Page 40 - 360.revista de Alta Velocidad - Nº 5

Schumann, Tilo. Meyer zu Hörste, Michael. Heckmann, Andreas. Lemmer, Karsten.

Wear is another aspect to be taken into account. In order to transmit tangential forces it is
required to violate the ideal rolling condition at the wheel-rail interface, i.e. there is a small
relative motion between the contact partners, which leads to sliding friction [14]. Wear or
more precisely the volume of abrasive removed material is related to the associated frictional
work [15]. However, wear and rail corrugation are very complex processes, so that a general
statement how they depend on the train speed is difficult and out of reach in the given context.
Just in order to get an idea, a multibody simulation of a today’s articulated highspeed train
with 6 cars, two bogies each car, 16t load per wheel-set, running on a straight track was
performed considering track irregularities. The material abrasion at the wheels per traveling
distance as a function of vehicle speed was evaluated on a trial basis. The exemplary results
in Figure 3 expose a rough trend: wheel wear for guidance grows progressively with the train
speed.

The wear partition associated to traction, i.e. longitudinal dynamics, grows less intense but
still with the fourth power of the vehicle speed as shown in Figure 3. This characteristic is based
on the fact that the longitudinal forces at the wheel-rail interface depend on the resistance
forces which in turn are dominated by the aerodynamic drag at very high velocities.
The traction potential itself is as well a function of the running speed. According to the prominent
historical survey by Curtius and Kniffler [16], the friction coefficient converges asymptotically
against μ = 0.16 on average for very high speeds, while the lower bound of the measurements
indicates μ = 0.1 to be a very reliable figure. The aerodynamic drag may approach values of
approximately 200 kN at 600 km/h, which requires 13 wheel axles each loaded with 16 t be
counterbalanced by traction with μ = 0.1. This appears to be feasible but indicates the necessity
to power as much wheels as possible in order to fully exploit the available traction potential.
That’s why one intermediate car of TGV 150 that set the world speed record of 574.8 km/h in
2007 was equipped with additional powered running gears [17].

3.2 Aerodynamics

Usually the aerodynamic forces like the drag scale with the stagnation pressure ρV²/2, where
 is the density of the air and V is the incident flow velocity in the reference frame of the
vehicle. In still air V corresponds directly to the driving speed U. It follows that the power which
is required to equalize the aerodynamic drag is proportional to U³, and at higher speeds the
aerodynamic drag will exceed the effect of mechanical friction [18].
However, today’s driving speeds up to 600 km/h correspond to a Mach number of M ≈ 0.5, so
that new aerodynamic effects associated to the compressibility of the fluid enter the picture.
The critical Mach number specifies the lowest Mach number at which the airflow over some
point of the train reaches the speed of sound. Above this critical Mach number the aerodynamic
quality of the vehicle will degenerate rapidly. To push the critical Mach number above M = 0.5 a
train requires a relatively long pointed nose similar to the Japanese Maglev train [19].
A highly safety relevant aerodynamic aspect concerns the crosswind stability in particular if
lightweight design is under consideration. Although newer train head designs show elements
to reduce the cross-wind forces [20], [21] , the optimization potential is limited in general.
Investigations with the NGT train concept support the assumption that operational train speeds
beyond 400 km/h require a specific device to prevent the lift-off and overturning of the vehicle
as it is proposed in [22] or as it is conceptually given by the MAGLEV guidance system. An
alternative way to deal with the cross-wind issue at higher speeds is to protect the train from
strong gusts using wind fences. Such fences could act as sound barrier at the same time and
help to reduce noise emissions of high speed trains.

Another safety relevant aspect concerns the aerodynamic loads which the flow around the train
induces on its surrounding. These loads typically as well scale with the square of the driving

38 360.revista de alta velocidad