STRUCTURAL DESIGN ENGINEERING OF WOVEN FABRIC BY SOFT COMPUTING: PART I - PLAIN WEAVE

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1 AUTEX Researc Journal Vol. June AUTEX STRUCTURAL ESIGN ENGINEERING OF WOVEN FARIC Y SOFT COMPUTING: PART I - PLAIN WEAVE Rajes Misra ana Kremenakova.K. eera & Jiri Militky Faculty of Textile Engineering Tecnical University of Liberec Czec Reublic eartment of Textile Tecnology Indian Institute of Tecnology eli India Abstract: Key words: An attemt as been made to otimise te engineering attributes of a lain weave fabric according to certain requirements. A simlified algoritm was used to solve fabric geometrical model equations and relationsis were obtained between useful fabric arameters suc as tread sacing and crim fabric cover and crim war and weft cover. Suc relationsis el in guiding te direction for moderating fabric arameters. Te full otential of te Peirce fabric geometrical model for lain weave as been exloited by soft comuting. Te interrelationsis between different fabric arameters for jammed structures non-jammed structures and secial cases in wic te cross-treads are straigt were obtained using a suitable algoritm. It is oed tat te fabric designer will benefit from te flexibility in coosing fabric arameters for acieving any end use wit te desired fabric roerties. esign engineering geometrical model jammed structure soft comuting. Introduction Fabric roerties are greatly affected by te coice of fabric arameters since te coice of fabric arameters influences te structure. Te beaviour and relationsi between fabric arameters is a recursor to te otimal solution for fabric engineering roblems. Many features of te clot are essentially deendent on geometrical relationsis. Te geometrical model of fabric rovides some simlified formulae to facilitate calculations and secific constants wic are of value for clot engineering structural roblems and mecanical roerties []. Tese fabric arameters are tools for an innovative fabric designer in creating fabrics for diverse alications. Te teoretical relationsi between fabric arameters enables te fabric designer to lay wit different fibres yarn tex treads/cm and weave to vary texture and fabric roerties. Te first study of fabric structural design was started in 937 by Peirce [] wic led to Peirce s model of lain-weave fabrics wit a circular yarn cross-section. He also roosed a fabric model wit an ellitical yarn cross-section. In 958 Kem roosed a racetrack model []. Hearle and Amirbayat roosed lenticular geometry for calculations in fabric mecanics by te energy metod in 988 [3]. Many studies related to fabric mecanical roerties on te basis of te fabric structural model were carried out by Grosberg [4] acker [5] and Postle [6]. Lindberg [7] extensively studied fabric mecanical beaviour related to tailorability. Subsequently a soisticated measurement system of fabric mecanical roerties was develoed by Kawabata and Niwa [8] wic is called te KES-F system. Anoter fabric mecanical measurement system called FAST was develoed by CSIRO in Australia [9]. Recently new objective measurement systems [] suc as te Virtual Image islay System (VIS) and te Fabric Surface Analysis System (FabricEye(r)) ave been develoed for te analysis of fabric geometrical roerties. On te oter and tere are currently many CA systems [] related to fabric design suc as weave construction colour and attern. Tere is also a attern design CA [3] including a visual wearing system (VWS) for garment designers. However tere is no fabric structural design system related to te decision on fabric density according to fibre materials yarn linear density and weave attern. Terefore a database system wic can easily calculate war and weft densities according to te various yarn counts weave constructions and materials is required troug te analysis of a design lan for nylon and olyester fabrics [45]. It is ossible to redict te fabric arameters and teir effect on te fabric roerties by soft comuting. Tis information is elful in making a decision regarding a secific buyer s need. A simlified algoritm is used to solve tese equations and to obtain relationsis between useful fabric arameters suc as tread sacing and crim fabric cover and crim as well as war and weft cover. Suc relationsis el in guiding te direction for moderating fabric arameters. For examle te arameters of a fabric requiring a certain crim in te war and weft even in te jammed state can be calculated. Alternatively it may be desirable to make a non-jammed fabric wit a certain amount of war and weft. Even fabrics wit maximum crim in eiter te war or weft direction can be estimated. In tis work an attemt as been made to otimise te engineering attributes of a lain weave fabric according to certain requirements. Metodology Aroac to develo soft comuting algoritm It is needless to mention tat te ioneering work of Peirce on te geometrical model rovides te basic latform for fabric engineering. Many basic fabric dimensional arameters can be worked out from te geometrical model by use of modern soft comuting metods. Fabric arameters for any relationsi between war and weft cover can be evaluated. Last but not least te relationsi between fabric mass and fabric cover can also be evaluated. Tis is te strengt of soft comuting wic cannot be acieved by any oter means including te graical or monogram metods. Te basic equations derived from te geometrical model are not easy to andle. In fact it is difficult to solve tese equations on many occasions. Many researcers ave tried to solve tese tt:// 37

