23 RD INTERNATIONAL SYMPOSIUM ON BALLISTICS TARRAGONA, SPAIN 16-2 APRIL 27 NOVEL EXAMINATION OF GUN BORE RESISTANCE ANALYSIS AND EXPERIMENTAL VALIDATION D. Carlucci 1, J. Vega 1, M. Pocock 2, S. Einstein 1, C. Guyott 2, R. Chaplin 1 1 U.S. Armament, Research and Development Center, Picatinny Arsenal, Dover, N.J. 7871, USA email: dcarl@pica.army.mil 2 Frazer-Nash Consultancy, Stonebridge House, Dorking Business Park, Dorking, Surrey, RH4 1HJ, UK, email: m.pocock@fnc.co.uk Abstract The resistance of a projectile to axial motion in a gun bore has been examined in the past [1] both experimentally and numerically. This resistance is an important aspect in accurately matching muzzle velocities in a computer simulation to experimental data. This resistance profile varies in magnitude as the projectile moves down the bore of a weapon. It initially increases as the rotating band or obturator is engraved and then decreases as travel continues. This profile is used in many computer codes in this form. The Analysis and Evaluation Technology Division at ARDEC designed the 155mm XM173E1 Instrumented Ballistic Test Projectile (IBTP) [2] as a strictly experimental vehicle to determine, among other things, bore resistance and blowby of a plastic obturating band. This projectile was instrumented with pressure transducers and accelerometers with the data telemetered to a ground station. The difference between the force applied and acceleration was reduced from the data and the result plotted to determine a bore resistance profile. The effect on internal ballistics of the experimentally derived engraving forces rather than simple assumed profiles (which are commonly used) has been started using the IBHVG2 [2] software. Additional work using a 1-dimensional modelling code, FNGUN [3], has been initiated to investigate further the correlation between experimental data and predictions. BACKGROUND In an attempt to better understand the interaction phenomena of projectiles inside a gun tube a procedure using the IBTP [1] Data was developed to obtain total resistance pressure opposing projectile travel. This so-called pressure is simply the resistive force expressed as a pressure using the bore area of the weapon. The desire for accurately predict muzzle velocity of cannon launched projectiles has necessitated an experimental method to determine total resistance in order to validate the numerical model and predict muzzle velocity with greater accuracy than ever before. Figure 1 depicts the IBTP projectile. The five pressure sensors utilized in this design were PCB 19C11 piezoelectric gages rated for 8, PSI. The accelerometer block consisted of one ENDEVCO 727A-2KG accelerometer in the axial direction 313
314 INTERIOR BALLISTICS and two 727A-6KG accelerometers in the balloting direction, 9 degrees apart. The ARRT-124 telemetry system incorporated was a 9 channel analog system with 5 KHz bandwidth for input signals. Figure 1: IBTP Projectile Over the last three years, approximately 28 IBTP projectiles of slightly different configurations were fired at Yuma Proving Grounds. Six of them were fired in a configuration as depicted in figure 1. This configuration allowed direct measurement of projectile base pressure, blow-by pressures, simultaneously with projectile axial and two balloting accelerations. The IBTP serial number (S/N) TM17 incorporated all the improvements and lessons learned from the previous five firings and was fired in 26 Axial Acceleration ( G s ) 165 YUMA 155 / PIMP+5% / Ambient / 26 January 26 145 135 125 115 15 95 85 75 65 55 45 35 25 15 5-5 -15-25 -35-45 -55 ACCELERATION TM17 Radial1 Radial2 W28: W3; overplot(col(w1, 2), lred); overplot(col(w1, 3), lgreen) Axial.2.4.6.8.1.12.14.16 Base Pressure- G1 ( PSI ) 51 48 45 42 3 3 3 27 24 21 18 Gage4 12 - - PRESSURE TM17 W27: W22; overplot(w23, lred); overplot(w24, lgreen); overplot(w25, black); overlay(w2, red) Gage2 Gage5 Gage3 Gage1.2.4.6.8.1.12.14.16.18 8 76 72 68 64 56 Blow-By Pressure- G2, G3, G4, G5 ( PSI ) 52 48 44 4 36 32 28 24 2 16 12 8 4-4 -8-12 -16-2 Figure 2. Acceleration data for TM17. Figure 3. Pressure data for TM17. from a M284 cannon at PIMP+5% (permissible individual maximum pressure +5 %, with peak pressure equivalent to roughly 5, PSI breech pressure or approximately 15,7g s for the projectile). TM17 data was used to calculate pressure resistance.
