Feed for a Target Turned Finish
The inverse of the turning-surface-finish tile: the fastest feed per revolution that still holds a target surface finish, f = sqrt(8 x nose_radius x Rt) (a target given as Ra converts with Rt = 4 x Ra). Holding 25 microinch Ra with a 1/32 in nose radius allows 0.005 IPR; a finer 16 microinch Ra drops it to 0.004 IPR. A larger nose radius lets you feed faster for the same finish. Answers 'how fast can I feed' instead of the finish at one feed. Theoretical; leave margin for tool wear and deflection.
Formula and source
f = sqrt(8 x nose_radius x Rt); Rt = 4 x Ra if the target is an Ra. The inverse of Rt = f^2 / (8 x r).
Theoretical surface roughness from feed and nose radius - first-principles scallop geometry as in Machinery's Handbook (Industrial Press), by name; public domain.
Audience
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