PDV in a Railgun. The Institute for Advanced Technology The University of Texas at Austin. Scott Levinson, Sikhanda Satapathy, Dwight Landen,

Transcription

1 PDV in a Railgun The Institute for Advanced Technology The University of Texas at Austin Scott Levinson, Sikhanda Satapathy, Dwight Landen, 8/14/27 17:51 2nd Annual PDV Workshop Aug 16-17, 27 Lawrence Livermore National Laboratory 1

2 Electromagnetic Launcher Armature Current (J) Force (JxB) Armature (Projectile) Rails Driving Current Magnetic Field (B) The current flowing in the rails causes a magnetic field which interacts with the current in the armature, generating a Lorentz (JxB) force. 2

3 Propulsion Force Energy Balance: t t 2 VIdt = dem + RI dt + Fzdz V I Fz Faraday s Law: V φ = RI + t => E = Idφ F dz m z => F z Em Em = ; and I = φ z φ z => F z 2 φ 1 L = = I z 2L 2 z 2 This is a geometric parameter. 3

4 Railgun Equations Propulsion force: F = ma = L I F ' f L is the inductance gradient, a geometric constant, and is around.5 μh/m 1 2 Ff 2 LI ' mv = Measured with Pearson coil Measured with PDV method 4

5 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 startup 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. 5

6 Typical measurement from B-Dot probes Breech Rowowski Current and BDot Measurements PDVanalMELshot6 1 5 units in legend ka IBreech (Peak: ka) Smoothed BDot pk to pk= 6inches Normalized: Breech Current pk to pk= 6inches Normalized: Bdot/ kgee - Lorentz Accleration time - ms B-dot coils 6

7 L' (Frictionless) Acceleration(t) = I 2M 2 (t) Muzzle exit 7

8 Axial Velocity Measurements with PDV on 1 m Railgun at IAT 1 m 3M μretroreflective Surfaces Beech Probe 2 independent axial velocity measurements With PDV Velocity (km/s) Breech Time (ms) Muzzle 1 12 Muzzle Probe Laser Detector Digitizer v i =.775 m/s Δf i MHz Detector 8

9 Breech Probe & Leading & Trailing Edges of Launch Package 9

10 Breech & Muzzle Probe Spectrograms 1 m Railgun s( Δ f,t) 2 = S( Δf,t) S(v,t) Muzzle Probe m/s v =.775 Δf MHz Breech Probe (bracketed) i C2PDVanalMELshot6 taken: , 15:4:41 N:496 novlap: v - m/s v - m/s Velocity (m/s) ( ΔV=λ Δf = λ fs/(2n)=.1892 m/s) (db) Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.96 μs), mav= 1-1 t (ms) t (ms) 1

11 Signal S(t) and S(t) /N(t) 248 k = 1 (, t) (, t) S(t) (, t) s v k 2 2 S(t) = max s Δ f = max s v S(t)/N(t) Muzzle Probe k k k k 2 S(t) Breech Probe 6 5 C4PDVanalMELshot6 Detection Quality Detected Signal Power PeakPower/Total Power 5 4 C2PDVanalMELshot6 Detection Quality Detected Signal Power PeakPower/Total Power db 2 db Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.96 μs), mav= 1 t (ms) Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.96 μs), mav= 1 t (ms) 11

12 4 v - m/s Velocity (m/s) ( ΔV=λ Δf = λ fs/(2n)=.1892 m/s) Muzzle Probe C4PDVanalMELshot6 taken: , 15:4:41 N:496 novlap: 248 +/- -2 db Intervals Above Peak -2 db Peak Power Below Peak -2 db Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.96 μs), mav= Velocity Statistics v - m/s Velocity (m/s) ( ΔV=λ Δf = λ fs/(2n)=.1892 m/s) Breech Probe C2PDVanalMELshot6 taken: , 15:4:41 N:496 novlap: 248 +/- - 2 db Intervals Above Peak -2 db Peak Power Below Peak -2 db Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.96 μs), mav= v - m/s Velocity (m/s) Time after trigger (ms),

13 Axial Position from PDV and B-Dot C4PDVanalMELshot6 - Heterodyne Position Measurement, Acceleration = L'/2M (I 2 (t) Positions of B-dot Peaks Kerrisk L'= uh/m, M=.177 g BestFit L'=.478 uh/m Integrated Muzzle Velocity from PDV.8 Position - m Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.96 μs), mav= 1 13

14 Breech and Muzzle PDV Velocities 45 4 Breech (C2) & Muzzle Velocities (C4) PDVanalMelShot6 N:496 novlap: 248 Velocity from Breech Probe (PDV) Velocity from Muzzle Probe (PDV) BestFit L'=.478 uh/m Velocity (m/s) ( ΔV=λ Δf = λ fs/(2n)=.1892 m/s) Velocity (m/s) ( ΔV=λ Δf = λ fs/(2n)=.1892 m/s) Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.96 μs), mav= Time after trigger (ms), (Δt= 1/fs =1 ns, ΔT= N Δt = 4.96 μs), mav= 1 14

