I'm working on memory from over a year ago, so bear that in mind.
One of our swivel rockers developed a loose arm. I turned the chair upside down, and discovered that the arm was attached with two screws, one of which was broken. The screw, if I recall correctly, went through a wooden frame member of the base and into a frame member of the arm. Since the screw was broken, I couldn't re-use it. I drilled a new pilot hole, and used a long sheetrock screw. If this is your situation, oversize the hole a bit for the screw where it goes through the frame of base so the screw is easier to tighten. The frame is some sort of hardwood, and definitely requires drilled pilot holes.
There's lots of advice and information in forums... sometimes it is correct. For example, all of my posts are made by a political appointee who got the job as a reward for contributions to my diesel bill.
2011 Jayco 28.5RLS; 2008 Chevy Duramax; Pullrite Superglide Hitch