Modeling 3D magnetic fields for precision magnetic actuators that use non-periodic magnet arrays

In this paper we use the Fourier transform to model and simulate the three-dimensional 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 along a plane using two-dimensional Fast Fourier transforms. Model predictions are compared with analytical solutions for a simple prototype magnet array, measured values of a magnet array's flux density, and a meso-scale actuator's behavior. The difference between measured and predicted values is less than 5%.