Influence of.....

INFLUENCE OF SPEED AND KNITTING DENSITY ON HAULING FORCE AND STRUCTURAL ELEMENTS OF WARP KNITS

Vojislav Gligorijevic1, Jovan Stepanovic1, Vasilije Petrovic2, Petar Stojanovic3

University of Nais1Faculty of Technology, Leskovac, Serbia

2Technical Faculty "Mihajlo Pupin", Zrenjanin, Serbia 3 Dunav AD Grocka, Grocka, Serbia

AbstractAn account of taffeta fabrics hauling force, immediately during haulage of knit from needles and between tensioning roller and directing knitted cloth beam, is given. The results obtained have shown that the hauling forces of knit between needles and tensioning roller are two to four times as great as knit hauling forces between directing and cloth roll of the machine. The measurement of knits hauling force has been performed at machine speeds of 8.5 min -1 and 580 min-1 for different knitting densities. The forces in elements of half-loop and loop elements were calculated and compared with forces obtained experimentally, using sensors and other accompanying equipment. A special attention has been paid to the behavior of the yarn on the machine itself, from tensioning mechanism to knitting needles at both low (8.5min-1) and high ( 580min-1) speeds of knitting at different densities of knitting. On the basis of average forces in the cycle of loop formation, properties as elongation and linear density of yarn in the moment of extension, cross section surface, elasticity modulus, self-radial frequency, conditional period of cycle, damping coefficient and logarithmic decrement, in other words, natural logarithm of the ratios of sequential maxima of solutions x(t), have been assessed.

Key words: hauling force of knit, half-loop, loop, density of knitting, speed of knitting

1. Experimental

Material and Methods

Using sensor and accompanying equipment (Fig.3) [1, 2] the hauling force of taffeta knit (Fig.2) on Rachel "Super Grant" RE-4 knitting machine (of. Karl Mayer) has been measured directly during its haulage from needles, respectively between needles and tensioning roller (Fig.1), (further in the text "zone 1"), and between tensioning roller- directing roller and knitted cloth roller (further in the text "zone 2").

2. Results and Discussion2.1 Forces in elements of half-loops and loops

The results of measurements are given in Tab.1. From experimental results it is obvious that hauling force in the zone 1 is two to four times as great as the hauling force in the zone 2, which can be explained by the forces acting in the knitting zone itself, respectively in the needle in the single phases of loops forming process. The

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diagrams of knit hauling force for the zone 1 at machine speeds 8.5 min -1 and 580 min-1 for knitting density I are presented in the Figs. 1.1. and 1.2. In the zone 2 the hauling force of knit at greater speed of knitting has been measured for all four densities of knitting. The diagram of knit hauling force for density I is shown in the Fig.1.3, for density II in the Fig.1.4, for density III in the Fig.1.5 and for density IV in the Fig.1.6.From these diagrams it may be seen that with an increase of the tension of the warp and of the knitted fabric, the hauling force of knit is changed as well as the density of knit. The forces in elements of half-loops and loops were also influenced in single phases of loops formation, as it has been proven experimentally.

Fig.1. The scheme of Rachel machine with measuring points and sensor

Legend: 1- bobbin; 2- warp; I-Compensation zone; 3- Directing bar; II- Compensation zone; III-Compensation

zone; 4- Tensioning mechanism; 5- Laying down of warp; 6- Needle with built-in sensor; IV – Knitted cloth;

7- Hauling roller; 8,9- Directing rollers; V- compensation zone; 10- Knitted cloth roller

a) b)Fig.2.Photograph of taffeta knitted fabric Fig.3.Measuring apparatusfrom right side (a) and reverse (b)

Tab. 1. Hauling forces of Taffeta knitted fabric in dependence on speed and density of knitting

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Speed of knitting [min-1]

Density of knitting[cm-1]

Hauling force of knit[cN]

Knitting zone

8.5 I 10.36 1580 I 22 1580 I 2 2580 II 2.5 2580 III 4.5 2580 IV 5 2

Fig.1.1- Diagram of taffeta knit Fig.1.2- Diagram of taffeta knit haulingforce at knitting speed of 8.5min-1 force at knitting speed of 580 min-1

and density I (zone 1) and density I (zone 1)

