@MASTERSTHESIS\{IMM2011-06105,
    author       = "D. Bigoni",
    title        = "Curving Dynamics in High Speed Trains",
    year         = "2011",
    school       = "Technical University of Denmark, {DTU} Informatics, {E-}mail: reception@imm.dtu.dk",
    address      = "Asmussens Alle, Building 305, {DK-}2800 Kgs. Lyngby, Denmark",
    type         = "",
    note         = "Supervised by Associate Professor Allan Peter Engsig-Karup, apek@imm.dtu.dk, {DTU} Informatics",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "This work presents a model for a generic railway vehicle running on straight or curved track with different profiles. The model employs the Newton-Euler formulation for dynamical systems. The wheel-rail interaction is modeled using the Hertz's static contact theory, corrected with the Kalker's theory for dynamical wheel-rail penetration. Tangential forces on the wheel-rail contact point are computed using the Kalker's linear theory with the appropriate corrections provided by the Shen, Hedrick and Elkins non-linear theory. Several type of elements of the suspension system have been modeled. The model is implemented in the program {DYTSI}. This is a framework for designing and testing railway vehicle models. {DYTSI} includes four numerical {ODE} algorithms that are used along the work: the Bulirsch-Stoer method, the Backward Differentiation Formula and two {ESDIRK} methods in the versions by Nielsen-Thomsen and by Jrgensen-Kristensen-Thomsen.
The hunting phenomenon has been studied on the Cooperrider model on straight and curved track. Results of previous works have been confirmed using {DYTSI}. The importance of precession forces on the dynamics, due to the high speed spinning of the wheel sets, has been highlighted. Additional results have been obtained for a complete wagon model and the symmetry assumption of the model running on straight track was rejected as different behaviors for the leading and trailing parts were obtained. On curved tracks the passage from the subcritical Hopf bifurcation to the super critical Hopf bifurcation was confirmed, for certain radii, also for the complete wagon model.
The dynamics of an {AGV} model, provided by {ALSTOM,} have been studied on curves with big radii and high cant deficiency. The results obtained, for the model running on smooth tracks, have been confirmed. Finally, the performances of the four {ODE} solvers have been compared on the highly stiff train dynamics problem. The {ESDIRK} methods have shown better stability for relaxed tolerances, but they require a big computational effort for finding accurate solutions. The {BDF} and the Bulisrch-Stoer methods turned out to be computationally more efficient, but they encountered stability problems on some of the test cases."
}