Free Milling Surface Finish & Scallop Height Calculator
Calculate theoretical cusp height (scallop crest), arithmetic surface roughness (Ra), and stepover percentage for 3D surface profiling and die sinking.
⚙️ Tool & Stepover Parameters
Stepover: 5.0% of Tool Diameter
• ISO Grade Class: N7 (Semi-Finish)
• Feed Mark Scallop: 0.16 μm (Feed marks are negligible compared to stepover cusps).
Die & Mold Rule: To eliminate manual hand benching and polishing on injection mold cavities, target a scallop cusp height $h le 2.5,mu ext{m}$ ($100,mu ext{in}$), typically requiring a stepover of 3% to 4% of cutter diameter.
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Understanding 3D Milling Scallop Height
When contouring complex 3D surfaces with a ball nose end mill, the spherical cutting tip leaves raised ridges of unmachined material between adjacent tool passes. The peak height of these ridges is termed the cusp height or scallop height ($h$).
Kinematic Formulas
Small Stepover Approx: h ≈ a_e² / (8 × R)
Theoretical Roughness: Ra ≈ h / 4 = a_e² / (32 × R)
Stepover for Target h: a_e = √(8 × R × h)
Theoretical Ra vs. Real World Shop Floor Ra
The formulas above calculate theoretical geometric finish based solely on tool kinematics. In real-world CNC machining, actual surface finish is typically 1.5× to 3.0× rougher due to:
- Tool Holder Runout: Even 5 microns of TIR runout creates single-flute cutting dynamics, doubling surface waviness.
- Zero Surface Speed at Center: A ball nose end mill has zero cutting speed ($V_c = 0$) at its exact tip, resulting in material burnishing, smearing, and tearing when cutting flat horizontal planes. Always tilt the tool 10° to 15° via 5-axis lead/lag angles.
- Tool Deflection & Chatter: Long-reach slender ball end mills vibrate under chip loads, creating chatter harmonics that imprint onto the finished wall.
Frequently Asked Questions
Why does my ball end mill leave a rough finish on flat floors?
At the very tip of a ball nose tool (axial center), the cutting diameter approaches zero, meaning the surface cutting speed (SFM) is zero. The flute cannot shear metal cleanly; instead, it plows and rubs the workpiece. Use a bull nose (corner radius) or flat end mill for planar floors, or tilt the tool axis using 3+2 positional machining.
How does a bull nose end mill compare to a full ball end mill for 3D machining?
A bull nose end mill has a flat center with rounded corner radii (e.g. 10mm tool with 1mm corner radius). On shallow sloped surfaces (< 30°), the flat bottom removes large swaths of stock with near-zero cusp height. However, on steep walls (> 60°), only the corner radius engages, behaving like a much smaller 2mm ball mill.
What stepover percentage is recommended for semi-finishing vs finishing?
For semi-finishing, a stepover of 15% to 25% of tool diameter balances rapid material removal with uniform stock allowance. For final finishing, stepover is typically reduced to 3% to 8% of cutter diameter to achieve Ra < 0.8 um (32 uin).