CNC Machining, High-Efficiency Milling (HEM), Trochoidal Toolpaths & CAM Feeds
CNC Milling Radial Chip-Thinning Factor & MRR Formula
Calculate Spindle Speed N (RPM), Exact Radial Chip-Thinning Compensation Factor RCTF, Compensated Table Feed Rate V_f (mm/min), and Volumetric Material Removal Rate MRR (cm³/min).
Why 10% radial stepover without Radial Chip-Thinning compensation rubs carbide flutes to death at 60% of target chip thickness!
Modern High-Efficiency Milling (HEM) uses full flute length a_p (mm) at shallow radial engagement a_e < 0.5 * D (e.g. 10% of endmill diameter D)! However, whenever radial stepover a_e is less than half the cutter diameter (50% D), no flute ever engages at 90° centerline—so programming catalog feed-per-tooth f_z = h_ex starves actual maximum chip thickness below the carbide edge hone, work-hardening stainless/titanium by rubbing instead of shearing! Exact chord geometry requires boosting programmed feed per tooth by the Radial Chip-Thinning Factor RCTF = IF(a_e >= 0.5 * D, 1.0, D / (2 * SQRT(a_e * (D - a_e)))), giving Spindle Speed N = (1,000 * V_c) / (PI() * D) RPM, Compensated Table Feed V_f = N * z * (h_ex * RCTF) mm/min, and Material Removal Rate MRR = (a_e * a_p * V_f) / 1,000 cm³/min!
Verify on a 16.0 mm 4-Flute Solid-Carbide Endmill Dynamic HEM Pass in 4140 Steel—Cutter_Diameter D = 16.0 mm (B2), Flute_Count z = 4 (B3), Surface_Cutting_Speed V_c = 180.0 m/min (B4 -> Spindle Speed = 3,581.0 RPM in E2), Target_Max_Chip_Thickness h_ex = 0.080 mm (B5), Radial_Stepover a_e = 1.60 mm (10% D, B6), and Axial_Depth a_p = 20.0 mm (B7): Radial Chip-Thinning Factor hits 16 / (2 * SQRT(1.6 * 14.4)) = 1.667x (E3!), boosting Compensated Table Feed from 1,145.9 up to 1,909.9 mm/min (E4) and delivering 61.12 cm³/min MRR with cool, thick chips (E5)!
| CNC HEM Milling KPI (D=16 mm, z=4, Vc=180 m/min, hex=0.08, ae=1.6, ap=20) | Formula | Verified Output |
|---|---|---|
| Spindle Speed N (RPM) | (1000 * Vc_m_min) / (PI() * D_mm) | 3,581.0 RPM |
| Radial Chip-Thinning Factor RCTF | IF(ae>=0.5*D, 1, D/(2*SQRT(ae*(D-ae)))) | 1.667x (1.000x @ ae = 8.0 mm 50% D) |
| Compensated Table Feed Vf (mm/min) | RPM * Flutes_z * Target_hex * RCTF | 1,909.9 mm/min (1,145.9 @ ae=8.0) |
| Material Removal Rate MRR (cm³/min) | (ae_mm * ap_mm * Vf_mm_min) / 1000 | 61.12 cm³/min (183.35 @ ae=8.0) |
Exact Chordal Radial Chip-Thinning Feed & Volumetric MRR Formula
Validate Cutter_Diameter D > 0, integer Flutes z >= 1, Surface_Speed V_c > 0, Target_Chip h_ex > 0, Radial_Stepover a_e in (0, D], and Axial_Depth a_p > 0!
=LET(dc_m, B2, fl_z, B3, vc_m, B4, hx_m, B5, ae_m, B6, ap_m, B7, IF(OR(dc_m <= 0, fl_z < 1, vc_m <= 0, hx_m <= 0, ae_m <= 0, ae_m > dc_m, ap_m <= 0), "Invalid Milling Input", LET(rp_m, (1000 * vc_m) / (PI() * dc_m), rc_f, IF(ae_m >= 0.5 * dc_m, 1, dc_m / (2 * SQRT(ae_m * (dc_m - ae_m)))), vf_m, rp_m * fl_z * hx_m * rc_f, ROUND((ae_m * ap_m * vf_m) / 1000, 2))))50% Cutter-Radius Centerline Engagement Unity Check (Set Radial Stepover a_e = 8.0 mm)
Widen Radial_Stepover B6 to 8.00 mm (exact 50% centerline engagement): Chip-Thinning Factor E3 drops cleanly to 1.000x, Table Feed E4 returns to uncompensated 1,145.9 mm/min, and Heavy-Roughing MRR E5 reaches 183.35 cm³/min!
=IF(ISTEXT(E5), E5, IF(B6 >= 0.5 * B2, 1, ROUND(B2 / (2 * SQRT(B6 * (B2 - B6))), 3)))Try the example
Use the original values or change them to test your understanding.