It is generally recognized that the weaving technique using the stiff warp yarn is troublesome.
This report deals with the interlacing construction between the cylindrical weft and the elastic warp yarns.
The curvature of the elastic warp yarn between of the weft yarns is determined by the contact conditions of the weft and warp yarns (
i.e. the frictional coefficient and the stress-resultants at the contact point), and also by the warp tension and the flexual rigidity
EI of the warp yarn.
The curve (see: Fig. 2) between the origin and the inflection point θ
1 may be expressed: and from θ
1 to the contact point between the warp and weft yarns: where, the origin of coordinates in the contact point between the warp and the weft yarns near the cloth-fell, and the coordinate
x coincides with the tangent at this contact point, and
k,
c, ψ; the constants in relation to the contact condition between the warp and the weft near the cloth-fell. θ: Angle formed by the tangent at the point on the curve of the warp and the coordinate
x θ
1: θ at the inflection point of the curve
Then calculating the coordinate
x2,
y2 at the contact point between the warp and the weft, being far from the cloth-fell, from the equations
(1)-(2), The following results are obtained:
(1) Both
x2,
y2 increase in proportion to
√EI,
(2) Under the contact conditions between the warp and weft, being near to the cloth-fell having the stress-resultants and tension and shearing force increased, show the same tendeny.
(3) The larger the warp tension is, the smaller
x2,
y2,
(4) The changing tendency of the curve of the warp is influenced by the frictional coefficient between the warp and weft yarns and the shedding angle.
(5) The stress-resultants are influence by the construction of the woven fabrics.
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