Polishing Aluminum

Bringing machined aluminum into a highly polished finish is a multi-step and sometimes challenging process.
The first step is to tumble (vibratory usually works best) the parts in an abrasive media such as a Plastic or Synthetic Media. Using as round a media shape as possible - cones vs triangles - will result in a smoother finish producing a better end result.
The second step is a polishing step using a Ceramic Media. Either an Angle Cut Cylinder or a Precision Ceramic Sphere will produce a smooth surface finish - again rounder is better.
In order to burnish the surface (if necessary), a third step can be to dry tumble the parts with a Walnut Shell Grit possibly treated with a fine abrasive such as jeweler's rouge.
It is important to make sure that the chemical compounds you use will not attack the aluminum. Depending on the final finish required, a small amount of hand polishing may be needed.