Control of liquid sloshing in open containers on industrial packaging lines (1)

Abstract: The sloshing control of the liquid in the open container on the industrial packaging line was studied. The equations of state of the linear filling control system for the rectangular container, the cylindrical container and the general upright rotational symmetry container were established. Using the optimal energy control scheme, a linear control law was obtained. The relationship curve between the motion time step and the response of the surface wave height was obtained. The numerical simulation experiment was performed for the shake control of the rectangular container. The difference between the theoretical results and the simulation results, as well as the analysis of the effect of the residual energy of the liquid sloshing, is compared, and the applicable range of the linear model is given.

Keywords: liquid sloshing; optimal control; industrial packaging line

It is a routine operation in the packaging industry to allow an open container of liquid to flow on the assembly line. Improving the flow process is extremely important for optimizing packaging costs and profits. Because the current packaging line has multi-purpose performance and can quickly change different packaging products, it is extremely important to input different optimized motion programs for different products. The operation of the packaging machine can be decomposed into: molding, filling and sealing, and 3 sub-operations are performed at the same time. Therefore, the conveyor belt movement is a gap type, when the packaging machine to perform the molding, filling and sealing operation, after the operation of the conveyor belt forward movement of a unit position. Since the residence time of the conveyor belt depends on the operating efficiency of the packaging machine, this time is usually fixed. Therefore, the optimization actually refers to the optimization of the time for one unit position of the conveyor belt movement.

Since the product between the filling machine and the sealing machine is an open container filled with liquid, the optimization of the movement of the conveyor belt must take into account whether the shaking of the liquid in the container will cause spillage. Because once it overflows, the product will be damaged and the packaging efficiency will be reduced.

This paper studies the optimal control of the movement of the open-filled container on the packaging line, corrects the Grundelius model, and generalizes the model to general rotationally-symmetric containers. For the approximation of the linear model, this paper uses ANSYS/FLOTRAN to simulate the system.

1 Liquid shaking model

The liquid sloshing model under the excitation motion outside the container has been extensively studied in the fields of aerospace, vehicle and ship dynamics and seismic engineering [2]. The most accurate liquid shaking model is described by a set of three-dimensional nonlinear partial differential equations. The model can be used for numerical simulation. Especially when the container is moving fast and the liquid wave height is quite large, the nonlinear effect is quite obvious. The liquid sloshing linear model established in this paper is suitable for the small wave height motion state.

(to be continued)