Evaluation of a Prototype Magnetic Gear

Evaluation of a Prototype Magnetic Gear S. Gerber and R-J. Wang Department of Electrical and Electronic Engineering Stellenbosch University Matieland 72, South Africa Email: sgerber@sun.ac.za Abstract In this paper, the design of a prototype concentrictype magnetic gear is evaluated. The effects that the mechanical bridges connecting the modulator segments have on the performance of the gear have been analyzed by using detailed twodimensional (2D) finite element (FE) analysis. The magnetic gear suffers significantly from end-effects, which result in a considerable decrease in the peak torque capability as well as excessive losses under high-speed operation. Three-dimensional (D) FE analysis is employed to identify the origin of the undesired endeffects and to determine which structural components have the greatest negative impact. Insight is then gained into how the prototype could be modified to reduce these end-effects. I. I NTRODUCTION In recent years there has been growing interest in the research of magnetic gears. This can be attributed to the availability of high energy density magnetic material and more importantly the novel topologies that can significantly increase the torque density of magnetic gears [1]. The unique advantages of magnetic gears over their mechanical counterparts are contact-less torque transfer, inherent over-load protection, reduced noise, high efficiency and low or no maintenance operation. For these reasons, magnetic gears would be the preferred choice in certain demanding and safety critical applications. Furthermore, because magnetic gears typically have a much higher torque density than electrical machines, the overall system torque density can be improved when a magnetic gear is used in conjunction with a higherspeed electrical machine [2]. In this paper, the design of a prototype concentric-type magnetic gear, first presented in [], is critically examined. The effect of the modulator bridges on the air-gap flux density harmonics and thus the performance in terms of torque, as well as efficiency, is analyzed. The magnetic design of the gear was done by using 2D FE analysis. It is, however, found that the practical measurement results in terms of peak torque capability (stall torque) and efficiency fell far short of the predicted ones. Several papers [2], [4] [] also reported this discrepancy, but only mentioned that the decrease of the stall torque may be ascribed to end-effects without further analysis and explanation. This paper presents a detailed investigation of the end-effects in the prototype. Measures that could be taken to alleviate the negative impact of these effects are then proposed. Relevant conclusions are drawn from this investigation. 78-1-47-458-2/1/$1. 212 IEEE Figure 1. Cross-sectional view of the prototype magnetic gear. II. T HE PROTOTYPE MAGNETIC GEAR In this section, the electromagnetic design, the mechanical layout and the predicted and measured performance characteristics of the prototype magnetic gear are discussed. A. Magnetic design Fig. 1 shows a cross-sectional view of the prototype magnetic gear. The modulator is kept stationary while the inner high-speed (HS) and outer low-speed (LS) assemblies rotate. For this configuration, the gear ratio may be expressed as follows [2]: ns ph (1) Gr = ph where ns is the number of flux modulator segments and ph is the number of pole pairs on the HS rotor. The number of pole pairs on the LS rotor is given by pl = ns ph (2) The detailed dimensions of the prototype magnetic gear are given in Table I. The type of permanent magnets used in the prototype is N5 grade NdFeB magnets. The modulator and the LS yoke were fabricated using.5 mm, M-1 electrical laminations. In order to ease the construction and increase the torsional stiffness of the flux modulator, the segments were 1

Table I P ROTOTYPE DESIGN PARAMETERS Parameter Value HS magnet pitch [fraction of pole pitch]. LS magnet pitch [fraction of pole pitch].87 Modulator tooth pitch [fraction of segment pitch].447 HS yoke inner diameter [mm] 41 HS yoke thickness [mm] 18.8 HS magnet thickness [mm] 5 HS air-gap length [mm].7 Modulator thickness [mm] 7 Modulator bridge thickness [mm].5 LS air-gap length [mm].5 LS magnet thickness [mm] 5 LS yoke thickness [mm] 7.5 LS yoke outer diameter [mm] 1 Stack length [mm] 4 Number of HS pole pairs 2 Number of LS pole pairs 21 Gear ratio 1.5 Figure. Flux density distribution of the prototype magnetic gear obtained using 2D FE analysis. (a) No bridges on the modulator (b) Bridges added on the HS side of the modulator Figure 4. Figure 2. Three-quarter section view of the prototype magnetic gear showing mechanical support structure, HS and LS shafts. connected with thin bridges on the HS side. The modulator was constructed by placing stainless steel rods in the slots between the modulator segments and filling these slots with epoxy resin. The HS yoke was