J. Cent. South Univ. (2017) 24: 1111-1120

DOI: 10.1007/s11771-017-3514-9

Length optimization of straight line connecting turnout on main line in high-speed railway station yard

YIN Guo-dong(尹国栋)¹, SHI Jin(时瑾)¹, WEI Qing-chao(魏庆朝)¹, LAI Lin(来琳)²

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

2. China Railway Design Corporation, Tianjin 300142, China

Central South University Press and Springer-Verlag Berlin Heidelberg 2017

Abstract: Taking the development of high-speed railway in China as background, and referring to the dynamic theory and wheel-rail contact mode, dynamic analysis model was established, considering the setting position of straight lines and running conditions of train in high-speed railway station yard. Using the established model, and choosing vehicle lateral acceleration and wheel suspension as the evaluation indexes, dynamic characteristic of vehicle traveling in turnout and adjacent area on main line was analyzed, and effects on travelling safety and stability of train aroused by length variation of straight lines were calculated based on analyzing the damping rules of vibration. The results show that, a certain length of straight lines can alleviate the vibration aroused in turnout and curve (turnout), length of straight lines connecting turnouts in different sections on main line was proposed to meet the demand of traveling stability, and shortening or cancelation of straight line for the scale limitation of station yard has less influence on operation safety of train.

Key words: high-speed railway; station yard; straight line; turnout; dynamic theory; length optimization

1 Introduction

As an advanced technology of railway transportation in the world, high-speed railway construction is developed in more and more countries. Technical and academic researches are more mature in countries with developed high-speed railway transportation, such as Japan, Germany, and France. Adapted to economic and transportation demand, high- speed railway developed rapidly in China in recent years, with the technology and development scale in great progress.

To countries with mature technology in high-speed railway construction, researches on station yard are focus on the improvements of bridge, tunnel and track [1-6]. Regulations about parameter of railway lines focus on the main line, with few researches on lines in station yard. To meet the high operation demand of high-speed railway station yard, Chinese scholars made certain researches on parameter selection of railway lines in station yard.

YANG [7] proposed technique standards on plane design, vertical section design and throat area turnout arrangement of station yard, according to the demand of speed increase of existing railway lines. Regulations were made on radius of curve connecting turnout, length of transition curve, selection of superelevation, and length of straight line between curve and turnout [8]. References were given to parameter selection of railway line in high-speed railway station yard, but in the researches above, static methods were applied mostly, with less consideration on influences on wheel-rail dynamic interaction and train travel stability aroused by parameter variation [9].

Based on dynamic theory and serpentine wave theory, SHI et al [10] calculated and analyzed effects on dynamic response caused by variation of curve radius, length of straight line between curve and turnout, and length of transition curve when train entering in and departing the station yard, using the established dynamic model. Although random irregularity of track and snaking motion of train were considered in the model, construction irregularity and complicated wheel-rail contact relation in turnout were ignored [11], so conclusions in the research are limited.

To adapt the frequent changes of railway lines as train traveling in high-speed railway station yard, turnouts are set to connect the main line, the arrival line and the departure line. For the intensive vibration aroused in turnout area and curvature transition point, straight line is suggested to be set to alleviate the vibration aroused in turnout and curve (turnout), and length selection of these straight lines is essential. Base on summarizing existing researches, taking the development of high-speed railway in China as background, and referring to the dynamic theory and wheel-rail contact mode, dynamics analysis model was established, considering the setting mode of railway lines and running conditions of train in high-speed railway station yard [12, 13]. Using the established model, and choosing vehicle lateral acceleration and wheel suspension as the evaluation indexes, dynamic character of vehicle traveling in turnout and adjacent area was analyzed, effects on travelling safety and stability of train aroused by length variation were calculated, and length of straight lines connecting turnouts in different sections on main line was proposed, based on analyzing the damping rules of vibration. Accordingly, suggestions were proposed to parameter optimization of railway lines in high-speed railway station yard.

2 Regulations on arrangement and parameter selection of railway lines connecting main line and arrival- departure line in high-speed railway station yard

With numerous railway lines laid in the station yard, high-speed railway station should not only meet the operation requirements of train to pass in high speed, but also satisfy the demand of high-speed train to arrive, depart and turn-back in station yard, arrangement of lines is shown in Fig. 1.

