理想纱条的纤维排列与随机过程分析The alignment of fibers in ideal sliver and its analysis by stochastic process
严广松,苏玉恒
摘要(Abstract)：
在Rao给出的理想纱条定义的基础上,进一步提出了理想纱条纤维排列的新定义.新定义考虑了纤维的长度分布,从纤维头端排列的概率分布角度指出了理想纱条的形态,新的理想纱条定义完全满足Rao理想纱条的4个条件.使用随机过程对这个新定义的理想纱条进行了分析,证明了这个随机过程是一个弱平稳过程,进一步求出了这个平稳过程的期望、方差和相关函数表达式,为理解理想纱条的意义和拟合非理想纱条建立了理论基础,也给出了理想纱条仿真的数学方法和途径.
关键词(KeyWords)： 理想纱条;纤维排列;纤维头端;随机过程
基金项目(Foundation): 国家自然科学基金项目(51173023);; 河南省高校科技创新团队支持计划项目(13IRTSTHN024)
作者(Author): 严广松,苏玉恒
参考文献(References)：
- [1]Martindale J G.A new method of measuring the irregularity of yarns with some observations on the origin of irregularities in worsted slivers and yarns[J].Journal of the Textile Institute,1945(36):35-47.
- [2]Brown G H,Ly G N.Statistics for the number of fiber ends in a segment of a random assembly of aligned fibers[J].Textile Research Journal,1985,55(4):206-210.
- [3]Suh M W.Probabilistic assessment of irregularity in random fiber arrays-effect of fiber length distribution on“variance-length curve”[J].Textile Research Journal,1976(45):291-298.
- [4]Zeidman M,Suh M W,Batra S K.A new perspective on yarn unevenness:components and determinants of general unevenness[J].Textile Research Journal,1998,56(4):1-6.
- [5]Yan G S,Zhu J Z,Yu C W.A new approach to theoretical yarn unevenness:a binomial distribution model[J].Journal of the Textile Institute,2010,101(8):753-757.
- [6]严广松,苏玉恒,朱进忠.纱线条干不匀的随机模拟[J].纺织学报,2012,33(1):33-37.
- [7]严广松,苏玉恒.棉纱线中纤维头端的等效分布研究[J].河南工程学院学报:自然科学版,2011,23(2):1-5.
- [8]Kuang X,Yan G,Jiang Z,et al.A new mathematical expression of yarn limit unevenness[J].Fibers and Polymers,2013,14(11):1943-1946.
- [9]Rao S J.The mathematical model for the ideal sliver and its applications to the theory of roller drafting[J].Journal of the Textile Institute,1961(52):570-600.
- [10]邱燕炜.理想纱条的数学建模[J].中国纺织大学学报,1999,25(3):6-9.