The basic construction of pole strength and armature winding characteristics determine the motor characteristics, when you apply a voltage to a DC motor the motor will increase in speed until the generated voltage approaches the applied voltage, i.e. the voltage will be almost equal, the difference between the two is the voltage the motor sees.
To increase the speed, the applied voltage has to be increased until again the generated voltage is again (almost) equal.
If you know the maximum rpm of the motor, you can find out the max. applied voltage to reach this.
Turning the motor over at a known rpm and reading the generated voltage at this RPM, you can extrapolate what the final max voltage can be applied.