Aerospace SAE J2277 / AMS 2430 Shot Peening, Compressive Residual Stress & Fatigue
Shot Peening Surface Coverage & Pass Count Formula
Calculate Multi-Pass Peened Dimple Coverage Cn = 1 - (1 - C1)^n (%), Residual Unpeened Parent Surface (%), Exact Continuous Passes for 98% Full Coverage, and Required Integer Nozzle Passes.
If 1 nozzle pass covers 62% of a gear root, 2 passes do NOT give 100%—random shot overlap leaves 14.4% unpeened fatigue-crack sites!
Controlled shot peening (AMS 2430 / SAE J2277) bombards aircraft landing gear, turbine disks, and valve springs with cast-steel or ceramic spheres to lock in `-600` to `-1,000` MPa of crack-arresting surface compressive residual stress. Because spherical shot impacts land as a spatial Poisson / Avrami random process, each subsequent nozzle pass of Single-Pass Coverage Fraction `c_1 = C_1% / 100` increasingly strikes ALREADY-dimpled metal! Consequently, Unpeened Virgin Area decays geometrically as `(1 - c_1)^n`, giving **`n`-Pass Surface Coverage `C_n = (1 - (1 - c_1)^n) * 100%`**! Because `100%` mathematical coverage would take infinite time, SAE J2277 defines **"100% Full Coverage" practically at `C_target = 98.0%`** (`200%` coverage = `2x` the exposure time needed to reach `98%`), requiring **`n_req = ROUNDUP(LN(1 - C_target/100) / LN(1 - c_1), 0)`** robotic nozzle passes!
Verify on a Robotic Turbine-Disk Root Peening Schedule—Calibrated_Single-Pass_Coverage `C_1` = 62.0% (`c_1 = 0.62`, B2), Programmed_Nozzle_Passes `n` = 4 (B3), and SAE_Full-Coverage_Threshold `C_target` = 98.0% (B4): `4` Passes achieve `97.91%` coverage (E2, leaving `2.09%` unpeened in E3—just shy of `98.0%`!), Exact `98%` Exposure equals `4.04` passes (E4), requiring **`5` Integer Robotic Passes** (`99.21%` actual) to certify `100%` AMS 2430 coverage (E5)!
| SAE J2277 Shot Peening KPI (Single-Pass C1=62.0%, n=4 vs 2 Passes, Target=98%) | Formula | Verified Output |
|---|---|---|
| Achieved n-Pass Coverage Cn (%) | (1 - ((1 - C1_Pct / 100) ^ n)) * 100 | 97.91% (85.56% @ 2 passes!) |
| Residual Unpeened Area (%) | 100 - Achieved_Coverage_Cn_Pct | 2.09% (14.44% fatigue risk @ 2 passes!) |
| Exact Exposure Passes for 98% | LN(1 - Target_Pct/100) / LN(1 - C1/100) | 4.04 passes |
| Certified Integer Nozzle Passes | ROUNDUP(Exact_Passes_For_Target, 0) | 5 Passes (certifies >= 98% AMS 2430) |
Poisson-Avrami Random Dimple Overlap & Certified Pass-Count Formula
Validate `Single_Pass C_1` in `(5%, 95%)`, `Nozzle_Passes n >= 1`, and `Target_Coverage` in `[80%, 99.9%]`!
=LET(cp_s, B2 / 100, np_s, B3, tg_p, B4 / 100, ex_n, LN(1 - tg_p) / LN(1 - cp_s), IF(OR(B2 <= 5, B2 >= 95, np_s < 1, B4 < 80, B4 > 99.9), "Invalid Peening Input", ROUNDUP(ex_n, 0)))Naive Two-Pass Linear-Addition Trap Check (Set Programmed Passes B3 = 2)
Cut robotic cycle time to `n` B3 = 2 passes assuming `2 * 62% > 100%`: Actual Coverage E2 stalls at `85.56%`, leaving `14.44%` of tensile-machined fillets completely unpeened (E3) where fluorescent-tracer (`Peenvis`) UV inspection immediately rejects the part!
=IF(ISTEXT(E5), E5, ROUND((1 - ((1 - (B2 / 100)) ^ B3)) * 100, 2))Try the example
Use the original values or change them to test your understanding.