The Effect OF Animal Fibre Diameter Distributions Within True Fibre

TheEffect OF Animal Fibre Diameter Distributions Within True FibreDiameter And Length On Yarn Unevenness prediction model

Fromdrafting theory the total relative variance (the square of thecoefficient of variation) of yarn is decomposed into threecomponents: roving variance, ideal variance and non-ideal variance(12):

Theideal unevenness is determined by the Martindale formula (13):

Theideal variance is the major component accounting for about 70% to 80%of the total variance. The formulae above is an indication that theappropriate unevenness result from random distribution of fibre whendrafting and exclusively depend on the amount of fibres in thecross-section of the yarn and the variability of diameter of thefibre. Roving variance is the total variance due to the inputcomponent and is usually as a result of top quality, the settings ofthe machine, the lubricant and the drawing system settings. Itseffect can be relatively small accounting for not less than 10% ofthe variance in total. Variance which is Non-ideal variance isusually created by drafting which is non-ideal in the spinningdrafting zone, and can be related to many factors such as fibrelength, crimp, spinning draft, roller setting, inter-fibre frictionand machine quality (12-16). This component accounts for about 15%-25% of the total variance. The relative importance of this componentincreases with increasing yarn linear density. Prediction of thenon-ideal unevenness is the key to the prediction of the totalunevenness. Fibre length and possible crimp effects are mainlyreflected through this component. The effect of machine quality canalso be incorporated into this component.

Yarnevenness can be improved either through improving roving quality orthrough reduction of the non-ideal unevenness, for example,optimising spinning draft and roller setting. In order to predict thenon-ideal unevenness it is important to have a good understanding ofthe mechanism of drafting which is not ideal. A mechanism that hasthe ability to move fibres in a non – random manner which isrelative to the array which is undrafted before accelerationcommences at a nip which is fixed leads to non-ideal drafting(17-18). The mechanisms of non-ideal drafting include the following:A) Sliver elasticity, which involves intermittent stretching of thesliver. The elasticity of sliver is accountable for only a negligibledegree of drafting irregularity in recent spinning systems (19). B)Roller eccentricity, which is machine dependent and generally hasonly a small effect on yarn irregularity. C) Floating fibres, thisrefers to fibres not gripped by either front or back rollers. This isa dominant cause of the additional yarn irregularity (12, 20-22).Fibre length makes a contribution to yarn unevenness mainly throughthis mechanism. As made known in Figure 1, the length of the fibrelength can influence the irregularity of the irregularity by a factorwhich is (L-H)/H, where (L-H) is the length of the zone which isfloating and (L-H)/H may be called the length of the floating zonewhich is normalised. Obviously, the smaller the length of the fibrethe lengthier the zone that is floating and the greater the chance ofthe fibre to change from the speed of a back roller to front rollerbefore it ranges the nip tip of the front roller.

Taylor(20) conducted detailed experiments, in a roller drafting system,showing that fibres change speed long before they reach the nip pointand that the acceleration point at which fibres change speed fromback roller speed to front roller speed is strongly correlated tofibre length, the shorter the fibre length, the greater is theprobability that it accelerates prior to that point. Fujino et al(21, 22) have further studied the regulation of movement of thefibres that float in apron of the drafting system. They suggestedthat the unsteady motion of floating fibres is the major cause of theadded variance during spinning drafting. However, it must be notedthat a fibre moving randomly out of turn does not increaseirregularity. Increased unevenness occurs only when fibre movementare correlated. Note that the perfect inequality is the dominantcomponent of the unevenness in total and how it relates with thefibre properties which have been described by the Martindale formula.The advantage of extrication of the non-ideal variance from the wholeis that it makes it easier to obtain a clear depiction of the effectsof the fibre length and other minor factors on yarn unevenness.



Yarn Unevenness Prediction Model 3


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TheEffect Of Animal Fibre Diameter Distributions Within True FibreDiameter And Length On Yarn Unevenness

YarnUnevenness Prediction Model

Froma drafting theory, it is possible to decompose the total relativevariance, which is the square of the coefficient of variation, of avan into three components: ideal variance, roving variance, andnon-ideal variance (12):

TheMartindale formula is applicable in the determination of idealunevenness (13):

Theideal variance is the major component accounting for about 70% to 80%of the total variance. The formula shown above indicates that thesource of ideal evenness as being the distribution in the process ofdrafting, which is random. Such an unevenness fluctuatesproportionately with the amount of fibres in the cross-section of theyarn, and the variation in the diameter of the fibre. Rovingvariance, on the other hand, entails the totals variance’s inputcomponent, and it is determined by the top quality settings of themachine’s drawing system, and the lubricant. Its effect isrelatively small accounting for about ten percent of the wholevariance. Non-ideal variance leads to the creation of non-idealvariance in the spinning drafting zone, and can be related to manyfactors such as fibre length, crimp, spinning draft, roller setting,inter-fibre friction and machine quality (12-16). This componentaccounts for about 15% -25% of the total variance, and its relativeimportance increases with the increasing yarn liner density: theprediction of the non-ideal unevenness is the key to the predictionof the total unevenness. Moreover, fibre length and possible crimpeffects are mainly reflected through this component, in which machinequality can also be incorporated. Yarn evenness can be improvedeither through improving roving quality or through the reduction ofthe non-ideal unevenness for example, optimising spinning draft androller setting.

