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Mathematical application in textiles
By :   N. Karthikeyan, J. Joshuva Alexander
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Abstract


It is not surprising that the various regions developed their own systems of textile measurement and textile vocabulary. In a world in which the pace of life was relatively slow, regional variations in systems of units were tolerable, but to-day communications are rapid, and commerce and technology need a uniform system of measurement that is universally accepted and understood. Errors of conversion are automatically eliminated, but, of course, during the transitional stage, there will be misunderstandings and arithmetical errors when old units are converted into new, even when prepared conversion tables are used. For textile calculations, it may be found that the usual sets of conversion tables do not include quantities peculiar to the textile industry. For these quantities, a conversion system has to be devised by using first principles and then published as a table or graph or left just as a conversion factor. Most of the calculations made by a textile technologist consist of a series of relatively simple steps, mainly arithmetical and at times using elementary aspects of trigonometry, geometry Algebra. The calculation is generally straightforward; it is the local thinking required that often presents most difficulty. It is usually worth spending a few minutes in considering various approaches to a problem before setting down the first line of calculation. An engineer or research scientist may employ more complex mathematics, a thorough training in pure and applied mathematics being required. The objective of any experiment or measurement should be to produce an answer that is as accurate as the instruments available and the skill of operator will allow. For many calculations, the person doing the necessary numerical work has a rough idea of the order of magnitude he should obtain. Scientific sampling, design of experiments, the analysis, presentation and interpretation of data through statistical techniques-all these created the concept of specification, production and inspection as a dynamic cycle. Inspection now is the source of data which, analyzed and interpreted through statistical methods, is continuously feed back to production people for corrective and preventive action. Inspection, that is, the act of screening out defectives before they reached the customer.



Need for Mathematics in Textiles


In any manufactured product no two articles are perfectly alike, For example, it is impossible to find two knots of yarn having exactly the same count, strength, evenness, length etc. this is because the raw material i.e. cotton itself varies from fibre to fibre within a bale, bale to bale, and season to season. The quality of the product in each process, therefore, varies according to the variation in the raw material used and degree of technical and refinement attained during processing. Further, machines and tools wear and tear due to long use it is neither possible nor economical to replace the machine. Superimposed on this is the variation arising from lack of fibre control during drafting and that from chance causes. Further, it is impossible to eliminate the effect of human factor entirely. Changes in atmospheric conditions also contribute towards an increase in overall variation in the quality of the product. These variations in various regions are often occurring problems in textile. Using various mathematical calculations can solve these variations.



Various Mathematical Calculation Methods Involved in Textile


Statistical Tests

Graphical Analysis

Distributions

Vectors

Trigonometric Functions

Matrix

Fourier series

Z and Laplace Transformation

Conversions and Formulas

General Mathematical Applications


Statistical Techniques


Statistics is defined as scientific method, which deals with collection, compilation, analysis and presentation of data. It is also defined as the science of average and the study of variability. They enable us to take corrective and preventive actions in case of variability and certainty. Some of the statistical techniques are:


  • Chi-square Test: This method is used when there is no prior knowledge of the distribution of test values. They are also used to identify the goodness of he fit of the given samples. End breakages in spinning, roving, carding, nep generation in blow room and carding are assessed using this test. The results are compared with the confidence limits and the performances are determined.


 

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Published On Tuesday, September 23, 2008
 
 
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