Comparative study on wheel-rail dynamic interactions of side-frame cross-bracing bogie and sub-frame radial bogie

Abstract

Improving freight axle load is the most effective method to improve railway freight capability; based on the imported technologies of railway freight bogie, the 27 t axle load side-frame cross-bracing bogie and sub-frame radial bogie are developed in China. In order to analyze and compare dynamic interactions of the two newly developed heavy-haul freight bogies, we establish a vehicle-track coupling dynamic model and use numerical calculation methods for computer simulation. The dynamic performances of the two bogies are simulated separately at various conditions. The results show that at the dipped joint and straight line running conditions, the wheel-rail dynamic interactions of both bogies are basically the same, but at the curve negotiation condition, the wear and the lateral force of the side-frame cross-bracing bogie are much higher than that of the sub-frame radial bogie, and the advantages become more obvious when the curve radius is smaller. The results also indicate that the sub-frame radial bogie has better low-wheel-rail interaction characteristics.

J. Mod. Transport. (2013) 21(1):18 DOI 10.1007/s40534-013-0001-3

Comparative study on wheelrail dynamic interactionsof side-frame cross-bracing bogie and sub-frame radial bogie

Chunlei Yang Fu Li Yunhua Huang

Kaiyun Wang Baiqian He

Received: 12 July 2012 / Revised: 29 December 2012 / Accepted: 7 January 2013 / Published online: 5 June 2013 The Author(s) 2013. This article is published with open access at Springerlink.com

Abstract Improving freight axle load is the most effective method to improve railway freight capability; based on the imported technologies of railway freight bogie, the 27 t axle load side-frame cross-bracing bogie and sub-frame radial bogie are developed in China. In order to analyze and compare dynamic interactions of the two newly developed heavy-haul freight bogies, we establish a vehicletrack coupling dynamic model and use numerical calculation methods for computer simulation. The dynamic performances of the two bogies are simulated separately at various conditions. The results show that at the dipped joint and straight line running conditions, the wheelrail dynamic interactions of both bogies are basically the same, but at the curve negotiation condition, the wear and the lateral force of the side-frame cross-bracing bogie are much higher than that of the sub-frame radial bogie, and the advantages become more obvious when the curve radius is smaller. The results also indicate that the sub-frame radial bogie has better low-wheelrail interaction characteristics.

Keywords Heavy haul Side-frame cross-bracing bogie

Sub-frame radial bogie Wheelrail dynamic interaction

1 Introduction

With its comprehensive advantages such as the large transport capacity, low energy consumption, light pollution, less occupation of the land, and high safety, the railway heavy-haul transport has developed rapidly all over the world. The side-frame cross-bracing bogie [13] and sub-frame radial bogie [49] are both main freight bogies applied in railway heavy-haul transport. In order to meet the needs of development of the Chinese railway transportation, the key technologies of both bogies were imported [10]; since then, many engineers and researchers in China began to study and investigate the technologies of the two bogies [1126] and successfully developed a 25 t axle load side-frame cross-bracing bogie named K6 [11] and a sub-frame radial bogie named K7 [24] to meet the needs of Datong-Qinhuangdao coal transportation.

In recent years, 27 t axle load side-frame cross-bracing bogie (Fig. 1) and sub-frame radial bogie (Fig. 2) were developed in China to further enhance the railway transport capacity. The two bogies mainly consist of three parts, the bolster, the wheel sets, and the side-frame. The main difference of the two bogies is in the side-frame. The former uses an elastic crossing bar to connect the left and the right side-frame, while the latter uses a sub-frame radial appliance to connect the front and the rear wheel sets. In this paper, the dynamic performances of the two bogies are analyzed and compared at various conditions based on the theory of vehicletrack coupling dynamics [27] and a vehicletrack coupling dynamic model [28] in order to nd which bogie has better low-wheelrail dynamic interaction

C. Yang F. Li Y. Huang

School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China

C. Yang (&)

Department of Product Development, CSR Meishan Company Limited, Meishan 620032, Chinae-mail: [email protected]

K. Wang B. He

State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China

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Fig. 1 27 t Side-frame cross-bracing bogie

Fig. 2 27 t Sub-frame radial bogie

Table 1 Main parameters of the two bogies

Bogie type Tare weight (kg)

Wheelbase (mm)

characteristics. The main parameters of the two bogies are shown in Table 1.

