People who rode “shotgun” many decades ago never dreamed that wagon wheels would find their way indoors and metamorphose into chandeliers, tables, stair railings, and wall art. You should remove the rust from any part of a wheel before you take it indoors in order to prevent any contact stains. It’s important to protect the patina of the wheel while removing the rust and you need to exercise care while completing the task.
Apply masking tape on the wooden parts of the wheel wherever wood abuts metal. If the wood is extremely porous use an “extra sticky” type of tape. Check to make sure the tape is firmly seated and will not let liquid seep into the pores of the wood.
Brush the metal parts of the wheel with a stiff-bristled brush. Do not use a wire brush as that will mar the patina of the metal. The goal is to remove the heavy areas of rust without going down to bare metal.
Rub the metal parts of the wheel with a coarse cloth such as burlap or canvas. Partially saturate the material in olive oil and apply pressure to the surface of the metal as you rub. Rub all the metal surfaces in this fashion until you have removed the rust. Repeat the process several times if necessary.
Buff off as much oil as you can with a clean cotton cloth. Apply pressure to the cloth, as you rub. An extremely light coating of oil will remain, no matter how hard you work, which will polish and protect the surface of the metal from future oxidation.
Remove the masking tape from the wheel and discard.