TEXTILE CALCULATION & EQUATION

Name : MAZADUL HASAN SHESHIRID: 2010000400008Batch: 13th Batch (Session 2009-2013)Department: Wet Processing Technology Email: mazadulhasan@yahoo.comBlog: www. Textilelab.blogspot.com Southeast UniversityDepartment of Textile Engineering

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SpinningCalculation and Equation

Basic Conversions (Spinning)

No Length Weight Time

1. 1 in = 2.54 cm 1 lb = 7000 gr 1 min = 60 sec

2. 1 yd = 36 in 1 lb = 16 oz 1 hr = 60 min

3. 1 m = 1.0936 yd 1 oz = 437.5 gr 1 shift = 8 hr

4. 1 Hk = 840 yd 1 kg = 2.2046 lb 1 day = 24 hr

5. 1 Hk = 7 leas 1 bag = 100 lb 1 day = 3 shifts

Count Conversion Table (Spinning)

Ne Nm Tex Grex Denier

Ne= 1 xNe 0.5905 xNm 590.5 /Tex 5905 /Grex 5315 /Den

Nm= 1.693xNe 1 xNm 1000 /Tex 10,000/Grex 9000 /Den

Tex= 590.5 /Ne 1000 /Nm 1 xTex 0.1 xGrex 0.111 xDen

Grex= 5905 /Ne 10,000 /Nm 10 xTex 1 xGrex 1.111 xDen

Denier= 5315 /Ne 9000 /Nm 9 xTex 0.9 xGrex 1 xDen

Draft & TPI Formulas

Efficiency Percentage (Spinning)

Cleaning Efficiency (%)

Efficiency (%)

Twists per inch

PRODUCTION CALCULATION FORMULAS

PRODUCTION FORMULAS

Yarn Count in Direct system

System

Unit weight Unit length Uses

Tex Grams 1,000m PolyesterDenier Grams 9,000m LycraD-Tex Grams 10,000m LycraPounds/Spyndle Pounds 14400yds Jute

Yarn Count in Indirect system

System Unit weight Unit length Uses

English (Ne) 1 lb 840 yds Cotton yarn

Metric (Nm) 1 kg 1 km Cotton yarn

Worsted 1 lb 560 yds Worsted yarn

Woolen 1 lb 256 yds Woolen yarn

•

Excellence of fiber quality by combing:

Fabric (Knitting & Weaving)Calculation and Equation

SIZING

Calculation:

Required Chemical &no. of Mixing of Sizing Recipe:

Production is calculated in accordance with the following equation-

Production calculation:

1. Production = no. of needle x no of feeder x RPM x stitch length/ yarn countProduction per shift in KG at 100% efficiency

Where,Ks = knitting constantCount = linear density of yarnGSM = gm per square meter

Another formulae is : Stitch length = (Tex × Ks) / GSM

Ks is a constant. Its value is different for different fabric structure and fabric type. Ks is calculated and estimated as below:

Ks = (GSM x Stitch length) / Tex

Production calculation:

Fabric type Color Value of Ks

Single jersey Average 19.55

Single lacoste Average 22.4

Double lacoste Average 22.75

Polo pique Average 25

Plain interlock Average 39.3

1 X 1 rib Light 24.5

1 X 1 rib Average 26.5

Ks = (GSM x Stitch length) / Tex

Relation between yarn count and m/c gauge seen in different m/c.:

GSM Calculation

DIFFERENT FABRIC GSM AND THEIR REQUIRED YARN COUNT

S/J without lycra -Fabric G.S.M Yarn Count

110 - 120 40 S – 36 S120 - 130 36 S - 32 S130 - 140 32 S – 28 S140 - 150 28 S150 - 160 26 S170 - 210 24 S

Rib without lycra -Fabric G.S.M Yarn Count

180 - 190 36 S - 32 S190 - 200 30 S200 - 215 28 S215 - 230 26 S230 - 250 24 S250 - 300 24 S

Interlock without lycra -

Fabric G.S.M Yarn Count200 - 220 34 S220 - 230 32 S230 - 250 30 S250 - 300 26 S

Lacoste without lycra -Fabric G.S.M Yarn Count

180 - 190 30 S190 - 210 28 S210 - 230 26 S230 – 250 26 S

40D Lycra Rib -Fabric G.S.M Yarn Count

230 - 240 32 S240 - 250 30 S250 - 280 26 S280 - 300 24 S

40D Lycra S/J –Fabric G.S.M Yarn Count

180 - 190 34 S190 - 210 32 S210 - 220 30 S220 – 240 28 S240 - 250 26 S

DIFFERENT FABRIC GSM AND THEIR REQUIRED YARN COUNT

Yarn DyeingCalculation and Equation

Production Calculation of Yarn singeing machine:

Length = Count * Weight = Count * Weight * 840 yards = (Count * Weight * 840) / rpm yards per minute = (Count * Weight * 840) / rpm * 60 * 8 * 3 yards per day = (Count * Weight * 840) / rpm * 60 * 8 * 3 * 0.914 =……X…meter/day.

