Theoretical Profile of Ring-Spun Slub Yarn and its Experimental Validation

Transcription

1 Chong-Qi Ma, Bao-Ming Zhou, Yong Liu, Chuan-Sheng Hu Schoo of Texties, Tianjin Poytechnic University, 399 West Binshui Road, Xiqing District, Tianjin, , China E-mai: Theoretica Profie of Ring-Spun Sub Yarn and its Experimenta Vaidation Abstract A mathematica mode for the yarn count of ring-spun sub yarn was estabished to predict the yarn profie based on process parameters such as the fibre ength, the veocities of roers and the time of over-feeding. The theoretica study shows that the sub ength depends mosty on the process parameters above. The actua sub ength is a fibre ength greater than the sub ength designed, and the actua ength of basic yarn is a fibre ength ess than the ength of basic yarn designed. The vaidity of the mode was then verified using four sets of experiments. The experimenta resuts agreed we with the mode predictions and showed that the present mode had high prediction accuracy, which may aid in the design and production of a desired sub yarn with controing spinning parameters. Key words: sub yarn, mathematica mode, sub profie, sub ength, basic yarn ength. Introduction Fancy yarns, because of their abundance of specia aesthetic and structura effects of the textie materias in which they are used, have attracted much interest in recent years [ - 3]. These yarns give decorativeness, improve the appearance of a garment and change the end-use properties of a fabric [4-6]. Sub yarn, as one of the fancy yarns, is now increasingy used for amost a kinds of textie products, such as denim garments, shirts and uphostery, due to its unique stye and bamboo-ike profie [7-9]. To date, a variety of methods are avaiabe for producing sub yarns, ike ring-spun sub yarns and rotor-spun sub yarns. In these methods, ring spinning is the eariest and aso the most common processing technoogy in sub yarn production at the present time. A weknown method in this process is to modify the ring spinning frame in such a way that the intermittent acceeration of the drafting roers causes constanty varying degrees of draft to be appied [0]. In earier research on sub yarn, Testore and Minero [] proposed and discussed a cassification and standardisation for the determination of the fundamenta parameters that characterise sub-type fancy yarns. Grabowska [] studied and characterised the basic parameters describing the structure and tensie properties of sub fancy yarn produced on a ring-twisting frame. Wang and Huang [3] discussed and anaysed the parameters of rotor spun sub yarns in detai. Recenty Lu, Gao and Wang [4] estabished a mathematica mode based on the bar torsion mode to describe twist distribution in sub yarn. Liu et a. [5] presented an anaytica method of determining sub yarn geometrica parameters Ma C-Q, Zhou B-M, Liu Y, Hu C-S. Theoretica Profie of Ring-Spun Sub Yarn and Its Experimenta Vaidation. FIBRES & TEXTILES in Eastern Europe 03;, (97: based on a D visuaisation image of a sub yarn. However, there is sti a ack of adequate understanding of this process, especiay the reationship between process parameters and the profie of sub yarn in the spinning process. For exampe, the actua sub ength of sub yarn is not exacty equa to the ength designed in actua yarn production. In this work, the intermittent acceeration of the drafting roers by controing stepper motors in ring spinning, causing constanty varying degrees of draft to form randomy distributed subs (thick paces in the yarn, was adopted to experimentay and theoreticay study the reationship between the yarn count and some important process parameters such as the fibre ength, roer veocity, running time. Mathematica mode In this study, sub yarn was produced by changing the speeds of the back-mid roers whie the front roer ran with a constant speed to deiver the siver at a constant rate, which caused a variation in the resutant