Lumped circuit-based sizing of quasi-Halbach PM excited T-LSMs: application to free piston engines

The study is aimed at a lumped circuit-based sizing of tubular-linear synchronous machines (T-LSMs) equipped by quasi-Halbach magnetised PMs in the mover. The proposed approach is initiated by the synthesis the T-LSM lumped circuit, taking into account: (i) the saturation of the magnetic circuit, (ii) the leakage fluxes, (iii) the armature magnetic reaction, and (iv) the variation of the mover position. Then, formulations of different no-load and load operation features are derived in terms of selected variables yielded by the proposed lumped circuit. Among these features, the main value of the developed force is selected as a sizing criterion whose variation with respect to different influent design parameters is investigated along with the armature current density. The lumped circuit-based sizing approach enables the selection of a set of appropriate design parameters for which the formulated no-load and load operation features are predicted. A dual validation of the obtained results by an analytical model based on the air gap flux density formulation on one hand, and a 2D finite element analysis on the other hand, proves the effectiveness of the proposed sizing approach.

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