2 Vehicletrack coupling dynamic model and various calculation conditions

A vehicletrack coupling dynamic model is established according to the structural characteristics of the bogie. The degrees of freedom (DOFs) of the vehicle and track parts as well as the non-linear characteristics such as wheelrail contact geometry, wheelrail normal force, and wheelrail

tangential creep force are all taken into account in the vehicletrack system. In addition, the elastic cross-bracing bar of the side-frame cross-bracing bogie and the sub-frame radial appliance of the sub-frame radial bogie are simplied as three-directional stiffness separately in the model. The vehicletrack dynamic model is a complex and huge dynamic system as shown in Fig. 3 and the DOFs of the whole dynamic system are shown in Table 2. More details about Fig. 3 and Table 2 can be found in the reference [27].

In order to compare and analyze the wheelrail interaction characteristics of the two bogies in various simulation conditions, we consider three scenarios: dipped rail joint, linear railway, and curve line. The detailed calculation conditions are shown in Table 3.

3 Analysis and comparison of wheelrail dynamic interaction

3.1 Wheelrail interaction at impulsive excitation

Figure 4 shows the wheelrail dynamic response comparisons of a heavy-haul freight car equipped with the side-frame cross-bracing bogie and the sub-frame radial bogie passing through the dipped joint at a speed of 80 km/h. In Fig. 4, we can see that the diagrams of the wheelrail dynamic interaction of both the bogies are basically the same and the amplitudes have little difference. Relatively, the wheelrail vertical force (Fig. 4a) and the vertical displacements of rail substructures (Fig. 4df) of the sub-frame radial bogie are slightly larger (about 2 %) than that of the side-frame cross-bracing bogie. That is because the sub-frame radial appliance is much heavier than that of the crossing bar, which increases the unsprung mass of the bogie. Therefore, to reduce wheelrail dynamic interactions, the sub-frame radial bogie should be lightened as much as possible.

3.2 Wheelrail interaction at random excitation on straight line

Figure 5 shows the mean values of the wheelrail vertical force, wheelrail wear, and wheelrail contact stress response as the heavy-haul freight car runs on the straight line at the speed of 80, 100, and 120 km/h, where the Chinese three-mainline spectrum excitation is considered. One can see that the mean values of the wheelrail responses of the two bogies almost have no changes with speed variation, and the wheelrail dynamic interactions of both bogies are basically the same.

Primary vertical stiffness (MN m-1)

Primary lateral stiffness (MN m-1)

Side-frame cross-bracing bogie

4,730 1,830 150200 1014

Sub-frame radial bogie

4,850 1,800 2550 2.55

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Comparative study on wheelrail dynamic interactions 3

(a)

Mc Yc(t)

c(t)

Icx

Zc(t)ds ds

Y

H cB

H Bt

H tw

(b)

Fp Fp

Kty

Cty

YtR(t)

Mt

XtL

tL

YtL

Ctz

Ktz

dw

Kpx Cpy

dw

Cty

Cty

YtL(t)

Cpz

Kpz

Cpx

Mw Yw(t) Iwx

w(t )

Kpy Cpy

Mw

Itz

Mw

Iwz

MB

IBz

Iwz

Zw(t)

w

XB

w

YrL(t)

YrR(t)

Mc Icz Yc

X

Cph

Kph

ZrL(t)

rL(t)

ZrR(t) rR(t)

Cbh

B

B

Ms

Ys(t)

s(t)

