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May 2004 NDIA Small Arms Las Vegas, 2004
1
If you can’t get a bigger target...
1
If you can’t get a bigger target...
Small CaliberEngraving ForceMeasurements
Jeff SiewertSystems Engineer
Arrow Tech Associates1233 Shelburne Rd., Suite D-8
S. Burlington, Vt. 05403802-865-3460 x19
May 2004 NDIA Small Arms Las Vegas, 2004
2
If you can’t get a bigger target...Sponsor
Contract: DAAE30-00-M-0236
Dr. Sheldon CytronAMSTA-AR-PC-H
973-724-3368 [email protected]
May 2004 NDIA Small Arms Las Vegas, 2004
3
If you can’t get a bigger target...Background
• Medium Caliber Measurements– 1972 GE ASD: Wolf & Cochran, 25mm
• Large Caliber Experimental Data– 1989, 1991 “Sticker” Testing, 155mm & 203mm
• Small Caliber Interior Ballistic Simulations– Missing: Change in Pmax as F(n) Small Change in Dia.– No direct push force measurement until Feb 2003
May 2004 NDIA Small Arms Las Vegas, 2004
4
If you can’t get a bigger target...
Barrel Sections for Push Force Testing
Instron Machine
Barrel Sections& Adapters
Push Test In Progress
May 2004 NDIA Small Arms Las Vegas, 2004
5
If you can’t get a bigger target...Bullet Construction
• Two Structural Configurations, Lubed & Unlubed
Lead Alloy Core
Copper Plated Steel Jacket
CavityCavity
Lead Alloy Core
Copper Plated Steel Jacket
CavityCavity
Pure Copper Body
Nose Cavity
Pure Copper Body
Nose Cavity
M80
Barnes “X”
May 2004 NDIA Small Arms Las Vegas, 2004
6
If you can’t get a bigger target...
7.62mm Barrel Configuration
1.2 FC Half Angle
May 2004 NDIA Small Arms Las Vegas, 2004
7
If you can’t get a bigger target...
“Standard” Barrel Cross Section
7.8225mm Dia.+ 0.03757.643mm Dia.
+ 0.0325
4.365mm+ 0.175
0.0898mm
7.62mm Barrel
Config. (con’t)
May 2004 NDIA Small Arms Las Vegas, 2004
8
If you can’t get a bigger target...Mod 7.62mm Reamer
• Fabricated from Muzzle End of Original 7.62mm Bbl
DimensionKey
Dimension, Inches
A: 0.4370
C: 0.474
D: 0.4570
E: 0.3460
F: 0.3440
G: 0.30850
H: (TBD, est.0.2897”)
K: 2.0250
L: 1.3560
M: 0.3300
N: 0.1200
O: 0.2000
Q: 20 Degree
R: 2 1/2 Degree
2.5 Deg. Forcing ConeHalf Angle
May 2004 NDIA Small Arms Las Vegas, 2004
9
If you can’t get a bigger target...Polygonal Barrel
Max Feature Depth
Barrel Radius
3 4 5 6 8
9 10
Note: All Barrel Corners Have 3.9116mm Radius x 0.508mm Wide
7
xAngle ()
Torque Sidewall Angle
Polygonal Barrels Attractive for Ceramic / Refractory Metals
May 2004 NDIA Small Arms Las Vegas, 2004
10
If you can’t get a bigger target...
Baseline 7.62mm Bbl
Avg. Push Force
• Function of Bullet Construction & Lube• Non-linear Behavior
1.2 Deg Half Angle FC Average Push Force vs. Travel
0
1000
2000
3000
4000
5000
6000
40 50 60 70 80 90 100 110 120Travel, mm
Pu
sh
Fo
rce
, N
Uncoated, Solid Copper ProjectilesMoly Coated, Solid Copper ProjectilesMoly Coated M80 ProjectilesUncoated M80 Projectiles
May 2004 NDIA Small Arms Las Vegas, 2004
11
If you can’t get a bigger target...
Baseline 7.62mm BblPeak Force vs. #
• Where is “Steady State”????
