Yarn diameter and Count Relationship between yarn count and
diameter is dependent upon specific volume of yarm. Specific volume, v, is the
ratio of the volume of yarn to that of the same weight of water. Specific volume
of yarn depends upon the raw material, type of spinning system, twist factor and
spinning parameters. Ring spun yarns have a lower specific volume than rotor
spun yarns. Acrylic and woolen yarns have a higher specific volume than cotton
yarns. Specific volume reduces with increase in twist factor. If d is diameter
in inches of yarn of count C v = 858Cd2. (1/d) = 29.3√C.
Specific volume of yarn is usually 1.1 to 1.2. If speific volume is assumed as
1.1 (1/d) = 28√C.
If d1
is diameter in cm and N is the count in tex units
then
d1=√N/267.3.
Twist Factor Twist factor indicates the amount of twist put into
the yarn and determines among other things the strength, elongation, specific
volume, liveliness of yarn. If twist factor is k and t is twists per inch
then, k = t/√C. If fibres follow helical path, Twist factor is equal the
angle surface fibres make with axis of yarn tan x =
√Πdt =√Π(√v)k/29.3 =0.107k(√v) When v = 1.1 tanx = k/9.
Tenacity Tenacity denotes intrinsic strength of yarn. Strength of
yarn is dependent on count and its intrinsic strength. It is usual to refer to
tenacity by the term Breaking length. This is the length whose weight is equal
to the breaking strength of yarn. If lea strength is used to denote strength,
intrinsic strength is given by CS where C is count and S is breaking strength.
This is commonly known as CSP or count strength product. As CS reduces with
count, corrected CSP is determined by correcting for the deviation of actual
count from nominal. If C1is the actual and C nominal count, corrected
CSP = CS - (C1 - C)18. If strength is by single thread then tenacity
is given by S/N where S is breaking strength and N is count in tex.
Irregularity Irregularity is an important characteristic of yarn
that determines appearance, sale value of yarn and fabric. It also has
considerable influence on strength realisation from fibre and performance of
yarn. The best possible regularity that can be achieved by current spinning is
that with random arrangement of fibres. Irregularity due to random arrangement
of fibres, CVr, is given by CVr = (√(1002 +
CVf2))/n where CVf = Coefficient of
variation of weight per unit length of fibre n = Number of fibres in yarn
crosssection. CVf for cotton varies within and between bolls,
between lots, stations but has a value roughly equal to 30%. In the case of wool
it is around 50% and for synthetics around 10%. Upon putting this figure in the
above formulae, CVr = 106/√n for cotton =112/√n for
wool =102/√n for synthetics.
Index of Irregularity Index of Irregulaity = Actual CV of
yarn/CVr. Index of irregularity indicates the scope for improving the
spinning processes for getting better regularity.
Imperfections These represent outlayers of variations in yarn
which have a profound influence on appearance of yarn and fabric and performance
of yarn. Uster imperfection tester measures three types of imperfections viz
Thin places, Thick places, Neps. Nep is differentiated from a thick place by the
length of the defect. The instrument evaluates nep as a thick place whose length
is shorter than 4mm and longer thick places are evaluated as thick. 4 classes of
each of these faults are measured as indicated in Table below.
Thin(%)
Thick (%)
Nep (%)
-30
+35
+140
-40
+50
+200
-50
+70
+280
-60
+100
+400
Thin places are influenced by fibre properties
combing and drafting conditions. Thick places are influenced by fibre
properties, blow room, carding and combing and drafting conditions. Neps are
influenced by fibre properties and blow room, carding and combing conditions.
Faults Faults are seldom occuring defects as agaist imperfections
which are frequent occuring defects. Faults show prominently in fabric and lead
to rejections. They also affect the performance of yarn in weaving and knitting.
Uster Classimat has facility to detect faults as per their size and length.
Longer and thicker size faults show up prominently and are termed as
objectionable
Short Length faults 16 categories of short length faults are
measured by Classimat.
