Calculation of Package Density in Yarn Dyeing

Package Density in Yarn Dyeing:
Package density has an important effect on yarn dyeing. When packages is 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 undyed 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 dying or none may occur. In this article, we will discuss yarn package density in yarn dyeing.

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Calculation of Package Density in Yarn Dyeing — Maintaining package density in yarn 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.