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Namangan muhandislik-texnologiya instituti 7-8 oktabr 2-tom
length)
c
1
The number of weft yarns attaching
together
ϕ
Yarn packing density
c
2
The
number
of
warp
yarns
attaching together
ϕ
L
Limited yarn packing density
C
p
Wetted perimeter of the cross-
section of pore (mm)
ρ
density(kg/m
3
)
d
p
Equivalent pore diameter (mm)
ρ
a
Air density(kg/m
3
)
d
y
Yarn diameter (m)
ρ
f
Fiber density (kg/m
3
)
k
Permeability coefficient
ρ
fa
Fabric density (kg/m
3
)
L
The length of tube or the thickness
of fabric (m)
η
Ratio of pore‘s
area to fabric
area in cross section
M
Constant value
ε
Porosity
N
1
The number of yarns per centimeter
in weft direction
μ
Dynamic
viscosity of the flow
(Pa·s)
N
2
The number of yarns per centimeter
in warp direction
Re
Reynolds number
Np
Pore number
2 Theoretical Analysis
2.1 Structural parameters of fabric
Yarn diameter
Assume that cotton yarn is a homogeneous cylinder, and according to the
definition of yarn fineness which is the ratio of yarn mass to yarn length. Then, the
yarn diameter can be obtained by[10, 11],
(1)
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Namangan muhandislik-texnologiya instituti 7-8 oktabr 2-tom
Where
d
y
is the yarn diameter (m),
T is yarn fineness (tex),
ϕ is packing density of
yarn,
ρ
f
is fiber density (kg/m
3
).
Yarn packing density
Yarn packing density is an index to determine the fiber volume in a yarn, which
can be expressed by [12],
(2)
Where
Z is yarn twist (numbers per unit length). It‘s worth noting that the packing
density is also influenced by materials and spinning technology. Some researchers
reported the suitable coefficients for different materials and spinning technologies
[13-16].
Therefore, the yarn packing density is a function of yarn twist and yarn fineness,
and their relationship can be obtained by solving Eq.(1) and Eq.(2),
(3)
Where
ϕ
L
is limited packing density, which is 0.8 for cotton yarn [16], M value is
0.0042 for cotton yarn produced by ring spinning technology[16]. The mean value
of packing density for ordinary yarn ranges from 0.4 to 0.5[16]. Thereby, the
relationship between yarn diameter and yarn twist
can be obtained by solving
Eq.(2) and Eq.(3). It‘s worth noting that the yarn material, the spinning technology
and the yarn fineness are certain before spinning. Therefore, yarn diameter can be
predicted from the only unknown parameter - yarn twist.
