Make sure to locate the knob so the grub screw aligns with one of the sides of the split shaft for a good fit ( do not align so the grub screw locates into the gap of the split shaft). These are screw fit, and can be tightened up with a small Allen Key using the grub screw on the side.
Not sure what year Les paul this is for. I bought it to use on my 59 Les Paul and although it is very nice, It's not the right shape or size for a late 50's Les Paul. I do have several original ones to compare it to and it didn't match up. I would recommend it for a vintage Les Paul if you want to add that vintage vibe!