Innovative Magnetic Gear Design Incorporating Electromagnetic Coils for Multiple Gear Ratios

Abstract

In this study, a novel magnetic gear design is introduced. Unlike conventional magnetic gears that can only achieve a single gear ratio using permanent magnetic poles, the proposed design incorporates electromagnetic coils that can adapt to various control strategies, resulting in a multiple gear ratio for the same machine design. We selected a gear system with five gear ratios to validate the new design. The performance of the proposed design was compared with that of the conventional magnetic gear. While permanent magnet poles offer high torque transmission with a small volume, they cannot provide different gear ratios for the same configuration. Therefore, this work suggests using a single-gear machine based on a fixed number of electromagnetic coils to achieve different gear ratios. This research outlines the design steps, simulation process, and detailed analysis. The results demonstrate the effectiveness of the proposed design strategy, which can be potentially applied to wind turbines, transportation, and other scenarios with comparable success.

1. Introduction

Gearboxes are essential components in various mechanical systems as they serve multiple critical functions. One of their primary roles is to adjust the speed and torque output of motors to match an application’s requirements. This can be achieved by using different gear ratios, allowing for an increase in torque at the expense of speed, or vice versa. Gearboxes are crucial for efficient power transmission and optimal utilization of motors in a wide range of industries, including automotive, manufacturing, aerospace, wind energy, and more. However, mechanical gearboxes have several drawbacks compared with other transmission systems due to their physical contact-based operation. These drawbacks include energy losses due to friction and heat [1], wear and fatigue over time [2], and undesirable noise and vibrations [3].

In recent years, magnetic gears have gained attention because of their high torque density and the advantages they offer over mechanical gears [4]. One significant advantage is that they eliminate physical contact between the driving and driven components. Unlike mechanical gears that rely on teeth meshing together, magnetic gears use magnets to transmit torque. This contactless interaction brings multiple benefits. Firstly, it reduces the need for lubrication and maintenance as there is no wear and tear from friction. Additionally, it improves efficiency by eliminating energy losses caused by mechanical contact. Magnetic gears also provide quieter and smoother operation as there is no noise from tooth engagement or vibrations. Furthermore, the absence of physical contact allows for higher torque density, enabling more compact and lightweight designs. Overall, magnetic gears offer improved durability, efficiency, and performance compared with mechanical gears.

Magnetic gears typically consist of the following three main components: an input rotor, an output rotor, and a magnetic coupling [5]. Both the input and output rotors are made up of permanent magnets (PMs) arranged in a pattern that alternates between north and south magnetic poles. These rotors are aligned in a way that attracts the north pole of the input rotor to the south pole of the output rotor, and vice versa, creating a magnetic field that transfers torque. The magnetic coupling, positioned between the input and output rotors, facilitates the transmission of magnetic force, allowing the rotors to rotate without direct contact. Additionally, housing may be included in the construction of a magnetic gear to enclose and protect the rotors and coupling. Overall, magnetism is utilized in the construction of magnetic gears to transmit power and torque effectively, offering benefits such as high efficiency, low noise, and maintenance-free operation.

Using PMs in magnetic gears makes it challenging to adjust the gear ratio. The gear ratio of a magnetic gear depends on the number of poles in the rotor, which remains fixed during operation. To obtain a multi-gear ratio, the number of poles on the input and output rotors must be variable. Designing a magnetic gear with multiple gear ratios using permanent magnets can be complicated. Trial-and-error approaches have been used to achieve the desired torque by referring to existing magnetic gears for the desired value of torque [6]. In [7], a novel magnetic variable gear design is introduced, presenting various speed ratios. In order to enable changing gear ratios, a high-remanence low-coercivity permanent magnet called aluminum–nickel–cobalt (Alnico) is employed. By integrating the magnetic gear and memory machine principles, an innovative double-deck structure for the stationary ring is devised to house the magnetizing winding. This winding has the capability to magnetize or demagnetize the Alnico PM in a dynamic manner. In [8], the concept of PM rotation is introduced as a means to achieve variable gear ratios in magnetic gears. This approach involves the use of circular diameter magnetization magnets instead of the conventional arc-shaped magnets typically employed in magnetic gears. The mechanical rotational motion of the magnets alters the order of magnetic harmonics, leading to a distinct coupling between the input and output of the gear system, thereby providing variable gear ratios. In addition to the complex design of this magnetic gear system, the rotational motion of the circular magnets can result in increased friction and wear within the system.

