Reuleaux triangle coaster

I was approached with a design for a coaster using a Reuleaux triangle in the middle. It is a shape of constant width so it is able to rotate within a square just like a circle would. I made some tweaks to the design like putting in a lip on the middle layer to stop the shape falling out. It works and is fairly functional but it's not very smooth and it squeaks as it turns, I've yet to come up with sensible solutions to those problems.