State of the Art of Magnetic Gears, their Design, and Characteristics with Respect to EV Application

Additional information is available at the end of the chapter Abstract This chapter briefly explains the advantage of using magnetic gears (MGs) for transportation applications. Usually, a traction EV unit consists of, besides the engine or motor, a mechanical gear. The drawbacks of using mechanical gears have been emphasized, especially with respect to high-speed motorization, where high transmis‐ sion ratio can be reached only by connecting multiple gears in series. A magnetic gear is capable of overcoming these issues. The chapter presents a state of the art on the available MGs, with fixed or variable transmission ratio, pointing out their applicabil‐ ity. Next, the possible design approaches (harmonic, magnetic reluctance equivalent circuit, and vector potential) are introduced. Furthermore, the output performances (power and torque) of two types of studied MGs are evaluated, with emphasis on the main loss criteria: iron losses in all the active parts of the MG. Finally, the influence of several materials is observed by means of numerical computation in order to decide, based on specific configuration, the most suited variant for transportation and aeronautic applications.

Since 2012, there has been an increase in the number of electric cars running on highways [3,6,8]. Most of them are powered by permanent magnet synchronous machines (PMSM)-due to their high energy from rare earths materials used for excitation-and sometimes by DC motors (DCM), for Renault ZOE model, induction machines (IM), or Tesla-S model. Table 1 presents few of the best-selling electric cars, in series production, with some technical characteristics and their cost/unit. Apart from Tesla-S model, which is extremely expensive, car manufacturers are generally proposing motorization variants with approximately the same performance and features. The best sold model today is the Nissan Leaf, launched in December 2010; by December 2016, it should reach over 200,000 units sold globally. Among European variants, Renault-Zoe and BMW-i3 are the bestsellers, noting that the German car manufacturer entered the market in the autumn of 2013 and by the end of this year, 2016, it should surpass 60,000 sold-ordered units. The number of electric units sold (globally surpassed the amount of 1 million units) is far from the number of internal combustion engine variants sold, one reason being the cost, in addition to the issue of autonomy. Basically, because of reduced autonomy and the reduced number of electric cars sold, the production cost/unit for EVs is high. Nevertheless, the trend is clear and with the increase in the number of supplying stations, the number of electric cars sold should increase exponentially. Table 1. Some of the best-selling electric cars, in series production: propulsion's characteristics and approximate cost/ unit. An interesting perspective was presented by the EVIG institute in 2013, see Figure 1. In their estimation, at the end of 2016 the number of cars sold should reach 2 million, and by the end of 2020 we should expect to have about 6 million electric cars running on streets. It looks promising, and we need to leave it to time to confirm their estimation.
The autonomy range of electric cars is affected by the load capacity and the energy storage capability, which is directly influenced by the total weight of the car and the propulsion's efficiency [2]. Thus, a closer look at the propulsion system should be considered.
The components of the drive chain are the electrical propulsion (electrical machine and transmission), the converter, and the battery-the energy flow within the system's components is bidirectional. The largest share of losses is in the electrical propulsion, 72%, on the static converter the loss is about 19%, and at the battery level the loss is about 9% (Figure 2).  Therefore, acting mainly on the electrical propulsion by improving its efficiency and power density will improve the overall autonomy of the EV [3][4][5].
With regard to the existing propulsion solution, it can be seen that over time, the operating speed has substantially increased [11][12][13][14][15][16][17][18][19]. As an example, let us take a look at few seriesmanufactured cars: if in 2003, the electric motor of the Toyota-Prius-Hybrid was at 6000 r/min, the latest model is running at 12,000 r/min [9]; for the BMW-i3 model, the nominal speed is 4000 r/min, while the maximum speed (in flux-weakening operating conditions) is 11,800 r/ min; for the present Mitsubishi-iMiev model, the speed of the motor is 9000 r/min. We can conclude that all car manufacturers are looking at increasing the speed of motorization, having in mind the improvisation of power density of the traction chain, as well as EV's autonomy.
In this context, we should recall that higher speeds are not easily and efficiently possible, since attached to the electric motor a gear is placed in order to transfer the torque-speed to the car's traction wheels. For a tire diameter of about 0.6 m and a circumferential speed of 1500 r/min coming from the gear, the vehicle's traveling speed is 47 m/s, meaning 169 km/h. In such a case, even if we would like to increase the speed of the propulsion motor, a classic mechanical gear with high transmission ratio is difficult to obtain; usually, we consider cascaded gear units, but this will affect the global power density of the traction system and its efficiency. Thus, a solution is needed to overcome this drawback. In this context, the use of a magnetic gear (MG) could be the right solution.
In Table 2, a weight comparison of the possible motorization solutions is presented, based on personal experience or technical data found on the available equipment.

