Torque density enhancement of 6/4 variable flux reluctance machine with 2nd harmonic current injection

Variable flux reluctance machines (VFRMs) are developed as magnetless electrical machines. To extend the application of VFRMs, the enhancement of torque density is a key during machine design. In this paper, a novel 2nd harmonic current injection method is developed for torque density enhancement for 6-stator-slot/4-rotor-tooth (6/4) VFRM. By using analytical method, the optimal current profile with injected 2nd harmonic current is obtained. The average torque of 6/4 VFRM is improved by 20% with the proposed method under all load conditions. Moreover, the proposed current profile has fixed harmonic proportions and is easily applicable to machines with different specifications. All the conclusions are confirmed by both finite element analyses and experimental results

Analysis of Stator/Rotor Pole Combinations in Variable Flux Reluctance Machines Using Magnetic Gearing Effect

The torque production of variable flux reluctance machines (VFRMs) is explained by the “magnetic gearing effect” in recent research. Based on this theory, this paper concludes the general principles for feasible stator/rotor pole selection and corresponding winding configuration for VFRMs. The influence of stator/rotor pole combination on torque performance is comprehensively investigated not only in terms of average torque and torque ripple, but also in terms of each single torque component. It is found that the synchronous torque is proportional to the fundamental rotor radial permeance component and has the dominant contribution in average torque for all the VFRMs. The stator slot number and rotor pole number should be close to each other to achieve the highest output torque. Meanwhile, the 6-stator-slot/(6i ± 2)-rotor-pole (6s/(6i ± 2)r) and their multiples are large torque ripple origins for VFRMs due to the large reluctance torque ripple. Also, it is proved that a lower stator slot number is preferable choice to obtain higher torque/copper loss ratio, whereas a higher stator slot number is more suitable for large machine scale scenario. Finally, the analyses and conclusions are verified by finite element analysis on the 6-, 12-, 18-, and 24-stator-slot VFRMs and by experimental tests on a 6s/7r and 6s/8r VFRMs

A PDEM-COM framework for uncertainty quantification of backward issues involving both aleatory and epistemic uncertainties

Uncertainties that exist in nature or due to lack of knowledge have been widely recognized by researchers and engineering practitioners throughout engineering design and analysis for decades. Though great efforts have been devoted to the issues of uncertainty quantification (UQ) in various aspects, the methodologies on the quantification of aleatory uncertainty and epistemic uncertainty are usually logically inconsistent. For instance, the aleatory uncertainty is usually quantified in the framework of probability theory, whereas the epistemic uncertainty is quantified mostly by non-probabilistic methods. In the present paper, a probabilistically consistent framework for the quantification of both aleatory and epistemic uncertainty by synthesizing the probability density evolution method (PDEM) and the change of probability measure (COM) is outlined. The framework is then applied to the backward issues of uncertainty quantification. In particular, the uncertainty model updating issue is discussed in this paper. A numerical example is presented, and the results indicate the flexibility and efficiency of the proposed PDEM-COM framework

Analysis of flux barrier effect of LCF PM in series hybrid magnet variable flux memory machine

Variable flux memory machines (VFMMs) with series hybrid magnets using both low coercive force (LCF) and high coercive force (HCF) permanent magnets (PMs) have been recognized as a viable candidate for wide-speed-range industrial applications due to the advantages of high torque density and wide speed range. Nevertheless, the adverse effects of LCF PM on the HCF PM in series-type VFMM under different magnetization states (MSs) are still unreported. In this paper, the flux barrier effect (FBE) of the LCF PM existing in series hybrid magnet VFMM is first revealed, and its causes are discussed as well as analyzed in depth on the basis of the equivalent magnetic circuit method and finite-element (FE) analyses. A topology of VFMM with dual-layer PMs is further developed to alleviate the FBE induced from LCF PMs. It can be found that the FBE can be effectively suppressed by employing the dual-layer (DL) PM arrangement and additional leakage flux paths. A prototype of the proposed design is built, and the theoretical and FE results are experimentally verified

Comparative Analysis of Variable Flux Reluctance Machines With Double- and Single-Layer Concentrated Armature Windings

In this paper, the variable flux reluctance machines (VFRMs) with double- and single-layer concentrated armature windings are comparatively analyzed. First, the single-layer winding is found to have an identical winding factor as a double-layer winding, but significantly larger peak value of magneto-motive force, which will result in severe local saturation in cores of VFRMs with single-layer winding. Then, based on the magnetic gearing effect and finite-element analysis, the electromagnetic performances of VFRMs with both winding types are compared. The VFRMs with single-layer winding are proved to be always lower in average torque, higher in torque ripple, larger in iron loss, and lower in efficiency than those with double-layer winding. Nevertheless, better fault-tolerance capability is achieved for a single-layer winding due to its physical separation between phases and larger phase self-inductance. Overall, the double-layer armature winding is the preferable choice for the VFRMs. Finally, a 6-stator-slot/4-rotor-pole VFRM with both double- and single-layer windings is prototyped for verification

