Semi-analytical Hopf bifurcation analysis of self-excited hunting motion in railway vehicles

Hunting stability is critical for the safe operation of high-speed railway vehicles, and reliable analysis of self-excited vibration systems supports efficient vehicle design and control. This work develops an efficient semi-analytical method for Hopf bifurcation analysis of railway vehicle hunting motion based on the Incremental Harmonic Balance (IHB) method. A lateral dynamics model incorporating carbody flexibility, Shen-Hedrick-Elkins creep forces with saturation characteristics, and Maxwell dampers is established. By introducing an implicit phase constraint strategy combined with FFT-accelerated Jacobian assembly and arc-length continuation, the proposed IHB method traces both stable and unstable solution branches and achieves a more than 100-fold speedup over conventional numerical integration. Based on this approach, comprehensive parametric Hopf bifurcation analyses reveal a hierarchical distinction in influence mechanisms: geometric parameters govern hunting instability through kinematic coupling and dominate both critical velocity and limit cycle amplitudes, whereas dissipative parameters primarily affect stability margins. The proposed method provides an effective alternative for hunting stability analysis of railway vehicle systems.