5-Axis CNC Die/Mold Machining & CAM Toolpaths, Ball-Nose Scallop & Effective Diameter
CNC Ball-Nose Scallop Cusp Height & Effective Vc Formula
Calculate 3D Mold Finishing Scallop Cusp Height h (um), Effective Engaged Cutting Diameter Deff (mm), True Cutting Surface Speed Vc,eff (m/min), and % of Nominal Diameter Speed.
Calculate spindle RPM from nominal 10 mm ball-nose diameter on a 0.08 mm finish pass and true cutting speed collapses 82%—plowing and work-hardening H13 tool steel!
During `3`- and `5`-axis CNC finish-sculpting of hardened `H13`/`P20` injection molds and titanium blisks with a **Hemispherical Ball-Nose End Mill** (`Nominal Diameter D` mm, `Radius R = D / 2` mm), adjacent parallel CAM passes spaced by **Radial Step-Over `a_e`** (`mm`) leave a periodic **Scallop Ridge / Cusp Height `h = (R - SQRT(R^2 - (a_e / 2)^2)) * 1,000`** (`um`, approximated parabolically as `a_e^2 / (4 * D)`—doubling step-over **quadruples** manual mold-polishing cusp height!)! Simultaneously, at shallow **Axial Finishing Depth of Cut `a_p`** (`mm < R` on flat/gentle surfaces), the flutes cut NOT at nominal diameter `D`, but at tiny **Chordal Effective Cutting Diameter `D_{eff} = 2 * SQRT(a_p * (D - a_p))`** (`mm`)—slashing **True Surface Cutting Speed `V_{c,eff} = (PI() * D_{eff} * RPM) / 1,000`** (`m/min`) to dead-zero right at the tool pole (`tilting 10°–15° lead/tilt angle` in `5`-axis CAM escapes the zero-speed dead center!)!
Verify on a `10.0` mm (`R = 5.0` mm) TiAlN Carbide Ball-Nose Finishing Pass—Nominal_Ball_Diameter `D` = 10.0 mm (B2), Radial_Stepover `a_e` = 0.45 mm (B3), Axial_Finish_Stock `a_p` = 0.35 mm (B4), and High-Speed_Spindle `N` = 18,000 RPM (B5): Scallop Cusp Height `h` equals a mirror-ready `5.07` um (E2), Effective Cutting Diameter `D_{eff}` shrinks to **`3.676` mm** (E3), True Surface Speed `V_{c,eff}` equals `207.9` m/min (E4—only **`36.8%`** of the `565.5` m/min nominal speed in E5)!
| CNC Ball-Nose Finishing KPI (D=10.0 mm Ball, N=18,000 RPM) | Formula | Verified Output |
|---|---|---|
| Scallop Cusp Height h (um) | ((D/2) - SQRT((D/2)^2 - (ae_mm/2)^2)) * 1000 | 5.07 um fine (64.41 um rough @ ae=1.6 mm!) |
| Effective Cutting Diameter Deff (mm) | 2 * SQRT(Axial_ap_mm * (Ball_D_mm - ap_mm)) | 3.676 mm (1.782 mm @ ap=0.08 mm skim!) |
| True Surface Speed Vc,eff (m/min) | (PI() * Effective_Deff_mm * RPM) / 1000 | 207.9 m/min (100.8 m/min carbide rubbing!) |
| % of Nominal Diameter Speed (%) | (Effective_Deff_mm / Nominal_D_mm) * 100 | 36.8% (17.8% at 0.08 mm skim!) |
Exact Circular-Arc Scallop Cusp Height & Chordal Effective Diameter Formula
Validate `Ball_Diameter D` in `[0.5, 50]` mm, `Radial_Stepover a_e` in `(0, D)`, hemispherical `Axial_DOC a_p` in `(0, D / 2]`, and `Spindle_RPM` in `[500, 80,000]`!
=LET(db_m, B2, ae_m, B3, ap_m, B4, nr_p, B5, de_f, 2 * SQRT(ap_m * (db_m - ap_m)), IF(OR(db_m < 0.5, db_m > 50, ae_m <= 0, ae_m >= db_m, ap_m <= 0, ap_m > 0.5 * db_m, nr_p < 500, nr_p > 80000), "Invalid Ball-Nose Input", ROUND((de_f / db_m) * 100, 1)))Coarse Semi-Finish Stepover (`a_e = 1.6` mm) + Ultra-Shallow Skim (`a_p = 0.08` mm) Rubbing Check
Open stepover to `B3 = 1.60` mm while taking a tiny `B4 = 0.08` mm spring pass: Scallop Height E2 explodes `12.7x` to **`64.41` um**, while `D_{eff}` E3 shrinks to `1.782` mm—dragging True Cutting Speed E4 down to `100.8` m/min (`17.8%` of nominal in E5) and chipping the chisel-edge tip!
=IF(ISTEXT(E5), E5, ROUND(((B2 / 2) - SQRT(((B2 / 2) ^ 2) - ((B3 / 2) ^ 2))) * 1000, 2))Try the example
Use the original values or change them to test your understanding.