A Schwarz-Christoffel (SC) mapping-based method is presented for accurately and efficiently predicting the thrust force of permanent magnet linear motors (PMLMs). It accounts for not only the slotting effect but also the end effect and the magnet shape. In this method, according to the magnet shape, the PMs are modeled as equivalent line currents on their surfaces. Through analyzing the invariant of the governing Poissonian field equation of line currents under a conformal mapping, the magnetic field boundary value problem in the air gap is mapped to a rectangle by the SC mapping, which is calculated with the SC Toolbox of MATLAB. Furthermore, the magnetic field solution is constructed with the line currents in a strip under the flux continuity condition. The cogging force due to the slotting effect and the end effect is obtained, respectively, by integrating the Maxwell stress tensor along the lines closely surrounding the slotted and finite-length iron core. The validity of the proposed method is examined by the finite-element method. The influences of the magnet shape on the thrust force pulsation characteristic are investigated for a PMLM equipped with rectangular PM and bread loaf PM.

Air vortex flow can induce small amplitude vibration of aerostatic bearings on the order of nanometers, which is known to be harmful to positioning accuracy of aerostatically supported devices in ultra-precision applications. In this paper, in order to suppress the vortex flow and reduce vibration of aerostatic bearings, a novel design of arrayed microhole restrictor (AMR) is proposed, and its effects are numerically and experimentally investigated. By computational fluid dynamics analysis, the transient flow features are studied for aerostatic bearings with AMR and conventional restrictors, and static performances of the bearings are also compared. Vibration strength of the bearing is measured experimentally to validate the effectiveness of AMR. The results show that vortex shedding in the recess is suppressed and the vibration can be effectively reduced by AMR, while load capacity and stiffness of the bearing remain unchanged.