Vibrationdata 1 Using Fatigue to Compare Sine and Random Environments Unit 35.
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Transcript of Vibrationdata 1 Using Fatigue to Compare Sine and Random Environments Unit 35.
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