc*(ta+tb));
[p6t]=forcein(fc*(0),fc*(tb));

t7=(tb+ta+tb+ta+tb+ta+tb):ta/l00:(tb+ta+tb+ta+tb+ta+tb+ta);
t7a=(tb+ta+ta+tb+ta+tb):ta/l 00:(tb+ta+ta+tb+ta+tb+ta);
t7b=(ta+tb+tb+ta+tb):ta/l00:(ta+tb+tb+ta+tb+ta);
t7c=(ta+tb+ta+tb):ta/l00:(tb+ta+ta+tb+ta);

t7d=(tb+ta+tb):ta/ 1002(tb+ta+tb+ta);

t7e=(ta+tb):ta/l OO:(ta+tb+ta);

t7f‘-=tb:ta/100:(tb+ta);

t7 g=0:ta/ 100:ta;
[p7]=forcein(fc*(tb+ta+tb+ta+tb+ta+tb),fc*(tb+ta+tb+ta+tb+ta+tb+ta));
[p7a]=forcein(fc*(tb+ta+ta+tb+ta+tb),fc*(tb+ta+ta+tb+ta+tb+ta));
[p7b]=forcein(fc*(ta+tb+tb+ta+tb),fc*(ta+tb+tb+ta+tb+ta));
[p7c]=forcein(fc*(ta+tb+ta+tb),fc*(tb+ta+ta+tb+ta));
[p7d]=forcein(fc*(tb+ta+tb),fc*(tb+ta+tb+ta));
[p7e]=forcein(fc*(ta+tb),fc*(ta+tb+ta));
[p71]=forcein(fc*(tb),fc*(tb+ta));

[p7g]=forcein(fc*(0),fc*(ta));

t8=(tb+ta+tb+ta+tb+ta+tb+ta):tb/l 00:(tb+ta+tb+ta+tb+ta+tb+ta+tb);
t8a=(tb+ta+ta+tb+ta+tb+ta):tb/l 00: (tb+ta+ta+tb+ta+tb+ta+tb);
t8b=(ta+tb+tb+ta+tb+ta):tb/l00:(ta+tb+tb+ta+tb+ta+tb);
t8c=(ta+tb+ta+tb+ta):tb/ 100:(tb+ta+ta+tb+ta+tb);

t8d=(tb+ta+tb+ta) :tb/ 100:(tb+ta+tb+ta+tb);

t8e=(ta+tb+ta):tb/ 100:(ta+tb+ta+tb);

t8 f=(tb+ta):tb/ 1 00:(tb+ta+tb);

t8 g=1a:tb/ 100:(ta+tb);

t8h=0ztb/100:tb;
[p8]=forcein(fc*(tb+ta+tb+ta+tb+ta+tb+ta),fc*(tb+ta+tb+ta+tb+ta+tb+ta+tb));
[p8a]=forcein(fc*(tb+ta+ta+tb+ta+tb+ta),fc*(tb+ta+ta+tb+ta+tb+ta+tb));
[p8b]=forcein(fc*(ta+tb+tb+ta+tb+ta),fc*(ta+tb+tb+ta+tb+ta+tb));
[p8c]=forcein(fc*(ta+tb+ta+tb+ta),fc*(tb+ta+ta+tb+ta+tb));
[p8d]=forcein(fc*(tb+ta+tb+ta),fc*(tb+ta+tb+ta+tb));
[p8e]=forcein(fc*(ta+tb+ta),fc*(ta+tb+ta+tb));
[p81]=forcein(fc*(tb+ta),fc*(tb+ta+tb));
[p8g]=forcein(fc*(ta),fc*(ta+tb));

