Yarn Count calculation: comprehensive 2 way of yarn numbering system

Yarn Count:

Count is a numerical expression of a yarn, which defines fineness & coarseness. A definition of yarn count is given by the textile institute-” Count, a number indicating the mass per unit length or length per unit mass of a yarn.”

Yarn Count Can Be Expressed In Two Ways :

1. Direct System
2. Indirect System

1. Yarn Count Measurement In Direct System:

In a direct yarn counting system, the yarn number or count is the weight of a unit length of a yarn.

Let,  

N  = The yarn number (Count)

W =  The weight of the sample at the official regain in the units of the system.

L =  The length of the sample

l  =  The unit of the length of the system.

Then, 

N = (W × l)/L

Example: Tex, Militex, Kilotex, Denier, Jute( lbs/spyndle) etc.

2. Yarn Count Measurement In Indirect System:

In an indirect system, the yarn number or count is the number of “ units of length” per “ unit of weight”.

Let, 

N = The yarn number (Count)

W = The weight of the sample at the official regain in the units of the system.

w = The unit of weight of the system

L  =  The length of the sample

l  =   The unit of length of the system

Then,  

N = (L ×w)/(l × W) 

Example: English count (Ne), Metric count (Nm), Worsted count ( Nw) etc.

Unit of Length & Weight in Direct Yarn Count System:

Count Calculation In Direct Yarn Count System:

Problem-1:

If a skim of 100 m of filament viscose yarn weights 1.67 gm. Calculate its Denier.

Calculation:

Here,

L  =  The length of the sample= 100 m

W = The weight of the sample at the official regain in the units of the system= 1.67 gm.

l  =  The unit of the length of the system

= 9 km

= (9 x 1000)m

= 9000 m

∴ N = (W × l)/L

= (1.67 gm ×9000 m)/(100 m)

= 150.3 den. (Ans)

Problem-2:

If a skim of 350 m of Polyester yarn weights 5 gm . Calculate its Tex.

Calculation:

Here,

L  =  The length of the sample= 350 m

W = The weight of the sample at the official regain in the units of the system= 5 gm.

l  =  The unit of the length of the system

= 1 km

= (1 x 1000)m

= 1000 m

∴N  =  (W × l)/L

=(5 ×1000)/(350)

= 14.28 Tex (Ans)

Unit of Length & Weight in indirect Yarn Count System:

Count Calculation In Indirect Yarn Count System:

Problem-1:

A lea of cotton yarn weights 25 grain. Calculate its count in the cotton or English system.

Calculation:

Here,  

L  =  The length of the cotton sample

= 1 lea

= 120 yds (we know, 1 lea= 120 yds)

W = The weight of the cotton sample at the official regain in the units of the system

= 25 grain

= 25/7000 lb ( we know, 1 lb= 7000 grain)

=0.0036 lb

l  =  The unit of the length of the system

= 840 yds

w = Unit of weight of the system = 1 lb

∴ N    = (L ×w)/(l × W) 

= (120 ×1)/(840 ×0.0036) 

= 120/3 

= 40 N_e (Ans)

Yarn Count Conversion System:

1. Conversion from Direct to Direct
2. Conversion from Indirect to Indirect
3. Conversion from Direct to Indirect
4. Conversion from Indirect to Direct

For Unknown Count :

Unknown Count = Multiplying conversion factor × known count

Conversion Chart From Direct to Direct:

Count Calculation From Direct To Direct Yarn Count System:

For, 

Denier to Tex,

Denier = 9 × Tex

For, 

Tex to Jute,

Tex = 34.45 × Jute

For, 

Tex to Denier,

Tex  = 0.111 × Denier

Conversion Chart From Indirect to Indirect:

Count Calculation From Direct To Direct Yarn Count System:

For,  

Metric to Cotton or English,

N_m = 1.7 × N_e       

For,  

Worsted to Cotton or English,

N_w = 1.5 x N_e

Conversion Chart From Direct to Indirect:

Count Calculation From Direct To Indirect and Indirect To Direct System:

For,

Denier to Cotton or English,

Denier = 5315/Ne

For, 

Tex to Cotton or English,

Tex = 590.5/Ne

For, 

Denier to Metric,

Denier = 9000/Nm

For, 

Tex to Metric,   

Tex = 1000/Nm

Mathematical Problem Related To Count Conversion:

Problem-1:

Find out the denier count, when Ne = 32 and Tex = 10.

Calculation:

We Know,

For,  

Denier to Ne

Denier = 5315/Ne

= 5315/32

= 166.0 (Ans)

For,

Denier to Tex

Denier = 9 x Tex

= 9 x 10

= 90 (Ans)

Problem-2:

Find out the metric count, when Ne = 32 and Tex = 10.

