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Influence of the Seam between Slab and CA Mortar of CRTSII Ballastless Track on Vibration Characteristics of Vehicle-Track System
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
SciVerse ScienceDirect SciVerse ScienceDirect Procedia Engineering 00 (2017) 000–000 Available online at www.sciencedirect.com Procedia Engineering 00 (2017) 000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Engineering 199 (2017) 2543–2548
X International Conference on Structural Dynamics, EURODYN 2017 X International Conference on Structural Dynamics, EURODYN 2017
Influence of the Seam between Slab and CA Mortar of CRTSII Influence of the Seam between Slab and CA Mortar of CRTSII Ballastless Track on Vibration Characteristics of Vehicle-Track Ballastless Track on Vibration Characteristics of Vehicle-Track System System Qingsong Feng, Hangyu Chao, Xiaoyan Lei Qingsong Feng, Hangyu Chao, Xiaoyan Lei
Engineering Research Center of Railway Environment Vibration and Noise Ministry Education,East China Jiaotong University, Nanchang 330013, ChinaMinistry Education,East China Jiaotong University, Nanchang Engineering Research Center of Railway Environment Vibration and Noise 330013, China
Abstract Abstract
With a lot of application of CRTSII slab ballastless track in China,a series of problems have arises during the slab With a lot of application of CRTSII slab ballastless track between in China,a problems arises during the slab track service. One of the most typical problems is the seam theseries trackofslab and CAhave mortar layer, namely CA track the influence most typical the seam between track slab CA mortar layer, namely mortarservice. seam. One This of may the problems vibration ischaracteristics of thethe vehicle and and CRTSII slab ballastless track.CA In mortar influenceaccording the vibration characteristics of theand vehicle ballastless In order toseam. study This this may phenomenon, to the actual engineering basedand on CRTSII the finiteslab element, a newtrack. vertical order to studycoupling this phenomenon, according to the actual and based the finite element, vertical vehicle-track dynamic model is established. Theengineering model consists of twoonparts, vehicle elementa new and CRTSII vehicle-track dynamicThe model is established. model consists of two parts, vehicle element and CRTSII slab ballastlesscoupling track element. former is regarded The as multi-rigid-body systems, while the latter is established by slab ballastless element. Theinformer regarded as system, multi-rigid-body whileconcrete the latterbase is established by means of finite track element method, which is rail, fastening track slab,systems, CA mortar, and subgrade means of finiteaselement in which rail,and fastening system, track CA mortar, concrete and subgrade are considered a wholemethod, body. The rail, slab the concrete base are slab, simplified as layered Eulerbase beam model. The are considered as a whole The rail, slablinear and the concrete base to areconsider simplified layered Euler of beam The fastener and subgrade are body. simplified as the spring. In order theascharacteristics the model. CA mortar fastener subgrade are simplified as the linear spring. In layer. order Based to consider the characteristics the CA model, mortar seam, theand nonlinear spring is used to simulate the CA mortar on vehicle-track couplingofdynamic seam, the nonlinear is used to simulate the CA mortar layer. Based dynamic of model, the influence law of spring CA mortar seam on the safety of vehicle operation, onon thevehicle-track displacementcoupling and acceleration each the lawstructures, of CA mortar seam onby thecomparing safety of vehicle operation, on the of displacement of each partinfluence of the track is revealed, the dynamics properties the CRTSIIand slabacceleration ballastless track of part of the trackwithout structures, is revealed, comparing theCA dynamics the CRTSII slabwhile ballastless of the conditions CA mortar seamby and those with mortar properties seam. The of result shows that there track is seam the conditions without CA mortar and thoseit with CA mortar seam. result shows that while there, is between the track slab and the CAseam mortar layer, has slight influence on The the smooth of vehicle operation butseam has between theimpact track slab and the CA mortar layer,ofitthe hasCRTSII slight influence on the smooth of vehicle , but has significant on the mechanical properties slab ballast-less track structure. Theoperation study is expected significant impact on the mechanical propertiesifofthere the CRTSII slabproblems ballast-less track to provide theoretical guidance for remediation are similar in the slabstructure. track. The study is expected to provide theoretical guidance for remediation if there are similar problems in the slab track. © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. © © 2017 The under Authors. Published by Ltd. committee Peer-review under responsibility responsibility of Elsevier the organizing organizing committee of of EURODYN EURODYN 2017. 2017. Peer-review of the Peer-review under responsibility of the organizing committee of EURODYN 2017. Keywords: CRTSII slab ballastless track;Dynamic coupling;Seam;Finite element method;Vibration characteristics Keywords: CRTSII slab ballastless track;Dynamic coupling;Seam;Finite element method;Vibration characteristics
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review©under the organizing committee 1877-7058 2017responsibility The Authors. of Published by Elsevier Ltd. of EURODYN 2017. Peer-review under responsibility of the organizing committee of EURODYN 2017.
