Title: Designing and experimentally testing a flux‐focusing axial flux magnetic gear for an ocean generator application
Abstract: IET Electric Power ApplicationsVolume 13, Issue 8 p. 1212-1218 Research ArticleFree Access Designing and experimentally testing a flux-focusing axial flux magnetic gear for an ocean generator application Mojtaba Bahrami Kouhshahi, orcid.org/0000-0001-9906-6090 Department of Electrical and Computer Engineering, Portland State University, 97201 Portland, OR, USASearch for more papers by this authorVedanadam M. Acharya, Department of Electrical and Computer Engineering, University of North Carolina at Charlotte, 28223 Charlotte, NC, USASearch for more papers by this authorMatthew Calvin, Department of Engineering Technology, University of North Carolina at Charlotte, 28223 Charlotte, NC, USASearch for more papers by this authorJonathan Z. Bird, Corresponding Author [email protected] Department of Electrical and Computer Engineering, Portland State University, 97201 Portland, OR, USASearch for more papers by this authorWesley Williams, Department of Engineering Technology, University of North Carolina at Charlotte, 28223 Charlotte, NC, USASearch for more papers by this author Mojtaba Bahrami Kouhshahi, orcid.org/0000-0001-9906-6090 Department of Electrical and Computer Engineering, Portland State University, 97201 Portland, OR, USASearch for more papers by this authorVedanadam M. Acharya, Department of Electrical and Computer Engineering, University of North Carolina at Charlotte, 28223 Charlotte, NC, USASearch for more papers by this authorMatthew Calvin, Department of Engineering Technology, University of North Carolina at Charlotte, 28223 Charlotte, NC, USASearch for more papers by this authorJonathan Z. Bird, Corresponding Author [email protected] Department of Electrical and Computer Engineering, Portland State University, 97201 Portland, OR, USASearch for more papers by this authorWesley Williams, Department of Engineering Technology, University of North Carolina at Charlotte, 28223 Charlotte, NC, USASearch for more papers by this author First published: 27 June 2019 https://doi.org/10.1049/iet-epa.2018.5931Citations: 6AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract The torque density characteristics for an axial flux magnetic gear using a flux-focusing topology is experimentally studied when using neodymium iron boron (NdFeB) rare-earth magnets. A geometric parameter sweep analysis was utilised in order to maximise both the calculated volumetric and mass torque density. The calculated torque and torque density was 628.6 N·m and 173.02 N·m/L while the experimentally measured torque and resultant torque density was 553.2 N·m and 152.3 N·m/L. 1 Introduction The very low rotational speeds created by ocean and wind renewable energy devices necessitate the need for the use of a mechanical gearing system or a very large direct-drive generator. Neither solution is ideal since the gearbox creates serious reliability and maintenance issues [1] and the direct-drive generators are very large in size [2]. The magnetic gear (MG) is becoming a contender for use in such low-speed, high torque, renewable energy applications [3, 4]. As a MG does not have the thermal torque density limiting characteristics associated with direct-drive generators a very high magnetic shear stress can be maintained in the air-gap. For instance, experimentally tested cycloidal and flux-modulating MGs have been demonstrated that can operate >200 N·m/L [5, 6]. The contactless speed conversion of the MG makes it particularly useful for applications in which reliability is paramount, as is required in marine hydrokinetic ocean generators. The non-contact torque–speed conversion operation also offers the potential for increasing generator operating efficiency. Cycloidal MGs [6-9] can simultaneously operate with a high torque density and high gear ratio; however, the radial cycloidal typology uses an eccentric air-gap, and this results in a large eccentric radial force that can seriously degrade the bearing life. Davey proposed and experimentally tested a 30:1 axial cycloidal typology in [8] which holds promise because it reduces the bearing wear problem. However, Davey's design only experimentally achieved a 14 N·m/L torque density and therefore higher torque density prototypes still need to be demonstrated. Radial coaxial MGs, as shown in Fig. 1a, create speed change using a central field modulation rotor, these MG designs have been studied to the greatest extent. In order to create field modulation coupling the slot and pole combination must satisfy (1) Fig. 1Open in figure viewerPowerPoint Radial and axial-flux MGs (a) An example of a radial coaxial MG, (b) A surface-mounted axial MG, (c) A flux-focusing axial MG. In each design the high-speed rotor has p1 = 6 pole-pairs, the low-speed rotor has n2 = 