Dinamics of ....

8/2/2019 Dinamics of ....

1/26

1

The dynamics of behavior in the process ofpolyester yarn from the knitting warp

Prof.dr Vojislav GligorijevicUniversity of NaisFaculty of Technology, LeskovacSerbia

E-maill: [email protected]

ApstractIn this study the dynamics of longitudinal tensile polyester yarn tex 19:53 mass in the knitting processandwithdrawal the taffeta knitwear knitting machine on Super Grant RE-4. The machine is operatedwith two knitting speed, low speed from 8.5 min -1 and higher speed of 580 min-1 with four differentdensities of knitting yarn. With the help of sensors, which were built on the needle segment in the zoneof compensation, and other parts, measured by the tensile force exceeds the compensation zone and thezone of knitting needles in themselves in order to monitor the dynamic behavior of polyester yarns inthe area of compensation and the process creating a loop in the individual phases. Based on the resultscalculated yarn tension in certain stages of the knitting of both speed knitting with four differentdensities.Based on the parameters of the machine, the moment of inertia of the spool with yarn, yarn longitudinal

mass in the zone of compensation, the module exceeds the elastic stiffness and other things, set thenonlinear differential equation of second order on the basis of which we have calculated the time of thecreation of a loop or cycle period and compared with the same period cycle of creating loops obtainedexperimentally. Discrepancies were minimal to neglect some of the parameters in the system of solvingdifferential equations.Based on the current elastic stiffness and friction coefficient exceeds in certain phases of the process ofmaking loops calculated tension in the yarn loops and half loops in the process of creation. .An important contribution is given in calculating the reduced friction angle of the yarn on the needlephase wefting with the forces at the ends of half loop and loop, the force of normal pressure whilemoving the needle half loop and the friction force to pull knitting down. As a novelty at this stage ofresearch.Key words: loop, half loop, wefting, friction, phases, tension, force, cycle time

Introduction

The warp knited knitwear (Figures 1 and 2) can be analyzed in view of a number of parameters in orderto obtain a uniform knitted structure. The yarn length in the loop is the most important parameter in theknitwear analysis. Equable yarn lengths in the loops, as well as their regular geometric shapecharacterizing the knitwear structure uniformity, are determined by the physical-mechanical propertiesof the yarn, the wefting depth, structure characteristics of the knitwear, and the intensity of the yarntension force variation in the compensation and knitting zones of the machine [1].

Certain influence on the yarn tension force at the wefting moment is exercised by the mechanicalproperties of the yarn, yarn stiffness, yarn feeding speed knitwear pulling force, yarn friction with thedevices for yarn guiding, feeding or tensioning, yarn friction with the loop creation elements, the friction between the yarns at the point of half loop passing over the needle butt, and the yarn contactangle with the needles.

The basic requirement of modern knitwear production on heavy duty warp-knitting machines is tomaintain the constant yarn length in the loops. To achieve this, the operation elements of the machinemust be supplied with precisely projected yarn lengths from the warp beam. The production of highquality knitwear is possible only in conditions of comprehensive and complete analysis of the knittingprocess, where the essential role is given to the dynamics of the yarn tension force in the compensationand knitting zones of the machine [2, 6, 7].

An important element in the process of warp knitting machine for knitting the optimization of addingwarp yarns in the area of compensation with respect to the minimum point of the load added to thewarp backThe machine is knited taffeta polyester yarn knitwear from the longitudinal mass of 19.53 tex knittingspeed of 8.5 and 850 lines per minute, for four variants of the loop length of yarn, knitting four densitiesand four levels of speed receipt of knitwear.


2/26

2

During the investigation, adding warp yarn length was variable.There are many approaches to the analysis knited process on knitting machines, including the analysisand modeling of process automation, optimization of production processes, quality of the process andthe yarn produced in strictly defined parameters estimates [13-16].From the technological point of view one of the parameters that have the greatest impact on the processof knitting the yarn in the warp geometry of zone passes, species and production of equipment for theadd, and the basic parameters-finesse needles or machines.

This publication aims to present the results obtained by nonlinear differential equations of second orderand the same compared with the results obtained experimentally on a machine with sensors designedspecifically for this type of machine in relation to the load dynamics in warp yarn and knitting zone,defined process of adding. Analysis of changes in force osnovinim yarns is differentiated depending onthe design parameters of the machine. In [17] discussed the process of yarn dodavanjawarp the constantlength of warp yarns addition, under certain conditions, as for example that the yarn viscoelastic bodyis not taking into account the stiffness, which is at this stage of research is of great importance.Mechanical designers in the process of technical and commercial designs focus their attention on theproblems of the kinematics and dynamics of sub-machines, types and properties of materials, as well asto optimize the dimensions of the machine, safety and ergonomics, among others [18].

1. Experimental

1.1. Investigation scope

The scope of this investigation is to determine the behavior and tension variation of yarn in thecompensation and the knitting zones of the knitting machine in the knitting process on a SUPERGRANT RE-4 warp-knitting machine as a function of the machine speed and the knitting density atvarious measuring points, in order to determine the influence of individual yarn guiding, directionaland feeding elements on the yarn tension structure as a condition for good quality of knitting.

1.2. Materials, machines and the testing equipment

In Table 1 given is the information on polyester yarn used for the measuring of the yarn tension force inthe compensation and knitting zones of the machine, the friction coefficients at all contact points of yarnwith the knitting, compensation and guiding elements of the machine, measuring of the current yarnstiffness, the contact angle between the yarn and the operation elements and yarn wefting depths. Themachine chosen for the knitting was a SUPER GRANT RE-4 Raschel machine produced by K. Mayerand installed in the knitting plant of the NITEX Company in Nais. The polyester yarn was knitted in thesingle warp right-left knitted fabrics, the diagram of which is knitted in figures 1a and b, in open and

closed layout, and the photo there of is knitted in figures 2a and b, front and reverse side of the taffeta.

