how to model motor+gearbox

[Ether]

What is the accepted wisdom here on CD of the "correct" way to model a motor plus gearbox combination[1]?

More specifically, if I have

- a motor with given free current, free speed, stall current, and stall speed, and

- a gearbox with given gear ratio and "efficiency"

... and I combine them together,

then what is the free current, free speed, stall current, and stall speed of that combination?


For example, 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?

- 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?

- the stall current should be exactly the same as the CIM stall current

- the stall torque would be less than 10 times the CIM's stall torque, but how much less?

- assume a linear behavior between free and stall points?



Endnotes:

1] I'm talking about a simple model for hand calculations for FRC purposes, not a complex simulation.