Journal of the Mechanical Behavior of Materials 2020; 29:195–202 Research Article Tran Anh Dung*, Mai Van Tham, Do Xuan Quy, Tran The Truyen, Pham Van Ky, and Le Hai Ha Numerical and experimental study of the dynamic factor of the dynamic load on the urban railway https://doi.org/10.1515/jmbm-2020-0020 (1972) had used dynamic load factor for high speed railway Received Jul 30, 2020; accepted Dec 24, 2020 track that incorporates train speed and the condition of the track [4]. The Office of Research and Experiments (ORE) of Abstract: This paper presents simulation calculations and the International Union of Railways and Birmann [5] had experimental measurements to determine the dynamic load proposed dynamic load factor for speeds up to 200 km/h factor (DLF) of train on the urban railway in Vietnam. Sim- incorporates the track geometry, vehicle suspension, ve- ulation calculations are performed by SIMPACK software. hicle speed, vehicle center of gravity, age of track, curve Dynamic measurement experiments were conducted on radius, super-elevation, and cant deficiency. The Germany Cat Linh – Ha Dong line. The simulation and experimental Railways (1943) using an equation with the train speed is no results provide the DLF values with the largest difference of more than 200 km/h to calculate the dynamic load factor 2.46% when the train speed varies from 0 km/h to 80 km/h only using train speed [6]. The dynamic load factor formula Keywords: dynamic load, dynamic load factor, urban rail- is used for South African Railways is similar to the Talbot way, train speed, track stiffness formula, but is calculated for narrow gauge track [2]. Clarke formula algebraically combines the Talbot and Indian Rail- ways dynamic load factors [7]. In 1968, a dynamic load fac- 1 Introduction tor only depended on the train speed was prepared for the Washington Metropolitan Area Transit Authority (WMATA) and used in subsequently recommended standards for tran- Dynamic load is an important value in the railway design sit trackwork [8]. In 2010, Sadeghi had proposed a dynamic process. Thus, accurate study of the DLF will lead to safe load factor in Iran. This factor depends on train speed [9]. and economical designs. However, determining the DLF is The speed of the train is no more 200km/h. The use of the a rather complicated problem because of the interaction AREMA recommendation for dynamic impact factor is sug- between rail and moving vehicles. gested for the railway with the train speed from 32 km/h The dynamic load is generally expressed as a function to 193 km/h [10]. The China Railways proposed dynamic of the static load (Eq. 1) [1] load factors that depend on train speed and wheel load Pd = ? · Ps (1) shift coefficient in curves. This factor is used for high speed railway [11]. In 2017, Leonid and Andrey had researched dy- Where Pd is the dynamic wheel load, ? is the dynamic namic live load factor for bridge structures on High speed wheel load factor (? > 1), and Ps is the static wheel load. railway [12]. Studies by authors around the world have published In this study, the authors studied the DLF for the ur- research results on dynamic load of railway. In 1953, Tal- ban railway based on field measurement and simulation bot [2] had given a dynamic load factor that relates to train calculations. The strain gage is used to measure relative speed and wheel diameter for heavy haul railway with the deformation. Simulation calculations are implemented by train speed less than 80 km/h. In 1969, Indian Railways SIMPACK software. had proposed dynamic load factor for narrow gauge track incorporates track modulus and train speed [3]. Eisenmann *Corresponding Author: Tran Anh Dung: University of Transport and Communications, Hanoi, Vietnam; Email: [email protected] Mai Van Tham, Do Xuan Quy, Tran The Truyen, Pham Van Ky, Le Hai Ha: University of Transport and Communications, Hanoi, Vietnam Open Access. © 2020 T. Anh Dung et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License 196 Ë T. Anh Dung et al. Figure 1: The strain gage 2 Experimental method to determinate DLF 2.1 Test equipments The rail is mounted the equipment to measure deformation. Relative deformation was measured by the strain gage with length 10mm. Strain gage was placed at the bottom center of the rail foot (Figure 1). Figure 2: The train of Cat Linh – Ha Dong urban railway line 2.2 Load test arrangements Test loads are trains on Cat Linh – Ha Dong urban railway Figure 3: Model of the train line as Figure 2. Each train includes 4 cars [13] with the following set-up method: + Tc-M + M-Tc such as Figure 3, in which: “M”: motor car “+”: semi-automatic central buffer coupler “Tc”: trailer car “−”: Semi-permanent central buffer coupler Load arrangement of