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This paper presents the simplified analytical optimization and comparison between electrically excited (EE) and permanent-magnet (PM) machines in terms of torque per volume T/V and torque per weight T/G for low-speed applications when their copper loss and overall size are the same. Analytical torque models for both machines are individually developed and optimized to obtain the optimal flux density ratio, split ratio, and maximum torque densities. Furthermore, the variation of optima with the number of poles and machine size is also investigated. The analytical analyses are validated by both finite-element analyses and experiments. It is concluded that torque densities of PM machines can be more than \sqrt2 times higher than those of EE machines. For EE machines, there is an optimal pole number to maximize torque densities, and large volume applications are preferred. In actual applications, EE machines are more likely to compromise the torque density to meet the thermal constraints. It also shows that the optimal T/G designs have significantly higher split ratio and are more cost- and weight-effective than the optimal T/V designs. [ABSTRACT FROM PUBLISHER]

This paper investigates the on-load cogging torque calculation in permanent magnet (PM) machines. The vast majority of existing methods for calculating the cogging torque, no matter whether analytical or numerical methods, neglect the influence of load, or are inappropriate in considering the influence of load. Without using the frozen permeability method, the torque calculated by the virtual work principle includes the magnetic energy due to the armature field. When using the frozen permeability method, the resultant torque based on the Maxwell stress tensor with the on-load PM field only has nonzero average torque and, hence, is not the on-load cogging torque. A new on-load cogging torque calculation method is proposed in this paper based on the combination of the virtual work principle and frozen permeability method. For its implementation, an improved frozen permeability method, which makes the magnetic energy with on-load PM field that can only be calculated according to the B–H curve, is also developed. By using the new method, all the shortcomings of existing methods can be avoided and, hence, the on-load cogging torque can be calculated appropriately in both linear and nonlinear cases. [ABSTRACT FROM PUBLISHER]

This paper investigates the influence of skewing on torque ripples, including the electromagnetic (EM) torque ripple, and the cogging torque, in permanent magnet (PM) machines. It is found that the effectiveness of skewing largely depends on the axial variation of a torque ripple phase but less on its magnitude under skewing. It is further found that, in both linear and nonlinear cases, the EM and the on-load torque ripple cannot be fully eliminated by skewing one on-load torque ripple period or any other angles, except 360^\circ electrical, which is impractical. This is due to the fact that the EM torque ripple, especially its phase, of each slice is different due to the axial variation of the equivalent current phase advance angle introduced by skewing. In nonlinear cases, the EM torque ripple variation is further aggravated by the axial variation of magnetic saturation. The EM torque ripple as well as the on-load torque ripple may be even increased by skewing, especially when the cogging torque is low and electric loading is high. [ABSTRACT FROM AUTHOR]

This paper investigates the average torque separation in permanent magnet (PM) synchronous machines. In order to accurately separate the PM and armature fields, and, hence, the torque components accounting for the magnetic saturation and crosscoupling, the frozen permeability (FP) method is often employed, while the torque can be calculated by different methods, such as Maxwell stress tensor and virtual work principle. Although these two methods result in identical torques in normal finite element (FE) analyses when appropriate FE meshes are used, the average torques calculated by these two methods are found to be different when the FP method is employed due to the influence of equivalent rotational magnetic saliency in the stator, which causes a part of PM torque being improperly attributed to the reluctance torque when Maxwell stress tensor method is employed. However, by using the virtual work principle, this is eliminated, and, hence, the average torque components can still be appropriately separated and analyzed. [ABSTRACT FROM AUTHOR]