Mechanism and Formation of Woven Selvage Lines
By Sei Uchiyama, Member,TMSJ Takatsuki Institute, Toyobo Co., Ltd. Takatsuki, Osaka Pref. Basedon Journalof the TxetileMachinery Society of Japan, Vol.19, No.11, T284-289(1966); Vol.19, No. 12, T309-315 (1966); Vol.20, No. 2, T49-56 (1967) ; Vol.20 , No.2, T57-60 (1967) Abstract This article discussestheoretically the mechanismof a woven selvage line and establishesbasic knowledgeabout, among other things, its dynamic construction, the differencesbetween the selvage and the body of a fabric, the process of stabilizingthe form of a selvage.
interlaced to form a selvage is x,=C. This location 1. Introduction is a function of T-,, a force which pulls the selvage- formation point to the left ; and of T+,, a force which This work is an attempt to clarify the weaving pulls that point to the right. mechanism of a selvage as part of a research into the xi=f (T-1, T+1) ...... (1) function of weaving. Seldom is the selvage of a fabric Assume that, with the progress of weaving cycles, specially woven. It is a by-product, so to say, of a fabric. xi transforms into, sucessively, x2, x3 and x; and is However, it should not be ignored, because it improves stabilized on reaching xn. xi, an optional point x at that the quality of a fabric, protects its ground and facili- time, is given as a function of xi-1. That is, tates the processing and handling of the fabric. It is xi=~5i-i(xi-,) believed, therefore, that establishing a theoretical basis xi-1=~Si-2(xi-2) for obtaining a uniform selvage is an undertaking of Also, practical value and will help to expand the range of x1~x2C"' "'.xi-1Cxi+1"' "'xn=xn+j reseach into weaving. This is continuous. Therefore, 2. Selvage Weave Analysis xn=cn-1 cn-2 ~csn-a"'O1(xl) j) On-1(n-2 {cn-3...~51(f(T-i, T+1))1) 2-1 Assumptions =m(f(T-1, T+1)) ...... (3) The process by which a selvage is woven and its Hence, the position where the selvage is stabilized position is stabilized is expressed schematically in Fig. is given as a function depending on variables which 1. Plot an optional point 0 on the fabric plane as the indicate the position of the first selvage-formation point. axis of coordinates. Draw the X axis parallel to the This point being determined by vectors T -, and T +1 fell of the cloh. Draw the Y axis at right angle to of warp and filling, the selvage is rectilinearly uniform, the X axis. Assume that the distance of the point if the above values are equal in all continuous weaving from the Y axis when the warp and filling are first cycles. It is not clear, however, when T-1 and T+1 influence the shape of a selvage during a weaving cycle. We look into this matter by taking the crank circle as a time axis. 1. Formation of a selvage begins when warp and filling threads begin to be interlaced on the edge of a fabric. This time corresponds to the space between the bottom center and the back center in the crank circle after picking as shown in Fig. 2. 2. With the completion of the insertion of filling, the shuttle stops in the shuttle box on the receiving side. The filling waits for the next picking, while retaining a degree of tension.
Vol. 14, No. 1 (1968) 21 3. Since initial picking corresponds to the dwell of a shedding cam, warp tension at this time does not change but keeps a value. 4. When the crank comes closer to the top center from the back center, the warp closes the shed, gripp- ing the pick and solidifying their lateral direction. 5. As the crank rotates further and beats the front center, a reed forces the filling yarn into the fell of the cloth. The filling thread then produces an elastic elongation load corresponding to the difference between width of the reed and the width of the fell. However, since frictional resistance acts on the inter- lacing points, the elastic elongation of the filling thread generates between the interlacing points, thus prevent- ing a lateral slip of the thread. 6. When the crank goes to the bottom center after beating, the temporary elastic elongation of the filling is regained and the initial selvage weave is fixed. 7. Then, the same motion is repeated, the selvage location repeats its elastic behavior-elongation and Fig,.,. 3 Warp and filling tensions in selvage regaining of elongation and reaches a stabilized position according to the conditions initially given. top center, the region where warp and filling begin to be interlaced and where filling slippage is avoided by the friction resistance of the warp sheet. Fig. 3 illustrates the yarn tension in this region on the selvage. The figure uses the following symbols : P=standard plane on the same surface as fabric plane XOY'. Q=plane made by warp threads OT' in over shed and warp threads OT" in under shed (P jQ) . xx'=standard line on plane P, which corresponds to the fell. YY'=standard line interlacing at right angles with XX' on plane P. 0=intersection where XX' and YY' meet, this being selvage-formation point. OW'=filling inside shed sheets. OW =orthogonal projection on plane P of OW'. OT' =warp on edge of fabric (over shed thread). OT" =warp on edge of fabric (under shed thread). OT =orthogonal projection on plane P of CT' and Fig. 2 shows an outline of the foregoing process. OT", which is a cross line between planes P and Q. The figure uses the following symbols : CS=extension line of selvage edge on plane P. A=time of picking. CS'=selvage edge after fabric passes temple. B=time when warp thread begins to contact filling K=temple. on the selvage. Lw=angle made by OX and OW on plane P. C=time when warp sheet begins to contact filling. Z B=angle made by OS and OY' on plane P. D=duration of shuttle stop. L82=angle made by OY and OT. /TOT" =dwell. F, =tension given to woven filling, the tension We may conclude from the reasoning conducted being parallel to the fell. thus far that the form and position of the selvage are F2'=tension of filling picked and remaining inside fixed in the region between the bottom center and the shed sheets.
