## Polyphase induction motor

The polyphase induction motor is the most commonly used industrial motor, finding application in many situations where speed regulation is not essential.

- It is simple and relatively inexpensive, and the absence of sliding contacts in the squirrel-cage machine reduces maintenance to a minimum.
- There are two general types of polyphase induction motors: the squirrel-cage type and the wound-rotor machine.
- Both motors have an armature or stator structure similar to that of the alternating current generator, consisting of a hollow cylinder of laminated sheet steel in which are punched longitudinal slots.
- A symmetrical polyphase winding is laid in these slots which, when connected to a suitable voltage source, produces a travelling MMF wave in the air gap, rotating at a synchronous speed equal to:
- RPMs = 120 f / p
- where f is the frequency and p the number of poles for which the stator is wound.

- This difference between synchronous speed and the rotor speed is commonly referred to as the slip of the rotor;
- in this case the rotor slip is ns – n, as measured in r/min.
- Slip is more usually expressed as a fraction of synchronous speed.

The fractional slip s is (ns -n) / ns

- The rotor speed in r/min can be expressed in terms of the slip and the synchronous speed as n =(1 – s) ns
- The relative motion of the stator flux and the rotor conductors induces voltages of frequency fr

fr = sfe

- called the slip frequency, in the rotor.

Above Typical polyphase squirrel-cage induction motor torque-speed curve.

The factors influencing the shape of this curve can be appreciated in terms of the torque equation, the resultant air-gap flux ~ sr in this equation is approximately constant when the stator-applied voltage and frequency are constant.

Also, recall that the rotor mmf Fr is proportional to the rotor current Ir. then be expressed in the form

T = – K Ir sin δr

where K is a constant and δr is the angle by which the rotor mmf wave leads the resultant air-gap mmf wave.