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the organizing committee of EURODYN 2017. 10.1016/j.proeng.2017.09.259
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Qingsong Feng et al. / Procedia Engineering 199 (2017) 2543–2548 Author name / Procedia Engineering 00 (2017) 000–000
CRTSII ballastless track structure features stable performance , comfort in ride, slow track deformation and less demand for maintenance. It is widely used in the high speed railway in China. At present, it has been applied in the Beijing-Shanghai high speed railway and most of the domestic passenger dedicated lines [1]. The CA mortar,which is one of key layers in CRTSII slab ballast-less track structure, is also the weakest link layer. The seam between track slab and CA mortar is a dynamic track irregularity. Once the seam occurred in the CA mortar, the repeated train loads will make the mortar seam area gradually expand. When the train runs across the seam area, the mortar loses its supporting role, this cause strong vibration of the vehicle-slab track system, thus affecting train operation safety. At present, domestic and foreign scholars have carried out a variety of theoretical and experimental studies on the CRTSII slab ballastless track structure in good condition. A finite element model of the CRTSII slab ballastless track on embankment has been established to study the dynamic stress distribution law of the track and subgrade under the moving load with different velocity[2]. Influence of the temperature load on deformation and stress conditions of CRTSII slab ballast-less track, and influence of track deformation on the running safety of vehicles are analyzed[3]. Apart from that, a finite element model of the CRTSII slab ballastless track on subgrade has also been established, and then subgrade constitutive model and structural material parameters are discussed[4]. The influence of uneven subgrade settlement and vehicle load on the track are studied [5]. However, there is few research on the stress of the CRTSII slab track with CA mortar seam. The influence of the changes of the length and the height of the CA mortar seam on the mechanical properties of CRTSII slab track structure is analyzed[6-8]. Therefore, based on the characteristics of CRTSII slab ballast-less track structure, the article establishes a finite element vertical coupling vibration model for CRTSII slab ballast-less track under the condition of the mortar seam by ABAQUS software. The CA mortar seam is simulated by nonlinear spring, and the wheel-rail model of the two subsystems is set up in accordance with the nonlinear Hertzian contact theory. After the track irregularity being introduced, then the vibration of coupling system is solved. The influence of length and height of seam on dynamic characteristics of the vehicle-track system are analyzed. The established method and results lay the basis for the further study of the seam between the track plate and the mortar layer, and thus provide guidance for practical engineering. 1. Vehicle-track vertical coupling model 1.1. Vehicle-track finite element model The CRTSII slab ballastless track structural is mainly composed of rail, fastening system, slab, CA mortar, concrete base and subgrade. The structure of the vehicle and track is transversely symmetrical structure. The vehicletrack coupling dynamics[9] shows that the vertical and the lateral coupling vibration effects of vehicle are very complicated. The results show that the transverse forces of track structure presents uniform distribution because of the high lateral stiffness[10]. Therefore, in order to facilitate the calculation, the model is simplified as a twodimensional vehicle-track coupled vertical vibration model, as shown in Fig. 1. The vehicle is assumed to be a 10 degree of freedom multi-rigid-body model[11]. We only take into consideration the ups and downs movement, the corner of car body and bogie, and the ups and downs of wheel. The car body, bogie and wheel are simulated by MASS element, and the suspension system by spring damping unit.
Fig. 1. 10 degree of freedom vehicle beam coupling model with three layers.
