Rail Temperature Rise Characteristics Caused By Linear Eddy Current .
Journal of Traffic and Transportation Engineering ( English Edition) 2014,1(6) :448-456 Rail temperature rise characteristics caused by linear eddy current brake of high-speed train Xiaoshan Lu', Yunfeng Li2 , Mengling Wu', Jianyong Zuo 1 ' 1 2 3 , Wei Hu' /nstitute of Railway Transit, Tongji University, Shanghai, China CSR Qingdao Sifang LDcomotive Co. , Ltd. , Qingdao, Shandong, China Ecole Nationale Supirieure d'Arts et Mitiers, Angers, Pays de la Loire, France Abstract: The rail temperarure rises when the linear eddy current hrake of high-speed train is working, which may lead to a change of rail physical characteristics or an effect on train operations. Therefore , a study concerning the characteristics of rail temperarure rise caused by eddy current has its practical necessity. In the research , the working principle of a linear eddy current brake is introduced and its FEA model is established. According to the generation mechanism of eddy current, the theoretical formula of the internal energy which is produced by the eddy current is deduced and the thennalload on the rail is obtained. ANSYS is used to simulate the rail temperarure changes under different conditions of thermal loads. The research result shows the main factors which contribute to the rising of rail temperarure are the train speed, brake gap and exciting current. The rail temperarure rises non-linearly with the increase of train speed. The rail temperarure rise curve is more sensitive to the exciting current than the air gap. Moreover, the difference stimulated by temperarure rising between rails of 60 kg/m and 75 kg/m is presented as well. Key words: high-speed train; linear eddy current brake; thennal load; rail temperarure rise 1 Introduction The traction and the braking are two main issues for a high -speed train ( Zhu and Zhang 1996 ) . As the drastic increasing in operation velocity of trains during recent years, the adhesion coefficient between the wheel and the rail at high speed decreases greatly as well as the coefficient of friction between the brake shoe and wheeL Therefore, it is necessary to use a Corresponding author: Jianyong Zuo , PhD , Associate Professor. E-maD: zuojy@tongji. edu. en. non-adhesive braking system for a supplementary braking force (Chen 2008; Yan eta!. 2010). The linear eddy current brake is such a non-adhesive form of non-contact brake system which has been already put into application on ICE3 (Chen 2001 ; Graber 2003 ; Kunz 2005 ; Treib 2013) , shown in Fig. 1. The linear eddy current brake has distinguished advantages including no wear, no pollution, low maintenance , quick response and so on (Ding et a!. 2012; Dong
449 Journal of Traffic and Transportation Engineering( English Edition) 2007 ; Xu 2011 ) . Thus , its application will greatly Fig. 1 enhance the safety of train operation. LECB installed on ICE3 However, due to the energy conversion principle of train braking, the kinetic energy of the train is converted to other forms of energy and dissipated ( Zhi et al. 1983; Zhu 1994; Zhang et al. 2011). The linear eddy current brake ( LECB ) achieves this by using eddy current effect converting the kinetic energy of the train into thermal energy of the rail. Based on the fact that the thermal energy on the rail caused by the eddy current effect can not be dissipated instantaneously, it will have a significant impact on the mechanical and electromagnetic performances of the rail and the effect of eddy current brake ( Li et al. 2011) . Therefore , a research on the rail temperature rise is necessary. In fact, LECB is still in the experimental stage , which means it is not be widely commercially applied and there exist several problems itself. As to research on the rail temperature rise caused by LECB , some results have been obtained by German researchers and Japanese researchers respectively and lead the world in this domain ( Hendrichs 1986 ; Kashiwagi et al. 2009) . Both of them are based on the experiment. Other papers usually focus on the thermal characteristics on a magnet pole ( Jung 2003 ) . Nevertheless, a systematic research on thermal characteristics of rail affected by LECB is deficient, which is the main focus in the paper. The study is set out based on simulation and a 3DFEM model of LECB and rail is established. According to electromagnetic theory , the heat load on the rail is calculated before simulation so that the complex electrical-thermal coupling calculation can be avoided. The main factors of LECB that affect the rail temperature rise are studied. 