Corresponding author’s email address: awahchukwuemeka@gmail.com 879 ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT ORIGINAL RESEARCH ARTICLE THE IMPACT OF STATOR TOOTH AND POLE COMBINATIONS ON OUTPUT OF A DUAL STATOR ELECTRIC MACHINE C. C. Awah*1, C. A. Amaghionyeodiwe2, G. C. Diyoke1, O. Obasi1, I. K. Nnabuenyi3 and S. E. Oti4 1Department of Electrical and Electronic Engineering, Michael Okpara University of Agriculture, Umudike 2Department of Mechanical Engineering, Michael Okpara University of Agriculture, Umudike 3Instrument QA/QC Arco M&E, NLNG Sub Contractor, Bonny, Rivers State, Nigeria 4Department of Electrical Engineering, University of Nigeria, Nsukka *Corresponding author’s email address: awahchukwuemeka@gmail.com ARTICLE INFORMATION ABSTRACT Due to the great influence of stator tooth and rotor pole combinations of electric machine on its output performance; the feasible permutations of these machine variables and its resulting electromagnetic effects on the output characteristics of a dual stator (DS) electric machine were analyzed and quantitatively compared in this study, for overall optimal yield. Finite element analysis technique was employed in the predictions through MAXWELL-2D computational software. The considered stator number (Ns) was six (6) while its corresponding rotor pole numbers (Nr) were: 10, 11, 13 and 14i.e. for Ns/Nr being 6/10, 6/11, 6/13 and 6/14, respectively. The study shows that machine type having 6/11 i.e. 6-stator tooth with11-pole number would exhibit the largest flux linkage amplitude, reasonably high voltage at low operating current and most promising torque in relation to the deployed magnet volume, albeit; with low operating speed range. The 6/10 and 6/14 machine topologies would have considerably high amount of torque ripple coupled with very low output performance in comparison to its equivalent6/11 and 6/13 machine types. Regrettably, high value of magnetic force on the rotor is acquired from 6/11 machine type. Consequently, the 6/11 machine type would most likely suffer from greater mechanical instability amongst other compared machine types; notwithstanding its other competitive merits. Submitted 01 April, 2024 Revised: 01 June, 2024 Accepted: 10 June, 2024 Keywords: Flux density Force Rotor Stator Voltage © 2024 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved. 1.0 Introduction Discussions on dual or double stator machines have drawn global attention of researchers over the decades, owing to its numerous merits over its single stator counterparts; ranging from enhanced thermal management, improved efficiency, larger torque and power densities, to higher fault-tolerant and reliability, amongst other advantages (Ali et al., 2021). Both the open-circuit torque and electromagnetic torque of a machine would be greatly affected by its applied number of poles, as demonstrated by Awah et al. (2022). Besides, right selection of pole and slot combinations could reduce or eliminate torque pulsation and other unwanted machine features (Choo et al., 2022). However, this present research is centred on the resulting impact of stator tooth and pole arrangements of a dual stator (DS) permanent magnet (PM) machine on a number of performance indices. Dual stator machines usually have higher mechanical complexity and cost than equivalent single stator machines; but this higher cost could be drastically reduced through application of consequent-pole design strategy, as demonstrated by Baloch et al. (2018). Zhao et al. (2020) established that similar analyses on dual rotor single stator configuration are also possible with almost similar trend in its resulting waveforms; however, with some noticeable differences on its output magnitudes. In order to enhance the torque densities of existing dual stator machines, Gao et al. (2019) and Song et al. (2019) developed two kinds of dual stator machines while also considering the tooth and pole possibilities of AZOJETE December 2024. Vol.20(4):879-890 Published by the Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria. Print ISSN: 1596-2490, Electronic ISSN: 2545-5818 www.azojete.com.ng mailto:awahchukwuemeka@gmail.com mailto:awahchukwuemeka@gmail.com http://www.azojete.com.ng/ Arid Zone Journal of Engineering, Technology and Environment, December 2024; Vol.20(4):879-890. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: awahchukwuemeka@gmail.com 880 the machines. The developed machines by Gao et al. (2019) and Song et al. (2019) are all dual stator machines and are distinctively different from that of the developed machine in this present investigation, structurally and otherwise. Pole arrangements of a machine would affect the machine’s pole ratios Li et al. (2015), winding factors (Awah and Okoro, 2018b) and subsequently, its resulting electromagnetic performances. The reliance of electrical machine’s output on its pole, winding factors and gear ratios is further ascertained by Hyoseok et al. (2017), Xie et al. (2019) and Cooke and Atallah (2017), respectively. It is worth mentioning that the studied machine in this present investigation belongs to the flux-switching permanent magnet (FSPM) machine family. FSPM machines have its feasible stator tooth and pole number combination peculiarities. This feasibility and peculiarities would naturally depend upon the basic operations of such machine i.e. as generator (Shao et al., 2020) and or as motor (Shi et al., 2016). Determination of tooth and pole possibilities via magnetic gearing principles can be extended to other electric machines, as detailed by Huang et al. (2019). Nevertheless, the research by Jia et al. (2016) shows that that a machine with high pole number may be associated with huge number of losses and by extension low efficiency regardless of its tremendous electromagnetic yield. Torque-speed path of a machine could be achieved by weakening its flux, usually by application of negative direct-axis (d-axis) current, which will customarily affect the resulting axis inductance. The flux-weakening strategy was applied in this present study; however, an extended torque-speed trajectory of a flux-switching machine could be obtained by appropriate modification of the machine’s d-axis inductance, through mechanical flux-adjusters, as presented in Zhao and Liu (2023) with validated experimental proof. This wider speed coverage is a desired quality for electric vehicle and traction applications. Similarly, a wider speed range could also be obtained in a machine by adopting a spoke-type magnetic rotor, owing to the associated high flux- focusing potential of this arrangement, for enhanced power, torque and efficiency values, amongst other admirable performance qualities. Again, the d-axis inductance worth of the system would be improved through this spoke-type arrangement; though, with suitable optimization of the machine’s other leading geometric variables, as established by Hu and Wang (2023). More so, power density and efficiency of a machine could be improved by employing suitable core materials, as presented in Hebri et al. (2023). Overall, stator tooth and pole arrangements of a dual stator machine is was analyzed in this current study and its impacts on the machine’s output are were also quantified, with a view to providing adequate guide to machine designers and practitioners on the need to implement suitable stator tooth and pole combinations, considering its consequent effects, for better-quality machine output. 2. Materials and Methods Investigated machine diagram is displayed in Figure 1. It is a double stator machine with magnets mounted on both stators. However, the alternating current armature conductors are placed only on the outer stator slot areas. The stators are separated by a rotor having field-modulating pole pieces. Both Maxwell-2D and MATLAB softwares were applied in the analyses. It is possible to carry out similar analyses using analytical methods, but finite element analysis approach is chosen and implemented in this study, owing to its high prediction accuracy compared to analytical procedures, which are associated with some electromagnetic assumptions. More so, field-weakening technique is adopted in obtaining the torque-speed trajectory through application of the machine’s direct-axis currents and adequate transformation of its axis variables. The considered stator tooth number (Ns) is 6 while the rotor pole numbers are: 10, 11, 13 and 14, i.e. Ns/Nr is: 6/10, 6/11, 6/13 and 6/14, respectively. The adopted pole numbers are chosen on basis of the established feasible combination principles provided in Awah and Zhu (2016). The predicted torque (T) is expressed in Eq. (1). The calculated magnetic force on the rotor axes is mathematically expressed in Eqs. (2) and (3), as implemented in Awah et al. (2023b). It is important to note that magnetic flux density amplitude plays major role in the output delivery of a given electric machine (Awah, 2023a and Awah, 2023b). http://www.azojete.com.ng/ mailto:awahchukwuemeka@gmail.com Arid Zone Journal of Engineering, Technology and Environment, December 2024; Vol.20(4):879-890. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: awahchukwuemeka@gmail.com 881 Figure 1: 3D diagram of the developed machine, 6/13(Awah, 2022) 332211 IEIEIET ++= (1) Where: ω is rotor speed, E1, E2 and E3 are three-phase voltages, I1, I2 and I3 are the matching phase currents (Oti and Awah, 2022). ss o r x Dl B F    =  cos 4 1 2 0 2 (2) ss o r y Dl B F    =  sin 4 1 2 0 2 (3) Where: Br is the radial flux density, D is stator inner diameter, l is stator axial length and ϴs is the stator angular coordinate. It is worth noting that high amount of UMF would certainly influence the noise and vibration levels of a machine and may even reduce the life span of the machine (Awah et al., 2018a). 