*Article* **Analytical Design of Sculpted Rotor Interior Permanent Magnet Machines**

**Steven Hayslett 1,\* and Elias Strangas 2**


**Abstract:** A computationally efficient design of interior permanent magne<sup>t</sup> (IPM) motor rotor features is investigated utilizing analytical methods. Over the broad operating range of IPM machines, interactions of MMF sources, permeances, and currents result in torque harmonics. The placement of traditional rotor features along with sculpt features are utilized to minimize torque ripple and maximize average torque. We extend the winding function theory to include the IPM rotor's primary and secondary reluctance paths and the non-homogeneous airgap of the rotor sculpt features. A new analytical winding function model of the single-V IPM machine is introduced, which considers the sculpted rotor and how this model can be used in the design approach of machines. Results are validated with finite elements. Rotor feature trends are established and utilized to increase design intuition and reduce dependency upon the lengthy design of experiment optimization processes.

**Keywords:** electric motor; interior permanent magnet; reluctance; MMF-permeance; winding function; torque ripple