2 Modeling for thermal simulation Figure 2 (SchOpf 2008) illustrates the working principle of LECB in which F represents magnetic force, Fa represents braking force and FA is attractive force. A LECB consists of the yoke, pole cores and coils. The magnetized directions of pole cores change alternatively. The LECB and the rail maintain a certain air gap ( called brake gap ) . When the train is running , there is a relative movement between the LECB and the rail , which generates an unsteady magnetic field on the head of rail. According to Faraday's law of electromagnetic induction, eddy currents are generated on the head of rail, shown in Fig. 3. The eddy currents generated on the rail interfere in the original magnetic field and distort it. The electromagnetic force between the rail and LECB has a horizontal component along the direction of the train speed ( direction Y) in addition to a vertical component ( direc-
450 Xiaoshan Lu et al. tion Z) . The horizontal component is just the train train is converted to the eddy current loss which cau- braking force F 8 Meanwhile the kinetic energy of the ses the rise of rail temperature. --- Relative velocity vis 0 -- r-- - -""' - v O - r--- F. 1 0 I (a) Non-operating state Fl FA (b) Operating state Fig. 2 - -Air gap -Rail I (c) Structure ofLECB Schematic of LECB Magnetic pole s N -f-:,. · :::·:.::::·::.:::::::·:::z" :··· ·· l:: --.f-7' . . . ::-:::·· .··· .···· ·· · ,·.·.·.··· ··· . ·· . ·. ···············.·.·.·.:.: "'''/ ··················· .·· . . - · Surface of rail Fig. 3 Schematic of eddy current The simplified model for illustrating the LECB is shown in Fig. 4. The load applied on the rail in this magnetic-thermal coupled system can be the thermal load only . Therefore, the simulation can be further simplified to an individual thermal simulation with its value deduced in advance. 2 .1 Determination of thermal load In order to further the simulation of the rail temperature rise trend under the thermal load of linear eddy current brake ( Liu and Liu 2008 ) , the derivation of the formula for simulation is required. The relative magnetic permeability is denoted by J.L, permeability of vacuum by J.Lo , the magnetic path length of the core by l, the brake gap by X 0 , magnetic induction intensity by B, the magnetic flux by Ps , the magnetomotive force ( MMF) by g., the magnetomotive force caused by coils by gm , the equivalent magnetomotive force caused by eddy currents by ge , the induced electromotive force (EMF) by g, the excitation current in coils by / 0 , the effective transient eddy current by i, the magnetic reluctance in the core by rm, the magnetic reluctance of the airgap by Rm , the yoke area of the magnetic pole by S, the number of coil turns of a
451 Journal of Traffic and Transportation Engineering( English Edition) pair of magnetic poles by N, the diameter of an eddy current area by D, the spacing of the adjacent magnetic poles of the same polarity by d, the relative movement speed between the rail and LECB by v, the penetration depth of eddy currents on the head of rail by 8 and the conductivity of the rail by 7J , the radius of eddy current area by r, time by t , the period time Fig. 4 2 by T. The magnetic flux in the circular area of the top surface of the rail corresponding to the poles changes continuously according to a law as "B7rr2 -O-B7rr2 -0" (Long et al. 2007). According to the cosine law, the period is d/ v and the magnetic flux P is ( Rodger et al. 1989; Tsuchimoto et al. 1992; Wang and Chiueh 1998; Xie 2001 ) Simplified model of LECB and rail - cP B7rr cos(27rvt/d) (1) Therefore , the EMF on the rail surface is g 2 - - - dt - B7rr (- 27rv/d)sin(27rvt/d) (2) The circular area above is deemed as an area constituted by several metal rings with the parameters shown in Fig. 5. The resistance of a ring is dR 2 7rrdr ( 3) 7]8 In Eq. ( 3 ) , the penetration depth of eddy currents 8 is (4) 8 d/ 7rV7JJ.l.I.Lo The instantaneous power in the circular area of diameter D is J D P I (2B 7r 7]8V /d )sin (27rvtld)r dr T 2 3 2 - 2 2 - 3 0 T1 Jr/dt B2 'IT3 7]8V2 D4 /64d- 2 Eddy current computing model The effective transient eddy current in the circular area of diameter D is ( Kunckel et al. 2003) i (5) The effective power in the whole area of diameter D within on circle T is p Fig. 5 (6) l B7r!J8vD fi 4d 2 ( 7) Since the eddy current on the surface of rail is relatively strong, the eddy current magnetic field has a weakening effect on excitation field. Therefore the magnetomotive force of the magnetic circuit is