Researchers have recently started exploring the use of magnetic coils instead of permanent magnets in magnetic gear designs [9,10]. These coils generate a magnetic field through the application of electric current, allowing for adjustable torque transmission in real time [11].

While limited research is available on the use of magnetic coils in magnetic gears, a few papers have shed light on this concept. In [12], the authors propose a novel magnetic gear design employing magnetic coils. They conduct simulations and experiments to evaluate the performance of the coil-based magnetic gear in terms of torque transmission, efficiency, and control. In [13], the researchers provide a comparative study between traditional permanent magnet-based magnetic gears and those utilizing magnetic coils. They investigate aspects such as torque ripple reduction, control strategies, and overall system efficiency.

Although further investigation is required, the use of magnetic coils in magnetic gears holds promise for applications that demand adjustable torque transmission and precise control. Such innovations could lead to improved performance, reduced maintenance requirements, and increased flexibility for various industries, including robotics, renewable energy systems, and automotive technology.

This study proposes a novel design for a multiple gear ratio magnetic gear within the same machine layout utilizing electromagnetic coils. The multiple gear ratio was obtained through proper control strategies. Five different gear ratios were selected as case studies. For each gear ratio, inner rotor and outer rotor control signals were extracted. After that, the proposed design and control were examined for every gear ratio using 2D Finite Element Magnetostatic Analysis (FEMM). Finally, the actual obtained gear ratios were compared to theoretical one for the sake of validation.

The main contributions of this work can be summarized in the following points:

• Introduction of a new design for magnetic gears incorporating electromagnetic coils to enable variable gear ratios within the same machine design.
• Ability to achieve five different gear ratios in a single gear system, demonstrating the versatility and adaptability of the proposed design.
• Implementation of a magnetic coupling rotation feature for adjusting output speeds while maintaining a consistent gear ratio.
• Comparison of the performance between traditional permanent magnet-based magnetic gears and the newly proposed electromagnetic coil-based system.
• Detailed analysis showcasing the efficacy of the proposed design strategy and its potential applicability to similar scenarios.

This paper is structured as follows: it begins with Section 2, outlining the fundamental theory of magnetic gears, followed by Section 3 and Section 4, which delve into the optimal thickness variation in the gear components. Section 5 introduces the proposed model construction and design for both high-speed and low-speed rotors, followed by Section 6, which discusses the new design analysis utilizing finite element simulation and presents the results. Finally, Section 7 concludes this paper.

2. Modeling of the Magnetic Gear

The conventional magnetic gear, as shown in Figure 1, is a type of magnetic gear that uses magnets instead of teeth to transmit torque. It consists of a number of magnetic pole pairs $p_i$ in the inner rotor, a number of pair poles $p_o$ in the outer rotor, and $n_s$ magnetic coupling pole pieces [14,15]. The induced flux due to inner rotor pole permanent magnets is modulated by the ferromagnetic pole pieces, which interact with the induced flux due to outer rotor pole permanent magnets. The relation between $p_o, p_i$ and $n_s$, which leads to maximum torque transmission, is given by Equation (1), where the relation between inner rotor speed ${\mathsf{\Omega }}_{\mathrm{h}}$, outer rotor speed ${\mathsf{\Omega }}_{\mathrm{L}}$, and magnetic coupling speed ${\mathsf{\Omega }}_{\mathrm{s}}$ is given by Equation (2) [14,16].

