Friction Stir Welding (FSW) Pitch, Heat Index & Power Formula

Fusion-weld 2xxx/7xxx aircraft aluminum and hot-cracking ruins the seam—Friction Stir Welding plasticizes metal 100 °C BELOW its melting point!

**Friction Stir Welding (`FSW`, AWS D17.3)** plunges a non-consumable shouldered H13/MP159 tool rotating at `N` (`RPM`) into aluminum rocket propellant tanks and EV battery extrusion trays, traversing along the butt joint at `v` (`mm/min`) under Measured Spindle Torque `M` (`N·m`) and Thermal Transfer Efficiency `eta` (`~0.85–0.92`). Defect-free dynamic recrystallization inside the stir nugget balances two kinematic invariants: **Revolution Pitch (Advance per Revolution) `APR = v / N`** (`mm/rev`—too high `>0.8` mm/rev starves plastic flow into internal **wormhole tunnel voids**; too low `<0.18` mm/rev churns excess **ribbon flash**!) and **Arbegast Pseudo-Heat Index `HI = N^2 / (v * 1,000)`** (`RPM²/(m/min)`), while torque directly measures **Mechanical Spindle Power `P_m = (2 * PI() * N * M) / 60,000`** (`kW`) and **Net Linear Heat Input `Q_{lin} = (eta * P_m * 1,000) / (v / 60)`** (`J/mm`)!

Verify on a `6` mm AA6061-T6 EV Cooling-Plate Butt Joint—Spindle_Speed `N` = 950 RPM (B2), Traverse_Feed `v` = 380 mm/min (B3), Measured_Spindle_Torque `M` = 44.0 N·m (B4), and Workpiece_Thermal_Efficiency `eta` = 0.88 (B5): Advance-per-Revolution equals `0.400` mm/rev (E2), Pseudo-Heat Index equals `2.375` (E3), Spindle Power draws `4.38` kW (E4), and Net Linear Heat Input equals `608.2` J/mm (E5)!

FSW Kinematic Pitch, Arbegast Heat Index & Torque-Based Linear Heat Formula

Validate `Spindle_RPM` in `[100, 4,000]`, `Traverse v` in `[20, 3,000]` mm/min, `Torque M > 1` N·m, and `Thermal_Efficiency eta` in `[0.50, 0.98]`!

=LET(nr_p, B2, vt_m, B3, mt_n, B4, et_h, B5, pk_w, (2 * PI() * nr_p * mt_n) / 60000, IF(OR(nr_p < 100, nr_p > 4000, vt_m < 20, vt_m > 3000, mt_n <= 1, et_h < 0.5, et_h > 0.98), "Invalid FSW Schedule", ROUND((et_h * pk_w * 1000) / (vt_m / 60), 1)))

Over-Hot 1,400 RPM / 220 mm/min Schedule T6 Precipitate Over-Aging Check

Spin up to `1,400` RPM while slowing feed to `220` mm/min (`B2 = 1400`, `B3 = 220`): Pitch E2 plunges to `0.157` mm/rev (extruding heavy shoulder flash!), Heat Index E3 jumps `3.75x` to `8.909`, and Linear Heat Input E5 surges `2.55x` to **`1,548.2` J/mm**—dissolving strengthening `Mg_2Si` precipitates across the Thermo-Mechanically Affected Zone (`TMAZ`)!

=IF(ISTEXT(E5), E5, ROUND((2 * PI() * B2 * B4) / 60000, 2))

Further reading

• Arte Sheets Lesson — Resistance Spot Welding Joule Heat & Nugget Size Formula
• Arte Sheets Lesson — Laser Powder Bed Fusion (LPBF) Volumetric Energy Density Formula