Abstract
A method of constructing a system of multi-moment balance equations, based on the statistical description of a production system is proposed. The need for research is determined by current trends in the development of production systems. The system of equations, which simulates the behavior of the production line for the transient conditions is obtained. It is shown that the resulting balance equations are not closed. The methods of closure of the self-linking chain of balance equations: the small-parameter method and the method of setting the equations of states for higher-order moments are considered. The known models using various methods of closure of the system of equations are analyzed. The model of the production line for the assembly-line production method is considered. The limitations and constraint equations, which enable the transition to single-moment PDE model of description of the assembly line and two-moment PDE model of the production line using the Burgers' equation are shown. The model of the production line for the company with the flow production method is considered. One-, two- and three-moment systems of equations for the two-level model of the production line are obtained. A general system of balance equations for the flow parameters of the production line is constructed.
Highlights
The models containing partial differential equations (PDE models) for designing production lines have been developed in recent decades [1,2,3,4,5,6,7]
The emergence of new types of models is due to trends of modern industrial production, the main of which is the trend to a continuous reduction of the product life cycle
This trend leads to the fact that, on the one hand, production lines operate for a considerable time in transient unsteady conditions, [3,4,5,6,7], on the other hand, the time for searching for the control mode of technological sites of the production line, is reduced [9]
Summary
The models containing partial differential equations (PDE models) for designing production lines have been developed in recent decades [1,2,3,4,5,6,7]. The emergence of new types of models is due to trends of modern industrial production, the main of which is the trend to a continuous reduction of the product life cycle This trend leads to the fact that, on the one hand, production lines operate for a considerable time in transient unsteady conditions, [3,4,5,6,7], on the other hand, the time for searching for the control mode of technological sites of the production line, is reduced [9]. The issue of justification of a method of constructing closed equations that define the model requires further development and determines the relevance of the chosen direction of research and its practical significance for modern flow production
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