Performance analysis of magnetic gear with Halbach array for high power and high speed

Abstract

In this study, we propose a non-contact 80 kW, 60,000 rpm coaxial magnetic gear (CMG) model for high speed and high power applications. Two models with the same power but different radial and axial sizes were optimized using response surface methodology. Both models employed a Halbach array to increase torque. Also, an edge fillet was applied to the radial magnetized permanent magnet to reduce torque ripple, and an axial gap was applied to the permanent magnet with a radial gap to reduce eddy current loss. The models were analyzed using 2-D and 3-D finite element analysis. The torque, torque ripple and eddy current loss were compared in both models according to the materials used, including Sm₂Co₁₇, NdFeBs (N42SH, N48SH). Also, the structural stability of the pole piece structure was investigated by forced vibration analysis. Critical speed results from rotordynamics analysis are also presented.

Keywords

Eddy current loss forced vibration analysis rotordynamics analysis Halbach array high speed and high power coaxial magnetic gear

1. Introduction

Mechanical gears have problems such as vibration, friction and heat. Magnetic gears are non-contact, and they have the following advantages over the mechanical gears: no friction, improved reliability, overload protection, and minimum acoustic noise. However, it is difficult to maintain mechanical concentricity with magnetic gears because of the double air gap. In addition, the magnetic gear transfers power through a magnetic field, so losses from the magnetic field must be taken into account. Since eddy current loss is dominant in magnetic gears, to reduce the eddy current loss we have proposed dividing the permanent magnets (PMs) in radial and axial directions.

Conventional magnetic gears used parallel axis gears and were unpopular because of their low torque density. Coaxial magnetic gears (CMGs) were developed to provide higher torque. These gears have a higher torque density than parallel axis magnetic gears because all of the PMs contribute to torque transfer at the same time [1–3]. With that factor in mind, we have employed a CMG with a Halbach array to increase the torque. The Halbach array, discovered by Mallinson, increases the magnetic field on one side, while the other side is canceled. The strong and weak sides of the magnetic field are determined by the direction of rotation. When the outer rotor rotates clockwise the fields are concentrated inside the array. On the other hand, when the inner rotor rotates counterclockwise the field is concentrated outside. Compared to conventional arrays, the magnetic field is stronger, and the control structure is simpler because it has a more purely sinusoidal curve. Also, it requires less shielding in the lower field areas [4,5].

Here we propose a Halbach model of 80 kW and 60,000 rpm for high speed and high power. The gear ratio is 10:1, the number of inner PMs is 8 and outer PMs is 80. This magnetic gear will be employed to replace the mechanical gear to the reducer in Vertical Take-off and Landing (VTOL) systems, as shown in Fig. 1. We studied two models with different radius and length with the same output power. Optimization was performed using statistical methods such as main effect analysis and response surface methodology (RSM). The final model was chosen considering torque, torque ripple, flux density and eddy current loss to improve performance. 2-D and 3-D performance analyses were performed using Ansys software. The eddy current loss in particularly was analyzed and compared using 3-D finite element analysis (FEA) to increase accuracy. In addition, the magnetic analysis was performed based on the material combinations used. Electrical steel 20PNF1200 for high speed application was employed as the core material to reduce core losses, and PM materials such as Sm₂Co₁₇ and NdFeB (N42SH, N48SH) were selected for performance.

Fig. 1.

Application of magnetic gear with quasi-Halbach array for VTOL system.

2. Magnetic gear with quasi-Halbach array considering torque ripple

Fig. 2.

Specifications of magnetic gears with surface-mounted PMs and quasi-Halbach array.

As shown in Fig. 2, the magnetic gear consists of an inner rotor (inner PMs and inner back yoke), an outer rotor (outer PMs and outer back yoke), pole pieces and double air gaps. The air gaps are between the inner PMs and the pole piece, the pole piece and the outer PMs. The relationship between pole pieces and inner and outer PMs becomes $\begin{eqnarray}\displaystyle n_{s}=p_{i}+p_{o} & & \displaystyle\end{eqnarray}$ (1) where p_i is the number of inner PM pole pairs, p_o is the number of outer PM pole pairs, and n_s is the number of pole pieces. When the pole pieces are fixed, the gear ratio G_r is given by $\begin{eqnarray}\displaystyle G_{r}=-(n_{s}-p_{i})/p_{i}=-p_{o}/p_{i}. & & \displaystyle\end{eqnarray}$ (2) The negative gear ratio means that the inner and outer rotors rotate in the opposite directions [1].

Torque ripple causes noise and vibration, so reducing torque ripple is essential. We propose applying an edge fillet to the PMs. Applying edge fillets to radial and circumferential magnetized PMs results in less torque than applying the edge fillet to radial magnetized PMs. Therefore, an edge fillet near the air gap was only applied to radial direction PMs in the inner and outer rotors. Figure 3 shows torque ripple depending on the edge fillet in the two models. The torque ripple was lowest with the 2 mm fillet. Above 2.5 mm the torque ripple increased. Therefore, the 2 mm fillet was applied considering torque maintenance.

Fig. 3.

Torque ripple results according to the edge fillet of radial direction PMs close to the air gap.

3. Magnetic performance analysis

3.1. Space harmonic analysis

Fig. 4.

Space harmonic analysis results for model A, B.

The magnetic fields generated in the inner and outer PMs of the magnetic gear are modulated by the pole pieces and produce space harmonics corresponding to each other’s pole pair. The number of pole pairs in the space harmonic flux density distribution is given by $\begin{eqnarray}\displaystyle p_{m,k}=|mp+kn_{s}| & & \displaystyle\end{eqnarray}$ (3) where p is the number of pole pairs per rotor, m is the space harmonic order of the magnetic flux density distribution equation and k is the space harmonic order in the modulation function. In the combination m = 1, k = −1, it has the largest value. Figure 4 shows the magnetic flux density distribution space harmonic order in the inner and outer air gaps. It can be seen that the 2^_nd harmonic order in the inner air gap and the 20^th harmonic order in the outer air gap have the highest values and correspond to the pole pairs of the inner and outer rotors [1,6]. These are the so-called working harmonics that contribute to torque.

3.2. Magnetic field distribution

When magnetic flux density is saturated, heat is generated. Therefore, it is necessary to check the magnetic flux density distribution. Figure 5 shows the flux density distribution of the two optimized models in 2-D. Both models used 20PNF1200 as a core material, and the saturation magnetic flux density of this material is 1.7 T. In Table 1, both models are reasonable because the maximum saturation magnetic flux density of the two models are below 1.7 T. Local magnetic flux density saturation occurs at the edge of the pole piece because of the magnetic flux concentrated on the pole piece, but this is an instantaneous value and can be ignored.

Table 1
Max. and RMS flux density of model A, B

Parameters Model A Model B

Max. flux density (T) RMS flux density (T) Max. flux density (T) RMS flux density (T)

Inner rotor 0.6 0.44 1.52 1.05

Outer rotor 1.46 0.99 1.68 1.11

Pole piece 1.3 0.67 1.17 0.6

Parameters	Model A	Model B
Inner rotor	0.6	0.44	1.52	1.05
Outer rotor	1.46	0.99	1.68	1.11
Pole piece	1.3	0.67	1.17	0.6

Fig. 5.

Flux density distributions of model A, B.

3.3. 3-D eddy current losses analysis

If the magnetic field of the conductor changes with time, an eddy current is generated by electromagnetic induction. Eddy current generates heat, which is called eddy current loss. The eddy current loss P_e can be expressed: $\begin{eqnarray}\displaystyle P_{e}=K_{e}(B_{max}tf)^{2} & & \displaystyle\end{eqnarray}$ (4) where K_e is the eddy current loss constant, B_max is the maximum magnetic flux density, t is the thickness of the PM and f is the frequency of the power source. Since the eddy current loss is related to the thickness of the PM, selecting the thickness of the PM per segment is an important factor [7].

Analyzing eddy current loss is necessary because it is related to efficiency. As shown in Fig. 6 and Table 2, axially divided PMs and air gaps in the axial and radial directions are proposed to reduce the eddy current loss. The losses and efficiency of the magnetic gear were confirmed and analyzed by 3-D analysis. The total loss in the 16 segments in both models was about 62% and 49% lower, respectively, than in the 1 segment.

Table 2

3-D performance analysis results of CMG with radial and axial gap

Model A		Axial division with radial gap				Model B		Axial division with radial gap
		1 segment		16 segments				1 segment		16 segments
Power (kW)		100.94		93.68		Power (kW)		89.29		96.03
Input speed (rpm)		60,000				Input speed (rpm)		60,000
Output speed (rpm)		6,000				Output speed (rpm)		6,000
Torque (Nm)		16.96		15.05		Torque (Nm)		14.39		15.39
Efficiency (%)		93.71		97.36		Efficiency (%)		94.44		97.29
Iron loss (kW)	PM loss (kW)	0.83	5.95	0.94	1.6	Iron loss (kW)	PM loss (kW)	0.88	4.38	1.29	1.39
Total loss (kW)		6.78		2.54		Total loss (kW)		5.26		2.68

Fig. 6.

Eddy current distributions of CMG with radial and axial gap.

4. Performance comparison by material combinations

Table 3 shows 2-D and 3-D magnetic analysis results for torque, power, core loss and PM loss for the developed models 16 divided segments, according to combinations of materials used. Since model B has more core, the core loss in Model B was about 300 W higher than Model A. Generally, neodymium magnets (NdFeBs) are used because of their strong magnetic field.

In this study, NdFeBs neodymium magnets (NdFeBs) were also used because of their strong magnetic field. NdFeBs (N42SH, N48SH) and samarium cobalt magnet (Sm₂Co₁₇) were compared to check torque and power characteristics of each material. The torque was highest when the PM material was N48SH, due to its strong magnetic field (N42SH:1.21 T, N48SH:1.28 T, Sm₂Co₁₇:1.06 T). Therefore, N48SH was more suitable for CMG, which requires high torque and high power. SmCo had lower torque than NdFeB because of a relatively weaker magnetic field.

If SmCo were used, the diameter or stack length would have to be greater than that of NdFeB to generate a similar output power. However, the thermal characteristic of SmCo (working temperature: 300-- 350 °C) is superior to that of NdFeB. Therefore, it is more suitable for aerospace, automotive, and similar applications, when a high working temperature is required.

Table 3
2-D and 3-D performance analysis results according to the combinations of materials used

Items (20PNF1200 material) Model A Model B

Sm₂ Co₁₇ NdFeB N42SH NdFeB N48SH Sm₂ Co₁₇ NdFeB N42SH NdFeB N48SH

2-D Torque Inner 12.73 15.54 16.62 12.73 15.68 16.83

(Nm) Outer 127.48 155.72 166.33 127.33 156.8 168.32

3-D (16 segments) Torque Inner 11.65 14.08 15.05 11.76 14.39 15.39

(Nm) Outer 113.27 139.23 149.1 115.04 142.11 152.84

Power (kW) 71.17 87.48 93.68 72.28 89.29 96.03

Efficiency (%) 96.53 97.44 97.36 96.54 97.37 97.28

Iron loss (kW) 0.7 0.86 0.94 0.97 1.19 1.29

PM loss (kW) 1.86 1.44 1.6 1.62 1.22 1.39

Total loss (kW, Iron loss + PM loss) 2.56 2.3 2.54 2.59 2.41 2.68

Items (20PNF1200 material)	Model A	Model B
2-D	Torque	Inner	12.73	15.54	16.62	12.73	15.68	16.83
	(Nm)	Outer	127.48	155.72	166.33	127.33	156.8	168.32
3-D (16 segments)	Torque	Inner	11.65	14.08	15.05	11.76	14.39	15.39
	(Nm)	Outer	113.27	139.23	149.1	115.04	142.11	152.84
	Power (kW)	71.17	87.48	93.68	72.28	89.29	96.03
	Efficiency (%)	96.53	97.44	97.36	96.54	97.37	97.28
	Iron loss (kW)	0.7	0.86	0.94	0.97	1.19	1.29
	PM loss (kW)	1.86	1.44	1.6	1.62	1.22	1.39
	Total loss (kW, Iron loss + PM loss)	2.56	2.3	2.54	2.59	2.41	2.68

5. Forced vibration analysis by magnetic force

Pole piece structures consist of laminated cores and supporting materials, so their structural stability is very weak. Therefore, the forced vibration analysis of magnetic gear must be considered. A forced vibration analysis was conducted by importing the magnetic forces applied to the pole piece. Figure 7 and Fig. 8 show the forced vibration according to pole passing frequency (60,000 × 4/60 = 4,000 Hz) [8]. It was confirmed that the maximum generated equivalent stress of both models was about 0.85 MPa and 2.07 MPa at the pole passing frequency, as shown in Fig. 7 and Fig. 8. The maximum yield strengths of the used materials were 115 MPa (PEEK) and 273 MPa (20PNF1200) respectively. It was structurally stable because the generated equivalent stress was within the yield strength of the used materials of the pole piece structure under forced vibration mode.

