After searching the internet for information on drill press chuck replacement I didn't come up with anything thorough on presses without a morse taper. My drill press has a Jacob's taper, but no morse taper. This instructable should help with chuck replacement and older drill press engineering.
Step 1: Remove Spring
Loosen the nut and carefully remove the quill feed return spring and housing. Make sure the spring does not come out of the housing because it is difficult to reassemble.
Step 2: Remove Feed Lever
Remove the feed lever and pull the quill, shaft and chuck unit from the press.
Step 3: Remove Ring
Remove the retaining snap ring.
Step 4: Remove Quill
Bearings hold the quill to the shaft. Place wood or metal between the chuck and the quill. Give the shaft a few taps with a rubber mallet and the quill should come loose.
Step 5: Remove Shaft
Rest the chuck on something so the shaft is free. Place a metal object through the top of the chuck and tap the shaft out from the back of the chuck. This is the Jacob's taper.
Step 6: New Chuck
The Jacob's taper on the new chuck should match that on the shaft. Tap the chuck onto the shaft with a rubber hammer.
Step 7: Reassemble Quill
Tap the quill and bearings back onto the shaft.
Step 8: Replace Ring
Replace the retaining ring.
Step 9: Reassemble Drill
Insert the quill into the drill press and reassemble the feed lever and return spring. Test the new chuck with a dial indicator for run out.