1. George Henderson GHI Systems, Inc. San Pedro, CA
Correlating End-Use Environments and ESS Machine Excitation Using Fatigue Equality
George Henderson
GHI Systems, Inc.
San Pedro, CA
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2. Scope Of Presentation Component Loading Response fr
gRMS and The PSD Spectrum
The Damage Potential Spectrum, DP(f)
Characterizing EUE Excitation
Characterizing 6DOF Vibration
Comparing EUE to 6DOF
We will be using certain terms and first need to define them.
I’m going to use the abbreviation SA to mean Spectrum Analyzer.
Here is the focus of what we will be covering today.
What is the basic mathematical algorithm on which the SA is based.
The basic details of the FFT
And as a focus on applications, we will use the chaotic pseudo-random HALT/HASS machine as a study example.

3. Component Loading Response
Parts vibrate at their natural frequency fr.
Vibration intensity depends on damping ratio and input loading.
If driven off fr response will decrease.
Fatigue only occurs when parts vibrate.
Products are assemblies of many parts.
Each with it’s own fr.
ESS stimulus should be uniform to uniformly stimulate all parts.

4. Response is Predictable
● Response bandwidth and
Gain depend on ζ .
● Higher response = more
fatigue vs time.
● Fatigue is produced only
if part is driven at fr *
● Loading must envelope all
part fr to achieve uniform
fatigue rates.
● Remember the TV Ad –
“Is it real or is it Memorex?
* Papoulis Law

5. gRMS & Hank's Rules 1: 6DOF gRMSs are not equivalent.
2: PSD scaled in g2/Hz is only measure of excitation power.
3: ∞ PSD’s can have the same gRMS.
4: gRMS with PSD jointly have meaning.
5: gRMS is unrelated to fatigue.
6: If you’re not stimulating the defect at its f, you’re wasting your time.*
It is elementary to show that gRMSs are unequal in fatiguing capability, UNLESS THEY RELATE TO IDENTAL SPECTRA.
The PSD is simply the root of the area under the PSD curve, of which there are an infinite number.
The machine’s gRMS meter is not measuring the energy transmitted to the product, nor it’s spectral components.
Hank Caruso, an ex Westinghouse test engineer and past president of the IEST, coined the famous Golden Rules.
A screen program that does not take into account the spectral power and fatigue experienced by screened components will eventually deliver problems to customers.
*Hank’s Golden Rule Number 1.

6. gRMS’s - Not Equally Effectivefr fr
g2/Hz
g2/Hz
“A”
“B”
Frequency
Frequency
Example: Consider two PSD’s: “A” and “B”.
Both PSD’s have the same gRMS – root of the area under the PSD curve.
Would they be expected to produce the same fatigue on a product who’s fr is as shown?
Difference is g2/Hz fr.

7. Example of gRMS Problem
The following slide shows results of identical screens using two different 6DOF machines.
Products were identical having a clock xtal defect. Fixturing was identical.
Machine set points were “10 gRMS”.
‘A’ found defect in 1/6th the time of ‘B’.
Reason was difference in excitation power g2/Hz at the fr of the defective part.

8. gRMS, a Non-Metric ‘B’ ‘A’ fr Spectral Intensity Spectral Intensity
This slide illustrates what we have been discussing about gRMS and PSDs.
The red curve is a PSD from a “segmented” table 6DOF machine, “A”. It’s gRMS was adjusted to be the same as a second “rigid plate” machine shown by the Blue PSD, “B”. The A spectrum almost envelopes the range of self resonance frequencies of the components of certain units under test. The B spectrum also does but is much lower at frx, the apparent resonant frequency of a failed component. The UUTs were ride control computers installed in a luxury car. All the products available had a common defect – a Quartz Crystal mounted above the circuit card and free to resonant in the plane of the board. During the tests, defects on machine A were precipitated in an average time of 8 minutes. 55 minutes were required for machine B. The difference is that although the gRMS was equal, there was a major difference in the spectral energy at the fatiguing resonance frequency of the components. This is shown graphically in the next slide.
,000
Frequency - Hz

9. gRMS– Not Related To Fatigue
Both Machines at “10 gRMS”
Defect Failure Level
Fatigue Magnitude
Rate = 4.1 E+6/Min
Rate = 1.7 E+8/Min
This is a plot of the fatigue accumulation versus time from the previous slide. Averages of several UUTs. Same meter indication of gRMS, but obviously different spectral shape.
Products on the two machines reached a total accumulated fatigue, but at different times. The times were related to the fatiguing intensity of excitation that enveloped the defect’s self resonant frequency.
Screen Duration- Min

