The Influence of Low-Order Wheel Polygonization on the Nonlinear Dynamic Transition Characteristics of the High-Speed Train Vertical System

The periodic excitation force generated by the wheel polygonal wear induces abnormal vibration, which affects the operational stability of the train. However, there are few reports on the influence of wheel polygonal order on the dynamic behavior of vehicle systems based on nonlinear dynamics theory. In this paper, the quarter high-speed train is taken as the research object, and a vertical vibration system model with nonlinear stiffness of the air spring is established. The influence of harmonic excitation on the vehicle vertical system is analyzed. The fourth-order R–K numerical method with variable step size is used to calculate the system response. Combined with the qualitative analysis method of nonlinear dynamics theory, the bifurcation form and transition characteristics of the motion state of the system under different orders of evolution are analyzed. The results show that with the evolution of the wheel polygonal order, the system transitions sequentially from period-doubling bifurcation, Neimark–Sacker bifurcation and boundary crisis to chaotic motion. Consequently, the nonlinear dynamic behavior of the system becomes increasingly complex. The wheel polygonal order is positively correlated with the vertical amplitude of the car body, but the amplitude changes gradually tend to be consistent after the evolution to the 7th harmonic. The chaotic vibration caused by the 5th- to 10th-order harmonics of the wheel polygonal wear can be suppressed by increasing the damping coefficient of the primary suspension. The nonlinear dynamic characteristics and chaotic motion evolution of the high-speed train vertical system under wheel polygonal excitation are further studied. It provides a theoretical basis for the prediction and control of chaos in train vibration reduction design and daily operation and maintenance.