Question

Problem 2: 50pts To monitor the rotation speed of a shaft, a generator motor attachment has been suggested. Here a permanent magnet motor, shown below, is directly attached to the shaft. Stator (magnet) Armature winding Bearing Power supply Brush Commutator Rotor A voltmeter is connected to the power supply connection and is calibrated for various voltage-rpm values. a) Determine the governing equations for this system. (use the motor rotation as the input and the voltage generated as the output) b) Develop a block diagram of the system. c) What is the transfer function?

Answer 1

This device is actually called Tachometer.

(a) In a DC machine, the EMF developed is directly proportional to the product of the field flux and the angular speed. Mathematically, $E = K\phi \omega$ , where $K = \frac{PZ}{2\pi A}$ and $\omega = \frac{2\pi N}{60}$

For a permanant magnet machine, take flux to be constant as well.

Putting all constants equal to K, we get E = K * N

(b)

(c) Transfer funtion = $\frac{E(s)}{N(s)} = K$