**Mathematical Problems and Solutions of Combing**

**Md. Abu Sayed**

Founder of Textile Apex

Pabna Textile engineering college, Pabna, Bangladesh

**Email:**sayed1952@facebook.com

**Cell :**+8801745214773

**What is Combing?**

**Combing**is the process in yarn spinning by which straightening and parallelizing of fibres and the removal of short fibres and impurities by using a comb on combs assisted by brushes and rollers is called combing. To produce a uniform sliver of required weight per unit length combing is necessary. Here goes the need to know the mathematical solutions.

**Some mathematical problems and solutions of combing are as follows –**

**1. Ribbon/feed lap weight per yd 580 grain. 6 laps are feeded in a combing machine. If delivered sliver weight per yds is 46.60 grain, then what will be the ribbon lap hank and draft?**

**Solution:**

Here given,

- Ribbon lap wt./yd = 580 grain
- Doubling = 6
- Delivered sliver wt./yd = 46.60 grain
- Ribbon lap hank =?
- Draft =?

Ribbon lap length/Length unit

**Ribbon lap hank**=

**…………………………………**

Ribbon lap weight/Weight unit

= Ribbon lap length/ Length unit X Weight unit/ Ribbon lap weight

= 1/840 X 7000/580

= 0.0144

**(ANS).**

Feed sliver weight

**Actual draft**=

**…………………………**X Doubling

Delivered sliver weight

= 580/46.60 X 6

= 74.68

Here given,

= (π X 2r X N) / 36

= (3.14 X 2 X 1 X 118) / 36

= 20.58

Sliver weight

7000

= 20.584 X 46.6/7000 X 60 X 8 X 90/100 lb/shift

= 59.20 lb/shift

Here given,

Again,

= (60.43 X 100)/(100 – 18)

= 6043 / 82

**(ANS).****2. In a combing machine coiler calendar roller speed is 118 rpm, radius 1”, Delivered sliver weight per yd is 46.6 grain. Calculate the production constant. If efficiency is 90% then also calculate the production per shift**.**Solution:**Here given,

- Coiler calendar roller speed (N) = 118 rpm
- Coiler calendar roller radius (r) = 1”
- Delivered sliver weight per yd = 46.6 grain
- Production constant =?
- Production/shift at 90% eff. =?

**Production constant**= Circumference speed of coiler calendar roller / 36= (π X 2r X N) / 36

= (3.14 X 2 X 1 X 118) / 36

= 20.58

Sliver weight

**Production/shift**= Production constant X**………………**X 60 X shift X Eff.7000

= 20.584 X 46.6/7000 X 60 X 8 X 90/100 lb/shift

= 59.20 lb/shift

**(ANS).****3. If in a combing machine draft constant is 2780 and DCP is 46, then what will be the mechanical draft of the machine? If waste is 18%, then what will be the actual draft?****Solution:**Here given,

- Draft constant = 2780
- DCP = 46
- Waste = 18%
- Mechanical draft =?
- Actual draft =?

**Mechanical draft**= Draft constant/DCP = 2780/46 = 60.43**(ANS).**Again,

**Actual draft**= (Mechanical draft X 100) / (100 – Waste%)= (60.43 X 100)/(100 – 18)

= 6043 / 82

= 73.70

Here given,

Again,

= (64 X 6) X 6.8

**(ANS).****4. Calculate the DCP of a combing machine from these parameters. Feed lap hank = 64 K Tex, Delivered single sliver hank = 3.40 K Tex, Doubling = 6, Waste = 15%, and draft constant = 1696. The machine is giving twine sliver delivery.****Solution:**Here given,

- Feed lap hank = 64 K Tex
- Delivered single sliver hank = 3.40 K Tex
- Doubling = 6
- Waste = 15%
- Draft constant = 1696
- DCP =?

**Delivered twin sliver hank**= 3.14 X 2 = 6.80 (Direct system)Again,

**Actual draft**= Feed lap hank / Delivered sliver hank X Doubling= (64 X 6) X 6.8

= 56.47

And,

= 56.47 X 85/100

And,

**Mechanical draft**= Actual draft X (100 – Waste%) / 100= 56.47 X 85/100

= 48

Now,

Now,

**DCP**= Draft constant / Mechanical draft
= 1696 / 48

= 35.33

= 35T

**(ANS)**.**5. Calculate the production for 8 hrs of a combing machine from the following data –**- Feed/Nip = 6.7 mm
- Waste = 16%
- Nip/min = 120
- Efficiency = 90%
- No. of head = 6 Feed lap hank = 68 K Tex

**Solution:**

Here given,

- Feed/Nip = 6.7 mm
- Waste = 16%
- Nip/min = 120
- Efficiency = 90%
- No. of head = 6 Feed lap hank = 68 K Tex
- Production/8 hrs =?

**We know that,**

**Production**= Nip/min X Feed/Nip X No. of head X Waste% X Eff.%

= 120 X 6.7 X 6 X {(100 – 16) / 100} X 90/100 mm/min

= 120 X 60 X 8 X 6.7/1000 X 68/1000 X 6 X 84/100 X 90/100

= 119.04 kg/8hrs

**(ANS).**

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