Table 1. Physical-mechanicalcharacteristics of the yarn

Average yarn fineness (tex) X 19.53

Fineness reliability range Q 0.06Fineness variation coefficient (%) CV 0.42Stretching (%) 31.90Stretching variation coefficient (%) CV 1.85Breaking strength (N tex-1)F 43.22Variation coefficient CV 2.52

Number of twist S 32

Uniformity to Uster (%) 0.50


3/26

3

Figure 1. Graphic representation of laying taffeta Figure 2. Knitwear taffeta photographedInterlacement in closed (a) and open laying (b) on the front side (a) and the reverse side (b)

1.2.1.Testing devices sensors

The apparatus used for measuring, together with the measuring equipment layout (Figure 3) consisted

of the following devices:

- LDSM, G-I and G-II TR sensors, Ljubljana- Typ Q11 Waggezelle measuring heads, HBM, Kraftaufnehmer, Germany- Adapter for yarn tension forces transformation,- Microprocessor measuring amplifier DMC 9012 A,- Warp feeding measuring device, AG Wahli, Switzerland,- Stroboscope, Strobotac Type 1538 A, Genera radio,

Figure 3. Measuring equipment layout

Legend : MV- measuring the size; EV- electrical size; DEV- strengthened by measuring the size; FOEV-filtered electrical size; MV,R- result of measuring the size measurement.

1.2.2. Methods and testing sequence

In order to carry out the experiment on the RE-4 Raschel machine it was necessary to prepare themachine for the warp tension measuring in the compensation and knitting zones of the machine.


4/26

4

Figure 4a shows the machine outlay with the measuring points indicated in the zones. In zone I,between the bobbin (1) and the guide bar (3), the yarn (2) (warp) tension variations were measured bysensors and supplementary equipment. The yarn tension variation was also monitored in zone II,

between the guide bar (3) and the tensioning device (4), and in zone III, at the tensioning device (4) andthe yarn feeder (5). In the knitting zone, the yarn tensioning was monitored in particular stages of theloop creation process by a sensor mounted directly on the needles (the needle segment).

The knitwear tension variation was observed in zone IV between the needles (6) and the directional

roller (7), and in zone V between the pressure roller (9) and the cloth roller (10).The knitwear is pulledby the pulling roller (8).

In figure 4b [10, 11] given is a simplified layout of the yarn motion from the warp beam (1) to needles(5). The yarn (2) passes below the guide bar (6), over the tensioning device (3) to be introduced into theyarn feeder (4), and thence knitted-in by the needles (5).

Figure 4. Scheme Raschel machines with a layout of measuring pointsand display the original image sensors up

sensor

sensor


5/26

5

2. The determination of the yarn length in the loop in the knitting process

To determine the yarn length directly in the knitting process, at the machine operation speed of 580 min -1, an AG Wahli yarn feeding measuring device was used and the gear wheel was changed in fourdensity levels. The total length of the fed yarn in the knitting determined was dividing by 480revolutions of the main machine shaft, giving the length of yarn per loop for particular density pervertical ribs Gv. In Table 2 given are the values of loop lengths and their average values with thecorresponding densities per vertical Gv, for all four knitting densities (I to IV).

2.1. Calculation of the wefting depth and the yarn-to-needle angle

To calculate the wefting depth, hk, from equation (1) it is necessary to know the dimensions of the basicoperational elements of the knitting machine. In the given case, the machine fineness was 20, accordingto the english numeration system, so the needle pitch would be P = 1.27 mm. The relation [1] is valid forthe warp-knitting machines, where p/P = 0.20, therefore, the sinker thickness is p = 0.20 1.27 = 0.254mm. For right-left machines, r1 = 0, and r2 = 0.4318 mm, which is the needle thickness, di, obtained fromthe relation di/P = 0.34.To calculate the contact angle, amounting to 1/2 of the sinker thickness, r1 mustalso be known; i.e., r1 = 0.5 0.254 = 0.127 mm.Table 2. Yarn length in the loop

Additional warp length L[mm]

Yarn length in the loop [mm]

Knittingdensity[cm-1] L1 L2 L3 Lsr 1 2 3 sr

DensityGv

[cm-1]

I 2514 2532 2506 2517 5,237 5,275 5,220 5,244 10,4

II 2512 2503 2508 2507 5,233 5,214 5,225 5,224 10,4

III 2474 2476 2470 2473 5,158 5,158 5,145 5,152 12,1

IV 2359 2359 2345 2351 4,895 4,914 4,885 4,898 13,1

According to Table 2, the yarn length in the loop at density I is 5.244 mm. The wefting depth, i.e., thelength of the yarn in the loop, can be calculated using equation (1). Garbaruk suggested use of equation(1.1) for approximate calculation of the yarn-to-needle contact angle.

hk = 0.5(-p + 2r1)sin-(r1 + r2 + d)X(sin+ cos- 1) - d, (1)

whence the length of the yarn in the loop is

= 2

+++++

sin

)1cossin())(()5.0( 211

dXdrrdhrp k [mm].

,0)(2

)(3

)(4

)2(3

21321

2

13 =++

+

++

+

drr

Pl

rrr

rpl (1.1)

Assuming that

)(4

)2(3

21

1

drr

rplK

++

+= and

)(2

)(3

11

2

drr

plm

++

= ,

we get

2

2

mK

+ = .

By solving this equation we get K = 5.672, calculated from the data for ,p, r1, r2, and d, and m2/2 =4.14 and = 1.525 rad. The same method is used to calculate other contact angle values for otherdensities.

Once the contact angles have been calculated, we can also calculate the wefting depth, the values thereof being given in table 3.

Known the wefting depth, we can calculate the yarn length in the loop for the four densities.


6/26

6

Table 3. Yarn wefting depth

Density Contact angle [rad]

Loop length [mm]

Wefting depth hk[mm]

I 1,525 5,244 1,9630

II 1,515 5,224 1,9528

III 1,490 5,152 1,9140IV 1,440 4,898 1,7807

For density I and the wefting depth 1.963mm we obtain

1

1.963 0.43183.014

0.5(1.27 0.2540tg

= =

, 1 = arctg 3.014 = 1.25 rad.