2 AUTEX Researc Journal Vol. June AUTEX equations and found some simlified relationsis. However te best metod so far as been found to be te graical metod. It was terefore decided to develo a simle algoritm from te Peirce geometrical model to establis te relationsi between various fabric arameters troug soft comuting. Programming Comuter rograms were develoed for establising relationsis between various fabric arameters originating from te Peirce geometrical model using MATLA-7. l l C sin θ θ θ sinθ Peirce s geometrical relationsis can be written in te following form: ( K θ ) sinθ [] Plot c ( K θ)sinθ ( cos θ ) were: tread sacing crim eigt d d d yarn diameter l modular lengt θ weave angle K l /. Start [] E 3 A θ. l /. θ. ( K θ ) sinθ ( K θ)sinθ ( cos θ ) l/ c / θ θ. x l [( θ ) sinθ ( )] x?. Plot c θ θ. A l sinθ θ θ.57 End l. E l θ sin l / c / Plot c θ C F tt:// 38

3 AUTEX Researc Journal Vol. June AUTEX F l. / / l sin θ θ. l θ sinθ / / Figure. Relationsi between tread sacing and crim eigt Plot c Start θ l /. 3 sinθ ( cos θ l/ ) c / Figure. Flowcart for solving Peirce s basic geometrical equations Suffix and reresent war and weft yarn resectively. Two similar equations for te weft direction can be obtained by intercanging suffix wit and vice-versa. Te relationsis between fabric arameters were graically obtained for various constructions like jammed structures non-jammed structures and also for fabric wen te cross-treads are straigt. Te flow cart for tis algoritm is sown in Figure. l / θ θ. θ cos sinθ l θ sinθ Results and discussion Te solution of / and / was obtained for different values of θ (war crim angle) ranging from. - π/ radians. Suc a relationsi is sown in Figure. Te Figure is similar to tat given by Peirce. It is a very useful relationsi between fabric arameters for engineering desired fabric constructions. One can see its utility for te following tree cases: Jammed structures n-jammed fabrics Secial case in wic cross-treads are straigt. Jammed structures Figure sows te non-linear relationsi between te two fabric arameters and on te extreme left. In fact tis curve is for jamming in te war direction. It can be seen tat te jamming curve sows different values of / for increasing Plot l / c / vs θ.57 c vs c End Figure 3. Flowcart for fabric arameters in jammed structures tt:// 39

4 AUTEX Researc Journal Vol. June AUTEX crim. Interestingly tis curve is a art of a circle and its equation is: Wit te centre at ( ) and a radius equal to. For jamming in te war direction of te fabric te arameters / and corresonding / can be obtained eiter from tis figure or from te equation above. Te relationsi between te fabric arameters over te wole domain of te structure being jammed in bot directions can be obtained by te algoritm given in Figure 3. Yarn sacing and crim amlitude deend uon bot yarn diameters and weave angle: We know tat ( ) (d d ) or in oter words. From Peirce s equations l sinθ sin ( ) cos From te above comutation te relationsi between different useful fabric arameters can be obtained and are given in Figure 4 to Figure 8. Figure 4 gives te relationsi between / and /. Tis figure sows tat te relationsi between tese arameters is less sensitive at te two extreme ends wile te relationsi is sensitive in a / range closer to. In fact tis sensitive range corresonds to maximum crim in one direction only. Te scoe for cange in and lies between.6 to.9 for bot arameters. eyond tis range a cange in tread sacing is ossible in only one direction. /..8.6 l sinθ sin l ( ) cos l [3] [4] [5] Weft crim ( c ) War crim ( c ) Figure 5. Relationsi between fraction war and weft crim for jammed fabric A useful relationsi between te crims in te two directions is sown in Figure 5. It indicates an inverse non-linear relationsi between c and c. Te intercets on te axis give maximum crim values wit zero crim in te cross direction. Tis is a fabric configuration in wic cross-treads are straigt and all te bending is done by te intersecting treads. It may be concluded ere tat at eiter end a small cange in te crim in one direction can ermit a large cange in te crim in te oter direction. ( c ) ( c ) Figure 6. Relationsi between c and c for jammed fabric Figure 6 sows te relationsi between / and / wit linearity between te arameters excet at te two extremes. Tis beaviour is in fact te relationsi between te square root of te crim in two directions; te constant is fixed for any jammed fabric. Oter ractical relationsis are obtained between te war and weft cover factor and between te clot cover factor and fabric mass (gsm) / Figure 4. Relationsi between war and weft tread sacing for jammed fabric Figure 7 gives te relationsi between war and weft cover factor for different ratios of weft to war yarn diameters (ß). Te relationsi between te cover factors in two directions is sensitive only in a narrow range for all values of ß. Te relationsi between te cover factors in two directions are inter-deendent for jammed structures. Maximum treads in te war/weft direction deend on te yarn count and weave. Maximum treads in one direction of te fabric will give unique maximum treads in te cross-direction. Te cange in te value of ß causes a distinct sift in te curve. A comaratively coarse yarn in one direction wit resect to te oter direction tt:// 4

