Design and Characteristics of Axial Magnetic Gear Using Rectangular Magnet

In recent years researchers have developed several models to improve the performance of magnetic gear using a pair of magnets or multi-pole [1, 2]. Generally, a magnetic gear transmission is understood to consist of motion or the transfer of torque through non-contacted gear using a driving gear wheel and a driven gear wheel. The principle of conversion of magnetic gear replaces the slot of the mechanical gear tooth to an iron core by using the north-pole (N) and south-pole (S) of the magnet. Magnetic gears are an alternative technology that may offer significant advantages such as, reduced maintenance and improved reliability, inherent overload protection, no mechanical loss, no mechanical fatigue, high efficiency, and physical isolation between input and output shafts [3-8]. In addition, slip and break away from the system when the overload compared with conventional gear when stopping or braking which could damage the machines [9].

There are several magnetic gear types has been introduced by previous researchers. These magnetic gear types consist of a permanent magnet rotor that guides the magnetic flux in iron segments. The other is the output rotor which is driven by this altering flux of the magnetic gear. Gear types are also found in many different configurations. Some of these configurations have the parallel axis and other configurations will transform rotational motion into linear motion. Li et al. [10] proposed a new transmission type using an involute SmCo magnetic gear. In 1993 and 1994, the magnetic worm gear and magnetic skew gear was also developed, respectively [11, 12]. However, both of them have the demerits of complexity and poor torque density.

Due order to avoid the complicated structure of magnetic worm and skew gears, Ikuta et al. [13] have proposed the simple parallel-axis magnetic gears which include two basic topologies: axial coupling and radial coupling. These magnetic gears can be categorized into the category of magnetic gears with closely spaced magnets. This gear type has typically a magnetic interaction in between magnets on two or more axes. The technology is with the two magnetic gear wheels covered with magnets on the surfaces. These magnets interact with each other and they create a driving force on drive magnet wheel. However, although, topology parallel-axis magnetic gear is very simple, but has not been widely used in industrial applications, because it has a low torque density [14]. The application of plastic bonded magnets for gears developed in recent years is an attractive alternative, and the trends are to use them in constructing such devices. They are low cost and do not present fragility in the manufacturing process. Preparation techniques and performance characteristics for the no-load and loaded operation of a magnetic gear system made of the Nd2Fe l4B plastic bonded magnet were reported by Tsamakis et al. [15].

On the other hand, to increase the torque of the magnetic gear, we focused the use of rare-earth permanent magnets of high energy, high remanence, and high coercivity such as neodymium-iron-boron (NdFeB) and samarium-cobalt (SmCo), which was found in 1980 [16, 17]. NdFeB magnet types have high performance compared with other magnets, the attention of researchers to examine the magnetic gear increases performances. In general, sector-shaped magnets were applied in magnetic gear fabrication, therefore it requires sufficient NdFeB magnetic material such as a parallel-axis magnetic gear [13, 18-20], radial magnetic gear [21-23], permanent magnetic spur gear [24], and magnetic planetary gearbox [25]. In addition, there are inherent problems such as price considered expensive and suffer from a shortage of supply. Therefore, a rectangular permanent magnet that can replace sector-shaped magnets in the manufacture of magnetic gears is an appropriate consideration. According to the paper [26], compared with the sector-shaped magnets, they have the merit of low cost due to available dimensional materials. From the geometry point of view, rectangular magnets have the advantages of standard product specifications, low manufacturing cost, and easy magnetization [27].

The purpose of this paper is to conduct experimental of the transmitted torque of a proposed axial magnetic gear with a variation of the rectangular magnet layer. According to the work [28], the use of rectangular magnets arranged in layers is the same as arranging magnetic circuits in parallel. By applying a magnetic circuit analysis approach, an increase in magnetic flux can be achieved by engineering rectangular permanent magnet arrangements in parallel (in layers). To perform magnetic circuit analysis, the electric circuit approach can be used. The resistance (R) and reluctance (Â) are inversely proportional to the area, indicating that the increased surface area will result in a reduction in value and will increase the desired result in the form of current and flux. Compared to the work [13], special attention is given to the application of rectangular magnets to reduce the NdFeB magnetic material used in axial magnetic gears. Unlike radial topology, axial magnetic gear does not require magnetic lengths in the magnetic flux region. They require an axially strong magnetic flux. Different topologies with 1-4 layers of permanent magnet mounted on acrylic discs are tested at 0-2400 rpm. To study the accuracy of the proposed axial magnetic-gear for different load conditions, measurement data obtained between axial magnetic gear and direct drive are compared.

