PDV in a Railgun PDV in a Railgun
Transcript of PDV in a Railgun PDV in a Railgun
11
PDV in a RailgunThe Institute for Advanced Technology
The University of Texas at Austin
PDV in a RailgunThe Institute for Advanced Technology
The University of Texas at Austin
Scott Levinson, Sikhanda Satapathy, Dwight Landen,
2nd Annual PDV WorkshopAug 16-17, 2007
Lawrence Livermore National Laboratory8/14/2007 17:51
22
Electromagnetic Launcher
Rails
DrivingCurrent Magnetic Field (B)
Armature(Projectile)
Force (JxB)ArmatureCurrent (J)
The current flowing in the rails causes a magnetic field which interacts with the current in the armature, generating a Lorentz (JxB) force.
33
Propulsion Force
2
0 0
t t
m zVIdt dE RI dt F dz= + +∫ ∫ ∫ ∫Energy Balance:
Faraday’s Law:
=>
=>
=>
V RItφ∂
= +∂
m zE Id F dzφ= −∫ ∫; and I = m m
zz
E EFz φ φ
∂ ∂= −
∂ ∂
221
2 2zLF I
z L zφ⎛ ⎞∂ ∂
= − =⎜ ⎟∂ ∂⎝ ⎠
This is a geometric parameter.
V
IFz
44
Railgun Equations
• Propulsion force:
• L’ is the “inductance gradient”, a geometric constant, and is around 0.5 μH/m
212 ' fF ma L I F= = −
212 'fF L I mv= −
Measured with Pearson coilMeasured with PDV method
55
Why is Friction Measurement Important?
• The start-up region requires initial external contact pressure to carry current.
• Due to long residence time of the armature at the start-up region, abnormal damage occurs to both rail and armature.
• Role of lubrication in the interface is under study.
• Accurate measurement of the initial motion is extremely important for studying lubrication effects.
66
Typical measurement from B-Dot probes
0 1 2 3 4 5 6-50
0
50
100
time - ms
units
in le
gend
Breech Rowowski Current and BDot Measurements PDVanalMELshot6
kA IBreech (Peak: 104.5286 kA)Smoothed BDotpk to pk= 6inches Normalized: Breech Currentpk to pk= 6inches Normalized: Bdot/0.098455kGee - Lorentz Accleration
B-dot coils
77
Muzzle exit
2
2M(t)L'(Frictionless) Acceleration(t) I=
88
Laser
Detector Digitizer
2.5
2.0
1.5
1.0
0.5
0
Velocity (km/s)
121086420Time (ms)
Breech
Muzzle
1 m3M
μRetroReflectiveSurfaces
Detector
Muzzle Probe
Beech Probe
2 independent axialvelocity
measurementsWith PDV
ii f0.775 vMHz
m/s Δ=
Axial Velocity Measurementswith PDV on 1 m Railgun at IAT
99
Breech Probe & Leading & Trailing Edges of Launch Package
1010
Breech & Muzzle Probe Spectrograms 1 m Railgun
( ) 2s f,t S ( f ,t) S (v ,t)Δ = Δ →
t (ms) t (ms)
Breech Probe (bracketed)
Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.096 μs), mav= 1
Velo
city
(m/s
) (Δ
V=λ Δ
f = λ
fs/(2
N)=
0.1
892
m/s
)
C2PDVanalMELshot6 taken: 17.4.2007, 15:40:41 N:4096 novlap: 2048
0 1 2 3 4 50
50
100
150
200
250
300
350
-10
-5
0
5
10
15
20
25
30
35
40
(dB)
v -m
/s
Muzzle Probe
v -m
/s
im/s
MHzv 0.775 f= Δ
1111
( ) ( )
( )2048
2
k1
2 2
S(t)
S(t)s v
max s f max s v
S(t)/N(t),
S(t)
t
, ,
k
k k k kt t
=
= Δ =
≅−∑
0 1 2 3 4 5 6-20
-10
0
10
20
30
40
50
Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.096 μs), mav= 1
dB
C2PDVanalMELshot6 Detection Quality
Detected Signal PowerPeakPower/Total Power
0 1 2 3 4 5 6-20
-10
0
10
20
30
40
50
60
Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.096 μs), mav= 1
dB
C4PDVanalMELshot6 Detection Quality
Detected Signal PowerPeakPower/Total Power
Breech Probe Muzzle Probe
t (ms) t (ms)
Signal S(t) and S(t) /N(t)
12
Velocity Statistics
0 1 2 3 4 5 60
50
100
150
200
250
300
350
400
Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.096 μs), mav= 1
Velo
city
(m/s
) (Δ
V=λ Δ
f = λ
fs/(2
N)=
0.1
892
m/s
)
C2PDVanalMELshot6 taken: 17.4.2007, 15:40:41 N:4096 novlap: 2048
V @ Above Peak -20 dBV @ Peak PowerV @ Below Peak -20 dB
Breech Probe ↓
+/-- 20 dB
Intervalsv -m
/s
0 1 2 3 4 5 60
50
100
150
200
250
300
350
400
Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.096 μs), mav= 1
Velo
city
(m/s
) (Δ
V=λ Δ
f = λ
fs/(2
N)=
0.1
892
m/s
)
C4PDVanalMELshot6 taken: 17.4.2007, 15:40:41 N:4096 novlap: 2048
V @ Above Peak -20 dBV @ Peak PowerV @ Below Peak -20 dB
Muzzle Probe ↓
+/-- 20 dB
Intervalsv -m
/s
0.2 0.3 0.4 0.5 0.6 0.7 0.80
2
4
6
8
10
12
14
16
18
20
Time after trigger (ms),
Velo
city
(m/s
)
0
0
400
200 6.0 0 6.0t - ms t - ms
0.2 0.8t - ms
v -m
/s
13
Axial Position from PDV and B-Dot
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50
0.2
0.4
0.6
0.8
1
1.2
Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.096 μs), mav= 1
Posi
tion
- mC4PDVanalMELshot6 - Heterodyne Position Measurement, Acceleration = L'/2M (I2(t)
Positions of B-dot PeaksKerrisk L'=0.66446 uH/m, M=0.0177 gBestFit L'=0.4708 uH/mIntegrated Muzzle Velocity from PDV
14
Breech and Muzzle PDV Velocities
0 1 2 3 4 5 60
50
100
150
200
250
300
350
400
450
Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.096 μs), mav= 1
Velo
city
(m/s
) (Δ
V=λ Δ
f = λ
fs/(2
N)=
0.1
892
m/s
)Breech (C2) & Muzzle Velocities (C4) PDVanalMelShot6 N:4096 novlap: 2048
Velocity from Breech Probe (PDV)Velocity from Muzzle Probe (PDV)BestFit L'=0.4708 uH/m
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
5
10
15
Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.096 μs), mav= 1
Velo
city
(m/s
) (Δ
V=λ Δ
f = λ
fs/(2
N)=
0.1
892
m/s
)
1515
PDV Acceleration Statistics
t - ms
50 % Confidence
Intervals
a -k
Gee
1616
PDV Acceleration &Friction
50 % Confidence
Intervals
x(m)
t - ms
v(m/s)
t - ms
a -k
Gee
a -k
Gee
1717
• Accurate velocity measurement is possible by measuring Doppler shift.
• Motion measurement is possible in the start-up region where use of B-dot probes is problematic.
• This method will help assess effects of lubrication on start-up armature behavior.
• The data shows interesting dynamic friction behavior at sliding contact.
• Future work: direct measurement of acceleration[1] "High resolution sliding velocity measurement for assessing dynamic friction effects," Sikhanda Satapathy,
Scott Levinson, Dwight Landen, David Holtkamp, and Adam Iverson, ASME Applied Mechanics and Materials ConferenceJune 3-7, 2007, University of Texas at Austin
Next Let's Consider:• Direct measurement of acceleration Incorporating VISAR principals
• Quick Look at Long range (18 m) and poor reflecting surfaces
• Feasibility of using Multiple probes for balloting measurement
So far . . .
