Connect the two motors by referring to Fig. 2.6. Connect a miniature lamp to one of the motors and another motor to the power supply and rotate the motor. The miniature lamp will light up.
You will learn from this experiment that a DC motor can generate power.
Now we move the wire across the field at a velocity of v without energizing the motor as Fig. 2.7 shows. We will learn that voltage e is generated in the wire. Let us compare this with the preceding Fig. 2.2.
The direction of the voltage is determined by Fleming's right-hand rule. The direction of the current is the opposite of the direction of the current shown in Fig. 2.2. Since this function reduces the current, it is called a counter-electromotive force. Supposing that the wire is part of the motor winding, we can express wire velocity v as v = ωR by referring to Fig. 2.3. Therefore, the counter-electromotive force that appears in this wire will be expressed according to the following equation:
e = BLRω ...... (2.6)
ω: Rotating speed [rad/s] R: Turning radius [m]
That means counter-electromotive force is proportional to rotating speed ω.
In the case of an actual DC motor, counter-electromotive forces working on all coils are combined and appear between the terminals.
Since it is also proportional to the rotating speed, it is expressed using back-emf constant KE.
e = KEω ...... (2.7)
e: Voltage generated in the motor terminals (counter-electromotive force) [V]
KE: Back-emf constant [Vs/rad]
ω: Rotating speed [rad/s]
When you measure this relationship on an actual motor, it will form a clean straight line as shown in Fig. 2.8.
Actually, back-emf constant KE and torque constant KT are the same thing, which may be verified as follows:
Supposing that the number of coil turns is N, the relationship between generated voltage e and back-emf constant KE will be as follows:
e = 2RNBLω = KEω ...... (2.8)
Here, substituting equation (2.7) for KT = 2RNBL of equation (2.4) and dividing both sides by ω, we obtain
KT = KE ...... (2.9).
If KT and KE are the same for DC motors, what will this mean?
Simply speaking, it means that a motor is a bidirectional energy converter between electricity and machine.
We can interpret that Fleming's left-hand rule views the energy conversion in the direction of "electricity to machine" whose conversion coefficient is KT.
Meanwhile, Fleming's right-hand rule views it in the direction of "machine to electricity" whose conversion coefficient will be KE
Thus, KT and KE are the same thing. In this book, however, we will continue to use KT and KE separately to clearly indicate the direction of conversion.