wheel-set and rail track - CiteSeerX

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TRANSPORT – 2002, Vol XVII, No 2, 46–51

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The pressure tensions σA(t) in sleepers at rail-seat have been calculated. The lowest 25 mode pairs and residual terms were included in the analysis. The normalised tension in the middle sleeper of track model due to the chosen loading case is depicted in Fig 2. One may now estimate how changes in track parameter levels will affect the maximum pressure tension. For instance, the results of calculations show that for the chosen loading case a change of the foundation stiffness kend from (-) level to (+) level will increase the pressure tension σA. Correspondingly, σA is decreased if the numerical value of Asleeper is raised from (-) level to (+) level. An empirical function (physical co-ordinate) σˆ A that gives an approximation of the maximum pressure tension σA was calculated by empirical formula according [9]. Using this function, the maximum pressure tension σA can be estimated for the combination of track parameter levels other than those. Note that low (-) and high (+) numerical levels of track parameters are investigated assigning the values -1 and +1, respectively, to the corresponding track parameter symbols. Values in the interval [-1,1] can also be assigned to the track parameter symbols for the linear interpolation of the approximate maximum pressure tension σˆ A inside the examined region of the eight-parameter design space. Further, the linear extrapolation of σˆ A can be performed assigning values to the track parameter symbols outside the interval [-1,1]. This approach should serve as a helpful tool in the process of designing track structures for the best performance. The best combination of track parameter levels inside the examined region as to the maximum pressure tension σA in the sleepers at rail-seat due to the investigated loading case can now be determined. The comparison with

Fig 2. Calculated pressure tensions σA, σB and σC in rail track elements

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the calculated maximum pressure tensions for track models shows that the lowest tension has been obtained. 3"/$$$ =$ !!0!/$$$

The pressure tensions σB(t) in mid sleeper crosssections have been calculated. The lowest 25 mode pairs and residual terms were included in the analysis. The normalised tension in sleeper 12 of track due to the chosen loading case is depicted in Fig 2. The largest effects on σB are obtained when the levels of the foundation stiffness varied. Note also a large two-factor interaction effect. From the inspection of the main effects and the abbreviated confounding pattern, logical explanation seems to be a large interaction effect between the two foundation stiffness.

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4. According to the estimation of stiffness parameters of rail track the maximum pressure tensions were obtained when the speed of the locomotive was about 3050 km/h. 5. A cost-benefit analysis with respect to the accumulated damages of the track or the sizing and number of track components required can be performed. $%$$ $

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The pressure tensions σC{t) in rail cross-sections have been calculated. The lowest 25 mode pairs and residual terms were included in the analysis. The normalised tension in the rail centrally of track model due to the chosen loading case is depicted in Fig 2. The largest effects are obtained varying the levels of the rail cross-sectional area and the foundation stiffness.

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1. In case of using a two level fractional factorial method, 24 dynamical parameters combinations are enough to investigate the mathematical model of track. 2. The calculated results show that the suggested mathematical model of track is sufficiently correct and is not contradictory to the mechanic fundamentals laws. 3. The pad viscous damping cpad seems to have only a small effect on the distribution of maximum pressure tensions among the components of track.

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Knothe K., Wille R., Zastrau B. W. Advanced contact mechanics - Road and rail. VEHICLE SYST DYN 35 (4-5): 2001, p 361– 407. Wu TX, Thompson D.J. Theoretical investigation of wheel/rail non-linear interaction due to roughness excitation VEHICLE SYST DYN 34 (4): 2000, p 261 – 282. True H. On the theory of non-linear dynamics and its applications in vehicle systems dynamics. VEHICLE SYST DYN 31 (5-6): JUN, 1999, p 393 – 421. Markova O., Kovtun H. A comparison of various theories on the interaction between wheel and rail. VEHICLE SYST DYN 33: Suppl. S. 1999, p 629 – 640. Cai Z. and Raymond G. P. Theoretical model for dynamic wheel/rail and track interaction. Proceedings Tenth International Wheel-set Congress, Sydney, Australia, 1992, p 128 – 142. Nielsen J. C. O. and Abrahamsson T. J. S. Coupling of physical and modal components for analysis of moving non-linear dynamic systems on general beam structures. International Journal for Numerical Methods in Engineering, Vol 33(9), 1992, p 1843-1859. Dahlberg T. and Nielsen J. C. O. Dynamic behaviour of free-free and in-situ concrete railway sleepers. Proceedings International Symposium on Precast Concrete Railway Sleepers. Madrid, 1991, p 393 – 416. # 



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