Fig.1.3- Diagram of taffeta knit hauling Fig.1.4- Diagram of taffeta knit hauling forceforce at knitting speed of 580 min-1 at knitting speed of 580 min-1

and density I (zone 1) and density II(zone 2)

Fig.1.5- Diagram of taffeta knit hauling Fig.1.6- Diagram of taffeta knit haulingforce at knitting speed of 580 min-1 force at knitting speed of 580 min-1andand density III (zone 2) density IV (zone 2)

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Tab.2- Forces in elements of half-loops and loops of taffeta knitted fabric

Forces in the stitching phase, Fomax [cN]

Friction of yarn [μ]

Contact angle α [rad]

Forces in half-loop/loop legF [cN]

Forces in half-loop/loop F [cN]

6 0.253 1.485 4.120⁄2.59 8.242⁄5.1816.5 0.253 1.485 11.332⁄0.5 22.664⁄1.00

3. Force in the elements of half-loops and loops According to Euler's formula

, .

forces in elements of half-loops and loops could be calculated and compared with forces obtained experimentally, using sensors and other accompanying equipment. In Tab.2 values of force in half-loop and loop are given, i.e.

, (1)

in one leg, or 8.241 cN in half-loop. According to the experiment, the average force of knitted fabric hauling is equal to 10.36 cN. Taking into account the condition that

F'p < Fo.cosβ + F1 + F2 , (2) in the case β = 52o and F1 = 4.120 = F2,

F'p < 6.cos.52o + 8.241, i.e.F'p <11.93 cN.

According to the expressions (1) and (2), Fp' will be equal to

.

Tension in the loop leg, according to the expression (1) will be

F= 0.25Fp = 0.25.10.36 =2.59 cNIn the half-loop leg this force will be equal to 4.12 cN.The hauling force of knitted fabric in the zone 2, according to the diagram from the Fig.1.3 equals to 2 cN, while the tension of the yarn in the loop leg is equal to F = 0.25x2 = 0.5 cN.From these data it is obvious that the force in the legs of loops in the zone 1 is twice as great as the force in loops legs in the zone 2 and in relation to half loop it is 3.5 times greater. In the case of greater speed and the density 1, when the hauling force of knitted fabric in the zone 1 (fig.1.2) is equal to 22cN and the in-coming force in the phase of stitching according to the diagram equals to 16.5 cN, the coefficient of friction is 0.253 and the contact angle of yarn on needles is 1.485 rad, the force in the half-loop leg will be

,

or 22.66 cN.The average hauling force, obtained experimentally, is 22 cN.From the expressions (1) and (2) it follows that the values of average hauling force are F p < 32.81 and Fp = 29.27 cN respectively.The tension of the yarn in the legs of loops according to the

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expression (1) is 5.5 cN, while in the leg of half-loop it equals to 11.332 cN; in other words, this force is twice as great as the force in the leg of loops and in relation to the loop in the zone 2, it is 5.5 times greater.

4.The influence of the force of warp tension and knitting density on the period of loop forming cycle of taffeta knits 4.1. Conditional resonance in the knitting process

Under conditional resonance, the increased amplitude in the case of coincidence of the self- and disturbance frequency is understood. If an increase of the amplitude is followed by corresponding increase of strain, occurring in oscillating elements during knitting process, it is clear that the resonance is of great importance for projecting and calculating of machine construction [9]. The greater the rigidity of the yarn, the greater the frequency of oscillating; it decreases with an increase of yarn length and the magnitude of oscillating of that yarn. By great speeds, when the force of resistance is proportional to the speed of movement, it is necessary to take into account the force of resistance in the equation of oscillating. In the works [1, 2, 3], on a "kettenstuhl" machine, the change of different yarns behavior in single processes of loops forming has been assessed by using a measuring head. However, the results obtained were not reliable because of greater faults that occurred during measurement. In order to obtain more reliable results, the inclusion of a sensor in the needle segment itself proved to be necessary. The special attention has been paid to the behavior of the yarn, in the zone from tensioning mechanism to knitting needles [6, 7, 8] at both low (8.5 min -1) and high (580min-1) knitting speed and with different densities of knitting. Before knitting, the length from tensioning mechanism to knitting needles was equal to 50 cm. According to the extension diagram, the extension of the initial yarn length (50 cm) for 1%, requested force equal to 2 cN and elongated yarn has been 50.5 cm long. In order to calculate the yarn cross section surface in the moment of extension, the determination of yarn linear density was necessary in the same moment. As the mass of initial yarn was 0,0092gr, the linear density of the yarn extended for 1% will be:

.

and the yarn cross section surface

.

