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A novel low-speed flux-modulated (FM) permanent-magnet (PM) motor that breaks the traditional design rule, which stipulates that the number of stator pole pairs and the number of rotor pole pairs must be the same, is proposed. The FM motor has a special physical structure with iron segments in the air gap to modulate the magnetic field. In the design, the free space between adjacent stationary iron segments also acts as ventilating ducts to help improving the heat dissipation and ventilation of the motor. Its cogging torque is very small. In this paper, a rule for comparing the power density of electric motors is proposed. The performance of the FM motor is compared with those of a magnetic-geared PM motor, a traditional PM motor, and a fractional-slot PM motor by using magnetic field finite-element analysis.