Thrust Force Calculation and Analysis for the Permanent Magnet Linear Motor Motion System Considering the Encoder Errors

In this article, we present the effects of encoder errors caused by the mechanical torsional vibrations on the characteristics of the thrust force for the permanent magnet linear motor (PMLM) motion system. First, the effects of the mechanical vibrations on the encoder errors are analyzed. Then, the three-phase current is calculated, considering the nonlinearity of the drive circuit. Based on Maxwell's equations and a Schwarz-Christoffel method, the analytical model of the magnetic field in airgap is established taking into account the slot effect. Finally, the thrust force considering the encoder errors is analytically presented using the electromagnetic energy method, and the experimental verification is carried out. The results show that the mechanical torsional vibrations will produce different kinds of encoder errors for the optical linear encoder. These encoder errors will be coupled with the harmonics in the magnetic field. Consequently, lots of new thrust harmonics appear, affecting the characteristics of the thrust force and the performance of the PMLM motion system.