Now You Know Complete Mathematics of Cotton Spinning

Complete Mathematics of Spinning or Spinning Problems

Lefayet Sultan Lipol
B.Sc in Textile Technology (BUTEX), M.Sc in Textile Engineering (Sweden)
Assistant Professor & Head, Fareast International University
E-mail: lefayetbd@gmail.com

Problems and Solutions of Blow Room

1. Find the number of lap per hour in Scutcher m/c of Bottom Calendar Roller dia = 7 inch, rpm = 12, efficiency = 80%, lap length 40 yards

Answer:

                                  𝜋∗7∗12∗80∗60
Production of m/c = -------------------------------------- yds/hr
                                       36∗100
= 351.85 yds/hr

                   351.85
No. of lap = ------------------
                      40
= 8.79 ≈ 9

2. Calculate the Production/hour of Blow room line with 2 Scutchers if B.C.R. dia=7 inch, r.p.m= 10, Efficiency=90%, waste 4%, lap weight 14 oz/yd. (B.C.R= Bottom Calendar Roller)

Answer:

                      3.14∗7∗10∗60∗90∗(100−4)∗2∗14
Production = ----------------------------------------------------------- lbs/hr
                                36∗16∗100∗100
= 553.896 lbs/hr

3. Calculate production/hour of a Blow Room line if, r.p.m of B.C.R r.p.m = 14, Dia= 18 cm, lap hank= 0.0012, efficiency 80%, no. of Scutcher =2

Answer:

                      3.14∗18∗14∗60∗0.80∗2
Production = -------------------------------------------------- lbs/hr
                       36∗2.546∗840∗0.0012
= 822.2 lbs/hr

4. Find out the beats/inch from the following data- Beater r.p.m= 720. No. of striker= 16, Feed roller r.p.m= 24, Dia of feed roller= 3 inch.

Answer:

Beats/min = Beater r.p.m* no. of striker
= 720*16
= 11520 no. of strikes

Surface speed of feed roller = πDN
= 3.14*3*24
= 226.08

                     11520
Beats/inch = -----------------
                     226.08
= 50.96

Solutions from Draw Frame to Auto Coner

5. Write the abbreviations:

Answer:

Elaboration:

TPI = Twist per inch

TM = Twist Multiplier

C.V = Co-efficient of variation

RPM = Revolution per minute

MPM = Meter per minute

GPS = Grams per spindle

TPM = Twist per metre

6. Delivery speed=150 MPM, Sliver hank=0.12, Tension draft =1.25 efficiency= 90%, what is the carding production/8 hrs?

Answer:

Here,

Delivery speed = 150 MPM
Sliver hank = 0.12
Tension draft = 1.25
Efficiency = 90%

                                          150∗1.09∗60∗8∗0.90∗1.25
Production/8hrs or shift = ----------------------------------------------------------- Kg/shift
                                                 0.12∗840∗2.204
= 397.4 Kg/shift

7. Front roller speed = 3500 r.p.m, roller dia=2.5 inch, delivery hank=0.12, efficiency=90%. What is the Draw Frame production/shift/machine?

Answer:

Surface speed = π *RPM*Roller dia
= 3.14*3500*2.5"
= 27475 inch/min

                                                    27475∗60∗8∗0.90
Production/shift/m/c (8 hrs) = ------------------------------------------------- Kg/shift
                                                   36∗840∗0.12∗2.2046
= 1483 Kg/shift

8. Feed Hank=0.1, Delivery hank=0.12, Doubling=8, what is the total draft?

Answer:

                      Delivery hank∗Doubling
Total draft = ------------------------------------------
                               Feed Hank
    0.12∗8
= --------------
       0.1
= 9.6

9. Spindle speed=1200 r.p.m, Roving hank=0.90, TPI=1.25, efficiency=80%, no. of spindles=120, what is the production/shift/machine?

Answer:

                                        1200∗60∗8∗120∗0.80
Production/m/c/shift = ----------------------------------------------- Kg/shift
                                      36∗840∗0.9∗1.25∗2.2046
= 737 Kg/shift

10. Spindle speed=12500, count=30/1 Ne, TM-3.70, Efficiency=92%, 1200 spindle/frame, what is the production/frame/shift?

Answer:

TM = 3.7, Ne = 30

TPI = TM * √Ne
= 3.7*√30
= 20.26

RPM = 12500

                                        12500∗60∗8∗1200∗0.92
Production/m/c/shift = ----------------------------------------------- Kg/shift
                                       36∗840∗30∗20.26∗2.2046
= 163 Kg/shift

11. Roving hank=0.90, count=26/1, what is the Ring Frame total draft required?

Answer:

Required draft = Delivery hank/Feed hank

    26
= ------
   0.90

= 28.88 ≈ 29

12. Roving hank=0.80, yarn count 20/1, roving make how many yard?

Answer:

                              20
Length of yarn = -------- yards
                             0.8
= 25 yards

13. What are the equipments require in quality control department in a standard spinning mills?

Answer:
AFIS, USTER tester, HVI, Wrap reel, Wrap block, Balance, Strength tester, TPI tester etc.

14. Drum speed=1500 MPM, no. of head (Drum) = 60, count=30/1 Ne, efficiency= 85%, what is the Auto Cone production/machine/shift?