1.2 Deg Half Angle FC Peak Push Force vs. Sequence #
y = 22.246x + 1217.1
y = 103.52x + 1108.1y = -65.112x + 3148.6
y = 95.025x + 4073.9
0
1000
2000
3000
4000
5000
6000
7000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Sequence #
Pea
k P
ush
Fo
rce,
NUncoated, Solid Copper Projectiles
Coated, Solid Copper Bullets
Moly Coated M80 Bullets
Std M80 Projectiles
Linear (Std M80 Projectiles)
Linear (Moly Coated M80 Bullets)
Linear (Coated, Solid Copper Bullets)
Linear (Uncoated, Solid CopperProjectiles)
May 2004 NDIA Small Arms Las Vegas, 2004
12
If you can’t get a bigger target...
Baseline 7.62mm BblPush Force Sigma
• Lowest w/ Bare Bullets in Std 7.62mm Bbl• Moly Lube Increased for this barrel
1.2 Deg Half Angle FC Push Force Standard Deviation vs. Travel
0
250
500
750
1000
1250
1500
1750
2000
40 50 60 70 80 90 100 110 120Travel, mm
Pu
sh
Fo
rce
Sig
ma
, N
Moly Coated, Solid Copper ProjectilesUncoated, Solid Copper ProjectilesMoly Coated M80 ProjectilesUncoated M80 Projectiles
May 2004 NDIA Small Arms Las Vegas, 2004
13
If you can’t get a bigger target...
M80 Projectile Resist Press vs. Travel, Lube & FC Angle
• Non-linear behavior• Differing Engraving Mechanism Assumed• Elastic in 1.2 Deg. Bbl, Plastic in 2.5 Deg. Bbl
M80 Bullet Resistance Pressure vs. Travel
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40 50 60Travel, mm
Re
sis
t P
ress,
MP
a
1.2 Deg FC, Moly Coated M80 Bullets1.2 Deg FC, Uncoated M80 Bullets2.5 Deg FC, Uncoated M80 Bullets2.5 Deg FC, Moly Coated M80 Bullets
May 2004 NDIA Small Arms Las Vegas, 2004
14
If you can’t get a bigger target...
2.5 deg FC Mod 7.62mm BBl
• Steeper FC Half-Angle = Lower Avg. Forces• Valid for Lubed and Unlubed Bullets
2.5 Deg Half Angle FC Average Push Force vs. Travel
0
1000
2000
3000
4000
5000
6000
40 50 60 70 80 90 100 110
Travel, mm
Pu
sh F
orc
e, N
Uncoated M80 Projectiles
Moly Coated M80 Projectiles
May 2004 NDIA Small Arms Las Vegas, 2004
15
If you can’t get a bigger target...
2.5 deg FC, Peak Force vs. #
• Steeper FC Angle = Lower Variability
2.5 Deg Half Angle FC, Peak Push Force vs. Sequence Number
y = 17.004x + 1016.9
y = 52.331x + 699.81
0
1000
2000
3000
4000
5000
6000
7000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sequence Number
Pe
ak P
ush
Fo
rce
, N
Moly Coated M80 ProjectilesUncoated M80 ProjectilesLinear (Moly Coated M80 Projectiles)Linear (Uncoated M80 Projectiles)
May 2004 NDIA Small Arms Las Vegas, 2004
16
If you can’t get a bigger target...
Radial Stiffness Effect
• Radial Stiffness Affects Engraving Forces• Bullet Construction Affects Radial Stiffness
Radial Stiffness vs. Interface Diameter
0.00E+00
5.00E+07
1.00E+08
1.50E+08
2.00E+08
2.50E+08
3.00E+08
3.50E+08
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Interface Diameter, inches
Rad
ial S
tiff
ne
ss, l
b/in
Copper/Tungsten Plastic/TungstenPure SteelCopper/Steel CorePure CopperSteel/Lead Core Copper/Lead CorePure Lead
May 2004 NDIA Small Arms Las Vegas, 2004
17
If you can’t get a bigger target...
