when you say rims, they are made out of all kinds of stuff
I recently did spoked wheels on '99 Honda Shadow motorcycle that were coated in cadmium....a dully gray metal
i was very careful with those, so as not to etch or damage that cadmium at all
as I've worked with chems it's a tedious process, I don't try and muscle the surface clean, but rather keep plenty of chems on the surface and use uniform repetition, either by hand, or with a foam attachment on a cordless hand drill
the results are always outstanding.....lot's of great chems and polishes, but of all the ones I've tried, I can usually get great results if give it plenty of elbow grease and time....again...i like the chems to do the heavy lifting, so my elbow grease is lots of back and forth, but not a lot hard pushing and rubbing...chrome is hard and durable, but can be marred....brushed aluminum is really fun to clean, a brushed aluminum finish can downright sparkle if you have the patience to take it down to nothing but pure aluminum, but these surfaces can be damaged and dulled
before i even touch wheels with any kind of polish, they get a general cleaning....I wash them with a good wash, rinse them, and then dry them....then they get a second wash with something like Sonax Wheel Cleaner Plus...i try to be really gentle and let the wash and chems do the work again here, there's a lot of dirt on wheels, and it's nasty stuff, so as much as I can, I try to avoid any hard rubbing so as not to gather and use the surface contaminants as abrasives on the surface by rubbing them into it in the cleaning process