yarn fineness. Sub yarns were considered using the overfeeding of the back-mid roer method in the 3-over- 3 apron drafting system. After initia stretching and drafting between the back roers and midde roers, the siver was fed into the drafting zone (midde and front roers. The speed of back-mid roers varied with an intermittent acceeration, which was equivaent to additiona fibre feeding into the drafting zone, aowing the production of sub yarns. Generay the characteristics of sub yarn depend mainy upon how and where the fibres in the siver are acceerated and overfed, hence the speed, acceeration 9

2 time, deceeration time and highest speed time of the acceerated roers are of crucia importance. In order to simpify the probem, we can make some assumptions: a The drawing process is idea for sub yarn production, i.e., a part of fibres, whose headend, which is defined as the eading end of the fibre whie moving, arrive at the front roer nip in a ring frame, are then gripped and move immediatey at a inear speed of the front roer, whie any other fibres in the drawing zone keep their origina speed of back-mid roers. There are no foating fibres during drafting. b A the fibres have the same fibre ength ( and fibre fineness (N tf. c The fineness of the siver (N tc and distribution density of fibre headends in the siver (m c are constant. Thus the number of fibres (n c in a cross-section of siver and the distribution density (m c of fibre headends in a siver can be expressed as m ( N Ntc N tc n N c tf c = = = tf ( Thus the yarn fineness can be expressed Generay the more the overfeeding fibres to the drawing zone, the greater the as sub. The size and profie of the sub wi aso vary with a number of other variabes, such as the inear veocities of the (5 drawing roers, the acceeration time, deceeration time and running time at As described above, N tc,, V are constant and we can et N tc /V = A. Thus the the highest speed of the back-mid roers. A of these may be varied to produce a above equation can be simpified as finished yarn with the quaities desired. (6 We assume that the inear veocity of the back-mid roers are V and V, respectivey, at the owest and highest constant Thus the average inear density of sub yarn between positions x and x D can speed during the running time of t and be written in the form of Equation 7, t, respectivey. The acceeration time xd xof D the x back-mid roers xd from x the owest Ntx = Ntx ( x dx = V x dx = V dx D D V constant speed (VD to the highest constant speed (V N xd x is t, and the deceeration time from V to V is t 3, as shown tc = V dx = D V (7 in Figure.a. Here we define the whoe A xd x = V dx time of sub spinning as D t = t t t 3. where the vaue of D is very sma. During the formation of sub yarn, the overfeeding of fibres, which can be caused by an acceeration of the backmid roers, which passes additiona fibres to the drawing zone, wi generay affect the size of the resuting sub. According to the spinning principe of sub yarn, some basic conditions such as t V, t V <, t 3 V <, V < V and V < V. are amost aways true. If we consider the front roer nip as the V (0 x < tv ordinate origin and take the traveing direction of the yarn as the X axis towards V V V ( x tv ( tv x < tv tv tv the right as positive, the distribution density (m x of fibre headends in the yarn at V V ( x = ( tv tv x < tv tv tv a random position x aong the X axis can V V V ( tv tv - x ( tv tv tv x < tv tv be expressed as t3v mc V ( x x mx = (3 A V dx = AV 0 x < tv x V AV AB( x tv tv x < ( t t V where V is the inear veocity of the front roer, and V (x is the instantaneous veocity of the back-mid roer when A( V V x AV( tv tv AV( tv tv AB( tv ( t t V x < tv the random position yarn moves through the front roer nip. A( V V x AB( x tv AV( tv tv The number of fibres in the cross-section Nt x( x= AV( tv tv AB( tv tv x < ( t t V of yarn at a random position x can be AV ( t t V x< ( t t t V written in the form of Equation 4. A( V V x AC[( x tv tv ( t3v ] AV( tv tv tv x x m x c V tc nx ( x = m x xdx = dx = V dx AV( tv tv tv ( t t t V x < ( t t V V Ntf V (4 A( V V x AC( t3v AV( tv tv tv AV( tv tv tv N x tc = V x dx Ntf V ( t t V x< ( t t t V AV AC( x tv tv ( t t t V x < ( t t t t3 V where n x (x is the number of fibres at a random position x in the X axis. Equations 8 and 9. (8 (9 30 FIBRES & TEXTILES in Eastern Europe 03, Vo., No. (97

