Vibrationdata

1

Using Fatigue to Compare Sine and Random Environments

Unit 35

Comparing Different Environments in Terms of Damage Potential

Base Input is Navmat P9492 PSD, 60 sec Duration

SDOF Response fn=300 Hz, Q=10

Assume fatigue exponent of 6.4 (Steinberg's value for electronic equipment)

What is equivalent sine level in terms of fatigue damage?

0.001

0.01

0.1

20 80 350 2000

Overall Level = 6.0 grms

+3 dB / octave -3 dB / octave

0.04 g2/ Hz

FREQUENCY (Hz)

PS

D (

g2 /

Hz

)

NAVMAT P9492 Synthesized Time History

Save as: accel_input

Synthesized Time History Histogram

Synthesized Time History PSD Verification

SDOF Response to Synthesis, Narrowband Random

Acceleration Response absolute peak = 64.7 G overall = 13.9 GRMS

Std dev = 13.9G (for zero mean)

Peak response = 4.6 sigma

Save as: accel_resp

= standard deviation

[ RMS ] 2 = [ ] 2 + [ mean ]2

RMS = assuming zero mean

Statistical Relation

SDOF Response to Synthesis, Narrowband Random, Histogram

A damage index D can be calculated using

i

m

1i

bi nAD

where

iA

in

b

is the response amplitude from the rainflow analysis

is the corresponding number of cycles

is the fatigue exponent

Damage Index for Relative Comparisons between Environments

Rainflow Cycles for SDOF (fn=300 Hz, Q=10) Response to PSD, Exponent=6.4

Equivalent Sine Level

What is equivalent Sine Input Level at 300 Hz for 60 second duration?

Again, SDOF Response fn=300 Hz, Q=10

Assume fatigue exponent of 6.4

Modified Relative Damage Index for Steady-state Sine Response

f Excitation Frequency

T Duration

Y Base Input Acceleration

Q Amplification Factor

b Fatigue Index

is the response bYQTfD YQ

Equivalent Sine Level (cont)

f 300 HzT 60 secQ 10b 6.4D 2.6e+13

Y=2.7 G (Sine Base Input at 300 Hz)

(QY) =27 G (Sine Response)

b1

Tf

D

Q

1Y

bYQTfD

Random Response overall = 13.9 GRMS = 13.9 G (1-sigma) for zero mean)

Equivalent Sine Response Amplitude 2-sigma Random Response

Repeat analysis for other Q and b values as needed. Run additional PSD synthesis cases for statistical rigor.

Equivalent Sine Level (cont)

vibrationdata > fatigue toolbox > Miscellaneous > Equivalent Sine Input for Given Damage Level

Histogram Comparison, Base Inputs

Random, Normal Distribution Sine, Bathtub Curve

Even though histograms differ, we can still do equivalent damage calculation for engineering purposes.

This is Engineering not Physics!

Converting a Sine Tone to Narrowband PSD

• Assume a case where the base input is a sine tone which must be converted to a narrowband PSD

• The conversion will be made in terms of the acceleration response of the mass to each input

• Assume Q and fatigue exponent

• Calculate fatigue damage for sine tone

• Select frequency limits for narrowband PSD

• One-twelfth octave band is used for this example

• Assume initial PSD level of 1 G^2/Hz

• Calculated SDOF response to narrowband PSD

• Calculate narrowband damage using Dirlik method

• Scale PSD level to match sine damage

Converting a Sine Tone to Narrowband PSD

vibrationdata > fatigue toolbox > Miscellaneous > Equivalent Narrowband Random PSD for Sine Input

Converting a Sine Tone to Narrowband PSD

Q b PSD (G^2/Hz)

10 4 19.9

10 6.4 15.0

10 9 12.0

30 4 31.7

30 6.4 23.9

30 9 19.1

18 G, 100 Hz, Sine Tone converted to One-twelfth Octave band PSD

Highest Q and lowest b give most conservative PSD level