22 Journal of The Textile Machinery Society of Japan F2=component on line OW of F2'. W, =tension given to selvage edge OS. W2'=tension of yarns in over shed. w2,, =tension of yarns in under shed. and W 2=sum of components on line OT of W2' and W2". If point 0 in Fig. 3 keeps a constant location between weaving cycles, then straight line OS may be considered a continuation of point 0. Therefore, selvage edge CS maintains a given relative position toward standard axis YY', and the selvage becomes rectilinear in shope. This condition can be defined as a function of warp and filling tensions by the following formula, considering the equilibrium of forces at point 0 : W 2 cos 02+F2 sin co=W 1 cos 81 W, sin 81+W2 sin 02=F2 cos w+F1 The condition of the contact of warp and filling threads at point 0 is represented in Fig. 4. Assume that the angle of contact of warp and filling is co , the angle of contact of filling and warp is ~ , and the angles of their projection to plane P are co and ~ ', where : cps=81+82, c '=rr-w. Assume, too, that the coefficient of friction between warp and filling is z
and for ~oaand ~o, and c=c ,' and Fig. 4 Angle of contact of warp and filling W 1=e'a~ a.W2 F2=e.F1 2-2 Experiments From formulas (4) and (5) is obtainable : 2-2-1 Angle of Selvage Line 8k-tan 1F2 - cos --W - w+e-R~Wr- - - - •F2-W2 -sin --02 ...... (61 2 cos 82+ F2 sin w Angles formed by warp and filling threads to the standard orthogonal axis have been measured and are In eq. (6), the angle formed by the selvage edge to the standard axis in a given weaving cycle is ex- shown as 8 and w in Fig. 3. The materials used in our experiments are listed pressed as a function of warp and filling tensions, assuming that w, 82, ~ and are constants determined in Tables 1 and 2. by weaving conditions. Cotton and filament looms, 180 and 160, respecti- Let 7=tan 8 and y be defined as a function of vely in r.p.m. and complete with shedding and positive selvage form. If 7 is constant in all weaving cycles, let-off motions, were used. the selvage becomes a uniformly straight line. Howe- Now to describe the procedure of the experiment. ver, a decrease in the differential coefficient of 7 for Leave alone several warp yarns drawn from the outer W2 and F2 lessens variations in selvage form. The end of a selvage which will be observed. Sever either differential coefficient of ry calculated by formula (6) over shed yarns or under shed yarns of a 10cm width
is : from the outer end to the center of the fabric width. Dye the warp of the other side pink, so that, when a7 _ (W2 cos 82+F2 sin w) (cos w+e-' ) a F2 W 2 (W2 cos 82+ F2 sin w) 2 the pink warp ends are lowered during opening and white picks are inserted into the under shed, the angle _ (F2 co_s_w+e (W F2-W2 sin 82) sin w 2 cos 82+ F2 Sin w) 2 can be observed clearly...... (7) Link a synchro-f lash (Model SF 3210B manufactured by Dempa Seiki) to the cam shaft. Synchronize the ,7 _ (W 2 cos 82+F2 sin w) sin 82 a W2 F2 (W2 cos 82+ F2 sin w)2 time of flash with the time when the cut sheet is on the over shed. Place a camera exactly above the _(F2 cos w+eF2-W2 sin 82) cos 82 (W2 cos 82+ F2 sin w) 2 object to be photographed to avoid any angle discre- ...... (8) pancy. Keep the room dark and open the aperture.
Vol. 14, No. 1 (1968) 23
_ Table 1 Properties of Yarn Specimens
Table 2 Weaves of Specimens
Table 3 Angles of Warp and Filling Threads on Selvage
Fig. 5 Apparatus for measuring angle of selvage warp and filling
sin 82=0, cos 82+1, and cos w l Therefore, from eq. (6) emerges : F2(1+e-µ3w) W2+ 0.13 F2 From formula (7) emerges : When the loom goes into operation, work the synchro- °7 W2(1+e µ3s) (10) f lash for continuous photographing of the loci of ends aF2 W2 (W2+0.13F2)2 and picks. The flash time in our experiment was 1 From eq. (8) emerges : ms and the wattage 350 w. pry -F2(1+e-' 3Ps) ) The experimental apparatus is shown in Fig. 5. aW2 F2 (W2+O.13F2) The results obtained are given in Table 3. Substituting measured results of 82 and w as con- We find from Table 3 that 02 and w vary slightly stants into theoretical formulas transforms the angles between weaving cycles and from specimen to specimen. of selvage formation and the partial differential of Let us apply these measured results to formulas selvage formation into practical and comprehensible (6), (7) and (8). Since 821.5° and w=7.4°, forms.