$$n_s=p_o+p_i$$

(1)

$${\mathsf{\Omega }}_{\mathrm{L}}={\displaystyle \frac{n_s}{p_o}}{\mathsf{\Omega }}_{\mathrm{s}}-{\displaystyle \frac{p_i}{p_o}}{\mathsf{\Omega }}_{\mathrm{h}}$$

(2)

In the general mode of operation of the conventional magnetic gear [17], the pole piece rotor is blocked, causing its speed ${\mathsf{\Omega }}_{\mathrm{s}}$ to equal zero. So, the corresponding gear ratio $G_r$ can be calculated with Equation (2)

$$G_r={\displaystyle \frac{{\mathsf{\Omega }}_{\mathrm{h}}}{{\mathsf{\Omega }}_{\mathrm{L}}}}=-{\displaystyle \frac{p_o}{p_i}}$$

(3)

3. Effect of the Thickness Variation in the Magnetic Gear Pieces

The thickness of the magnetic gear rotor is a crucial factor in determining the torque values of the gear system. Torque is directly proportional to the magnetic flux passing through the system, which is influenced by the thickness of the rotor [18]. Increasing the thickness of the magnetic gear rotor allows for a greater magnetic flux to pass through, resulting in higher torque values. On the other hand, reducing the thickness of the rotor decreases the magnetic flux and subsequently decreases the torque values [19]. When selecting the optimal thickness of the magnetic gear rotor, various factors should be considered. Firstly, the desired torque output for a specific application needs to be determined. If a high torque output is required, a thicker rotor should be chosen. Conversely, for low-torque applications, a thinner rotor may suffice. In addition, material properties and manufacturing constraints should be taken into account [20]. The material used in the rotor should possess the necessary structural integrity and magnetic properties for the desired thickness. Manufacturing limitations, such as machining precision and cost considerations, should also be considered. Furthermore, system efficiency needs to be evaluated [21]. Thicker rotors generally result in higher torque values but may increase power losses due to eddy currents and magnetic saturation. Therefore, an optimal thickness that strikes a balance between torque output and system efficiency should be chosen.

To determine the optimal thickness of the magnetic gear rotor, this paper introduces an optimal design for the magnetic gear thickness. The flowchart in Figure 2 demonstrates the procedure of varying the thickness of the magnetic coupling pole pieces (W4), inner rotor permanent magnet (W2), and outer rotor (W6). It is important to note that the external radius of the outer rotor and the lengths of air gaps (W3, W5) remain fixed during the calculations. Additionally, Figure 3 illustrates the relationship between inner rotor torque (T_i) and inner rotor magnet thickness (W2), while Figure 4 shows the relationship between outer rotor torque (T_o) and outer rotor magnet thickness (W6). It is clear that torque increases with an increase in either the inner rotor magnet thickness or the outer rotor magnet thickness, with the outer rotor magnet thickness having a more pronounced effect. It is necessary to note that during the calculations, the value of the external radius of the external rotor and length of air gaps W3 and W5 are always fixed.

4. Optimal Gr Ratio and ${\mathit{p}}_{\mathit{o}}$, ${\mathit{p}}_{\mathit{i}}$, and ${\mathit{n}}_{\mathit{s}}$ Combination

The gear ratio between the rotors is the number of magnetic pole pairs on the high-speed rotor to the number of magnetic pole pairs on the low-speed rotor, as shown in Equation (3). To select the optimal values for $p_o$, $p_i$, and $n_s$ in order to achieve a desired torque ratio Gr [22], it is important to minimize torque ripples by ensuring that the cogging factor $C_f$ is kept to a minimum [23]. Equation (4) [24] can be used to calculate $C_f$, and the goal is to achieve a value of 1, which will result in minimum torque ripples.

$$C_f={\displaystyle \frac{2p_o\times n_s}{LCM\left(2p_o,n_s\right)}}$$

(4)

To estimate the torque ratios Gr, the best combination of $p_o$, $p_i$, and $n_s$ can be determined using the flowchart in Figure 5. This combination will provide the necessary torque ratio with the least amount of torque ripples. From the results obtained in

Table 1. List one of $p_i$, $p_o$, $n_s$, G_r, ppcm, and c_bien values.

