Enkele stochastische eigenschappen van een uit vezels ge‐sponnen garen voor het ideale klassieke spinproces en enkele ermee samenhangende problemen

Abstract

SummarySome stochastic properties of a yarn spun from fibres for the ideal classic spinning process and some connected problems.For the ideal classic spinning process {for definition cfi section 2) the characteristic functions of the cross‐section of a yarn and the volume of a yarn‐piece are derived. It is assumed that the fibres possess a two‐dimensional probability distribution for their length and cross‐section, however with the restriction that the fibre‐length has an upper bound with probability one.For the case that the fibres have uniform cross‐section the spectral functions of the foregoing quantities are given.Under the same condition of a uniform cross‐section of the fibres analogous results have been obtained by H. BRENY [7], however in quite another and partly more tedious way. The spectral function of the yarn‐cross‐section has also been independently obtained by KIYOHISA FUJINO and SUEO KAWABATA [8].In spinning practice the coefficient of variation of the yarn‐cross‐section for the ideal classic spinning process {the so called coefficient of MARTINDALE) is denoted an optimal character in so far as it should be the minimum coefficient of variation, which is attainable. This is certainly the case if the disturbances in the spinning process are independent of the irregularities already contained by the yarn.However, if the disturbances are dependent on the yarn‐irregularity, then it is a priori not sure that the irregularity will always increase. Perhaps the opposite may occur.In this connection it seems an interesting problem to determine the implications on the yarn irregularity by using servo‐mechanisms in the spinning process. Some investigations in this direction have already been done by the Japanese (cf. the references).