Answer:

                                      1500∗60∗8∗0.85∗60∗0.9144
Production/m/c/shift = ---------------------------------------------------- Kg/shift
                                              30∗840∗2.2046
= 604 Kg/shift.

15. Find out the production/day/comber in tons from the following parameters: Nips/min: 350, Feed/Nip= 7.5 mm, Head: 8, Noil extraction: 18%, Lap weight: 1200 grains/yd and efficiency: 85%.

Answer:

Nips/min = 350

                                        7.5
Feed/Nip = 7.5 mm = ---------------- yd = 0.0082 yd (36"=1 yard, 2.54 cm=1", 10 mm=1 cm).
                                 2.54∗10∗36

                                                 1200
Lap weight = 1200 grains/yd = -------------- lb/yd = 0.17 lb/yd (1 lb=7000 grains)
                                                 7000

Head = 8
Noil extraction = 18%
Efficiency = 85% = 0.85

Production/day/chamber =?
                                                Nips      Feed                               (100−noil)
Production = Feed lap weight * ---------- * ---------- * No. of head*time * ------------ efficiency%
                                                 min        Nip                                    100
= 0.17*350*0.0082*8*60*24*0.82*0.85
≈ 3917 lb/day
≈ 1777 Kg/day
≈ 1.777 ton/day

Spin plan

16. Problem: Per day required production of a spinning mill is 30 ton of 32 Ne carded yarn, make a spin plan.

Solution:

1 ton =1000 Kg

30 ton = 30*1000 = 30,000 Kg

Machine required:

1. Blow room, 2. Carding, 3. Draw Frame-I, 4. Draw Frame-II, 5. Roving Frame/ Flyer Frame/ Simplex, 6. Ring Frame, 7. Auto Coner.

No. of Automatic Cone Winding machine:

Winding speed (delivery speed) = 1500-2000 m/min
No. of head (Drum) = 60
Efficiency = 85-95%
No. of winding machine =?
Yarn count = 32 Ne
Time = 1 Day = 24 hours

                                                                              1500∗1.09∗60∗60∗24∗0.85∗1
Production of automatic cone winding machine = ------------------------------------------- (1m=1.09 yards)
                                                                                        32∗840∗2.204
= 2026.8 Kg/day/m/c

No. of Auto Coner required = 30,000/2026.8 = 14.8 ≈15

No. of Ring Frame Required:

Spindle speed = 15000-25000 rpm
No. of spindle = 480-1000
TM = 3.5-4.8
Count = 32Ne
Efficiency = 85-95%
Wastage = 0.5-1.5%

So, the production of Ring Frame should be = 30,000+30,000*1.5%
= 30,450 Kg

                            Spindle RPM
Delivery speed = ----------------------
                                 TPI

   Spindle RPM
= -----------------------------
    TM √Count

   15,000
= -------------------
   4.2√32

= 631.35 inch/min

                     631.35∗60∗24∗1∗1000∗0.9
Production = ------------------------------------------
                          32∗840∗36∗2.204

= 383.7 Kg/day

No. of Ring Frame required = 30450/383.7
= 79.4 ≈ 80

No. of Simplex Machine Required:

Spindle speed = 900-1200 rpm
No. of spindle = 120
Roving count = 0.7-2 hank
TM = 0.9-1.3
Efficiency = 85-90%
Waste = 0.5%

Required production = 30,450+30,450*0.5%
= 30,602 Kg/day

                            Spindle speed
Delivery speed = ------------------------
                                 TPI
    Spindle speed
= -----------------------------
    TM √Count

      1200
= -------------------
    1.1√1.2

= 995.85 inch/min

                                            995.85∗1∗0.85∗60∗24∗120
Production/day/machine = ------------------------------------------------
                                                  840∗36∗1.2∗2.204
= 1836 Kg/day

No. of Simplex required = 30602/1836 ≈ 17

No. of Draw Frame-I & Draw Frame-II required:

Delivery speed = 600-800 m/min
Sliver hank = 0.12-0.2 hank
Efficiency = 90-95%
Waste = 0.5%
Time= 1 day= 24 hours

Required production of Draw Frame-I = 30602+30602*0.5%
= 30755 Kg/day

                                  700∗1.09∗60∗24∗0.95
Production/day/m/c = ----------------------------------------
                                    0.16∗840∗2.204
= 3524 Kg/day

No. of Draw Frame-I = 30,755/3524
= 8.7 ≈ 9

Similarly, no. of Draw Frame-II

≈ 9

No. of Carding Machine Required:

Production/Carding m/c = 30-70 Kg/hr
Waste = 4-5%

Required Carding machine = 30,755+30755*4%
= 31985 Kg/day

Carding machine production/day = 60*24 = 1440 Kg/day

No. of Carding machine required = 31985/1440
≈ 22

No. of Blow Room Line Required:

Production = 800 Kg/hr
Waste = (3-5) %

Required Blow room production = 31985 + 31985*3%
= 32945 Kg/day

Per day production/Blow room line = 800*24 Kg/day = 19200 Kg/day

No. of Blow room line required = 32945/19200 ≈ 2

So the calculated spin plan for the 30 ton/day production of 32 Ne carded yarn is:

Blow room line = 2
Carding machine = 22
Draw Frame-I = 9
Draw Frame-II = 9
Simplex = 17
Ring Frame = 80
Auto Coner = 15

References: