Abstract Summary
Magnetic track brakes (mtbs) are additional braking systems used in railway vehicles at emergency situations and low adhesion conditions. While the mtb is active, the electromagnets create magnetic attraction forces between the rail and the brake and occurring friction forces in the mtb—rail contact are transmitted to the bogie. At low velocities, mtbs were typically deactivated to avoid stopping jerks. However, trends of increasing operational speed put highest demands on the braking performance of railway vehicles and require activation until full stop. This can cause harmful self-excited vibrations of the mtb. Some passive countermeasures are already published, [1], but may not always be reasonable, because of constraints in the design or negative aspects regarding weight or braking performance. To overcome these drawbacks and to gain deeper system understanding, strategies for active vibration control of an mtb are investigated, not addressed in literature so far. This paper builds on preliminary work from [1], where the stability behavior of the mtb was studied in detail and on considerations from [2], where the input of mechanical energy, during one oscillatory period, is used for stability investigations. There, an active control of the normal force on a basic friction oscillator was presented, which minimizes the input energy and diminish the vibrations. In this study, the electromagnet of the mtb serves as actuator and the electric voltage as the regulated variable of the implemented state feedback. Since the states of the coupled electromagnetic-mechanical system cannot be measured directly a state observer based on the electric current (system output) and voltage (system input) is used. To ensure the functionality of the controller, necessary requirements of the system, such as controllability and state-observability are discussed. Different approaches to diminish self-excited vibrations are studied, based on reducing the energy fed into the oscillating system. Considering a minimal model of the mtb the input energy depends on the electromagnetic-mechanical coupling and the friction force in the mtb—rail contact, which were both identified as self-excitation mechanisms in [1]. With a harmonic approach for the states the input energy is calculated for the linearized system. The obtained equation shows dependencies of the phase shift between magnetic flux and the oscillatory mechanical motion, the model parameters and the steady state values. For certain parameters an optimal phase shift between flux and motion is identified to minimize the calculated energy. These findings are used together with the electromagnetic model to obtain a control law for the input voltage. By comparison of the numerical simulations, the obtained control strategies applied on the linearized and the non-linear model, are evaluated with respect to effectiveness and necessary energy effort. [1] Tippelt D. et al. Modelling, analysis and mitigation of self-excited vibrations of a magnetic track brake, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2021 [2] Popp K. Modelling and control of friction-induced vibrations. Mathematical and Computer Modelling of Dynamical Systems. 2005.