The rail, track slab and concrete base of track structure are simulated by Euler beam element. In order to eliminate the influence of boundary effect, the line length of track is 221 m. The fastener system is simplified as a
Qingsong Feng et al. / Procedia Engineering 199 (2017) 2543–2548 Author name / Procedia Engineering 00 (2017) 000–000
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discrete spring damping; subgrade support and CA mortar are simulated by distributed spring damper. In the seam area shown in Fig. 2, the damping effect is not taken into consideration. Nonlinear spring element is used in the simulation; the nonlinear characteristics of the spring are shown in Fig. 3. The maximum value of the height of seam of CA mortar u 0 is 3mm in the spring force-displacement curve of nonlinear spring, as shown in Fig. 3. The length of the curve slope with 0 is to simulate the height of seam of CA mortar, and the slope of the curve is mortar stiffness. Wheel-Rail coupling is realized by contact module, after analyzing the relations between the contact force and the elastic compression of wheel and rail. According to the Hertz nonlinear elastic contact theory[12], we define the wheel-rail contact model by importing ABAQUS contact properties with the table form of force-displacement.
Fig. 2. Mortar void area in the track structure.
Fig. 3. Nonlinear spring force displacement curve
1.2. Track irregularity and numerical simulation Track irregularity considered simultaneously consists of medium long wave irregularity and short wave irregularity in this paper. In this model, the Germany low interference spectra is used for medium long wave irregularity while the weld joint irregularity spectrum is used for the short wave irregularity. Track irregularity simulation sample is obtained by using the frequency of power spectrum equivalent algorithm. By using the selfwriting MATLAB program, we could modify the vertical coordinate value of rail joint in the file to further introduce the track irregularity. The simulation results of the irregularity are shown in Fig. 4 and Fig. 5.
Fig. 4. German low interference irregularity.
Fig. 5. Irregularity of rail joint in rail welding area.
2. Model validation To test and verify the correctness of the model, compared with the calculation results of literature[13] , the calculation conditions for a single high-speed train running on the track at a speed of 200 km/h, the wavelength is 12.5 m and the amplitude is 3 mm of the periodic sine function for track irregularity excitation. The results of this paper are shown in Figs. 6~9.
(a) The result of literature [13]
(b) The result of this paper
Fig.6. Vertical force of wheel-rail
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Qingsong Feng et al. / Procedia Engineering 199 (2017) 2543–2548 Author name / Procedia Engineering 00 (2017) 000–000
(a) The result of literature [13]
(b) The result of this paper
Fig.7. Vertical acceleration of car body
(a) The result of literature [13]
(b) The result of this paper
Fig.8. Vertical acceleration of slab
(a) The result of literature [13]
(b) The result of this paper
Fig.9. Vertical Displacement of slab
As can be seen from Figs.6~9：the response amplitude and waveform of this paper are basically consistent with the calculation results of the literature[13],and the feasibility and correctness of this method are proved. 3. The calculation and analysis of Vehicle-track coupling model A calculation example is given using the vehicle-track coupling finite element model established in ABAQUS software. The vehicle is the high-speed train CRH3 in China. Train speed is 300 km/h. the rail is 60kg/m continuously welded rail. Fastener is WJ-8 fastener system, spacing of 0.65m. Track slab is CRTSII track slab. The line length of track is 221m. Contact model is Hertz nonlinear elastic contact, the grid size of finite element model is 0.01m, for convergence, the computing time step is equal to the rail grid size divided by the speed is 0.00012s. Two kinds of working conditions need to be considered: CA mortar seam and CA mortar seamless.
Qingsong Feng et al. / Procedia Engineering 199 (2017) 2543–2548 Author name / Procedia Engineering 00 (2017) 000–000
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3.1 The analysis of vehicle system vibration response The calculation results of vibration response of vehicle system includes the time history contrast curve of the wheel-rail contact force (as shown in Fig. 10), and the maximum vertical acceleration of vehicle (as shown in Table 1).
(a) Seamless
(b) Seam Fig. 10. The contrast of vertical wheel-rail contact force Table 1 The maximum vertical acceleration of vehicle parts.
working conditions
Car body
Bogie
wheel
seamless
0.977
10.854
48.634
seam
0.984
10.871
48.951
When train moves through the upper part of the mortar seam region, the wheel-rail force changes slightly compared with the seamless, as can be seen in Fig.10. The Table 1 shows that vertical acceleration of vehicle system components changes slightly compared with the seamless. So at this time the wheel-rail interaction and dynamic response of vehicle system are mainly inspired by track random irregularities. 3.2 Vibration response analysis of track structure system The calculation results of vibration response of track structure system includes the time history contrast curve of the track displacement (as shown in Fig. 11), and the maximum vertical acceleration of track structure system (as shown in Table 2).
(a) seamless
(b) Seam Fig. 11. The vertical displacement of track structure system
Table 2. The maximum vertical acceleration response of track system components. working conditions
rail
Track slab
Concrete base
seamless
72.287
25.163
23.838
seam
73.462
62.159
31.227
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Qingsong Feng et al. / Procedia Engineering 199 (2017) 2543–2548 Author name / Procedia Engineering 00 (2017) 000–000
According to Fig. 11, when the train runs through the mortar seam region, the vertical displacement of the slab and support layer is more noticeable, compared with the seamless. Table 2 shows that the seam has the greatest effect on the acceleration of track slab almost 3 times higher than seamless; the seam has an obvious influence on the concrete base, increased by 31%; Its effect on rail is not obvious, mainly due to the fact that the wheel-rail interaction is mainly inspired by track random irregularities. 4. Conclusions In view of CA mortar seam of the CRTSII type ballastless track problems, ABAQUS finite element method is utilized to set up the calculation model of vertical coupling vibration vehicle-track under condition of CA mortar seam. Two different working conditions are taken into consideration: seam of the mortar and seamless of the mortar, aimed at analyzing and comparing the influence of CA mortar seam on vibration response of vehicle and track structure. The main conclusions are as follows: (1) The establishment of simplified calculation model of vehicle-CRTSII slab ballastless track system with CA mortar seam is reasonable and feasible. (2) The CA mortar seam has an obvious influence on the vibration of track slab, concrete base, compared with the seamless; however, its effect on rail vibration is not obvious, the main reason is that the wheel-rail interaction is still dominated by random irregularity excitation. (3) When the mortar seam exists under the slab, the track dynamic irregularity plays an important role in wheel rail interaction, whereas mortar seam has little effect on the wheel-rail force and the acceleration of vehicle system components. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant No.51008123, 51368020, 51308493） . References [1] HE Wuhua. Technology of ballastless track. Beijing:China Railway Science, 2005. [2] SONG Xiaolin, ZHAI Wanming. Dynamic Stress Distribution of the Infrastructure of CRTSII Slab Ballastless Track under High Speed Moving Load. China Railway Science, 2012, 33(4):1-7. [3] ZHU Xiaojia. Analysis on CRTSII track slab temperature effects and its influences on the running safety of the vehicle. South West Jiao Tong University, 2012. [4] WANG Xuan, ZHANG Jiasheng, WANG Qiyun. Three-dimensional Numerical Simulation for Vehicle Dynamic Load and Dynamic Response of Ballastless Track Subgrade. China Earthquake Engineering Journal, 2014, 36(4): 857-867. [5] YI Funan. Study of the stress and deformation of ballastless track of Different types of high speed railway on different loads. Changsha: Central South University ,2010:31 57. [6] XU Hao, LIU Xiao, XU Jinhui, WANG Ping. Influence on CRTSII Slab Track Structure Caused by the Debonding between Slab and CA Mortar under the Action of Temperature Load. Railway Standard Design, 2013(9):9-12. [7] YANG Rongshan, DUAN Yuzhen, LIU Xueyi. Influence induced by sleeper looseness of bi-block slab track on dynamic property of wheeltrack system. China railway science, 2014, 35(5): 13−18. [8] LI Peigang, LIU Xueyi, LI Guoqing. Influence of CA mortar void on dynamic characteristics of unit slab track on bridge. China railway science, 2014, 35(3): 20−27. [9] ZHAI Wanming. Vehicle-track coupling dynamics.science press, 2007. [10] ZHAO Pingrui, ZHANG Yuanai, LIU Xueyi, GUO Likang. Beam-Plate Model on the Elastic Foundation of Ballastless Track. CHINA RAILWAY SCIENCE,2009,30( 3):1-4. [11] JN Varandas, P Holscher, MAG Silva.Settlement of ballasted track under traffic loading: Application to transition zones.Proceedings of the Institution of Mechanical Engineers,2014,228:242-259. [12] FENG Qingsong, LEI Xiao-yan, LIAN Song-liang. Vibration analysis of high-speed railway tracks with geometric irregularities. JOURNAL OF VIBRATION ENGINEERING ,2008,21(6):559-564. [13] XIANG Jun, HE Dan, ZENG Qing-yuan. Analysis Method of Vertical Vibration of Train and Ballastless Track System with the Lateral Finite Strip and Slab Segment Element. JOURNAL OF THE CHINA RAILWAY SOCIETY, 2007, 29(4).
