Determination of woven fabric impact permeability index

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1 Ida Joural of Fbre & Textle Research Vol. 34, September 009, pp Determato of wove fabrc mpact permeablty dex M Tokarska a & K Gotek Departmet for Automato of Textle Processes, Techcal Uversty of Lodz, Zeromskego 6, Lodz, Polad Receved 7 July 008; revsed receved ad accepted 6 February 009 A ucertaty measurg a feature of techcal fabrcs called mpact permeablty has bee assessed the form of mpact permeablty dex. Impact permeablty descrbes the dfferece the behavour of a fabrc dyamc arflow codtos relato to ts behavour statc codtos. A mathematcal model of pressure drop wove fabrc, whch s formed as a result of mpact arflow through the product, has bee preseted. For the assessmet of accuracy mpact permeablty dex determato, the procedures descrbed gude to the expresso of ucertaty measuremet are used. A example of calculatg ucertaty budgets of the parameters aalysed has also bee reported. It s observed that the method of determato of mpact permeablty dex s useful. The dex s a good measure of mpact permeablty for the techcal fabrcs wth respect to ther flow propertes. Keywords: Ar permeablty, Impact permeablty dex, Ucertaty, Wove fabrc Itroducto Wove fabrcs are ofte used as cavas covers, parachutes, arbags, tets or protectve clothg. The behavour of textle products depeds o the codtos that they are used. Durg the use of such products, the fabrcs are subjected to statc ad dyamc ar pressures whch cause ar streams to move a skew maer through ther structure,. Statc codtos 3 are assumed to be a referece pot sce the steady arflow through a porous membrae (a fabrc takes place. The szes ad shapes of pores do ot chage ths state. I the codtos of traset ar flows, all the quattes are fact tme depedet; ths refers both to ar flow parameters ad the fbrous structure mafestg all rheologcal features,4. The studes of dffereces the behavour of fabrcs durg steady ad traset arflows s based o the mpact permeablty of flat textle products,5. The mpact permeablty of fabrcs s greatly affected by ther structural parameters. A eural etwork has bee used to model ths property 6. I the preset study, a ucertaty measurg a feature of techcal fabrcs called mpact permeablty has bee assessed the form of mpact permeablty dex. A mathematcal model of pressure drop wove fabrc, whch s formed as a result of a To whom all the correspodece should be addressed. E-mal: emagda@p.lodz.pl mpact arflow through the product, has bee preseted. Materals ad Methods Te specmes ( = 0 of polyester wove fabrc were used to determe the ar mpact permeablty. The fabrc parameters are gve Table. Fabrc parameter Raw materal Weave Table Wove fabrc parameters Value Polyester Pla Thckess 0.8 mm Surface mass 9 g/m Apparet desty 45 kg/m 3 Number of threads warp weft Lear desty warp weft Breakg force warp weft Crmp 48/cm 6/cm 9.7 tex 8. tex 6 cn 4 cn warp 3. % weft 0.3 % Twst of threads Twstless