3. Results and Discussion Flux density contours of the machine configurations are presented in Figure 2; intensity of the flux is considerably high at the tips of both the stator and rotor teeth. The implemented flux density magnitude is 2.0 Tesla. Consequently, the resulting air-gap flux density wave forms of the machine types in one electric revolution are shown in Figure 3(a). The generated flux linkage outlines on no-load and at different speed settingsare depicted in Figure 3(b). Outer magnet Outer stator core Shaft location Inner stator segment Inner magnet Rotor http://www.azojete.com.ng/ mailto:awahchukwuemeka@gmail.com Arid Zone Journal of Engineering, Technology and Environment, December 2024; Vol.20(4):879-890. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: awahchukwuemeka@gmail.com 882 (a) 6/10 (b) 6/11 (c) 6/13 (d) 6/14 Figure 2: Magnetic flux density (a) Flux density versus rotor position -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 0 60 120 180 240 300 360 R a d ia l a ir g a p f lu x d en si ty ( T ) Rotor position (mechanical deg) Ns/Nr = 6/10 Ns/Nr = 6/11 Ns/Nr = 6/13 Ns/Nr = 6/14 http://www.azojete.com.ng/ mailto:awahchukwuemeka@gmail.com Arid Zone Journal of Engineering, Technology and Environment, December 2024; Vol.20(4):879-890. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: awahchukwuemeka@gmail.com 883 (b) Flux linkage versus speed Figure 3: Flux density and linkage waveforms Figure 4 (a) shows the produced voltage values at varying speed. A linear relationship exists between the applied speed and generated voltage, in-line with theoretical impression. Voltage variations with applied current are compared in Figure 4 (b). It is observed that the 6/10 and 6/13 machine types would yield the lowest and highest voltage values, respectively; at extreme electric loadings. Meanwhile, the generated voltage values of 6/11 and 6/13 machine types are almost similar at all speed ratings, as presented in Figure 4(a), as well as at the rated current, as shown in Figure 4 (b). This similarity trend also repeated on the generated electromagnetic torque, as shown in Figure 5. It is worth mentioning that 6/10 and 6/14 machine types have dip pulsation effects on its torque, as shown in Figure 5 (a). It is worth noting that output torque of a machine is directly related to its induced-voltage. Thus, the presence of 3rd harmonic component of torque shown in Figure 5(b) is indications that the investigated machine would most probably possess even order voltage harmonics. (a) Voltage versus speed 0 2 4 6 8 10 12 14 0 500 1000 1500 2000 2500 3000 3500 4000 F lu x l in k a g e m a g n it u d e( m W b ) Speed (r/min) Ns/Nr = 6/10 Ns/Nr = 6/11 Ns/Nr = 6/13 Ns/Nr = 6/14 0 5 10 15 20 25 30 35 40 45 50 0 500 1000 1500 2000 2500 3000 3500 4000 F u n d a m en ta l v o lt a g e a m p li tu d e (V ) Speed (r/min) Ns/Nr = 6/10 Ns/Nr = 6/11 Ns/Nr = 6/13 Ns/Nr = 6/14 http://www.azojete.com.ng/ mailto:awahchukwuemeka@gmail.com Arid Zone Journal of Engineering, Technology and Environment, December 2024; Vol.20(4):879-890. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: awahchukwuemeka@gmail.com 884 (b) Voltage versus load current Figure 4: Comparison of voltage 3. (a) Outlines (b) Harmonics Figure 5: Torque comparison at constant copper loss, 30W 0 2 4 6 8 10 12 0 10 20 30 40 50 60 V o lt a g e a m p li tu d e (V o lt s) Applied load (Amperes) Ns/Nr = 6/10 Ns/Nr = 6/11 Ns/Nr = 6/13 Ns/Nr = 6/14 0 1 2 3 4 5 0 60 120 180 240 300 360 T o rq u e (N m ) Angular position (deg) Ns/Nr = 6/10 Ns/Nr = 6/11 Ns/Nr = 6/13 Ns/Nr = 6/14 0 1 2 3 4 5 0 1 2 3 4 5 6 7 8 9 T o rq u e (N m ) Spectra Ns/Nr = 6/10 Ns/Nr = 6/11 Ns/Nr = 6/13 Ns/Nr = 6/14 http://www.azojete.com.ng/ mailto:awahchukwuemeka@gmail.com Arid Zone Journal of Engineering, Technology and Environment, December 2024; Vol.20(4):879-890. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: awahchukwuemeka@gmail.com 885 The computed average torques at different current densities is compared in Figure 6 (a). The 6/13 machine produced the largest output torque at certain current density range, but 6/11 seems to possess highest ability to sustain electric overload at saturated condition. The 6/11 machine type is more promising in terms of its potential to generate the largest torque for a given volume of applied magnet material, as could be observed from Figure 6(b). Similarly, torque-speed routes of the analyzed machine types are presented in Figure 7. Although, 6/11 and 6/13 machine configurations have relatively high value of shaft torque compared to 6/10 and 6/14 equivalents, the latter has reasonably high speed coverage; which is an esteemed electric motor drive property. Nonetheless, the 6/10 and 6/14 machine categories may most likely face distortion issues during its drive period; particularly, at high speed, as could be observed from its reluctance torque outlines. (a) Torque versus current density 4. (b) Torque versus PM volume Figure 6: Torque comparisons at different load conditions 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 14 16 18 20 22 24 T o rq u e (N m ) Applied load (A/mm2) Ns/Nr = 6/10 Ns/Nr = 6/11 Ns/Nr = 6/13 Ns/Nr = 6/14 0 50 100 150 200 250 300 350 0 10 20 30 40 50 60 T o rq u e/ M a g n et v o lu m e (k N m /m 3 ) Applied load (Watts) Ns/Nr = 6/10 Ns/Nr = 6/11 Ns/Nr = 6/13 Ns/Nr = 6/14 http://www.azojete.com.ng/ mailto:awahchukwuemeka@gmail.com Arid Zone Journal of Engineering, Technology and Environment, December 2024; Vol.20(4):879-890. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: awahchukwuemeka@gmail.com 886 5. (a) 6/10 (b) 6/11 (c) 6/13 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 1000 2000 3000 4000 5000 6000 7000 8000 T o rq u e (N m ) Speed (r/min) Total output torque Magnet torque Reluctance torque -0.2 0.2 0.6 1 1.4 1.8 2.2 2.6 3 0 500 1000 1500 2000 2500 3000 3500 4000 T o rq u e (N m ) Speed (r/min) Total output torque Magnet torque Reluctance torque -0.2 0.2 0.6 1 1.4 1.8 2.2 2.6 3 0 1000 2000 3000 4000 5000 6000 7000 T o rq u e (N m ) Speed (r/min) Total output torque Magnet torque Reluctance torque http://www.azojete.com.ng/ mailto:awahchukwuemeka@gmail.com Arid Zone Journal of Engineering, Technology and Environment, December 2024; Vol.20(4):879-890. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: awahchukwuemeka@gmail.com 887 (d) 6/14 Figure 7: Torque characteristics Resulting torque ripple values of the investigated machine types are displayed in Figure 8. Again, the calculated torque ripples are in agreement with the observations of Figure 5. The 6/10 machine topology has consistently exhibited the most deplorable electric machine characteristics. Figure 8: Torque ripple magnitudes at 15A Magnetic force characteristics of the machine are presented in Figure 9. High value of unbalanced magnetic force (UMF) on the rotor is realized from the 6/11 machine type, this is followed by the 6/13 machine category. Negligible magnetic forces are obtained in the 6/10 and 6/14 machines types, owing to its suitable tooth and pole arrangements. This low value of magnetic force is a desired machine quality. Obviously, the resulting magnetic force would be large at low electric load condition, as shown in Fig. 9 (a) and (b). 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 1000 2000 3000 4000 5000 6000 7000 T o r q u e ( N m ) Speed (r/min) Total output torque Magnet torque Reluctance torque http://www.azojete.com.ng/ mailto:awahchukwuemeka@gmail.com Arid Zone Journal of Engineering, Technology and Environment, December 2024; Vol.20(4):879-890. ISSN 1596-2490; e-ISSN2545-5818; www.azojete.com.ng Corresponding author’s email address: awahchukwuemeka@gmail.com 888 (a) Force at 10 W (b) Force at 30 W Figure 9: Rotor magnetic force 4. Conclusion The impact of stator and rotor pole combinations of a dual stator permanent magnet machine is presented in this work. Most of the desirable machine outputs are produced by the machine type that is designated as 6/11; though, with a poorer speed coverage. It is observed that the machine types having 6/10 and 6/14 topologies exhibit poor output performances compared to its counterparts. Moreover, the machine type that is equipped with 13-pole would yield the most economic benefit, considering its higher torque in relation to the consumed lesser magnet material/volume. The analyzed machine would be most suitable in low speed and direct drive applications. The 6/11 machine type has the greatest potential against electromagnetic overloading; however, high amount of rotor magnetic force is also realized from the 6/11 machine type, and this is unattractive machine characteristics. References Ali, H., Sulaiman, E., Aziz, R., Jenal, M., Ahmad, MZ. and Khan, F. 2021. Review of double stator flux switching machines with various arrangements of excitation sources. Alexandria Engineering Journal, 60(5): 4393–4410. Awah, CC. 2022. Performance comparison of double stator permanent magnet machines. Archives of Electrical Engineering, 71(4): 829–850. 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The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 42(1): 250–260. http://www.azojete.com.ng/ mailto:awahchukwuemeka@gmail.com