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

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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 <formula formulatype="inline"><tex Notation="TeX">${\rm x}$</tex></formula>-winding and <formula formulatype="inline"> <tex Notation="TeX">${\rm y}$</tex></formula>-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 <formula formulatype="inline"><tex Notation="TeX">${\rm x}$</tex></formula>-winding and the <formula formulatype="inline"><tex Notation="TeX">${\rm y}$</tex> </formula>-winding in the core-type SPMPM. By using virtual work principle, <formula formulatype="inline"><tex Notation="TeX">${\rm x}$</tex></formula>-direction thrust force, <formula formulatype="inline"><tex Notation="TeX">${\rm y}$</tex> </formula>-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 <formula formulatype="inline"><tex Notation="TeX">${\rm d}\hbox{-}{\rm q}$</tex></formula> 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. </para>