5 AUTEX Researc Journal Vol. June AUTEX Weft cover factor o r c t e r fa o v c W eft eta eta eta.5 desired value of / icks/cm war and weft yarn tex as well as war and weft crim. One can coose any oter four arameters to obtain all fabric arameters. Te algoritm described in Figure can be used to obtain several solutions for non-jammed fabric. Straigt cross-treads In te Figure te intersection of te orizontal line corresonding to / gives all ossible structures ranging from relatively oen to jammed configurations. In tis case. Te fabric designer is allowed te otion to coose te ossible fabric construction. Tese otions include jamming and oter loose constructions War cover factor Figure 7. Relationsi between war and weft cover factor for different ß for jammed fabric. els in increasing te cover factor. For ß.5 te war yarn is coarser tan te weft wic causes an increase in te war cover factor and a decrease in te weft cover factor. A similar effect can be noted for ß in wic te weft yarn is coarser tan te war yarn. Clot cover factor ( KK) Fabric areal density (g/m ) Figure 8. Relationsi between fabric cover factor and fabric mass for jammed structures Te relationsi between fabric mass in gsm wit clot cover (K K ) is ositively linear as sown in Figure 8. Te trend may aear to be self-exlanatory. Practically an increase in fabric mass and clot cover factor for jammed fabrics can be acieved in several ways suc as zero crim in te war direction and maximum crim in te weft direction zero crim in te weft direction and maximum crim in te war direction equal crim in bot directions and dissimilar crim in bot directions. Tis exlanation can be understood by referring to te non-linear art of te curve in Figure. n-jammed structures It can be seen tat te relationsi between / and corresonding / is linear for different values of crim. Tis relationsi is useful for engineering non-jammed structures for a range of values of crim. Te fabric arameters can be calculated from te above non-jammed linear relationsi between / and / for any desired value of war crim. Ten / can be obtained from (- /) and for tis value of / one can obtain te value of / for te desired value of weft crim. Tus all fabric arameters can be obtained for a 7 Using te above logic it is also ossible to obtain fabric arameters for: A fabric jammed in bot directions A fabric wit maximum crim in one direction and straigt cross-treads A fabric wic is neiter jammed nor as zero crim in te cross-treads. Conclusion Te full otential of te Peirce fabric geometric model for lain weave as been exloited by soft comuting. Te interrelationsis between different fabric arameters as sown for jammed structures can be obtained for te oter two cases using te algoritm. It is oed tat te fabric designer will benefit from te flexibility in coosing fabric arameters for acieving any end use wit te desired fabric roerties. References:. F. T. Peirce J. Text. Inst. 8 3 (937).. A. Kem J. Text. Inst. 49 (958). 3. J. W. S. Hearle and J. Amirbayat J. Text. Inst (988). 4. P. Grosberg and S. Kedia Text. Res. J. 36 (966). 5. S. acker Text. Res. J. (95). 6. R. Postle G. A. Carnaby and e S. Jong Te Mecanics of Wool Structures Halsted Press New York J. Lindberg. ere and. alberg Text. Res. J. 3 (96). 8. S. Kawabata R. Postle and M. Niwa Objective Secification of Fabric Quality Mecanical Proerties and Performance Te Textile Macinery Society of Jaan N. G. Ly. H. Tester P. uckenam A. F. Roczniok A. L. Adriaansen F. Scaysbrook and e S. Jong Text. Res. J. 6 7 (99).. J. Hu Structure and Mecanics of Woven Fabrics.9-86 Woodead Publising Limited Great Abington 4.. tt:// i-esigner.. tt:// Texro. 3. T. Harada and M. Saito Sen-I Gakkaisi (986). 4. S. J. Kim Proceedings of nd International Fibre Symosium in Fukui. Jaan. 5. S. J. Kim Proceedings of 3rd International Conference on Advanced Fibre/Textile Materials in Ueda.3 Jaan 5. tt:// 4