Design, fabrication, and testing of a scalable series Black, Brian C.

Design, fabrication, and testing of a scalable series Black, Brian C.
Calhoun: The NPS Institutional Archive
Theses and Dissertations
Thesis Collection
2006-03
Design, fabrication, and testing of a scalable series
augmented railgun research platform
Black, Brian C.
Monterey, California. Naval Postgraduate School
http://hdl.handle.net/10945/2855
NAVAL
POSTGRADUATE
SCHOOL
MONTEREY, CALIFORNIA
THESIS
DESIGN, FABRICATION AND TESTING OF A SCALABLE
SERIES AUGMENTED RAILGUN RESEARCH PLATFORM
by
Brian C. Black
March 2006
Thesis Advisor:
Co-Advisor:
William B. Maier II
Terry R. McNelley
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TITLE AND SUBTITLE: Design, Fabrication, and Testing
a Scalable Series Augmented Railgun Research Platform
AUTHOR(S) Brian C. Black
PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
Naval Postgraduate School
Monterey, CA 93943-5000
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Master’s Thesis
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13. ABSTRACT (maximum 200 words)
12b. DISTRIBUTION CODE
The design and material properties of rails and projectiles are
critical to the success of the Navy railgun. This thesis addresses the
design,
fabrication,
and
testing
of
a
scalable
square
bore
electromagnetic railgun.
This railgun is designed to permit series
augmented operation, and incorporates disposable rail liners to
facilitate investigating the suitability of various rail materials. A
series
of
shots
has
demonstrated
performance
consistent
with
theoretical modeling, including significant performance enhancement as
a result of both slotted rail geometry and augmentation over solid rail
and un-augmented configurations.
A capacitor based stored energy
supply input of 35 kJ resulted in a measured velocity of 294 m/s for an
11.4 gram projectile. Suggestions are provided for future power supply
configurations, rail materials and surface treatments, and a variety of
armature geometries.
14. SUBJECT TERMS
Railgun, Rail-gun, Augmentation, Electromagnetic launch, Armature,
Pulsed Power, Hypervelocity launch, Hypervelocity Projectile, Ion
beam surface treatment, IBEST, Laser peening, Electromagnetic Weapon
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135
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OF ABSTRACT
CLASSIFICATION OF
ABSTRACT
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Approved for public release; distribution is unlimited
DESIGN, FABRICATION AND TESTING OF A SCALABLE SERIES
AUGMENTED RAILGUN RESEARCH PLATFORM
Brian C. Black
Lieutenant, United Stated Navy
B.A., Political Science, Dickinson College, 1991
B.S., Mechanical Engineering, University of Pittsburgh, 1998
Submitted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
from the
NAVAL POSTGRADUATE SCHOOL
March 2006
Author:
Brian C. Black
Approved by:
William B. Maier II
Thesis Advisor
Department of Physics
Terry R. McNelley
Co-Advisor
Department of Mechanical and
Astronautical Engineering
Anthony J. Healey
Chairman, Department of Mechanical and
Astronautical Engineering
iii
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iv
ABSTRACT
The
design
projectiles
railgun.
and
are
material
critical
to
properties
the
of
success
of
rails
and
the
Navy
This thesis addresses the design, fabrication,
testing
railgun.
of
This
augmented
liners
and
to
a
scalable
railgun
operation,
is
and
facilitate
square
designed
electromagnetic
to
incorporates
investigating
various rail materials.
bore
permit
series
disposable
the
rail
suitability
of
A series of shots has demonstrated
performance consistent with theoretical modeling, including
significant performance enhancement as a result of both the
slotted
rail
geometry
configurations.
A
and
augmentation
capacitor
based
over
stored
solid
energy
rail
supply
input of 35 kJ resulted in a measured velocity of 294 m/s
for an 11.4 gram projectile.
future
power
supply
Suggestions are provided for
configurations,
rail
materials
surface treatments, and a variety of armature geometries.
v
and
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vi
TABLE OF CONTENTS
I.
INTRODUCTION ............................................1
A.
BACKGROUND .........................................1
B.
OBJECTIVE ..........................................3
II.
RAILGUN TEST PLATFORM DESIGN ............................5
A.
GENERAL ............................................5
B.
MATERIAL PROPERTIES ................................5
C.
IMPROVED
INDUCTANCE
GRADIENT
WITH
SERIES
AUGMENTATION .......................................7
D.
IMPROVED INDUCTANCE GRADIENT WITH SLOTTED RAIL
GEOMETRY ..........................................13
E.
ADDITIONAL COMPONENTS .............................14
III. PULSED POWER SUPPLY ....................................19
A.
PRESENT SYSTEM ....................................19
B.
REDESIGNED POWER SUPPLY ...........................22
IV.
DESIGN VERIFICATION ....................................25
A.
PARAMETER MODEL ...................................25
B.
CONSERVATION OF ENERGY CIRCUIT MODEL ..............26
C.
STRUCTURAL DESIGN .................................28
V.
RESULTS ................................................33
A.
SHOT DIAGNOSTICS ..................................33
VI.
CONCLUSION .............................................41
A.
PERFORMANCE SUMMARY AND RECOMMENDATIONS ...........41
B.
MATERIALS PROCESSING METHODS ......................43
APPENDIX A. MATERIAL PROPERTY DATA SHEETS ...................45
APPENDIX B. PRODUCTION DRAWINGS .............................55
APPENDIX C. MODELING .......................................71
A.
KERRISK’S METHOD SPREADSHEETS [3] .................71
B.
PARAMETER BASED MODELING [7] ......................72
C.
CONSERVATION OF ENERGY INTEGRATION [4] ............79
D.
STRUCTURAL DESIGN VERIFICATION ....................84
APPENDIX D. MAGNETIC FIELD AND CIRCUIT SIMULATIONS .........87
A.
COMSOL MULTIPHYSICS MODELING ......................87
B.
ORCAD 10.3 P-SPICE CIRCUIT MODELING ...............99
APPENDIX E. BREAK SCREEN AND CURRENT PROFILE SCREEN
CAPTURES ..............................................103
APPENDIX F.
TYPICAL POST-SHOT MATERIAL CONDITIONS .........111
LIST OF REFERENCES .........................................115
INITIAL DISTRIBUTION LIST ..................................117
vii
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viii
LIST OF FIGURES
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Figure 12.
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
Figure 33.
Figure 34.
Figure 35.
Figure 36.
Figure 37.
Exploded Railgun Assembly .........................5
Series Augmented Current Path .....................8
Augmented Railgun Geometry where R = 3/16” .......10
Augmented Conductor Assembly .....................12
Slotted Rail Geometry ............................14
Railgun Loading Apparatus ........................15
3.0-µH Series Inductor and Components ............16
Target Chamber ...................................17
Power Supply Cabinet .............................20
Power Supply Cabinet Interfaces ..................21
Fixed End Distributed Load Beam Model [After Ref.
9] ...............................................30
Augmented Rail to Conductor Threaded and Braised
Joint ............................................42
Armature Geometry Alternatives (Appendix B) ......43
Top Containment Half .............................55
Bottom Containment Half ..........................56
Solid Primary Conductor Rails ....................57
Slotted Primary Conductor Rails ..................58
Ceramic Insulators ...............................59
Augmented Rails, Rail liners, and Spacer .........60
Augmenting Conductor Components ..................61
External Conductor Connectors and Muzzle Shunt ...62
Full Conductor Assembly ..........................63
Full CAD Assembly with Loader and Muzzle Shunt ...64
Full Assembled Railgun with Loader ...............64
Basic U-Shape Armature ...........................65
Flared M-shape Armature ..........................66
Square M-shape Armature ..........................67
Altered U-shape Armature with Center Hollow ......68
Railgun Mounting Base ............................69
Kerrisk’s Method Rail Parameters [After Ref. 2] ..71
Simplified Beam Geometry (Not to scale) ..........84
Transformed Homogenous Beam Geometry (Not to Scale)
.................................................84
Solid Non-Augmented Magnetic Flux Density ........87
Solid Non-Augmented Magnetic Field Across Bore ...88
Solid Non-Augmented Magnetic Field Across Rail
Surface ..........................................89
Slotted Non-Augmented Magnetic Flux Density ......90
Slotted Non-Augmented Magnetic Field Across Bore .91
ix
Figure 38. Slotted Non-Augmented Magnetic Field Across Rail
Surface ..........................................92
Figure 39. Solid, Augmented Magnetic Flux Density ...........93
Figure 40. Solid Augmented Magnetic Field Across Bore .......94
Figure 41. Solid, Augmented Magnetic Field Across Rail Surface
.................................................95
Figure 42. Slotted Augment Magnetic Flux Density ............96
Figure 43. Solid Augmented Magnetic Field Across Bore .......97
Figure 44. Solid Augmented Magnetic Field Across Rail Surface
.................................................98
Figure 45. P-SPICE Single Module LRC Circuit Model ..........99
Figure 46. Single Power Module Current Profile .............100
Figure 47. P-SPICE Four-Module LRC Circuit Model ...........101
Figure 48. Four-Module Current Profile Output from Figure 46
Circuit Model ...................................102
Figure 49. Solid Non-Augmented Velocity Measurement ........103
Figure 50. Solid Non-Augmented Current Profiles ............104
Figure 51. Slotted Non-Augmented Velocity Measurement ......105
Figure 52. Slotted Non-Augmented Current Profiles ..........106
Figure 53. Solid Augmented Velocity Measurement ............107
Figure 54. Solid Augmented Current Profiles ................108
Figure 55. Slotted Augmented Velocity Measurement ..........109
Figure 56. Slotted Augmented Current Profiles ..............110
Figure 57. Typical Post-Shot Rail and Insulator Wear .......111
Figure 58. Typical Post-Shot Armature Wear .................112
Figure 59. Muzzle Block Indicating Muzzle Flash Arcing .....113
x
LIST OF TABLES
Table
Table
Table
Table
Table
Table
1.
2.
3.
4.
5.
6.
Table 7.
Table 8.
Table 9.
Table 10.
Table 11.
Table 12.
Table 13.
Table 14.
Table 15.
Table
Table
Table
Table
Table
Table
Table
16.
17.
18.
19.
20.
21.
22.
Table
Table
Table
Table
Table
Table
23.
24.
25.
26.
27.
28.
Nominal EM Gun Parameters, [From Ref. 1] ..........2
Summary of Rail Properties [After Ref. 2] .........6
Experimental Data Results ........................33
Predicted vs. Experimental Gain Factors ..........35
Total System Resistance and R/L’ Results .........38
Chromium Copper Rail Liner Material Properties
[After Ref. 2] ...................................45
Oxygen Free Copper Rail Liner Material Properties
[After Ref. 2] ...................................46
Phosphor Bronze Rail Liner Material Properties
[After Ref. 2] ...................................47
Copper Tungsten Rail Liner Properties [After Ref.
2] ...............................................48
Aluminum 7075 T-651 Rail Liner Material Properties
[After Ref. 2] ...................................49
Aluminum 6063 T-5 Armature Material Properties
[After Ref. 2] ...................................50
G-11 FR-5 Containment Material Properties [After
Ref 10] ..........................................51
Ceramic Insulator Material Properties [After Ref.
11] ..............................................52
Mylar Film Insulator Material Properties [After
Ref. 12] .........................................53
Kerrisk’s
Method
and
Augmentation
Adjusted
Inductance Gradient (L’) Calculations ............71
1500 m/s Solid Non-Augmented Parameter Model .....72
1500 m/s Slotted Non-Augmented Parameter Model ...73
1500 m/s Solid Augmented Parameter Model .........74
1500 m/s Slotted Augmented Parameter Model .......75
265 m/s Solid Augmented Parameter Model ..........76
290 m/s Slotted Augmented Parameter Model ........77
Parameter Estimate of Peak Current and Final
Velocity for 3/8” diameter Grade 2 Bolts .........78
35 kJ Velocity Integral, Solid Non-Augmented. ....79
35 kJ Velocity Integral, Slotted Non-Augmented. ..80
35 kJ Velocity Integral, Solid Augmented. ........81
35 kJ Velocity Integral, Slotted Augmented. ......82
83 kJ Velocity Integral, Slotted Augmented. ......83
Transformed Geometry Moment of Inertia Calculation
.................................................85
xi
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xii
ACKNOWLEDGEMENTS
Thank you Professor Bill Maier for your confidence and
support
throughout
this
project,
and
for
facilitating
exposure to resources beyond the Naval Postgraduate School.
Thank you to Professor Terry McNelley and both the Physics
and Mechanical Engineering Departments for facilitating a
mixed curriculum tailored to this research.
Snyder,
George
professional
Jaksha,
expertise
and
and
Frank
personal
Thank you Don
Franzen
for
commitments
your
which
turned theory into practice in the fabrication and testing
of this railgun prototype.
Renk
for
your
materials
Thank you Tania Zaleski and Tim
professional
processing
courtesy
collaboration
in
between
supporting
the
Laboratories and the Navy Postgraduate School.
the
National
Thank you
to all of the professional engineers at the Institute for
Advanced Technology and the Center for Electromechanics at
the University of Texas at Austin for direct contributions
to
the
materials,
throughout
this
design,
thesis.
and
Thank
modeling
you
Fred
methods
Beach,
used
Donald
Gillich, Michael Lockwood, Michael Graham, and Juan Ubiera
for building the NPS Railgun Laboratory infrastructure and
establishing a standard of excellence.
Finally, thank you
Romina, Sophia, and Carmen for making success important.
xiii
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xiv
I.
A.
INTRODUCTION
BACKGROUND
The
military
electromagnetic
missions
is
potential
railgun
well
of
for
the
U.S.
Naval
defined.
The
Navy’s
notional
surface-fire
focused
support
investment
and
research of both Army and Navy sponsored programs through
the
Office
identified
of
Naval
the
Research
remaining
and
U.S.
engineering
Army
ARDEC
obstacles
overcome prior to fielding a practical system.
Postgraduate
leverage
School
such
(NPS)
is
investments
uniquely
in
order
has
to
be
The Naval
positioned
to
to
investigate
alternatives.
The Center for Electromechanics (CEM) and
the
for
Institute
Advanced
Technology
(IAT)
from
the
University of Texas at Austin have pushed the envelope in
terms of materials, pulsed power, and systems engineering
approaches to applied railgun technology.
IAT
engineers
published
an
IEEE
In January 2005,
article
entitled
“Development of a Naval Railgun” summarizing the status of
Naval railgun development and detailing areas where further
research is warranted [1].
directly
10,000
related
shots.
identifying
to
extending
Although
the
The railgun specific issues are
bore
progress
destructive
life
has
mechanisms
to
as
been
of
high
made
as
toward
transitioning
contacts and hyper-velocity gouging, no design parameters,
material combination, or processing treatment have resolved
their impact on bore life.
Simultaneously
parameters
listed
achieving
the
in
1
Table
full
while
scale
notional
achieving
shot
frequencies of 6-12 rounds per minute is presently beyond
the
capacity
of
even
large
scale
1
laboratory
facilities.
Therefore,
economy
of
simulation
and
scalable
applied
research is critical to the success of the railgun program.
Table 1.
Over
produced
Nominal EM Gun Parameters, [From Ref. 1]
the
past
several
decade,
iterations
NPS
of
railgun
small
research
scale
weapons to facilitate applied research.
has
demonstrator
During the 2005
fiscal year, the NPS Railgun program has made a substantial
investment
in
laboratory
infrastructure
including
the
purchase of ten 11 kV 830 µ−Farad capacitors from General
Atomics and advanced high current switches, supplementing
the existing pulsed power energy storage capacity by an
order of magnitude.
By leveraging the collaborative direct
input of CEM, IAT, material modifications research support
from Lawrence Livermore and Sandia National Laboratories,
as well as multi-curriculum contributions from within the
campus,
NPS
railgun
research
is
now
more
than
ever
positioned to confront railgun technological deficiencies
through applied engineering.
2
B.
OBJECTIVE
The
objective
fabrication,
bore,
and
of
this
testing
conventional
of
railgun
thesis
a
is
scalable,
capable
of
square
bore
between
single
rail
slotted
rail
performance
configuration
and
series
geometries.
comparisons
Shot
are
design,
reconfigurable
achieving
package velocities in excess of 1500 m/s.
(19mm)
the
The initial 3/4"
supports
comparisons
augmentation,
repetition
accomplished
launch
solid
and
with
and
materials
disposable
rail liners at the rail to armature interface to protect
the permanent main conductor rail structure.
The railgun
test platform incorporates a manual loading apparatus to
facilitate consistent initial conditions including armature
firing position and an interference armature fit which does
not
require
Alternative
full
disassembly
armature
conditioning
are
geometries
provided
Unreliable
performance
spontaneous
triggering
practical
capacitor
between
to
of
proposals
inform
the
above
charge
and
consecutive
7,000
limit
6500
power
testing.
switches
volts,
of
for
follow-on
TVS-40
shots.
caused
requiring
volts
and
a
a
corresponding total stored energy limit of 35 kJ.
Chapter II examines weapon design including decisions
regarding materials, geometry, and firing configurations.
Chapter III discusses the design and limits of the existing
pulsed power supply, as well as a proposed multi-module
system.
including
static
Chapter IV provides design verification analysis
ideal
railgun
deflection
conservation
of
parameter
considerations,
energy
model.
3
modeling,
and
Chapter
containment
an
V
applied
discusses
experimental
results.
recommendations
geometries,
for
and
future
Chapter
VI
testing,
alternative
processing
materials.
4
methods
concludes
for
with
armature
rail
liner
II. RAILGUN TEST PLATFORM DESIGN
A.
GENERAL
The exploded assembly of Figure 1 below depicts the
main structural elements of the railgun design without the
loading
apparatus.
SolidWorks
CAD
software
was
used
extensively for 3D modeling and for creating the technical
drawings required for fabrication.
comprehensive
collection
of
Appendix B includes a
individual
parts
and
assemblies.
Figure 1.
B.
Exploded Railgun Assembly
MATERIAL PROPERTIES
Materials selections were based on an analysis of the
property tables included in Appendix A.
These values were
either obtained directly from the vendor or from the MATWEB
online material database.
None of the material selections
are entirely new to railgun applications.
The thickness and placement of the two insulating bars
fixes the bore dimensions given the clamshell containment
design.
Due to superior compressive dimensional stability,
5
adequate
over
dielectric
glass
CoorsTek
fired
reinforced
Alumina
subsequent
constant,
to
epoxy
(Al203)
fabrication
and
ceramic
required
specification
of
phenolics
AD-96
was
ease
as
including
refurbishment
such
was
as
G-10,
chosen.
these
+/-1%
parts
No
were
positional
tolerances of through holes for the containment bolts and
outer
surface
tolerance.
dimensions
finished
to
+/-0.005
inch
Surface dimension tolerances were verified by
micrometer measurements for both insulators.
The main conductor and a range of rail liner materials
were selected after a lengthy process that began with a
much
larger
list
extracted
directly
from
materials
handbooks based strictly on parameters of conductivity and
hardness.
This
list
was
subsequently
limited
after
a
literature review of previously proven railgun materials,
and
by
the
final
process
of
locating
vendors
with
an
inventory of 1/8” thick bar or plate stock suitable for the
liner geometry.
interest.
Table 2 below summarizes the properties of
The stainless alloy properties are included as a
point of comparison.
Untreated Material Properties
Hardness Conductivity
Rockwell B
%IACS **
Material
density
(g/cm3)
oxygen free
copper
50
101
1.71E-06
8.94
chromium
copper
79
80
2.16E-06
8.89
phosphor bronze
93
20
8.70E-06
8.86
copper tungsten
98
45
3.83E-06
14.84
aluminum 7075
87
33
5.15E-06
2.81
Stainless alloy
410
* 110
3
5.70E-05
7.8
* linear extrapolation from
Rockwell C
Table 2.
Resisitivity (ohm-cm)
@ 200C
** based on %IACS = (172.41e-6 / Resistivity)
Summary of Rail Properties [After Ref. 2]
6
At the time of completion of this thesis, testing has
been restricted to the chromium copper rail liners in order
to preserve processed samples for higher velocity regimes.
Several
alternative
armature
geometries
were
fabricated by using three variants of aluminum including
Al-6063,
Al-6061,
and
Al-1100.
All
testing
has
been
conducted using standard u-shaped Al-6063 armatures shown
in Figure 25 of Appendix B.
The main containment clamshell pieces were fabricated
from 2” thick blocks of G-11 FR-5 glass reinforced epoxy
laminate.
This
common
small-bore
railgun
containment
material has high resistance, high strength, and excellent
machinability.
3/8”
Grade
2
Containment
stainless
hardware
steel
hex
includes
cap
nuts,
twenty-two
bolts,
and
washers.
C.
IMPROVED INDUCTANCE GRADIENT WITH SERIES AUGMENTATION
One of the critical railgun design parameters is the
inductance gradient, or inductance per unit length (L’).
This parameter is a function of the rail and bore geometry.
The most fundamental method for determining this parameter
is based on modeling the rails as two infinite wires with a
fixed radius, separated by a fixed distance representing
the bore width between the rails.
approximation,
extensive
more
results
accurate
empirical
applicable
Although this is a fair
research
has
to
case
the
produced
of
the
rectangular rail and square bore configuration, commonly
referred to as Kerrisk’s Method [3]. Appendix C includes
the spreadsheets used to evaluate the inductance gradient
for the rail geometries selected for this design.
7
The energy efficiency of a small scale railgun driven
through a pulse forming network is significantly limited
even under ideal modeling conditions neglecting dissipative
losses such as electrical resistance and friction.
This
ideal efficiency can be expressed by the following equation
[4].
η=
L'x
( L + L ' x)
L’ is the inductance gradient, L is the total system
inductance, and x is the rail length.
values
L=
of
5.5
micro-Henries
Applying the actual
and
L’
=
0.683
micro-
Henries/meter for this specific design to a 10 meter gun
length predicts an ideal energy efficiency approaching 50%.
Using the actual effective railgun length of 50 cm, based
on
these
same
efficiency
performance
is
values
only
L
of
5.8%.
emphasizes
L’,
and
This
the
need
the
entering
for
maximum
ideal
argument
maximizing
L’
for
while
minimizing the total system inductance of the pulse forming
network.
There
are
several
methods
for
enhancing
the
L’
parameter by enhancing the magnetic field in the bore above
that created by a single rail pair.
My design permits the
use of series augmentation by incorporating a second pair
of rails and connecting conductors to create the circuit
path illustrated in Figure 2 below.
Figure 2.
Series Augmented Current Path
8
The result is an enhanced magnetic field in the bore
region due to contributions from the same current pulse
flowing through both rail pairs.
Current through the outer
rail pair establishes a field in the bore region ahead of
the advancing armature as indicated in Figure 2.
A review
of literature regarding series augmentation indicates that
for
large
fixed
scale
Lorentz
high
velocity
force,
the
applications,
benefits
of
based
lower
on
a
current
requirements due to stronger magnetic fields in the bore
region are offset by the resistive losses [5].
However,
for my design, given the short rail length, no requirement
to recover energy for high frequency repetitive shots, and
considering
supply,
the
constraint
series
of
augmentation
a
is
limited
a
stored
practical
energy
method
to
improve projectile velocity.
Whereas Kerrisk’s method for evaluating the inductance
gradient is well defined for the simple railgun, a method
for determining the new inductance gradient as a result of
the augmenting rail contribution has not been empirically
developed.
The augmented L’ can be approximated by modeling
each
as
rail
integrating
a
the
long
magnetic
thin
current
field
carrying
contribution
region contributed by each wire.
to
wire
and
the
bore
Based on 1/4" outer rail
width, and 3/8” width for the combined inner rail plus rail
liner
thickness,
and
making
the
assumption
that
current
flows down the rail centerlines, the augmented geometry can
be expressed in terms of the half-thickness of the inner
rail, R as depicted in Figure 3.
The factors used in
Figure 3 are based on the actual augmented railgun geometry
9
with bore spacing of 3/4", a 1/32” insulation gap of mylar
film
and
adhesive
laminating
sheets
separating
the
rail
surfaces, and R = 3/16”.
Figure 3.
The
geometry
Augmented Railgun Geometry where R = 3/16”
magnitude
depicted
of
in
the
Lorentz
Figure
following equation where
µ0
3
is
force
(F)
approximated
for
the
by
the
is the permeability constant
and I is current.
⎡
⎛
⎞ ⎛
⎞⎤
⎜
⎟
⎜
µ0 I
1
1 ⎟⎥
⎛1⎞ ⎛ 1 ⎞
F=
+
+
+
⎢
⎜
⎟
⎜
⎟ ⎥dx
4π R∫ ⎢⎜⎝ x ⎟⎠ ⎜⎝ 6 R − x ⎟⎠ ⎜ 11 + x ⎟ ⎜ 47 − x ⎟ ⎥
⎜
⎟ ⎜
⎟
⎝ 6
⎠ ⎝ 6
⎠ ⎥⎦
⎣⎢
2
5R ⎢
After integrating and reducing,
⎡
⎛ 41 ⎞
⎛ 41 ⎞ ⎤
⎣⎢
⎝ 6
⎝ 6
⎜ 6 R⎟
⎜ 6 R ⎟ ⎥ µ 0 I2 ⎡
µ 0 I2 ⎢ ⎛ 5R ⎞
⎛ 41 ⎞ ⎤
⎛ 5R ⎞
F=
⎢ln ⎜
⎢ 2ln ( 5 ) + 2ln ⎜ ⎟ ⎥
⎟ + ln ⎜
⎟ + ln ⎜ 17 ⎟ + ln ⎜ 17 ⎟ ⎥ =
4π ⎣
4π ⎢ ⎝ R ⎠
⎝ R ⎠
⎝ 17 ⎠ ⎦
⎜ R⎟
⎜ R ⎟⎥
⎠
⎠ ⎦⎥
The equation can be written in terms of the components
of the total L’.
10
F=
µ 0 I2
1 ⎡ µ0
1
⎤
3.22 + 1.76 ) ⎥ I 2 = ⎡⎣ L ' pri + L ' aug ⎤⎦ I 2
⎡⎣3.22 + 1.76 ⎤⎦ = ⎢
(
4π
2 ⎣ 2π
2
⎦
It is convenient to express the augmented inductance
gradient
as
Kerrisk’s
a
gain
method
factor
L’
that
can
calculated
for
be
applied
the
to
the
non-augmented
configuration.
L ' pri + L ' aug 6.44i10 −7 + 3.52i10 −7
=
= 1.55
L ' pri
6.44i10 −7
This gain factor of 1.55 is used for all subsequent
discussions of the augmented inductance gradient for both
slotted and solid rail configurations as demonstrated in
the calculations of Appendix C.
Appendix D applies COMSOL
Multiphysics finite element software to model the relative
improvement of the magnetic field and flux density across
the center of the bore region and across the inner rail
surface.
liner
COMSOL modeling neglects the geometry of the rail
for
all
configurations.
Electrical
separation
between inner and outer rail surfaces is accomplished by
wrapping the outer rail in two full layers of 1.0 mil Mylar
film.
Although even a single layer of this film is rated
to hold off the magnitude of breech voltage experienced
across the rails, a slightly more robust physical interface
was necessary to prevent defects in the rail surface finish
from compromising the film integrity and short-circuiting
the augmenting rails.
Three layers of 3.0 mil adhesive
laminating film supplementing the 2 layers of mylar film
between
the
adjoining
rail
faces
prevented
the
circuits seen in initial efforts to fire augmented.
11
short-
Augmented Conductor Assembly
-Initial configuration is 19mm (3/4”) square bore
augmented / non-augmented firing options
-Maximum non-augmented configuration: 38mm x
38mm (1-1/2” x 1-1/2”)
-Ceramic insulator symmetry doubles working life
Figure 4.
Augmented Conductor Assembly
Figure 4 demonstrates the augmented conductor assembly
and
bore
geometry.
By
removing
the
external
copper
conducting rods the gun can be fired in the non-augmented
configuration.
external
For initial non-augmented testing, both the
conductor
rods
and
the
augmented
rails
were
removed and a pair of G-11 FR-5 phenolic insulators was
substituted to avoid eddy current losses in a disconnected
rail pair.
The inner rail pair is configured to support the use
of a muzzle shunt.
A copper conductor bar was used to
short the muzzle shunt connection during initial testing
prior to using actual armatures.
The limited energy and
short duration current pulse available for initial testing
produced a minor muzzle flash.
required
to
optimize
muzzle
Follow-on work will be
shunt
circuit
elements
for
operating the gun at high power in order to prevent damage
to the conductors as the armature breaks contact with the
muzzle.
At higher energies, an effective muzzle shunt may
12
become
critical
to
preventing
muzzle
flash
interference
with the velocity measuring breaks-screens because of the
confined operating range of the laboratory environment.
D.
IMPROVED
GEOMETRY
INDUCTANCE
GRADIENT
WITH
SLOTTED
RAIL
Another technique to boost the L’ is to alter the rail
geometry by a series of slots cut in to either side of the
rails.
The slotted geometry still provides the common rail
height
necessary
for
mechanical
mounting
of
the
rails
within the containment structure, but confines current flow
to a narrower center channel.
This technique results in a
more concentrated magnetic field within the bore region.
To
predict
narrowed
the
rail
gain
provided
height
by
dimension
slotted
of
1”
geometry,
was
the
the
input
parameter into the Kerrisk’s method calculation rather than
the full exterior height, resulting in an expected gain
factor of 1.45.
Verifying an improvement in final armature
velocity for a fixed input energy is significant because it
has potential applications for both thermal management and
rail containment designs for more advanced railgun systems.
Figure 5 demonstrates the slotted rail geometry.
detailed
drawing
is
included
in
Appendix
B,
Figure
A
17.
Appendix D demonstrates COMSOL Multiphysics finite element
software modeling of the relative magnitude of improvement
of the magnetic field (H) and magnetic flux density (B=µoH)
for slotted and non-slotted rail configurations.
Figure 30
demonstrates how the altered slotted rail geometry affects
the
input
parameters
used
to
gradient.
13
calculate
the
inductive
Figure 5.
E.
Slotted Rail Geometry
ADDITIONAL COMPONENTS
High tolerance structural design is required to limit
rail
deflection
and
maintain
a
consistent
bore
profile.
Maintaining stiffness and straightness in a short, small
bore railgun is significantly easier than for a large bore
10
m
gun.
In
interference
order
fit
when
to
achieve
loading
a
the
tight
rail
armature,
to
rail
the
gun
incorporates a manual screw auger which advances a breech
block and protruding 3” ram contoured to the back of the
armature.
The 3” ram provides a consistent longitudinal
starting point for testing and places the armature in a
region where magnetic fields are well established.
effective
railgun
position is 50 cm.
length
beyond
the
loaded
The
armature
The loading apparatus is mounted at
four points to the containment shells via 3/8” stainless
steel threaded rods and helicoil inserts.
This apparatus
is currently under-utilized because the lack of sufficient
power to overcome static friction mandates a loose armature
fit.
Although a slight interference fit was used for the
preliminary
testing
discussed
14
herein,
the
armatures
fabricated
to
actual
design
bore
geometry
required
some
volume reduction via polishing in order to prevent binding.
During testing, prior to installing the loading apparatus,
a bore ram is used to force the polished armature through
the entire length of the gun to identify excessive regions
of binding.
Figure 6 shows a side and overhead view of the
assembled loading apparatus.
Figure 6.
The
railgun
Railgun Loading Apparatus
design
also
includes
a
muzzle
block
mounted with four 1/4" stainless steel bolts into helicoil
inserts set in the containment shells.
The current muzzle
block has a 1-1/4” diameter hole through which the armature
exits.
Although this design is adequate for testing at 35
kJ,
must
it
supply.
be
improved
prior
to
upgrading
the
power
A square muzzle port properly sized to the bore
dimension may assist in confining the deleterious effects
of the muzzle flash to the rail liner rather than to the
underlying
main
conductor
rail.
The
photograph
of
the
muzzle block in Appendix F Figure 59, was taken immediately
following a shot, and hints at the potential for arcing
damage at the muzzle exit at higher energies.
15
A series inductor was constructed by tie-wrapping 4/0
welding cable around a PVC shape.
Although a much larger
inductor was initially fabricated, optimized to maximize
the pulse length, its effect of diminishing peak current
resulted in the inability to overcome static friction when
firing with a stored energy of 35 kJ.
A final compromise
between peak current and pulse length was accomplished by
using
the
three
turn
inductor
pictured
among
other
components in Figure 7.
3-turn series inductor of welding cable
wound around 13-1/2” diameter shape
threaded through a protective hose
Bore ram with G-10 endpiece
G-11 rail substitute for
non-augmented
configuration
Figure 7.
