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# Textile Calculations (Spinning) Part-I

Updated: Dec 22, 2023

Q: What is the relation between CV% and U%? Also, write the difference between both.

### Ans:

C.V. % = 1.25 X U%

• The irregularity U% is proportional to the intensity of the mass variations around the mean value.

• The U% is independent of the evaluating time or tested material length with a homogeneously distributed mass variation.

• The larger deviations from the mean value are much more intensively taken into consideration in the calculation of the coefficient of variation C.V. %.

• C.V. % has received more recognition in modern statistics than the irregularity value U%.

• The coefficient of variation C.V.% can be determined extremely accurately by electronic means, whereas the calculation of the irregularity U% is based on an approximation method.

### Ans:

The probability of faults is due to damaged front roller cots or rollers in the R/F drafting zone. Explanation:

The front roller diameter is 27 mm so the circumference of the front roller is (3.14 * 2.7 = 8.6 cm i.e. approximately 9 cm). so the cause of the fault is due to the front roller or cots in the R/F drafting zone.

### Ans:

The average no. of fiber in yarn cross section = (20 * 1000) / 150 = 134

For cotton limit irregularity CVlim = 106 / √134 = 9.15%

Index of irregularity = CVact / CVlim = 23.2 / 9.5 = 2.54%

### Ans:

CV% yarn w/o addition of CV in R/F is = CV% / √n = 8 / √2 = 5.7%

CV % of output yarn = √(5.7+18) = 18.88%

### Ans:

Sliver Linear density = 20 kTex = 20,000 Tex

Polyester = 20000 x 0.67 = 13400 tex

Cotton = 20000 x 0.33 = 6600 tex

No. of cotton fibres in the sliver cross section = (6600 * 9)/1.2 = 49500 = N1

No. of polyester fibres in the sliver cross section = (13400 * 9)/1.5 = 80400 = N2

Total no. of fibres = 49500 + 80400 = 129900 = NT

CVlim = 100 / √ NT = 100 / √129900 = 0.28

CVdoub = √(NcVc2 + NpVp2 ) / (Nc + Np)

Nc & Np are no. of cotton and polyester sliver ends

CVdoub = √(2 * 42 + 4 * 32 ) / (2+4) = 1.37%

Actual CV% of input sliver

CVactual = √(CVd2 + CVdraft2 ) = √(1.372 + 22 ) = 2.427

Index of Irregularity = CVact / CVlim = 2.427 / 0.28 = 8.66

### Ans:

CV of single yarn is = 1.25 * U%

= 1.25 * 17.3 = 21.625 %

CV% of 3 ply yarn = CV of single yarn / √n where n = no. of doublings

= 21.625 / √3 = 12.5%

### Ans:

The formula is

CV% of doubling = CV% of single / √n where n = no. of doublings

1.8 = CV% of single / √6

CV% of singles = 4.41%

i.e. CV% of comber sliver is 4.41%.

### Ans

CV of ring yarn (exclude of CV% added in R/F) = CV% of roving / √n

= 7.8 / √2 = 5.52

CV% of ring yarn with added

CV% in Ring frame = √ (5.522 + 4.82 ) = 7.32

CV% doubled yarn having 3 single of above yarn = 7.32 / √3 = 4.23

### Ans

CV of doubling = 2.5 / √N = 2.5/√8 = 0.88

CVoutput = (CVdoub2 + CVadd2 ) 1/2 or CVadd = (CVo/p 2 - CVdou 2 ) 1/2

= (2.52 – 0.882 ) 1/2 = 2.34%

### Ans

Schlafhorst has incorporated a yarn monitoring system on the rotor spinning machines using an optoelectronic sensor ‘Corolab7’ - It measures yarn diameter online and can provide details about the evenness, imperfections, detection of faults etc. Uster poly guard is an online yarn supervisory attachment for the automatic rotor spinning machines - Based on the capacitive measuring principle. - Gives detailed information for all the rotor heads.

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