Single Nozzle Air-jet Loom

Indian Journal of Fibre & Textile Research

Vol. 33, March 2008, pp. 45-51

Simulation analysis of weft yarn motion in single nozzle air-jet loom to study the

effective parameters

H Nosratya, Ali A A Jeddi & Y Mousaloo

Textile Engineering Department, Amirkabir University of Technology, Tehran 15914, Iran

Received 25 July 2007; accepted 14 February 2008

A simulation model has been suggested for a single nozzle air-jet loom to analyse weft yarn motion under different

conditions of weaving procedure. For this purpose, weft yarn motion equation has been derived using this model, physical

laws and combination of air velocity and air-yarn friction coefficient equations. This analytical model for drum storage

system is developed to investigate the weft yarn behaviour during weft insertion, i.e. displacement, velocity, and yarn

tension. Numerical solutions of yarn motion equations have been obtained. Tension analysis of weft insertion has been

carried out both theoretically and experimentally using different cotton-polyester yarn counts under different air pressures.

The results show good agreement between theoretical and experimental values of weft yarn tension.

Keywords: Air-jet loom, Air-yarn friction coefficient, Simulation model, Weft insertion, Weft yarn motion

IPC Code: Int. Cl.8 D03D

1 Introduction Air-jet weaving is an advanced weaving method

with high efficiency and productivity. However, the

weft yarn motion in air-jet filling insertion is very

complicated. It is not a positively controlled process,

and the air stream during the filling insertion process

is turbulent and unsteady with regard to its velocity, it

could be compressible. The transferred material, i.e.

weft yarn, also has its complications, especially in the

case of staple yarns. The weft yarn propulsion force is

provided by the friction between the yarn surface and

the air stream.

Many researches in the field of simulating the air-

jet filling insertion have been performed. Salama and

Mohamed1 simulated the air-jet filling insertion by

using a single nozzle for insertion and a tube to guide

the air. They presented the air velocity distribution

along regular and slotted tubes in terms of the tube

configuration and its interaction with the air-jet at the

tube entrance. Adanur and Mohamed2 modified this

simulator with automatic data acquisition and

analysis, and measured the weft insertion time, air and

weft yarn velocity, air pressure, and weft yarn tension.

They2 reported the influence of different weft

insertion system parameters and yarn characteristics

on yarn velocity. They found that the increase in yarn

linear density and twist increases the insertion time.

Adanur and Bakhtiyarov3 presented an analytical

model to simulate air flow through the channel. They

calculated the drag coefficient in the guide channel

and propelling force acting on the yarn, and found the

results in good agreement with the experimental data

obtained for the same conditions. Nosraty et al.4

obtained the weft yarn position, the weft yarn velocity

and the weft yarn tension graphs by using a

simulation model for weft yarn motion.

Adanur and Mohamed5 developed analytical

models to investigate the air-jet filling insertion.

These models enable yarn velocity to be calculated

from measured values of air velocity. Then they5

compared the predictions of the models with

experimental results. Ishida and Okajima6

in an

experimental study analyzed the flow characteristics

inside the main nozzle of the loom by changing

air tank pressures and acceleration tube lengths, to

obtain basic data for an optimum design of the main

nozzle.

In the present study, different theoretical and

experimental equations of the air velocity of the

nozzle (U) and the friction coefficient between air

and yarn (Cf), as reported by previous researchers,

have been applied in the weft yarn motion

equation. Thereafter, the equation, which has the

theoretical results nearest to the experimental results,

has been suggested as an analyzing model to predict

the weft yarn motion at different conditions.

___________ aTo whom all the correspondence should be addressed.

E-mail: [email protected]

INDIAN J. FIBRE TEXT. RES., MARCH 2008

46

2 Materials and Methods

2.1 Theoretical Background

Hitherto, several models have been presented in the

literature to describe the yarn motion during insertion.

Many parameters influence yarn motion equation.

Some of them are due to yarn diameter and surface

properties7, and the others depend on the loom setting,

such as air velocity. Uno8 expressed the air velocity

distribution along the guide channel as follows:

1300

13 0

+=

x

UU …(1)

where x is the distance from the nozzle (m); U0, the

initial air velocity at the core of nozzle (m/s); and U,

the air velocity at distance x from the nozzle (m/s).

