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.
