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Characteristics of Cloth Formation in Weaving and Their Influence on Fabric Parameters XIAOGANG CHEN Department of Textiles, University of Manchester Institute of Science and Technology, Manchester M60 1QD, United Kingdom ABSTRACT This paper discusses the characteristics of cloth formation in weaving as regards continuous weaving, the concept of balanced weaving is put forward, and an equation of balanced weaving is then established for analyzing the response of the weaving process to disturbances of various kinds. Based on the analysis of beat-up resistance and weft yarn bouncing back, the cloth formation area is defined as an indicator of the weaving conditions. These discussions lead to control of fabric parameters.

Research into the cloth formation theory in weaving started, arguably, in the 1950s, most notably by Greenwood et al. [4, 5, 6]. Such research has furthered the understanding of the weaving process and has led to the establishment of loom setting procedures, enabling the use of shed timing, imbalanced shed, and so on, to achieve the required geometric, physical, and mechanical characteristics of woven fabrics. Understanding of the nature of cloth formation in weaving and applying electronic controls have enabled the loom to become a much more precise machine for producing fabrics. Because of this, the loom’s ability to produce fabrics with complicated structural features has widened and fabric quality has been much improved for various end-use applications. Another line of work is the analysis and modeling of woven fabrics to attempt to engineer fabrics with certain properties. Chen and Leaf, for instance, worked on a computer system that is able to determine fabric parameters based on specifications of physical and mechanical properties, such as the cover factor and tensile modulus [1, 3]. Being able to make fabrics with engineered structural parameters is more important today because woven fabrics are used not only for domestic but also for technical applications. Satisfying the property requirements becomes vital in some technical applications such as in the aeronautics industry. In this paper, we attempt to analyze the characteristics of the cloth formation process by defining balanced weaving and describing beat-up resistance. We also address the problem of how a fabric should be made with engineered parameters in order to perform properly.

Textile Res. J. 75(4), 281–287 (2005) DOI:10.1177/0040517505054737

Balanced Weaving Process It is important that weaving is kept continuous and weft density kept constant at a pre-specified level. For continuity, we may treat the loom as a black box with warp and weft yarns as input and grey fabric output, as indicated in Figure 1. Under stable weaving conditions, the material flow through the black box must be constant, though the amount of flow can be stabilized on different levels. In fabric terms, the flow level corresponds to the amount of yarns going into the system or the grey fabric coming out of the system. The steadiness of the flow can also, more conveniently, be measured by the weft density of the grey fabric. If the loom is running under the normal conditions, the weft density of the grey fabric should be consistent. To express it another way, a varying weft density is always a sign that the loom is not working under acceptable weaving conditions. During weaving, the warp and weft yarns enter the weaving system and grey fabric comes out of the weaving system in a continuous fashion; at the same time, the input to and output from the system must, for normal weaving, be at equilibrium. Hence, weaving is a dynamically balanced process. The level at which the balance is established is determined by the fabric specifications and realized by loom setting-up. Obviously, any interference or disturbance to this equilibrium or bal-

FIGURE 1. Weaving viewed as a system.

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ance will lead to a fault in the fabric, and severe disturbance of balanced weaving may make it impossible to continue the process. Therefore, it is critical that weaving conditions be balanced during weaving, when the beat-up distance and the level of the base warp tension should both be constant. Because the weft density of the fabric is a direct result of the weaving status, it can be used as an indicator for the levels of balanced weaving. Balanced weaving has two features: when the ratio of input to output of the weaving system remains unchanged, balanced weaving will remain on the same level, and this level is a response to the stimulation of

any interruption. Figure 2 shows weaving responses to different kinds of stimulations to the weaving system, where (a) is the response to a step signal caused by the braking weight change, (b) is the response to a pulse signal caused by the variation in let-off length, and (c) is the response to a pulse signal caused by an irregular take-up length. However, the response of weaving to interference is not instantaneous, but rather delayed. This is due to the fact that the warp tension change caused by interference takes time to correct. EQUATION

