sustainability

Article Design and Operating Mode Study of a New Concept Car Employing Permanent Magnet Electrodynamic Suspension Technology

Ze Zhang 1, Zigang Deng 1,* , Shuai Zhang 1, Jianghua Zhang 1, Li’an Jin 2, Xiaochen Sang 1, Pengfei Gao 3, Jing Li 1 and Jun Zheng 1

1 State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China; [email protected] (Z.Z.); [email protected] (S.Z.); [email protected] (J.Z.); [email protected] (X.S.); [email protected] (J.L.); [email protected] (J.Z.) 2 School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China; [email protected] 3 School of Architecture and Design, Southwest Jiaotong University, Chengdu 610031, China; [email protected] * Correspondence: [email protected]

Abstract: Based on the principle of permanent magnet electrodynamic suspension (PMEDS), a new concept maglev car was designed by using rotary magnetic wheels and a conductor plate. It has the advantages of being high-speed, low-noise, environmentally friendly, safe and efficient. The PMEDS   car is designed to use a permanent magnet electrodynamic wheel (EDW) to achieve the integration of levitation force and driving force. The levitation force is generated by the repulsive force of the eddy Citation: Zhang, Z.; Deng, Z.; Zhang, current magnetic field, and the driving force is generated by the reaction force of magnetic resistance. S.; Zhang, J.; Jin, L.; Sang, X.; Gao, P.; A simplified electromagnetic force model of the EDW and a dynamics model of the PMEDS car were Li, J.; Zheng, J. Design and Operating established to study the operating mode. It shows that the PMEDS car can achieve suspension when Mode Study of a New Concept Maglev Car Employing Permanent the rotational speed of the EDWs reaches a certain threshold and the critical speed of the EDWs is Magnet Electrodynamic Suspension 600 rpm. With the cooperation of four permanent magnet EDWs, the PMEDS car can achieve stable Technology. Sustainability 2021, 13, suspension and the maximum suspension height can reach 7.3 mm. The working rotational speed of 5827. https://doi.org/10.3390/ EDWs is 3500 rpm. At the same time, the movement status of the PMEDS car can be controlled by su13115827 adjusting the rotational speed of rear EDWs. The functions of propulsion, acceleration, deceleration, and braking are realized and the feasibility of the PMEDS car system is verified. Academic Editors: Antonio Ometto and Gino D’Ovidio Keywords: permanent magnet; electrodynamic suspension; maglev car; electromagnetic force; operating mode Received: 14 March 2021 Accepted: 17 May 2021 Published: 21 May 2021 1. Introduction Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in According to the suspension mechanism, the maglev scheme is divided into a high published maps and institutional affil- temperature superconducting (HTS) maglev, electromagnetic suspension (EMS) and elec- iations. trodynamic suspension (EDS). The HTS maglev makes use of the unique strong magnetic flux pinning ability of high-temperature superconductors in the external magnetic field, so that the superconductor can induce the superconducting current that hinders the change of the applied magnetic field. This unique electromagnetic interaction macroscopically realizes self-suspension and self-stability. Based on this characteristic, HTS maglev has Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. been successfully applied in , flywheel energy storage, rail transit, and This article is an open access article other fields. Magnetic bearing has been studied for nearly 20 years in the United States [1], distributed under the terms and Germany [2], and [3], and has gradually been extended to large-scale commercial conditions of the Creative Commons applications. Other countries, such as South Korea [4], are gradually increasing their invest- Attribution (CC BY) license (https:// ment in this field. The HTS flywheel energy storage system (HTS-FESS) has the advantages creativecommons.org/licenses/by/ of a simple control, high energy storage density, high efficiency, long service life and wide 4.0/). application range. Several teams in the United States [5], Japan [6,7], and Germany [8]

Sustainability 2021, 13, 5827. https://doi.org/10.3390/su13115827 https://www.mdpi.com/journal/sustainability Sustainability 2021, 13, 5827 2 of 20

are developing the HTS-FESS prototype. In 2000, the first man-loading HTS maglev test vehicle “Century” was successfully developed in Southwest Jiaotong University, Chengdu, China [9]. In 2013, the team manufactured a 45-m-long HTS maglev ring test line and the second-generation HTS maglev vehicle “Super-Maglev” [10]. In addition, institutions in Germany [11], Japan [12], Brazil [13], and Italy [14] also developed HTS maglev vehicles in succession. The EMS is based on the force of attraction between the energized conductor and rail ferromagnets and maintains the gap through active control. Germany’s “ (TR)” series is an outstanding representative of EMS in the field of maglev transportation, which has been developed into the TR09 train. The low-speed EMS maglev system is represented by Japan’s HSST, which runs at a maximum speed of 130 km/h and is oriented towards a medium and low-speed urban rail transit system. The EDS [15] is composed of magnetic materials and non-magnetic passive tracks that induce eddy current flowing inside, while magnetic materials move above it. The induced current forms the magnetic field opposite to that of the magnetic materials, which produces the force in the vertical and horizontal directions. The main applications of EDS are low-temperature superconducting EDS and permanent magnet EDS. Japan is in the leading position in the low-temperature superconducting EDS and the has set a world record of 603 km/h [16]. The permanent magnet EDS field is dominated by the United States. In 1998, the US state of Georgia [17] adopted the [18] technology developed by Lawrence Livermore National Laboratory in its urban maglev transportation technology development project. Compared with other maglev methods, EDS has a simpler track structure which can achieve self-stabilizing suspension and does not require a complex control system [19]. Because of low cost, EDS is being studied as a substitute for existing high-speed maglev systems [20–22]. Therefore, it has become one of the hot spots in maglev research. However, the traditional structure of EDS has the limitations of a large electromagnetic resistance, high energy consumption, and incapability to achieve static suspension. Reduc- ing magnetic resistance or effectively using magnetic resistance is the key to promoting the development of EDS technology. Various methods are used to reduce this kind of magnetic resistance, but their cost is huge. R. F. Post and D. L. Trumper et al. have proposed that linear Halbach arrays can provide a low cost means of providing sufficient levitation force for a maglev system [23–25]. But such a system still creates magnetic resistance and requires a separate expensive linear synchronous motor to generate thrust. Another option is to try to use the magnetic resistance for propulsion. This can be achieved by rotating the magnetic source instead of simply translating. The generation of magnetic thrust is similar to the generation of the car wheel thrust that uses friction. The magnetic rotor rotates and translates above the track at the same time. This generates eddy currents and a reverse field which interacts with the source field to generate not only levitation force but also propulsion force [26–28]. In the 1970s, it was proposed that rotating superconducting magnets on a non- magnetic conductive track could provide an integrated suspension and propulsion mech- anism for high-speed ground transportation [29,30]. This structure is almost certainly complicated by the need to rotate a superconductor cooled by helium. With the rapid improvement of a rare earth magnet, it is thought that it may use a permanent magnet instead of a superconductor to create a low-cost rotor with a small air gap [31]. N. Fujii et al. [32,33] proposed a vertical permanent magnet wheel structure which was placed above the edge of the conductive track. It can not only generate levitation force, but also generate propulsion force and lateral force. Meanwhile, when the track is inclined, it will also increase the lateral force. However, there are few examples in the literature that report on the performance and thrust efficiency of such maglev systems during translation, and discussion on the prototype of the axial magnetic rotating maglev system has not been carried out. T. Lipo et al. [32,34] proposed a horizontal permanent magnet wheel structure where a radial Halbach permanent magnet array mechanically rotates above a non-magnetic conductive track to form a time-varying magnetic field, which interacts with the track to induce levitation and propulsion force at the same time. This structure can be Sustainability 2021, 13, 5827 3 of 20

used to build a relatively inexpensive form of maglev transportation because the track does not require electrical installation, and the levitation and propulsion force will be generated by a single mechanism. J. Bird et al. [35] used a two-dimensional steady-state method to study various parameters that affect the performance of this maglev system and proposes corresponding methods to improve the performance. In this paper, in order to make full use of the advantages of permanent magnet electrodynamic suspension (PMEDS), we introduced the PMEDS technology into the automobile structural system, designed a new concept maglev car structure based on the radial Halbach permanent magnet array, and fabricated the principal prototype. The PMEDS car applies EDS technology to the structure of the car system, which breaks the traditional driving mode and can realize the functions of suspension, propulsion, braking, etc. Combined with finite element analysis, a simplified electromagnetic force model was established, and the dynamics model was designed and built in Adams dynamics simulation software. Based on the dynamics model, the operating mode of the PMEDS car under static suspension, acceleration, uniform speed, and deceleration were studied. The simulation results provide a groundbreaking exploration for the application of new concepts of maglev transportation.