Calculation:

We Know,

For,  

Metric to Ne

Nm = 1.7 x Ne

= 1.7 x 32

= 54 (Ans)

For,

Metric to Tex

Nm = 1000/ Tex

= 1000/10

= 100 (Ans)

Relation Between Yarn Diameter & Count:

Let,

Yarn Count  = N Tex [ For, Direct System]

∴ Length of N gm of yarn = 1 km

= 1000 m

= (1000 x 100) cm

= 10⁵ cm

∴ Length of 1 gm of yarn   = 10⁵/ N cm

Assuming,

The specific volume of the yarn = 1.1 [ By experiment, an apparent specific volume of 1.1 for cotton was found]

∴ Volume of 1 gm of yarn   = 1.1 cm³

∴ Length of the 1.1 cm³ of yarn  = 10⁵/N cm

We Know,

Volume = Length x Cross-sectional Area

or, 1.1  = 10⁵/N  x (πd²)/4    cm

or, d² = (1.1 ×N ×4)/(10⁵× π)

or, d  = 0.375/100 × √N 

or, d  = k × √N   

∴ d  ∝ √N [For, Direct System]

For,

Indirect System,

1 inch = 2.54 cm

∴   d  = = 0.375/100 × √N × (1/2.54) inch

In Indirect System,

We can assume Ne instead of Tex,

∴ Ne = 590.5/Tex

Or, Tex = 590.5/Ne

∴ d = 0.375/100 × √N × (1/2.54) inch

Or, d  = (0.375 ×√590.5 )/(100 ×2.54) × (1/√Ne)   inch

or, d = k x 1/(√Ne)

∴ d ∝ 1/√Ne  [For Indirect System]

Methods Or Ways Of Yarn Count Measurement:

1. Warp Reel And Analytical Balance Method:

Overview:
This is a standard method used to determine the yarn count, which tells us how fine or coarse the yarn is.

Concept:
Yarn count is a numerical value that describes the thickness of yarn. There are two types of systems:

1. Indirect system
2. Direct system

Formula:

1. Indirect system [N = (L ×w)/(l × W)]
2. Direct system [N = (W × l)/L]

• N = The yarn number (Count)
• W = The weight of the sample at the official regain in the units of the system.
• w = The unit of weight of the system
• L  =  The length of the sample
• l  =   The unit of length of the system

Tools Required: Warp reel, weighing balance, and a set of standard weights.
Sample Used: Cotton yarn in hank form.

Working Process:

• The warp reel is set up and the yarn is guided from the cone through the reel.
• The reel’s counter measures the yarn length.
• For cotton, the reel has a 1-yard circumference and winds 120 yards. For jute, it’s 2.5 yards circumference with 300 yards needed.
• The cotton reel is motor-driven and stops automatically once the target length is wound; for jute, it’s operated manually.
• The wound yarn is then weighed using a balance.
• This process is repeated 12–16 times. The average is used to calculate the yarn count using the direct count system.

2. Warp Reel And Quadrant Balance Method:

Overview:
Quadrant balance is a direct-reading instrument used to determine the count of short yarn lengths.

Scope:
Can measure counts for yarns up to 40 yards. Also usable for weighing fabric samples.

Principle:
Measures the fineness or thickness of yarn using either:

1. Indirect system [N = (L ×w)/(l × W)]
2. Direct system [N = (W × l)/L]

Tools Required: Quadrant balance, scale, and blade.
Sample Used: Cotton yarn in roving or sliver form.

Working Steps:

• Measure 4 yards of cotton yarn with a scale.
• Hang the sample on the hook of the quadrant balance.
• Read the count directly from the appropriate scale.
• The balance includes three scales:
  • 4 yards for sliver
  • 20 yards for roving
  • 840 yards for yarn
• Repeat the process 16 times and take the average to find the final count.

3. Warp Reel And Knowles Balance Method:

Structure:

• A beam balance used to find yarn count.
• It has a hexagonal rod with five faces (A to E), each calibrated for different count ranges.
• A screw allows rotation of the rod to bring the required scale into view.
• Matching weights (A to E) go with each scale.
• A sliding rider helps balance the beam.

Procedure:

• Place 120 yards of yarn on the right pan.
• Choose a matching weight (A to E) and place it on the left pan.
• Turn the screw to align the correct scale with the viewer.
• Adjust the rider on the scale until the beam is balanced.
• The rider’s position shows the yarn count.

4. Beesleys Balance Method:

Usage:
Used when only a short piece of cotton yarn is available, either loose or removed from fabric.

Principle:

• A beam with a hook on one end and a pointer on the other.
• The beam is leveled initially with a standard weight on the pointer side.
• Yarn samples are cut using a template and added to the hook until the pointer aligns with the reference line.
• The number of yarn pieces needed for balance gives the count.

Working Steps:

• Choose the right template based on yarn length (short or long cotton).
• Cut yarn pieces using the template and blade.
• Hang them one by one on the hook and count the pieces.
• Repeat the process 10 times and calculate the average for the final count.

Application:
Helps determine the count of yarn taken from a small fabric sample.

Some Important Conversion:

• 1 lb = 7000 grain
• 1 lea = 120 yds.
• 1 yds = 0.914 m
• 1 inch = 2.54 cm
• 1 kg = 2.204 lb
• 1 Hank = 840 yds.

References:

1. Principles of Textile Testing by J E Booth.
2. Handbook of Textile Testing and Quality Control by E. B. Grover, Elliot Brown Grover, Dame Scott Hamby.
3. Physical Testing of Textiles by B.P. Saville.

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