[p8h]=forcein(fc*(0),fc*(tb));

t9=(tb+ta+tb+ta+tb+ta+tb+ta+tb)tta/l 00:(tb+ta+tb+ta+tb+ta+tb+ta+tb+ta);
t9a=(tb+ta+ta+tb+ta+tb+ta+tb):ta/l 00:(tb+ta+ta+tb+ta+tb+ta+tb+ta);
t9b=(ta+tb+tb+ta+tb+ta+tb):ta/ l 00:(ta+tb+tb+ta+tb+ta+tb+ta);
t9c=(ta+tb+ta+tb+ta+tb):ta/ l 00:(tb+ta+ta+tb+ta+tb+ta);
t9d=(tb+ta+tb+ta+tb):ta/ 100:(tb+ta+tb+ta+tb+ta);

t9e=(ta+tb+ta+tb):ta/ 100:(ta+tb+ta+tb+ta);

t9f=(tb+ta+tb):ta/ 100:(tb+ta+tb+ta);

t9g=(ta+tb):ta/100:(ta+tb+ta);

t9h=tb:ta/100:(tb+ta);

t9i=0:ta/ 1 00:ta;

[p9]=forcein(fc*(tb+ta+tb+ta+tb+ta+tb+ta+tb),fc*(tb+ta+tb+ta+tb+ta+tb+ta+tb+ta));
[p9a]=forcein(fc*(tb+ta+ta+tb+ta+tb+ta+tb),fc*(tb+ta+ta+tb+ta+tb+ta+tb+ta));

156

[p9b]=forcein(fc*(ta+tb+tb+ta+tb+ta+tb),fc*(ta+tb+tb+ta+tb+ta+tb+ta));
[p9c]=forcein(fc*(ta+tb+ta+tb+ta+tb),fc*(tb+ta+ta+tb+ta+tb+ta));
[p9d]=forcein(fc*(tb+ta+tb+ta+tb),fc*(tb+ta+tb+ta+tb+ta));
[p9e]=forcein(fc‘(ta+tb+ta+tb),fc*(ta+tb+ta+tb+ta));
[p9t]=forcein(fc*(tb+ta+tb),fc*(tb+ta+tb+ta));
[p9g]=forcein(fc*(ta+tb),fc*(ta+tb+ta));
[p9h]=forcein(fc*(tb),fc*(tb+ta));

[p9i]=forcein(fc*(O),fc*(ta));

t10=(tb+ta+tb+ta+tb+ta+tb+ta+tb+ta):tb/l 00:(tb+ta+tb+ta+tb+ta+tb+ta+tb+ta+tb);
t10a=(tb+ta+ta+tb+ta+tb+ta+tb+ta):tb/100:(tb+ta+ta+tb+ta+tb+ta+tb+ta+tb);
t l Ob=(ta+tb+tb+ta+tb+ta+tb+ta):tb/ 1 00: (ta+tb+tb+ta+tb+ta+tb+ta+tb);
t10c=(ta+tb+ta+tb+ta+tb+ta):tb/ 1 00:(tb+ta+ta+tb+ta+tb+ta+tb);

tl Od=(tb+ta+tb+ta+tb+ta):tb/ 100:(tb+ta+tb+ta+tb+ta+tb);
t10e=(ta+tb+ta+tb+ta):tb/ 100:(ta+tb+ta+tb+ta+tb);

tl 0f=(tb+ta+tb+ta):tb/ 100:(tb+ta+tb+ta+tb);
t10g=(ta+tb+ta):tb/l00:(ta+tb+ta+tb);

t10h=(tb+ta): tb/ l 00: (tb+ta+tb);

t10i=taztb/100:(ta+tb);

t10j=0:tb/100:tb

[p 1 O]=forcein(fc *(tb+ta+tb+ta+tb+ta+tb+ta+tb+ta),fC "'(tb+ta+tb+ta+tb+ta+tb+ta+tb+ta+tb));
[p l Oa]=forcein(fc"‘(tb+ta+ta+tb+ta+tb+ta+tb+ta),fc*(tb+ta+ta+tb+ta+tb+ta+tb+ta+tb));
[p l Ob]=forcein(fc*(ta+tb+tb+ta+tb+ta+tb+ta),fc*(ta+tb+tb+ta+tb+ta+tb+ta+tb));

