A Simple Model-Based Method for Sloshing Estimation in Liquid Transfer in Automatic Machines

Abstract

This paper studies the phenomenon of sloshing in the field of automatic machines for packaging of liquid products, with specific reference to containers with planar motions. After introducing two equivalent discrete models based on a mass-spring-damper system borrowed from the literature (one linear and one non-linear), a novel method is proposed to evaluate the sloshing height of the liquid, namely the deviation of its free surface at the wall of the container from the equilibrium condition. The merits of this method are that it is easy to use, requiring no experimental evaluation of the system parameters or computationally-expensive fluidodynamical simulations, and it gives good results also for highly dynamical motions. Moreover, though this paper focuses on cylindrical containers performing rectilinear movements, the technique therein presented can be extended to containers of arbitrary shape and generic planar motions. The method is validated by experimental tests using cylindrical containers of different dimensions and a large number of rectilinear motion laws with maximum accelerations up to 12m/s 2 . The results are compared with those that may obtained by using other methods of equal complexity available in the literature, showing the effectiveness of the proposed technique.

Sloshing dynamics estimation for liquid-filled containers performing 3-dimensional motions: modeling and experimental validation

“…A novel technique for the sloshing-height estimation of a liquid inside a cylindrical container subject to 2-dimensional planar motions was proposed, extending what was presented in [17]. The technique is based on simple discrete mechanical models, rather than machinelearning or complex fluid dynamics methodologies, thus granting a reliable and easy-tocompute estimation.…”

“…To overcome this drawback, a novel approach, based on the mass-spring-damper model [16], is proposed in [17] for the sloshing-height estimation. This model is validated for 1-dimensional motions in [17] and it is exploited in [18] and [19] to plan antisloshing trajectories.…”

“…To overcome this drawback, a novel approach, based on the mass-spring-damper model [16], is proposed in [17] for the sloshing-height estimation. This model is validated for 1-dimensional motions in [17] and it is exploited in [18] and [19] to plan antisloshing trajectories. The same technique is used in a software application presented in [20] to execute simulations of liquid sloshing in cylindrical and rectangular containers.…”

“…The same technique is used in a software application presented in [20] to execute simulations of liquid sloshing in cylindrical and rectangular containers. In [17], the authors propose the possible extension to planar motions, but no experimental validation is provided. The latter is the objective of this paper, particularly referring to 2-dimensional planar motions of a cylindrical container, with accelerations up to 9.5 m/s 2 .…”

Sloshing Dynamics Estimation for Liquid-filled Containers under 2-Dimensional Excitation

“…However, estimating the sloshing height by means of the tangent of the pendulum angles may lead to singularity conditions, when the container acceleration is high, since in this case these angles can approach 90 • and the tangent tend to assume unrealistic high values. To overcome this drawback, a novel approach, based on the mass-spring-damper model [11], is proposed in [12] for the sloshing-height estimation. This model is validated for 1-dimensional motions and the authors propose the possible extension to planar motions, but no experimental validation is provided.…”