Theoretical Estimation of End-Breakage Rate in Spinning

Hajime Kawakami; Masaaki Hashimoto; Fumihiko Yamamoto

doi:10.4188/jte1955.20.1

Hajime Kawakami, Masaaki Hashimoto, Fumihiko Yamamoto

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Keywords: END BREAKAGES, SPINNING, WORSTEDS FINENESS, FIBER STRENGTH

JOURNAL FREE ACCESS

1974 Volume 20 Issue 1 Pages 1-7

DOI https://doi.org/10.4188/jte1955.20.1

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Published: 1974 Received: - Available on J-STAGE: July 07, 2008 Accepted: - Advance online publication: - Revised: -
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Date of correction: July 07, 2008 Reason for correction: - Correction: ABSTRACT Details: Wrong : End-breakage is assumed to occur in the fiber bundle which forms a triangle zone between a front roller nip line and a twisting point.
On the this assumption a theoretical investigation into end-breakage encountered during spinning has been made together with such factors as tension, yarn irregularity, number of fibers and fiber strength.
The following equation for calculating absolute values of end-breakage rate during spinning has been derived:
where R is the end-breakage rate for a predetermined spun length; Q is the stationary end-breakage rate; τ is the average spun length during end-breakage; m is the number of fibers which are caught simultaneously between the front rollers and the twisting point; n is the cross sectional number of fibers; λn is the probability that fibers n are caught between the front rollers; T is the tension exerting on the triangle zone, k(T) is the probability density function of T;p=1-q, q is the probability that a fiber is caught simultaneously between the front rollers and the twisting point; and g(x) is the probability density function of X in which X=T-S-R where S is the strength of the fiber bundle in the triangle zone and R is a mutual resistance against slippage.
Since the values calculated by the equation lie substantially within the scope of the empirically known end-breakage, it has been proved that the equation can be of practical use.
Right : End-breakage is assumed to occur in the fiber bundle which forms a triangle zone between a front roller nip line and a twisting point.
On the this assumption a theoretical investigation into end-breakage encountered during spinning has been made together with such factors as tension, yarn irregularity, number of fibers and fiber strength.
The following equation for calculating absolute values of end-breakage rate during spinning has been derived:
where R is the end-breakage rate for a predetermined spun length; Q is the stationary end-breakage rate; τ is the average spun length during end-breakage; m is the number of fibers which are caught simultaneously between the front rollers and the twisting point; n is the cross sectional number of fibers; λn is the probability that fibers n are caught between the front rollers; T is the tension exerting on the triangle zone, k(T) is the probability density function of T;p=1-q, q is the probability that a fiber is caught simultaneously between the front rollers and the twisting point; and g(x) is the probability density function of X in which X=T-S-R where S is the strength of the fiber bundle in the triangle zone and R is a mutual resistance against slippage.
Since the values calculated by the equation lie substantially within the scope of the empirically known end-breakage, it has been proved that the equation can be of practical use.

Date of correction: July 07, 2008 Reason for correction: - Correction: CITATION Details: Wrong : [1] Hori; J. Text. Mach. Soc. Japan, 8, 248 (1955) De Barr; J. Text. Inst., 50, T 284 (1950)
[2] Fujino, Uno, Shiomi, Yanagawa; J. Text. Mach. Soc., Japan, 14, 566 (1961)
[3] Ono; Handbook of Wool Industry (1968)

Right : [1] Hori; J. Text. Mach. Soc. Japan, 8, 248 (1955) De Barr; J. Text. Inst., 50, T284 (1950)
[2] Fujino, Uno, Shiomi, Yanagawa; J. Text. Mach. Soc., Japan, 14, 566 (1961)
[3] Ono; Handbook of Wool Industry (1968)

Date of correction: July 07, 2008 Reason for correction: - Correction: PDF FILE Details: -

Abstract

End-breakage is assumed to occur in the fiber bundle which forms a triangle zone between a front roller nip line and a twisting point.
On the this assumption a theoretical investigation into end-breakage encountered during spinning has been made together with such factors as tension, yarn irregularity, number of fibers and fiber strength.
The following equation for calculating absolute values of end-breakage rate during spinning has been derived:
where R is the end-breakage rate for a predetermined spun length; Q is the stationary end-breakage rate; τ is the average spun length during end-breakage; m is the number of fibers which are caught simultaneously between the front rollers and the twisting point; n is the cross sectional number of fibers; λn is the probability that fibers n are caught between the front rollers; T is the tension exerting on the triangle zone, k(T) is the probability density function of T;p=1-q, q is the probability that a fiber is caught simultaneously between the front rollers and the twisting point; and g(x) is the probability density function of X in which X=T-S-R where S is the strength of the fiber bundle in the triangle zone and R is a mutual resistance against slippage.
Since the values calculated by the equation lie substantially within the scope of the empirically known end-breakage, it has been proved that the equation can be of practical use.

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