I'm doing a gear design project, and I'm using a multivariate mixed integer non-linear optimization suite known as
Couenne distributed by COIN-OR. Within Python, I use this solver to solve for all aspects of the gears in a 2 ratio reverted gear-train given 2 target gear train ratios (4.3 fwd, 9.1 rev). My classmates are telling me that the diametral pitch for each gear pair must be an integer value, or a value with a well known fraction in decimal form. Is this true? I've found that placing this constraint makes it much harder to approach the 2 target ratios. Perhaps it was a consideration about manufacturing, because It would be exceedingly hard to machine a diameter that is an irrational number. However, couldn't the same be said for any diameter? Manufacturing shouldn't depend on the dimension because for any given manufacturing precision we will never know what is after the decimal place. For both irrational and integer diametral pitches, the manufacturing error would be the same. So why would gear diametral pitches have to be integer values?
Without this constraint, I'm able to achieve a total gear train ratio error of 1.3*10^-8 percent from the target ratios.
EDIT: when I refer to "diametral pitch" I am referring to the gear module, number of teeth per inch