Design of New Energy-Efficient Permanent Magnetic Maglev Vehicle Suspension System

In view of the current traffic criticism faced by urban construction and the quality development and personalized trend of future rail transit system, a new type of maglev rail transit system is proposed in this paper. The principles of the modules of train suspension guidance, linear drive and on-board communication are also introduced and analyzed in this paper. Additionally, the feasibility of train suspension structure is studied based on Ansoft Maxwell finite element simulation, which includes: under three-dimensional magnetic field, the static magnetic force of Halbach permanent magnet array is changed, and the safety and reliability of the permanent magnet suspension array are verified by comparing with the actual test vehicle sampling data; the critical stability characteristics of suspension structure under static magnetic field are proved by physical modeling. Therefore, the electromagnetic damping structure is introduced into the vehicle suspension frame to constitute the hybrid suspension control system of permanent magnet electromagnetic, and the hybrid suspension model is established, which proves that the hybrid suspension system has controllable observability. Finally, the linearized state feedback control strategy is designed for the single-point electromagnetic levitation ball system to simulate the compensation and regulation of the static magnetic field by the electromagnetic damping system. The excellent performance of the electromagnetic levitation ball also proves the feasibility and rationality of the electromagnetic control strategy. Compared with the traditional electromagnetic hybrid suspension system, this system realizes “zero” power suspension, and the energy consumption of train suspension is only consumed in the instant that the electromagnetic damping system is regulated.


I. INTRODUCTION
The problem of traffic congestion has been and abroad, such as the new energy suspension monorail train of CRRC Corporation Limited [1] and the BYD straddle-type Sky Rail [2,3] in China, and the Israeli Sky Tran [4][5][6] and the Russian Sky Way rail cable car [7,8], Germany's Dortmund Air Rail [9], Japan's Chiba Monorail [10], and so on.
Among these types of sky train, most of them still use wheel-rail suspension and rotating motor drive mode, while train is devoted to the development of Personal Rapid Transit(PRT), introducing the advanced maglev technology, but the structure of it is complex.The processing of the support system is very difficult, so it is hard to be applied widely.On the other hand, the proposing of "zero" power control strategy [11,12] promotes the development and application of the

II. A NEW PERMANENT MAGNET RAIL TRANSIT SYSTEM
In this paper, a new intelligent permanent magnet maglev rail transit system named "Rainbow" is proposed, which means that the system will be a smart colorful cloud over the city and contributes to the urban aerial landscape construction.The system uses the magnetic force of rare earth permanent magnetic material to realize a For the system function, the "Rainbow" system can be divided into six modules, which are electromagnetic permanent magnet hybrid suspension control system, electromagnetic guidance control system, intelligent communication system, permanent magnet linear drive system, track and vehicle operation control system, ground power supply system.
In the suspension guide structure, the system realizes the vertical suspension of the vehicle through Halbach permanent magnet array, and realizes the real-time dynamic suspension adjustment of train safety by combining with electromagnetic stability control.There are two sets of preset suspension limit wheels at the top of the suspension frame to prevent vertical suspension collision.In the horizontal direction, the electromagnetic steering structure completes the stable control on both left and right side, and the upper and lower end of the electromagnetic guide structure are respectively installed with mechanical limit pulley to form the two-stage guide protection structure of the guide system.In addition, Secondary rubber wheels are installed on the outside of permanent magnetic levitation structure to prevent vehicle from colliding with permanent magnet array under unsteady conditions such as turning and tilting.
In the train drive system, the long stator permanent magnet synchronous linear motor is adopted.The long stator of the motor is arranged alternately by three phase AC windings, fixed on the upper wall of the inner side of the suspension beam, and the corresponding electric motor mover is composed of permanent magnets and placed at the top of the suspension frame.The traveling wave magnetic field generated by the armature winding and the static magnetic field produced by the permanent magnet form the electromagnetic traction force and drag the suspension frame and the carriage to move forward.In the actual driving control strategy, the conventional linear motor multi-modal control method is adopted.According to the vehicle state, different driving strategies is switched to adapt the situation, including slip frequency control, vector control, direct thrust control and so on.
In order to improve the safety degree of vehicle operation and the intelligence of train service, the "Rainbow" system has applied the technology of Internet of Things and artificial intelligence in the on-board system.The former collects and preprocesses all kinds of field data (including levitation height, magnetic field center deviation, car body position, etc.) for the intelligent front-end system.The wireless communication equipment connects the car to the cloud control terminal to realize the exchange of data information.The latter realizes the intelligent unmanned driverless and human-car friendly interactive system of running, organizing, managing and serving.The mobile terminal can be implemented through APP, WeChat public number and other ways to implement the operation and personalized services, which mainly include: man and machine interface interaction, traffic data display, multimedia conversion and so on, to ensure that passengers have good and comfortable experience.
In addition, the "Rainbow" system is equipped with the safety facilities of the conventional rail transit system, such as emergency brake button, escape ladder, smoke alarm and so on, to ensure the overall safety and reliability of the system.
To sum up, the "Rainbow" system is a new type of medium and low speed rail transit system with the functions of stable suspension, safety   The mass of suspension frame and car about 1.5 Ton

