3D Modeling of Tramway Bogies equipped with independent wheels

Details

Written by Nicolas Docquier

 

Aim of the project

The goal of this research project was to model and analyse the dynamic behaviour of a complex bogie (the 'BA2000' bogie) which consists of an articulated chassis equipped with four independent wheels. This bogie equips the full-length low floor 'T2000' urban tramway.

The bogie has been originally designed to satisfy severe geometrical requirements (tracks with very low curve radius: up to 15 m, and low-floor carbody: less than 20 cm high). The present study was carried out with ROBOTRAN, developed by the CEREM, to analyse the dynamical behaviour of the system, in terms of lateral stability on straight track and entry curving. In particular, the independent wheel concept coupled with an articulated bogie frame was a possible source of instability, that a model must reveal.

System description

The BA2000 bogie (see figure) consists of an articulated chassis : a main crossbar, four articulated longitudinal beams, rods to close the loops and a special eccentric mechanism to ensure a 'sufficiently constant' wheel gauge when the bogie deforms. As regards deformation, in addition to the 'in-plane' one, an 'out-o-plane' deformation is also allowed (most of the joints are compliant spherical joints) to overcome track cross-level irregularities, the bogie being not equipped with primary suspension (except some very stiff bushing in the articulations).

The T2000 is composed of three carbodies whose the central one (shorter) is mechanically constrained by a roof bisector mechanism to keep a centred orientation during slope–downhill transitions. The front and the rear carbodies are carried by two BAS 2000 bogies, the central one by a classical rigid bogie.

Model special features

As regards the wheel/rail contact, a non-linear 3D model for an single independent wheel on a rail was developed [1] for general wheel/rail profiles, including flange contact. Tread forces are computed using the well-known Kalker’s theory and routines (linear theory, Fastsim, …).

From the numerical point of view, a particular attention was paid to the geometrical wheel/rail contact solution, by using a combined iterative method combining a dichotomic procedure and the Newton-Raphson method to find each wheel/rail contact point and to close the multibody loops of the system [1].

The dynamical multibody model of the BA2000 bogie (22 generalized relative coordinates) and/or the full tramway (3 carbodies + 3 bogies : 84 coordinates) were generated with our symbolic multibody software ROBOTRAN, including:

• the “open-loop” system equations of motion;
• the constraints equations (at algebraic, velocity and acceleration levels);
• the wheel kinematics (required by wheel/rail contact models).

Typical results

The desired analysis mainly dealt with transitory motions, to check for the vehicle lateral stability. Two typical results are presented here, on related to a straight track motion, the other one to a real entry curving in the Brussels railway network.

A BA2000 bogie carrying half a carbody was simulated on a perfect straight track. The ROBOTRAN modal analysis has unfortunately revealed an unstable mode involving the yaw deformation of the bogie. Practically, the flange contact prevents from derailment but the intermittent behaviour was obviously far from being acceptable since each contact involves a transverse impact force on the wheel, as illustrated in the next result (showing the intermittent yaw deformation of the bogie).

A full Tramway T2000 was simulated in entry curving (velocity: 7 m/sec, curve radius : 50 m). An interesting result is the time history of the so-called wheel/rail angle of attack (see figure on the right), that is responsible of the wheel wear due to friction.

In this case, as expected, the BA2000 wheels angle of attack is approximately 10 times lower than that of a classical bogie, thanks to its deformation capabilities (see next figure)

References

1. A New Wheel/Rail Contact Model for Independent Wheels, Fisette, P. et Samin, J.C., Archive of Applied Mech., 64 (1994), pp 180-191.
2. Lateral Dynamics of a Light Railway Vehicle with Independent Wheels, Fisette, P. et Samin, J.C., Supplement to Vehicle System Dynamics, 20 (1992), pp 157-171.