Transcript Slide 1

Dynamic Concepts, Inc.
Huntsville, Alabama
Vibrationdata
Using a Random Vibration Test Specification to Cover a
Shock Requirement via a Pseudo Velocity Fatigue
Damage Spectrum
By Tom Irvine
3rd International Conference on Material and Component Performance
under Variable Amplitude Loading, VAL2015
1
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Introduction
Shock Fatigue
1. Determine whether a given PSD can cover an SRS Specification
2. Derive an Optimized PSD which will cover an SRS
References
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H. Gaberson, Shock Severity Estimation, Sound & Vibration Magazine, Bay Village,
Ohio, January 2012
•
H. Caruso and E. Szymkowiak, A Clarification of the Shock/Vibration Equivalence in MilStd-180D/E, Journal of Environmental Sciences, 1989
•
Dave Steinberg, Vibration Analysis for Electronic Equipment, Second Edition, WileyInterscience, New York, 1988
•
ASTM E 1049-85 (2005) Rainflow Counting Method, 1987
•
Halfpenny & Kim, Rainflow Cycle Counting and Acoustic Fatigue Analysis Techniques for
Random Loading, RASD International Conference, Southampton, UK, July 2010
•
Halfpenny, A Frequency Domain Approach for Fatigue Life Estimation from Finite
Element Analysis, nCode International Ltd., Sheffield UK
Electronics Solder Joints
•
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Aerospace and military
components must be
designed and tested to
withstand shock and vibration
environments
Cracked solder Joints for Piece Part with “J leads”
Introduction
•
Consider a launch vehicle component which will be
exposed to random vibration and pyrotechnic shock
during flight
•
The random vibration occurs primarily during liftoff
and the transonic and maximum dynamic pressure
phases of ascent.
•
The corresponding random vibration specification is
in the form of a base excitation power spectral
density (PSD)
•
The pyrotechnic shock is due to staging and
separation events, with the resulting shock
requirement given as a shock response spectrum
(SRS)
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Shock & Vibration Testing
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Shaker Table Vibration Test
Shock Testing using a Resonant Plate
Usually straightforward to
meet specification
Typically excited by mechanical impact
from pneumatic piston. Requires trial-anerror configuration to meet specification
Test Concerns
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•
Aerospace Pyrotechnic-type SRS tests are almost always more difficult to
configure and control in the test lab and are thus more expensive than
shaker table PSD tests
•
Some lower and even mid-level SRS specifications may not have the true
damage potential to justify shock testing
•
The purpose of this presentation is to demonstrate a shock and vibration
comparison method based on the fatigue damage spectrum (FDS)
•
The comparison results can be used with other considerations to determine
whether the random vibration test covers the shock requirement
•
A related method is also demonstrated for deriving an optimized PSD to
envelop an SRS
•
These methods are found to be effective comparison and derivation tools
within a framework of assumptions
Test Concerns
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Gaberson, et al, have characterized shock damage potential in terms of
pseudo velocity
•
A typical velocity severity threshold is 100 in/sec (254 cm/sec) for military
quality equipment
•
some references apply a 6 dB margin which reduces this limit by one-half.
•
This threshold is defined in part by the observation that the velocity which
causes yielding in mild steel beams is about 130 in/sec
•
Also note that some aerospace and military standards for electronic
equipment define a shock severity threshold as 0.8 G/Hz times the natural
frequency in Hz, which is equivalent to 50 in/sec
•
References: MIL-STD-810E & SMC-TR-06-11
Test Concerns
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Shock tests may be omitted for some components if the pseudo velocity is <
50 in/sec
•
The argument to skip shock testing can be strengthened if the random
vibration test is rigorous enough to cover the shock requirement
•
The study in this webinar uses numerical simulations to compare the effects
of random vibration and shock via rainflow cycle counting and fatigue
damage spectra
•
The comparison can then be used with other factors to determine whether
a random vibration test covers a shock requirement
Assumptions
•
The component can be modelled as a linear
single-degree-of-freedom (SDOF) system
•
The peak shock and vibration pseudo velocity
response levels fall below the threshold for the
corresponding material, or below 100 in/sec for
an electronic component
•
The resulting shock and vibration response
stress levels are below the material yield point
•
Fatigue is the only potential failure mode
•
The lower level, longer duration random
vibration test may be effectively substituted for
the high-amplitude, brief-duration shock test
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Assumptions (cont)
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There are no failure modes due to peak relative displacement, such as
misalignment, loss of sway space, mechanical interference, etc
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There are no shock-sensitive mechanical switches, relays or reed valves,
which might experience chatter or change-of-state during shock
•
There are no extra-sensitive piece parts such as crystal oscillators, klystrons,
travelling wave tubes, magnetrons, etc
•
The piece parts are Mil-spec quality and have been previously qualified to
shock levels similar to those in MIL-STD-202, MIL-STD-883, etc
•
The natural frequency, amplification factor Q and fatigue exponent b, can be
estimated between respective limits
Rainflow Cycle Counting
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•
SDOF responses must be calculated for each fn and Q of interest, for both
the PSD and the for SRS
•
A representative time history can be synthesized for the SRS
•
The Smallwood, ramp invariant, digital recursive filtering relationship is then
used for the response calculation per Reference
•
The rainflow cycles can be calculated from the time domain response
•
In addition, response PSDs can be calculated for the base input PSD using
the textbook SDOF power transmissibility function
•
The rainflow cycles are then tabulated from the response PSDs via the Dirlik
method
Fatigue Damage Spectrum
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• A relative damage index can be calculated from the response rainflow
cycles using
D   A ib n i
i 1
• The FDS expresses the damage D as a function of natural frequency with
the Q and b values duly noted
• The amplitude convention for this paper is: (peak-valley)/2
Example
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• Determine whether a given PSD envelops an SRS in terms of fatigue
damage
• Natural frequency is an independent variable, 20 to 2000 Hz
• Vary amplification factor Q = 10 or 30
• Vary fatigue exponent b = 4 or 9
The natural frequency, damping and fatigue exponent respective estimates are
“wide open” because electronic boxes are typically “black boxes” for mechanical
engineering purposes
Wide estimates also allow for a rigorous test of the method.
