1. 1 Induction Motors ©Dr. B. C. Paul 2001

2. 2 The Induction Motor Most motors have a problem in that the rotor moves To run a current to it and create an electromagnet you must have rings and brushes This is a high wear part In the induction motor the rotor is a squirrel cage Electric loops run around the squirrel cage but are connected only to themselves

3. 3 The Induction Motor Trick Eliminating the electromagnet rings and contacts save wear, but how can it work? Three phase currents moving through the stator create a rotating magnetic flux The trick is the rotor has closed electrical loops embedded Faraday’s law says that a voltage is produced by a loop enclosing a changing flux v = N dФ/dt

4. 4 Happenings on a Rotor The rotor wire loops have only the resistance of the wire itself Its almost a short circuit When voltage is supplied a large current is produced in the rotor Now we have a current flowing through a loop creating its own magnetic field in a magnetic field The magnetic field link up the rotor and cause it to move in the same direction as the rotating flux in the stator

5. 5 The Secret of the Induction Motor We use the magnetic field from the stator current to induce the current that makes the rotor behave as an electromagnet That way we have a rotor that tries to follow the current without any ring or brush connections The rotating action of the current in the stator makes the magnetic flux revolve around in the motor

6. 6 The Speed of an Induction Motor Problems strike - Suppose the Rotor is turning at the same rate the magnetic flux is rotating? Now there is no change in the magnetic flux through the loops in the rotor no changing magnetic flux means no induced voltage no induced voltage means no induced current no induced current means no electromagnet on the rotor no electromagnet on the rotor means no torque Jumping Jelly Beans - An induction motor can only develop torque if its turning slower than the 3 phase voltage frequency

7. 7 Speed and Induction Torque is developed from the rotor falling behind the 3 phase current The speed of an induction motor is at least partially a function of the torque it must develop Obviously not a good choice for a strict speed control application Running a water pump motor a bit slower than 3600 or 1800 rpms isn’t going to kill us It will also save us big bucks on the motor

8. 8 Getting Torque on an Induction Motor Torque = KBi i K is a proportionality constant B is the magnetic flux density produced by the currents in the stator i i is the current induced in the rotor loop The total torque is the sum of the torque produced by each loop in the rotor The induced current and magnetic flux are sinusoidal - get the highest torque when they peak in sync

9. 9 Magnetic Flux Peaks The magnetic flux is produced by the current flowing through the loops in the Stator and the rotor falling behind producing the frequency of the magnetic flux seen by the rotor Magnetic flux should be a sinusoid with the same frequency as the induced voltage Now we need to get the behavior of the induced current in the rotor

10. 10 Timing of Peaking Characteristics The thing that makes the flux change relative to the loops on the rotor is the speed difference between the two flux changes most rapidly when the rotor is standing still V g = V g0 ( 1 - η r / η s ) The English translation of this real cool equation is the voltage induced in the rotor is maximum when the rotor is still and decreases linearly to zero as the speed of the rotor approaches synchronous speed with the frequency of the current in the stator

11. 11 Timing the Peaking of the Current Since the voltage drives the current, the current should do as the voltage - except Wire coils are inductors and this loop wire thing in the rotor probably has inductance inductance throws the current out of syc with the voltage inducing it Of course that wire also has some resistance Sounds like we need the impedance of that rotor loop to figure out when current will peak

12. 12 Sizing up the Impedance Z = R + j(ωL - 1/(ωC)) Resistance will be the resistance of the short circuited wire loop - it will be a constant for the motor design Since no one put a capacitor on the rotor the capacitance term will drop out That leaves us with ωL L is the inductance of the loop - it too is a constant for the motor design ω is the angular frequency of the the voltage inducing the current in the rotor

13. 13 Frequency of the Induced Voltage Voltage is induced by the relative motion of the changing flux and the rotor That means the voltage has the same frequency as the flux only when the rotor is standing still Otherwise ω r = ω s ( 1 - η r / η s )

14. 14 Significance of the Induced Voltage Frequency The induced voltage frequency packs a double whammy it controls the impedance of the loop in the rotor the impedance controls the lag of the current behind the voltage

15. 15 Phase of the Induced Current When the rotor is still ω r is large creating a large inductive reactance When inductive reactance is large relative to resistance the current phasor will lag the voltage by a large amount Since Flux and Voltage are in sync a lagging current phasor will peak the i i when B (the flux term is near a minimum torque = KB i i Means induction motors have whimmpy starting torque

16. 16 Speeding up the Motor As the motor speeds up the frequency of the induced voltage falls as the voltage frequency falls the inductive reactance drops - resistance becomes more dominant The current phasor moves into syc with the flux This tends to drive torc up Remember though the induced voltage is falling

17. 17 Speed Torque Relations Torque Speed Product of current magnitude and power factor eventually maximize Beyond this the impedance is mostly resistance and the current falls directly with the voltage which falls linearly as the speed of the rotor comes into sync with the current in the stator Steady State induction motor operation is in the linear region

18. 18 Induction Motor Observations Using induced currents to make the rotor an electromagnet saved us rings, brushes, and the need for a separate current source to magnetize the rotor This made the induction motor cheaper to build and lower maintenance to operate We had to accept some losses and weaknesses to gain these advantages

19. 19 Weaknesses of Induction Motors We had to accept a weak starting torque We had to accept a non fixed motor speed it will be something like the frequency of the three phase current but slower how much slower is determined by the torque it must exert to pull its load We had to accept a motor that could not be turned into a generator by reversing torque and having the load turn the machine The motor that could do this was a synchronous AC motor explained earlier