Phenomenon of cross winding delivered yarn onto packages takes place on several yarn spinning/rewinding/processing machines. Among different modes of winding like random, precision and step precision winding, step precision winding offers distinct advantages. Step precision winding combines positive characteristics of random and precision winding to form a pattern free package with coil angle varying over a narrow range (Koranne 2013).

In step precision winding, package starts winding in precision mode with a non-pattern forming traverse ratio giving coil angle very close to desired. Upon winding, coil angle keeps on reducing. After some interval, when coil angle has decreased to some extent, traverse ratio is instantaneously shifted to a new lower value that will bring coil angle closer to desired mean value. On continuing winding, coil angle again decreases and after certain interval traverse ratio is again instantaneously shifted to a new a non-pattern forming value to restore mean coil angle. Thus, a step precision wound package is wound with several non-pattern forming traverse ratios that are decreased progressively in steps to build a package with coil angle varying over a narrow range.

For applications like dyeing, warping and weft supply packages for shuttleless looms, open wind traverse ratios are taken. Manufacturer of a winding system has to take utmost care to select all traverse ratios that are open not giving “diamond” and/or “honeycomb appearance”. To build a package with minimal variation of coil angle, traverse ratios taken during winding of entire package need to be sufficiently large in number closer to one another. With use of a few traverse ratios, coil angle varies over a wide range. At change over from one traverse ratio to next lower one; if coil angle variation is large, traverse length on package suddenly change from a higher to lower value that adversely affects appearance of side flanks of packages. This may be permissible for applications like assembly winding where close winding giving high package density (and thereby high yarn content on package) is of main importance. But for other applications like dyeing, warping and weft supply packages for shuttleless looms, it is always advantageous to have several non-pattern forming open wind traverse ratios (Koranne 2013).

Several patents are available on step precision winding (German Patent 1999, 1992; United States Patent 1987, 1995, 2000, 2002) but none exactly describe the procedure of finding out non-pattern forming open traverse ratios that are acceptable visually also from the point of view of diamond or honeycomb appearance. Traverse ratios selected for step precision winding on commercial winding systems are not accessible to the user of winding system.

In cross wound packages, yarn is laid in form of helices reversing at extremes. Traverse ratio (also known as winding ratio/crossing ratio) is an important parameter associated with cross wound packages that is defined as number of coils laid on the package in a double traverse. If traverse ratio is expressed in form of fraction X/Y (with X and Y as natural numbers without any common factor except 1), Y indicates number of double traverses after which yarn comes to same place. With a smaller value of Y, yarn comes to same place after fewer double traverses causing overlapping of yarn wraps one above the other forming undesirable ribbons (patterns). For example, a traverse ratio of 11/3 would form ribbons as wraps of yarn after every three double traverses overlap on one another. Such ribbon forming number shall be termed as “nominal traverse ratio”. To avoid ribbon formation, traverse ratio for winding should be incremented or decremented from 11/3 so that yarn is displaced at least equal to its diameter that would eliminate overlapping and lay yarn adjacent to one another giving “close wind”. If number is taken such that the displacement of yarn is substantially more, say four times yarn diameter, it becomes “open wind”. Such non-ribbon forming numbers derived from “nominal traverse ratios” shall be called as “actual traverse ratios”.

For end user applications like dyeing, warping and shuttleless loom weft supply open wind traverse ratios are usually selected in which wraps of yarn are seen substantially away from one another forming an open package facilitating flow of dye liquor during package dyeing or allowing withdrawal of yarn without tension peaks or slough off.

It is very essential to find out methods to determine suitable traverse ratios for step precision winding when task of manufacture of a step precision winding system is undertaken. The study reported in this paper discusses a novel approach developed to find out several suitable open wind traverse ratios for step precision winding. The outcome of this paper is very useful for manufacturers desirous to develop open step precision winding systems.

It can be mathematically shown that pattern forming ratios lie very close to one another. Their interval depends upon package diameter. Winding a cylindrical package with traverse length of 150 mm for package diameter range of 45 mm to 200 mm at constant angle of 16°, traverse ratio decreases progressively between 7.4005 and 1.6651 from empty to full package. During this build up fractions between 1 and 11 occur 241 times where ribbon formation is most likely. If traverse ratio is selected as any of these numbers, there would be occurrence of ribbon formation. If a traverse ratio is selected nearer to any of these numbers, partial overriding of yarns wraps is caused that result into formation of ridges and hollows on package surface (called as honeycomb formation). Even if yarns are adequately apart, certain numbers as traverse ratio give appearance of diamond pattern on package. This is also regarded as unacceptable by the users. Figure 1 shows unacceptable packages (with honeycomb formation and diamond appearance) and an acceptable package. Apart from this, other fractions of number higher than this can also become unacceptable depending upon yarn linear density and package diameter. Therefore, finding a suitable traverse ratio is a critical job as problematic ratios lie closer to one another.