${\mathit{p}}_{\mathit{i}}$	${\mathit{n}}_{\mathit{s}}$	${\mathit{p}}_{\mathit{o}}$	Gr	ppcm
2.0	7.0	5.0	2.5	28.0
2.0	9.0	7.0	3.5	36.0
3.0	11.0	8.0	2.667	66.0
3.0	13.0	10.0	3.333	78.0
4.0	15.0	11.0	2.75	120.0
4.0	17.0	13.0	3.25	136.0
5.0	19.0	14.0	2.8	190.0
5.0	21.0	16.0	3.2	210.0
6.0	23.0	17.0	2.833	276.0
6.0	25.0	19.0	3.167	300.0
7.0	25.0	18.0	2.571	350.0
7.0	27.0	20.0	2.857	378.0
7.0	29.0	22.0	3.143	406.0
7.0	31.0	24.0	3.429	434.0
7.0	35.0	26.0	3.889	560.0
8.0	29.0	21.0	2.625	464.0
8.0	31.0	23.0	2.875	496.0
8.0	33.0	25.0	3.125	528.0
8.0	35.0	27.0	3.375	560.0
9.0	37.0	28.0	3.111	666.0
9.0	37.0	27.0	2.7	740.0
10.0	41.0	31.0	3.1	820.0
10.0	43.0	33.0	3.3	860.0

, combinations were obtained, which gave the required torque ratio with $C_f$ equal 1.

5. Proposed Design Strategy

In order to achieve a variable gear ratio, the conventional magnetic gear’s permanent magnet poles need to be replaced with electromagnetic coils. The polarity of these coils should be adjustable based on the control strategy. By using this technique, a single magnetic gear with a set dimension and fixed number of coils can provide multiple gear ratios. This study presents the design of a magnetic gear with five different gear ratios, which are listed in

Table 2. Gear ratio combination.

	Pi	ns	Po	Gr
Gr1	9	25	16	1.778
Gr2	8	25	17	2.125
Gr3	7	25	18	2.571
Gr4	6	25	19	3.167
Gr5	4	25	21	5.25

. The selection of these combinations is based on the principle of least common multiple, as referenced in [25].

The outer and inner rotors are designed to generate a magnetic field using a coil instead of permanent magnets. To achieve the desired gear ratio, as stated in Table 2, the controller regulates the coil connection to ensure the inner and outer rotors have the correct number of poles. The magnetic coupling pole pieces facilitate the connection between the inner and outer rotors, and it is necessary for them to have a constant number of poles, equal to the sum of the poles in the inner and outer rotors, as indicated in Equation (2). Thus, a permanent magnetic pole with a pair of 25 poles is utilized.

To achieve a compact gear size while meeting the requirements of the five gear ratio combinations outlined in Table 2, it is crucial to determine the optimal number of coils that can be evenly distributed among the inner and outer rotor poles. The maximum number of poles for the inner rotor is 18, while for the outer rotor, the maximum number is 42.

Hence, the main objective is to strike a balance between the number of coils and the poles in each combination, ensuring equal distribution.

5.1. Design Construction

The proposed design for variable-speed magnetic gears aims to achieve precise speed control, stability, and optimal performance by continuously adapting the gear ratio based on speed sensor feedback. This process involves speed measurement using sensors on both input and output shafts, a control loop for comparing desired and actual speeds, gear ratio adjustment driven by speed error, feedback tuning to minimize discrepancies, and the incorporation of additional algorithms for enhancing stability and performance.

The speed box is engineered to generate five different speeds by manipulating the poles of the fast and slow rotors with the coils. The coil feeding and pole quantity are regulated through sliding rings, as illustrated in Figure 6. Speed sensors are strategically positioned, transmitting signals to the control unit where calculations are made to determine the best conversion ratio. Subsequently, the coils are activated to achieve the required polarities.