2. Structural Design and Schematic The PMEDS car system consists of a maglev car and maglev lane, as shown in Figure1. The entire body of a maglev car is similar to a traditional car, except that the rubber wheel is embedded with the ring-shaped permanent magnet wheel. A non-ferromagnetic conductor plate is paved on the surface of ordinary roads as a special maglev lane. The PMEDS car can get rid of the constraints of the track existing in other classical maglev systems, and steer actively rather than being passively guided by the track. At the same time, the flat and simple maglev lane structure can be more easily integrated into the existing traffic infrastructure. In addition, the PMEDS car has strong adaptability, and can switch freely between a maglev car and conventional electric car. When the speed is low, a maglev car can run on ordinary roads, which is no different from a traditional car. When the maglev car needs to run at high speed, it can switch to the maglev lane and enter suspension Sustainability 2021, 13, x FOR PEER mode,REVIEW so as to reduce the resistance and greatly improve the driving speed. Therefore,4 itof is 21

expected to be a promising transportation tool in the future.

Figure 1. Concept map of the PMEDS car. Figure 1. Concept map of the PMEDS car.

Our group designed and built a 1:50 PMEDS car model. Figure 2 shows its structure diagram and Figure 3 shows the experimental prototype of the PMEDS car. A maglev car is composed of four permanent magnet electrodynamic wheels (EDW), four brushless outer rotor DC motors, a chassis, and four auxiliary wheels. The permanent magnet EDW adopts the annular Halbach structure. The motors use a brushless outer rotor DC motor. The controller controls four motors separately.

Figure 2. Structure diagram of the PMEDS car model.

Figure 3. Experimental prototype of the PMEDS car. Sustainability 2021, 13, x FOR PEER REVIEW 4 of 21 Sustainability 2021, 13, x FOR PEER REVIEW 4 of 21

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Figure 1. Concept map of the PMEDS car. Figure 1. Concept map of the PMEDS car. Our group designed and built a 1:50 PMEDS car model. Figure 2 shows its structure OurOur group group designed designed and and built built a a 1:50 1:50 PMEDS PMEDS car car model. model. Figure Figure 2 shows its structure diagram and Figure 3 shows the experimental prototype of the PMEDS car. A maglev car diagramdiagram and and Figure Figure 33 shows shows the the experimental experimental prototype prototype of ofthe the PMEDS PMEDS car. car. A maglev A maglev car is composed of four permanent magnet electrodynamic wheels (EDW), four brushless iscar composed is composed of four of four permanent permanent magnet magnet electrodynamic electrodynamic wheels wheels (EDW), (EDW), four four brushless brushless outer rotor DC motors, a chassis, and four auxiliary wheels. The permanent magnet EDW outerouter rotor rotor DC DC motors, motors, a a chassis, chassis, and and four four auxiliary auxiliary wheels. wheels. The The permanent permanent magnet magnet EDW EDW adopts the annular Halbach structure. The motors use a brushless outer rotor DC motor. adoptsadopts the the annular annular Halbach Halbach structure. structure. The The mo motorstors use use a abrushless brushless outer outer rotor rotor DC DC motor. motor. The controller controls four motors separately. TheThe controller controller controls controls four four motors motors separately. separately.

FigureFigure 2. 2.StructureStructure diagram diagram of ofthe the PMEDS PMEDS car car model. model. Figure 2. Structure diagram of the PMEDS car model.

Figure 3. Experimental prototype of the PMEDS car. Figure 3. Experimental prototype of the PMEDS car. Figure 3. Experimental prototype of the PMEDS car.

Magnetic wheels are the core components of a maglev car, and they are the direct source of levitation force and driving force. Figure4 shows the structure and operating state of a permanent magnet EDW. The magnetic wheel adopts a four-pole annular Halbach structure, including 16 magnetic monomers. The permanent magnet array adopts radial and tangential magnetization methods to form the Halbach permanent magnet array, which has a strong magnetic field outside and a weak magnetic field inside. The Halbach array is fixed on a horizontally placed outer rotor of the motor that rotates at high speed, which forms a time-varying magnetic field on the surface of the secondary induction plate that is located below the permanent magnet array. According to Lenz’s law, eddy current will be generated in the secondary induction plate. The interaction between the eddy current field and the external magnetic field will generate a repulsive force related to the magnetic induction intensity of the external magnetic field and the relative speed of movement. The tangential force is expressed as a driving force in the horizontal direction and the normal force is expressed as a levitation force that overcome the self-weight of the EDW. It makes full use of the characteristics of the annular Halbach structure permanent magnet array and converts the inherent magnetic resistance into the driving force in the direction of travel by rotating. Sustainability 2021, 13, x FOR PEER REVIEW 5 of 21

Magnetic wheels are the core components of a maglev car, and they are the direct source of levitation force and driving force. Figure 4 shows the structure and operating state of a permanent magnet EDW. The magnetic wheel adopts a four-pole annular Hal- bach structure, including 16 magnetic monomers. The permanent magnet array adopts Sustainability 2021, 13, 5827radial and tangential magnetization methods to form the Halbach permanent magnet ar- 5 of 20 ray, which has a strong magnetic field outside and a weak magnetic field inside.

Figure 4. SchematicFigure 4. ofSchematic the structure of the and structure operatin andg state operating of a permanent state of a permanentmagnet EDW. magnet EDW.

The HalbachAt thisarray time, is fixed the driving on a horizontally force and the placed levitation outer force rotor have of athe strong motor coupling that ro- relationship. tates at highThe speed, onlyfactor which affecting forms a themtime-varying is the relational magnetic speed field between on the surface the magnetic of the wheelsec- and the ondary inductioninduction plate plate. that Under is located the action below of the the permanent driving force, magnet the magneticarray. According wheel generates to the Lenz’s law,traveling eddy current speed will in the be forwardgenerated direction, in the secondary which makes induction the relative plate. rotationalThe interac- speed of the tion betweenmagnetic the eddy wheel current with field the inductionand the external plate decrease magnetic and field the will suspension generatecapacity a repul- gradually sive force reduce,related soto athe single magnetic suspension induction unit cannot intensity achieve of the the external integration magnetic of suspension field and and driving. the relative speedThe of rotational movement. speed The oftangential four permanent force is expressed magnet EDWs as a driving are controlled force in bythe motors to realize the suspension function and operating state control function. Figure5 shows horizontal direction and the normal force is expressed as a levitation force that overcome the schematic diagram of a PMEDS car model. The front EDWs turn counterclockwise the self-weight of the EDW. It makes full use of the characteristics of the annular Halbach at the rotational speed of ω and the direction of magnetic resistance F is backward, structure permanent magnet array and1 converts the inherent magnetic resistance intod1 the while the rear EDWs turn clockwise at the rotational speed of ω and the direction of driving force in the direction of travel by rotating. 2 magnetic resistance F is forward. The suspension function is achieved by synchronizing Sustainability 2021, 13, x FOR PEERAt this REVIEW time, the driving forced2 and the levitation force have a strong coupling rela- 6 of 21 the rotational speed of the front and rear EDWs and turning in opposite directions, which tionship. The only factor affecting them is the relational speed between the magnetic generates driving force of the same size and opposite directions that offsets each other. wheel and the induction plate. Under the action of the driving force, the magnetic wheel At the same time, the levitation force F +F generated by the four EDWs overcomes the generates the traveling speed in the forward direction,l1 l2 which makes the relative rotational weightof the entire of the device entire deviceto achieve to achieve in-situ in-situ suspen suspension.sion. Then, Then,the difference the difference in driving in driving force speed of the magnetic wheel with the induction plate decrease and the suspension capac- forcebetween between the front the front and andrear rearEDWs EDWs formed formed by bydifferent different rotational rotational speed speed is isused used to to form form a ity gradually reduce, so a single suspension unit cannot achieve the integration of suspen- aforward forward propulsion propulsion when when Fd1FFd2d1 to>F realized2 to realize a pro- sion and driving.apulsion propulsion and braking and braking function. function. In addition, In addition, by adjusting by adjusting the difference the difference in rotational in rotational speed The rotationalspeedon the on left thespeed and left rightof and four rightsides, permanent sides, the device the ma device isgnet driven isEDWs driven by aredifferent by controlled different propulsion propulsion by motors forces forcesto on the on theleft realize theleftand suspension and right right sides function sides and and achieves and achieves operatin a steering a steeringg state function. control function. function. Figure 5 shows the schematic diagram of a PMEDS car model. The front EDWs turn counterclockwise at the rotational speed of ω1 and the direction of magnetic resistance Fd1 is backward, while the rear EDWs turn clockwise at the rotational speed of ω2 and the direction of magnetic re- sistance Fd2 is forward. The suspension function is achieved by synchronizing the rota- tional speed of the front and rear EDWs and turning in opposite directions, which gener- ates driving force of the same size and opposite directions that offsets each other. At the same time, the levitation force Fl1+Fl2 generated by the four EDWs overcomes the weight

Figure 5. Schematic diagram of the PMEDS car model. Figure 5. Schematic diagram of the PMEDS car model.

