Wire-EDM Spark Pulse Energy, Overcut & Kerf Offset Formula

Programming CNC wire-EDM path offsets by half the 0.250 mm brass wire radius (0.125 mm) forgets the +41.9 um radial plasma spark gap—cutting punch dies 83.8 um undersize!

**Traveling-Wire Electrical Discharge Machining (`Wire-EDM`)** vaporizes `62` HRC hardened `D2` / tungsten-carbide stamping dies inside deionized water (`< 10` uS/cm) without mechanical cutting force—using `10,000` K plasma micro-craters of **Single-Pulse Discharge Energy `E_p = (V_d * I_p * t_{on}) / 1,000`** (`mJ` at Gap Discharge Voltage `V_d` V, Peak Spark Current `I_p` A, and Pulse-On Duration `t_{on}` us) cycled at **Pulse Duty Factor `DF = (t_{on} / (t_{on} + t_{off})) * 100%`** (`kept <= 35%–40%` so `t_{off}` flushes debris before stationary DC arcs snap the brass wire!)! Because crater depth and plasma channel expansion scale as **`g_r ~= 4.2 * (I_p^0.4) * (t_{on}^0.3)`** (`um` radial overcut per side on tool steel), **Total Wire Kerf Width equals `W_{kerf} = d_{wire} + (2 * g_r) / 1,000`** (`mm` -> `CNC` Cutter-Radius Offset `H = W_{kerf} / 2` plus skim stock)!

Verify on a Roughing Main-Cut Pass in `50` mm `D2` Tool Steel—Gap_Discharge_Voltage `V_d` = 28.0 V (B2), Peak_Pulse_Current `I_p` = 36.0 A (B3), Pulse-On_Time `t_{on}` = 18.0 us (B4), Pulse-Off_Flush_Time `t_{off}` = 42.0 us (B5), and Brass_Wire_Diameter `d_{wire}` = 0.250 mm (B6): Single-Spark Energy equals `18.14` mJ (E2), Pulse Duty Factor equals `30.0%` (E3), Radial Spark Gap `g_r` equals **`41.9` um per side** (E4), and Total EDM Kerf Width equals **`0.3338` mm** (`0.1669` mm centerline offset + finish allowance! E5)!

Wire-EDM Spark Crater Energy, Duty Flushing & Kerf Compensation Formula

Validate `Discharge_Voltage V_d` in `[15, 60]` V, `Peak_Current I_p` in `[0.5, 500]` A, `Pulse_On t_{on}` in `[0.1, 200]` us, `Pulse_Off t_{off}` in `[1.0, 1,000]` us, and `Wire_Diameter` in `[0.02, 0.36]` mm!

=LET(vd_v, B2, ip_a, B3, tn_u, B4, tf_u, B5, wd_m, B6, sg_u, 4.2 * (ip_a ^ 0.4) * (tn_u ^ 0.3), IF(OR(vd_v < 15, vd_v > 60, ip_a < 0.5, ip_a > 500, tn_u < 0.1, tn_u > 200, tf_u < 1, tf_u > 1000, wd_m < 0.02, wd_m > 0.36), "Invalid EDM Input", ROUND(wd_m + (2 * sg_u) / 1000, 4)))

Third-Skim Mirror Finish Pass (`I_p = 4` A, `t_on = 1.5` us, `t_off = 12` us) Recast Removal Check

Switch the generator to a low-capacitance finish trim (`B3 = 4.0` A, `B4 = 1.5` us, `B5 = 12.0` us): Spark Energy E2 drops **`108x` to `0.17` mJ** (`11.1%` duty in E3), shrinking Radial Spark Gap E4 from `41.9` down to **`8.3` um** (`0.2665` mm kerf in E5) so the wire shaves off the brittle white thermal recast layer to `Ra < 0.25` um!

=IF(ISTEXT(E5), E5, ROUND(4.2 * (B3 ^ 0.4) * (B4 ^ 0.3), 1))

Further reading

• Arte Sheets Lesson — CNC Ball-Nose End-Mill Stepover, Scallop Cusp & Effective Diameter
• Arte Sheets Lesson — Electrochemical Machining (ECM) Equilibrium Gap & Brine Rise