Why does RPM increase at shallow contact?

Maintaining the same cutting speed on a smaller effective diameter requires higher spindle speed.

Does the calculator select safe cutting data?

No. It provides a geometric starting point that must be checked against cutter-maker data and tool and machine limits.

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Ball-nose effective cutting diameter

Q: Why is effective diameter smaller than nominal diameter?

On the spherical part of the cutter, the contact circle is smaller than nominal diameter, especially close to the tool axis.

Calculate actual cutting diameter Dcap, RPM for a target Vc and table feed after applying the spindle-speed limit.

Tip depth ap or angle βDcap, Vc, RPM and VfContact cross-sectionLocal calculations

Why Dcap matters

A ball-nose cutter does not always cut at its nominal diameter.

Near the tip, peripheral speed is much lower than at full diameter. Using D instead of Dcap can therefore produce insufficient RPM for the intended cutting speed.

Depth from the tip

For an ideal sphere the calculator uses Dcap = 2√(ap(D − ap)), with ap measured from the lowest cutter point.

Contact angle β

When the angle from tool axis to the contact-point radius is known, effective diameter is Dcap = D · sin β.

Spindle limit

Theoretical RPM is compared with the machine maximum. If limited, the calculator reports achieved Vc and feed from the actual RPM.

Transparent assumptions

Geometry provides a starting point, not complete cutting data.

The real contact point also depends on toolpath direction, tool-axis tilt, radial engagement, edge geometry and deflection. The cutter's own RPM limit may be lower than the spindle limit.

FAQ

Common ball-nose questions

Why is effective diameter smaller than nominal diameter?

The spherical cutter section meets the contact plane on a circle smaller than nominal diameter. The circle shrinks towards the tip and tool axis.

Why does RPM rise at shallow contact?

Cutting speed depends on diameter and RPM. Maintaining the same Vc at a smaller Dcap requires more spindle speed.

What does angle β mean?

It is the angle between the tool axis and the radius from the ball centre to the considered contact point. At β = 90°, Dcap equals D.

Can I use the result at the exact tip?

Not directly. At the axis Dcap approaches zero and theoretical RPM approaches infinity. Change contact strategy or tilt rather than increasing RPM without limit.

Is this a complete cutting-data recommendation?

No. Check cutter maximum RPM, material, coating, overhang, runout, coolant, rigidity and manufacturer guidance.

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