3. Simplified Model of Electromagnetic Force To provide electromagnetic force input for dynamic simulation to accurately analyze the dynamic response of the PMEDS system, it is necessary to transform the interaction relationship between the EDW and the conductor plate and establish a simplified electro- magnetic force model. The main core of the PMEDS electromagnetic model is an induction eddy current model composed of a moving permanent magnet and an induction plate. There are two main research methods: one is the analytical approach, and the other is the numerical approach (mainly the finite element method). The circular geometry of the EDW combined with the linear geometry of the lane makes the analytical approach a for- midable problem and both 2D and 3D analytical calculations lack an accurate and univer- sal analytical equation. On the other hand, the research on the linear Halbach structure accounts for the majority of the PMEDS based on the Halbach structure. The research on the annular Halbach structure is less extensive and the methods are mostly equivalent to the linear Halbach structure. The calculation results are quite different. Therefore, in this paper we used the finite element method to carry out numerical calculations of the force of the suspension system, and studied the law of the levitation force and driving force with the system parameters, so as to obtain a simple and effective electromagnetic force mathematical model of the suspension system. Finally, the mathematical model was used to quantitatively describe the levitation force and driving force, which provides an effec- tive reference for the characteristic analysis of PMEDS systems. We used the finite element analysis software Maxwell to numerically analyze the electromagnetic force characteris- tics of the EDW and proposed a simplified mathematical model of electromagnetic force for dynamic calculations. The mathematical model has a simple expression form and is more suitable for engineering calculations. The outer radius of EDW was fixed to 50 mm according to the size ratio of car model. In order to reduce the eddy current loss and increase the levitation force, other parameters of EDW were optimized by Maxwell 2D simulation. The values of model parameters are shown in Table 1. In order to make the simulation result closer to the experimental data, a simplified three-dimensional finite element model of the permanent magnet EDW was established, as shown in Figure 6. The model includes five parts: EDW, conductor plate, motion domain Band, and solution region. Since the EDW is rotating, the motion domain Band uses a polygonal cylinder to wrap the EDW. The material of EDW is N35 whose remanence is 1.42 T and the magnetization direction is set according to the ring Halbach. The material of the conductor plate is set to aluminum, and the motion domain Band and solution region are set as a vacuum. The rotational speed is set to 0 to 6000 rpm, while the air gap is set to 5 to 15 mm and the length step is 1 mm. Sustainability 2021, 13, 5827 6 of 20

3. Simplified Model of Electromagnetic Force To provide electromagnetic force input for dynamic simulation to accurately analyze the dynamic response of the PMEDS system, it is necessary to transform the interaction relationship between the EDW and the conductor plate and establish a simplified electro- magnetic force model. The main core of the PMEDS electromagnetic model is an induction eddy current model composed of a moving permanent magnet and an induction plate. There are two main research methods: one is the analytical approach, and the other is the numerical approach (mainly the finite element method). The circular geometry of the EDW combined with the linear geometry of the lane makes the analytical approach a formidable problem and both 2D and 3D analytical calculations lack an accurate and uni- versal analytical equation. On the other hand, the research on the linear Halbach structure accounts for the majority of the PMEDS based on the Halbach structure. The research on the annular Halbach structure is less extensive and the methods are mostly equivalent to the linear Halbach structure. The calculation results are quite different. Therefore, in this paper we used the finite element method to carry out numerical calculations of the force of the suspension system, and studied the law of the levitation force and driving force with the system parameters, so as to obtain a simple and effective electromagnetic force mathematical model of the suspension system. Finally, the mathematical model was used to quantitatively describe the levitation force and driving force, which provides an effective reference for the characteristic analysis of PMEDS systems. We used the finite element analysis software Maxwell to numerically analyze the electromagnetic force characteristics of the EDW and proposed a simplified mathematical model of electromagnetic force for dynamic calculations. The mathematical model has a simple expression form and is more suitable for engineering calculations. The outer radius of EDW was fixed to 50 mm according to the size ratio of car model. In order to reduce the eddy current loss and increase the levitation force, other parameters of EDW were optimized by Maxwell 2D simulation. The values of model parameters are shown in Table1. In order to make the simulation result closer to the experimental data, a simplified three-dimensional finite element model of the permanent magnet EDW was established, as shown in Figure6. The model includes five parts: EDW, conductor plate, motion domain Band, and solution region. Since the EDW is rotating, the motion domain Band uses a polygonal cylinder to wrap the EDW. The material of EDW is N35 whose remanence is 1.42 T and the magnetization direction is set according to the ring Halbach. The material of the conductor plate is set to aluminum, and the motion domain Band and solution region are set as a vacuum. The rotational speed is set to 0 to 6000 rpm, while the air gap is set to 5 to 15 mm and the length step is 1 mm. The boundary condition is defined as the infinity boundary condition which is called Balloon Boundary. The introduction of this boundary condition is a very ideal processing method because it removes the necessity of drawing the solution domain in a way that is too large, thereby reducing the overhead of computing resources such as the memory and CPU.

Table 1. The parameters in the Maxwell 3D simulation.

Parameter Value Pole pairs, P 4 Remanence of permanent, Br/T 1.42 Inner radius of EDW, Ri/mm 34 Outer radius of EDW, Ro/mm 50 Width of EDW, Ww/mm 35 Width of Conductor Plate, Wp/mm 100 Thickness of Conductor Plate, Tp/mm 10 Conductivity of Conductor Plate, σ/(S/m) 3.8 × 107 Rotational speed ω/rpm 0~6000 Air gap, G/mm 5~15 Sustainability 2021, 13, x FOR PEER REVIEW 7 of 21

Table 1. The parameters in the Maxwell 3D simulation.

Parameter Value Pole pairs, P 4 Remanence of permanent, Br/T 1.42 Inner radius of EDW, Ri/mm 34 Outer radius of EDW, Ro/mm 50 Width of EDW, Ww/mm 35 Width of Conductor Plate, Wp/mm 100 Thickness of Conductor Plate, Tp/mm 10 7 Sustainability 2021, 13, 5827 Conductivity of Conductor Plate, σ/(S/m) 3.8 × 10 7 of 20 Rotational speed ω/rpm 0~6000 Air gap, G/mm 5~15

FigureFigure 6. Permanent 6. Permanent magnet magnet EDW EDW model model in Maxwell. in Maxwell.

