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…