# Mathematical Problems and Solutions of Warping in Textile Weaving

What is Warping in Weaving?

The parallel winding of warp ends many winding packages (cheese or cone) on to common packages (warp beam) is known as warping. Warping is so importance in textile weaving due to construction of warp yarn beam, construction of parallel of yarn sheet and also combination of small packages.

 Warping process in weaving
Warping Calculation in Textile Weaving Industry:

Problem-01:
Calculate the time required to prepare of 8 warpers beam on 2 improved high speed beam warpers with warping speed of 560yds (calculated) per minute. The length of warp on each beam is required to be 36000 yds, where efficiency is 80%. Also find here the efficiency.

Solution:
Here,
Total length of warp in yds= 36000,
Yarn count=20s,
Number of beams=8,
Number of machines=2,
Calculated production in yds per machine per hour= 560,
Efficiency= 80%=0.8
Required time=?
Efficiency=?

Now,
Time required,
Total length of warp in yds × number of beams
=……………………………………………………………………………………………………………………………. (1)
Actual production in yds per machine per hour × number of machines

Again,
Actual production in yds per machine per hour,
= Calculated production in yds per machine per hour ×60 × efficiency
= 560×60×0.8
= 26880 yds

Now, from equation (1), we get,
Time required,
36000×8
=………………
26880×2
=  5.36 hours.

So, time required for this calculation is 5.36 hours.

Again,
Efficiency= {(Actual production/Calculated production) ×100}
= {(26880/36000) ×100}
= 74.67%

So, efficiency for this calculation is 74.67%

Problem-02:
A modern high speed beam warping machine produces 8 beams each containing 222720 yds of warp per day of 8 hours. If the calculated warping speed of the warper is 580 yds per minute then calculate its efficiency.

Solution:
Here,
No. of beams=8,
Total production=222720 yds,
Time= 8 hours,
Calculated production per minute=580 yds,
Efficiency=?

So,
Efficiency= {(Actual production/Calculated production) ×100} …………… (1)

Now,
Calculated production per hour=580×60=34800 yds,

And,
Actual production in yds per hour= (Total production/ Time) = (222720/8) = 27840 yds

Now, from equation (1), we get,
Efficiency= {(27840/34800) ×100} = 80%

So, efficiency for this calculation is 80%.