Textile calculations

all calculations for textile technology students

1. 10/27/13 TEXTILE CALCULATIONS
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TEXTILE CALCULATIONS

FIBRE FINENESS, YARN COUNTS AND CONVERSIONS
Micronaire Value (Cotton) : The unit is micrograms per inch. The average weight of one inch
length of fibre, expressed in micrograms(0.000001 gram).

Denier (Man-Made Fibres) : Weight in grams per 9000 meters of fibre.
Micron (Wool) : Fineness is expressed as fibre diameter in microns(0.001mm)
Conversions:
· Denier = 0.354 x Micronaire value
· Micronaire value = 2.824 x Denier
YARN COUNTS
It is broadly classified into;
1. DIRECT SYSTEM
2. INDIRECT SYSTEM
INDIRECT SYSTEM
· English count (Ne)
· French count(Nf)
· Metric count(Nm)
· Worsted count
Metric system: Metric count(Nm) indicates the number of 1 kilometer(1000 meter) lengths per
Kg.
Nm = length in Km / weight in kg (or)
Nm = length meter / weight in grams
DIRECT SYSTEM
· Tex count
· Denier

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CONVERSION TABLE FOR YARN COUNTS
Tex Den Nm Grains/yd
Tex den/9 1000/Nm gr.yd x 70.86
Ne 590.54/tex 5314.9/den Nm x .5905 8.33 / gr/yd
Den tex x 9 9000/Nm gr/yd x 637.7
Nm 1000/tex 9000/den 14.1 / gr/yd
Grains/yd tex / 70.86 den / 637.7 14.1/Nm
Where, Nm – metric count, Nec – cotton count
CONVERSION TABLE FOR WEIGHTS
Ounce Grains Grams KilogramsPounds
Ounce 437.5 grains28.350 grams
Grains
0.03527
ounces
0.0648 grams
Grams 0.03527 grains15.432 grains 0.001 kgs
Kilograms 35.274 ounces15432 grains1000 grams
2.2046
pounds
Pounds 16.0 ounces 7000 grains453.59 grams0.4536 kgs
CONVERSION TABLE FOR LINEAR MEASURES
Yard Feet Inches Centimeter Meter
Yard 3 feet 36 inches 91.44 cms
0.9144
meter
Feet 0.3333 yards 12 inches 30.48 cms
0.3048
meter
Inches 0.0278 yards0.0833 feet 2.54 cms
0.254
meter
Centimeter 0.0109 yards0.0328 feet0.3937 inches 0.01meter
Meter 1.0936 yards3.281 feet39.37 inches 100 cms
CALCULATIONS
Grams per meter = 0.5905 / Ne
Grams per yard = 0.54 / Ne
Tex = den x .11 = 1000/Nm = Mic/25.4
Ne = Nm/1.693
DRAFT = (feed weight in g/m) / (delivery weight in g/m)
DRAFT = Tex (feed) / Tex(delivery)
DRAFT = delivery roll surface speed / feed roll surface speed
No of hanks delivered by m/c = (Length delivered in m/min) / 1.605

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BLOW ROOM

% trash in cotton - % trash in lap
(1) Blow-room Cleaning Efficiency% (CE) = -------------------------------------------
% trash in cotton

(2) Lint in waste (%) = 100 - CE

CARDING
(1) P =( L x 1.0936 x 60 x Effy ) / (Hank (Ne) x 36 x 840 x 2.2045)
P - production in kgs / hr
L - delivery speed in m/min
effy- efficiency
Ne - English count ( number of 840 yards in one pound)
840 - constant
2.2045- to convert from lbs to kilograms
(2) Production In Kgs / Hr = (L x Ktex x 60 x Effy) / ( 1000)
L - delivery speed in m/min
Ktex- sliver count in Ktex (kilotex)
effy - efficiency
1000- to convert to kilograms from grams
(3) Production In Kgs / 8 Hrs = (0.2836 x L x Effy) / (Ne)
L - delivery speed in m/min
effy - efficiency
Ne - English count

(4) Prodn / 8 Hrs = (Hank x Nd) /( Ne x 2.2045)
Hank = no of hank (840 yards)delivered by the machine
Nd = no of deliveries
Ne = hank of the material
(5) Total Draft in Card = (Feed Weight in g/m) / (Sliver Weight in g/m)

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Wt. per yard of lap fed
(6) Actual draft = ------------------------------------------------
Wt. per yard of card sliver delivered


Length of card sliver delivered
(7) Mechanical draft = ----------------------------------------
Length of lap fed

or

Draft constant of card machine
= ------------------------------------------
Draft change pinion

(8) Actual draft is always greater than the mechanical draft in carding because it is the
carding waste% that increases the actual draft.

