for a DC motor/generator:
voltage = speed/speed_constant ( in rpm/V), current = current *
torque_constant ( in Nm/A)
Typo: torque = current * torque_constant
For speed, I'd be inclined to measure frequency rather than voltage, with
a tacho sensor if necessary (e.g. if the load is a DC generator and
the AC component's fundamental can't be reliably separated from its
harmonics).
why shouldn't it still work if shorted?, torque will be determined by the
current through the DC resistance of the motor.
The main issue is that the constants only provide an approximation.
Depending upon the precision, that may be enough. Or beyond that, it may
suffice to perform a one-time calibration step to measure torque as a
function of current and speed (and temperature if that can be measured
easily) and use the results to interpret subsequent electrical
measurements.
the voltage across the DC resistance will be determined by the speed.
There are two components to the voltage drop: back-EMF and current through
the winding resistance. The former increases with speed, the latter with
current (and thus torque). The speed constant only determines the former.
When free-running (high speed, low torque), back-EMF dominates;
near stall (low speed, high torque), winding resistance dominates.
If voltage = speed/speed_constant was an absolute, any given voltage would
produce a fixed speed regardless of load (up to and including welding the
axle to the body).
lots of dynamometers are a simple drum or disc with a know moment of
inertia, with speed being sampled and acceleration thus torque
calculated from that
That only works if it's desired (or acceptable) for the speed to vary as
the integral of the applied torque (e.g. rolling road scenario). It won't
work if you want to measure behaviour under varying loads, or stall torque
(although for the latter, a passive load won't work either).