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Correlating End-Use Environments and ESS

Machine Excitation Using Fatigue Equality

George HendersonGHI Systems, Inc.

San Pedro, CA

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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

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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.

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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

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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.**Hank’s Golden Rule Number 1.

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gRMS’s - Not Equally Effective

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 power @ fr.

Frequency Frequency

g2/H

z

g2/H

z

fr fr

“A” “B”

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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.

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gRMS, a Non-Metric

10 1000 10,000 Frequency - Hz

Sp

ectr

al

Inte

nsit

yS

pectr

al In

ten

sit

y

fr

‘A’

‘B’

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gRMS– Not Related To Fatigue

Defect Failure Level

1.0 8 10 55 100 Screen Duration- Min

Fati

gu

e M

ag

nit

ud

e

Rate

= 1.7

E+8/M

in

Rate = 4.1

E+6/Min

Both Machines at “10 gRMS”

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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 g2/Hz @ fr, not the gRMS is what counts

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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

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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.

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Global DP(f) Limits

Frequency

DP(f) A

DP(f) B

● 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 validfor this case

DP

Am

plitu

de

DP(f) C

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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’

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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

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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.

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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.

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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 = 140.4. Σ of Micro spectrum, f(RMS)590 – 610 Hz =

17.83.

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Global EUE - Diesel Engine

f(RMS) = 14.03

fRMS = 140.4

fr ≈ 600 Hz

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Micro EUE – 590 – 610 Hz

fRMS = 17.278

Fr ≈ 600 Hz

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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.

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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.

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6DOF Global fRMS 200- 2KHz

Global fRMS = 67.47

Fr=612 Hz

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6DOF Micro DP(f) @ 612 Hz

DP(f) = 63.8

Fr=612 Hz

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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.

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EUE/6DOF DP(f)s Overlay

EUE DP(f) = 0.176DOF DP(f)= 0.43

Fr= 612 Hz

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Final Step Micro is zoomed to center on known

defective part fr of 612 Hz. Following plot shows Global 500-700 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.

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It’s All About Product fr!!!

fRMS = 500-700 Hz

EUE fRMS = 0.786DOF fRMS = 1.30

@ fr 612 HzEUE DP(f) = 0.76DOF DP(f) = 1.3

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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.

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References

1. Source of DP(f) theory. Henderson, G. and Piersol, A., “Fatigue Damage Descriptor ForRandom Vibration Environments”.Sound & Vibration, October, 1995.

2. Validation by use. Connon, S., “Assessment of HydraulicSurge Brake Effects On Fatigue Failures Of A Light Trailer”, AberdeenTest Center, US Army, 2002.

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Thanks For Your Kind Reception.

George Henderson, President, GHI Systems, Inc.

800-GHI-SYST (444-7978) george@ghisys.com