Enhancement of power law model for accelerated life testing

Transcription

1 Enhancement of power law model for accelerated life testing 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. Naval Undersea Warfare Center Slide

2 Outline 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 22 Oct 7-9, Toronto, Ontario, Canada Slide 2

3 Test Specimen 8 cold rolled mild steel Ø annealed Full failure was defined when tip touched bar located ~ in below tip at start Full Failure Point Slide 3

4 Excitation profiles. G 2 /Hz... ED SMOOTH RS-4 WHITE-MED WHITE-LOW ED SIM RS Frequency (Hz) 5 test specimens used for each profile RS-4 ED SIM RS-4 Excitation Response ASTR 22 Oct 7-9, Toronto, Ontario, Canada Slide 4

5 Time to Failure ED SIM RS-4 ED SIM RS-6 Power Law using PSD Time-Predicted Time-Measured ED SMOOTH RS-4 ED SMOOTH RS-6 Power Law Method Profile WHITE-LOW WHITE-MED G 2 /Hz TTF ( PSD) =.... n kpsd ED SMOOTH RS-4 WHITE-MED WHITE-LOW ED SIM RS Frequency (Hz) Use measured TTF and initial PSD from and WHITE-LOW, combined with the power law to predict TTF of other profiles. ASTR 22 Oct 7-9, Toronto, Ontario, Canada Slide 5

6 Crack Propagation during Failure EXAMINE IN DETAIL 6 Slide 6

7 Failure Videos Slow Motion Video Time Elapsed Video Slide 7

8 Stress State changes..349 G 2 /Hz 8 Grms-5 min Natural frequency shift affects time to failure G 2 /Hz. F t 4. F t G 2 /Hz 8 Grms- 3 min. F t 2 F t ED SIM RS-4 F t. 2 2 Frequency (Hz) Slide 8

9 Natural Frequency Shift During Failure Fn (Hz) Slope is Rate of Natural Frequency Change (RFC) RFC ED SIM RS-4 i = fn t i i t fn i i Time(min) Slide 9

10 Accelerated Life Model Implementation Step - Subject a test item to a vibration profile. Measure the RFC(f n ) and ξ(f n ) Step 2- Compute the SDOF relative displacement y rms Step 3- Perform maximum likelihood estimate (or equivalent) to determine C and p. N p Δf RFC = Cy rms ω ni n TTF = RFC( f ( f, fn) = w!! PSD ( f ) df ( ) ( ) π fn f + (2ξ n f fn) i= ni ) Slide

11 Comparison to Power Law using PSD MTTF (min) ED SIM RS-4 ED SIM RS-6 Beam 2-SEL Model ED SMOOTH RS-4 Time-Predicted Time-Measured ED SMOOTH RS-6 Profile WHITE-LOW WHITE-MED Time to Failure ED SIM RS-4 ED SIM RS-6 Power Law using PSD Time-Predicted ED SMOOTH RS-4 ED SMOOTH RS-6 TTF ( PSD) = Time-Measured Profile n kpsd WHITE-LOW WHITE-MED Use measured RFC and PSD from to predict TTF of other profiles. Only need to test one excitation profile Slide

12 3 Rate of Frequency Change 2.5 White-High Meas. White-High Pred. RFC(Hz/s) Natural Frequency (hz) Prediction of RFC is more accurate in the elastic region Modeling can be done over any frequency change that is desired ASTR 22 Oct 7-9, Toronto, Ontario, Canada Slide 2

13 ζ = 2Q 8 A Note About Damping Factor Q=2*sqrt(fn) Q=linear Q=meas. 8 Q=2*sqrt(fn) Q=linear Q=meas. Q(G/G) 6 4 Q(G/G) fn(hz) Damping ratio can be related to quality factor by Q = 2 from Steinberg f n Measured value of Q from experiment Item dependent Amplitude and frequency dependent 2 3 fn(hz) WHITE-LOW ζ = 2Q Linear approximation gives reasonable results Slide 3

14 Comparison of Damping Models MTTF(min) Beam 2 SEL Model - Linear Q Time-Predicted Time-Measured MTTF (min) Beam 2-SEL Model Time-Predicted Time-Measured Profile ED SIM RS-4 ED SIM RS-6 ED SMOOTH RS-6 ED SMOOTH RS-4 Profile WHITE-LOW WHITE-MED ASTR 22 Oct 7-9, Toronto, Ontario, Canada Slide 4

15 Conclusions 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 ASTR 22 Oct 7-9, Toronto, Ontario, Canada Slide 5

16 QUESTIONS? 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. 22. DOI:./j x Ø M.E. Paulus, A. Dasgupta, Semi-empirical life model of a cantilevered beam subject to random vibration, International Journal of Fatigue, 45 (22) ASTR 22 Oct 7-9, Toronto, Ontario, Canada Slide 6