DRAWFRAME
(1) Break Draft = Surface Speed of 2nd Roller / Surface Speed of Back Roller
(2) Main Draft = Surface Speed of 1st Roller / Surface Speed of 2
nd
(Middle)
Roller
(3) Total Draft = Surface speed of delivery roller / surface of feed roller
(4) Production In Kgs / 8 Hrs = (0.2836 x L x Effy x Nd) / (Ne)
L - delivery speed in m/min
effy - efficiency
Ne - english count
Nd - No of delvieries
(5) Prodn In Kgs / Hr = (FRD x Fr. rpm x 3.14 x 60 x Effy x Nd) / (Ne x 840 x 36 x
2.2045)
FRD - front roller dia in inches
FRrpm - front roller rpm
effy - efficiency
Ne - Sliver hank
Nd - number of deliveries
SPEEDFRAME + RINGFRAME
(1) Twist / Inch (TPI) = Spindle Speed / FRS
FRS - front roller surface speed in inches/min

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(2) FRS = Fr. rpm x 3.14 x FRD
FRS - Front roller surface speed
FRD - front roller diameter
(3) T.P.I = T.M. x Sqrt (Count or Hank)
T.M. - Twist multiplier
sqrt - square root

(4) Prodn in Kgs / 8 Hrs = (7.2 x SS x Effy) / (TPI x Ne x 1000)
SS - spindle speed
(5) Spindle Speed = M/Min x TPI x 39.37
(6) Hank Delivered = Spindle Speed / ( Tpi x 62.89)

Single yarn strength (gm)
(7) RKM = -----------------------------------
Tex number of yarn

(8) Ring bobbin content = 3.1 LD
2
(L = Lift in inch, D = ring dia in inch)

(9) Doubling bobbin content = 3.7 LD
2


Actual count x (1 + Present regain)
(10) Corrected count = ------------------------------------------------
1 + Standard regain

Weight per yard of roving fed
(11) Actual draft of ring frame = -----------------------------------------------------------
Weight per yard of yarn delivered on bobbin

Surface speed of front roller
(12) Mechanical draft of ring frame = --------------------------------------
Surface speed of back roller

Draft constant
= --------------------------
Draft change pinion

(13) Twist contraction % = It is basically the percent shortening in length of
yarn between the front roller and the bobbin. The length at the
front roll is taken as 100%. For example 5% twist contraction
means, the yarn length on the bobbin is 95% of the length at the

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front roll.

Yarn count at front roll - yarn count at bobbin
(14) TC% = ------------------------------------------------------------ x 100
Yarn count at front roll

(15) Example of twist contraction given yarn;

Count on bobbin = 10
s

Twist contraction = 5%

10 x 1.00
Yarn count at front roll = -------------- = 10.53
s
95%

(16) Mechanical draft is always greater than actual draft in ring spinning?

It is necessary to draft the roving to a finer yarn count at front roll that what is to be
bobbin. Because due to twist contraction of yarn, the count of yarn on bobbin becomes
coarser than the count of yarn at front roller.

Twist per inch (TPI)
(17) Twist multiplier or Twist factor = ----------------------------
Ö Count (Ne)




(18) TPI = Twist multiplier x ÖCount (Ne)

or

Twist constant of ring frame
(19) TPI = -------------------------------------
Twist change pinion

(20) Turns per metre (TPM) = Twist factor ÖNm

(21) TPI = TPM x 0.0254

(22) Ring Traveller Speed
Ring Traveller Speed in m/Sec= (Spindle Speed x Ring Dia in mm x 3.14)/
(60 x 1000)

Actual ring traveler speed ?

Assume, spindle speed = 9,000 rpm
Ring Diameter = 57 mm

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Front roll delivery = 64 metre/min.
Package circumference = 102 mm (avg)

Front roll delivery (m/min) x 1000
Traveller lag (rpm) = Spindle speed - ——————————————
Package circumference (mm)

14x1000
= 900 - ———— = 8363 rpm
102


Traveller lag 900 – 8863 = 137 rpm


Uncorrected traveller speed (m/sec.) :

Spindle speed x Ring diameter (mm) x p
= ——————————————————
1000 x 60

9000 x 57 x 3.142
= ——--—————— = 26.8 m/sec.
1000 x 60



Corrected Traveller speed (m/sec.) :

Ring dia (mm) xp x Trav. Lag (rpm)
Traveller speed (m/sec) – —————————————————
60 x 1000

57x 3.142 x 137
= 26.8 - ———————— = 26.39 m/sec.
60 x 1000


(23) Weights of ring travellers No. 1 and 1/0.