Analysis of power factor in variable flux reluctance machines with MMF-permeance model

This study investigates the underlying mechanism of low-power factor issue of variable flux reluctance machines (VFRMs) from the perspective of magneto-motive force (MMF)-permeance model. On the basis of a simplified analytical model, the relationship between the design parameters and the power factor is identified and systematically summarised into three predictable ratios: the rotor permeance ratio, stator/rotor-pole ratio and DC/AC winding ampere turns ratio. Specifically, the smaller the rotor-pole arc, the air-gap length, the rotor-pole number and the AC/DC winding ampere turns ratio are, the higher the power factor will be. In addition, the weak coupling between the field and armature windings caused by the modulation effect of the salient rotor is responsible for the low-power factor issue of VFRMs, regardless of the control scheme, winding configuration or saturation effect. A 6-stator-pole/4-rotor-pole VFRM is prototyped and tested for verification

A hybrid field model for open-circuit field prediction in surface-mounted PM machines considering saturation.

This paper presents a nonlinear hybrid field model to predict the open-circuit magnetic field distribution in surface-mounted permanent-magnet machines. It combines the complex permeance model (CPM) with the magnetic equivalent circuit (MEC). The saturation effect is accounted for in the CPM by considering the magnetic potential distribution on the stator bore, which is calculated by the MEC and can be transformed to the virtual current on the slot. The proposed model significantly improves the calculation accuracy for saturated machines, which is verified by the finite-element analysis and the experimental results

Rotor shaping method for torque ripple mitigation in variable flux reluctance machines

In this paper, four rotor shaping methods, i.e., eccentric circular, inverse cosine, inverse cosine with third harmonic, and multi-step shaping methods, are developed and compared for torque ripple mitigation in variable flux reluctance machines (VFRMs). By using a 6-stator-pole/7-rotor-pole (6/7) VFRM as an example, the design criterions and capabilities of these four methods are illustrated. It is found that all the rotor shaping methods are capable of torque ripple mitigation and applicable to all the VFRMs except those with 6 k /(6 i ± 2) k ( k , i = 1, 2, 3…) stator/rotor pole combinations. Moreover, the inverse cosine with third harmonic and multi-step shaping methods are found to have the best performance. They are able to reduce the torque ripple by 90% at a cost of only 3% torque density reduction. A 6/7 VFRM with both conventional and shaped rotors is prototyped and tested for verification

On-load field prediction of surface-mounted PM machines considering nonlinearity based on hybrid field model

Analytical models show weakness in dealing with saturation in surface-mounted permanent-magnet machines. A hybrid field model (HFM) integrating complex permeance method (CPM) and lumped parameter magnetic circuit model (LPMCM) is proposed in this paper for predicting the on-load magnetic field considering nonlinearity effect of stator lamination. In the proposed model, the CPM calculates the field in the air gap and magnet regions, while LPMCM calculates the magnetic potential distribution inside the iron reflecting nonlinearity effect. The equivalent current sheet is obtained to replace such distribution on the stator bore. Moreover, local magnetic saturation of tooth tip is also transformed into equivalent current on the tooth surface. A solving procedure is proposed to calculate the equivalent current and guarantee the convergence. Compared with CPM, the proposed model considering the saturation effect significantly improves the prediction accuracy of the on-load performance. The HFM predictions are compared with finite element and experimental results. The excellent agreement validates its effectiveness

Analysis of bilinear oscillators under harmonic loading using nonlinear output frequency response functions

In this paper, the new concept of Nonlinear Output Frequency Response Functions (NOFRFs) is extended to the harmonic input case, an input-independent relationship is found between the NOFRFs and the Generalized Frequency Response Functions (GFRFs). This relationship can greatly simplify the application of the NOFRFs. Then, beginning with the demonstration that a bilinear oscillator can be approximated using a polynomial type nonlinear oscillator, the NOFRFs are used to analyze the energy transfer phenomenon of bilinear oscillators in the frequency domain. The analysis provides insight into how new frequency generation can occur using bilinear oscillators and how the sub-resonances occur for the bilinear oscillators, and reveals that it is the resonant frequencies of the NOFRFs that dominate the occurrence of this well-known nonlinear behaviour. The results are of significance for the design and fault diagnosis of mechanical systems and structures which can be described by a bilinear oscillator model