[p l Oc]=forcein(fc*(ta+tb+ta+tb+ta+tb+ta),fc*(tb+ta+ta+tb+ta+tb+ta+tb));

[p 1 0d]=forcein(fc"'(tb+ta+tb+ta+tb+ta),fc*(tb+ta+tb+ta+tb+ta+tb));

[p 10e]=forcein(fc*(ta+tb+ta+tb+ta),fc*(ta+tb+ta+tb+ta+tb));

[p 1 0f]=forcein(fc*(tb+ta+tb+ta),fc*(tb+ta+tb+ta+tb));

[pl 0g]=forcein(fc*(ta+tb+ta),fc*(ta+tb+ta+tb));
[p10h]=forcein(fc*(tb+ta),fc*(tb+ta+tb));

[pl0i]=forcein(fc*(ta),fc*(ta+tb));

[p 10j]=forcein(fc*(0),fc*(tb));

t l l =(tb+ta+tb+ta+tb+ta+tb+ta+tb+ta+tb) 2 ta/ 1 00:(tb+ta+tb+ta+tb+ta+tb+ta+tb+ta+tb+ta);
t1 la=(tb+ta+ta+tb+ta+tb+ta+tb+ta+tb):ta/100:(tb+ta+ta+tb+ta+tb+ta+tb+ta+tb+ta);
t1 lb=(ta+tb+tb+ta+tb+ta+tb+ta+tb):ta/ 1 00:(ta+tb+tb+ta+tb+ta+tb+ta+tb+ta);

t1 lc=(ta+tb+ta+tb+ta+tb+ta+tb):ta/ 1 00:(tb+ta+ta+tb+ta+tb+ta+tb+ta);

tl 1d=(tb+ta+tb+ta+tb+ta+tb):ta/l 00:(tb+ta+tb+ta+tb+ta+tb+ta);

t1 1e=(ta+tb+ta+tb+ta+tb):ta/l 00:(ta+tb+ta+tb+ta+tb+ta);

t1 1 f=(tb+ta+tb+ta+tb):ta/100:(tb+ta+tb+ta+tb+ta);

t1 1g=(ta+tb+ta+tb):ta/ 100:(ta+tb+ta+tb+ta);

t1 lh=(tb+ta+tb):ta/ 100:(tb+ta+tb+ta);

t1 1 i=(ta+tb):ta/ 100:(ta+tb+ta);

tl 1j=tb:ta/lOO:(tb+ta);

tl lk=0:ta/100:ta;

[pl 1 ]=forcein(fc*(tb+ta+tb+ta+tb+ta+tb+ta+tb+ta+tb),fc*(tb+ta+tb+ta+tb+ta+tb+ta+tb+ta+tb+ta));
[pl 1a]=forcein(fc*(tb+ta+ta+tb+ta+tb+ta+tb+ta+tb),fc*(tb+ta+ta+tb+ta+tb+ta+tb+ta+tb+ta));

[pl 1b]=forcein(fc"'(ta+tb+tb+ta+tb+ta+tb+ta+tb),fc*(ta+tb+tb+ta+tb+ta+tb+ta+tb+ta));

[p l l c]=forcein( fc*(ta+tb+ta+tb+ta+tb+ta+tb),fc*(tb+ta+ta+tb+ta+tb+ta+tb+ta));

[pl 1 d]=forcein(fc*(tb+ta+tb+ta+tb+ta+tb),fc*(tb+ta+tb+ta+tb+ta+tb+ta));

[pl 1 e]=forcein(fc*(ta+tb+ta+tb+ta+tb),fc*(ta+tb+ta+tb+ta+tb+ta));

