This article is devoted to mathematical modelling of the production ow lines of the conveyor-type. Here is an analytical method for calculating the parameters of a production line with a regulated speed of the movement of the subjects of the labour along the conveyor developed. The description of the parameters of the state of the production line is made in the one-moment approximation using partial dierential equations. There has been derived a solution that determines the state of the parameters of the production line for a given technological position as a function of the time. The transitional period during which the initial condition of the distributing of the subjects of the labour along a conveyor has the inuence on the state parameters of a production line is certain. The developed method of the calculation of the ow parameters of the production line allows designing control systems of the production line of the conveyor-type with a regulated rate of the movement of the subjects of the labour.
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.
Purpose. Development of algorithms for controlling the speed of the conveyor belt, based on the distributed model of the transport system, containing partial differential equations methodology. To calculate the parameters of a conveyor line with a variable speed of material motion, an instrument of math ematical physics is used. findings. Comparative analysis of conveyor transport system models is performed. Application of partial differential equations for simulating transport systems of conveyor type, which are complex dynamic distributed systems, is substantiated. A nondimen sional model of a conveyor system in instantaneous approximation with the use of partialderivative equations is presented. A sys tem of characteristic equations is recorded and a solution is developed which defines the value of material flow and material den sity at an arbitrary point of time for the given point of the transportation route. An expression is obtained which defines the value of material delay in the transport system depending on the velocity defect law for conveyor belt movement. Transition period time is determined during which the output material flow is defined by linear density of material disposition along the transportation route. Dependences for the material linear density and material flow for the steady state condition are defined. The performance criterion of control of flow parameters of the conveyor system is recorded and a solution of the problem of optimal control of con veyor belt speed providing the relay control mode with the minimum power consumption for material movement is found. An example of control algorithm development is given. originality. PDEmodels of transport systems of conveyor type and energysaving algorithms for controlling such systems have been improved. Practical value. The proposed method for calculating the parameters of the conveyor line, which is a dynamic distributed sys tem, can be used to design systems for optimal control of flow parameters of transport systems of conveyor type
In this paper, a model of a transport conveyor system using a neural network is demonstrated. The analysis of the main parameters of modern conveyor systems is presented. The main models of the conveyor section, which are used for the design of control systems for flow parameters, are considered. The necessity of using neural networks in the design of conveyor transport control systems is substantiated. A review of conveyor models using a neural network is performed. The conditions of applicability of models using neural networks to describe conveyor systems are determined. A comparative analysis of the analytical model of the conveyor section and the model using the neural network is performed. The technique of forming a set of test data for the process of training a neural network is presented. The foundation for the formation of test data for learning neural network is an analytical model of the conveyor section. Using an analytical model allowed us to form a set of test data for transient dynamic modes of functioning of the transport system. The transport system is presented in the form of a directed graph without cycles. Analysis of the model using a neural network showed a high-quality relationship between the output flow for different conveyor sections of the transport system.
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