Salama et al.9 found experimentally that the air

velocity of the nozzle is a function of time, as shown

below:

τ= tUU 0 …(2)

where τ is a constant and is related to the running

speed and the air pressure.

Duxbury et al.10

estimated velocity distribution

along the axis of air jet with steady flow, as follows:

L/C0

−= eUU …(3)

where C is the constant = 30 (dimension of length);

and L, the distance from the nozzle to be expressed as

a function of time in the form as shown below:

cx(t)0eUU = …(4)

Friction coefficient between air and yarn which

would be depended on the nature of used yarn has

been suggested by previous workers, like:

Uno8 found experimentally for spun yarn:

2)(

102.0f

+−+=

VUC …(5)

where Cf is the friction coefficient ; U, the air

velocity(m/s); and V, the yarn velocity (m/s).

Adanur and Mohamed11

found experimentally the

relationship between friction coefficient and air

velocity (range of 1-350 m/s) in the form of:

2c1f

−= UcC …(6)

where

c1 = 0.4193 and c2 = −0.4883 for cotton yarn.

c1 = 0.4274 and c2 = −0.4887 for textured polyester

yarn.

The dimensionless coefficient Cf is function of the

Reynolds number Re=UD/V, where U is the air

velocity in channel (m/s); D, the channel diameter

(m); and V, the air dynamic viscosity (m2/s). The

following equations have been presented for Cf

according to Reynolds number:

Smith and Goud12

:

61.0

f Re27.0 −=C …(7)

Matsui13

:

61.0

f Re24.0 −=C …(8)

Orii and Sano14

:

64.0

f Re27.0 −=C …(9)

Selwood15

:

61.0

f Re37.0 −=C …(10)

Limming and Ming16

:

1111.0xro

f)Re.e(

0706.0

RKC = …(11)

where 787.0Re.

3566.0

ro

+=V

K

Rero = Reynolds number on the weft yarn radius

Rex = Reynolds number on the weft yarn length

Adanur and Bakhtiyarov4:

Re

96f

ψ=C …(12)

where ψ is the function of guide channel and its slots

dimensions.

2.2 Proposed Model for Yarn Motion

The present model17

is based on the Adanur and

Mohammed5

model on an Investa single nozzle air-jet

loom with weft yarn drum storage (Fig.1). The

general assumptions for this model are:

NOSRATY et al.: SIMULATION ANALYSIS OF WEFT YARN MOTION IN SINGLE NOZZLE AIR-JET LOOM

47

(i) Weft yarn has uniform properties, such as linear

density and diameter, and is inextensible.

(ii) The fluctuation in the movement of the yarn due

to turbulent and unsteady flow is not taken into

account. Therefore, the yarn moves along a

straight line inside the confusor along the center.

(iii) The effect of gravitational force on the yarn

motion is neglected, since its value is small.

(iv) The starting point for the weft yarn motion is

taken as the confusor entrance and its

displacement in confusor is chosen on X-axis.

Newton’s second law governs the yarn motion

during the course of insertion. Thus, the equation for

the yarn motion can be written as5:

21

)(FFF

dt

MVd−=Σ= …(13)

where M is the total yarn mass involved in the motion

(kg); V, the yarn velocity (m/s); t, the time (s); ΣF, the

total force acting on the yarn; F1, the air friction force

on the yarn; and F2, the force applied by the yarn

guide.

)()(5.0 6542

0f1 lllVUdCF ++−πρ=

∫ πρ−−πρ+

7l

0

22

f2

f 5.0)(5.0 lVdCdxVUCd ...(14)

where Uo is the initial air velocity at the core of

nozzle (m/s); U, the air velocity at a distance from the

nozzle (m/s); V, the yarn velocity (m/s); d, the yarn

diameter (m); ρ, the air density (kg/m3); Cf, the

friction coefficient between air and yarn; l2 = the yarn

length between the guide and nozzle; l4 + l5 + l6, the

lengths of yarn exposed to nozzle’s air flow; and x,

the distance from the confusor entrance (m).

µα= emVF2

2 5.0 …(15)

where m is the linear density of the yarn (kg/m); µ, the

friction coefficient between yarn and guide; and α, the

angle of wrap around the guide (rad).

