Analytical calculation of interaction force between orthogonally magnetized permanent magnets

In an advanced micro-lithographic system, it is of critical importance that components are resiliently isolated from external vibrations. A passive/active electromagnetic device is a feasible solution to perform such vibration isolation. Within this device, passive permanent magnets provide the gravity compensation and active electromagnets accurate positioning. The focus of this article is on permanent magnet modeling, since a precise model is inevitable to achieve the high accuracy required for such application. This article describes a study on interaction force along three degrees of freedom (DoF) between permanent magnets having an unaligned magnetization direction for use in a permanent-magnet based suspension application. Feasibility of finite element modeling (FEM) and analytical modelling for such structures is discussed, implemented and verified with measurements