1818
" Standard" PDV Directly Yields Velocity
VariableRetro-
Reflector
Single ModeLaser
DirectionalCirculator
Powermeter
OpticalDetector
90:103-port coupler
90 %
10 %
CollimatorProbe
Projectile
V(t)
x(t) xr0
12
3Main
ω0ω0ω0ω0ω0
w1z w1ω1
ω1
ω1
ω0,
ω1
ω0,
( )0t 1 ts(t) 2 I I cos ω(t) t≅ ⋅ ⋅ Δ ⋅
ω0
ω0ω0
Detected signal: ( ) t t00t 1 t 0 t 1 t
v a ts(t) 2 I I cos ω(t) t 3.8V/mW I I cos 2ω tc+ ⋅⎧ ⎫≅ ⋅ ⋅ Δ ⋅ = ⋅ ⋅ ⎨ ⎬
⎩ ⎭.
Terms incorporated in a subscript t indicate that they are calculated or measured by averaging
over a small time interval τ centered about t . Note that the amplitude of the detected signal |s(t)| is
proportional to the square-root of the received signal amplitude ( 1tI ), and is adjustable by
simply varying laser source amplitude ( 0tI ).
Laser frequency ω0Doppler shifted frequency ω1Interference: ( )0 1ω ω ωΔ ≡ −
1919
Use "VISAR-Like" PDV for AccelerationCollimator
Probe
ω0
ω1
MainMain
50 %
50 %
50 %
50 %
ω0
ω1ω0
ω1
ω0
ω1a
ω0
ω1
VariableRetro-
Reflector
Single ModeLaser
DirectionalCirculator
Powermeter
OpticalDetector
90:103-port coupler
90 %
10 %
12
3Main
ω0
ω0
ShortDelay
Ta
LongDelay
Tb
ω1b
ω0 ω0
50:502:1-port coupler
50:502:1-port coupler
ω1a
ω1bω0ω1aω1b
S(t)
( )( ) ( )( )( )( )0 1a 0 1b0t 1at 0t 1bt
1a 1b1at 1bt
I I cos ω ω t I I cos ω ω t
I I cos ω ω tS(t) 3.8V/mW
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
⋅ − ⋅ + ⋅ − ⋅≅
+ ⋅ − ⋅
Noting: 1 02v(t)ω (t) ω 1
c⎛ ⎞= +⎜ ⎟⎝ ⎠
, we observe that
( )
( )
at t1a 0
bt t1b 0
v a T tω ω 1 2
c
v a T tω =ω 1 2
c
⎛ ⎞+ ⋅ −= +⎜ ⎟⎜ ⎟
⎝ ⎠⎛ ⎞+ ⋅ −+⎜ ⎟⎜ ⎟
⎝ ⎠
2020
"VISAR-Like" PDV for Acceleration cont.
Three signal components offer an independent means to detect the velocity in the vicinity
of time Ta and Tb, and with average acceleration between them. They have respective
frequencies & amplitudes:
1) ( )at t1a 0 0
v a T tω ω 2ω
c+ ⋅ −
− = at amplitude 0t 1atI I⋅
2) ( )bt t
1b 0 0
v a T tω ω 2ω
c+ ⋅ −
− = at amplitude 0t 1btI I⋅
3) ( )b at1b 1a 0
a T Tω ω 2ω
c⋅ −
− = at amplitude 1at 1btI I⋅
The 3rd component’s frequency is proportional to acceleration ⇒ directly measurable!
However, it’s amplitude, 1a t 1b t
I I⋅ , is typically 10-20 dB smaller than the other 2
components ⇒ may result in poor S/N.