3 Thus the veocities of the back-mid roers can be written as Equation 8. This function is a piecewise inear function with 4 pieces. In order to simpy, we et V V = B tv V V = C t V 3 in the anaysis beow. Theoretica prediction of the yarn number (inear density and profie of ring-spun sub yarn In the manufacturing process of sub yarn, the ength (t V of yarn deivered from the front roer during the time of t pays a key roe in the yarn number (inear density and profie of the sub yarn. Generay the yarn number and profie of sub yarn mainy depends upon the reationship between the above ength and that of fibres. Hence the yarn number (inear density and theoretica profies of sub yarn are anaysed and discussed under the foowing conditions. Thickest yarn ength of sub yarn greater than the fibre ength, t V > In this condition, the thickest yarn ength (t V of the yarn deivered from the front roer in the time of t is greater than the fibre ength. The veocity of the back-mid roers increases from the owest speed V to the highest V during the time of t, then keeps the speed during the time of t, and finay decreases from V to V. The graph of function V (x can be drawn as the ower poyine in Figure.a according to Equation 8. Substituting Equation 8 into Equation 6 and integrating, function N tx (x can be written as a piecewise continuous function with 8 pieces presented as Equation 9. In the first piece, when 0 x < t V -, we get N tx (x - AV. It is a inear function and the graph of the function is a straight ine. In the second piece, it is a quadratic function and its shape is a paraboa that opens up between the two ends, (t V -, AV and ((t t V -, AV AB(t V /. The third piece is aso a inear function, the range of which is [AV AB(t V /, AV - AB(t V /]. FIBRES & TEXTILES in Eastern Europe 03, Vo., No. (97 a b Figure. a Graphs of functions N tx (x & V (x and b theoretica profie of sub yarn under condition of t V >. The fourth piece is aso a quadratic function and its shape is a paraboa that open down. In the fifth piece, when (t - t V - x < (t t t V -, we obtain N tx (x - AV. It is aso a inear function, the graph of which being a straight ine. The graphs of other pieces are simiar and symmetrica to those of the first three pieces. According to the x vaue (domain and graph of each piece, the piecewise graphs of a eight functions are drawn by taking each piece and treating it as a separate function, as shown in Figure.a. The yarn number (inear density, N tx (x, indicates the yarn diameter or fineness to which that particuar yarn has been spun. Hence the profie of sub yarn is simiar to that of the function graph, as shown in Figure.b. Additionay the three important parameters: the ength of basic yarn (L b, the sub ength (L s and the ength of the thickest yarn (L M can be obtained from Equation 9 and Figure. L b = t V (0 L s = t V ( L M = [(t t t V ] [(t t V ] = t V ( From the above equations and discussion, we can draw the foowing concusions:. Athough the veocity of the back-mid roers (V can be increased or decreased ineary, the inear density of sub yarn, N tx (x, can not be increased or decreased ineary.. Athough the veocity of the back-mid roers (V has reached its maximum, the thickest part of sub yarn wi not occur unti after the yarn has run over the distance of the fibre ength, or over a time of /V. 3. In this condition, the actua ength of the sub is t V, i.e., the sub ength is a fibre ength onger than the sub ength designed. And