Guys,
ABEC, which was the
Anti-Friction Bearing Engineering Committee when I was an apprentice and was
reformulated into the
Annular Bearing Engineering Committee some years back (I must have missed that memo), puts out the standard load requirement equations in a rather expensive set of books. I have never understood their approach of making such information (gathered by
taxpayer funded research) so costly as, it seems to
me, more people would
use bearings if they had that information more readily available -- but that has been the trend for the past few decades. One of the things I am looking for is a
public domain basis for such information I can use in my ongoing work towards writing a new mechanical design engineer's handbook (the reason I am posting stuff over at
http://www.scribd.com/Lew%20Merrick).
In any case, the limiting factor on rolling element bearing design is the
Hertzian contact stress concentration that occurs when a round surface impinges on another surface. The smaller the radius, the larger the
Hertzian contact stress concentration factor. Since a ball bearing has a sphere (one
Hertzian contact stress concentration factor) rolling in a radial round groove (a second
Hertzian contact stress concentration factor), the effect of the stress concentration is approximately doubled -- making the
nomograph curve of overall stress concentrations take the form of
concentration factor = 1/
roller diameter².
Back in the pre-computer days things requiring more complex calculations were reduced to
nomographs[/] to simplify things. There were whole rafts of mathematical graph people who created them for government agencies and major corporations. If you look hard enough (older editions of Joe Shigley's Machine Design leap to mind), you will find nomographs for most mechanical design calculations.