machines Article Design Procedure for High-Speed PM Motors Aided by Optimization Algorithms Francesco Cupertino ID , Riccardo Leuzzi, Vito Giuseppe Monopoli * ID and Giuseppe Leonardo Cascella Department of Electrical and Information Engineering, Politecnico di Bari, 70126 Bari, Italy; francesco.cupertino@poliba.it (F.C.); riccardo.leuzzi@poliba.it (R.L.); g.l.cascella@gmail.com (G.L.C.) * Correspondence: vitogiuseppe.monopoli@poliba.it Received: 30 December 2017; Accepted: 8 February 2018; Published: 11 February 2018 Abstract: This paper considers the electromagnetic and structural co-design of superficial permanent magnet synchronous machines for high-speed applications, with the aid of a Pareto optimization procedure. The aim of this work is to present a design procedure for the afore-mentioned machines that relies on the combined used of optimization algorithms and finite element analysis. The proposed approach allows easy analysis of the results and a lowering of the computational burden. The proposed design method is presented through a practical example starting from the specifications of an aeronautical actuator. The design procedure is based on static finite element simulations for electromagnetic analysis and on analytical formulas for structural design. The final results are validated through detailed transient finite element analysis to verify both electromagnetic and structural performance. The step-by-step presentation of the proposed design methodology allows the reader to easily adapt it to different specifications. Finally, a comparison between a distributed-winding (24 slots) and a concentrated-winding (6 slots) machine is presented demonstrating the advantages of the former winding arrangement for high-speed applications. Keywords: AC machines; design automation; design optimization; finite element analysis; high- speed electrical machines; synchronous permanent magnet machines 1. Introduction In several application areas, there is a growing interest in high-speed electrical machines [1], because they allow compactness and reliability. For example, direct-drive high-speed actuators permit the elimination of the need for a mechanical gearbox, reducing system weight and increasing its efficiency [2]. As the rotational speed of the electrical machine grows, structural integrity of the rotor tends to become a critical issue [3]. Moreover, core loss quickly grows with the electrical frequency that is proportional to the mechanical speed, resulting in an augmented thermal stress. Among the variety of high-speed brushless machines, Surface Permanent Magnet (SPM) synchronous machines exhibit the highest torque density but also the highest cost, due to rare earth permanent magnets (PMs). Moreover, a retaining sleeve is mandatory in SPM machines, to withstand centrifugal stress and ensure rotor integrity [4,5]. So far, several kinds of optimized design procedures of permanent magnet machines have been presented in the literature, each addressing a particular issue related to this topic (i.e., computational time, optimal solution reliability, integrated mechanical-electromagnetic design, etc.). In [6] a viable automatic design procedure to enlarge the high-efficiency operation area while keeping low computational burden is proposed. In fact, the finite element method (FEM) is highly time-consuming, above all when efficiency calculations are performed, while the coarse-mesh FEM is a basic technique allowing a reduction of the computational burden through a limited number of Machines 2018, 6, 5; doi:10.3390/machines6010005 www.mdpi.com/journal/machines