10. Summary Rules On gRMS #1: Equal gRMSs are not equally effective
The PSDs must also be identical
An ∞ number of PSDs can have equal gRMS
#2: gRMS doubling does not double fatigue
Nor does halving it reduce fatigue by 50%
#3: gRMS on the chamber readout is not related to accumulated fatigue
fr, not the gRMS is what counts
It is elementary to show that gRMSs are unequal in fatiguing capability, UNLESS THEY HAVE IDENTAL SPECTRA.
The PSD is simply the root of the area under the PSD curve, of which there are an infinite number.
The machine’s gRMS meter is not measuring the energy transmitted to the product, nor it’s spectral components.
Hank Caruso, an ex Westinghouse test engineer and past president of the IEST, coined the famous Golden Rules.
A screen program that does not take into account the spectral power and fatigue experienced by screened components will eventually deliver problems to customers.

11. Introducing The DP(f)*1,2
A velocity spectrum which includes:
Duration of excitation/response.
Damping of component.
The materials S/N Beta Slope of Fatigue.
And which indicates:
Magnitude of fatigue at fr - “Micro Value”
Wide Spectrum Area fRMS – “Global Value”
Principal Use:
Analysis/Comparison of accumulated fatigue.
* Henderson/Piersol Damage Potential Descriptor

12. Global DP(f)
Like the PSD and its gRMS, the Global DP(f) and fRMS are related
The “Micro” DP(f) applies only one fr frequency
One Special Case of fRMS from different Global DP(f) spectra can be misinterpreted.
See next Slide
fRMS of similar spectra gives a ‘global’ measure of overall affectivity of fatigue potential.
The Micro Case DP(f)g2/Hz at a specific fr is valid and similar to the PSDs g2/Hz.

13. Global DP(f) Limits ● Case A envelopes B and Global fRMS is valid
● DP(f) magnitude valid for all fr
● Case C is not enveloped by A or B
● Global fRMS valid
for this case
DP(f) A
DP Amplitude
DP(f) B
DP(f) C
Frequency

14. The PSD Measures spectral power only.
In terms of Power per unit bandwidth - g2/Hz.
Dynamic Power of a vibrating item is proportional to the square of its g amplitude.
Does NOT Include exposure time or fatigue variables.
Σ of PSD over entire f range equals the total mean-square value of the random variable x(t)
The root of the area under the PSD is the 1 σ Standard Deviation, known as ‘gRMS’

15. Fatigue Accumulation Physics
For most materials, fatigue is proportional to the Σ of stress loadings.*
Loading and total cycles are the coordinates of the material’s S/N fatigue failure diagram.*
S, stress magnitude, relates to the velocity of the 1st bending mode. Modal frequency is proportional to loading count N. Stress is not related to acceleration.
The DP(f) velocity spectrum provides stress magnitudes at discreet loading frequencies.
* Miners Rule of Fatigue Accumulation

16. DP(f), A Better Metric.
DP(f) is a velocity spectrum that shows the Σ of fatigue (magnitude) vs exposure time.
Fatigue constants, S/N β, damping ζ, and exposure time, t are entered by the user.
6DOF Screens may be correlated with EUEs.
Based on Σ of fatigue at fr of components.
Both Global and Micro solutions result.
Global for wideband comparisons.
Micro for specific fr.

17. How to Characterize EUE
Monitor the wideband time record of the End-Use-Environment with an analyzer.
Specify DP(f) inputs – time, ζ, and β.
Perform a DP(f) on the time data.
Read f(RMS) for Global value.
Zoom and read DP(f) at fr for Micro value.
Retain DP(f) & values for future comparisons.
General Use “Hanks Golden Rule #1”. Before an effective screen can be undertaken, it is necessary to understand some machine/fixture characteristics.
If the true excitation is not balanced at multiple product fixture points, the degree of fatigue and hence screen results will not be uniform.
As part of this survey, it must be determined if the spectral power available from the machine envelopes all the resonant frequencies of the products components to be screened. If this is not the case, Hanks, LAW #1 Applies: “If your not stimulating the defect, you’re wasting you time.
Depending on your use – HALT, HASS, HASSA, etc. spectral power uniformity is an underlying requirement.
In particular, verification of fatigue accumulation relates to just about all the steps of the processes used.

