Jtam-A4.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 54, 3, pp. 871-879, Warsaw 2016 DOI: 10.15632/jtam-pl.54.3.871 NUMERICAL AND FIELD INVESTIGATIONS OF TRACK DYNAMIC BEHAVIOR CAUSED BY LIGHT AND HEAVY RAILWAY VEHICLES Jabbar Ali Zakeri, Seyed Ali Mosayebi, Morteza Esmaeili School of Railway Engineering, The Center of Excellence in Railway Transportation, Iran University of Science and Technology, Tehran, Iran e-mail: zakeri@iust.ac.ir; mosayebi@iust.ac.ir; m esmaeili@iust.ac.ir Dynamic behavior of a track-train system is a function of axle loads and support stiffness because of non-linear supports.Therefore, it is expected that the support stiffness affects the behavior of the railway track during passing of a light or heavy car body. Since the effects of axle loads caused by light and heavy railway vehicles and support stiffness of ballasted railway tracks due to passing railway vehicles have not been studied adequately, therefore the present study focused on this issue. For this purpose, this issue was first investigated by passing a light and heavy car body including bogies with three axle loads as field tests. Then, numerical analyses of the railway track causedby the passing of these railwayvehicles were studied, and the numerical results were compared with the field results. There was a good agreement between the values of field responses and numerical analyses. Subsequently, a series of sensitivity analyses on effects of the axle loads caused by light or heavy loading and support conditions was done on the ballasted railway track. The results indicated that themaximumvertical displacements increasedby axle loads, increased sleeper distances and decreases support stiffness. Finally, equations of track behavior based on support stiffness and axle loads were derived. Keywords: numerical and field investigation, railway track, track dynamics, railway vehicles 1. Introduction In order to understand themechanism of railway tracks and reduction ofmaintenance costs, the dynamic behavior of the railway track should be investigated. Since it was difficult to measure responses of the railway track directly in field, thereforemodels of railway tracks were investiga- ted usually. The available technical literature indicated that differentmodels andmethods were presented for the analysis of railway tracks by various researchers. Usually, numerical models for analyzing the railway track are: one-dimensional model of a railway including lumpedmas- ses, two-dimensional model of a track including beam on an elastic foundation with continuous supports or discrete supports. There aremany researchers in the field of modeling and dynamic analysis of railway tracks. In these studies, several models have been proposed for investigating the railway track and its components. Generally, the research fields of these researchers could be divided into three categories: dynamic analysis of railway tracks, simulation of the vehicle and railway track, and train-track interaction. Some of the most prominent researchers who studied these fields are: Cai (1992), Zhai and Sun (1994), Knothe (1995), Zhai and Cai (1997), Fryba (1999), Zakeri (2000), Popp et al. (2003), Zakeri and Xia (2008), Bogacz and Czyczuła (2008), Dahlberg (2010) and Zakeri and Ghorbani (2011). Among the most important parameters in the analysis of railway tracks, axle loads of railway vehicles and support conditions of ballasted railway tracks could be pointed out. Some of researchers worked in the field of the effects of stiffness of railway track components. For example, Kerr (2003) investigated the behavior of the rail on elastic supports due to moving load. Zhai et al. (2004) studied vibrations of the railway 872 J.A. Zakeri et al. ballast in tracks. Witt (2008) studied the behavior of under sleeper pads in railway tracks. Pu- zavac et al. (2012) investigated vertical stiffness of the railway track due to passing loads. Zakeri and Abbasi (2012) investigated stiffness of the railway track in desert areas. Also, Esmaeili et al. (2014) studied the sand fouled ballast on train induced vibrations. In the mentioned studies and the available technical literature, the effects of a passing light railway vehicle (Draisine) and a heavy railway vehicle including bogies with three axle loads on ballasted railway tracks have not been studied adequately. Also considering that the behavior of the railway track support is nonlinear and depends on train loads, the effects of various passing train loads including the light and heavy railway vehicles have been studied in this paper. Therefore, the simulation of light and heavy car bodies has been explained in this paper. Afterward, a series of field tests by using light or heavy loadingwas done for validating the numerical analyses. After validation and in continuation, the effects of axle loads caused by light and heavy railway vehicles and support stiffness of the railway track were studied. Finally, equations of the track behavior based on the support stiffness and then the axle loads were derived. 