I had to set up a part in the lathe today and wanted to centre an existing hole. My expanding mandrels are not that flash (and are the hammer type), and I did not have a turned to suit mandrel available.
Solution -
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Use an adjustable reamer. Instead of adjusting the blades to ream, place the reamer in the hole and adjust up to a light but snug fit. Provided the reamer has not been bent, good enough to help get the hole on the axis of the lathe.

Michael