TheThe boundary excitation condition source consists is defined of two as the parts: infinity the first boundary is the main condition excitation which magnetic is called field Balloonprovided Boundary. by the permanent The introduction magnet, of which this boundary has been completed condition in is the a very material ideal setting, processing and the methodsecond because is the eddy it removes current the effect necessity of the conductor of drawing plate, the which solution is set domain in the excitations.in a way that is

Sustainability 2021, 13, x FOR PEERtoo REVIEW large,Due thereby to the reducing regular size the of overhead the model, of computing the mesh division resources adopts such manual as the memory division.8 of and Since21 CPU.the EDW and the motion domain band need to calculate their motion properties, their meshesThe excitation are refined. source The consists conductor of two plate parts: is a fixedthe first part, is the so itsmain mesh excitation size can magnetic be slightly fieldenlarged. provided The by meshthe permanent of the solution magnet, region which can has be been divided completed into the in maximum the material size. set- The Figure 9 shows the distribution of eddy current in the conductor plate when the ro- ting,meshing and the diagram second ofis the the eddy permanent current magnet effect of EDW the modelconductor is shown plate, inwhich Figure is 7set. The in the total tational speed of EDW is 3000 rpm and the air gap is 10 mm. The eddy current is mainly number of meshes is 217,659. excitations.concentrated in the rearward position below the wheel, and there are two current loops. Due to the regular size of the model, the mesh division adopts manual division. Since the EDW and the motion domain band need to calculate their motion properties, their meshes are refined. The conductor plate is a fixed part, so its mesh size can be slightly enlarged. The mesh of the solution region can be divided into the maximum size. The meshing diagram of the permanent magnet EDW model is shown in Figure 7. The total number of meshes is 217,659. Figure 8 shows the distribution of magnetic flux density in the conductor plate when the rotational speed of EDW is 3000 rpm and the air gap is 10 mm. The direction of the induction magnetic field is opposite to the magnetic field of EDW. The induction magnetic field below the EDW is stronger, which affects the levitation force and driving force. The maximum magnetic flux density can reach 0.4931 T.

Figure 7. The meshing diagram of the permanent magnet EDW model. Figure 7. The meshing diagram of the permanent magnet EDW model.

Figure 8. Distribution of magnetic flux density in the conductor plate. Sustainability 2021, 13, x FOR PEER REVIEW 8 of 21

Figure 9 shows the distribution of eddy current in the conductor plate when the ro- tational speed of EDW is 3000 rpm and the air gap is 10 mm. The eddy current is mainly concentrated in the rearward position below the wheel, and there are two current loops.

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Figure8 shows the distribution of magnetic flux density in the conductor plate when the rotational speed of EDW is 3000 rpm and the air gap is 10 mm. The direction of the

induction magnetic field is opposite to the magnetic field of EDW. The induction magnetic fieldFigure below 7. The the meshing EDW diagram is stronger, of the which permanent affects magnet the levitation EDW model. force and driving force. The maximum magnetic flux density can reach 0.4931 T.

Figure 8. Distribution of magnetic flux density in the conductor plate. Figure 8. Distribution of magnetic flux density in the conductor plate.

Sustainability 2021, 13, x FOR PEER REVIEWFigure 9 shows the distribution of eddy current in the conductor plate when9 of the 21 rotational speed of EDW is 3000 rpm and the air gap is 10 mm. The eddy current is mainly concentrated in the rearward position below the wheel, and there are two current loops.

Figure 9. Distribution of eddy current in the conductor plate.

Figure 1010 shows shows the the levitation levitation force force and and driving driving force force of the of EDW the EDW with differentwith different rotational ro- tationalspeeds under speeds different under different suspension suspension air gaps. As air shown gaps. As in Figureshown 10 ina, Figure the levitation 10a, the force levitation firstly forceincreases firstly rapidly increases with rapidly the increase with the of theincrease rotation of the speed rotation of the speed EDW of and the starts EDW to and increase starts toslowly increase around slowly 2000 around rpm. This 2000 is rpm. because This the is because higher the the rotational higher the speed rotational of the speed EDW is,of the EDWgreater is, the the magnetic greater the density magnetic passing density through passing the conductor through the plate conductor per unit time,plate whichper unit is time,equivalent which to is a equivalent faster frequency to a faster of the frequency time-varying of the electromagnetic time-varying field,electromagnetic which induces field, a which induces a larger eddy current magnetic field in the induction plate so that the levi- tation force becomes greater. The levitation force tends to be stable at higher rotational speeds due to the saturation of the eddy current magnetic field. As shown in Figure 10b, the driving force firstly increases rapidly with the increase of the rotation speed of the EDW, reaching a peak at about 1200 rpm, and continues to decrease thereafter. This is because when the EDW runs at a low speed, the ampere force is related to the speed of the magnetic induction wire cutting induction plate, so the driving force is positively re- lated to the speed. When the EDW runs at a high speed, the induced current is concen- trated on the surface of the induction plate, and the vertical magnetic field related to the driving force is weakened, so the driving force is negatively related to the speed. Consid- ering the actual application requirements, the finite element simulation model only calcu- lates up to 6000 rpm. Under ideal conditions, as the speed increases indefinitely, the levi- tation force tends to stabilize, and the driving force attenuates close to zero. This phenom- enon verifies the conclusion that PMEDS is suitable for high-speed and ultra-high-speed application scenarios. For the EDW, the total power, Ptotal, includes the rotational power of EDW, PEDW, for levitation and driving and the loss power, Ploss, in the form of heat in the conductor plate [27]. The PEDW is computed from:

× × × = = (1) 9550 9550

where T is the torque computed by multiplying the load force by the outer radius, FT is the load force, Ro is the outer radius, and n is the rotational speed. The Ploss in the conductor plate is obtained by Maxwell simulation. The EDW efficiency, ηEDW, is given by:

= = (2) + Sustainability 2021, 13, 5827 9 of 20

larger eddy current magnetic field in the induction plate so that the levitation force becomes greater. The levitation force tends to be stable at higher rotational speeds due to the saturation of the eddy current magnetic field. As shown in Figure 10b, the driving force firstly increases rapidly with the increase of the rotation speed of the EDW, reaching a peak at about 1200 rpm, and continues to decrease thereafter. This is because when the EDW runs at a low speed, the ampere force is related to the speed of the magnetic induction wire cutting induction plate, so the driving force is positively related to the speed. When the EDW runs at a high speed, the induced current is concentrated on the surface of the induction plate, and the vertical magnetic field related to the driving force is weakened, so the driving force is negatively related to the speed. Considering the actual application requirements, the finite element simulation model only calculates up to 6000 rpm. Under ideal conditions, as the speed Sustainability 2021, 13, x FOR PEER REVIEWincreases indefinitely, the levitation force tends to stabilize, and the driving force10 attenuates of 21 close to zero. This phenomenon verifies the conclusion that PMEDS is suitable for high-speed and ultra-high-speed application scenarios.

(a) (b)

FigureFigure 10. 10.Force Force variation variation of of the the EDWEDW withwith differentdifferent rotational speeds speeds under under different different suspension suspension air airgaps. gaps. (a) (Levitationa) Levitation force; (b) Driving force. force; (b) Driving force. This ratio indicates the proportion of power that is used to create the levitation and For the EDW, the total power, Ptotal, includes the rotational power of EDW, PEDW, driving forces. for levitation and driving and the loss power, Ploss, in the form of heat in the conductor The rotational speed of EDW has a significant effect on the performance. When the plate [27]. The PEDW is computed from: air gap is 10 mm, the power requirements with different rotational speed are shown in Figure 11. Figure 12 shows that the EDWT effici× nencyF increases× R × withn the increasing rotational P = = T o (1) speed. This is because at higher EDWrotational9550 speeds, the 9550electrical frequency becomes higher and the induced eddy current in the conductor plate saturates gradually, which causes wherethe lossT ispower the torque to stop computed increasing. by The multiplying result is thethat load the forceEDW bypower the outerincreases radius, withFT anis the loadincreasing force, Rrotationalo is the outer speed radius, compared and nwithis the the rotational loss power speed. and the The EDWPloss inefficiency the conductor in- platecreases. is obtained The EDW by efficiency Maxwell is simulation. higher thanThe 80% EDW when efficiency, the rotationalηEDW speed, is given is higher by: than 4500 rpm. PEDW PEDW ηEDW = = (2) Ptotal PEDW + Ploss This ratio indicates the proportion of power that is used to create the levitation and driving forces. The rotational speed of EDW has a significant effect on the performance. When the air gap is 10 mm, the power requirements with different rotational speed are shown in Figure 11. Figure 12 shows that the EDW efficiency increases with the increasing rotational speed. This is because at higher rotational speeds, the electrical frequency becomes higher and the induced eddy current in the conductor plate saturates gradually, which causes the loss power to stop increasing. The result is that the EDW power increases with an increasing rotational speed compared with the loss power and the EDW efficiency increases. The EDW efficiency is higher than 80% when the rotational speed is higher than 4500 rpm.

