施撚の基礎理論および実験
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概要
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Mechanical properties such as load-deflection relationship and modulus of rigidity on the twisting of yarn in stationary state have been studied by many researchers. But on the twisting of yarn in rnnning state there are few fundamental studies, experimental or theoretical, except Tobisch's theory. Tobisch derived his theory on the assumption that the number of twists of yarn per unit length, or twist density, was uniform everywhere in the twisting field, but this is true only when the delivery velocity is very small or the internal friction of yarn is negligible. The author has made theoretical and experimental studies on the twisting of yarn in running state, considering it as a visco-elastic body made of homogeneous and uniform materials. The studies may be briefly summerized in the following outline. (1) A yarn of total length L is fixed at both ends. This yarn is divided into two parts, the length l of it being twisted and the other length L-l free from twisting. If a point fixed between these two parts is suddenly released, twisting will be transmitted to the untwisted part. The theory of this transient transmission of twisting has been treated by solving the following partial differential equation : p(∂^2θ/∂t^2) = G(∂^2θ/∂x^2) + η(∂^3θ/∂t∂x^2) where p = the density of yarn θ = angle of torsion at x along the yarn t = time G = modulus of rigidity of yarn. η = tangential coefficient of viscosity at the cross section of yarn. In the case under consideration, let the angles of torsion along the yarn and at the end of the lenght l be Θ and θ_0 respectively. Then the following relation holds : θ=Θ-θ_(0x)/L. The solution of the above differential equation by the use of this relation and initial and boundary conditions in this case has shown that the twist density of yarn transmitted to the untwisted part is exponentially increased with time and approaches to θ_0/L. (2) A high speed camera by which 64 pictures could be taken per second was used in order to confirm the above theory. The results measured coincided satisfactorily with the theory. (3) When the yarn was fixed at one end and free at the other and the twisting moment was applied at the free end, the above differential equation was solved under the initial and boundary conditions in this case. The twist density of yarn in this transient case also approaches exponentially to θ_0/L with time. (4) In the running yarn, the following transformation of coordinates was used : x=ξ+vt, where v is the velocity of the running yarn, x is a fixed coordinate in yarn and ξ is in space. By solving this transformed equation, it has been shown that the twist density of running yarn with only internal friction is in steady state exponentially decreased from the twisting element, say the aperture of flyer, to the nip point of delivery roller. (5) Also by the solution of the above transformed equation, Ball's distribution diagram of twist in the twisting fields of the ring frame and mule has proved to be the distributed one in a case when the yarn is considered as a visco-elastic body with solid friction. (6) In the yarn with plasticity, the twisting field is divied into two Zones : an elastic zone ξ=0-ξ_1. and a plastic zone ξ=ξ_1-L. The equations of twist density in elastic and plastic zones have been derived under considerations of the boundary conditions. An experiment of twisting rayon yarn with the flyer frame showed that these twe zones occurred and could be explained by substituting appropriate numerical values into the above derived equations. (7) When the internal friction of yarn is negligible or the delivery velocity of yarn is very small, Tobisch's theory is applicable. So, in such a state, the double twisting principle of tyre cord has been analyzed by this theory. (8) The re-distribution of twists in the twisting field by the invasion of twisted yarn into the untwisted field or by its regression from the twisting field with the introduction of untwisted yarn is occasionally important in spinning operation, especially in false twisting of worsted spinning and rotating funnel of high draft system in cotton spinning. The state of this re-distribution was experimentally studied by photographing the twisting operation in one twisting field, and the results measured could be qualitatively explained by the above described theorics. (9) The permanent deformations of twisted yarn set by steam or initially applied tension were studied by measuring the free rotating angle about the axis of the yarn loaded axially. According to these experiments, the permanent sets are 0-28% of the initial number of twists of yarn.
- 山形大学の論文
- 1953-12-18