In Equation (3), the gear ratio is determined without any motion of the magnetic gearbox’s central component. However, by rotating the magnetic coupling, variable output speeds can be achieved while maintaining a consistent gear ratio. The speed adjustment is facilitated by controlling the direction of rotation of the central rotor, enabling the magnetic gear to function as a continuously variable system. To achieve this, a low-speed motor is incorporated to rotate the central component at ±10 rpm. For example, with a Gr4 of 3.167, when the low-speed shaft spins at 100 rpm, the high-speed shaft will rotate at 316.7 rpm. When the middle rotor is stationary, the high-speed shaft will also rotate at 316.7 rpm. However, when the middle rotor spins at +10 rpm or −10 rpm, the high-speed shaft speeds up to 358.67 rpm and slows down to 275 rpm, respectively.

5.2. High-Speed Rotor Coils Design

In order to determine the minimum number of turns for all coils that can be divided into groups to accommodate all five gear combinations, the total number of turns must be evenly divisible by the number of poles (18, 16, 14, 12, or 8) with no remainder. After investigating, it was determined that the initial integer value needed for this purpose was 4032 turns. The specific details for each gear can be found in

Table 3. High-speed rotor coil turn distributions for each gear.

	Pole Pair	Pole	Turns /Pole	Total Turns
Gr1	9	18	224	4032
Gr2	8	16	252	4032
Gr3	7	14	288	4032
Gr4	6	12	336	4032
Gr5	4	8	504	4032

Total number of turns of all coils = 4032. Initial total coils = 68.

and

Table 4. High-speed rotor coil turn summation steps.

Gr1	Gr2	Gr3	Gr4	Gr5
224	252	288	336	504
448	504	576	672	1008
672	756	864	1008	1512
896	1008	1152	1344	2016
1120	1260	1440	1680	2520
1344	1512	1728	2016	3024
1568	1764	2016	2352	3528
1792	2016	2304	2688	4032
2016	2268	2592	3024
2240	2520	2880	3360
2464	2772	3168	3696
2688	3024	3456	4032
2912	3276	3744
3136	3528	4032
3360	3780
3584	4032
3808
4032

. Additionally, there are a total of 68 groups, matching the number of poles for the five gears. It is worth noting that each gear is represented by a different color for simplicity.

Table 4 was consolidated into a single column and rearranged in ascending order in the first column of

Table 5. High-speed rotor coils per group and their distribution numbers among the five gear combinations with their control signal strategies.

Coil No.	Turns/ Coil	Total No. Turns	Gr1	Gr2	Gr3	Gr4	Gr5
1	224	0	1	1	1	1	1
2	28	224	−1	1	1	1	1
3	36	252	−1	−1	1	1	1
4	48	288	−1	−1	−1	1	1
5	112	336	−1	−1	−1	−1	1
6	56	448	1	−1	−1	−1	1
7	72	504	1	1	−1	−1	−1
8	96	576	1	1	1	1	−1
9	84	672	−1	1	1	1	−1
10	108	756	−1	−1	1	1	−1
47	24	3784	1	-1	−1	−1	−1
48	224	3808	−1	−1	−1	−1	−1

. By following the processing approach outlined in Table 5, the number of coils was reduced from 68 to 48. According to Table 5, the first north pole for the first gear (Gr1, red color) consists of a single coil with 224 turns. The subsequent south pole is made up of a series of four coils (with 28, 36, 48, and 112 turns, respectively) whose total sum also equals 224 turns, ensuring magnetic design balance.

The detailed information from Table 5 can be found in Figure 7 and Figure 8. Figure 7 displays the recommended number of turns for each coil for Gr1, while Figure 8 illustrates the control circuit pulses for each coil and gear ratio.

5.3. Low-Speed Rotor Coil Design

Using the same method described in the previous section, the minimum integer total number of turns for all coils is 9409. Additionally, the number of groups was reduced from 9409 to 168 groups. Details of

Table 6. Low-speed rotor coil turn distributions for each gear.