Figure 11. EDW power and loss power with different rotational speeds. Sustainability 2021, 13, x FOR PEER REVIEW 10 of 21

(a) (b) Figure 10. Force variation of the EDW with different rotational speeds under different suspension air gaps. (a) Levitation force; (b) Driving force.

This ratio indicates the proportion of power that is used to create the levitation and driving forces. The rotational speed of EDW has a significant effect on the performance. When the air gap is 10 mm, the power requirements with different rotational speed are shown in Figure 11. Figure 12 shows that the EDW efficiency increases with the increasing rotational speed. This is because at higher rotational speeds, the electrical frequency becomes higher and the induced eddy current in the conductor plate saturates gradually, which causes the loss power to stop increasing. The result is that the EDW power increases with an increasing rotational speed compared with the loss power and the EDW efficiency in- Sustainability 2021, 13, 5827 10 of 20 creases. The EDW efficiency is higher than 80% when the rotational speed is higher than 4500 rpm.

Sustainability 2021, 13, x FOR PEER REVIEW 11 of 21

FigureFigure 11. 11. EDWEDW power power and and loss loss power power with with different different rotational rotational speeds. speeds.

Figure 12. EDW efficiencyefficiency with differentdifferent rotationalrotational speeds.speeds.

The establishmentestablishment ofof a a mathematical mathematical model model requires requires determining determining the the correlation correlation coeffi- co- cientefficient according according to the to data the fitting,data fitting, and then and obtaining then obtaining the final the mathematical final mathematical fitting formula. fitting Theformula. utilization The utilization of the MATLAB of the MATLAB fitting toolbox fitting fortoolbox data for fitting data has fitting the has characteristics the character- of aistics convenient of a convenient solution solution and high and accuracy. high accuracy. Therefore, Therefore, the MATLAB the MATLAB fitting fitting toolbox toolbox was selectedwas selected as the as surfacethe surface fitting fitting tool, tool, and and the the best best fitting fitting formula formula was was selected selected accordingaccording to the goodnessgoodness of fitfit testtest resultresult thatthat isis thethe finalfinal mathematicalmathematical modelmodel ofof thethe suspensionsuspension characteristic curve. In this article, the polynomial fitting of Matlab’s curve fitting toolbox cftool was se- lected as the method of data fitting. With the parameters of the suspension system fixed, the levitation force and driving force could be regarded as a binary function of the rota- tional speed of the EDW and the suspension air gap. We assumed that its functional form is: = (3) where x is the rotational speed of the EDW, y is the suspension air gap, F is the electro- magnetic force, pij is the polynomial coefficient, n1 is the highest order of the rotational speed of the EDW, and n2 is the highest order of the suspension air gap. When using the fitting algorithm, the appropriate highest power should be selected, but a higher power is not better. This is because the Runge phenomenon is prone to occur when the power is too high, which results in large deviations in data point that outside the test point. The best fitting coefficients of the suspension characteristics are obtained by polynomial fitting. Finally, the mathematical models of the levitation force Fl and driv- ing force Fd are:

= 0.13 − (2.23 × 10 ) − 0.02 + (1.39 × 10 ) + (2.78 × 10)+(1.35 × 10) − (1.43 × 10) − (1.28 × 10) − (4.65 × 10) (4) + (4.01 × 10) + (2.12 × 10) + (6.63 × 10) Sustainability 2021, 13, 5827 11 of 20

In this article, the polynomial fitting of Matlab’s curve fitting toolbox cftool was selected as the method of data fitting. With the parameters of the suspension system fixed, the levitation force and driving force could be regarded as a binary function of the rotational speed of the EDW and the suspension air gap. We assumed that its functional form is:

n1 n2 i j F = ∑ ∑ pijx y (3) i=0 j=0 where x is the rotational speed of the EDW, y is the suspension air gap, F is the electromag- netic force, pij is the polynomial coefficient, n1 is the highest order of the rotational speed of the EDW, and n2 is the highest order of the suspension air gap. When using the fitting algorithm, the appropriate highest power should be selected, but a higher power is not better. This is because the Runge phenomenon is prone to occur when the power is too high, which results in large deviations in data point that outside the test point. The best fitting coefficients of the suspension characteristics are obtained by polynomial fitting. Finally, the mathematical models of the levitation force Fl and driving force Fd are:

−5 2 −9 3 Fl = 0.13x − 2.23 × 10 x − 0.02xy + 1.39 × 10 x +2.78 × 10−6x2y + 1.35 × 10−3xy2 − 1.43 × 10−10x3y −1.28 × 10−7x2y2 − 4.65 × 10−5xy3 (4) +4.01 × 10−12x3y2 + 2.12 × 10−9x2y3 +6.63 × 10−7xy4

−5 2 −8 3 Fd = 0.13x − 6.14 × 10 x − 0.02xy + 1.16 × 10 x +5.90 × 10−6x2y + 8.48 × 10−4xy2 − 9.44 × 10−13x4 −7.67 × 10−10x3y − 2.00 × 10−7x2y2 (5) −1.97 × 10−5xy3 + 2.31 × 1017x5 + 3.63 × 10−14x4y +1.17 × 10−11x3y2 + 2.52 × 10−9x2y3 +1.37 × 10−7xy4 As the R-square of levitation force is 0.9896, and the R-square of driving force is 0.9874, the fitting degree is high. Therefore, the fitting model can be used as the electromagnetic force simplified mathematical model of EDW in the following dynamic simulation.

4. Operating Mode The Adams is used to simulate the suspension performance and observe the changes in suspension air gap, levitation force, driving force, and translation speed in real time. The virtual prototype simulation software Adams developed by MSC in the United States, which is Automate Dynamic Analysis of Mechanical Systems, was developed based on the Lagrangian equation method of multi-body system dynamics and integrates system modeling, solving, and visualization technologies. Users can use Adams to perform statics, kinematics, and dynamics simulation analysis and it can be used to test the performance, peak load, and motion range of the mechanical system and calculation of the finite element input load. At the same time, its open program structure and multiple external interfaces can provide a secondary development research platform to analyze special types. It has always been favored by major automobile companies and researchers, and has been widely used in the automotive industry. The use of Adams to solve dynamic problems mainly includes two steps: modeling and solving. Modeling is completed manually or imported by other software. In order to make the virtual prototype and the real object have a high degree of similarity, special solid modeling software Solidworks is used to model, assemble each part, and finally import. The total weight of PMEDS car model is 9.2 kg. During dynamic simulation with Adams, it is necessary to arrange the position coordinates of each component in the space, restrict the movement of each component by applying constraints, and import the simplified electromagnetic force model of the levitation force and driving force. It is also possible to Sustainability 2021, 13, 5827 12 of 20

add rotational speed function to left front (LF), right front (RF), left rear (LR), and right rear (RR) wheels separately. The three degree of freedom dynamic model of the PMEDS car is shown in Figure 13. Solving is completed through the software’s own solver. We Sustainability 2021, 13, x FOR PEER REVIEWanalyzed the operating mode under three typical working conditions of static suspension,13 of 21 Sustainability 2021, 13, x FOR PEER REVIEW 13 of 21 acceleration, and uniform speed, as well as deceleration and braking.

Figure 13. PMEDS car dynamic model in Adams. Figure 13. PMEDS car dynamic model in Adams. Figure 13. PMEDS car dynamic model in Adams. 4.1.4.1. StaticStatic SuspensionSuspension 4.1. Static Suspension WhenWhen thethe PMEDS car car is is at at static static suspension suspension,, the the front front and and rear rear EDWs EDWs rotate rotate at the at the When the PMEDS car is at static suspension, the front and rear EDWs rotate at the samesame speedspeed inin differentdifferent directions. By By gradua graduallylly adjusting adjusting the the speed speed of ofEDWs EDWs from from 0 to 0 to same speed in different directions. By gradually adjusting the speed of EDWs from 0 to 40004000 rpm, rpm, the the process process shift shift of of the the PMEDS PMEDS car car from from a stationarya stationary state state on on the the ground ground to to static 4000 rpm, the process shift of the PMEDS car from a stationary state on the ground to suspensionstatic suspension is simulated. is simulat Theed. relationshipThe relationship between between the th suspensione suspension air air gap gap and and rotational rota- static suspension is simulated. The relationship between the suspension air gap and rota- speedtional ofspeed EDWs of EDWs is shown is shown in Figure in Figure 14. 14. tional speed of EDWs is shown in Figure 14.