2 40 INDIAN J. FIBRE TEXT. RES., SEPTEMBER 009. Impact Permeablty Idex To determe the mpact permeablty dex, the real ad hypothetcal mpulse pressures of the fabrc are ecessary. The real mpulse pressure s measured o a specally costructed measurg stad (Fg.,4. The stad s equpped wth the followg measurg devces: ( a sesor for measurg the psto travel [x(t], type PJ 50+WG04 of Peltro make, measurg rage 0-50 mm, resoluto mm, accuracy class 0.5; ( a sesor for measurg the movemet of the specme surface [h(t], type Z4M-W00RA of OMRON make, rage ±40 mm relato to the focus, resoluto 0.06 mm, accuracy class 0.; ( a sesor for measurg the pressure of the ar over the psto [p(t], type FPM-0PG of Fujkura make, measurg rage ±3.79 kpa, olearty 0.5%, pressure hysteress of a order of 0.4 %, accuracy class 0.9; ad (v a system for measurg the curret of the electromaget, whch causes the travel of the psto the cylder [(t], measurg rage 0-0 A, accuracy class 0.5. The measuremet of the quattes s performed o a vrtual strumet bult o the bass of the LabVew program. The hypothetcal mpulse pressure s determed as follows: Based o the comparatve studes carred out, a hypothetcal pressure drop p (t o the deal fabrc s deduced, assumg that the product propertes wll rema the same, rrespectve of the codtos of use. A fabrc made of deally elastc ad weghtless threads s regarded as deal. The absece of frcto betwee threads s also assumed. After the effect of arflow dsappears, the pores of such a product retur to ther orgal shape. By aalysg the chages Fg. Schematc dagram of a measurg stad [x(t the psto travel; p(t the pressure of the ar over the psto; h(t the movemet of the specme surface; (t the travel of the psto the cylder; t the tme; ad Uz the power supply] the geometrcal parameters of the space betwee the specme placed ad the movg sealed psto, the hypothetcal pressure drop p (t o the deal fabrc has bee determed usg the followg sem-emprcal relatoshp 7 : d x( t π d h( t p '( t = a π r ( r + h ( t dt dt ( where a s a slope of the statc characterstc p s (w; w, the ar volume stream; p s, the pressure drop statc codto; t, the tme; ad r, the radus of the psto. Relatoshp as show Eq. ( s based o the results of the measuremets of psto travel x(t ad the deflecto of the textle product specme h(t. The tme characterstcs obtaed are approxmated by meas of eural etwork 8. The approxmated quattes are substtuted to Eq. ( ad the pressure pulse p (t s thus calculated. Whe the real [p(t] ad hypothetcal [p (t] pressure pulses are kow, the mpact permeablty of wove fabrc the form of the dex (IP ca be calculated usg the followg relatoshp: IP = IP * 0.5 ( where IP = max p ( t * t 0 = + t 0 t 0 max p ( t max p' ( t (3 where IP * s the assstat dex calculated for -th specme of a wove fabrc; p, the real pressure pulse; ad p, the hypothetcal pressure pulse both obtaed for -th specme of a wove fabrc; =,,...,; ad, the umber of measuremets. The IP dex makes t possble to compare the dffereces that occur durg statc ad dyamc vestgatos of the wove fabrc. Negatve value of the IP dex meas that the shapes ad dmesos of the ter-thread caals wll cause a decrease the arflow resstace o the fabrc the traset flow codtos as compared to that the steady flow codtos. The postve IP dex meas that the shapes ad dmesos of the ter-thread caals wll cause a crease the arflow resstace o the textle product the traset flow codtos as compared to that the steady flow codtos.

3 TOKARSKA & GNIOTEK: DETERMINATION OF WOVEN FABRIC IMPACT PERMEABILITY INDEX 4 Zero values of the dex dcate that the dfferece the pressure occurred o both sdes of the fabrc specme s the same, rrespectve of the vestgato codtos. Thus, the structure of the fabrc, the shapes ad the dmesos of ts pores should ot chage durg vestgatos dyamc codtos as compared to those statc codtos.. Aalyss of Iaccuracy of Impact Permeablty Idex The mpact permeablty dex (IP s a measure of a complex structure ad umerous factors fluecg t. Its aalyss volves a detaled study o the basc system of physcal codtos of the measuremet as well as costructg a mathematcal model descrbg the behavour of fabrcs durg traset arflows. The expermet whose purpose s to determe the mpact permeablty dex of a flat textle product, such as wove fabrcs, etals several drect measuremets. The aalyss of the accuracy mpact permeablty determato was made as reported earler 9-. The measure of the accuracy determato of the IP dex s assumed as: U( IP = k u ( IP (4 p C for the coverage factor k p = (the cofdece level s 0.95 Applyg the law of ucertaty propagato 9, a depedece of the complex ucertaty u C (IP of the estmate of the IP o the stadard compoet ucertates p ad p s gve by the followg formula: IP uc ( IP = u ( p = p IP + ( ' u p (5 = p ' The square of stadard ucertaty u (p of the estmate p amoutg to u ( p ' = u ( p ' C ad beg the same for each =,,..,; where s the umber of measuremets (vestgated specmes. The complex ucertaty u C (p s determed usg the followg equato: ' uc ( p' = u ( ws + u ( ps ws ps where + u ( x + u ( x x x + u ( h + u ( h h h + u r ( r (6 ps x x π h h p ' = π r ( r h w + t ' t ' ; (7 s t = t t [t, the cremet equals 0.00 s; t, the tme to whch the maxmum hypothetcal pressure correspods; ad t = t 0.00]; h = h(t ; h = h(t ; x = x(t ; x = x(t ; ad p s, the pressure value calculated from the formula ps ( w = aws, where w s s the maxmum value of the ar volume stream obtaed o the fabrc statc codtos. Usg Eqs ( ad (3, partal dervatves of Eq. (5 were determed. Fally, accordg to Eq. (4, the accuracy determato of the mpact permeablty dex s obtaed usg the followg relatoshp: U ( IP = ( p k p u p = ( p + p ' p + u = ( p + p ' ( p ' (8 where the square of stadard ucertaty s expressed by the followg geeral equato: u ( x = u ( x u ( x (9 A + B where u A s the varace of type A; ad u B, the varace of type B.

