Fred swigs a 12-pack of Bass Ale onto the table

I have a couple of cheap drill chucks that feel like they've been lubed
with a mix of rubber cement and swarf. Just soaking them in solvent then
relubing might work but taking them apart would let me look for burrs.
After guessing that they are assembled with a right-hand thread between
the top part (with the taper hole) and the lower part (with the 3 holes
for the key) I tried a judicious use of force and saw no movement at all.

Before I employ a meticulously calculated lever arm (which happens to
match the length of my largest wrench) and an oh-so-gentle tap of a BFH,
could anyone tell me if this is how they are supposed to come apart? I'd
appreciate it; the chucks would appreciate it; so would my wife, kids,
and neighbors.
--
Fred R
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