Production Calculation of reeling machine:

Production Calculation of hank to cone winding machine:

Machine Parameter Yarn quality Speed (rpm)58/2, 60/2 450

All single count 500 to 550

Length = Count Weight = Count * Weight 840 yards = (Count Weight 840) / rpm yards per minute = (Count Weight 840) / rpm 60 8 3 yards per day = (Count Weight 840) / rpm 60 8 3 0.914 =……X…meter/day.

GSM Calculation:WPI = 32CPI = 45Stitch length = 3 mmYarn Count = 20’S Ne

No. of Needle = π × Machine Diameter (D) × Machine Gauge (N) = 3.1416 × 30 × 24 = 2262Yarn Count = 30/1 Ne No. of Feeder = 96Machine RPM = 28Stitch length = 3 mmEfficiency = 85% = 0.85Shift = 8 hr. = 8 × 60 = 480 min

Production Calculation Of Yarn Dyeing Machine :

Production of the machine is 146.407 Kg/Shift.

Note: If any parameter in this calculation is changed then production capacity per shift will be changed.

Package Density Calculation (Yarn Dyeing):

Formula

Density Calculation for Several Counts (Yarn dyeing):

1**Before Pressing• Yarn Quality: 30/1 cc• Package Height (H) = 162mm = 16.2cm• Total Package Dia (D1) = 162mm = 16.2cm• Total Package Weight (W1) = 1.38kg = 1380gm• Spring Weight (W2) = 0.185kg = 185gm• Spring Dia (D2) = 65 mm = 6.5cm

2 **After Pressing Yarn Quality: 30/1 ccPackage Height (H) = 145mm = 14.5cmTotal Package Dia (D1) = 165mm = 16.5cmTotal Package Weight (W1) = 1.38kg = 1380gmSpring Weight (W2) = 0.185kg = 185gmSpring Dia (D2) = 65 mm = 6.5cm

**So we can sure that after pressing for every count, yarn package density will be increase.

Density Calculation for Several Counts (Yarn dyeing):

Length Calculation in Package:

To maintain the constant package density same length of yarn should be wound to all the packages of a batch or lot. The dyeing machine capacity is calculated on weight, so it is necessary to maintain the uniform weight throughout the packages. To do this for a definite count of yarn following calculation is followed,

In this machine length is pre selected. For different count of yarn different length of yarn is pre selected. This is due to maintain the constant package weight and package density.

Package density Calculation

We know package density ρ =mass (m)/volume (v) gm/ccVolume= π (R2-r 2) h

R= outer radius of packageR= inner radius of packageh= height of package

Now we consider a sample of 40/1 cotton yarn whoseR=4.138r= 1.59h=15.24Mass m=1000gm

So package density ρ=1000/π (4.1382-1.592)15.24 gm/cc =1.433 gm/cc

Production calculation:We know production= speed (m/min) ×60×24 ×1.09/(840×40×2.2045) Kg/day/head When speed is 800m/min at 80% efficiency Production=800×60×24×1.09/ (840×40×2.2045)kg/day/head =10.5976kg/day/head Total production=10.5976×54×12kg/day =6867.2448kg/day

Production calculation of RF Dryer :

Length of RF Dryer = 13m

At 28rpm it takes 21 min 9 sec to pass this length

Along this length it can accommodate 416 package 416kgs

So at 21 min9sec or 1269sec it can dry 416kgs

So in 1hr or 3600sec it can dry = 416×3600/1269 kg/hr = 1180.14 kg/hr

So Production per day = 1180.14×24kg = 22658.688 kg = 22.66 tons

Production calculation of RF Dryer

Knit DyeingCalculation and Equation

Calculations related to batch section:

Now, when a gram per linear meter is low then meters per chamber will be more. Thus, fabric loading should be reduced to avoid jamming in the winch. In this case 80-85% fabric

loading is given. But when gram per linear meter is more then rope length will reduce and in this case up to 90% fabric loading can be given.