FOR

BALANCED WEAVING

We will use the plain weave fabric geometry to illustrate the establishment of the balanced weaving equation. After passing the cloth formation area during weaving, the fabric enters a temporary stable stage, where the picks will not move relative to the warp ends. As well, both warp and weft yarns are still under tension and thus have yet not started to retract. Figure 3 shows the cross section along the warp direction of the plain woven fabric taken at such a stage. In this illustration, S is the take-up length per loom cycle, l is the let-off length of warp ends per loom cycle, ⌬l is the extension of l due to the existence of the warp tension, and ␣ is the weaving angle. In real fabrics, the yarn path may assume different configurations affected by many factors ranging from fiber type to fabric construction. Along with many other researchers [7, 8], we have assumed that the modular length of the warp yarn in the fabric can be expressed by a straight line.

FIGURE 3. Fabric cross section.

Based on Figure 3, it is easy to establish that FIGURE 2. Weaving response to different stimulations.

S ⫽ 共l ⫹ ⌬l 兲 cos ␣ .

(1)

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During a balanced weaving, S and l are constants. For this reasons, the base warp tension level will remain unaffected and thus ⌬l will remain unchanged. Obviously, the weaving angle ␣ will not change during balanced weaving. Because this equation describes the stable relationship between the input and output of the weaving system, we refer to it as the balanced weaving equation in this context. It is necessary to add three more facts about the balanced weaving equation. First, ⌬l is closely related to the warp tension level and yarn type. However, we have proved [2] that for most (if not all) fabrics, ⌬l is fully recoverable, and this recovery will contribute to fabric shrinkage when the fabric is removed from the loom. Different levels of ⌬l therefore will lead to different levels of fabric off-loom shrinkage. Second, cos ␣ reflects the crimp interchange during weaving. A smaller value of cos ␣, i.e., a larger ␣, corresponds to a higher level of yarn crimp in the warp direction, a smaller level of yarn crimp in the weft direction, and vice versa. Third, in a balanced weaving situation, both l and ⌬l are constants, and therefore (l ⫹ ⌬l) is a constant. However, the let-off length in practice may not always be the same. If the variation in let-off length is small enough, a change in ⌬l will compensate for the variation in l. In this situation, the weaving is no longer balanced even though (l ⫹ ⌬l) is still constant. Any change in l and ⌬l will affect the weft density of the fabric. DISTURBANCES TO BALANCED WEAVING CONSEQUENCES

AND

THEIR

Balanced weaving produces a uniform weft density in the fabric. However, such weaving can be destroyed by various disturbances, which will cause variations in weft density. From the balanced weaving equation we see that the disturbance mainly comes from the take-up of fabric and the let-off of warp ends. In weaving, one of these disturbances may happen or both may take place at the same time. Obviously, the probability of both happening together is much smaller. We will discuss the two kinds of disturbances separately. Take-up Disturbance Mechanical faults of the take-up gear system are the most likely causes of disturbances of this type. A sudden insertion of extra thick or thin warp ends may also cause a take-up disturbance. In order to see the consequences of a take-up disturbance, we consider the first-order derivative of Equation 1, which is dS ⫽ cos ␣(dl ⫹ d⌬l) ⫺ (l ⫹ ⌬l) sin ␣ d␣, where dS is the change in take-up length of fabric, dl is the change in the let-off length of the warp ends, d⌬l is the change in ⌬l, and d␣ is that in

the weaving angle; dl, d⌬l, and d␣ come into existence because of dS. We assume that the disturbance to balanced weaving is only from the take-up motion and that the let-off of the loom works under normal conditions, that is dl ⫽ 0. The expression for dS then reduces to dS ⫽ cos ␣ d⌬l ⫺ 共l ⫹ ⌬l 兲 sin ␣ d␣

.

