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This book investigates the utilization of harmonics in the permanent magnet (PM) or rotor shape to improve the torque density of PM brushless AC machines including three-phase inner rotor and outer rotor machines, five-phase machines, dual three-phase machines, linear machines, by means of analytical, finite element analyses, and as well as experimental validation. 
The torque density can be improved while the torque ripple remains low in PM shaping utilizing the 3rd harmonic. In this book, the analytical expression of output torque is derived for PM machines with rotor shape using the 3rd harmonic, and then the optimal 3rd harmonic for maximizing torque is analytically obtained. 
The book compares the PM shape in surface-mounted PM (SPM) machines and the rotor lamination shape in interior PM (IPM) machines utilizing the 3rd harmonic, and it becomes clear that their shaping methods and amount of torque improvement are different. 
In a five-phase PM machine, the 3rd harmonic can be utilized in both the current waveform and PM shapes to further improve the output torque. For the dual three-phase SPM machines without deteriorating the torque more than 30% when the optimal 3rd harmonic into both the current and PM shape are injected.
The harmonics in airgap flux density have significant influence on the cogging torque, stator iron flux distribution, and radial force between the rotor and stator. These effects has been investigated as well in this book.

Third Harmonic Utilization in Permanent Magnet Machines

General Introduction.- Torque Enhancement of Three Phase Surface-Mounted Permanent Magnet Machine Using 3rd Order Harmonic.- Average Torque Improvement of Three Phase Interior Permanent-Magnet Machine Using 3rd Harmonic in Rotor Shape.- Third Order Harmonic Utilization in In-Wheel Machines to Improve Output Torque.- Influence of Airgap Flux Density Waveform on Optimal Split Ratio and Torque Density of SPM Machines.- Investigation of Stator Flux Density and Iron Loss in 3rd Order Harmonic Shaped Surface-Mounted Permanent Magnet Machines.- Analysis of Cogging Torque in Surface-Mounted Permanent Magnet Machines with Shaped Magnets.- Influence of Harmonics on Radial Force and Vibration of Surface-Mounted Permanent Magnet Machines.- Multi-Objective Optimization of Surface-Mounted Permanent Magnet Machine with Third Harmonic Shaped Rotor.- Using Third Harmonic for Shape Optimization of Flux Density Distribution in Slotless Linear Permanent-Magnet Machine.- Design and Analysis of Permanent Magnet Linear Synchronous Machine with Third Harmonic Shaping Mover.