Calculating the chamber loading

In the following table are listed general recommendations covering rope cycle times and speeds for a wide range of fabrics:

Fabric Rope cycle times in minutes

(Cycle Time)

Rope circulation speed m/min

(Reel speed)

Knit fabric

PES unfixed 1 250PES heat set 1-1.5 200

PC 1-2 250Co - reactive 2-3 225-275

Preparation and storage of stock dyes and chemicals Available stock solution:

1. Red-0.1%, 0.5%, 1%, 2% 2. Yellow-0.1%, 0.5%, 1.0%, 2.0%, 3. Blue- 0.1%, 0.5%, 1.0%, 2.0%.

Preparation: To prepare 0.1% stock solution, it necessary to mix 0.1 gm dye with 100cc water. To prepare 0.5% stock solution, it necessary to mix 0.5 gm dye with 100cc water. To prepare 1.0% & 2.0% stock solution similar procedure is followed. To prepare 10% stock solution of soda ash, it necessary to mix 10 gm soda with

100cc water.

SHADE % STOCK SOLUTION %

0.0001-0.009 0.1

0.10-0.99 0.5

1-1.99 1

2-3.99 2

4 ( or above) 4

Stock solution preparation:

Stock Solution Making Procedure (Dyeing lab)

For solid, X gm chemicals/dyes/auxiliaries in the 100 ml water is called x%

stock solution.For liquid,

X ml/cc chemicals/dyes/auxiliaries in the (100 - x ml/cc) water is called x% stock solution.

Conversion formula from percentage to g/l is asg/l = Required amount (%)× 10

Recipe Calculation

Dyes and chemicals measuring formula for laboratory:

The amount of dye solution (ml) is calculated as follow –

The amount of chemical soln (ml) is measured as follow –

Fabric Type GSM Pump Speed % Reel Speed(MPM)Single Jersey Up to 140 80 250

140 – 180 85 230180 – above 90 210

Polo Pique, Back Pique

& Bubble Knit

Up to 160 85 280160 – 200 90 260220 – above 90 240

Interlock Up to 180 85 260180 – 220 90 240220 – above 90 220

Machine Setup On The Basis Of Fabric Type & GSM

MONTHLY EFFICIENCY OF KNITTING FLOOR:

Daily production – 6500 kgs. Approx.

Daily production capacity – 10000 kgs approx.

So, monthly production – 6500 x 30 kgs.

Monthly production capacity – 10000 x 30 kgs. So, Monthly production efficiency = (6500x30x100)/ (10000x30) % = 65%

GarmentsCalculation and Equation

COSTING OF THE PRODUCT:

Let

price of yarn is $ 3.00/ kg.

Process loss of yarn for knitting (10%) = $0.30

Knitting fabric cost = $3.30

Cost of dyes & chemicals = $2.50

Process loss for dyeing (12%) = $0.30

Dyed fabric cost = $ 6.10

Packing cost = $0.05

Production cost of fabric=$6.15

Fabric price (with 25% margin) =$7.79

Fabric consumption/ doz. = (Body length + Sleeve length +10) x Chest length x 2 x GSM x12 /10000000

Garments specification: Body length=78 cm Sleeve length=33 cm

Chest length=62 cmGSM=210

Fabric consumption/ doz. = {(78+33) x62x2x210x12}/ 10000000= 3.469 kg

Fabric consumption/doze (with 10% wastage) = 3.816 kg

Body fabric cost / doz. =$(7.79x 3.816)= $29.73

Cost of collar& cuff/doz = $ 4.00Cost of Trims=$ 2.25Cost of Trims (with 5% Process loss) = $2.36Production Cost of Garments/ doz=$36.09Garments Price/doz (with 25% Profit) =$45.12

COSTING OF THE PRODUCT:

Costing of Men’s shirt

Fabric consumption for a dozen of shirt π × L size of basic shirt.═Width of body of shirt 1/2 chest═ ═ 24"+1"(sewing allowance) ═ 25"Body length 32"+1"(sewing allowance)═

═ 33"Sleeve length 23"+2.5(cost) +1.5"(sewing allowance)═

═ 27"

Consumption of a body shirt:═{1/2 chest× (body length) ×2} / 36× fabric width. (Sq. inch)

