Enhancement of power law model for accelerated life testing - ieee … of... · Mark Paulus-NUWC...

Mark Paulus-NUWC Keyport!

Slide 1

Enhancement of power law model for accelerated

life testing

Naval Undersea Warfare Center

Abhijit Dasgupta, PhD

University of Maryland

CALCE-Center for Advanced Life Cycle Engineering

Mark Paulus, PhD Principal Engineer, Advanced Test Development

Distribution Statement A: Approved for Public Release; Distribution is unlimited.


Slide 2

♦ Discuss the limitations of the Power Law Model when comparing different excitation vibration profiles

♦ Discuss the effects of a change in natural frequency and the resulting change in stress state

♦ Introduce the new semi-empirical model which accounts for the changing stress state

ASTR 2012 Oct 17-19, Toronto, Ontario, Canada

Outline


Slide 3

Test Specimen ♦ 1018 cold rolled mild steel

Ø annealed

♦ Full failure was defined when tip touched bar located ~1 in below tip at start

Full Failure Point


Slide 4 ASTR 2012 Oct 17-19, Toronto, Ontario, Canada

Excitation profiles

0.00001

0.0001

0.001

0.01

0.1

1

100 100020 2000

ED SMOOTH RS-40WHITE-MEDWHITE-LOWWHITE-HIGHED SIM RS-40

Frequency (Hz)

G2 /H

z

• 5 test specimens used for each profile RS-40 ED SIM RS-40 WHITE-HIGH Excitation WHITE-HIGH Response


Slide 5

0.00001

0.0001

0.001

0.01

0.1

1

100 100020 2000

ED SMOOTH RS-40WHITE-MEDWHITE-LOWWHITE-HIGHED SIM RS-40

Frequency (Hz)G

2 /Hz


Power Law Method

nkPSDPSDTTF 1)( =

Power Law using PSD

0

20

40

60

80

ED SIM R

S-40

ED SIM R

S-60

ED SMOOTH R

S-40

ED SMOOTH R

S-60

WHITE-HIG

H

WHITE-LOW

WHITE-MED

Profile

Tim

e to

Fai

lure Time-Predicted

Time-Measured

♦ Use measured TTF and initial PSD from WHITE-HIGH and WHITE-LOW, combined with the power law to predict TTF of other profiles.


Slide 6

6

Crack Propagation during Failure

EXAMINE IN DETAIL


Slide 7

Failure Videos

Slow Motion Video Time Elapsed Video


Slide 8

0.00001

0.0001

0.001

0.01

0.1

1

100 100020 2000

ED SIM RS-40WHITE-HIGH

Frequency (Hz)

G2 /H

z

Stress State changes

.0349 G2/Hz 8 Grms-15 min

Fn@ t0

.347 G2/Hz 8 Grms- 31 min

Fn@ t1

Fn@ t2

Natural frequency shift affects time to failure

Fn@ t3

Fn@ t4


Slide 9

0

50

100

150

200

250

300

350

400

0 10 20 30Time(min)

Fn (H

z)

ED SIM RS-40WHITE-HIGH

Natural Frequency Shift During Failure

1ii

1iii tt

fnfnRFC

−

−

−

−=

Slope is Rate of Natural Frequency Change (RFC)


Slide 10

Accelerated Life Model Implementation

♦ Step 1- Subject a test item to a vibration profile. Measure the RFC(fn) and ξ(fn)

♦ Step 2- Compute the SDOF relative displacement

♦ Step 3- Perform maximum likelihood estimate (or equivalent) to determine C and p.

np

rmsCyRFC ω=

( ) ( )∫∞

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎠⎞⎜

⎝⎛ +−

=0 22224 )2(2

1)(),( dfffff

fwffynnn

PSDnrmsξπ

!!

∑=

Δ=

N

i in

in

fRFCf

TTF1 )(


Slide 11

Comparison to Power Law using PSD

♦  Use measured RFC and PSD from WHITE-HIGH to predict TTF of other profiles.

♦  Only need to test one excitation profile

nkPSDPSDTTF 1)( =

Power Law using PSD

0

20

40

60

80

ED SIM R

S-40

ED SIM R

S-60

ED SMOOTH R

S-40

ED SMOOTH R

S-60

WHITE-HIG

H

WHITE-LOW

WHITE-MED

Profile

Tim

e to

Fai

lure Time-Predicted

Time-Measured

Beam 2-SEL Model

01020304050607080

ED SIM

RS-40

ED SIM

RS-60

ED SMOOTH R

S-40

ED SMOOTH R

S-60

WHITE-HIG

H

WHITE-LOW

WHITE-MED

Profile

MTT

F (m

in)

Time-PredictedTime-Measured


Slide 12 ASTR 2012 Oct 17-19, Toronto, Ontario, Canada

Rate of Frequency Change

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250 300 350

RFC

(Hz/

s)

Natural Frequency (hz)

White-High Meas.White-High Pred.

• Prediction of RFC is more accurate in the elastic region • Modeling can be done over any frequency change that is desired


Slide 13

A Note About Damping Factor

0

20

40

60

80

100

0 100 200 300fn(Hz)

Q(G/G)

Q=2*sqrt(fn)Q=linearQ=meas.

0

20

40

60

80

100

0 100 200 300fn(Hz)

Q(G/G)

Q=2*sqrt(fn)Q=linearQ=meas.

WHITE-HIGH WHITE-LOW

•  Damping ratio can be related to quality factor by

•  from Steinberg

•  Measured value of Q from experiment

• Item dependent

• Amplitude and frequency dependent

•  Linear approximation gives reasonable results

nfQ 2=

Q21

=ζ

Q21

=ζ


Slide 14

Comparison of Damping Models


Beam 2-SEL Model

01020304050607080

ED SIM

RS-40

ED SIM

RS-60

ED SMOOTH R

S-40

ED SMOOTH R

S-60

WHITE-HIG

H

WHITE-LOW

WHITE-MED

Profile

MTT

F (m

in)


010203040506070

MTT

F(m

in)

Profile

Beam 2 SEL Model - Linear Q



Slide 15

♦ Power Law model does not account for a change in natural frequency

♦ A change in natural frequency leads to a change in the stress state

♦ New semi-empirical model accounts for changing stress state which improves prediction accuracy


Conclusions


Slide 16

Mark Paulus, PhD NUWC-Keyport

Principal Engineer- Advanced Test Development Further Reading:

Ø M.E. Paulus, A. Dasgupta and E. Habtour, Life estimation model of a cantilevered beam subjected to random vibration, Fatigue and Fracture of Engineering Materials. 2012. DOI:10.1111/j.1460-2695.2012.01693.x

Ø M.E. Paulus, A. Dasgupta, Semi-empirical life model of a cantilevered beam subject to random vibration, International Journal of Fatigue, 45 (2012) 82–90.


QUESTIONS?

Enhancement of power law model for accelerated life testing - ieee … of... · Mark Paulus-NUWC...

Documents

Transcript of Enhancement of power law model for accelerated life testing - ieee … of... · Mark Paulus-NUWC...