24 Journal of The Textile Machinery Society o f Japan Eq. (9) shows that the higher the filling tension Table 4 Selvage Tension of Cotton Broadcloth and the lower the warp tension, the greater the angle of selvage formation and that the effects of warp-f fill- ing friction are small in number. Eqs. (10) and (11) show that even if warp and filling tensions vary, the angles of selvage formation vary only slightly, resulting in a neat or well-made selvage. 2-2-2 Warp tension Variations in warp tension are closely related to variations in selvage form, as we have shown. While measuring variations in warp tension between weaving cycles and within a cycle, it was studied how to estimate warp tension between the fell and the heddle, which tension seems to have direct influence on selvage formation.
Table 5 Selvage Tension of Nylon Taffeta
Fig. 6 Pickup device for measuring yarn tension
Fig. 6 shows the schematic pickup action of the tension analyzer used in our experiment. M in the chart is a fixed plate, with thread guides A and A' at both ends. The back of M has cantilevers L and L' fixed to axis 0, with four gages R and R' sticking to yarns in the heddles in the front row, the measuring the cantilevers. Yarn guides B and B', fixed to L and being done between the lease rod and the back rest. L', run through the dent in M and are placed on the The results of the test are given in Tables 4 and 5. same horizontal level as A and A'. From these measured results emerge the following With tension given to a yarn, L and L' bent facts : through B and B', with 0 as the center. The yarn became almost rectilinear and a distortion showed up In broad- In nylon cloth taffeta on gages R and R'. This change in resistance value Average selvage tension W2 =32.8 g W2 =15.9 g was relayed to the bridge circuit. The amount of Variations in selvage S output distortion is 950x 10-5, measured tension ranged tension w=S. 6 g Sw=2.8 g from 0 to 150 g, and the maximum error after a Percentage variations CV= 17 % CV= 17 ° comparative experiment was within +1%. in selvage tension o Measurement was done on the same conditions as After measuring tension variations between weav- described in the preceding section. The amount of ing cycles, we measured those within a weaving cycle. tension was read from a tension chart formed at the The conditions of measurement were the same as time of beating by the reed. This meant accurate above. reading of timing The threads measured were selvage Tension variations in cotton broadcloth within a
Vol. 14, No. 1 (1968) 25 cycle are given in Fig. 7. In the chart, one weaving cycle ranges from 0 to 7200. Table 6 shows warp tension which fits crank angles obtained from the chart.
Table 6 Warp Tension Variations within Weaving Cycle Warp tension (g)
Fig. 7 Tension variations within one weaving cycle of cotton broadcloth
Such warp tension variations within a weaving cycle are presumably due to warp distortions which Fig. 8 Warp line of cotton broadcloth vary according to crank angles. Table 7 lists warp distortions made by various motions of the loom and actually measured under the same conditions as in Fig. 8 shows the warp line of cotton broadcloth, Table 6. Increases and decreases in distortions were having the same measuring conditions as in Table 6, measured on the assumption that the distance between in under-shed state. TA=yarn tension between the the fell of the cloth and the back rest in the closed fell of the cloth and the heddle ; TB=yarn tension state of warp yarn was the standard length. between the heddle and the lease rod ; Tc=yarn tension By calculating the correlation coefficient between between the lease rod and the back rest ; Bi=angle the total amount of deformations in Table 7 and the formed by T A and TB; 02 =angle of contact formed by warp tension in Table 6 concerning crank angles, it is the lease rod and the yarn ; a=perpendicular distance determined as +0. 85, and we find a correlation be- between the fell and the heddle ; b=vertical distance tween them with 99% confidence. between the heddle and lease rod ; and c=vertical Tension variations within a weaving cycle are distance between the lease rod and the back rest. observable between the back rest and the dropper box, Assume that the thread in equilibrium state in the as we have said. However, it is warp tension between heddle eyelet is pulled to the fell of the cloth. The the fell and the heddle that directly influences selvage vertical pressure on the eyelet, then, is : shape. Direct measurement of this yarn tension being 2TB'cos (81/2) difficult, we studied how to estimate it from the Assuming that the frictional coefficient of the yarn actually measured yarn tension between the back rest and the eyelet is tension T A when the yarn begins and the dropper and found a correlation between the to move is expressible thus : two. TA=TB+2TB cos(0l/2)p1=TB(1+2 cos(0i/2),ai}
Table 7 Variations in Warp Distortion within Weaving Cycles
26 Journal of The Textile Machinery Society of Japan and As a result, we can predict warp tension between TB=Tc e2•B2 the reed and the fell of the cloth, which tension is where ~2 is the frictional coefficient between the yarn directly related to weaving. and the lease rod. Therefore, if Tc=1, the tension 2-2-3 Filling tension ratio among TA, T B and T c is calculable by the follow- Filling tension was measured while filling yarns ing formula : were pulled from a fixed shuttle at the same speed as TA : TB : Tc= (1+2 cos (01/2) f~11e'2A2 : e~292: the shuttle speed. Townsend reports that there is no ...... (12) difference in filling tension between commercial weav- In the light of Fig. 8, 01 and 02 in eq. 12 are : ing and this method. The pickup and recording 01= tan -1(a/d) + tan -' (b/d ) apparatus was the same as that used for warp tension 02=,r-tan 1fb/(d-R)) ...... ,13) measurement. Fig. 9 illustrates schematically the -sin-' R/f ~ b2+d-R)211/2 1 J device to draw filling yarn. where R=radius of lease rod. B1, 02, , and ,u2 have different values according to warp shedding conditions. The calculated values of 01 and 02 and measured values of, and ,u2 are given in Table 8.
