Warping Calculations

Lecture 12: Warping CalculationsW. A. WimalaweeraOUSLContentsBeam Warping calculationsSectional Warping CalculationsBeam Warping Calculation

The first stage of beam warping is the preparation of a set of back beams (or section beams) each containing a fraction of the total number of ends to be in the fabric. Then we have to assemble these back beams to one beam in a second stage. Lets consider the following example.Example 1: A weaver has an order for 25,000 metres from a loom state plain weave fabric having following construction: Cotton 45s x Cotton 45s X 48 inches 103 EPI x 65 PPIAssume C1 = 5% and C 2 =7%. Assume a waste percentage of 2% for warp yarn.Calculate the number of section beams to be prepared, number of supply packages (Warp) to be ordered, amount of warp in each package and the requirement of warp and weft yarns

Calculation of number of beams and packagesThe weaver has to produce a large quantity of a plain weave loom state fabric. To produce such a quantity, best method of warping is direct warping. As the warp yarn is a single yarn it has to be sized after warping. During sizing we can assemble the back beams to the final weavers beam.

The construction details are given for the loom state fabric. Loom state fabric is the fabric delivered by the weaving machine. After finishing the fabric specifications such as warp yarn density, weft yarn density, area density etc. may change a little. We are not concerned about this in this particular exampleCalculation of warp beamsFirst of all we must calculate the number of back beams to be prepared and how many warp ends must be there in one beam. For that we must know the details about the warping machine creel capacity available in the mill. Assume that the creel capacity of the warping machine is 750. That means the maximum number of ends we can warp at a time is 750.

Calculation of the number of beamsTotal number of warp ends in the fabric= 103 ends/inch x 48 inches= 4944 The number of back beams = Total number of ends in the fabricCreel capacity

= 4944 / 750=6.592 7

We have to make 7 back beams to have the total number of ends of 4944 . Each bean contains (4944 / 7 = 706.28 ) 707 ends.

The exact number of ends in one back beam = 707That means we are using only 707 spindles of the creel although we have a total number of spindles of 750.The weaver has to order from the winding department 707 yarn packages each containing sufficient weight of yarn for 25000 m of fabric. Yarn requirement is calculated as follows. The width of the beam = warp width at reed = un-crimped length of the weft= 48 inches (1.07) = 51.4 inches

Yarn requirementFirst of all let us calculate the total amount of warp yarn requirement.Total length of the warp yarn requirement= 4944 x 25000 m x (1.05)= 129,780,000 m

Total length of the warp yarn requirement= 129780000 m x 1.083 yds/m= 140,594,957 yardsTotal weight of warp yarn requirement= 140594957 lbs (pounds) 45 x 840= 3719.44 lbs

Total weight to be ordered (consider waste)= 3719.44 x 1.02 lbs= 3793.88 lbs

The weight in of yarn in one package = 3793.88 / 707= 5.37 lbsThe weaver has to order 707 yarn packages each containing 5.37 lbs from the winding factory so that he can prepare the beam on his warping machine.

Beam warping calculation 2An order for 24200 m of the following finished fabric has been received. Cotton 15 tex X Cotton 15 tex X 1.2 m 38 1/cm X 35 1/cm

Warp Crimp, C1 = 9%, Weft Crimp, C2 = 8%, Warp and weft waste = each 2.5%

A beam warper with a creel capacity of 600 is available. Calculate,a) The number of back beams to be prepared and the width of the beams.b) Total requirement of warp and weft yarn.c) Number of yarn packages required for warping and the weight of yarn to be wound on to each package.

Sectional Warping CalculationIn sectional warping also we have two stages. In the first stage we wind a certain number of warp ends, which depends on the creel capacity, on to a warping drum. The density of the warp ends wound on to the drum is similar to the warp density on the weavers beam. Therefore the number of warp ends wound on to the drum represents only a section of the complete warp beam. To complete the total number of ends required on the weavers beam we have to wind several sections on to the drum. Once all the sections are wound on to the drum we have to transfer the whole set of ends to the weavers beam. This is the second stage of sectional warping. This step is known as Beaming.

Sectional Warping CalculationExample A weaver receives an order to weave 2500 m of a fabric having following specifications:Nylon 75d/24f X Nylon 75d/24f X 48 inches102 1/inches X 83 1/inchesThe above details are of the finished fabric. The finished fabric has following crimps: Warp crimp, C1 = 6%, Weft crimo, C2 = 5%, assume a warp waste of 3%. The fabric has warp way strips in white and red colours of 0.5 inch width. Now the weaver has to determine the warping details and yarn requirements.

Why Sectional warping?The fabric quantity ordered is small (2500 m), and it has warp way stripes. Therefore the most suitable method of warping is sectional warping.The sectional warping machine available in the factory has a creel capacity of 600.First of all let us calculate the total number of warp ends in the fabric.

Total number of ends in the beamTotal number of warp ends in the fabric= 102 1/inch x 48 inches= 4896The warp and weft crimps of the finished fabric are given.When we consider the weft, the un-crimped length of the weft is equal to the width of the warp sheet at the reed. The width of the warp sheet at reed (reed-in width) is approximately equal to the width of the warp on the beam.

