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

An interior permanent magnet machine comprising:

• a wound stator;
• a rotor core including a plurality of poles, with each pole defining a plurality of pole cavities;
• wherein each of the plurality of pole cavities includes a cross section, perpendicular to a central axis of rotation, defining a cross sectional shape having a centerline;
• wherein the cross sectional shape of each of the plurality of pole cavities includes a radially outer barrier portion and a central portion;
• wherein the centerline of the cross sectional shape of the radially outer barrier portion of each pole cavity is defined by a generally arcuate segment;
• wherein the generally arcuate segment of the centerline of the radially outer barrier portion of each pole cavity is defined by the equation:
• Ax2|Bxy|Cy2|Dx|Ey|F=0
• wherein A, B, C, D, E, and F are constants, x is a value along an x-axis of a Cartesian coordinate system, and y is a value along a y-axis of a Cartesian coordinate system;
• wherein the centerline of the cross sectional shape of the central portion of each pole cavity is defined by a linear segment;
• and
• a plurality of magnets, with one of the plurality of magnets disposed within the central portion of one of the plurality of pole cavities.