In
3.0-µH Series Inductor and Components
preparation
for
shooting
at
high
velocities,
a
target chamber was custom designed and fabricated by MGM
Targets.
It consists of a three foot long, 10” diameter
steel tube with a 6” entry portal.
The tube is filled with
ground rubber contained by solid rubber sheets at the entry
point and along the top, where a bolted access panel allows
projectile recovery.
The target chamber is pictured in
Figure 8.
16
Figure 8.
Target Chamber
17
THIS PAGE INTENTIONALLY LEFT BLANK
18
III. PULSED POWER SUPPLY
A.
PRESENT SYSTEM
The stored energy supply consists of two 830 µF, 11 kV
rated
Maxwell
Model
32327
capacitors
switched
parallel Maxwell TVS-40 vacuum switches.
by
two
These capacitors
discharge through dedicated pairs of high power rectifier
diodes
connected
crowbar
the
current waveform at peak value to prevent oscillation.
The
diodes
by
ABB
pair
is
are
to
model
Switzerland
Ltd.
a
common
5SDD
ground
50N5500,
which
manufactured
Semiconductors.
Each
diode
constrained by an ABB diode clamp model 5SAC 18V9001, rated
at 90 kN.
Downstream of the diode strings, current output
from
individual
each
capacitor
is
monitored
Pearson Model 1330 wide band current monitors.
with
two
The outputs
from the parallel TVS-40 switches are connected by a single
bus
bar
Pearson
and
currents
model
1423
up
to
current
500
kA
monitor.
are
monitored
Output
and
by
a
return
leads extend through the side of a steel framed, plexiglass
covered enclosure, allowing connection to the railgun leads
with 4/0 Flex-a-Prene heavy duty welding cable rated for
600 Volts.
The input side welding cable is wound around a
13-1/2” PVC shape to serve as a series inductor as pictured
in Figure 7.
from
extreme
In order to protect the inductor cable run
compressive
forces
experienced
during
discharges, the 3/4" cable is threaded through a 7/8” inner
diameter rubber hose.
Figure 9 shows an overhead view of
the power supply cabinet.
19
Figure 9.
The
Pearson
output,
and
attenuator
Agilent
Power Supply Cabinet
1330
is
produces
further
before
Infinium
being
S4852
an
initial
conditioned
processed
m-Volt/Amp
through
for
oscilloscope.
5
display
The
a
10:1
using
Pearson
an
1423
produces a 1 m-Volt/Amp output, and is sent through both a
10:1 attenuator and 2:1 divider for display.
screen
captures
for
each
included in Appendix E.
shooting
Oscilloscope
configuration
are
Peak currents registered by the
combined Pearson 1423 output ranged from 88-98 k-Amps for
all
four
rail
configurations
when
discharged
from
an
initial capacitor voltage of 6500 volts.
PSpice circuit
modeling
the
is
included
in
Appendix
D
for
6500
Volt
initial charge and other experimentally determined values
for
the
railgun
test
platform
including,
inductance,
resistance and railgun resistance as specified in Figure
45.
The
railgun
resistance
20
value
of
0.3
m-Ohm
was
initially calculated based on the material properties and
cross-sectional
areas
of
the
entire
railgun
conductor
apparatus from input to output leads.
The
main
capacitor
pair
is
charged
with
a
Bertan
Associates Series 105 1kW High Voltage Power Supply through
a
separate
capacitor
circuit
is
of
monitored
diodes
by
a
and
resistor
dedicated
bars.
voltmeter
Each
display
panel.
Simultaneous triggering of the TVS-40 switches is done
with a Glassman High Voltage Inc. Series LX High Voltage
Power
Supply
via
catalog #315DM410.
two
100
µF
General
Atomics
capacitors
On a single firing signal, each 100 µF
capacitor discharge is stepped up to 5kV using homemade
transformers.
Figure
10
demonstrates
the
power
supply
cabinet interfaces for charging, triggering, and supply and
return to the railgun test platform.
Figure 10.
Power Supply Cabinet Interfaces
Throughout various stages of testing, elements within
the pulsed power circuit delayed progress due to arcing,
21
failed
diodes,
non-triggering
switches,
and
ruptured
transmission cable leads. Although the initial goal was to
operate the capacitors at 9 kV, which would have supplied a
total stored energy of 67.2 kJ, erratic switch output and
spontaneous triggering above 7 kV demanded that final data
collection
be
conducted
at
6.5
kV,
which
limited
total
stored energy to 35 kJ.
As the TVS-40 switches are rated
beyond
documented
these
limits,
a
trigger
rejuvenation
procedure may restore them to improved functionality [6].
The
oscilloscope
current
traces
in
Appendix
E
clearly
identify both uneven current peaking and pulse decay rates
from
the
two
capacitors
attributed
to
uneven
coupling
across the TVS-40 switches.
B.
REDESIGNED POWER SUPPLY
The Naval Postgraduate School Physics Department has
invested in ten new General Atomics capacitors with the
same catalog number and ratings as the Maxwell Laboratories
pair used for testing.
limited
to
35
kJ,
Where testing for this research was
incorporating
the
present
and
new
capacitors into a multiple module system will provide a
maximum
stored
energy
capacity
of
600
kJ.
The
older
capacitors have been cycled at high voltages since at least
June of 1999 and might be contributing to uneven power
sharing
through
the
TVS-40
switches.
In
addition
to
investigating switch refurbishment, a comparison of output
current profiles using a pair of the new capacitors within
the
existing
power
supply
would
indicate
whether
the
irregular discharge can be solely attributed to the TVS-40
switches.
22
In
addition
to
the
new
capacitors,
two
new
high
current Titan ST-300A high action spark gap switches and
associated triggering apparatus have been purchased.
The
Titan switches are rated for 600 kA peak current and 55 kV
peak voltage and will permit a single switch to control the
output of a module pair of capacitors.
Figures
practical
47
four
and
48
module
of
Appendix
ripple
fired
D
demonstrate
circuit
designed
a
to
maintain an average 280 kA current pulse for 0.67 ms, which
should accelerate an 11.4 gram armature to 1500 m/s over
the
50
cm
configuration
rail
(See
length
Table
for
the
19).
slotted,
The
model
augmented
circuit
incorporates a 1 m-Ohm muzzle shunt resistor for a first
look at the dynamics which occur as the armature breaks
electrical contact with the muzzle.
This model requires
that each module be charged to near capacity at 10 kV, and
incorporates optimized delay times and series inductors.
Achieving the effective rise time and peak current required
to overcome the static friction of a tight interference fit
requires firing the first two modules simultaneously.
Such
a fit is critical to maintaining the solid armature to rail
interface necessary to delay transition to arcing and to
prevent
rail
damage
from
intermittent
within the bore.
23
armature
caroming
THIS PAGE INTENTIONALLY LEFT BLANK
24
IV. DESIGN VERIFICATION
A.
PARAMETER MODEL
On May 6, 2004, Dr. Mark Crawford, Pulsed Power and
Electromagnetic Launch Team Leader from IAT, presented a
colloquium lecture to the Naval Postgraduate School Physics
Department
[7].
The
parameter-based
system.
dissertation
approach
The
to
outlined
designing
applicable
a
a
top
basic
thumb-rules
are
level
railgun
based
on
simplifying assumptions such as a symmetric acceleration
profile
which
accelerations
performance,
allows
for
conservative
rail
containment.
identifying
geometry,
Appendix
C
both
average
modeling
electrical
applies
and
of
velocity
action,
this
peak
and
rail
parameter-based
approach to the four physical configurations, solid nonaugmented,
slotted
non-augmented,
solid
augmented,
and
slotted augmented, and to a range of energy inputs as a
basis of comparison to other modeling techniques in order
to
validate
containment
bolt
sizing,
and
to
correlate
average current to final velocity.
P-Spice circuit model predictions in Appendix D for
the average current required to reach 1500 m/s over the 50
cm
effective
railgun
length
are
based
on
the
average
required current calculated from the parameter-based model.
The
experimental
results
from
the
solid
augmented
and
slotted augmented experimental shots are also inputted into
the parameter model (Tables 21 and 21) for comparison.
The
parameter model predicts that a final armature velocity of
1500 m/s requires a peak current of nearly 500 kA for the
solid, non-augmented configuration as detailed in Table 16.
Therefore, 500 kA is used to assess containment deflection,
25
and bolt diameter and spacing in Section C below.
A final
application of the parameter model uses bolt diameter and
yield strength to predict the maximum current of 355 kA,
and
maximum
achieved
on
final
the
velocity
railgun
of
1085
test
m/s
platform
which
with
can
be
Grade
2
stainless 3/8” bolts, per Table 21.
B.
CONSERVATION OF ENERGY CIRCUIT MODEL
In order to evaluate experimental results and estimate
velocity performance for an effective rail length of 50 cm,
a
simplified
circuit
model
was
developed
for
module capacitive stored energy power supply.
a
single
Appendix C
details the process which applies conservation of energy
principles to Kirchhoff’s Voltage law, coupling inductive
energy transfer to projectile kinetic energy via Lorentz
force parameters.
In the following equation,
F is the
Lorentz force accelerating the armature, m is the armature
mass, dv/dt is armature acceleration, L’ is the inductive
gradient of the rails, and I is the time dependant value of
current.
F =m
The
model
neglects
dv 1
= L'I2
dt 2
frictional
losses
and
relies
on
several simplifying assumptions including assuming that the
total system inductance L is much larger than the product of
L’ and rail length x.
effective
system
The model also assumes that the total
resistance
R
is
much
larger
than
the
resistance R’x, where R’ is the rail resistance per unit
length.
In both cases, L and R are verified experimentally
to be an order of magnitude larger then L’x and R’x for the
26
L is calculated based on the rise time
60 cm test platform.
to
peak
current
in
a
oscilloscope at 150 µs.
discharge
cycle,
measured
by
The following equation for the
period of oscillation T demonstrates how inductance can be
solved based on the known capacitance C of 1.66 mF.
T = 4∆trise = 2π LC
In order to simplify the model to a purely inductive
energy transfer between the total system inductance and the
railgun, the capacitive stored energy is eliminated from
the final expression by neglecting the initial 150 µs of
current ramping up to its peak value.
The increase in
armature velocity during the rise time is small. The time
dependent
expression
for
current
is
an
exponentially
decaying waveform:
I ( t ) = I o exp
⎛ − Rt ⎞
⎜
⎟
⎜ L ⎟
⎝
⎠
,
where the peak current Io is determined by:
1
2
⎛C ⎞
⎟ Vo
L
⎝ ⎠
.
I0 = ⎜
Vo is the initial state of capacitor voltage which for
my experimental data runs was 6500 Volts.
The resulting
expression provides for a separable differential equation
for rail length as a function of velocity [4].
dv 2 Rv L ' v 2 L ' I o2
v +
+
=
dx
L
L
2m
27
An integral table gives the expression including the
integration constant D.
(
1
2
∫ dx = 2a ln av + bv + c
⎡
⎛ 2av + b − b 2 − 4ac ⎞ ⎤
1
⎢
⎟⎥ + D
ln ⎜
2
2
⎜
⎟
2a ⎢ b − 4ac
⎝ 2av + b + b − 4ac ⎠ ⎦⎥
⎣
)− b
The circuit parameters which comprise factors
a ,b ,
and c , are defined below.
a=
−L '
L
b=
−2R
L
c=
⎡ ⎛1
2 ⎞⎤
⎢ L ' ⎜ CVo ⎟ ⎥
⎠⎦
⎣ ⎝2
( mL )
The integration constant D scales the solution such
that zero velocity corresponds to a zero length railgun.
The actual values used for each variable are included in
Tables 22-26 of Appendix C.
Table
25
gives
the
integration
for
parameters
associated with the slotted augmented rail configuration,
and predicts a final velocity of 293 m/s corresponding to
the 50 cm effective rail length, and total stored energy of
35 kJ.
I have neglected the minimal projectile velocity
which exists when I = Io, as well as losses due to friction
between
the
rails
and
armature,
the
effects
of
which
compensate for each other to some extent.
C.
STRUCTURAL DESIGN
The 24” railgun containment halves are clamped by a
total of 22 Grade 2 stainless hex-head steel bolts of 3/8”
diameter, rated by the vendor at 57 ksi in accordance with
the
SAE
J420
1985
abstract
[8].
The
bolts
are
longitudinally spaced at 2” intervals down the length of
the containment beginning 1” from either end.
28
Conservative static modeling assumptions were applied
to assess the overall containment design in terms of rail
deflection, bolt spacing and diameter.
augmented
configuration
and
the
From the solid non-
500
kA
peak
current
predicted in Table 16 of Appendix C, rail repulsion force
per unit length, p, is calculated by using the following
equation.
−7
lb f
F µo I 2 ( 4π • 10 ) ( 500kA )
MN
p= =
=
≈ 1.75
≈ 9983
x 2π d
m
in
( 2π • 0.0286 )
2
In
the
previous
equation,
F
is
the
rail
repulsion
force, x is the total rail length, µo is the permeability
constant, I is peak current, and d is the length in meters
between
rail
centerlines
considering
the
rail
liner
and
primary rail as a single solid conductor.
Two
specific
structural
design
objectives
are
investigated.
Maximum rail deflection must be limited to less than
0.0001 inches,
Under worst case loading, the containment bolts must
not exceed their static yield strength.
A
2-D
model
of
the
distributed
longitudinal
rail
repulsion force between any two consecutive bolt pairs is
represented by the fixed-end beam model in Figure 11.
29
L
ymax
pL4
⎛L⎞
= y⎜ ⎟ =
⎝ 2 ⎠ 384 EI
p
ymax
Figure 11.
Fixed End Distributed Load Beam Model [After
Ref. 9]
Maximum
deflection,
ymax,
occurs
at
the
midpoint
between bolts spaced at a distance L, of 2”. E is the
modulus of elasticity, and I is the moment of inertia based
on
the
beam
demonstrates
materials
cross-section.
the
and
Appendix
method
used
to
geometry
into
a
simplify
single
C,
Section
the
C,
composite
representative,
homogenous beam in order to determine maximum deflection.
For 9983 lbf/in loading, the calculated deflection is less
than
0.00002
inches,
confirming
adequate
containment
stiffness.
The validity of the previous deflection calculation
depends on achieving the fixed boundary conditions of no
slope and no deflection based on bolt loading conditions.
Here I consider the total rail length, x = 24”, and the
total of 22 bolts of 3/8” diameter to determine the maximum
load per unit length (pmax) achievable at the bolt Yield
Strength (YS) threshold of 57 ksi.
pmax
lbf ⎞
⎛
22 *0.1104in 2 i57,000 2 ⎟
⎜
# bolts i Abolt iYS ⎝
lbf
lbf
in ⎠
=
=
≈ 5770
< 9983
x
in
in
24in
30
The maximum sustainable load of 5770 lbf/in is less
than
that
which
results
from
the
500
kA
peak
current
condition corresponding to a 1500 m/s exist velocity for
As such, pmax is
the solid non-augmented configuration.
used
to
determine
the
actual
peak
current
capacity
to
Converting 5770 lbf/in to metric
inform follow on testing.
units yields approximately 1.01 MN/m.
I max =
The
2π d i pmax
µo
resulting
≈
2π i0.0286mi1.01
4π i10−7
calculation
N
A2
MN
m ≈ 380kA
shows
that
the
present
containment design is capable of maintaining bolt loading
below yield strength up to a maximum current of 380 kA.
Based on parameter modeling in Table 22, this peak load
capacity
correlates
with
the
alternative
method
of
rail
repulsion force and bore height to calculate the force per
unit length.
Table 22 indicates that the Grade 2 bolt
yield strength threshold is achieved at 355 kA, correlating
to a final velocity of about 1085 m/s.
Therefore, in order
to achieve the no-yield requirement at 500 kA, the grade 2
stainless
bolts
must
be
upgraded
to
grade
8.
The
ACF
Components vendor quotes grade 8 hex head bolts at a yield
strength of 130,000 ksi [8].
pmax
kip ⎞
⎛
22*0.1104in 2 i130 2 ⎟
⎜
# bolts i Abolt iYS ⎝
lbf
lbf
in ⎠
≈ 13,156
=
=
> 9983
24in
x
in
in
The grade 2 hardware currently in use will suffice
until considerable additional stored energy is integrated
into the pulsed power supply.
All containment modeling is
based on conservative static loading rather than the actual
31
dynamic loading which occurs during firing.
The previous
design
demonstrate
an
efforts
improve
verification
containment
such
methods
that
future
to
adequate
bore
tolerance should concentrate on deficiencies in the rail
liner
surface
finish
rather
than
design.
