Air Bearing Upgrade for Split-Hopkinson Pressure Bar (SHPB) Experiment

Donald Hayes II, Joseph Chason, Sarah Napier, Zachary Johnson Department of Mechanical Engineering

Sponsor Dr. Joel House

Eglin Air Force Base Research Laboratory

AdvisorErica Cosmutto

FAMU/FSU College of Engineering

April 12, 2012

Overview Introduction Concept Generation & Selection Final Concept Components Functional Diagram Results & Discussion Project Budget Safety Concerns Conclusion Acknowledgements Questions

2

Introduction: SHPB Basics

StrikerMechanism

Incident Bar / Strain Gauges / Bushings

Transmitter Bar / Strain Gauges / Bushings

MaterialSample

Momentum Trap

Initial Strain Pulse

Reflected Pulse Transmitted Pulse

3

Introduction: SHPB Basics

StrikerMechanism

Strain Gauges Strain GaugesMaterialSample

Momentum Trap

Data

Data Acquisition System

4

Introduction: Needs Assessment Research air bearings for existing 5/8 inch

diameter journal bearing system Develop:

Bar alignment method System upgrade from journal bearings to air bearings

Determine efficiency of air bearings over journal bearings

5

Introduction: Objectives Analyze SHPB design based on use of air bearings Analyze:

Hardware cost Interface requirements Installation procedures Impact on bar geometry

Assess strain gauge technology Develop procedure to align bars Design a working prototype to show knowledge of

system Remain within $2500 budget

6

Generating Concepts: Methodology

Break system into base components Treat components as individual systems Generate multiple solutions per system Determine most suitable components Combine and implement into design

7

Generating Concepts: Components & Concerns

SHPB Components Base Structure Striker Mechanism Incident & Transmission Bars Strain Gauges Air Bushings Momentum Trap Air Supply System

Concerns Bar Alignment Method Data Acquisition

8

Generating Concepts: Criteria

Cost Weight Size Simplicity Durability

Portability Scalability Accuracy Data Quality Ease of Use

9

Selecting Concepts

10

Selecting Concepts

11

Selecting Concepts

CostMass

SizeSimplicity

Durability

PortabilityScalability

Accuracy

Data Quality Ease of use

Score

12

Final Concept Component Final SelectionBase Structure T-Slotted Framing

Striker Mechanism Electric Solenoid

Incident, Transmission & Striker Bars 0.75” dia. 1566 Steel

Strain Gauges Foil Type (Vishay Co.)

Air Bushings 0.75” ID (New Way Air Bearing Co.)

Momentum Trap Custom

Gas Supply Compressed Argon

Data Acquisition NI Hardware & Software (LabView)

Bushing Alignment Method Laser Insert

13

Components: Striker Mechanism

Solenoid Striker barMcMaster Carr

336 ozf.

14

Striker bar tube

Components: Air Bushings

Air lineBushing block

housing Air bushing

New Way Air Bearings0.75” Inner Diameter30 lb. Radial Load

15

Components: Strain Gauges and Material Sample

Strain gauges

16

Components: Strain Gauges and Material Sample

Strain gauges

Vishay MicromeasurementsGauge factor ≈ 2Resistance = 120 ΩLocated 6” from sample

17

Components: Strain Gauges and Material Sample

Copper specimen ~ 0.3” diameter~ 0.3” thick

18

Components: Momentum Trap (bar stopper)

19

Final ConceptIncident bar

Copper specimen

Momentum trap

Transmitter bar

Strain gauges

Air bushing

Striker bar mechanism

Length = 8 ft.Width = 7 in.Height = 3.5 in.

20

Functional Diagram

Activation Switch

StrikerMechanism

Incident Bar / Strain Gauges / Bushings

Transmitter Bar / Strain Gauges / Bushings

MaterialSample

Momentum Trap

WheatstoneBridges

Gas Supply

DC PowerSupply

Data Acquisition

System

DataPowerGas

120 Volts AC Data

Recording & Storage

21

Strain Pulse: VisualizationVisualizing the Sample

CopperSample

SteelIncident Bar

SteelTransmitter Bar

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Strain Pulse: VisualizationReduced Sample Area Increases Applied Stress

Dsteel DCopper 0.75 in 0.31 in

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Visualizing the Strain PulseSurface: Von Mises Stress

Yield Stress

σy Copper

½ σy Steel

24

Geometric Definitions + Boundary Conditions

Material Description

Strain Waves Strain Energy

Analyzing Data LabView hardware & software 250 kHz Sampling rate

Measured Voltage Calculated Strain

25

Data Acquired

26

Incident Wave Equal to Consequent Waves

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Elastic Impulse Wave Area

Incident Reflected Transmitted "Absorbed"

Strain-Seconds 1.15 x 10-8 4.47 x 10-9 5.46 x 10-9

% of Initial Pulse 100 % 38.7 % 47.3 % 14 %

Low sampling rate error

∫dε*dt (s)

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Discussion Potential improvements in system

Use of stainless steel bars Potential improvements in testing

Annealed copper specimen Higher data rates

Used 250 kHz Recommend 1 MHz

Implement friction imitation method to evaluate efficiencies between air bushings and journal bearings

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Project Budget Within budget Total budget

$2,500 Total expenditures

$2117 Percentage under budget

15%

30

Striker2.8%

Support Systems3.0%

Frame3.1%

Bars11.9%

Budget Savings15.3%

Bearings64.0%

Allocation of Expenditures

31

Safety Concerns

Pinching/crushing fingers

Flying Fragments

Electrocution

32

Review Analyzed:

SHPB design based on use of air bushings Interface requirements Installation procedures

Designed alignment tool Impact on bar geometry

33

Review Assessed strain gauge technology

Foil gauges sufficient Semiconductor gauges if high accuracy required

Designed a working prototype that shows knowledge of system

Remained within $2500 budget Total expenditures ≈ $2100

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Conclusion Accomplished major requirements! Critical Factors

Segmented design Ease of manufacture Team cooperation Excellent support

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AcknowledgementsWe would like to thank the following people for their help and support which

made this project a success…

Dr. House – Eglin AFRLDr. Shih – FAMU/FSU COEDr. Kosaraju – FAMU/FSU COE, CAPSDr. Dalban-Canassy – FAMU/FSU COE, ASCDr. Hovsapian - CAPSMr. Bob Walsh - NHMFLMr. Dustin McRae – FAMU/FSU COE, NHMFLDr. Solomon – FAMU/FSU COEMr. Ryan Jantzen – FAMU/FSU COE, HPMIMr. Bill Starch - ASCDr. Hellstrom – FAMU/FSU COE, ASC

THANK YOU!

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Questions?

Comments?

Quantity Unit Cost Total CostSolenoid 1 69.94 $69.94T-slot Framing 1 1/2 inch (96 inch length) 2 48.15 $96.30Incident & Transmission Bar: 1566 Steel Bar 0.75 inch (36inch length) 2 29.42 $58.84

T-slot Framing 1 1/2 inch (4 foot length for 6 inch braces) 1 25.15 $25.15Air Manifold (72 inches) 1 16.34 $16.34Striker Bar: 1566 Steel Bar 0.75 inch (6inch length) 2 5.17 $10.34Right Angle Fastener 16 4.06 $64.96Fasteners (Packs of 4) 16 2.71 $43.36Strain Gauges (Pack of 10) 3 20 $60.00Air Bushings 0.75 inch 4 265 $1,060.00Bushing Block 0.75 ID 4 135 $540.000.25”x3”x72” Aluminum Sheet 1 40.35 $40.35

0.75” Diameter x 12” Long High Tolerance Aluminum Bar 1 12.1 $12.1012” Aluminum U-Channel 1 14.19 $14.190.75” diameter x 6” Long High Tolerance Steel Bar 1 5.26 $5.26Total $2,117.13

Detailed Budget

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Velocity CalculationsThe velocity of the striker bar is neededThe only requirement is that the specimen plasticaly deform while the incident and transmitter bars are only loaded elasticalyThe following equations show the process

yc 70MPa Yield stress of copper

Areac .42

in

2 0.126in2 Area of the copper

F yc Areac 5.675kN Force Required to reach Yield

Next the mass of the steel bar is computed

7.85gm

cm3 Density of steel

v 0.75

2

2 in2 6 in 2.651in3

Volume of the 3/4 inch diameter, 6 inch striker bar

mass v 0.341kg Mass of the striker bar39

Velocity CalculationsNext the amount of time the striker bar will impact the incident bar

c 6100ms

Speed of wave propogation in steel

Length of Striker barL 6in

Pressure wave propogating down the strikerbar and returning = 2 x length/speed

t 2Lc

4.997 10 5 s

t 49.967s Duration of impact

Finaly the minimum velocity of the striker bar needed to plasticaly deform the specimen

VF

masst 0.832

ms

Minimum velocity of striker barneeded to plasticaly deform the copper specimen

V 1.86mihr

40

Velocity CalculationsAcc

130ozfmass

105.993m

s2 Acceleration available from the

chosen solenoid

Lsol 1in Length of piston with given force

D Do Vo t .5A t2 Generic dynamic position equation

timesolLsol

0.5 Acc

.5

0.022s Derived time, from previous equation

Vstkr Acc timesol 5.191mihr

Calculated velocity from given solenoid

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Plastic Energy Derivation

• Stress σ = F/A

• Strain ε = (Li – Lo) / Lo

• Gauge Factor GF = [ (Ri - Ro) / Ro] / ε

• Data Strain ε (Ri) = [ (Ri - Ro) / Ro] / GF

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Plastic Energy Derivation

• Strain in Specimen:

dεavg / dt = ( cb / Ls ) * (εI – εR – εT)

• Integration:

εs = (Cb / Ls) * ∫0t [(εI – εR – εT) *dt]

Strain through the specimen

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Plastic Energy Derivation

• Strain energy for each wave

Kinetic energy = 0.5 * m * v2

• Initial EI = 0.5* AB * CB * EB * T *εI2

• Reflected Er = 0.5* AB * CB * EB * T *εR2

• Transmitted Et = 0.5* AB * CB * EB * T *εT2

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Plastic Energy Derivation

• Strain energy

δSE = EI – ER – ET

• Plastic Energy absorbed by specimen

Es = 2 * δSE45

Solenoid Optimization

0 10 20 30 40 50 60 70 80 90 1000

500

1000

1500

2000

Cost ($)

Appl

ied

Forc

e (o

z F)

Unacceptable Region

Acceptable Region

Unacceptable Region

Unacceptable Region

46

Weak Formulation for FEA

A 2tTd

d

2

xE A

xud

d

dd

f x t( ) 0

x t( )w A 2tTd

d

2 w

xE A

xud

d

dd w f x t( )

d 0

x t( ) A( )twd

d

tTd

d

w f x t( )

d w A tTd

d

0

47

Weak Formulation for FEA

48