SciVerse ScienceDirect SciVerse ScienceDirect Procedia Engineering 00 (2017) 000–000 Available online at www.sciencedirect.com Procedia Engineering 00 (2017) 000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Engineering 199 (2017) 2543–2548
X International Conference on Structural Dynamics, EURODYN 2017 X International Conference on Structural Dynamics, EURODYN 2017
Influence of the Seam between Slab and CA Mortar of CRTSII Influence of the Seam between Slab and CA Mortar of CRTSII Ballastless Track on Vibration Characteristics of Vehicle-Track Ballastless Track on Vibration Characteristics of Vehicle-Track System System Qingsong Feng, Hangyu Chao, Xiaoyan Lei Qingsong Feng, Hangyu Chao, Xiaoyan Lei
Engineering Research Center of Railway Environment Vibration and Noise Ministry Education,East China Jiaotong University, Nanchang 330013, ChinaMinistry Education,East China Jiaotong University, Nanchang Engineering Research Center of Railway Environment Vibration and Noise 330013, China
Abstract Abstract
With a lot of application of CRTSII slab ballastless track in China,a series of problems have arises during the slab With a lot of application of CRTSII slab ballastless track between in China,a problems arises during the slab track service. One of the most typical problems is the seam theseries trackofslab and CAhave mortar layer, namely CA track the influence most typical the seam between track slab CA mortar layer, namely mortarservice. seam. One This of may the problems vibration ischaracteristics of thethe vehicle and and CRTSII slab ballastless track.CA In mortar influenceaccording the vibration characteristics of theand vehicle ballastless In order toseam. study This this may phenomenon, to the actual engineering basedand on CRTSII the finiteslab element, a newtrack. vertical order to studycoupling this phenomenon, according to the actual and based the finite element, vertical vehicle-track dynamic model is established. Theengineering model consists of twoonparts, vehicle elementa new and CRTSII vehicle-track dynamicThe model is established. model consists of two parts, vehicle element and CRTSII slab ballastlesscoupling track element. former is regarded The as multi-rigid-body systems, while the latter is established by slab ballastless element. Theinformer regarded as system, multi-rigid-body whileconcrete the latterbase is established by means of finite track element method, which is rail, fastening track slab,systems, CA mortar, and subgrade means of finiteaselement in which rail,and fastening system, track CA mortar, concrete and subgrade are considered a wholemethod, body. The rail, slab the concrete base are slab, simplified as layered Eulerbase beam model. The are considered as a whole The rail, slablinear and the concrete base to areconsider simplified layered Euler of beam The fastener and subgrade are body. simplified as the spring. In order theascharacteristics the model. CA mortar fastener subgrade are simplified as the linear spring. In layer. order Based to consider the characteristics the CA model, mortar seam, theand nonlinear spring is used to simulate the CA mortar on vehicle-track couplingofdynamic seam, the nonlinear is used to simulate the CA mortar layer. Based dynamic of model, the influence law of spring CA mortar seam on the safety of vehicle operation, onon thevehicle-track displacementcoupling and acceleration each the lawstructures, of CA mortar seam onby thecomparing safety of vehicle operation, on the of displacement of each partinfluence of the track is revealed, the dynamics properties the CRTSIIand slabacceleration ballastless track of part of the trackwithout structures, is revealed, comparing theCA dynamics the CRTSII slabwhile ballastless of the conditions CA mortar seamby and those with mortar properties seam. The of result shows that there track is seam the conditions without CA mortar and thoseit with CA mortar seam. result shows that while there, is between the track slab and the CAseam mortar layer, has slight influence on The the smooth of vehicle operation butseam has between theimpact track slab and the CA mortar layer,ofitthe hasCRTSII slight influence on the smooth of vehicle , but has significant on the mechanical properties slab ballast-less track structure. Theoperation study is expected significant impact on the mechanical propertiesifofthere the CRTSII slabproblems ballast-less track to provide theoretical guidance for remediation are similar in the slabstructure. track. The study is expected to provide theoretical guidance for remediation if there are similar problems in the slab track. © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. © © 2017 The under Authors. Published by Ltd. committee Peer-review under responsibility responsibility of Elsevier the organizing organizing committee of of EURODYN EURODYN 2017. 2017. Peer-review of the Peer-review under responsibility of the organizing committee of EURODYN 2017. Keywords: CRTSII slab ballastless track;Dynamic coupling;Seam;Finite element method;Vibration characteristics Keywords: CRTSII slab ballastless track;Dynamic coupling;Seam;Finite element method;Vibration characteristics
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review©under the organizing committee 1877-7058 2017responsibility The Authors. of Published by Elsevier Ltd. of EURODYN 2017. Peer-review under responsibility of the organizing committee of EURODYN 2017.