Table 8 Measured Values of 01, 02, h1 and ,u2 in Cotton Broadcloth
Fig. 9 Filling tension measured
In Fig. 9, the yarn drawn out of a spool in the Table 9 Longitudinal Warp Tension Distributions shuttle is held by a revolving disk and a nip roller. in Cotton Fabric Drive the disk so as to adjust the circumferential speed of the disk to the shuttle speed and then measure yarn tension. Let the end of the yarn be sucked into a vacuum nozzle lest the yarn should get entangled.
Table 10 Longitudinal Warp Tension Distribution in Nylon Taffeta
Substituting the values in Table 8 into formula (12) and applying the measured values in Table 6, to the substitution gives us Table 9, which lists length- wise warp tension distributions in the cotton fabric. Table 10 lists those in the nylon fabric.
Table 11 Shuttle and Spool in Filling Tension Measurement
Vol. 14, No. 1 (198) 27
- Table 12 Filling-drawing Tension
Fig. 10 Tension diagrams of unwinding filling
Fig. 11 Tension variation of filling within The shuttle speed in our experiment was from 9 tc one cyle 11 m/sec. Table 11 gives the size of the spool and the shuttle condition for the next experiment. A=shuttle begins its picking-motivated flight. In Fig. 10, the reeling tension of the filling yarn B=point where filling generates pretension. The is measured. The line drawn was converted into filling located between the edge of the selvage and numerical values by the methods described in what the eyelet of the shuttle enters the warp sheet ; the follows, to facilitate analysis and comparison. shuttle continues to fly. Hence, the pirn begins to The whole reeling section was cut into three equal unravel. It receives static friction, and tension be- parts. They were referred to as the first stage, the ocmes intense. intermediate stage and the final stage. Each stage C=warp is closed. Warp and filling begin to was divided into 10 equal parts. Assume that the contact with each other. The shuttle has already upper and lower limits of the yarn tension amplitude passed through the shed formed by the warp. During at the partition points are hn and h'n. Then, average this time, the filling contacts no warp, except the warp tension h, percentage variation CV, and average total in the selvage. amplitude a are obtainable by hn and h'n, as follows : D=shuttle reaches the box and stops. E=beating imparts stretch tension to filling and h° (hn+h'~)/2110 increases yarn tension. CV==L~ ° (hn+h'n)/2 }2/911~2/h ...... (14) To know the pre-tension in B, (1) loosen the yarn sufficiently between the shuttle eyelet and the measur- a=~;°(hn-h'n)/10 ing pickup device before it is pulled out, and (2) divide Converting Fig. 10 into numerical values by this the yarn-drawing direction into two : the front of the method results in Table 12. shuttle (hereinafter referred to as condition A) and Now to study variations in filling tension in the its rear of it (condition B). There is a difference light of these measured results. hn-h' n is the ampli- between A and B in the state of contact between the tude of filling tension in one chase. Assume that yarn and the eyelet of the shuttle, as shown in Fig. the yarn length in one chase is 2 inches and the actual 12. The results of this experiment are given in Table reed width 50 inches. A line drawn for tension varia- 13. tions within a pick shows an amplitude of a and a The initial load was higher than the average runn- frequency of 25. Fig. 11 is a typical pattern. The ing tension. The greater the angle of contact between behavior of filling in relation to the crank angle is the yarn and the eyelet, the higher the initial load examined with the aid of the symbols in Fig. 11. and the running tension.
28 Journal of The Textile Machinery Society of Japan Observe the starting-point of contact between warp and filling near point C and the intensity of frictional resistance between them. The procedure of observation is as follows : Keep warp in the open shed and insert filling. Fix one end of the filling to a phosphor-bronze plate with a strain gauge attached to it. Attach to the other end of the filling a hook from which a load can be suspended. Outside the warp sheet, install a guide pulley to support the filling. Suspend a load from the hook and gradually in- crease the load. The filling then begins to slide at a point where the frictional resistance of the warp sheet Fig. 12 Contact of and eyelet of shuttle yarn is overcome. The overcoming force is detectible and measurable
Table 13 Pretension of Unwound Filling with a strain gauge. We may interpret the force at this time as a force which overcomes the frictional resistance of the warp sheet and displaces the filling. This force varies depending on the condition of the interlacing of the warp and filling. The test results are illustrated in Fig. 13.
The angle CA where the condition A arises is calculated by the following formula : ° CA=360 x 2WS x - N 60 ...... (15) where eA=crank angle of rotation from picking to point A. W =distance between eyelet of shuttle kept in box and selvage edge. S=shuttle speed. N=r.p.m. of loom.
