Mathematical Problems and Solutions of Winding

Mathematical Problems and Solutions in Winding

Md. Abu Sayed
Founder of Textile Apex
Pabna Textile engineering college, Pabna, Bangladesh
Email: sayed1952@facebook.com
Cell : +8801745214773





Winding:
The process of transferring yarns from ring bobbins, hank etc. into a suitable package is called winding. It may be electrical or mechanical.
winding problems
Formulas for winding

1. Production per hour of winding machine (For cotton) = Surface speed of winding drum (yds/min) X 60/(840 X Yarn count) X No. of drums X Efficiency% X Waste% (lb/hr)
 
= Production or surface speed of each spindle X /(840 X Yarn count) X No. of spindle X Efficiency% X Waste% (lb/hr)

= Production or surface speed of each spindle X 60 X 8 X (No. of spindle/1 Spindle (Spindle)

2. Production per hour of winding machine (For Jute) = Surface speed of winding roller (inch/min) X 60 X Count/(36 X 14400) X No. of spindle X Eff% (lb)

3. Production per hour of winding machine (Tex system)

= Surface speed of winding roller or spindle (cm/min) X 60 X Count/(100 X 1000) X No. of spindle x Eff.% (gm)

                                        Actual production
4. Machine efficiency = ………………………. X 100
                                    Calculated production

Mathematical Problems and Solutions in Winding


1. Production per minute of a high speed winding machine is 630 yds. What is the time required for winding 54S number’s 60,000 lb yarn onto same 500 drums. Here efficiency is 90%.

Solution:

Here,
  • Production of machine = 630 yds/min
  • Yarn count = 54S
  • No. of drums = 500
  • Machine eff. = 90%
  • Amount of yarn = 60,000 lb
  • Required time =?
Production/hr (lb) = Production per min of 1 drum X 60/(840 X yarn count) X No. of drum X Machine eff.%

= 630 X 60/(840 X 54) X 500 X 90/100

= 375 lb

                                                   Total amount of yarn
Time required for winding yarn = …………………………
                                                     Production per hr

                                              = 60,000/375 hr (ANS).

2. Production per min of a winding machine is 651 yds with 100% efficiency, then calculate the required no. of winding drums to produce 46S numbers 1600 lb yarn within 8 hr with the same machine.

Solution:

Here,
  • Production of a winding drum = 651 yds/min
  • Machine efficiency = 92%
  • Yarn count = 46S
  • Amount of yarn = 1600 lb
  • Required no. of drums in 8 hr =?
We know,

Production per 8 hr of a winding drum,

                                            60 X 8
= Production per min X ……………………. X Eff.%
                                    840 X Yarn count

= 651 X (60 X 8)/(840 X 46) X 92/100

= 7.44 lb

                                                                  Amount of yarn
Now, Required no. of drums = ………………………………………
                                                 Production per 8 hr of a winding drum

                                              = 1600/7.44 = 215.05 = 215 (ANS).

3. Calculate the production per shift of each spindle of a auto-coner Winding machine from the following data –

  • Drum speed = 2400 rpm
  • Dia of drum = 3”
  • Warp yarn count = 30S
  • Efficiency = 68%
Solution:
  • Drum speed = 2400 rpm
  • Dia of drum = 3”
  • Warp yarn count = 30S
  • Efficiency = 68%
  • Production/Spindle/8 hr =?
We know,

                                       Drums Surface speed X 60 X 8
Production/Spindle/8 hr = ………………………………… X Eff.%
                                              36 X 840 X Count

     3.14 X 3 X 2400 X 60 X 8            68
= ……………………………….. X ……….
              36 X 840 X 30                  100

= 8.13 lb (ANS).

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