The relation between Taper Angle and Amount of Yarn on a Beam is discussed below:

Let,

s = Traverse length.

L = Axial

d = Empty beam dia.

D = Full beam dia.

**Relation between Taper Angle and Amount of Yarn on a Beam is:**

**dm = (D+d)/2 = mean dia. **

Where,

X = Tape distance

α = Taper angle

v = Volume of yarn stored on beam.

Let, s > x so as to maintain stability

…….∏D2L ∏d2L

V = ………. – ………….

……….4…………….4

…..∏L

= …….. (D2 – d2)

……4

………….D+d D-d

= ∏L (………) (……….)

…………….2 . 2

From the figure, it is clear that

……….D+d……..D-d

dm = ……… & ………… = x tan α

…………..2………..2

So, v = π L dm (x tanα)

V > π L dm S tan α if, x > s

V < π L dm S tan α if, x < s

So, V ∞ S tan α if α = 90° then V = α

So unlimited amount of yarns can be wound if the flange stays perpendicular to the beam barrel. Practically this is impossible. But this type of package permit’s wind a high amount of yarn.

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Author of this Article:Rofiquzzaman RajuFabric Technologist, B.J.Group, Mawna, Gazipur Email: [email protected]