[pl 1 fl=forcein(fc*(tb+ta+tb+ta+tb),fc*(tb+ta+tb+ta+tb+ta));

[p1 1g]=forcein(fc*(ta+tb+ta+tb),fc*(ta+tb+ta+tb+ta));

[pl lh]=forcein(fc*(tb+ta+tb),fc*(tb+ta+tb+ta));

[pl 1 i]=forcein(fc*(ta+tb),fc*(ta+tb+ta));

157

[pl 1 j ]=forcein(fc*(tb),fc*(tb+ta));
[pl lk]=forcein(fc*(0),fc*(ta));

f0=p0.*exp(-i*kl *pol); % force history that no vibration

f1 =p1.*exp(-i*kl *pol)-lr*pla.*exp(-i*kl*(2*le-pol));

f2=p2.*exp(-i*k1*pol)-lr*p2a.*exp(-i*kl I"(2"‘le-pol))+lr"‘lf"‘p2b."‘exp(-i"'kl *(2*le+pol));
f3=p3.*exp(-i*k1*pol)—lr*p3a.*exp(-i*kl *(2*le-pol))+lr*lf*p3b.*exp(~i*k1*(2*le+pol))-
lr"2*lf*p3c.*exp(-i*kl *(4*le-pol ));

f4=p4.*exp(-i*kl *pol)-lr*p4a.*exp(-i*kl *(2*le-pol ))+lr*lf*p4b.*exp(—i*kl*(2*1e+pol ))-
lr"2*lt*p40.*exp(-i*kl *(4*le-pol))+lr"2*lf"2*p4d.*exp(-i*k1*(4*le+pol));
f5fi)5.*exp(-i*kl*pol)-lr*p5a.*exp(-i*k1 *(2*le-pol))+lr*lf‘"p5b.*exp(-i*k1*(2*le+pol))—
lr"2*lf*p5c.*exp(-i*kl *(4*le-pol ))+1r"2*1f"2*p5d.*exp(-i*kl *(4*le+po1))-lr"3*1f"2*p5e.*exp(-
i*kl *(6*le-pol));

f6=p6.*exp(-i*kl *po 1 )-lr*p6a.*exp(-i*kl *(2*le-pol ))+lr*lt"‘p6b.*exp(-i*kl *(2*le+po 1 ))-
lr"2*lt"'p6c.*exp(-i*kl *(4*1e-pol ))+1r"2*lf"2*p6d.*exp(-i*k1 *(4*le+pol))-1r"3*lf"2*p6e.*exp(-
i*k1*(6*1e-pol ))+1r"3*1f"3*p6f.*exp(-i*kl*(6*le+pol ));
f7=p7.*exp(-i*k1*pol)-lr*p7a.*exp(-i*kl*(2*le-pol))+lr*lt‘p7b.*exp(-i*k1*(2*le+pol))-
lr"2*lt*p7c.*exp(-i*kl *(4*le-po l ))+lr"2*lt“2*p7d.*exp(-i*k1 *(4*1e+po 1))-lr"3*lf"2*p7e.*exp(-
i*kl *(6*le-po l ))+lr"3*lf"3 *p7f.*exp(-i*k1 *(6*le+po l ))-lr"4*lf"3*p7g.*exp(-i*k1 *(8*le-po 1 ));
f8=p8.*exp(-i*k1*pol)-lr*p8a.*exp(-i*kl *(2*le-pol ))+lr*lf"‘p8b.*exp(-i*kl *(2*1e+pol))-
lr"2*lf"‘p80.*exp(-i*kl *(4*le-pol ))+lr"2*lf"2*p8d.*exp(-i*kl *(4*le+po l ))-lr"3*lf"2*p8e.*exp(-
i*kl *(6*le-po 1 ))+lr"3*lf"3 *p8f.*exp(-i*kl *(6*le+po 1 ))-lr"4*lf"3 *p8g.*exp(-i*kl *(8*le-

pol ))+lr"4*lf"4*p8h.*exp(-i*k1 *(8*le+pol ));

f9=p9.*exp(-i*kl *pol)—lr*p9a.*exp(-i*k1*(2*le-pol))+lr*lf*p9b.*exp(-i*kl*(2*le+pol))-
lr"2*lf"‘p9c.*exp(—i*kl*(4*1e-pol))+lr"2*lf"2*p9d.*exp(-i*k1*(4*le+pol))-lr"3*lf"2*p9e.*exp(-
i*k1 *(6*le-pol ))+lr"3*lf"3*p9£*exp(-i*kl *(6*le+po 1))-lr"4*lf"3*p9g.*exp(-i*kl *(8*le-
pol))+1r"4"'lf"4*p9h.*exp(-i*k1*(8*le+pol))-lr"5*lf"4*p9i.*exp(-i*kl*(10*le-pol));

f1 0=plO.*exp(-i*k1*pol)-lr*p10a.*exp(-i*kl*(2*le-pol))+1r*lt*p10b.*exp(-i*kl*(2*le+pol))-
1r"2*lf*p10c.*exp(-i"'kl *(4*le-pol ))+lr"2*lf"2*plOd.*exp(-i*kl *(4*le+pol))-lr"3 *lf"2*p10e.*exp(-
i*kl *(6*le-pol))+lr"3*lf"3*p10f.*exp(-i*k1*(6*le+pol))-lr"4*lf"3*p10g.*exp(-i*k1*(8*le-

pol ))+1r"4*lf"‘4*p10h.*exp(-i*kl *(8*le+pol ))-lr"5*lf"4*pl 0i.*exp(-i*k1 *(l 0*le-

pol ))+1r"5*1f"5*ple.*exp(-i*kl *(10*1e+pol ));

f1 lwl 1.*exp(-i*kl *pol)-lr*p1 la.*exp(-i*kl *(2*le-po 1 ))+lr*lt"'p1 lb.*exp(-i*k1*(2*le+pol))—
lr"2*lt"'pl 1c.*exp(-i*kl I"(4"‘le-pol))+lr"2"‘lf"2"‘pl ld.*exp(-i*kl *(4*le+pol))—lr"3*lf"2*pl le.*exp(-
i*k1*(6*1e-pol))+lr"3*lf"3*pl 1f."‘exp(-i"'kl *(6*le+po l ))-lr"4*lf"3*pl lg.*exp(-i*kl *(8*1e-

pol ))+lr"4*lf"4*pl 1h.*exp(-i*kl *(8*le+pol))-lr"5*lf"4*pl li.*exp(-i*k1 *( 10*le-

pol ))+1r"5*lf"5*p1 lj.*exp(-i*l<l *(10*le+pol ))-lr"6*lf"5*pl lk.*exp(-i*kl *(12*1e-pol ));

%fl=pl .*exp(-i*kl *pol)+p2.*exp(-i*kl *(2*le-pol ));
%fl =p1.*exp(-i*kl*pol)-p2.*6XP(-i*k1*(2*13‘P°1));

%plot(t/lO,yO,t/10,yl,t/l0,y2,t/lO,y3,(t+5)/10,yl,(t+10)/10,y2,(t+l5)/10,y3);

plot(ds+dt*t0,da*p0,'k--',ds+dt*tl ,da*p1,'k--',ds+dt*t2,da*p2,'k--',ds+dt*t3,da"‘p3,'k--',ds+dt*t4,da*p4,'k--
',ds+dt*t5,da*p5,'k--',ds+dt*t6,da*p6,'k--',ds+dt*t7,da*p7,'k--',ds+dt*t8,da*p8,'k-—',ds+dt*t9,da*p9,'k--
',ds+dt*tlO,da*p10,'k--',ds+dt*tl l,da*p1 1,'k--');

hold on;legend('input');hold on;