2. Modeling of the railway track Inmodeling of the railway track with the concept of railway tracks on a viscoelastic foundation, twomodels can be considered.These are: (a) railway trackwith one layer including a continuous rail, (b) railway track with two layers including the rail and sleepers. In Fig. 1, the railway track with two layers is presented. The first layer is the rail as a continuous support and the second layer are sleepers as discrete supports. Fig. 1. Railway track with two layers (rail and sleeper) As can be observed from Fig. 1, the sleepers are modeled as a series of lumped masses. In this figure, Kp and Kb are pad and support stiffnesses, respectively. Figure 2 shows the rail and sleeper in the model of the railway track with two layers. Fig. 2. Rail and sleeper in the railway trackmodel By using the finite element method, the rail is divided into several elements, and thematrix of each element is derived. Then the total matrix of the rail is derived by assembling all rail elements. In each element of the rail, vertical stiffness of rail pads is considered in beam joints. Also, stiffness, damping andmassmatrix of the railway track with two layers can be considered as a submatrix of the whole system (Zakeri, 2000). Numerical and field investigations of track dynamic... 873 3. Modeling of railway vehicles In this Section, the passing railway vehicles including light and heavy railway car bodies are simulated. In this regard and by using the finite element method, the equations of motion of all components of the light and heavy railway vehicles are derived and their matrices are formed. Then by assembling the matrices of railway vehicles and tracks, the derived equation is solved with available numerical methods. Next, the models of light and heavy railway vehicles are presented. 3.1. Heavy railway vehicle In order to model a rail vehicle for heavy loading, a car body including bogies with three axle loads is considered, see Fig. 3. Fig. 3. Heavy railway car body including bogies with three axle loads InFig. 3,Lc andLt are halves of the bogies andwheels axes, respectively. In this figure,Mc is car body mass, Mt – bogie mass, Mw – wheel mass, Jc – car body rotational inertia and Jt is bogie rotational inertia. As can be seen in Fig. 3, the car body has bogies with three axle loads. Cw, Kw, Ct and Kt are primary and secondary suspension damping and stiffness, respectively. So, Zc is the vertical displacement of the car body, ψc – rotation of the car body, Zt – vertical displacement of the bogie, ψt – rotation of the bogie and Zw is vertical displacement of the wheel. 3.2. Light railway vehicle Also, in order to model a railway vehicle for ight loading, a draisine with two axle loads is considered as shown in Fig. 4. InFig. 4,MD andJD aremass and rotational inertia of thedraisine, respectively. Kw andCw are suspension system damping and stiffness, respectively. Also, ZD is the vertical displacement of the draisine, ψD – its rotation and Zw is the vertical displacement of the wheel. In the following, the procedure of field tests caused by a passing light draisine and a heavy car body is presented. 874 J.A. Zakeri et al. Fig. 4. Light railway draisine with two axle loads 4. Field tests For investigating the behavior of a ballasted railway track in field, a railway track was selected in Iran. In order to obtain time histories of the vertical displacement of the railway track in field tests, two types of railway vehicles including light and heavy railway vehicles were utilized. For applying light loading, a draisine with two axle loads was used. Specifications of that draisine were: total weight 4 tons, axle load 2 tons, wheel load 1 ton, length 4m and vehicle speed 30km/h. Also, locomotive GT26CW was used to apply heavy loading. Specifications of the locomotive were: total weight 110 tons, axle load 18.3 tons, wheel load 9.2 tons, length 18mand vehicle speed 30km/h (Zakeri andAbbasi, 2012). Figure 5 indicates the passing of the light and heavy railway vehicles. Fig. 5. Railway vehicles for field tests; (a) GT26CW locomotive including bogies with three axle loads, (b) draisine with two axle loads For measuring the vertical displacement of the railway track caused by the rail vehicles, linear variable differential transformers (LVDT’s) located on sleepers were utilized (Fig. 6). Fig. 6. Linear variable differential transformer (LVDT) for measuring the vertical displacement of the railway track In next Section, results of numerical analyses are compared and validatedwith the responses from field tests. Numerical and field investigations of track dynamic... 875 5. Validation of the railway model In order to validate the results of numerical analyses, they have been compared and validated with the results of field tests. Figure 7 shows numerical and field vertical displacement time histories of the railway track caused by the car bodies. Fig. 7. Vertical displacement time histories of the railway track caused by railway vehicles; (a) heavy vehicle, (b) light vehicle By observing and comparing vertical displacement time histories of the railway track caused by passing railway vehicles and those obtained from numerical simulation and field studies, two important points could be extracted. Firstly, the range of field responses is in a good agreement with the values of numerical analyses. Secondly, the trend of field responses shows a good agreement with the numerical analyses. Hence, it could be concluded that the modeling and numerical analyses of the railway track caused by a light draisine and a heavy car body have been done correctly. In the next Section, equations of the railway track according to the support stiffness and axle loads are derived. 