**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.

**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)

= 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

Calculated production

Here,

= 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

Here,

60 X 8

= Production per min X

840 X Yarn count

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

= 7.44 lb

Amount of yarn

Production per 8 hr of a winding drum

= 1600/7.44 = 215.05 = 215

Drums Surface speed X 60 X 8

36 X 840 X Count

3.14 X 3 X 2400 X 60 X 8 68

=

36 X 840 X 30 100

= 8.13 lb

= 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 100Calculated production

Mathematical Problems and Solutions in WindingMathematical 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 =?

**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 =?

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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