I suppose if there's a "sci.engr.mechanical" group I should post it there

-- but r.c.m has some smart mechanical types, and s.e.c may still have some lurkers who might come out of the woodwork for this one.

So here's a question for the mechanical engineers in the group(s).

I was giving a seminar on control systems last week, and had the embarrassment of not only having a huge mathematical error in one of my slides, but had one of the smarter audience members question my underlying assumptions -- and I didn't have answers for either problem while standing there.

The basic problem is this:

If I'm putting a gearbox into a control system, and I have a data sheet (or measurements) for the gearbox that tell me it's efficiency in the designed direction of power transfer (usually when it's gearing down), I would like to know what its efficiency is in the backward direction.

In other words, if I have a gearbox with a gear-down ratio of K:1 and

100% efficiency, then when I drive a torque into the thing I should get K*** torque out. But what I really get is K ***torque * efficiency.

I know both from experimentation with one sample, and from working out the math, that if I have a single-stage worm gear that I try to back- drive, its efficiency in the backward direction is pretty close to

h_b = h_f / (1 - 2 * h_f), where h_f is the efficiency in the forward direction.

But I don't know if this is general to all gearboxes, or even to all worm gear trains -- it's quite possible that I messed up my calculation and then lucked out on the one sample that I experimented on.

So -- anyone know? Are there any mechanical engineering texts that I should buy to check up on this?