Determination of the Weight Functions of the Edges of an Undirected Graph in the Computer Search of the Optimal Path Using Dakystre’s Algorithm

Abstract

The use of algorithms and computer programs to find the optimal path of the graph using the Dijkstra algorithm allows determining the tension and changes in the relative tension in the filling zones of knitted and textile machines, taking into account the specifics of the design of the thread feeding system. This makes it possible to reduce the breakage of threads, to optimize thread tension in the working zone of the formation of the original product. Determining the weight functions of the edges of an undirected graph during the computer search for the optimal path is an important component of the optimization of thread tension in the working zone of the formation of the output product. Tension optimization is carried out on the basis of its minimization, which allows to reduce the probability of a break in the working area. Optimization of the geometric parameters of the thread feeding system on the technological equipment, namely the construction of such a broken form of the thread, in which the total angle of coverage of the constructive structural elements of the technological equipment in the form of cylindrical and torus-shaped guides, elements of tensioning devices, devices for monitoring breakage will have a minimum value. This will reduce the amount of friction force between the thread and the guide surfaces and obtain minimum tension in the working area. Taking into account the large number of structural elements of the thread feeding system on technological machines, their location in the plane and space, there is a need to use modern information technologies. The imperfect shape of the thread filling line on technological machines of light industry, the low quality of complex threads and yarns when the tension increases along the filling depth leads to their breaks. The use of algorithms and computer programs for finding the optimal path of the graph using Dijkstra’s algorithm allows determining tension and changes in relative tension in the filling zones of knitted and textile machines. The improvement of the process of thread processing on technological machines of light industry consists in minimizing tension and should be based on theoretical and experimental studies of the process of interaction of threads with structural elements of the feeding system, in particular, tensioning devices to control breakage and guides of large and small curvature. Determination of the weight functions of the edges of the unoriented graph of the broken form of the thread allows us to obtain the total, minimum angle of coverage of the constructive structural elements of technological machines. The structural elements of the technological equipment represent the basis of cylindrical and torus-shaped guides, elements of tensioning devices, devices for monitoring breakage. This makes it possible to reduce tension and relative tension in the refueling zones of technological equipment.