For specific mass of polyester yarn the value of 1.38 mg.mm-3 has been used. The elastic rigidity modulus, as the relation of the force and the surface of yarn cross section, will be equal to

.

In the case of slow machine work, the average force of 13 cN (Tab.3) in the cycle of yarn forming will provoke an elongation of 6% and the length of the yarn will be 53cm. The yarn linear density in the moment of extension will be 17.358 tex, yarn cross section surface will be 0, 01 257 mm 2

and the module of elasticity will be 103 420.8 cN.cm -2.The self radial frequency (Tab.4) will amount to 1.0104s, and the conditional period of cycle to 6.215s. The coefficient of damping is valued at 0.009336s, and the logarithmic decrement at 4.766.10-3. "Logarithmic decrement", 2.π.h/ω =0.0339637, is, as already mentioned, the natural logarithm of the ratios of sequential maxima of solutions x (t). In this case the oscillating is damped, too. The conditional period of cycle decreases with an increase of the force in relation to the period of cycle obtained experimentally. With an increase of knitting density the average force in the cycle amounts to 1.5 cN, while the elongation of the yarn equals to 7%, which corresponds to the length of the yarn of 53.5 cm. Elasticity modulus

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equals to 108338 cN.cm-2, self radial frequency to 1.025 s and conditional period of cycle to 6.126s. The decrease of the conditional period of cycle is evident.

Table 3 Impact different density of the knitting speed of 8.5 and 580 min-1 at fineness of stressed yarn

Speed of knitting [min-1]

Density of knitting without stress [cm -1]

Initial length of yarn without stress [cm]

Yarn fineness before stress [tex]

Average force in the cycle of knitting [cN]

Yarn elongation [%]

Length of stressed yarn [cm]

Fineness of stressed yarn [tex]

8.5 I 50 19.53 13 6 53.00 17.3588.5 II 50 19.53 13.50 7 53.50 -8.5 III 50 19.53 13.63 7.75 53.875 -580 I 50 19.53 16.80 8 54.00 17.037580 II 50 19.53 15.655 - - -580 III 50 19.53 19.836 - - -580 IV 50 19.53 21.64 - - -

At the greatest knitting density allowed, the average force in the cycle amounts to 13.63 cN and the elongation to 7.75%, this value corresponding to the yarn length of 52.875 cm. The elasticity modulus is valued at 110185.93 cN.cm-2, the self radial frequency at 1.0264 s, the period of cycle at 6.118s. With a minimum difference between forces, the conditional period of the cycle is still decreasing.In the case the machine is working at the speed of 580 min -1, at the initial density I, the average force in the cycle of loops forming is 16.8 cN and elongation of the yarn is 8%. The yarn linear density in the moment of extension is 17.037 tex, yarn cross section surface is 0.01234 mm2 and elasticity modulus is 136142.6 cN.cm-2. The self radial frequency is equal, for all 20 cycles, to 3.73211s and the conditional period of one cycle to 0.0841 s. The period of one cycle, obtained experimentally, is 0.103s. The damping coefficient in this case is 0.1345, and the logarithmic decrement is 0.0472.For the second density the average force in the cycle is 15.655 cN, the self radial frequency is 0.1235 s, and the conditional period of one cycle is 0.12s.For the third density the average force in the cycle is 19.836 cN, the self radial frequency is 0.1235 s, and the conditional period of one cycle is 0.123 s.For the fourth maximally allowed density of knitting, the average force in the cycle is 21.64 cN, elasticity modulus is 178547 N.cm-2, self radial frequency of all cycles is 2.9924 s and the conditional period is 2.098 s or 0.104 s for one cycle.