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the organizing committee of EURODYN 2017. 10.1016/j.proeng.2017.09.259
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Qingsong Feng et al. / Procedia Engineering 199 (2017) 2543–2548 Author name / Procedia Engineering 00 (2017) 000–000
CRTSII ballastless track structure features stable performance , comfort in ride, slow track deformation and less demand for maintenance. It is widely used in the high speed railway in China. At present, it has been applied in the Beijing-Shanghai high speed railway and most of the domestic passenger dedicated lines [1]. The CA mortar,which is one of key layers in CRTSII slab ballast-less track structure, is also the weakest link layer. The seam between track slab and CA mortar is a dynamic track irregularity. Once the seam occurred in the CA mortar, the repeated train loads will make the mortar seam area gradually expand. When the train runs across the seam area, the mortar loses its supporting role, this cause strong vibration of the vehicle-slab track system, thus affecting train operation safety. At present, domestic and foreign scholars have carried out a variety of theoretical and experimental studies on the CRTSII slab ballastless track structure in good condition. A finite element model of the CRTSII slab ballastless track on embankment has been established to study the dynamic stress distribution law of the track and subgrade under the moving load with different velocity[2]. Influence of the temperature load on deformation and stress conditions of CRTSII slab ballast-less track, and influence of track deformation on the running safety of vehicles are analyzed[3]. Apart from that, a finite element model of the CRTSII slab ballastless track on subgrade has also been established, and then subgrade constitutive model and structural material parameters are discussed[4]. The influence of uneven subgrade settlement and vehicle load on the track are studied [5]. However, there is few research on the stress of the CRTSII slab track with CA mortar seam. The influence of the changes of the length and the height of the CA mortar seam on the mechanical properties of CRTSII slab track structure is analyzed[6-8]. Therefore, based on the characteristics of CRTSII slab ballast-less track structure, the article establishes a finite element vertical coupling vibration model for CRTSII slab ballast-less track under the condition of the mortar seam by ABAQUS software. The CA mortar seam is simulated by nonlinear spring, and the wheel-rail model of the two subsystems is set up in accordance with the nonlinear Hertzian contact theory. After the track irregularity being introduced, then the vibration of coupling system is solved. The influence of length and height of seam on dynamic characteristics of the vehicle-track system are analyzed. The established method and results lay the basis for the further study of the seam between the track plate and the mortar layer, and thus provide guidance for practical engineering. 1. Vehicle-track vertical coupling model 1.1. Vehicle-track finite element model The CRTSII slab ballastless track structural is mainly composed of rail, fastening system, slab, CA mortar, concrete base and subgrade. The structure of the vehicle and track is transversely symmetrical structure. The vehicletrack coupling dynamics[9] shows that the vertical and the lateral coupling vibration effects of vehicle are very complicated. The results show that the transverse forces of track structure presents uniform distribution because of the high lateral stiffness[10]. Therefore, in order to facilitate the calculation, the model is simplified as a twodimensional vehicle-track coupled vertical vibration model, as shown in Fig. 1. The vehicle is assumed to be a 10 degree of freedom multi-rigid-body model[11]. We only take into consideration the ups and downs movement, the corner of car body and bogie, and the ups and downs of wheel. The car body, bogie and wheel are simulated by MASS element, and the suspension system by spring damping unit.
Fig. 1. 10 degree of freedom vehicle beam coupling model with three layers.