B. Static Magnetic Field Analysis of permanent Magnet Array
Combined with the basic structure of vehicle suspension frame, the static levitation force generated by permanent magnet array is simulated by Finite Element Method [13,14]   The effects of different horizontal deviations on the suspension force are shown in Table 3 below.It can be seen from the sample data that the distribution of the actual magnetic field intensity is in good agreement with the finite element simulation curve.The energy of the magnetic field is distributed in the position of B and C, whose trend is high in the middle and low on the sides, and the width of the isopotential line on both sides is relatively narrow, that is, the variation span of the magnetic field intensity is large.On the other hand, Figure 7 and Table 4 further illustrate that the magnetic energy of Halbach permanent magnetic arrays is basically within the centimeter level of space, The distance between the car position and the suspension module of the "Rainbow" system is more than one meter and the design height of the column is about 7.9 meters.Structurally, the magnetic energy of the suspension module is basically shielded from the beam.Therefore, for passengers in the car and pedestrians along the track of the "Rainbow" system, residents, they will not be affected by the magnetic field intensity of the permanent magnet.

C. Simulation Discuss and Structural Optimization
In order to verify the simulation results, the    In the mixed suspension structure, the static suspension mainly depends on the permanent magnet, which needs a large number of permanent magnets laid along both sides of the track in the engineering construction.However, the precious rare earth resources lead to the high price of the high-performance permanent magnet in the market.This will also affect the application of the "Rainbow" system.As far as construction cost is concerned, compared with the traditional rail transit system, the system has the advantage of lower cost, but in engineering and design, it should save materials and reduce engineering cost as much as possible while ensuring the basic requirements of vehicles.Therefore, the combination of Halbach permanent magnet array is simulated in this paper.
From the simulation results of levitation force and horizontal force, it can be seen that the static magnetic field force between permanent magnets is large, which is very difficult for engineering assembly and can easily cause bumps between permanent magnets.For this purpose, non-magnetic materials (such as epoxy resin) were filled in the Halbach permanent magnet array combination gap.In this way, not only the difficulty of permanent magnet assembly can be effectively reduced, but also the demand for permanent magnets in practical construction can be reduced to a certain extent.It can be seen from the simulation that the thickness of the laminated plate has a certain influence on the levitation magnetic force, and the influence degree of the thickness is shown in Figure 9. estimate and so on.

