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In this paper, a new double-stator cup-rotor permanent-magnet brushless DC (PMBDC) machine is proposed and analyzed. Since the machine structure is so unique while its operating principle is so distinct, a numerical field approach, namely the circuit-field-torque grid-model time-stepping finite-element method (CFT-GM-TS-FEM), is newly developed to analyze the steady-state and dynamic characteristics of the machine. Particularly, the analysis of eddy-current loss in both the PMs and iron core of the machine is conducted. Experimental results are given for verification.