Knurling Blank Diameter for Clean Tracking

The blank circumference must be a whole number of teeth, so teeth = round(pi x D x TPI) and blank = teeth / (pi x TPI). A 0.750 in target at 21 TPI wants 49 teeth, so turn the blank to 0.7427 in (0.0073 in under); a 1.000 in target at 33 TPI rounds to 104 teeth and 1.0032 in (0.0032 in over) -- the adjustment is signed and always within half a tooth. Diamond and straight TPI knurls; diametral-pitch knurls and the knurl maker's tracking chart govern the finished pattern.

teeth = round(pi x target_diameter_in x knurl_tpi); blank_diameter_in = teeth / (pi x knurl_tpi); adjustment_in = blank_diameter_in - target_diameter_in.

Knurl tracking rule, first-principles; a circular-pitch (TPI) knurl tracks cleanly only when the blank circumference is a whole number of teeth.

The tracking relation is public first-principles geometry (circumference = whole number of teeth); the target diameter and knurl TPI are user-supplied.

Estimate. AHJ and licensed professional govern.

Field names used by the API: target_diameter_in, knurl_tpi, teeth, blank_diameter_in

• Whole-tooth circumference clean tracking needs pi x D x TPI to round to a whole number of teethknurl tracking geometry
• TPI form circular-pitch (teeth-per-inch) knurl; diametral-pitch knurls differscope of this tile