DELIVERABLE 2.8 - urban track

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Figure 3.4 D0208_STIB_M24.doc TIP5-CT-2006-031312 Page 28 of 44 URBAN TRACK Issued: August 13, 2008 Quality checked and approved by project co-ordinator André Van Leuven LCC (Life Cycle Cost) analyses have very clearly shown the positive effect on life cycle costs and maintenance work. This optimum course taken by the forces involved will result in a reduction of both rail and wheel wear. The track serves as guidance for the moving vehicle and is responsible for its dynamics. For the investigation of kinematics, at least a general point in the cross section of the vehicle has to be observed, not a point in the track plane, which is from a mathematics view a singular plane. For the dynamics, Newton’s and Euler’s laws have to be taken into consideration. For both, the centre of gravity is the decisive point. Therefore, track alignment design has to be performed for this centre. The track should provide continuous variations for at least velocities and accelerations and preferably also jerks everywhere within the vehicle. On the other hand, the track is the support structure for internal forces (in the rails) and external forces caused by the moving vehicles. The continuous welded rails have to be bent and kept in the required shape. This is only possible with a special continuous variation of cant gradient. In a ramp, the railroad track is always stressed. The normalized pattern and derivatives look like: Normalized constant cant gradient and curvature and derivatives The kinematics induced by a constant cant gradient without rounded connections are typical. There is a step in the elevation angles of the cant gradient at the boundaries. The sway (roll) angular velocity is discontinuous, therefore the sway (roll) angular acceleration is infinite, which causes also the non- compensated transverse acceleration in the centre of gravity to be infinite. The sway (roll) angular jerk is infinite, which causes also the non-compensated transverse jerk in the centre of gravity to be infinite. If only the outer rail is elevated also vertical acceleration and jerk are infinite. Rounded connections are needed to remove these singularities, which elongate the cant gradient in an undefined manner. With circular rounded connections, only accelerations are limited, but not the jerks. Another important aspect is to consider the rail(s) as (a) bended beam(s). For the bending of the rail, in that context a simple Bernoulli - Euler – model suffices.
Figure 3.5 D0208_STIB_M24.doc TIP5-CT-2006-031312 Page 29 of 44 URBAN TRACK Issued: August 13, 2008 Quality checked and approved by project co-ordinator André Van Leuven It has to be applied biaxial, in the stiff up direction of the web and in the weak transverse direction of the foot For a conventional geometry, the ideal position of the continuous welded rails in plain lines lead in the maximum to the following discontinuities: Transverse direction: Small steps in the curvature (connections of two circular curves without transition curve) or kinks in the curvature (at a clothoid). Up direction: Steps in the angles (at a constant cant gradient) equalling kinks in the position. As can be detected immediately, up direction are two orders worse than transverse direction! 180 160 140 120 100 80 60 40 20 0 VA71 UIC60 UIC54E S49 -80 -60 -40 -20 0 20 40 60 80 Typical rail cross sections Taking into consideration the formulas of basic bending theory, for the nowadays used cant gradient can be derived: All nowadays used cant gradients have discontinuities at the ends, if one order does not match that of the neighbouring rough track alignment design element (straight all derivatives = 0, circle only zero th derivative (cant) � 0 ). The discontinuity is forced by a continuous distribution of the loadings due to the rail fastenings analogous formula of Zimmermann (Hetényi). Assuming a special shape of the loading distribution, which generates the wanted geometry of the rail in the cant gradient, either the amplitude of the force or the length of the rounded connection can be calculated. The prescribed geometry is not realized there!
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Page 11 and 12: Figure 2.3 Figure 2.4 Lateral widen
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Page 15 and 16: 2.4. SAARBAHN Figure 2.7 Rail profi
Page 17 and 18: 2.6. KARLSRUHE (VBK) Figure 2.9 Rai
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Page 23 and 24: 3. THE VIENNESE CURVE 3.1. INTRODUC
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Page 31 and 32: Figure 3.6 Figure 3.7 Bezogene Übe
Page 33 and 34: 3.3. IMPLEMENTATION Figure 3.9 Figu
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DELIVERABLE 2.8 - urban track

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