Fig. 7.

The results of force density and forced vibration stress results of model A.

Fig. 8.

The results of force density and forced vibration stress of model B.

6. Rotordynamics analysis

Rotordynamics analysis is essential to verify the presence of critical speeds within the operating speed range. The critical speed of the developed magnetic gear must be above the operating speed, 60,000 rpm in this case, to avoid resonance with the natural frequency of the rotating body. A 1^st forward whirling critical speed around 90,000 rpm was found for model A and model B in the rotordynamics analysis. Each model had sufficient separation margins, as shown in Fig. 9. Hence, the rotor structures of the two models were structurally stable, because there was no critical speed within the operating speed range.

Fig. 9.

Campbell diagrams of model A and B.

7. Conclusion

An 80 kW, 60,000 rpm CMG with Halbach array was successfully developed for a 10:1 reducer in a VTOL system, using magnetic and mechanical performance analyses. This study considered new ways to reduce torque ripple and eddy current losses. Torque ripples and eddy current losses were greatly reduced, by 50% or more, using an edge fillet on the radial magnetized PMs, and axial and radial PM gaps. 2-D and 3-D magnetic analyses for the developed models were conducted according to the of combinations of materials used, for high speed and high power. Also, the structural stabilities of the pole piece and rotor structure were verified by forced vibration analysis and rotordynamics analysis. These results have never been reported in previous CMG development journals, and represent a new approach for magnetic-mechanical coupled systems.

Footnotes

Acknowledgements

This research was supported by Korea Electrotechnology Research Institute (KERI) Primary research program through the National Research Council of Science & Technology (NST) funded by the Ministry of Science and ICT (MSIT) (No. 20A01018).

References

Atallah

Calverley

S.D.

and Howe

, Design, analysis and realisation of a high-performance magnetic gear, IEE Proceedings-Electric Power Applications151(2) (2004), 135–143.

Jian

and Chau

K.T.

, Analytical calculation of magnetic field distribution in coaxial magnetic gears, Progress in Electromagnetics Research92 (2009), 1–16.

Chau

K.T.

Cheng

and Hua

, Comparison of magnetic-geared permanent-magnet machines, Progress in Electromagnetics Research133 (2013), 177–198.

Choi

J.S.

and Yoo

J.H.

, Design of a Halbach magnet array based on optimization techniques, IEEE Transactions on Magnetics44(10) (2008), 2361–2366.

Jian

and Chau

K.T.

, A coaxial magnetic gear with Halbach permanent-magnet arrays, IEEE Transactions on Energy Conversion25(2) (2010), 319–328.

Shin

H.M.

and Chang

J.H.

, Design of coaxial magnetic gear for improvement of torque characteristics, Journal of Magnetics19(4) (2014), 393–3982.

Kim

S.H.

Kim

D.W.

Lee

D.Y.

Gim

C.S.

and Kim

Y.J.

, Analysis of efficiency and loss due to number of poles in magnetic gears, Journal of the Korea Institute of Electronic Communication Science13(5) (2018), 1023–1028.

Hong

D.K.

and Jeong

Y.H.

, Multiphysics analysis of a high speed PMSM for electric turbo charger, International Journal of Applied Electromagnetics and Mechanics59(3) (2019), 835–843.

Performance analysis of magnetic gear with Halbach array for high power and high speed

Abstract

Keywords

1. Introduction

3.1. Space harmonic analysis

Table 1 Max. and RMS flux density of model A, B Parameters Model A Model B Max. flux density (T) RMS flux density (T) Max. flux density (T) RMS flux density (T) Inner rotor 0.6 0.44 1.52 1.05 Outer rotor 1.46 0.99 1.68 1.11 Pole piece 1.3 0.67 1.17 0.6

Footnotes

Acknowledgements

References

Table 1
Max. and RMS flux density of model A, B

Parameters Model A Model B

Max. flux density (T) RMS flux density (T) Max. flux density (T) RMS flux density (T)

Inner rotor 0.6 0.44 1.52 1.05

Outer rotor 1.46 0.99 1.68 1.11

Pole piece 1.3 0.67 1.17 0.6