(2)

Equation 2 indicates that a disturbance in the take-up dS will cause ⌬l and ␣ to change. Remember that the warp extension ⌬l1 is fully recoverable when tension is removed. Thus d⌬l is the change in ⌬l due to the disturbance. Although ⌬l is always positive, d⌬l may be either positive or negative depending on different circumstances. If the disturbance is caused by taking up more fabric length than required, dS is positive; otherwise, dS is negative. According to Equation 2, a positive dS will cause an increase in ⌬l, i.e., a positive d⌬l, and a decrease in ␣, i.e., a negative d␣. More explicitly, it can be described as [dS (⫹) 3 d⌬l (⫹), d␣ (⫺)]. Similarly, for a negative dS, we have [dS (⫺) 3 d⌬l (⫺), d␣ (⫹)]. Let us now discuss the influence of the take-up disturbance on the fabric’s weft density. A positive dS can only happen when the take-up motion accidentally takes up more fabrics length than required. The immediate effect of this disturbance on the weft density of the fabric is that the on-loom weft density is reduced from its normal level to a certain extent. Meanwhile, this disturbance will raise the warp tension, leading to stretched warp ends, i.e., a positive d⌬l, and a decreased weaving angle ␣, i.e., a negative d␣. When the fabric is removed from the loom and fully relaxed, the warp extension ⌬l will recover, contributing to a higher weft density at the place where the weft density was made smaller by the disturbance. Because the weaving angle ␣ was made smaller in the on-loom fabric, in the course of crimp interchange in a relaxing fabric, the weaving angle in the warp direction can only be increased. This change will also increase the weft density, which was made smaller. The influence of a positive dS and a negative dS is described below, with symbols 1 and 2 representing increase and decrease, respectively.

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From this discussion, we can conclude that when balanced weaving is disturbed from the take- up by an amount of dS, the change in weft density for the on-loom fabric is likely to be compensated by the change in ⌬l1 and ␣i when the fabric has been removed from the loom. Note that the compensation will not be enough to recover the change in weft density when the disturbance is too large. Let-Off Disturbance From Equation 1, we can write that l ⫽ S cos ␣ ⫺ ⌬l. Differentiation of this expression leads to dl ⫽

cos ␣ dS ⫹ S sin ␣ d␣ ⫺ d⌬l cos2 ␣

.

In this case, we assume that the disturbance is from the let-off motion only. Therefore, there is no change in the take-up length of the fabric, i.e., dS ⫽ 0. This leads to dl ⫽ S

tan ␣ d␣ ⫺ d⌬l cos ␣

.

(3)

As indicated in Equation 3, a positive dl leads to an increased weaving angle, i.e., a positive d␣, a decreased extension, i.e., a negative d⌬l, and vice versa. These can be illustrated by the expressions [dl (⫹) 3 d␣ (⫹), d⌬l (⫺)] and [dl (⫺) 3 d␣ (⫺), d⌬l (⫹)]. When balanced weaving is disturbed from the let-off by sending in extra warp length, the warp tension will be reduced and the cloth fell will move forward because of the tension balance between the warp ends and the fabric, resulting in a lower weft density. Since the warp tension becomes lower, the warp extension ⌬l is reduced by d⌬l. This means that when the fabric is removed from the loom, less elastic recovery will occur to the warp ends in the fabrics, and thus a smaller contribution will be needed to increase the weft density in the off-loom fabrics. This disturbance will also lead to a larger weaving angle, and the fabric will have a larger warp crimp. Because of the lower warp tension during weaving, the warp yarns in an off-loom fabric will have little potential to undo the crimp. For this reason, the weft density in the off-loom fabric is less likely to increase. This situation is illustrated by the following expressions.

From the discussion on the let-off disturbance, we can conclude that when the balanced weaving is interrupted from the let-off motion by an amount of dl, the change in weft density occurring during weaving is unlikely to be compensated by the recovery in ⌬l and ␣ during fabric relaxation.

Resistance to Beat-up During beat-up, the newly inserted weft yarn, or the pick, is pushed toward the cloth fell along the warp ends by the reed. In this time interval, the reed must overcome the friction between the warp ends and the new pick. At the same time, due to the elasticity of textile yarns, the beat-up action causes greater extension in the warp ends, which in turn causes an elastic resistance against beat-up.

