Methodology for Dynamic Model Development of Iron-Less Axial Flux Permanent Magnet Synchronous Machine Constructed by Additive Manufacturing

The paper develops a dynamic model for ironless axial-flux permanent-magnet synchronous machines (AFPMSMs) fabricated using 3D-printing techniques. The model employs lumped parameters determined through an efficient two-dimensional (2D) magnetic-field analysis. The proposed methodology is based on the machine’s state differential equations, enabling an overall dynamic representation through time-stepping simulations in software defined by the corresponding block diagrams. The state equations of the electrical subsystem are formulated in the time domain using a per-phase lumped-parameter equivalent circuit of the stator winding. The mechanical subsystem is represented by modeling the rotor motion equation as the dynamics of a rotating concentrated mass. The lumped parameters of the dynamic model are then evaluated, including the flux linkage, the resistance and inductance of the electrical subsystem, and the inertia and damping coefficients of the mechanical subsystem. The electrical parameters are computed using finite element analysis (FEA) with a specifically developed, computationally efficient 2D representation. The accuracy of this approach is verified through comparison with a corresponding three-dimensional (3D) analysis, which requires substantially greater computational resources. Although ironless machines exhibit increased leakage magnetic-field components owing to the 3D field distribution in the end regions, these components primarily affect the inductance terms and contribute negligibly to the electromagnetic forces. Finally, the mechanical parameters—such as the moment of inertia and the damping coefficients—are evaluated using classical formulas. The calculated parameters are further validated through experimental measurements performed on a prototype machine.