25 ferromagnetic segments and the fixed rotor has p3 = 19 pole-pairs. While the gear ratios are not as high in these MGs compared with cycloidal MGs both a high torque density and balanced air-gap bearing force have been demonstrated [10-12]. An axial version with surface-mounted permanent magnets (PMs) has also been proposed [13]. The axial field modulation typology is shown in Fig. 1b. The axial MG enables the axial stack length to be short. However, a robust mechanical structure is needed to maintain the small air-gap. Mezani et al. [13] first demonstrated the performance of a 5.75:1 axial flux MG and calculated that a 70 N·m/L torque density could be achieved when using a 200 mm outer diameter. Subsequently, Johnson et al. [14] and Hirata et al. [15] experimentally studied surface-mounted axial MGs, however, both designs did not achieve torque densities greater than equivalent direct-drive generators. For instance, the axial surface-mounted MG design tested by Johnson et al. had a 6.67:1 gear ratio with a 5 mm air-gap, the resulted torque density was only 22 N·m/L. Gardner et al. [16] recently conducted a sizing analysis for surface-mounted axial and radial MGs and showed that while the radial MG often can have a higher torque density the axial MG can be better when a short axial length is needed or when the outer diameter is large. In order to increase the torque density Halbach rotor and flux-focusing axial rotor typologies have also been investigated. Johnson et al. [17] showed that using a Halbach rotor magnet typology the torque density could be increased 65% relative to the equivalently sized surface-mounted magnet rotor design. However, the Halbach magnets are difficult to mechanically assemble. A flux-focusing axial MG typology was first studied by Acharya et al. [18]. An example of a flux-focusing axial MG is shown in Fig. 1c. The torque density in a flux-focusing rotor typology can be increased by changing the magnet area facing the rotor air-gap. Acharya et al. [18, 19] calculated that a 4.16:1 gear ratio flux-focusing axial MG could operate with a torque density of 257.6 N·m/L when using an outer diameter of 280 mm [20]. Yin et al. [21] suggested that this torque density could be increased further by utilising the transverse radial flux that is present in the flux-focusing typology and Yin et al. [21] calculated that the torque density could be as high as 282 N·m/L. However, Yin's proposed design would be mechanically challenging to fabricate. In [22] an interesting 3-D printed flux-focusing axial MG was presented by Tsai et al. The 4.16:1 gear ratio design used ferrite magnets and so the torque density was only 3 N·m/L. A disadvantage of the flux-focusing MG rotor topology is that the magnitude of the higher order rotor harmonics can be quite high. Recently, Dong et al. [23] has proposed to further increase the torque density of axial MGs by utilising bulk superconducting magnets. However, only initial simulation analysis results were presented. It may be advantageous to consider using the superconducting magnets on the non-rotating high-pole count rotor as this would then enable it to be cooled with relative ease. A number of authors have tried to combine an axial flux MG with a stator. For instance, Bronn designed an axial flux MG with an integrated axial stator [24, 25]. Bronn computed that the torque density would be 105 N·m/L when using an outer radius of 320 mm; however, the measured torque density was reduced to 34.8 N·m/L due to the 4 mm air-gap that was used. Johnson et al. [26] also integrated a stator into a 9.33:1 gear ratio axial MG, the stator was inserted within the inner radius of the MG structure. While the simulated torque density was 60 N·m/L the experimentally tested axial MG only achieved a 10.4 N·m/L torque density when using a 260 mm diameter rotor. This was in part due to the 4.8 mm air-gap that was used. Researchers have also proposed replacing one of the MG rotors with a stator [27] while this does enable a variable gear ratio to be achieved it results in the torque density being no higher than when using a direct-drive motor [28]. This paper tries to add to the body of research on axial flux MGs by presenting the design and experimental testing of a flux-focusing axial MG. The paper first summarises the analysis work discussed in [19, 20] and then presents the experimental verification of the flux-focusing axial-flux MG. Unlike in [25, 26] a small air-gap was maintained so as to try to maximise the torque density capability of the axial MG typology. 