Component
Electric propulsion For the sake of comparison, we have considered three possible variants: one motorization with 6500 r/min, another one with high-speed motor (running at 26,000 r/min), while the traction is used with a fixed mechanical gear ratio, or with multilevel gear (to reach the desired ratio), or when, for the same high-speed machine, we have a magnetic gear (MG) excited with rare earth material. Table 2 shows how for the same converter and battery pack, high-speed motorization has a reduced weight with about 80 kg (with fixed mechanical gear). Otherwise, when using an MG with high transmission ratio, the performance and power density are high, while the weight of the entire propulsion system is decreased by about 130 kg-which is a huge win for an EV.
The detailed structure of a magnetic gear will be presented in the next section. Here, we should recall that the main materials found on a magnetic gear are the permanent magnet for excitation, and the steel. Thus, the MG has one important disadvantage: it is extremely expensive because the excitation (on both rotating parts-the low-speed rotors-which are interacting for the production of the torque) is generally made of Nd-Fe-B. According to As a result, an important decision was first taken in 2012, when the European Research Agency (ERA) said that it will not fund research projects that use rare earth materials, such as Nd-Fe-B or Sm-Co type; it is for this reason that research institutes and universities have lately reconsidered the use of ferrite material (5 €/kg) or the possibility to avoid any excitation material, by means of passive rotors, such as reluctance synchronous machines (RSM). Some others are trying to reduce the volume of rare earth materials, calling such machines as PMassisted ones.
Otherwise, from previous research experience and information found in the literature, it has been observed that a magnetic gear with specific configuration of poles/teeth will induce specific torque ripples in the propulsion system [25][26][27][28][29][30][31]. Thus, when thinking of an MG, we are interested in finding an appropriate configuration which produces the lowest vibration and noise level. These elements will be considered with respect to the MG topic, while considering it for the EV application.

Principal of operation of magnetic gears, available topologies, and design approaches
A classic gear, meaning a mechanical one, which relies on the contact of two wheels with different number of iron teeth (see Figure 3 left), has some important drawbacks. First of all, physical contact is needed, which involves local friction and heat (and consequently losses). Besides, lubrication is needed from time to time, in appropriate quantity. Moreover, the teeth are physically and irreversibly damaged with time due to material friction and fatigue. Thus, the losses increase after several hours/years of operation. All these disadvantages are eliminated in the case of a magnetic gear (MG). Above all, another important benefit of MG use should be indicated here: in order to obtain high transmission ratio, one should use complex gears, with more than two integrated wheels. Usually, two or more mechanical gears are cascaded (linked) in the transmission chain. Such configurations drastically affect the power density and the efficiency of mechanical transmission. This is not the case for MGs: the most important amount of loss is found in the iron loss component, while the mechanical one (due to friction with the air and on the bearings) is in the same range as that of mechanical gears. The first reference of a gear without mechanical contact dates back to 1916 [20,34]. Since then, the benefits of MG were highlighted, namely: no need for lubrication, no local heating (no friction losses), and no risk of breaking the elements used to transfer power . However, the first built viable solution dates to the 1980s (see a similar configuration of such an MG in Figure 3 right)-evaluated from the torque capability point of view in [35]-but its efficiency was somewhere in the 25-30% range (only a part of magnetic poles was in active magnetic contact). The first efficient MG solution that fully exploits all the gear magnets dates back to early 2000 [20]-see Figure 4. Numerous other configurations of MGs have been proposed with time . Some of these variants will be shown here in order to have a clue about the state of the art, but before that, we will see the principal of operation of a regular MG.

