Analysis and Optimization of a New 2-D Magnet Array for Planar Motor

This paper presents a new 2-D permanent-magnet array for a planar motor, in which the angle between the magnetization directions of any two adjacent magnets is 45$^{\circ}$ . The harmonic model for flux density distribution of the array is solved by the scalar magnetic potential equation and validated by the finite-element method. An analytical model for real-time control is derived by taking the first harmonic of the magnetic flux density distribution. The ignored higher harmonics in $z$-component of the magnetic flux density distribution is minimized by the genetic algorithm such that the analytical model becomes more accurate. Compared with the well-known Halbach magnet array, the proposed magnet array has lower higher harmonic components and higher $z$ -component of the magnetic flux density, which will reduce the force ripples of the planar motor.