John Wanjiku

Influence of Slot Openings and Tooth Profile on Cogging Torque in Axial-Flux PM Machines

Slotted axial-flux machines have excellent power and torque densities. However, it is difficult to reduce their cogging torque due to the complexity associated with implementing classical techniques. In this paper, slot-opening widths and tooth profiles will be shown to be significant in mitigating cogging torque in these machines. In particular, varying the slot opening reduced it by 52%, whereas a parallel-tooth (rectangular) profile lowered it by 24%, when compared with a conventional trapezoidal-tooth profile. An analytical quasi-3-D analysis was formulated and used to analyze and determine cogging torque. It was validated numerically and experimentally. Its versatility is in its ability to analyze different shapes of poles and slot openings, which can be extended to model air-gap nonuniformity. This paper also presents cogging torque minimization techniques that maintain the ease of manufacture of the parallel-tooth stator. Experimental results showed 73% and 48% reduction in cogging torque, which are achieved by the use of alternating pole arcs and skewed poles.

The Effect of Two- and Three-Level Inverters on the Core Loss of a Synchronous Reluctance Machine (SynRM)

The paper shows the reduction of core losses by using a three-level inverter over a two-level inverter for the same dc-bus voltage and switching frequency. A synchronous reluctance machine stator-core toroid was used in the analysis. Hence, the analysis is realistic as it accounts for mechanical effects through the stator core, and the distorted supply of the line-to-line inverter voltage supplies. The paper also shows the limitations of using finite element-derived excitation; hence, the toroid was directly supplied by the inverter. The reduction of core losses by use of a three-level inverter is significant at very high flux densities and frequencies; approximately 60% lower core losses. Therefore, it can reduce the cooling burden especially in the hard to cool teeth, increase the service life, and allow increased output. The latter is because the output of the three-level fundamental voltage is higher for the same dc-bus and switching frequency at lower machine losses.

The effect of tooth-width on the distribution of rotational core losses

This paper examines the effect of tooth-width in the mapping of pulsating, elliptical and rotational losses in a tooth body for a given slot-pitch. Core loss distribution in the tooth is done with the use of FEA and 2-D core loss measurement results. The core loss distribution is computed using two methods, i.e., pulsating losses assuming all the flux-density in the stator is pulsating and elliptical losses including rotational losses. The two are compared and discussed in detail. A methodology that reduces the FEA geometrical size for core loss analyses to a slot-pitch is also presented.

Shielding of the z-component of the magnetic field in a 2-D magnetizer with a deep yoke

Compact two-dimensional magnetizers with deep yokes can achieve very high flux densities (~2 T) at the expense of increasing the z-component of the magnetic field (Hz), in the measurement region. Hz is often reduced by shielding, where the shields are placed at an optimum distance from the sample. The paper will show that a given shield distance is not effective in minimizing Hz over the entire flux density range. Larger spacings (> 18 mm) were effective at high flux densities, while lower ones (9 to 10 mm) were effective at low flux densities. This was validated experimentally where the shield distances of 10 mm and 22.5 mm reduced Hz of the unshielded case by 83 % at 0.5 T and 72 % at 1.5 T, respectively. In addition, the paper will show that the magnetic properties and the interaction of the sample and shields, reduces the effectiveness of shielding in deep saturation.

Investigating the sources of non-uniformity in 2-D core loss measurement setups

Two-dimensional (2-D) core loss measurements have low reproducibility and repeatability, due to several errors such in data acquisition, sensing systems and the magnetizer. The latter contributes to the variation in the samples flux density (B) under rotational magnetization. The variation in B requires a reduction of the measurement region, stresses the power source, lowers the circularity of B and modifies its locus. This variation is analysed in four magnetizers, where sinusoidal distribution of the magnetizing winding and increasing the yoke depth, are proposed. A deep yoke will be shown to increase the magnetic loading of the sample, and mitigates the variation in B in magnetizers with non-sinusoidal fields such as the square tester. The location of B-coils can result to the overestimation or underestimation of the measured B values; affecting the core loss. Experiments showed a 14% (at ∼0.8 T) and 6% (at ∼1.6 T) difference at two locations. B-holes also increase non-uniformity in the sample; spiking of B and H at the hole regions. Numerical results will show that it has minimal effects on B (< 1%), but the local increase in the field (H) is in the order of 10 4 A/m at saturation.

Design of a Sinusoidally Wound 2-D Rotational Core Loss Setup With the Consideration of Sensor Sizing

The design of a two-dimensional rotational core loss setup that considers sensor sizing and the airflux leakage field is presented. The length of the flux density (B) coils is evaluated based on the magnetic degradation caused by holes used to locate the B-coils. The measured core loss is shown to be independent of the planar magnetic field (H) coil size, but depends on the location and the thickness of the enclosed core area. This determines the extent of the airflux leakage field in the measured field. This field links through the air close to the sample surface, and is shown to bias the shape, magnitude, and phase of the measured magnetic field. Core losses measured using three testers show that the airflux leakage field reduces with increasing magnetizer diametrical size. However, it is independent of the stack length in compact magnetizers. Finally, the performance of the proposed magnetizer is assessed at 60 Hz, 400 Hz, and 1 kHz.

Design of a 2-D magnetizer with the consideration of the z-component of the magnetic field

A magnetizer design methodology that takes into account systematic errors such as the variation in flux density (B), and the z-component of the magnetic field (Hz), is proposed. The effect of the sample diameter and the effective length of the yoke, i.e. yoke depth on Hz are analysed. Experimental results at 1.5 T and 60 Hz showed a reduction of 81 %, 72 % and 30 % by a large magnetizer, shielding and reducing the yoke depth from 80 mm to 10 mm, respectively. This was in comparison to an unshielded compact magnetizer. Hz is also dependent on magnetic loading. Furthermore, at 2 T and 60 Hz, magnetic contributions dominated Hz such that the effectiveness of shielding and reducing the yoke depth decreased to 27 % and 4 %, respectively. To achieve these very high flux densities, the magnetizers were designed to be compact (sample diameter of ≤ 100 mm and narrow airgaps of ≤ 2 mm). This reduction in size increases the leakage field above and below the sample to the same level of magnitude as the applied field, which affects the measurement of the magnetic field (H). Two H-coil sizes with a sensitivity difference of 60 % are used to show that the measured H is independent of the coil size, but depends on the leakage field. Their measured core loss difference under pulsating and rotating fields was about 6 %.

Design considerations of 2-D magnetizers for high flux density measurements

The Fieldmetric measurement of 2-D core losses requires the use of orthogonal magnetic field H and flux density B sensors that are placed in a region of very high uniformity. It is difficult to achieve uniformity in the entire measurement region, in addition to the variation of B with magnetization directions. Therefore, there is a need to eliminate and/or reduce any contribution of a 2-D magnetizer to this variation, which contributes to systematic errors. Uniformity due to the magnetizer can only be controlled at the design stage. In that regard, four 2-D magnetizers are compared based on the variation of B with changes in magnetization directions. At high flux densities, any non-uniformity in B results in very H values, thus the errors due to the magnetizer are significant. Another effect of high non-uniformity is a reduction of the measurement area. It will be shown that the choice of the magnetizer design (hence the sample shape) significantly affects the variation of B with magnetization direction. In addition, the effect of the yoke depth in mitigating this problem is presented where it reduces this variation by 50%, for certain magnetizers.