Topredict the non-ideal unevenness, it is important to have a goodunderstanding of the mechanism of non-ideal drafting. Non-idealdrafting encompasses the mechanism that has the potential of makingfibres move randomly in relation to the array that is undrafted priorto their acceleration, which takes place in an immovable nip (17-18).Such mechanisms of drafting include:

Sliverelasticity:this involves intermittent stretching of the sliver, and it has justa light impact on the irregularity of drafting modern systems ofspinning (19).

Rollereccentricity:this is machine dependent, and generally has only a small effect onyarn irregularity.

Floatingfibres:this refers to fibres not gripped by either front or back rollers. Itis a dominant cause of the additional yarn irregularity (12, 20-22),and the mechanism through which the length of the fibre contributesto yarn unevenness.

Ascan be seen from figure I, the yarn irregularity is influenced by thelength of the fibre by factor (L-H)/H, where (L-H) is represents thelength of the zone that is afloat. In this case, (L-H)/H is themoderated length of the zone that is afloat. It is obvious that thelength of the affects the ability of a fibre to shift between being aback roller and a front roller speed until such a point that itattains the nip point of the front roller. Taylor (20) conducteddetailed experiments, in a roller drafting system, showing thatfibres change speed long before they reach the nip point.

Moreover,the very experiments showed that the acceleration point at whichfibres change speed from back roller speed to front roller speed isstrongly correlated to fibre length: the shorter the fibre length,the greater the probability that it accelerates prior to that point.Fujino et al (21, 22) have further studied the regulation of themovement of floating fibres within the systems of apron drafting.They suggested that the instability in the motion of the fibres thatare afloat is the major cause of the added variance during spinningdrafting. However, it must be noted that a fibre moving randomly outof turn does not increase irregularity. Increased unevenness occursonly when fibre movements are correlated. It is important to notethat the primary component of the total unevenness is the ideal one:Martindale formula is handy in describing the relationship between itand the properties of the fibre. The advantage of the separationbetween the non-ideal variance and the total is its ability to makeobtaining a clear image of the respective effects of the lengths ofthe fibres as well as other minor factors such as the unevenness ofthe yarn easier.

The Effect of Animal Fibre Diameter Distributions and the Predicted Resultant Yarn Unevenness within True Fibre Diameter and Length on Yarn Strength

TheEffect of Animal Fibre Diameter Distributions and the PredictedResultant Yarn Unevenness within True Fibre Diameter and Length onYarn Strength

Themass irregularity along a yarn leads to staple fibre yam thatconsists of a fracture zone at each length. The strength of theweakest fracture zone is referred to as yarn strength while the meanstrength of the fracture zone is known as intrinsic yarn strength.

Thestrength of a yarn intrinsic can be determined by the use of animproved yarn heliacal structure (model) that follows the Hearle’stheory. According to the model, there are factors that determine thestrength of the yarn main factors are the strength, length, radius,twist, friction and migration of the fibre.

Accordingto the Hearle’s theory and experiments, the tenacity of fibrebundle varies proportionally to the tenacity of the fibre. Forinstance, if one doubles the tenacity of the fibre the tenacity ofthe yarn doubles too. In relation to Hearle’s theory, fibretenacity strongly correlates to its diameter and length however, itis hard to demonstrate the effect of fibre tenacity by using woolwith a matched diameter and duration.

Thelength of a fibre can affect its strength this is-through slippageeffect. In a staple fibre, the transverse forces generated by theyarn generate grip. This means that the central length of fibre isfully gripped by its neighbours and therefore, contributing to thestrength of the yarn, while the end fibres make no contribution tothe strength of the fibre and in return, the end fibre makes anegative contribution to the strength of the yarn. In relation tothis, as the length of the yarn increases, the portion of the endfibre involved in slippage is reduced and thus resulting to anincrease in the strength of the yarn.

Fibretwist is also another determinant factor of the strength of the yarn,as pointed out in Hearle’s theory, twist and fibre migration arethe only reasons why short fibres hold together as yarn. An increasein the twist of a yarn results to increase in its strength but onlyto a certain maximum strength where later the strength falls afterreaching the maximum point. The increase in strength is because astwist increases in the yarn the transverse force increases andbecomes larger making the portions involved in slippage shorten andthus resulting in small contribution twist. The falling of tenacityat high twist levels is because of fibre obliquity effect. With thisexplanation, it is clear that for an increase in the strength of ayarn less twist is needed for longer fibres and vice versa (for adecrease in the strength of a yarn more twist is required in shortfibres).

Weak-linktheory has been adopted to determine the effect of yarn unevenness onits strength in accordance to the Spencer-Smith’s model. The modelexplains that the linear dependence of a yarn`s tenacity on anunevenness yarn is given by the following equation: Sn1= S1* (1- β * CV% / 100).

Wherebyβ is constant and S1is the result of the increase in the strength of the yarn intrinsic.The computer-stimulated yarns have proved this model, where thestrength of the yarns is assumed to be proportional to the thinnestplace of any specific length. From the equation, it is clear thatintrinsic strength is always bigger than the strength of the yarnand, therefore, the strength of the yarn is determined by theunevenness of the yarn. This is because an increase in the length offibre not only increases the intrinsic fibre strength, but alsoimproves the evenness of the yarn.