A Theoretical Approach to the Problem of Yarn Strength

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Abstract
An idealized yarn composed of fibers with specified properties is treated analytically with the aim of determining the yarn strength at any degree of twist. The results are presented in the form of equations and curves which relate the yarn strength to the fiber properties and the degree of twist. Two cases are studied: (1) All fibers alike; (2) fiber properties variable from fiber to fiber. In the latter case the mathematical expectation of the yarn strength at any yarn cross section is obtained. It is found that the optimum twist multiplier is largely determined by the fiber length, fiber fineness, and coefficient of friction, whereas the maximum yarn strength (corresponding to the optimum twist multiplier) is more strongly dependent upon the intrinsic fiber strength than upon the other fiber properties studied.