My bronze sleeve bearing's outer diameter is exactly 5/8" and the inner diameter of my pillow block is 5/8", so the sleeve bearing won't quite fit into the pillow block.
If you are sure about those dimensions, I would try press fitting the sleeve bearing into the pillow block. This can be done in a vise. You must be sure that the pressure of one jaw of the vise is on the inner race of the pillow block bearing and not on the entire bearing. The easiest way is to use a socket that is the same size as the inner race. You must be sure that the parts are square to each other before applying pressure.
The bronze sleeve bearing's inner diameter is slightly larger than the 11mm stainless steel shaft and so the bronze ring slides up and down the shaft pretty easily.
After press fitting the sleeve bearing, the inner diameter of the sleeve bearing may be slightly smaller so the shaft may fit more tightly.
- Scotty