Using Fatigue Damage Spectrum for Accelerated Testing with

Automotive Testing Expo 2016
Stuttgart Germany
31th May - 02th June 2016
Using Fatigue Damage Spectrum for Accelerated Testing
with Correlation to End-Use Environment
Lecturer: Holger Boller Vibration Research
About Vibration Research
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Vibration Research formed as a private company in 1995
45 employees in development, research and production
More as 4.500 installed Vibration Control system world wide
Global Customer Base
In 2014 new building in Jenison
§  Pioneered many vibration testing techniques
§  First to perform long time history replication on ED shakers - We call it F.D.R. Field Data
Replication
§  New featuring kurtosis control (Kurtosion®)
§  VRC has received U.S. patent number 4,726,726 for its Kurtosion® software
§  Introduced FDS - Fatigue Damage Spectrum
§  Introduced iDOF - Instant Degrees of Freedom
Using Fatigue Damage Spectrum for Accelerated
Testing with Correlation to End-Use Environment
§  Key Point´s and Questions for the customer are:
1.  Can I reproduce the measured different complex time signals in an easy way?
2.  How can I generate PSD profiles from the time signals in a realistic and reproducible way?
3.  Comparison of the fatigue damage between the Time signal and the generated RANDOM
signal
Actual Situation - Where are we?
Actual Situation
§  Simulation of mechanical stress is included in the design, development
and qualification of products
§  Use of mathematically generated time signals
§  Derivation of parameterized models
§  Good correspondence between failures in the field and in the
laboratory simulation
None of the signals thus generated is identical to the load in the field.
We can´t reproduce and justify all failures.
Vibration Testing in the Real World
§  Use of standardized test specifications
§  ISO 16750; MIL 810; RTCA DO160; VW 80000; ASTM 4728; EN 60068; IEC 17025
§  Can´t answer all Questions
§  A lot of possibilities and an a big field of interpretation
§  Many papers to read
Handling of the Time Signal
§  Create a Test Profile from Time History Data
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Method 1: Peak Hold PSD
Method 2: Average PSD
Method 3: Field Data Replication
Method 4: PSD Profile with the same Fatigue
Method 1 - Peak Hold PSD
§  PEAK HOLD - FFT based on peaks, from each time block
AccelerationSpectralDensity(G²/Hz)
§  Extracts the peaks from the blocks of data
§  Max Values from each Time Block are used to create the PSD Spectrum
§  Critical for time signals with short events (pulses)
AccelerationSpectralDensity
Demand
1x100
1x10-1
1x10-2
1x10-3
1x10-4
1x10-5
1x10-6
5
10
Frequency(Hz)
100
200
Method 2 – Average PSD
§  AVERAGE - FFT of each block of data is averaged together
AccelerationSpectralDensity(G²/Hz)
§  Creates a uniform average - power of the test
§  Critical for time signals with highly variable RMS value
§  This method “lose” short events
AccelerationSpectralDensity
Demand
1x100
1x10-1
1x10-2
1x10-3
1x10-4
1x10-5
1x10-6
5
10
Frequency(Hz)
100
200
Method 3 – Field Data Replication
§  Exact replication of the Time History – Amplitude, Phase, Fatigue Cycles
§  Maintains ordering of Stress Cycles
§  Cannot be easily accelerated
Comparison between
PEAK HOLD PSD, AVERAGE , TIME SIGNAL
Signal
gRMS
gPEAK
vRMS
vPEAK
dPEAK
KURTOSIS
TIME SIGNAL
0,44
-3,9 / 4,7
0,05
-0,25 / 0,27
-6,2 / 7,4
~6
PEAK HOLD PSD
1,86
-11,1 / 11,1
0,21
-1,3 / 1,3
-36,6 / 25,7
~6
PEAK HOLD PSD
1,87
-5,9 / 5,8
0,21
-0,75 / 0,73
-21,1 / 19,3
~3
AVERAGE PSD
0,44
-2,6 / 2,6
0,05
-0,39 / 0,31
-7,9 / 7,2
~6
4 Key Questions came up with our comparison
§  Is it possible to design a vibration test (profile and test time) that accurately
simulates the End-Use Environment of a product throughout its lifetime?
§  Is it possible to confidently combine multiple, complex time signals into a single
test profile?
§  Is it possible to reliably accelerate a test and maintain an accurate simulation of
imported field data?
§  How I can compare all my new test profiles?