═25"×33"×2 (Sq. inch ). {Let assume fabric width 25"effective width 25"−1" 24"}═ ═Fabric length 25×33×2 / 44 inch═

Fabric consumption 25×33×2 / 44×36 yds═Consumption of sleeve (length of sleeve × width sleeve) ×2 sq. inch═ ═27"×24"×2" (Sq. inch)

Fabric consumption in length width ═ 27×24×2 / 44×36 sq. inch

Total fabric consumption of one dozen shirt ═ [(25×33×2 / 44×36 + / 27×24×2 / 44×36) ×2+ wastage of 8%] ═ 22.75 yds + 8% wastage

═24.6 yds

Sewing threads consumption:It is calculated by measuring the total of different kind of seam. Normally sewing

threads consumption per shirt , 120m.So, sewing threads consumption per dozen,

═ 120 × 12 ═ 1440m

Costing of Men’s shirt

Costing of T- shirt

Fabric Type :Single jerseyG.S.M :180Yarn count :24/1Measurement of Garments:Body length : 54 cmChest length : 43 cmSleeve length : 15 cmFabric Consumption = {(Body length + sleeve length + allowance) *(Chest length + 3)} * 2 /10,000 * G.S.M / 1000 * 12 * 10 % (+)

= {( 54 + 15 + 10 ) * ( 43 + 3 )} * 2 / 10,000 * 180 / 1000 * 12 * 10% (+)=1.72 kg=1.72* 0.18 = 1.90 kg / doz. Costing

Fabrics cost : 17.10Cost of making : 4.5Print cost : 3.5Lab cost : 0.20Accessories cost : 2.5Washing cost : 1

Total = $ 28.80 / Doz. = $ 2.40 / pcs.

How can we get Fabric Consumption & Fabrics Price?Say:

** Body Length = 85, Chest Width = 52, Sleeve Length = 44 & G.S.M = 240

Fabric Description: 100 % Cotton S/J

Fabric Need = [(85+5+44+5) 52+5] 2 12 240/10000000+10%= [(90+49) 57] 2 12 240/10000000+10% = (13957) 2 12 240/10000000+10% = 7923 12 240/10000000+10% = 45636480/10000000 + 10%= 4.563648 +10%= 4.563648 + .4563= 5.02 Kgs Fabrics

Say Per Kgs Price: US$ 6.00/Kgs

Poly bag costing :Total Length X width X Thickness= 36cm X 28cm X 10mm= 10080/72000= 0.14pcs/lb

Fabrics Price:Total Fabric Need 5.00 Kg $ 6.00 = $ 30.00Trim/ Accessories (Minimum Charge) = $ 2.50Cutting & Making Charge (C.M) = $ 5.00Printing Charge (If any) = $ 0.00Embroidery Charge (If any) = $ 0.00Buying Commission (If necessary) 5% = $ 1.97

Final/Total = $ 39.47/12

Costing of a garment:Fabric cost + Accessories cost + Trimming cost + Production cost + Transport cost + Commission + Profit

Consumption of T-Shirt:

Equation: {(Body length + Sleeve length) Chest} 2 GSM 10000 1000 5000

Solution:Body Length = 50 + 6 (Allowance) = 56 cmSleeve Length = 15 + 3 (Allowance) = 18 cm Chest = 37 + 3 (Allowance) = 40 cmGSM = 180 cm

= {(56 + 18) 40} 2 180 10000 1000 5000= 532.8 kg.

Consumption of Collar:

Equation: {(Neck width + Front neck drop) collar depth} 2 GSM 10000 1000 5000

Solution:Neck width =22 2 = 44 cm Front neck drop =5 cm Collar depth =2.5 cm 2 = 5 cm GSM = 240

= {(44 + 5) 5} 2 140 10000 1000 5000= 58.8 kg.

Total = 532.8 + 58.8 kg = 591 kg

Collar & Cuff measurements

Size Collar measurement (cm) Cuff measurement (cm)

S 40 x 9 40 x 3.5

M 42 x 9 40 x 3.5

L 44 x 9 40 x 3.5

XL 46 x 9 40 x 3.5

XXL 48 x 9 44 x 3.5

XXXL 50 x 9 44 x 3.5

Consumption of bottom part:

Equation: Length*(width*4)*G.S.M÷10000÷1000*12

Length=53=8=2=63cmWidth= 18*4+6= 78cmG.S.M= 260Solution

[(63*78*260)÷10000÷1000*12=1.53kgs

Consumption of Pocket:

Equation: Length*width*G.S.M÷10000÷1000*12

Length=11+2=13cmWidth=10cmG.S.M= 260Solution

(13*10) *260÷10000÷1000*12=0.04056kg

Total= 1.53+0.04056 1.5705kg

Costing process:Finish fabric cost: (Yarn price + Knitting cost + dyeing cost)

Body fabric cost: (Total fabric consumption + Total yarn consumption)

Cost of making (CM):……………………………$Accessories cost:…………………………………..$Overhead cost………………………………………$Others cost:………………………………………….$Buyer commission:……………………………….$Total cost..................................................$

Costing process:

PRICE OF THE PRODUCT:Generally price of product is determined by the required profit adding to the total expenses. So,Price of products= (Direct expenses + Indirect expenses + Factory Overhead) + Required profit

MARKER EFFICIENCY: The marker planner measures his success by the efficiency of the marker plan. The following formula is used to measure the efficiency:

Marker efficiency=Area of the pattern in the marker plan/ Total area of the marker plan X 100%.

MARKER EFFICIENCY:

STANDARD TIME = Normal time + Allowances = Normal time + (Normal time ×Allowances)

= NT (1+ Allowances).In garments production world, the terms SMV or SAM used frequently. SMV stands for Standard Minute Value. SAM for Standard allocated minute or Standard Allowed Minute.

SMV CALCULATION:SMV calculation of a basic T-shirt from a time study sheet of a garments industry. Following formulas are use-

Normal time = (Average observed time) × (Performance rating factor).

SMV (Standard Minute Value) = Basic Time + (Allowances × Basic time). = Basic Time× (1+ Allowance).

Allowances are assumed for this calculation is 20%.

SMV

SMV

Target Production /Hour = (No Of worker -1) x 60 / SMV

SMV= standard Mean Value (the Time Required to Complete garments by sewing )

SMV=( Basic time +Allowance )

To select sewing thread, thread size or number is very important. The number which is used to express the fineness of a sewing thread is called sewing thread number or ticket number. It has 2 system as follows-

Cotton system : It is derived from English cotton system.

Cotton ticket number in Ne = ( Yarn count in Ne / Number of ply ) x 3

Metric system : It is derived from Metric count system.

Ticket number in Nm = ( Yarn count in Nm / Number of ply ) x 3

sewing thread number or ticket number

Equation For Find Yarn Count (If GSM is Known)

Single Jersey = 4300 /GSM

Pique = 5200 / GSM

Fleece = 7200 / GSM

Interlock = 7200 / GSM

1x1 rib = 6000 / GSM

Locoest =5500 / GSM

2x2 rib = 6250 / GSM

Terry = 6240 / GSM

Find out Required Yarn Count (If GSM is Known)

Equation :

S/j Ne = (0.141x GSM) + 50.22

Pique Ne = (0.146x GSM) + 57.16

Double Lacost Ne = (0.167 X GSM) + 64.36

1X1 Rib Ne = (0.123X GSM) + 54.57

Interlock = (0.206X GSM) + 80.56

Lycra 1X1 Rib = (0.119 X GSM) + 59.12

Lycra 2X2 Rib = (0.108X GSM) + 56.62

Conversion of (GSM Equation )

Kg To YardsEquation :

= GSM / 39.37 X 36 X fabric Width

=Result .Kg

=1000/ Result .yds

[It is converted Kg To yards ]

Per Yards Fabric price Equation :

= GSM / 43” X Width / 1000 X Per kg Prize

=Result .

[This the Equation define per yards Fabric price ]

Conversion of (GSM Equation )

Yards To meterEquation :

= Length X 36 X 2.54 /1000

=Result

[It is converted yards to Meter ]

Meter To YardsEquation :

= Length /36 / 2.54 X 1000

=Result

[ It is converted Meter To yards ]

Conversion of (GSM Equation )

Find Out How many Yds / KgEquation :

= 714//GSM

=Result (yds in Kg)

[Only For 58’’/60’’ Width]

Price/YardsEquation :

= GSM /43 / 2.54 X Width

=Result / 1000 X Price

= price/yds

Textile TestingCalculation and Equation

Four point grading systemSize of defects Penalty 3 inches or less 1 pointOver 3 inch but not over 6 inch 2 pointOver 6 inch but not over 9 inch 3 pointOver 9 inch 4 point

Four point grading system

Shrinkage Test:

Spirality test: