An oxide layer will form whenever the copper surface is undisturbed for a period of time (minutes). A patina usually refers to the much longer term surface film that has a greenish tinge to it.
With a standard DC commutator motor, or a slip ring machine, the copper wear rate per pass of the brush is extremely low. On copper/carbon current collection systems where the copper surface is only occasionally wiped, such as on the motor you describe or an overhead wire on an electrified railway, the copper wear rate per pass of the carbon is much higher (say 100x) because in the intervening period between brush passes, an oxide layer forms on the copper surface which is eroded by the passage of the carbon.
I have some typical wear rate figures (though not with me) if you want them.
I'm not sure how close I have come to your question. To simulate this type of problem you need a test rig where the brush lifts and lowers, I once operated such a rig.