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