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PSD Specification
Power Spectral Density, 24 GRMS Overall
2
Accel (G /Hz)
1
0.1
0.01
20
100
Frequency (Hz)
Duration 180 sec/axis
1000
2000
Freq
(Hz)
Accel
(G^2/Hz)
20
0.04
150
0.30
2000
0.30
Miscellaneous > Fatigue Toolbox > PSD Input > VRS & FDS for Base Input PSD
Run this for all four (Q, b) permutations. Save each Pseudo Velocity FDS.
SRS Specification
Three shocks/axis
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Natural
Frequency
(Hz)
Accel
(G)
10
10
2000
2000
10,000
2000
SRS Specification Pseudo Velocity
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Shock Response Spectrum > Convert Accel SRS to Pseudo Velocity SRS
SRS Specification Pseudo Velocity
Maximum PV = 61 in/sec
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Synthesize a time history from scratch or use library file: srs2000G_accel
Only need one time history because spec is always Q=10 even though two Q values are used for FDS
Synthesized Time History
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SRS Specification
Shock Response Spectrum Q=10
10000
Peak Accel (G)
Spec & 3 dB tol
Negative
Positive
1000
Natural
Frequency
(Hz)
Accel
(G)
10
10
2000
2000
10,000
2000
100
10
5
10
100
1000
Natural Frequency (Hz)
Three shocks/axis
10000
Run this for all four (Q, b) permutations. Save each Pseudo Velocity FDS.
Legend:
PSD
SRS
Pseudo Velocity FDS Q=10 b=4
Pseudo Velocity FDS Q=10 b=9
10
18
Damage (in/sec)
Damage (in/sec)
9
10
4
10
9
10
8
10
7
10
20
14
10
12
100
1000
10
2000
20
100
1000
Natural Frequency (Hz)
Natural Frequency (Hz)
Pseudo Velocity FDS Q=30 b=4
Pseudo Velocity FDS Q=30 b=9
11
2000
20
Damage (in/sec)
9
10
4
10
Damage (in/sec)
16
10
10
10
9
10
8
10
20
18
10
16
10
14
100
1000
2000
Natural Frequency (Hz)
PSD Covers SRS for b = 4 (plots in left column)
10
20
100
Natural Frequency (Hz)
1000
2000
SRS Specification
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• Now consider the case where a PSD is to be derived to cover an SRS
requirement.
• The component will be assumed to have Q=30 and b=6.4 (single pair for
brevity)
• The natural frequency is left as an independent variable.
• Candidate PSD functions can be derived via trial-and-error
• Each PSD is scaled so that its pseudo velocity FDS just envelops that of the
time history synthesized for the SRS specification
• The optimal PSD is that which satisfies the enveloping with the least
possible acceleration, velocity and displacement RMS levels
Time History > PSD Envelope via FDS
Power Spectra Density 47.2 GRMS Overall, 180 sec
10
Pseudo Velocity FDS Q=30 b=6.4
10
16
10
15
10
14
10
13
10
12
6.4
Damage (ips)
1
2
Accel (G /Hz)
SRS
PSD
0.1
0.01
20
100
1000 2000
Frequency (Hz)
Freq
(Hz)
Accel
(G^2/Hz)
20
0.026
137
0.65
2000
1.476
20
100
Natural Frequency (Hz)
The equivalent PSD is conservative in
terms of fatigue damage.
1000 2000
The equivalent PSD does not completely envelop the SRS.
Increase the level or duration if peak enveloping is required.
Peak Enveloping
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• A conservative PSD can be generated to envelop an SRS in terms of
peak response
• But PSD is limited to about 2000 Hz for practical shaker test
• This limitation is okay as long as component is an SDOF system with fn <
2000 Hz
Shock Response Spectrum > Envelope SRS via PSD, peak response
Peak Envelope PSD
But too high for a shaker table test!
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Comparison
The peak VRS is based on the Rayleigh distribution.
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Conclusions
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Rainflow FDS curves can be calculated for both PSD and SRS functions
•
The curves can then be superimposed on the same graph to compare the damage
potential for each environment
•
The relative differences between the FDS curves for the PSD and SRS for the first
example were rather insensitive to Q but very sensitive to b
•
The FDS comparison technique can also be used as a basis for enveloping a shock
event with a PSD optimized in terms of the least possible overall levels, as shown in
the second example
•
These methods can be used more efficiently if the natural frequency, damping and
fatigue exponents respective estimates can be narrowed
•
Matlab scripts for performing these calculations are available at:
https://vibrationdata.wordpress.com