Principal of operation
The operation of the MG is based on the modulation of the magnetic field created by the rotating magnetic poles of the high-speed rotor within the iron poles of the static part [20,33].
The main components of such MG are shown in Figure 4. The field developed in the static iron will interact with the field created by the magnetic poles of the low-speed (outer) rotor and will force it to run in the opposite direction [20,33].
It has been shown that the highest torque transmission is obtained with the following equality [20]: where p in , N s , and p out are the number of poles pair for the inner (high-speed) rotor, of the fixed iron part and of the outer (low-speed) rotor, respectively. The correspondences between the output (ω out ) and input (ω in ) speed and the gear ratio (gr) are: Besides, with a specific configuration of the MG, it is possible to obtain smooth mechanical characteristics-the lowest possible torque ripples are obtained if the ripples coefficient (k r ) equals unity (the ideal case) [33].
where LCM denotes the 'least common multiple' between the number of poles of the inner rotor and the fixed iron teeth.
These are just a few elements showing the operating principle of an MG in general. The analytical modeling of different MGs found in the literature will be summarized later, after the presentation of a detailed state of the art on the existent configurations.

State of the art of magnetic gears with fixed or variable transmission ratio
The first efficient MG, having radial configuration, was proposed by Attalah [20]. Next, other variants have been proposed. For example, in [34] a concentrated flux variant (or the so-called spoke configuration) was considered for the inner (high-speed) rotor; for the low-speed and hightorque rotor, the surface-mounted variant is almost exclusively used-because the surface-mounted topology proposes the best power density, and because at low speed the risk of magnet's detaching is reduced. Such a topology, like the one presented in [34], is shown in Figure 5. This variant is again of radial flux. Thus, one could imagine all types of configurations for the high-speed rotor, which are usually used for classic permanent magnet synchronous machines (PMSM)-see different rotor configurations in Figure 6.  Since in an MG we are not interested in the flux-weakening capabilities of the structure itself, the structure with surface-mounted magnets based on Nd-Fe-B material on the high-speed rotor (shown in Figure 4) is almost exclusively used. When cheaper magnet material such as the ferrite is used, the concentrated flux (or spoke) variant can be considered (Figure 5). The partially or entirely inset magnet variants in Figure 6 could be appropriate solutions when very high speeds are to be considered, in order to avoid the use of a consolidating ring of carbon or Titan material-which increases the air gap of the MG and drastically reduces its capability of producing the torque.
Axial flux variants [28,29], such as the ones shown in Figure 7, have also been analyzed, since the axial configuration offers the best power density (due to reduced volume and weight on the passive elements: shaft and housing). Usually, the MG is attached at the inner rotor side to an electric motor, to transfer the desired speed and torque to a load. In order to reduce the passive elements, some researchers have proposed integrated configurations. Such configurations are usually built on in-wheel motor variants, meaning that the motor has an inner stator and an outer rotor. Next, attached to the outer rotor is the inner rotor of the MG above, the static part with iron teeth, and on top of it the second rotor of the MG. Such compact variants have been studied in [26,30,31,39,40]. The transition from in-wheel motor to integrated MG-motor is shown in Figure 8. Other types of MGs, such as the cycloid [27] and even the ones with variable transmission ratio [24,29] have been proposed. Thus, we can emphasize that this topic is of real interest in the field of EVs (for the majority of applications) and power generation for wind turbines [39]. Next, the reader's attention will be focused on the existent analytical approaches that can be used for MG's design and modeling.

Analytical approaches for the design of MGs
There are three main design techniques for the analytical modeling of magnetic gears, similar to the case of electrical machines: the harmonic approach [25,27,30,36], the magnetic reluctance equivalent circuit [22,38], and vector potential algorithm [26,28,37,41].

Analytical design of MG through harmonic approach
For the solution presented in [20], later we had the formularization of the operating principal, given by Atallah [36] and others [25, 27 , 30]. In order to express the torque produced by the two rotors rotating in opposite direction, we first need to express the flux density in the air gap. This flux density has two components: a radial and a tangential one. Also, the influence of the stationary part (the iron teeth) has to be evaluated as a modulating component.
The two components of flux density, the radial and tangential one, produced by the inner rotor of the MG, are: where a n , b n , and α 0 are the Fourier coefficients and the initial shift angle of the rotor. Next, the modulating component of the fixed iron teeth, similarly obtained, is function of Fourier coefficients and initial shift angle of this armature, meaning a n , b n , and α 0 : Similar to (5), one can get the flux density components to the outer rotor of the MG. In [30] some detailed formulation was given for the harmonic components with the pole pair number equal to (n ⋅ p in ) and (m ⋅ N s -n ⋅ p out ), or equal to (n ⋅ p out ) and (m ⋅ N s -n ⋅ p in ).
The torque produced by the inner and outer rotor is a function of the pull-out torque, T min and T mout (γ 0 is the shift angle of the outer rotor of the MG) [30]:

