A Finite Element Solution for Lateral Track Buckling Problem.

Transcription

1 A FINITE ELEMENT SOLUTION FOR THE LATERAL TRACK BUCKLING PROBLEM by Javier Gallego and David Gómez-Rey Department of Railways Systems Technology TIFSA-Grupo RENFE Madrid, ESPAÑA Telephone: Fax: Abstract: People and freight transport have increased in the last few years. With the introduction of CWR several problems caused by traditional tracks have been solved, but new ones have arisen. The CWR track lateral instability generated by thermal and mechanical loads, due to temperature changes and the pass of vehicles respectively, is one of the most critical troubles because the circulation becomes unsafe and causes catastrophic derailments. In the past traditional theoretical analysis were developed for solving track buckling but they were not appropriated enough for modelling actual situations due to the hypothesis introduced. Although there was not a general theory accepted by researches, they applied traditional results to cases like on curves of more than 500 m radius. The fast development of computers in recent years has made it possible that nowadays investigations can be based on the finite element methods (F.E.M). A non-linear, three-dimensional finite element study of lateral track buckling is presented to solve traditional limitations. Lateral ballast resistance and rail lifting wave due to vertical loads generated by the pass of vehicles are considered as they are the most influential parameters, are considered. The finite element model has been developed for tight, metric curves, particularly, for less than 150 meters curves radius where the problem of lateral track buckling becomes critical. As a conclusion of the investigations, values of buckling temperatures have been obtained in order to predict lateral track buckling. Figures comparing results for different radius, lateral resistance and defect of alignment are also included. Final theoretical results shall be validated with field tests

2 1. Introduction: Widespread introduction of Continuous Welded Rails (CWR), instead of the traditional jointed ones, has caused an increase of accidents and incidents due to track buckling problems, that is why nowadays this phenomena has become more interesting. Track buckling can be caused only by thermal loads due to temperature changes or by mixture of thermal and mechanical loads generated by the pass of vehicles (dynamic buckling). [1] In the past were developed different analytical methods but they used to be very complex mathematically and with lot of disadvantages.[7] [8] Later in time different finite element models were programmed to study track buckling. [2] [4] In this survey, finite element models have been developed to eliminate disadvantages of the previous methods. The presented models are non-linear. There is one for the vertical direction and other for lateral direction, being the vertical direction results used in the lateral one. They have been generated with multi-purpose packaged software for simulating tight metric curves, this is, curves with a radius between 100 and 150 meters where track buckling is being increased. Multi-purpose finite element packaged software have been strongly developed and they include powerful numeric resolution methods, that is why this kind of software has become very useful for solving complex mathematical problems like track buckling. The purpose of this packaged software modelling is to find a simple way to predict track buckling. The important point of this model is the determination and the evaluation of the track parameters that will affect the problem s solution, this is the generation of the model. The following parameters have been considered in this model: Lateral resistance. Longitudinal resistance. This parameter does not seem to be very influential so a typical value has been chosen.[2] Vertical resistance. Simulated and Non-simulated track interaction. Rail lifting wave. Initial track geometric imperfections amplitude. Curve radius. Tie spacing. Rail profile. Torsion resistance has not been considered as advice the sensitive figure shown in [2]

3 2. Development of non-linear multi-purpose packaged software generated models: A finite element packaged software has been used for developing the non-linear models. The initial non-linear and three-dimensional model, shown in figure 1, has been divided in two new models, one for the vertical direction and another for the lateral direction. Figure 1: Three-dimensional model. They works as follows: The first model is used for vertical direction modelling. With this one, raillifting wave generated by the pass of vehicles has been obtained, this will allow to calculate modified lateral resistance s values to be introduced in second model. Figure 2 shows the vehicle characteristics and the static rail lifting wave generated. Reduced lateral resistance ties and increased ones can be identified on figure 2. Figure 2: Rail lifting wave

4 In this first model, thermal loads have not been introduced because these will be responsible of lateral track buckling but they will nor have significant influence in the rail-lifting wave. Gap element have been used for modelling the vertical resistance, those elements work as the ballast do. When the gap is under compression force its behaviour is like a spring and if the element is under traction force, rail become free and gap element can not do anything to keep the rail on its position. The ties have been modelled by rigid elements. Longitudinal resistance has been modelled by non-linear spring element. To calculate the rail lifting wave it has been used force control numerical methods, this means that the force s evolution followed a control curve that grew to the vertical force s value induced by the vehicles. The second model is used for lateral direction modelling. Using the rail lifting wave calculated with first model and experimental correlation shown in [1], the modified lateral resistance s values can be calculated and finally introduced in lateral model. Thermal loads have been introduced in this second model. The lateral loads generated for the vehicle must also be introduced but after several simulations it can be concluded that this loads did not have a significant influence in final results. Non-linear spring elements have been used for modelling the lateral resistance. Spring s characteristic curve came from the field tests data. To calculate the critical buckling temperatures it has been used displacement control numerical methods, this means that the displacement s evolution followed a control curve that grew linearly to the maximum lateral displacement s value simulated. For each iteration, the packaged software gave the temperature needed to get the step s displacement, so at the end the track buckling evolution could be drawn. 50 meters track length have been simulated, as the model shown in [2]. 3. Validation of the multi-purpose finite element packaged software generated model: To validate the model, several field tests have been done to obtain the different track parameters values in buckled tracks. A lateral resistance test is shown in figure

