43RD ANNUAL ARMAMENT SYSTEMS: GUN & MISSILE SYSTEMS CONFERENCE Gun-Barrel Vibrations of Rapid-Fire Medium Caliber Guns Prof Tom Dawson U. S. Naval Academy April 23, 2008 with support from NAVSEA Naval Gunnery Project Office and Naval Surface Warfare Center Dahlgren
I. Background
Barrel Vibrations Barrel vibrations can affect accuracy of both slow firing and rapid firing guns by causing positive or negative muzzle jump during projectile launch. Vibrations can arise from gravity-caused barrel droop or barrel curvature from manufacturing or both. Possible enhanced effect with rapid-fire guns where vibrations from one round continue to exist and can be reinforced by subsequent rounds.
Present Interest in rapid-fire medium-caliber gun mounts and the effects of barrel vibrations on their accuracy. Motivation generated by evaluation and selection of gun mounts for the new Littoral Combat Ships and for other similar Navy needs
Early Navy Work Near-muzzle barrel vibrations of 3-in/70 Gun Mount during travel of projectile through the barrel -Single Firings
Dahlgren Report of 1951 B. M. Gurley & S.E. Hedden Novel use of optical reflections and Fastax camera to measure rotations (slopes) of barrel section near muzzle during projectile launch
and Early Record of Barrel Vibrations Section Rotation Δφ = φ 1 φ 2 φ 2 φ 1
Early Army Work Dispersion of machine-gun fire as influenced by firing rate. Increased dispersion measured when firing rate near fundamental barrel vibration frequency - or twice that frequency. Basis for design criterion that: barrel frequency in cycles/sec should generally be 4 (or more) times the firing rate in rounds/sec.
1955 Report on Barrel Vibrations D. E. Wente R. L. Schoenberger B. E. Quinn First study of dynamic amplification of barrel vibrations from tuned firing rates
Dynamic Amplification of Barrel (from 1955 Army Report) Dispersion R Avg Circle Barrel curvature from manufacture
Previous Numerical Work on Barrel Vibrations Numerical studies were carried out at the Army s Watervliet Arsenal during 1970 s (and onward) with attention restricted to barrel vibrations before projectile exit: No multiple firings.
II. Computer Model
Lumped-Mass Model & Mechanic 16 mass model mass m n P n-1 Pn V s & M s depend on v s at n-1, n, n+1 & projectile load P (if between n-1 and n+1) If P between n-1 and n P n-1 = F Otherwise 0 If P between n and n+1 P n = F Otherwise 0
Projectile Forces on Barrel Centrifugal Forces Simple Example Actual Case Friction Forces Typical Coeff of Friction μ 0.20 to 0.30
III. Generic 3in /60 Gun Mount (Firing 14 lb Projectiles)
Generic Barrel 5 Rigid Barrel (No attachments) 10 Flexible Assumed Fixed vibration frequencies ω 1 = 62.0 rad/sec = 9.87 cycles/sec ω 2 = 387 rad/sec = 61.6 cycles/sec etc Flexible Length Inside Dia = 3 in Outside Dia = 4 in Flexible section divided into 16 lumped masses. Accuracy checked by increasing number to 32 and then to 48 as shown in the following
Assumed Projectile Velocity in Barrel 3500 3000 2500 S VELOCITY (F/S) 2000 1500 1000 500 2.25 ft From Leduc Formula assuming 50% of muzzle velocity achieved at first 15% of barrel length V Muzzle (15 ft) as = S + b 0 0 2 4 6 8 10 12 14 16 DISTANCE ALONG BARREL S (ft)
Demonstration of Adequacy of Lumped-Mass Model - Idealized Case- Negligible Friction between Spinning Projectile and Barrel
Convergence with number of mass elements 0.014 Displacemnet (in). 0.012 0.01 0.008 0.006 0.004 0.002 0-0.002-0.004-0.006 32 Mass Model 16 Mass Model 48 Mass Model Friction Coeff μ = 0 Projectile Location at X=5 VERTICAL DISPLACEMENTS (Relative to static values) Distance X 0 1 2 3 4 5 6 7 8 9 10 11 Distance X along Barrel (ft)
Adequacy of Computer Solution 0.014 0.012 0.01 VT P Vertical Deflection (in). 0.008 0.006 0.004 0.002 0-0.002 Computer Program From Analytical (Exact) Theory Instantaneous Projectile Position at VT=5' Simplified Case Constant Projectile Force P=2000 lbs Constant Projectile Velocity V= 2500 ft/sec Friction Coeff μ =0-0.004-0.006 0 2 4 6 8 10 12 Distance along Barrel (ft)
Detailed Results -Actual Case- First-Round Barrel Response Free Vibrations following First Round Response Characteristics after Multiple Rounds
First-Round Barrel Response
Muzzle Deflections vs. Time 0.02 Vertical Displacement (in). 0.01 0-0.01-0.02 Muzzle Deflections (relative to static values) First Round F H F V Friction μ =0.2 Friction μ = 0.3 f= μ F H -0.03 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (msec)
Dynamic Section Rotation Comparison with 1951 Dahlgren Data 0.002 Relative Section Rotation (rad) 0.0015 0.001 0.0005 0-0.0005-0.001-0.0015-0.002 Data Round D Optical Measurements B. M. Gurley & S. E. Hedden NPG Report 804 Dahlgren (1951) Theory (μ = 0.2) 0 0.5 1 1.5 2 2.5 3 3.5 Time (msec) Theory (μ = 0) (solid line) Time Normalized to Generic 3" / 60 Rotations as Measured
