An analytic description of reluctance torque in function of pole shape, with regards to local saturation
Electric mobility, which is essential in terms of sustainable development and renewable power, is partly based on permanent magnetic electric motors of high power density. The magnets of these motors unfortunatelly need rare earth metals (Dysporsium and Neodymium) which can only be found in limited quantities and practically on areas of single state, namely in China. Rarity of reserves and the monopolistic commercial status inevitably make purchase and production expensive and unstable to a great extent. Use of switched reluctance motors (SRM) could mean viable solution to the problem (since these kind of motors do not have magnets as component parts), but widespread application of these motors is impeded by its typical significant level of noise and high torque ripple, nevertheless these disadvantages can be reduced with the aid of proper fine-tuning designs of motors, especially by forming of the pole surfaces.
In my paper I introduce a formula, which gives the description of the reluctance torque taking the nonlinear BH curve of laminations, the rotary angle and the current as well as the pole shape into consideration, in view of local saturation in pole corners. Since magnetization curves do not have explicit forms, my derivation is based repeated approximation, observation and FEM-experience. Furthermore, in order to derive relations I resort to the magnetic equivalent circuits as well as the integral form of Maxwell-equations. (Although finite element method modelling is inapplicable in a direct way to designing electromagnetic instruments, it is suitable for verifying calculations and for fine-tuning and optimalization of local parts.) At the starting of planning we definitely take the first step with analytic formulas usable for scaling as well, then comes fine-tuning with finite element analysis. The pole-side function introduced by myself as well as the derived relations make it possible to design instruments based on reluctance torque more accurately, also it gives aid and guideline in case of pole shape optimization. Since the formula allowes change even of axial direction on pole surfaces, COMSOL Multiphysics had to be applied in 3D in order to verify the relations set up beforehand. (In case of 2 dimensional observations besides COMSOL the Matlab PDE Toolbar also meant assistance.)