2

0.56646sin 0.351

0.25806 2.3445 =

+, 2 = arcsin 0.351 = 0.358 rad.

whence the angle

= 1 +2 = 1.608 rad.In Table 4 given are the corresponding values of the angles and the yarn lengths in the loop for knownwefting depths. The calculated values for the yarn length in the loop differ from the experimental values

because we have obtained approximate values for the wefting depth and contact angles. To enableprecise calculation of the angles the fifth grade equation should be applied.

Table 4. Yarn length in the loop

Density Contact angle [rad]

Wefting depth hk[mm]

Loop length [mm]

I 1,608 1,9630 4,9875

II 1,601 1,9528 4,9670

III 1,609 1,9140 4,8900

IV 1,613 1,7807 4,6720

2.2. Yarn stiffness and friction coefficient determination

To calculate the maximum tension forces of warp yarns in the wefting phase (point 0 in the loopcreation cycle density I (Table 4), the existing stiffness and yarn friction coefficient in that phase must becalculated. From D-10 graph ( Figure 6), the maximum force in cycle I in the compensation zone is 6 cN,and from the knitting zone graph in the wefting phase point zero 14.21 cN, making a total of 20.21cN in the half loop wefting phase.

From D-11 graph (Figure 7),the maximum force in cycle I in the compensation zone is 8 cN, and fromthe knitting zone graph 14.21 cN, which amounts to 22.21 cN.

To calculate the stiffness and the friction coefficient of the yarn the two equations with density data Iand II are brought together. The maximum forces in the wefting phase are the forces in the half loop,and in this case the necessary force is in the half loop side. In the first instant, the force in the half loopside is 20.21:2 = 10.105 cN, and in the second 22.21:2 =11.105 cN .

max 2 1 2exp exp 1

2( )

R B RT T T

R r R rR r

= = +

+ ++ ,

i.e,

10.105 = 6exp2.75 ( )175.2exp4982.0

+ B

,


7/26

7

11.105 = 8exp2.75 ( )175.2exp4982.0

+ B

,

where2.75 = K.

Solving the equation gives the friction coefficient = 0.253, and stiffness B = 7.031 cN mm2.The yarn stiffness can be calculated from the formula

B = 0.05 Ed4,

where d yarn diameter,

E longitudinal yarn elasticity module.This formula can be used only to calculate the initial stiffness, and the existing stiffness in the knittingprocess itself is interesting.

2.2.1. The determination of the yarn diameter and the yarn cross section area

In the knitting process we have used texturized polyester of fineness 19.53 tex with 32 filaments andspecific mass 1.38 gcm-3.

The fineness of the elementary fiber:

11000 32 1638.519.53

tT mg

= = .

The area of the fiber cross section:

2

3

6

32 1S 0.01415

1.6385 10 1.38 10mm

= =

.

where the length of the elementary fiber L is assumed to be 163850 mm, and 1g in mass.

The yarn diameter:

21/2

1/2

3.57 1019.53 0.134645

1.38d mm

= = .

3. Yarn tension forces in the phases of the loop creation process

In figure 5 given is the diagram of the yarn tension force in the loop creation process with several cycles.The period of one cycle at the machine knitting speed of 8.5 min-1 is 7.05 s. The maximum yarn tensionin the loop creation process is in points 5, 8 and 0. Points 5 and 8, the maximum tension, correspond tothe motion of the warp (yarn) feeder in final front and rear positions. The tensioning of the yarn is at itsmaximum at the end of the wefting phase (point 0), when the needles reach the lowest position. Theminimum yarn tension corresponds to the feeder section between latch needles during the forward and

backward motion (points 4 and 7), and during the needle rising for latch opening (point 9). The tensionvariations were also observed in other loop creation process phases. For example, during the half looppass over the other half of the needle latch (points 10 and 10a) [3, 4, 5].This tension variation can beexplained by the fact that the yarn has a lower tension on its way from the warp beam towards theneedles than the yarn moving toward the half loops, i.e., from the zone between the feeder and the latchneedles that have an increased tension in the loop creation zone from the additional part of the yarnmoving towards the warp beam, when it is added to the half loop at an increased tension [12]. Theincreased yarn unwinding resistance also increases the maximum yarn tension, but, at the same time,the scattered tension is also increased, thus producing a decreased average yarn tension.Such yarntension variations lead us to investigate the yarn tension from the aspect of both maximum tensionvalue and the average tension value [8]. In table 5 given are the forces per phases in the knitting zone fordensity I at machine speed of 8.5 min-1, based on the input forces from the compensation zone I in thegraph D-10 (Figure 6) and at machine speed of 580 min-1as shown in graph D-13 in figure 9. Diagram ofthe yarn tension in knitting phases and compensation zone at a speed knitting machines 8.5 min -1 and580 min-1 density in the knitting and the diagram in Figure 6, and 9.


8/26

8

In figures 7, 8 and 9 shown are the diagrams of the yarn tension at the knitting speed of 8.5 min-1 for thecompensation zones I, II and III, and in figures 10, 11and 12 at the speed of 580 min-1 or the samecompensation zones.

I

Figure 5. Diagram of the yarn tension forces in the loop creation processwith several cycles

The average values of the force in the knitting process, and the maximum values in the wefting phase ofthe compensation zone are given in table 6.