2 Axial flux MG operating principle The flux-focusing axial MG structure being studied is shown in Fig. 1c—it contains p1 = 6 pole-pairs on the high speed rotor (HSR), p3 = 19 pole-pairs on the stationary rotor and n2 = 25 ferromagnetic steel slots on the low speed rotor (LSR). The central modulation rotor is the LSR as it has two air-gaps and so it experiences the highest torque. With ω3 = 0 this pole combination yields the speed relationship [29] (2) where the gear ratio is Gr = n2/p1 = 4.16. This gear ratio has a repeating decimal term that limits the number of non-fundamental harmonics that interfere to create torque ripple. The cogging factor for this design is 1 [20]. The operation of the axial MG can be understood by considering the superposition of the air-gap fields created within the MG. Fig. 2a shows the axial flux density near the fixed rotor due to the p1 = 6 pole-pairs on the HSR (rotor 1), with and without the n2 = 25 modulation slots. The corresponding spatial harmonics for these two cases is shown in Fig. 2b. It can be seen that without the LSR the p1 = 6 pole-pair harmonic is dominant, and the following additional harmonics are also created: (3) where k = 2, 3, … . Fig. 2Open in figure viewerPowerPoint Axial flux density, Bz, near the fixed rotor 3 due to magnets only on the high-speed rotor (rotor 1) with and without the n2 = 25 LSR slots (a) Waveforms, (b) Corresponding harmonics. The field is plotted at a radius of r = 137 mm and at an axial distance of 0.5 mm With the n2 = 25 slots added the HSR rotor field is modulated via the Prosthaphaeresis identity, giving rise to the additional positive-valued harmonic terms: (4) where m = 1, 2, 3, … . The parameters for the experimental design shown in Table 1 were used to create these plots. Table 1. Initial, final and experimental prototype geometric parameter Parameter Value Unit Initial Final Experiment High speed rotor pole-pairs, p1 6 6 6 — steel pole span, θ1s 15 15 15.6 deg axial length, l1s 40 25 27 mm air-gap length, g 0.5 0.5 1 mm concentration ratio, C1 6.8 1.7 1.9 — Low speed rotor pole pieces, n2 25 25 25 — steel pole span, θ2s 10 8.5 9.5 deg axial length, l2s 8 8 8 mm pole pairs, p3 19 19 19 – Fixed rotor pole span, θ3s 4.74 4.74 4.96 deg axial length, l3s 30 15 22 mm concentration ratio, C3 16.1 3.3 4.8 — MG radial outer radius, ro 55 140 140 mm inner radius, ri 35 80 80 mm Material NdFeB magnet, Br, NMX-40CH 1.25 T 1080 steel resistivity 18 μΩ-cm 430FR steel resistivity 76.4 — μΩ-cm 416 steel resistivity — 57.0 μΩ-cm Fig. 3 shows the spatial harmonic content of the modulated axial flux density next to the HSR when only the fixed p3 = 19 pole-pairs are present. In this case, the fixed rotor creates the harmonics: (5) and with the n2 = 25 LSR slots present the additional positive-valued modulated harmonics are: (6) Fig. 3Open in figure viewerPowerPoint Axial flux density, Bz, near the high-speed rotor due to magnets only on the fixed rotor 3 with and without the n2 = 25 LSR slots (a) Waveforms, (b) Corresponding harmonics. The field is plotted at a radius of r = 137 mm and at an axial distance of 0.5 mm It is interesting to note that the higher odd harmonics associated with both the p1 and p3 pole-pairs don't meaningfully interact with the LSR slot harmonics. 3 Parametric sweep analysis In order to develop a design that could be constructed a 3-D finite element analysis (FEA) parameter sweep analysis was conducted using JMAG software. The initial geometric and material parameters used in the analysis are shown in Fig. 4 and defined in Table 1. The magnets were Nd–Fe–B magnet (grade NMX-40CH, with residual flux density, Br = 1.25 T), the HSR and stationary ferromagnetic poles were assumed to be made of 1080 steel and the low-speed rotor poles were assumed to be made of 430FR steel. Fig. 4Open in figure viewerPowerPoint Geometric parameters used in the axial MG analysis The original intent of the parameter sweep analysis was to develop a good, but not optimal, design that could be constructed quickly. As only a few key geometric parameters were studied the use of a simple parameter sweep technique provided key physical trade-off insights. The mass torque density defined as (7) where m1, m2 and m3 are the mass of rotor 1, rotor 2 and rotor 3, respectively. The volumetric torque density, defined as (8) are the primary objective functions used in the sweep analysis. In the parameter analysis, the HSR and LSR magnet and steel pole span are equal such that (9) and (10) The flux focusing was achieved by increasing the ratio between the steel pole magnet surface area and the steel pole area facing the air-gap. For the HSR, the flux-focusing ratio is defined as [18] (11) and for fixed rotor it is given by (12) In order to increase the torque density a parameter sweep was conducted that involved sweeping both the outer radius ro and inner radius ri of the axial MG while keeping all other variables constant it can be seen from Figs. 5 and 6 that by doing this the peak volumetric torque density keeps increasing with an increasing outer radius and a decreasing inner radius but the mass torque density is maximised at a specific inner radius value. Fig. 