Novel examination of gun bore resistance analysis and experimental validation 315 Figure 2 displays the acceleration data and Figure 3 shows the pressure data taken from the test in which projectile number TM17 was fired. Significant data distortions were present in the pressure data and these were greatest when recording pressures below 1, PSI. An investigation indicated these data anomalies were induced by the pressure sensor and the more significant ones were: a). The negative pressure readings (figure 3) were caused by the gage inability to return to zero or by an initial condition of the gage when power was applied forcing the gage to sit at a positive value before the round is fired in which the negative pressure. PRESSURE TM17 PRESSURE TM17 Pressure Compensations ( PSI ) 54 51 48 45 42 3 3 3 27 24 21 18 12 - - YUMA / PIMP+5% W13: w7; / overplot(w4, Ambient lred); overplot(w6, / black); 26 overplot(-w3, January lgreen) 26 G-Compensation Factor Compensated Pressure Base Pressure None-Return to Zero Factor Figure 4. Compensation factor for TM17. Figure 5 compensated pressure data for TM17. value shifts to the true zero. b). The G-compensation residuals (figure 3) caused by the blind gage built into the gage affected the reading. In both cases, correction factors have been determined to compensate the pressure for the effects of these distortions as shown in figures 4 and 5. PRESSURE RESISTANCE CALCULATION YUMA / PIMP+5% / Ambient W12: W3; overplot(w11*3.31, / 26 lred) January 26 5 Two different methods have been used to determine resistance pressure. The experimental method using the axial acceleration and base pressure data from the IBTP TM17 firing as shown in figure 6 and a numerical model using all the parameters described in figure 7. After a comparison of the results, the numerical model was updated using the experimental data to fine tune critical propellant parameters and predict muzzle velocity with great accuracy. Compensated Pressure Vs. Px ( PSI ) 5 5 47 44 41 38 35 32 2 2 2 2 17 14 11 8 5 2-1 Pressure Derive from Axial Compensated Pressure
316 INTERIOR BALLISTICS Gun Tube P P1 P2 PB PX Propellant Charge PB IBTP Projectile PA PR F = M. α PX = F / A Experimental Profile PX =( W. α ) /( A. gc ).(1) PB Projectile Base Pressure ( PSI ) PX Pressure Derived from the Axial acceleration ( G s ) PR Pressure Resistance ( PSI ) M Mass of the IBTP projectile ( Lbs ) A Projectile Cross tion (Square Inches ) α Axial Acceleration (G s ) W = M. gc gc = gravitational Constant g = Acceleration units Figure 6. Empirical Free Body Diagram Numerical Model profile P Breech Pressure ( PSI ) P1 Mid-Chamber Pressure ( PSI ) P2 Fwd Chamber Pressure ( PSI ) PA Pressure due to the Air in front of the Projectile ( PSI ) PB Projectile Base Pressure ( PSI ) PR Resistance Pressure ( PSI ) P Total Pressure ( PSI ) W Weight of Projectile ( Lbs ) A Bore Cross tion ( Square inches ) gc Gravitational Constant α Projectile Axial Acceleration ( G s ) PR = Total Friction + Blow-By + Engraving Forces Figure 7.- Analytical Free Body Diagram. EXPERIMENTAL PROCEDURE Step1: Determine force from pressure and Newton s second law Identify muzzle exit time for the acceleration from figure 2 and for the pressure from figure 4 and extract the acceleration and pressure up to this point. This is the setback portion of the axial event. Double integrate the axial acceleration to determine projectile travel distance and verify that muzzle exit corresponds to 2 inches of projectile travel. If not, make adjustments on the sampling frequency to match the travel distance. Step 2: Smooth measured data The operations required to determine resistance pressure can not be done with noisy data, because it usually results in negative values which have no physical meaning. To avoid this the data is smoothed by using filtering and curve fitting techniques as shown in figures 8 and 9.
Novel examination of gun bore resistance analysis and experimental validation 317 Axial Acceleration ( G s ) 1 14 1 12 11 1 8 7 5 4 2 ACCELERATION TM17 YUMA / PIMP+5% W19: / Extract(W2,,313); Ambient overplot(w18, / 26 lred) January 26 Raw Axial Acceleration Filtered Axial Acceleration 1-1 Figure 8. Smoothed acceleration data for TM17. Base Pressure ( PSI ) 5 51 4 47 45 4 41 3 37 35 3 31 2 27 25 2 21 1 17 1 11 7 5 PRESSURE TM17 YUMA / PIMP+5% / W22: Ambient W21; overplot(w2*3.3, / lred) 26 January 26 Raw - Base Pressure Filtered Base Pressure 1-1 Figure 9. Smoothed pressure data for TM17. Step 3: Compensate pressure data Compensate the pressure data as previously described. Step 4: Subtract the force required to generate the acceleration from the force generated by the base pressure Determine the pressure required to yield the axial acceleration and subtract it from the compensated pressure (the actual pressure acting on the base of the projectile). This is the resistance pressure in the time domain. Step 5: Plot the resistance curve Perform an XY Plot with the resistance from step 4 up to the travel distance calculated in step 1. The result is the resistance pressure vs. travel as shown as the lower trace in figure 1.
