Torque Production Limit of Surface Permanent Magnet Synchronous Machines and Their Electromagnetic Scalability

In view of the increasing demand in torque density, this article propounds the idea of looking for an upper bound of the torque production and average shear stress for surface permanent magnet (SPM) synchronous machines. The derivation is based on the assumption of an infinite permeability of the iron core and employs the transfer relation between the normal magnetic flux density and the tangential magnetic strength. The result is written as functions of the machine's major geometries and excitation conditions. The ratio of the actual value and this upper bound may be used as a metric of measuring the usage of materials’ electromagnetic capability, or reversely as an indicator of the marginal gain of the iron core of higher relative permeability. The result is further investigated to discuss the electromagnetic scalability and the sizing law of SPM machines. Specifically, the reason for increasing volumetric torque density as the machine size goes up is revealed. The optimal remanence flux density of permanent magnets is also predicted at
$1.91\,\mathrm{T}$
, providing that the lamination saturates at
$2\,\mathrm{T}$
.