Frictional Resistance (Rf) At the moment of beat-up in the weaving cycle, the newly inserted pick has already been embraced by the warp ends because of shedding. In order to move forward, the reed must overcome the friction between the pick and the warp ends. Let us consider a fabric unit, shown in Figure 4a, taken from the cloth fell, where Tf is the warp tension within the fabric, ␪ is the warp angle in the fabric unit, and ␤ is the warp wrapping angle over the pick. Suppose that the tension of the fabric, corresponding to one warp end width, at beat-up is Tfabric. Then, the relation between Tf and Tfabric is Tf ⫽

T fabric . cos ␪

(4)

FIGURE 4. A fabric unit from the cloth fell with (a) geometric and (b) mechanical relations.

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In order for the weft yarn to overcome the frictional resistance, the force acting on the new pick should be at least the same as the frictional resistance. According to Euler’s equation, with reference to Figure 4b, the frictional resistance Rf ⫽ Tf e␮␤, i.e., Rf ⫽

T fabric ␮␤ e cos ␪

(5)

where ␮ is the frictional coefficient between the warp and weft yarns, ␤ is the warp-wrapping angle, and ␪ is the warp angle in the fabric unit. Equation 5 shows that Rf increases when any of ␮, ␤, and ␪ increase. A higher fabric tension at the beat-up moment Tfabric will lead to higher beat-up resistance, too. Obviously, the warp wrapping angle ␤ and the warp angle ␪ in the fabric unit describe in part the fabric geometry at the beat-up moment. ␤ is governed by the loom setting up. For example, if the loom is set to early shedding, the wrapping angle ␤ will be larger at beat-up, and that in turn will produce a higher frictional resistance Rf ␪, on the other hand, is related to the fabric weft density and the thickness of the weft yarn. A higher weft density and a thicker weft yarn will lead to a larger ␪, which will contribute to a higher beat-up resistance. ELASTIC RESISTANCE (RE) Because of the elastic nature of most textile yarns, the warp ends will provide elastic resistance to the weft at beat-up. Figure 5 illustrates the mechanical model of the fabric unit from the cloth fell. Figure 5a describes the tension situation for the new pick with Twarp being the warp tension at beat-up, and Figure 5b depicts the elastic resistance. N is the resultant force of the warp tension from the fabric side and warp end side.

The elastic resistance Re is the horizontal component of N, shown in Figure 5b, which is Re ⫽ N cos ␸, i.e., R e ⫽ 冑T warp2 ⫹ Tf 2 ⫹ 2Twarp Tf cos ⬔共Twarp ,Tf 兲 cos ␸ . (7) It is evident from Equation 7 that the elastic resistance Re is dependent on the warp tension on the warp side and on the fabric side, the angle between the directions of these two tensions, and angle ␸. Basically, the larger the Twarp and Tf , the larger the elastic resistance Re and the smaller the angle ␸, the larger the Re. For a fabric with a given weft density and a given yarn linear density, the angle ␸ in the fabric may be taken as a constant. Under such a situation, angle ⬔(Twarp, Tf) is determined by the direction of Twarp only, which is, in turn, governed by the selection of shedding time. An early shedding time means that at the beat-up moment, the shed is well open and the angle between Twarp and the horizontal line is large. It is evident from Figure 5a that a larger angle between Twarp and the horizon makes angle ⬔(Twarp, Tf) smaller. Thus, an early shedding time, producing a larger shed angle at the beat-up moment, will result in a larger resultant force N, which will increase the elastic resistance. However, a larger shed angle at the beat-up moment will cause a larger angle ␸ between N and the horizon, which will reduce the elastic resistance. In general, therefore, the influence of shedding time on the elastic resistance depends on both the tensions Twarp and Tf and the shed size. TOTAL RESISTANCE

TO

BEAT-UP

We stated earlier that the frictional resistance and the elastic resistance form the total resistance to beat-up. If we use R to denote the total beat-up resistance, then R⫽

T fabric ␮␤ e cos ␪ ⫹ 冑Twarp2 ⫹ Tf 2 ⫹ 2Twarp Tf cos ⬔共Twarp ,Tf 兲 cos ␸ . (8)

FIGURE 5. Mechanical model of a woven fabric at beat-up.

