# Mathematical Problem of Jute Drawing

These functions of the drawing stages are (1) Drafting the finisher card sliver to a count suitable for feeding the spinning frame; (2) Reduction of weight irregularities by doubling; (3) Straightening the fibers and laying them along the sliver axis so that when they come to be spun on the spinning frame they will be evenly drafted and twisted to form an acceptable yarn. In this article, we will discuss the mathematical problem of jute drawing.

### Mathematical Problem of Jute Drawing

Problem-1:
Calculate lbs/100 lbs sliver from the drawing frame with particulars as below:

Finisher card delivered sliver =16 lbs/100 yds.

Drawing frame draft =4

Doubling at drawing frame = 2: 1

Solution :

………………………………………….Doubling at D/F
Finisher card sliver wt. = 16× ………………………. = Drawing frame sliver wt.
…………………………………………….Draft at D/F

Then, Drawing sliver wt.= 16×(2÷4) = 8 lbs/ 100 yds. (ANS).

Problems-2:
3 finisher cards supply slivers to 2 first drawing frames calculate the speed of the back roller of the drawing frame in balance. Each finisher card produces 400 lbs/100 yds sliver; Drawing frame 2 heads, 2 deliveries/head, doubling 2 each into 1.

Solution:

2  1st D/F =3 Finisher card production/hr.
= 3×400
= 1200 lbs/hr

Then 1  1st D/F production/hr = 1200 ÷ 2
= 600 lbs/min.

1st D/F feed /min = 600 ÷ 60 = 10 lbs/min.

Total no of sliver feed at D/F
= 2×2×2 slivers

Length of sliver available/ min to feed = 10 × (100÷16) yds /min.

To each D/F = (10×100×3)÷16 ft/min.

…………………………………………..10×100×3
Surface speed of back roller = ……………….. ÷ 2×2×2
…………………………………………………16

= 23.44 ft/ min. (ANS)

You may like also: Twist, Yarn Count and Twist Change Pinion in Jute Spinning

Problem-3:
Calculate prod/hr of Double thread screw gill drawing frame from particulars:

Back R/r S.Speed =15.52 ft /min.

Draft = 6

Delivered sliver = 4 lbs /100 yds.

Solution:

Delivery roller S.Speed =15.52×6 = 93.12 ft/min.

Total length of delivery = 93.12×5×2 ft/min.

….93.12×5×2×60
= ……………………. yds /hr.
……………3

….93.12×5×2×60×4×90
= ……………………………….. lbs/ hr[ at 90% eff ]
…………3×100×100

= 670 lbs /hr (ANS).

```Author of this article:
Engr Avijit Dey
Production Officer
Fabian Group, Chittagong
Mobile: 01836124490
E-mail: [email protected]```

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