HI Guy's …I've a few old drill press's bought used and the chuck's used to work loose after a while….
I used 222 Locktight or screw – lock to keep them together…..clean the chuck and its mating face…just a couple of drops of the fluid, hand fit…spin to check for run out…once ur satisfied place a block of wood under the chuck and hang a weight on the operation arm to keep the chuck tight…overnight shoud do it……one of mine was real bad, had tram lines in it, used a little extra fine valve grinding paste to lap it in, a good clean up and Locktite…it's never come of…….only do this if u'll never want the chuck off again say for say MT drill bits….
Frank in France