	Pole Pair	Pole	Turns/Pole	Total Turns
Gr1	16	32	295	9409
Gr2	17	34	277	9409
Gr3	18	36	262	9409
Gr4	19	38	248	9409
Gr5	21	42	225	9409

,

Table 7. Low-speed rotor coil turn summation steps.

Gr1	Gr2	Gr3	Gr4	Gr5
295	277	262	248	225
589	554	523	496	449
883	831	785	743	673
9409	8856	8364	7924	7169
	9133	8625	8171	7393
	9409	8887	8419	7617
		9148	8667	7841
		9409	8914	8065
			9162	8289
			9409	8513
				8737
				8961
				9185
				9409

and

Table 8. Low-speed rotor coils per group and their distribution numbers among the five gear combination with their control signal strategies.

Coil No.	Turns/ Coil	Total No. Turns	Gr1	Gr2	Gr3	Gr4	Gr5
1	225	0	1	1	1	1	1
2	24	225	1	1	1	1	−1
3	14	249	1	1	1	−1	−1
4	16	263	1	1	−1	−1	−1
5	18	279	1	−1	−1	−1	−1
6	155	297	−1	−1	−1	−1	−1
7	48	452	−1	−1	−1	−1	1
8	28	500	−1	−1	−1	1	1
9	31	528	−1	−1	1	1	1
10	35	559	−1	1	1	1	1
167	24	9161	−1	−1	−1	−1	1
168	225	9185	−1	−1	−1	−1	−1

can be found in Figure 9 and Figure 10, in detail, which provide complete data. Figure 6 shows the proposed initial number of turns for each coil, while Figure 7 displays the control circuit pulses for each coil and gear ratio.

5.4. Control System and Increased Technological Complexity

The proposed magnetic gear design incorporates electromagnetic coils to achieve variable gear ratios, which naturally introduces a higher level of technological complexity compared with traditional fixed-ratio gears with permanent magnets (PMs). In fixed-ratio magnetic gears, the gear ratio is determined by the number of magnetic poles, which remain constant during operation. However, in the proposed system, the coils can be dynamically controlled to adjust the gear ratios.

To obtain different gear speed ratios, the process involves the following control steps:

• Speed Measurement: The speed of the rotors entering the system (slow rotation axis) is measured.
• Conversion Ratio Calculation: The required speed on the fast rotation axis is specified, and the appropriate conversion ratio is calculated based on the known input speed.
• Coil Interconnection: Once the conversion ratio is determined, the coil connections are modified to match the desired gear ratio, as shown in Figure 8 and Figure 10. The controller ensures that the inner and outer rotors are configured with the correct number of poles.
• Signal Transmission: A signal is sent to the slip rings of the fast and slow rotation members to convert the coils and achieve the required gear ratio.

While this method requires the integration of control circuits, which adds to the overall system complexity, it provides significant advantages. These include not only the ability to achieve multiple gear ratios within a single design but also the flexibility to control the field intensity. By adjusting the current supplied to the coils, the system can also control the torque output, adding a level of adaptability that fixed-ratio systems cannot offer.

This control system, as shown in Figure 6, ensures the system can continuously adapt the gear ratio in real time based on operational requirements. Although this approach introduces more complexity compared with traditional mechanical or fixed-ratio magnetic gears, the flexibility, precision, and efficiency gained by controlling both speed and torque make it a valuable innovation for applications requiring variable transmission.

6. Finite Element Simulation and Results Discussion

To ensure the precision of the suggested design, the magnetic gear, which incorporates electromagnetic coils, was examined for every gear ratio in this study. The analysis of different scenarios was carried out using 2D Finite Element Magnetostatic Analysis (FEMM), as mentioned in [26]. Furthermore, the outcomes obtained from the proposed model were compared with those of the conventional magnetic gear, which employs permanent magnet poles.

To design a magnetic gear comparable to a conventional gear and to facilitate a meaningful comparison between the proposed and conventional gears, the dimensions of both gears must be the same.