32
the
overall
structural
V.
A.
RESULTS
SHOT DIAGNOSTICS
Table 3 lists the experimental results.
Shot
1
2
3
4
5
6
7
Configuration
L'
System Voltage
(uH/m) L (µH)
solid, non-aug 0.3037
5
solid, non-aug 0.3037 2.5
solid, non-aug 0.3037 5.5
slot, non-aug 0.4405 5.5
solid, aug
0.4707 5.5
slotted, aug 0.6828 5.5
slotted, aug 0.6828 5.5
Table 3.
Shots
3-7
Initial
Final
Input Energy
Ipeak
Velocity
KE
Efficiency
(KJ)
53
35
35
35
35
35
35
(k-Amps)
N/A
110
97.8
88.0
95.0
91.4
88.9
(m/s)
246
168
105
117
265
294
286
(J)
332.8
160.9
62.8
78.0
393.3
492.7
466.2
0.63%
0.46%
0.18%
0.22%
1.12%
1.41%
1.33%
(V) Mass(g) Mass(g)
8000
11
10.2
6500
11.4
10.6
6500
11.4
11
6500
11.4
10.9
6500
11.2
10.6
6500
11.4
11.2
6500
11.4
11.1
Experimental Data Results
were
all
conducted
with
the
same
series
inductor and initial capacitor charge of 6.5 kV in order to
compare
each
configuration.
Shot
1
was
taken
with
a
capacitor charge of 8 kV and a 5 µH total system inductance.
This 8 kV shot produced two in a longer series of testing
delays
caused
pulsed
power
by
the
supply.
failure
On
of
this
components
shot
in
within
the
particular,
the
series inductor solid copper cable lead separated from the
cable run.
coils
Also, the forces squeezing the series inductor
together
axially
ruptured
the
sheath and rendered the line unusable.
rubber
insulating
The peak current
value for the 8 kV shot was unreadable due to over-ranging
the oscilloscope settings.
After the 8 kV shot, the TVS-40
switches began to spontaneously trigger when charged up to
7 kV, ultimately demanding that the data runs be limited to
6.5 kV.
Prior to re-introducing a new series inductor, a
new sheathed cable run was threaded through a 7/8” inner
diameter rubber hose to prevent a similar rupture, and new
cable leads were fabricated.
33
The 2.5 µH inductance listed for shot 2 represents the
total system inductance with no additional series inductor.
Although the resultant velocity of 168 m/s surpassed all
other subsequent non-augmented shots which did incorporate
a series inductor, the higher current peaking resulted in
one TVS-40 switch failing completely.
Upon obtaining a
replacement switch, a 3 µH series inductor was used for all
further testing in order to avoid over-stressing the system
while
permitting
consistent
test
parameters
for
all
shooting configurations.
The remaining experimental firings, shots 3-7 of Table
3, were conducted at 6.5 kV with a total system inductance
of 5.5 µH.
Although statistically insignificant for the
single point sampling, the resultant velocities demonstrate
a trend consistent with each improvement in the inductance
gradient, ranging from 105 m/s for the solid non-augmented
configuration to an average of 290 m/s for the two slotted
augmented shots.
The
respective
gain
factors
for
slotted
geometry,
series augmentation, and their combined totals as predicted
by the L’ and magnetic field models detailed in Appendix C
are compared to the experimental gain in Table 4.
The
experimental gain factors are determined by the following
ratios.
2
maug vaug
2
mslotted vslotted
= Gaingeometry
2
msolid vsolid
2
mnon − aug vnon
− aug
= Gainaug
For all cases other than solid augmented, the initial
mass
is
11.4
grams
and
cancels
square of the final velocities.
34
leaving
a
ratio
of
the
The augmented gain factor
is an average of the gains calculated for both the slotted
and
solid
rail
geometries.
The
lower
than
expected
velocities for the non-augmented configurations in shots 3
and 4, suggest that given only 35 kJ of stored energy and
diminished
magnetic
accelerating
static
force
fields
is
friction.
configuration
near
Shot
with
no
without
2
augmentation,
the
threshold
for
the
series
of
solid
inductor
the
overcoming
non-augmented
produced
a
final
velocity closer to the value expected by the conservation
of energy model in Table 23.
non-augmented
shot
without
Although data for a slotted
a
series
inductor
is
not
available at this time, the experimentally determined gain
factors in Table 4 marked with an asterisk (*) use the 168
m/s velocity result of shot 2.
L' Geometry Modeling
1.55
1.45
2.25
Gain Factors
Series Augmentation
Slotted Geometry
Total Gain
Table 4.
Magnetic Field Modeling
1.66
1.5
2.49
Experimental Results (mv2)
6.26 ( * 2.49 )
1.22
7.63 ( * 2.98 )
Predicted vs. Experimental Gain Factors
There is close agreement between gain factors produced
by the two respective modeling techniques.
limited
data
runs,
the
experimental
unreliable and deviate from the models.
the
augmentation
and
the
slotted
Due to the
gain
factors
are
In all cases, both
geometry
resulted
in
improvements in final velocity.
Additional
operational
velocity
shots
velocity
results
from
which
were
diagnostics
shots
3
performed
suggest
and
4
may
that
have
prior
the
to
lower
been
the
result of insufficient power to overcome static friction.
During two early shots at the 35 kJ level, using a 22.5 µH
series inductor intended to match the current pulse length
35
to the total rail length, the armature in one case did not
break static friction at all, and in another traveled only
3 inches down the barrel.
Significant enhancement of the stored energy supply is
necessary
to
generate
valid
experimental
results
for
comparison to the idealized models which neglect frictional
losses.
Furthermore, the moderately loose interference fit
between
the
entirely
armature
inadequate
and
for
bore
used
maintaining
contact at higher velocity regimes.
in
these
effective
tests
is
electrical
When the pulsed power
supply is adequately hardened to permit extracting stored
energy near the capacity of individual modules, and when
multiple modules contribute to building an adequate current
waveform, the loader mechanism can be used to provide an
appropriately tight interference fit.
The consistency of
this fit along the bore length as indicated by the torque
required to manually advance a test round, and the use of a
torque wrench on the loading mechanism may be critical to
establishing conditions necessary to validate gain factors
experimentally.
The parameter based modeling in Appendix C predicts no
violations of generally accepted thresholds such as rail
heating and linear current density for all configurations
when the muzzle velocity is 1500 m/s.
The peak current,
parameter based calculations for the minimum adequate bolt
diameter
performed
are
in
using
close
classic
agreement
beam
with
bending
the
calculations
analysis.
Both
methods indicate that the Grade 2 bolt will reach their
yield strength threshold between 335 and 380 kA, with the
resulting exit velocity ranging from 1085-1150 m/s.
36
The conservation of energy model prediction of 293 m/s
velocity for the slotted augmented configuration with 35 kJ
of
stored
energy
compares
velocity of 290 m/s.
with
the
average
experimental
The conservation of energy model was
also evaluated to predict the maximum velocity which could
be achieved by a single module of two capacitors charged to
10 kV, which corresponds to 83 kJ of stored energy.
The
resultant velocity for the 50 cm effective rail length is
495 m/s.
The current traces in Appendix E from the experimental
shots indicate that the magnitude of current (I) is small as
the projectile exits the gun.
A total system resistance of
3.3 m-Ohm has been used for all simulations.
The power
supply resistance was measured to be 3 m-Ohm and the rail
resistance
was
calculated
to
be
0.3
m-Ohm
from
the
resistivity and geometry of the copper conductors within
the railgun assembly from input to output leads.
calculated for each shot in Table 5.
calculated
by
the
following
equation
R/L’ is
The R/L’ ratio is
where
each
of
the
terms is defined in Table 5.
R
1
=
(Wo _ − KE )
L ' 2mv
Shots 1-2, and 5-7 support the model parameter of 3.3
m-Ohms of total system resistance.
The two low velocity
non-augmented results for shots 3 and 4 are outliers at
4.44 and 5.78 m-Ohms respectively, suggesting additional
frictional losses.
37
Shot
Configuration
L'
Armature
Input Energy Velocity Kinetic Energy
(uH/m) Mass(g)
1
2
3
4
5
6
7
solid, non-aug
solid, non-aug
solid, non-aug
slot, non-aug
solid, aug
slotted, aug
slotted, aug
0.3037
0.3037
0.3037
0.4405
0.4707
0.6828
0.6828
Table 5.
R/L'
R
Wo (KJ)
(m/s)
KE (J)
(Ohm-m/H )
(m-Ohm)
53
35
35
35
35
35
35
246
168
105
117
265
294
286
332.8
160.9
62.8
78.0
393.3
492.7
466.2
9793
9137
14620
13120
5896
5221
5367
2.97
2.77
4.44
5.78
2.78
3.57
3.66
11
11.4
11.4
11.4
11.2
11.4
11.4
Total System Resistance and R/L’ Results
Appendix
F
includes
photographs
insulator, and armature wear.
of
typical
rail,
Every shot resulted in a
thin coating of melted aluminum deposited along the rail
length.
Gaps in the presence of the coating correlated to
the localized damage in the chromium copper rail material
suggesting
specific
locations
where
between the armature and rail.
the
as-fabricated
measure
at
0.748”
3/4"
the
developed
Micrometer measurements of
square
where
arcing
Aluminum
same
6063
measurements
armatures
for
the
ceramic insulator thickness hold the tighter tolerance of
0.750” +/- 0.0001 along the entire length.
Although these
dimensions suggest an ideal fit, the surface finish in the
bore region of the rail liner is accomplished by 400 grit
belt
sanding
followed
by
600
grit
hand
sanding.
Hand
feeding of the armatures down the bore length indicates
alternating regions of binding and slipping.
As a result,
the final loose sliding fit was accomplished by polishing
the outer armature faces.
The volume of material removed
by this polishing was significant: all of the as-fabricated
armatures had an initial mass of 11.6 grams but the typical
final armature launch mass was 11.4 grams.
In general, the
more material removed from the armature during polishing to
provide a working fit, the more rail damage observed postfiring due to caroming of the round back and forth between
38
the
rails
during
launch.
The
extreme
variation
in
electrical contact during launch which results from such a
poor fit contributed to the rail damage as demonstrated by
localized
blackened
aluminum
and
copper
regions
where
arcing likely occurred.
In one shot, the results of which are not included in
Table 3 due to occurring prior to effective diagnostics,
the as-fabricated armature provided a working fit without
polishing.
This particular shot produced an even aluminum
coating down the entire rail length with no visible damage
to the underlying rail liner.
Inspections of the spent
armatures reveal that the highest velocity shots experience
the least loss of armature mass, and the least deformation
of the trailing arms.
Root radius wear for the augmented
higher velocity shots was grainy but retained the aluminum
metallic tone whereas the root radius of the non-augmented
shots was obscured by blackened deposits.
Although the
current levels experienced in this testing are far less
than the 900 kA threshold for root radius melting observed
by Francis Stefani and Trevor Watt for a 40 mm square bore
railgun, visual inspection of the spent armatures suggest
that the onset may occur at significantly lower currents
for this small bore test platform [13].
39
THIS PAGE INTENTIONALLY LEFT BLANK
40
VI. CONCLUSION
A.
PERFORMANCE SUMMARY AND RECOMMENDATIONS
The
trend
of
improved
velocity
corresponding
to
engineered inductance gradients, and qualitative agreement
between
alternative
modeling
approaches
indicates
that
there are no immediate impediments to scaling the stored
energy supply in order to experiment with higher velocity
regimes
on
this
railgun
test
platform.
However,
incremental advances are recommended in order to allow the
development
of
diagnostics.
pulsed
power
supply
components
and
Before moving to multi-module pulsed energy
configurations,
fully
harnessing
single
must
be
module
the
stored
demonstrated.
energy
As
of
a
previously
discussed, a 10 kV charge corresponding to a total stored
energy of 83 kJ should produce nearly 500 m/s.
Concurrent
with fully utilizing a single module, the armatures can be
loaded
into
a
mid-bore
position,
reducing
the
effective
rail length to an appropriate value such as 25 cm in order
to investigate behavior when there is significant current
as the armature exits the rails.
This would provide the
opportunity to experiment with a muzzle shunt present.
The present method of connecting the series inductor
welding cable directly to the railgun conductor leads must
be
improved
decouple
the
railgun
by
the
physical
itself.
directly
addition
coupled
Such
to
stress
a
the
of
of
fixed
fixed
the
manifolds
inductor
manifold
railgun
from
could
supply
which
and
then
the
be
return
conductors via a solid copper bus-bar.
The basic mechanical containment is sound for scaling
to
at
least
1085
m/s
using
41
Grade
2
stainless
bolts.
Upgrading to Grade 8 stainless steel bolts permits scaling
above 1500 m/s for all configurations.
weak
points
threaded
related
and
to
braised
augmenting
rails
conductor
rods
the
mechanical
conductor
connect
used
to
However, the likely
connections
the
for
design
containment
augmented
are
the
where
the
penetrating
operation,
as
demonstrated in Figure 12.
Potential for thermal and
mechanical failure at location of
threaded / braised joint
connecting conductor rod to
augmented outer rail
Figure 12.
As
Augmented Rail to Conductor Threaded and
Braised Joint
adequate
addition
to
stored
targeting
energy
becomes
increases
in
available,
the
degree
in
of
interference fit, incorporating a bore rider in front of
the
armature
either
attached
or
as
an
independent
projectile load may help both seal the bore in front of the
armature
to
prevent
blowing
by
of
the
liquid
interface
layer, and stabilize the armature ride within the bore,
preventing
the
damage
due
to
caroming
which
currently
exists.
A variety of armature geometries, pictured in Figure
13, have been fabricated to provide options for improving
42
the
elastic
response
in
the
trailing
arms
in
order
to
maintain solid to solid electrical contact with the rails.
Figure 13.
B.
Armature Geometry Alternatives (Appendix B)
MATERIALS PROCESSING METHODS
Anticipating
the
maturation
of
the
power
supply,
preparations for the first application of the railgun test
platform
have
been
initiated.
A
collaboration
between
Lawrence Livermore (LLNL) and Sandia National Laboratories
(SNL) is underway in order to conduct in-bore testing of
laser
peened
untreated
[13],
rail
ion-beam
liner
surface
samples
for
treated
the
[14],
chromium
and
copper,
phosphor bronze, copper tungsten, and aluminum 7075 alloys
discussed in Table 2.
Timothy
Applications
Modification
Renk,
of
Project
Ion
Beams
Materials
Sandia’s
Materials
surface
treatments on pairs of each of these materials.
Tania
Project
Leader
has
at
for
beam
Zaleski,
Laboratory,
Leader
for
43
performed
Laser
ion
Peening
at
LLNL,
has
conducted
preliminary
micro-hardness
testing
on
each
material treated by a range of laser parameters in order to
determine the optimal parameters to be used on the full
rail
liners.
Following
completion
of
the
rail
liner
peening, and nano-hardness testing on the ion beam treated
samples, LCDR Paul Clifford, USN, will conduct a series of
shots at the Naval Postgraduate School in order to assess
the suitability of these processes for enhancing rail life
over untreated liner materials.
44
APPENDIX A. MATERIAL PROPERTY DATA SHEETS
Rail liner: Chromium Copper UNS C18200, TH04
MatWeb Data Sheet
Date: 7/12/2005
Chromium Copper, UNS C18200, TH04 Temper flat products, aged
KeyWords: CDA 182, CC101, ISO CuCr1, CEN CW105C, A2/1
SubCat: Copper Alloy, Nonferrous Metal, Metal
Material Notes: Good to excellent corrosion resistance. Excellent cold workability; good hot
Applications: resistance welding electrodes, seam welding wheels, switch gear, electrode
Available as flat products, wire, rod, tube, and shapes.
Component
Value
Min
Max
Chromium, Cr
0.6
1.2
Copper, Cu
99.1
Iron, Fe
0.1
Lead, Pb
0.05
Silicon, Si
0.1
Properties
Value
Min
Max Comment
Physical
8.89
--at 20°C (68°F)
Density, g/cc
Mechanical
Hardness, Rockwell B
79
--460
--Tensile Strength, Ultimate, MPa
Tensile Strength, Yield, MPa
405
--Elongation at Break, %
14
--In 50 mm
130
--Modulus of Elasticity, GPa
Poissons Ratio
0.3
--UNS C36000 (free-cutting
Machinability, %
20
--brass) = 100%
Shear Modulus, GPa
50
--Electrical
Electrical Resistivity, ohm-cm
2.16E-06
--at 20°C (68°F)
Thermal
CTE, linear 20°C, µm/m-°C
Heat Capacity, J/g-°C
Thermal Conductivity, W/m-K
Melting Point, °C
Solidus, °C
Liquidus, °C
Processing
17.6
0.385
171
-1070
1075
---1070
---
-from 20-100°C (68-212°F)
--TB00 temper at 20°C (68°F)
1075
---
Solution Temperature, °C
Aging Temperature, °C
Hot-Working Temperature, °C
----
980
425
800
For 10-30 minutes, water
1000 quench
500 For 2-4 hours
925
Table 6.