Calcutate, with the aid of eq. (15), BAfor a fabric Fig. 13 Frictional resistance between warp 38 inches wide woven on a loom 52 inches in reed space and filling and 180 in r.p.m. In this case, the shuttle eyelet is ahead of the traveling direction of the shuttle when The starting time of frictional resistance in cotton the shuttle runs from the left selvage to the right selvage ; behind, when the shuttle runs in the reverse broadcloth is about 30° earlier than in nylon taffeta, because of the difference in shedding between filament direction. The calculated results are given in Table and cotton looms. We also find that cotton surpasses 14. the nylon fabric in frictional resistance. By combining Tables 13, 14 and Fig. 13, we obtain
Table 14 Point Where the Pretension of Raveling Filling Fig. 14. The chart concerns cotton broadcloth 38 Occurs inches wide woven on a cotton loom 52 inches wide and 180 in r.p.m. The chart shows that : (1) The left selvage forms when the filling is firmly held by the warp at a crank angle of about 298°. Filling tension at this time is 5 g. In other words, filling tension involved in forming of the left selvage is presumably 5 g.
Vol. 14, No. 1 (1968) 29 Y
Fig. 15 Selvage-forming point and selvage angle
Q'P=varied selvage edge. LL'=front edge line of temple. Assume CQ'=o-o0, PO'=oo /PQ'M=B,, LP00'=ao 00' =A, and if OQ 1Q'P, QY=o, LQ XY=8, The amount of displacement when selvage-forma- tion point 0 in Fig. 15 shifts to point Q' is calculable Fig. 14 Filling tension vs. warp frictional by the following expression : resistance OQ'=o-oo=4o=A(tan 0 =tan 0o) ...... (16) However, in the light of eq. (9), tan 0 F2(1+e-a~R) _ (2) The right-hand selvage forms when the filling W2+0.13 F2 _1 (17) is firmly held by the warp at a crank angle of 310°. Also, if tan Bo=tan ,=m, This is about the time when filling pre-tension gener- 4o=A(1'-m) ...... (18) ates. Therefore, filling pre-tension is presumably In other words, the surface contour of the selvage- about 7 g. Clearly, then, the left and right selvages formation point is calculable if warp and filling ten- differ in the degree of filling tension which directly sions are known. affects selvage formation. This filling tension we call With the aid of Table 4, "Warp tension of cotton "effective filling tension ." broadccloth," the loci of the selvage surface contour The shuttle stops at a crank angle of 372° in the have been estimated by eq. (18) and are given in Fig. shuttle box. At this time, the filling is firmly held 16. The photograph under the chart pictures the in place by the warp and has no bearing on filling shape of the same section illustrated in the chart. It tension related to weaving, even if "beating repercus- sions" occur. 2-2-4 Variations in selvage form Knowing the angle formed by the selvage edge, the angle which is the standard line at the time of weaving, we shall know how uneven is the formed selvage. Fig. 15 illustrates this relationship. The following symbols are used in the figure : XX' and YY'=orthogonal standard axes. 0=selvage-forming point. OR=warp in selvage edge. OP=stationary selvage edge.
30 Journal of The Textile Machinery Society of Japan is seen that both the chart and the photograph agree well with each other. The estimate assumes A=3 mm, filling tension F2=10 g=const. and 1+e=1. The space between picks was actually (about 0.3 mm but is given 3 mm in the chart. Therefore, the calculated value of unevenness was ten-fold. 2-3 Conclusions Fig. 16 proves that the deviation of the surface from the plane of the selvage form depends upon warp and filling tensions at the time of selvage-weav- ing; and that the selvage edge angle is a parameter of the deviation. How does the selvage-formation point varies accord- ing to warp and filling tensions and how do the tens- ions affect the coefficient of variations? If point P in Fig. 15 is stationary, the vertical distance between P and the selvage-formation point is expressible thus : PM=B In the light of eqs. (16) and (17), P ~=A•1'=F(W2.F2) ...... (19) Distance o when warp tension W2 varies from 16 to 56 g and filling tension F2 from 5 to 20 g is calcu- lated from eq. (19) with the results given in Fig. 17. Fig. 18 Variations in filling tension and Variations in warp and filling tension vs. variati- coefficient of variations in ons in the selvage edge position have been estimated selvage-forming angle by eqs. (10) and (11) and are shown in Figures 18 and 19. Fig. 18 shows variations in filling tension
Fig. 19 Variations in warp tension vs. Fig. 17 Warp and filling tensions coefficient of variations in and selvage position selvage-forming angle
