Dooh!!!
Both models are correct: the linear applies to the brake mode and the nonlinear to the coast mode.
The commutator, friction, pwm rates , motor inductance etc are all secondary distraction factors. The key is the darn protection diode in the off pwm pulse phase. Under simplifying assumptions, we can think of Vemf as a battery that is allowed to charge or discharge the motor coil. In the on phase, it is there for both the brake and coast mode. In the off phase, Vemf is only there for the brake mode where a current loop is created by switching on the lower legs of the H bridge. In the coast mode , these lower legs are switched off but there is a diode in the path instead. The diode essentially blocks Vemf from modifying the current once the current has reached zero and Vemf battery can be assumed removed from the ckt for most of the off phase. So in the coast mode we can replace Vemf with Vemf*duty. This leads to the two simple math equations I spoke of earlier. What I called the inductive model corresponds to the coast mode and the resistive model corresponds to the brake mode.
Brake mode: only 12 v chopped, Vemf present all the time so:
i_free*R = 12* duty -Vemf ---> Vemf = 12*duty - i_free*R ...................... linear with duty
Coast mode: both 12v and Vemf chopped
i_free*R = (12-Vemf)*duty --> Vemf = 12 - i_free*R/duty ........................varies inversely with duty
It is clearly a little more complicated than this, but these models capture the crux of the matter:
So all we need now is for someone to run the Victors and JAG in both coast and brake modes to see if theory holds up.
Hmmmmm how do I change the title of this thread
Doesn't someone owe me a beer?!