Improving the existing technological processes of processing complex threads on knitting machines and looms requires determining the change in relative tension in the areas of refueling. The change of tension occurs due to the interaction of complex threads with guides of large curvature, taking into account and without taking into account the radial coverage of the complex thread by the surface of the guide. The task of determining the tension should be based on the use of dichotomy algorithm software in computer determination of the tension of complex threads. Determining the change in relative tension in the areas of filling of complex threads on knitting machines and looms, taking into account and without taking into account the radial coverage of the complex thread by the guide surface, will improve the technology of production of knitwear and fabrics. Improvement of technological processes of the knitting and textile industry should be based on complex researches of process of interaction of complex threads with directing surfaces of big curvature. Obtaining theoretical dependences will allow to obtain equations for determining the tension of the thread in the area of fabric formation and knitwear, reduce the percentage of thread breaks, improve the quality of finished products. Many studies do not take into account the nonlinear relationship between force and coefficient of friction in obtaining the final equations. All this leads to significant differences between theoretical and experimental dependences, which does not allow the use of the former in specific calculations. Downtime of technological equipment associated with the elimination of cliffs is 75-80% of the total downtime. It is possible to significantly reduce the number of breaks by using quality raw materials and optimizing the conditions of thread processing on knitted and textile machines, where their interaction with the guides and working bodies of great curvature takes place. The tension dependences of complex threads have the form of a system of transcendental equations, for the solution of which it is necessary to use numerical methods. The dichotomy method is the most effective.

Computer implementation of the recursion algorithm allows at the initial stage to determine the thread tension, which occurs after passing the comb tension device of the hosiery feed system depending on the physical and mechanical properties of raw materials, geometric parameters of structural elements of the hosiery thread feed system. Computer determination of the change in relative tension on stocking machines is based on the use of the dichotomy algorithm in solving transcendental equations. Determining at the initial stage of the tension of the thread feed process on hosiery machines allows to determine the tension after passing the comb tensioning device, which will occur during the interaction of the thread with the structural elements of the cylindrical comb tension device depending on the type of raw material, curvature for bending, deformation in the area of ​​contact with the guide, the feed rate of the thread. The increase in tension after passing the comb tensioning device is due to the increase in friction between the thread and the cylindrical guide. This is due to the increase in the coverage angles of the cylindrical guide rods of the comb tensioning device. The development of a computer program for determining the tension of the thread on stocking machines should be based on the use of object-oriented programming languages. Determining the tension and changes in relative tension in the refueling zones of hosiery machines, taking into account the specifics of the design of the thread feed system of hosiery machines, will reduce thread breakage, optimize thread tension in the working area of ​​hosiery machines. The improvement of the technological process of thread processing on hosiery machines should be based on theoretical and experimental studies of the process of interaction of threads with structural elements of the feed system, including comb tensioning device and guides of large and small curvature. The main element of the structural elements of the feed system of stocking machines is a comb device for tension. Theoretical dependences for determining the tension after the comb device will allow to obtain algorithmic and mathematical software, which is used in computer software to calculate the tension and change the relative tension in the areas of refueling stocking machines. Optimization of tension in the working area will reduce the change in relative tension in the refueling areas of hosiery machines, improve the quality of hosiery.

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.

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.

Ensuring the minimum tension during thread processing on technological equipment allows to reduce equipment downtime due to the elimination or significant reduction of thread breaks. Minimization of tension is ensured by optimization of the shape of the thread filling line, in which the total angle of coverage of the guides will be minimal. This problem is solved by using Dijkstra’s algorithm in finding the optimal path of a directed graph. The computer program for implementing this algorithm allows you to optimize the form of filling the thread on the technological equipment. The development of application packages of computer programs allows to reduce the time for the design of technological processes in the light and textile industry as much as possible. This is due to the modernization of the thread filling line on the technological equipment, which allows to minimize thread tension in the working area. Minimization of tension is ensured by optimization of the shape of the thread filling line, in which the total angle of coverage of the guides will be minimal. This problem is solved by using Dijkstra’s algorithm in finding the optimal path of a directed graph. Construction of the optimal path of the directed graph will allow to obtain the minimum tension in the working area. Constructive structural elements in the form of guides, elements of tensioning devices, break control devices, which have a cylindrical, elliptical shape, and discrete segments of a straight line act as obstacles in the path of the thread. Straight line segments can have an inclination relative to the vertical axis. Taking into account the large number of structural elements of the thread feeding system on light and textile industry machines and their location, there is a need to develop a special computer program for determining the optimal shape of the thread feeding line using the Dijkstra algorithm when searching for the optimal path of a directed graph. The objective function in the problem is the minimum necessary tension, which is the minimum sum of the angles covered by the thread of guide surfaces that have a cylindrical, elliptical shape, discrete segments of a straight line. The use of a computer program allows you to determine tensions and changes in relative tension in the filling zones of light and textile industry machines, which allows you to optimize the shape of the thread supply line even at the stage of designing the technological process. The use of algorithms for computer programs for finding the optimal path of an undirected graph, for cylindrical, elliptical guides, discrete segments of a straight line, allows you to determine the influence of coverage angles on the target tension function. Determining the effect of coverage angles, for cylindrical, elliptical guides, discrete segments of a straight line, on the objective function during the computer determination of the optimal path for an oriented graph is an important component of the optimization of thread tension in the working area of machines of the light and textile industry, the formation of knitted and textile products.