Vol. 14, No. 1 (1968) 31 with warp tension constant ; Fig. 19, vice versa. The l2=oc, R1 >R2 + 0, and if the mass of warp in OL is variations range from 16 to 56 g for warp tension ; extremely small, the elasticity of flexure in OL may from 5 to 20 g for filling tension. be ignored. Therefore, load P and the rigidity of (1) Fig. 17 shows that : warp in MO are the main factors in flexure o pro- (a) The lower the warp tension and the higher duced by P. That is, o is approximately obtainable by the filling tension, the greater the selvage-formation thinking of warp as a cantilever, provided the cross angle. section of the warp is uniformly circular. (b) The lower the warp tension and the higher Therefore, the filling tension, the steeper the gradient of the ° -___P 3E1 l3 ...... (20) selvage-formation angle to the progress of warp and filling tensions. I=D 64 4 ...... (21) (2) Figs. 18 and 19 show that : Hence, (a) Percentage variations in the selvage-formation 0~.6.6P 3 angle with variations in warp and filling tensions are -:- ED4 l1 ...... (22) conspicuous when warp tension is low. When warp The size of P in eq. (22) can be expressed as in what tension is high, the percentage is low. follows. Point 0 at which vertical force P acts as in (b) The curve of variations in the selvage-form Fig. 20 corresponds to selvage-forming point 0 in Fig. ation angle is approximately of the first order when 3. Therefore, force P whick shifts point 0 to the filling tension varies ; of the secondary order when direction of the X axis is : warp tension varies. P= (W1 sin 81+W 2 sin 02) - (F2 cos w+F1) However, approximately 3. Features of Selvage Contrasted to Body sin 02 0, cos w---l, and F1 : F2 of Fabric Accordingly, P=W1 sin 81-2 F1 23) Substituting the foregoing equation into eq. (22) What follows discusses the of the selvag e conrasted to the body of fabric and how the border line between gives us : 6.6(W1-- sin e1-2F1) them should be handled. ED4 - - l1 34 Analysis Taking Warp Yarn as Beam Assume 6.6ED4 1, 3--p' _ then : o =p . P ...... (25) although o is influenced by the spacing between warp yarns also. Fig. 21 shows the relationship between the spacing among strands of warp yarn and flexure o, in which H=spacing between strands of warp yarn ; D=diameter of warp yarn. If o -(H, only one strand of warp yarn supports force P. If o >H, more than one strand of warp yarn support P, which is uniformly distributed to each strand. Thus, when o1 <_H, 01= pP, when H 32 Journal of The Textile Machinery Society of Japan 3 Table 15 Table of On WARPNOT FLEXED Y' Table 16 nH Calculated Fig. 21 Flexure of warp Assume D=0.15 mm Then, p=2.7 mm/kg x 103 Now to calculate load P. Warpt ension W, and fill- ing tension F1 are, as we have shown, approximately Table 17 P & H VS. On 40g>W,)-20g and lOg>F1>1g And B1 17° Therefore, P is calculable as follows from eq. (23), the positive and negative signs indicating a loading direction : 8g~P>-10g, IPI<10g Assume p=2.7 mm/kg. 0, when P is varied from 0 to 10 grams and n from 1 to 12, is calculable by eq. Since On Vol. 14, No. 1 (1968) 33 Fig. 22 on and nH curves Fig. 23 P & H vs Unl Table 17 is graphically given in Fig 23. The figure shows that : 0 (1) The higher the compressive force given to the selvage-formation point, the higher the selvage flexure. However, the percentage increase in flexure under a load decreases gradually. This is because strands of warp yarn carrying a load increases in num- ber. (2) The greater the spacing between strands of warp yarn, the higher the selvage flexure under the same compressive force. The larger the spacing between strands of warp yarn, the higher the selvage flexure. This phenomenon, too, can be explained by the rate of increase in the number of strands of warp yarn carrying a load. (3) Selvage flexure in 40 s cotton broadcloth is ±2.3 mm in relation to the center line if the spacing between strands of warp yarn is 0.2 mm; approxima- tely ±3. 3 mm, if th space is 0.4 cm, as in, say, cotton Fig. 24 Contact of reed and warp yarn shirting. 3-2 Features of Selvage Produced by Beating with Reed angle. The distribution of warp tension toward the fabric MRR'Q=warp line. width is considered another factor distinguishing the I J =reed, selvage from the body of the fabric. It is quite con- T1, T 2 =warp tension. ceivable that weaving function and the quality and 02=LYMR. quantity of a fabric vary with variations in warp ten- 0 = LX 1 RM. sion. Beating with the reed is discussed here as d~c=angle formed by T2 with reed at point R. influencing the distribution of warp tension. Fig. 24 The force with which a reed squeezes warp at illustrates the relations between the warp yarn and the point R is expressed as the difference between com- reed. The figure uses the following symbols : ponents of T1 and T2 in the X1X1' direction. Assume M=warp-weaving point on fell. this force to be P and reed dents perpendicular to R, R'=points of contact of warp and reed. X1X1'. XX'=fell of cloth. P=T1cos 0-T2 cos (__-z1cc) X1'X1=straight line passing R and parallel to XX'. YY'=warp axis intersecting with XX' at right =T1 cos (---_ o2) -T2 cos (-----4c) ...... (27) 34 Journal of The Textile Machinery Society of Japan The angles formed by warp yarn located from the selvage edge to the central section and the standard axis YY' perpendicular to the fell of the cloth shrink as warp gets close to the center, finally dwindling to zero when warp is parallel to YY' (sec Fig. 25). Eq. (27) can be approximately transformed into : P=T1cos '~ - 02-T2 cos 2 -dc2 T 1 - cos2 +82 sin-) __T2(_ cos' 2 +dc sin's 2 =+Ti02-T2dcc Assume that the vertical distance between the reed and XX' are y. Assume d~ + 0. Assuming T 24c 0, then P=+-dx 'Y .T1, because 82 Ax7 , as in