J. Cent. South Univ. (2012) 19: 2681-2688 

DOI: 10.1007/s11771-012-1327-4

Effects of wheelset vibration on initiation and evolution of rail short-pitch corrugation

YAN Zi-quan(闫子权)^1,2, GU Ai-jun(谷爱军)¹, LIU Wei-ning(刘维宁)¹, V. L. Markine ², LIANG Qing-huai(梁青槐)¹

1. School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China;

2. Faculty of Civil Engineering and Geo-Sciences, Delft University of Technology, Delft, 2600GA, Netherlands

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: The initiation and evolution of short-pitch corrugation in Beijing metro line 4 was studied from the viewpoint of wheelset vibration. A three-dimensional elastic model was set up. Numerical simulations were undertaken with this model to analyze the corrugation by the wheelset vertical vibration and torsional vibration. Based on numerical results, the relation between rail corrugation and wheelset vibration, and the relation between the position of electromotor and wheelset vibration were indicated. It is found that avoiding the wheelset-rail resonance is one method of controlling the rail short-pitch corrugation and solving the vibration and noise problem in metro lines.

Key words: rail corrugation; wheelset vertical vibration; wheelset torsional vibration; finite element modeling

1 Introduction

Corrugations have occurred on almost every railroad system since the inception of railways. It is one of the most serious problems in railway engineering now. Its initiation and evolution cause fierce vibrations of railway vehicle and track, noise and reduction of the use life of the structural parts [1-4]. A prodigious volume of research has been undertaken in this area, and a vast literatures exist, from which it is clear that corrugation arises from a variety of different causes [5-8]. However, it is also clear that, corrugation continues to be a problem whose principal means of control is grinding of the rail now. These countermeasures take large amount of labor and huge cost [9-10].

Most of the experimental investigations performed at British Rail (BR), partially together with Cambridge University, could be found in Refs. [11-12]. A survey of the problem including the influence of steel grade was given. The metallurgical structures of corrugations as well as the effects of grinding and initial rail roughness were discussed in detail. Reference [13] showed how measured receptances to quantify the dynamic response of the wheel and rail to vertical, lateral and longitudinal forces could be combined with creep/force-creep laws and with formulae for rail wear. It was shown that this hypothesis was able to explain observations of short-pitch corrugations on tangent track of BR lines. HEMPELMANN and KNOTHE [14] reviewed 128 papers, described the development of complete wear pattern in the sleeper bay and performed a large number of parametric investigations in order to identify critical parameters.

Recently, the viewpoint that rail corrugation is bound up with wheelset vibration, was accepted by more and more research scholars. GRASSIE and ELKINS [15] studied the rail corrugation in North American Transit System, and indicated that corrugation at 300-350 Hz was associated with the second torsional resonance of the driven wheelsets. The corrugation at 750-1 000 Hz was associated with the so-called “pinned-pinned” mode of the track, in which the rail vibrated as if it was pinned at the fastenings. Other types of corrugation, which were observed only in individual transit systems, were associated with unusual dynamic features of particular trackforms or vehicles. KURZECK [16] studied heavy vibrations at the running gear of a metro vehicle with a typical frequency of 80 Hz with a radius between 50 and 200 m. It was found that the oscillation was characterized by high vertical amplitudes at the axle box of the inner wheel of the leading wheelset, and these high amplitudes occur without the need of an excitation by the rails. COLLETTE et al [17] considered that torsional vibrations of metro wheelsets were involved in the wavelength-fixing mechanism of the rutting-type rail corrugation. The basic conditions for this type of wear to appear were established using a theory developed in the frequency domain.

So, analysis on the initiation and evolution of rail short-pitch corrugation from the wheelset vibration viewpoint is reasonable. In this work, firstly, investigation and filed test were carried out on the corrugation sections in Beijing metro line 4. Then, the realistic elastic FEM of wheelsets was set up and numerical simulations were undertaken with this model. Based on numerical results, it was attempted to explain the relation between rail corrugation and wheelset vibration. Finally, the mechanism of corrugation and countermeasure were discussed.

