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A coupled field-circuit model of a 5-phase permanent magnet tubular linear motor A method for modeling of the dynamics characteristics for a 5-phase permanent magnet tubular linear motor (PMTLM) is presented. Its electromagnetic nonlinear field analysis with finite element method (FEM) has been coupled with the circuit model. The calculation model includes the equations for electrical circuits and mechanical quantities as well. They have been obtained using Lagrange's method. The calculated and measured waves of the mover position have been compared for several values of the excitation current. This comparison yields a good agreement. Presented calculation model is very useful in designing and optimization of the PMTLM and in the calculation of the parameters for the control algorithms intended for such a type of actuators.

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Purpose The purpose of this paper is to create a reliable nonlinear magnetic equivalent circuit (NMEC) of the hybrid magnetic bearing (HMB). Commonly used magnetic equivalent circuits of HMB omit a saturation effect of the magnetic material as well as the leakage and fringing flux. It results in imprecise modelling of the magnetic field distribution. On the other hand, only 3D finite element analysis (FEA) can be used to precisely simulate the magnetic field in this type of the magnetic bearing. The proposed NMEC incorporates the saturation effect of the magnetic material, as well as the leakage and fringing flux. Design/methodology/approach The magnetic equivalent circuit of presented HMB is proposed to obtain a reliable model that ensures short calculation time. Developed NMEC incorporates the phenomena as the saturation effect, as well as the leakage and fringing flux. The reluctance of the air gap that includes the fringing flux was calculated using 3D FEA. Kirchhoffs’ laws were used to create a set of nonlinear equations that were iteratively solved by Broyden’s method. Findings Incorporating into NMEC of the HMB a saturation effect of the magnetic material, as well as the leakage and fringing flux, resulted in the accurate model that was in good agreement with 3 D finite element model and the real object. The developed NMEC offers the calculation time in the range of miliseconds, therefore can be successfully used in the engineering design instead of the FEM. Originality/value Presented NMEC can be considered as a fundamental model that can be successfully used for accurate and fast simulation of the HMB. Proposed NMEC includes considerable factors that decide about the model accuracy such as the saturation effect of the ferromagnetic material and the leakage and fringing flux. The developed NMEC can be used in the optimization procedures and for simulations of dynamic responses.