Hydrodynamic Model of Transport System

A hydrodynamic model of production systems with a flow method of organizing production is considered. The basic macro-parameters 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.