Table 5. Forces in the knitting zone, per phases

Knitting zone at8.5 min-1

Compensation zone at8.5 min-1

Compensation zone at580 min-1

PhaseYarn tension force T

[cN]Yarn tension force T

[cN]Yarn tension force T

[cN]

0 14,21 17,49 21,27

1 13,23 16,51 20,29

2 11,27 14,55 18,33

3 5,39 8,67 12,45

4 1,47 4,75 8,535 20,09 23,37 27,15

6 5,88 9,16 12,94

7 0,735 4,01 7,79

8 16,17 19,45 23,23

9 0,49 3,77 7,55

10 12,25 15,53 19,31

10a 11,27 14,55 18,3311 14,21 17,49 21,27

Averagevalue

9,743 13,022 16,8

Table 6. The average and maximum tensionforces in the knitting process

F[cN[

0

n = 8,5 min-1

/ 2s cm-1

1cm 4,9 cN

T = 2 / = 7,o5s


9/26

9

0

5

10

15

20

25

30

1 3 5 7 9 11 13

Phase Phase

Phase Phase

Phase Knitting

zone T cN

Phase Zone

compensation T

cN

Phase Zone

compensation

In Figure 6. gives a diagram of the yarn tension in knitting phases and compensation zone at aspeed knitting machines 8.5 min-1 and 580 min-1 for the density and knitting I.The diagram on the basis of values given in Table 5 shows that in the knitting zone of maximumforce in a process of creating loops in phase 5 minimum phase in the 7 In the zone ofcompensation at a speed knitting of 8.5 min-1 maximum force in the process of creating loops inphase 5, the minimum in the fourth phase In the zone of compensation at a speed knitting 580min-1 exceeds the maximum tension force is also in phase 5, the minimum in the 4 phase.

Figure 6. Diagram of theyarn tension in knittingphases and compensationzone at a speed knittingmachines 8.5 min-1 and 580min-1 for the density andknitting I

Figure 7. Diagram D-10 of the yarn tension force in the compensation zone Iat the knitting speed of 8.5 min -1 and the knitting density I

3.1. Determination of coefficient of friction in the closing phase of the needle

Consider the closing phase of the needle in the figure 13,a, r = arctg r.., which will be the tiltingangle of the half loop repulsive even 0-0 in the closing stage of the needle. To find the reducedfriction coefficient, we count the conditional section is a needle in a plane in which lies half loopcircular (Figure 13, b)in which the normal pressure force N half loop acts in motion by the needle,a friction force Ft pulls up half loop.

Figure 8. Diagram D-11 of the yarn tension forces in the compensation zone IIat the knitting speed of 8.5 min -1 and the knitting density I

T= 3,28 cN

T s

T s

T = 2,47 cN

T cN

Phase


10/26

10

Figure 9. Diagram D-12 of the yarn tension forces in the compensation zone IIIat the knitting speed of 8.5 min -1 and the knitting density I

Figure 10. Diagram D-13 of the yarn tension forces in the compensation zone Iat the knitting speed of 580 min -1 and the knitting density I

The slope of the resultant R force N and Ft determine a reduced friction angle r, respectively,.if the resultant R is known, it will force acting on the ends of half loop to be equal 0.5 R. Friction

between the yarn and needles reduces the transmitting power of 0.5 R along the needles. At pointA the force will act

The point B on the axis of the yarn tension this is minimal and when = 0.200 is

Friction force is

( )( )1 exp 0,5 .t rF N R = =

3.1.1. Forces in the half loop and loop elements

According to Euler formula the forces in the half loop (Figure 14) are

11

01

exp

TT = ,

22

12

exp

TT = .

The forces in the elements of half loops and loops [9] can be calculated and compared with theexperimentally obtained forces. The maximum input force T0max in the wefting phase according to thediagram on the compensation zone I (Figure 7) is 6 cN, the yarn friction against the needles is 0.253 andthe angle is 1.485 rad. The force in one side of the half loop will be:

1 0.2531.485

64,120 cNT

e

= = ,

T = 1,89 cN

T s

T s

T =7,06 cN


11/26

11

i.e. 8.241 cN in the half loop. According the test the average knitwear pulling force amounted to 10.36cN.

Since

'

pF < T0 cos +T1 + T2

and in the given case, = 52o, and T1= 4.120 = T2

Fp


12/26

12

Figure 12. Diagram D-15 of the yarn tension forces in the compensation zone IIIat the knitting speed of 580 min-1and the knitting density I

Figure 14. Phaze closing needle with tongue Figure 14. The intersection of the needle in the plane

Table 7. Reduced coefficient and the friction angle in the wefting phase

Angle [rad]

Frictioncoefficient

[]

Reducedfriction

coefficient[r]

Reducedfrictionangle

[r]

Normalpressureforces in

half loop N[cN]

Forceresultant R

[cN]

Forces athalf loopends inpoint A

[cN]

Forces athalf loopends inpoint B

[cN]

0,6981 0,2540 0,3289 0,3178 7,376 7,768 3,251 2,605

0,6981 0,2540 0,3289 0,3178 7,494 7,890 3,303 2,6470,6891 0,2540 0,3289 0,3178 7,623 8,025 3,360 2,692

0,6981 0,2540 0,3289 0,3178 7,784 8,195 3,431 2,749

T s

T =5,81cN


13/26

13

Table 8. Reduced coefficient and friction angle in the needle closing phase

Frictioncoefficient

[ ]

Reducedfriction

coefficient[r]

Reducedfrictionangle[ r]

Forceresultant

R[cN]

Normalpressureforces N

[cN]

Angle [rad]

Forcesat halfloop

ends inpoint A

[cN]

Forcesat halfloop

ends inpoint B

[cN]

0,257 0,332 0,320 7,765 7,369 0.698 3,244 2,5920,257 0,332 0,320 7,890 7,487 0.698 3,297 2,634