Cbv

Js

Zs(t)

Kbv

Kbh

Cty Kty

Mt Itz YtR XtR

Lc Lt

tR

Mb Mb

Kw Cw

d d

Ls

Y

Cfv Cfv

Kfv Kfv

Fig. 3 Vehicletrack coupling dynamic model. a End view. b Top view

Table 2 DOFs of the vehicletrack coupling dynamic model

Freedom Longitudinal Lateral Vertical Rolling Yawing Pitching

Car body Xc Yc Zc uc wc bc

Bolster (i = 1,2) XBi YBi ZBi uBi wBi

Side-frame (i = 1,2) Xt(L,R)i Yt(L,R)i Zt(L,R)i wt(L,R)i bt(L,R)i

Wheel set (i = 14) Ywi Zwi uwi wwi bwi

Rail Yr(L,R) Zr(L,R) ur(L,R)

Sleeper Ys Zs us

Ballast Zb(L,R)

Table 3 Calculation conditions Serial number Railway Excitation Speed (km/m)

1 Linear railway line Dipped rail joint 80

2 Linear railway line Chinese three-mainline track spectrum

80, 100, and 120

3 Curve railway line of R = 300 m Without track irregularity 55

4 Curve railway line of R = 300 m Chinese three-mainline track spectrum

55

3.3 Wheelrail interaction on curve negotiation

Figure 6 shows the wheelrail lateral force and the wheel rail wear power of the external side wheel of the two bogies as the vehicle passes through a smooth curve at a speed of 55 km/h; the curve radius is 300 m. In Fig. 6, we can see that the wheelrail lateral force and wheelrail wear power of the

side-frame cross-bracing bogie are apparently much higher than those of the sub-frame radial bogie. For example, the maximum wheelrail lateral force of the side-frame cross-bracing bogie is 28.16 kN, while that of the sub-frame radial bogie is 15.68 kN. The former is about 1.8 times larger than the latter. The maximum wheelrail wear power of the side-frame cross-bracing bogie is 88.89 Nm m-1, while that of

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(a) (b)

400

150

Wheel-rail vetical force (kN)

Vertical acceleration of rail (g)

350

Side-frame cross-bracing bogie

Sub-frame radial bogie

100

Side-frame cross-bracing bogie

Sub-frame radial bogie

300

50

250

0

200

150

-50

100 0 2 4 6 8 10

-100 0 2 4 6 8 10

Time (ms)

Time (ms)

(c) (d)

10

1.2

Vertical acceleration of ballast (g)

Vertical displacement of rail (mm)

Side-frame cross-bracing bogie

Sub-frame radial bogie

5

1.0

Side-frame cross-bracing bogie

Sub-frame radial bogie

0

0.8

-5

0.6

-10 0 4 8 12 16 20

0.4 0 10 20 30 40 50

Time (ms)

Time (ms)

(e) (f)

Vertical displacement of sleeper (mm)

Vertical displacement of ballast (mm)

0.8

0.5

Side-frame cross-bracing bogie

Sub-frame radial bogie

0.4

Side-frame cross-bracing bogie

Sub-frame radial bogie

0.6

0.3

0.4

0.2

0.2

0.1

0.0 0 10 20 30 40 50

0.0 0 10 20 30 40 50

Time (ms)

Time (ms)

Fig. 4 Wheelrail dynamic interactions of the two bogies at impulsive excitation. a Wheelrail vertical force. b Vertical acceleration of rail. c Vertical acceleration of ballast. d Vertical displacement of rail. e Vertical displacement of sleeper. f Vertical displacement of ballast

the sub-frame radial bogie is 30.16 Nm m-1, which is about

2.95 times than the former. These indicate that the sub-frame radial bogie can reduce the wheelrail lateral interactions and can particularly reduce the wheelrail wear signicantly when negotiating a curve.

