Ball nose feed calculator accounts for a ball-nose end mill’s reduced effective diameter at shallow depths of cut, converting target surface speed and depth of cut into spindle RPM.
Ball nose end mills only cut with part of the ball at shallow depths of cut. This finds the effective cutting diameter at your depth of cut, then the spindle speed adjusted for it.
De = 2 x sqrt(R^2 – (R – doc)^2), where R = D/2. RPM uses De in place of full diameter: RPM = (SFM x 3.82) / De.
How it works
At shallow depths, only a small chord of the ball is actually cutting, so using the full ball diameter for RPM badly understates the real surface speed at the cutting edge. Effective diameter corrects for this.
FAQ
What if depth of cut exceeds the radius? Past the radius, the full diameter is engaged, so effective diameter caps at the full ball diameter.
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How it works
A ball-nose cutter’s tip is spherical, so at shallow depths of cut only a small portion near the center of the ball is actually engaged; this effective cutting diameter is smaller than the tool’s full diameter and shrinks further as depth of cut decreases. Using full tool diameter to calculate RPM at a shallow depth of cut significantly understates actual surface speed at the cutting edge, so effective diameter should be used instead.
FAQ
Why does my ball-nose tool wear out faster than expected at light depths of cut? At very shallow depths of cut, the true surface speed at the small effective diameter can be much lower than intended if RPM was set using full tool diameter, leading to rubbing rather than clean cutting, which accelerates edge wear. Recalculating RPM from effective diameter for the actual depth of cut in use corrects this.
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CNC Calculators · Stepover Calculator · Spindle RPM Calculator