452 Xiaoshan Lu et al. (8) In Eq. ( 8) , k. is a conversion coefficient usually at a value 1. 5 ( He et al. 2004) . According to loop theorem , there are (9) l!J.1.1.L0 S Rm 2X0 IJL 0 S ( 10) (11) Substituting Eqs. ( 7) , ( 8) , ( 10) and ( 11 ) into Eq. ( 9 ) , it can be concluded rm 16Nl0 JLod ( 12) /ik . 'ITTJ8vD 2JL 0 16X0 d According to the device dimension of LECB , the value of Dis 0.175 m, dis 0. 35m. Then it can be concluded 1. 4074/0 B -------- -(13) 0. 455V 5. 6X0 where / 0 represents the excitation current, whose unit is A; X 0 represents the brake gap, unit mm; V represents the train velocity, unit km/h. Equation ( 6 ) can also be rewritten by the device dimension, shown as follow (14) P 23. 7B 2 V2 Then the thermal flux is B q 4 P 76. 03B 'ITDz 2 V2 (15) Equation ( 15) is the formula that can be used to calculate the thermal flux on the rail when the LECB is working. When braking parameters / 0 , X0 and V are given, the thermal power per unit area on the rail surface when LECB is working can be deduced. 2.2 FEA model of rail for thennal simulation According to what has been concluded, there is no need to keep LECB model for simulation analysis. The thermal load can be applied to the top of rail directly. The rail of model type 60 kg/m ( GB 2585-2007 hot-rolled steel rails for railway) with the length of 350 mm is adopted as simulation model and the proftle of the rail is not simplified for keeping high simulation accuracy. The material of the rail is set to U71Mn and the initial temperature is set to 20 't. The rail FEA model and its meshing result are shown in Fig. 6. The total number of elements after meshing is 14565 . Fig. 6 Rail model and meshing result Because the operation speed of the train is high and the relative short action length of LECB is only 1. 05 m (including three pairs of magnetic poles and each of them is 0. 35 m long) , the period change is so quick that the time in which a pair of magnetic poles passing over the corresponding region of the rail where the eddy current is generated is merely 0. 0033 s to 0. 2520 s. Therefore, the thermal effects generated by adjacent pole pairs passing over the same position on the rail can be superimposed. Here assumes that the load of thermal flux is generated by one pair of magnetic poles. The rail temperature rise affected by the whole LECB can be superposed by several pairs of magnetic poles. Consequently when effects of the whole brake device are researched, the result of temperature rise can be directly obtained by superposing the simulation results. 3 Simulation result analysis In order to study trends of rail temperature rise under different brake gaps, excitation currents and train speeds, the simulation analysis is done according to conditions listed in Tab. 1. The conditions sum up to 45 , so that not all the results are listed in the paper. Fig. 7 shows the simulation result in the condition where the brake gap is
453 Journal of Traffic and Transportation Engineering( English Edition) 7 mm, excitation current is 50 A and the train speed is 200 km/h. The result shows that the maximum rail temperature rise is 25. 94 'C and the penetration depth is about 2 mm. 20.000 20.660 Tab. 1 List of parameters required for simulation 21.321 21.981 Brake gap Excitation (mm) current (A) 30 Train speed ( km/h) 22.641 23 .302 50, 100, 200, 300, 380 23 .962 24 .622 6 7 8 50 50, 100, 200, 300, 380 70 50, 100, 200, 300, 380 30 50, 100, 200, 300, 380 50 50 , 100 , 200, 300, 380 70 50, 100, 200, 300, 380 30 50, 100, 200, 300, 380 50 50, 100, 200, 300, 380 70 50, 100 , 200 , 300 , 380 25 .283 25 .943 (a) Temperature distribution along the rail surface 20.000 20.660 21.321 2 1. 981 The effects of train speed, brake gap and excitation current on rail temperature rise are shown as follows. 