Computation of Cogging Force of a Linear Tubular Flux Switching Permanent Magnet Machine Using a Hybrid Analytical Modeling

Permanent magnet flux switching machines are gaining more and more interest due to their relatively good characteristics. Indeed, the presence of all magnetic field sources in the stator (armature windings, permanent magnets and/or field windings), which implies a completely passive rotor, makes it suitable for a large variety of applications [1] [2]. Different flux switching machines topologies have been studied in scientific literature. In this contribution, a relatively new modeling approach [3] based on the coupling of mesh based generated reluctance networks (MBGRN) and analytical models (AM), based on the formal solution of Maxwell’s equations, is used for the accurate prediction of cogging force of a linear tubular flux switching machine. This type of machines could be favorably used in oceanic renewable energy conversion. Figure 1(a) illustrates how the two approaches are combined for the case of a tubular linear flux switching structure. In this example the analytical solution is used for modeling the mechanical air-gap, and inner and outer airs, and the RN method is used to model the moving and static armatures. In order to have a more generic approach, the stator and moving armatures are modeled using mesh based generated reluctance network (MBGRN) technique [3]. This technique, as classical RN method, can be used with a minimum number of reluctances for regions where flux tubes are not highly affected by topology changes. As for finite elements analyses (FEA), the studied domain in MBGRN should be finely meshed in some regions (air-gap for example) and coarsely meshed in other regions. However, in contrast to FEA, the mesh relaxation in MBGRN can be done more easily conducting to reduced system matrix dimensions, and consequently reduced computation time. Indeed, while in FEA two adjacent elements should share an edge, it is no more necessary for RN method, as illustrated in Fig. 1(b). This new modeling approach has been used to analyze the performance of different electromagnetics devices (2D and 3D) [3]–[7]. In this contribution, this technique is used for the computation of cogging force of a linear tubular flux switching permanent magnet structure, something which has never been reported yet, to the best of our knowledge, in scientific literature. The goal is to further extend the investigation of this technique for the computation of relatively sensitive quantities, such as the cogging force, in more complex structures. Another goal is to highlight advantages of HAM as compared to other modeling techniques, and more particularly FEA, in order to obtain reduced order equations system [8] [9].