Ball nose end mills

An ideal 6 mm ball nose cutting a flat surface 0.30 mm deep without tilt engages an outer diameter of 2.615 mm. At 10,000 rpm that is 82.2 m/min, versus 188.5 m/min calculated from nominal diameter. Use the engaged geometry and check actual tool, holder and spindle limits.

Geometry and applications

A ball-nose end mill has a rounded end for contours and radius features. An ideal full-ball profile has radius equal to half the nominal diameter. Harvey Performance, Ball nose milling strategy guide, 26 June 2017

The geometric profile does not by itself specify the substrate, coating, flute count, neck, reach or allowable workpiece material. A 6 mm ball profile and a 6 mm shank are also different dimensions. Nominal size describes only part of the tool's cutting and clearance envelope; it does not establish that the holder and shaft can reach an arbitrary concave feature.

Nominal diameter is not always the active diameter

At a shallow axial engagement, only part of the spherical end cuts. Harvey's guide distinguishes effective diameter from nominal diameter when axial depth is less than the ball radius. It also describes inclination as a way to avoid the zero-surface-speed point at the tool center. These relationships concern contact geometry; they do not prescribe one tilt angle for every machine or toolpath. Harvey Performance, effective diameter and tilt discussion

For an ideal, untilted ball of diameter D and radius R = D/2, engaging a flat surface to axial depth a, with 0 ≤ a ≤ R, the largest engaged diameter is:

D_eff = 2 × sqrt(R² − (R − a)²) = 2 × sqrt(a × (D − a)).

IMCO's ball-nose technical resource uses this shallow-engagement geometry and distinguishes it from engagement reaching at least half the tool diameter. Its speed/feed treatment also includes axial chip-thinning and tool-projection adjustments, rather than substituting nominal diameter into every calculation. IMCO, Adjustments for ball nose end mills, printed pp.134–135

The expression reaches D at a = R. Extending it beyond the equator would incorrectly make the computed diameter decrease; it is not a universal formula for deeper or tilted engagement. Surface slope and tool inclination can move contact to another region of the sphere. In an actual cut, the engaged region can contain a range of local cutting speeds.

Cutting speed and feed are different quantities

Sandvik identifies effective cutting diameter at the actual depth as important for true cutting-speed calculations with ball nose and other large-radius cutters. In metric units, surface speed follows v = π × D_eff × n / 1000, with diameter in mm and spindle speed n in revolutions per minute. Table feed instead relates to spindle speed, effective tooth count and feed per tooth. Feed per tooth is not automatically equal to maximum chip thickness. Sandvik Coromant, Milling formulas and definitions

At the exact rotational axis, the local radius is zero, so rotational surface speed is zero even at a high spindle speed. A higher RPM does not eliminate that geometric fact. Tilting can move the active cutting zone away from the tip, but changes engagement and clearance at the same time.

Scallops and stepover

Adjacent passes of a rounded tool can leave cusps, commonly called scallops. IMCO's resource relates smaller radial stepover to lower geometric scallop height and gives the approximation h ≈ s²/(8R), where s is stepover and R the ball radius. This is a geometric relationship, not a measured roughness guarantee. IMCO, Surface finish, printed p.135

For an ideal flat surface, parallel passes, an exact spherical profile and 0 ≤ s ≤ 2R, the circular cross-section gives the exact expression:

h = R − sqrt(R² − (s/2)²).

Solving for spacing at a chosen geometric height gives s = 2 × sqrt(2Rh − h²). These are elementary circle-geometry deductions under the stated assumptions. Curved surfaces, changing contact direction, tool deflection, runout, vibration, wear and material behavior can make the actual surface differ. A computed cusp height is not automatically Ra, Rz or a complete description of surface integrity.

Original example: shallow contact and surface speed

Use the hypothetical 6 mm ball, 0.30 mm axial engagement and 10,000 rpm on a flat surface without tilt.

D_eff = 2 × sqrt(0.30 × 5.70) = 2.615 mm, approximately.

The local result is π × 2.615 × 10,000 / 1000 ≈ 82.2 m/min. Nominal diameter gives 188.5 m/min.

A hypothetical target of 100 m/min at the calculated diameter corresponds to approximately 12,171 rpm. That arithmetic does not establish that the tool, holder, spindle or workpiece can operate at that speed, nor does it determine chip load or cutting force. A flute near the axis still has a lower local speed than one at the outer engaged radius.

Original example: stepover and geometric finish

Using the same 3 mm ball radius on an ideal flat surface, a 0.50 mm stepover gives:

h = 3 − sqrt(9 − 0.25²) = 0.010435 mm ≈ 10.43 µm.

The small-step approximation gives 0.50²/(8 × 3) = 0.010417 mm, close under these assumptions. Reducing stepover to 0.25 mm gives an exact height of approximately 0.002605 mm, or 2.61 µm: about one quarter of the original geometric height.

For a hypothetical 5 µm geometric-height target, the inverse expression gives approximately 0.346 mm spacing. None of these values determines measured roughness, allowable machining stock or a universal finishing pass. A nominally smaller scallop can coexist with poorer actual finish if other cutting conditions dominate.

Source versions and limits

Reviewed 2026-11-02 PST. Harvey's guide is dated 26 June 2017. IMCO's extract prints pages 134–135 but no independently verified issue date; the upload path is not treated as a publication date. Sandvik's live definitions have no separately verified technical issue date here. The equations and original examples are bounded geometry and dimensional arithmetic. They establish no default RPM, feed, depth, stepover, tool life or workpiece compatibility for a particular operation.