ANALYTICAL MODELLING OF THREAD TENSION ON A SYSTEM OF SURFACES

The paper deals with the determination of the tension of a flexible thread using numerical methods. The equilibrium of a homogeneous inextensible heavy thread, when statically interacting with a system of surfaces of various shapes, has been simulated. The paper presents the results of analytical modelling of thread tension. The formulas for calculating the tension at any point of thread by characteristic sections and the normal pressure at critical points have been derived. An example of calculation of thread tension on two smooth cylindrical surfaces and a rough surface of a cone simulating some working bodies of textile machines has been given. The normal pressure on the thread sections at the points dangerous, with respect to contact disturbance, has been determined. After solving all the equations and determining their components, a mathematical model of heavy thread tension at static equilibrium has been constructed using the points found.