Do I need a voltage converter to run an imported bandsaw?
As the others have suggested in the notes, the frequency of the supply has an effect on the induction motors that power the bandsaw and the dust collector.  

If you move a motor designed for 50Hz onto 60Hz power, it will turn faster, by roughly 20%.  It will also draw more current (possibly a lot more, it depends on the motor as to how much).   The speed may exceed design tolerances on parts such as bearings, the impeller in the dust collector, etc.  If the current increases over the motor's full load amperage rating, the motor (or possibly other wiring of the device) would fail.

It seems likely to me that you would be able to buy replacement motors of the correct type cheaper than a frequency converter.