Free Vibrations following First Round
Free Vibration of Muzzle (note check of analytical solution & damping value) 0.6 0.4 Muzzle Vibration about Static Position after First-Round Projectile Exit Displacement (in) 0.2 0-0.2-0.4-0.6 Free-Vibration Analytical Solution Computer Solution 0 100 200 300 400 500 Time (msec) Moderate Damping K = 0.03
Response Characteristics after Multiple Rounds
Dynamic Amplification Relative Displacement (in). 1.5 1 0.5 0-0.5-1 -1.5 Muzzle Deflection after 4 Round Burst Relative to Static Values 71 81 60 70 80 90 100 110 120 130 140 Firing Rate (rds/min) 113 Damping K = 0.03 Friction Coefficient 0.30 3''/60 Generic 124 126
Barrel Deflections (note continuing input of energy 1 0.8 Actual Deflections Firing Rate 113 rds/min Deflection (in) 0.6 0.4 0.2 0 Moderate Damping K = 0.03 Friction Factor μ = 0.30 Begin Round 5 Begin Round 3 Begin Round 4-0.2-0.4 Initial Static Droop 0 2 4 6 8 10 12 Distance along Barrel (ft)
IV. Application to USN Mark 75 (80 rds/min)
Mark 75 3"/62 (80 rds/ min) USS Curts FFG 38
Barrel Details Mark 75 (3in/62) Gun Mount Muzzle Break 10 ft (effective) Barrel & Water Jacket Bore Evacuator & Lock Nut
Mark 75 - Idealized Barrel Description Barrel (with attachments) 62 120 Rigid Flexible 97 lbs 56 lbs Gas Evac & Lock Nut & ½ Al Cover Muzzle Break & ½ Al Cover Modal Frequencies ω 1 = 41 rad/sec (6.5 cycles/sec) ω 2 = 276 rad/sec (44 cycles/sec) etc Flexible Length Inside Dia = 3 in Outside Dia = 4 in Leduc formula for projectile velocity
Variable Firing Rates Normal (Bell-Shaped) Distribution 0.12 Probabiliy Density (1/rds/min). 0.1 0.08 0.06 0.04 0.02 0 Average 80 rds/min Std Dev = 4 rds/min 68 % ±4 rds/min 95 % ±8 rds/min Normal Distribution -14-12 -10-8 -6-4 -2 0 2 4 6 8 10 12 14 Differrence between Firing Rate & Average Firing Rate (rds/min)
Dispersion: Theory vs. Measurement +8 20 20 Round Bursts Target Target Distance Distance 1500' 1500' 8 6 Moderate Damping Damping (K =0.03) (K =0.03) Friction Coeff (μ = 0.20) (μ = 0.20) 0 4 2 Std Dev R(Theory) = 2.91 R(Data) = 2.93 R = 2.93' =2mrad R = 2.93' =2 mrad 0-8 -6-4 -2 0 2 4 6 8-2 USN.Mark 75 3 / 62 Gun Mount.firing.14 lb Projectiles -8 Two Bursts -Theory Two Bursts- Dahlgren Data Two Burst Dahlgren Data -4-6 -8 Mean Firing Rate 80 rds/min Std Dev 4 rds/min Freq Ratio = 4.9-8 0 +8
V. Application to Study of Oto Melara 76 mm/62 SR (120 rds/min)
Oto Melara 76mm/62 SR (Super Rapid Gun Mount
Mark 75 vs 76mm SR Mark 75 Mark 75 ( 1970) SR( 2000) Firing Out of Battery In Battery Avg Firing rate 80 rds/min 120 rds/min Accuracy (10-rd burst) 1.9 mrad 0.30 mrad* *Reported on web page 76mm SR with standard shield
Extracted From Web Page: Italian 76mm/62 (3 ) The SR is an improved faster-firing version of the Mark 75. Accuracy improved partly by reducing the weights of the moving parts. Claims are that these changes have reduced the radial-error standard deviation values to less than 0.3 mrad for 10-round burst
Examination with Theory What if firing rate of Mark 75 is increased 50% to 120 rds/min? See table. Dispersion increased from about 1.9 mrad at 80 rds/sec to about 6.5 mrad at 120 rd/min (for 10-Rd Bursts) Mark 75 (modified) Firing Rate Radial Dispersion* (rds/min) (Std Dev in mrad) 80 1.9 mrad 120 6.5 mrad * 10 Rd Bursts (avg of 4)
What if weights of gas evacuator & muzzle break are then reduced by 50%? (Avg of data from generic and Mark 75) Dispersion reduced from about 6.5 mrad to about 4.5 mrad (for 10-rd bursts) Conclusion: Cannot achieve reported accuracy for 120 mm SR with only a reduction of add-on weights of Mark 75 when modified for 120 rds/min
What if increased damping of barrel vibrations? See graph below. Dispersion (dashed line) reduced from about 4.5 mrad to about 0.5 mrad for 200% increase in damping. Std Dev of Radial Dispersion (mrad). 7 6 5 4 3 2 1 0 0.03 present Mark 75 Mark 75 (Avg 120 rds/min) Average Curve for (50% reduction in add-on weights) Generic 3''/60 (Avg 120 rds/min) 10 Round Bursts Avg of 4 Bursts (circles) 0.02 0.04 0.06 0.08 0.1 0.12 Damping Coefficient
VI. Concluding Remarks
Barrel Vibrations Work Analysis can explore performance aspects of rapid fire guns not possible with limited testing. Can be of value in assessing factors for Navy needs when considering cost, accuracy, sensitivity to firing rate, inherent damping of vibrations, age effects, etc. Barrel vibrations can affect gun effectiveness and barrel wear. Longer term implications of work are improved fire control & accuracy and improved maintainability regarding barrel wear