84 th Shock and Vibration Symposium 2013 NASA

84 th Shock and Vibration Symposium 2013

NASA Engineering & Safety Center (NESC) Dynamic Concepts, Inc. Huntsville, Alabama

The software programs for this tutorial session are available at: http: //www. vibrationdata. com Username: lunar Password: module

Now consider that the bracket assembly is subjected to the random vibration base input level. The duration is 3 minutes.

Continuous Beam Subjected to Base Excitation

Continuous Beam Natural Frequencies

Continuous Beam Stress Levels

Continuous Beam, Sample Stress Time History

Time Scaling Equivalence

Project Goals

Fatigue Curves

Sample Base Input PSD

Synthesize Time History

Synthesized Time History PSDs

SDOF Response

Relative Displacement Response Statistics

Rainflow Counting on Relative Displacement Time Histories

Miner’s Accumulated Fatigue

Derivation of the RD-N Curve

Cycle Scale Factor

Numerical Results

Fatigue as a Function of 3 -sigma Limit for 20 million cycles

RD-N Equation for High-Cycle Fatigue

Damage Equivalence

Conclusions

Comparing Different Environments in Terms of Damage Potential

NAVMAT P 9492 Synthesized Time History

Synthesized Time History Histogram

Synthesized Time History PSD Verification

SDOF Response to Synthesis, Narrowband Random

Statistical Relation

SDOF Response to Synthesis, Narrowband Random, Histogram

SDOF Response to Synthesis, Rainflow Analysis

Damage Index for Relative Comparisons between Environments A damage index D was calculated using where b

Damage Index for SDOF (fn=300 Hz, Q=10) Response to PSD

Equivalent Sine Level

Equivalent Sine Level (cont) Random Response overall = 14. 50 GRMS = 14. 5 G (1 -sigma) for zero mean) Equivalent Sine Response Amplitude � 2 -sigma Random Response

Histogram Comparison, Base Inputs Random, Normal Distribution Sine, Bathtub Curve

Converting a Sine Tone to Narrowband PSD

Converting a Sine Tone to Narrowband PSD (cont) Set

Converting a Sine Tone to Narrowband PSD (example)

Converting a Sine Tone to Narrowband PSD, Verification

Converting a Sine Tone to Narrowband PSD, Verification (cont)

Converting a Sine Tone to Narrowband PSD, Verification (cont)

Converting a Sine Tone to Narrowband PSD, Verification (cont)

Converting a Sine Tone to Narrowband PSD, Rainflow Cycle Count b

Converting a Sine Tone to Narrowband PSD, Fatigue Damage The damage index is only intended to compare the effects of the two base input types. The Narrowband PSD is thus has a greater fatigue damage potential that the Sine input for b > 6. 4 Un-notched aluminum samples tend to have a value of b � 9 or 10.

Recall the formula for the overall GRMS response to narrowband base input The response levels are

Note that some references use smaller fatigue exponents which yield more conservative, higher PSD base input levels. Old Martin-Marietta document gives a value of b=4. 0 for “Electrical Black Boxes. ”

Base Input: Half-Sine Pulse (11 msec, 50 G)

The smallest difference is 692 at 190 Hz. 692^(1/6. 4) = 2. 78 1/2. 78 = 0. 36 So rescale time history amplitude by 0. 36 And PSD (G^2/Hz) by 0. 36^2 = 0. 13

CPU Time Comparison Language Program Time (min) rainflow. exe 1 rainflow_mex. cpp 1 Fortran RAINFLOW 2 Matlab rainflow_bins. m 23 Python rainflow. py 38 C/C++ Matlab MEX

Complete paper with examples and Matlab scripts may be freely downloaded from http: //vibrationdata. wordpress. com/ Or via Email request tom@vibrationdata. com tirvine@dynamic-concepts. com