Figure 7 shows the diagrams of the wheelrail lateral force of the four wheel sets. Seen from the gure, the values of the four wheel sets of the side-frame cross-

bracing bogie are very uneven. The maximum value of the rst and the third wheel set is nearly 3 times greater than that of the second and the fourth wheel set; this means the guiding wheel sets will wear more quickly than that of the non-guiding wheel sets and cause the guiding wheel sets to repair and change, or even scrapped in advance. But, for sub-frame radial bogie, the values of the four wheel sets are basically the same, and the maximum is also much lower

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Comparative study on wheelrail dynamic interactions 5

(a) (b)

Mean wheel-rail vertical force (kN)

180

150

Side-frame cross-bracing bogie

Sub-frame radial bogie

Side-frame cross-bracing bogie

Sub-frame radial bogie

90

Mean wheel-rail wear power (Nmm-1)

20

120

15

10

60

5

30

0

0

80 100 120

80 100 120

Running speed (kmh-1)

Running speed (kmh-1)

Running speed (kmh-1)

(c)

Mean wheel-rail contacl stress (MPa)

1,400

1,200

Side-frame cross-bracing bogie

Sub-frame radial bogie

1,000

800

600

400

200

0

80 100 120

Fig. 5 Wheelrail dynamic interactions of the two bogies with random excitation on straight line. a Mean wheelrail vertical force. b Mean wheelrail wear power. c Mean wheelrail contact stress

0 0 50 100 150 200

(a) (b)

30

90

25

Wheel-rail lateral force (kN)

Wheel-rail wear power (Nmm-1)

20

60

15

Side-frame cross-bracing bogie

Sub-frame radial bogie

10

30

5

Side-frame cross-bracing bogie

Sub-frame radial bogie

0 0 50 100 150 200

Curve distance (m)

Curve distance (m)

Fig. 6 Wheelrail dynamic interactions of the two bogies negotiating without excitation. a Wheelrail lateral force. b Wheelrail wear power

than that of the side-frame cross-bracing bogie; so relatively, the wheelrail wear would be reduced and the life of the wheel set would be extended.

Figure 8 shows the comparison of the peak values of the wheelrail lateral force and the wheelrail wear power as

the vehicle passes through smooth curved lines with different radii. As shown from Fig. 8, the peak values of the wheelrail lateral force and the wheelrail wear power of the side-frame cross-bracing bogie are signicantly larger than those of the sub-frame radial bogie, and the difference

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(a) (b)

30

20

R=300 m V=55 kmh-1

25

Wheel-rail lateral force (kN)

Wheel-rail lateral force (kN)

R=300 m V=55 kmh-1

15

20

15

The first wheelset

The second wheelset

The third wheelset

The fourth wheelset

10

10

5

The first wheelset

The second wheelset

The third wheelset

The fourth wheelset

5

0 0 50 100 150 200

0 0 50 100 150 200

Curve distance (m)

Curve distance (m)

Fig. 7 Wheelrail lateral forces of different wheel sets while negotiating without excitation. a Side-frame cross-bracing bogie. b Sub-frame radial bogie

(a) (b)

35

Wheel-rail lateral force (kN)

Wheel-rail wear power (Nmm-1)

30

100

Side-frame cross-bracing bogie

Sub-frame radial bogie

Side-frame cross-bracing bogie

Sub-frame radial bogie

25

80

20

60

15

40

10

20

5

0 300

400

500

600

800

1000

1500

0 300

400

500

600

800

1000

1500

Radius of curve (m)

Radius of curve (m)

Fig. 8 Peak values of wheelrail dynamic interaction of the two bogies. a Wheelrail lateral force. b Wheelrail wear power

becomes gradually larger with the reduction of the radius. For instance, when the radius is 1,500 m, both the bogies have little difference; when the radius is 1,000 m, the peak value of the wheelrail lateral force and wheelrail wear power of the side-frame cross-bracing bogie is, respectively, 11.24 kN and 18.44 Nm m-1, while that of the sub-

frame radial bogie is correspondingly 8.3 kN and7.1 Nm m-1, the former being about 1.35 times and 2.6

times larger than the latter, respectively. As the curve radius is 300 m, the peak values of the former are, respectively, 28.16 kN and 104.7 Nm m-1, while that of

the latter are 15.68 kN and 30.16 Nm m-1, respectively,

the former being about 1.8 times and 3.47 times larger than the latter, respectively.