the actua ength of basic yarn is ess than that of the basic yarn designed, i.e., t V. Thickest yarn ength of sub yarn ess than the fibre ength, t V < In this condition, the thickest yarn ength (t V of the yarn deivered from the front roer during the time of t is ess than the ength of fibres. Generay the acceeration time (t and deceeration time (t 3 of the back-mid roer are equa in order to produce high-quaity sub yarn, i.e., t = t 3. Thus we get B = C. A graph of the function V (x can be drawn as the ower poyine in Figure.a (see page 3 according to Equation 8. Based on the function V (x, function N tx(x can be integrated as Equation 3 where N tx(x is a piecewise continuous function with 6 pieces. In this function, the first three pieces and sixth piece are the same as the first and eighth piece in 3

4 Equation 9. The fourth piece is a paraboa that open down with the range, [AV - AB(t V /, AV ]. The fifth piece is a inear function, the range of which is [AV AB(t V /, AV - AB(t V /]. The graphs of a six functions are drawn in Figure.a. The profie of sub yarn is simiar to that of the function graph, as shown in Figure.b. Figure. a Graphs of functions N tx (x & V (x and b theoretica profie of sub yarn under condition of t V <. 3 a b a b Figure 3. a Graphs of functions N tx (x & V (x and b theoretica profie of sub yarn under condition of t V = 0. x A V dx = AV 0 x < tv x AV AB( x tv tv x < ( t t V A( V V x AV( tv tv AV( tv tv AB( tv ( t t V x < tv Nt x ( x= (3 AV AB[( x tv ( x tv tv ] AB( tv tv x < ( t t V AV ABtV ( x tv AB( tv ( t t V x < tv AV AC( x tv tv tv x < ( t t t t3 V Equation 3. Additionay the three important parameters: the ength of the thickest yarn (L M, the sub ength (L s and yarn number (inear density of the thickest yarn (N tm can be obtained from Equation 3 and Figure.a. L M = 0 (4 L s = t V (5 N tm = AV. (6 Two extreme conditions The first contition t V = 0 In this condition, it is cear that t = 0. We can aso get t = t 3 and B = C in the same manner as in the previous cases. The graph of function V (x can be drawn as the ower poyine in Figure 5 according to Equation 8. According to V (x, there are 5 pieces in the piecewise function (7 of the yarn number (inear density N tx(x. In this function, the first two pieces and the fifth piece are the same as that in Equation 9. The functions of the third and fourth pieces are the same, but the domain is different. The graphs of a five functions are drawn in Figure 3.a. Hence the profie of sub yarn is simiar to that of the function graph and can be drawn as in Figure 3.b. The three important parameters: the ength of the thickest yarn (L M, the sub ength (L s and yarn number (inear density of the thickest yarn (N tm can be obtained from Equation 7 and Figure 3.a. L M = 0 (8 L s = (9 N tm = AV L AB(t V (0 The second contition t V = Like the above three conditions, the graphs of the two functions, V (x and FIBRES & TEXTILES in Eastern Europe 03, Vo., No. (97

5 N tx(x, and the profie of sub yarn can be drawn as in Figures 4.a and 4.b, respectivey. The four important parameters: the ength of the thickest yarn (L M, the sub ength (L s, the yarn number (inear density of the thickest yarn (N tm and ength of the base yarn (L j can be obtained from Figure 4.a. L M = 0 ( L s = (t t 3 V ( N tm = AV (3 L j = 0 (4 a Experimenta vaidation In order to verify the theoretica prediction, we carried out some experiments with the different conditions above. Generay the sub ength of sub yarn made from the same raw materias cannot be obtained correcty by the direct observationa method due to its unidentifiabe boundary between the base yarn and sub. In order to avoid this probem, two strands of back poyester fiament yarns (5.3 tex, Fangyuan chemica fibre Co. Ltd., Suzhou, China were used as the base yarn, and (30 tex, fibre ength = 9 mm was fed into the drafting zone to produce the sub. A schematic diagram of the spinning