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Gun-Barrel Vibrations of Rapid-Fire Medium Caliber Guns
Prof Tom DawsonU. S. Naval Academy
April 23, 2008
with support fromNAVSEA Naval Gunnery Project Office
and Naval Surface Warfare Center Dahlgren
43RD ANNUAL ARMAMENT SYSTEMS:GUN & MISSILE SYSTEMS CONFERENCE
I. Background
Barrel VibrationsBarrel 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-calibergun 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. HeddenNovel use of
optical reflections and “Fastax”
camera to measurerotations (slopes) of barrel section near
muzzle during projectile launch
…and Early Record of Barrel Vibrations
Section RotationΔφ = φ1−φ2
φ1
φ2
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)
Barrel curvature from manufacture
Avg CircleR
Dispersion
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 mn
Pn
V’s & M’s dependon v’s at
n-1, n, n+1& projectileload P (if
between n-1 and n+1)
Pn-1
If P between n-1 and nPn-1 = FOtherwise 0
If P between n and n+1 Pn = F Otherwise 0
Projectile Forces on BarrelCentrifugal Forces
Friction Forces
TypicalCoeff of Frictionμ ≈ 0.20 to 0.30
Simple Example
Actual Case
III. “Generic” 3in /60 Gun Mount
(Firing 14 lb Projectiles)
Generic Barrel
Flexible section divided into 16 lumped masses. Accuracy checked by increasing number to 32 and then to 48 … as shown in the following
vibration frequenciesω1 = 62.0 rad/sec = 9.87 cycles/secω2 = 387 rad/sec = 61.6 cycles/sec
etc
Flexible LengthInside Dia = 3 in
Outside Dia = 4 in
Assumed Fixed
10’5’
Rigid Flexible
Barrel (No attachments)
Assumed Projectile Velocity in Barrel
0
500
1000
1500
2000
2500
3000
3500
0 2 4 6 8 10 12 14 16DISTANCE ALONG BARREL S (ft)
VELO
CIT
Y (F
/S)
From Leduc Formula assuming 50% of muzzle velocity
achieved at first 15% of barrel length
Muzzle (15 ft)
2.25 ft
S
bSaSV+
=
Demonstration of Adequacy of Lumped-Mass Model
- Idealized Case-Negligible Friction between Spinning
Projectile and Barrel
Convergence with number of mass elements
-0.006
-0.004
-0.002
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0 1 2 3 4 5 6 7 8 9 10 11Distance X along Barrel (ft)
Dis
plac
emne
t (in
).
32 Mass Model16 Mass Model48 Mass Model
VERTICAL DISPLACEMENTS(Relative to static values)
Friction Coeff μ = 0
Distance X
Projectile Location at X=5’
Adequacy of Computer Solution
-0.006
-0.004
-0.002
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0 2 4 6 8 10 12Distance along Barrel (ft)
Ver
tical
Def
lect
ion
(in) .
Simplified Case Constant Projectile Force
P=2000 lbsConstant Projectile Velocity
V= 2500 ft/sec Friction Coeff μ =0
Instantaneous Projectile Position
at VT=5'
From Analytical
(Exact) Theory
ComputerProgram
VT
P
Detailed Results -Actual Case-
First-Round Barrel ResponseFree Vibrations following First RoundResponse Characteristics after
Multiple Rounds
First-Round Barrel Response
Muzzle Deflections vs. Time
-0.03
-0.02
-0.01
0
0.01
0.02
0 0.5 1 1.5 2 2.5 3 3.5 4Time (msec)
Vert
ical
Dis
plac
emen
t (in
).