The rail, track slab and concrete base of track structure are simulated by Euler beam element. In order to eliminate the influence of boundary effect, the line length of track is 221 m. The fastener system is simplified as a
Qingsong Feng et al. / Procedia Engineering 199 (2017) 2543–2548 Author name / Procedia Engineering 00 (2017) 000–000
2545 3
discrete spring damping; subgrade support and CA mortar are simulated by distributed spring damper. In the seam area shown in Fig. 2, the damping effect is not taken into consideration. Nonlinear spring element is used in the simulation; the nonlinear characteristics of the spring are shown in Fig. 3. The maximum value of the height of seam of CA mortar u 0 is 3mm in the spring force-displacement curve of nonlinear spring, as shown in Fig. 3. The length of the curve slope with 0 is to simulate the height of seam of CA mortar, and the slope of the curve is mortar stiffness. Wheel-Rail coupling is realized by contact module, after analyzing the relations between the contact force and the elastic compression of wheel and rail. According to the Hertz nonlinear elastic contact theory[12], we define the wheel-rail contact model by importing ABAQUS contact properties with the table form of force-displacement.
Fig. 2. Mortar void area in the track structure.
Fig. 3. Nonlinear spring force displacement curve
1.2. Track irregularity and numerical simulation Track irregularity considered simultaneously consists of medium long wave irregularity and short wave irregularity in this paper. In this model, the Germany low interference spectra is used for medium long wave irregularity while the weld joint irregularity spectrum is used for the short wave irregularity. Track irregularity simulation sample is obtained by using the frequency of power spectrum equivalent algorithm. By using the selfwriting MATLAB program, we could modify the vertical coordinate value of rail joint in the file to further introduce the track irregularity. The simulation results of the irregularity are shown in Fig. 4 and Fig. 5.
Fig. 4. German low interference irregularity.
Fig. 5. Irregularity of rail joint in rail welding area.
2. Model validation To test and verify the correctness of the model, compared with the calculation results of literature[13] , the calculation conditions for a single high-speed train running on the track at a speed of 200 km/h, the wavelength is 12.5 m and the amplitude is 3 mm of the periodic sine function for track irregularity excitation. The results of this paper are shown in Figs. 6~9.
(a) The result of literature [13]
(b) The result of this paper
Fig.6. Vertical force of wheel-rail
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Qingsong Feng et al. / Procedia Engineering 199 (2017) 2543–2548 Author name / Procedia Engineering 00 (2017) 000–000
(a) The result of literature [13]
(b) The result of this paper
Fig.7. Vertical acceleration of car body
(a) The result of literature [13]
(b) The result of this paper
Fig.8. Vertical acceleration of slab
(a) The result of literature [13]
(b) The result of this paper
Fig.9. Vertical Displacement of slab
As can be seen from Figs.6~9：the response amplitude and waveform of this paper are basically consistent with the calculation results of the literature[13],and the feasibility and correctness of this method are proved. 3. The calculation and analysis of Vehicle-track coupling model A calculation example is given using the vehicle-track coupling finite element model established in ABAQUS software. The vehicle is the high-speed train CRH3 in China. Train speed is 300 km/h. the rail is 60kg/m continuously welded rail. Fastener is WJ-8 fastener system, spacing of 0.65m. Track slab is CRTSII track slab. The line length of track is 221m. Contact model is Hertz nonlinear elastic contact, the grid size of finite element model is 0.01m, for convergence, the computing time step is equal to the rail grid size divided by the speed is 0.00012s. Two kinds of working conditions need to be considered: CA mortar seam and CA mortar seamless.
Qingsong Feng et al. / Procedia Engineering 199 (2017) 2543–2548 Author name / Procedia Engineering 00 (2017) 000–000
2547 5
3.1 The analysis of vehicle system vibration response The calculation results of vibration response of vehicle system includes the time history contrast curve of the wheel-rail contact force (as shown in Fig. 10), and the maximum vertical acceleration of vehicle (as shown in Table 1).
(a) Seamless
(b) Seam Fig. 10. The contrast of vertical wheel-rail contact force Table 1 The maximum vertical acceleration of vehicle parts.
working conditions
Car body
Bogie
wheel
seamless
0.977
10.854
48.634
seam
0.984
10.871
48.951
When train moves through the upper part of the mortar seam region, the wheel-rail force changes slightly compared with the seamless, as can be seen in Fig.10. The Table 1 shows that vertical acceleration of vehicle system components changes slightly compared with the seamless. So at this time the wheel-rail interaction and dynamic response of vehicle system are mainly inspired by track random irregularities. 3.2 Vibration response analysis of track structure system The calculation results of vibration response of track structure system includes the time history contrast curve of the track displacement (as shown in Fig. 11), and the maximum vertical acceleration of track structure system (as shown in Table 2).