2 Investigation and filed test

Nowadays, short-pitch rail corrugation has grown on Beijing metro line 4, as shown in Fig. 1(a), which is one of the most important metro lines in Beijing. Consequently, the detailed examination of the mechanism of rail corrugation on Beijing metro line 4 is started.

Fig. 1 Rail corrugation on Beijing metro line 4: (a) Short-pitch rail corrugation; (b) Detailed measurements

In this work, at first, the measurements using a tape measure were carried out in order to clarify the characteristics of short-pitch rail corrugation of Beijing metro line 4. The detailed measurements are shown in Fig. 1(b). It is known that the wavelength is 5.5 cm of the rail corrugation. The running speed of the measured section is 60 km/h. So it could be concluded that the vibration frequency of this section approaches 300 Hz.

Then, field test was carried out, including two types of fastening: one was Cologne Egg fastening III, and the other was Cologne Egg fastening IV. Figure 2 shows the time-acceleration of two types of fastening. Frequency-acceleration relation is shown in Fig. 3. It is found that the rail vibration is very severe at 300 Hz.

Fig. 2 Time-acceleration relation of fastening: (a) Cologne Egg fastening III; (b) Cologne Egg fastening IV

Fig. 3 Frequency-acceleration relation of fastening

3 Model of wheelset vibration

The adoption of a realistic wheelset model has a large influence on the computational accuracy of the simulation. Thus, the realistic wheelset geometric dimension of Beijing metro line 4 was used in this work, as shown in Fig. 4.

Based on the wheelset of Beijing metro line 4, the wheelset parameters are listed in Table 1.

Fig. 4 Wheelset of Beijing metro line 4 (Unit: mm)

Table 1 Parameters of wheelset

In this model, the flexibility effects due to vertical and torsional vibration of the wheelset were considered. The modal properties of the wheelset were calculated from a finite element model (Fig. 5 shows the mesh of the wheelset).

4 Analysis of wheelset vertical vibration

4.1 Vertical vibration of wheelset with electromotor

Simulations were carried out for vertical vibration of the wheelset with electromotor, using the mechanical model (Fig. 6 shows the model) [18].

In Fig. 6, F_y is the reaction force of rail to wheelset, Part A is the left half of axletree between two wheels, Part B is the right half of axletree between two wheels, Part C is the outside of left wheel (wheel-I), and Part D is the outside of right wheel (wheel-II).

The analysis results are shown in Fig. 7. The wheelset (wheel-I and wheel-II) vertical vibration

Fig. 5 Finite element mesh of wheelset with electromotor

Fig. 6 Mechanical model for vertical vibration wheelset with electromotor

Fig. 7 Wheelset vertical vibration receptance

receptances at 0-1 000 Hz frequency are shown. For the analysis of the vertical vibration characteristics at peak values, the wheelset shapes at these peaks are shown in Table 2.

Table 2 Wheelset with electromotor shapes at peak values

The wheelset vertical vibration characteristic is upward bending vibration, and the wheels and axletree are perpendicular, at 0-100 Hz. Its vertical vibration characteristic is left oblique vibration at 200 Hz, and right oblique vibration at 205 Hz. Its vertical vibration characteristic is that the vibration directions of all parts (A, B, C and D) are downward and the wheels have lateral bending vibration at 285-300 Hz. At 375 Hz, its vertical vibration characteristic is upward bending vibration, but the wheels vibration direction is opposite to the direction at 0-100 Hz. The axletree has elongated vibration and the wheels are perpendicular to axletree at 425 Hz. Only the wheels have lateral bending vibration at 475 Hz. Part C and Part D are downward bending vibration and the wheels are lateral bending vibration at 565 Hz. Part B and Part C have upward bending vibration, and Part D has downward bending vibration, but the wheels have little vibration at 650 Hz. The wheelset vibration at 670 Hz is opposite to that at 650 Hz. Only Part C and Part D have upward bending vibration at 850 Hz, and are downward bending at 875 Hz.

