Electric motor
Torque

Electromagnetic motors derive torque from the vector product of the interacting fields. Calculating torque requires knowledge of the fields in the air gap. Once these have been established, the torque is the integral of all the force vectors multiplied by the vector's radius. The current flowing in the winding produces the fields. For a motor using a magnetic material the field is not proportional to the current.

A figure relating the current to the torque can inform motor selection. The maximum torque for a motor depends on the maximum current, absent thermal considerations.

When optimally designed within a given core saturation constraint and for a given active current (i.e., torque current), voltage, pole-pair number, excitation frequency (i.e., synchronous speed), and air-gap flux density, all categories of electric motors/generators exhibit virtually the same maximum continuous shaft torque (i.e., operating torque) within a given air-gap area with winding slots and back-iron depth, which determines the physical size of electromagnetic core. Some applications require bursts of torque beyond the maximum, such as bursts to accelerate an electric vehicle from standstill. Always limited by magnetic core saturation or safe operating temperature rise and voltage, the capacity for torque bursts beyond the maximum differs significantly across motor/generator types.

Electric machines without a transformer circuit topology, such as that of WRSMs or PMSMs, cannot provide torque bursts without saturating the magnetic core. At that point, additional current cannot increase torque. Furthermore, the permanent magnet assembly of PMSMs can be irreparably damaged.

Electric machines with a transformer circuit topology, such as induction machines, induction doubly-fed electric machines, and induction or synchronous wound-rotor doubly-fed (WRDF) machines, permit torque bursts because the EMF-induced active current on either side of the transformer oppose each other and thus contribute nothing to the transformer coupled magnetic core flux density, avoiding core saturation.

Electric machines that rely on induction or asynchronous principles short-circuit one port of the transformer circuit and as a result, the reactive impedance of the transformer circuit becomes dominant as slip increases, which limits the magnitude of active (i.e., real) current. Torque bursts two to three times higher than the maximum design torque are realizable.

The brushless wound-rotor synchronous doubly-fed (BWRSDF) machine is the only electric machine with a truly dual ported transformer circuit topology (i.e., both ports independently excited with no short-circuited port). The dual ported transformer circuit topology is known to be unstable and requires a multiphase slip-ring-brush assembly to propagate limited power to the rotor winding set. If a precision means were available to instantaneously control torque angle and slip for synchronous operation during operation while simultaneously providing brushless power to the rotor winding set, the active current of the BWRSDF machine would be independent of the reactive impedance of the transformer circuit and bursts of torque significantly higher than the maximum operating torque and far beyond the practical capability of any other type of electric machine would be realizable. Torque bursts greater than eight times operating torque have been calculated.
oulipo:avoid_letter[a]