7/31/2019 Me 34308

1/4

Analysis and Simulation on the Braking Force of

Permanent Magnetic Brake

Ming YaoDepartment of Traffic Engineering

Jiangsu University

Zhenjiang, Jiangsu, P.R.China; 212013

Email: ymluck@ujs.edu.cn

Zhuohua TangDepartment of Traffic Engineering

Jiangsu University

Zhenjiang, Jiangsu, P.R.China; 212013

AbstractThe structure and working principle of permanent

magnetic brake were introduced and the main factors of

influencing braking ability of the permanent magnetic brake were

analyzed with theory formula. By using of software as Ansoft, an

finite element simulation model for magnetic brake were built up,

and compare simulate value with theoretical one express that they

have better consistency. Based on the simulation model,influencing factors of the braking force about permanent magnetic

brake were analyzed, and the simulate results express that the

height of gap between brake and track has a great influence on the

braking force, so it must pay much more attention on brake design.

Keywords-permanent magneti brake; braking force;

Simulation; design of brake

I. INTRODUCTIONWith the development of rail transit, the passenger train has

already got into the high-speed rail era. With the increasing of

speed, there are so many people looking at trains safety, so the

braking performance of train face a great challenge. Currently,braking mode of medium-low speed trains are mainly friction

brake, such as block brake, disk brake etc. However, these

methods belong to adhesion braking, as the train speeds

increase, the adhesive coefficient reduces quickly, which

makes braking force reduces correspondingly. For this reason,

high-speed train is hard to stop in limited braking distance by

adhesion braking mode alone. The other braking mode such as

Eddy current brake, magnetic brake and other non-adhesion

braking are widely used in high-speed train, the braking force

of train come from the rail directly and free from adhesion

coefficient, so if the high-speed train use the combination

control strategy that combine adhesion braking and non-

adhesion braking, the braking performance of the train will begreat improved. Permanent magnetic track braking technology

is a new type of brake mode developed in recent decades,

which has been widely focused because of its non-consumption

of energy, maintenance-free and good braking performance in

high speed. This new technology, which has made good effect

in the Shinkansen, was proposed by the Japan Railway

Technical Research Institute (RTRI) at first. On the ICE high-

speed train of German, it has also adopted liner type of

permanent magnet brake produced by the Knorr Company in

Swiss.

At present, the rail transit is in the process of increasingspeed in China, whereas permanent magnetic track brakingtechnology is still in its initial stage. So it has a greatsignificance to study the permanent magnetic track braketechnology in-depth. In this paper, the working principle andstructure of permanent magnetic track brake was introduced,

and with theoretical formula the braking force was calculated;in addition, by using the software as Ansoft, an finite elementsimulation model for magnetic brake were built up. With thesimulation model, it analyzed the main factors which affect the

braking force by changing the design parameters of magnetictrack brake so as to provide a reference for the design of

permanent magnetic track brake.

II. WORKING PRINCIPLE OF PERMANENT MAGNETIC TRACKBRAKE

A liner type of permanent magnet brake is showed inFigure 1; its magnet axis is composed of permanent magnetand semi-circular diaphragm. Brake connects to the train by

ring flange on the top cover and fixed on the bogeys. Both endsof the brake have fringe cover, and the rotation of magnet axiscan be achieved by the hydraulic cylinder which is inside of thefringe cover, so it can to close or separate the magnetic field

between brake and track.

The working principle of permanent magnetic track brake isas follow: When the trains run normally at high speed, becauseof the lift cylinder of train has taken the brake into a high

position, there is no braking force between the brake and thetrack no matter how the magnet axis rotates; When the high-speed train need to brake, pole shoes are 5~7mm away fromthe track with the working of the lift cylinder that fixed on

Supported by Jiangsu Province Key Laboratory of Automotive EngineeringQC200705

Supported by Jiangsu Province Ordinary University Science Research Project08KJD580005

Figure 1. A liner type of permanent

7/31/2019 Me 34308

2/4

train, at the same time, the hydraulic cylinder drives magnetaxis to the position that the permanent and U-shaped

permanent magnet were separated by the semi-circulardiaphragm(Figure 2a), the pole shoes will form differentmagnetic poles, and the closed magnetic field can cross the

pole shoes and the track, because of the pole shoes are veryclosed to the track, the brake produces a kind of non-contacteddy current braking force.

When the train need to remove the non-contact eddycurrent braking force, the magnet axis was rotated to a positionthat the permanent magnet is relative to the U-shaped

permanent magnet by controlling the hydraulic cylinder(Figure2b), and there is no closed magnetic field formed between the

pole shoes and the track, so braking force is not generated;When the speed of train decreased, the pole shoes will beadsorbed on the track under the magnetic suction to achieve thefriction brake; When the train stopped, parking brake can berelied on the suction of the magnetic field.

III. THE INFLUENCING FACTORS AND CALCULATIONMETHOD ABOUT THE SUCTION OF PERMANENT MAGNETIC

TRACK BRAKEBased on the top analysis, we can see that the size of the

braking force depends on the suction between the brake and thetrack, so it is necessary to analysis the method of calculationabout the magnetic track brake. The suction can be calculated

by following formula.