0,257 0,332 0,320 8,025 7,616 0.698 3,353 2,679

0,257 0,332 0,320 8,195 7,777 0.698 3,424 2,736

0,252 0,326 0,315 7,765 7,380 0.698 3,256 2,613

0,252 0,326 0,315 7,890 7,449 0.698 3,308 2,655

0,252 0,326 0,315 8,025 7,628 0.698 3,365 2,701

0,252 0,326 0,315 8,195 7,789 0.698 3,436 2,758

0,248 0,322 0,312 7,765 7,389 0.698 3,265 2,629

0,248 0,322 0,312 7,765 7,389 0.698 3,265 2,629

0,248 0,322 0,312 7,890 7,508 0.698 3,317 2,672

0,248 0,322 0,312 8,025 7,637 0.698 3,374 2,718

0,248 0,332 0,312 8,195 7,799 0.698 3,446 2,775

4. Determination of the suspended period of one

cycle in the process of creating a loop

To determine the conditional period of one cycle in the process of creating a loop taffeta knitwear it wasnecessary to determine the total moment of inertia, which consists of the moment of inertia coil, where itwas necessary to know its dimensions and the specific weight of the material from which the coil ismade. Total moment of inertia of the coil is from the moment of inertia of trees and moment of inertiareel spool pages. It was also necessary to calculate the moment of inertia of polyester yarn that is woundon the coil with a diameter of 15.1 cm, weighing 9.632 kg and specific gravity exceeds 1.38 g cm-3exceeds that in our case is 2991276.6 g cm2, or with a total moment of inertia of the coil, 52475.2 g cm s2..Poisson coefficient of 0.5 is taken from the literature

Elastic modulus of stiffness was determined by the expression

211 ,

PE cN

S

=

where S is the cross-section of yarn in cm3;P1-load of yarn in the yarn cN which deforms by 1%.

Home zone length exceeds the compensation machinery was 50 cm. For the yarn elongation for 1%elongation according to the diagram was necessary powers of 2 cN and we got the yarn length 50.5 cm.Longitudinal weight yarn at this point was Tt = 18.217 tex.Cross sectional Yarn: S = 0.01320 mm2. Based on the specific weight of polyester yarn from the ratio offorce and cross-sectional area, we calculated the cross module "elastic stiffness: E1 = 15151.5 cN cm-2.Equation object, for experimental verification, can be written in the form of:

2

2 2 2 2 222 2 2 2 2

0 0 0

+1 .kMd T A I dT d d L A I A I I dI I dr

TS r dt S r dt S r dt r r dt r dt r dt

+ + = + +

In 2v const = and, the slow change I = const, r = const, to disregard the last member of the equation,

we get


14/26

14

2

2 2 222 2 2

0 0

2 2

2 21 1 0 1 0

2

2 222

,

22 2where A= ; ; ; .

100 100 100

1respectively .

k

k

Md T A v I dT L A IT

S r dt S r dt r

v I vL IQ R R Q

E E r S E r S L

d T dT Q R T M

dt dt r

+ + =

= = =

+ + =

Connecting with the tension T2 braking torque Mk transfer function can be written as::

( )

( )

( )

12

2.

1

p

p

k p

T rK

M Q p R p

= =+ +

From the transfer function shows that the transfer coefficient transfer function is equal to r-1, or in steadymode, T2 r = Mk.

Now we can calculate the Q and R:2

2

2 2

2 52,5 5475,2 2 0,5 101,293 ,

100 100 76776,98 15,1 0,01269

L IQ s

E r S

= = =

2

2 2

2 0,5 5475,2 2 0,5 100,0123 .

100 100 76776,98 15,1 0,01269

IR s

E r S

= = =

As the

2

2 222

1.k

d T dT Q R T M

dt dt r + + =

replacement values for Q and R and to disregard the Mk we get T2 = x

3

1, 293 0,0123 0,

respectively x+9,512 10 0,77339 0

x x x

x

+ + =

+ =

How is the general form of nonlinear differential equations of second order

( ) ( )

2

0

2 2

0

2 0,

and its general solution:

exp cos ;

where

x h x x

x k ht t

h

+ + =

= +

=

Conditional period damped oscillatory system amount to

.

2.usT

=

As in our case

The coefficient of attenuation amount:


15/26

15

3

0

5

.

2 9,512 10 , 0,77339; substituting we get

0, 77339 2, 26 10 0,8794 .

Conditional cycle period amount to

6,28T 7,14 .

0,8794Substituting values for h and the general solution of the equatio

us

h a

s

s

= =

= =

= =

3

n, we get

x= k exp(-4,756 10 ) cos(0,8794 ).t t +

0,01230,01081 .

1,293 1s = =

As in our case 0 1 , oscillation is damped.The occurrence of high amplitude in the coincidence of their own and disturbance frequency ofoscillation is called resonance, and only matching resonance frequencies are called conditional. If theincrease in the amplitude follows the corresponding increase in stress that occurs in the oscillatingelements of the then clear resonance in the design-construction design of machines is very important.The frequency of oscillation is even greater if the yarn is greater rigidity and decreases with increasinglength of the yarn and the yarn size of the oscillation. At high speeds, when the drag force is

proportional to the velocity, it is necessary in preparing the oscillation equations take into account theforce of resistance.

Based on the solution of nonlinear differential equations of second order we get the period of one cyclein the process of creating a loop, or one row of loops on the whole working width of the machine, the

knitting of the knitwear taffeta polyester yarn. This is a novelty at this stage of research, however, toshow that we need to be verified experimentally in the process of knitting machine with a sensor that ismounted on the needle segment, and the same set of rail together with other segments of the needle,which is also a novelty in this stage of research.

5. The interrelation of force acting on the loopwarp tension and withdrawal knitwear

With the help of G-2 sensors and related equipment, we measured the force the withdrawal of knitwearimmediate withdrawal of the needle or the needle and the tensioning roller, the below zone 1, and thetension roller-directing and roll merchandise at below zone 2 .Force the withdrawal of knitwear in zone 1 is two to four times the force of pulling in the second zone,which is understandable by the forces acting inside the knitting zone, or on the needle in certain stagesof the process of creating a loop. Force diagram for the withdrawal of knitwear and density is shown infigure 15, where the force the withdrawal of knitwear 2 cN. Force the withdrawal of knitwear fordensity II (Figure 16) was 2.5 cN, density III (Figure 17) and density of 4.5 cN IV (Figure 18) 5 cN.This is also reflected on the elements of the force in half loop and the loop in various stages of theprocess of creating loops, we have experimentally proved.Figure 19 shows a diagram of the filtered force the withdrawal of knitwear in the knitting zone at aspeed 8.5 min -1 and the density of knitting I. At high speed knitting of 580 min-1 density and knitting I,knitwear withdrawal force of 22 cN (Figure 20).The above diagram shows that the increase of tension warp and drag force change knitwear knitted .


