Modeling Magnetic Fields for Precision Magnetic Actuators That Use Non-perioduc Magnet Arrays

In this paper we use the Fourier transform (FT) to model and simulate the 3-D magnetic field created by finite, planar permanent magnet arrays that are Fourier-transformable and possess vertical magnetization. This approach captures the three dimensional characteristic of the fields, including the field components near the ends of the array. These end effects are important in small-scale precision actuators where geometric constraints preclude the use of larger, finite arrays that emulate the behavior of infinite arrays. We demonstrate how to model and compute the field characteristics using 2-D Fast Fourier transforms (FFTs). Model predictions for a prototype magnet array are compared with measured values of a magnet array’s flux density. The difference between measured and predicted values is within the expected error (5%) of the measurement system. INTRODUCTION Permanent magnet arrays are important to precision actuators such as linear motors that use Halbach arrays [1, 2] and multi–axis magnetic levitation machines [3-5]. These devices often consist of long, repeating coils and permanent magnet arrays. In order to design such systems, infinitely periodic magnetic field models are used in performance models [1, 5]. However, meso-scale instruments and precision machines such as probe-based data storage systems [6, 7] employ non-periodic magnetic structures due to geometric constraints, and therefore modeling them requires a departure from conventional periodic field models. Mesoscale devices often include a set of permanent magnets that interact with an energized planar coil, as shown Fig. 1. In order to predict the performance of these actuators, non-periodic field models should be employed to capture end effects. Furthermore, accurate force models of these structures must consider field effects in three dimensions. This leads to a need to develop accurate, yet computationally effective field models for the prediction of meso-scale magnetic actuator forces.