Energy and Power of DC Motors

Every motor outputs a torque that varies as a function of motor speed. The motors in the robot kit are permanent magnet motors, and there is a linear relationship between the motor speed and torque. See Overview of DC motors.

With no load on the motor, the shaft rotates at its maximum speed, referred to at the “no load speed.” As torque is applied to the shaft the torque the motor slows down, until the torque reaches the “stall torque” at which point the motor stops rotating. The torque speed curve of DC Permanent magnet motors is a straight line, but other types of motors have different shape curves.

Measure the “no load speed” of both the geared and non geared motors. Use a stop watch for the geared motor, and the optical sensor setup for non geared motor that rotates too fast to count by hand. Also measure the stall torque using the setup in the lab. Show the torque and speed calculations on a separate sheet. Plot the straight line torque speed curves for both motors below.

The power output for a motor is given by the torque, τ, times the angular velocity, ω (in radians per second):

(units of Nm/s)

By looking at torque speed curve one can see that the power output is zero when the motor is stalled, and zero when the motor spins with no torque output at its “no load speed.” The maximum power output occurs when the motor is operating at the midpoint of its operating range, where the speed is half the “no load speed” and the torque is half of the stall torque (for a proof take the derivative of the power).

The power is equal to δE/δtime. Thus the energy output of a motor is:

(where δθ is the amount of rotation in degrees)

The maximum amount of rotation that can occur in the robot contest is the angular speed at multiplied by the contest duration (60 seconds)

(radians)