16/26

16

Figure 15. Diagram of tensile force at density I taffeta knitwearand speed of 580 min-1

Slika.16. Diagram of force withdrawal taffeta density II of knitwearand knitting speed of 580 min-1

Figure 17. Diagram of force withdrawal taffeta density III of knitwear and knittingspeed of 580 min-1


17/26

17

Figure 18. Diagram of force withdrawal taffeta density IV of knitwearand knitting speed of 580 min-1

Figure 19. Diagram of force withdrawal taffeta knitting knitwear in the zone directlyfrom the density of needle knitting and knitting and speed of 8.5 min-1

Figure 20. Diagram of force withdrawal taffeta knitwear in the zone directly

from the density of needle knitting and knitting and speed 580 min-1

In table 9 are given force by stages of the process of creating a loop for knitting density N at kniting 8.5min-1, based on input forces from the zone of compensation according to the diagram in figure20, and at the speed machines 580 min-1 at D-13 chart in figure 23.In figure 21, and 22 are shown diagrams of the yarn tension during knitting speed of 8.5 min -1 for thecompensation zone 2 and 3, and figure 23, 24 and 25 at a speed knitting 580 min-1 zone compensation of1, 2 and 3.Table 10 give the average values of the force in the knitting process and the maximum force in the areawefting phase compensation.


18/26

18

Table 9: The tension in the yarn in phase knitting zoneIn Figure 21, based on forcevalues given in table 9 shows thediagram changes in tension in theknitting yarn in knitting zone andthe zone of compensation at aspeed of 8.5 knitting and 580 min -1. In the knitting zone maximalforce is in phase 5, the minimumphase in 9. In the zone ofmaximum force compensation isalso in phase 5 (23.37 and27.15cN), the minimum phase 9(3.77 and 7.55 cN).Why does occur in phase 5 themaximum tension, and theminimum phase 9. This questionis for now not to give answerswithout a deeper study of theprocesses of creating the loop onthis machine.

0

5

10

15

20

25

30

1 3 5 7 9 11 13

Phase

Knitting zo ne at8.5 m in-1 Yarntension force T[cN]

Compensationzone at 8.5 m in-1

Yarn tension forceT [cN]

Compensationzone at 580 m in-1Yarn tension forceT [cN]

Figure 21. Diagram showing changes in tension on the yarn and knitting phases in the area of

compensation for the different two-speed knitting with a density of I..

Diagram of the yarn tension in knitting phases and compensation zone at a speed knitting machines 8.5min-1 and 580 min-1 density in the knitting and the diagram in figure 22 and 25.

Table 10. Average and maximum force inphase wefting the compensation zone

Sped knitting 8,5 min-1

Sped knitting 580 min-1

Diagram T cN Tmax cN T cN Tmax cN

D-10 3,28 6 - -

D-11 2,47 7 - -

D-12 1,89 4

D-13 - - 7,06 16,5

D-14 - - 5,81 15,75

D-15 - - 4,81 12,5

PhasePhase Knitting

zoneZone

compensationZone

compensation

T cN TcN/8,5min-1 TcN/580 min-1-

0123456789

1010a11

14,2113,2311,27

5,391,47

20,095,88

0,73516,17

0,4912,2511,2714,21

17,4916,5114,558,674,75

23,379,164,01

19,453,77

15,5314,5517,49

21,2720,2918,3312,458,53

27,1512,947,79

23,237,55

19,3118,3321,27

Averagevalue

9,743 13,022 16,8

T cN

Phase


19/26

19

Figure .22. Diagram of tensile forces in the area of compensationat a speed knitting 8.5min-1 density I and knitwear

Figure 23. Diagram of tension in the zone 2 at a speed compensation knitting 8.5 min-1density I and knitwear

Figure 24. Diagram of the yarn tension in the zone 3 of compensationat a speed knitting 8.5 min-1 density I and knitting

6. Yarn tensile force by phases of the process of creating loopsthe density of yarn II

In Table 11 are given by the yarn tension phases of the process of creating a loop for density knitting II,based on the input force on the charts. As seen from table values of tension move in different phases atthe speed machines of 8.5 min-1 are different, caused by input forces. At high speed knitting of 580min-1forces are greater in certain phases for larger loads at higher speeds yarn knitting.

T =1,89 cN

T s

T s

T=2,47 cN


20/26

20

Figure .25. Diagram of the yarn tension in a compensation zone 1at a speed knitting 580 min -1 and the density I and knitting

Figure .26. Diagram of the yarn tension in a compensation zone 2at a speed knitting 580 min -1 density I and knitting

Figure 27. Diagram of the yarn tension in the zone 3 of compensationat a speed knitting 580 min -1 density I and knitting

.In table.12 give the average values of maximum force and the phase velocity for both wevting knittingdensity.Figure 28. Diagram showing changes in tension on the yarn and knitting phases in the zone ofcompensation for the different two-speed knitting with a density II. Table13 are given force bystages ofthe process of creating the loop density III based on the input force on the diagram which are not shownhere. Table 14 are given as mean values and the maximum force being wefting by zones. Table 15 are


21/26

21

given force in stages IV to the density in the knitting zone and the zone of compensation based on thediagrams for both speed knitting machines. In Table 16 are given the average and maximum values ofthe force being wefting.

