Gearbox efficiencies and backdriving check

[Infraviolet]

Is it true for all forms of reduction gearbox that if the overall efficiency is <50% backdriving will be impossible (gear teeth would break before input would spin, even with no load at the input), and that if the efficiency is >50% backdriving will always be possible so long as any load on the input shat is minimal? Or does this rule ony apply to worm gear systems which use a sliding wedge contact, and not to more typical bevel/spur/planetary gears which have a rolling contact?

I ask because some differt designs of planetary gears which I've 3d printed have similar reduction ratios, yet if I backdrive one of them even with the motor present the input spins smoothly, yet the other won't backdrive at all (even with no motor present). Does this mean the latter one will have a poor efficiency (<50%) and give a lot less output torque than would be expected from the input torque and reduction ratio?

Thanks

[Doctorandus_P]

No, that simplification is not true.
Consider for example a simple gear reduction box with gears of 100 and 101 teeth, and with exceptionally bad bearings. Even when efficiency goes below 50% it will still be back drivable. It won't matter much from which side you drive it.

Also, some worm gear boxes are back drivable too. I have a worm gear box with a 1:10.5 ratio (with a dual start worm, and 21 teeth on the brass gear) and it is back drivable. It is also possible to make a "worm gear" with cam rollers and these are back drivable too, even with higher transmission ratios.

https://www.youtube.com/results?search_query=worm+gear+cam+roller

Whether a worm gear set is back drivable depends on the average contact angle and the friction cooficient between the used (& lubricated) materials.

[Infraviolet]

Ok, I can see with the 100 and 101 example that poor efficiency doesn't mean a gear system can't be backdriven, but what about the converse statement, if some gear set is not backdrivable does that automatically mean poor efficiency. Thanks

[Doctorandus_P]

Again, if you take it to the extreme: Think of a 6 stage gearbox, with each stage a ratio of 1:10. Overall efficiency may be high, but even a tiny bit of friction in the fist stage gets amplified by a million and probably something will break before it's being back driven. (A billion for 9 stages and a trillion for 12 stages, etc...)

And there are also special devices that can not be back driven such as "one way bearing" and a sprag clutch.

https://en.wikipedia.org/wiki/Sprag_clutch

(A sprag clutch can be integrated in such a one-way bearing, but there are other mechanisms too.)

[Infraviolet]

Thanks, makes sense put like that.

[Doctorandus_P]

If you want to know if "something works", then I find that thinking about an exaggerated test case often helps to get some clarity.