3.1 Magnetic flux measurement

Before the magnetic layer is installed, the flux value of each bar magnet layer is measured using the WT 110A Teslameter type. Tables 3 and 4 show the results of the flux measurements of the primary and secondary gear magnetic layers.

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(a) Testing with direct-drive

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(b) Testing with magnetic gear

Figure 3. Sketch of dynamic test bench

Table 3. Magnetic layer flux measurements of primary disc

Table 4. Magnetic layer flux measurements of secondary disc

$s=\sqrt{\frac{n \sum_{i=1}^{n} X_{i}^{2}-\left(\sum_{i=1}^{n} X_{1}\right)^{2}}{n(n-1)}}$  (9)

and,

$s_{e}=\frac{s}{\sqrt{n}}$  (10)

where, s_e = standard error.

In statistics, the standard deviation is used to measure the number of variations or the distribution of a certain number of data values. The lower the standard deviation approaches the average value, on the contrary, if the standard deviation value is higher the width of the data range varies. Thus, the standard deviation is the difference in the value of the sample with the mean value. From Tables 5 and 6, for example, based on the preceding formula, it is obtained in the table for both primary and secondary plates, such as the mean, the variance, and the standard deviation. Then the standard error is specifically obtained as a measuring tool to determine the sampling error used. The larger the number (n enlarged), then the standard error will decrease. That is, increasing the sample size (n) will minimize the error or average deviation (estimator) of the population parameter. Based on these two tables’ shows that the standard error obtained is still small, the highest is 5.2 for 4 layers of the magnet on the secondary magnetic gear.

3.2 Performance measurement

Figure 4 shows the test apparatus of the magnetic gear (n₁ < n₂). In the figure, both the magnetic gear is connected to the DC motor (n₁) and DC generator (n₂). The test system is able to measure the performance characteristics both accelerating and decelerating the magnetic gear. Measurements were taken in the loaded condition at variable speed, variable load, and the magnetic layer was varied, respectively. The measured data such as load current, output voltage, speed, and output power. The results of the comparison test of direct-drive with magnetic gear at speeds from 0-2400 rpm with a load of 200, 300, and 400 ohms are shown in Figures 5, 6, and 7, respectively.

Table 5. Variance and standard deviation of the magnetic layer flux of the primary magnetic gear

Table 6. Variance and standard deviation of the magnetic layer flux of the secondary magnetic gear

From Figures 5, 6, and 7, it can be seen that the addition of four magnetic layers in the magnetic gear can improve the magnetic force, therefore, we choose to arrange a piece magnet in parallel to meet assembly in gear's design. In other words, the addition of any one piece of the magnetic layer to the magnetic flux of 85.33 mT can improve magnetic-gear torque. Table 7 shows the increase in output power to the influence of the magnetic flux between the 4 magnetic layers and the direct drive with loads of 200, 300, and 400 ohms, respectively.

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Figure 4. Axial MG prototype placed on the test bench (g=0.5mm)

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Figure 5. The comparison between direct-drive and magnetic gear at load of 200 Ohm

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Figure 6. The comparison between direct-drive and magnetic gear at load of 300 Ohm

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Figure 7. The comparison between direct-drive and magnetic gear at load of 400 Ohm

Table 7. A comparison of the output power produced between a 4-layer magnetic gear with a direct drive with varying loads

No	Loads (ohm)	Output Power (Watts)
		Direct Drive	Magnetic gear (4 layers)
1.	200	2.24	2.4
2.	300	1.56	1.52
3.	400	1.2	1.1

 

To compare the torque with varying loads with respect to each additional magnetic layer, the magnetic torque of the gear as a function of the number of magnetic layers with varying loads is shown in Figure 8. It is clear that the torque of magnetic gear will decrease in proportion to the output load at speed 2400 rpm. The figure indicates that the maximum load torque is applied to the direct coupling between the motor and the generator with a 200 Ohm loading of 0.19 x 10^-3 (N-m).

Maximum load torque that occurs decreases proportional to the addition of load on the DC generator. Axial magnetic gear as proposed in Figure 1, each rectangular magnetic layer with 85.33 mT is capable of carrying a maximum load torque of 0.12 x 10^-3 (N-m). The period of adding each layer to the rectangular magnet of the magnetic gear affects the increase in load torque. That is, the presence of four magnetic layers with the same magnetic flux strength approaches the maximum torque produced by the direct drive of 0.18 x 10^-3 (Nm). In this test, the torque load ratio is only measured at the maximum load for direct drive. The aim is the basis of investigating the ability of each rectangular magnetic layer used in magnetic gear assembly.

