Susumu Kase

Extension of plane rubber films

Extension of thin plane films, uneven in initial thickness and obeying the constitutive equation of rubber‐like elasticity, was analyzed mathematically with the following results. (i) The plane extension of rubber films is governed by two simultaneous partial differential equations whose independent variables are (u,v) and dependent variables are ( f,g) where (u,v) is the position in Cartesian coordinates of a rubber particle constituting the film occupied before the extension and ( f,g) is the position of the same particle after the extension. (ii) The axisymmetrical stretching mode is governed by a single ordinary differential equation which can readily be solved analytically or numerically upon specification of film thickness known at any one radial position. (iii) Uniform thickness extension is possible only when the film is initially uniform in thickness and the mode of extension is uniform biaxial, i.e., the two principal strains in x and y directions, respectively, are independent of position (u,v)...

Study on Electrostatic Spinning

An electrostatic spinning system consisting of fiber-opening roll, electrostatic field for formation of yarn, yarn twister, and take-up roll developed by the authors is described. The opening roll covered with garnet wires opens the entangled fibers, and individual fibers are blown to the electrostatic field by the centrifuge of the roll. It was found that the opening-roll diameter should be increased with increasing fiber length to insure best performance and to prevent roll wraps. The electrostatic field is created by a pair of cone electrodes facing each other either in horizontal or vertical arrangement. In the horizontal type, the yarn formed is drawn out of the electrostatic field through a small hole at the tip of the cathode. In the vertical type, the cathode is placed above the anode, with the yarn drawn out of a small hole at the tip of the anode. The yarn twister resembles the false twister, and the take-up roll is driven by friction. The size and the shape of electrodes, the distance between the electrode pair, the geometry of fiber supply to the electrostatic field, and the air-conditioning, etc. were found to affect the fiber yield. Vertically-positioned electrodes were found to be better than horizontal ones with respect to the filer yield and compactness of the equipment. Revolving anode and sharply-pointed cathode were found to be effective in straightening bent fibers, thereby obtaining uniform yarns.

THEORETICAL ANALYSIS OF FILM CASTING PROCESS WITH A PINNING DEVICE UNDER A TRANSIENT STATE

In previous reports, we proposed the model describing the catenary of the steady state of film casting in consideration of gravity or the electrostatic power of a pinning device. In this report, the model of the steady state was developed, and the perturbation transient solution around the steady state, the frequency response transfer function and the analysis of stability were calculated. The stability criterion of Nyquist, well known for control engineering, was used to determine stability. A new analytical model of film casting process that had been developed to judge stability by turbulence had an excellent practicality. Through an analysis of the film casting in transient states, it was found that (1) the stability limit grew wider when the electrostatic force was stronger, the chill roll radius was longer, and the vertical distance from the die exit to the landing point was longer, and (2) a thickness variation of about 10% occurred in response to a stepwise change in the extrusion viscosity by 1%.

Thin filament equations. Part 1. Equations in simplest form and their solutions

The present paper is the first of a series of manuscripts which are devoted to extensive discussion of thin filament equations, i.e., the simultaneous partial differential equations governing the continuous drawing and transient stretching of liquids taking the shape of thin filaments. This paper exclusively deals with thin filament equations in their simplest form, namely the equations governing the isothermal melt spinning of Newtonian fluids. Subjects covered are (1) formulation of the equations, (2) solution for the steady state spinning, (3) perturbation equations around the steady state spinning, (4) analytical transient solution of the perturbation equations, (5) numerical transient solution of perturbation equations for the constant take‐up speed spin line, (6) frequency response transfer functions, (7) stability of spin line, (8) numerical solution of the nonlinear thin filament equations simulating the draw resonance oscillation, (9) analysis of spin line transients in Lagrangian (τ,τ’) coordina...

Extension of uneven flat films

Extension of flat films uneven in thickness and lying on the (x,y) plane is analyzed mathematically. Constitutive models assumed are isothermal Newtonian fluids and rubber‐like elastic solids. Governing equations reduce to the Cauchy–Riemann equations when the material is Newtonian fluid and the film is uniform in thickness. Many unusual modes of extension exist in this case. In both cases of Newtonian fluids and rubberlike elastic solids, governing equations reduce to readily solvable ordinary differential equations when the extension is axisymmetrical. Conditions of wrinkle free extension are introduced. Numerical solutions are obtained for the general extension of the films of rubber‐like elastic solids.

Study on Crinkle Design of Crepe. Part 2 Analysis of the Phase Difference between Contiguous Hard Twisted Yarn in Crepe.

目的 よこ糸に強撚糸を挿入したクレープの布中で隣接する強撚糸が作るらせんの位相差が決まる機構を明らかにする.成果 たて糸のひずみエネルギーが最小になる位置に位相差が決まると考え, たて糸とよこ糸の交差点を点接触と仮定した布モデルにより, 単純化した条件下で位相差によるらせん発生時のたて糸のひずみの2乗の総計を比較した.また実際のクレープを試作し強撚糸が作るらせんの位相差を観察した.得られた結果の概要は次のとおりである. (1) モデルによる解析では, 同方向の撚り糸が隣接すると位相は一致する.(2) モデルによる解析では, 異方向の撚り糸が隣接するとらせんの断面形状により位相差は異なり, らせんが布面に対して垂直方向につぶれた楕円らせんか真円に近い場合は位相は半周期ずれ, 布面に対して水平方向につぶれた楕円らせんでは位相が一致する.(3) 試作結果は, (1), (2) のモデル解析結果により良く説明できる.

Study on Crinkle Design of Crepe. Part 3. Theoretical Analysis of the Helix Number of Hard Twisted Yarn in Crepe.

目的 よこ糸に強撚糸を挿入したクレープの布中で強撚糸が作るらせん数を, たて糸による拘束とよこ糸同士の拘速を考慮したモデルにより解析を行う.成果 たて糸による拘束を線形な弾性拘束, よこ糸同士の拘束は布面に水平方向の見掛け上の断面2次モーメントを大きくすると仮定し解析を行った結果次の式を得た. n=l/2√2aπ√ (Mt/EI) 2+√ (Mt/EI) 4-4ka2/EI (n=1, 2, ……) n : 長さlのよこ糸に発生するらせん数l : よこ糸の試料長α : Ix/I I : よこ糸の断面2次モーメント Ix : 布中でのよこ糸の見かけ上の断面2次モーメント Mt : よこ糸のねじりモーメントE : よこ糸のヤング率 k : たて糸による弾性拘束の単位長さ当たりのバネ定数この式から次の結果が得られた.(1) よこ糸のねじりモーメントが大きくなると, らせん数は多くなる.(2) たて糸による拘束のバネ定数はらせん数にほとんど影響しない.(3) 見掛け上の断面2次モーメントが大きくなると, らせん数が減少する.

Sizing Process using Water-soluble Vinylon Filaments

A new method for warp sizing is attempted by means of twisting agent filaments. The method uses a running yarn composed of a warp yarn twisted with water-soluble vinylon (PVA) filaments. And the running yarn is passed between upper roller coated with rubber and lower roller wetted by warmed water, and then is transformed to a sized warp yarn with PVA filaments acted as agent.This sizing treats at the temperature from 60°C to 95°C and at the speed from 10m/min to 30m/min with the running yarn twisting from 100turns/m to 300turns/m. The characteristics of the sized cotton yarn such as size add-on, penetration of PVA into warp yarn, mechanical properties, and abrasion resistace are evaluated. Under the condition of the water temperature more than 80°C, it is found that properties of these sized yarns are similar to those of conventonal sized yarns. The advantage of this method is providing the new simple sizing process.