Outer and inner constructions, having important effects upon the quality of woven fabrics, are completed by the behaviors of the warp & weft yarns during the following weaving periods;
(I) Behaviors of the warp & weft yarns during the weft inserting motion.
(II) Behaviors of the warp & weft yarns during interlacing period which is effected by the beating motion.
(III) Relaxation of the warp & weft yarns which built the fabric constructions at an equilibrated state being not influenced by the beating motion.
The calculation concerning the behaviors of the warp & weft yarns when the reed leaves the cloth-fell and while the reed is beating the cloth-fell during the above-mentioned period (II) is shown in this report.
When the reed leaves the cloth-fell, the equilibrated position of the last weft yarn inserted is calculated by the following equation; where β (=α
0): Shedding angle (q. v. Fig. 1) α
1: Interlacing angle (q. v. Fig. 1) μ: Frictional coefficient between warp & weft yarns
Then the interlacing angle of the weft yarn beaten at the cloth-fell before
n beatings, is calculated by the following formula;
Moreover, while the reed beats the cloth-fell, the interlacing angle concerning the weft yarn beaten last is calculated by the following formula too; where
T0: Tension of warp yarn before the reed beats the cloth-fell
T0′: Tension of warp yarn increased owing to the beating
k:
T0′/
T0 And, for
n, after the weft yarn last beates up the cloth-fell, we obtained the following equation:
Therefore, by
n>1 we can calculate from the equation (2)-(4) easily the interlacing angles α
1, α
2, ……α
n and α
1′, α
2′, ……α
n′ with which one warp crosses each weft before and after each beating, when numerical values of β,
k and μ are given
Then, comparing α
1, α
2, ……α
n with α
1′, α
2′, ……α
n′, we observed the theoretical interlacing phenomena between the warp & weft yarns, and established a guide for future experimental studies.
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