[Ether]

Attached screenshot "tetrix.png" shows Tetrix data gleaned from Richard Wallace's posts.

The purple dots are the two data points from post #1. These are actual dynamometer data on a Tetrix motor-plus-gearbox.

The blue dots are eyeballed from the dyno data graph attached to post #15 for the same motor, but without the gearbox. To facilitate visual comparison, this data was then adjusted for a "perfect" (100% efficient) 52:1 gearbox so it could be compared graphically to the data with the actual gearbox.

It's quite apparent that, for this gearbox at least, the "threshold torque boundary" consideration can be ignored, and a "constant torque loss" assumption is not valid¹. The torque loss in this gearbox is essentially zero with no load torque, and increases linearly² as the load torque is increased. This data suggests that modeling torque loss as a linear² function of load torque would work well for this gearbox.


Assuming this data is typical, the answers to the questions raised in the original post would be:

...suppose I bolt a CIM to a gearbox that has ratio 10:1 and efficiency 90%. Then:

- the free speed at the gearbox shaft should be slightly slower than 1/10th of the CIM's free speed, because of the friction in the gearbox... but how much slower? answer: for practical purposes, no slower.

- the free current should be slightly more than the CIM's free current (because of the torque load of the gearbox friction), but how much more? answer: for practical purposes, no more.

- the stall current should be exactly the same as the CIM stall current answer: of course.

- the stall torque would be less than 10 times the CIM's stall torque, but how much less? answer: assuming that "90% efficient" means "the maximum power with the actual gearbox is 90% of the maximum power with the ideal gearbox", and assuming that the speed vs torque curve is linear, the answer is "10% less" (see attached sketch "efficiency.png" which assumes linear speed vs torque with actual gearbox)

- assume a linear behavior between free and stall points? answer: probably a good enough approximation.

¹ the assumption is not valid, but it may still be possible to come up with an average value which can be tweaked to give useful results for certain problem domains

² probably roughly linear, but can't tell for sure from only two data points :-(