I found something out today that I never knew. There are some situations where I would like to use a ball bearing on a shaft, but the outer diameter of a ball bearing is too large for my application. I have always been under the impression that needle bearings which come with the outer race but no inner race must use a purchased inner race, (which again makes the outside diameter too large) or else they must run on a hardened shaft to keep from galling the shaft material. I spoke with a rep for Koyo bearings today, and they make a needle bearing with an outer race that needs no inner race nor a hardened shaft. The rollers run directly on a 1045 steel shaft that is not hardened and they will not gall it. I will go over to Canadian Bearings on Monday and find out more about this. If it's really true, it will get me out of a bind. The outer diameter of a 3/8" ball bearing is 0.875". The outer diameter of a 3/8" needle bearing is 9/16". This is a B68 Koyo bearing.