Numerical and experimental study of the dynamic factor of the dynamic load on the urban railway

Tran Anh Dung , Mai Van Tham , Do Xuan Quy , Tran The Truyen , Pham Van Ky and Le Hai Ha

Abstract

This paper presents simulation calculations and experimental measurements to determine the dynamic load factor (DLF) of train on the urban railway in Vietnam. Simulation calculations are performed by SIMPACK software. Dynamic measurement experiments were conducted on Cat Linh – Ha Dong line. The simulation and experimental results provide the DLF values with the largest difference of 2.46% when the train speed varies from 0 km/h to 80 km/h

1 Introduction

Dynamic load is an important value in the railway design process. Thus, accurate study of the DLF will lead to safe and economical designs. However, determining the DLF is a rather complicated problem because of the interaction between rail and moving vehicles.

The dynamic load is generally expressed as a function of the static load (Eq. 1) [1]

(1)Pd=Ps

Where Pd is the dynamic wheel load, ∅ is the dynamic wheel load factor (∅ > 1), and Ps is the static wheel load.

In this study, the authors studied the DLF for the urban railway based on field measurement and simulation calculations. The strain gage is used to measure relative deformation. Simulation calculations are implemented by SIMPACK software.

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 1

The strain gage

Test loads are trains on Cat Linh – Ha Dong urban railway line as Figure 2.

Figure 2

The train of Cat Linh – Ha Dong urban railway line

Each train includes 4 cars [13] with the following set-up method: + Tc-M + M-Tc such as Figure 3, in which:

Figure 3

Model of the train

“+”: semi-automatic central buffer coupler

“−”: Semi-permanent central buffer coupler

“M”: motor car

“Tc”: trailer car

Load arrangement of the train is set up such as Figure 4

Figure 4

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 5

Dynamic deformation versus time for train speed V = 30km/h

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. The maximum of dynamic deformation is 0.000127.

Figure 6

Dynamic deformation versus time for train speed V = 50km/h

Figure 7 shows the dynamic deformation time-history 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.

Figure 7

Dynamic deformation versus time for train speed V = 80km/h

Measuring the static deformation of the rail we have the following results:

Table 1

Table of results of static deformation

No.Measurement timesStatic deformation
1The first0.00010735
2The second0.00010519
3The third0.00010004
Average value0.00010419

Some typical results of the dynamic load factors are depicted in the form of graphs comprising load histories under different train speeds (Figure 8).

Figure 8

Dynamic load factors increasing due to speed for urban railway

By using linear regression analysis of the DLF. Using Minitab simulation software. The results from the minitab software are as follows

Regression equation

Φ=0.9909+0.004853.V

Coefficients

TermCoefSE CoefT-ValueP-ValueVIF
Constant0.99090.012479.940.000
V0.0048530.00025019.380.0031.00

Model Summary

0.014602699.47%99.21%96.25%

Analysis of variance

Regression10.0800740.080074375.520.003
V10.0800740.080074375.520.003
Error20.0004260.000213
Total30.080500

The equation of DLF is proposed such as Eq. 2.

(2)Φ=0.9909+0.004853.V

Where V is velocity (km/h)

It can be seen that the values of dynamic load factor increasing due to speed such as Eq. 2. It was created based on support stiffness, rail material, train load and train speed.

3 Application of software to simulate dynamic model vehicle-track interactions

3.1 Numerical simulation process

The model of vehicles is included 3 parts: car body, bogie and wheel set. Each part of the system has five degrees of 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 elastic point support model uses a series of point support spacing intervals of the discrete elastic (Figure 9, 10).

Figure 9

Track structure lateral view

Figure 10

Track structure side view

These models are established using SIMPACK software to simulate the model of urban railway dynamic such as Figure 11 to 14.

Figure 11

Simulation of wheel model of Cat Linh – Ha Dong line

Table 2

Vehicle vibration model degrees of freedom

FreedomBouncingLateralRollingYawingPitching
Car bodyZcYcϕcψcβc
Front bogieZt1Yt1ϕt1ψt1βt1
Rear bogieZt2Yt2ϕt2ψt2βt2
First wheel setZw1Yw1ϕw1ψw1βw1
Second wheel setZw2Yw2ϕw2ψw2βw2
Third wheel setZw3Yw3ϕw3ψw3βw3
Fourth wheel setZw4Yw4ϕw4ψw4βw4
Table 3

