Prediction of structure-borne vibrations induced into large structures by train transit

Transcription

1 Prediction of structure-borne vibrations induced into large structures by train transit F. Braghin, S. Bruni, A. Collina, G. Traini2 and F. Natoni2 Mechanical Engineering Department, Politecnico di Milano, Milano, Italy. 2 Italferr S.p.a., U. 0. Infiastrutture, Rome, Italy. Abstract The paper presents an approach for the evaluation of train induced structural noise in large civil structures. The procedure is based on time domain simulation of train-track interaction. The calculation is split into two stages, in order to manage also structure representations with a high number of degrees of freedom. 1 Introduction The development of a high speed railway system requires the consideration of major railway stations as the nodal points of the high speed network but also as exchange points with the regional and urban railway. In this context, an example is given by the widening of the Bologna railway station, in conjunction with the realization of the loop rail connection which will enable the high speed line to pass through the downtown ( Collegamento Ferroviario Passante, in short CFP). The structure of the new Bologna station is made of 60m long concrete modules with a total length of 600m. It has three different floors below the actual railway station level: from the lowest floor to the top floor there is the High Speed Platform (HSP), the High Speed Hall, the so called Kiss & Ride floor (devoted to shops and other social activities), the FS Platform (FSP) for ordinary trains at ground level, and above the gallery level with a restaurant. Every

2 2 12 Computers in Railways VIII 12m there is a transversal frame of horizontal beams and columns to which the different floors are connected (see fig. 1). For this kind of structures, due to the presence of people, both structure-borne and air borne noise problems are critical. The most efficient way to keep these problems under control is to carefully design the track system, which means to choose an appropriate track system and to optimize its parameters. In this work an efficient approach, based on numerical simulation and able to evaluate structural noise due to rail transit in large civil structures, is presented. The dynamical analysis is carried out first considering the track and that part of the structure directly interacting with the track system. Subsequently, the forces transmitted by the track system are applied to an extended model of the structure, in order to evaluate the propagation of structural noise. CSllPry. R.ala"ra"f li Figure 1: Front view of the railway station 2 Rail runnability analysis The runnability analysis has been performed by means of the simulation code A.D.Tre.S. ([2]) developed at Politecnico di Milano, Mechanical Engineering Department. It includes t he following topics: - Vibrations transmitted to the structure according to the prescriptions of IS Safety of running (derailment, track gauge variation, skew) which can be critical for a deformable track system with higher deformability than traditional ballasted track ([5]). - Impact factor defined as the ratio between the maximum dynamical stress Q d and the corresponding statical stress Qs.

3 Computers in Railways VIII 2 13 The evaluation of the vibrations transmitted to the structure, of the safety assessment and of the impact factor is done considering the interaction between train, track and structure, as explained in the following paragraphs. 3 Model of Interaction Between Train and Track - Structure In the simulation code A.D.Tre.S. ([2]) these two subsystems (train and track-structure) are modelled separately: the track and the structure are schematized through FEs while for the rail vehicle a hybrid multibody - deformable model is used: carbody and bogies are schematized trough rigid bodies while the wheelsets are represented by means of their rigid and deformable modes. The model adopted for the creepage contact forces is the heuristic model by Shen - Hedrik - Elkins ([6]). The equations of motion of this two subsystems are integrated numerically in the time domain. The equations of the rail vehicle are: [MW] a l l, + [&I 'ZW + [Kwl.X, = F,t (X,,Aw,Xt,Xt,t) (1) [A&], [R,] and [K,] being the mass, damping and stiffness matrices of the rail vehicle, X, the vector of the corresponding degrees of freedom. The Fwt vector represents the generalized forces due to the wheel - rail contact forces, function of both vehicle motion (X,) and track motion (X,). The dependence on time is due to the fact that track and wheel irregularity is considered. The equations of motion that govern the dynamics of the whole track- structure system are: where [Mtt],[Rtt] and [Ktt] are the mass, damping and stiffness matrices of the track while [Mss], [R,,] and [K,,] are the matrices of the structure. [R,t] and [Kst] represent the coupling terms related to visco-elastic elements such as, for instance, the ballast layer or the elastic supports of the slab in the slab track system. Xt is the vector containing the degrees of freedom of the track, while XS contains