5 Figure 3: Lateral resistance test. The data from field tests was introduced in the models generated for each of the validation curves. The results obtained, once a safety criteria shows in [1] for progressive buckling and in [3] for sudden buckling is used, were compared with the temperature data from the place where track buckling appeared. With this comparison it can be concluded whether the packaged software generated model would be useful to predict track buckling or not. The places where the validations curves are, as well as the most important characteristics of the track are shown on table 1. A non-buckled curve has also been considered. Table 1: Validation curves characteristics. Figures 4, 5 and 6 show the validation results and table 2 contains the maximum temperatures at the curve location and those obtained with the finite element model

6 Figure 4: Lateral track buckling evolution for buckled validation curve 1. Figure 5: Lateral track buckling evolution for buckled validation curve 2. Figure 6: Track buckling evolution for non-buckled validation curve

7 Table 2: Validation results. From the validation figures it can be stated that the finite element packaged software generated model would have predicted track buckling properly in the case of buckled curves. For a non-buckled curve, the model would have also given an appropriate result, predicting that track buckling would have not appeared. 4. Practical application: In the last few years accidents and incidents due to track buckling, particularly in tight curves, have increased. Some abacuses have been prepared to study the problem. UIC 54 track with 0.6m tie spacing has been used. Curve radius between 100 and 150 meters have been used. For each of the curve radius, three initial track geometric imperfection amplitude levels have been modelled by a half-sine wave, to sum up, 10, 20 and 50mm. Finally for each of the three amplitude levels of initial track geometric imperfection, 8 different lateral resistance levels have been considered: 7, 8, 10, 12, 14, 16, 18 and 20 kn per meter of track. Therefore 96 simulations, that will fill most of the tight curves situations, have been made. The practical application of the finite element model included let obtain the following results: The first category shows the track buckling process for different lateral resistance values with curve radius and initial track geometric imperfection amplitude kept constant. An example of this type of results is showed on figure

8 Figure 7: First category of results. It can be concluded that when the lateral resistance value is increased, critical buckling temperatures also increase and the buckling process changes form progressive buckling to sudden buckling appearing then both, the upper and lower, critical buckling temperatures. With second category of results presented, the initial track geometric imperfection amplitude effect can be observed. This influence is shown on figure 8 (W 0 is the imperfection s amplitude). Figure 8: Second category of results. It can be concluded that as the initial track geometric imperfection amplitude increases critical buckling temperatures values decrease. Third category of results shows the evolution of critical buckling temperatures for each of the radius considered, related to initial track geometric imperfection s amplitude. An example is shown on figure

9 Figure 9: Third category of results. As the curve radius is reduced, the critical buckling temperatures decrease and the buckling process becomes progressive. Finally, safety criteria have been used to obtain fourth category results. An example is shown on figure 10. Figure 10: Fourth category of results. This kind of abacus can be used simply and quickly to predict track buckling. It can be used in two ways. The first one is to calculate the minimum lateral resistance required to avoid track buckling from the value of the maximum temperature expected, once obtained it can be compared with field tests results. If the calculated lateral resistance value is higher than the one of the field test track buckling will not appear. Second way is just the opposite, to calculate the maximum track temperature before buckling appears from the lateral resistance value, once obtained it can be compared with the maximum temperature expected. If the temperature calculated is lower than the expected buckling will appears

10 5. Conclusions: The multi-purpose finite element packaged software generated models are an alternative to the traditional methods based on difficult to solve non-linear equation systems and also to specific finite element models programmed on purpose to study track buckling. In the survey it is shown the initial track geometric imperfection amplitude effect as well as the influence of the lateral resistance and the curve radius. The models have been validated for buckled and for non-buckled curves. With the model shown, easy and quick using result abacus can be obtained, in a simple way, to predict track buckling. 6. References: [1] ORE D 202 RP 3: Théorie de la stabilité de la voie en longs rails soudés, February [2] C. Esveld, How safe is CWR?, WCRR, [3] C. Esveld, A new set of computer models for analysing CWR, WCRR,1997. [4] Bao, Y and Barenberg, E.J. Three Dimensional Buckling Analysis of Continuous Welded Rail (CWR) Track, WCRR, [5] Bao, Y and Barenberg, E.J Innovative methods to enhance the stability of continuous welded rail (CWR) track and railroads productivity, WCRR, [6] J. Eisenmann, The significance of the rail lifting wave, Rail International, October 1976, pp [7] A. Kerr, An analysis of thermal track buckling in the lateral plane, DOT/FRA/ORD-76/285, September [8] G. Samavedam, A. Kish & D. Jeong, Parametric Studies on Lateral Stability of Welded Rail Track, DOT/FRA/ORD-83/07, May