Effect of liquid sloshing in lateral and longitudinal directions on railway tank cars based on an improved equivalent model

Additional slosh forces and moments are generated owing to the movement of the liquid inside a partly filled tank car. The loads may have a great influence on the structure reliability and dynamic performance of the vehicle. An improved equivalent model of liquid sloshing is put forward to obtain the forces and moments of sloshing liquid acting on the tank during the lateral and longitudinal sloshing processes. An improved method is proposed to obtain the equivalent masses and stiffness for the improved equivalent model. The equivalent model is integrated into the multi-body dynamic model of a railway tank car with 68 degrees of freedom. Furthermore, the equivalent liquid-vehicle model is used to investigate the effects of fluid sloshing on dynamic characteristics. The influence of the filling ratio on the dynamic response of the tank car is discussed based on the forces and the corresponding moments between the tank car body and the liquid in different layers. The railway tank car is obviously influenced by the liquid sloshing during passing the curved and sloped tracks. The influence of liquid sloshing on the pitching motion of the tank is heavy if the tank is about half filled. The derailment coefficient and the wheel unloading rate are slightly influenced by the filling ratio of tank cars on curved tracks while the indices of the tank cars on sloped tracks are the greatest if the filling ratio is 40%.