Jpearman has done some great lab testing with Vex motors. This post shows the motor current response for both 269 and 393 motors to a step response. The steady state is achieved in around 100ms for both motors.
Good data. It appears that both motors have a time constant tau = 20 ms based upon the initial slope or using 100ms as a 5*tau value.
We can use this data to calculate the approximate moment of inertias of the motors. Since the motor time constant tau = max speed/max accel and the max speed is the same for both motors … we know that the motor max accelerations are identical for both motors. Since max speed = 10.4 rad/s and max accel = stall torque/Izz we can calculate Izz for a 269 as
Izz_269 = tau*stall torque/max speed = 2.8 in_lb*.113 nm/in_lb*tau/10.4 = 6.085*E-4 kgm^2
Using the equality of motor max accelerations gives a ratio to get Izz_393 from Izz_269 and the motor torques. So
Izz_393 = Izz_269*Istall_393/Istall_269 = 6.085E-4*14.7/2.8 = 3.19E-3 kgm^2
So we now have enough data to do a pretty good motor model.