Cutter Diameter for a Spindle RPM
The inverse of the machining-speed tile: the cutter or work diameter that runs at a target (or the machine's maximum) spindle RPM for a given surface speed, diameter = 12 x SFM / (pi x RPM). 100 SFM at 1,000 RPM is a 0.382 in diameter. Because a larger diameter turns slower, a machine RPM ceiling sets the SMALLEST cutter that still reaches the full SFM - a smaller one tops out the spindle first. Surface speed from the tool / material chart; the machine and rigidity govern.
Formula and source
diameter(in) = 12 * SFM / (pi * RPM); the inverse of RPM = 12 * SFM / (pi * dia); 12/pi = 3.8197.
First-principles cutting geometry; the speeds-and-feeds method as in Machinery's Handbook (Industrial Press), by name, solved for the diameter.
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