The specifications of the urban railway train

1Mass of car bodyMc [ton]22.4
2Mass of frameMt [ton]3.52
3Mass of wheel setMw [ton]1.539
4The car body around the X axes’ rotational inertia;Icx [ton.m2]23.2
5The car body around the Y axes’ rotational inertia;Icy [ton.m2]943
6The car body around the Z axes’ rotational inertia;Icz [ton.m2]941
7The bogie around the X axes’ rotational inertia;Itx [ton.m2]1.43
8The bogie around the Y axes’ rotational inertia;Ity [ton.m2]1.76
9The bogie around the Z axes’ rotational inertia;Itz [ton.m2]2.96
10The wheel set around the X axes’ rotational inertiaIwx [ton.m2]0.801
11The wheel set around the Y axes’ rotational inertiaIwy [ton.m2]0.104
12The wheel set around the Z axes’ rotational inertiaIwz [ton.m2]0.814
13The distance between two bogie centre plates2L [mm]12,600
14The distance between two wheel axesLt [mm]2,200
15The hight from the rail surface to the center of the bodyHc [mm]1,800
16The height from the rail surface to the center of the bogieHf [mm]500
17The lateral distance between two axle box springs2dw [mm]1,930
18The lateral distance between two air springs2ds [mm]1,850
19The longitudinal distance between two axle box springs2c1 [mm]550
20The height from the top of the air spring to the center of the bodyhc [mm]1,005
21The height from the bottom of the air spring to the center of the bogiehf [mm]196.8
22Height from rail surface to damperH2 [mm]697
23The height from the rail face to the restraining barH3 [mm]465
24Diameter of wheelD [mm]840
25Distance between two wheel rollers2S [mm]1,493
26Longitudinal stiffness of one side of the air springKsx [MN/m]0.21
27Lateral stiffness of one side of the air springKsy [MN/m]0.21
28The vertical stiffness of one side of the air springKsz [MN/m]0.45
29Longitudinal stiffness of an axle boxKpx [MN/m]10.6
30Lateral stiffness of an axle boxKpy [MN/m]7.8
31Vertical stiffness of an axle boxKpz [MN/m]1.7
32Lateral damping coefficient of air springsCsy [kN.s/m]30.0
33Vertical damping coefficient of air springsCsz [kN.s/m]60.0
34Vertical damping coefficient of axle box springsCpz [kN.s/m]10.0
Figure 12

Simulation of bogie model of Cat Linh – Ha Dong line

Figure 13

Simulation of car body model of Cat Linh – Ha Dong line

3.2 Results

The dynamic load of the wheels acting on the rails when the cars of Cat Linh – Ha Dong line run on the rails with train speed V = 30 km/h are shown in Figure 15. The maximum of dynamic load is 48.625 kN.

Figure 14

3D model calculating dynamic of car of Cat Linh – Ha Dong line

Figure 15

Graph of vertical dynamic force of wheel load acting on rail with V = 30 km/h

The dynamic load of the wheels acting on the rails when the cars of Cat Linh – Ha Dong line run on the rails with train speed V = 50 km/h are shown in Figure 16. The maximum of dynamic load is 52.883 kN.

Figure 16

Graph of vertical dynamic force of wheel load acting on rail with V = 50 km/h

The dynamic load of the wheels acting on the rails when the cars of Cat Linh – Ha Dong line run on the rails with train speed V = 80 km/h are shown in Figure 17. The maximum of dynamic load is 59.228 kN.

Figure 17

Graph of vertical dynamic force of wheel load acting on rail with V = 80 km/h

It can be seen that the experimental results of dynamic load factors are similar to the simulation values. These results are compared with the results of other authors that are suitable [7].

Table 4

Experiment resultsSimulation resultsration
30 km/h1.131.151.77%
50 km/h1.221.252.46%
80 km/h1.391.400.72%
Figure 18

Comparison of dynamic load factor with other authors

4 Conclusions

The authors performed DLF research and proposed a DLF function for the urban railway in Vietnam. The results can be used to provide design flexibility and broadening the design principle. Besides, this study may also support in calculating railway maintenance and repair. There are many dynamic load factors for railway, but in this article, the authors assess DLF on the urban railway in Vietnam (1,435 mm gauge). In the future, the next development direction is to study DLF for prestressed concrete sleepers of narrow railway (1,000mmgauge) and high speed railway (1435mm gauge) in Vietnam.

Acknowledgement

This research is funded by University of Transport and Communications (UTC) under grant number T2019-CT-01TD.

1. Conflict of Interest

Conflict of Interests: The authors declare no conflict of interest regarding the publication of this paper.

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