D. Stability Analysis of suspension system
In the electromaglev system composed of Halbach permanent magnet array, due to the lack of damping term in the equation of state of the system, the system presents a critical stable state [15]; At the same time, the static suspension system also presents a certain volatility in the actual suspension magnetic force detection, so this paper will combine the magnetic force analysis of the suspension system to judge the stability of the static suspension system.
Since the 1970s, researchers have put forward many strategies for the study of magnetic field of Halbach permanent magnetic arrays, which can be divided into: finite element simulation [16], sinusoidal approximation [17], electronic circulation analysis [ 18 ], magnetic charge method [19].However, in many research methods, magnetic field analysis is often carried out for the modes of rotating motor [20] and electric suspension structure [21], but there are few references for static magnetic force analysis between double-layer Halbach permanent magnetic arrays.Therefore, in this paper, the finite element magnetic simulation curve is obtained by MATLAB fitting tool between vertical levitation force and suspension clearance.
According to the fitting function, the steady state analysis of the static suspension system is carried out.
The fitting function is as follows: the confidence interval is 95%.
The magnetic force function of the levitation height h is the F(h), and the fitting parameter is: For this kind of time-varying suspension systems, researchers often study the stability of the controlled system by analyzing the stability of the system at the equilibrium point.In reference [ 22 ], it is shown that there is a nonlinear exponential function relationship between the magnetic field of single layer Halbach and the suspension gap.In the actual suspension control, the adjustable control range of the general electromagnetic maglev train is kept within the 3mm, while the "Rainbow" suspension system is designed to develop the "personal rapid rail transit system", that is, the In the formula ( 5), the parameters can be calculated or measured in practice, that is, when the mass of the vehicle is known, the suspension height under the static magnetic field will be stabilized at ℎ 0 and the vertical displacement velocity will be zero.
When formula ( 3) is expanded by Taylor formula, the linearized equation of state is obtained as follows: Among them,k = (−)  , assume that x = ℎ − ℎ 0 ,y = .The equation of state space of the system can be obtained : From the formula ( 7), the characteristic equation of the suspension system is obtained as follows: λ 2 +  = 0 From (1) we know that  < 0,  ≫  .
Therefore, the state matrix equation of the system is the second order system, and its eigenvalue has a pair of imaginary real roots with the real part as zero, that is, the system is in the state of zero damping[ 23 ](pp.51-63), λ 1,2=±j√ .In other words, the equilibrium point of the suspension system under the static magnetic field is critical stable after linearization.
Combined with the above deduction, the formula ( 7) is solved numerically at a certain equilibrium point by using MATLAB simulation platform.Taking  = 750， = 10/ 2 , initial value (ℎ 0 ,  0 ) = (28, −1), 23mm is the height of suspension in response to the equilibrium point, and the dynamic trend of suspension frame under the action of static magnetic field can be obtained, as shown in Figure 10.From the velocity curve and displacement curve, it can be seen that a single static permanent magnet structure can realize the relative stability of the suspension system, but the response of the system will be close to the equal-amplitude oscillation when there is a slight external disturbance.Moreover, it is not controllable by itself.

E. Design and Analysis of Electromagnetic Constrained Damping System
In the analysis of the above section, the train suspension system cannot meet the requirements of train safety and stability only by static magnetic force.Combined with the development of modern electromagnetic permanent magnet hybrid magnetic levitation technology, electromagnetic constrained damping system is introduced into the "Rainbow" suspension system, and the static magnetic field force is supplemented and slowed down by using the controllability of electromagnetic force.The hybrid suspension structure can be divided into permanent magnet array and electromagnetic coil, and its structure is three views, as shown in Figure 11.

F. physical models
First, it is assumed that there is no magnetic field coupling between the electromagnetic winding and the Halbach permanent magnet array, and the electromagnet is in the state of non-magnetic saturation and so on.In ideal conditions, the suspension is subjected only to magnetic field force and vehicle gravity, in the vertical direction of the dynamic equation: In the formula:   --magnetic field force,   (, ) --Electromagnetic force,   () -magnetic field force of permanent magnet,  --gravity acceleration, The equation of electromagnetic force for single point electromagnetic system [24]: The relationship between voltage and current in the electromagnet winding can be expressed as follows: In the formula: R--electromagnet winding resistance,   --equivalent inductance of electromagnet winding.
When the suspension system is in the equilibrium position, the suspension system under the static magnetic field realizes the critical stable state, and the electromagnetic constrained damping system achieves the effect of fine tuning the suspension state, then the real-time control of the hybrid system belongs to a kind of bounded regulation.From the expressions (1) and ( 9), we can see that the magnetic force of the suspension system has a complex nonlinear relationship.
Therefore, in this paper, the nonlinear system is linearized by Taylor series at the suspension equilibrium.
Suppose that ( 0 , ℎ 0 ) is an equilibrium point of a hybrid suspension system, which is obtained by ( 8): It is easy to obtain the Taylor formula expansion (neglecting the higher-order term) for the magnetic force of (8): F  ( 0 , ℎ 0 ), F ℎ ( 0 , ℎ 0 ) is derived from the differential partial derivative formula: The controlled output relationship between gap and current is described in formula (16), and the controlled relation between voltage and gap can be transformed by formula (10).
In addition, the characteristic equations of electromagnetic permanent magnet hybrid open loop suspension system can be obtained by (16).There is an open loop pole in the right half plane on the complex plane of the system.
According to the Routh Criterion, the hybrid suspension structure composed of permanent magnet array and electromagnetic constrained damping system belongs to an unstable structure of its own, but the system is still observable and controllable.The suspension control model can be adjusted by external control strategy to make the whole suspension system stable.

