Optimal Tank Geometry to Enhance Static Roll Stability of Partially Filled Tank Vehicles

A generic tank cross-section is formulated to describe the geometry of currently used tanks in transportation of fuel oils and bulk liquids, and to explore optimal tank geometry for enhancement of roll stability limit of tank vehicle combinations. The tank periphery, composed of 8 circular arcs symmetric about the vertical axis, allows more design flexibility in view of the roll stability limits than the conventional tank shapes. A shape optimization problem is formulated to minimize the overturning moment imposed on the vehicle due to c.g. height of the liquid load, and the lateral and vertical movement of the liquid bulk within the partly filled tank. Different optimal tank cross-sections are proposed corresponding to varying fill conditions, while the total cross-sectional area, overall height and overall width are constrained to specified values. A static roll plane model of the tank is developed and analyzed to study the potential performance benefits of the optimal cross-sections under various fill volumes, vehicle lateral acceleration and sprung mass roll angle. The magnitudes of lateral and vertical translation of the c.g. of the cargo within the proposed optimal cross-sections under a constant lateral acceleration field are compared with those obtained with currently used cross-sections to demonstrate the performance potentials of the optimal shapes. The proposed optimal tank geometry and the steady-state fluid slosh model are integrated with the static roll model of a tractor-semitrailer vehicle to derive the performance gain in terms of rollover threshold lateral acceleration limit of the vehicle for different liquid fill conditions. The analyses are performed for conventional as well as for the proposed optimal tank cross-sections. A comparison of the results revealed that the rollover threshold of the vehicle equipped with the proposed optimal tank geometry is approximately 15% higher than that of the vehicle equipped with modified oval or circular cross-section tanks.