ORIGINAL PAPER Journal of Textile Engineering (2007), Vol.53, No.5, 203-210 2007 The Textile Machinery Society of Japan Analyzing the Path and the Tension of a Yarn under a False-twist Process Using a Doubly Stacked Multi-disk Spindle KANEDA Naoto, SHINTAKU Sukenori *, KINARI Toshiyasu, SHIMOKAWA Tomotsugu Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa 920 1192, Japan Received 5 April 2007; accepted for publication 13 September 2007 Abstract The path followed by and the tension generated along a yarn under a false-twist process using an enlarged model unit of a doubly stacked multi-disk spindle are measured and analyzed on the basis of a theory, an extension of authors earlier proposition. The geometrical quantities necessary to reproduce the yarn path, i.e. the inclination angle made by the yarn against a disk surface, the length along which the yarn runs on the disk, etc., are estimated from the CCD image of the yarn configuration. The twisting tension, the inter-disk yarn tension, and the untwisting tension of the running yarn are also detected. It is revealed that the theoretical analysis can successfully elucidate and predict the inter-disk yarn tension as well as the relation between the twisting tension and the untwisting tension only if the yarn configuration is observed. This study will give a novel and useful clue to the manufacturing technology related to false-twist processing using multi-disk spindles. Key Words: Textured yarn, Doubly stacked multi-disk spindle, Friction twisting, Yarn tension, Yarn path 2 * 3 Thwaits[1, 2] Du [3, 4] 1 3 [5 10] 2 3 2 2 [5, 6] * 920-1192 E-mail: sintaku@t.kanazawa-u.ac.jp, Tel: +81-76-234-4693, Fax: +81-76-234-4695 203
KANEDA Naoto, SHINTAKU Sukenori, KINARI Toshiyasu, SHIMOKAWA Tomotsugu 2 2 4 Fig. 1(a) ( 140 dtex 36F / POY ) (83 dtex DTY ) Fig. 1(b) 1 Fig. 7(b) D = 50 mm D = 200 mm 24 mm (a) Schematics of experimental apparatus (a) Yarn tension T (b) Dimension of a large scaled model disk (b) Yarn angle θ and yarn adhesion width h (c) Position of guide holes Fig. 1 Outline of a model machine. (c) Yarn adhesion angle u Fig. 2 Measurement parameters in an experiment. 204
Journal of Textile Engineering (2007), Vol.53, No.5, 203-210 [5] μ = 0.15 Fig. 1(c) 10 mm 6 mm 4 11 Fig. 1(c) (1-1) (1-11) (4-1) (4-11) (1-6) (4-6) 1 3 2 4 V D / V F T1 T2 - T6 T7 ( CM250-R CM100-PS) Fig. 2(a) Table 1 Experimental conditions. θ Fig. 2(b) h Fig. 2(b) 360 μ Fig. 2(c) CCD Table 1 Fig. 3 H = 50 mm L = 130 mm (1-1) Y V D D D/Y (a) T (b) θ (c) h D/ Y (d) D/Y u Fig. 3(a) D/Y T1 T2 - T6 T7 Fig. 3(b) D/Y 1 2 θ 3 4 θ Fig. 3(c) Fig. 3(d) h u D/Y Fig. 4 H = 90 mm L = 130 mm (1-1) Fig. 3 Fig. 4(a) D/Y T1 - T4 D/Y T5 T6 T7 Fig. 4(b) D/Y 2 θ2 3 θ3 1 θ1 4 θ4 Figs. 3(a), (b) Figs.4(a), (b) H θ Fig. 2(b) μf sinθ2 (a) Relation between yarn tension T and speed ratio D/Y (b)relation between yarn angle θ and speed ratio D/Y (c) Relation between yarn adhesion width h and speed ratio D/Y Fig. 3 Experimental result (H = 50 mm, L = 130 mm, line1-1). (d) Relation between yarn angle u and disk number 205