Method 4: Fatigue Damage Spectrum
§  Same recording duration - same test time
§  Same Frequency Range
§  Accounts for time history, duration, and fatigue damage
TimeSignal
AVERAGEPSD
PEAKHOLDK=3
PEAKHOLDK=6
1.00E+08
FATIGUEDAMAGE
1.00E+05
1.00E+02
1.00E-01
1.00E-04
1.00E-07
1.00E-10
1.00E-13
1.00E-16
1.00E-19
3
30
Frequency[Hz]
300
Theory Fatigue Damage Calculation
§  S-N Curve (S for stress, N for cycles):
§  Miner’s Rule:
time
strength
N = c ∗ S −b
permanently
§  N=Numberofstresscyclestofailure
§  S=peakamplitudeofcyclicalstress
§  b=faQgueparameter
§  c is experimentally found to be between 0.7 and 2.2.
Usually for design purposes, c is assumed to be 1.
k
ni
=c
∑
i =1 N i
How works the Calculation of the
Fatigue Damage Spectrum?
§  The acceleration waveform is converted to a velocity waveform
§  Velocity is desired because Henderson-Piersol equations
utilize velocity - Velocity has a direct relationship to stress
§  Stress waveform is narrow-band filtered and the defined Q value
is used
§  Q value determines filter bandwidth
§  Cycle counting and damage calculation ensure in each frequency-bin
to determine damage contributions over a spectrum of frequencies.
§  Spectrum spacing determines number of points in spectrum
(number of frequency bins)
How works the Calculation of the
Fatigue Damage Spectrum?
b Fatigue
and
c Factor
Acceleration
Waveform 1
Integrator
Acceleration
Waveform 2
Integrator
Acceleration
Waveform 3
Integrator
Velocity
Waveform 1-3
Multiply
Narrow Band
Filter
Q-Factor
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Rainflow
Counting
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•
•
Fatigue
Damage
Calculation
Henderson
Piersol
Conversion
Kurtosion™
PSD
Spectrum
How works the Calculation of the
Fatigue Damage Spectrum?
Fatigue Monitor - VibrationView Software
§  We have 4 different time signals and would like to make a random test that
recreates the same fatigue.
§  We want to run an equivalent of 10.000 hours of desired life time in 30 hours
vibration test
§  select a ‘b’ and ‘Q’ value for your data and product.
−b
§  “b” is calculated with: N i = c ∗ Si
§  “Q” or quality factor is used in narrow band pass filter calculations, and will affect the
smoothness of the Fatigue damage
§  If you are not sure then MIL-Std 810 suggests b = 8 and Q = 50.
(see pg. 288 of MIL-STD 810G)
Creating a RANDOM Vibration Test with the
Fatigue Damage Module
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Import the Time History file(s)
Set the frequency range
Enter m and Q Values
Enter Target Life
Define the Test Duration
Add Kurtosis
Create the PSD Profile Table
Combining FDS and Accelerated Test Time
Cobblestone
RailroadCrossing
ComfortRoad
ResonanceRoad
Combined
1.00E+07
FATIGUEDAMAGE
1.00E+04
1.00E+01
1.00E-02
1.00E-05
1.00E-08
1.00E-11
3
30
Frequency[Hz]
300
Same Fatigue - without Test Time compression
§  Weight each waveform by exposure time, and / or number of discrete events
§  Accelerate the test creating a Gaussian PSD profile that is the damage equivalent
to the total target life
PSDSpectrum[g²/Hz]
Cobblestone
RailroadCrossing
ComfortRoad
ResonanceRoad
Combined
Frequenz[Hz]
300
1.00E-01
1.00E-03
1.00E-05
3
30
Same Fatigue - with Test Time Compression
§  Weight each waveform by exposure time, and / or number of discrete events
§  Accelerate the test creating a Gaussian PSD profile that is the damage equivalent
to the total target life
Cobblestone
RailroadCrossing
ComfortRoad
ResonanceRoad
30
Frequency[Hz]
Combined
PSDSpectrum[g²/Hz]
1.00E+07
1.00E+04
1.00E+01
1.00E-02
1.00E-05
1.00E-08
3
300
Conclusions
§  With the FDS Software Module from Vibration Research:
§  We have a powerful tool for our customers
§  To compare given Time Signals in Ratio to the generated Damage
§  To combine Multiple & Complex measured Time Signals
§  To create easily a Random PSD Profile that is the Fatigue Damage equivalent to the imported &
weighted time history file(s)
§  To integrate higher Kurtosis Values into the calculated PSD Profiles
§  Accelerate testing using FDS and Kurtosion®
F.D.R Replication Software
§  Reproduce complex time signals in an easy way
§  The repeating rate can reflect the life time and the true environmental condition
Any Questions?
Thank you very much for your attention.
Any Questions ??
Come to our Booth: 1268
or
Send E-Mail: vrsales@vibrationresearch.com
or
Visit our website: www.vibrationresearch.com
Thank You!