Short Length Faults
Size of Fault
A - 0.1 to 1cm
B - 1 to 2cm
C - 2 to 3cm
D - above 4cm
+100 to +150%
A1
B1
C1
D1
+150 to +250%
A2
B2
C2
D2
+250 to +400%
A3
B3
C3
D3
above +400%
A4
B4
C4
D4
Very short thick places are
caused by the presence of seed coats, broken seeds, trash in the case of cotton
and cutterfibres in synthetics. Medium size short thick places are caused by
embedded fluff, loose lint among others. Faults of 4cm and above are caused by
slubs, undrafted ends, bad piecings etc.
Long Thick Faults 5 catergories of long thick faults are measured
by classimat. E - Above 8cm length and above +100% crosssection size.
Size of fault
8 - 32cm
above 32cm
+45 - +100%
F
G
Long thick places of E category are known as
'Spinner's double' and are caused by lashing of an end with adjoining end at
roving or ring frame. F and G faults are due to drafting defects at earlier
stages, sliver splitting in creel at roving and long overlap of sliver at the
time of sliver break at drwaframe.
Long Thin Faults 4 types of thin places are measured
Size of Fault
8 - 32cm
above 32cm
-30 to -45%
H1
I1
-45 to -75%
H2
I2
Long thin faults are due to raw
material defects, drafting faults in roving and drawing, split sliver in creel
of roving, mal functioning of stop motion at drawframe.
Correlogram If r(l) is the (Auto)correlation coefficient of
thickness( or weight per unit length)of yarn at points 'l' apart, then the plot
of r(l) against l is Correlogram. Correlogram is a useful tool for detecting the
presence of periodicities in yarn. Let t1 and t2 denote
thickness(or weight per unit length) of yarn at points separated by 's'
distance Auto Correlation Function r(s) = (N(∑titi+s -
∑ti∑ti+s)/∑{(N∑ti2
-∑(ti)2)(N∑ti+s2
-∑(ti+s)2)}. For lengths below fibre length, correlogram
is determined by the fibre length distribution of cotton. Since part of the
fibres are common to both crossections, there will be a positive auto
correlation coefficient. Corrleation coefficient between points x
aprt,
r(x) = I/la(l - x)
f(l)dl where la is mean fibre length and f(l) is frequency of
fibres of length l and lm is maximum fibre length
Variance Length curve Variance length curve is a graph relating
variance of weight of length of yarn and the length. This is a very useful tool
in characterising the various types of irregularities in yarn and will assist in
locating processes which require improvement. Irregularity in a yarn is given
by Variance(x L). Here L denotes the total length of yarn taken for study
and x denotes the length of pieces cut from the yarn and weighed. If x is varied
keeping L constant, variance length curve obtained is known as Between length
curve or BL curve. On the other hand, if x is kept constant and L is varied, the
curve obtained is known as Within length curve or VL curve. At lengths shorter
than longest fibre length, BL curve is influenced by fibre length distribution
of fibre as some fibres will be common to both sections. Variance length curve
is related to correlogram of yarn as indicated below
B(x) = B(O)(2/L2) (x-u)r(u)du where r(u) denotes auto correlation coefficient
of thickness between points u distance apart, B(x) = Variance of weight of
lengths x long. When x is less than lt, where lt is half
the length biassed mean fibre length of fibre,lc B(x) = B(O)(1 -
(x/3la)) Where lais mean fibre length. For lengths
longer than longest fibre length, B(x) = B(O)lc/x, if there
are no other irregularities( no extra auto correlation coefficients) where
lc is length biassed mean length of fibre. This enables one to find
out how much the actual variance length curve deviates from the ideal. Variance
length curve shows the amount of short, medium and long term variations present
in a yarn. While short term variations come from ring frame, medium term
variations arise from roving frame and long term variatons from drawframe.
