This paper models a huge family of electrical machines featuring simple salient poles in a unified way based on the general airgap field modulation theory. The modulation principle is analyzed by introducing the magnetomotive force (MMF) modulation operator, which characterizes the influence of variable reluctance block on the primitive magnetizing MMF distribution established by field winding. Popular machine topologies are investigated in detail from the perspective of airgap field modulation mechanism. The iron core magnetic potential drop due to the finite slot opening depth and the impact of iron saturation on the parameters are considered by proper theoretical indication. In addition, the modulation effect of salient poles highly depend on the slot-opening-width- to-pole-pitch ratio $\epsilon$. The effect can be neglected when $\epsilon$<0.3 and the best modulation results will be achieved when $\epsilon$=0.5. It is also found that mainly three different harmonics parts modulated by salient poles contribute on airgap flux density and torque production. Straightforward relations between the frequency-domain or amplitude information of performances indexes and topological parameters can be obtained obviously by certain analytical expressions without heavy finite-element analysis (FEA). Analytical results are verified by 2D FEA and experiments measurements.

This tutorial paper presents the mathematics behind the widely observed air-gap field modulation phenomena in electrical machines and derives the duality between electrical machines and switching converters. A bibliometric analysis of the existing research on various machine types is presented to show the historical development of electrical machines from the perspective of the number of publications, showing the necessity and urgency of unifying the analysis of operating principles/torque production mechanisms before the development of the general air-gap field modulation theory in 2017. The theoretical framework and its applications are reviewed. Detailed examples of how to use the developed theory to analyze the operating principle/torque production, conduct the quantitative analysis of parameters and basic performance, and make innovations from topologies of typical electrical machines are also included for verification as well as self-study.

This paper investigates the natures of induction machine (IM) and synchronous machine (SM) from a new point of view based on the general airgap field modulation theory. The equivalent airgap model containing three critical elements is proposed to expound their modulation principles and common features in a unified way, thus the electromagnetic performance analysis, i.e., back-electromotive force (EMF) and torque, of IM and SM can be put together from the perspective of airgap field modulation principle while the only difference exists in the modulators. The modulators are optimized by considering the nonlinearities like rotor coils resistance and leakage inductance of IM and the actual magnetomotive force (MMF) distribution of SM. Theoretical expressions of airgap flux density distribution, flux linkage and EMF, general average torque, torque density comparison, and inductance characteristics are developed to reveal the relation between the performances and initial key topological parameters systematically and verify the model feasibility entirely. The iron saturation is treated as a constant discount on the airgap MMF to provide general mechanism comprehension and reasonable parameters calculation. All the theoretical predictions are verified by two-dimensional (2-D) finite element analysis together with experiment achieving good agreement.

The flux guides are adopted in a number of electric machines, such as the synchronous reluctance machine (SynRM) and the brushless doubly fed reluctance machine (BDFRM). This article further develops a novel and unified theoretical approach for the category of machines with flux guides. Specifically, the magnetomotive force (MMF) modulation operator of variable flux guides is proposed based on the general airgap field modulation theory, to describe the modulation behavior on the source magnetizing MMF distribution in detail. Both machine topologies with flux guides, namely, the SynRM and BDFRM, are addressed in detail from the perspective of airgap field modulation mechanism. It is proven that, three kinds of harmonic components with pole pairs of $p_{f}$ and $(lN_{MB}\pm p_{f})$ correspond to $p_{f}$ pole-pair source magnetizing MMF and their relative amplitudes can be characterized by three magnetic field conversion factors. The magnetic field modulation effects of flux guides and simple salient poles are compared in terms of the torque production ability. In addition, electromagnetic performances such as airgap flux density, torque density, and inductance characteristics are correlated with their initial key topological parameters by certain analytical expressions and compared fairly between the SynRM and BDFRM. The agreement among the theoretical analysis and the two-dimensional (2-D) finite element analysis together with experimental test verifies the effectiveness of the proposed analysis.

Given its high torque density, robust structure, and efficient heat dissipation, the in-wheel flux-switching machine has garnered significant interest in e-bike applications. This paper introduces an in-wheel hybrid-excitation flux-switching (IW-HEFS) machine to reduce the reliance on the costly PM materials. Specifically designed for in-wheel applications, the optimization issue for the IW-HEFS machine involves six variables, six objectives, and two primary constraints. To streamline the optimization process, three principles are proposed to improve the solving efficiency by means of the Kriging model, sensitivity analysis, and dimensionality reduction strategies. On this basis, the electromagnetic performance of the IW-HEFS machine is significantly enhanced, particularly in terms of the torque and efficiency characteristics. Moreover, the optimization results are compared, along with the analysis of their strengths and weaknesses. Additionally, an evaluation of the proposed IW-HEFS machine is conducted to further reveal its potential in in-wheel applications by comparing with an existing outer-rotor flux-switching permanent magnet machine. Finally, the prototype experiment is launched with the consideration of manufacturing friendliness to estimate the analytical discussion.

The accurate calculation of stray load loss has an important contribution to increasing motor efficiency. The stray load loss can be regarded as the difference of the total iron losses and harmonic rotor cage losses between the no load and load conditions. A method combining the general airgap field modulation theory (GAFMT) and 2D finite element analysis (FEA) is proposed for calculating the stray load loss of the squirrel cage induction motor (SCIM). Firstly, the amplitudes and rotation speeds of the main space harmonics of the airgap magnetic flux density are calculated based on the GAFMT. And the relationships between these space harmonics and stray load loss are analyzed. Secondly, these space harmonics are synthesized by the equivalent current layers in the airgap and then are substituted into the 2D FEA models to calculate the losses. At last, the stray load loss calculated by the proposed method is compared with that obtained by practical motor tests.