# Winding Mathematical Problems and Solutions

Winding:
The process of transferring yarns from ring bobbins, hank, etc. into a suitable package is called winding process. It may be electrical or mechanical. in this article, we will discuss the winding mathematical problems and solutions.

### Mathematical Problems and Solutions in Winding

Formulas for winding

1. Production per hour of the 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 a 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 the 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 the 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).

#### You may read also: Winding Mathematical Formulas, Problems and Solutions

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

• Drum speed = 2400 rpm
• Dia of drum = 3”
• Warp yarn count = the 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).

```Author of this Article:
Md. Abu Sayed
Founder of Textile Apex
Pabna Textile engineering college, Pabna, Bangladesh
Email: [email protected]
Cell : +8801745214773```

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