Computer implementation of a recursion algorithm for determining the tension of a thread on technological equipment based on the derived mathematical dependences

Abstract

The current study of computer implementation of the algorithm for determining a thread tension on technological equipment using recursion has established the values of thread tension before a zone where fabric and knitwear form on the technological equipment. It has been proven that the magnitude of thread tension before the formation zone is influenced by the number of guides in each particular technological machine, the curvature radius of each guide, the angle at which a thread wraps the guide, the angle of a thread’s radial wrap, the thread’s physical-mechanical and structural characteristics. The values of the angles at which a thread wraps the guides and the radial angles at which a thread is wrapped by the surface of a guide are defined by the geometric parameters and the design of both the thread feed system on technological equipment and specific guides. As a result, it has become possible at the initial stage of designing a technological process to determine thread tension before the formation zone, depending on the equipment geometric and structural parameters and the thread physical-mechanical and structural characteristics. The difference of 2–6 % between the experimental and calculated values of the tension confirms the correctness of the assumptions made when constructing the model of interaction between the thread and the guide, taking into account its physical, mechanical and structural characteristics, and the possibility of using recursion to sequentially determine the tension in the zones of technological equipment from the entrance zone to the fabrics and knitwear formation zone. Specifically, it has been established that the thread tension increases from a zone to a zone and reaches its maximum before the formation zone. It has been shown that the increase in tension by 9‒15 % leads to a disruption of the technological process and the break of the thread. Thus, there is reason to argue about the possibility, at the initial stage of designing the technological process of fabric and knitwear production, to regulate the thread tension before the zone where fabric and knitwear form. This could be achieved by adjusting the geometric parameters and design of both the thread feed system on the technological equipment and specific guides, which would minimize the value of thread tension