Application of hopf bifurcation at infinity to hunting vibrations of rail vehicle trucks

Many models of train wheelset systems involve Coulomb friction terms and model the flange rail forces as stiff linear springs with dead bands. For such systems, the regular theory of Hopf bifurcation is not applicable, whereas a newly developed theory of Hopf bifurcation at infinity can be used. This is because such systems are basically linear as far as very large amplitude motions are concerned. In this paper, we apply this theory to study the oscillations of a wheelset using a numerical algorithm. Comparisons with the results obtained by the describing function method are also made.