[JVN]

There are plenty of complex ways to look at this. I know I've played with many of them. When I started learning how to do this stuff, I used some fairly complex models, however these really aren't needed.

For our applications, a simple model is MORE than sufficient. In fact, I frequently use approximations and get well within the ballpark for our type of systems.

I always tend to think in terms of an equivalent "super-motor" which represents the two motors geared together. In this case, you can assume the system will spin at some fixed speed (the super-motor represents the two motors and all the gearing in between them.) Based on this speed, each motor will see some percentage of the applied loading. This percentage is a function of the relationship of the speeds the motors are running at. (If both motors are identical and are geared the same, it makes sense that they will each see 1/2 the overall loading.)

To see these relationships in action you can take a peak at the attached (old-school) spreadsheet I used to use for motor combiner design. Digging through this should help you. (Your mileage may vary, this sheet is a few years old.)

One thing to think about:
Some of the best advice I ever got on this subject was "There is no voodoo involved, the motor torques add together, sometimes one motor may drag a little depending on how good your speed matching is, but if they are in the ballpark they will both contribute. Match them at free-speed and go about your business."

Hope this helps. Feel free to email me if you have any specific questions. This sort of thing has been a hobby of mine for a while. (Teaching it to others has turned into a hobby of it's own.)

Regards,
John