5Open in figure viewerPowerPoint Volume torque density as a function of outer radius, ro, and inner radius ri Fig. 6Open in figure viewerPowerPoint Mass torque density as a function of outer radius, ro, and inner radius, ri Curves in Figs. 5 and 6 for respective outer radii are almost parallel to each other, which implies that the volumetric and mass torque densities change with ri and ro independently from other geometric parameters. Therefore, in order to maximise mass torque density, the outer radius was chosen to be ro = 140 mm and the inner radius was chosen to be ri = 80 mm. Further parameter variation was then carried out by consecutively changing the axial lengths l1s, l2s, l3s and angular span θ2s. Fig. 7 shows how the peak torque density changes when l1s was varied while keeping all other variables constant. The peak torque density was at l1s = 25 mm. Then keeping l1s = 25 mm fixed l3s was varied, as shown in Fig. 8, and this resulted in l3s = 15 mm yielding a calculated peak volumetric and mass torque density of 252.6 N·m/L and 52.3 N·m/kg, respectively. Fig. 7Open in figure viewerPowerPoint Volume and mass torque density as a function of LSR axial length, l1s Fig. 8Open in figure viewerPowerPoint Volume and mass torque density as a function of stationary rotor axial length, l3s With l1s and l3s held fixed Fig. 9 shows how the torque density changed with variations in the LSR pole arc span, θ2s. It can be seen that the peak torque density was maximum when θ2s = 8.5°. Keeping θ2s = 8.5° and only changing the LSR axial length l2s Fig. 10 was obtained. It is observed that a peak torque density occurs at l2s = 8 mm. Fig. 9Open in figure viewerPowerPoint Volume and mass torque density as a function of LSR steel pole span, θ2s Fig. 10Open in figure viewerPowerPoint Volume and mass torque density as a function of LSR axial length, l2s The final obtained values from this basic variable sweep are shown in Table 1. Using the final geometric values, a pole-slip plot as shown in Fig. 11 was created. Under magnetostatic conditions, the rotor torques must satisfy (13) Fig. 11Open in figure viewerPowerPoint Torque as a function of pole slip angle on different parts when using final geometric parameters The MG rotors pole slipped when the LSR torque exceeded T2 = 869.4 N·m. The calculated volumetric and mass torque density using the final active region geometric parameters was 289.8 N·m/L and 60.7 N·m/kg, respectively [19]. 4 Experimental prototype In order to fabricate the axial MG as well as lower its construction cost rectangular magnets were utilised. The dimensions for the HSR magnets were 36 × 60 × 25 mm3 and the fixed rotor magnets dimensions were 11 × 60 × 20 mm3. In order to retain the magnets in place a magnet retaining lip on the LSR and HSR steel poles was also added, this increased the axial length on both rotors by 2 mm. In addition, for mechanical stiffness reasons the axial length of the fixed rotor was increased by further 5 mm and for mechanical assembly purposes the air-gap was increased to g = 1 mm. All of these dimensional design changes are summarised in Table 1. An exploded view of the final experimental prototype is shown in Fig. 12. Fig. 12Open in figure viewerPowerPoint Exploded view of the experimental prototype The JMAG 3-D magnetostatic FEA calculated torque, on different parts of the experimental prototype, when only the LSR is rotating, is shown in Fig. 13. In order to obtain an accurate result 16.5 million mesh elements were used, with a 2 ms time step size. The maximum calculated torque on the LSR was T2 = 628.6 N·m, which resulted in the torque density reducing to 173.2 N·m/L. Fig. 13Open in figure viewerPowerPoint Torque on different parts of the AFMG when LSR was rotated with practical design considerations The torque and axial force on the different parts of the axial-flux MG when both the HSR and LSR were rotated at the peak torque angle are shown in Figs. 14 and 15, respectively. The large axial forces created challenges when trying to maintain a uniform air-gap. An outer ring bearing was added as shown in Fig. 12 to help maintain a uniform air-gap. Fig. 14Open in figure viewerPowerPoint Torque on different parts of the axial-flux MG when both rotors were rotated with practical design considerations Fig. 15Open in figure viewerPowerPoint Axial force on different parts of the axial-flux MG with practical design considerations when both rotors were rotated 5 Experimental results The experimentally constructed HSR, LSR and fixed rotor are shown in Fig. 16. The measured axial magnetic flux density, Bz, when the rotors are surrounded by air for the high-speed rotor is compared in Fig. 17. While Fig. 18 shows the field comparison next to the fixed rotor. The high-speed rotor's measured 6th harmonic and fixed rotor's measured 19th harmonic are, respectively, 1.7 and 5.2% lower