Initial design of two-stage magnetic gear for high power density according to gear ratio

Abstract

The magnetic gears which can replace the mechanical gear system are actively studied recently. Improving the power density is growing importance because the characteristics that as gear ratio grows so power density decreases were observed. This paper analyzes the various characteristics (power density, efficiency, torque ripple, loss, and so on) according to the gear ratio in detail, and proposes a concept that high gear ratio by combining two low gear ratio. A target gear ratio is 10 to 1 and application is 1 kW wind turbine. To obtain the optimal combination, 30 gear ratios were considered, and initial design process was shown about this concept to propose the direction of improving the power density. All models were analyzed with 2D-FEM by numerical analysis.

Keywords

Finite element analysis magnetic gears power density high gear ratio

1. Introduction

Mechanical gearboxes employed in a wind turbine are used to increase the rotor speed of the generator. Gears transfer power by gear teeth interlocking but it generates vibration and friction loss. The vibration and friction cause some wear and damage on the gears, and eventually increase maintenance costs [1–3]. Because magnetic gears which have no mechanical contact are suit to address those problems, lots of researches have been conducted over the past few decades [4–7]. Here are major two advantages of magnetic gears: First, problems caused by physical contact such as vibration, noise, equipment wear, and damage do not exist. Second, when the gear overloaded, it would be slipped and protects the gear, then makes each rotor working respectively [7–9].

Among various type of magnetic gears, a coaxial magnetic gear is selected due to high power density in this research. The gear ratio of the coaxial magnetic gear which is first proposed by Atallah is established by the number of poles in the permanent magnets attached to two rotors. If there are one pair of magnets on a first rotor, it would be needed fifty pair of magnets on the other rotor to make a 100:1 gear ratio. However, employing many magnets on a rotor leads to problems such as a power density reduction and increasing the cost of the manufacturing. It is very simple to overcome if only low gear ratio is used. Based on this idea, a two-stage magnetic gear is proposed [10,11]. It is able to make high gear ratio only using two low-gear ratios. Those past papers shown that two-stage magnetic gears (100:1) have a higher power density than single coaxial magnetic gear (100:1). However, they didn’t research in detail. Only one case was considered among the various parameters.

In this study, it has been performed that initial research on developing a two-stage magnetic gear with a 10:1 gear ratio to apply to an 1 kW wind turbine for the base study of 100:1 and prototype of the laboratory level. The two-stage magnetic gear employs two coaxial magnetic gears that called a primary magnetic gear and a secondary magnetic gear. First, torque ripple, power density, loss, and efficiency of single coaxial magnetic gears are analyzed according to gear ratios, through the 2D-FEM. Second, summary graphs are created according to the characteristics respectively. The last, the most suitable gear ratio of the secondary magnetic gear is shown for each characteristic of the coaxial magnetic gear.

2. Two-stage magnetic gear

2.1. Structure and principle of magnetic gear

As shown in Fig. 1, coaxial magnetic gears are mainly composed of three parts: inner rotors and outer rotors, and pole pieces. Two rotors rotate independently. Pole pieces transfer the magnetic flux between the two rotors and they are the most important part of making a gear ratio. Permanent magnets are attached to the two rotors, and the gear ratio is determined by the number of inner and outer poles. Normally, the number of permanent-magnet poles on the inner rotor is designed to be smaller than that of the outer rotor, and the inner rotor rotates with higher speeds and less torque than the outer rotor.

Fig. 1.

Structure of a traditional coaxial magnetic gear.

Equation (1) shows the relationship between the gear ratio of the coaxial magnetic gear and speed, and torque. The minus sign indicates that the torque and the rotation direction of the two rotors are opposites. Here, P _o and P _i are the number of poles on the outer rotor and inner rotor, respectively. ω_o and ω_i are the rotational speeds of the outer rotor and inner rotor, respectively. τ_o and τ_i are the torque of the outer rotor and inner rotor, respectively [7–9]. $\begin{eqnarray}\displaystyle \text{Gear ratio}=\frac{-P_{o}}{P_{i}}=\frac{{\omega}_{i}}{{\omega}_{o}}=\frac{{\tau}_{o}}{{\tau}_{i}}. & & \displaystyle\end{eqnarray}$ (1)

The pole pieces adjust the direction of the inner rotor magnetic flux and the outer rotor magnetic flux by altering the gap flux between the two rotors. The number of pole pieces N _p is expressed in (2) [7–9]. $\begin{eqnarray}\displaystyle N_{p}=\frac{P_{o}+P_{i}}{2}. & & \displaystyle\end{eqnarray}$ (2)