( )frq

mmm

KKL

VBHF = (1)

WheremmBH for the energy product of permanent

magnet when working; mV for the volume of permanent

magnet; qL for the height of air gap between the bottom ofbrake and the track; rK for the reluctance coefficient, it isrelated to the length of magnetic yoke and the size of work gap,

in general, it changes from 1.05 to 1.45; fK for the leakage

coefficient, it depends on leakage magnet of the entirestructure, and it is generally between 2.5 and 20.

Formula (1) shows that the suction of permanent magnettrack brake is not only related to the maximum energy productof permanent magnet, the volume of permanent magnet and so

on but also affected by the reluctance coefficient, the leakagecoefficient and the height of air gap between the bottom of

brake and the track etc. Therefore, the key to the design ofmagnet track brake is to optimize the entire structure of brakeand to reduce the air gap and so on when the material andvolume of permanent magnet are certain. We can achieve this

purpose by establishing the simulation model of magnet trackbrake and using the model to analysis the parameters of entire

structure. Ansoft Maxwell 2D/3D software is a powerful two-dimensional/three-dimensional finite element analysissoftware, and it can be used to analyze motors, sensors,transformers, permanent magnet devices, actuators and otherelectromagnetic devices which are in the static, steady state,transient, normal condition and fault condition etc., Therefore,this article choose the Ansoft software to simulate and analyzethe magnet track brake.

IV. THE FINITE ELEMENT SIMULATION ANALYSIS OFPERMANENT MAGNETIC TRACK BRAKE

A. The establishment of finite element simulation modeAs the structure of permanent magnet track brake is simple,

and the default length of graphics that imported into theMaxwell 2D is one meter along the Z axis, therefore, wechoose two-dimensional static magnetic module to analyze thesuction between the brake and the track.

1) In order to simplify the simulation calculation, we make

two assumptions:

a) Assuming that the assembly gap of brake is 0.5mm;b)assuming that the permeability of entire structure is a constant.

So we use Maxwell 2D to establish a two-dimensionalfinite element model of magnetic track brake.

2) the process is as follows:a) Selecting the solver; b) determining the size of the brake

structure, and drawing the model; c) determining the material

properties of brake; d) determining the boundary conditions ofcalculation and the loads; e) determining the subdivision andsolving the issue. Figure 3 is the two-dimensional model of

permanent magnet brake which is established in the Ansoftenvironment.

Finite element mesh is the base for solving; we need tomesh carefully so as to ensure the accuracy of calculation. Weuse the form of six node triangle to split the solving field. In

Figure 3. Two-dimensional model of permanent magnetic t

brake

Figure 2. Working principle of permanent magnetic track

brake

7/31/2019 Me 34308

3/4

order to enhance the accuracy of the solution in the region,some small triangles need to be split in some place where themagnetic field is strong or the change of magnetic field is huge,other triangles can be split according to the demands. Figure 4is the subdivision result of two-dimensional finite elementsubdivision mesh.

B. The determination of material properties on permanentmagnet brake

In the Ansoft software environment, the model can haveone or more material regions which are air, paramagneticmaterials, conductive materials and permanent magneticmaterial. When establishing the model, the area of eachmaterial should enter the appropriate material properties, andthe material properties can be linear or non-linear. The varietyof material parameters which used in the brake are shown inTable 1.and defined as follows:

1) Describing the linear material properties:

a) The relative permeability;b) Coercive force (for permanent magnet);

2) Describing the non-linear material properties:

a) The B/H curve can be used to represented the non-linear materials;

b) Dont consider hysteresis with a curve;

c) We can describe the B/H curve respectively if it is

anisotropy in the three directions, and the default B/H curve is

isotropic.

TABLE I. THE MATERIAL PARAMETERS OF THE BRAKE COMPONENTS

Permanentmagnet

Top cover, Bottom

partition, Sideplank, Semi-circular

diaphragm

Fixed U-

groove,Pole shoe,

Track

Airgap

Material NdFe35 Al_NSteel_101

0Air

Rel. Permeability 1.1 1B-H Curve

Entry1.0

Mag. Coercivity

A/m -8.9e+5 0 0 0

Mag.

retentivity(T)1.23 0 0 0

Magnetization

(A/m)9.79e+5 0 0 0

C. The analysis on the results of finite element simulationmodel

With the above-mentioned simulation model and therelevant parameters in Table 1, it simulated the magnetic fluxthroughout the brake which is shown in Figure 5.

The figure shows that the flux of brake mainly has threeparts: First, the main magnetic flux which comes frompermanent magnet and through the pole shoes, air gap to thetrack; this part produces the suction for brake, and its flux ismaximum; Second, the leakage magnetic flux which throughthe interval of magnetic board; this magnetic flux is small

because of the separators are non-magnetic materials; Third,the magnetic flux which comes from the end of pole shoe andthrough the surrounding air to reach the other end of pole shoe.The suction value of the simulation is 254.5KN when the airgap between brake and track is 4mm, and the suction valuecalculated with formula (1) is 298.7KN when the energy

product of NdFe35 takes 310KJ/m3 and other parameters, suchas the reluctance coefficient, the leakage coefficient, take themiddle value in the formula. Because the leakage magnet

which comes from the assembly gap of various components ofthe brake has not considered in the process of theoreticalcalculation, the theoretical value larger than the simulation oneis in line with practice, and it also shows that the simulationmodel has a good consistency with the theoretical formula. Sothe simulation model is successful and it can be used as a basisfor further research and analysis.

