Protecting PVC rod in 3 jaw lathe chuck

Best way would be soft jaws; bore the 20mm profile into them. If it's not for production, though, that's a nuisance. Otherwise, consider thick pads (1/8" rubber, or even cork). Or, maybe just make a socket for the rod, slip-fit, and drive the socket on a center.

You could use a larger piece of PVC, bore it and slit it and use it as soft jaws. Or if your chuck uses top jaws you could make some soft jaws if you don't already have some, and then bore them to hold the work. One type of soft jaw that works well for parts that don't need high gripping force is made from round stock. Saw up three pucks from some aluminum round bar, Face both ends parallel, cut two slots at 90 degrees on one face that are just slightly deeper than the key part of the bottom jaws, turn around, drill and c'sink for one jaw screw in the center of the puck. This method only uses one screw per jaws so clamping pressure will be lower but you get 4 chances to bore the jaws, not just two. And the bored jaws will have lots of surface area to spread the clamping. Eric

A piece of 3/4" PVC water pipe, slit.