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. In 1824, the French physicist François Arago formulated the existence of rotating magnetic fields, termed Arago's rotations. By manually turning switches on and off, Walter Baily demonstrated this in 1879, effectively the first primitive induction motor. [2] [3] [4] [5] [6] [7] [8] 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}

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. The power factor of induction motors varies with load, typically from about 0.85 or 0.90 at full load to as low as about 0.20 at no-load, [39] due to stator and rotor leakage and magnetizing reactances. [45] Power factor can be improved by connecting capacitors either on an individual motor basis or, by preference, on a common bus covering several motors. For economic and other considerations, power systems are rarely power factor corrected to unity power factor. [46] 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

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]

Paraphrasing from Alger in Knowlton, an induction motor is simply an electrical transformer the magnetic circuit of which is separated by an air gap between the stator winding and the moving rotor winding. [28] The equivalent circuit can accordingly be shown either with equivalent circuit components of respective windings separated by an ideal transformer or with rotor components referred to the stator side as shown in the following circuit and associated equation and parameter definition tables. [39] [46] [51] [52] [53] [54] Steinmetz equivalent circuit In a single-phase split-phase motor, reversal is achieved by reversing the connections of the starting winding. Some motors bring out the start winding connections to allow selection of rotation direction at installation. If the start winding is permanently connected within the motor, it is impractical to reverse the sense of rotation. Single-phase shaded-pole motors have a fixed rotation unless a second set of shading windings is provided. See also: Fleming's left-hand rule for motors Standard torque [ edit ] Speed-torque curves for four induction motor types: A) Single-phase, B) Polyphase cage, C) Polyphase cage deep bar, D) Polyphase double cage Typical speed-torque curve for NEMA Design B Motor Transient solution for an AC induction motor from a complete stop to its operating point under a varying load

Universal motors

In certain smaller single-phase motors, starting is done by means of a copper wire turn around part of a pole; such a pole is referred to as a shaded pole. The current induced in this turn lags behind the supply current, creating a delayed magnetic field around the shaded part of the pole face. This imparts sufficient rotational field energy to start the motor. These motors are typically used in applications such as desk fans and record players, as the required starting torque is low, and the low efficiency is tolerable relative to the reduced cost of the motor and starting method compared to other AC motor designs. There are three basic types of small induction motors: split-phase single-phase, shaded-pole single-phase, and polyphase. Induction motor improvements flowing from these inventions and innovations were such that a modern 100- horsepower induction motor has the same mounting dimensions as a 7.5-horsepower motor in 1897. [12] Principle [ edit ] 3-phase motor [ edit ] A three-phase power supply provides a rotating magnetic field in an induction motor. Inherent slip – unequal rotation frequency of stator field and the rotor