Anisotropy of the Static Friction. of Plain-woven Filament Fabrics

Transcription

1 Anisotropy of the Static Friction of Plain-woven Filament Fabrics By Masayasu Ohsawa and Satoru Nam iki, Members, T M S J Faculty of Technology, Tokyo University of Agriculture and Technology, Koganei, Tokyo. Based on the Journal of the Textile Machinery Society of Japan, Transactions, Vol. 19, No. 1, T7-16 (1966) Abstract The relationship between the geometrical structures of plain-woven filament fabrics and the directional effect of fabric-on-fabric static friction has been investigated with the following results : (1) Frictional force F per unit area for every relative direction of rubbing is related to pressure N by the relation F=kNn, where k and n are constants. (2) The term "coefficient of the directional effect of fabric-on-fabric friction" is used here and given a quantitative significance by defining it as o= (/iff vww)i (uff+vww) where pff and Nww are the friction coefficients of sliding, "filling-along-filling" and "warp-along-warp", respectively. Their values ~, obtained from experimental results, show the same tendencies as those obtainable by cloth geometrical calculations. (3) The structure of a high crown of warp or filling has marked influence upon the anisotropy of the friction of a given fabric. 1. Introduction The surface friction of woven fabrics has an essential bearing on handling and abrasion. Previous inquiry into the friction of fabrics deals almost exclusively with the fabric texture[l], [2]. There is no published work on the geometrical structures of woven fabrics. Observation of the friction of every fabric reveals a difference between a spun fabric and a filament fabric. Continuous-filament fabrics are more uniform in their construction than spun fabrics, and their geometrical character makes them a fitting object for the study of fabric anisotropy. the filling direction f and of the lower cloth in the direction of the deflecting angle B. 2. Experiment and Its Results 2-1, Fabric-on-Fabric Contact The state of fabric-on-fabric contact is shown in Fig. 1, where the symbols w and f represent warp and filling respectively. Warp-along-warp contact (w-w) of fabrics is shown in Fig. (a). Filling-along-filling contact (f - f) is shown in Fig. (b). The filling direction is taken as a base line, and the angle between the base line and the direction of motion is called deflecting angle, and is represented by B (deg). Accordingly, (f -B) denotes a relative motion of the upper cloth in Fig. 1 Model of fabric-on-fabric contact Vol. 12, No. 5 (1966) 197

2 In our experiment, motion of the upper cloth moved in the direction of warp or filling, while the direction of motion of the lower cloth was varied. Frictional force was then influenced by deflecting angles. Assuming that this fact depends upon i ie fabric structure, we use as the coefficient of the differential frictional effect (D.F.E.) of the fabric. ~-- (,...(1), where,~ is coefficient of static friction, and there is no anisotropy when o= Apparatus Rubbing directions of the upper cloth : 2 levels Rubbing directions of the lower cloth : 7 levels Variations of load : 6 levels Frequency of experiment : 5 times The motion of the upper cloth was in the directions of warp and filling. The angles between the direction of motion of the lower cloth and their base line were multiples of 15 less than 90. All samples were tested under standard atomospheric conditions Results of Experiment The frictional force versus time plot usually had the highest peak at the start of the motion, and then declined gradually, accompanied by a stick-slip motion. The point of the highest peak is used in this article as static frictional force, expressed by the symbol F. The relation between the static friction F and the pressure N is linear on logarithmic paper, as shown in Fig. 3. This relation was proved by statistical analysis to be linear in character for the various directions of rubbing. Thus a law of friction F=kN" was obtained. Fig.2 Schematic diagram of apparatus for friction test The instrument, shown diagrammatically in Fig. 2, consisted of a horizontal flat base on which a piece of the lower cloth tested was held in place by a cramp. Another piece of the same cloth to serve as the test upper cloth was fastened to a flat slider. The frictional force resisting the horizontal motion of the base acted on the wire of the slider. The force was, therefore, measured with an unbonded strain-gauge dynamometer and recorded on pen-writing oscillograph paper Experimental Procedure The samples used were three kinds of commercially sold fabrics differing in anisotropy (Table 1). Conditions of the experiment : Size of specimens : Upper cloth 5 cm >< 14 cm Lower cloth 7cm x 14cm Apparent contact area : 35cm2 Rubbing speed of the base : 13.8cm/min Experimental elements : Fig. 3 Example of normal force sample sample relation A shown C : shown between by by solid dotted frictional lines. lines force and 198 Journal of The Textile Machinery Society of Japan

3 2-5. Calculation of D.F.E. of Fabrics The coefficient of friction was calculated by the following formula from k and n : Ng '2 = N2 -N I, F N dn N, =k(n;n-n,n)/n(n;-n,)...(2) The calculated results are given, with k, n and p in Table 2. was calculated by formula (1) for the various directions, and is shown diagrammatically in Fig Discussion a) Values of k, n and ~~ Sample A (Table 2-a) p increased abruptly with a decrease in 0 in the range of (f-45 ) and (f_00). k did likewise. This agrees with Wilson's findings[21. The largeness of k and the smallness of n at (f -0 ) are presumably the influence of interlocking action at the contact points. Sample B (Table 2-b) Fig. 4-c Experimental D.F.E. on sample C Fig. 4-a Experimental D.F.E. on sample A Fig. 4-b Experimental D.F.E. on sample B Vol. 12, No. 5 (1966) 199

