**Introduction: **

In this article, we will know about the mathematical solution of jute spinning frame problems. The three essential tasks of the spinning process are as:

- Drafting
- Twisting
- Winding-on

Drafting is carried out by the usual arrangement of retaining rollers and drawing rollers where drawing rollers rotate faster than retaining rollers.

After emerging out from the nip of drafting rollers the thin ten-uous sliver passes down to the top of the flyer goes through its hollow leg and wound onto the bobbin. During flyer ration, it is imparted necessary amount of twist.

Winding on function is carried out by builder mechanism. As the builder moves up and down the bobbins alternatively rise into and withdraw from the flyer and thus winds yarn on the bobbin in a continuous spiral.

**Mathematical Solution of Jute Spinning Frame Problems**

**Problem 1:**

What will be the prodn for 8 hrs working of a spg. From of 100 spyndles with particulars as below:

- R.P.M of flyer = 3300;
- TPI = 3.35
- Sliver from finisher drawing frame = 0.5lbs/100yds.
- Spg frame efficiency = 80%

**Solution:**

………………….14400×0.5

Spg count = ……..………….. = 8lbs/spyndle.

……………………..9×100

……………………….3300×60×8×100×8×0.8

Prodn/ shifts = ……………………………………… = 583.747 lbs. (ANS)

……………………………..3.35×36×14400

**Problem 2:**

Find out the required input sliver in-lbs of jute spg mills having 10 Apron draft sliver spinning frame to produce 10 lbs/spindle. Hessian warp yarn (Assume necessary parameters)

**Solution:**

Here, no of Apron draft sliver spg frame =10

Hessian warp yarn count = 10 lbs/spindle.

Let, Spindle speed =4000 r.p.m,

K factor = 12

No of spindle = 100

Wastage = 2%, Efficiency = 90%

TPI =12÷ √10 = 3.8

Then, prodn/ spg frame/day in lbs

….4000×60×24×10×100×90×10

= ……………………………………………..

……………..14400×3.8×36

Then, input sliver in lbs = 26315.78947× {(100+L)÷100}

= 26842.10526 . (ANS)

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**Problem 3:**

Find the prodn /shift of 8 hrs of a jute mill having 28 frames of 100 spindles each running with the following particular:

- Flyer speed=3800 r.p.m
- T.P.I=3.2
- Count=8.6 lbs/spindle
- Eff=84%

Comment on the quality of the yarn produced if 10% root cutting is used in the mixing along with good fiber.

Solution:

…………………………….3800×60×8×8.6×.84×100×28

Production/Shift = ……………………………………………….

………………………………………3.2×36×14400

= 22240.556 lbs. (ANS)

Author of this Article:Engr Avijit DeyProduction Officer Fabian Group, Chittagong Mobile: 01836124490 E-mail: [email protected]