Abstract: Based on some truck suspension model consisting of primary and subsidiary spring, a two-degree-of-freedom system with piecewise-Based on truck suspension model consisting of primary andsubsidiary springs, a two-degree-of-freedom system with piecewise-linearityinvolved in discontinuous damping force is established The stroboscopicPoincaré map is established, and the saltation matrix is deduced byzero-time discontinuity mapping method at the interface. The resultindicates that the saltation matrix is independent on spring rate, but isnot independent on damping force. The Neimark-Sacker bifurcation point isinvestigated by the numerical calculation. The research on bifurcation andchaos can contribute to optimizing design in impacting systems.