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

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