2.2. Background of two-stage magnetic gear

As mentioned, in a coaxial magnetic gear, the gear ratio is determined by the number of poles of the two rotors. Therefore, the following analysis is performed to determine the relationship between the gear ratio and the output. The number of poles on the inner rotors of all the coaxial magnetic gear models was fixed at two, and the number of poles on the outer rotors are increased from 4 to 40 by units of two poles. Their volumes of magnets and steel-sheets are fixed, and gear ratios are between 2 and 20. As shown in Fig. 2, the results shows that the outer power is highest when the gear ratio is 4. Increasing waveform is shown from 2 to 4 and decreasing is shown after 4. However, inner power decreased as the gear ratio increased. It can be expected that using a small gear ratio, approximately 4, will be beneficial in terms of power density. Based on previous research [10,11], and those results, it can be confirmed that possibility of coaxial magnetic gear with high power density and high gear ratio through the two-stage magnetic gear.

Fig. 2.

Gear ratio vs. power of magnetic gear.

The two-stage magnetic gear was proposed to deal with power density problem, and its structure is shown in Fig. 3. It is composed of a primary magnetic gear, a secondary magnetic gear, and couplings. The coupling that links the two magnetic gears performs the role of transferring the primary magnetic gear’s output to the input axis of the secondary magnetic gear. In this manner, the overall gear ratio of the two-stage magnetic gear is the product of two gear ratios, as in (3). $\begin{eqnarray}\displaystyle R_{o}=R_{1}\times R_{2} & & \displaystyle\end{eqnarray}$ (3) where, R _o is the overall gear ratio of the two-stage magnetic gear, and R ₁ and R ₂ are the gear ratio of the primary and secondary magnetic gears, respectively. From this principle, two-stage magnetic gear is able to achieve a higher power density than single magnetic gear. Aside from power density, there are several indicators that demonstrate the performance of a magnetic gear, such as torque ripple, loss, and output. A comprehensive comparative analysis is needed to determine whether using a two-stage magnetic gear is truly advantageous.

Fig. 3.

Structure of two-stage magnetic gear.

Table 1

Gear ratio of two-stage magnetic gears

Primary magnetic gear	Secondary magnetic gear	Overall
1.5	6.67
2	5 (overlap)
2.5	4 (overlap)
3	3.33
3.5	2.86
4	2.5 (overlap)
4.5	2.22
5	2 (overlap)
5.5	1.82	10
6	1.67
6.5	1.54
7	1.43
7.5	1.33
8	1.25
8.5	1.18
9	1.11
9.5	1.05

Fig. 4.

The standard model of a magnetic gear (Gear ratio: 2).

Table 2

Specification of the standard coaxial magnetic gear model

Item		Value	Unit
B _r of magnet material		1.0	T
Material of steel sheet		35JN230	-
		63	mm
Thickness	Outer PM	3.5	mm
	Inner PM	3.5	mm
Velocity	Outer rotor	2,000	rpm
	Inner rotor	4000	rpm
Torque	Outer rotor	6.6	Nm
	Inner rotor	2.5	Nm
Power	Outer rotor	1,391	W
	Inner rotor	1,046	W
Efficiency		74	%

Table 1 shows the possible combinations of 10:1 gear ratios. There are 30 single gear ratios because some gear ratios are overlapped. To design the standard coaxial magnetic gear models, 2:1 gear ratio model is selected as shown in Fig. 4. Table 2 shows the specification of the standard model and the attached magnets are NdFeB series. Each model was designed by changing the number of magnets with some conditions; fixed the inner rotor external diameter, fixed the outer rotor internal diameter, fixed the cross sectional area of the pole pieces, fixed the thickness of the magnets, and fixed the length of the air gaps between two rotors and the pole piece structure. They are designed 1 kW power, 2.5 Nm inner torque, and 4,000 rpm inner speed as an output power of the coaxial magnetic gear. Additionally, models which have same gear ratio but different the number of poles are analyzed to determine an optimal number of poles.

