Your instructor did you a favor - he taught you what you need to do
to get a mirror finish. While he might have taught you how to use
tumblers, the technique you are trying to emulate with a machine
requires that you know what is happening in the finishing process
whether manual or automated.
Finishing involves smoothing and burnishing. The tumbler processes
you have seen are all burnishing - steel with rotary or vibratory
machines and the magnetic finishers all burnish. Then do not remove
metal, they hammer it in tiny bits.
The first part of finishing is to smooth the metal - you can do it
by hand with sandpaper or on the buff with Tripoli. You can also do a
very good job of smoothing with a tumbler - my favorite is a
vibratory flow thru with various grades of abrasive - depending on
what you started with. Cast work differs from fabricated, and silver
works differently from brass or gold or pmc.
After you have smoothed the work in your vibratory tumbler, you can
burnish it to bring up a reflective surface. The magnetic tumblers
work well on detail pieces - filigree, fine wire pieces such as ear
wires, and heads. They are pretty small and don't accommodate large
pieces. My work horse is a rotary tumbler with stainless steel.
My solution to a perfect shiny finish, is this. After smoothing and
burnishing, the work is run in a dry media in a vibratory tumbler -
walnut shells or wood chips charged with simichrome or chrome oxide
or rouge. It runs for quite a while - 24 hours or more - and the
resulting finish is flawless.
I love my magnetic tumbler, but I don't use it as much as the
vibratory or rotary. There is a bit more to this tumbling than which
one to buy.
There is a lot of on finishing on Orchid. There are also
reference books on the process. I've written a basic book on the
process - available from most of the major suppliers - Rio, Gesswein,
Otto Frei, Elaine Luther.