Fig. 1 Sketch of lines arrangement in high-speed railway station yard

No. 18 turnout with movable frog is the main type of turnout used in high-speed railway station yard in China. When the curve of closure rail in No. 18 turnout is 1100 m, permissible maximum speed is 80 km/h as train passing through turnout in side direction, and permissible maximum speed is 350 km/h as train passing through turnout in straight direction. As shown in Fig. 1, No. 18 turnouts are arranged on main line in high-speed railway station yard.

According to design code of high-speed railway in China [8], intermediate line is proposed to set to connect turnout and curve on arrival-departure line, with the distance between turnout and terminal of superelevation slope not less than 20 m, and not less than the sum of superelevation slope length and distance from switch heel to terminal switch sleeper in difficulty conditions. Length of intermediate line connecting curve and turnout on main line in station yard is not mentioned, and in the high-speed railway code, lines with length not less than 50 m (not less than 32 m in difficulty conditions) is proposed to be inserted between two facing turnouts on main line in the high-speed railway station yard, when the two side lines of two facing turnouts may be passed by train at the same time, and lines with length not less than 25 m is proposed to be inserted between two facing turnouts on main line in the high-speed railway station yard, when the two side lines of two facing turnouts not be passed by train at the same time.

3 Dynamic model

3.1 Vehicle model

With each component of a system be abstracted as a rigid body, interaction of each body and its influence on system dynamics behavior are researched in rigid multi-body dynamics. To assist the kinematical and dynamic analysis of the complex system, mathematic model solved by computer program is established, and to find a stable numerical solution method with high efficiency is a key step in rigid multi-body dynamics. SIMPACK is a multi-body dynamics analysis software with advanced algorithm. For the adoption of relative coordinate recursive algorithm, dynamic equations are relatively few in SIMPACK, and that increases the calculation speed and gives obvious advantage to this software. With abundant modeling elements, track and vehicle can be established rapidly based on substructures.

For the less effect on wheel-rail vertical and lateral interaction aroused by longitudinal interaction of vehicles, single vehicle model was established to simulate train in this research, as shown in Fig. 2, and the vehicle model comprises a car body, two bogles, four wheelsets, and the connecting components. The car body, bogles, wheelsets are assumed as rigid bodies, and the stiffness and damping of primary suspension andsecondary suspension springs are considered as linear. The car body and each bogle is assigned 6 DOFs, which are vertical, lateral, longitudinal, pitching, rolling, and yawing movements, while each wheelset is assigned 4 DOFs, i.e. lateral, longitudinal, rolling, and yawing movements, with totally 34 DOFs be considered in the vehicle model.

Fig. 2 Vehicle model in SIMPACK

3.2 Turnout model

No. 18 turnout with movable frog is the main type of turnouts used in high-speed railway station yard in China. The main plane dimension of No.18 turnout is given in Table 1.

Table 1 Main plane dimension of No.18 turnout

A turnout is comprised by a switch panel and a crossing panel connected by a closure panel, and the arrangement of rail lines in turnout area is shown in Fig. 3.

Fig. 3 Location of rail lines in turnout

Assumptions are adopted in turnout model:

1) Train load is carried by switch rail and stock rail jointly in area where the two rails attached closely. Assuming the displacement of switch rail equal to that of stock rail in closely attached area, these two rails are combined to one rail that be assumed as Euler beam with variable cross sections and be supported on elastic foundation, meanwhile, same assumption is made in closely attached area of point rails. Rails in unattached areas are assumed as Euler beams with constant cross section.

2) Vibration of switch rail in curve is not considered when train running through the turnout in straight direction, and vibration of switch rail in straight line is not considered when train running through the turnout in side direction [14].

LMA tread is adopted and variable cross section is established in the track model, referring to actual cross section shapes of rail in No.18 turnout, as shown in Figs. 4 and 5 [15, 16].

Fig. 4 LMA wheel tread

3.3 Wheel-rail contact model

Wheel-rail contact geometry relationship in turnout area is more complex than that of ordinary railway line. Several static wheel-rail contact states in switch area are shown in Fig. 6. In Fig. 6(c), two-point contact or three-point contact might appear between wheel tread and rail, as single-point contact or two-point contact appears in other figures, and wheel-rail contact point transfers to switch rail completely in Fig. 6(d) [16, 17]. With assumptions in Section 3.2, switch rail and stock rail are combined to one rail in area where the two rails attached closely, distribution of wheel-rail forces on switch rail and stock rail is not considered, the same assumption is made in crossing area, so single-point contact is used in the dynamic model to analyze contact relation between wheel tread and rail in turnout area [18-21].

An important aspect on simulating train running in turnout area is to establish a contact model between wheel back and wing rail (guard rail). Contact between wheel back and wing rail (guard rail) is shown in Fig. 7.

For the short time contact between wheel back and wing rail (guard rail), elastic contact model is adopted, and spring-damping force component is set between wheel back and rail. Normal force F_N is determined by wheel-rail relative displacement and speed, using the real-time calculation. The algebraic expression is given by

                       (1)

where p represents wheel-rail relative lateral displacement;represents wheel-rail relative lateral speed; c_b and d_b represents lateral stiffness and damping coefficient respectively.

Although the rails were regard as one rail in area where the two rails attached closely, when train running on turnout, wheel-rail contact point may transfer from one rail to another rail, that lead to the abrupt changing and discontinuity of wheel-rail contact point. The

vertical irregularity brought by contact point variation generates horizontal and vertical impact and relative displacement between wheel and rail, and the variation of wheel-rail static contact geometry parameter is reflected on the changes of distance from contact point to track center, rolling radius difference between left wheel and right wheel and wheel-rail contact angle. Based on analyzing the variation of contact point, dynamic wheel-rail contact relation is calculated by established model, considering dynamic lateral and vertical displacement as well as yaw angle displacement between wheel and rail aroused by wheel-rail horizontal and vertical impact. Normal force between wheel and rail is calculated based on Hertz nonlinear contact theory, and wheel rail creep force is calculated using simplified theory of Kalker. Considering the dynamic variation of wheel-rail contact relation, the research of wheel-rail dynamic contact geometry is more suitable to analyze the dynamic interaction between wheel and rail.

Fig. 5 Several cross sections used in turnout:

Fig. 6 Wheel-rail contact positions as train running through switch area:

Fig. 7 Illustration of contact between wheel back and wing rail (guard rail)

4 Effect on dynamic interaction between vehicle and track induced by length variation of straight line connecting curve and turnout on main line in high-speed railway station yard

Intensive vibration is aroused in curvature transition point and turnout area for the break of curvature and the constructional irregularity of turnout when train running into turnout (curve) after passing through the curve (turnout). Theoretically, process of vibration damping on intermediate straight line can alleviate the superposition of vibration generated on turnout area and that generated on curvature transition point, and it has important significance to riding quality of high-speed railway.

In different operation requirements, train runs through turnouts at different speed and in various directions. As shown in Fig. 1, No. 18 turnout connect main line curve and lines in station yard, probable running directions of train in this area are shown in Fig. 8.

Fig. 8 Train running through turnout and curve in different directions:

According to regulations in design code of high-speed railway in China, route parameters were chosen as calculation condition: length of transition curve L_t=200 m, length of circular curve L_c=200 m (curve radius R=8000 m, and superelevation h=120 mm), length of intermediate straight line L_s=200 m (when train runs through turnout in straight direction, length of intermediate straight line L_s=200 m; when train runs through turnout in side direction, length of intermediate straight line L_s=100 m). By choosing vehicle lateral acceleration and wheel suspension as the evaluation indexes, relations between riding quality of high-speed railway and length of straight line connecting curve and turnout on main line in station yard were calculated, using the established dynamic model.

4.1 Dynamic responses of train running through turnout in straight direction at speed of 350 km/h

Time history of vehicle lateral acceleration is shown in Fig. 8, when train runs into turnout in straight and forward direction after passing through curve and intermediate straight line at the speed of 350 km/h. As shown in Fig. 9, impact vibration is generated on vehicle lateral acceleration in curvature transition point such as ZH sport and HY sport when train running through the curve, and vibration of lateral acceleration in turnout is more intensive. Lateral acceleration of vehicle damps constantly as train runs on the intermediate straight line, with 80% vibration damps in the range of 35 m after train running into the intermediate straight line, as shown in Fig. 9(b).

Fig. 9 Lateral acceleration of vehicle with train running into turnout in straight and forward direction after passing through curve and intermediate straight line:

Time history of vehicle lateral acceleration is shown as Fig. 10, when train runs into the curve passing through intermediate straight line at the speed of 350 km/h, after running through turnout in straight and reverse direction. Lateral acceleration of vehicle damps constantly as train runs on the intermediate straight line, with 60% vibration damps in the range of 35 m after train running into the intermediate line, and the rest vibration damps less in each following period of vibration, it damps completely exceed the range of 200 m after train running into the intermediate line.

Accordingly, in operation conditions above, the location of intermediate straight line with length not less than 35 m can alleviate the superposition of vibration generated on turnout (curve) and vibration generated on curve (turnout) in a great degree, and the traveling stability of train can be ensured.

Wheelsets suspension variation of the first axle is shown in Figs. 11 and 12, when train runs into turnout in straight and forward direction after passing through curve and intermediate straight line, as well as train runs into the curve passing through intermediate straight line after running through turnout in reverse direction.Suspension of wheelsets on curves is much less than that on turnout. Thus, the arrangement of intermediate straight line has rarely influence of wheelsets suspension in these two operation conditions.

Fig. 10 Lateral acceleration of vehicle with train running into curve passing through intermediate straight line, after running through turnout in straight and reverse direction:

Fig. 11 Wheel suspension of first bogle with train running into turnout in straight and forward direction after passing through curve and intermediate straight line

4.2 Dynamic responses of train running through turnout in side direction at speed of 80 km/h

Time history of vehicle lateral acceleration is shown in Fig. 13, when train runs into turnout in side and forward direction after running through curve and intermediate straight line at the speed of 80 km/h. As shown in Fig. 13, lateral acceleration of vehicle generated on curve and intermediate straight line is much less than that generated on turnout. Thus, the arrangement of intermediate straight line has rarely influence on traveling stability in this operation condition.

Fig. 12 Wheel suspension of first bogle with train running into curve passing through intermediate straight line, after running through turnout in straight and reverse direction

Fig. 13 Lateral acceleration of vehicle with train running into turnout in side and forward direction after running through curve and intermediate straight line

Time history of vehicle lateral acceleration is shown as Fig. 14, when train runs into the curve passing through intermediate straight line at the speed of 80 km/h, after running through turnout in the side and reverse direction. As shown in Fig. 14, vibration of vehicle lateral acceleration damps rapidly when train runs into the intermediate straight line, and vibration of lateral acceleration in curvature transition point such as ZH sport and HY sport is weak. Thus the arrangement of intermediate straight line has rarely influence on traveling stability in this operation condition.

Wheelsets suspension variation of the first axle is shown in Figs. 15 and 16, when train runs into turnout in side and forward direction after running through curve and intermediate straight line, as well as train runs into the curve passing through intermediate straight line after running through turnout in side and reverse direction. Suspension of wheelsets on curve is much less than that on turnout, thus the arrangement of intermediate straight line has rarely influence of wheelsets suspension in these two operation conditions.

Fig. 14 Lateral acceleration of vehicle with train running into curve passing through intermediate straight line, after running through turnout in side and reverse direction

Fig. 15 Wheel suspension of first bogle with train running into turnout in side and forward direction after running through curve and intermediate straight line

Fig. 16 Wheel suspension of first bogle with train running into curve passing through intermediate straight line, after running through turnout in side and reverse direction

By summarizing the calculation results in Section 4.1 and Section 4.2, suggestions were given to arrangement of lines in high-speed railway station yard: to meet the demand of traveling stability, intermediate straight line with length not less than 35 m was proposed to connect curve on the main line and turnout in high- speed railway station yard in the calculation conditions above; meanwhile, shortening or cancelation of intermediate straight line for the scale limitation of station yard has less influence on operation safety of train. For the limitation of assumed route parameters, the regulations on intermediate straight line should change with radius of circular curve and length of transition curve.

5 Effect on dynamic interaction between vehicle and track induced by length variation of insertion straight line between two facing turnouts laid on different main line tracks

As shown in Fig. 1, No. 18 turnouts in different tracks may be arranged oppositely in high-speed railway station yard, and the running route of train in this area is shown in Fig. 17. Theoretically, the superposition of vibration generated on the two turnouts can be alleviated in a great degree for the insertion of line between the two facing turnouts in different main line tracks.

Fig. 17 Train running into later turnout in side and reverse direction after running through former turnout in side direction

Effects on traveling ability induced by length variation of insertion straight line between two facing turnouts were calculated. In the calculation model, length of insertion straight line was set as 100 m.

Time history of vehicle lateral acceleration is shown in Fig. 18, when train runs through two facing turnouts laid on different main line tracks at the speed of 80 km/h. Lateral acceleration vibration on the two turnouts is intensive, and damping of lateral acceleration impact ends basically in the range of 9 m after train running into the insertion straight line. With the insertion of line notless than 9 m between two facing turnouts, travelling stability of train on lateral turnout is nearly unaffected by vehicle vibration generated on former turnout for the opposite direction of lateral acceleration vibration in the two turnouts.