Figure 9 shows the comparison of the mean values of wheelrail lateral force and wheelrail wear power as the vehicle passes through curved lines of different radii, where Chinese three-mainline spectra as the random excitation is considered. Seen from the gure, regardless of whether the

mean value of the wheelrail lateral force or the wheelrail wear power, the values of the side-frame cross-bracing bogie are always higher than those of the sub-frame radial bogie; and, the smaller the curve radius, the greater the difference. Only when the curve radius is beyond 1,000 m do the mean values of the wheelrail lateral force and the wheelrail wear power of both bogies tend to be the same.

3.4 Actual wheelrail wear comparison between two types of bogies

The 25 t axle load side-frame cross-bracing bogie named K6 and the 25 t axle load sub-frame radial bogie named K7 have been used on Datong-qinghuangdao heavy-haul line for about 2 9 105 km. Figure 10 shows the difference of the ange wear of the different bogies. One can see from the gure that the mean value of the ange wear of the K6-type bogie is 0.52 mm, while that of the K7-type bogie is 0.15 mm, less than one-third of the K6-type bogie. The

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Comparative study on wheelrail dynamic interactions 7

(a) (b)

Mean wheel-rail wear power (Nmm-1 )

25

70

Mean wheel-rail lateral force (kN)

60

20

Side-frame cross-bracing bogie

Sub-frame radial bogie

Side-frame cross-bracing bogie

Sub-frame radial bogie

50

15

40

10

30

5 300 600 900 1,200 1,500

20 300 600 900 1,200 1,500

Radius of curve (m)

Radius of curve (m)

Fig. 9 Mean values of the wheelrail dynamic interaction of the two bogies. a Wheelrail lateral force. b Wheelrail wear power

0.0

(a) (b)

0.8

4.0

0.68

3.5

3.15

2.95

0.6

3.0

Flange wear (mm)

0.52

0.4

Tread wear (mm)

2.5

2.0

1.5

0.2

0.15

1.0

0.5

0.0

K7

K6

K7

K6

K5

Bogie type

K5

Bogie type

3.35

Fig. 10 Comparisons of actual ange and tread wear of different type bogies. a Mean ange wear. b Mean tread wear

mean value of tread wear of the K6-type bogie is 3.15 mm, while that of the K7-type bogie is 2.95 mm, also less than that of the K6-type bogie. These indicate that application of the sub-frame radial bogie would be more effective to decrease wheelrail wear.

4 Conclusions

(1) Passing through the dipped rail joints, the vertical wheelrail dynamic interaction of both the side-frame cross-bracing bogie and the sub-frame radial bogie is basically the same, but because of the heavier unsprung mass of the sub-frame radial bogie, the dynamic responses of the rail substructures are slightly larger.

(2) Running on a straight line at random excitation, the wheelrail dynamic responses of both the bogies are basically the same with a little difference, and the

running speed has almost no inuence on the wheel rail vertical dynamics performance.(3) Negotiating curves, the wheelrail lateral force and wheelrail wear power of the side-frame cross-bracing bogie are apparently larger than those of the sub-frame radial bogie, and the smaller the curve radius, the larger the difference. Only when the curve radius is beyond 1,000 m, the wheelrail dynamic responses of the two bogies are basically the same. These indicate that the sub-frame radial bogie has advantages on dynamic performance, especially on curve negotiation.

Acknowledgments This work was supported by the National Natural Science Foundation of China (No. 50975238).

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

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