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Shafts and bearings usually use interference or transition fits - they shouldn't slide and for installation you should use force - some kind of press or clamping tool would be best, eventually if such tools are not available - few gentle hits with a hammer (you shouldn't hit the bearing directly to avoid damage, use something, for example piece of wood, to spread the force onto the whole bearing). Alternatively, you can heat/cool one of the parts to make use of thermal expansion.

InductionBearingHeater

I often build things (3D printers, skateboard wheels, bicycle parts) that use off-the-shelf ball-bearings. These ball bearings are available in nominal mm sizes, and to the limit of my measuring tools, tend to be ground exactly to size. For example, a bearing with 15mm ID and 24mm OD will have ID and OD of exactly 15 and 24mm, to my ability to measure.

Typically you want an interference fit on a bearing ID since the shaft is usually the element that's rotating and whatever the bearing OD goes into will have a looser fit. If your shaft is rotating and has a loose fit with the bearing ID it can start to score and cause a whole bunch of issues. You can typically find undersized dowels which could work in your instance.

To get a bearing and a shaft which fit each other with a close sliding fit, is it more normal to use an undersize shaft or an oversize bearing? If the former, why does it seem so hard to find shafts commonly available to fit nominal bearing sizes?

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As for the undersize/oversize I suggest you to read some basic information about engineering tolerances. The nominal size is obviously only theory, so we use tolerances to describe the allowed variation in the actual dimenisions. Depending on the type of tolerance we allow them to be for example only higher than nominal, only lower, always higher by certain number, either lower or higher etc. And when we assemble 2 parts that have certain tolerances we have engineering fit.

In cases where you want a bearing to have a close sliding fit on a shaft, it seems two things are possible: Either you could buy special ball bearings with slightly over-nominal size (i.e. 15.15mm ID), or you could buy shafts with slightly under nominal size (14.85mm). However, there doesn't seem to be a common "standard undersize" shaft or "standard oversize" bearings for each nominal mm size; neither thing seems to be common. This leaves a world of 15mm shafts and 15mm bearings which don't fit each other except by interference fit.

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Standard practice is to heat the bearing with a bearing heater, or cool the shaft, prior to assembly. The thermal expansion (or contraction) allows just enough clearance for assembly. Shaft fits are also dependent on the load and application of the bearing, usually based on ISO clearances. This is a useful resource from a reputable manufacturer. For a 15 mm bearing with line to line fit or a little tighter you may be able to just use an arbor press and some elbow grease.

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Bearing manufacturers will give values for interference based on the application. This does not involve buying shafts off the shelf. It involves setting the spec and having a machinist create the right sized shaft. Pump and motor manufacturers make their shafts to the right specification, which is most certainly not by buying them off the shelf. We are talking micrometers as the measurement accuracy required. All the major bearing manufacturers have guides for this (SKF, FAG, etc.). A millwright's handbook provides guidance on installation procedures. Not all bearings can be put on in a press, so field techniques also exist (yes, hammers are involved).

Obviously there is in-depth engineering that goes into setting the standards and the resultant specs, but no engineering knowledge is necessary to use the guides. The skillset for installation is a mechanic's, not an engineer's.

It's also easy to buy linear or rotary shafts ground to nominal diameters. For example, I can buy 15mm ground rotary shafts. These are usually ground to a +/- tolerance which means half of them won't fit the bearings, or the more precise ones are ground to an upper spec of 15mm and very small tolerance smaller. Usually, even with the 15mm upper spec, the size is too close to 15mm for a bearing to slide on. I have to polish the shaft down with sandpaper (destroying the nice finish) in order to get an bearing that can be assembled by sliding, such as for a bicycle hub axle.

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