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# Linear density_AyBee Marwat

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### Linear density_AyBee Marwat

1. 1. Abu Bakkar Marwat-Textile Engineer LINEAR DENSITY 1/7 LINEAR DENSITY: The thickness or diameter of a yarn is one of its most fundamental properties. However, it is not possible to measure the diameter of a yarn in any meaningful way. This is because the diameter of a yarn changes quite markedly as it is compressed.  Yarn is a soft assembly of fibres  There are voids spaces between the fibres within yarn (Most methods of measuring the diameter of yarn involve compressing the yarn and hence the measured diameter changes with the pressure used. So mechanical means, devices can’t be used for measuring the diameter of the yarn.)  yarn is thinner at twisted places and thicker where twist is less  Yarn appears vivid because of the hairiness; it has protruding fibres upon its surface and also sometimes loops of fibers (kinks). (Due to undefined boundaries, optical methods e.g. microscope can’t be used to measure yarn diameter)  Also there are lots of differences in the structure and cross section of different fibres  Wool has nearly round cross-section  Silk has a triangular cross-section  Cotton is like flattened tube  Man-made fibres are often made with trilobal (nylon), star or hollow cross-section for particular purposes. Due to these problems, there are no such devices to measure the diameter of a yarn. Instead, systems of denoting the fineness of a yarn by weighing a known length have evolved. This is known as the linear density. Simply it the yarn thickness or coarseness. There are two systems: 1) Direct system 2) Indirect system 1: Direct System: w/l In this system of counting, length unit is fixed and weight unit is variable. It is defined as weight per unit length. When count increases, fineness decreases (count↑ fineness↓). It is further classified as: a) Tex system b) Denier system c) Grex system a) Tex System (Tt): It is defined as no of grams per 1000 meters length. Multiples are based on weight unit and are as under Milli-tex (mTex): no of mg per 1000 meters length. It is used for yarn and roving. Deci-tex (dTex): no of decigrams per 1000 meters length. It is used for sliver. Kilo-tex (KTex): no of kilograms per 1000 meters length. It is used for laps. Tex is universal system either for spun or filament yarn. b) Denier System (Td): It is defined as no of grams per 9000 meters length. texengr05@yahoo.com
2. 2. Abu Bakkar Marwat-Textile Engineer LINEAR DENSITY 2/7 c) Grex System (Tg): No of grams per 10000 meters length 2: Indirect System: l/w In indirect count system weight unit is fixed and length is variable on which basis measurement is done. When count increases, fineness increases. (count↑ fineness↑) This includes: a) English Count (Ne): In this system, the weight unit is in lbs and length unit is hanks; No of hanks per pound. Hank length varies for different fibers or yarns.      Cotton = 840yards Wool = 256yards Spun Silk = 840yards Bast fibers (linen) = 300yards Worsted = 560yards b) Metric Count (Nm): It is defined as no of 1000 meters length/Kg. It is commonly used for heavy yarns. Count Conversion Table: Ne= Nm= Tex= Grex= Denier= Ne 1 xNe 1.693xNe 590.5 /Ne 5905 /Ne 5315 /Ne Simplified calculations: Calculations for Tex: 1000 m  1 g (1 Tex) 1m  1 mg (1 Tex) 100 cm  1 mg (1 Tex) 50 cm  0.5 mg (1 Tex) Calculations for Denier: 9000 m  1g (1 denier) 9m  1 mg (1 denier) 900 cm  1 mg (1 denier) 9 cm  0.01 mg (1 denier) Nm 0.5905 xNm 1 xNm 1000 /Nm 10,000 /Nm 9000 /Nm Tex 590.5 /Tex 1000 /Tex 1 xTex 10 xTex 9 xTex Grex 5905 /Grex 10,000/Grex 0.1 xGrex 1 xGrex 0.9 xGrex Denier 5315 /Den 9000 /Den 0.111 xDen 1.111 xDen 1 xDen Calculations for Grex: 10,000 m  1g (1 Grex) 10 m  1mg (1 Grex) 1m  0.1mg (1 Grex) 50 cm  0.05mg (1 Grex) Calculations for Ne: 840 yd  1lb (1 Ne) 840 yd  453.6g (1 Ne) 1.85 yd  1g (1 Ne) 66.67in  1g (1 Ne) 33.33in  0.5g (1 Ne) Calculations for Nm: 1000 m * X(count)  1kg (X Nm) 1000 m * 1  1000g (1 Nm) 1m  1g (1 Nm) 50 cm  0.5g (1 Nm) texengr05@yahoo.com
3. 3. Abu Bakkar Marwat-Textile Engineer LINEAR DENSITY 3/7 Effect of linear density on Hairiness: Yarn linear density is statistically significant when evaluating both yarn counts together with SPSS. We found a direct relationship between yarn linear density and hairiness; the hairiness increases when the yarn linear density increases. In other words, coarse yarns have more hairs than fine yarns for all the observed hair lengths. This can be explained by the increase of fibres in the cross-section of yarn. Designation/Nomenclature of Yarn:  Single Yarn: (spun or cotton) It is identified through one group of three symbols: 24/S/15 Where 24-count, S-direction of twist, 15-twist level or TPI  Single Yarn: (filament yarn): 100(15)/S/80 Where 100-denier count, (15)-no of monofilaments in filament yarn, S-direction of twist, 80-level of twist i.e TPM  Plied Yarn: It is identified through two groups of three symbols: 24/S/15, 2/Z/12 Where 24-Ne (cotton count), S-direction of twist, 15-TPI, 2-no of plies, Z-direction of twist of "yarns", 12-TPI  Cabled yarn: It is identified by three groups of three symbols: 20/Z/10, 2/S/8, 2/Z/6 Where 20-Ne, Z-direction of twist in individual yarn, 10-TPI, 2-no of plies of single yarn, Sdirection of twist, 8-TPI, 2-no of plies of plied yarns, Z-direction of twist, 6-TPI Measuring Linear Density: Sampling: For lots that contain five cases or less, the sample should consist of all the cases. Ten packages are selected at random but in approximately equal number from each case. For lots that consist of more than five cases, five cases should be selected at random from each of these cases. In all cases, sampling ends up with ten cases. Effect of Moisture Content: Yarns contain a varying amount of moisture depending on the constituent fibres and the moisture content of the atmosphere where they have been stored. The additional moisture can make an appreciable difference to weight and hence the linear density of yarn. So there are three conventional methods of expressing linear density. Each of which has a different way of dealing with moisture content. texengr05@yahoo.com
4. 4. Abu Bakkar Marwat-Textile Engineer LINEAR DENSITY 4/7 a) Linear density as received: In this method no allowance is made for the moisture content, the linear density measured on the yarn as it is. Numbers of skeins are wound on a wrap reel which has a circumference of a convenient length e.g., 1 meter. Then linear density is calculated from the total length and total weight. When measuring the length of a piece of yarn or when reeling a given length of yarn it is important that the operation is carried out using a standard tension. On wrap reel while reeling a hank of yarn, tension is set by introducing the correct amount of friction into the yarn path. Skein gauge: The skein gauge shown in the fig checks the length of a 50 wrap skein under a standard tension. The test hank is passed round the lower fixed peg and the upper peg which forms one arm of a balance. The load on the other end of the balance is set at 50g x the nominal tex of the yarn. If the length of the hank is correct the pointer will be opposite the zero mark. Any deviation from the correct length is shown directly as a plus or minus percentage. The length of the skein should be within 0.25% of the actual girth of the reel, the reeling tension of the wrap reel being adjusted to achieve this. Because the yarn on a package may be under Jaw tension it is correct practice first to wind a hank from the package of sufficient length for all the tests which Hank Load are to be carried out. This is then allowed to relax without any tension for 4h before winding the actual test skeins from it. Jaw b) Linear density at standard testing atmosphere: In this method the skeins of yarn are preconditioned for 4h by drying in an oven at 50º C. They are then conditioned in the standard atmosphere (20±2 º C, 65±4% RH) for 24 h. The reason for preconditioning the yarn is so that the equilibrium moisture content is approached from the same side each time, thus avoiding the effects of hysteresis. The reeling of the hanks and calculation of the linear density are then carried out as above. c) Linear density at correct condition: This method is more accurate than the previous one as the amount of moisture contained by the fibres in equilibrium with the standard atmosphere can vary. In the method, the hanks are reeled as above and then dried to oven dry weight (105C-two consecutive weighing the same) and weighed. The dry weight then has the appropriate standard regain allowance added to it and the linear density is then calculated from this weight. Weight at correct condition = dry weight x (100 + standard regain)/100 texengr05@yahoo.com
5. 5. Abu Bakkar Marwat-Textile Engineer LINEAR DENSITY 5/7 Linear density from a fabric sample:  When the linear density of a yarn has to be determined from a sample of fabric, a strip of the fabric is first cut to a known size.  A number of threads are then removed from it and their uncrimped length is determined under a standard tension in a crimp tester.  All the threads are weighed together on a sensitive balance and from their total length and total weight; the linear density can be calculated. Yarn from a finished fabric may have had a resin or other type of finish applied to it so that its weight is greater than that of the original yarn. Alternatively it may have lost fibres during the finishing process so that its weight may be lower than that of the original yarn. For these reasons the linear densities of yarn from finished fabrics can only represent an estimate of the linear density of the yarn used to construct. When yarn is removed from a fabric it is no longer straight but it is set into the path that it took in the fabric as shown in fig. This distortion is known as crimp and before the linear density of the yarn can be determined, the crimp must be removed and the extended length measured. Shirley crimp tester: The crimp tester is a device for measuring the crimpfree length of a piece of yarn removed from a fabric. The length of the yarn is measured when it is under a standard tension whose value is given in Table. The instrument is shown diagrammatically in Fig. and consists of two clamps, one of which can be slide along a scale and the other which is pivoted so as to apply tension to the yarn. The sample of yarn removed fro the fabric is placed in the clamps with each end a set distance into the clamp; this is because the length of yarn in the clamps has to be allowed for in the measurement. The right hand clamp can be moved along the scale and it has an engraved line on it at which point the extended yarn length can be read. The left hand clamp is balanced on a pivot with a pointer arm attached. On the pointer arm is a weight which can be moved along the arm to change the yarn tension, the set tension being indicated on a scale behind it. At zero tension the left hand clamp assembly is balanced and the pointer arm lines up against a fixed mark. As the weight is moved along the arm the clamp tries to rotate around the pivot, so applying a tension to the yarn. When a measurement is being made the movable texengr05@yahoo.com
6. 6. Abu Bakkar Marwat-Textile Engineer LINEAR DENSITY 6/7 clamp is slid along the scale until the pointer is brought opposite the fixed mark. At this point the tension in the yarn is then the value which was set on the scale. The length of the yarn can then be read off against the engraved line. The crimp, which is the difference between the extended length and the length of the yarn in the fabric, is defined as: Percentage crimp: (Li + Lo)/Lo x 100 Lo = distance between ends of the yarn as it lies in the fabric Li = straightened length of yarn Yarn tensions for the crimp tester: Yarn type Woolen & worsted Cotton Man made continuous filament yarn Linear density 15 to 60 tex 61 to 300 tex 7 tex or finer Coarser than 7 tex All Tension (cN) (0.2 x tex) + 4 (0.07 x tex) + 12 0.75 x tex (0.2 x tex) + 4 0.5 x tex Applications of Linear density: 1) Total length on a yarn package: 1) Package wt: 2.5 lb & Ne 20: Cotton: 840 x count = 1 lb 840 x 20 = 1 lb 16800 = 1 lb i.e 16800 yards length weighs 1 lb Then 2.5 lb cone length: 16800 x 2.5 = 42000 yards Worsted: 560 x count = 1 lb 560 x 20 = 1 lb 11200 = 1 lb i.e. 11200 yards length weighs 1 lb Then 2.5 lb cone length: 11200 x 2.5 = 28000 yards Woolen: 256 x count = 1 lb 256 x 20 = 1 lb 5120 = 1 lb i.e. 5120 yards length weighs 1 lb Then 2.5 lb cone length: 5120 x 2.5 = 12800 yards 2) Package wt: 2 lb, 80 spun polyester: (Spun polyester means that it is cut into small fibres like cotton) 840 x count = 1 lb 840 x 80 = 1 lb 67200 = 1 lb i.e. 67200 yards length weighs 1 lb Then 2 lb package length: 2 x 67200 = 134400 yards 3) Package wt: 2 kg, 100/2 denier Nylon filament (For filament yarn, 100/2=200, 50/2=100) 9000 m = 200 g Then 2 kg cone length: (9000 x 2)/0.2 = 90,000 m (30/2 viscose spun=15, 20/2=10) 4) Package wt: 3 kg, 100 denier Polyester: 9000 m = 100 g 9000 m = 0.1 g Then package weighing 3 kg have length: (9000 x 3)/0.1 = 270,000 m 5) Package wt: 2 lb, Tex count = 20 1000 m = 20 g 1000 m = 0.0441 lb 2 lb package will have length: texengr05@yahoo.com
7. 7. Abu Bakkar Marwat-Textile Engineer LINEAR DENSITY 7/7 (1000 x 2)/0.041 = 45351 m 2) Fabric cost: Fabric construction: 20 x 16/ 128 x 60 60” 3/1 S twill Leno Warp crimp = 6% Weft crimp = 8% Total length = 36000 yards Warp weight = (total ends x tape length)/(840 x warp count) {lbs} ----- (1) Now for total ends, we have = (ends/in x width of fabric)+selvage ends + extra ends = (128 x 63) + (2*24) + 10 = 8064 + 48 + 10 = 8122 For tape length: Ly = Lf (1 + C) = 36000 (1+6%) = 36000(1.06) = 38160 yards Putting values in equ. 1: = (8122 x 38160)/(840 x 20) = 18448.54 lbs Total bags = 18448.54/100 = 184.48 (one bag=100lbs) Total cones = 184.48*40 = 7379 cones (one cone=2.5lb & one bag = 40 cones) Warp cost: price of cone x No of cones = 240*7379 = 1770960 rupees Weft weight = (total picks x reeded width)/(840 x weft count) ----- (2) Now for total picks, we have = picks/inch x fabric length + Extra picks = (60*36) x 36000 + 10 = 77760010 For reeded width: Ly = Lf (1 + C) = 63 (1+8%) = 63 (1.08) = 68.04” = 68.04/36 = 1.89 yd Putting values in equ 2: = (77760010 x 1.89)/(840 x 16) = 10935 lbs Total bags = 10935/100 = 109.35 bags Total cones = 109.35*40 = 4374 cones Weft cost: price of cone x No of cones = 225*4374 = 984150 rupees Total cost = 77760010 + 984150 = 2755110 rupees texengr05@yahoo.com