The paper provides a model to describe the dynamical performances of the three-piece-fright truck. The model has 19 rigid bodies and 81 degrees of freedom. The focus is put on the two-dimensional dry friction on the surfaces of the wedges in the lateral and vertical directions, and on the contact surfaces between the side frames and the adapters (wheelsets). The stick- slip motion between the corresponding components caused by the friction and the structure varying systems occurring together with the stick-slip motion are considered. The friction direction angle, the switch condition and the acting friction force are used in the model. The critical speed is determined through Hopf bifurcation analysis. The phase diagram and first return map are used to verify the chaotic motion of the systems. The dynamic responses and the wheel/rail contact forces to the irregularity track are provided.