Fast Analytical Force Estimation in Active Magnetic Bearings using a Magnetic Equivalent Circuit Model

This paper presents a fast analytical force estimation in active magnetic bearings for high speed electrical machines. A magnetic equivalent circuit has been proposed considering material non-linearity in the rotor and stator laminations. An 8-pole, hetero-polar radial active magnetic bearing has been designed using pure analytical methods and finite element analysis. In conventional closed loop control schemes, mathematical AMB models usually assume unsaturated, high relative permeability iron core in electromagnets for simplicity of the whole system. A non-linear magnetic equivalent circuit model can be therefore beneficial while setting up a model based design of an active magnetic bearing control scheme to improve the overall accuracy considering non-linear effects of magnetic materials. Magnetic equivalent circuits require numerical approaches such as Newton-Raphson iterations and in magnetic equivalent circuits, relative permeability values of the iron need to be updated in every iteration to consider material's B/H curve. In this study, an incremental loading of current has been considered to account highly loaded cases in the analytical model of the radial magnetic bearing to estimate the force more accurately without coupling finite element simulations with a model based design. It is shown that incremental loading of current improves the convergence of Newton-Raphson iterations and highly nonlinear AMB electromagnets can be modelled within the control scheme with a higher accuracy. The proposed approach might eliminate the necessity of finite element simulations of radial AMBs in line with different control approaches. The results have been validated by performing electromagnetic finite element simulations.