Relation between Taper Angle and Amount of Yarn on a Beam

Relation between Taper Angle and Amount of Yarn on a Beam
Rofiquzzaman Raju
Fabric Technologist,
B.J.Group, Mawna, Gazipur
Email: rtextile.finance@gmail.com



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


Let, 

s = Traverse length.
L = Axial
d = Empty beam dia.
D = Full beam dia.
 

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 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 flange stays perpendicular to beam barrel. Practically this is impossible. But this type of package permit’s to wind high amount of yarn.