# GATE (TF) Textile 2010 Question Paper Solution | GATE/2010/TF/49

A speed frame with all the drafting rollers of 25.4 mm diameter has the following process parameters: Roving count – 1.5g Ne; Front drafting roller speed – 220 rpm; Roving diameter – 3.0 m; Roving Twist Multiplier – 1.2 tpi Ne-1/2, Empty bobbin diameter – 76.2 mm.

###### Question 49 (Textile Engineering & Fibre Science)

The ideal bobbin rack speed for the first layer of roving being directly wound on the empty bobbin will be approximately

Diameter of all drafting rollers(D)=25.4 mm

Roving count=1.5s Ne

Roving diameter=3.00 mm

Front roller speed(N)=220 rpm

Empty bobbin diameter=76.2 mm
Let bobbin speed=N rpm

For first layer of roving being wound-

Surface speed of empty bobbin=surface speed of the front rollers

Bobbin speed x dia of empty bobbin=Front roll speed x dia of roller

N x 76.2=220 x 25.4

N=220 x 25.4 /76.2

N=5588/76.2

Bobbin speed(N)=73.33 rpm

Now,

Ideal bobbin rack speed=Bobbin speed x dia of roving

Ideal bobbin rack speed=73.33 x 3

Ideal bobbin rack speed=220 mm/min (Ans)