Table 9. Dimensions of the conventional magnetic gear.

Section	Value
Inner radius of the outer rotor (mm)	541
Inner radius of back iron in the outer rotor (mm)	636
External radius of the outer rotor (mm)	765
External radius of the inner rotor (mm)	400
Shaft radius in the inner rotor (mm)	142
Inner rotor magnet thickness (mm)	83
Air gap (mm)	2
Outer rotor magnet thickness (mm)	95
Axial length (mm)	100

presents the dimensions of the conventional magnetic gear. Figure 11 shows the results of the 2D FEMM simulation analysis for static torques, instantaneous torques, and flux density in the inner and outer air gaps of the conventional magnetic gear. This analysis was performed for the first gear ratio (Gr1) to verify the accuracy of the design. The maximum torque achieved by the inner rotor is 6500 Nm, with a maximum flux density of 2 Tesla.

In accordance with the flowchart in Figure 2,

Table 10. Details dimensions for the proposed magnetic gear.

Thickness (mm)	Radius (mm)
W1 = 175	R1 = 317
W2 = 83	R2 = 400
W3 = 2	R3 = 402
W4 = 137	R4 = 539
W5 = 2	R5 = 541
W6 = 95	R6 = 636
W7 = 129	R7 = 765
W8 = 142	R8 = 142

displays the dimensions of the proposed magnetic gear. The dimensions and angle of each coil are proportionate to their ampere turns. While the coils remain fixed, employing the appropriate control strategy, as depicted in Figure 8 and Figure 10, enables the magnetic gear to achieve various gear ratios. Figure 12 illustrates the layout of the magnetic gear flux flow, where a current supply capable of 10 A is utilized to generate a magnetic field and power the inner and outer poles. This setup ensures a flux density of 0.5 tesla.

6.1. Proposed Model Analysis

To calculate the first gear ratio ($p_i$= 9, ns = 25, $p_o$ = 16, Gr = 1.778), Figure 7 and Figure 9 provide the number of turns for the inner and outer coils, respectively. The control pulses for each ratio can be found in the fourth columns of Table 5 and Table 8. Figure 13 displays the obtained results, including the static and instantaneous torques, as well as the flux density in the inner and outer air gaps.

The provided set of graphs illustrates the dynamic performance of the magnetic gear system. In Figure 13a, the static torque of the inner rotor is plotted against the rotor angle. The graph reveals that the torque oscillates between positive and negative values, with both peaks and valleys that indicate significant variations in torque as the rotor moves. The positive peaks occur when the magnetic fields between the rotors are in favorable alignment, allowing for effective torque transmission, while the negative values represent moments of misalignment, resulting in torque reversal.

Figure 13b shows the variation in the maximum instantaneous torque on both the inner and outer rotors over the rotor angle. The torque of the inner rotor (in blue) fluctuates between negative and positive values, following the same pattern as in Figure 13a, while the outer rotor torque (in red) remains mostly positive with smaller fluctuations. The torque in the middle part (in green) shows less variation, indicating consistent torque transmission. The outer rotor’s behavior demonstrates that the magnetic gear can still maintain torque output despite the fluctuating torque on the inner rotor, highlighting the stability of torque transfer between components.

In Figure 13c, the radial flux density waveform in the inner air gap is shown. The flux density fluctuates periodically as the rotor rotates, with peaks corresponding to the maximum magnetic field strength when the rotor poles align. The variations in flux density are indicative of the magnetic coupling’s effectiveness in transmitting torque, and the pattern correlates with the torque variations observed in Figure 13a.

Similarly, Figure 13d presents the radial flux density waveform in the outer air gap. The flux density here follows a similar pattern to that in the inner air gap but with smaller amplitude fluctuations. This indicates that the outer rotor experiences a more stable magnetic field compared with the inner rotor, which explains the relatively stable outer rotor torque seen in Figure 13b.

