When aluminum oxide forms it covers the metal with a hard grey coating. A process called anodising makes the coat thicker. It won't rub off, and many products, including professional cookware, have an anodised finish. It does protect aluminium, but it's hard to clean. There are some ways to clean anodised aluminium without ending up with a dull looking item.
Apply Bar Keeper's Friend to the anodised aluminium. Rub with a damp rag until the aluminium is clean. Rinse under running water and dry with a soft rag.
Try cleaning your anodised aluminium with Copper-Glo. Though formulated for copper, it can clean anodised aluminium as well as Bar Keeper's Friend, and you don't have to rub as hard. Put Copper-Glo on the anodised aluminium. Rub with a damp rag, rinse, and dry with a soft rag.
Use Bon Ami cleanser and a plastic scrubber to gently clean anodised aluminium. Rinse with warm water and dry with a soft rag.
Apply SafeRestore to remove oxidation from anodised aluminium and to keep new oxidation from forming. After cleaning with SafeRestore, apply a coat of Anodized Restoration Treatment to clean the dry surface.Air dry the piece. Both SafeRestore and Anodized Restoration Treatment are available from the Eaco Chem website.
Place the piece of aluminium in a shallow pan. Put on rubber gloves and eye protection. Cover the aluminium with warm water and add 1 tbsp of drain cleaner dry crystals. Mix the drain cleaner in the water. Lift the aluminium out of the water every two minutes to remove the residue from the item. When the stains are gone, take the aluminium out of the pan, rinse, and dry with a soft rag. Repeat the process if you see any dark spots. Sand the surface of the aluminium with 800 grit sandpaper to remove any scratches and buff it with a soft rag. Apply olive oil or a coat of wax to keep the piece from tarnishing, or spray it with clear lacquer.
When using drain cleaner, make sure you're in a well ventilated area.