how to model motor+gearbox

[Ether]

@James Critchley

Interesting question.

A flat mechanical efficiency (single number such as 90%) is a Coulomb friction model. It represents the load dependent binding of the gears and shafts due to tolerances in the bearings and the relative sliding of gear tooth surfaces under load.
…
By definition there is no load at free speed. At no load, there is no friction.

So, going back to the original post (excerpt appended below), what I hear you saying is this (the highlighted parts):

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? answer: no load, no friction, so the free speed at the gearbox output of the combo would be modeled as exactly 1/10th motor free speed (ignoring windage for simplicity)

• 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: no load, no friction, so the free current of the combo would be the same as the motor-alone free current

• the stall current should be exactly the same as the CIM stall current answer: yes

• the stall torque would be less than 10 times the CIM’s stall torque, but how much less? answer: 10% less

• assume a linear behavior between free and stall points? ** answer: if you ignore windage for simplicity, then yes**

So:

Ncombofree = Nmotorfree/G

Tstallcombo = TstallmotorGeff

… and connect those points with a line to get the speed vs torque for the combo.

The “no friction at no external load” assumption is (as previously stated) an approximation, and I suspect that approximation becomes increasingly less tenable as the gear ratio increases. Does anyone have free speed data for a Banebots motor with and without a 256:1 gearbox?

**