Fig. 25. Presumably, warp yarn near the selvage edge Fig. 25 Warp angle at weaving point generates surplus tension equivalent to distortion, be- cause the frictional force of the reed exceeds that of warp yarn near the center. Presumably, too, the deformation and permanent elongation of yarn are, therefore, higher. These assumptions were experi- mentally verified. The conditions of the experiment are given in Table 18. Table 18 Specimen for Testing Warp Tension Distributi Fig. 26 Warp tension distribution from selvage to center of fabric distinguishing the selvage from the body of the fabric is filling tension, which influences the two differently. We proceed to discuss the difference in weaving and weave between the selvage and the ground by using a function of selvage form. One of the features of selvage weaving construction is that the filling yarn bends on the warp yarn. Except in the selvage, the filling is straight and connects side by side with warp. The bending may be considered analogous to the condition shown in Fig. 3, in which angle w of the filling expands 180° along axis XX'. The function of selvage form is expressible by the following formula in the light of eq. (6) 7 -_ F2 cosW w+e-~ -F2-W2 sin_02_ Fig. 26 gives the average values of the experiment 2 cos 02+F2 sin w involving three tests. The warp yarn was all front-row Except in the selvage edge, w = -180 °, for the above- heddle yarn. The chart shows that warp tension near mentioned reason. Therfore, in the above formula, the selvage is higher than in the central part. The sin w=0 and cos w=-1 border line between the selvage and the central part is not clear but is located about 70 mm from the And from the experimental results, selvage toward the center. sin 02+ 0 and cos 82+ 1 3-3 Effects of Filling Tension on Selvage Hence, assume 7 at this time to be 70. The preceding section discussed warp tension dis- F2(e-µT P-1) tribution and distortion as characterizing the boundary 70- between the selvage and the ground. Another feature where yo=dynamic equilibrium at the point of intlerac- Vol. 14, No. 1 (1968) 35 ing of warp and filling, hereinafter referred to as a from the body, as we have said. function of equilibrium at the interlacing point. yo 3-4 Density of Warp and ry are both obtainable from the ratio of filling We have seen that the effects of warp and filling tension to warp tension, but F2 in yo differs from F2 tensions on weaving construction differ between the in ry. F2 in y is the tension of the filling bent on selvage and the other areas of a fabric. Presumably, the selvage egge and has a force to hold the selvage then, warp and filling densities vary, depending on the construction fabric. F2 in yo has an entirely opposite width direction of a fabric. Fig. 27 shows the areas force, because the filling does not flex. Filling ten- where warp and filling densities were measured in sion on the selvage edge restricts weaving construction our experiment-with the results given in Table 19. toward the center of the fabric. However, except on the selvage edge, it works in the opposite way to the warp at every pick and has no influence similar to that at the selvage edge. We now proceed to obtain percentage transforma- tions of function ry of the selvage line and function rya of equilibrium at the interlacing point in relation to variations in warp and filling tensions and to investi- gate the behaviors of such functions. Percentages transformations of ry and ryoare calculable, respectively, by the following equations : ary W2(1+e-' ) aF2 W2 (W2+0.13 F2)2 aW2 F2~ (W2+0.13 F2)2 and Fig. 27 Positions where warp and filling aryl - (e-~Pc'P-1) densities were measured aF2 W2 W2 aryu F2 (e- 1) The figures in Table 19 are the average of two W2 )F2 W22 - - readings in the same measured area. Five measure- These calculation formulas show that the higher ments were made in different areas within one sec- the warp and filling tensions, the lower the percentage tion. Therefore, the average per section was obtained transformations of the function of the selvage line ; from 10 measured values. but that the percentage variations in the function of As shown in Table 19, warp density withion 10 mm equilibrium at the interlacing point is independent of of the right and left edges of the selvage is higher the amount of filling tension or variations in the than in the other areas of the fabric. Warp density tension. within 10-20 mm of the edges of the selvage is about The fact that the direction, function and size of the same as in the central part. Filling density is filling tension and its variations all differently influ- almost the same in the whole width. These experi- ence the equilibrium behavior of the interlacing point mental findings also seem to illustrate that filling is, in our opinion, one point distinguishing the selvage tension in the selvage operates to pull fabric con- Table 19 Warp and Filling Densities in Fabric Width Direction (weaving on shuttle-equipped loom) 36 Journal o f The Textile Machinery Society of Japan struction inward. Transform this expression as follows : Ii + - v 2_-v h y Fo Wo Wo Fo Wo 4. Transitional Characteristics of Stabiliza- m•8 = • 70 