Chromium Copper Rail Liner Material
Properties [After Ref. 2]
45
Main conductor rails: OFE Copper C10100, H04
MatWeb Data Sheet
Date: 7/12/2005
Oxygen-free Electronic Copper (OFE), UNS C10100, H04 Temper, flat products
KeyWords: BS C110, C103 , ISO Cu-OFE, CEN CW009A, oxygen-free high conductivity copper (OFHC), CDA 101
SubCat: Copper Alloy, Nonferrous Metal, Wrought Copper, Metal
Material Notes: Flat test specimens, 1mm and 6mm thick, H04 temper.
Applications: busbars, bus conductors, waveguides, hollow conductors, lead-in wires and anodes for vacuum tubes,
Processing: Excellent hot and cold workability; good forgeability. Fabricated by bending, coining, coppersmithing,
Corrosion Resistance: Good to excellent. Susceptible to galvanic corrosion when coupled with iron, aluminum,
Component
Value
Min
Max
Copper, Cu
99.99
Properties
Value
Min
Max Comment
Physical
Density, g/cc
8.94
--at 20°C (68°F)
Mechanical
Hardness, Rockwell B
50
--Hardness, Rockwell F
90
--Hardness, HR30T
57
--1mm thick flat specimen
Tensile Strength, Ultimate, MPa
345
--Tensile Strength, Yield, MPa
310
--0.5% extension
Elongation at Break, %
6
--1mm thick flat specimen
Elongation at Break, %
12
--6 mm specimen.
Modulus of Elasticity, GPa
115
--Poissons Ratio
0.31
--Fatigue Strength, MPa
90
--1E+09 cycles, 1 mm thick flat test specimen.
Machinability, %
20
--UNS C36000 (free-cutting brass) = 100%
Shear Modulus, GPa
44
--Shear Strength, MPa
195
--Electrical
Electrical Resistivity, ohm-cm
1.71E-06
--at 20° C (68°F)
Thermal
CTE, linear 20°C, µm/m-°C
17
--from 20-100°C (68-212°F)
CTE, linear 100°C, µm/m-°C
17.3
--from 20-200°C (68-390°F)
CTE, linear 250°C, µm/m-°C
17.7
--from 20-300°C (68-570°F)
Heat Capacity, J/g-°C
0.385
--at 20°C (68°F)
Thermal Conductivity, W/m-K
391
--at 20°C (68°F)
Melting Point, °C
1083
--Processing
Annealing Temperature, °C
-375
650
Hot-Working Temperature, °C
-750
875
Recrystallization Temperature, °C
18.3
--C37700 (forging brass) = 100%
Table 7.
Oxygen Free Copper Rail Liner Material
Properties [After Ref. 2]
46
Rail liner: Phosphor bronze C51000, H06
MatWeb Data Sheet
Date: 7/12/2005
Phosphor bronze 5% Sn, UNS C51000, H06 Temper flat products
KeyWords: CDA 510, PB102, ISO CuSn5
SubCat: Copper Alloy, Nonferrous Metal, Bronze, Metal
Material Notes: Good to excellent corrosion resistance. Excellent cold workability. Fabricated by blanking,
Applications: bellows, bourdon tubing, clutch discs, cotter pins, diaphragms, fasteners, lock washers, wire
brushes, chemical hardware, textile machinery, welding rod.
Trace content of Phosphorus.
Test specimen: flat products - 1mm
Component
Value
Min
Max
Copper, Cu
93.6
95.6
Iron, Fe
0.1
Phosphorous, P
0.03
0.35
Lead, Pb
0.05
Tin, Sn
4.2
5.8
Zinc, Zn
0.3
Properties
Physical
Density, g/cc
Mechanical
Hardness, Rockwell B
Tensile Strength, Ultimate, MPa
Tensile Strength, Yield, MPa
Elongation at Break, %
Modulus of Elasticity, GPa
Poissons Ratio
Fatigue Strength, MPa
Machinability, %
Shear Modulus, GPa
Electrical
Electrical Resistivity, ohm-cm
Thermal
CTE, linear 250°C, µm/m-°C
Heat Capacity, J/g-°C
Thermal Conductivity, W/m-K
Melting Point, °C
Solidus, °C
Liquidus, °C
Processing
Annealing Temperature, °C
Table 8.
Value
Min
Max
8.86
--
--
93
535
550
6
110
0.341
205
20
41
----------
----------
8.70E-06
--
--
17.8
0.38
84
-975
1060
---975
---
---1060
---
--
475
675
Comment
at 20°C (68°F)
0.5% extension under load
In 50 mm
At 10^8 cycles, 1 mm strip
UNS C36000 (free-cutting brass) = 100%
at 20°C (68°F)
from 20-300°C (68-570°F)
at 20°C (68°F)
Phosphor Bronze Rail Liner Material
Properties [After Ref. 2]
47
Rail liner: CW 75 Class 11 25%Copper 75%Tungsten
MatWeb Data Sheet
Date: 7/12/2005
CMW ELKONITE® 10W3 (Copper Tungsten) RWMA Class 11
SubCat: Metal Matrix Composite, Copper Alloy, Tungsten Alloy, Nonferrous Metal, Metal
Material Notes: Electrical contacts resistant to arcing, power transformer switches, resistance /
projection welding electrodes, and EDM electrodes
Information provided by CMW Inc.
Component
Value
Min
Max
Copper, Cu
25
Tungsten, W
75
Value
Min
Max Comment
Properties
Physical
Density, g/cc
14.84
--Mechanical
Hardness, Rockwell B
98
--Flexural Modulus, GPa
1.03
--Electrical
Electrical Resistivity, ohm-cm
3.83E-06
--(45% IACS)
Thermal
Thermal Conductivity, W/m-K
220
--Melting Point, °C
-1085
3410
Solidus, °C
1085
--Liquidus, °C
3410
---
Table 9.
Copper Tungsten Rail Liner Properties [After
Ref. 2]
48
Rail liner: Aluminum 7075-T651
MatWeb Data Sheet
Date: 7/12/2005
Aluminum 7075-T6; 7075-T651
Material Notes: General 7075 characteristics and uses (from Alcoa): Very high strength material used for highly stressed
structural parts. The T7351 temper offers improved stress-corrosion cracking resistance.
Applications: Aircraft fittings, gears and shafts, fuse parts, meter shafts and gears, missile parts, regulating valve parts, worm
gears, keys, aircraft, aerospace and defense applications; bike frames, all terrain vehicle (ATV) sprockets.
Data points with the AA note have been provided by the Aluminum Association, Inc. and are NOT FOR DESIGN.
Component
Value
Min
Max
Aluminum, Al
87.1
91.4
Chromium, Cr
0.18
0.28
Copper, Cu
1.2
2
Iron, Fe
0.5
Magnesium, Mg
2.1
2.9
Manganese, Mn
0.3
Silicon, Si
0.4
Titanium, Ti
0.2
Zinc, Zn
5.1
6.1
Properties
Value
Min
Max Comment
Physical
Density, g/cc
2.81
--AA; Typical
Mechanical
Hardness, Brinell
150
--AA; Typical; 500 g load; 10 mm ball
Hardness, Knoop
191
--Converted from Brinell Hardness Value
Hardness, Rockwell A
53.5
--Converted from Brinell Hardness Value
Hardness, Rockwell B
87
--Converted from Brinell Hardness Value
Hardness, Vickers
175
--Converted from Brinell Hardness Value
Ultimate Tensile Strength, MPa
572
--AA; Typical
Tensile Yield Strength, MPa
503
--AA; Typical
Elongation at Break, %
11
--AA; Typical; 1/16 in. (1.6 mm) Thickness
Elongation at Break, %
11
--AA; Typical; 1/2 in. (12.7 mm) Diameter
AA; Typical; Average of tension and
compression. Compression modulus is about 2%
Modulus of Elasticity, GPa
71.7
--greater than tensile modulus.
Poissons Ratio
0.33
--Fatigue Strength, MPa
Fracture Toughness, MPa-m½
Fracture Toughness, MPa-m½
Fracture Toughness, MPa-m½
Machinability, %
Shear Modulus, GPa
Shear Strength, MPa
Electrical
Electrical Resistivity, ohm-cm
Thermal
CTE, linear 68°F, µm/m-°C
CTE, linear 250°C, µm/m-°C
Heat Capacity, J/g-°C
Thermal Conductivity, W/m-K
Melting Point, °C
Solidus, °C
Liquidus, °C
Table 10.
159
29
20
25
70
26.9
331
--------
--------
5.15E-06
--
--
23.6
25.2
0.96
130
-477
635
----477
---
----635
---
AA; 500,000,000 cycles completely reversed
stress; RR Moore machine/specimen
K(IC) in L-T Direction
K(IC) in S-L Direction
K(IC) in T-L Direction
0-100 Scale of Aluminum Alloys
AA; Typical
AA; Typical at 68°F
AA; Typical; Average over 68-212°F range.
Average over the range 20-300ºC
AA; Typical at 77°F
AA; Typical
AA; Typical
AA; Typical
Aluminum 7075 T-651 Rail Liner Material
Properties [After Ref. 2]
49
Armature: Aluminum 6063-T5
Date: 7/12/2005
MatWeb Data Sheet
Aluminum 6063-T5 UNS A96063; ISO AlMg0.5Si; Aluminium 6063-T5; AA6063-T5
KeyWords: UNS A96063; ISO AlMg0.5Si; Aluminium 6063-T5; AA6063-T5
SubCat: Aluminum Alloy, Nonferrous Metal, 6000 Series Aluminum Alloy, Metal
Material Notes: Data points with the AA note have been provided by the Aluminum Association, Inc. and are
Component
Value
Min
Max
Aluminum, Al
97.5
0.1
Chromium, Cr
Copper, Cu
0.1
Iron, Fe
0.35
Magnesium, Mg
0.45
0.9
Manganese, Mn
0.1
Silicon, Si
0.2
0.6
Titanium, Ti
0.1
Zinc, Zn
0.1
Value
Min
Max Comment
Properties
Physical
Density, g/cc
2.7
--AA; Typical
Mechanical
Hardness, Brinell
60
--AA; Typical; 500 g load; 10 mm ball
Hardness, Knoop
83
--Converted from Brinell Hardness Value
Hardness, Vickers
70
--Converted from Brinell Hardness Value
Ultimate Tensile Strength, MPa
186
--AA; Typical
Tensile Yield Strength, MPa
145
--AA; Typical
Elongation at Break, %
12
--AA; Typical; 1/16 in. (1.6 mm) Thickness
AA; Typical; Average of tension and
compression. Compression modulus is about
Modulus of Elasticity, GPa
68.9
--2% greater than tensile modulus.
Poissons Ratio
0.33
--AA; 500,000,000 cycles completely reversed
Fatigue Strength, MPa
68.9
--stress; RR Moore machine/specimen
Shear Modulus, GPa
25.8
--Shear Strength, MPa
117
--AA; Typical
Electrical
Electrical Resistivity, ohm-cm
3.16E-06
--AA; Typical at 68°F
Thermal
CTE, linear 68°F, µm/m-°C
23.4
--AA; Typical; Average over 68-212°F range.
CTE, linear 250°C, µm/m-°C
25.6
--Average over the range 20-300ºC
Heat Capacity, J/g-°C
0.9
--Thermal Conductivity, W/m-K
209
--AA; Typical at 77°F
AA; Typical range based on typical composition
for wrought products 1/4 inch thickness or
Melting Point, °C
-616
654 greater
Solidus, °C
616
--AA; Typical
Liquidus, °C
654
--AA; Typical
Processing
Annealing Temperature, °C
413
--hold at temperature for 2 to 3 hr; cool at 50 °F
Solution Temperature, °C
521
--Aging Temperature, °C
204
--hold at temperature for 1 hr
Aging Temperature, °C
182
--hold at temperature for 1 hr
Table 11.
Aluminum 6063 T-5 Armature Material
Properties [After Ref. 2]
50
Containment: G-11 FR-5 Glass-reinforced epoxy
G-11 NEMA Grade FR5
Glass reinforced, high temperature epoxy, laminate
Tensile Strength
lengthwise, PSI
crosswise, PSI
40,000
35,000
flatwise, PSI
edgewise, PSI
60,000
35,000
lengthwise, PSI
crosswise, PSI
55,000
45,000
6
2.7
2.2
19,000
Compressive Strength
Flexural Strength
Modulus of Elasticity in flex
lengthwise, PSI x 10
6
crosswise, PSI x 10
Shear Strength, PSI
IZOD Impact
flatwise, ft lb per inch of notch
edgewise, ft lb per inch of notch
Rockwell Hardness M scale
Specific Gravity
Coefficient of Thermal Expansion
cm/cm/ deg C x 10
-5
7
5.5
110
1.82
0.9
Water Absorption
.062" thick, % per 24 hrs
.125" thick, % per 24 hrs
.500" thick, % per 24 hrs
0.25
0.15
0.1
.062" thick
.125" thick
500
400
Dielectric Strength, volt/mil
perpendicular to laminations; short
Dissipation Factor
condition A, 1 megacycle
0.025
condition A, 1 megacycle
5.2
Dielectric Constant
Insulation Resistance
Condition:
96 hours at 90%
relative humidity
(in mega ohms)
200,000
Flame Resistance
94V-0
Underwriter Labs, Classification
1,600
Bond Strength, in lbs
Max Continuous Operating Temperature All Phenolics can withstand -100º F
300
Approximate degrees F
sheet mil spec:
Mil-I-24768 / _ _
28
Table 12.
G-11 FR-5 Containment Material Properties
[After Ref 10]
51
Insulator: CoorsTek AD-96 alumina ceramic
AD-96 Alumina Material Properties
Trade Name: AD-96
Composition: Nominal 96% Al2O3
2/23/2006
Color: White
Units
gm/cc
Microns
%
--
Value
3.72
6
0
0
358 (52)
GPa (psi x 10 )
ASTM-F417
303 (44)
--
ASTM-C848
0.21
ASTM-C773
2068 (300)
Property
Density
Crystal Size
Water Absorption
Gas Permeability
Flexural Strength (MOR), 20 degrees C
Elastic Modulus, 20 degrees C
Test
ASTM-C20
Thin-Section
ASTM-373
-6
Poisson's Ratio, 20 degrees C
3
Compressive Strenght
MPa(psi x 10 )
Hardness
GPa(kg/mm )
KNOOP 1000 gm
Rockwell 45 N
11.5 (1175)
78
3
ACMA TEST #4
NOTCHED BEAM
ASTM-C408
221 (32)
5-Apr
24.7
1 x 10 /degrees
C
J/kg*K
ASTM-C372
ASTM-E1269
8.2
880
degrees C
NOTE 3
250
degrees C
ac-kV/mm
(acV/mil)
25 degrees C
25 degrees C
ohm-cm
ohm-cm
ohm-cm
---
NO-LOAD COND.
1700
ASTM-D116
ASTM-D150
ASTM-D2520
ASTM-D1829
ASTM-D1829
ASTM-D1829
Note 4
Note 4
8.3 (210)
9
0.0002
14
>10
9
4 x 10
6
1 x 10
0.5
0.6
2
Tensile Strength, 25 degrees C
Fracture Toughness K(Ic)
Thermal Conductivity, 20 degrees C
Coefficient of Thermal Expansion, 25-1000
degrees C
Specific Heat, 100 degrees C
MPa (psi x 10 )
1/2
Mpa m
Wm degrees K
-6
Thermal Shock Resistance, (delta)Tc
Maximum Use Temperature
Dielectric Stength
Dielectric Constant, 1MHz
Dielectric Loss (tan delta) 1MHz
Volume Resistivity
25 degrees C
500 degrees C
1000 degrees C
Impingement
Rubbing
Table 13.
Ceramic Insulator Material Properties [After
Ref. 11]
52
Augmenting Rail Insulator: Mylar (polyester)
Table 14.
Mylar Film Insulator Material Properties
[After Ref. 12]
53
THIS PAGE INTENTIONALLY LEFT BLANK
54
APPENDIX B. PRODUCTION DRAWINGS
Top Containment Half
Figure 14.
Top Containment Half
55
Bottom Containment Half
Figure 15.
Bottom Containment Half
56
Solid Primary Conductor Rails
Figure 16.
Solid Primary Conductor Rails
57
Slotted Primary Conductor Rails
Figure 17.
Slotted Primary Conductor Rails
58
Ceramic Insulator
Figure 18.
Ceramic Insulators
59
Augmented Rails, Rail liners, and Spacer
Figure 19.
Augmented Rails, Rail liners, and Spacer
60
Augmenting Conductor Components
Figure 20.
Augmenting Conductor Components
61
External Conductor Connectors and Muzzle Shunt
Figure 21.
External Conductor Connectors and Muzzle
Shunt
62
Full Conductor Assembly
Figure 22.
Full Conductor Assembly
63
Full Assembly CAD Model and Finished Result
Figure 23.
Figure 24.
Full CAD Assembly with Loader and Muzzle
Shunt
Full Assembled Railgun with Loader
64
Basic U-shape Armature
Figure 25.
Basic U-Shape Armature
65
Flared M-shape Armature
Figure 26.
Flared M-shape Armature
66
Square M-shape Armature
Figure 27.
Square M-shape Armature
67
Altered U-shape Armature with Center Hollow
Figure 28.
Altered U-shape Armature with Center Hollow
68
Railgun Mounting Base
Figure 29.
Railgun Mounting Base
The mounting base is fabricated from a 1.5” thick slab
of insulating phenolic.
bolts
extend
through
the
Three pairs of the containment
base
for
mounting.
The
base
itself is then bolted directly to the firing line table.
69
THIS PAGE INTENTIONALLY LEFT BLANK
70
APPENDIX C.
A.
MODELING
KERRISK’S METHOD SPREADSHEETS [3]
Inductance Gradient Calculations for Solid and Non-
slotted Rail Geometries
Kerrisk's Method for L' Determination - Los Alamos National Laboratory 1981 [Ref.2]
L' = [A + B*ln(1 + a1*(w/h) + a2*(w/h)*(s/h))*ln(b1 + b2*(s/h) + b3*(w/h) + b4*(s/h)*(w/h)]
s = bore spacing(mm)
h = rail height (mm)
w = rail width (mm)
( NOTE: Augmented configurations apply gain factor of 1.55 over their respective non-augmented L' )
Solid Rails
Slotted Rails
Solid Augmented
Slotted Augmented
A
0.440641
0.440641
0.440641
0.440641
B
-0.07771
-0.07771
-0.07771
-0.07771
a1
3.397143
3.397143
3.397143
3.397143
a2
-0.06603
-0.06603
-0.06603
-0.06603
b1
1.07719
1.07719
1.07719
1.07719
b2
2.743651
2.743651
2.743651
2.743651
b3
0.022093
0.022093
0.022093
0.022093
b4
0.263739
0.263739
0.263739
0.263739
s
19
19
19
19
h
50.8
25.4
50.8
25.4
w
9.5
9.5
9.5
9.5
s/h
0.374015748
0.748031496
0.374015748
0.748031496
w/h
0.187007874
0.374015748
0.187007874
0.374015748
Solid Rail L'
Solid augmented L'
Slotted Augmented L'
Slotted L'
0.30368
0.44051
0.47070
0.68279
Table 15.
Kerrisk’s Method and Augmentation Adjusted
Inductance Gradient (L’) Calculations
Table 14 input parameters of bore spacing (s), rail
height (h), and rail width (w) are demonstrated in Figure
28 below.
h
s
w
Figure 30.
Kerrisk’s Method Rail Parameters [After Ref.
2]
71
B.
PARAMETER BASED MODELING [7]
1500 m/s Solid Non-Augmented Parameter Modeling
Solid Rail Non-Augmented Parameter Model
µH/m
L'
0.30368
Target velocity:
Projectile mass:
Effective length:
Armature height:
t = 2x/(delta v)
2
aavg =2x/(t )
Avg. Current: Iavg = (2ma/L' )
0.5
Peak Current
Ipeak = (Iavg2/0.7)0.5
Linear current density:
Ipeak' = Ipeak / armature height
Electrical Action: G=2mv/L'
∆T=
(ρe/ρmCp)*(G/A2)
1500
11.4
50
19
t (ms)
m/s
grams
cm
mm
0.67
2.25E+06
aavg (m/s )
225
aavg (kG's)
411.01
k-Amps
491.25
k-Amps
25.86
(kA/mm)
1.13E+08
Amp s
Electrical Action is a measure of heating due
to current flow
40.00
Kelvin (K)
Based on thumbrule of a delta T of 40 K
across the rail due to resistive heating, where
A = conductor cross-sectional area
2
2
Conductor Area =
2
[(ρe/ρmCp)(G/∆Τ)]0.5
118.65
mm
Required rail width (mm)
Actual rail width
(1/4" rail + 1/8" rail liner)
Lorentz Force at peak current:
6.24
mm
9.53
mm
36642.86
N
F = (1/2)L'Ipeak
2
2
2
m
0.000361
Bore Area (m )
Base Pressure = F/A
102
Mpa
Repulsion force per unit length
(Base Pressure x Bore height)
1.93
MN/m
Grade 2 SAE J429 3/8" diameter stainless steel bolts
Minimum Yield Strength
Individual bolt area required to avoid exceeding Yield Strength for
static longitudinal repulsion force along entire 24" rail length
distributed between 22 bolts
Minimum Bolt Diameter Required
Actual Bolt Diameter
Table 16.
Assume: average acceleration is 70% of
peak acceleration and this ratio is
2
proportional to (Iavg
/Ipeak2)
Note: linear current densities > 45 kA/mm are
regarded as unstable for railgun design
The expression (ρe/ρmCp) is a ratio of
electrical resistivity to the product of mass
density and specific heat capacity, a typical
value for the ratio for copper is
0.005
2
4
(K/Amp s)/mm .
8238
lbf
0.56
14.73
square inches
ksi
11.05
kip/in
57000
psi
0.21
square inches
0.519
0.375
inches
inches
1500 m/s Solid Non-Augmented Parameter Model
72
1500 m/s Slotted Non-Augmented Parameter Modeling
Slotted Rail Non-Augmented Parameter Model
µH/m
L'
0.44051
Target velocity:
Projectile mass:
Effective length:
Armature height:
t = 2x/(delta v)
1500
11.4
50
19
t (ms)
m/s
grams
cm
mm
0.67
2.25E+06
aavg (m/s )
225
aavg (kG's)
341.26
k-Amps
407.88
k-Amps
21.47
(kA/mm)
7.76E+07
Amp s
40.00
Kelvin (K)
[(ρe/ρmCp)(G/∆Τ)]0.5
98.51
mm
Required rail width (mm)
Actual rail width
(1/4" rail + 1/8" rail liner)
Lorentz Force at peak current:
5.18
mm
9.53
mm
36642.86
N
2
aavg =2x/(t )
Avg. Current: Iavg = (2ma/L' )
0.5
Peak Current
Ipeak = (Iavg2/0.7)0.5
Linear current density:
Ipeak' = Ipeak / armature height
Electrical Action: G=2mv/L'
∆T=
(ρe/ρmCp)*(G/A2)
2
2
Conductor Area =
F = (1/2)L'Ipeak
2
2
2
2
m
Bore Area (m )
0.000361
Base Pressure = F/A
102
Mpa
Repulsion force per unit length
1.93
(Base Pressure x Bore height)
MN/m
Grade 2 SAE J429 3/8" diameter stainless steel bolts
Minimum Yield Strength
Individual bolt area required to avoid exceeding Yield Strength for
static longitudinal repulsion force along entire 24" rail length
distributed between 22 bolts
Minimum Bolt Diameter Required
Actual Bolt Diameter
Table 17.
Assume: average acceleration is 70% of
peak acceleration and this ratio is
2
proportional to (Iavg
/Ipeak2)
Note: linear current densities > 45 kA/mm are
regarded as unstable for railgun design
Electrical Action is a measure of heating due
to current flow
Based on thumbrule of a delta T of 40 K
across the rail due to resistive heating, where
The expression (ρe/ρmCp) is a ratio of
electrical resistivity to the product of mass
density and specific heat capacity, a typical
value for the ratio for copper is
0.005
2
4
(K/Amp s)/mm .
8238
lbf
0.56
14.73
square inches
ksi
11.05
kip/in
57000
psi
0.21
square inches
0.519
0.375
inches
inches
1500 m/s Slotted Non-Augmented Parameter
Model
73
1500 m/s Solid Augmented Parameter Modeling
L'
0.47070
Target velocity:
Projectile mass:
Effective length:
Armature height:
t = 2x/(delta v)
Solid Rail Augmented Parameter Model
µH/m
1500
11.4
50
19
t (ms)
m/s
grams
cm
mm
0.67
2.25E+06
aavg (m/s )
225
aavg (kG's)
330.13
k-Amps
394.58
k-Amps
20.77
(kA/mm)
7.27E+07
Amp s
40.00
Kelvin (K)
[(ρe/ρmCp)(G/∆Τ)]0.5
95.30
mm
Required rail width (mm)
Actual rail width
(1/4" rail + 1/8" rail liner)
Lorentz Force at peak current:
5.02
mm
9.53
mm
36642.86
N
2
aavg =2x/(t )
Avg. Current: Iavg = (2ma/L' )
0.5
Peak Current
Ipeak = (Iavg2/0.7)0.5
Linear current density:
Ipeak' = Ipeak / armature height
Electrical Action: G=2mv/L'
∆T=
(ρe/ρmCp)*(G/A2)
2
2
Conductor Area =
F = (1/2)L'Ipeak
2
2
2
2
m
Bore Area (m )
0.000361
Base Pressure = F/A
102
Mpa
Repulsion force per unit length
1.93
(Base Pressure x Bore height)
MN/m
Grade 2 SAE J429 3/8" diameter stainless steel bolts
Minimum Yield Strength
Individual bolt area required to avoid exceeding Yield Strength for
static longitudinal repulsion force along entire 24" rail length
distributed between 22 bolts
Grade 2 Minimum Bolt Diameter Required
Grade 8 SAE J429 3/8" diameter stainless steel bolts
Minimum Yield Strength
Individual bolt area required to avoid exceeding Yield Strength for
static longitudinal repulsion force along 2" rail length distributed
between 4 bolts
Grade 8 Minimum Bolt Diameter Required
Actual Bolt Diameter
Table 18.
Assume: average acceleration is 70% of
peak acceleration and this ratio is
2
proportional to (Iavg
/Ipeak2)
Note: linear current densities > 45 kA/mm are
regarded as unstable for railgun design
Electrical Action is a measure of heating due
to current flow
Based on thumbrule of a delta T of 40 K
across the rail due to resistive heating, where
The expression (ρe/ρmCp) is a ratio of
electrical resistivity to the product of mass
density and specific heat capacity, a typical
value for the ratio for copper is
0.005
2
4
(K/Amp s)/mm .
8238
lbf
0.56
14.73
square inches
ksi
11.05
kip/in
57000
psi
0.21
square inches
0.519
inches
130000
psi
0.09
square inches
0.344
0.375
inches
inches
1500 m/s Solid Augmented Parameter Model
74
1500 m/s Slotted Augmented Parameter Modeling
Slotted Rail Augmented Parameter Model
µH/m
0.68279
L'
Target velocity:
Projectile mass:
Effective length:
Armature height:
t = 2x/(delta v)
2
aavg =2x/(t )
Avg. Current: Iavg = (2ma/L' )
0.5
Peak Current
Ipeak = (Iavg2/0.7)0.5
Linear current density:
Ipeak' = Ipeak / armature height
Electrical Action: G=2mv/L'
∆T=
(ρe/ρmCp)*(G/A2)
1500
11.4
50
19
t (ms)
m/s
grams
cm
mm
0.67
2.25E+06
aavg (m/s )
225
aavg (kG's)
274.10
k-Amps
327.62
k-Amps
17.24
(kA/mm)
5.01E+07
Amp s
40.00
Kelvin (K)
2
2
Conductor Area =
2
[(ρe/ρmCp)(G/∆Τ)]0.5
79.13
Required rail width (mm)
Actual rail width
(1/4" rail + 1/8" rail liner)
Lorentz Force at peak current:
4.16
mm
9.53
mm
36642.86
N
F = (1/2)L'Ipeak
2
mm
2
2
m
Bore Area (m )
0.000361
Base Pressure = F/A
102
Mpa
Repulsion force per unit length
1.93
(Base Pressure x Bore height)
MN/m
Grade 2 SAE J429 3/8" diameter stainless steel bolts
Minimum Yield Strength
Individual bolt area required to avoid exceeding Yield Strength for
static longitudinal repulsion force along entire 24" rail length
distributed between 22 bolts
Grade 2 Minimum Bolt Diameter Required
Grade 8 SAE J429 3/8" diameter stainless steel bolts
Minimum Yield Strength
Individual bolt area required to avoid exceeding Yield Strength for
static longitudinal repulsion force along 2" rail length distributed
between 4 bolts
Grade 8 Minimum Bolt Diameter Required
Actual Bolt Diameter
Table 19.
Assume: average acceleration is 70% of
peak acceleration and this ratio is
2
proportional to (Iavg
/Ipeak2)
Note: linear current densities > 45 kA/mm are
regarded as unstable for railgun design
Electrical Action is a measure of heating due
to current flow
Based on thumbrule of a delta T of 40 K
across the rail due to resistive heating, where
The expression (ρe/ρmCp) is a ratio of
electrical resistivity to the product of mass
density and specific heat capacity, a typical
value for the ratio for copper is
0.005
2
4
(K/Amp s)/mm .
8238
lbf
0.56
14.73
square inches
ksi
11.05
kip/in
57000
psi
0.21
square inches
0.519
inches
130000
psi
0.09
square inches
0.344
0.375
inches
inches
1500 m/s Slotted Augmented Parameter Model
75
265 m/s Solid Augmented Parameter Modeling
Solid Rail Augmented Parameter Model for Experimental Velocity Result: 265 m/s
µH/m
L'
0.47070
Target velocity:
Projectile mass:
Effective length:
Armature height:
t = 2x/(delta v)
265
11.4
50
19
t (ms)
m/s
grams
cm
mm
3.77
7.02E+04
aavg (m/s )
7.0225
aavg (kG's)
58.32
k-Amps
69.71
k-Amps
3.67
(kA/mm)
1.28E+07
Amp s
40.00
Kelvin (K)
[(ρe/ρmCp)(G/∆Τ)]0.5
40.06
mm
Required rail width (mm)
Actual rail width
(1/4" rail + 1/8" rail liner)
Lorentz Force at peak current:
2.11
mm
9.53
mm
1143.66
N
2
aavg =2x/(t )
Avg. Current: Iavg = (2ma/L' )
0.5
Peak Current
Ipeak =
(Iavg2/0.7)0.5
Linear current density:
Ipeak' = Ipeak / armature height
Electrical Action: G=2mv/L'
∆T=
(ρe/ρmCp)*(G/A2)
2
2
Conductor Area =
F = (1/2)L'Ipeak
2
2
2
2
m
0.000361
Bore Area (m )
Base Pressure = F/A
3
Mpa
Repulsion force per unit length
0.06
(Base Pressure x Bore height)
MN/m
Grade 2 SAE J429 3/8" diameter stainless steel bolts
Minimum Yield Strength
Individual bolt area required to avoid exceeding Yield Strength for
static longitudinal repulsion force along entire 24" rail length
distributed between 22 bolts
Grade 2 Minimum Bolt Diameter Required
Grade 8 SAE J429 3/8" diameter stainless steel bolts
Minimum Yield Strength
Individual bolt area required to avoid exceeding Yield Strength for
static longitudinal repulsion force along 2" rail length distributed
between 4 bolts
Grade 8 Minimum Bolt Diameter Required
Actual Bolt Diameter
Table 20.
Assume: average acceleration is 70% of
peak acceleration and this ratio is
2
proportional to (Iavg
/Ipeak2)
Note: linear current densities > 45 kA/mm are
regarded as unstable for railgun design
Electrical Action is a measure of heating due
to current flow
Based on thumbrule of a delta T of 40 K
across the rail due to resistive heating, where
The expression (ρe/ρmCp) is a ratio of
electrical resistivity to the product of mass
density and specific heat capacity, a typical
value for the ratio for copper is
0.005
2
4
(K/Amp s)/mm .
