Rubber mandrel Bushings that expand

I turn a lot of salt shaker pepper grinder combination pieces for sale at craft shows. I have a 3/8 inch threaded mandrel that has two rubber bushings on it that can be expanded to hold the ID of the pieces I am turning (the ID of the pieces is 1 1/16 inch which is the OD of the rubber bushing) . When I tighten the nuts on the mandrel against these rubber bushings they expand to hold the pieces steady for turning the OD of the pieces.
The rubber is wearing out and I would like to get another set. Due to poor memory I have no idea where I got the originals. I have looked online to no avail. Even tried McMaster Carr. Nothing yet. Maybe I am using the wrong nomenclature. Perhaps they are not called bushings? I don't know but, I would really like to get another set before these ones give up the ghost completely.

Does anyone know where I might find anything like this or by whatever other name I can search for a match?
Thank you guys and Gals,
Denny

I would just stack up section of rubber hoses one inside the other. perhaps get a rubber stopper of the correct od and drill a hole. Stationary sander spindles may work. They can be 3d printed in something like rubber.
BilLD

Drill or punch the mandrel hole. then grind or sand the od to fit

https://www.supplyhouse.com/Wal-rich...CABEgJdXvD_BwE

https://www.zoro.com/zoro-select-bum...SABEgIdIPD_BwE

https://www.homebrewit.com/products/...-5-16-x-1-1-16

https://www.mcmaster.com/products/ru...e-rubber-rods/

https://www.marcospecialties.com/pin...ts/RUBB-SLEEVE

Expanding jam chucks or sanding drums for a drill. Same thing basically just different names.

Shot in the dark here but can you maybe turn new bushings out of something like delrin and keep the original mandrel?

Penn State industries has some salt peppermill kits that use what they call a jam chuck like you described. They have one that is 1" that will probably expand to what you need. 1in Jam chuck for Mini Salt and Peppermill at Penn State Industries
Another option is to turn a wooden jam chuck. I find the rubber expanding jam chuck don't always center up like I prefer.

I would suggest looking at Rubber Chucky
https://www.rubberchucky.com/store/c...isms%29.html#/

I would suggest a pin chuck. I make mine out of hardwood. https://www.youtube.com/watch?v=Odu1cT3AwUE

Searching for "rubber freeze plugs" might get you what you're looking for.

I believe I have a set of these. I will check when I get out to my shop later and get back to you if I have that size. I know it is daunting to make a round rubber sleeve with a center hole that will spin without wobble.