Analytical design of MG through magnetic reluctance equivalent circuit
Based on the literature research, we have found a first approach on MG modeling through magnetic reluctance equivalent circuit in [22]. This approach is interesting because it also takes into account the steel material characteristic (through curve fitting). Actually, this paper was an adaptation of the method presented in [38] where the analytical design approach was applied to a brushless permanent magnet machine.
The method consists in computing the torque, as a function of a flux (Ψ m ) and magneto-motive force (F m ) product, produced in each element of the equivalent circuit. Such a magnetic reluctance equivalent circuit is shown in Figure 9.
where n θ is the number of elements of reluctances on the considered equivalent circuit. The magnetic flux is a function of the magnetic reluctance, which can be expressed through curve fitting for each specific material. For a certain iron sheet, the magnetic reluctance can be expressed as: where h is the length of the flux for a specific trajectory and the S is the area of the flux on a specific element of the geometry-a or n index varies the function of material. These reluctances (and finally the fluxes) are calculated on radial and tangential direction.
The magneto-motive force, F m , can be computed as well on each specific element, recalling that: where H m is the magnetic field intensity calculated on each element of the magnetic circuit.

Analytical design of MGs through vector potential algorithm
The vector potential expressions, in both air gaps of the MG, have been detailed for radial and axial flux topologies in [28,41]. Since the mathematical modeling for such an approach is quite laborious and goes beyond the scope of this state-of-the-art presentation of MGs, it will not be presented here. (It's worth mentioning that even the integral coefficients are detailed in the previous references; thus, the reader can investigate this topic if needed.) With this, we have concluded a short presentation on the available analytical models used in the design of process of MGs. Next, we will consider two of the available configurations to evaluate their performances (in terms of iron loss and torque) and we will rapidly investigate the influence of certain materials used in the construction of MGs.

Characteristics of MGs with respect to their use in EV application
Two of the previously presented MG variants will be investigated here: the first one is an integrated motor-gear variant having an in-wheel configuration for the electric motor, and the second MG will be a high-speed variant with buried permanent magnets. Evaluation of the performances of these two topologies in terms of iron loss and torque (or output power) will be employed numerically, by means of finite element method (FEM) and the Flux2D software.

Integrated in-wheel motor magnetic gear topology
The considered in-wheel motor gear topology is the one presented in Figure 8. The motor is a fractional slot permanent magnet synchronous machine (FS-PMSM)-17 pairs of poles and 39 slots. Above the outer rotor of the FS-PMSM and attached to it, we have an inner rotor of the MG, having the same number of pairs of poles (p in =17), and a reduced number of pairs of poles for the outer rotor of the MG (p out =5). It means that the magnetic transmission will produce a higher speed, at a lower torque: it is a multiplier, or reversed gear [40]. Numerically computed results are shown in Figures 10-12.   A first result of this analyzed integrated motor-gear variant is shown in Figure 10, where the field lines and flux density distribution within the active parts of the topology are presented.
The reader can observe the influence of modulated teeth in the transfer of the flux (torque) from the inner to outer rotor. In the air gap layers of this machine-gear topology, the FEM software computed the following air gap flux densities, plotted in Figure 11: here, Gap1 refers to the in-wheel motor's air gap, Gap2 stands for the inner rotor air gap of the MG and Gap3 refers to its outer rotor air gap. More results are plotted in Figure 12.
The delivered torque and power, as well as the iron loss within the active parts of the integrated motor-gear studied variant are plotted in Figure 11. Some torque ripples can be identified, both on the inner and on the outer rotors of the integrated motor-gear variant. Since the major loss component within an MG is the iron loss, it is obvoius that the efficiency of the transmission is very low. One could sum the iron loss components (for the inner and outer rotor, as well as for the static part poles or teeth-SPP) and of the in-wheel motor to get 130 W. These results are not optimized. Based on the image of the flux density distribution (Figure 10 right), we could consider to reshape the teeth's geometry and the outer rotor yoke, in the perspective of increasing the efficiency.
In order to prove the important advantage of MGs against classic mechanical gear, that is the possibility to obtain a very high transmission ratio for high-speed applications, and to get a very compact magnetic traction system with very good power density, the reader's attention will be oriented toward a high-speed MG.

