Dynamic analysis of a partially filled tanker train travelling on a curved track is studied in this paper. A partially filled tanker is dynamically modelled when it is travelling along a real curved track. For three classes of tracks, rail irregularities are randomly generated by using Monte Carlo simulation. An equivalent dynamic system is used to model the sloshing motion of the fluid. Two derailment indexes, i.e., derailment quotient and unloading ratio, are obtained numerically as safety indicators. A parametric study is carried out to investigate how different parameters such as the operational speed, fluid modelling, rail irregularities, and fluid density may affect the derailment potential. It is found that ignoring the sloshing may lead to ١٨% and ٢٥% error in the calculation of derailment quotient and unloading ratio, respectively. It is also found that lowering the centre of gravity and consequently reduction of the moment arms is more dominant than the oscillating forces due to sloshing motion. © ٢٠١٠ Inderscience Enterprises Ltd.

The movement of the liquid cargo within a partly filled tank car is known to impose additional slosh forces and moments that may adversely affect the dynamic responses of the vehicle. This study is aimed at analyzing the liquid cargo slosh in a partly filled tank car and its effects on vehicle responses during a switch-passing maneuver. A two-dimensional analytical liquid slosh model is formulated for the analyses of the liquid load shift in the roll plane, lateral slosh force, and roll moment through summation of first four antisymmetric modes of the liquid. The analytical slosh model is integrated to a 114 degrees-of-freedom multibody dynamic model of the railway tank car comprising nonlinear wheel–rail contact and contact pairs of the suspension system. The validity of the slosh model is illustrated by comparing the responses with those reported in other studies and those obtained from a nonlinear computational fluid dynamic model. The coupled fluid–vehicle model is subsequently used to study the effects of fluid slosh during switch-passing maneuvers on different response measures, namely roll motion of the tank car, lateral and vertical wheel–rail contact forces, and derailment ratio. The significance of the liquid cargo slosh in the partially filled state is demonstrated by comparing the responses with those of the car with equivalent rigid cargo. The results show that liquid sloshing within the partly filled car can lead to higher magnitudes of car body roll angle and thereby the unloading ratio compared to the conventional rigid cargo car. Switch-passing critical speeds are further identified for different fill ratios and switch geometries. For fill ratios below 80%, the switch-passing critical speeds of the partly filled car are substantially lower compared to those of the equivalent rigid cargo car. Neglecting the contributions due to dynamic slosh force and roll moment arising from a partially filled railway tank car may thus lead to underestimation of the critical speed in switch-passing maneuvers.

In this study, the nonlinear damping characteristics of friction wedges in the secondary suspension of a freight wagon are investigated considering nonsmooth unilateral contact, multiaxis motions, slip-stick conditions, and geometry of the wedges. The parameters of the contact pairs within the suspension were identified to achieve smooth and efficient numerical solutions, while ensuring adequate accuracy. A simulation model of the friction wedge was formulated and analyzed, which revealed highly nonlinear dependence on vertical, roll, and lateral motions between the bolster and the side frames. The friction wedge model was integrated into the multibody dynamic model of a three-piece bogie to study the effects of wedge properties on hunting characteristics. The resulting 114-degrees-of-freedom wagon model incorporated constraints due to side bearings, axle boxes, and the center plates, while the wheel-rail contact forces were obtained using the FASTSIM algorithm. The simulation results were obtained to study hunting properties of the wagon in terms of critical speed and the predominant oscillation frequency, and the effects of wedge friction and geometry on stability characteristics of the freight car. The results showed subcritical Hopf bifurcation of dynamic responses of the wagon. Moreover, an increase in the wedge angle, friction coefficient, and springs free length resulted in a higher critical speed.

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General purpose railway tank cars similar to road tankers are known to transport liquid cargo in partial-fill state due to variations in liquid cargo density and governing axle load limits. It is widely reported that the cargo movements constitute additional forces and moments that could strongly affect the wheel-rail interactions and coupling forces, and thereby the directional dynamics of the wagon. In this study, the linear slosh theory is used to describe the liquid cargo movement in the roll plane by a simple pendulum, which is integrated into a comprehensive nonlinear multi-body model of a three-piece truck to study the effects of liquid cargo slosh on lateral dynamics of the tank car. The model also incorporates the nonlinear secondary suspension restoring and damping forces, attributed to friction of the wedges, using the non-smooth contact method in addition to the geometric constraints of various components. The wheel/rail contact forces are simulated considering non-elliptical wheel-rail contact using the FASTSIM algorithm. The lateral dynamic responses of the multi-body model of a freight car with partially filled liquid load and an equivalent rigid cargo are evaluated to study the effect of cargo movement on the critical speed and the wheelset hunting oscillations frequency. The results obtained considering different fill ratios of the liquid cargo suggest that the fluid slosh yields additional damping effect on the lateral dynamics of the car. Liquid cargo movement within partly-filled tank car could thus yield a beneficial influence on the wheelset hunting. This was evidenced from the phase relationship between the lateral oscillations of the pendulum and the bogie/wheelset. Consequently, a partially filled tanker resulted in relatively higher critical hunting velocity compared to that of the wagon with equivalent rigid cargo.