D. The simulation analysis on the factors which affect thesuction of brake

According to the analysis above, the suction of permanentmagnet brake are affected by the energy product of permanentmagnet, the volume of permanent magnet and the air gap

between the bottom of brake and track besides the reluctance

coefficient and the leakage coefficient. The formula (1) showsthat the reluctance coefficient, the leakage coefficient and thevolume of permanent magnet are linear correlation with thesize of suction value, however, the energy product of

permanent magnet and the air gap between the bottom of brakeand track are not linear correlation with the suction value

because of the energy product of permanent magnet at workingpoint is closed related to the air gap between the bottom ofbrake and track. So it is necessary to use the simulation modelto analyze the brake. The simulation results about the suction

Figure 5. The magnetic flux of brake

Figure 4. Two-dimensional finite element

subdivision meshes

7/31/2019 Me 34308

4/4

by changing the air gap between the bottom of brake and thetrack is calculated and shown in Table 2.

TABLE II. THE SIMULATION RESULTS OF SUCTION ON DIFFERENT AIR GAP

The height of air

gap(mm)

0.5 1 2 4 6 8 12 20

The simulation

value(KN)

259.2 258.5 257.2 254.5 252.8 251.1 248.8 245.6

We get the air gap suction curve by taking the height of airgap as horizontal ordinate and the simulation value of suctionas vertical coordinate, and the curve is shown in Figure 6.

Figure 6 shows that the suction of brake declines with theincreasing of the height of air gap, and the suction will increaselargely when the air gap decreases. The relationship betweenthe air gap and the suction looks like the logarithmic function.So the suction can be improved significantly by reducing theheight of the air gap between the bottom of brake and the trackwhen the brake is working.

CONCLUSION

According to the analysis above, we know that the suctionof the permanent magnet track brake is mainly affected by theenergy product of the permanent magnet at working point andthe height of air gap when the material and the volume of the

permanent magnet are constant, and the suction of thepermanent magnet track brake will increase significantly withthe decreasing of the air gap which shows a non-linearrelationship. Therefore, we can optimize the brake in the

process of designing by reducing the size of the magnetic yokeand increasing the size of the permanent magnet when theexternal size of brake is constant, meanwhile, it should payattention to the rigor of the entire structure of brake, to reducethe interval between the permanent magnet and magnetic yoke

and to decrease the air gap between the bottom of brake and thetrack. When the train is carrying on the friction brake, becausethe debris result from the rub of brake and track will furtherincrease the air gap between the bottom of brake and the track,it should exclude the debris smoothly to ensure the brake has agood braking performance.

REFERENCES

[1] Ming Yao, Ren He, Study on permanent magnetic brake systemapplication and strategy of combination control, ManufacturingAutomation, pp.57-60,2010(9) (In Chinese).

[2] Bing-heng Shao, Xin Zhang, Xian-fu Zhu, The study of the modes onbraking of high speed trains, Electric Drive for Locomotive, pp.10-15,1995(5) (In Chinese).

[3] Kyung-Ho Ha, Jung-Pyo Hong , Gyu-Tak Kim, A Study of the Designfor Touch Free Linear Eddy Current Brake. IEEE TRANSACTIONSON MAGNETICS, VOL 35. pp.4031-4033, SEPTEMBER 1999

[4] Ren He, Run-xin Niu, Ying Dong, Application of permanent magnettrack braking technique in railway. China safety science journal, Vol 17(1), pp.167-170, January 2007 (In Chinese).

[5] Ming Yao, Zhuo-hua Tang, A kind of linear permanent magnet trackbrake, 201110086650.9[P], 2011(4) (In Chinese).

[6] Ming Yao, Ren He, Xiao-na Zhang, A kind of permanent magnet trackbrake, 200910213026.3[P], 2009(12) (In Chinese).

[7] Ming-xi Mo, Bao-xia Zhang, Permanent magnet track brakingtechnique and correlative calculations, Electric Locomotives & MassTransit Vehicles, pp.23-25, 2009(3) (In Chinese).

[8] Sohel Anwar, A Parametric Model of an Eddy Current ElectricMachine for Automotive Braking Applications. IEEE Transactions on

Control Systems Technology, Vol. 12, No. 3, MAY 2004.

[9] Cai-hong Zhu, Magnetic Field Finite Element Analysis of PermanentMagnet Brushless DC Motors Based on Ansoft, Micromotors, pp.103-105,2010(6) (In Chinese).

[10] Zhong-yang Sun, Practical tutorial for procedures of train tractioncomputation. China railway publishing house, Beijing, 1999 (InChinese).

Figure 6. Air gap suction curve of the simulation model