3 .1 Effects of train lire eeds 22.641 23.302 on rail temperature 23.962 24.622 25 .283 When the brake gap is 6 mm and excitation current is 70 A ( the condition where the rail temperature reaches its maximum of all ) , the rail temperature rise trend caused by eddy current brake is shown in Fig. 8 . The lower curve represents the maximum rail temperature trend under an pair of magnetic poles and the upper curve represents the maximum rail temperature trend when the LECB (including three pairs of magnetic poles) is passing over. As the figure indicates, the rail temperature increases non-linearly with the increase of train speed. According to Faraday's law of electromagnetic induction , with the train speed increasing, the amount of change of magnetic flux per unit time at some point of the rail is increased and the eddy current generated is correspondingly increased. The increase of eddy current will lead to an increase of rail temperature rise inevitably which is relatively sensitive to the speed of the train at low speed while tending to ease at high speed according to Fig. 8. The result can be confirmed by theoretical arithmetic ( Guo et al. 2012). 25 .943 (b) Temperature distribution on the cross section of rail Fig. 7 Simulation results of one condition Besides, Fig. 8 also indicates that the maximum rail temperature in all conditions reaches 111. 28 'C. 3.2 Effects of bra!E gaps on rail temperature lire When the excitation current is selected at 50 A constantly , the maximum rail temperature curves by taking different brake gaps ( 6, 7, 8 mm) are shown in Fig. 9. Comparing the three curves illustrated in Fig. 9 , a conclusion can be drawn that as the brake gap increases , the maximum rail temperature will be slightly reduced though the level of the reduction limited by 1% to 3% per 1 mm change of brake gap. According to magnetic circuit theory , the total magnetic circuit reluctance increases in pace with the brake gap increas-
454 Xiaoshan Lu et al. ing, which leads to the decrease of magnetic field intensity and eddy currents generated. In short, with an equivalent input of the excitation currents, the influence of the brake gap on the rail temperature rise trend is minimized. 120 111.28 '"'"'100 2" . 80 "8"" -WholeLECB -- -- One pair of magnetic poles .B 8 60 " .§ the entire magnetic field intensity, the excitation current has greater influence on the eddy current effects , which leads to a greater effect on braking torque and temperature. The analysis data demonstrate that at the speed of 50 km/h, the maximum temperature increased by 3% to 7% per 20 A increase in the excitation current while the maximum temperature increased by 22% to 27% for each 20 A increase in the excitation current with the train speed up to 380 km/h. Therefore , it can be obtained that the excitation current has a greater effect on temperature rise under high train speed; otherwise, the influence is relatively small under the low-speed case. I "' :::E 40 33.12 35.94 37.09 20 ------ -------- ------ ------ 100 0 200 300 400 - - 30 A ----50 A . 70 A '"'"' 100 2". Train speed (km/h) Fig. 8 110 . " Curves of rail maximum temperature trend 90 "" 8 .B 8 s 90 80 · "' :::E - - 6mm ---- 7mm . 8mm 70 60 0 100 200 300 400 Train speed (km/h) Fig. 10 Maximum temperature curves under different excitation currents 65 3.4 60 ------ -------- ------ ------ 0 100 200 300 400 Train speed (km/h) Fig. 9 3.3 Maximum temperature curves under different brake gaps Effects of excitation currents on rail temperature rise When the brake air gap is selected at 7 mm constantly, for example, the maximum rail temperature curves by taking different excitation currents ( 30 , 50 , 70 A) are shown in Fig. 10. It is manifested in Fig. 10 that the effects of excitation currents on the rail temperature are more explicit compared with brake gaps. Having a great impact on Effects of types of rail on rail temperature rise Holding steady values of all other parameters , the rail temperature rises on different types of rail are studied as well. The mode type 60 kg/m is usually used in high-speed lines while the mode type 75 kg/misused in heavy-haul railways. The maximum rail temperature curves by taking different types of rail are shown in Fig. 11. Obviously, the maximum temperatures of rail types of 75 kg/m and 60 kg/m have little difference. Although there are many different dimensional parameters of these two types of rail , the penetration depth is about 2 mm on the top surface of the rail where the contour shapes of them have few differences in term of the whole rails.
