Modeling Transient Liquid Slosh Behavior at Variable Operating Speeds Induced by Intermittent Motions in Packaging Machines

The present paper deals with the problem of modeling liquid slosh occurring in the packaging process of containers filled with liquid. Sloshing effects are induced by one-dimensional intermittent motions and are undesired due to the necessity of quality control processes, such as weighing. Therefore, motion optimizations are often applied with the intention to minimize the residual vibrations. Valid process models are required to do so. The aim of this paper is to derive models for describing the liquid slosh behavior for different motions and for common practical circumstances, e.g., different container geometries as well as machine operating speeds, and to state the model's limits of use. Known model approaches are discussed, and their assumptions are reviewed experimentally. This leads to a set of limited ranges of operating speeds in which the applied models' assumptions are valid. The models are derived for these sets from experimental data, and a comparison is executed that enables the determination of the models' validity concerning their operating speed dependency. Finally, the validity of the derived models is investigated by comparing their predictive efficiency of describing the vibration for different motion profiles.