Textile Calculation

Count
Count is the measure of fineness or coarseness of yarn.

Systems of Count Measurement
There are two systems for the measurement of count.

1. Direct System
2. Indirect System

Direct System
It is used for the measurement of weight per unit length of yarn. When count increases, fineness decreases. ( count↑ fineness↓ ). Commonly used units in this system of measurement are:-

1. Tex ( 1 Tex = 1g/ 1000m )
2. Grex ( 1 Grex = 1g/ 10,000m )
3. Denier ( 1 Denier = 1g/ 9000m )

Indirect System
It is used for the measurement of length per unit weight of yarn. When count increases, fineness increases. ( count↑ fineness↑ ). Commonly used subsystems of indirect system are:-

1. English System ( 1 Ne = 1 Hank/ lb )
2. Metric System ( 1 Nm = 1 Km/ kg )

For cotton yarn, length of 1 Hank = 840 yards. Whenever the type of count is not mentioned with the count, it is understood that it is the English count.

Count Conversion Table


Calculate the length of a package of 80/1 and cone weight 2.083 lb.

Yarn type = 80/1
Cone wt. = 2.083 lb
Cone length = ?

Solution:

Length = Ne x lb x 840 yards
= 80 x 2.083 x 840 yards
= (139977.6÷ 1.0936 )m
= 127997.07 m                            [Ans.]

Calculate the length of yarn with Ne (80/2) and weight 4.166 lb.

Yarn type = 80/2
Cone weight = 4.166 lb
Cone length = ?

Solution:

Length = Ne x lb x 840 yards
= (80÷2)x 4.166 x 840 yards
= (139977.6÷1.0936)m
= 127997.07 m                            [Ans.]

Calculate the draft at drawing frame if the feeding sliver is 68 grains/yard, delivered sliver is 48 grains/ yard and the number of doublings is 8 :-

Count of feeding sliver = 68 gr/ yd
Count of delivered sliver = 48 gr/ yd
Doubling = 8 (8 sliver cans used)
Draft = ?

Solution:

Actual draft = (count fed x doubling) ÷ (count delivered) (direct system)
= (68 x 8)÷ 48
= 11.33                                      [Ans.]

Calculate the grains/ yard of delivered sliver if feeding sliver is 68, doubling is 6 and the draft is 7 :-

Count of F.S = 68
Count of D.S = ?
Doubling = 6
Draft = 7

Solution :

A.D = (F.S x D)÷ D.S
=> 7 = (68 x 6)÷D.S
=>D.S = 68 x 6 = 58.28 grains/ yard                         [Ans.]

Calculate the TPI on simplex if the diameter of back roller is 15/16”, rpm of B.R is 10, rpm of flyer is 1000 and draft is 6 :

TPI on simplex = ?
Dia. of B.R = 15/16”
Dia. of F.R = ?
Rpm of B.R = 10
Rpm of flyer = 1000 rpm
Draft, D = 6

Solution :

S.S of B.R = πDN = π x 15/16” x 10 = 29.45”/ minD = (S.S of F.R) ÷ (S.S of B.R)
=> 6 = (S.S of F.R)÷29.45
=> S.S of F.R = 6 x 29.45 = 176.71”/ min
TPI = rpm of flyer ÷ S.S of F.R = 1000 ÷ 176.71 = 5.66                         [Ans.]

Calculate the TPI (twists per inch) produced on a simplex with diameter of front roller 28 mm and its rpm be 30. The rpm of flyer is 1000.

TPI on simplex = ?
Dia. of F.R = 28 mm = 2.8 cm
Rpm of F.R = 30
Rpm of flyer = 1000

Solution : Dia. of Front roller = 2.8 cm / 2.54 (1 in= 2.54 cm)
= 1.1023 inchSurface speed of F.R, ^DN = π x dia. of F.R x rpm of F.R
= π x 1.1023 x 30
= 103.88 “/ min.TPI = rpm of flyer ÷ S.S of F.R = 1000 ÷ 103.88
= 9.63                                         [Ans.]