Table 4 Impact different density of the knitting speed of 8.5 and 580 min-1 at coefficient of dumping and logarithmic decrement

Speed of knitting [min-1]

Density of knitting [cm-1]

Surface of yarn cross section [mm2]

Self radial frequency [s]

Conditional period of cycle [s]

Coefficient of dumping [s]

Logarithmic decrement

8.5 I 0.01257 1.0104 6.215 0.009336 4.76610-3

8.5 II - 1.025 6.126 - -8.5 III - 1.0264 6.118 - -580 I 0.01234 0.186 0.0841 0.1345 0.0472580 II - 0.1235 0.123 - -580 III - 0.144 0.108 - -580 IV - 0.149 0.104 - -

Conclusion

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By using sensor, built in the needle segment, the change of yarn strain and the hauling force in the knitting and compensation zones of the knitting machine have been assessed at different speeds and knitting densities.The hauling force in the zone 1 is twice to four times as great as the hauling force of the knit in the zone 2, this fact being attributed to the forces acting in the knitting zone itself in the single phases of loops forming process.On the bases of the diagrams obtained, it is obvious that with an increase of tension of the warp and the knit, the hauling force is also changed, as well as knitting density. This specially influenced forces in half-loop and loop elements in the single phases of loops formation.Time period of one cycle at 8.5min-1 equals to 7s, and at 580min-1 to 0.103 s. The calculated values of time periods differ from experimental values thanks to deformation instantaneously appearing in yarns during the work of the machine and to entanglement of yarn in the knitting process.During loops formation process, the hauling force of knit must be inferior to the force in half-loop. In this case Fp' < 11.93 cN because, according to the experiment, Fp' = 10.36 cN. In one moment these forces will equalize, so that Fp' = 10.64 cN. At higher speed of the machine the hauling force of the knitted fabric in zone 2 attains 22 cN. The initial force in the stitching phase is 16.5 cN and the force in the half-loop leg is 22.66 cN. In this case, too, the force Fp' < 29.27 cN. Yarn tension in the loop leg is 5.5 cN and in the half-loop leg is 11.333 cN.As illustrated by the data in tables, the forces change in single zones and at greater speeds these forces are substantially greater because of increased yarn tension obtained on account of an increase of machine speed and knitting density.The difference among calculated end experimental time constant in one cycle originates from the deformation of the yarn in the knitting and compensation zones, the total deformation being composed from three components: elastic, viscoelastic and plastic part. These deformations are acting instantaneously and are dominating only at greater speeds, in other words by greater yarn tension. At lower speeds only elastic part is dominating, thanks to the lower yarn tension. This is confirmed by the results obtained for time constants of cycles at the lower knitting speed, where the stress of yarn is law in comparison with stress of yarn at high speeds of knitting, when the damping coefficient is significantly greater.

References: [1] Gligorijević R. V., Uticaj dinamičkih karakteristika mehanizama za zatezanje osnove na prugavost pletiva, magistarski rad, VTO Tekstilna tehnologija, Ljubljana, 1986, 47s.[2] Gligorijević R. V., Upliv dinamike in trenja niti v kompenzacijski in pletilni zoni na strukturo pletiva, disertacija, VTO Tekstilna tehnologija, Ljubljana, 1990.[3] Vera Havas, V.A. Petrova, Influence of the yarn strukture on the processing behaviour and the properties., Melliand Textilberichte, 3/1980, 240-241p.[4] Vera Havas, V.A. Petrova, Influence of the yarn strukture on the processing behaviour and the properties., Melliand Textilberichte, 4/1980, 326 p.[5] Vera Havas, V.A. Petrova, Influence of the yarn strukture on the processing behaviour and the properties., Melliand Textilberichte, 5/1980, 426p.[6] Gligorijević V., Stupica I., Srđak M., Petrović T., Dinamika zatezanja niti u procesu pletenja, Tekstil Vol. 40 broj 9 ,. 415-420s ., Zagreb, 1991.7] V.Gligorijević, M.Stamenković, J.Stepanović, Dinamika zatezanja i oscilovanja pređe u procesu pletenja, Monografija, TF Leskovac, 2001.8] V. Gligorijević, M. Đorđević, N. Ćirković, D. Trajković; " Yarn tension and oscillation in the process of warp knitting"; FIBRES & TEXTILES in Eastem Europe, Vol. 11, 1, 25 – 27 (2003)9 Kazimierz Kopias., Fadenzugkrafte im Bereich des Fadenspanners an Kettenwirkmaschinen., Melliand Textilberichte, 9/ 1985, 646 p.

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