Theoretical Surface Finish
Theoretical turned surface finish from feed and tool nose radius.
Example
You enter
- Feed per revolution f (IPR) 0.005
- Tool nose radius r (in) 0.03125
You get
- Rt (in) 0.0001
- Ra (in) 0.000025
- Theoretical Rt 100
- Estimated Ra 25
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopePeak-to-valley Rt = f^2 / (8 x r) with an estimated Ra ~= Rt / 4, in microinches and micrometres (first-principles scallop geometry).
Formula or tableTheoretical peak-to-valley Rt = f^2 / (8 x r); estimated arithmetic average Ra ~= Rt / 4 (= f^2 / (32 x r), about 0.031 x f^2 / r).
Source and editionTheoretical surface roughness from feed and nose radius - first-principles scallop geometry as in Machinery's Handbook (Industrial Press), by name; public domain.
Free accessPure geometry, public; the measured finish is rougher than this theoretical value.
What governsEstimate. AHJ and licensed professional govern.
API field namesfeed_ipr_in, nose_radius_in, rt_in, ra_in, rt_uin, ra_uin
- Round-nose tool the feed is fast enough that the round nose scallops the surface (the dominant regime); Ra ~= Rt / 4 is an estimatescallop geometry