455 Journal of Traffic and Transportation Engineering( English Edition) 115 110 .a."' 105 . 100 1'1. s"' 95 90 111.28 ----60km/m - -75km/m Acknowledgments . 2 .§ . I ::E This project is supported by the Fundamental Research Funds for the Central Universities (No. 2860219030) and Foundation of State Key Laboratory of Traction Power, Southwest Jiaotong University ( No. TPL1308). 85 80 75 70 0 100 200 300 400 Train speed (km!h) Fig. 11 75 kg/m. The maximum rail temperature in all conditions reaches 111. 28 't: . Maximum temperature curves under different types of rail References Chen, A. F. , 2001. ICE 3 pioneers application of eddy-current rail brakes. Foreign Rolling Stock, 38(4): 37-39. Chen, J. D. , 2008. Research on non-adhesive brake technology for railcar. Master thesis, Dalian Jiaotong University, Dalian. 4 Conclusions By theoretical derivation and simulation analysis, the effects of eddy current brake on the rail temperature rise are studied. The results show that there are three main aspects of LECB that affect the rail temperature rise: the train speed, brake gap and excitation current. The influence of these three aspects on rail temperature rise is quantitatively analyzed by simulation. Because the simulation of rail temperature rise of LECB is an electrical-thermal coupling problem, the heat load on the rail is calculated by electromagnetic theory before simulation in order to avoid the complex electrical-thermal coupling calculation. Therefore, the simulation process has been greatly simplified. If the brake gap and excitation current keep constant, the rail temperature rises non-linearly with the increase of train speed. The rail temperature rise curve is relatively sensitive to the speed of the train at low speed while tending to ease at high speed. Under the specific circumstances with the same train speed and excitation current , rail temperature rise would decrease with a gain of brake gap which has a light effect on the temperature rise. And if keep brake gap and train speed as constant , the increasing excitation current will lead to the increase of rail temperature rise. What's more, the excitation current has greater influence on temperature rise with higher train speed. There is no significant difference of rail temperature rise trends between the rail types of 60 kg/ m and Ding, F. Y., Lv, B. J., Gu, L. L., 2012. Summary of eddy current braking technology of high speed train. Railway Locomotive & Car, 32(6): 1-4,20. Dong, X. M. , 2007. Working principle and structural characteristics of high-speed EMU. China Railway Publishing House, Beijing. Graber, J. , 2003. The linear eddy-current brake on ICE3--operational concept and first experience. Foreign Locomotive & Rolling Stock Technology, (5): 1-6, 14. Guo, Q. Y., Huang, S. Z. , Wu, W. Y., et al. , 2012. Research on pyrometric effect on eddy current brake for maglev train. Journal of the China Railway Society, 34(1): 29-33. He, R., Yi, F. Y., He, J. Q., 2004. A computation method for braking torque of eddy current retarder. Automotive Engineer, 26(2): 197-200. Hendrichs, W. , 1986. The thermal behaviour of the eddy-current brake. Elektrische Bahnen, 84(5): 139-144, 146-148. Jung, S. J. , 2003. Thermal analysis and test of eddy-current braker for high-speed train. Transactions of the Korean Institute of Electrical Engineers, 52 ( 5 ) : 197-202. Kashiwagi, T. , Sakamoto, Y. , Sasakawa, T. , et al. , 2009. Basic characteristics of rail brake systems using linear motor technology. Quarterly Report ofRTRl, 50(3): 173-178. Kunckel, S. , Klaus, G. , Liese, M. , 