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In the linear and planar motors, the 1D Halbach magnet array is extensively used. The sinusoidal property of the magnetic field deteriorates by analyzing the magnetic field at a small air gap. Therefore, a new 1D Halbach magnet array is proposed, in which the permanent magnet with a curved surface is applied. Based on the superposition of principle and Fourier series, the magnetic flux density distribution is derived. The optimized curved surface is obtained and fitted by a polynomial. The sinusoidal magnetic field is verified by comparing it with the magnetic flux density of the finite element model. Through the analysis of different dimensions of the permanent magnet array, the optimization result has good applicability. The force ripple can be significantly reduced by the new magnet array. The effect on the mass and air gap is investigated compared with a conventional magnet array with rectangular permanent magnets. In conclusion, the new magnet array design has the scalability to be extended to various sizes of motor and is especially suitable for small air gap applications.

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In this paper, the changing of magnet shape in Halbach magnet array of planar motor is analyzed for the magnetic flux density. It is the rectangular magnets that are replaced by pyramidal magnets. The magnetic flux density of Halbach magnet array with rectangular magnets is derived by Fourier series and scalar potential. The magnetic flux density of pyramidal magnet array is obtained through superposition and dividing the magnet array in several layers. Then the harmonic model has good agreement with the finite element model (FEM) by comparing the [Formula: see text]-component of magnetic flux density. The division layer [Formula: see text] is decided by analyzing the amplitude error of [Formula: see text]-component of magnetic flux density between harmonic and FEM. The pyramidal magnet array is analyzed from the items such as the waveform, peak value and total harmonic distortion (THD) of [Formula: see text]-component of magnetic flux density. Above all, the smaller the rotation angle is, the bigger the peak value of [Formula: see text]-component of magnetic flux density will be obtained and the smaller the total harmonic distortion will be simultaneously achieved.