Based on Table 2, it can be found that the wheelset vertical vibration at 285-300 Hz is the most adverse vibration to rail. Figure 8 shows the wheelset vibration characteristic at 285-300 Hz. It can be divided into vertical vibration characteristic and lateral bending vibration characteristic. The vertical vibration leads to the severe vibration of rail, and the bending vibration arouses the tangential force between the wheelset and rail. Rail vibration will react with the wheelset, and increase its vibration.

It is found that wheelset vibration at 285-300 Hz easily arouses and amplifies the rail vibration of the same frequency, and leads to shot-pitch rail corrugation easily.

4.2 Vertical vibration of wheelset without electromotor

Simulations were carried out for vertical vibration of the wheelset without electromotor using the mechanical model (Fig. 9 shows the model).

In Fig. 9, F_y is the reaction force of rail to wheelset, Part A is the left half of axletree between two wheels, Part B is the right half of axletree between two wheels, Part C is the outside of left wheel (wheel-I), and Part D is the outside of right wheel (wheel-II).

The analysis results are shown in Fig. 10. The wheelset vertical vibration receptances at 0-1 000 Hz frequency are indicated. For the analysis of the vertical vibration characteristics at peak values, the wheelset shapes at these peaks are also shown in Table 3.

The wheelset vertical vibration characteristic is upward bending vibration, and the wheels and axletree are perpendicular, at 0-95 Hz. Its vertical vibration characteristic is downward bending vibration at 105 Hz, and it is opposite to the shape at 0-95 Hz. Its vertical vibration characteristic is that the vibration directions of all parts (A, B, C and D) are downward and the wheels are lateral bending vibration at 300 Hz. The axletree has elongated vibration, the wheels have bending vibration at 420 Hz, and the axletree has shortened vibration at 425 Hz. Only the wheels have lateral bending vibration at 475 Hz. Part C and Part D have downward bending vibration and the wheels have lateral bending vibration at 570 Hz. Part B and Part C have upward bending vibration, and Part D has downward bending vibration, but the wheels have little vibration at 705 Hz. The wheelset vibration at 710 Hz is opposite to that at 705 Hz. Only Part C and Part D have upward bending vibration at 865 Hz, and are downward bending at 895 Hz.

Fig. 8 Wheelset with electromotor vibration characteristic at 285-300 Hz

Fig. 9 Mechanical model for vertical vibration of wheelset without electromotor

Fig. 10 Wheelset vertical vibration receptance

Table 3 Wheelset without electromotor shapes at peak values

Based on Table 3, it can be found that the wheelset vertical vibration at 300 Hz is the most adverse vibration to rail. Figure 11 shows the wheelset vibration characteristic at 300 Hz. It can be divided into vertical vibration characteristic and lateral bending vibration characteristic. The vertical vibration leads to the severe vibration of rail, and the bending vibration arouses the tangential force between the wheelset and rail. Rail vibration will react with the wheelset, and increase its vibration.

It is found that wheelset vibration at 300 Hz easily arouses and amplifies the rail vibration of the same frequency, and leads to shot-pitch rail corrugation easily.

4.3 Effect of electromotor location on wheelset vertical vibration

In order to analyze the effect of electromotor location on wheelset vertical vibration, Fig. 12 shows the different electromotor locations, where L is the distance of electromotor location to the symmetry axis of axletree.

Figure 13 shows the analysis results. It is indicated that the effect of electromotor location on wheelset vertical vibration, especially at 285-300 Hz (the frequency that leads to short-pitch rail corrugation) is little. Namely, the frequency of 285-300 Hz is the most likely to cause rail corrugation, no matter where the motor is located.

