The focus of this research topic is on the dynamic, in particular, vibrational behaviour of the mtb and its unknown influence on the braking behaviour. Therefore, a system model, including the elastic frame of the mtb, the frictional contact, the electric wiring, and the magnetic attraction for a number of magnets, electrically and mechanically linked with each other, will be derived and investigated in detail. Systems including frictional contact are prone to (in the application already observed) self-excited vibrations. Limit cycles with possibly harmful amplitudes may emerge. Consequently, system parameters affecting stability and vibrational behaviour will be analysed. To reduce adverse effects of self-excited vibrations, or vibrations after impacts of the magnets with the rails, strategies to control the current/voltage of the electromagnets will be investigated.

Bifurcation theory and continuation methods will be applied to analyse post-critical stability behaviour. A minimal model, including as few (electromagnetic and mechanical) degrees of freedom as possible to map the system behaviour, will allow for a more fundamental understanding. Basic findings will then be reviewed by experiments and by a full multibody dynamics system (MBS) model, including the mechanical (rigid and elastic) parts and the electromagnetic models for the four corner electromagnets. The conditions for the onset of possible self-excited vibrations, i.e. loss of stability, will be studied with both modelling approaches. Passive and control-based countermeasures will be developed and investigated with the minimal model and tested on the complex model.

The general aims of this research topic are:

  • Investigation of the dynamic behaviour of the mtb on straight tracks: coupling effects of the vibrational behaviour of the elastic frame on the frictional and electromagnetic forces at the contacts of the pole shoes will be studied.
  • Passive and active ways to limit amplitudes of occurring limit cycles, when braking to full stop, will be derived and investigated in detail.
  • Investigation of occurring limit cycles and the post-critical behaviour of complex electromagnetic-mechanical systems.
  • Implications of possible lightweight design for the mtb on the braking performance as well as on the vibrational behaviour will be investigated.
  • The dynamic behaviour of the mtb when braking over switches and crossings that is the most complex and critical in particular considering lightweight will be studied in detail.
Graphical model of dynamical behaviour

First three eigenmodes of the brake frame: (a) first asymmetric mode; (b) first symmetric mode; (c) second asymmetric mode.