Calculation of Cogging Force in Permanent Magnet Linear Motor Using Analytical and Finite Element Methods

In a permanent magnet (PM) linear motor, there is a force ripple which is detrimental to positioning. This force ripple is mainly due to a cogging force and a mutual force ripple. These forces are affected by the geometric parameters of a brushless PM motor, such as the width of the magnet, the height of the magnet, the shifted length of the magnetic pole, the length and height of the armature and the slot width. The optimal design can be found by considering force ripple as a cost function and the geometric parameters as design variables. In this paper, we calculate the flux density distribution in the air gap using the analytic solution of Laplace and Possion equations in the function of geometric parameters. The cogging force is obtained by integrating the Maxwell stress tensor, which is described by the flux density distribution on the slot face and end face of the iron core of an armature. Finally, a finite element method is presented in order to compare with the previous method.