May 2004NDIA Small Arms Las Vegas, 2004 11 Small Caliber Engraving Force Measurements Jeff Siewert Systems Engineer Arrow Tech Associates 1233 Shelburne.

May 2004 NDIA Small Arms Las Vegas, 2004

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If you can’t get a bigger target...

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Small CaliberEngraving ForceMeasurements

Jeff SiewertSystems Engineer

Arrow Tech Associates1233 Shelburne Rd., Suite D-8

S. Burlington, Vt. 05403802-865-3460 x19

[email protected]


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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]


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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


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Barrel Sections for Push Force Testing

Instron Machine

Barrel Sections& Adapters

Push Test In Progress


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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”


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7.62mm Barrel Configuration

1.2 FC Half Angle


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“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)


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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


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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

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xAngle ()

Torque Sidewall Angle

Polygonal Barrels Attractive for Ceramic / Refractory Metals


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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


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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)


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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


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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


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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


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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)


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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


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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


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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


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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


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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


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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)


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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


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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

May 2004NDIA Small Arms Las Vegas, 2004 11 Small Caliber Engraving Force Measurements Jeff Siewert Systems Engineer Arrow Tech Associates 1233 Shelburne.

Documents

ndia small arms las

barrel slide

bbl slide

progress slide

cont slide

force prediction slide

radial stiffness slide

fn small change