15 PDV Acceleration Statistics 5 % Confidence Intervals a - kgee 15

16 PDV Acceleration &Friction a - kgee 5 % Confidence Intervals a - kgee x(m) v(m/s) 16

17 So far... 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 Conference June 3-7, 27, 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 17

18 " Standard" PDV Directly Yields Velocity Projectile Collimator Probe 9:1 3-port coupler Directional Circulator ω ω ω 9 % Main w 1z w ω 1 1 ω ω 1 ω ω Single Mode Laser V(t) x(t) Laser frequency ω Doppler shifted frequency ω 1 Interference: Δω ( ω ω1) x r 1 % ω ω Variable Retro- Reflector ω, ω 1 ω, ω 1 Power meter Optical Detector t 1t ( ) s(t) 2 I I cos Δω(t) t v + a t s(t) 2 I I cos Δω(t) t = 3.8V/mW I I cos 2ω t Detected signal: ( ) t t t 1t t 1t c. 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 ( I 1t ), and is adjustable by simply varying laser source amplitude ( I t ). 18

19 ω ω 1 Collimator Probe ω 5:5 2:1-port coupler Main Use "VISAR-Like" PDV for Acceleration 5 % ω 1 ω 5 % ω ω 1 ω 1 Short Delay T a 5:5 2:1-port coupler 5 % Main 5 % ω ω 1a ω 1b 9:1 3-port coupler 9 % 1 % Main ω ω 1a 2 Directional Circulator 3 1 Power meter ω 1b ω ω Single Mode Laser Long Delay T b ω ω Variable Retro- Reflector ω 1a ω 1b Optical Detector S(t) ( ) It I1at cos( ( ω ω1a) t) It I1bt cos ( ω ω1b ) t S(t) 3.8V/mW + + I I cos ( ω ω ) t 1at 1bt 2v(t) Noting: ω 1(t) = ω 1+, we observe that c ( ) vt + at Ta t ω1a = ω 1+ 2 c ( ) vt + at Tb t ω 1b =ω 1+ 2 c ( 1a 1b ) 19

20 "VISAR-Like" PDV for Acceleration cont. Three signal components offer an independent means to detect the velocity in the vicinity of time T a and T b, and with average acceleration between them. They have respective frequencies & amplitudes: 1) 2) 3) ω ω 2ω ( ) v + a T t t t a 1a = at amplitude t 1at ω ω 2ω c ( ) v + a T t t t b 1b = at amplitude t 1bt ω ω 2ω c ( ) a T T t b a 1b 1a = at amplitude 1at 1bt c The 3 rd component s frequency is proportional to acceleration directly measurable! However, it s amplitude, I I, is typically 1-2 db smaller than the other 2 1a t 1b t components may result in poor S/N. I I I I I I 2

21 Quick Look at PDV w/ 3 probes over LONG (18-m) Range - Reflecting Surface - Balloting Arrange 3 Oz Optics Probes in array At 18 m downrange from probes, wave reflector surfaces (by hand) : Reflexite P66 unpolished al 775 no surface Observe Spectrograms s( v,t k ) Probe 1 Probe 3 Probe 2 21

22 1-way Source to IR card Range: 18. m 75 mw - each channel 15 mw - each channel 3 mw - each channel RetroReflective Unpolished 775 Surface.85 in 22

23 Velocity (m/s) (ΔV=λ Δf = λ fs/(2n)=.946 m/s) Trial 5: Moving RetroReflective Surface 3 mw - each channel, Adjustable Retro: - 2 db each ch Probe - Reflector Range: 18. m trial5manual sigs_ch1.wfm taken: 26-Jul-27 15:41:12 N:496 novlap: Probe Probe (db) S(v,t) Velocity (m/s) (ΔV=λ Δf = λ fs/(2n)=.946 m/s) trial5manual sigs_ch2.wfm taken: 26-Jul-27 15:41:12 N:496 novlap: (db) Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= 1-1 Velocity (m/s) (ΔV=λ Δf = λ fs/(2n)=.946 m/s) Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= 1 trial5manual sigs_ch3.wfm taken: 26-Jul-27 15:41:14 N:496 novlap: 372 Probe (db) Velocity (m/s) ( ΔV=λ Δf = λ fs/(2n)=.946 m/s) trial5manual sigs_ch1.wfm taken: 26-Jul-27 15:41:12 N:496 novlap: 372 V - m/s Ch 1 Ch 2 Ch Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= 1 23

