Abstract:

In order to study the relationship between the alignment of fibers and the uneven distribution of fiber numbers in the cross-sections of a staple yarn, a mathematical model describing the distribution of fibers at the left ends of yarn segments cut at equal intervals and the expectation of the fiber numbers in the yarn cross-section was established using geometric probability method, and a parameter to characterize the arrangement of fibers in yarn was defined. The variation of fiber numbers in the cross-sections of yarn segments against the fiber alignment parameter was simulated by Monte Carlo method. The results showed that the CV value of fiber numbers in the cross-sections of the segments of the staple yarn was negatively proportional against the parameters of the alighment state of staple fibers in the yarn, and demonstrated no relation with the distribution of the fiber length and the division of the simulation interval. When the alighment parameter is close to 1, that is when the number of fibers in the left end of the yarn segment is fixed, the variation in fiber numbers in the cross-sections was the lowest. When the alignment parameter tends to 0, meaning that when the number of fibers in yarn segments follows a Poisson distribution, the variation of the fiber numbers was the highest.

Key words: fiber end, fiber alignment, random simulation, yarn unevenness, fiber number in the cross-section of staple yarn