made of solid mild steel and integrated with the HS shaft as shown in Fig. 2, which also shows the modulator supported from the casing as well as the LS shaft. The flux density distribution of the magnetic gear at its maximum torque position obtained using 2D FE analysis is shown in Fig.. According to the 2D FE analysis, the Close-up view of the magnetic gear stall torque of the LS rotor is 5. Nm. This results in a torque density of 11 knm/m based on the active material volume. Bearing in mind that N5 are a low grade Neodymium magnets, this result seems to verify that stall torque densities exceeding 1 knm/m is practically achievable. B. Effect of the modulator bridges Fig. 4 shows the modulator of the magnetic gear without bridges and added. The radial flux density distribution in the HS air-gap due to HS magnets and LS magnets respectively are displayed in Fig. 5. Figs. and 7 show the radial air-gap flux density spectra in the HS and LS air-gaps respectively. It can be observed from Fig. that the bridges can suppress the undesired higher order harmonics (e.g. 21st and 25th harmonics) in the HS air-gap, which helps to minimis unwanted losses in the HS magnets and solid yoke. The fundamental harmonic (2nd) in the HS air-gap due to the HS magnets is actually slightly stronger. 2

Radial flux density [T] 2. 1.5 1..5..5 1. 1.5..2.4. Normalised angle.8 1..5.4..2.1. (a) Due to HS magnets Radial flux density [T].2.1..1.2..2.4. Normalised angle.8 1. Radial flux density waveform in the HS air-gap..8.4.2. Space harmonics present in the LS air-gap. 12.2 (b) Due to the LS magnets. Space harmonics present in the HS air-gap. However, this harmonic due to the LS magnets is slightly weaker. From Fig. 7 it is clear that the bridges have very little impact on the harmonics in the LS air-gap due to either the HS or LS magnets. In order to illustrate the benefits of reducing higher order harmonics in the HS air-gap, simulations of the gear with the HS rotor operating at a speed of 12 rpm was performed. 21 Torque [Nm] Figure. 4 2.1.2..4 Time [ms].5. Fig. 8 shows a comparison of the ohmic losses in the HS magnets. The losses are almost 4 times smaller in the case of the bridged modulator. The advantages in terms of torque ripple on the HS rotor is illustrated in Fig.. Two-dimensional FE analysis indicates that the stall torque of the gear is 52 Nm without bridges and 5.4 Nm with.4 Figure 8. Total ohmic losses in the HS magnets with the HS rotor rotating at 12 rpm.. 8..8 1 (a) Due to the HS magnets.. Figure 7..1. (b) Due to the LS magnets. Ohmic loss [W].8.7..5.4..2.1. 1. (b) Due to LS magnets Figure 5. (a) Due to the HS magnets..4. 2.8 2.7 2. 2.5 2.4 2. 2.2 2.1 2.. Figure..1.2..4 Time [ms].5. Torque on the HS rotor operating at a speed of 12 rpm.

25 4 2 Loss [W] Torque [Nm] 5 2 15 1 1 5 4 2 1 1 2 HS rotor angle [degrees] 4 Figure 1. Torque on the LS rotor vs. position of the HS rotor. The LS rotor is kept at a fixed position. The position at corresponds to the maximum torque position in Fig. Figure 12. 5 1 nhs [rpm] 15 2 Total no-load losses vs. speed of the high-speed rotor. 5 Efficiency [%] 85 8 75 7 5 Figure 11. Experimental setup used to test the prototype magnetic gear. bridges. Fig. 1 shows a plot of the torque on the LS rotor as a function of the HS rotor position. These results agree well with those presented in [5], which also indicate that bridges on the HS side of the modulator do not have a significant impact on the stall torque. Thus, in the case of this prototype, the bridged modulator shows not only the benefits of simplified mechanical construction, but also a distinct advantage of suppressing unwanted high order flux harmonics in the HS air-gap with little impact on the flux harmonics in the LS air-gap and the stall torque of the gear. C. Predicted versus measured results The experimental setup used to test the prototype is shown in Fig. 11. The measured stall torque of the LS rotor was only Nm which amounts to a 8% reduction when compared with that of 2D FE predicted results. Furthermore, the prototype suffered significantly from rotational losses as can be seen in Fig. 12 which shows the no-load losses of the gear as a function of the rotational speed. To identify the regions in the gear where the losses are concentrated, Thermax temperature indicators were placed at various parts of the prototype. A significant temperature rise was found on the side of the casing supporting the modulator during high speed operation, which is caused by the time-varying end leakage flux in the casing. These losses substantially decreased the efficiency of the prototype gear, especially at higher speeds. Fig. 1 shows the efficiency of the gear at a constant load of 2 Nm. III. A NALYSIS OF END - EFFECTS In this section, detailed D FE modeling of the prototype magnetic gear is presented. The purpose of this analysis is 5 1 nhs [rpm] 15 2 Figure 1. Efficiency vs. speed of the high-speed rotor at a