4 214 Computers in Railways VIII those of the supporting structure. It is pointed out that external forces only act on the track:.ftv is the generalized force vector which contains the wheel - rail contact forces function of the track (&) and of the vehicle (X,) motion. Since the contact forces change their application point, the expression of the generalized forces on the track is explicitly dependent of the time t. In order to take into account the coupling of the two subsystems, at each integration step an iterative procedure is adopted which allows the equilibrium of the subsystems and their congruence at the contact points ([2]) to be satisfied. Due to the structural complexity of the station, a particular technique is used to manage the high number of degrees of freedom of the model. The calculation is split into two stages: in the first stage the problem of dynamic interaction between train, track and a condensed representation of the supporting structure is solved, in order to predict the forces transmitted by the track system to the structure. In order to obtain reliable results, the simplified model of the structure, used at this stage, must reproduce the local behaviour of the complete building near the track. In the second stage, the forces previously evaluated are applied to a complete model of the station in order to predict the vibrations of the structure in several locations of interest. Step I: Train - Track Interaction with Equivalent Structure The simplified schematization of the supporting structure, used in this first stage, is represented by an equivalent beam. Each 60m module is schematized through a span supported by equivalent springs. The parameters of the equivalent structure are identified in order to match the frequency response of the detailed model of the structure at floor level (FSP) on which the track is placed. This approach leads to a dynamical equivalence of the simplified and complete structure for the first modes of vibration. The system composed by eq. 1 and 2 is solved introducing the simplified structure which reproduces the local behaviour of the complete structure under the track. Hence the forces locally transmitted to the structure take into account the dynamics of the track interacting with the first modes of the floor:

5 Computers in Railways VIII 2 15 where the hatted terms are referred to the simplified structure. The time history of the forces transmitted by the track to the equivalent structure during a train transit are stored in order to be subsequently applied to the complete FE model of the structure. The stiffness and damping matrices of the simplified structure can be split into two contributions, one due to the structure itself (tagged by the single apostrophe) and one due to the track, namely the ballast or the elastic supports (tagged by the double apostrophe): R,, = q, The generalized forces transmitted by the track to the simplified structure are equal to: + RY,; K,, = KL, + K:, (4) Step 11: Analysis with the Full Model of the Structure In the second step a complete FE model of the supporting structure is used. In order to evaluate the response of the complete structure, also far from the track, the second part of eq. 2 is integrated in the time domain using the FE model of the whole structure (this second integration is marked by subscript 2): - Zs + [R:,]. 2, + [K;,]* X, = [A]. &(t) (6) [Mss] * where the right-hand side of eq. 6 represents the lagrangian component of the forces, due to train transit, transmitted to the structure, function of the motion of the track Xt and of the simplified structure - X, both calculated at step I. The matrix [A] is a boolean matrix used to refer the forces transmitted by the track to the corrisponding nodes of the complete structure. In order to evaluate the structure-borne vibrations, accelerations due to train transit have been calculated in several points of the structure with particular attention given to the areas occupied by passengers.

6 2 16 Computers in Railways VIII 4 Application: the "Collegamento Ferroviario Passante - Bologna" 4.1 The proposed slab track Two different track typologies have been compared, the standard ballasted track and a massive track. For the latter one, a parameter optimisation procedure was performed. The modulus of the proposed slab track (fig. 2) is made of a concrete platform (2.4x3x0.55 m) placed over four elastic supports. On each platform there are four prestressed concrete sleepers elastically connected to the platform. Furthermore there are two lateral elastic elements, called stoppers, which permanently connect the lateral side of the platform to the supporting structure. c Sloppel suppart (b) Front view Figure 2: Modulus of the slab track As is well known, a massive track is able to attenuate vibrations induced by train transit since the concrete platform behaves as a suspended foundation ([4]). The stiffness of the elastomeric elements under the platform has been chosen in order to obtain a first vertical frequency at 15Hz (vertical rigid mode of the platform) as shown in figure 3a where the acceleration/force transfer function in the vertical direction is reported for the rail and for the slab. Since the shear stiffness of the elastic elements under the platform is lower than the vertical stiffness, the horizontal natural frequency of the track, in ab-

7 Computers in Railways VIII 2 17 sence of the lateral stopper, would be located at 5Hz as shown in figure 3b, in a range in which an interaction with the yaw movements of the wheelsets is possible. Such an interaction could lead to vibrations of great entity in the horizontal plane, as found experimentally in [l]. This led to the adoption of the two lateral stoppers mentioned above, raising the first lateral eigenfrequency of the track to 14Hz (see fig. 3b). Figure 3a also shows the vertical flexural frequency of the rail at 11OHz. In this mode rails and sleepers vibrate in phase relative to the slab. Figure 3: Calculated transfer function (acceleration/force) of the slab track; (a) vertical: rail (continous line) and slab (broken line); (b) lateral: with lateral stoppers (continuous line) and without stoppers (broken line) 4.2 Simulations with track and equivalent structure At first simulations have been carried out in order to compare the performances of the standard ballasted track and of the slab track with respect to the attenuation of vibrations, adopting an equivalent schematization of the local dynamic behaviour of the supporting structure (step I). The parameters of the equivalent structure have been identified from the dynamic response of the complete structure modelled by means of beam elements for the columns and for the transversal beams and plate elements for the floors and the roof. To this purpose, the transfer function between vertical acceleration and vertical force at midspan of the central module has been used. The results show several frequencies in the range of interest (0-100Hz):

