Electromagnetic Forces Acting on the Planar Armature of a Core-Type Synchronous Permanent-Magnet Planar Motor

The core-type synchronous permanent-magnet planar motor (SPMPM) discussed in this paper includes one or more planar armatures each of which contains two sets of three-phase windings named ${\rm x}$-winding and ${\rm y}$-winding. For each planar armature, a magnetic field energy equation is established first. This equation describes the mechanism of the coupling between the permanent-magnet array, the ${\rm x}$-winding and the ${\rm y}$ -winding in the core-type SPMPM. By using virtual work principle, ${\rm x}$-direction thrust force, ${\rm y}$ -direction thrust force and vertical force acting on the planar armature are modeling analytically. For eliminating the coupling in these force models, the excitation flux linkages and phase currents are all transformed into ${\rm d}\hbox{-}{\rm q}$ synchronous reference frame. From the decoupling force equations, some characteristics of the vertical component of force on the planar armature are obtained. The electromagnetic force model is helpful for the design of the contactless planar bearing and the servo control system of the SPMPM.