24 Trial 7: Moving Unpolished 775 Surface 3 mw - each channel, Adjustable Retro: - 2 db each ch Probe - Reflector Range: 18. m Probe 1 Probe 2 S(v,t) Probe 3 Velocity (m/s) ( ΔV=λ Δf = λ fs/(2n)=.946 m/s) mmtrial7manual sigs_ch1-3: 26-Jul-27 15:47:5 N:496 novlap: Ch1 Ch2 1.8 Ch V - m/s Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= 1 24

25 Trial 4: Moving RetroReflective Surface 75 mw - each channel, Adjustable Retro: - 6dB each ch Probe - Reflector Range: 18. m Probe 2 Probe 1 S(v,t) Probe 3 V - m/s 25

26 Use Multiple (Muzzle) Probes Muzzle Probe Array (Oz Optics) Muzzle Mirror Downrange into Muzzle Mirror (1-mW 65 nm signal from FIS "Fault Detector" split into 3 probes) Up-range into IR card at breech (IR Laser signal from each probe) 26

27 35 Breech and Muzzle Velocities with new Laser (with appropriate bracketing) pdv1_ch4.wfm taken: 25-Jun-27 13:44:54 N:16384 novlap: v - m/s Velocity (m/s) (ΔV=λ Δf = λ fs/(2n)=.7396 m/s) ch 4 Breech Probe ch 3 Muzzle Probe ch 2 Muzzle Probe ch 1 Muzzle Probe Time (ms), (Δt= 1/fs =.64 ns, ΔT= N Δt = μs), mav= 1 27

28 (2 nd ) Summary 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 [1] "Photonic Doppler Velocimetry in the Bore of a Railgun, [2] High resolution acceleration measurements, [3] "Balloting Motion Measurement in Railgun," 28

29 Extras 29

30 Spectrogram of New Laser S(v,t) v - m/s db Multiple Velocities result from aliasing & multiple lines (1.667 GHz) (from new IPG Laser, which is now fixed) 3

31 Trial 8: No Moving Surface 3 mw - each channel, Adjustable Retro: - 2 db each ch Probe - Reflector Range: 18. m Probe 1 Probe 2 S(v,t) trial8manual sigs_ch3.wfm taken: 26-Jul-27 15:5:4 N:496 novlap: Velocity (m/s) (ΔV=λ Δf = λ fs/(2n)=.946 m/s) Probe (db) V - m/s Velocity (m/s) ( ΔV=λ Δf = λ fs/(2n)=.946 m/s) trial8manual sigs_ch3.wfm taken: 26-Jul-27 15:5:4 N:496 novlap: 372 Above Peak -2 db Peak Power Below Peak -2 db Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= 1 31

32 1 Trial 8: No Moving Surface 3 mw - each channel, Adjustable Retro: - 2 db each ch Probe - Reflector Range: 18. m trial8manual sigs_ch1 Detection Quality Detected Signal Power PeakPower/Total Power 1 5 trial8manual sigs_ch2 Detection Quality Detected Signal Power PeakPower/Total Power 5 S db -5 db Probe 1 Probe 2 S/N Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= trial8manual sigs_ch3 Detection Quality Detected Signal Power PeakPower/Total Power Tektronix Scope Traces db -5-1 Probe Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= 1 32

33 4 Trial 5: Moving RetroReflective Surface 3 mw - each channel, Adjustable Retro: - 2 db each ch trial5manual sigs_ch2 Detection Quality Probe - Reflector Range: 18. m 4 trial5manual sigs_ch1 Detection Quality 3 3 db Detected Signal Power PeakPower/Total Power Probe 1 Probe Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= 1 S S/N db Detected Signal Power PeakPower/Total Power Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= 1 4 trial5manual sigs_ch3 Detection Quality 3 2 Tektronix Scope Traces db 1 Probe 3 Detected Signal Power PeakPower/Total Power Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= 1 33

34 Trial 7: Moving Unpolished 775 Surface 3 mw - each channel, Adjustable Retro: - 2 db each ch Probe - Reflector Range: 18. m 3 25 trial7manual sigs_ch1 Detection Quality Detected Signal Power PeakPower/Total Power 1 trial7manual sigs_ch2 Detection Quality Detected Signal Power PeakPower/Total Power 5 2 db S db S/N Probe 1 Probe Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= trial7manual sigs_ch3 Detection Quality Detected Signal Power PeakPower/Total Power Tektronix Scope Traces db 5-5 Probe Time after trigger (ms), (Δt= 1/fs =2 ns, ΔT= N Δt = μs), mav= 1 34

35 Trial 4: Moving RetroReflective Surface 75 mw - each channel, Adjustable Retro: - 6dB each ch Probe - Reflector Range: 18. m S S/N Probe 1 Probe 2 Tektronix Scope Traces Probe 3 t (ms) t (ms) 35