For the drill press to work properly, the belt must be under considerable amonunt of tension. If it is not, there won't be sufficient friction and the belt will creep. The belt is made from rubber and textile core. It's quite flexible, but if you leave it tensioned for longer time, the belt wil deform plastically around the pulleys creating bends, As you start your drill press, these bends will run around the pulleys creating those unwanted vibrations.
Step 1: Fix It!
Fortunately, there is an easy fix for it! Only thing you have to do is, that every time you know you´re not going to use your belt powered tool for longer time, you simply loosen the tightening mechanism. This means, that your belt won´t be under unnecessary tension, and it wont stretch undesirably.
This also works for other belt driven tools, like table saw. Let me know what you think about this tip or if you have som easy maintenance tricks make sure to share them in comment, subscribe to my YouTube channel, I post QuickTip like this every monday and project video every thursday and don´t forget: get inspired, use what you have and make the best out of it!