the train is set up such as Figure 4 Figure 4: Model of test train load Numerical and experimental study of the dynamic factor of the dynamic load on the urban railway Ë 197 2.3 Test results Figure 5 shows the dynamic deformation time-history curves of the rail foot in the first test point on Cat Linh – Ha Dong urban railway line with train speed V = 30 km/h. The maximum of dynamic deformation is 0.00011732. Figure 7: Dynamic deformation versus time for train speed V = 80km/h Table 1: Table of results of static deformation No. Measurement times Static deformation Figure 5: Dynamic deformation versus time for train speed V = 1 The first 0.00010735 30km/h 2 The second 0.00010519 3 The third 0.00010004 Average value 0.00010419 Figure 6 shows the dynamic deformation time-history curves of the rail foot in the second test point on Cat Linh – Ha Dong urban railway line with train speed V = 50 km/h. Some typical results of the dynamic load factors are The maximum of dynamic deformation is 0.000127. depicted in the form of graphs comprising load histories under different train speeds (Figure 8). Figure 6: Dynamic deformation versus time for train speed V = 50km/h Figure 7 shows the dynamic deformation time-history Figure 8: Dynamic load factors increasing due to speed for urban railway curves of the rail foot in the third test point on Cat Linh – Ha Dong urban railway line with train speed V = 80 km/h. The maximum of dynamic deformation is 0.000145. Measuring the static deformation of the rail we have the following results: 198 Ë T. Anh Dung et al. By using linear regression analysis of the DLF. Using 3 Application of software to Minitab simulation software. The results from the minitab software are as follows simulate dynamic model vehicle-track interactions Regression equation 3.1 Numerical simulation process Φ = 0.9909 + 0.004853.V The model of vehicles is included 3 parts: car body, bogie and wheel set. Each part of the system has five degrees of Coeflcients freedom: bouncing, lateral, rolling, yawing and pitching. So, each car has 35 degrees of freedom as follows in Table 2. The model of track structure with the continuous elas- Term Coef SE Coef T-Value P-Value VIF Constant 0.9909 0.0124 79.94 0.000 tic point support model uses a series of point support spac- V 0.004853 0.000250 19.38 0.003 1.00 ing intervals of the discrete elastic (Figure 9, 10). Model Summary Figure 9: Track structure lateral view S R-sq R-sq(adj) R-sq(pred) 0.0146026 99.47% 99.21% 96.25% Analysis of variance Figure 10: Track structure side view Source DF Adj SS Adj MS F-Value P-Value Regression 1 0.080074 0.080074 375.52 0.003 These models are established using SIMPACK software V 1 0.080074 0.080074 375.52 0.003 to simulate the model of urban railway dynamic such as Error 2 0.000426 0.000213 Figure 11 to 14. Total 3 0.080500 The equation of DLF is proposed such as Eq. 2. Φ = 0.9909 + 0.004853.V (2) Where V is velocity (km/h) It can be seen that the values of dynamic load factor in- creasing due to speed such as Eq. 2. It was created based on support stiffness, rail material, train load and train speed. Figure 11: Simulation of wheel model of Cat Linh – Ha Dong line Numerical and experimental study of the dynamic factor of the dynamic load on the urban railway Ë 199 Table 2: Vehicle vibration model degrees of freedom Freedom Bouncing Lateral Rolling Yawing Pitching Car body Zc Yc ϕc ψc βc Front bogie Zt1 Yt1 ϕt1 ψt1 βt1 Rear bogie Zt2 Yt2 ϕt2 ψt2 βt2 First wheel set Zw1 Yw1 ϕw1 ψw1 βw1 Second wheel set Zw2 Yw2 ϕw2 ψw2 βw2 Third wheel set Zw3 Yw3 ϕw3 ψw3 βw3 Fourth wheel set Zw4 Yw4 ϕw4 ψw4 βw4 Table 3: The specifications of the urban railway train No. Technical parameters Symbols, units Values 1 Mass of car body Mc [ton] 22.4 2 Mass of frame Mt [ton] 3.52 3 Mass of wheel set Mw [ton] 1.539 2 4 The car body around the X axes’ rotational inertia; Icx [ton.m ] 23.2 2 5 The car body around the Y axes’ rotational inertia; Icy [ton.m ] 943 2 6 The car body around the Z axes’ rotational inertia; Icz [ton.m ] 941 2 7 The bogie around the X axes’ rotational inertia; Itx [ton.m ] 1.43 2 8 The bogie around the Y axes’ rotational inertia; Ity [ton.m ] 1.76 2 9 The bogie around the Z axes’ rotational inertia; Itz [ton.m ] 2.96 2 10 The wheel set around the X axes’ rotational inertia Iwx [ton.m ] 0.801 2 11 The wheel set around the Y axes’ rotational inertia Iwy [ton.m ] 0.104 2 12 The wheel set around the Z axes’ rotational inertia Iwz [ton.m ] 0.814 13 The distance between two bogie centre plates 2L [mm] 12,600 14 The distance between two wheel axes Lt [mm] 2,200 15 The hight from the rail surface to the center of the body Hc [mm] 1,800 16 The height from the rail surface to the center of the bogie Hf [mm] 500 17 The lateral distance