2003. Calculation of eddy current losses and temperature rises at the stator end portion of hydro generators. COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering , 22(4): 877-890. Kunz, M., 2005. Integration of the ICE 3's linear eddy-current brake in the infrastructure-technical aspects and operational experience. Converter Technology & Electric Traction, ( 2) : 4-8. Li, B. G., Qiao, F., Ding, F. Y. , 2011. Study on optimization analysis of braking force blending for high-speed EMU with eddy current brake. Railway Locomotive &Car, 31 (5): 132-134. Liu, Y. B., Liu, G. H. , 2008. Key techniques and thermal analysis of ftnite element analysis software ANSYS. Journal of Chongqing University of Science and Technology: Natural Sciences Edition,
456 10(6)' 104-107. Long, X. L., Zhang, B. F., She, L. H., 2007. Eddy brake of maglev train. Ordnance Industry Automation, 26(9), 58-59. Rodger, D., Karaguler, T., Leonard, P. J., 1989. A formulation for 3D moving conductor eddy current problems. IEEE Transactions on Magnetics, 25(5), 4147-4149. SchHpf, M. , 2008. Eddy current brake-an innovative wear-free braking system independent from wheel-rail adhesion. 6th World Congress on High Speed Rail, Amsterdam. Treib, L. , 2013. Operation experience of linear eddy current brake device. Foreign Locomotive &Rolling Stock Technology, (3) , 38- 43. Tsuchimoto, M. , Miya, K. , Yamashita, A. , et al. , 1992. An analysis of eddy current and Lorentz force of thin plates under moving magnets. IEEE Transactions on Magnetics, 28(2): 1434-1437. Wang, P. J., Chiueh, S. J., 1998. Analysis of eddy-current brakes for high speed railway. IEEE Transactions on Magnetics, 34 ( 4) : 1237-1239. Xie, D. X. , 2001. Finite element analysis of 3D eddy current field. Xiaoshan Lu et al. China Machine Press, Beijing. Xu, X. F., 2011. Study of the application efficiency of eddy current brake on high-speed train. Master thesis, Tongji University, Shanghai. Yan, G. B. , Fang, Y. T. , Zhang, F. , 2010. Design and analysis of hybrid excitation rail eddy current brake system of high-speed train. Journal of Mechanical & Elec1rica1 Engineering, 27 ( 8) , 19-22. Zhang, J. B. , Peng, H. S. , Ni, D. C., eta!. , 2011. Overviewing braking technology of the high-speed trains. ffiectric Drive for Lo- comotives, (4): 1-4. Zhi, L. Q. , Un, T. P. , Sun, F. X., 1983. Braking technology of modem railway. China Railway Publishing House, Beijing. Zhu, X. F., 1994. Electromagnetic analysis of the linear eddy cunent braking. Journal of Shanghai Institute of Railway Technology, 15(2)' 55- i3. Zhu, X. F. , Zhang, X. R. , 1996. Analysis and calculation of braking force on rail eddy current braking of high speed trains. Journal of Shanghai Tiedao University, Natural Science, 17 ( 4) , 1-ll.
cessity. In the research , the working principle of a linear eddy current brake is introduced and its FEA model is established. According to the generation mechanism of eddy current, the theoretical formula of the internal energy which is produced by the eddy current is deduced and the thennalload on the rail is obtained.
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Rail Transportation and Engineering Center (RailTEC) 205 N Mathews Ave. Urbana, IL, United States 61801. ABSTRACT . Previous research has focused on the effect of rail cant on rail wear and wheel/rail interaction, indicating that a steeper rail cant results in increased wear on rails and wheels. However, no research has investigated the effect .
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