combined free speed of 3 motors

[James Kuszmaul]

Originally Posted by Ether

Perhaps it will help to present the math in a slightly different way. Attached is a derivation for the torque vs speed curve for the 3-motor combination directly from the torque vs speed curves for the individual motors.

It's straightforward algebra. It follows naturally from the assumptions that 1) all three motor speeds are the same (since they are mechanically linked) and 2) the individual motor torques are additive.

As you can see, the combination behaves exactly like a single motor with torque = Tstall*(1-Speed/Sfree), where:

Tstall = T1s + T2s + T3s .... and .... Sfree = (T1s + T2s + T3s)/(T1s/S1f + T2s/S2f + T3s/S3f)

This is definitely the right step getting to where I want to be, however, although I do see the linear relationship between net speed and torque, I do not see how that necessarily allows us to use the single motor equations (V=IR + v/Kv and I = KtI) for the combined motors. I have worked out some of the equations and attached the derivations. Hopefully you will be able to see where I am going and can help get it that last few steps.