KANEDA Naoto, SHINTAKU Sukenori, KINARI Toshiyasu, SHIMOKAWA Tomotsugu (a) Relation between yarn tension T and speed ratio D/Y (b)relation between yarn angle θ and speed ratio D/Y (c) Relation between yarn adhesion width h and speed ratio D/Y Fig. 4 Experimental result (H = 90 mm, L = 130 mm, line1-1). (d) Relation between yarn angle u and disk number (a) Relation between yarn tension T and speed ratio D/Y (b)relation between yarn angle θ and speed ratio D/Y (c) Relation between yarn adhesion width h and speed ratio D/Y Fig. 5 Experimental result (H = 90 mm, L = 150 mm, line1-1). (d) Relation between yarn angle u and disk number T H T θ Figs. 4(c), (d) Fig. 3(c), (d) D / Y h u h u H Fig. 5 H = 90 mm L = 150 mm (1-1) Fig. 3 Fig. 4 Fig. 5(a) T Fig. 4(a) T1 - T5 T6 T7 D / Y Fig. 5(b) Fig. 4(b) D/Y 2 θ2 3 θ3 1 θ1 4 θ4 Figs. 5 (c), (d) Figs. 3(c), (d) D/Y Figs. 4(a), (b), (c) Figs. 5(a), (b), (c) L T θ1 θ2 h1 h2 L θ 2 h T L h T Fig. 3(d) Fig. 4(d) Fig. 5(d) u D/Y 2 Fig. 6 Yarn path in a friction-twisting process using a doubly stacked multi-disk spindle. Fig. 6 206
Journal of Textile Engineering (2007), Vol.53, No.5, 203-210 2 [5] [6] Fig. 7(a) (1) dt ξ 1 + T (k ne + k gη) + Fe + μfe s = 0 (1) ds T F T ξ 1 k n k g e η e ξ 1 Fig. 7 (b) Y D (D/Y = α) [5] ω ω, u, v, T ω, u, v T (u, v) ω P ω P P ω P [6] R r v u (5) Fig. 7(b) P (x, y, z)=p (u, v)=((r+rcosv)cosu, (R+rcosv)sinu, rsinv) (5) Fig. 8 (f, b, k) Q P (u 1 v 1) [6] f (R + rcosv 1) b (R + rcosv 1) k rsinv 1 sinu 1 cosu 1 0 = 1 (6) sinv 1 cosu 1 sinv 1 sinu 1 cosv 1 g = R f cosu 1 b sinu 1 rh ± g k 2 + g 2 r 2 sinv 1 = (7) k 2 + g 2 v 1 (7) k b h u 1 v 1 du 1 = ρ = R/r (2) dv (ρ + cosv) tanω dω μα cosv cos 2 ω = ( + sin ω) 2 dv α 2 2α cosω + 1 ρ + cosv sinv (3) (ρ + cosv) tanω dt μt(α cosω 1) cosvcos 2 ω = ( + sin 2 ω) (4) dv sinω α 2 2α cosω + 1 ρ + cosv (a) Vectors on the curved surface (b) The geometry of a torus Fig. 7 Course of a thread on a torus model. Fig. 8 Yarn path from the initial point Q (f, b, k), through the contact point P, to the escape point N on the disk. 207
KANEDA Naoto, SHINTAKU Sukenori, KINARI Toshiyasu, SHIMOKAWA Tomotsugu P t = ( sinu 1, cosu 1, 0) (8) QP {(R+rcosv 1)cosu 1 f, (R+rcosv 1)sinu 1 b, rsinv 1 k} (9) t QP ωp QP t ω P = cos ( ) 1 (10) QP 1 [5, 6] 4 Fig. 9 ω, u, v T 1 1 Q P (6) (10) P ω T1 (2) (4) P N 2 2 1 N 2 Q P 1 1 2 T3 1 3 4 3 4 4 N T7 Q P T1 T7 Fig. 10 H=90 mm, L=130 mm, (1-1) T (T1-T7) Fig. 11(a) (Z = 200 mm) (Z = 200 mm) Fig. 10 Fig. 11(a) Z T D/Y Fig. 10 D/Y T (Z = 200 mm) Z = 135 mm 1 Z = 45 mm 2 Z = 45 mm 3 Z = 135 mm 4 (Z = 200 mm) V D/V F = 1.68 Fig. 10 2 (Z = 45 mm ) Fig. 11(b) 2 D/Y Fig. 10 T ω, u, v, T T Fig. 12 Fig. 10 D/Y = 1.5 + Fig. 9 Calculation procedure. 208
Journal of Textile Engineering (2007), Vol.53, No.5, 203-210 Fig. 10 Comparison result of yarn tension. 2) H L θ T 3) 2 2 2 4) 2 T (a) coordinate axis (b) influence of feed effect Fig. 11 Influence of the speed ratio (D/Y). 2 ω P, u 1, v 1 T1 ω, u, v T 2 1) D/Y T References [1] Thwaits JJ (1984) J Text Inst, 75, 285 297 [2] Thwaits JJ (1985) J Text Inst, 76, 157 170 [3] Du Guang-Wu, Hearle JW (1991) Text Res J, 61, 289 297 [4] Du Guang-Wu, Hearle JW (1991) Text Res J, 61, 347 357 [5] Shintaku S, Endo T, Kinari T, Tamamura R (1999) J Text Mach Soc Japan, 52, T217 T224 [6] Shintaku S, Endo T, Kinari T, Tamamura R (2000) J Text Mach Soc Japan, 53, T53 T61 [7] Shintaku S, Endo T, Kinari T, Kobayashi S (2000) J Text Mach Soc Japan, 53, T155 T164 [8] Endo T, Shintaku S, Kinari T, Sasaya R (2001) J Text Mach Soc Japan, 54, T119 T125 [9] Endo T, Shintaku S, Kinari T (2003) Text Res J, 73, 139 146 [10] Endo T, Shintaku S, Kinari T (2003) Text Res J, 73, 192 199 209
KANEDA Naoto, SHINTAKU Sukenori, KINARI Toshiyasu, SHIMOKAWA Tomotsugu Fig. 12 Comparison result of yarn path. 210