257
lbf
0.56
0.46
square inches
ksi
0.34
kip/in
57000
psi
0.01
square inches
0.092
inches
130000
psi
0.00
square inches
0.061
0.375
inches
inches
265 m/s Solid Augmented Parameter Model
76
290 m/s Slotted Augmented Parameter Model
Slotted Rail Augmented Parameter Model for Experimental Velocity Result: 290 m/s
µH/m
L'
0.68279
Target velocity:
Projectile mass:
Effective length:
Armature height:
t = 2x/(delta v)
2
aavg =2x/(t )
Avg. Current: Iavg = (2ma/L' )
0.5
Peak Current
Ipeak = (Iavg2/0.7)0.5
Linear current density:
Ipeak' = Ipeak / armature height
Electrical Action: G=2mv/L'
∆T=
(ρe/ρmCp)*(G/A2)
290
11.4
50
19
t (ms)
m/s
grams
cm
mm
3.45
8.41E+04
aavg (m/s )
8.41
aavg (kG's)
52.99
k-Amps
63.34
k-Amps
3.33
(kA/mm)
9.68E+06
Amp s
40.00
Kelvin (K)
2
2
Conductor Area =
2
[(ρe/ρmCp)(G/∆Τ)]0.5
34.79
Required rail width (mm)
Actual rail width
(1/4" rail + 1/8" rail liner)
Lorentz Force at peak current:
1.83
mm
9.53
mm
1369.63
N
F = (1/2)L'Ipeak
2
mm
2
2
m
Bore Area (m )
0.000361
Base Pressure = F/A
4
Mpa
Repulsion force per unit length
0.07
(Base Pressure x Bore height)
MN/m
Grade 2 SAE J429 3/8" diameter stainless steel bolts
Minimum Yield Strength
Individual bolt area required to avoid exceeding Yield Strength for
static longitudinal repulsion force along entire 24" rail length
distributed between 22 bolts
Grade 2 Minimum Bolt Diameter Required
Grade 8 SAE J429 3/8" diameter stainless steel bolts
Minimum Yield Strength
Individual bolt area required to avoid exceeding Yield Strength for
static longitudinal repulsion force along 2" rail length distributed
between 4 bolts
Grade 8 Minimum Bolt Diameter Required
Actual Bolt Diameter
Table 21.
Assume: average acceleration is 70% of
peak acceleration and this ratio is
2
proportional to (Iavg
/Ipeak2)
Note: linear current densities > 45 kA/mm are
regarded as unstable for railgun design
Electrical Action is a measure of heating due
to current flow
Based on thumbrule of a delta T of 40 K
across the rail due to resistive heating, where
The expression (ρe/ρmCp) is a ratio of
electrical resistivity to the product of mass
density and specific heat capacity, a typical
value for the ratio for copper is
0.005
2
4
(K/Amp s)/mm .
308
lbf
0.56
0.55
square inches
ksi
0.41
kip/in
57000
psi
0.01
square inches
0.100
inches
130000
psi
0.00
square inches
0.066
0.375
inches
inches
290 m/s Slotted Augmented Parameter Model
77
Solid Non-Augmented Parameter Model for Peak Current,
Maximum Velocity for Grade 2 Bolt Diameter
Solid Rail Non-Augmented Parameter Model for Actual Grade 2 Bolt Design
µH/m
L'
0.30368
Target velocity:
Projectile mass:
Effective length:
Armature height:
t = 2x/(delta v)
2
aavg =2x/(t )
Avg. Current: Iavg = (2ma/L' )
0.5
Peak Current
Ipeak = (Iavg2/0.7)0.5
Linear current density:
Ipeak' = Ipeak / armature height
Electrical Action: G=2mv/L'
∆T=
(ρe/ρmCp)*(G/A2)
1085
11.4
50
19
t (ms)
m/s
grams
cm
mm
0.92
1.18E+06
aavg (m/s )
117.7225
aavg (kG's)
297.30
k-Amps
355.34
k-Amps
18.70
(kA/mm)
8.15E+07
Amp s
Electrical Action is a measure of heating due
to current flow
40.00
Kelvin (K)
Based on thumbrule of a delta T of 40 K
across the rail due to resistive heating, where
A = conductor cross-sectional area
2
2
Conductor Area =
2
[(ρe/ρmCp)(G/∆Τ)]0.5
100.91
mm
Required rail width (mm)
Actual rail width
(1/4" rail + 1/8" rail liner)
Lorentz Force at peak current:
5.31
mm
9.53
mm
19171.95
N
F = (1/2)L'Ipeak
2
2
2
m
0.000361
Bore Area (m )
Base Pressure = F/A
53
Mpa
Repulsion force per unit length
(Base Pressure x Bore height)
1.01
MN/m
Grade 2 SAE J429 3/8" diameter stainless steel bolts
Minimum Yield Strength
Individual bolt area required to avoid exceeding Yield Strength for
static longitudinal repulsion force along entire 24" rail length
distributed between 22 bolts
Grade 2 Minimum Bolt Diameter Required
Grade 8 SAE J429 3/8" diameter stainless steel bolts
Minimum Yield Strength
Individual bolt area required to avoid exceeding Yield Strength for
static longitudinal repulsion force along 2" rail length distributed
between 4 bolts
Grade 8 Minimum Bolt Diameter Required
Actual Bolt Diameter
Table 22.
Assume: average acceleration is 70% of
peak acceleration and this ratio is
2
proportional to (Iavg
/Ipeak2)
Note: linear current densities > 45 kA/mm are
regarded as unstable for railgun design
The expression (ρe/ρmCp) is a ratio of
electrical resistivity to the product of mass
density and specific heat capacity, a typical
value for the ratio for copper is
0.005
2
4
(K/Amp s)/mm .
4310
lbf
0.56
7.71
square inches
ksi
5.78
kip/in
57000
psi
0.11
square inches
0.375
inches
130000
psi
0.05
square inches
0.249
0.375
inches
inches
Parameter Estimate of Peak Current and Final
Velocity for 3/8” diameter Grade 2 Bolts
78
C.
CONSERVATION OF ENERGY INTEGRATION [4]
35 kJ Solid Non-Augmented Velocity Integration
Rail length as an integral function of velocity for solid/non-augmented input parameters:
∫ dx =
(
1
ln av 2 + bv + c
2a
⎡
⎛ 2av + b − b 2 − 4ac
1
⎢
ln ⎜
2a ⎢ b 2 − 4ac ⎜ 2av + b + b 2 − 4ac
⎝
⎣
)− b
⎞⎤
⎟⎥ + D
⎟⎥
⎠⎦
2
Table integral form: V = av + bv + c
Input Parameters:
Velocity (m/s)
mass (g)
0.0114
120
C (farads)
1.66E-03
121
L (Henries)
5.50E-06
122
R (ohms)
3.30E-03
123
Volts
6.50E+03
124
W 0 (J)
3.51E+04
125
First Term:
-9.17E+01
-9.13E+01
-9.08E+01
-9.03E+01
-8.98E+01
-8.92E+01
Second Term:
-6.23E+01
-6.28E+01
-6.32E+01
-6.37E+01
-6.43E+01
-6.48E+01
Required Rail Length (m):
0.12
0.13
0.13
0.14
0.14
0.15
126
127
128
129
130
-8.86E+01
-8.80E+01
-8.73E+01
-8.65E+01
-8.57E+01
-6.54E+01
-6.60E+01
-6.67E+01
-6.75E+01
-6.83E+01
0.16
0.16
0.17
0.18
0.19
-3.75E+04
131
-8.48E+01
-6.91E+01
0.20
1.44E+06
1.09E+04
132
133
-8.38E+01
-8.27E+01
-7.01E+01
-7.12E+01
0.21
0.23
Square Root (b - 4ac)
134
-8.14E+01
-7.25E+01
0.24
1.22E+03
135
-8.00E+01
-7.39E+01
0.26
1/Square Root(b - 4ac)
136
-7.82E+01
-7.57E+01
0.28
8.23E-04
D = Integration Constant:
154.17
137
138
139
-7.60E+01
-7.31E+01
-6.87E+01
-7.79E+01
-8.08E+01
-8.50E+01
0.31
0.35
0.40
140
-6.01E+01
-9.36E+01
0.51
141
-5.54E+01
-9.82E+01
0.57
L' (H/m)
3.04E-07
Integral factors:
a = -L'/L
-5.52E-02
b= -2R/L
-1.20E+03
c =(L' W o)/(mL)
1.70E+05
4ac
2
b
b / 2a
2
2
Table 23.
35 kJ Velocity Integral, Solid NonAugmented.
79
35 kJ Slotted Non-Augmented Velocity Integration
Rail length as an integral function of velocity for slotted/non-augmented input parameters:
∫ dx =
(
1
ln av 2 + bv + c
2a
⎡
⎛ 2av + b − b 2 − 4ac
1
⎢
ln ⎜
2a ⎢ b 2 − 4ac ⎜ 2av + b + b 2 − 4ac
⎝
⎣
)− b
⎞⎤
⎟⎥ + D
⎟
⎠ ⎦⎥
2
Table integral form: V = av + bv + c
Input Parameters:
Velocity (m/s)
mass (g)
0.0114
160
C (farads)
1.66E-03
162
L (Henries)
5.50E-06
164
R (ohms)
3.30E-03
166
Volts
6.50E+03
168
W 0 (J)
3.51E+04
170
L' (H/m)
4.41E-07
Integral factors:
a = -L'/L
-8.01E-02
b= -2R/L
-1.20E+03
c =(L' W o)/(mL)
2.46E+05
4ac
172
174
176
178
180
First Term:
-6.78E+01
-6.75E+01
-6.72E+01
-6.69E+01
-6.65E+01
-6.62E+01
Second Term:
-3.58E+01
-3.61E+01
-3.64E+01
-3.67E+01
-3.71E+01
-3.74E+01
Required Rail Length (m):
0.13
0.13
0.14
0.15
0.15
0.16
-6.58E+01
-6.53E+01
-6.49E+01
-6.44E+01
-6.39E+01
-3.78E+01
-3.82E+01
-3.87E+01
-3.91E+01
-3.97E+01
0.17
0.18
0.19
0.20
0.21
-7.89E+04
182
-6.33E+01
-4.02E+01
0.23
1.44E+06
7.49E+03
184
186
-6.27E+01
-6.19E+01
-4.08E+01
-4.15E+01
0.24
0.26
Square Root (b - 4ac)
188
-6.11E+01
-4.23E+01
0.28
1.23E+03
190
-6.02E+01
-4.32E+01
0.30
1/Square Root(b - 4ac)
192
-5.91E+01
-4.43E+01
0.33
8.11E-04
D = Integration Constant:
103.74
194
196
-5.78E+01
-5.62E+01
-4.55E+01
-4.72E+01
0.36
0.40
198
200
-5.39E+01
-5.03E+01
-4.94E+01
-5.29E+01
0.46
0.55
202
-4.09E+01
-6.20E+01
0.80
2
b
b / 2a
2
2
Table 24.
35 kJ Velocity Integral, Slotted NonAugmented.
80
35 kJ Solid Augmented Velocity Integration
Rail length as an integral function of velocity for solid/augmented input parameters:
∫ dx =
(
1
ln av 2 + bv + c
2a
⎡
⎛ 2av + b − b 2 − 4ac
1
⎢
ln ⎜
2a ⎢ b 2 − 4ac ⎜ 2av + b + b 2 − 4ac
⎝
⎣
)− b
⎞⎤
⎟⎥ + D
⎟⎥
⎠⎦
2
Table integral form: V = av + bv + c
Input Parameters:
Velocity (m/s)
mass (g)
0.0114
150
C (farads)
1.66E-03
152
L (Henries)
5.50E-06
154
R (ohms)
3.30E-03
156
Volts
6.50E+03
158
W 0 (J)
3.51E+04
160
First Term:
-6.61E+01
-6.59E+01
-6.57E+01
-6.55E+01
-6.53E+01
-6.51E+01
Second Term:
-3.05E+01
-3.07E+01
-3.09E+01
-3.11E+01
-3.12E+01
-3.14E+01
Required Rail Length (m):
0.08
0.09
0.09
0.09
0.10
0.10
162
164
166
168
170
-6.49E+01
-6.47E+01
-6.44E+01
-6.42E+01
-6.40E+01
-3.17E+01
-3.19E+01
-3.21E+01
-3.23E+01
-3.26E+01
0.11
0.11
0.12
0.12
0.13
-9.01E+04
172
-6.37E+01
-3.28E+01
0.13
1.44E+06
7.01E+03
174
176
-6.34E+01
-6.31E+01
-3.31E+01
-3.34E+01
0.14
0.15
Square Root (b - 4ac)
178
-6.28E+01
-3.36E+01
0.16
1.24E+03
L' (H/m)
4.71E-07
Integral factors:
a = -L'/L
-8.56E-02
b= -2R/L
-1.20E+03
c =(L' W o)/(mL)
2.63E+05
4ac
2
b
b / 2a
2
180
-6.25E+01
-3.40E+01
0.16
1/Square Root(b - 4ac)
182
-6.22E+01
-3.43E+01
0.17
8.08E-04
D = Integration Constant:
96.65
184
186
188
190
192
194
196
198
200
202
204
206
208
-6.18E+01
-6.15E+01
-6.11E+01
-6.06E+01
-6.02E+01
-5.97E+01
-5.91E+01
-5.85E+01
-5.78E+01
-5.70E+01
-5.61E+01
-5.51E+01
-5.38E+01
-3.46E+01
-3.50E+01
-3.54E+01
-3.58E+01
-3.63E+01
-3.67E+01
-3.73E+01
-3.79E+01
-3.86E+01
-3.93E+01
-4.02E+01
-4.12E+01
-4.25E+01
0.18
0.19
0.20
0.21
0.22
0.24
0.25
0.27
0.29
0.31
0.34
0.37
0.40
210
212
-5.21E+01
-4.98E+01
-4.41E+01
-4.64E+01
0.45
0.52
214
-4.58E+01
-5.02E+01
0.64
2
Table 25.
35 kJ Velocity Integral, Solid Augmented.
81
35 kJ Slotted Augmented Velocity Integration
Rail length as an integral function of velocity for slotted/augmented input parameters:
∫ dx =
(
1
ln av 2 + bv + c
2a
⎡
⎛ 2av + b − b 2 − 4ac
1
⎢
ln ⎜
2a ⎢ b 2 − 4ac ⎜ 2av + b + b 2 − 4ac
⎝
⎣
)− b
⎞⎤
⎟⎥ + D
⎟⎥
⎠⎦
2
Table integral form: V = av + bv + c
Input Parameters:
Velocity (m/s)
mass (g)
0.0114
150
C (farads)
1.66E-03
155
L (Henries)
5.50E-06
160
R (ohms)
3.30E-03
165
Volts
6.50E+03
170
W 0 (J)
3.51E+04
175
First Term:
-4.91E+01
-4.90E+01
-4.89E+01
-4.87E+01
-4.86E+01
-4.85E+01
Second Term:
-1.57E+01
-1.59E+01
-1.60E+01
-1.61E+01
-1.63E+01
-1.64E+01
Required Rail Length (m):
0.05
0.05
0.05
0.06
0.06
0.07
180
185
190
195
200
-4.83E+01
-4.82E+01
-4.80E+01
-4.78E+01
-4.76E+01
-1.65E+01
-1.67E+01
-1.69E+01
-1.70E+01
-1.72E+01
0.07
0.08
0.09
0.09
0.10
-1.90E+05
205
-4.74E+01
-1.74E+01
0.11
1.44E+06
4.83E+03
210
215
-4.72E+01
-4.70E+01
-1.76E+01
-1.78E+01
0.12
0.12
Square Root (b - 4ac)
220
-4.68E+01
-1.80E+01
0.13
1.28E+03
L' (H/m)
6.83E-07
Integral factors:
a = -L'/L
-1.24E-01
b= -2R/L
-1.20E+03
c =(L' W o)/(mL)
3.82E+05
4ac
2
b
b / 2a
2
225
-4.66E+01
-1.82E+01
0.14
1/Square Root(b - 4ac)
230
-4.63E+01
-1.84E+01
0.16
7.83E-04
D = Integration Constant:
64.93
235
240
245
250
255
260
265
270
275
280
285
-4.61E+01
-4.58E+01
-4.55E+01
-4.52E+01
-4.48E+01
-4.44E+01
-4.40E+01
-4.35E+01
-4.29E+01
-4.23E+01
-4.15E+01
-1.87E+01
-1.90E+01
-1.92E+01
-1.96E+01
-1.99E+01
-2.03E+01
-2.07E+01
-2.12E+01
-2.17E+01
-2.23E+01
-2.30E+01
0.17
0.18
0.20
0.21
0.23
0.25
0.27
0.30
0.33
0.36
0.41
290
295
-4.05E+01
-3.93E+01
-2.39E+01
-2.51E+01
0.46
0.53
300
305
310
-3.74E+01
-3.37E+01
-3.07E+01
-2.69E+01
-3.03E+01
-3.32E+01
0.64
0.86
1.03
2
Table 26.