Relative Stiffness Effect on Resistance Pressure
Relative Resistance Factor vs. Interface Diameter
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Interface Diameter, Calibers
Re
sis
tan
ce
Fa
cto
rCopper/Tungsten Plastic/TungstenPure SteelCopper/Steel CorePure CopperSteel/Lead Core Copper/Lead CorePure Lead
Multiplier on baseline engraving force prediction
May 2004 NDIA Small Arms Las Vegas, 2004
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If you can’t get a bigger target... Effect on P-T
• Resistance Pressure Change Before Peak Pressure Affects Pmax• Smaller Effect than originally expected
7.62mm M80 Pressure vs. Time
0
50
100
150
200
250
300
350
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
Time, msec
Ch
amb
er P
ress
ure
, MP
a
Uncoated M80 in 7.62mm Baseline BbL
Moly Coated M80 in 7.62mm Baseline BblUncoated M80 in 2.5 Deg FC Mod 7.62mm Bbl
Moly Coated M80 in 2.5 deg FC Mod 7.62mm Bbl
May 2004 NDIA Small Arms Las Vegas, 2004
19
If you can’t get a bigger target...Effect on P-T
• Changes to Peak Pressure within “normal” limits• FC Increase: Reduced Pmax, Lube: No Effect
7.62mm M80 Pressure vs. Time
200
225
250
275
300
325
350
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Time, msec
Cha
mbe
r P
ress
ure,
M
Pa
Uncoated M80 in 7.62mm Baseline BbL
Moly Coated M80 in 7.62mm Baseline BblUncoated M80 in 2.5 Deg FC Mod 7.62mm Bbl
Moly Coated M80 in 2.5 deg FC Mod 7.62mm Bbl
May 2004 NDIA Small Arms Las Vegas, 2004
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If you can’t get a bigger target...Observations
• Non-linear Engraving Behavior– F(n) of Projectile Construction
– F(n) of Projectile Lubrication
– F(n) of Forcing Cone Half Angle
– F(n) of Bullet: Diameter, Engraved Length
• Reduced P-T Sensitivity– Due to Travel of Resistance wrt Pmax
• >15 Shots Req’d to Attain SS Engraving
May 2004 NDIA Small Arms Las Vegas, 2004
21
If you can’t get a bigger target...
Small Caliber Resistance Pressure Algorithm
KRatioL
GCos
FStiffnessFlFFBandMatBandlengthBandDiaPP refrr
*2
*9.16
*'**)0.1(*
PrN PrN Travel,
PSI MPa Band Lengths
2000 137.9 0.0
372650 25700.0 1.4-FC Len
478500 33000.0 (4.74+ FC Len)/2
507500 35000.0 4.0- FC Len
5400 372.4 4.87+ FC Len
5400 372.4 8.00
5400 372.4 10.00
5400 372.4 30.00
5400 372.4 60.00
5400 372.4 2000.00
Where:
Pr = Computed Resistance Pressure
PrN = Normalized Resistance Pressure
BD = Band Diameter, Calibers
BL= Band Length, Calibers
Mat’ FF = Material Code, 1.0 for Fe & Cu, 0.2 for Plastics
Stiffness FF = Stiffness Factor from chart
FC Len = Forcing Cone Length
K = Small Residual Constant
= Forcing cone angle (included angle)
May 2004 NDIA Small Arms Las Vegas, 2004
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If you can’t get a bigger target...
Predicted vs. CalcResistance Pressure
Small Cal Predicted vs. Calc. Engraving Pressure
0
20
40
60
80
100
120
0 10 20 30 40 50 60 70 80 90 100
Travel, mm
Pre
ss
ure
, MP
a Measured Barnes 1.2 Deg FC
Computed Barnes 1.2 Deg FC
Measured M80, 1.2 Deg. FC
Computed M80, 1.2 Deg. FC
Measured M80, 2.5 Deg. FC
Computed M80, 2.5 Deg FC
Data Collection Length Limited by Column Buckling of Punch
May 2004 NDIA Small Arms Las Vegas, 2004
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If you can’t get a bigger target...Conclusions
• Small Caliber Engraving is a More Complex Relationship Than Expected
• Closed Form Equation Can Be Used For Approximations
• Detailed Knowledge Req’d of:– Barrel: Lands & Grooves, FC angle– Bullet: Construction, Lubrication
• More Sophisticated Barrel Geometries (Polygonal) are under study