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Figure 8. Characteristics of load torque vs magnetic flux

3.3 Basic analogy of magnetic circuits vs electric circuits

Based on the theory of magnetism, there is a similar analogy to the electrical circuit. Therefore, to analyze the magnetic flux can be done with an electric circuit approach, known as Ohm's law:

$I=\frac{V}{R}$  (11)

where,

• I = current [Ampere]
• V = voltage [Volt]
• R = resistance [Ohm]

Thus, the replacement value of the above equation is:

$\Phi=\frac{\mathcal{F}}{\Re} \quad \leftrightarrow \quad I=\frac{V}{R}$  (12)

where,

• Ф = flux [T], (the desired effect),
• (ℱ) = magnetic force, (form of external force required to establish the lines of magnetic flux in the magnetic material),
• (ℜ) = Reluctance, (resistance to the determination of the flux).

From Eqns. (11) and (12), it can be described in terms of the circuit as shown in Figure 9.

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Figure 9. Magnet circuit and electrical circuits: (a) Equivalent magnetic circuit and (b) Electrical circuit analogy

As an illustration, Figure 10 shows a comparison of the measurements of 1 magnetic bar with a thickness of 3 mm and 3 pieces of the magnet in parallel with a thickness of 1 mm. In this study, the result of magnetic flux measurements of magnetic layers in parallel with a thickness of 1 mm is 223 mT slightly higher than a magnet with a thickness of 3 mm, i.e. 196 mT. In addition, Figure 11 shows a magnet with a thickness of 4 mm versus 4 magnetic layers with a thickness of 1 mm. Here, the magnetic pole is illustrated that 1 rectangular magnet bar only has 2 poles, whereas a four-layer magnet has 8 poles.

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Figure 10. Magnetic size 3 mm versus magnetic size 1 mm with 3 layers

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Figure 11. An overview of the comparison of an NdFeB magnet pieces: (a) One layer of NdFeB magnets, (b) 4 layer of NdFeB magnets

3.4 Discussion

According to the paper [28], when rectangular magnetic tooth layers are arranged in parallel compared to in series, the magnetic reluctance decreases and increases magnetic flux. On the other hand, the presence of magnetic rectangular arranged in layers also leads to an increase in the number of poles. The torque of a magnetic gear depends on the number of magnetic poles, the area of the poles covered by the magnets, the magnetic field strength of magnets, and the separation distance between magnets of the coupling [19, 21].

For different multi-pole of the magnetic gears with the same magnetic field strength, the torque of magnetic coupling increases as the number of magnetic poles increases for distances smaller than the critical separation distance. This means that the magnetic force increases in proportion to the addition of four magnets arranged in parallel or it equals to add to 8 poles pairs. In this case, there are differences in the magnetic torque between four rectangular magnets arranged in parallel (multi-pole) with a thickness of 4 mm compared with a rectangular magnetic (2 poles) with the same thickness (Figure 11).

Table 8. Comparison of torque of several magnetic gear topologies

Topology	Ratio	Magnet Shape	Remanence (T)	Torgue (N-m)	Ref.
Planetary	-	sectoral	1.09	24.13	[31]
Coaxial	1:5.5	coaxial	1.25	24.5	[32]
Spur (Radial)	1:4	sectoral	1.183	16.3 (analytic) 13.1 (measured)	[24]
Radial	1:1	Rectangular	1.16	5.29	[27]
Radial	1:16	sectoral	1.3	2.6	[8]
Parallel	1:1	sectoral	1.16	6.43	[33]
Axial	1:1	sectoral	1	3.9	[33]
Axial (serial)	1:2	Rectangular	0.099	1.9.10-3 (measured)	[28]
Axial (layers)	1:2	Rectangular	0.254	2.24.10-3 (measured)	in this work

 

On the other hand, Wu et al. [26] described an analytical approach for the transmitted torque calculation of an external magnetic gear set with rectangular magnets by employing the technique of the current sheet model. Based on the analytical model, the effects of design parameters, including the number of magnetic poles, the length of the air gap and the remanence of permanent magnets, affect the transmitted torque of magnetic gear.

Furthermore, the rectangular magnet composition of the layered system proposed in this paper is an attractive offer in the design of magnetic gear with several advantages. Among them, easy to make, very simple, it can provide increased torque compared to previous designs. Table 8 provides a comparison with some axial magnetic designs that have been made by previous researchers.

The authors would like to acknowledge the support of the Laboratory of Electrical Engineering, University of Nusa Cendana - Kupang and scholarship support from the Ministry of Research Technology and Higher Education.