18. EUE Example
Data is from vibration loading on an electrical part during rev-up, installed on a Diesel Engine.
PSD showed flat impulsive spectrum but nothing about fatigue.
DP(f) was computed for 100 Hrs of exposure.
Σ of Global f(RMS) 200 Hz – 2 KHz =
Σ of Micro spectrum, f(RMS)590 – 610 Hz =

19. Global EUE - Diesel Engine
fr ≈ 600 Hz
f(RMS) = 14.03
fRMS = 140.4

20. Micro EUE – 590 – 610 Hz
Fr ≈ 600 Hz
fRMS =

21. Characterizing 6DOF shaker
Specify DP(f) inputs – time, ζ, and β.
Monitor at product mounting point.
Perform DP(f).
Read f(RMS) for Global Σ of fatigue.
Read DP(f) for Micro Σ of fatigue at fr.
Retain DP(f) & values for future comparisons on same machine.
General Use “Hanks Golden Rule #1”. Before an effective screen can be undertaken, it is necessary to understand some machine/fixture characteristics.
If the true excitation is not balanced at multiple product fixture points, the degree of fatigue and hence screen results will not be uniform.
As part of this survey, it must be determined if the spectral power available from the machine envelopes all the resonant frequencies of the products components to be screened. If this is not the case, Hanks, LAW #1 Applies: “If your not stimulating the defect, you’re wasting you time.
Depending on your use – HALT, HASS, HASSA, etc. spectral power uniformity is an underlying requirement.
In particular, verification of fatigue accumulation relates to just about all the steps of the processes used.

22. 6DOF Example
Following plots are DP(f) of 6DOF machine at product mounting point for critical part.
PSD was chaotic, strongly mixed with hammer harmonics, has no fatigue indication.
DP(f) computed for 1 Hr of excitation.
Global magnitude f(RMS) = 67.46
Micro spectrum magnitude f(RMS) = 63.8.
Peaks (hammer harmonics) can be seen below 500 Hz.

23. 6DOF Global fRMS KHz
Global fRMS = 67.47
Fr=612 Hz

24. 6DOF Micro 612 Hz
Fr=612 Hz
DP(f) = 63.8

25. Correlating EUE with 6DOF
Process 6DOF time history.
Adjust time of exposure, to equalize with EUE Micro DP(f) value.
Compare Global fRMS values spanning fr for relative numerical comparison.
Zoom/overlay plots for graphic comparison.
Use Micro DP(f) spectrums about fr for precise correlations.

26. EUE/6DOF DP(f)s Overlay
Fr= 612 Hz
EUE DP(f) = 0.17
6DOF DP(f)= 0.43

27. Final Step
Micro is zoomed to center on known defective part fr of 612 Hz.
Following plot shows Global Hz fRMS) and Absolute 612 Hz DP(f) values.
This case shows precise correlation between EUE and 6DOF excitations at part fr, in terms of Σ fatigue.
Solves for machine excitation and time to match EUE fatigue.

28. It’s All About Product fr!!!
fRMS = Hz
EUE fRMS = 0.78
6DOF fRMS = 1.30
@ fr 612 Hz
EUE DP(f) = 0.7
6DOF DP(f) = 1.3

29. Conclusions DP(f) can be applied to both EUE’s as well as 6DOF’s.
DP(f)s can be adjusted for exposure time, ζ, and β, for more accurate Σ of fatigue.
DP(f)’s may be overlaid to show correlation.
6DOF exposure time can then be adjusted to duplicate the EUE at the product fr.
This uniquely process is based on Σ of fatigue.
Read of Conclusions.

30. References 1. Source of DP(f) theory. Henderson, G. and Piersol, A.,
“Fatigue Damage Descriptor For
Random Vibration Environments”.
Sound & Vibration, October, 1995.
2. Validation by use. Connon, S., “Assessment of Hydraulic
Surge Brake Effects On Fatigue
Failures Of A Light Trailer”, Aberdeen
Test Center, US Army, 2002.

31. Thanks For Your Kind Reception.
George Henderson, President, GHI Systems, Inc.
800-GHI-SYST ( )
Thank you very much for attending. I hope you have found something in today’s program to improve your screening program.