Tool247: You are partially correct, the maximum speed is limited by the available voltage, but as the voltage drops the current demand rises to do the same amount of work so the motor will heat up which may then destroy the motor. Speed on a DC motor is best controlled by pulsing the manufacturer specified voltage on and off rapidly (50khz+) and varying time ratio of time the voltage is on verses off in each cycle, the more time the voltage is on vs off per cycle the faster the motor will run and vice versa. Since the motor is always being supplied the maximum voltage, but only for a limited time in each cycle, the current demand is optimized and the motor does not overheat. This process is known as Pulse Width Modulation (PWM), if you would like more detail check this URL:
https://www.electronics-tutorials.ws/blog/pulse-width-modulation.html.
Richard.