From Figure 5a, it is obvious that the resultant force N can be expressed by Equation 6, where ⬔(Twarp, Tf) refers to the angle between Twarp and Tf : N ⫽ 冑T warp2 ⫹ Tf 2 ⫹ 2Twarp Tf cos ⬔共Twarp ,Tf 兲 .

(6)

Because of the two kinds of resistance to beat-up, the new pick moves into the cloth fell in an alternating fashion during beat-up. When the beat-up force is large enough to overcome the frictional resistance, the new pick will move relative to the warp ends and toward the cloth fell. However, when the new pick has moved some distance toward the cloth fell, the beat-up force is unable to move the new pick any further. What happens at this stage is that the new pick will move together with the warp ends, enduring the frictional resistance and the elastic resistance. This will cause the fabric tension to

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decrease and the warp sheet tension to increase. This change of tension balance will help the beat-up force to push the new pick further into the fabric. We believe that these two modes of movement continue until the end of beat-up. This kind of movement of the new pick may be termed the intermittent movement. Obviously every measure should be taken to reduce the number of cycles of slack-tension movement in order to create good weaving conditions, and setting the base warp tension to a higher level is one measure that has been widely used. PICK BOUNCING BACK

AND

␺⫽

1 共␪ ⫺ ␾兲 2

.

(10)

CLOTH FORMATION AREA

The new pick is pushed to the fell position during beat-up. However, this weft yarn, together with some of its previous ones, will tend to bounce back to an extent when the reed retreats due to the unbalanced tension between the fabric and warp sheet. Figure 6 is a unit taken from the cloth fell when the reed just starts to retreat. In Figure 6, N⬘ is the resultant force on the weft, Rf⬘ is the friction on the weft, ␺ is angle between N⬘ and the perpendicular, ␾ is half of the shed angle, and ␪ is the weaving angle. At the moment when the reed starts to move back, the weft yarn tends to bounce back, mainly because of the tension difference on the two sides of the new pick. Basically, the tendency for the new pick to move outward is governed by the friction Rf⬘ and the new resultant force N⬘ of the warp tension. The latter tends to cause the new pick to bounce back. To stop the new pick from bouncing back, the projections of N⬘ and Rf⬘ must be at least equal to each other, i.e., N⬘ sin ␺ ⱕ Rf cos ␺, i.e., tan ␺ ⱕ

this equation that a smaller ␺ is desirable for preventing the weft yarn from bouncing back. When the weft density of a fabric is given, a smaller ␺ can only be reached when an early shedding time is arranged. That is, an early shedding type helps stop the new pick from bouncing back. In Figure 6,

Rf ⬘ ⫽␮ , N⬘

(9)

where ␮ by definition is the frictional coefficient between the warp and weft yarns. Equation 9 states that if tan ␺ is less than the frictional coefficient between the warp and weft yarns, the new pick will not bounce back. For this reason, Equation 9 is called the nonbouncing-back equation. It is clear from

FIGURE 6. Mechanical model of fabric when reed retreating.

This shows that the larger the shed angle ␾, the smaller the angle ␺; ␺ becomes zero only when ␪ ⫽ ␾. This means that the new pick does not tend to bounce back under such weaving conditions. In practice, it is not possible to satisfy the condition ␪ ⫽ ␾. Consequently, in practical weaving, angle ␺ is always larger than zero, indicating that there will always be some bouncing back of the new pick. In another words, apart from fabrics that require very low weft density, the new picks are not pushed to the correct position by just one beat-up action. Normally, it takes a number of successive beat-ups to reach a pre-set weft density. Therefore, when weaving fabrics with normal to high weft densities, there will always be a length of fabric at the cloth fell whose weft density is lower than required and changes as a new beat-up action takes place. This length of fabric is known as the cloth formation area, which is illustrated in Figure 7. In Figure 7, ⌬1 refers to the bounce-back distance of the new pick when the reed has retreated, ⌬2 is that of the previous weft, and so on; p2 is the required on-loom pick

FIGURE 7. Existence of cloth formation area.