6. Track behavior versus support stiffness In this Section, effects of axle loads of light and heavy car bodies are investigated in terms of the behavior of a ballasted railway track. Figure 8 indicates a sample of the vertical displacement time history of the railway track due to passing of light and heavy railway vehicles. As can be observed in Fig. 8, the vertical displacement time history of the railway track has two and six peaks due to passing of a light draisine and a heavy car body, respectively. Figure 9 shows the ratio of the maximum vertical displacement with respect to the light and heavy axle loads [mm/ton] against the support stiffness [MN/m] for various distances between the sleepers. As canbe seen inFig. 9, themaximumvertical displacementperunit axle load is constant for higher support stiffness. The maximum vertical displacements decrease for growing axle loads. Also, the increase of the sleeper distances and decreasing of the support stiffness make them 876 J.A. Zakeri et al. Fig. 8. Vertical displacement time history of ballasted railway track; (a) passing of a light draisine, (b) passing of heavy car body Fig. 9. Ratio of the maximum vertical displacement with respect to light and heavy axle loads versus the support stiffness greater. The effect of the sleeper distance is significant as it decreases the support stiffness. The trend observed in Fig. 9 is close to the power equation as y = axb. The corresponding equations are presented in Table 1. Table 1 indicates that the coefficients of the equations increase with the increasing distance of the sleepers. Numerical and field investigations of track dynamic... 877 Table 1.Equations of themaximumvertical displacementperunit axle load against the support stiffness Distance of sleepers Equations R-Squared 50cm y =0.5x−0.63 R2 =0.98 60cm y =0.6x−0.64 R2 =0.98 70cm y =0.73x−0.66 R2 =0.98 ∗ x and y are the support stiffness [MN/m] and themaximumvertical displacement per unit load [mm/ton], respectively 7. Track behavior versus axle loads In the previous Section it has been shown that by increasing axle loads, the track behavior may be stabilised by increasing the support stiffness. Figure 10 indicates themaximum vertical displacement [mm] versus the axle load [ton] for various distances between the sleepers. Fig. 10. Themaximum vertical displacement for light and heavy axle loads As can be observed is Fig. 10, themaximumvertical displacements increase with an increase in the axle loads. Also, they grow for greater sleeper distances. The effect of the sleeper distance is significant as it increases the values of axle loads. The trend of the diagrams is close to a logarithmic equation y = a ln(x)+ b. The corresponding equations are given in Table 2. Table 2.Equations for the maximum vertical displacement versus axle loads Distance of sleepers Equations R-Squared 50cm y =0.25ln(x)−0.15 R2 =0.97 60cm y =0.29ln(x)−0.17 R2 =0.97 70cm y =0.32ln(x)−0.18 R2 =0.97 ∗ x and y are axle loads [ton] and themaximumvertical displacement [mm], respec- tively In Table 2, the coefficients of the equations increase with the distance between the sleepers. 878 J.A. Zakeri et al. 8. Conclusion A review of technical literature indicates that the behavior of track supports is nonlinear and depends on train loads. For this reason, the effects of passing light and heavy railway vehicles have been studied in this paper. So, the simulation procedure of light and heavy car bodies has been explained. Afterward, results of a series of field tests with two light and heavy loadings have been presented for validating the numerical analyses. After validation, the effects of axle loads of light and heavy railway vehicles as well as support stiffness have been studied. The important findings of the present study can be summarized as follows: • The range of the field responses is in a good agreement with the values of numerical analyses. Also, the trend of field responses is in a good agreement with the numerical analyses. • By increasing thedistancebetween the sleepers from50 to 70cm, the ratio of themaximum vertical displacement with respect to the axle load increased by 33 and 25 percent at the support stiffness of 20 and 120MN/m, respectively. • For the sleeper spacing 60cm, the ratio of themaximumvertical displacementwith respect to the axle load decreased by 68 percent due to increasing of the support stiffness from 20 to 120MN/m. • The trend of the ratio of themaximumvertical displacement with respect to the axle load against the support stiffness is close to a power equation y = axb. The coefficient a in this equation is 0.5, 0.6 and 0.73 for the distance of between sleepers of 50, 60 and 70cm, respectively. Correspondingly, the coefficient b is −0.63, −0.64 and−0.66, respectively. • By increasing the axle loads from 8 to 18.5 tons, the maximum vertical displacement increased the 83 percent for sleeper spacing 60cm. • By increasing the distance between the sleepers from 50 to 70cm, the maximum vertical displacement increasedby30and27percent at theaxle loads of 2 and20 tons, respectively. • The trend of the maximum vertical displacement against the axle loads is close to a loga- rithmic equation y = a ln(x)+ b. The coefficient a in this equation is 0.25, 0.29 and 0.32 for the distance between the sleepers 50, 60 and 70cm, respectively. Correspondingly, the coefficient b is−0.15, −0.17 and−0.18, respectively. Acknowledgment The authors are grateful to dr. S.Mohammadzadeh for his help in this study. The authors would like to thank technical engineers, R. Abbasi, M.Mehrali andM. Nouri, for their assistance during the course of this project. References 1. 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