than calculated. These values are different from reported values in [30] because wrong dimensions for the gauss metre probe were considered. This resulted in a larger difference between FEA and measured values. As the fixed rotor contains a higher number of poles the measurement accuracy is less than that for the HSR, and larger discrepancy in this case could be partly related to measurement error. Fig. 16Open in figure viewerPowerPoint Experimentally assembled axial flux-focusing MG (a) High-speed rotor, (b) Low-speed rotor, (c) Fixed rotor Fig. 17Open in figure viewerPowerPoint HSR axial magnetic flux density at a radius of r = 137 mm and at an axial distance of 1.04 mm above the rotor when surrounded by air (a) Waveforms, (b) Corresponding spatial harmonic comparison showing the 6th, 18th, 30th and 42nd harmonic for the measured and FEA calculated axial flux density Fig. 18Open in figure viewerPowerPoint Fixed rotor axial magnetic flux density when the rotor surrounded by air at a radius of r = 137 mm and at an axial distance of 1.04 mm above the rotor when surrounded by air (a) Waveforms, (b) Corresponding harmonic analysis showing the 19th, 57th, 95th and 133rd harmonic for the measured and FEA calculated axial flux density The axial MG assembly on the test bed is shown in Fig. 19. The LSR was driven by an induction motor, while the high-speed rotor was connected to a PM generator. The high-speed rotor was rotated at ω1 = 50 rpm and using the torque control method, a stepped load torque was applied to the MG until it reached the pole-slip torque point. The resulted torque plot is shown in Fig. 20. The peak measured torque was 553.2 N·m which resulted in the measured active region volumetric and mass torque density being 152.3 N·m/L and 42.3 N·m/kg, respectively. This is 12% lower than calculated. The reason for this discrepancy is believed to be primarily due to the mechanical frictional losses within the axial bearings as well as for the unaccounted-for eddy current losses within the solid steel poles and support mechanical structure. The large axial forces present within the MG create significant challenges with respect to mechanical construction and will cause mechanical losses within the bearings. Fig. 19Open in figure viewerPowerPoint Axial MG on the test bed Fig. 20Open in figure viewerPowerPoint Measured torque on high speed and LSRs The measured no-load torque on the high speed and LSR is shown in Fig. 21. Whilst Fig. 22 shows the power loss as a function of load. It can be seen that the power loss does not change with increasing load when the MG input speed is held fixed at ω1 = 50 rpm. This therefore results in the efficiency increasing significantly with increased applied load. The measured torque ripple as a function of the load for the low speed and HSRs is shown in Figs. 23 and 24, respectively. As can be seen the torque ripple for different loads is relatively unchanged, this results in a very high percentage torque ripple at light loads. A summary of the above experimental analysis results is given in Table 2. Table 2. Measured average torque and calculated power, loss and efficiency at each load step Load, % Power loss, W Efficiency Torque ripple, N·m HSR LSR 0 49.2 43.07 11.55 19.58 20 48.1 63.02 9.01 15.06 36 50.5 77.41 10.28 16.64 52 50.6 84.06 10.89 15.96 68 50.0 87.86 11.46 16.72 84 49.8 90.01 11.67 17.55 100 49.6 91.79 12.18 16.64 Fig. 21Open in figure viewerPowerPoint Measured no-load torque on low speed and high-speed rotors Fig. 22Open in figure viewerPowerPoint Power loss and efficiency as a function of the load torque at 50 rpm HSR speed Fig. 23Open in figure viewerPowerPoint Torque ripple as a function of load for LSR Fig. 24Open in figure viewerPowerPoint Torque ripple as a function of load for HSR 6 Conclusion The design and experimental performance of an axial flux-focusing MG have been presented for the first time. The experimentally tested axial MG had a peak torque of 553.2 N·m which resulted in an active region torque density of 152.3 N·m/L. While this is 12% lower than the calculated value it is significantly higher than prior tested axial MGs. The large axial forces present within the axial MG created significant construction and testing challenges with respect to maintaining the mechanical air-gap. An additional outer bearing needed to be retrofitted to create air-gap uniformity. The MG power loss was shown to not increase with load and therefore, good efficiency was demonstrated at the high torque, low speed operating conditions that were tested. It was also shown that the torque ripple does not depend on the load and this therefore resulted in a high torque ripple at low load conditions. 7 Acknowledgments The authors would gratefully like to thank the JMAG Corporation for the use of their FEA software. 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