I read this thread yesterday and thought it over. I DO have a cat or 2 that whirs -- I just can't remember which ones!

Mine do it when they are obviously on a mission - not at a full gallop, but a very quick walk. I've never seen them start or stop a whir; they are always just passing through the room I am in on the way from one place to another. Yes it is a happy sound!

It reminds me of the friction cars my brother had as a boy. You hold the car on the ground, roll it backwards to "wind" it up, then release, and off it goes.

Oh, and when mine do the whir, they are not interested in a quiet walk either. More like stomping he hee.