Transcript Correlating End-Use-Environments with 6DOF HALT/HASS vibration

Correlating End-Use
Environments and ESS Machine
Excitation Using Fatigue
Equality
George Henderson
GHI Systems, Inc.
San Pedro, CA
1
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
2
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.
3
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
4
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.
5
gRMS’s - Not Equally Effective
“A”
Frequency




fr
g2/Hz
g2/Hz
fr
“B”
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 power @ fr.
6
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.
7
Spectral
Intensity
Spectral Intensity
gRMS, a Non-Metric
‘B’
‘A’
10
fr
1000
Frequency - Hz
10,000
8
gRMS– Not Related To Fatigue
Fatigue Magnitude
Both Machines at “10 gRMS”
Defect Failure Level
1.0
8 10
55
Screen Duration- Min
100
9
Summary Rules On gRMS

#1: Equal gRMSs are not equally effective



#2: gRMS doubling does not double fatigue


The PSDs must also be identical
An ∞ number of PSDs can have equal gRMS
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
10
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
11
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.
12
DP Amplitude
Global DP(f) Limits
DP(f) A
DP(f) C
DP(f) B
Frequency
● 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
13
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’
14
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
15
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.
16
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.
17
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.
18
Global EUE - Diesel Engine
fr ≈ 600 Hz
f(RMS) = 14.03
fRMS = 140.4
19
Micro EUE – 590 – 610 Hz
Fr ≈ 600 Hz
fRMS = 17.278
20
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.
21
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.
22
6DOF Global fRMS 200- 2KHz
Global fRMS = 67.47
Fr=612 Hz
23
6DOF Micro DP(f) @ 612 Hz
Fr=612 Hz
DP(f) = 63.8
24
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.
25
EUE/6DOF DP(f)s Overlay
Fr= 612 Hz
EUE DP(f) = 0.17
6DOF DP(f)= 0.43
26
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.
27
It’s All About Product fr!!!
fRMS = 500-700 Hz
EUE fRMS = 0.78
6DOF fRMS = 1.30
@ fr 612 Hz
EUE DP(f) = 0.7
6DOF DP(f) = 1.3
28
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.
29
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.
30
Thanks For Your Kind
Reception.
George Henderson, President,
GHI Systems, Inc.
800-GHI-SYST (444-7978)
[email protected]
31