Choosing a linear bearing is not only about shaft diameter. You must check:
Shaft hardness and tolerance (basic conditions)
Bearing format – raw LM vs housed SC/SBR units
Open vs closed type – floating shaft vs supported rail
Standard vs long type – stability and moment rigidity
Hardness
LM linear ball bearings are designed to run on hardened shafts (typically HRC 60+).
If you use soft mild steel or soft 304 stainless with steel balls, the balls will quickly dig grooves into the shaft and destroy accuracy.
Tolerance
The ID of LM bearings is made to fit precision ground shafts with g6 or h6 tolerance.
If the shaft is too small (e.g. generic cold-drawn rod with big minus tolerance or poor roundness), the bearing will feel loose and wobble.
If the shaft is too large (e.g. k6 or positive tolerance chrome bar), the bearing may jam, run rough or even break the ball cage.