Influence of Boundary Conditions on the Objective Function in the Computer Determination of the Optimal Path for an Undirected Graph

Abstract

The minimum necessary tension will be determined by the objective function, which is the minimum sum of the angles of coverage of the guiding surfaces by the thread. A recursive approach is used to determine the thread tension in the working zone, in which the output tension after the obstacle in the previous zone will be the input before the obstacle in the next zone. Algorithms and computer programs were used to find the optimal path of an undirected graph using Dijkstra’s algorithm, which made it possible to determine the influence of boundary conditions on the objective function, taking into account the specifics of the design of the thread feeding system. This leads to a decrease in thread breakage. Minimizing thread tension on technological machines allows to reduce the probability of breakage in the working area. The minimum necessary tension will be determined by the objective function, which is the minimum sum of the angles of coverage of the guiding surfaces by the thread. The use of algorithms and computer programs for finding the optimal path of an undirected graph using Dijkstra’s algorithm allows determining the influence of boundary conditions on the objective function. Determination of tension and changes in relative tension in the filling zones of knitted and textile machines, taking into account the specifics of the design of the thread feeding system, allows to reduce the breakage of threads, to optimize thread tension in the working zone of the formation of the output product. Determining the influence of boundary conditions on the objective function during the computer determination of the optimal path for an undirected graph in the 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. Reducing the friction force between the thread and the guide surfaces is achieved by optimizing the geometric parameters of the thread feeding system on the technological equipment. Practically, this is realized by building such a broken form of the thread, in which the total angle of coverage of the constructive structural elements of the technological equipment will have a minimal value. Constructive structural elements are presented in the form of guides of cylindrical shape and in the form of a torus, elements of tensioning devices, devices for monitoring breakage. Construction of the optimal path of an undirected graph will allow obtaining the 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.