4 1 Table 2-e 3. Geometrical Analysis of Cloth Structure 3-1 Geometrical Contact of Yarn Crowns of Fabrics Fig. 5 Example of cross-section of fabric (sample A) /2 was nearly independent of 0. This showed the absence of anisotropy. Sample C (Table 2-c) /2 increased with an increase in 0 in the range of (w-45 ) to (w-90 ). k did likewise. This is similar to the results for sample A. b) o-values Sample"A o at =0 and,~=90 was 0.50 (/c ff>l!wtu), and increased along the axis and decreased along the axis ~, thus clearly showing the presence of anisotropy. As for the degree of variations in o, we found that ~cf for axis graduated on (f --0) varied more than did /Jww. On the other hand, /1w, for axis varied less than did The diagram exhibited no noticeable variations, though. Sample B o at =0 and,~=90 berg 0.07 (/(ww>/off), sample B was influenced hardly at all by ~c. The complex undulations in the diagram were mostly small in height and, therefore, practically free from anisotropy. Sample C o at =0 and =90 being 0.30 (/2ww>/,c f f), there clearly was anisotropy which was in the opposite direction to anisotropy in sample A. In other words, samples A and C were opposite to each other in the warp and filling. The three samples, when compared in o, were A >C>B. A comparison of samples A and C in only showed that t~ f f was nearly equal to tlww. The obvious conclusion, then, is that there was no difference in the maximum value between samples A and C ; and that, therefore, the measuring of o relative to anisotropy served a useful purpose. Fig. f Unit cell The cross-section of a fabric woven of continuousfilament yarns is shown in Fig. 5. Its unit cell is shown in Fig. 6. It seems reasonable to assume that the cross-sectional shape of yarns consists of two equal arcs of a fusiform shape. Fig. 6 uses these nomenclatures : a : width of thread b : thickness of thread d : yarn diameter calculated from yarn count e : b/a E : b/d S : cross-sectional area of thread r : radius of sector 0 : angle of sector (rad.) then S=r20--a(r-b/2) therefore E= 1- -1( 2 -I-11)2sin-'-2e (_2-1 2 n 2 e 1--f e e e b was directly measured, the yarn diameters were estimated from the count, and then E, e and a were calculated. 1 in plain coven fabric 200 Journal of The Textile Machinery Society of Japan

5 Bent crowns around a transverse thread protruded from the fabric surface to a height of h, which was calculated as follows, using the principle of cloth geometry to non-circular threads : h.=bw-hf=hw-bf or h~=b f-hw=hf-bw where hw : warp crimp amplitude h1: filling crimp amplitude The structural elements of fabric construction are given in Table 3, where c is crimp percentage. Table 3 Elements of Fabric Structure where a and ko are constants. a of filament fabrics were approximately equal to unity and k0 =tan A, where A was the angle of friction of fibers. Within the load range used in our experiments, F/N=tan (c2+a) where was the angle of frictional effect of crowns shown in Table 4. Surface roughness is a major contributing factor to friction between filament yarns if filaments are arranged side by side. This is not the Coulomb effect in the true sense of the term. It is essentially an effect of mechanical interlockingl3]. Table Geometrical Aspects Geometrical coef f icent lated coefficient of D.F.E., of D.F.E. z- of friction and the o7, were deduced. calcu. Assume (i) that the surface roughness of a yarn, like the roughness of a metal surface, comes from form factor ky ; and (ii) that ~b is approximately equal to 90 x (1-k,). The effect of mechanical interlocking can, then, be estimated from the angle cb. With this additional effect added, z is equal to tan (~o±cb+a). ~~ and z- are plotted against D in Fig. 8, a; are represented in Fig. 9. Fig. 7 Contact of two protruding-crowns In Fig. 7 P is the point of contact of the protruded crowns of upper and lower fabrics. Then, F cos y-n sin q=k0 (F sin y N cos ro) Fig. 8-a Variations in of sample A p and z- plotted against 0 Vol. 12, No. 5 (1966) 201

6 I Fig. 9-b Geometrical D.F.E. on sample B Fig. 8-b Variations in ii of sample B and z plotted against B Fig. 9-c Geometrical D.F.E. on sample C.f L Fig. 8-c Variations in,u and z plotted against 8 of sample C Fig. 9-a Geometrical D.F.E. on sample A 3.3 Geometrical Calculations Discussed (1) Table 4 shows that ~o decreased with an increase in 6 in samples A and B ; but that this was the other way round in smaple C. r had the same tendencies with co, but z- had higher values than,u. It is clear that,u was essentially different from z, but the figures have shown that both were about the same in the degree of variation. From this result, it seems reasonable to introduce ~o and ~b into the discussion of the directional effect. (2) Figs. 9 and 4 show the same tendencies, except as to sample B. It follows, then, that the contributing factor to anisotropy was located in the protruding crowns ; and that the direction of the higher values of friction coefficient is determinable by the height of the crowns of warp or filling. The degree of balance between warp and filling yarns was very high in sample B. Therefore, bw = b f and also hw = h1. It was reasonable to think of the construction of the protruding crowns, because there is no way to analyze geometrically a sample in which the count, flattening and crimp are completely balanced. 202 Journal of The Textile Machinery Society of Japan

7 This explains anisotropy to c (3) The a method in ponded to the and took no yarns and the the structural important bear therefore, to assume a close relationship between anisotropy and structual unbalance. aic uue w lvlr. 1. nato who cooperated fully in our experiments. 4. Conclusions Literature Cited Experiments were made to look into the directional friction of typical plain-woaven fabrics. With close observation of the unit cell in the structure of fabrics, a geometrical analysis was made of structural unbalance and anisotropy. [1] Y. Miura, J. Soc. Fib. Sci. Tech. Japan, 10, 558 (1954) [2] D. Wilson, J. Text. Inst., 54, T143 (1963) [3] H. G. Howell, et al., Friction in Textiles. Butterworths Pub. Ltd., P5 (1959) Vol. 12, No. 5 (1966) 203