A machine for retreading tires includes a rotatable hub that includes a moveable conical element, and an expandable rim disposed around the rotatable hub. The expandable rim includes a plurality of shoes. Each shoe of the plurality of shoes may have a base portion and a rim portion. The base portion may have a two-piece construction that allows for replacement of a worn interface that may include a channel and a ramp. A method for assembling an expandable rim for use in a tire retreading machine, and a method for servicing a machine having an expandable rim are also disclosed.