constant load of 2 Nm. to determine the causes for the large difference between the results from 2D FE analysis and measurements. Simulations were performed using MagNet 7 from Infolytica Corporation. A. Laminated material modeling Considering the three-dimensional nature of the problem under investigation and specifically the deviation between 2D and D FE results, special attention was paid to the modeling of the laminated material used for the LS yoke and the modulator. Electrical laminations have significantly different BH-curves between the parallel and perpendicular directions to the lamination plane. To fully exploit the D FE computational advantage, this needs to be adequately accounted for in the D FE modeling. Given a BH-curve, B(H), for a uniform sample of steel, the BH-curves in the plane of the laminations, Bxy (H), and perpendicular to this plane, Bz (H), can be deduced from the following relations [7]: Bxy (H) = γb(h) + (1 γ)µ H B Hz (B) = γh(b) + (1 γ) µ () (4) with γ the stacking factor, taken as.5 in this study. The difference between a simple isotropic model and an anisotropic model of the laminated material is illustrated in Fig. 14, which shows the axial component of the flux density in the modulator for the model with the supporting casing described in the following section. This axial component of flux is not accounted for in 2D simulations. 22

B. Identification of end-effect origins (a) Isotropic BH-curve. (b) Anisotropic BH-curve. Figure 14. Flux density color map of Bz in the modulator for the model including the surrounding casing. φls RLS RLS LS RHS e yok φhs φleak F Rleak φleak Rleak RHS φhs r ato dul o M F et agn m HS e yok HS Figure 15. Simplified magnetic equivalent circuit explaining the mechanism behind the end-effects which have a negative impact on the performance of the gear. A simplified representation of the magnetic circuit of the gear is presented in Fig. 15. This circuit will be used throughout this section to describe the difference between the simulation models used to calculate the stall torque of the gear. Note that in this circuit, only the HS magnets are represented for the sake of simplicity. The principles discussed, however, are valid for both magnet layers. In Fig. 15, the sources represent the MMF of the north and south poles of the magnets. The reluctance, RHS, represents the total reluctance of the HS magnet and HS air-gap. Similarly, the reluctance, RLS, represents the equivalent air-gap on the LS side of the gear. The reluctance of the steel yokes and the modulator is considered negligible in this discussion. The leakage path reluctance is represented by Rleak. The results of the simulations in this section are summarized in Fig. 17, to which reference will be made in each case. The first step taken in the analysis of the end-effects was to do a D simulation of the ideal gear, i.e. without any structural parts in the model. The stall torque obtained in this way should be less than in a 2D simulation because in a 2D simulation Rleak =. Considering the D case, Rleak is always less than infinity and some leakage flux will exist. The stall torque obtained from the D simulation was 4. Nm (Fig. 17: D, ideal case), a drop of only 1% compared to the 2D value. From this, it appears that the torque reduction is not only caused by the unavoidable endeffects associated with the finite stack length, but also by the surrounding structural components that form part of the flux leakage path. In other words, the actual value of Rleak must be smaller than accounted for in this simulation. One difference between the prototype and the ideal D model was that the modulator in the prototype was slightly extended. This was done in the belief that this would enhance the coupling between the HS and LS rotors. Taking this extension of the modulator into account in the D model actually yielded a 5% lower stall torque of 44.2 Nm (Fig. 17: D, extended modulator). While it is true that the extended modulator increases the total flux linkage of the magnets, the assumption that this improves the torque capability of the gear is incorrect. What is important to the torque capability is the coupling of the appropriate harmonics between the HS and LS rotors. Extending the modulator results in a lower Rleak, resulting in a greater leakage flux, φleak. Because of the somewhat reduced overall reluctance seen by the HS magnets, the flux φhs increases and thus causes a larger MMF drop across the HS rotor reluctance, RHS. As a result of the above, the flux coupling to the LS rotor, φls, is actually reduced. This explanation is consistent with observations made in the D FE model, namely more flux linked by the HS magnets but reduced flux coupling to the LS rotor. In order to determine the cause of the additional drop in stall torque, a D simulation including all the relevant structural components in the model was done. This simulation reported a stall torque of only 5. Nm (Fig. 17: D, support 2