Figure 14. Relationship between suspension air gap and rotational speed of EDWs. FigureFigure 14.14. RelationshipRelationship between suspension suspension air air gap gap and and rotational rotational speed speed of ofEDWs. EDWs. From Figure 15, it can be known that the levitation force and driving force of the EDWsFromFrom gradually FigureFigure increases 1515,, it can with be be known knownthe increase that that theof the rotationallevitation levitation speedforce force andbefore and driving suspension. driving force force of After the of the EDWsEDWsthe rotational graduallygradually speed increases of EDWs with with reaches the the increase increase 600 rpm of of(a rotationalfter rotational 3 s), the speed speed levitation before before forcesuspension. suspension. of the EDWs After After thetheis sufficient rotational rotational to speedspeed balance of theEDWs deadweight reaches reaches 600 600of therpm rpm PMEDS (a (afterfter 3 car 3s), s), theand the levitation achieve levitation suspension. force force of the of the AsEDWs EDWsthe isrotationalis sufficient sufficient speed toto balancebalance of EDWs the continuesdeadweight deadweight to increaseof of the the PMEDS PMEDS, the levitation car car and and forceachieve achieve needs suspension. suspension. to balance As with Asthe the therotational gravity, speed at which of EDWs time continuesit remains toat increaseabout 23, theN and levitation no longer force increases, needs to whichbalance causes with the gravity,suspension at which air gap time to increase.it remains Due at about to the 23 fact N thatand nothe longer damping increases, of PMEDS which is almostcauses zero,the suspension the levitation air gapforce to and increase. the suspension Due to the air fact gap that fluctuates the damping and cannotof PMEDS be stabilized, is almost zero, the levitation force and the suspension air gap fluctuates and cannot be stabilized, Sustainability 2021, 13, 5827 13 of 20

rotational speed of EDWs continues to increase, the levitation force needs to balance with Sustainability 2021, 13, x FOR PEER theREVIEW gravity, at which time it remains at about 23 N and no longer increases, which14 of causes 21 the suspension air gap to increase. Due to the fact that the damping of PMEDS is almost zero, the levitation force and the suspension air gap fluctuates and cannot be stabilized, and the maximum suspension air gap reaches 7.3 mm. The driving force gradually decreases and the maximum suspension air gap reaches 7.3 mm. The driving force gradually de- andcreases is stable and atis stable around at 4around N under 4 N the under combined the combined effect of effect the increasing of the increasing of the rotational of the speedrotational of the speed EDWs of the and EDWs the suspension and the suspensi air gap.on Stableair gap. suspension Stable suspension is achieved is achieved when the rotationalwhen the speed rotational of the speed EDWs of reachesthe EDWs 3500 reaches rpm. As3500 shown rpm. inAs Figure shown 14 in, whenFigure the 14, rotational when speedthe rotational of the EDWs speed is of around the EDWs 3500 is rpm, around the maglev3500 rpm, car the reaches maglev the car maximum reaches the suspension maxi- airmum gap suspension and suspends air gap stably. and At suspends the same stably. time, At as shownthe same in time, Figure as 15 shownb, when in Figure the rotational 15b, speedwhen isthe more rotational than 3500 speed rpm, is more the drivingthan 3500 force rpm, decreases the driving gradually. force decreases In order gradually. to produce aIn larger order driving to produce force a larger and improve driving force thedriving and improve efficiency the driving of a maglev efficiency car, of the a maglev working rotationalcar, the working speed of rotational EDWs was speed set of as EDWs 3500 rpm.was set as 3500 rpm.

(a) (b)

FigureFigure 15. 15.Electromagnetic Electromagnetic force force variation variation ofof EDWsEDWs duringduring static suspension. suspension. (a ()a )Levitation Levitation force; force; (b ()b Driving) Driving force. force.

4.2. Acceleration and Uniform Speed 4.2. Acceleration and Uniform Speed The method adopted for acceleration is decelerating the rotational speed of the rear The method adopted for acceleration is decelerating the rotational speed of the rear EDWs and keeping the rotational speed of the front EDWs constant, so that the forward EDWs and keeping the rotational speed of the front EDWs constant, so that the forward driving force is greater than the backward driving force, which generates forward propul- driving force is greater than the backward driving force, which generates forward propulsion sion force to drive the PMEDS car to accelerate. From 1 s to 8 s, the rotational speed of all force to drive the PMEDS car to accelerate. From 1 s to 8 s, the rotational speed of all EDWs EDWs increases from 0 to 3500 rpm. The PMEDS car moves from a standstill state to static increasessuspension. from From 0 to 3500 9 s to rpm. 10 s, The the PMEDS rotational car speed moves of from the arear standstill EDWs state decreases to static from suspension. 3500 Fromrpm 9to s 3000 to 10 rpm, s, the and rotational the PMEDS speed car of thebegins rear to EDWs accelerate. decreases From from 10 s 3500 to 13 rpm s, due to3000 to the rpm, andexistence the PMEDS of the carcar’s begins translation to accelerate. speed, the From rota 10tional s to speed 13 s, dueof the to front the existence EDWs relative of the to car’s translationthe induction speed, plate the increases rotational and speed the driving of the force front decreases, EDWs relative while the to therotational induction speed plate increasesof the rear and EDWs the driving relative force to the decreases, induction while plate the decreases rotational and speed the driving of the rearforce EDWs increases. relative toIn the other induction words, platethe difference decreases between and the the driving driving force force increases. of the front In other EDWs words, and rear the differenceEDWs betweenbecomes the larger driving and larger. force of In thethis front way, EDWsthe propulsion and rear force EDWs and becomes the car’s largertranslation and larger.speed In thiswill way, continue the propulsion to increase, force which and makes the car’s the translation rotational speedspeed willof the continue rear EDWs to increase, relative which to makesthe induction the rotational plate decrease, speed of and the eventually rear EDWs results relative in toa reduction the induction in the plate levitation decrease, force and eventuallyand the loss results of suspension in a reduction capacity. in theTherefore, levitation the force rotational and the speed loss of of the suspension EDWs needs capacity. to Therefore,be adjusted the twice, rotational so that speed the rotational of the EDWs speed needs of the to befront adjusted EDWs twice,and rear so thatEDWs the relative rotational speedto the of induction the front plate EDWs are and equal, rear the EDWs driving relative forceto offsets the induction each other plate again, are and equal, the thePMEDS driving forcecar enters offsets a eachuniform other speed again, driving and the state. PMEDS From car 13 enterss to 14 as, uniform the rotational speed speed driving of state.the rear From 13EDWs s to 14 increases s, the rotational from 3000 speed rpm ofto the4000 rear rpm EDWs and the increases translation from speed 3000 rpmof the to PMEDS 4000 rpm car and thestabilizes translation at 1.1 speed m/s. The of the entire PMEDS acceleration car stabilizes process at lasted 1.1 m/s. 5 s and The the entire average acceleration acceleration process lastedof PMEDS 5 s and car the is 0.22 average m/s2. accelerationThe rotational of speed PMEDS regulation car is 0.22 process m/s2 of. Thethe EDWs rotational during speed regulationacceleration process and uniform of the EDWs speed during is shown acceleration in Figure and16. The uniform relative speed rotational is shown speed in Figure of the 16. TheEDWs relative and rotationalthe translation speed speed of the of EDWsthe PMEDS and the car translation are respectively speed shown of the PMEDSin Figure car 17 are respectivelyand Figure shown18. in Figures 17 and 18. Sustainability 2021, 13, 5827 14 of 20 Sustainability 2021, 13, x FOR PEER REVIEW 15 of 21

Sustainability 2021, 13, x FOR PEER REVIEW 15 of 21

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FigureFigure 16. 16.Rotational Rotational speed variation variation of of EDWs EDWs du duringring acceleration acceleration and anduniform uniform speed. speed. Figure 16. Rotational speed variation of EDWs during acceleration and uniform speed. Figure 16. Rotational speed variation of EDWs during acceleration and uniform speed.

