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High-speed machines with a solid rotor or a high- strength retaining sleeve could offer design and performance advantages. For a specific application, if the use of a high-strength nonmagnetic metallic retaining sleeve is more advantageous than a nonmetallic (e.g., carbon fiber) one, one needs to evaluate the eddy-current losses due to armature reaction space and time harmonics and/or tooth ripple, as they can be significant. This problem is aggravated furthermore in fractional-slot concentrated-winding machines due to their inherent sub- and super nonsynchronous MMF harmonic components. In this paper, the impact of the number of phases is quantified to help design a lower eddy loss rotor sleeve for a high-speed surface-mounted permanent-magnet rotor machine with fractional-slot concentrated armature winding, FSPCW-SPM. The goal of this paper is to provide a general method for laying out preferred FSPCW configurations. Also, a general method for screening and choosing the optimal slot/pole combinations is presented.