In summary, Figure 13 illustrate the periodic nature of torque and magnetic flux density in the magnetic gear system. The significant fluctuations in inner rotor torque and flux density are typical for such systems because of the alternating alignment and misalignment of magnetic poles. However, the consistent torque output on the outer rotor and middle part, as well as the relatively stable flux density in the outer air gap, demonstrate the overall reliability and efficiency of the system. These observations highlight areas where the design could be further optimized, such as reducing torque ripples to enhance smoothness and improve overall performance.

When comparing the results of the proposed gear shown in Figure 13 with the conventional magnetic gear results in Figure 11, it is noted that the new magnetic gear provides lower torque values at the same dimensions. However, these results still provide valuable information regarding the desired gear ratio. Additionally, the lower torque values can be attributed to the low current supplied to the coils (10 ampere producing 0.5 Tesla). In future work, we plan to optimize this issue to achieve maximum torque density in these configurations. Similar to the analysis of gear ratio 1 shown in Figure 13, the analyses for the other four gear ratios are presented in Figure 14, Figure 15, Figure 16 and Figure 17.

6.2. Results Discussion

Table 11. The proposed magnetic gear average torque for each case and their obtained gear ratios.

Gear Ratio No.	Data According to the Control Strategy	TLav (Nm)	Thav (Nm)	Tppav (Nm)	Obtained Gear Ratio Gr = TLav/Thav
1	$p_i$ $=9, n_s$ $=25, p_o$ $=16, G_r$ = 1.778	−120.681	−221.807	342.173	1.837
2	$p_i$ $=8, n_s$ $=25, p_o$ $=17, G_r$ = 2.125	−102.068	−208.821	310.598	2.0459
3	$p_i=7,$ $n_s=25, p_o$ $=18, G_r$ = 2.571	−93.1981	−250.713	343.522	2.6901
4	$p_i$ $=6, n_s$ $=25, p_o$ $=19, G_r$ = 3.167	−72.0579	−225.327	297.236	3.1270
5	$p_i$ $=4, n_s$ $=25, p_o$ $=21, G_r$ = 5.25	−43.9432	−242.951	286.507	5.5288

provides a summary of the average maximum torque values for the proposed magnetic gear at five different gear ratios. The second column displays the data for each case after the application of various control strategies. For instance, the first objective gear ratio is calculated as Gr = 1.778, determined by dividing the average maximum output rotor torque (TL_av) by the average maximum inner rotor torque (Th_av) (Gr = TL_av/Th_av = −221.807/−120.681 = 1.837). It is observed that the two gear ratios (1.778, 1.837) are very close to each other. This small discrepancy can be attributed to the cogging torque nature of the machine, which is discussed in Equation (4).

Furthermore, the sixth column confirms that all obtained gear ratios align with the objective gear ratio presented in the second column. This alignment supports the proposed theory within this research.

7. Conclusions

In this research, a newly proposed design of a magnetic gear with a variable gear ratio based on electromagnetic coils is presented. Conventional magnetic gears typically cater to only one gear ratio by utilizing permanent magnetic poles. In this study, the gear poles are crafted with electromagnetic coils, enabling adaptation for multiple control strategies that facilitate the generation of varying numbers of poles. This novel approach results in a variable gear ratio within the same machine design. To validate this innovative concept, a magnetic gear system with five gear ratios is selected for examination in comparison to conventional magnetic gear systems. While permanent magnet poles enhance transmitted torque efficiently within minimal volume, they are limited in providing diverse gear ratios within a single configuration. Consequently, we advocate for a single-gear machine design based on a fixed number of electromagnetic coils capable of producing various gear ratios. This research outlines detailed design steps and simulation analyses to support the newfound strategy. The results obtained underscore the effectiveness of the proposed design approach, which shows promise for broader applications in similar contexts. It should be noted that five different gear ratios were simulated in this study. For the lowest gear ratio (Gr1), the predicted maximum static torque was approximately 200 Nm. In contrast, for the highest gear ratio (Gr5), the predicted maximum static torque was about 50 Nm.