G. Electromaglev control strategy
Because the oscillation amplitude of the hybrid suspension control system is relatively small under the stable state, the suspension force under the static magnetic field can be approximately considered as a constant value, while the electromagnetic constrained damping system can suppress and adjust the momentum of the suspension oscillation.
Combined with the formulas ( 8) and (11), it is obtained that: The state space equation of the electromaglev control system is obtained by expanding at the equilibrium point： In the formula, x 1 and x 2 represent suspension displacement and suspension displacement velocity, respectively.Clearly, in the matrix rank discriminant of the equation of state: The system has complete controllability and observability.

H. Experimental verification and discussions
At present, the project is still in the basic research stage, and the electromagnetic constrained damping system is still in the theoretical stage, but its structure and principle are basically the same as the electromagnetic suspension ball system.In this paper, the control strategy of electromagnetic constrained damping in a single point suspension ball system is studied.
The state space model of the suspension system based on the parameters of the real single point suspension ball system is as follows: In the formula, x1 and x2 represent the displacement and velocity of the suspension ball respectively, and the matrix rank discriminant   >0,  >0 ,respectively.
For linearized systems, the state feedback control of linear time-invariant systems can be used for pole assignment of formula (22).
According to the expected performance of actual control, this paper selects the dynamic control performance index: the overshoot quantityδ 1 ≤ 5% ,and the adjustment time is less than 3 s.
Combined with the reference [25] The linearized state space equation after the state feedback pole assignment method is as follows: ]  (26) The state feedback control strategy is tested on a single point suspension ball system, as shown in figure 12-14.
According to the above theoretical derivation, the system model with linearized pole assignment is simulated in MATLAB/Simulink.
Among them, the output voltage is set to 5.8 V, the suspension ball position is basically stable at  device, digital-to-analog converter, etc.) will also affect the quality of the system response output.
Therefore, there are a few burr pulses in the voltage response of the system, which can be regarded as the signal output within a reasonable range.(5) Application and promotion: in view of the strong climbing ability, small turning radius and light weight of the system, instead of occupying land, the "Rainbow" system will actively seek to promote and apply the complex environment, such as bay, valley, channel, cross-river and so on, as well as the special town, campus and so on, to provide a reference and reference for modern intelligent traffic.
criticized during the development of domestic cities.With Beijing, Shanghai and Guangzhou as the typical large cities, the continuous growing scale of the cities leads to the increasingly significant contradiction between the transportation demand of urban area and the transit capacity of the traditional ground /underground transportation system, especially the traffic congestion problem.To a large extent, this reduces the efficiency and liveability of the city.At the same time, with the development of small and medium-sized cities, traffic congestion has become more and more obvious.Following the publication of the National New Urbanization Plan (2014-2020), the Central Urban Work Conference and the outline of the 13th Five-Year Plan put forward a specific discussion on the construction of livable cities.After that, livable city construction becomes the important goal of our country's urban construction, and it is particularly urgent to upgrade and perfect the urban public transportation system.Urban rail transportation is considered to be a green mode of transportation because of its large carrying capacity, safety, speed, energy and resource saving character.Research shows that the energy consumption of rail transit is only 1/9 of that of a car and 1/2 of a bus under the same capacity.Therefore, it is a common understanding of the world to give priority to the development of public transport system with rail transit as its backbone and use it as an important way to solve urban traffic problems.At present, there are seven main types of urban rail transit systems at home and abroad, such as subway, light rail, monorail, tram, maglev, etc..The functional orientation and technical advantages and disadvantages of these systems are different, as shown in Table 1.The rail transit system like subway is mainly used to solve the problem of large volume transportation and commuting, which has been developed rapidly since the 12th Five-Year Plan.With the publication of "Opinions of the General Office of the State Council on further strengthening management of urban rail transit planning and construction", the blind construction on urban rail transit has been standardized.At the same time, with the rapid changes in the economic situation since July, there is an urgent need for the infrastructure construction, especially like railway, to exert its pull effect on the national economy.Therefore, the small and medium-sized rail transit with the goal of promoting tourism and achieving rural revitalization has been given a special mission of the times.Suspension monorail train (also called sky train) is very popular among the cities because of the advantages of low cost, short time of construction and flexibility.It has great market potential for the development of small and medium-sized cities in the future, especially the urban areas built around the mountains, those connecting the end of the subway and residential areas, etc.. Progresses in scientific and industrial technology have also promoted the rapid development of sky train.A variety of suspended rail transit systems have been put forward at home FIGURE 1. "Rainbow" rail transit system has strong climbing ability, small turning radius and flexible driving, intelligent service and other advantages, which is suitable for small volume and scattered mode transportation, and it has a good application prospect for the development of small and medium-sized cities in the future.

