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Correlating End-Use Environments and ESS Machine Excitation Using Fatigue Equality

Correlating End-Use Environments and ESS Machine Excitation Using Fatigue Equality. George Henderson GHI Systems, Inc. San Pedro, CA. Scope Of Presentation. Component Loading Response f r gRMS and The PSD Spectrum The Damage Potential Spectrum, DP(f) Characterizing EUE Excitation

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Correlating End-Use Environments and ESS Machine Excitation Using Fatigue Equality

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  1. Correlating End-Use Environments and ESS Machine Excitation Using Fatigue Equality George Henderson GHI Systems, Inc. San Pedro, CA

  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

  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.* *Hank’s Golden Rule Number 1.

  6. 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 frisas shown? • Difference is g2/Hz power @ fr. fr fr g2/Hz g2/Hz “A” “B” Frequency Frequency

  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 Spectral Intensity ‘B’ Spectral Intensity fr ‘A’ 10 1000 10,000 Frequency - Hz

  9. gRMS– Not Related ToFatigue Both Machines at “10 gRMS” Defect Failure Level Fatigue Magnitude Rate = 4.1 E+6/Min Rate = 1.7 E+8/Min 1.0 8 10 55 100 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 • g2/Hz @ fr, not the gRMS is what counts

  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 envelopesB 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.

  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 = 140.4. • Σ of Micro spectrum, f(RMS)590 – 610 Hz = 17.83.

  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 = 17.278

  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.

  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 200- 2KHz Global fRMS = 67.47 Fr=612 Hz

  24. 6DOF Micro DP(f) @ 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 frfor 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 frof 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.

  28. It’s All About Product fr!!! fRMS = 500-700 Hz EUE fRMS = 0.78 6DOF fRMS = 1.30 @fr612 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.

  30. References 1. Source of DP(f) theory. Henderson, G. and Piersol, A., “Fatigue DamageDescriptor 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 (444-7978) george@ghisys.com

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