3. Characteristics analysis of coaxial magnetic gear

3.1. Power density

Power density is an important characteristic because it is directly related to the size and manufacturing cost of the electrical equipment. The output of each rotor was divided by the total weight of the coaxial magnetic gear, and they are compared how much power was output per unit weight. Figure 5 shows the mean, standard deviation, and minimum and maximum power densities of the magnetic gears by each gear ratio. Four different number of poles are employed to one gear ratio. For instance, 2:1 gear ratio could be consist of 2 inner poles and 4 outer poles, 4 inner poles and 8 outer poles, 6 inner poles and 12 outer poles, and 8 inner poles and 16 outer poles. It would be confirmed that the top 3 highest mean power density are gear ratio of 1.25, 1.33, and 1.5. Gear ratio 1.43 shows the largest range of changes. That is, in the magnetic gear with a gear ratio of 1.43, the number of poles on rotors had a close relationship with the power density.

Fig. 5.

Power density of coaxial magnetic gear’s (a) outer rotor and (b) inner rotor.

3.2. Torque ripple

Coaxial magnetic gears are magnetically joined without direct contact, such that they are free of the vibration and noise caused by physical contact. However, torque ripple occurs due to several harmonics because the magnetic flux is modulated by the pole pieces. Torque ripple is a source of vibration and noise in the equipment, so it must be considered when designing equipment. As shown in Fig. 6(a), the torque ripple of the outer rotor was less than 40% for all models except gear ratio of 2 and 3. In these two magnetic gear models, the mean values were above 40%, and the maximum values were 70.4% and 81.9%. The model with a gear ratio of 6.5 had the smallest mean value of 0.2%. As shown in Fig. 6(b), the mean value of the inner torque ripple was less than 10% except integer gear ratios such as 2, 3, 4, 5, 6, 7, 8, and 9. Magnetic gears with an integer gear ratio had over 30% mean torque ripple value. The highest ripple is 222.5% on 3:1 gear ratio and the lowest ripple is 0.2% on 1.25:1 gear ratio. Torque ripple changing degree according to the number of poles was completely different even they have the same gear ratio. When the gear ratio of the coaxial magnetic gear was 1.25, 2.86, 5.5, 6.5, or 7.5, the fluctuation rate according to the number of poles and the values were smaller than in models with different inner rotor and outer rotor torque ripple.

Fig. 6.

Torque ripple of coaxial magnetic gear’s (a) outer rotor and (b) inner rotor.

Fig. 7.

Loss that occurs when the coaxial magnetic gear is operating, (a) iron loss, (b) magnet’s eddy current loss, and (c) overall loss.

Fig. 8.

Coaxial magnetic gear’s power transfer efficiency.

3.3. Loss and efficiency

Losses occurred in a coaxial magnetic gear can be divided into two categories; the iron loss generated in the ferromagnetic part of pole piece and the back yoke, the eddy current loss generated in the magnet due to its conductivity. Figure 7 shows the relationship between the coaxial magnetic gear losses and the gear ratio. It also used four different number of poles per one gear ratio. The lowest mean iron loss of 5.3 W was generated when the gear ratio was 1.5. The lowest mean eddy current loss of 1.5 W was generated when the gear ratio was 2.22. The lowest total loss of 13.03 W was generated when the gear ratio was 2.5.

Figure 8 shows efficiencies according to gear ratio. Efficiency graph is very similar to total loss graph because output power of all models are same. Therefore, the highest efficiency model is 2.5:1 gear ratio and its efficiency is 98.6%.

4. Conclusion

This paper shows initial research for designing a 1-kW two-stage magnetic gear with a 10:1 gear ratio. Power density, torque ripple, loss, and efficiency was analysed according to gear ratio. The results showed that the gear ratio with the maximum power density was 1.33, and the gear ratios with the minimum torque ripple in the outer and inner rotors were 6.5 and 1.25, respectively. The gear ratio with the smallest loss and the highest transfer efficiency was 2.5. As the result, it seems like that finding an optimal model using these data is not clear. 17 combinations were used to get a 10:1 gear ratio and 120 models were analysed in detail. Even though an optimal model is decided among them, the partner gear ratio may not be a superior. If power density and efficiency are considered in same weight, the best combination is 2.5:1 and 4:1. However, torque ripple of this combination should be improved. Therefore, a two-stage magnetic gear has high power density than single-stage but it should be careful in the design process. The total solution will be proposed in next paper, which shows the primary magnetic gear design as a future work. The analytical method of this paper will be a big milestone in the final design of the two-stage magnetic gear.

Footnotes

Acknowledgements

This work was supported by the Technology Innovation Program (10076577, Development of optimum design technology of non-contact magnetic gear driving module for electrical supercharger) funded By the Ministry of Trade, Industry & Energy (MOTIE, Korea).

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