Tools › Reliability › Physics of Failure › PCB Vibration and Thermal Cycling Fatigue › Example
6 × 8 in FR-4 board, simply supported, 0.04 g²/Hz: Miles response, Steinberg 3σ displacement limit, three-band Miner life, lead frame and plated-through hole
| Tool | PCB Vibration and Thermal Cycling Fatigue |
| Source | National Aeronautics and Space Administration (2001). Dynamic Environmental Criteria. NASA-HDBK-7005, NASA, Washington, DC. Eq. 5.27 (Miles) and Section 7.1.2 (b = 6.4); Leissa, A. W. (1969). Vibration of Plates. NASA SP-160, eq. 4.16 (Warburton's formula, exact for simply supported edges); Savoie, T., and Babuška, V. (2014). SAND2014-1768C, eqs. 10–13 (Rayleigh Miner sum) and p. 9 (E, ν of the test board); Delgado, I. R., et al. (2004). NASA/TM-2004-212985, eq. 6 (Method of Universal Slopes); Steinberg, D. S. (1988). Vibration Analysis for Electronic Equipment, 2nd ed., cited for the 0.00022 B/(c h r √L) limit, Q = √f_n, b = 6.4 and the octave rule. |
| Level | Professional |
Problem
An 8 × 6 × 0.062 in glass-epoxy board (E = 3.795 Msi, ν = 0.266, 0.065 lb/in³, 0.15 lb of parts) is simply supported on four edges and sees a flat 0.04 g²/Hz spectrum from 20 to 2,000 Hz. A 1 in standard DIP (c = 1.0, 1 g, 14 leads of 0.018 × 0.010 in Alloy 42, shoulder 0.06 in, vertical leg 0.05 in) sits at the centre (r = 1) parallel to the 8 in edge. Find the board's fundamental frequency, Miles' response with Q = √f_n, the 3σ relative displacement against Steinberg's limit, the lives by the 3σ relation, the three-band Miner sum and the Rayleigh sum, the resonant 5 g sine dwell, the response to a 50 g 11 ms half-sine shock, the lead stress and octave ratio, and the plated-through-hole barrel strain and life for a 100 °C swing (hole 0.035 in, 0.001 in copper, α_z 60 ppm/°C, E_z 0.5 Msi, column 0.070 in, copper 36 ksi, ε_f 0.3).
Inputs to Enter
- Board 8 × 6 × 0.062 in, E 3.795 Msi, ν 0.266, rib factor 1, 0.065 lb/in³, parts 0.15 lb, edges S S S S; PSD 20 0.04 / 2000 0.04 g²/Hz, Q blank (√f_n), exposure 1 h
- Component L 1 in, c 1.0 (DIP), r 1.0 (centre), parallel to a, 0.0022 lb, 14 leads; lead 0.018 × 0.010 in, E 20 Msi, l_s 0.06 in, h_L 0.05 in, allowable 20 ksi
- Sine 5 g; shock 50 g, 11 ms; isolator off; PTH α_z 60, α_cu 17 ppm/°C, ΔT 100 °C, E_cu 17 Msi, d 0.035 in, t_cu 0.001 in, E_z 0.5 Msi, D_eff 0.070 in, S_u 36 ksi, ε_f 0.3
Answers
- D = 81.11 lb-in, ρ_A = 0.007155 lb/in², λ = π²(1 + (8/6)²) = 27.42, f_n = 142.6 Hz (exact SSSS = Warburton)
- Q = √142.6 = 11.94; G_rms = √(π/2 · 142.6 · 11.94 · 0.04) = 10.35 g; Z_1 = 386.1 · 10.35/(2π · 142.6)² = 0.004973 in, Z_3 = 0.01492 in
- Z_lim = 0.00022 · 8/(1.0 · 0.062 · 1.0 · √1) = 0.02839 in, ratio 0.526, margin +0.90; N = 2 × 10⁷ (0.02839/0.01492)^6.4 = 1.227 × 10⁹ cycles = 2,390 h at 3σ; three-band D = 2.665 × 10⁻⁵ per hour → 37,519 h; Rayleigh sum 37,928 h
- Sine 5 g: 59.7 g peak, Z = 0.02871 in (ratio 1.01, margin −0.01), 9.31 × 10⁶ cycles = 18.1 h; shock 50 g 11 ms: z_max = 0.03366 in, SRS 70.0 g (ratio 1.40), allowable 6 Z_lim = 0.1703 in, margin +4.06
- Lead: K = 1,071 lb/in, f_c = 8,166 Hz (octave ratio 57, passes), foot rotation 0.0659°, P = 0.00488 lb, M = 0.00221 lb-in, stress 7.38 + 0.28 = 7.67 ksi, margin +1.61 against 20 ksi
- PTH: free mismatch 0.0043, copper share 0.436, ε = 0.001873 (elastic 31.8 ksi, 0.88 S_u), Universal Slopes life 308,400 cycles (transition 6,082)
Notes
The tool's default inputs are this case; press Submit. The board, the input level and the component are illustrative (not a printed example); the board stiffness is the Sandia test board's measurement, the constants are Steinberg's as cited, and every number is checked in test_pcb_vibration_fatigue.php against closed forms and the independent numpy script References/PCB-Vibration/checks/pcb_check.py (Miles against the exact SDOF integral, the Rayleigh sum against a quadrature of the peak distribution, the half-sine against solve_ivp, the lead frame against a numpy stiffness solve, twenty randomly generated boards).