1. Circuit Board Fatigue Response to Random Vibration Part 2
Unit 38
Circuit Board Fatigue Response
to Random Vibration Part 2

2. Reference

3. 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.

4. 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

5. Fatigue Introduction The following method is taken from Steinberg:
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 random-vibration environment, based upon the 3 circuit board relative displacement

6. Empirical Fatigue Formula
The allowable limit for the 3-sigma relative displacement 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

7. 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

8. 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.

9. RD-N Equation for High-Cycle Fatigue
The final RD-N equation for high-cycle fatigue is
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.

10. RD is the zero-to-peak relative displacement.6x
20 million cycles
The derived high-cycle equation is plotted in along with the low-cycle fatigue limit.
RD is the zero-to-peak relative displacement.

11. Exercise 1 (20 million cycles)
A DIP is mounted to the center of a circuit board.
Thus, C = and r = 1.0
The board thickness is h = 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
(20 million cycles)

12. vibrationdata > Miscellaneous > Steinberg Circuit Board Fatigue

13. Exercise 1
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?

14. Exercise
Read NAVMAT PSD

15. Exercise
SDOF Response to Base Input

16. Exercise

17. Acceleration PSD

18. Relative Displacement

19. Steinberg Relative Displacement PSD Fatigue

20. Fatigue Results ***************************************************
PSD filename: rd_psd
Overall level = inch RMS
Max amp =
Max rd_Z_ratio =
Duration = 60 sec Cycles=
CDI =
Damage Rate = 2.796e-06 per sec
Time to failure (R=0.7): e+05 sec Cycles=5.6703e+07
69 hr 32 min 37 sec

21. Exercise 2
Repeat exercise 1 using a time domain synthesis.

22. Exercise

23. Synthesized Time History

24. PSD Comparison

25. Exercise

26. Relative Displacement Response

27. Exercise

28. Exercise 2, Time Domain Results
Max amp =
Max rd_Z_ratio =
Duration = 60 sec Cycles=
CDI =
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 = , % lower than Time Domain

29. Exercise 3, Solid Rocket Motor Resonant Burn

30. Exercise 3, Resonant Burn Time History
Nonstationary
kurtosis =
Rice Characteristic Frequency = Hz

31. Exercise 3, Resonant Burn Histogram
Non-Gaussian!

32. Exercise 3, Resonant Burn Waterfall FFT

33. Exercise 3, Solid Rocket Motor Base Input
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 = inch (3-sigma)
Apply solid rocket motor acceleration as base input.
Calculate relative displacement time history
Perform Steinberg calculation

34. Exercise 3, Solid Rocket Motor Base Input

35. Exercise 3, Solid Rocket Motor Base Input