Role of sprag angle in friction-induced vibration in catenary–pantograph systems

Suppressing friction-induced vibration (FIV) in catenary–pantograph systems is critical because it impacts both stable transportation and maintenance costs. Numerous studies have investigated FIV using analytical, experimental, and numerical methods. However, none of these studies considered the sprag angle—the upper-frame angle of the pantograph—although its role in brake squeal has been extensively investigated. This study integrates full-scale experiments, a flexible multibody dynamics (MBD) model, and theory to elucidate the role of the sprag angle in FIV in catenary–pantograph systems. Experiments with an actual pantograph demonstrate that FIV is self-excited, and transitions to impact vibration, and that larger sprag angles and higher friction destabilize the system and shift the dominant FIV frequency. On the numerical side, we propose a fast equilibrium solver for the pantograph that enables efficient flexible MBD simulations. Moreover, complex eigenvalue analysis reproduces the measured stability boundaries, growth rates, and dominant frequencies. Mechanistically, a circulatory matrix induced by Coulomb friction drives mode coupling; the eigenvalues depend strongly on the sprag angle, explaining the observed frequency shifts. The model further shows that effective countermeasures require both adjusting the sprag angle and mitigating mode coupling. We also clarify, theoretically, the relationship between the eigenvalue perturbation and mode displacement methods. The results demonstrate that combining these approaches enables a deeper understanding of FIV and that FIV can be captured, both qualitatively and quantitatively, by a three-degree-of-freedom system. This combined approach advances FIV research and contributes to other fields that address mode coupling.