The function of the total yarn mass involved in the

motion is given as follows:

)()( 1kxmxM += …(16)

where k1 = l1 + l2 + l3 + l4 + l5 + l6

Thus

2

2

1

2

)()(

dt

xdkxm

dt

dxm

dt

MVd++

=

Thereafter

20f2

2

1

2

)(5.0)( VUdCdt

xdkxm

dt

dxm −πρ=++

∫ −πρ+++

7

0

2f654 )(5.0)(

l

dxVUCdlll

µα−π− emVlVpdC2

22

f 5.05.0

With simplified assumptions as A= 0.5πρd and k2 =

l4 + l5 + l6, the following second-order non-linear

differential equation for weft yarn motion is obtained:

)(])([

)(

])([

)(

1

2f

1

20f2

2

2

txktxm

VUAC

ktxm

VUCAk

dt

xd

+

−+

+

−=

]5.0[])([

2f

1

2

mmelACktxm

dt

dx

+++

− µα …(17)

Fig. 1 — Schematic diagram of the drum - storage model for single nozzle air - jet loom19 [1— Weft package, 2— Weft yarn, 3— Weft

yarn feeder, 4 —Weft yarn drum storage, 5— Yarn clamp, 6— Yarn guide,, 7— Air nozzle, 8— Scissors, 9— Confusor, 10— Suction

pipe, and 11— Suction tank]


48

In solving Eq. (17), the parameters Cf and U should

be substituted in according to distance (x) or time (t),

and the initial conditions taken into account.

2.3 Numerical Solutions

2.3.1 Initial Conditions

The confusor entrance was taken as the starting

point, i.e. at this point the distance of yarn is zero

(x = 0). At this instant (t = 0, x = 0), the length of the

yarn that is under the influence of the air-jet is equal

to l4 + l5. Therefore, the total force on the yarn is

given by the following relationship:

)(5.0 54

2

0f llUdCF +πρ=Σ …(18)

and the yarn mass, when the clamp opens but the yarn

is still stationary, is given by using the following

equation:

)( 54321 lllllmM ++++= …(19)

Since there is a force acting on the yarn, the yarn

acceleration is not zero, while the yarn velocity is

zero (V = 0) because still clamped.

Hence

)(

)(5.0

54321

54

2

0

lllllm

llUdC

dt

dVa

f

++++

+πρ== …(20)

Owing to the fact that the distance l6 is very small, the

yarn acceleration along this distance can be assumed

not changed. Thus, the yarn velocity at the starting

point, i.e. the entrance of confusor, can be written as:

60 2alV = …(21)

2.3.2 Solution Procedures

By substituting each of the air velocity distribution

equations [Eqs (1), (2), & (4)] and friction coefficient

equations [Eqs (5), (6), (7), (8), (9), (10), (11), and

(12)] into weft yarn motion equation [Eq. (17)], a

numerical equation was obtained for yarn motion.

These second-order non-linear equations with initial

conditions were solved by using 4th order Runge-kutta

numerical method. Then, weft yarn displacement,

velocity, and tension graphs were obtained from the

yarn motion equations for a cotton-polyester 30/2Ne

weft yarn under 3 bar pressure and compared with

experimental results. It was concluded that the nearest

theoretical prediction with experimental results is

made when Eqs (4) and (5), respectively for air

velocity and friction coefficient, are substituted into

the yarn motion Eq. (17). Consequently, the following

equation was selected as the simulating model for

weft yarn motion:

+

+−+

−

= 02.0

2

1

])([ cx(t)0

1

2

02

2

2

dt

dxeU

ktxm

dt

dxUAk

dt

xd

)(02.0

2

1

])([ cx(t)0

1

2

cx(t)0

tx

dt

dxeU

ktxm

dt

dxeUA

+

+−+

−

+

])([ 1

2

ktxm

dt

dx

+

−

++

+

+−

× µαmme

dt

dxeU

Al 5.002.0

2

1

cx(t)0

2

…(22)

3 Results and Discussion

3.1 Influence of Variable Parameters in Model

The parameters that could be changed practically

on the air-jet loom are yarn count and air-supply

pressure. Yarn count causes a change in the yarn

diameters (d) and linear density (m) in the model, and

air-supply pressure could change air density (ρ) and

initial air velocity (U0). Therefore:

Nem

410905.5 −×= …(23)

Ned

510745.8 −×= …(24)

RT

P=ρ …(25)

where P is the air pressure (N/m2); ρ, the air density

(kg/m3); T, the air absolute temperature (Kelvin); and

R, the gas constant equals to 287 j/kg.K.


