Before the development of semiconductor power electronics, it was difficult to vary the frequency, and cage induction motors were mainly used in fixed speed applications. Applications such as electric overhead cranes used DC drives or wound rotor motors (WRIM) with slip rings for rotor circuit connection to variable external resistance allowing considerable range of speed control. However, resistor losses associated with low speed operation of WRIMs is a major cost disadvantage, especially for constant loads. [40] Large slip ring motor drives, termed slip energy recovery systems, some still in use, recover energy from the rotor circuit, rectify it, and return it to the power system using a VFD. O u t p u t M e c h a n i c a l P o w e r ÷ I n p u t E l e c t r i c a l P o w e r {\displaystyle \eta =OutputMechanicalPower\div InputElectricalPower} Slip, s {\displaystyle s} , is defined as the difference between synchronous speed and operating speed, at the same frequency, expressed in rpm, or in percentage or ratio of synchronous speed. Thus There are three basic types of small induction motors: split-phase single-phase, shaded-pole single-phase, and polyphase.

The number of magnetic poles, p {\displaystyle p} , is equal to the number of coil groups per phase. To determine the number of coil groups per phase in a 3-phase motor, count the number of coils, divide by the number of phases, which is 3. The coils may span several slots in the stator core, making it tedious to count them. For a 3-phase motor, if you count a total of 12 coil groups, it has 4 magnetic poles. For a 12-pole 3-phase machine, there will be 36 coils. The number of magnetic poles in the rotor is equal to the number of magnetic poles in the stator.

Universal motors

Although polyphase motors are inherently self-starting, their starting and pull-up torque design limits must be high enough to overcome actual load conditions. Over a motor's normal load range, the torque's slope is approximately linear or proportional to slip because the value of rotor resistance divided by slip, R r ′ / s {\displaystyle R_{r}'/s} , dominates torque in a linear manner. [38] As load increases above rated load, stator and rotor leakage reactance factors gradually become more significant in relation to R r ′ / s {\displaystyle R_{r}'/s} such that torque gradually curves towards breakdown torque. As the load torque increases beyond breakdown torque the motor stalls. Larger single phase motors are split-phase motors and have a second stator winding fed with out-of-phase current; such currents may be created by feeding the winding through a capacitor or having it receive different values of inductance and resistance from the main winding. In capacitor-start designs, the second winding is disconnected once the motor is up to speed, usually either by a centrifugal switch acting on weights on the motor shaft or a thermistor which heats up and increases its resistance, reducing the current through the second winding to an insignificant level. The capacitor-run designs keep the second winding on when running, improving torque. A resistance start design uses a starter inserted in series with the startup winding, creating reactance. Standardized NEMA & IEC motor frame sizes throughout the industry result in interchangeable dimensions for shaft, foot mounting, general aspects as well as certain motor flange aspect. Since an open, drip proof (ODP) motor design allows a free air exchange from outside to the inner stator windings, this style of motor tends to be slightly more efficient because the windings are cooler. At a given power rating, lower speed requires a larger frame. [44] Rotation reversal [ edit ]

Rotor resistance, leakage reactance, and slip ( R r {\displaystyle R_{r}} , X r {\displaystyle X_{r}} or R r ′ {\displaystyle R_{r}'} , X r ′ {\displaystyle X_{r}'} , and s {\displaystyle s} ). n s = 2 f p ⋅ ( 60 s e c o n d s m i n u t e ) = 120 f p ⋅ ( s e c o n d s m i n u t e ) {\displaystyle n_{s}={2f \over p}\cdot \left({\frac {60\ \mathrm {seconds} }{\mathrm {minute} }}\right)={120f \over {p}}\cdot \left({\frac {\mathrm {seconds} }{\mathrm {minute} }}\right)} . [32] [33] Many useful motor relationships between time, current, voltage, speed, power factor, and torque can be obtained from analysis of the Steinmetz equivalent circuit (also termed T-equivalent circuit or IEEE recommended equivalent circuit), a mathematical model used to describe how an induction motor's electrical input is transformed into useful mechanical energy output. The equivalent circuit is a single-phase representation of a multiphase induction motor that is valid in steady-state balanced-load conditions. For rotor currents to be induced, the speed of the physical rotor must be lower than that of the stator's rotating magnetic field ( n s {\displaystyle n_{s}} ); otherwise the magnetic field would not be moving relative to the rotor conductors and no currents would be induced. As the speed of the rotor drops below synchronous speed, the rotation rate of the magnetic field in the rotor increases, inducing more current in the windings and creating more torque. The ratio between the rotation rate of the magnetic field induced in the rotor and the rotation rate of the stator's rotating field is called "slip". Under load, the speed drops and the slip increases enough to create sufficient torque to turn the load. For this reason, induction motors are sometimes referred to as "asynchronous motors". [31] Breakdown torque T max {\displaystyle T_{\text{max}}} happens when s ≈ R r ′ / X {\displaystyle s\approx R_{\text{r}}'/X} and I s ≈ 0.7 L R C {\displaystyle I_{\text{s}}\approx 0.7\;LRC} such that T max ≈ K V s 2 / 2 X {\displaystyle T_{\text{max}}\approx KV_{\text{s}}The first commutator-free single-phase AC induction motor was invented by Hungarian engineer Ottó Bláthy; he used the single-phase motor to propel his invention, the electricity meter. [9] [10]

In both induction and synchronous motors, the AC power supplied to the motor's stator creates a magnetic field that rotates in synchronism with the AC oscillations. Whereas a synchronous motor's rotor turns at the same rate as the stator field, an induction motor's rotor rotates at a somewhat slower speed than the stator field. The induction motor stator's magnetic field is therefore changing or rotating relative to the rotor. This induces an opposing current in the rotor, in effect the motor's secondary winding. [28] The rotating magnetic flux induces currents in the rotor windings, [29] in a manner similar to currents induced in a transformer's secondary winding(s).For example, for a four-pole, three-phase motor, p {\displaystyle p} = 4 and n s = 120 f 4 {\displaystyle n_{s}={120f \over 4}} = 1,500RPM (for f {\displaystyle f} = 50Hz) and 1,800RPM (for f {\displaystyle f} = 60Hz) synchronous speed.