For No. 1 = 90 grains / 100 travellers

For No.1/0 = 80 grains/100 travellers

WINDING
1. Slub catcher settings :

a. Fixed Blade = Carded - (2.0 to 2.5) x diameter
Combed - (1.5 to 2.0) x diameter

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b. Electronic yarn clearer = 3 cm x 3 diameter

Diameter in inch = 1/( 28 x Öcount )
for Blended yarn
= 10 to 15% more settings

2. Yarn clearer efficiency = Number of
objectionable thick faults removed by slub catcher
= x 100
Total objectionable thick faults present in yarn before winding

Total breaks during winding (at faults)
3. Knot factor =
No. of breaks due to objectionable yarn faults

Strength of spliced joint x 100
4. Retained splice strength =
Strength of parent yarn

5. Winding Tension = 0.1 x Single yarn strength in grams


4500 x Y
6. Expected efficiency E =
S x N (12 + 98)

7. Winder’s workload (0.17 min/operation on conventional winding m/c = 2300 operations
per shift of 8 hours

where,
1 creeling or 1 piecing = 1 operation
1 doffing = 2 operations

8. Winder’s workload on autoconer (0.08 min per operation) = 4800 operations/shift of 8
hours

where,
1 bobbing feeding = 1 operation
1 doffing (manual) = 4.5 operation


Y = Length/Bobbin (metres)
B = Breaks per bobbin
S = Winding speed (metres/min)
C = English count

(9) Production in Kgs / 8 Hrs = (0.2836 x L x Effy x Nd) / (Ne)

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L - delivery speed in m/min
effy - efficiency
Ne - english count
Nd - No of delvieries
(10) P =( L x 1.0936 x 60 x Effy ) / (Hank (Ne) x 36 x 840 x 2.2045)
P - production in kgs / hr
L - delivery speed in m/min
effy- efficiency
Ne - English count ( number of 840 yards in one pound)
840 - constant
2.2045- to convert from lbs to kilograms


WARPING

R x 100
1. Machine Efficiency E =
R + S
R = Uninterrupted running time for 1,000 meters (in sec)

1000 x 60
=
Machine speed in mtr/min.
S = Total of time in seconds for which the machine is stopped for a production of
1,000 meters

B X N X T1 T2 T3
= R + --------------- + ----- + ---------- + T4
400 L L x C

B = Ends breaks/400 ends/1,000 meters
N = Number of ends
L = Set length in 1,000 meters
C = Beams per creel

Timing of activities in seconds are :

T1 = To mend a break
T2 = To change a beam
T3 = To change a creel
T4 = Miscellaneous Time loss/1,000 mtrs.

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2. Production in metres per 8 hrs. (K) = 480 x mtrs/min x E/100 kgs.

3. Production in Kgs. per 8 hrs. = (K x N)/(1693 x English Count)

4. Warping Tension = 0.03 to 0.05 x Single thread strength


SIZING

Length in metre x 1.094 x Total ends
1. Warp weight = x 100
(in kg.) 840 x 2.204 x Warp count


Sized warp weight - Unsized warp weight
2. Size pick-up = x 100
%age Un-sized warp weight

3. Weight of size = Warp Weight x Size pick up %

Sized warp length - Unsized warp length
4. Stretch %age = x 100
Un-sized warp length

Total-ends x Warp length in yards
5. Sized yarn =
count Sized warp weight (lbs) x 840

Wt. of sized yarn - Wt. of oven dried yarn
6. %age Moisture= x 100
content Wt. of sized yarn

Deliver counter reading - Feed counter reading
7. %age Stretch = x
100 Feed counter reading

840,000 x D x C
8. %age Droppings = x 100
on loom 454 Y x N x P

D = Dropping in gms. C = English Count
Y = Length woven (yds.) N = Number of Ends
P = % size add on

9. Invisible Loss% =

Amount of size material issued - Amount of size added on yarn
= x 100
Amount of size issued

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Steam, Consumption (Sizing M/c) = 2.0 kg/kg of sized yarn

(Cooker) = 0.3 kg/kg of liquor

(Sow box) = 0.2 kg/kg of yarn

No. of Cylinder x 1,000 x English count
10. Max. Speed of machine =
(metres/min) Number of ends

Number of ends x 0.6
11. Wt. of warp in gms/mtr =
English count

WEAVING

1. Reed Count :

It is calculated in stock port system.

