Can you elaborate on what rod you sourced? For example if its drill rod, they are typically ground with stated tolerance +/- 0.0005" My experience is they can vary that much across the axis (elliptical) as opposed to diametric but now we are getting into the weeds. Its pretty good stuff. But if you bought nominal stock of pretty much anything else, all bets off.The rod is 3/16 at 4.7mm diameter
Just eyeballing the size/fit I'd aim for something like 0.0005" diameter over shaft size but for this purpose could even be a bit more, say 0.001".
Class III Medium Fit Tolerance Chart for Holes and Bolts
Medium running fits - tolerances are intended for higher running speeds, or heavy journal pressures, or both.
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