# Mathematical Problem and Solution of Winding in Textile Weaving

Winding Production Calculation:
The person who wants to make career in textile weaving sector has to know the different calculation method of winding process. This article has presented some key calculation methods of winding with examples such as winding production calculation, required time calculation and number of drum calculation in winding.
 Winding production calculation in weaving
Winding Speed Calculation:
Problem-01:
How much time will be required for a winder to wind 2000 pounds of 20s cotton yarn if the cone winder operates at 900 yds per minute, where the winding efficiency is 90% and number of drum is 30? Also calculate winding production per drum per hour for this calculation.

Solution:
Here,
Quantity of yarns in pounds= 2000,
Yarn count=20s,
No. of drums=30,
Calculated rate of winding in minutes= 900 yds= (900/840) hank= 1.07 hank,
Winding efficiency=90%=0.9,
Required time=?

So,
Time required,
Quantity of yarns in pounds × yarn count
=…………………………………………………………………………………………….… (1)
Actual production in hanks per hour × no. of drums

Again,
Actual production per hour per drum in hank,
= Calculated rate of winding in minutes × 60× Efficiency
= 1.07×60×0.9
= 57.86 hank

Now, from equation (1), we get,
Time required,
2000×20
=………………
57.86×30
=  23.04 hours.

So, time required for this calculation is 23.04 hours and winding production per hour per drum is 57.86 hank.

Problem-02:
Yarns are required to wind 1600 pounds of 46s in 8 hours on a high speed winding machine with 651 yds as the rate of winding (calculated) of the machine runs with 92% efficiency. How many drums would be required?

Solution:
Here,
Quantity of yarn= 1600 pounds,
Yarn count= 46s,
Calculated production per minute= 651 yds= (651/840) hank= 0.78 hank,
Time= 8 hours,
Efficiency=92%=0.92,
Number of drum=?

So,
Number of drums,
Quantity of yarns in pounds × yarn count
=……………………………………………………………………………………………….… (1)
Actual production in hanks per hour × Time required

Now,
Actual production in hanks per hour,
= Calculated production per minute × 60× efficiency
= 0.78×60×0.92
= 42.78

Now, from equation (1), we get,
Number of drums,
1600×46
=……………………..
42.78×8
=   215 drums

So, total no. of drums required for this calculation is 215.

Problem-03:
Calculate the time required for winding 60000 pounds of 50s yarn on 500 high speed winding drums each of which has a calculated rate of winding of 630 yds per minute. The efficiency is 90%.

Solution:
Here,
Quantity of yarns in pounds= 60000,
Yarn count=50s,
Number of drum=500,
Calculated production per minute= 630 yds= (630/840) hank= 0.75 hank,
Winding efficiency=90%=0.9
Time required =?

So,
Time required,
Quantity of yarns in pounds × yarn count
=………………………………………………………………………………………………………….… (1)
Actual production in hanks per hour × number of drums

Now,
Actual production in hanks per hour,
= Calculated production per minute in hank × 60× efficiency
= (0.75×60×0.9) hanks
= 40.5 hanks

Now, from equation (1), we get,
Time required,
60000×50
= ………………………
40.5×500
=  148. 15 hours

So, time required for this calculation is 148.15 hours.