DELIVERABLE 2.8 - urban track

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.