Width of the Finished fabric= 48 inchesCalculation of the width of the warp sheetIf the width of the warp sheet at reed is W,

The crimp of the weft of finished fabric is defined as follows: Length of the un-crimped weft Width of the fabricWeft Crimp, % = C2 = _________________________________________x 100 Width of the fabric Therefore, C2, % = (W 48) 100/ 48 W = (48 x 5/100) x + 48= 50.4 inches

Reed-in width and beam widthIn this calculation we assume that any permanent change of the length of the weft takes place due to finishing or weaving processes.

Width of the warp sheet at the reed = 50.4 inches Therefore width of the warp to be wound on to the drum = 50.4 inches {This can be little larger than 50.4 (reed-in width) for practical reasons}

Number of sections to be wound onto the drum = 4896 / 600= 8.16 Sections

Number of sections to be woundIn this case,We can either wind 8 sections with 600 ends and then a 9th section with a reduced number of ends (600 x 0.16 = 96) or We can wind 9 sections with 4896/9 (= 544) ends per section or we can select the width of a section depending on the numbers of threads in the colour repeat of the warp.

Which method is better?The second method is better than method 1because1. We have to creel a lesser number of yarn packages at the beginning and we do not have to remove some packages after 8 sections. 2. Further we can use 544 packages with the same amount of yarn in each package. However we must be careful to maintain the number of threads in the colour repeat. If the number of threads in one section (544) is not equal to a multiple of the threads in the colour repeat we will have to change the packages in the creel during change overs from one section to the other.

Consider the method 2If we are going to wind 9 equal sections on to the drum,The width of one section on the drum = 50.4 / 9 = 5.6 inchesSo we have to wind 9 sections each having 544 ends amounting to 4896 ends per beam. We do not use the available creel capacity of 600 spindles.This fabric has two colours, white and red in the warp. In the case fabrics with coloured stripes we have to consider colour repeat also when we decide for the width of one section.Number of yarns in one 0.5 inch wide strip = 102 /2 = 51Therefore we have to arrange warp yarns in the following order for warping:51 Black, 51 White, 51 Black , 51 White so on (48 white strips and 48 black strips)The number of threads in one section (544) is not a multiple of 51. Hence it is better to change the number of threads per one section to 510 and wind 9 sections with 510 threads (9 x 510 = 4590) and to have 4896 4590 (= 306=51 x6) ends for the last section.

Now Consider the method 3If we want to select a section width depending on the colour repeat we have to follow the following method.Total number of coloured strips in the fabric = 4896 /51 = 96Maximum number of colour strips in one section = 600 / 51 = 11.7The number of cololur strips in one section must be less than 11. It is better if this number is equal to a multiple of 2 as we have two colours of same width. Further is advisable to select a number which is a fraction of 96. The largest number which fulfils both the conditions is 8.Therefore the number of colour strips per section = 8Number of threads per section = 8 x 51 = 408(We use only 408 positions of the creel which has 600 capacity.)Number of sections to be wound= 96 / 8 = 12This method is the best method as we do not have to change the creeling during the process of warping.

Requirement of warp yarnThe requirement of warp has to be calculated separately for white and red threads.

Total length of the fabric= 2500 mTotal length of the warp yarn = 2500 x 1.06 x 4896 = 12,974,400 mLength of the warp yarn with waste = 12974400 x 1.03 m= 13,363,632 mTotal weight= 13363632 x 75 g 9000 = 111363.6 = 111.36 kgAmount of white yarn = amount of red yarn = 111.36/2 = 55.68 kgNow we must calculate the amount of yarn to be wound onto individual packages. It depends on the which of the above mentioned methods we want to use

Yarn amount per packageIf we use the method 2 aboveEach of 204 (510 -306) packages must have a length of 2500 x 9 x 1.03 x 1.06 m of yarn.Each of 204 packages must have 24566 m of yarn from which 102 must be wound with white yarn and other 102 with red yarn.Each of 306 packages must have a length of 2500 x 10 x 1.06 x1.03 m (=25750 m) of yarn from which 153 must be wound with white and other 153 with red yarn.Yarn requirement is as follows:

YarnNo. of packagesLength / packageWeight / packageTotal /kg2. White10224566 m204.71 g20.8815327295 m227.5 g34.803. Red10224566 m204.71 g20.8815327295 m227.5 g34.804. Total510111.36Yarn amount per packageIf we use the method 3 aboveTotal number of packages= 408Total number of white packages = 204Total number of red packages= 204Number of sections= 12The length of yarn to be wound to each package = 2500 x 12 x 1.03 x 1.06 mThe mass of yarn to be wound to each package = 2500 x 12 x 1.03 x 1.06 x 75/9000 g= 275.95 g

Yarn amount per packageYarn requirement is as follows:

YarnNo. of packagesLength / packageWeight / packageTotal /kgWhite20432754 m272.95 g55.68Red20432754 m272.95 g55.68Total40832754 m272.95 g111.36Even though we use a higher creel capacity in the case 2, it appears to be difficult to carry out. We have to take more care in winding of packages and creeling has to be changed after winding of 9 sections.Exercise Sectional WarpingA warper has to prepare a beam to weave 3000 m of the following polyester gabardine fabric using his sectional warping machine.

PE, 150 dTex/36f x PE, 150 dTex/36f x 130 cm 25 1/cm X 24 1/cmThe finished fabric has warp way stripes of 1 cm width of grey and white colours. C1 = 6%, C2 = 5 %, Warp waste = 3%Calculate,a. Number of sections to be wound on to the warping drum and width of each section.b. Number of yarn packages required from each colour andc. The quantity of yarn to be wound on to each package so that winding of yarn packages as well as warping is carried out efficiently.

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