plot(ds+dt*t0,da*f0,'k-',ds+dt*t1 ,da*fl ,'k-',ds+dt*t2,da*f2,'k-',ds+dt*t3,da*f3,'k-',ds+dt*t4,da* f4,'k-
',ds+dt*t5,da*f5,'k-',ds+dt*t6,da*f6,'k-', ds+dt*t7,da*f7,'k-',ds+dt*t8,da*t‘8,'k-',ds+dt*t9,da*f9,'k-
',ds+dt*t10,da*f1 0,’k-',ds+dt*tl l ,da*fl 1,'k-');

hold on;

legend('input','output');hold on;

AXIS ([0.1 0.55 -7 25]);

datal3=xlsread('test3-gage1-3'); %load the experimental data from the Excel file 'test3-gagel'
chtl3=data13(:,1); %give the first column tote, that is the time

158

chl=datal3(:,2); %give the second column to chl, that is the gage one
ch3=datal3(:,3);

data2=xlsread('3inch l 50rev');
cht2=data2(:,l);
ch2=data2(:,2);

%plot(chtl3,ch1,chtl3,ch3); hold;
plot(cht2,ch2,':'); hold;
hold on;

xlabel('t (ms)');

ylabel(‘Force (unit)')

title('3inch1 50, impactinterfacelose=20%')

%legend('input','output')

%subplot

%plot(t+1 00000,y)

%for each Y, the reflect wave should be added in. that is: the inverse Y
%with x value as 2L-x; the t should be something like 2L-t but some how
%different, LN =t0; if t is from 0 to pi/1000, then it travels almost 3 or
%4 times along the bar.

% be careful, at each stage, the force history is the sum of all the input
% and reflects

B. SUBPROGRAM FOR THE INPUT CURVE

function [b]=forcein(x, y)

t=x:(y-x)/100:y;

s=0;

cl=l; kl=0.15;

%ml=0.00; m2=0.; m3=0.; m4=0.; m5=0.;

%dl=0.00; d2=0.00; d3=0.; d4=0; d5=0.;

data=xlsread('impactforcehistory'); %load the experimental data from the Excel file 'test3-gage1'
time=data(:,l); %give the first column tote, that is the time

force=data(:,2 ); %give the second column to chl , that is the gage one

p=polyfit(time, force, 10)
%f=polyval(p,time)

for i=1 :101,
if(s>=0)

%f(i)=sin(t(i))/0.9+sin(3*t(i))/3+sin(5*t(i))/5+sin(7*t(i))/7+sin(9*t(i))/9+sin(1 l*t(i))/1 1+sin( 1 3*t(i))/l3+si
n(15*t(i))/15+sin(l7*t(i))/l7+sin(l9*t(i))/l9+sin(2l*t(i))/2l+sin(23*t(i))/23;
f(i)=cl*(sin(t(i)));

%f(i)=P(l)*t(i)"10+P(2)*t(i)"9+P(3)*t(i)"8+p(4)*t(i)"7+P(5)*t(i)"6+P(6)*t(i)"5+P(7)*t(i)A4+P(8)*t(i)"3+P
(9)*t(i)"2+P(10)*t(i)"1+p(1 1);

% f(i)=cl*sin(t(i))+k1*(cos(t(i))—
l)+ml*sin(l.1*t(i))+m2*sin(l.3*t(i))+m3*sin(l.5*t(i))+m4*sin(1.7*t(i))+m5*sin(l .9*t(i))+d1*sin(t(i)/1.l
)+d2*sin(t(i)/l .3)+d3*sin(t(i)/ l .5)+d4*sin(t(i)/l .7)+d5*sin(t(i)/1.9);

b(i)=f(i);
if (t(i)>3.14159265)

159

b(i)=0;

if (b(i)<0)
b(i)=0;

end

end
end
end

160

APPENDIX E

LABVIEW PROGRAM FOR THE NUMERICAL METHOD

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