318 INTERIOR BALLISTICS 118 112 16 1 94 88 82 76 Resistance ( PSI ) 7 64 58 52 46 4 34 28 22 RESISTANCE TM17 YUMA / PIMP+5% / Ambient W8: W1; overplot(w7, / 26 lred) January 26 16 1 4-2 2 4 6 8 1 12 14 16 18 Inches Figure 1. - Resistance Profile for TM17. Numerical Model Resistance Experimental Resistance ANALYSIS CODE A lumped parameter interior ballistics model, IBHVG2 [2], was used to generate analytical interior ballistic predictions. After generating an empirical resistance profile for the projectile in the tube, the model was exercised to determine if the new resistance profile would yield an acceleration profile for the projectile which would show a reasonable correlation to the empirical data. The model employs basic physics and thermo-chemistry to drive the projectile down a launch tube. Both the energy balance and the equation of motion utilize the resistance profile. In the energy balance, the energy available to accelerate the projectile is reduced by losses. One of the losses is the energy lost due to engraving the projectile, the energy lost to friction with the bore and the energy lost to gas blow-by. All these losses were lumped together in the resistance profile. The resistance profile itself is a set of data points with a resistive pressure at an axial position down the tube. The model interpolates values between the data points. In the equation of motion, the base pressure is reduced by the resistive pressure prior to the acceleration being calculated. The model was exercised with the new resistance profile from the empirical analysis replacing the previously estimated resistance profile. The previous resistance profile was a scaled representation of the way a metallic rotating band is represented historically.
Novel examination of gun bore resistance analysis and experimental validation 319 17 1 14 1 Axial Acceleration ( G s ) 12 11 1 8 7 5 4 2 ACCELERATION TM17 YUMA / PIMP+5% / Ambient W34: Extract(W3,,313); / overlay(w33, 26 January lred) 26 Empirical Axial Acceleration Analytical Axial Acceleration 1-1 Figure 11. Comparison of measured and calculated axial acceleration for TM17 The metallic band resistance pressure is greatest at approximately 75% of its insertion through the forcing cone of the tube. It then reduces through the rest of its engraving process and remains at a relatively low level during the rest of the ballistic cycle. The empirical resistance profile does not track with the physical representation of the rotating band obturator. It increases through the first 6 inches of travel, approximately, and then decreases through the rest of its in-bore flight. Utilizing this resistance profile, the model was recalibrated to adjust the closed bomb burn rate by modifying the burn rate coefficient to achieve the appropriate peak breech pressure. SUMMARY A data input file was generated using the specifics from the test round under study. The model was adjusted to match the peak pressure. A reasonably correlation was generated between the analytical model and empirical data. Limitations of using a lump parameter model are believed to be the prime source of error between the two. The pressure gradient within the chamber and tube is calculated by a Lagrangian approximation with no explicit hydrodynamics.
32 INTERIOR BALLISTICS FUTURE EFFORTS Currently efforts are underway to characterize KULITE pressure sensors with piezoresistive sensing elements and features such as 1 MHz resonant frequency and acceleration sensitivity of 5 1-8 % of full scale acceleration. A perceived advantage is that piezoresistive gages do not require charge amplifiers so the return to zero may not be present. Additionally, this gage is not G-compensated and the acceleration error is around 4 G s for a 15 kg shot therefore it is free of the G-compensation residuals issue As refinements in the analysis of test data are realized, the modeling effort will be updated. Additionally, a 1-dimensional modeling effort will be initiated to attempt to get a more refined correlation between the test derived data and the model. Utilizing a hydrodynamic model should minimize the discrepancy between the acceleration plots. REFERENCES [1] M. Hollis, B. Flyash, A. Bahia, J. Potucek, D. Carlucci, Empirical Measurements of Cannon Launch Pressures on a Finned 155-mm Artillery Projectile, 21 st International Symposium on Ballistics, 19-23 April 24. [2] R. D. Anderson, K. D. Fickie, IBHGV2 A User Guide, Technical Report BRL-TR-2829, US Army Ballistic Research Laboratory, July 1987 [3] J. Hodson, C. C. Guyott, FNGUN User Manual, Report Ref. FNC/895R, Frazer-Nash Consultancy Ltd, October 1994