Table 11. Tension in the phasesthe processs creating a loop

0 14,21 17,74 19,51

1 13,23 16,76 19,15

2 11,27 14,80 17,19

3 5,39 8,92 11,31

4 1,47 5,00 7,39

5 20,09 23,62 26,01

6 5,88 9,41 11,80

7 0,735 4,26 6,65

8 16,17 19,70 22,09

9 0,49 4,02 6,41

10 12,25 15,78 18,17

10a 11,27 14,80 17,1911 14,21 17,74 20,13

Averagevalue

9,74 13,264 15,655

Figure 28. Diagram ofthe yarn tension inknitting phases andcompensation zone at aspeed knitting machine8.5 min-1 and 580 min-1for knitting II density atthe input forcesFrom the diagram we

see that the maximumtensile force in the yarnknitting zone in phase 5,the minimum phase inthe 9. In the zone ofcompen sation at a speed knitting 8.5 min-1maximum ten sile forceis also.In phase 5, theminimum phase in 9. Athigh speed knitting of580min-1 maximumtensile force is in phase

5, the minimum phase in 9.

Table 12 .The average and maximum force in phases wefting8,5min-1 580min-1Diagram T

cNTmaxcN

TcN

TmaxcN

D-16 3,53 8 - -

D-17 2,41 7 - -

D-18 2,14 4 - -

D-19 - - 5,30 15

D-20 - - 4,94 13,5

D-21 - - 4,25 8,25

Knitting zone Zonecompensation

Zonecompensation

Phase T cN T cN at8,5 min-1 T cN at580 min-1

T cN

0

5

10

15

20

25

30

1 3 5 7 9 11 13 15

Knitting zone

Knitting zone

Zone

compensation

Zonecompensation TcN at 8,5 min-1Zonecompensation

Zonecompensation TcN at 580 min-1

T cN

Phase


22/26

22

Table 13. Tension in the phases ofthe processs creating a loop

0 14,21 18,1 24,33 6 5,88 9,77 15,98

1 13,23 17,21 23,33 7 0,735 4,625 10,83

2 11,27 9,28 21,37 8 16,17 20,06 26,27

3 5,39 9,28 15,49 9 0,49 4,38 10,59

4 1,47 5,36 11,57 10 12,25 16,39 22,35

5 20,09 23,89 30,19 10a 11,27 15,16 21,37

11 14,21 18,01 24,31Average

value 9,74 13,171 19,836

Table14. The averageand maximumforceinphaseswefting

Figure 29. Diagram of the yarn tension inknitting phases and compensation zoneat a speed knitting machines 8.5 min-1and 580 min-1 III on the knitting density

of the input forces.

In Figure 25.2 gives a diagram of changesin tension on the yarn and knittingphases in the knitwear of compensationfor the different two-speed knitting withdensity III.The diagram shows the change in yarntension in various stages of the process ofcreating the loop (0 - 11), where the

maximum tension force in stage 5, the minimum in the phase 3 (blue line). In the area of compensation

Knitting zoneZonecompensa-tion

Zonecompen-sation

T cN at580 min-1

Phase T cN T cN at 8,5min-1

Diagram 8,5 min-1 580min-1

T cN TmaxcN T cN TmaxcN D-25 - - 10,1 21,5

D-22 3,807 6,5 - - D-26 - - 7,98 23,25

D-23 3,73 10 - - D-27 - - 11 12,25

D-24 3,057 6 - -

0

5

10

1520

25

30

35

Knitin

gzo

ne

Phas

e 0 2 4 6 8 10 11

T cN


23/26

23

(cyclamen color) at a speed knitting 8.5 min-1 exceed the maximum tension force is also in phase 5, theminimum in the third stage At high speed knitting of 580 min-1 (yellow line) the maximum tensile forceis in phase 5, the minimum in the third stage

Table 15. Tension in the phases ofthe processs creating a loop

Table 16. The average and maximumforce in phases wefting

Knitting zoneZonecompen-sation

Zonecompen-sation

Phase T cNT cN at8,5 min-1

T cN at580min-1 6 5,88 9,77 17,77

0 14,21 18,1 26,1 7 0,735 4,625 12,625

2 11,27 9,28 17,28 8 16,17 20,06 28,06

3 5,39 9,28 17,28 9 0,49 4,38 12,38

4 1,47 5,36 13,36 10 12,25 16,39 24,39

5 20,09 23,89 31,98 10a 11,27 15,16 23,16

11 14,21 18,01 26,10

Aver-age

value9,74 13,171 21,646

Diagr-

am8,5 min-1 580min-1

T cN TmaxcN T cN

TmaxcN

-

D-28 3,89 10 - - D-31 - - 11,89 23,5

D-29 5,67 8,5 - - D-32 - 8,30 21

D-30 5,27 7 - - D-33 - - 6,53 13,5


24/26

24

CONCLUSIONS

Based on the results obtained by calculations and by experimental method, the following conclusionscan be given:

1. At slow knitting speed of 8.5 min -1 and knitting density I, the yarn tension forces in the

compensation zone decrease from the warp beam towards the knitting zone of the machine.

2. At knitting speed of 580 min-1 and density I, there occurred a tension force decrease in the secondcompensation zone, while in the third zone there was an increase of the yarn tension forcecompared to the second zone. In our opinion, this yarn tension increase was due to the tensioningdevice itself, because it could not evenly compensate the yarn tensioning and feed the exactprojected yarn length to the needles, which had a negative effect on the loop size.

3. In the needle closing phase, the yarn friction coefficient decreased at higher yarn tensioning forces,with the proportional decrease of the reduced coefficient and friction angle, while the forces at thehalf loop ends and the normal pressure forces increased.

4. The normal pressure forces in the half loop and the forces at its ends increased in the wefting phase,the contact angle and yarn friction values remaining unchanged.

5. The knitwear pulling forces obtained mathematically differ insignificantly from the pulling force

obtained experimentally by a sensor.6. The mathematical model of the process added, referring to the isotropic and anisotropic knitwear

knitted on the assumptions defined for dynamical systems of equal length and adding yarn forholding variables knited force structure and characteristics of the warp knitting process on knittingmachines, should be helpful in choice of optimal conditions in the knitting process.

7. Theoretical and experimental research shows that the analyzed structural parameters on knittingmachines have an impact on the optimal conditions for the knitting, the second of great importanceis the use of yarns of different segments in the composition of raw material addition, a compre

hensive corner of ranging from 30 to 70 , and 0 . In the case of anisotropic structures, it isvery important to produce them on the basis of knitting machine knitting needle high division, theaddition of segments from a number of warp yarns back, EBC-controlled system.