Figure 17. Relative rotational speed variation of EDWs during acceleration and uniform speed. Figure 17. Relative rotational speed variation of EDWs during acceleration and uniform speed. Figure 17. Relative rotational speed variation of EDWs during acceleration and uniform speed. Figure 17. Relative rotational speed variation of EDWs during acceleration and uniform speed.

Figure 18. Translation speed variation of the PMEDS car during acceleration and uniform speed. Figure 18. Translation speed variation of the PMEDS car during acceleration and uniform speed. Figure4.3. Deceleration 18. Translation and speedBraking variation of the PMEDS car during acceleration and uniform speed. Figure4.3. Deceleration 18. Translation and Braking speed variation of the PMEDS car during acceleration and uniform speed. The method commonly adopted for deceleration is to accelerate the rotational speed 4.3.of rearDecelerationThe EDWs, method andand commonly Braking the front adopted EDWs arefor decelerationkept at a constant is to accelerate rotational the speed, rotational so that speed the of rearThe EDWs, method and commonly the front adopted EDWs arefor decelerationkept at a constant is to accelerate rotational the speed, rotational so that speed the of rear EDWs, and the front EDWs are kept at a constant rotational speed, so that the Sustainability 2021, 13, 5827 15 of 20

Sustainability 2021, 13, x FOR PEER REVIEW4.3. Deceleration and Braking 16 of 21

Sustainability 2021, 13, x FOR PEER REVIEWThe method commonly adopted for deceleration is to accelerate the rotational16 of speed21 of

rear EDWs, and the front EDWs are kept at a constant rotational speed, so that the forward drivingforwardforce driving is force smaller is smaller than thethan backward the backward driving driving force, force, which whichgenerates generates a a back- backward brakingwardforward braking force driving toforce driveforce to is thedrive smaller PMEDS the thanPMEDS car the to backwardcar decelerate. to decelerate. driving The The simulationforce, simulation whichprocess generates process of a theof back- the first 17 s isfirstward the 17 samebraking s is the as theforcesame process toas drivethe process of the acceleration PMEDS of accele car andration to decelerate. uniform and uniform speed. The speed.simulation Then Then in theprocess in casethe case of of the constantof translationconstantfirst 17 s istranslation the speed, same from asspeed, the 17 process from s to 18 17 of s, s accele theto 18 rotational rations, the androtational speed uniform ofspeed thespeed. rearof theThen EDWs rear in theEDWs increases case in- of from 4000creasesconstant rpm from translation to 45004000 rpm rpm, speed, to and 4500 from the rpm, PMEDS17 and s to the 18 car PMs, the beginsEDS rotational car to begins decelerate. speed to decelerate. of Fromthe rear From 18 EDWs s to 18 22.5 s in- to s, the translation22.5creases s, the from translation speed 4000 rpm of thespeed to PMEDS4500 of rpm,the carPMEDS and gradually the ca PMr graduallyEDS decreases car begins decreases to to zero. decelerate. to Similarly,zero. Similarly, From the 18 rotational sthe to speedrotational22.5 s, ofthe the speedtranslation EDWs of the isspeed EDWs adjusted of is the adjusted twice.PMEDS twice. From car gradually From 22.5 s22.5 to decreases s 23.5 to 23.5 s, the s,to the zero. rotational rotational Similarly, speed speed the of the rearofrotational the EDWs rear speed EDWs decreases of decreases the EDWs from from 4500is adjusted 4500 rpm rpm totwice. 3500to 3500 From rpm. rpm. 22.5 The The s to relativerelative 23.5 s, the rotational rotational speed speed speed ofof the fronttheof the front and rear and rear EDWs rear EDWs decreases EDWs are synchronizedare from synchronized 4500 rpm again. to ag 3500ain. The rpm.The driving driving The relative force force offsets rotationaloffsets each each speed otherother of again. Theagain.the PMEDSfront The and PMEDS car rear is carEDWs at staticis at are static suspension, synchronized suspension, thus agthusain. enabling enabling The driving thethe braking force offsets function. function. each The other The en- entire again. The PMEDS car is at static suspension, thus enabling the braking function. The en- decelerationtire deceleration process process lasts lasts 6.5 6.5 s and s and the the average average acceleration acceleration of of the the PMEDS PMEDS carcar isis 0.17 m/s2. m/stire 2deceleration. The rotational process speed lasts regulation 6.5 s and process the average of the acceleration EDWs during of theacceleration, PMEDS car uniform is 0.17 The rotational speed regulation process of the EDWs during acceleration, uniform speed, speed,m/s2. The deceleration rotational and speed braking regulation is shown process in Figure of the 19. EDWs The relative during rotational acceleration, speed uniform of the deceleration and braking is shown in Figure 19. The relative rotational speed of the EDWs EDWsspeed, anddeceleration the translation and braking speed is of shown the PMEDS in Figure car 19. are The respectively relative rotational shown in speed Figures of the 20 and the translation speed of the PMEDS car are respectively shown in Figures 20 and 21. andEDWs 21. and the translation speed of the PMEDS car are respectively shown in Figures 20 and 21.

FigureFigure 19.19. Rotational speed speed variation variation of ofEDWs EDWs during during deceleration deceleration and braking. and braking. Figure 19. Rotational speed variation of EDWs during deceleration and braking.

Figure 20. Relative rotational speed variation of EDWs during deceleration and braking. FigureFigure 20.20. Relative rotational rotational speed speed variation variation of EDWs of EDWs during during deceleration deceleration and braking. and braking. Sustainability 2021, 13, 5827 16 of 20 Sustainability 2021, 13, x FOR PEER REVIEW 17 of 21

Figure 21. Translation speed variation of the PMEDS car during deceleration and braking. Figure 21. Translation speed variation of the PMEDS car during deceleration and braking.

4.4.4.4. Efficiency Efficiency ForFor thethe PMEDS car, car, there there are are two two kinds kinds of ofefficiency: efficiency: EDW EDW efficiency efficiency and PMEDS and PMEDS car car efficiency.efficiency. WeWe evaluatedevaluated the performance performance of of PMEDS PMEDS car car from from different different perspectives. perspectives. The efficiency of EDW, ηEDW, indicates the efficiency of the EDW using motor power The efficiency of EDW, η , indicates the efficiency of the EDW using motor power to rotate and is given by: EDW to rotate and is given by: + = = (6) PEDW+ +PEDW+1 +PEDW+2 ηEDW = = (6) where the PEDW is the rotationalPEDW +powerPloss of thePEDW four1 +EDWsPEDW including2 + Ploss 1the+ Protationalloss2 power of the front wheels, PEDW1, and the rotational power of the rear wheels, PEDW2. The Ploss is wherethe loss the powerPEDW ofis the four rotational EDWs power and incl ofudes the fourthe loss EDWs power including of the front the rotational wheels, P powerloss1, of theand front the loss wheels, powerPEDW1 of the, andrear thewheels, rotational Ploss2. While power the of PEDW1 the rearand P wheels,EDW2 are PcomputedEDW2. The byP loss is therotational loss power speed of as the shown four by EDWs (1), the and Ploss1 includes and Ploss2 the are loss computed power ofby therelative front rotational wheels, Ploss1, andspeed the of loss EDWs power in a of Maxwell the rear simulation. wheels, P loss2When. While the PMEDS the PEDW1 car runsand atPEDW2 a constantare computed speed, by rotationalthe Ploss1 is speed equal asto shownthe Ploss2 bybecause (1), the theP loss1drivingand forcePloss2 isare zero computed and the relative by relative rotational rotational speedspeed of are EDWs equal. in The a MaxwellPEDW1 is different simulation. from Whenthe PEDW2 the because PMEDS under car runs the influence at a constant of the speed, translation speed, the front and rear EDWs rotate at different speed. the Ploss1 is equal to the Ploss2 because the driving force is zero and the relative rotational When the air gap is 10 mm, the EDW efficiency with different translation speeds is speed are equal. The PEDW1 is different from the PEDW2 because under the influence of the translationshown in Figure speed, 22. the When front the and translation rear EDWs speed rotate is 0 atm/s, different the PMEDS speed. car is at static sus- pensionWhen and the the air efficiency gap is of 10 EDW mm, is the 59.5%. EDW As efficiencythe translation with speed different increases, translation the EDW speeds efficiency increases because of the increasing of the rotational speed. When the translation is shown in Figure 22. When the translation speed is 0 m/s, the PMEDS car is at static speed is 15 m/s, the EDW efficiency achieved is 82.9%. suspension and the efficiency of EDW is 59.5%. As the translation speed increases, the EDW The power of the car, Pcar, indicates the efficiency of EDW to levitate and drive the car efficiencyand is given increases by: because of the increasing of the rotational speed. When the translation speed is 15 m/s, the EDW efficiency achieved is 82.9%. The power of the car, Pcar, indicates=( − the) efficiency +( + of EDW) to levitate and drive(7) the car and is given by: where the Vx is the horizontal speed and the Vz is the vertical speed of the PMEDS car. When the PMEDS car in the Pprocesscar = ( Fofd 2accelera− Fd1)Vtion,x + the(Fl 1PMEDS+ Fl2) Vcarz efficiency is shown in (7) Figure 23. The variation of the horizontal speed is shown in Figure 18. When speed and where the Vx is the horizontal speed and the Vz is the vertical speed of the PMEDS car. Whenair gap the of PMEDSthe PMEDS car are in the constant, process the of driving acceleration, force calculated the PMEDS by F card2 − efficiencyFd1 is zero and is shown Vz in Figureis zero, 23 so. Thethe power variation and of the the efficiency horizontal of the speed PMEDS is shown car is always in Figure zero. 18 .From When 8 s speed to 14 s, and air the horizontal speed increases from 0 to 1.1 m/s, while the efficiency of the PMEDS car gap of the PMEDS are constant, the driving force calculated by F − F is zero and V is increases because of the increasing of the horizontal speed and drivingd2 powerd1 and reaches z zero, so the power and the efficiency of the PMEDS car is always zero. From 8 s to 14 s, the maximum value of 8.56% at 12.7 s. Due to getting rid of the ground friction and the theneglecting horizontal of air speed resistance, increases the PMEDS from 0 car to needs 1.1 m/s, only while a small the amount efficiency of driving of the force PMEDS to car increasesaccelerate. because Due to ofthe the small increasing speed in ofthe the starting horizontal stage, speedthe efficiency and driving of PMEDS power car and is not reaches the maximum value of 8.56% at 12.7 s. Due to getting rid of the ground friction and the neglecting of air resistance, the PMEDS car needs only a small amount of driving force to accelerate. Due to the small speed in the starting stage, the efficiency of PMEDS car is not high. When the PMEDS car runs at a higher speed, it has better efficiency and performance. Sustainability 2021, 13, x FOR PEER REVIEW 18 of 21