EPI
Reed width =
1 + Weft crimp %age

No. of dents in 2 inches is called Reed Count

2. Reed Width :

100 + Weft crimp %age
Reed width = Cloth width x
100
3. Crimp %age :

Warp length - Cloth length
Warp Crimp %age = x 100
Cloth length

Weft length - Cloth length
Weft Crimp %age = x 100
Cloth length

EPI
4. Warp cover factor =
ÖWarp Count
PPI
5. Weft cover factor =
ÖWeft count

Wp.C.F. x Wt. C.F.
6. Cloth cover factor = Wp.C.F. + Wt.C.F. -

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28

7. Maximum EPI for particular count :

a. For plain fabrics = 14 x ÖCount

b. For drill fabrics = ÖCount x 28 x 4/6

c. For satin fabric = ÖCount x 28 x 5/7

Ends/repeat x 1 / yarn diameter
d. Other design =
No. of intersections / repeat + ends/repeat

1
8. Yarn diameter =
28 x ÖCount

Weave Density

1. Warp density = Ends/cm x ÖTex x K
= < 250

2. Filling density = Picks/cm x ÖTex x K
= < 350

(Warp density - 100) x F.D.- 100
3. Weave Density = 50 +
(Weft density - 100) x F.D.- 100

4. Effective weave density = W.D. x K of loom width x K of Design = < 72




To change the count and number of thread/inch, keeping the same denseness of the
fabric :

1. To change the EPI without altering the denseness :

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EPI in given cloth x Ö Warp count in expected cloth
EPI in Exp.Cloth =
Ö Warp count in given cloth
2. To change the count without altering the denseness :

EPI in exp. cloth
2

EPI in exp. cloth = x Count in given cloth
EPI in given cloth

Warp requirement to weave a cloth :

Total ends x 1.0936 x 453.59 x crimp%
1. Warp weight in gms/mtrs. = x
Waste 840 x Count %age



2. Weft weight in gms/mtrs. =
R.S. in inches x 453.59 x PPI
= x Crimp %age x Waste %age
840 x Count

Weft wt. in kgs. x Weft count x 1848 x 0.9144
3. Cloth length in mtrs.with =
the given weft weight PPI x R.S. in inches


For Silk and Polyester :


1. Warp weight in gms/mtrs. =


Total ends x Count (Denier)
= x Crimp% x Waste %age
9000
2. Weft weight in gms/mtrs. =
RS in inches x PPI x Count (Denier)
= x Crimp% x Waste %age
9000

Allowance for count in Bleached and Dyed Fabric :

¨ Count becomes 4%

¨ Finer Dyed counts become max.6% Coarser

FABRIC PRODUCTION

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Motor pulley diameter
1. Loom speed = Motor RPM x
Loom pulley diameter


Actual production
2. Loom Efficiency %age = ----------------------------- x 100
Calculated production

Yarn weight - Dryed yarn weight
3. Moisture Regain %age = --------------------------------------------- x 100
Dryed yarn weight


Yarn weight - dried yarn weight
4. Moisture Content %age = -------------------------------------------- x 100
Yarn weight

Total ends x Tape length in metre
5. Warp weight in Kg. = ----------------------------------------------
1693.6 x Warp count

RS in centimetres x Coth length in metres x PPI
6. Weft weight in Kg. = ----------------------------------------------------------------
4301.14 x Weft count

EPI PPI
7. Cloth weight in GSM = ----------------- + ----------------- x 25.6
Warp count Weft count

GSM (Grams per sq. metre)
8. Oz (Ounce) per sq.yard = -------------------------------------
34

Material measurement :

For calculating of length of any rolled fabrics :

0.0655 (D - d) (D + d)
L = -------------------------------
t
Where,
L = Length of material (feet)
t = Thickness of fabrics (inches)
D = Outside diameter (inches)
d = Inside diameter (inches)


Weight of yarn in a cloth :

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The weight of cloth manufactured on loom depends upon the weight of yarns in the warp and
weft : ends/inch, picks/inch and the weight of size on the warp.

Therefore, Cloth weight = Weight of warp + Weight of weft + Weight of size (All in lbs.)

Total No. of Ends x Tape length in yds.
Where as Weight of warp in lbs = ----------------------------------------------------
840 x Warp yarn count




Also Weight of weft in lbs. =

Length of cloth (yds) x Picks/inch in cloth x Reed width (inch)
= -----------------------------------------------------------------------------------
840 x Weft yarn count