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The Influence of Dimensional Stability on Overfeed Sewing
Shrinkage of Wool Fabric
Tong-hong Xu 1,2, a, Hong Sun1,2,b 1 Changzhou Textile and Garment Institute, Changzhou, 213164 China
2 Changzhou key Laboratory of New textile material, Changzhou,213164,China
Keywords: water shrinkage; dimensional stability; overfeed sewing shrinkage; wool fabric
Abstract. In order to analyze the influence of dimensional stability on overfeed sewing shrinkage of
wool fabric, the paper used theoretical analysis equation to evaluate and overfeed sewing shrinkage of
wool-type fabrics and took water shrinkage as index of dimensional stability to analyze its influence
on overfeed sewing shrinkage characteristic value such as connection length, fabric connection length
ratio. The research revealed the relationship of dimensional stability and overfeed sewing shrinkage,
and derived calculation method of oblique shrinkage based on analysis of warp and weft shrinkage. It
provided the theory reference on sewing quality of wool fabric in apparel manufacture and use.
Introduction
We have established theory equation of physical characteristics about overfeed sewing shrinkage
and fabric connection length. Fabric connection length ratio which can change with variation of
moisture absorption, water absorption, thus it can influence sewing shrinkage change in garment
processing and consumer process.
There are many literature reported about dimensional change of wool fabric after moisture
absorption and water absorption. For example R.L.Shishoo [1] etc. of Sweden Textile Research
Institute had researched length change of wool fabric with change in air relative humidity.
P.G.Cookson [2] had studied hygroscopic expansion influence on wool fabric appearance. He thought
excess hygroscopic expansion could cause garment appearance change. The sewing parts of garment
could come into crepe in lower relative humidity and wearing in higher relative humidity environment
especially in producing garment. He went on to research that breaking elongation was liner with
hygroscopic expansion and relaxation shrinkage.
It uses index of relaxation shrinkage rate and hygroscopic expansion rate to show fabric size change
process which denotes the same with shrinkage or steam shrinkage with the difference of testing
method on FAST test instrument. Using fabric water shrinkage as an example, the paper analyzes
dimensional change influence on overfeed sewing shrinkage characteristic value such as connection
length, fabric connection length ratio which can illustrate the influence of dimensional stability on
overfeed sewing shrinkage ratio in the processing and use.
Relationship of shrinkage with connection length and connection length ratio
Here is theory equation of overfeed sewing shrinkage with physical characteristic value such as
fabric connection length and fabric connection length ratio [3].
euu ls
aD
as)1(
1. (1)
In the equation, e
c
l
la is ratio of fabric connection length or unit.
Advanced Materials Research Vol. 796 (2013) pp 593-597Online available since 2013/Sep/18 at www.scientific.net© (2013) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMR.796.593
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D is the ratio of fabric bending modulus and tensile elasticity coefficient that is flexural modulus
ratio. The unit is m2.
el and cl identifies connection length of corresponding point 1 to 2 of long fabric A and short fabric
B which are called long and short fabric connection length
as shown in the figure 1.
Influence of shrinkage on sewing connection length. Fabric
shrinkage is the value of change in relative length after shrinkage.
Supposing that l (cm)is fabric connection length on condition of
overfeed sewing original length， 'l (cm)is connection length after
shrinkage. k stands for shrinkage. So it can get equation 1 from
definition of shrinkage.
100'
l
llk . (2)
That is,
lkl )1(' . (3)
Supposing that el (cm) is fabric connection length on condition of overfeed sewing, '
el (cm) is
fabric connection length after shrinkage. ck is corresponding shrinkage .It can draw equation 4 from
equation 3.
ece lkl )1(' . (4)
It is obvious that if ck >0, '
el will become smaller, if ck <0, '
el will become larger, which show that
fabric connection length is changeable according to shrinkage.
Influence of shrinkage on connection length ratio. Supposing that dk is short fabric shrinkage, '
cl is short fabric connection length after shrinkage. cl is original connection length of short fabric. It
can get calculation equation 5 of short fabric connection length after shrinkage from equation 4 as
show below.
cdc lkl )1(' . (5)
Supposing that 'a is connection length ratio after shrinkage, thus it can get equation 6.
)1(
)1('
'
'
ce
dc
e
c
kl
kl
l
la
. (6)
It can derive equation 7 from equation 6 from definition of c
e
la
l .
)1(
)1('
c
d
k
kaa
. (7)
Equation 7 shows that fabric shrinkage changes with connection length from.
Relationship of oblique shrinkage with warp shrinkage and weft shrinkage
In sewing garment, the sewing direction is not only along warp and weft, but also oblique. So it is
necessary to analyze oblique dimension change in fabric sewing process. In order to analyze
dimension change of any direction quickly, it discusses relationship between warp or weft shrinkage
with oblique shrinkage which takes fabric shrinkage as an example.
Fig .1 Fabric overfeed
sewing dimension
594 Silk, Protective Clothing and Eco-Textiles
Theoretical analysis. Supposing that opa is fabric length, opb is fabric width, oc is intercepted
length along oblique direction, as shown in figure 2. pa1 , pb1 is length and width after shrinkage.
jsk , wsk is warp shrinkage and weft shrinkage .The calculation is as follow.
