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In order to further reveal the vertical random vibration characteristics of railway vehicles, using the system engineering method, taking the passenger, the train system, and the track system (ballast track) as a unified whole, a passenger-train-track vertical coupling dynamic model is established, and the vibration differential equations of the model are derived. In the model, passengers are regarded as a single-degree-of-freedom system attached to the bottom of the carriage, the train system is represented as a 10-degree-of-freedom multi-rigid body model, the track system is regarded as the infinite long Euler beam model with three layers of continuous elastic point support, and the Hertz nonlinear elastic contact theory is applied to the wheel and rail coupling relationship. Based on this, the time-domain numerical solution of the passenger-train-track vertical coupling dynamic model is given by using Newmark- β implicit integration algorithm, and the correctness of the model is verified by the real vehicle test. This study can provide some theoretical basis for the design of railway vehicles and provide fundamentals for the coordinated control and system optimization of railway vehicle ride comfort.

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The strong vibration responses of the cab system can be restrained by the damper force and the friction of the suspensions for trucks. After the failures of dampers, especially in the case of the complete failure, the anti vibration effect of the friction is prominent. However, the nonlinear vibration response characteristics of the cab subject to the damper complete failure have not been revealed. In order to reveal the nonlinear vibration response characteristics, a dynamic model of the cab system was established and its vibration equations were given. The friction forces existing in the suspensions were determined by the bench test. The influences of the friction forces on the cab vibration under different amplitude harmonic inputs were investigated when the dampers completely fail. The cab vertical displacement changes with the excitation amplitude and the vibration represents various motion states, including the periodic motion, the quasi-periodic motion, and the chaotic motion. The simulation results show that when the dampers fail, the proper friction forces help to suppress the quasi-periodic motion and the chaotic motion of the cab and to reduce the amplitude of the periodic motion. The proper friction forces can make the cab movement far away from the chaos area. They also help to avoid the fatigue damage of the cab floor and suspension parts to improve the service life of the suspension parts and to reduce the maintenance cost of the cab suspensions.