Drawing 2
Minimum theoretical variation and effect of drafting and doubling.
Minimum theoretical variation
The basic requirement to produce even yarns would be a constant number of fibers and each fiber should be of same fineness. Also in every case, the end of one single fiber would have to connect with the beginning of the following fiber. No available spinning process can produce such yarn.
In practice the fibers overlap each other and spun yarn has a certain minimum irregularity CVlim is given by
where, n is the mean number of
fibers in the cross-section.
where T is tex of sliver,roving or yarn and is the tex of fiber.
From the formula (1) it can be seen that with the increase in the number of fiber in the cross-section CV% decreases, (because the irregularity of faults are usually averaged out in this case).
Effect of drafting and doubling.
Addition of irregularities
Each machine in spinning process odds a certain amount of irregularity to the finished yarn. Suppose the CV of a sliver is C1, and it is fed to a machine which adds irregularity C2 to the sliver during processing. Let C, be the CV of the processed sliver. Then C is given by the formula
C2= C12 + C22
C=Ö( C12 + C22 )………(2)
Where C2 is the irregularity produced by the machine. Irregularity is increased due to drafting (The square of CV is called relative variance)
Reduction of Irregularities
One of the objects of doubling is to reduce the irregularity. If ‘n’ strands of materical, each having same CV are doubled, then CV of the combined strands is
Here n = no. of strands or no. of doubling
Irregularity is reduced because of doubling.
In practice when slivers and ravings are doubled they are usually dratted at the same time. The process of drafting adds to the variation. The final product will therefore have an irregularity value which depends on whether the reduction due to doubling is greater than the increase due to drafting.
Example: 1 (for addition of irregularities)
A draw frame sliver with a CV value of 4% is fed to the speed frame. The resulting roving has a CV value of 8.4% find the irregularity produced (added) by the speed frame.
Example:2 ( for reduction of irregularities)
8 carding slivers, each having the same CV value of 7%, are fed to a drawframe. What will be the CV of the combined strands after doubling?
Irregularities of fiber strands( sliver, roving, yarn etc.)
Evenness of yarn means the degree of its uniformity in respect of mass per unit length, diameter, twist, colour, hairiness strength etc. However popular approach is to consider the variation in mass per unit length or thickness. Evenness of laps, slivers and roving also is considered as the variation in mass per unit length of fibre strands. Variation in mass/unit lenght is generally due to variation in number of fibre in the cross section of the fibre strand.
Classification of variation
There are mainly two types of variation
a. Random variation and
b. Periodic variation
Random variation:
Random variation is the variation that occurs randomly in textile material without any definite order.
Suppose a yarn is cut into short equal lengths, say, of one inch and the weight or mass of each consecutive length is found out. The weights are plotted in a graph against the lengths similar to the following figure (fig-1)
By joining the points a trace is produced, called the irregularity trace or graph. This shows how the mass per unit length varies about a central value or the mean. The deviation of each point from the mean and hence standard deviation and co-efficient of variations (CV%) can be derived and used as measure of irregularity or unevenness.
Formula of standard deviation.
Where,
Formula of co-efficient of variation.
This method of cutting and weighing the fibre stand is a technique used for the measurement of irregularity. The disadvantage with the method is that it is slow and laborious.
Application of basic statistical analysis:
Compare two fibre stands from the following:
Test no
|
Sample-1
5 test
|
Sample -2
5 test
|
1
|
27.2
|
27.5
|
2
|
27.8
|
26.7
|
3
|
27.1
|
26.9
|
4
|
26.2
|
27.3
|
5
|
27.0
|
27.0
|
Mean
|
27.06
|
27.06
|
Std. deviation
|
0.57
|
0.33
|
CV%
|
2.10
|
1.21
|
The CV sample 2 (1.21) is less than the CV% of sample 1 (2.10). This means that the quality of sample 2 is better than that of sample 1