MG with buried permanent magnets for high-speed applications
The second analyzed MG is with high-speed inner rotor, running at 26,000 r/min (with p in =1), and outer rotor for low-speed rotor (with p out =15) running at approximately 1500 r/min. The number of static part iron teeth is N s =16. The magnets are buried in order to avoid the surfacemounted pieces which need a consolidating ring. A preliminary check on the mechanical resistance of the inner rotor steel needs to be employed numerically, to check if the iron bridges have not been damaged during MG's operation. A cross section of the high-speed MG is shown in Figure 13. This MG will be evaluated for different steel material characteristics (M335, M400, and Vacoflux48), and permanent magnet types (Nd-Fe-B, Ferrite, Alnico). As a reference variant, the MG with Nd-Fe-B and M400 steel is considered. The first result of this configuration is shown in Figure 14, where the field lines and flux density distribution are shown. An obvious saturation is found on the inner rotor core, on the iron's bridge, which is normal behavior since the flux needs to pass the air gap.   An amount of 365 W of iron loss was computed here. By comparing these iron losses (for the M400 steel, given in Figure 17, and the ones from Figure 18, for Vacoflux48), the huge advantage of the structure equiped with Vacoflux material is obvious, for which the iron loss is less than half of the M400-which is neither a bad material nor a cheap one. Of course, products based on Vacoflux48 are rather exclusive units and meant for special applications (like racing cars)-the cost of one prototype is almost prohibitively expensive. For ordinary applications, even the M400 steel is considered an expensive material-it is usually used for prototypes and low series manufacturing. Otherwise, a cheaper variant based on M335 is suitable in terms of output performances, giving similar results as the ones using M400.
A more complete comparison of the performances of the high-speed MG, when equipped with different types of materials and their magnetical characteristics is given in Tables 4 and 5the width of the considered steel sheet (0.2, 0.35, and 0.5mm) is given also in Table 4. Some comments need to be made with respect to the Alnico and ferrite, the results of which are summarized in Table 4: for this specific configuration of the MG, because of the iron bridge which needs to support important centrifugal forces (we recall that the high-speed rotor is running at 26,000 r/min), and the low level of remanent flux density (for Ferrite material) or coercivity (for Alnico), the magnetic flux is not sufficiently strong to cross the air gap. Different rotor configurations (with concentrated flux or halback array) need to be considered-which means that a topology with more than one pair of poles is requested. To prove this, one can investigate the field lines and the flux densities depicted in Figure 16, given within the active parts of the MG while ferrite or Alnico materials are used (Figure 19). Figure 19. Investigation of the MG field lines and flux density distribution, when ferrite (top) and Alnico (bottom) magnets were considered.
As 15 years have passed since the first efficient MG proposition, we could expect, in the next years, improvements in the field of MGs, especially for the ones with variable transmission ratio, which could be extremly useful in transportation and aeronautical domains. With the advancement in the field of materials, for rare earth materials and ferromagnetic steel, the future of fully electromagnetic propulsion systems could be considered as a viable industrial solution, and not only a new research subject.

Conclusions
This chapter proposes an overview of the challenges in EV application, where the speed limits were pushed forward in the last decade. Practically, all the car manufacturers are proposing mobility solutions based on electrically propelled traction systems, which are limited because of the drawbacks of the mechanical gear, which needs to be continuously lubricated, presenting important heat and local losses; moreover, higher speeds drastically decrease the power density of motorization. To overcome these drawbacks, researchers have proposed in the last decade possible solutions based on magnetic gears (MGs). We have presented in this chapter the existent configuration of fixed transmission ratio MGs, we have also indicated some references in which the variable transmission was studied and we have presented the main analytical approaches used for the design of MGs: the harmonic, magnetic reluctance equivalent circuit, and vector potential algorithms. A quasi-complete reference list was given with respect to this topic. Next, we have investigated two variants of MG, one with integrated motor and a second one for high-speed applications and a transmission ratio of 1/16. Through numerical computation we have investigated the output mechanical performances of the studied MGs, as well as the major loss component of such devices: the iron loss within the active parts of the MG. The influence of different materials on the active parts, meaning ferromagnetic steel and permanent magnets, was evaluated and a comparison of the obtained performances was depicted.
The research on MG has gained interest in the last decade and we expect that based on advancements in materials, the performances of these devices will be even more improved and will be of real interest, especially in the field of transportation and aeronautics.