Hydrodynamic Model of Transport System

Abstract

A hydrodynamic model of production systems with a flow method of organizing production is considered. The basic macroparameters of the state of the production flow line and the relationship between them are determined. The choice of a lot of moment approximation for modelling the production line is justified. It is shown that the conveyor-type flow line is a complex dynamic system with distributed parameters. The boundary value problem is formulated for the longitudinal vibrations of the conveyor belt when the material moves along the transportation route. It is assumed that there is no sliding of material along the conveyor belt, and the deformation that occurs in the conveyor belt is proportional to the applied force (Hooke's elastic deformation model). The significant effect of the uneven distribution of the material along the transportation route on the propagation velocity of dynamic stresses in the conveyor belt is shown. When constructing the boundary and initial conditions, the recommendations of DIN 22101: 2002-08 were used. The mechanism of the occurrence of longitudinal vibrations of the conveyor belt when the material moves along the transportation route is investigated. The main parameters of the model that cause dynamic stresses are determined. It is shown that dynamic stresses are formed as a result of a superposition of stresses in the direct and reflected waves. Analytical expressions are written that make it possible to calculate the magnitude of dynamic stresses in a conveyor belt and determine the conditions for the occurrence of destruction of the conveyor belt. The characteristic phases of the initial movement of the material along the technological route are considered. The process of the emergence of dynamic stresses with the constant and variable acceleration of the conveyor belt is investigated. The dynamics of stress distribution along the transportation route is presented. It is shown that the value of dynamic stresses can exceed the maximum permissible value, which leads to the destruction of the conveyor belt or structural elements. The transition period is estimated, which is required to ensure a trouble-free mode of transport operation during acceleration or braking of the conveyor belt. The use of dimensionless parameters allows us to formulate criteria for the similarity of conveyor systems.

Hydrodynamic Kelvin-Voigt Model Transportation System

“…The article [15] analyzes the models of the elastic element Kelvin-Voigt element, the combination of Hooke and Kelvin-Voigt element, as well as the combination of two Kelvin-Voigt elements. The analysis of long-wave oscillations in the conveyor belt of the transport system for the Hooke element model and the analytical model of the transport system is presented in [1]. The mechanical properties of composite materials for the manufacture of a rubber conveyor belt with polyester and polyamide cartridges are given in [16].…”

“…The analysis of the arising deformations in accordance with Hooke's law was investigated in [1]. Substituting expression (7), which determines the relationship between stress and strain, into equation 6, we obtain…”

“…In article [1], the hydrodynamic Hooke's model of a transport system is considered, which was used to analyze the mechanism of the occurrence of longitudinal vibrations in a conveyor belt when material moves along a transportation route. To construct a model of the transport system, the equations of two-moment description (2) were used in the form [1,2]:…”

“…is located can be calculated as follows [1,Fig. 1]: where dm is the total mass acting on the belt; B is conveyor belt width; h is conveyor belt height; ) , ( S t  is conveyor belt tensions; W F is sum of total resistances to belt movement [1]:…”

“…Descriptions of each component of the secondary resistance (5) are discussed in detail in [1]. Detailed information on the methods for calculating secondary resistances is given in [4].…”