Coupled axisymmetric analytical and finite element analysis for induction devices having moving parts

An analytical solution is determined in a simple shape region considered between the moving part and the fixed one, and it is built as a special finite element called "Macro-Element (ME)". The rest of the domain is finite element meshed. The coupling between both solutions is carried out when assembling finite element and ME matrices. The movement is then considered only by the modification of the ME matrix. In this way, the matrix due to the finite element discretization is calculated once and used for every relative position of the moving part. The formulation is elaborated in the case of an axisymmetrical structure and its validity is achieved when applying it to study an electromagnetic actuator. The proposed model proves itself economic and accurate.