Transcript Webinar_38_circuit_board_fatigue_part_2

Unit 38
Vibrationdata
Circuit Board Fatigue Response
to Random Vibration
Part 2
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Reference
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• Electronic components in vehicles are subjected to shock and vibration
environments.
• The components must be designed and tested accordingly
• Dave S. Steinberg’s Vibration Analysis for Electronic Equipment is a widely
used reference in the aerospace and automotive industries.
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• Steinberg’s text gives practical empirical formulas for determining the fatigue
limits for electronics piece parts mounted on circuit boards
• The concern is the bending stress experienced by solder joints and lead wires
• The fatigue limits are given in terms of the maximum allowable 3-sigma relative
displacement of the circuit boards for the case of 20 million stress reversal
cycles at the circuit board’s natural frequency
• The vibration is assumed to be steady-state with a Gaussian distribution
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Fatigue Introduction
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The following method is taken from Steinberg:
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•
•
Consider a circuit board that is simply supported about its perimeter
A concern is that repetitive bending of the circuit board will result in cracked
solder joints or broken lead wires
Let Z be the single-amplitude displacement at the center of the board that
will give a fatigue life of about 20 million stress reversals in a randomvibration environment, based upon the 3 circuit board relative
displacement
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Empirical Fatigue Formula
The allowable limit for the 3-sigma relative displacement
0.00022B
Z 3 limit 
Ch r L
Z
is
(20 million cycles)
B =
length of the circuit board edge parallel to the component, inches
L =
length of the electronic component, inches
h = circuit board thickness, inches
r =
relative position factor for the component mounted on the board
C =
Constant for different types of electronic components
0.75 < C < 2.25
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Derivation of the RD-N Curve
• Develop Steinberg methodology into a “Relative Displacement vs. Cycles” curve
• Derivation details are given in:
T. Irvine, Extending Steinberg’s Fatigue Analysis of Electronics Equipment
Methodology to a Full Relative Displacement vs. Cycles Curve, Revision C,
Vibrationdata, 2013
• An overview of results are given in the following slides
Derivation of the RD-N Curve (cont)
Steinberg gives an exponent b = 6.4 for PCB-component lead wires, for both sine and
random vibration.
The goal is to determine an RD-N curve of the form
log10 (N) = -6.4 log10 (RD) + a
N
is the number of cycles
RD
relative displacement (inch)
a
unknown variable
The variable a is to be determined via trial-and-error.
RD-N Equation for High-Cycle Fatigue
The final RD-N equation for high-cycle fatigue is

RD  6.05- log10 (N)
log10 

Z
6.4
 3 limit 
The low cycle portion will be based on another Steinberg equation that the
maximum allowable relative displacement for shock is six times the 3-sigma
limit value at 20 million cycles for random vibration.
RD-N CURVE
ELECTRONIC COMPONENTS
RD / Z 3- limit
10
6x
1
20 million
cycles
0.1
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
CYCLES
The derived high-cycle equation is plotted in along with the low-cycle fatigue limit.
RD is the zero-to-peak relative displacement.
Exercise 1
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A DIP is mounted to the center of a circuit board.
Thus, C = 1.0
and r = 1.0
The board thickness is h = 0.100 inch
The length of the DIP is L =0.75 inch
The length of the circuit board edge parallel to the component is
B = 4.0 inch
Calculate the relative displacement limit
0.00022B
Z 3 limit 
Ch r L
(20 million cycles)
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vibrationdata > Miscellaneous > Steinberg Circuit Board Fatigue
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Exercise 1
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A circuit board has a natural frequency of fn = 200 Hz and an amplification
factor of Q=10.
It will be exposed to the NAVMAT P-9492 PSD base input.
What is the board’s 3-sigma displacement?
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Exercise
Read NAVMAT PSD
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Exercise
SDOF Response to Base Input
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Exercise
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Acceleration PSD
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Relative Displacement
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Steinberg Relative Displacement PSD Fatigue
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Fatigue Results
***************************************************
PSD filename: rd_psd
Overall level = 0.002719 inch RMS
Max amp = 0.01083
Max rd_Z_ratio =
1.083
Duration = 60 sec Cycles=
13589
CDI = 0.0001678
Damage Rate = 2.796e-06 per sec
Time to failure (R=0.7): 2.504e+05 sec Cycles=5.6703e+07
69 hr 32 min 37 sec
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Exercise 2
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Repeat exercise 1 using a time domain synthesis.
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Exercise
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Synthesized Time History
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PSD Comparison
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Exercise
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Relative Displacement Response
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Exercise
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Exercise 2, Time Domain Results
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Max amp = 0.0119
Max rd_Z_ratio =
1.19
Duration = 60 sec Cycles=
13560
CDI = 0.0001988
Damage Rate = 3.313e-06 per sec
Time to failure = 2.113e+05 sec Cycles=4.7744e+07
= 58 hr 41 min 5 sec
Dirlik PSD results was: CDI = 0.0001678,
15% lower than Time Domain
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Exercise 3, Solid Rocket Motor Resonant Burn
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Exercise 3, Resonant Burn Time History
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Nonstationary
kurtosis = 3.597
Rice Characteristic
Frequency = 456.9 Hz
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Exercise 3, Resonant Burn Histogram
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Non-Gaussian!
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Exercise 3, Resonant Burn Waterfall FFT
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Exercise 3, Solid Rocket Motor Base Input
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Assume the previous circuit board is in an avionics box mounted adjacent to accelerometer
measurement location for solid rocket resonant burn event.
But change natural frequency to match Rice frequency for transient resonant excitation.
Set fn=459.6 Hz, Q=10, Z = 0.010 inch (3-sigma)
Apply solid rocket motor acceleration as base input.
Calculate relative displacement time history
Perform Steinberg calculation
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Exercise 3, Solid Rocket Motor Base Input
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Exercise 3, Solid Rocket Motor Base Input
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