49

Equation (25) shows that with the increase in air

pressure at a constant temperature, air density (ρ) is

increased. Therefore, the constant value of A= 0.5πdρ

in simulating model is increased. Owing to the

increase in air pressure, the weft yarn acceleration and

the force acting on the yarn are increased. Thus, the

initial air velocity at the core of nozzle can be

calculated with different air pressure by using the

following equation18

:

CMU .0 = …(26)

where

−

−γ= −γγ 1

1

2 1/

)/ln(

2

0PP

eM …(27)

4.1v

p==γ

C

C …(28)

where M is the Mach number; C, the sonic velocity

(335 m/s); Cp, the isopiestic specific heat ; Cv, the

isovolumetric specific heat ; γ, the adiabatic index for

air ; P0, the atmosphere pressure (105 Pascal ); and P,

the air supply pressure .

Thereafter, the theoretical solutions to simulating

model Eq. (22) were obtained by 4th order Runge-

kutta method by using a written program19

and Matlab

software. Theoretical results were achieved for

different conditions of variable factors of the yarn

counts 20/2, 30/2, and 40/2Ne, and air-supply

pressures 2.5, 3.0, 3.5, 4.0, and 4.5 bar. The following

information of the Investa single nozzle air-jet

loom model is necessitated to solve the model: reed

width = 1.5m; l1 = 0.01m; l2 = 0.085m; l3 = 0.055m;

l4 = 0.015m; l5 = 0.015m; and l6 = 0.015m; channel

diameter (D) = 0.018m; angle of wrap around the

guide (α) = 21.42 rad; machine speed = 300 rpm;

and timing— yarn release = 105○, and clamp

closes = 235°. Thus, time ( t) = 0.075 s; and air

temperature (T) = 298 K (25°C).

Figures 2 and 3 show the influence of variable

factors theoretically on the weft yarn tension under

different conditions.

Weaving trials were made commercially on an

Investa single nozzle air-jet loom (Model 15Zs–8MZ–

1979–PN155) at the air pressure for weft insertion

from 2.5 bar to 4.5 bar with 0.5 bar intervals using

blends of 20/2, 30/2, 40/2Ne cotton (33%) and

polyester (67%) yarns. It is worth noting that the

maximum weft yarn tension plays an important roll

on machine efficiency. If it is less than the yarn

breaking strength, the efficiency increases and hence,

the production costs decrease. This parameter can be

obtained easily from the weft yarn tension graphs. On

the other hand, measuring of weft yarn displacement

and velocity needs more complex instruments. For

this reasons, the peaks of theoretical and experimental

tension graphs have been compared at a weft insertion

cycle to consider the simulating model equation.

All weft yarn tension measurements were made by

an electronically Rothschid tensiometer. The average

of the maximum tension of weft yarn was calculated

for 100 successive weaving cycles. In all experiments,

the weaving room temperature was kept nearly

constant at 25○C. The experimental results were

Fig. 2 — Effect of weft yarn count on weft yarn tension from

theoretical model (under 3 bar air pressure)

Fig. 3 — Effect of air pressure on weft yarn tension from

theoretical model (yarn count 30/2 Ne)


50

compared with the theoretical values (Table 1).

Statistical analysis at 95% level of confidence shows

that there is no significant difference between the

average yarn tension peaks of theoretical and

experimental results. However, in 2.5 and 4.5 bar of

air-supply pressure the difference is nearly

considerable in comparison with the medium pressure

(Fig. 4). This can be attributed to the yarn buckling

which is created due to turbulent and unsteady flow,

neglecting the simulating model. Perhaps, this

phenomenon at lower and higher air pressure is more

effective on yarn tension than at medium pressure.