35 kJ Velocity Integral, Slotted Augmented.
82
83 kJ Slotted Augmented Velocity Integration
Rail length as an integral function of velocity for slotted/augmented input parameters:
∫ dx =
(
1
ln av 2 + bv + c
2a
⎡
⎛ 2av + b − b 2 − 4ac
ln ⎜
2
2
⎜
⎣ b − 4ac ⎝ 2av + b + b − 4ac
) − 2ba ⎢⎢
1
⎞⎤
⎟⎥ + D
⎟
⎠ ⎦⎥
2
Table integral form: V = av + bv + c
Input Parameters:
Velocity (m/s)
mass (g)
0.0114
350
C (farads)
1.66E-03
355
L (Henries)
5.50E-06
360
R (ohms)
3.30E-03
365
Volts
1.00E+04
370
W 0 (J)
8.30E+04
375
First Term:
-5.26E+01
-5.25E+01
-5.25E+01
-5.24E+01
-5.24E+01
-5.23E+01
Second Term:
-1.20E+01
-1.21E+01
-1.21E+01
-1.22E+01
-1.22E+01
-1.23E+01
Required Rail Length (m):
0.10
0.33
0.34
0.34
0.34
0.35
380
385
390
395
400
-5.22E+01
-5.22E+01
-5.21E+01
-5.21E+01
-5.20E+01
-1.23E+01
-1.24E+01
-1.24E+01
-1.25E+01
-1.26E+01
0.35
0.36
0.36
0.37
0.37
-4.49E+05
405
-5.19E+01
-1.26E+01
0.38
1.44E+06
4.83E+03
410
415
-5.19E+01
-5.18E+01
-1.27E+01
-1.27E+01
0.38
0.39
Square Root (b - 4ac)
420
-5.17E+01
-1.28E+01
0.39
1.37E+03
L' (H/m)
6.83E-07
Integral factors:
a = -L'/L
-1.24E-01
b= -2R/L
-1.20E+03
c =(L' W o)/(mL)
9.04E+05
4ac
2
b
b / 2a
2
425
-5.17E+01
-1.29E+01
0.40
1/Square Root(b - 4ac)
430
-5.16E+01
-1.29E+01
0.40
7.28E-04
D = Integration Constant:
64.93
435
440
445
450
455
460
465
470
475
480
485
490
-5.15E+01
-5.14E+01
-5.14E+01
-5.13E+01
-5.12E+01
-5.11E+01
-5.10E+01
-5.10E+01
-5.09E+01
-5.08E+01
-5.07E+01
-5.06E+01
-1.30E+01
-1.31E+01
-1.31E+01
-1.32E+01
-1.33E+01
-1.34E+01
-1.34E+01
-1.35E+01
-1.36E+01
-1.37E+01
-1.38E+01
-1.38E+01
0.41
0.42
0.42
0.43
0.44
0.44
0.45
0.46
0.46
0.47
0.48
0.49
495
-5.05E+01
-1.39E+01
0.50
500
505
510
-5.04E+01
-5.03E+01
-5.02E+01
-1.40E+01
-1.41E+01
-1.42E+01
0.51
0.52
0.53
2
Table 27.
83 kJ Velocity Integral, Slotted Augmented.
83
D.
STRUCTURAL DESIGN VERIFICATION
Rail containment deflection is modeled based on static
loading from 500 kA peak current conditions predicted for
the solid non-augmented configuration in Table 15.
railgun
test
simplified
platform
by
considering
The
cross-sectional
geometry
is
the
primary,
and
rail
liner,
augmenting conducting rails as a single solid oxygen free
copper conducting bar.
The homogenous beam bending model
considers only the 1-3/8” G-11 material from the outer face
of
the
augmenting
containment.
geometry
conductor
rail
to
the
top
of
the
The resultant combined rail and containment
contributing
to
the
beam
bending
model
are
represented in Figure 30.
G-11
4-3/4”
1-3/8”
5/8”
Figure 31.
OFE Copper
2”
Simplified Beam Geometry (Not to scale)
The transformed geometry after expressing the copper
in terms of G-11 for purposes of calculated the rectangular
moment of inertia is depicted by Figure 31.
xG −11 = 4.75"
yG-11=1.375”
YG-11
yc=0.625”
y
Ycentroid
Yc
xc = ηc i2" = 12.4"
Figure 32.
Transformed Homogenous Beam Geometry (Not to
Scale)
84
The centroid and moment of inertia for the transformed
geometry of Figure 31 are based on the following equations.
⎛ y A + yG −11 AG −11 ⎞
Ycentroid = ⎜ c c
⎟
Ac + AG −11
⎝
⎠
2⎤
⎡1
I = ∑ ⎢ xi yi3 + Ai Ycentroid − Yi ⎥
⎣12
⎦
Table
27
lists
the
values
used
in
the
previous
equations to calculate the rectangular moment of inertia
for the transformed cross-section.
Centroid and Moment of Inertia Calculations for Equivalent Homogenous Beam
Section Elasticity Modulus (psi) Area ( in2 ) y (in) yA ( in3 ) Centroid ( in ) Moment of Inertia ( in4 )
Copper
1.67E+07
7.75
0.1875 1.453
0.6448
8.370
G-11
2.70E+06
6.5313 1.1875 7.756
Table 28.
Transformed Geometry Moment of Inertia
Calculation
85
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86
APPENDIX D.
A.
MAGNETIC FIELD AND CIRCUIT SIMULATIONS
COMSOL MULTIPHYSICS MODELING
100 k-Amp DC, Solid Non-Augmented
Figure 33.
Solid Non-Augmented Magnetic Flux Density
X and Y axes units are in meters.
87
Figure 34.
Solid Non-Augmented Magnetic Field Across
Bore
X axis is in units of meters, Y axis is Magnetic field
strength A/m.
88
Figure 35.
Solid Non-Augmented Magnetic Field Across
Rail Surface
X axis is in units of meters, Y axis is Magnetic field
strength A/m.
89
100 k-Amp DC, Slotted Rail, Non-Augmented
Figure 36.
Slotted Non-Augmented Magnetic Flux Density
X and Y axes units are in meters.
90
Figure 37.
Slotted Non-Augmented Magnetic Field Across
Bore
X axis is in units of meters, Y axis is Magnetic field
strength A/m.
91
Figure 38.
Slotted Non-Augmented Magnetic Field Across
Rail Surface
X axis is in units of meters, Y axis is Magnetic field
strength A/m.
92
100 k-Amp DC, Solid Rail, Augmented
Figure 39.
Solid, Augmented Magnetic Flux Density
X and Y axes are units are in meters.
93
Solid Augmented Magnetic
Field Across Bore
Figure 40.
Solid Augmented Magnetic Field Across Bore
X axis is in units of meters, Y axis is Magnetic field
strength A/m.
94
Solid Augmented Magnetic Field
Across Rail Surface
Figure 41.
Solid, Augmented Magnetic Field Across Rail
Surface
X axis is in units of meters, Y axis is Magnetic field
strength A/m.
95
100 k-Amp DC, Slotted Rail, Augmented
Figure 42.
Slotted Augment Magnetic Flux Density
X and Y axes units are in meters.
96
Solid Augmented Magnetic
Field Across Bore
Figure 43.
Solid Augmented Magnetic Field Across Bore
X axis is in units of meters, Y axis is Magnetic field
strength A/m.
97
Solid Augmented Magnetic Field
Across Rail Surface
Figure 44.
Solid Augmented Magnetic Field Across Rail
Surface
X axis is in units of meters, Y axis is Magnetic field
strength A/m.
98
B.
ORCAD 10.3 P-SPICE CIRCUIT MODELING
LRC Model of the existing power supply, and resultant
current profile at 35 kJ
Rail Resistance
System Inductance
System Resistance
Diode delay
Capacitance
0.3 m-Ohms
5.5 µH
3 m-Ohms
100 µs
1.66 mF
Figure 45.
P-SPICE Single Module LRC Circuit Model
99
Figure 46.
Single Power Module Current Profile
100
Four-Module Ripple Fired 332-kJ Circuit Model
1.0 mOhm
0.3 mOhm
Circuit Parameters
Rail Resistance
3.0 mOhm
0 µs
Shunt Resistance
100 µs
Resistance per Module
Diode delay
Switch delay
2.5 µH
3.0 mOhm
1.66 mFarad
Inductance
0 µs
Resistance
100 µs
5.0 µH
Diode delay
200 µs
Switch delay
Inductance
300 µs
3.0 mOhm
Switch delay
3.0 mOhm
Resistance
Resistance
Diode delay
400 µs
12.0 µH
Switch delay
500 µs
Inductance
Diode delay
14 µH
3.0 mOhm
101
Capacitance per Module
Module 1
Module 2
Module 3
Module 4
Inductance
Resistance
P-SPICE Four-Module LRC Circuit Model
Figure 47.
Figure 48.
Four-Module Current Profile Output from
Figure 46 Circuit Model
102
APPENDIX E. BREAK SCREEN AND CURRENT PROFILE SCREEN
CAPTURES
6500 Volts, Solid Rail, Non-augmented
TVS-40 switches triggered
Armature exits muzzle
Figure 49.
Solid Non-Augmented Velocity Measurement
Green and yellow traces are from break screens located
at 0.5 meter interval for velocity measurement.
103
Figure 50.
Solid Non-Augmented Current Profiles
Green and Purple Traces are the Pearson 1330 current
monitor traces through the individual TVS-40 switches, the
Yellow
curve
is
the
Pearson
railgun.
104
1423
total
current
to
the
6500 Volt, Slotted Rail, Non-Augmented
6500 volts / slotted / non-augmented
Figure 51.
Slotted Non-Augmented Velocity Measurement
See caption for Figure 49.
105
Figure 52.
Slotted Non-Augmented Current Profiles
See caption for Figure 50.
106
6500 Volt, Solid Rail, Augmented
Figure 53.
Solid Augmented Velocity Measurement
See caption for Figure 49.
Fluctuation in green trace
is due to loose electrical connection and vibration during
shot at break-screen mount, corrected for subsequent shots.
107
Figure 54.
Solid Augmented Current Profiles
See caption for Figure 50.
108
6500 Volts, Slotted, Augmented
Figure 55.
Slotted Augmented Velocity Measurement
See caption for Figure 49.
109
Figure 56.
Slotted Augmented Current Profiles
See caption for Figure 50.
110
APPENDIX F.
TYPICAL POST-SHOT MATERIAL CONDITIONS
Rails and Insulators
Figure 57.
Typical Post-Shot Rail and Insulator Wear
111
Armature Wear
Figure 58.
Typical Post-Shot Armature Wear
112
Muzzle
Figure 59.
Muzzle Block Indicating Muzzle Flash Arcing
113
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114
LIST OF REFERENCES
1.
McNab,I.R., Stefani,F., Crawford,M., Erengil,M.,
Persad,C., Satapathy,S., Vanicek,H., Watt,T., and
Dampier,C., Development of a Naval Railgun, IEEE
Transactions on Magnetics, Vol.41, No.1, pp.206-213,
January 2005.
2.
Materials Web website, last accessed 23 February
2006, http://www.matweb.com/search/
3.
Kerrisk,J.F., Current Distribution and Inductance
Calculations for Rail-Gun Conductors, LANL report LA-9092MS, Nov. 1981.
4.
Maier, B., Selected Topics in Railgun Technology
Course Notes, Naval Postgraduate School, July 2005.
5.
Kotas,J.F., Guderjahn,C.A., Littman,F.D., A
Parametric Evaluation of Railgun Augmentation, IEEE
Transactions on Magnetics, Vol.22, No.6, November 1986.
6.
Chen,Y.G., Dethlefsen,R., Crumley,R., HighCoulomb Vacuum Switch, IEEE International Digest of
Technical Papers, Pulsed Power Conference 1993,Digest of
Technical Papers, Vol.2, pp.938-941, June 1993.
7.
Crawford, M., Railgun System Technology, Naval
Postgraduate School Physics Department Colloquium Lecture,
May 2004.
8.
ACF Component & Fasteners, Inc. Specification
Handbook, 2005 Edition, last accessed 05 March 2006,
www.acfcom.com
9.
Ugural, A.C. and Fenster, S.K., Advanced Strength
and Applied Elasticity, Fourth Edition, Prentice Hall
Publishers, Upper Saddle River, NJ, 2003, pp.527.
10. K-Mac Plastics website, last accessed 23 February
2006, www.k-mac-plastics.net/data%20sheets/Acculamtechnical-data.htm
115
11. CoorsTek Ceramics website, last accessed 23
February 2006, www.coorstek.com/materials/ceramics/
alumina/ad96.asp
12. American Micro-Industries website, last accessed
23 February 2006, www.electricalinsulationmaterial.com/
electrical-insulation-products/mylar_polyester_film/ mylarpolyester-film.html#mylar-properties
13. Stefani,F., Watt,T., Experimental and
Computational Investigation of Root-Radius Melting in CShaped Solid Armatures, IEEE Transactions on Magnetics,
Vol.41, No.1, pp.442-447, January 2005.
14. Hackel,L., Chen,H., Laser Peening – A Processing
Tool to Strengthen Metals or Alloys to Improve Fatigue
Lifetime and Retard Stress-Induced Corrosion Cracking,
Lawrence Livermore National Laboratory Laser Science and
Technology Program UCRL-ID-155327, September 2003.
15. Renk,T., Buchheit,R., Sorensen,N., Senft,D.,
Thompson,M., Grabowski,K., Improvement of Surface
Properties by Modification and Alloying with High-Power Ion
Beams, Physics of Plasmas, Vol.5, No.5, pp.2144-2150, May
1998.
116
INITIAL DISTRIBUTION LIST
1.
Defense Technical Information Center
Ft. Belvoir, VA
2.
Dudley Knox Library
Naval Postgraduate School
Monterey, CA
3.
Professor William B. Maier II, Code PH/MW
Department of Physics
Naval Postgraduate School
Monterey, CA
4.
Professor Terry McNelley, Code MAE/MC
Department of Mechanical and Astronautical Engineering
Naval Postgraduate School
Monterey, CA
5.
Engineering and Curriculum Office, Code 34
Naval Postgraduate School
Monterey, CA
6.
LT Brian C. Black
Pittsburgh, PA
7.
Tania Zaleski
Laser Peening Project Leader
Lawrence Livermore National Laboratory
Livermore, CA
8.
Tim Renk
Beam Applications and Initiatives Project Leader
Sandia National Laboratory
Albuquerque, NM
9.
Prof. Hans Mark
Institute for Advanced Technology
Austin, TX
10.
Prof. Ian McNabb
Institute for Advanced Technology
Austin, TX
117
11.
Dr. Mark Crawford
Institute for Advanced Technology
Austin, TX
12.
Francis Stefani
Institute for Advanced Technology
Austin, TX
13.
Dwayne Surls
Institute for Advanced Technology
Austin, TX
14.
Chadee Persad
Institute for Advanced Technology
Austin, TX
15.
Fred Beach
Institute for Advanced Technology
Austin, TX
16.
Robert Hebner
Center for Electromechanics
Austin, TX
17.
John Pappas
Center for Electromechanics
Austin, TX
18.
Dr. Roger McGinnis
Air Warfare and Naval Weapons Applications Division
Office of Naval Research
Arlington, VA
19.
Roger Ellis
EM Railgun INP
Office of Naval Research
Arlington, VA
20.
John Kinser
Office of Naval Research
Arlington, VA
20.
Elizabeth D’Andrea
Office of Naval Research
Arlington, VA
118
21.
Dr. Irwin Singer
Tribology Section, Naval Research Lab
Washington, DC
22
Robin Keesee
US Army Research and Development Command
Aberdeen Proving Ground, MD
23.
Mark McCormick,
Northrop Grumman Corporation Ship Systems
Pascagoula, MS
119
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