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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