Woven Fabric Woven Fabric CalculationsCalculations

Dr. Jimmy LamDr. Jimmy Lam

Institute of Textiles & ClothingInstitute of Textiles & Clothing

AgendaAgenda

Calculations on weft consumptionCalculations on weft consumption Calculations on warp preparationCalculations on warp preparation Calculations on warp/weft crimp percentageCalculations on warp/weft crimp percentage Calculations on fabric weight (g/mCalculations on fabric weight (g/m2))

Weft consumption of a loomWeft consumption of a loomQuestionQuestion

A loom runs at 210 picks/min at an overall A loom runs at 210 picks/min at an overall efficiency 82%. The warp width in the reed is efficiency 82%. The warp width in the reed is 1.2m and the linear density of the weft is 30 tex. 1.2m and the linear density of the weft is 30 tex. What is the weft consumption per 8 hoursWhat is the weft consumption per 8 hours

AnswerAnswerWeft consumptionWeft consumption

A) Length of weft used per hour at 100% efficiencyA) Length of weft used per hour at 100% efficiency=1.2 X 210 X 60 /1000km =15.12km per hour=1.2 X 210 X 60 /1000km =15.12km per hour

B) At 82% efficiency, the length used in 8 hoursB) At 82% efficiency, the length used in 8 hours=15.12 X 0.82 X 8 =99.19km=15.12 X 0.82 X 8 =99.19km

C) Weft consumption, for 30 tex yarn is:C) Weft consumption, for 30 tex yarn is:=30 X 99.19 /1000kg =29.76 kg per 8 hours=30 X 99.19 /1000kg =29.76 kg per 8 hours

Warp PreparationWarp PreparationQuestionQuestion

An order for 220 pieces of woven fabric, each An order for 220 pieces of woven fabric, each 110m in length and 1.2m in wide, is received. 110m in length and 1.2m in wide, is received. In the finished fabric, the warp crimp is 9% and In the finished fabric, the warp crimp is 9% and there are 38 ends/cm. The creel of the direct there are 38 ends/cm. The creel of the direct warping process has a maximum capacity of warping process has a maximum capacity of 500 cones.500 cones.– A) How many back beams are requiredA) How many back beams are required– B) What length of warp is on each?B) What length of warp is on each?

Warp PreparationWarp PreparationAnswerAnswer

A) Total number of ends:A) Total number of ends:– Ends/cm x finished width in cmEnds/cm x finished width in cm

– =38 x 120 =4560 ends=38 x 120 =4560 ends

– Since the creel can hold 500 cones, the number of ends per Since the creel can hold 500 cones, the number of ends per back beam could be 456, and 10 back beams should be usedback beam could be 456, and 10 back beams should be used

B) The total length of warp is given byB) The total length of warp is given by– Number of pieces X piece length X (100+crimp)/100Number of pieces X piece length X (100+crimp)/100

– =220X110X109/100 =26,378m=220X110X109/100 =26,378m

Crimp Percentage of Woven FabricCrimp Percentage of Woven Fabric

The crimp percentage is the difference between The crimp percentage is the difference between straightened thread length and the distance between straightened thread length and the distance between the ends of the thread in the fabric.the ends of the thread in the fabric.

Crimp % = (l-s)/s x 100Crimp % = (l-s)/s x 100 Measuring crimp practically is not always a simple Measuring crimp practically is not always a simple

procedure. The length of the crimped yarn may be procedure. The length of the crimped yarn may be easily measured, but to decide when the crimped easily measured, but to decide when the crimped yarn removed no longer retains crimp is not easy.yarn removed no longer retains crimp is not easy.

Example Example Crimp %Crimp %

Crimp % , (Formula 1)Crimp % , (Formula 1) C=(L-S)/S * 100%C=(L-S)/S * 100%

– Where L is warp length, S is cloth lengthWhere L is warp length, S is cloth length Warp Length (L), (Formula 2)Warp Length (L), (Formula 2) L=(1+C)* SL=(1+C)* S

– Where C is crimp %, S is cloth lengthWhere C is crimp %, S is cloth length Cloth length (S), (Formula 3)Cloth length (S), (Formula 3) S=L/(1+C)S=L/(1+C)

– Where L is warp length, C is crimp %Where L is warp length, C is crimp %

Question 1Question 1Crimp %Crimp %

A cotton cloth is analysed, and from a tested A cotton cloth is analysed, and from a tested strip of 20cm, the mean warp length is 21.2cm. strip of 20cm, the mean warp length is 21.2cm. Determine both the crimp and take-up Determine both the crimp and take-up percentage.percentage.

AnswerAnswer

Crimp Percentage: Crimp Percentage: (21.2 – 20.0) / 20 = 6.0%(21.2 – 20.0) / 20 = 6.0%

Take up PercentageTake up Percentage (21.2-20.0)/21.2 = 5.66%(21.2-20.0)/21.2 = 5.66%

N.B In many fabrics, there is not too great difference between the N.B In many fabrics, there is not too great difference between the warp and weft crimps, but there are examples of quite large warp and weft crimps, but there are examples of quite large differences. E.g. in cotton poplin, the warp cirmp could be 14% differences. E.g. in cotton poplin, the warp cirmp could be 14% and the weft crimp in only 2%and the weft crimp in only 2%

Example 2Example 2Crimp %Crimp %

Ex2: Ex2: Calculate the length of warp required to weave Calculate the length of warp required to weave

160m of cloth if the warp crimp is 12%160m of cloth if the warp crimp is 12% Ex3Ex3 What length of cloth can be woven from 800m What length of cloth can be woven from 800m

of warp if the warp crimp is 8%of warp if the warp crimp is 8%

AnswerAnswer

Ex2Ex2 S= cloth length = 160mS= cloth length = 160m Crimp = c = 0.12 and therefore warp length will Crimp = c = 0.12 and therefore warp length will

be: be: C= (l-s)/s X100%; and c =l/s -1 and l=(1+c)*sC= (l-s)/s X100%; and c =l/s -1 and l=(1+c)*s L=(1+0.12)*160 = 179.2mL=(1+0.12)*160 = 179.2m

AnswerAnswer

Ex3Ex3 Warp Length, L =800m , find cloth length, sWarp Length, L =800m , find cloth length, s S=L/(1+c) = 800/(1.08)S=L/(1+c) = 800/(1.08) =740.8m=740.8m

Fabric Weight CalculationsFabric Weight Calculations(Areal Density)(Areal Density)

In the imperial system, fabric weight is expressed in In the imperial system, fabric weight is expressed in ounces per square yard.ounces per square yard.

In SI, the mass per unit area is grams per square meter.In SI, the mass per unit area is grams per square meter. If we get a 10 cm x 10 cm fabric, the fabric is easy to If we get a 10 cm x 10 cm fabric, the fabric is easy to

measure and multiplied by 100 to give fabric weight measure and multiplied by 100 to give fabric weight (g/m(g/m22).).

However, if we don’t have the fabric, the fabric weight However, if we don’t have the fabric, the fabric weight can be calculated by fabric density (sett), yarn count can be calculated by fabric density (sett), yarn count and crimp percentage.and crimp percentage.

Fabric WeightFabric WeightCalculationCalculation

Question 1:Question 1: A cotton fabric is woven from 18 tex warp and A cotton fabric is woven from 18 tex warp and

21 tex weft. The fabric has 28 ends/cm and 25 21 tex weft. The fabric has 28 ends/cm and 25 picks/cm, and the warp and weft crimp picks/cm, and the warp and weft crimp percentages are 2.5 and 9.0 respectively. percentages are 2.5 and 9.0 respectively. Estimate the areal density (fabric weight g/mEstimate the areal density (fabric weight g/m22))

AnswerAnswer Mass of warp per square meterMass of warp per square meter

– =(ends/m)/1000 x (100+crimp%)/100 x tex=(ends/m)/1000 x (100+crimp%)/100 x tex– =(28 x 100)/1000 x (102.5 *18)/100=(28 x 100)/1000 x (102.5 *18)/100– =51.5 g =51.5 g

Note factor 1000 is introduced because tex is defined in Note factor 1000 is introduced because tex is defined in terms of g/km terms of g/km

Mass of weft per square meterMass of weft per square meter– =(picks/m)/1000 x (100+crimp%)/100 x tex=(picks/m)/1000 x (100+crimp%)/100 x tex– = (25*100)/1000 x (109*21)/100= (25*100)/1000 x (109*21)/100– =57.2g=57.2g

Fabric weight =51.5 + 57.2 =108.8 g/mFabric weight =51.5 + 57.2 =108.8 g/m22

If we use ends/cm in the formula, we could If we use ends/cm in the formula, we could omit the factor of 100 on the bottom line, the omit the factor of 100 on the bottom line, the total mass per square meter will be written:total mass per square meter will be written:

{(ends/cm x 100+crimp% x tex) + (picks/cm x {(ends/cm x 100+crimp% x tex) + (picks/cm x 100+crimp x tex)} /1000100+crimp x tex)} /1000

={(28*102.5*18) +(25*109*21)}/1000={(28*102.5*18) +(25*109*21)}/1000 =51.6+57.2 =108.8g/m=51.6+57.2 =108.8g/m22

Fabric WeightFabric WeightCalculationCalculation

Question 2Question 2 A satin strip cotton fabric is woven from a warp of 25 A satin strip cotton fabric is woven from a warp of 25

tex in the plain sections and from one of 12 tex in the tex in the plain sections and from one of 12 tex in the satin weave. There are 40 repeats of the pattern in a satin weave. There are 40 repeats of the pattern in a fabric width of 1.28m, each repeat being made up of 48 fabric width of 1.28m, each repeat being made up of 48 ends of plain weave and 72 ends of satin weave.ends of plain weave and 72 ends of satin weave.

The crimp is 8% in the plain weave and 5% in the satin The crimp is 8% in the plain weave and 5% in the satin weave. The weft is 14 tex, with 28 picks/cm and has 6% weave. The weft is 14 tex, with 28 picks/cm and has 6% crimp.crimp.

Calculate the aerial density of this fabric (g/mCalculate the aerial density of this fabric (g/m22))

AnswerAnswer For this patterned fabric in which varied yarns are used, For this patterned fabric in which varied yarns are used,

each type of yarn will require separate treatment.each type of yarn will require separate treatment. Number of pattern repeats per meter width= 40x1/1.28 Number of pattern repeats per meter width= 40x1/1.28

=31.25=31.25 Fabric Weight (Warp Yarn)Fabric Weight (Warp Yarn) Hence, number of plain weave ends/m =31.25 x 48; andHence, number of plain weave ends/m =31.25 x 48; and Mass of plain weave ends/mMass of plain weave ends/m (31.25*48)/1000 *(108*25)/100 =40.5g(31.25*48)/1000 *(108*25)/100 =40.5g Similarly, mass of satin weave ends/mSimilarly, mass of satin weave ends/m (31.25*72)/1000 * (105*12)/100=28.4 g(31.25*72)/1000 * (105*12)/100=28.4 g

Fabric Weight (Weft yarn)Fabric Weight (Weft yarn) Mass of weft per meterMass of weft per meter =28*106*14*100/1000 =41.6 g=28*106*14*100/1000 =41.6 g Fabric weight (warp +weft) per square meterFabric weight (warp +weft) per square meter =40.5+28.4+41.6=110.5 g/m=40.5+28.4+41.6=110.5 g/m22

Fabric WeightFabric Weight(Imperial System)(Imperial System)

Sometimes, we need to express fabric weight in Sometimes, we need to express fabric weight in Imperial System (oz/ydImperial System (oz/yd22), the calculation is as ), the calculation is as follows:follows:

Question 3Question 3 Calculate the fabric weight (oz/yd2) for the Calculate the fabric weight (oz/yd2) for the

following cotton cloth:following cotton cloth: 22s x18s, 64 x 60 and 6.5% x 8.5%22s x18s, 64 x 60 and 6.5% x 8.5%

Convert the system to SIConvert the system to SI Tex = 590.5/cotton countTex = 590.5/cotton count Warp =590.5/22 =26.8 texWarp =590.5/22 =26.8 tex Weft=590.5/18=32.8 texWeft=590.5/18=32.8 tex Sett /cm =Ends per inch /2.54Sett /cm =Ends per inch /2.54 Ends/cm =64/2.54=25.2 Ends/cm =64/2.54=25.2 Picks/cm =60/2.54 =23.6Picks/cm =60/2.54 =23.6

Fabric Weigth (g/mFabric Weigth (g/m22)) {(25.2*106.5*26.8)+(23.6*108.5*32.8)}/1000{(25.2*106.5*26.8)+(23.6*108.5*32.8)}/1000 =155.g/m=155.g/m22

Since 1 g/mSince 1 g/m22 =0.029 oz/yd =0.029 oz/yd22

Fabric Weight (oz/ydFabric Weight (oz/yd22) = 155*0.029) = 155*0.029 =4.52 oz/yd=4.52 oz/yd22

Fabric WeightFabric WeightDenierDenier

Question 4Question 4 Calculate the weight of the fabric (oz/lb2) for Calculate the weight of the fabric (oz/lb2) for

the following nylon fabrics:the following nylon fabrics: 45 denier x 45 denier; 104 x 96 and 4% x 5%45 denier x 45 denier; 104 x 96 and 4% x 5%

Convert it to SIConvert it to SI Tex = Denier /9Tex = Denier /9

– Warp tex =45/9 =5Warp tex =45/9 =5– Weft tex =45/9=5Weft tex =45/9=5

Ends/cm =ends per inch /2.54Ends/cm =ends per inch /2.54– Ends/cm= 104/2.54=40.9Ends/cm= 104/2.54=40.9– Picks/cm =96/2.54=37.7Picks/cm =96/2.54=37.7

Fabric Weight (g/mFabric Weight (g/m22)) {(40.9 x 104 x 5) + (37.7 x 105 x 5)}/1000{(40.9 x 104 x 5) + (37.7 x 105 x 5)}/1000 41 g/m41 g/m22

Since g/mSince g/m22 =0.029 oz/lb =0.029 oz/lb22

Fabric Weight (oz/lbFabric Weight (oz/lb22) = 41 x 0.029) = 41 x 0.029 =1.19 oz/lb=1.19 oz/lb22