process modified is shown in Figure 5. A digita sampe spinning machine (DSSP-0, Digitized Textie Technoogy Institute of Tianjin Poytechnic University, China which can contro every roer s speed by means of a computer was empoyed to produce sub yarns using intermittent acceeration of the back-mid roers under different conditions in the experiments. The spinning parameters are isted in Tabe. The four sets of parameters correspond to: # t V >, # t V =, 3# t V <, 4# t V =0. After spinning, the sub yarns produced were recorded by digita camera (Canon G0, Canon Co. Ltd., Japan, as shown in Figure 6 (see page 34. In order to reduce the error, each sub yarn was measured at east 0 times at different positions under each condition and the mean vaue was cacuated. The experimenta resuts obtained from the different spinning conditions are isted in Tabe (see page 34. The experimenta resuts showed that the FIBRES & TEXTILES in Eastern Europe 03, Vo., No. (97 b Figure 4. a Graphs of functions N tx (x & V (x and b theoretica profie of sub yarn under condition of t V =. Roving Figure 5. Schematics of the ring-spun sub yarn spinning process. Tabe. Spinning parameters in the experiments; V ss - spinde speed, Mdr - mechanica draft ratio, Dt - designed twist. # 40 # 9 3# 5 4# 0 Midde roer Fiament yarn V V Front roer Sub yarn t V, mm t V, mm t 3 V, mm t V, mm V ss, R/min Mdr Dt, turns/m x A V dx = AV 0 x < tv x AV AB( x tv tv x < ( t t V AB Nt x ( x= AV ( x t V AB( t V ( t t V x < t V AB AV ( x t V AB( t V t V x < ( t t V AV t t V x t t t Equation 7. ( < ( 3 V (7 33

6 a b c d Figure 6. Images of the sub yarns produced from the four experiments under different conditions, a t V >, b t V =, c t V <, d t V = 0. sub ength and that of basic yarn measured agreed we with the theoretica predictions and showed that the mode has high prediction accuracy. Concusions 34 A theoretica mode was proposed to dea with the yarn count and yarn profie of the ring-spun sub yarn spinning process according to the process parameters. Spinning experiments were carried out to vaidate the mode. The experimenta resuts show very good agreement with those obtained from the theoretica predictions. The concusions presented provide a genera way of understanding and producing sub yarn with the profie desired in the ring-spun sub yarn spinning process. Acknowedgments The present work is supported by the Nationa Science Foundation of Tianjin No.0JCY- BJC000. References. Petruyte S. FIBRES & TEXTILES in Eastern Europe 008; 6, 3: Ragaišienė A. FIBRES & TEXTILES in Eastern Europe 009; 7, 4: Grabowska KE. FIBRES & TEXTILES in Eastern Europe 008; 6, 6: Kumpikaitė E, Ragaišienė A, Barburski M. FIBRES & TEXTILES in Eastern Europe 00; 8, 3: Tabe. Resuts obtained from the different spinning conditions; L db - ength of basic yarn designed, L d - ength of sub designed, L tb - theoretica ength of basic yarn, L t - theoretica ength of sub, L mb - measured ength of basic yarn, L m - measured ength of sub. A parameters is in mm. t V L db L d L tb L t L mb L m # # # # Kumpikaitė E, Ragaišienė A, Barburski M. FIBRES & TEXTILES in Eastern Europe 00; 8, 4: Grabowska KE. FIBRES & TEXTILES in Eastern Europe 00; 8, : Liu X, Wen Z, Su Z, Choi K.-F. Textie Research Journa 008; 78, 4: Edaat-Pour S. The Textie Magazine 008; 49, 5: Gong RH, Wright RM. Fancy yarns: Their manufacture and appication. Woodhead Pubishing Limited, UK, 00, pp Gong RH, Wright RM. Fancy yarns: Their manufacture and appication. Woodhead Pubishing Limited, UK, 00, pp Testore F, Minero G. Journa of the Textie Institute 988; 79, 4: Grabowska KE. Fibres & Texties in Eastern Europe 00; 9, : Wang J, Huang XB. Textie Research Journa 00; 7, : Lu Y, Gao W, Wang H. Internationa Journa of Cothing Science and Technoogy 007; 9, : Liu J-H, Li Z-X, Lu Y-Z, Jiang H-X. FI- BRES & TEXTILES in Eastern Europe 00; 8, : Received Reviewed FIBRES & TEXTILES in Eastern Europe 03, Vo., No. (97