2121
Quick Look at PDV w/ 3 probes over LONG (18-m) Range
• Arrange 3 Oz Optics Probes in array• At 18 m downrange from probes, wave reflector surfaces (by hand) :
• Reflexite P66• unpolished al 7075• no surface
• Observe Spectrograms
Probe 1 Probe 3
Probe 2
( )ks v ,t
- Reflecting Surface- Balloting
22
75 mW - each channel
1-way Source to IR card Range: 18.0 m150 mW - each channel
300 mW - each channel
Unpolished 7075 Surface
RetroReflective
0.85 in
2323
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
Vel
ocity
(m/s
) (Δ
V= λ
Δf =
λ fs
/(2N
)= 0
.000
946
m/s
)
trial5manual sigs000_Ch1.wfm taken: 26-Jul-2007 15:41:12 N:4096 novlap: 3072
50 100 150 200 250 300 3500
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
-10
-5
0
5
10
15
20
25
30
35
40
(dB)
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
Vel
ocity
(m/s
) (Δ
V= λ
Δf =
λ fs
/(2N
)= 0
.000
946
m/s
)
trial5manual sigs000_Ch2.wfm taken: 26-Jul-2007 15:41:12 N:4096 novlap: 3072
50 100 150 200 250 300 3500
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
-10
-5
0
5
10
15
20
25
30
35
40
(dB)
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
Vel
ocity
(m/s
) (Δ
V= λ
Δf =
λ fs
/(2N
)= 0
.000
946
m/s
)
trial5manual sigs000_Ch3.wfm taken: 26-Jul-2007 15:41:14 N:4096 novlap: 3072
50 100 150 200 250 300 3500
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
-10
-5
0
5
10
15
20
25
30
35
40
(dB)
0 50 100 150 200 250 300 350 4000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
Velo
city
(m/s
) (Δ
V=λ Δ
f = λ
fs/(2
N)=
0.0
0094
6 m
/s)
trial5manual sigs000_Ch1.wfm taken: 26-Jul-2007 15:41:12 N:4096 novlap: 3072
Ch 1Ch 2Ch 3
Trial 5: Moving RetroReflective Surface300 mW - each channel, Adjustable Retro: - 2 dB each chProbe - Reflector Range: 18.0 m
S(v,t)Probe 1 Probe 2
Probe 3
V - m/s
t - ms t - ms
24240 50 100 150 200 250 300 350 4000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
Velo
city
(m/s
) (Δ
V=λ Δ
f = λ
fs/(2
N)=
0.0
0094
6 m
/s)
1.2 W @ 18 mmtrial7manual sigs000_Ch1-3: 26-Jul-2007 15:47:05 N:4096 novlap: 3072
Ch1Ch2Ch3
Trial 7: Moving Unpolished 7075 Surface300 mW - each channel, Adjustable Retro: - 2 dB each chProbe - Reflector Range: 18.0 m
Probe 1 Probe 2
V - m/sProbe 3
S(v,t)
t - ms t - ms
2525
Trial 4: Moving RetroReflective Surface75 mW - each channel, Adjustable Retro: - 6dB each chProbe - Reflector Range: 18.0 m
Probe 1 Probe 2
Probe 3
S(v,t)
V - m/s
t - ms t - ms
2626
Use Multiple (Muzzle) Probes
Muzzle Probe Array
(Oz Optics)
Muzzle Mirror
Downrange into Muzzle Mirror (1-mW 650 nm signal from FIS "Fault Detector" split into 3 probes)
Up-range into IR card at breech (IR Laser signal from each probe)
2727
Breech and Muzzle Velocitieswith new Laser (with appropriate bracketing)
0 1 2 3 4 5 60
50
100
150
200
250
300
350
Time (ms), (Δt= 1/fs =0.64 ns, ΔT= N Δt = 10.4858 μs), mav= 1
Vel
ocity
(m/s
) (Δ
V= λ
Δf =
λ fs
/(2N
)= 0
.073
906
m/s
)pdv001_Ch4.wfm taken: 25-Jun-2007 13:44:54 N:16384 novlap: 8192
ch 4 Breech Probech 3 Muzzle Probech 2 Muzzle Probech 1 Muzzle Probe
v -m
/s
2828
• Like VISAR, use of time delayed signals may allow direct PDV measurement of the acceleration
• A Quick-look shows PDV is likely to work over – long ranges, – with multiple, independent, closely-spaced signals, – & (maybe) w/ untreated launch-package surfaces.