Torque [Nm] 5 4 2 1 2D case lator cture plied sured ed 1 ed 2 p ifi ifi a al ru du ide mo rt st ces a e me mod mod, D nded uppo leran totyp D, D, te to Pro,s, ex D D, D Figure 1. Flux density distribution plot clearly showing the severe leakage through the modulator supporting structure. Figure 17. structure). A flux density distribution plot produced by this simulation is shown in Fig. 1. It can be seen that flux leaks into the surrounding casing, especially where the modulator is supported. In terms of the circuit of Fig. 15, the effect of the casing is to reduce the leakage reluctance, Rleak, even further. Even with almost all the structural components included in the model, the simulated stall torque is still % higher than the measured result. This discrepancy is due to manufacturing tolerances, specifically the dimensions of the magnets, which is slightly smaller and unintentional skewing of the modulator. A simulation with the magnets within the tolerance specified and skewing the modulator by 1 electrical results in a stall torque of.5 Nm (Fig. 17: D, tolerances applied), which is very close to the measured results. IV. R ECOMMENDED DESIGN IMPROVEMENTS The simplest modification that can be made to the design that will significantly reduce the end-effects is to replace the connecting ring of the modulator with a nonmagnetic one. Making only this modification results in a stall torque of 41.5 Nm (Fig. 17: D, modified 1). Alternatively, if the supporting plate on the side connected to the modulator is replaced with a nonmagnetic one, the stall torque is 4.7 Nm (Fig. 17: D, modified 2). In both cases, however, the stall torque is still significantly lower than the ideal D case and it may be worthwhile to construct most of the casing from nonmagnetic material or to move the supporting casing further away from the active parts of the gear. Because the end-effects are significant in magnetic gears, the stack length should be included as a design variable whenever possible when design optimizations are performed. V. C ONCLUSIONS The evaluation of the design and end-effects of a prototype magnetic gear have been presented in the above sections. Introducing connecting bridges on the flux modulator helps simplify the construction and also dampen some potentially harmful harmonics in the HS air-gap. Two-dimensional FE analysis promises very good performance and indicates that torque densities exceeding 1 knm/m is practically achievable. However, end-effects have a significant detrimental impact on the stall torque capability of concentric magnetic gears and must be taken into consideration if accurate performance estimates are to be obtained. For concentric magnetic gears it is vitally important that the flux modulator is magnetically insulated. It must be kept in place by components with low permeability, e.g. austenitic stainless steel, aluminium or epoxy. Failure to do this can result in significant leakage flux, especially when surrounding structural parts are fabricated using soft magnetic materials. The leakage flux not only reduces the torque capability of the gear, but will also reduce the efficiency of the gear depending on the conductivity of the surrounding structural parts as well as the speed of operation. ACKNOWLEDGEMENT The authors would like to thank Mr. L. Bronn for his contribution in the design and construction of the prototype. This project is in part supported by the National Research Foundation (NRF) and Stellenbosch University, all of South Africa. R EFERENCES [1] K. Atallah and D. Howe, A novel high-performance magnetic gear, Magnetics, IEEE Transactions on, vol. 7, no. 4, pp. 2844 284, July 21. [2] K. Atallah, S. Calverley, and D. Howe, Design, analysis and realisation of a high-performance magnetic gear, Electric Power Applications, IEE Proceedings -, vol. 151, no. 2, pp. 15 14, March. [] L. Bro nn, R.-J. Wang, and M. J. Kamper, Development of a shutter type magnetic gear, in Proceedings of the 1th Southern African Universities Power Engineering Conference, 21. [4] P. Rasmussen, T. Andersen, F. Jorgensen, and O. Nielsen, Development of a high-performance magnetic gear, Industry Applications, IEEE Transactions on, vol. 41, no., pp. 74 77, May-June 25. [5] N. Frank and H. Toliyat, Analysis of the concentric planetary magnetic gear with strengthened stator and interior permanent magnet inner rotor, Industry Applications, IEEE Transactions on, vol. 47, no. 4, pp. 152 1, July-Aug 211. [] P. Rasmussen, T. V. Frandsen, K. K. Jensen, and K. Jessen, Experimental evaluation of a motor integrated permanent magnet gear, in Energy Conversion Congress and Exposition (ECCE), 211 IEEE, September 211, pp. 82 8. [7] J. Bastos and G. Quichaud, D modelling of a non-linear anisotropic lamination, Magnetics, IEEE Transactions on, vol. 21, no., pp. 2 2, Nov 185. Powered by TCPDF (www.tcpdf.org) Stall torque of the low-speed rotor from different sources.