5 Analysis of wheelset torsional vibration

5.1 Wheelset torsional vibration

Simulations were carried out for wheelset torsional vibration, including the wheelset with electromotor and without electromotor. The analysis results are shown in Fig. 14. The wheelset torsional vibration receptances at 0-1 000 Hz frequency are indicated. In order to analyze the torsional vibration characteristics at peak values, the wheelset shapes at these peaks are shown in Table 4.

Fig. 11 Wheelset without electromotor vibration characteristic at 300 Hz

Fig. 12 Different electromotor locations: (a) Middle; (b) L=215 mm; (c) L=431 mm; (b) No electromotor

Fig. 13 Effect of electromotor location on wheelset vertical vibration receptance

It is known that the basic torsional frequency of the wheelset with electromotor is 80 Hz, and the second torsional frequency is 505 Hz. The wheelset without electromotor only has basic torsional frequency, and it is 75 Hz. The basic torsional vibration characteristic is that the wheel-I vibration direction is opposite to that of wheel-II. The second torsional vibration characteristic is that the vibration directions of two wheels are coincident, and the direction of electromotor is opposite to that of the wheels.

Fig. 14 Wheelset torsional vibration receptance

5.2 Effect of electromotor location on wheelset torsional vibration

In order to analyze the effect of electromotor location on wheelset torsional vibration, Fig. 12 shows the different electromotor locations, where L is the distance of electromotor location to the symmetry axis of axletree.

The analysis results are shown in Fig. 15. The basic torsional frequency of the wheelset without electromotor is 75 Hz, and 80 Hz is the basic torsional frequency of the wheelset with electromotor. The second torsional frequency is 275 Hz for middle electromotor, 305 Hz for L=215 mm, 505 Hz for L=431 mm, and there is only basic torsional frequency for wheelset without electromotor. It is indicated that the effect of electromotor location on wheelset fundamental torsional vibration is little, but its effect on the second torsional vibration is large.

Table 4 Wheelset shapes at peak values

Fig. 15 Effect of electromotor location on wheelset torsional vibration receptance

6 Conclusions

1) Based on the investigation and field test, it is known that the rail vibration of Beijing metro line 4 is very severe at 300 Hz.

2) The vertical vibration of Beijing metro line 4 wheelset (including the wheelset with electromotor and without it) has the greatest impact on the rail at 285-300 Hz. The theoretical analysis is validated by the field test and survey results. It is indicated that the short-pitch rail corrugation has a close contact with wheelset and rail vibration.

3) The effect of electromotor location on wheelset vertical vibration, especially at 285-300 Hz (the frequency leading to shot-pitch rail corrugation) is little. Namely, the frequency of 285-300 Hz is the most likely to cause rail corrugation, no matter where the motor is located.

4) The basic torsional frequency of the wheelset with electromotor is 80 Hz, and the second torsional frequency is 505 Hz. The wheelset without electromotor only has basic torsional frequency, and it is 75 Hz. The basic torsional vibration characteristic is that the wheel-I vibration direction is opposite to that of wheel-II. The second torsional vibration characteristic is that the vibration directions of two wheels are coincident, and the direction of electromotor is opposite to the wheels.

5) The effect of electromotor location on wheelset fundamental torsional vibration is little, but the effect on the second torsional vibration is large.

6) The wheelset-rail resonance is one of the reasons of initiation and evolution of rail short-pitch corrugation, so avoiding the resonance is a method of controlling the rail corrugation.

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(Edited by YANG Bing)

Foundation item: Project(C11H00021) supported by Beijing Municipal Science & Technology Commission of China; Project(KCJB11063536) supported by Beijing Jiaotong University, China

Received date: 2011-07-20; Accepted date: 2011-11-28

Corresponding author: YAN Zi-quan, PhD; Tel: +86-13811209805; E-mail: Ziquan.Yan@hotmail.com