1 _ Wv 2 tion of Selvage Form o As sume the above formula to be : As warp and filling tensions vary, so the point of h Vol. 14, No. 1 (1968) 37 - _7a Wo o (s)== F0 70 H (s) 1+ W 00s 7 Assuming therefrom : WO--Ta 70 ...... '39) 7o =k FO Q Then, -ka'Ta•s O(s) 1+T Fig. 28 Filling tension = 15g, warp tension a s H(s) ...... ,40) = 10 --> 15g and step input Dive Laplace formation to eq. (38) and assume : F0 =Tb 7° ...... (41) 70 = kb J W0 Then, D( kb•Tb's s) _ 1+T_ (s) ...... (42) b•s Eqs. (40) and (42) are formulas of a transfer function which gives the response of the selvage form function to variations in warp and filling tensions. The element, which has a transfer function gener- ally represented by the above expression, turns out to be an element connecting, in a series, the first-order element and the differential element. By using the transfer function obtained here, we Fig. 29 Warp tension - 15g, filling tension calculate the output response to the fixed input and 15 -~ 2g and step input draw the standard curve of the response. On the basis of eq. (40), we study a case where filling tension 1 mm. However, the value is not of an absolute but varies abruptly. relative index. The time constant is 22.7 picks. Condition 1 Warp tension (low) 15 g Condition 2 Warp tension (low) 15 g Filling tension (high) 10 g-45 g Filling tension (high) 15 -~ 2 g (low) (higher) H(s)=215=--13 In the light of eq. (32), s s y0-0.66, provided k-1 0 =13 ka e n'Tg ka=0.066, Ta=15 H(s)== 15--10 -- 5- s s Fig 29 shows a response curve. In this case the rela- Substituting this into eq. (40) gives us : tive index of d~ is 2.5 mm and the time constant 15 picks. ~ (s) _ _ 5 kaT a s_ s(1+Ta s) Condition 3 Warp tension (high) 30 g which, when inversely transformed, is : Filling tension (low) 5-x10 g(higher) TSkaTas . 1_ _-SkaTa The response curve in this case is shown in Fig. 30. 1+Tas s I+Tas Here, do is low enough to be ignored and the time -1 - 5kg constant is as high as 176 picks. -_5 ka e-"'Ta ...... (43) s+-1 T Now to investigate abrupt variations in warp ten- a sion with the aid of eq. (42). From formula (41) is obtainable ka=0.066, Ta=22.7 Condition 4 Filling tension (high) 10 g By applying this to eq. (43), the relationship between Warp tension (low) 25->20 g (lower) n and 0 is obtainable as shown in Fig. 28. If we vary V(s) = 5 filling tension in Fig. 28 from 10 to 15 g, then B indicates 0.33. Assuming that 0= (l-) of formula Substituting this into eq. (42) and inversely (18), then the unevenness of selvage form 4~=approx transforming it results in 38 Journal of The Textile Machinery Society of Japan s Fig. 30 Response curve of n and B = 30g, filling Fig. 32 Response curve of n and B (filling tension = 5 -~ lOg and step input tension =10g, warp tension = 30 -~ 35g and step input) 0.7 Fig. 31 Response curve of n and B (filling tension = 10g, warp tension = 25- 20g and step input) Fig. 33 Response curve of n and B (filling & 5kae n~Tb tension 5g, warp tension 15 -~ 10g, kb=0.044, Tb=15.1 step input) The response is shown in Fig. 31. In this case, time constant is 15 picks and the unevenness is 0.6 mm. a selvage line function and thus obtained a clue to Condition 5 Filling tension (high) 10 g clarifying selvage-weaving. The selvage line function Warp tension (higher) 30 -->35 g clarifies the effects of warp and filling tensions on The response is illustrated in Fig. 32. The time selvage form and appearance, thus giving us basic constant is 30 picks and corrugation is extremely slight. knowledge of how to make a neat or well-built selvage. Condition 6 Filling tension (low) 5 g We have also grasped the features of a selvage in Warp tension (lower) 15 -->10 g contrast to those of the ground by thinking of selvage Here the time constant is 15 and the unevenness is warp as a beam and by observing reed oscillation approximately 0.3 mm. resistance, the effects of filling tension, etc., which The surface contour of the selvage has so far been are weaving factors featuring a selvage. investigated by calculating the response of the selvage Finally, we have calculated, by means of a function form function when warp or filling tension is subjected of the selvage line, the response of the stabilizing to abrupt variations. The experiment just described process of selvage form. The response process has shows that, with a high time-constant and slight been expressed schematically. A selvage must be unevenness of selvage form, the variation curve of such as to add to the good appearance of the fabric selvage form is mild ; but that, with a low time and be uniform if it is to facilitate subsequent oper- constant and notable unevenness of selvage form, the ations and finishing However, uniform weaving con- selvage form varies considerably. ditions are indispensable for making a neat and uniform selvage, so much so that a fabric is judged by its 5. Summing up selvage. It is from this point of view that the present article discusses some aspects of selvage-weaving. The By analyzing the mechanism and formation of a author will be happy if this work gives some new selvage through weaving structure, we have deduced knowledge about weaving technology. Vol. 14, No. 1 (1968) 39