Modelling, analysis and mitigation of self-excited vibrations of a magnetic track brake

Abstract

Magnetic track brakes work independently of the wheel–rail contact as an additional braking system in railway vehicles. In the past, magnetic track brakes were usually deactivated at velocities below 25 km/h in mainline applications to avoid stopping jerks. However, current demands on braking performance require activation until full stop. During field tests on this subject, severe self-excited vibrations were measured at velocities below 25 km/h. This study analyses the oscillations observed by focusing on the stability behaviour of a simplified linear coupled electro-magneto-mechanical model of the track brake. Key parameters are identified by applying established criteria of linear stability theory. To account for essential nonlinear effects, a detailed multibody dynamics model with flexible bodies including a more enhanced electro-magnetic model is introduced and parameterised by using measurement data. Simulation results reveal two separate (or combined) mechanisms that may lead to self-excitation. On the one hand, friction-induced vibrations between the magnets and the rail; on the other hand, coupling effects between the electro-magnetic and the mechanical subsystems of the track brake may be the cause of the self-excited vibrations observed. Stability behaviour is influenced by various design parameters and in particular by the contact conditions between track brake and rail. Finally, a few passive methods are briefly discussed that may help to mitigate or reduce self-excited vibrations at low velocities in future designs of track brakes.

Active mitigation of self-excited vibrations of a magnetic track brake

“…The brake forces rise towards low velocities, which is expected because of the friction characteristic of the mtb-rail contact. The coefficient of sliding friction increases with decreasing velocity, while the gradient becomes even steeper at small velocities, [5]. At v v ≈ 20 km/h (t ≈ 17 s), vibrations start to occur and amplitudes of the brake forces rise up to FBx ≈ 8 kN with a mean value of approximately FBx ≈ 13 kN and a frequency of f osc = 28.5 Hz.…”

“…The amplitudes of the bending moments MCBz,l and MCBz,r at the opposite connecting beams are in phase while braking forces show a phase shift of 180 • , which implies that the excited eigenmode of this vibration is an asymmetric mode with a measured frequency of 28.5 Hz. The mode was identified as the first asymmetric bending mode by FE-analysis in [5]. Detail (a) in Fig.…”

“…2 shows that the electric current i C and the vehicle velocity v v remain approximately constant during the amplitude increase of the bending moments in (c). In [4] and [5] the stability behaviour of an mtb was studied for a simplified linearized quarter model, tuned to match the eigen-mode and frequency of the real system. Investigations with this model revealed two self-excitation mechanism as mentioned previously and were validated with a full system model.…”

“…with parameters a hyp , a hyp0 , b hyp and the vertical distance z between magnet and rail. The electromagnetic (EM) forces, acting on the mechanical system, can be derived from the partial derivative of the magnetic co-energy, [5], with lateral displacement from the middle of the rail head y = lα:…”

“…It was shown that system parameters can be tuned, within reasonable limits, to get positive real parts of the eigenvalues of the linearized system, indicating a loss of asymptotic stability. In [5] passive remedies to mitigate self-excited vibrations at mtbs and their positive influence were presented, but may not always be reasonable, because of constraints in the design or negative aspects regarding weight or braking performance. To overcome drawbacks from passive mitigations and to gain deeper system understanding, this paper presents first investigations on active vibration control at the coupled electromagnetic-mechanical system of an mtb, which is not addressed in literature so far.…”