(a) seamless
(b) Seam Fig. 11. The vertical displacement of track structure system
Table 2. The maximum vertical acceleration response of track system components. working conditions
rail
Track slab
Concrete base
seamless
72.287
25.163
23.838
seam
73.462
62.159
31.227
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Qingsong Feng et al. / Procedia Engineering 199 (2017) 2543–2548 Author name / Procedia Engineering 00 (2017) 000–000
According to Fig. 11, when the train runs through the mortar seam region, the vertical displacement of the slab and support layer is more noticeable, compared with the seamless. Table 2 shows that the seam has the greatest effect on the acceleration of track slab almost 3 times higher than seamless; the seam has an obvious influence on the concrete base, increased by 31%; Its effect on rail is not obvious, mainly due to the fact that the wheel-rail interaction is mainly inspired by track random irregularities. 4. Conclusions In view of CA mortar seam of the CRTSII type ballastless track problems, ABAQUS finite element method is utilized to set up the calculation model of vertical coupling vibration vehicle-track under condition of CA mortar seam. Two different working conditions are taken into consideration: seam of the mortar and seamless of the mortar, aimed at analyzing and comparing the influence of CA mortar seam on vibration response of vehicle and track structure. The main conclusions are as follows: (1) The establishment of simplified calculation model of vehicle-CRTSII slab ballastless track system with CA mortar seam is reasonable and feasible. (2) The CA mortar seam has an obvious influence on the vibration of track slab, concrete base, compared with the seamless; however, its effect on rail vibration is not obvious, the main reason is that the wheel-rail interaction is still dominated by random irregularity excitation. (3) When the mortar seam exists under the slab, the track dynamic irregularity plays an important role in wheel rail interaction, whereas mortar seam has little effect on the wheel-rail force and the acceleration of vehicle system components. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant No.51008123, 51368020, 51308493） . References [1] HE Wuhua. Technology of ballastless track. Beijing:China Railway Science, 2005. [2] SONG Xiaolin, ZHAI Wanming. Dynamic Stress Distribution of the Infrastructure of CRTSII Slab Ballastless Track under High Speed Moving Load. China Railway Science, 2012, 33(4):1-7. [3] ZHU Xiaojia. Analysis on CRTSII track slab temperature effects and its influences on the running safety of the vehicle. South West Jiao Tong University, 2012. [4] WANG Xuan, ZHANG Jiasheng, WANG Qiyun. Three-dimensional Numerical Simulation for Vehicle Dynamic Load and Dynamic Response of Ballastless Track Subgrade. China Earthquake Engineering Journal, 2014, 36(4): 857-867. [5] YI Funan. Study of the stress and deformation of ballastless track of Different types of high speed railway on different loads. Changsha: Central South University ,2010:31 57. [6] XU Hao, LIU Xiao, XU Jinhui, WANG Ping. Influence on CRTSII Slab Track Structure Caused by the Debonding between Slab and CA Mortar under the Action of Temperature Load. Railway Standard Design, 2013(9):9-12. [7] YANG Rongshan, DUAN Yuzhen, LIU Xueyi. Influence induced by sleeper looseness of bi-block slab track on dynamic property of wheeltrack system. China railway science, 2014, 35(5): 13−18. [8] LI Peigang, LIU Xueyi, LI Guoqing. Influence of CA mortar void on dynamic characteristics of unit slab track on bridge. China railway science, 2014, 35(3): 20−27. [9] ZHAI Wanming. Vehicle-track coupling dynamics.science press, 2007. [10] ZHAO Pingrui, ZHANG Yuanai, LIU Xueyi, GUO Likang. Beam-Plate Model on the Elastic Foundation of Ballastless Track. CHINA RAILWAY SCIENCE,2009,30( 3):1-4. [11] JN Varandas, P Holscher, MAG Silva.Settlement of ballasted track under traffic loading: Application to transition zones.Proceedings of the Institution of Mechanical Engineers,2014,228:242-259. [12] FENG Qingsong, LEI Xiao-yan, LIAN Song-liang. Vibration analysis of high-speed railway tracks with geometric irregularities. JOURNAL OF VIBRATION ENGINEERING ,2008,21(6):559-564. [13] XIANG Jun, HE Dan, ZENG Qing-yuan. Analysis Method of Vertical Vibration of Train and Ballastless Track System with the Lateral Finite Strip and Slab Segment Element. JOURNAL OF THE CHINA RAILWAY SOCIETY, 2007, 29(4).