Abstract
The idea that mathematical simulation of the process of textile yarn stretching which reveals new features of its destruction in technological processes is substantiated in the paper. Mathematical model should take into account textile yarn motion velocity in technological processes, acting external forces, and the reliable law of yarn strain under stretching. Secant moduli of cotton yarn strain were determined from experimental diagrams of cotton yarn stretching. A significant nonlinearity of the change in strain modulus depending on the strain value is shown. An account of this factor leads to physically nonlinear laws of cotton yarn strain. Therefore, as the basis of a mathematical model of the motion process, a physically developed nonlinear elastic-viscoplastic law of cotton yarn strain is proposed. The main properties of the proposed law and the methods for determining its support dependencies are discussed. An algorithm for using the law in a mathematical model of the process of yarn strain to a break is proposed.
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