Unit 38 Vibrationdata Circuit Board Fatigue Response to

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

Reference Vibrationdata 2

Vibrationdata • 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. 3

Vibrationdata • 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 4

Fatigue Introduction Vibrationdata 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 randomvibration environment, based upon the 3 circuit board relative displacement 5

Empirical Fatigue Formula Vibrationdata 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 6

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 log 10 (N) = -6. 4 log 10 (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 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.

6 x 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.

Exercise 1 Vibrationdata 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 (20 million cycles) 11

Vibrationdata vibrationdata > Miscellaneous > Steinberg Circuit Board Fatigue 12

Exercise 1 Vibrationdata 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? 13

Exercise Read NAVMAT PSD Vibrationdata 14

Exercise SDOF Response to Base Input Vibrationdata 15

Exercise Vibrationdata 16

Acceleration PSD Vibrationdata 17

Relative Displacement Vibrationdata 18

Steinberg Relative Displacement PSD Fatigue Vibrationdata 19

Fatigue Results Vibrationdata ************************** 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. 796 e-06 per sec Time to failure (R=0. 7): 2. 504 e+05 sec Cycles=5. 6703 e+07 69 hr 32 min 37 sec 20

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

Exercise Vibrationdata 22

Synthesized Time History Vibrationdata 23

PSD Comparison Vibrationdata 24

Exercise Vibrationdata 25

Relative Displacement Response Vibrationdata 26

Exercise Vibrationdata 27

Exercise 2, Time Domain Results Vibrationdata Max amp = 0. 0119 Max rd_Z_ratio = 1. 19 Duration = 60 sec Cycles= 13560 CDI = 0. 0001988 Damage Rate = 3. 313 e-06 per sec Time to failure = 2. 113 e+05 sec Cycles=4. 7744 e+07 = 58 hr 41 min 5 sec Dirlik PSD results was: CDI = 0. 0001678, 15% lower than Time Domain 28

Exercise 3, Solid Rocket Motor Resonant Burn Vibrationdata 29

Exercise 3, Resonant Burn Time History Vibrationdata Nonstationary kurtosis = 3. 597 Rice Characteristic Frequency = 456. 9 Hz 30

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

Exercise 3, Resonant Burn Waterfall FFT Vibrationdata 32

Exercise 3, Solid Rocket Motor Base Input Vibrationdata 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 33

Exercise 3, Solid Rocket Motor Base Input Vibrationdata 34

Exercise 3, Solid Rocket Motor Base Input Vibrationdata 35