Muzzle Deflections (relative to static values)
First RoundFriction μ = 0.3
Friction μ =0.2
f= μ FH
FH
FV
Dynamic Section RotationComparison with 1951 Dahlgren Data
-0.002
-0.0015
-0.001
-0.0005
0
0.0005
0.001
0.0015
0.002
0 0.5 1 1.5 2 2.5 3 3.5
Time (msec)
Rel
ativ
e Se
ctio
n R
otat
ion
(rad
)
Data Round D
Theory (μ = 0)(solid line)
Time Normalized to Generic 3" / 60
Rotations as Measured
Optical Measurements B. M. Gurley & S. E. Hedden NPG Report 804 Dahlgren (1951)
Theory (μ = 0.2)
Free Vibrations following First Round
Free Vibration of Muzzle(note check of analytical solution
& damping value)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 100 200 300 400 500Time (msec)
Dis
plac
emen
t (in
)
Free-Vibration Analytical Solution
Computer Solution
Moderate Damping K = 0.03
Muzzle Vibration about Static Position after First-Round Projectile Exit
Response Characteristicsafter Multiple Rounds
Dynamic Amplification
-1.5
-1
-0.5
0
0.5
1
1.5
60 70 80 90 100 110 120 130 140Firing Rate (rds/min)
Rel
ativ
e D
ispl
acem
ent (
in).
81
113
124
126
71
Damping K = 0.03Friction Coefficient 0.30
3''/60 Generic
Muzzle Deflection after 4 Round BurstRelative to Static Values
Barrel Deflections(note continuing input of energy
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12Distance along Barrel (ft)
Def
lect
ion
(in) Moderate Damping
K = 0.03 Friction Factor
μ = 0.30
Actual DeflectionsFiring Rate 113 rds/min
Initial Static Droop
Begin Round 4
Begin Round 3
Begin Round 5
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
10 ft (effective)
Barrel & Water Jacket
Bore Evacuator & Lock Nut
Muzzle Break
Mark 75 - Idealized Barrel Description
Flexible Length
Inside Dia = 3 in
Outside Dia = 4 in
Modal Frequencies ω1 = 41 rad/sec (6.5 cycles/sec)ω2 = 276 rad/sec (44 cycles/sec)
etc
120’’62’’
Barrel (with attachments)
97 lbs 56 lbs
Muzzle Break & ½ Al Cover
Rigid Flexible
Gas Evac & Lock Nut & ½ Al Cover
Leduc formula for projectile velocity
Variable Firing Rates Normal (Bell-Shaped) Distribution
0
0.02
0.04
0.06
0.08
0.1
0.12
-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14
Differrence between Firing Rate & Average Firing Rate (rds/min)
Prob
abili
y D
ensi
ty (1
/rds
/min
).
Normal Distribution
Average 80 rds/min
Std Dev = 4 rds/min
68 % ±4 rds/min
95 % ± 8 rds/min
Dispersion: Theory vs. Measurement
-8
-6
-4
-2
0
2
4
6
8
-8 -6 -4 -2 0 2 4 6 8
Two Bursts - Theory
Two Bursts- DahlgrenData
Moderate Damping (K =0.03) Friction Coeff (μ = 0.20)
R = 2.93' =2mrad
20 Round BurstsTarget Distance 1500'
Std DevR(Theory) = 2.91’
R(Data) = 2.93’USN
.Mark 75 …3”/ 62 Gun Mount ….firing ….14 lb Projectiles
Mean Firing Rate 80 rds/min
Std Dev 4 rds/minFreq Ratio = 4.9
R = 2.93' =2 mrad
-8´
+8´
-8´ +8´
0
0
Damping (K =0.03) Friction (μ = 0.20)
20 Round BurstsTarget Distance 1500'
Two Burst -Theory
Two Burst –Dahlgren Data
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 (∼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
Mark 75
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 TheoryWhat 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 mrad120 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.
0
1
2
3
4
5
6
7
0.02 0.04 0.06 0.08 0.1 0.12Damping Coefficient
Std
Dev
of R
adia
l Dis
pers
ion
(mra
d).
Generic 3''/60(Avg 120 rds/min)
Mark 75 (Avg 120 rds/min) 10 Round Bursts
Avg of 4 Bursts (circles)Average Curve for
(50% reduction in add-on weights)
0.03 present Mark 75
VI. Concluding Remarks
Barrel Vibrations WorkAnalysis 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…