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spacing of the fabric, which is the inverse of the weft density. Obviously, ⌬1 ⬎ ⌬2 ⬎ . . . ⬎ ⌬n⫺1 ⬎ ⌬n ⫽ 0 and limi 3 n ⌬i ⫽ 0. This shows that a weft yarn is beaten into its required position, where the pick spacing becomes p2 , only after n successive beat-up actions. The length of this cloth formation area indicates the weaveability of the fabric under the current loom setting. A large length of this area means the fabric is difficult to weave, whereas a short length of this area is a hint that the fabric is easy to weave.

Making Fabrics with Required Parameters For given warp and weft yarns and weave structure, the practical parameters for a woven fabric are the warp and weft densities and yarn crimps in the fabric. All these parameters together with the fiber types influence fabric performance. The earlier discussions on balanced weaving and on weaving resistance are helpful in achieving specified values for these parameters. CONSTANT WARP

AND

WEFT TENSION

Based on our discussion of balanced weaving, any change in base warp tension destroys balanced weaving, and will lead to variations in the final weft density of the fabric. The on-loom weft density may remain unchanged when warp tension changes and the configuration of the warp ends in the fabric change. Also, and probably more importantly, the warp end extension has changed. The change in warp end extension will affect off-loom fabric shrinkage and thus weft density. It is less likely that weft tension will change in modern weaving. If it does, the effect on warp density will be similar. Weaving tension affects the yarn configuration in the fabric. It is well known that a higher tension leads to a smaller yarn crimp, and a lower tension results in a larger yarn crimp. The configuration of yarns within the fabric influences many aspects of the fabric’s performance, such as tensile modulus and fabric thickness. LOOM SETTING To weave more effectively, there is no doubt that the cloth formation area should be small. A number of measures can be taken to achieve a small length of the cloth formation area. The use of early shedding is common for reducing the length of the cloth formation area. The early

shedding arrangement may increase the frictional resistance to beat-up, but it produces a good locking effect from the shed layers to the new pick, preventing bouncing back. An imbalanced shed geometry has also been implemented for a smaller length of the cloth formation area.

Conclusions The concept of balanced weaving is put forward in this paper, and a simple equation is established for analyzing weaving responses to disturbances, providing a convenient and useful method for this purpose. The cloth formation process is examined in detail, beat-up resistance is analyzed, and the two kinds of resistance, frictional and elastic, are expressed mathematically. Bouncing back of the new pick is discussed, and the conditions for no bouncing back are established. The cloth formation area is introduced and is related to the weaveability of a fabric. The length of the cloth formation area can be used as an indicator of fabric weaveability. Based on the discussion of balanced weaving and the cloth formation area, measures for achieving the required fabric parameters are recommended.

Literature Cited 1. Chen, X., and Leaf, G. A. V., Engineering Design of Woven Fabrics for Specific Properties, Textile Res. J. 70(5), 437– 442 (2000). 2. Chen, X., Masters thesis, Northwest Institute of Textile Science and Technology, Xi’an, China, 1984. 3. Chen, X., Doctoral thesis, The University of Leeds, Leeds, U.K., 1991. 4. Greenwood, K., and Cowhig, W. T., The Position of Cloth Fell in Power Looms, Part I: Stable Weaving Conditions, J. Textile Inst. 47, T241–T254 (1956). 5. Greenwood, K., and Cowhig, W. T., The Position of Cloth Fell in Power Looms, Part II: Disturbed Weaving Conditions, J. Textile Inst. 47, T255–T273 (1956). 6. Greenwood, K., and Vaughan, G. N., The Position of Cloth Fell in Power Looms, Part III: Experimental, J. Textile Inst. 47, T274 –T286 (1956). 7. Kawabata, S., Niwa, M., and Kawai, H., The Finite-deformation Theory of Plain Weave Fabrics, Part I: The Biaxial Deformation Theory, J. Textile Inst. 64, 21 (1973). 8. Leaf, G. A. V., and Kandil, K. H., The Initial Load Extension Behaviour of Plain-Woven fabrics, J. Textile Inst. 71, 1–7 (1980). Manuscript received March 5, 2003; accepted August 13, 2003.