• Multiple-independent signal detection in small railgun is feasible • Future work:
– Routinely characterize axial velocity profiles in large EM guns (e.g., HeMCL)
– Test direct measurements of axial acceleration & 3d balloting
(2nd) Summary
[1] "Photonic Doppler Velocimetry in the Bore of a Railgun”, http://www.emlsymposium.org/about.html,[2] “High resolution acceleration measurements,” http://www.emlsymposium.org/about.html
[3] "Balloting Motion Measurement in Railgun," http://www.emlsymposium.org/about.html
29
Extras
3030
Spectrogram of New Laser
Multiple Velocities result from aliasing & multiple lines (1.667 GHz)(from new IPG Laser, which is now fixed)
S(v,t)v
-m/s dB
3131
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
Vel
ocity
(m/s
) (Δ
V= λ
Δf =
λ fs
/(2N
)= 0
.000
946
m/s
)
trial8manual sigs000_Ch3.wfm taken: 26-Jul-2007 15:50:04 N:4096 novlap: 3072
50 100 150 200 250 300 3500
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
-10
-5
0
5
10
15
20
25
30
35
40
(dB)
0 50 100 150 200 250 300 350 4000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
Velo
city
(m/s
) (Δ
V=λ Δ
f = λ
fs/(2
N)=
0.0
0094
6 m
/s)
trial8manual sigs000_Ch3.wfm taken: 26-Jul-2007 15:50:04 N:4096 novlap: 3072
V @ Above Peak -20 dBV @ Peak PowerV @ Below Peak -20 dB
Trial 8: No Moving Surface300 mW - each channel, Adjustable Retro: - 2 dB each chProbe - Reflector Range: 18.0 m
t - ms
Probe 1 Probe 2
Probe 3
S(v,t)
V - m/s
t - ms
3232
0 50 100 150 200 250 300 350 400-20
-15
-10
-5
0
5
10
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
dB
trial8manual sigs000_Ch3 Detection Quality
Detected Signal PowerPeakPower/Total Power
0 50 100 150 200 250 300 350 400-20
-15
-10
-5
0
5
10
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
dB
trial8manual sigs000_Ch2 Detection Quality
Detected Signal PowerPeakPower/Total Power
-50 0 50 100 150 200 250 300 350 400-20
-15
-10
-5
0
5
10
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
dB
trial8manual sigs000_Ch1 Detection Quality
Detected Signal PowerPeakPower/Total Power
Trial 8: No Moving Surface300 mW - each channel, Adjustable Retro: - 2 dB each chProbe - Reflector Range: 18.0 m
S/N
S
TektronixScope ⇒Traces
Probe 1 Probe 2
Probe 3
t - ms t - ms
3333
0 50 100 150 200 250 300 350 400-20
-10
0
10
20
30
40
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
dB
trial5manual sigs000_Ch1 Detection Quality
Detected Signal PowerPeakPower/Total Power
0 50 100 150 200 250 300 350 400-20
-10
0
10
20
30
40
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
dB
trial5manual sigs000_Ch2 Detection Quality
Detected Signal PowerPeakPower/Total Power
0 50 100 150 200 250 300 350 400-20
-10
0
10
20
30
40
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
dB
trial5manual sigs000_Ch3 Detection Quality
Detected Signal PowerPeakPower/Total Power
Trial 5: Moving RetroReflective Surface300 mW - each channel, Adjustable Retro: - 2 dB each chProbe - Reflector Range: 18.0 m
S/N
SProbe 1 Probe 2
TektronixScope ⇒Traces
Probe 3
t - ms t - ms
3434
0 50 100 150 200 250 300 350 400-20
-15
-10
-5
0
5
10
15
20
25
30
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
dB
trial7manual sigs000_Ch3 Detection Quality
Detected Signal PowerPeakPower/Total Power
0 50 100 150 200 250 300 350 400-20
-15
-10
-5
0
5
10
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
dB
trial7manual sigs000_Ch2 Detection Quality
Detected Signal PowerPeakPower/Total Power
0 50 100 150 200 250 300 350 400-20
-15
-10
-5
0
5
10
15
20
25
30
Time after trigger (ms), (Δt= 1/fs =200 ns, ΔT= N Δt = 819.2 μs), mav= 1
dB
trial7manual sigs000_Ch1 Detection Quality
Detected Signal PowerPeakPower/Total Power
Trial 7: Moving Unpolished 7075 Surface300 mW - each channel, Adjustable Retro: - 2 dB each chProbe - Reflector Range: 18.0 m
S
Probe 1 Probe 2S/N
TektronixScope ⇒Traces
Probe 3
t - ms t - ms
3535
Trial 4: Moving RetroReflective Surface75 mW - each channel, Adjustable Retro: - 6dB each chProbe - Reflector Range: 18.0 m
Probe 1 Probe 2
Probe 3
t (ms)
S/N
S
t (ms)
TektronixScope ⇒Traces