**Winding:**

Winding is the process of transferring yarns from ring, bobbin, hank into a suitable package. The purpose of winding is to create a more manageable package that can be easily handled and processed in downstream operations. It is one of the most important operations, which is mainly occurred in the spinning section. Besides, it is also important in fabric manufacturing. In fabric manufacturing, directly winding is not so much important, but rewinding and its winding mathematical formulas are so important.

The formation of big yarn packages that could be smoothly unwound, during the next process is known as winding. Winding is the most essential process in both yarn and fabric manufacturing. The main objective of winding is to produce a suitable package for both woven and knitted fabric production.

**Winding Mathematical Formulas, Problems, and Solutions**

**Types of winding:**

There are three types of the winding process. These are:

- Parallel winding
- Nearly parallel winding
- Cross winding

**Formulas of Winding:**

……………………………………Quantity of yarn in-lbs to be wound

1. Time required = ………………………………………………………………………..

………………………………Actual production in-lbs/hrs X No. of drums

…………………………………………Actual Production

2. Winding Efficiency = …………………………………………… X 100%

…………………………………………Calculated Production

Note: Actual Production < Calculated Production

………………………………Calculated Production – Actual Production

3. Efficiency loss = ……………………………………………………………………. X 100%

…………………………………………Calculated Production

**Mathematical Problems and Solutions**

***How much time will be required to wind 2388 lbs of 20s cotton on 40 drums of a super speed cone winder if the calculated of winding is 1298 yds per min and the efficiency is 80%.

**Solution:**

Given that,

**Quantity of yarns in-lbs = 2388 lbs

**Yarn count = 20s

**No. of drums = 40

**Calculated rate of winding in minutes = 1298 yds

…………1298

= ………………….. Hank

…………840

**Efficiency = 80%

………80

= …………….

………100

**Required time = ?

We know,

……………………………………Quantity of yarn in-lbs to be wound

Time required = …………………………………………………………………………..

……………………………Actual production in-lbs/hrs X No. of drums

…………………………………………Quantity of yarn in hank

OR, Time required = ………………………………………………………………..

………………………………Actual production in hanks X No. of drums

……………………………………Quantity of yarns in-lbs X Yarn count

OR, Time required = ……………………………………………………………………. _________(1)

………………………………Actual production in hanks X No. of drums

Again we know,

Actual production per hour per drum in Hank = Calculated rate of winding in minutes X Efficiency X 60

………………..80

= 1298 X ………… X 60 yds

………………..100

……..1298…………80

= ……………. X …………. X 60 hanks

……..840…………..100

= 74.17 hank

Now from (1) No. equation we get,

………………..………………..2388 X 20

Time required = …………………………………

………………..………………..74.17 X 40

= 16.098 hrs (Ans)