With regard to a good agreement between the

theoretical values obtained for the weft yarn tension

peaks and the experimental results, the suggested

simulating model equation Eq. (22) for weft yarn

motion is a suitable prediction method for the

behaviour of weft insertion. The importance of

simulating model is that with this method, it is

possible to minimize the air-supply pressure for

different yarn with different characteristics.

Therefore, it is avoided from the extra-consumed

energy and also the number of weft yarns breaking

during weft insertion due to using extra air pressure.

For this reason, weaving machine efficiency increases

and the energy cost decreases.

4 Conclusions Weft yarn motion using a single nozzle is highly

affected by the air velocity distribution and the feed

yarn structure and conditions. Hence, to consider the

weft yarn behaviour through weft insertion channel

and to establish the most suitable conditions of weft

insertion, a simulating analysis model is found to be

very useful. For this purpose, the equation has been

developed for weft yarn motion by using different

equations of air velocity distribution and air-yarn

friction coefficient. Finally, a theoretical model is

suggested to describe the weft yarn motion, i.e. yarn

displacement, yarn velocity and yarn tension.

In the second part of this work, maximum peak of

weft yarn tension has been determined analytically

and compared with the obtained experimental data

under different conditions of air-supply pressure and

yarn count. The results show good agreement between

theoretical and experimental values. This model

enables the air-supply pressure to be minimized for

different conditions of yarn and weft insertion.

Therefore, this kind of simulation is useful to increase

machine efficiency and decrease energy costs.

References

1 Salama M & Mohamed M, Text Res J, 56 (1986) 721.

2 Adanur S & Mohamed M, J Text Inst, 79 (1988) 297 & 316.

3 Adanur S & Bakhtiyarov S, Text Res J, 66 (1996) 401.

4 Nosraty H, Kabganian M & Jeddi Ali A A, Esteghlal J Eng,

19 (2001) 161.

5 Adanur S & Mohamed M, J Text Inst, 83 (1992) 45 & 56.

6 Ishida M & Okajima A, Text Res J, 64 (1994) 10.

7 Yoshida K & Hasegawa J, J Text Maxh Soc Japan, 37 (1991)

45.

Table 1 — Average of maximum yarn tension under different

air pressure

Yarn

count

Ne

Air pressure

bar

Theoretical yarn

tension peak

cN

Experimental

yarn tension

peak, cN

40/2 2.5 99.64 102.64

3.0 102.65 104.58

3.5 105.68 106.41

4.0 109.79 108.21

4.5 112.44 110.24

30/2 2.5 106.40 111.94

3.0 111.21 114.19

3.5 115.69 116.44

4.0 120.09 118.70

4.5 125.12 120.95

20/2 2.5 145.32 148.57

3.0 150.54 152.45

3.5 155.76 155.73

4.0 161.24 159.39

4.5 166.34 163.02

Fig. 4 — Theoretical and experimental graphs for maximum yarns

tension under different air pressures


51

8 Uno M, J Text Mach Soc Jpn, 18 (1972) 47.

9 Salama M, Adanur S & Mohamed M, Text Res J, 57 (1987)

44.

10 Duxbury V, Lord P R & Vaswani T B, J Text Inst, 50 (1959)

P558.

11 Adanur S & Mohamed M, J Text Inst, 61 (1991) 259.

12 Smith F S & Gould J, J Text Inst, 71 (1980) 38.

13 Matsui M, Trans Soc Rheol, 20 (1976) 465.

14 Orii K & Sano Y, Sen-I-Gakkaishi, 24 (1968) 212.

15 Selwood V, J Text Inst, 53 (1962) T576.

16 Liming W & Ming C, Proceedings, ATC 95, The 3rd Asian

Textile Conference (The Hong Kong Polytechnic University)

1995, 38.

17 Nosraty H, Jeddi A A A, Kabganian M & Bakhtiarnejad F,

Text Res J, 76 (2006) 637.

18 Streeter V L, Fluid Mechanics, 5th edn ( Mc Grow-Hill, New

York), 1971.

19 Mousaloo Y, The study of weft yarn motion in an air- jet

loom, M.Sc. thesis, Amirkabir University of Technology,

Tehran, Iran, 2003.

Documents

Single Nozzle Air-jet Loom