Abstract
The Maglev vehicle Transrapid is levitated by magnetic forces which pull the vehicles levitation frames toward the guideway from below. The magnets possess poles with alternating fluxes which are part of the synchronous long stator linear motor. Although the Transrapid glides along its guideway without mechanical contact, this alternation as well as the loading and unloading of the guideway girders excite vibrations of the ground. In order to calculate the time behavior of the vibrational emissions, a simulation of the transfer of a Transrapid vehicle over several guideway girders is proposed. The equations of motion for the vehicle and the girders are calculated separately by the MBS software NEWEUL and assembled and numerically integrated in MATLAB/SIMULINK. The control law for the magnet forces is simplified by the characteristics of linear spring-damper elements. The controlled magnet forces travel along the guideway continuously and include the dynamic component due to the alternating fluxes and the geometry of the poles and stator. Results of a complete vehicle moving along a guideway consisting of several girders can be obtained within a few minutes of computation time. Therefore, the mechanism of excitations can be analyzed by numerical time integration in the full state space. The results are validated by measurements of the forces in the joints of the guideway girders. The vibrational emission along the Transrapid guideway differs from the vibrations of contact-afflicted vehicles as no impacts and fewer stochastic effects occur.
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References
Deutsches Institut für Normung: Messung von Schwingungsimmissionen. DIN–Norm, DIN 45669 (1995)
Deutsches Institut für Normung: Erschütterungen im Bauwesen. DIN–Norm, DIN 4150 (2001)
Eisenbahn Bundesamt: Regeln der Technik—Magnetschnellbahn Ausführungsgrundlagen, Gesamtsystem. Published on EBA’s website, Doc.-no. 50630 (2006)
Gottzein, E.: Das Magnetische Rad als autonome Funktionseinheit modularer Trag- und Führsysteme für Magnetbahnen. VDI–Fortschritt-Berichte, Reihe 8, vol. 68. VDI Verlag, Düsseldorf (1984)
Hägele, N.: Vertikaldynamik der Magnetschwebebahn Transrapid unter besonderer Berücksichtigung der Fahrwegdynamik. Diploma Thesis DIPL–112, Institute B of Mechanics, University of Stuttgart (2006)
Kreuzer, E., Leister, G.: Programmsystem NEWEUL’90. Institute B of Mechanics, University of Stuttgart, AN-24 (1991)
Meisinger, R.: Beträge zur Regelung einer Magnetschwebebahn auf elastischem Fahrweg. Ph.D. thesis, Fachbereich für Maschinenwesen, Technical University of Munich (1977)
Meisinger, R.: Optimale Regelung periodischer Systeme mit sprungförmiger Zustandsänderung. Z. Angew. Math. Mech. 57, T79–T81 (1977)
Meisinger, R.: Simulation of a single and double-span guideway under action of moving maglev vehicles with constant force and constant gap. Schriftenreihe der Georg-Simon-Ohm-Fachhochschule Nürnberg (14) (2002)
Miller, L.: Transrapid, Innovation für den Hochgeschwindigkeitsverkehr. Bayerischer Monatsspiegel (4), 34–45 (1998)
Müller, G., Lutzenberger, S.: Vibrations induced by maglev-trains—a hybrid numerical-analytical-engineering approach. In: Proc. of the 6th German Japanese Bridge Symposium, München (2005)
Popp, K.: Beiträge zur Dynamik von Magnetschwebefahrzeugen auf geständerten Fahrwegen. VDI–Fortschritt-Berichte, Reihe 12, vol. 35. VDI Verlag, Düsseldorf (1978)
Popp, K., Schiehlen, W.: Dynamics of magnetically levitated vehicles on flexible guideways. In: Pacejka, H. (ed.) The Dynamics of Vehicles on Roads and on Railway Tracks, pp. 479–503. Swets & Zeitlinger B.V., Amsterdam (1976)
Raschbichler, H.G.: Entwicklungslinie Magnetschnellbahn Transrapid. In: Rausch, K.F., Rießberger, K., Schaber, H. (eds.) Sonderheft Transrapid. ZEVrail, Glasers Annalen, vol. 127, pp. 10–16. Georg Siemens Verlag, Berlin (2003)
Rausch, K.F., Rießberger, K., Schaber, H.: Sonderheft Transrapid. ZEVrail, Glasers Annalen, vol. 127. Georg Siemens Verlag, Berlin (2003)
Schach, R., Jehle, P., Naumann, R.: Transrapid und Rad–Schiene–Hochgeschwindigkeitsbahn. Springer, Berlin (2006)
Schiehlen, W., Eberhard, P.: Technische Dynamik. Teubner, Wiesbaden (2004)
The Mathworks: MATLAB/SIMULINK. Version 7, R14. www.themathworks.com (2005)
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Hägele, N., Dignath, F. Vertical dynamics of the Maglev vehicle Transrapid. Multibody Syst Dyn 21, 213–231 (2009). https://doi.org/10.1007/s11044-008-9136-0
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DOI: https://doi.org/10.1007/s11044-008-9136-0