Fig. 18 Lateral acceleration of vehicle with train running through two facing turnouts laid on different main line tracks:

Suspension variation of wheelsets in front bogle is shown in Fig. 19. Wheelsets suspension changes intensively in turnout area, and suspension of wheelsets on the former turnout decreases rapidly after the wheelset running through crossing area. With no suspension as train running on the insertion line, wheelsets suspend after train traveling for a certain distance on the second turnout, and the distance exceeds bogie wheelbase. Thus, the arrangement of insertion straight line has rarely influence on wheelsets suspension when train running through facing No. 18 turnouts laid on different main line tracks.

Fig. 19 Wheel suspension of first bogle with train running through two facing turnouts laid on different tracks

Accordingly, to meet the demand of traveling stability, insertion straight line with length not less than 9 m was proposed to be set to connect two facing No. 18 turnouts laid on different main line tracks. Shortening or cancelation of insertion straight line for the scale limitation of station yard has less influence on operation safety of train.

6 Effect on dynamic interaction between vehicle and track induced by length variation of insertion straight line between two facing turnouts laid on same main line track

As shown in Fig. 1, No. 18 turnouts may be arranged oppositely on the same track in high-speed railway station yard, and the running route of train is shown in Fig. 20 with two facing No. 18 turnouts laid on the same main line track.

Fig. 20 Train running into later turnout in straight direction after running through former turnout in straight and reverse direction

Effects on traveling ability induced by length variation of insertion straight line between two facing turnouts were calculated. In the calculation model, length of insertion straight line was set as 300 m.

Time history of vehicle lateral acceleration is shown in Fig. 21, when train runs through two facing turnouts laid on the same track at the speed of 350 km/h. Lateral acceleration of vehicle damps constantly as train running on the insertion straight line, with 60% vibration damps in the range of 20 m after train running into the insertion straight line, and the rest vibration damps less in each following period of vibration, it damps completely exceed the range of 300 m after train running into the insertion straight line. Thusly, for the limitation of station yard scale, insertion straight line with length not less than 20 m is proposed to connect two facing No. 18 turnouts laid on the same track to meet the demand of traveling stability.

Wheelsets suspension variation of the first axle is shown in Fig. 22. Same as suspension changes in Section 5, wheelsets suspension changes intensively in turnout area, and suspension of wheelset on the former turnout decreases rapidly after the wheelset running through crossing area. With no suspension as train running on the insertion line, wheelsets suspend after train traveling for a certain distance on the second turnout, and the distance exceeds bogie wheelbase. Thus, the arrangement of insertion straight line has rarely influence on wheelsets suspension when train passing through two facing No. 18 turnouts laid on the same main line track.

Fig. 21 Lateral acceleration of vehicle with train running through two facing turnouts laid on same main line track:

Fig. 22 Wheel suspension of first bogle with train running through two facing turnouts laid on same main line track

Accordingly, to meet the demand of traveling stability, insertion straight line with length not less than 20 m was proposed to connect two facing No. 18 turnouts laid on the same main line track. Shortening or cancelation of insertion straight line for the scale limitation of station yard has less influence on operation safety of train.

7 Conclusions

1) To meet the demand of traveling stability, intermediate straight line with length not less than 35 m was proposed to be set to connect curve and turnout on main line in high-speed railway station yard under the calculation condition. For the limitation of route parameters, these regulations on intermediate straight line should change with radius of circular curve and length of transition curve, etc.

2) To meet the demand of traveling stability, insertion straight line with length not less than 9 m was proposed to be set to connect two facing No. 18 turnouts laid on different main line tracks.

3) To meet the demand of traveling stability, insertion straight line with length not less than 20 m was proposed to be set to connect two facing No. 18 turnouts laid on the same main line track.

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(Edited by YANG Bing)

Cite this article as: YIN Guo-dong, SHI Jin, WEI Qing-chao, LAI Lin. Length optimization of straight line connecting turnout on main line in high-speed railway station yard [J]. Journal of Central South University, 2017, 24(5): 1111-1120. DOI: 10.1007/s11771-017-3514-9.

Foundation item: Project(2014JBZ012) supported by the Fundamental Research Funds for the Central Universities, China

Received date: 2015-09-28; Accepted date: 2016-03-22

Corresponding author: YIN Guo-dong, PhD Candidate; Tel: +86-13811705153; E mail: 08115240@bjtu.edu.cn