4 4 INDIAN J. FIBRE TEXT. RES., SEPTEMBER Results ad Dscusso Based o the aalyss of measuremet results obtaed o the statc vestgato stad, the squares of stadard ucertates of compoets of Eq. (7 were determed,.e. u (w s ad u (p s, whch are ecessary for Eq. (6. O the statc vestgato stad, a statstcal aalyss of the measuremet results obtaed was carred out. The expaded ucertaty of the ar volume stream measuremet U(w s = dm 3 /s ad the expaded ucertaty of the pressure measuremet U(p s = 7 Pa were obtaed for the coverage factor k p =. Thus, the complex varace u (w s s (dm 3 /s. However, the complex varace u (p s s.5 (Pa. Further, the measuremet results obtaed o the dyamc vestgato stad were also aalysed. Based o ths aalyss, squares of stadard ucertates of the followg compoets of Eq. (7 whch are ecessary for Eq. (6 were determed: u (r, u (x, u (x, u (h ad u (h. The psto radus (r, equal to the cylder radus whch the psto travels, was measured by meas of a slde calper of a mmum graduato of d e (0.000 dm. To determe the stadard ucertaty of type B, the uform dstrbuto was used. The varace of ( de type B calculated for the slde calper s u B = = dm. The varace of type A calculated o the bass of measuremets s u A = dm. Hece, the square of the complex stadard ucertaty of the estmate of r (Eq. s u (r = dm. To determe the expaded ucertaty of the psto travel (x, x the cylder, stadard plates of class II of a executo accuracy of ±0.005 mm ad a aalog-dgtal DAQ board were used. The values of the stadard ucertates of type B were also calculated based o the formato gve by the producer ad assumg uform dstrbuto. I the case of usg gauge blocks, the ucertaty of type B ( a a ( s ub = + = = mm. 3 3 Hece, u B = dm. Furthermore, the voltage sgal from the sesor of lear dsplacemets of type PJ 50+WG04 of Peltro make s set to the A/C measurg card o the computer. The voltage values of the rage 0-0 V correspod to the dsplacemet values of the rage 0-00 mm. Thus, the dcato terval of the sesor s Y m = 00 mm. Sce a measurg card of bts was used, the mmum graduato, ths case, s as gve below: Y m 00 a = = = mm Thus, the varace of type B, resultg from the use of a measurg card, s u B = dm. The varace of type B s u B =. 0-8 dm. The varace of type A s u A =. 0-9 dm. Thus, the square of the complex stadard ucertaty of the estmate of both x ad x s u (x = u (x =. 0-8 dm. To determe the expaded ucertaty of the movemet of the specme surface h ad h, as doe prevously, gauge blocks of class II ad the same A/C measurg card were used. Hece, the varaces of type B s u B =. 0-8 dm. The varace of type A was also calculated [ u = dm ]. Thus, the square of the complex stadard ucertaty of the estmate of h ad h s u (h = u (h = dm. The, for each of the 0 specmes, the value of the expaded ucertaty U(pʹ = k p u C (pʹ was calculated for the coverage factor k p =. O ths bass, the authors calculated the mea value of the ucertaty U ( p' of the determato of the maxmum hypothetcal pressure pʹ of the fabrc. The ucertaty budget of determato of the maxmum value of the hypothetcal pressure pulse for oe specme of the fabrc studed s show Table. The mea value of the maxmum hypothetcal pressure for a gve fabrc uder vestgato s foud to be 583 Pa, whle the mea value of the expaded ucertaty s 64 Pa. To determe the expaded ucertaty [U(IP] of the real value of IP dex, the value of the square of the complex stadard ucertaty [u (p ] of the real pressure measuremet dyamc codtos was calculated. The expaded ucertaty of ths measuremet (for k p =, accordg to the aalyss made, s U(p = 3 Pa. Hece, the square of the complex stadard estmate of p s u (p = u C(p = 4.5 Pa for each =,,..,. Usg Eq. (8, the value of the expaded ucertaty [U(IP] of the IP estmate of the real value A