SummaryQuality knitwear largely depends on the management and control of the length of yarn needed to create

a loop. That is why more and more attempts to measure the improvement of the system exceeds thatinclude monitoring the size of the yarn tension, yarn tension oscillation in the knitting process, bringing

balance and expenditure for each knitting yarn system, measuring the speed of the yarn, the yarn lengthequal to the loop, as well as their proper geometric shape, are conditioned by the depth and intensitychanges wefting .] 3.4 [tension in countertrade yarn and knitting machines zone This means that theintensity change of the yarn tension to some extent characterized by the geometry of the loop or thedegree of uniformity of structure of knitwear.Due to the complexity of the process of knitting on the knitting machines, has not yet reached a highdegree of automation, and new studies are necessary to conception, development of new mechanisms,in which it would be easier to monitor and regulate all the relevant parameters with the main objectiveto achieve even greater automation system this process. For this purpose it is necessary to carry out thesynthesis of mechanisms for the purpose of keeping communication with the control system.Dynamic analysis of the time yarn tensioning process is the basis for setting up mathematical models ofthe dynamics of yarn tension from the moment of separation of the warp yarn bobbins to point weftingor trawl for determining the force acting on the cross at the moment wefting. The results can be used todevelop and design new systems for measurement and control, in order to find possibilities to improvethe process of knitting in terms of its automation. Based on these studies to cross the appropriatemixtures of certain longitudinal mass can make recommendations for the optimal processing conditionson the machine, in order to obtain the parameters of quality knitwear.From the dynamic point of view of a particular innovation is obtained by comparing the experimentalperiod of one cycle with a period of damped oscillatory process obtained from the nonlinear differentialequations of second order. Comparing the values of the period we have confirmed the experimentalvalue of the results as a valuable input for further research in this field of research.Many studies and investigations of modern machines can be made using traditional methods that donot allow to achieve the required accuracy of the results and meet the research to the extent necessary.


25/26

25

Installing sensors in the knitting zone and countertrade allowed to control the yarn tension, yarn,tension oscillation mechanism at any point of time during the operation of the machine, especially whenstopping and starting the machines in operation in order to obtain information relating to theproduction process, increase quality knitwear, expanded range of possibilities of machine, increase thechoice and use of synthetic yarn, increase the possibility of sampling, and more.

References[1] Gligorijevi R. V., Uticaj dinamikih karakteristika mehanizama za zatezanje osnove na prugavost

pletiva, magistarski rad, VTO Teks tilna tehnologija, Ljubljana, 1986, 47s.

[2] Gligorijevi 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, 240-24lp.[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, 426 p.[6] Gligorijevi V., Stupica I., Srak M., Petrovi T., Dinamika zatezanja niti u procesu pletenja, Tekstil

Vol. 40 broj 9 str. 415-420 ., Zagreb, 1991.

[7] V.Gligorijevi, M.Stamenkovi, J.Stepanovi, Dinamika zatezanja i oscilovanja pree u procesu

pletenja, Monografija, TF Leskovac, 2001.[8] Gligorijevi V., Dorevi M., The influence of the force of yarn tension in the compensational andknitting zone on the structure uniformity of the right-left knitted fabrics, 31. Simpozij o novostih v

tekstilstvu, Ljubljana, 1997.

[9] V. Gligorijevi., M. Dorevi., M. Stamenkovi., D. Trajkovi., Ravnoteni poloaj polupetlje uprocesu pletenja, Zbornik izvoda radova , IV simpozijum, Savremene tehnologije i privredni razvoj,

Tehnoloki fakultet, Leskovac 2001.

[10] V. Gligorijevi., M. Dorevi., M. Stamenkovi, The influence of the force of yarn tension in thecompensational and knitting zone on the structure uniformity of the right-left knitted knitwear, The

Indian Textile Journal, Mumbai (India), July 1999, page 8-13.

[11]Kazimierz Kopias., Fadenzugkrafte im Bereich des Fadenspanners an Kettenwirkmaschinen.,Melliand Textilberichte, 9/1985, 646 p.

[12]Vojislav Gligorijevi, Miodrag Dorevi, Nenad irkovi, Duan Trajkovi, Zatezanje i oscilovanje

pree u procesu osnovinog pletenja, Zbornik izvoda radova, VI simpozijum, Savremene tehnologije i

privredni razvoj, Tehnoloki fakultet, Leskovac, 23 i 24 oktobar 2005.[13]. Grzubowski W. W., Radziewskij W. A.; Isledowanie dynamiki osnowiazalnowo procesa kakobiekta awtomatczeskowo regulirowania, Technologia liegkoj promyslennosti, Nr 1, 1972, pp. 129-134.[14]. Radziewskij W. A.; K teorii awtomaticzeskowo uprawlenia osnowiazalnym procesom, Technologialiegkoj promyslennosti, Nr 3, 1975, pp. 124-129.[15]. Kopias K.; Technologia dzianin kolumienkowych, WNT, Warszawa 1986, 177p.[16] Backmann R.; Modellierung der Fadenzufhrung in Maschinen zur Herstellung textilerFlchengeblide, Textiltechnik 36, 1986, Nr 10, pp. 518-520.[17]. Mikoajczyk Z.; Model of the Feeding Process of Anisotropic Warp Knitted Fabrics, Fibres &Textiles in Eastern Europe, Vol. 11, No 2 (44) 2003, pp. 58-62.[18]. Pahl G., Beitz W.; Nauka konstruowania, Translation from German, WNT, Warszawa 1984, 505p.

Address author:

Prof. dr Vojislav Gligorijevic,Ph.D.Head of Textile Department

University of Nais

Faculty of Technology Leskovac

Bulevar Oslobodjenja 124

16000 Leskovac

Serbia

email: [email protected]./Fax.: +381 16 215 440


26/26

Dinamics of ....

Documents