Fig. 2 Coordinate transformation of sample shrinkage
)1(
)1('
c
d
k
kaa
. (8)
)1(
)1('
c
d
k
kaa
. (9)
In figure 2, coordinate system is established from o point as the origin, horizontal ordinate is the X
axis, longitudinal coordinates is the Y axis. It will set a certain point c (x0,y0)of original coordinate
system mapping to new point coordinate system which produces corresponding point 'c
(x1,y1).According to linear mapping principle, here is equation 10.
. (10)
In equation 8, 11s , 22s can calculate based on warp shrinkage and weft shrinkage. Specific express
is shown by equation 11 and equation 12.
wsks 111. (11)
jsks 122. (12)
Supposing that r is distance of oc，so it can be calculated by formula 13.
2
0
2
0 yxr . (13)
The distance of 'oc can be calculated by formula 14.
2
0
2
0
' )1(2)1( ykxkoc jsws . (14)
Assuming that is dip angle of oblique and horizon, it can get equation 15 according to polar
coordinate theorem.
01 11
221 0
0
0
xx s
sy y
Advanced Materials Research Vol. 796 595
cos,sin 00 ryrx . (15)
So it can derive calculation formula 16 of 'oc .
2222' cos)1(sin)1( wsjs kkroc . (16)
Assuming that fabric oblique shrinkage is k ，it can get formula 17 from definition of shrinkage,
and derive formula 18.
100'
oc
ocock . (17)
2222 cos)1(sin)1(1 wsjs kkk . (18)
It explains oblique shrinkage after fabric moisture or water absorption which is not only relative to
warp shrinkage and weft shrinkage, but also to sample dip angle in equation 18.
Comparison of oblique shrinkage with warp shrinkage and weft shrinkage.The first
comparison condition is that if jsk = wsk , It can get comparison formula as follow.
2222 cos)1(sin)1(1 wsjs kkk .
)1(1 jsk )1(1 wsk .
So it can draw a conclusion: k = jsk = wsk .
The second comparison condition is that if jsk > wsk ,
2222 cos)1(sin)1(1 wsjs kkk > 2222 cos)1(sin)1(1 wsws kk .
And k > wsk ,
Meanwhile,
2222 cos)1(sin)1(1 wsjs kkk < 2222 cos)1(sin)1(1 jsjs kk .
And k < jsk ,
So it can get wsk < k < jsk .
If wsk > jsk , similarly available under conclusion: jsk < k < wsk .
It can draw fabric oblique shrinkage change was centered on warp shrinkage and weft shrinkage.
Prediction of overfeed sewing shrinkage characteristic value in oblique sewing process
In sewing garment, there are three conditions except for overfeed sewing of same fabric in the same
direction .The first is same fabric sewing each other along different direction. The second is different
fabric sewing each other along same direction. The third is different fabric sewing each other along
different direction. Different fabric can produce different shrinkage in different direction. Thus it is
necessary to analyze fabric overfeed sewing shrinkage characteristic in different fabric and direction.
The following paper analyzes overfeed sewing characteristic (fabric connection length, connection
length ratio) change based on warp and weft shrinkage in fabric oblique process.
Change of connection length in oblique sewing process. As sewing fabric in oblique, it can
derive connection length equation 19 from equation 3 and 18.
2222'
e cos)1(sin)1( wsjse kkll . (19)
596 Silk, Protective Clothing and Eco-Textiles
The following article gives an illustration of the calculation formula 19. It supposes that 2el ,
%5.1jsk , %7.0wsk . varies from 0 degree to 90 degree. The final relationship of connection
length and is shown in figure 3.
Fig. 3 Relationship of connection length and fabric cutting out angle
Change of connection length ratio in different direction’s sewing of same fabric. A fabric is
cut in two parts of different direction to sew. It supposes that is the angle of long fabric and weft
direction, and a is the angle of short fabric and weft direction. So it can get formula 20.
akakl
kkla
wsjse
wsjsc
2222
2222
'
cos)1(sin)1(
cos)1(sin)1(
. (20)
That is ,
akak
kkaa
wsjs
wsjs
2222
2222
'
cos)1(sin)1(
cos)1(sin)1(
. (21)
It shows that different fabric has different shrinkage which can cause connection length change. In
equation 21.
Summary
Wool fabric is processed by steam pressure repeatedly. It will produce dimension change as a result
of hygroscopic expansion and relaxation shrinkage which can influence connection length and
connection length ratio, and overfeed sewing shrinkage. The paper analyzes relationship of dimension
change with overfeed sewing shrinkage characteristics.
Fabric is cut and processed generally along oblique in garment processing, thus it is necessary to
learn about fabric oblique dimension change. It uses index of warp or weft hygroscopic expansion
ratio and relaxation shrinkage ratio to evaluate fabric’s dimension change on FAST test system. The
paper develops dimension change equation in any direction. It provides theory reference to forecast
change of overfeed sewing shrinkage characteristics.
References
[1] R.L.Shishoo and M .Choroszy. Textile Machinery Society of Japan, Osaka, (1990) : p. 316.
[2] P.G.Cookson. Journal of Textile Research (1992), p. 44.
[3]Tong-hong Xu,Ping Gu.Journal of Fiber Bioengineering and Informatics and Textile
Bioengineering and Informatics Symposium Proceedings (2010), p. 635.
Advanced Materials Research Vol. 796 597
Silk, Protective Clothing and Eco-Textiles 10.4028/www.scientific.net/AMR.796 The Influence of Dimensional Stability on Overfeed Sewing Shrinkage of Wool Fabric 10.4028/www.scientific.net/AMR.796.593