Fig 2 .FIGURE 3 .
Fig 2. Sample car schematic with the help of Ansoft Maxwell software.At the same time, combining with the actual test data, we carry out comparative verification and analysis.Because the magnetic force between Halbach permanent magnets is greatly affected by the vertical gap and horizontal offset of permanent magnet array, therefore, in the magnetic simulation analysis, we set the horizontal offset between permanent magnets as in [0-5]; In the vertical direction, the gap interval is [0-40], and six groups of sample data are used to explain it, as shown in Figure 5 below.Combined with actual project construction, in the simulation analysis of this paper, the size of the permanent magnet block is taken as 150*30*30 (corresponding to the length, width and height of the permanent magnet in figure 3 respectively).The permanent magnet adopts the sintered NdFeB N45 model.The vertical gap, the horizontal offset and the size of the permanent magnet which are described above are of millimeter magnitude (mm).The simulation data in this paper mainly focus on the analysis of the single point suspension structure without considering the coupling relationship between adjacent levitation points.

FIGURE 5 .
FIGURE 5. Finite Element magnetic simulation curve According to the above figure, the static levitation force of Halbach array and the gap and horizontal offset of permanent magnet decreases nonlinearly, and the attenuation rate of magnetic force decreases gradually with the increase of height.The levitation height of medium and low speed maglev trains in China generally are around 10 mm, while the control range of vehicle operation is stable within the controllable range of 3mm.Referring to the basic data of the medium and low speed maglev train, the static levitation force of the "Rainbow" suspension system can reach 3.33kN when the horizontal deviation is 0 mm and the suspension gap is 0 mm.The maximum load of the permanent maglev structure can reach about 1.2 Ton.When

FIGURE 6 .
FIGURE 6. Static Magnetic Field Force Curve Under Finite Element Simulation Interface The figure shows:(a) The trend of static vertical force changes under different levitation gap conditions, (b) the horizontal magnetic force with several horizontal displacements under the levitation gap, (c) the longitudinal magnetic force along the orbital direction under different levitation gaps (d) 3D magnetic force trend with different suspension gap and horizontal offset.In (a), when the suspension gap is in hight='15mm' Force_x magnetic direction reverses (from the original repulsive force to the attractive force), and the rate of change is different before and after the magnetic direction flipping.That is, the magnetic suction attenuation rate is slightly smaller than the magnetic force attenuation rate.In (b), the horizontal magnetic force increases nonlinearly with the increase of horizontal offset, and then decreases gradually.The smaller the gap, the faster the magnetic growth and the larger the amplitude.The maximum horizontal magnetic force is obtained when the offset reaches about 25mm (when the suspension gap is 0 mm, the maximum magnetic force is 3.03 kN; when the suspension gap is 25mm, the horizontal magnetic force is up to 1.04 kN).It can be seen that under the ideal condition, which means the horizontal deviation is 0 mm, the horizontal steering force can realize "zero" power operation.When the horizontal offset is larger than 5mm, the permanent magnet array has strong horizontal lateral force, especially when the suspension gap is small, which requires the guidance control system to have strong anti-disturbance and correction ability, as well as the necessity of introducing the secondary steering structure.In (c), the amplitude of magnetic force generated by the permanent magnet array in the direction of travel along the orbit is basically zero, and will not change with the horizontal offset, but the direction is basically irregular.The influence of magnetic force along the track direction wasn't taken into account in the actual engineering design.In (d), the horizontal offset and levitation clearance of the upper and lower permanent magnetic arrays are taken as the variable axis, and the three-dimensional integrated magnetic force (scalar) between the permanent magnetic arrays is drawn by finite element simulation.The magnetic force relationship between the gap and the offset is more intuitively reflected For the distribution of magnetic field intensity, as shown in Figure7below:

( a )FIGURE 7 .
FIGURE 7. Magnetic field intensity distribution in several states It can be seen from the diagram that the magnetic field intensity on the track line is basically concentrated on the contact surface between the Halbach permanent magnets with the maximum intensity of 1.048 kT, which is nonlinear attenuated with the increase of the distance.The magnetic field intensity between the suspension points is obviously increased.The magnetic field energy is mostly concentrated on the surface of the central magnet, and the maximum internal intensity can reach 1.8346kT.
actual test sample data are compared with the finite element simulation data, as shown in Table5.The actual data obtained the mean value of the corresponding suspension gap by increasing the load on the vehicle suspension frame.
bearing capacity has a certain attenuation compared with the theoretical one, but the overall attenuation rate is relatively low, which basically meets the magnetic requirements of the actual vehicle operation.The deviation rate of magnetic force at the 26mm moment of suspension gap is about 19%.Combined with chapter C, the bearing capacity of suspension frame is not only related to suspension clearance, but also affected by horizontal deviation.Some of the sample points in Table 5 are affected by the detection position, resulting in a large magnetic deviation rate, which likely the error caused by the horizontal offset.Several sets of sample data and simulation data in Figure 5 are drawn into line diagram verification analysis, as shown in Figure 8.

FIGURE 8 .
FIGURE 8. Finite element Simulation and actual Measurement Curve (Vertical Force)

FIGURE 9 .
FIGURE 9 .Halbach permanent magnet array gridding and the effect of laminated plate thickness on vertical magnetic force Figure (a), we pay attention to the skin effect between permanent magnets, the simulation surface depth is set to 2 mm; In figure (b), x1 denotes the thickness of the adding layer, x denotes the displacement of the short rail along the direction of the track, and the starting point of the short rail is set to (150+ X) mm, the thickness of adding layer is set to (5+X) mm; the starting point of the long rail is set to 0 mm, the thickness of the adding layer is [0,5] and the sampling step is 1 mm.It can be seen from the above figure that the thickness of the laminated plate has obvious

2 ) 3 )
−  = 0.9996 > 0.9  = 0.01747 (According to formula (2), the fitting function is in excellent agreement with the actual levitation magnetic force.According to Newton's second law and equation of suspension (1), the equation of state of levitation system in vertical magnetic field can be obtained, without considering the influence of horizontal deviation.{ ℎ ̇=  ̇= (ℎ)/ −  (In the formula, v denotes the displacement velocity of the vehicle in the vertical direction and m represents the mass of the whole suspension structure.

carrying capacity of the car can contain 4- 6 people.
Combined with the simulation curve of suspension force, the height of suspension control is basically kept within the adjustable range of 5 mm, in addition, on the suspension frame mechanical protective wheels with horizontal and vertical direction are set to avoid large suspension fluctuation of suspension structure.Therefore, by obtaining the equilibrium point, the stability of the equation of state of the system is analyzed by using the Taylor formula in the local linearization expansion at the equilibrium point.At the equilibrium point, the equation of suspended state is : { ℎ ̇=  = 0 ̇=  *  ( * ℎ) +  −  = 0(4)By formula (4), we can get:

FIGURE 10 .
FIGURE 10.Response Waveform of Vertical displacement and Velocity

FIGURE 11 .
FIGURE 11.. Three views of hybrid suspension structure

5 .
1mm (distance to the bottom of the winding coil), and the adjusting time is about 2 s, as shown in Figure12below.

Figure 12 .
Figure 12.Output Curve of suspension system under Linear State Control

Figure 13 .
Figure 13.Output response of suspension ball systemIn the suspension structure of the "Rainbow"

Figure 14 .
Figure 14.Actual suspension ball position control curve

Acknowledgments:
Since the establishment of the project in 2015, the research, development, and construction of the system have been strongly supported by the Ministry of Industry and Information Technology.It has also obtained the help from Southwest Jiaotong University, Beijing Jiaotong University, National University of Defense Technology, Tongji University, and Institute of Electrical Engineering of Chinese Academy of Sciences, China CRRC, Ganzhou Fortune, Shandong Laigang Construction, Dongguan Hongcan, Changzhou Pacific and other units for their support and assistance.Here, the author expressed sincere gratitude to the above units.At the same time, I am very grateful to all the teachers and students of our school's "Rainbow" rail transit system research group for their long-term support and guidance.Funding: National Natural Science Foundation of China ( No.61763016 and 61603306 ) ; National key research and development plan advanced rail transit special (No.2017YFB1201105-12); Jiangxi Provincial Natural Science Foundation (No.20171BAB202030 ); Jiangxi Provincial Department of Education Science and Technology Research Key Project ( No. GJJ170514 and GJJ150620).

TABLE III .
SUSPENSION ATTENUATION RATES AT DIFFERENT HORIZONTAL OFFSETS

TABLE V SIMULATION
OF SUSPENDED VERTICAL MAGNETIC FORCE AND PRACTICAL MEASUREMENT DATA SHEET In the above table, the actual single point