Calculation of Package Density in Yarn Dyeing

Calculation of Package Density in Yarn Dyeing 

Package Density in Yarn Dyeing:

Package density has important effect on yarn dyeing. When package are too soft then liquor flowing through it will find the course of least resistance and cause channeling, which leaves some parts of the package relatively un dyed or lighter. If the packages are wound too hard, a point can be reached where the flow of liquor is impeded to such an extent that poor dyeing or none may occur. In this article we will discuss on yarn package density before dyeing.

The ratio of mass and volume is called density.

• Density = ρ
• Mass = m
• Volume = v

Here, 

m = (Bobbin weight with yarn – Bobbin weight without yarn) gm.

v = π (R12 – R22) × h

• R1 = Outer radius of the bobbin (with yarn).
• R2 = Inner radius of the bobbin.. 

Say, for example, 

• Outer Radius, R1=16.3/2 = 8.15 cm. 
• Inner Radius, R2 = 6.96/2 =3.48 cm.
• Height = 16 cm.. 

We know = πr2h. 

So, total volume, V1 = π R12h 

=3.1416 X (8.15) 2 X 16

=3339 cm3

Steel bobbin, V2= π R22h 

= 3.1416 X (3.48)2 X16.

= 609 cm3 

Original volume = (3339-609) = 2730 cm3

Package Density, ρ = m/v = (1395-235)/2730 = 0.42 gm/cm3.

Package density in soft winding for cotton must be 0.36 to 0.40 gm/cm3 and for polyester or CVC it would be higher than 0.40 gm/cm3.

We measure the package density of different bobbins in this section which are:

Count (Ne)	Package density (gm/cm3)
20s	0. 387
24s	0. 375
26s	0. 382
28s	0. 35
30s	0. 345
34s	0. 37
40s	0. 378

For filament (Polyester):

Count (denier)	Package density (gm/cm3)
30	0. 44
75	0. 376
100	0. 46

For spun yarn:

Count (denier)	Package density (gm/cm3)
40/2	0. 39
50/2	0. 4197

For CVC yarn:

Count (Ne)	Package density (gm/cm3)
30s	0. 40
26s	0. 39