5 TOKARSKA & GNIOTEK: DETERMINATION OF WOVEN FABRIC IMPACT PERMEABILITY INDEX 43 Table Ucertaty budget of determato of maxmum value of hypothetcal pressure for a selected fabrc specme [Complex ucertaty square u C(p Pa, ad Mea expaded ucertaty U ( p ' 64 Pa] Symbol of Estmate of Varace Varace Assumed Varace Sestvty Estmates of Cotrput put of type A of type B dstrbuto [u (x ] factor varaces of buto of quatty quatty [u A(x ] [u B(x ] of compoets of estmates a (x dm dm probablty x, Pa w s dm 3 /s - - Uform (dm 3 /s 87.6 Pa s/dm p s 056 Pa - - Uform.5 Pa r dm Uform dm Pa/dm x dm Uform. 0-8 dm Pa/dm x dm Uform. 0-8 dm Pa/dm h dm Uform dm Pa/dm h dm Uform dm Pa/dm w s Maxmum value of the ar volume stream obtaed o fabrc statc codtos; p s Pressure drop statc codto; r Radus of psto; x Psto travel [x = x(t ad x = x(t ]; h Movemet of specme surface [h = h(t ad h = h(t ]; ad t & t Tme. a Percetage cotrbuto of estmates of varaces of compoets of x to complex ucertaty square [u C (p ]. Symbol of put quatty (x Table 3 Ucertaty budget of determato of mpact permeablty dex of sample fabrc Estmate of put quatty Pa Square of stadard ucertaty u (x of compoets x, Pa Mea value of sestvty factor Pa - Estmates of varace of compoets x Square of complex ucertaty u C(IP Cotrbuto of estmates a % Expaded ucertaty u (IP Value of IP dex p p a Percetage cotrbuto of estmates of varaces of compoets of x to complex ucertaty square [u C (IP] of the mpact permeablty dex of the fabrc studed for the coverage factor k p = s obtaed. The ucertaty budget s preseted Table 3 where mea values of the sestvty factors for the partcular put quattes p, pʹ stead of the set of 0 coeffcets for each of these quattes (0 fabrc specmes studed are show. The percetage cotrbuto of the estmates of varace of the compoets p ad pʹ to the square of the complex ucertaty u C(IP (Table 3 was calculated for a sample fabrc. The calculated expaded ucertaty U(IP whch s a measure of accuracy of determato of the mpact permeablty dex of fabrc allows determg the terval whch wth a probablty of 0.95 (k p =, the real value of the IP dex les. The value of the calculated IP dex of the fabrc s foud to be The accuracy terval of determato of IP dex s [ (lower lmt, (upper lmt]. Moreover, the value of the relatve expaded ucertaty (3.6% ad the value of the coeffcet of varato of the IP dex (.3% are juxtaposed. 4 Coclusos The method of determato of mpact permeablty dex reported ths study s foud to be useful for arragg techcal fabrcs wth respect to ther flow propertes. The value of the relatve expaded ucertaty (3.6% results from the accuracy of the model of the hypothetcal pressure pulse assumed. The relatoshp s obtaed o the bass of assumptos. As a sem-emprcal relatoshp for determg the maxmum value of the hypothetcal pressure, t requres measurg the put quattes defed the model. Thus, errors of modelg ad measuremet ucertates are volved here.

6 44 INDIAN J. FIBRE TEXT. RES., SEPTEMBER 009 The value of the varato coeffcet of the mpact permeablty (.3 % for the fabrc studed testfes to the fact that the measuremet of the mpact permeablty of fabrc s a repeatable measuremet. Idustral Importace: The measurg stad ca be used as a referece pot for the costructo of the devce teded to seral producto ad dustral measuremets. Studes o the mpact permeablty of fabrcs (comparatve studes allow ths feature to be shaped at the desg ad costructo stage. The results obtaed ca be used to desg cavas covers, parachutes, arbags, tets or protectve clothg. Refereces Gotek K & Tokarsk P, Text Res J, 70 ( Gotek K & Tokarska M, Text Res J, 7 ( Textles, Determg the Ar-permeablty of Textles PN-EN ISO 937:998 (Polsh Commttee for Stadardzato, Tokarska M, Research ad Aalyss of Impact Permeablty of Wove Fabrcs, Ph.D. thess, Departmet for Automato of Textle Processes, TUL, Lodz, Polad, Gotek K, Fbres Text Easter Eur, 4 ( Tokarska M, Text Res J, 74 ( Tokarska M & Gotek K, Fbres Text Easter Eur, 3 ( Taylor J G, Neural Networks ad ther Applcatos (Joh Wley & Sos, Chchester, USA, Gude to the Expresso of Ucertaty Measuremet (Iteratoal Orgazato for Stadardzato, Warsaw, Polad, Cohe E R & Tusky V S, IEEE Trasactos o Istrumetato ad Measuremet, 44 ( Deck R H, Measuremet Ucertaty Methods ad Applcatos (The Iteratoal Socety of Automato, Aust, USA, 997.

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