This is the inside my my chrome wheels. The chrome is just stuck on the outside of the wheel. This inside is probably clear coated (it is not bare metal)



What can I use to clean this to get all of the old caked-on brake dust, as well as the adhesive from weights? Degreaser works a little bit, as does wheel cleaner.
Is there anything more effective that I can use?

 

Might try a pressure washer.

 

As suggested, a pressure washer with the soap should work. With hyraflouric acid content of the soap it would take the paint off your car.

Honestly, I've never had a problem using simple green or similar product for brake dust.....although mine has never been that bad.

On the wheel weights a good cleaning first then using a solvent type product and elbow grease. When I had my Vette wheels rebalanced (I took just the wheels to the dealer) I pulled the old glued on weights and cleaned with a couple different products ......paint thinner and something else that I can't remember. Then I washed them well and "polyed" them.

Looks like you have the polished aluminum wheels and the display side is clear coated. Use a moderately stiff brush on the inside with a strong soap of your choice

 

The aluminum wheels on my Dodge truck look like that. Once they get that bad it's like concrete.
I use white wall cleaner and a SOS pad every couple years. AND, lots of elbow grease. Mine are factory silver painted and the brake dust seems to etch itself into the paint.

 

Just list the cleaners, I 've ever used in such cases :
1. Cleaner from bitumen stains . I used the tool "Profoam 1000 " Korean company "KANGAROO". But there are a lot of funds from different manufacturers ;
2 . Means for removing the adhesive , paint , etc. This branch of the " production of advertising structures ." Chose him as the most powerful , peeling plastic upholstery from a evil mounting tape. I do not remember the name of Means, but many of these liquids too;
4 . Cleaner engine from oil deposits . Manufacturer - LIQUI MOLY. The same manufacturer produces cleaner of brakes - also very good . One drawback - both are a bit expensive;
5 . Handy tools : brake fluid or Coca Cola . Coca Cola an amusing incident , but cleans better than soapy water . ( as you Americans drink this chemical solution? !) .
I wish you luck .

 

Call me weird, and lot's of folks here do.

But everytime I rotate my tires, I make up a bucket of hot soapy water and scrub the back of each rim.

It's kind of a pain, but it kills nasty brake dust build-up.

Unfortunately, brake dust is highly corrosive, and even a good quality rim cleaner will probably fail at getting those wheels back to "good as new".

 

I'm OCD with clean so, I'm with 843de, wash them every tire rotation, a lot less work, but for this problem X2 to the above mentioned pressure washer

 

I know this is an old post, but I just bought my 2006 HHR a couple of weeks ago and the back side of the wheels had so much tar and build up on them it was affecting the balance. I started with a scrub brush and some wheel foam, that got a lot of the dirt and brake dust off. Then for the tar I used some glass cook top cleaner which has a slight abrasive to it with a scrubbing pad. The real stubborn spots I softened with brake cleaner and then repeated with the scrubbing pad and liquid cleaner. It worked pretty well I would say. Some of the tar pieces were as big as a dime and I had to scrape them off with a plastic putty scraper.