Rotor geometry for interior permanent magnet machine having rare earth magnets with no heavy rare ea

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An interior permanent magnet machine includes a wound stator, and a rotor core defining a plurality of pole cavities. Each of the pole cavities includes a cross section, perpendicular to a central axis of rotation, that defines a cross sectional shape having a centerline. The cross sectional shape of each of the pole cavities includes a radially inner barrier portion, a radially outer barrier portion, and a central portion. The centerline of the cross sectional shape of each of the radially outer barrier portion and the radially inner barrier portion, of each pole cavity, is defined by a generally arcuate segment. The centerline of the cross sectional shape of the central portion, of each pole cavity, is defined by a linear segment. One of a plurality of rare earth magnets, having no heavy rare earth elements, is disposed within the central portion of one of the plurality of pole cavities.