8 2 18 Computers in Railways VIII [=I Figure 4: Accelerations of the slab at mid span with massive and ballasted track this points out the importance of adopting a track which filters out all the frequencies over 15-20Hz. The simulations have been carried out with a freight train composed of a six axles locomotive and a four axles freight wagon running at 60 km/h and with high level track irregularity, defined by the standard ORE B176, and wheel irregularity deduced from vertical rail acceleration measurements ([3]). The third octave band representation of the acceleration of the structure under the track (see fig. 4) shows the better filtering performance of the slab track especially above 30Hz. Figures 5a and 5b show the time histories of the vertical displacement of the rail of the slab track and the forces transmitted from the slab to the equivalent structure due to the transit of the freight train: the same forces are subsequently applied to the complete structure for the second step of the calculation procedure. For the ETR500 and the freight train rail runnability has been verified: maximum values of the calculated derail coefficients are respectively equal to 15% and 31%, well below the limit value of 80%. 4.3 Evaluation of the structural noise Adopting the procedure explained in par. 3, the structural noise in several points of the structure has been evaluated. Tab. 1 shows the pondered level obtained with different trains: as prescribed by IS the pondered limit value is set at 89.5dB, corresponding to a RMS value of [m/s2]. The first two columns in Table 1 show the comparison between ballasted and massive track, considering the

9 Computers in Railways VIII 2 19 (a) (b) Figure 5: Vertical displacement of the rail at the border and at the center of the slab of the massive track due to the transit of a freight train at 60 km/h (a), force transmitted by the single rubber element under the slab (b) freight train running on the FSP at 6Okm/h: the better performance of the slab track is evident. The simulation with the intercity train has been done at the speed of 60km/h. The values, as expected, are lower than those obtained with the freight train because of the lower load per axle and because of the lower suspended mass of the passengers vehicles with secondary suspension. In order to determine the influence of velocity on the interaction between track and structure a simulation has been done with an intercity train running at 100 km/h. Comparing the levels with those obtained in the previous simulation, the levels increase showing the dependence of the dynamical interaction from the velocity of the vehicles. Considering the ETR500 train, running at 120 km/h on the HSP, due to the lower deformability of the HSP with respect to FSP, it is found that, despite the higher speed, the levels of acceleration induced on the structure are lower than those seen in the previous cases. Using the results obtained in the previous cases, the levels of vibration induced in the structure have been evaluated in the case of contemporaneous transit of an ETR500 train at 120 km/h on the HSP and of an intercity train at 60 km/h on the FSP. The computation has been done considering the two transits completely uncorrelated. As can be seen in tab. 1 the level is slightly greater than that due to the transit of the intercity train only.

10 220 Computers in Railways VIII Platform Track Speed [km/h] HSP Kiss&Ride Restraurant Roof Freight Freight IC IC ETR5OO ETR5OO IC FSP FSP FSP FSP HSP HSP FSP ballast massive massive massive massive massive massive k < <70.0 <70.0 Table 1: Maximum RMS value of the vertical acceleration [m/s2] in different areas of the structure. Ref. value a, = 10-6[m/s2] 5 Conclusions In the present work, a time-domain based methodology to evaluate transmitted vibrations and structural noise due to train transit, in the case of large civil structures, has been presented. This proposed methodology can consider both the interaction between train and track and the influence of the structure on the track, limiting the computational effort. References Bocciolone M., Cigada A., Falco M.: Train-structure interaction: measurement in the subway of Milan ; Heavy Vehicle Systems, Vol. 6, N. 1-4, 1999, Inderscience Enterprises Limited Diana G., et al.: A.D. Tre.S.: A software for railway runnability analysis ; WCRR 97 Congress, Florence Italy, nov Diana G., Bruni S., Cheli F., Collina A.: Train-track interaction: a comparison between a numerical model and full-scale experiments ; Heavy Vehicle Systems, Vol. 6, N. 1-4, 1999, Inderscience Enterprises Limited Eisenmann J.: Oberbau bei Stadtbahnen und U-Bahnen unter besonderer Berucksichtigung der Korperschallemission ; Internationales Verkehrswesen, Vol. 33, N 1, 1981 Elkins J.A., Carter A.: Safety assessment of rail veichles ; Vehicle System Dinamics, V01.22, N. 3-4, 1993, Swets & Zeitlinger B.V, Lisse, The Netherlands Shen Z.Y., Hedrick J.K., Elkins J.A.: A comparison of alternative creep force models for rail vehicle dynamic Analysis ; Vehicle System Dinamics, V01.12, N. l, 1983, Swets & Zeitlinger B.V, Lisse, The Netherlands