Hydrodynamic Kelvin-Voigt Model Transportation System
Abstract
The hydrodynamic Kelvin-Voigt model of production systems with a flow method of organizing production is considered. The main macro parameters of the state of the production line and the relationship between them are determined. The analysis of the main characteristics of models of elastic elements, which are used to analyze the occurrence of the dynamic stresses in a moving conveyor belt, is presented. A boundary value problem for elastic longitudinal vibrations in a conveyor belt with a moving material is formulated. It is assumed that the deformation of the conveyor belt element corresponds to the Kelvin-Voigt model and there is no sliding of the moving material on the belt. When determining the forces of resistance to motion acting on an element of the belt, the recommendations of DIN 22101: 2002-08 were used. The analysis of the Kelvin-Voigt model of the elastic element is carried out and the distinctive features of the model are demonstrated. The justification of the choice of the Kelvin-Voigt model of an elastic element for describing the process of occurrence of the longitudinal vibrations in a conveyor belt is given. The dependence of the non-uniform flow of material and the magnitude of tensions in the belt is estimated. An expression is written for the speed of propagation of disturbances along a moving conveyor belt with the material. The reasons for the acceleration and deceleration of the conveyor belt associated with the uneven supply of material at the entrance of the transport system are determined. The relationship between the speed of a conveyor belt and the mass of material along a section of the conveyor is demonstrated. It is shown that an increase in the power of the electric motor at the start and acceleration of the conveyor belt, as well as a decrease in power during the braking and stopping of the conveyor belt, is the cause of the appearance of dynamic stresses in it. The characteristic phases of the initial movement of the conveyor belt with the material are analyzed. The process of occurrence of dynamic tensions with the constant and variable acceleration of the conveyor belt for the phase of acceleration and deceleration of the conveyor belt is investigated. For the analysis, a dimensionless model of a conveyor line was used. An expression is obtained for static and dynamic tensions in the conveyor belt. The amplitude of oscillations of dynamic stresses and the characteristic time of damping of oscillations in a conveyor belt is estimated. A quadratic dependence of the speed of damping of a wave of dynamic tensions with an increase in the oscillation frequency is demonstrated. An inversely proportional dependence of the characteristic decay time of the generated dynamic tensions on the value of the viscosity coefficient of the composite material of the conveyor belt is shown.
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