Spectrogram Spectrogram is a fourier analysis of variations
present in the material. The amplitude of the variations are sorted as per their
wavelength and plotted as a amplitude vswavelength curve. The spectrogram
of a yarn due to random fibre arrangement has a "hill" whose maximum wavelength
lies in the region of 2.5 to 3 times fibre length. On the top of it, waves
introduced by drafting waves is superimposed. Wavelength of drafting wave is
also 2.5 to 3 times fibre length and so in normal yarn the "hill" is pronounced
depending upon the amplitude of drating wave. With cut staple fibres peak value
of spectrogram lies at 2.7 times fibre length. A shorter but a smaller amplitude
wave will also be found at half the fibre length and this is a lower harmonic.
In between these two peaks, there will be a valley. In cotton, wollen and other
material with variable staple diagram, the spectrogram has a hump like shape
with maximum around 2 to 3 times mean length. Thus spectrogram of cotton yarns
has a maximum at 6 to 8cm, of woolen yarn at about 20cm. OE rotor yarns have a
peak at a slightly lower length than ring yarns because fibres are curled with
hooks leading to a lower projected length on yarn axis. When periodic variation
is present, spectrogram will show a sharp peak at the point corresponding to
wavelength of periodicity. So spectrogram is a useful tool for detecting the
periodicities in the material. It also gives their wavelength which can be used
to trace the cause of periodicity and rectify it.
Blend Variability Blend variation is an important parameter to be
controlled in blends in view of their influence on appearance, fault incidence,
grade, and sale value of fabric. Two types of blend variability have to be
minimised.
Variations in blend proportion of the component fibres in cross section
along the length of yarn
Inadequate intermixing of components within a cross section.
Longitudinal blend variation If black and white fibres are
randomly mixed, white fibres in cross section will have a mean equal to np and a
variance equal to npq where n is the avearge number of fibres in yarn cross
section, p proportion of white fibres and q is proportion of black fibres in
yarn. This represents the minimum blend variability that will be present in yarn
with the best possible mixing of components. Index of blend variability is a
quantity used to assess the extent of departuture of actual blend variation from
random mixing. Index of blend irregularity = √((1/N)∑((wi - p
ni)2/pqni) where wi,
bi and ni denote the number of white, black and total
number of fibres in a crossection and N total number of yarn cross sections
examined. IBI compares the observed deviation in blend proportion in each
section against theoretically estimated value of that section and determines the
avearge of this over a number of sections.
Intimacy of lateral mixing To assess intimacy of mixing the ribbon
of fibres emerging from front roller nip is examined.Two measures of intimacy
mixing are used 1.Index of mixing,Π = proportion of white fibres that have a
white right hand neighbour. 2. Measure of mixing, g = number of groups of
white fibres in the strand. Π = (w - g)/g. If mixing is random Π= p. g
= npq. Degree of mixing is the ratio gactual/grandom
» left by Kashan Rizvi from Karach Sindh Pakistan (1 year 311 days ago.)
which TPI is suitable for 26/S,30/S and 40/S for knits fabric. Are there any formula to find right TPI for different count. Respond to this comment
» left by Bala(609) (1 year 310 days ago.)
Normally twist Factor of 3.5 to 3.7 is used in medium counts like 26s, 30s and 40s in knit fabrics. But you may go in for even lower twist factor if you use superior cottons. Respond to this comment
» left by Anonymous (1 year 72 days ago.)
Can you please provide guidance over proof of theory to get "1/d = 28C. " Respond to this comment
» left by Prasad from Tanzania (262 days 16 hours ago.)
Suggest yarn strength by RKM method should be included and conversion formulae from CSP to RKM and vice-versa. Respond to this comment
» left by ali naqvi from maxco karachi pakistan (61 days 16 hours ago.)
How to measure the DENSITY of soft wind cone is there any effective and easy formula. (syed muhammad Ali naqvi) MAXCO PVT KARACHI SINDH PAKISTAN.
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(l - x)
f(l)dl
(x-u)r(u)du 