Sustainability 2021, 13, x FOR PEER REVIEW 18 of 21

Sustainability 2021, 13, 5827 17 of 20 high. When the PMEDS car runs at a higher speed, it has better efficiency and perfor- mance.high. When the PMEDS car runs at a higher speed, it has better efficiency and perfor- mance.

Figure 22. EDWEDW efficiency efficiency with a different translation speed. Figure 22. EDW efficiency with a different translation speed.

Figure 23. PMEDS car efficiency in the process of acceleration. FigureFigure 23.23. PMEDSPMEDS carcar efficiencyefficiency inin thethe processprocess ofof acceleration.acceleration. 4.5. Feasibility of Real Size Car 4.5. FeasibilityThe parameters of Real usedSize Car for the real size PMEDS car are given in Table 2. The parameters used for the real size PMEDS car are given in Table 2.

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Sustainability 2021, 13, x FOR PEER REVIEW4.5. Feasibility of Real Size Car 19 of 21

The parameters used for the real size PMEDS car are given in Table2.

TableTable 2.2. TheThe parameters of of the the real real size size PMEDS PMEDS car. car.

ParameterParameter Value Value Inner radius of EDW/mm 400 Inner radius of EDW/mm 400 OuterOuter radius radius of of EDW/mm 260 260 WidthWidth of of EDW/mm EDW/mm 280 280 PolePole pairs pairs of of EDW EDW 4 4 WheelbaseWheelbase of of car/mm 2920 2920 Wheel-trackWheel-track of of car/mm 1640 1640 Mass of car/kg 2540 Mass of car/kg 2540

InIn orderorder toto directlydirectly reflectreflect thethe forceforce characteristics characteristics of of the the PMEDS PMEDS car, car, a a three-dimensional three-dimen- transientsional transient finite element finite element model model is established is established with Maxwell. with Maxwell. FigureFigure 2424 showsshows the the levitation levitation force force and and driving driving force force of the of real the size real EDW size with EDW dif- with differentferent rotational rotational speeds speeds under under different different suspension suspension air gaps. air Wh gaps.en the When air gap the is air less gap than is less than40 mm 40 and mm the and rotational the rotational speed speedis greater is greater than 500 than rpm, 500 an rpm, EDW an can EDW produce can producemore than more than10 kN 10 levitation kN levitation force. force.Four EDWs Four EDWscan produc can producee more than more 40 than kN of 40 levitation kN of levitation force and force andthe PMEDS the PMEDS car achieves car achieves suspension suspension and is andmanned. is manned. When the When air gap the is air 40 gap mm, is the 40 max- mm, the maximumimum driving driving force force is 3.7 iskN. 3.7 kN.

(a) (b)

FigureFigure 24. 24.Force Force variationvariation of of the the real real size size EDW EDW with with different different rotational rotational speeds speeds under under different different suspension suspension air gaps. air (a gaps.) Levitation force; (b) Driving force. (a) Levitation force; (b) Driving force.

5.5. ConclusionsConclusions We presented a new concept maglev car employing PMEDS which achieve the inte- We presented a new concept maglev car employing PMEDS which achieve the inte- gration of suspension and driving. It applies maglev technology into the automotive field gration of suspension and driving. It applies maglev technology into the automotive field to design a new type of car, which provides constructive guidance for the development of to design a new type of car, which provides constructive guidance for the development ground transportation. The mathematical model of levitation force and driving force were of ground transportation. The mathematical model of levitation force and driving force established through data fitting combined with the finite element method, and the dy- were established through data fitting combined with the finite element method, and the namic model of PMEDS car was established in Adams. Based on the dynamics model, the dynamicoperating model mode ofof PMEDSthe PMEDS car wascar establishedunder static insuspension, Adams. Based acceleration on the dynamicsand uniform model, thespeed, operating deceleration mode and of the braking PMEDS ware car analyzed under static. The suspension,results showacceleration that the critical and speed uniform speed,of the EDWs deceleration for suspension and braking is 600 ware rpm, analyzed.and the maximum The results suspension show that air thegap criticalfor stable speed ofsuspension the EDWs can for reach suspension 7.3 mm. isThe 600 working rpm, and rotational the maximum speed of suspension EDWs is 3500 air rpm. gap At for the stable suspensionsame time, the can movement reach 7.3 mm.status The of the working PMEDS rotational car can be speed controlled of EDWs by only is 3500 adjusting rpm. the At the Sustainability 2021, 13, 5827 19 of 20

same time, the movement status of the PMEDS car can be controlled by only adjusting the rotational speed of rear EDWs and in turn reducing the complexity of control system. The acceleration is related to the reduction of the rotational speed of rear EDWs. When the rear EDWs are reduced by 500 rpm, the PMEDS car can obtain 0.22 m/s2 acceleration. Furthermore, this control method can accurately regulate the translation speed of a PMEDS car. After the 5 s acceleration process, the translation speed of the PMEDS car stabilizes at 1.1 m/s. The EDW and PMEDS cars are more efficient when they run at higher speeds. The levitation force of real size PMEDS car is more than 40 kN to achieve suspension while being manned. The functions of propulsion, acceleration, deceleration, and braking are realized and the feasibility of the PMEDS car system is verified by the experimental prototype. The simulation method has provided a valuable reference for the future design of the PMEDS car and a new maglev transportation system.

Author Contributions: Conceptualization and Supervision, Z.D.; Investigation, Z.Z., S.Z., L.J., X.S., and P.G.; Software, J.Z. (Jianghua Zhang), J.L. and J.Z. (Jun Zheng). All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: This work was supported in part by the National Natural Science Foundation of China (U19A20102), the Sichuan Science and Technology Program (21RCYJ0064), the Chengdu International S&T Cooperation Program (2019-GH03-00002-HZ), and the Fundamental Research Funds for the Central Universities (2682020ZT96). Conflicts of Interest: The authors declare no conflict of interest.

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