Analytical calculation of air gap magnetic field in permanent magnet linear motors

A mathematical modeling is established by analytical method to study the air gap magnetic field in the Permanent Magnet Linear Motors (PMLM) with Halbach array. The two-dimensional vector magnetic potential of air gap magnetic field is calculated by solving the Maxwell equations, and then the analytical expression of the air gap magnetic flux density is obtained. The analytical results are in very good agreement with those obtained by the FEM, which confirms the accuracy of the analytical method. Halbach array is contrasted with radial array, thus, its advantage is proved. The impact of the height and the width coefficient of the permanent magnets on the fundamental amplitude and sine distortion rate of air gap magnetic flux density is discussed. The measurement system of magnetic flux density is built to further verify the correctness of the analytical method. The reference for the design of corresponding linear motors is offered by the analysis of air gap magnetic field.