Textile Calculation: Fibre to Finished Garment (The Textile Institute Book Series) [1 ed.] 032399041X, 9780323990417

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Textile Calculation

The Textile Institute Book Series Incorporated by Royal Charter in 1925, the Textile Institute was established as the professional body for the textile industry to provide support to businesses, practitioners, and academics involved with textiles and to provide routes to professional qualifications through which Institute Members can demonstrate their professional competence. The Institute’s aim is to encourage learning, recognize achievement, reward excellence, and disseminate information about the textiles, clothing, and footwear industries and the associated science, design, and technology; it has a global reach with individual and corporate members in over 80 countries. The Textile Institute Book Series supersedes the former Woodhead Publishing Series in Textiles and represents a collaboration between the Textile Institute and Elsevier aimed at ensuring that Institute Members and the textile industry continue to have access to high-caliber titles on textile science and technology. Books published in the Textile Institute Book Series are offered on the Elsevier website at: store. elsevier.com and are available to Textile Institute Members at a substantial discount. Textile Institute books still in print are also available directly from the Institute’s website at: www.textileinstitute.org To place an order, or if you are interested in writing a book for this series, please contact Sophie Harrison, Acquisitions Editor: [email protected]

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The Textile Institute Book Series

Textile Calculation Fibre to Finished Garment

Edited by

R. Chattopadhyay Professor, Department of Textile and Fibre Engineering, Indian Institute of Technology, Delhi, India

Sujit Kumar Sinha Professor, Department of Textile Technology, National Institute of Technology Jalandhar, India

Madan Lal Regar Assistant Professor, Department of Fashion Design, National Institute of Fashion Technology, Jodhpur, Rajasthan, India

Woodhead Publishing is an imprint of Elsevier 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States The Boulevard, Langford Lane, Kidlington, OX5 1GB, United Kingdom Copyright © 2023 Elsevier Ltd. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. ISBN: 978-0-323-99041-7 For information on all Woodhead Publishing publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Matthew Deans Acquisitions Editor: Sophie Harrison Editorial Project Manager: Rafael G. Trombaco Production Project Manager: Prasanna Kalyanaraman Cover Designer: Victoria Pearson

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Contents

List of contributors 1

2

3

Introduction: textile manufacturing process R. Chattopadhyay, S.K. Sinha and Madan Lal Regar 1.1 Raw material and its characteristics 1.2 Expression of fineness 1.3 Importance of fiber properties 1.4 Ranking fiber properties for various spinning technologies 1.5 Estimation of fiber parameters from fiber linear density 1.6 Flow chart of spinning process 1.7 Flow chart of weaving process 1.8 Flow chart of weft knitting process 1.9 Garmenting process flow chart Applications of selected response surface design of experiments and advanced control charts in textile engineering Subhankar Maity 2.1 Role of statistics for textile engineers 2.2 Design of experiment 2.3 Response surface design 2.4 Process control in textiles by advanced control chart 2.5 EWMA control charts 2.6 Conclusions References Man made fiber manufacturing process Supriyo Chakraborty 3.1 Introduction 3.2 Degree of polymerization 3.3 Number average molecular weight, weight average, and viscosity average molecular weight of polymers 3.4 Quantitative concepts of polymeric molecules for fibers 3.5 Relation between filament fineness (denier) and it’s diameter 3.6 Tensile strength of a filament 3.7 Temperature dependence of polymer viscosity

xi 1 1 1 2 6 7 7 10 11 11

13 13 15 16 35 50 53 54 57 57 57 59 62 63 64 65

vi

Contents

3.8 3.9 3.10 3.11 3.12

4

5

6

7

Melt spinning variables Temperature profile of filaments in melt spinning Determination of degree of crystallinity from DSC study Determining crystallinity of the spun polymeric fibers Conclusion References

67 69 73 75 76 76

Prespinning processes (opening and cleaning, carding and drawing) R. Chattopadhyay 4.1 Introduction 4.2 Opening and cleaning 4.3 Carding 4.4 Draw frame Practice problems

77 77 77 90 97 106

Combing, roving preparation, and spinning R. Chattopadhyay 5.1 Combing 5.2 Roving frame 5.3 Ring spinning

111

Yarn structure and mechanics R. Chattopadhyay 6.1 Yarn fineness/count conversion 6.2 Yarn diameter 6.3 Number of fibers in yarn cross-section 6.4 Linear density of plied yarn 6.5 Torsion and bending of a fiber within twisted yarn 6.6 Yarn contraction/extension due to twisting/untwisting 6.7 Relationship between structural parameters 6.8 Packing coefficient 6.9 Close pack geometry 6.10 Fiber migration in spun yarn 6.11 Tensile behavior of twisted filament yarn 6.12 Radial pressure in twisted yarn 6.13 Wrap yarn 6.14 Blended yarn 6.15 Self-locking structure of spun yarn 6.16 Core sheath yarn 6.17 Exercise problems References

139

Fabric preparatory Akhtarul Islam Amjad and Madan Lal Regar 7.1 Introduction

171

111 120 128

139 140 141 142 143 143 145 149 153 155 157 160 161 162 166 168 169 170

171

Contents

7.2 7.3 7.4 7.5 7.6

8

9

10

11

vii

Winding of yarn Splicing Production calculation of winding machine Warping Sizing References

171 179 179 181 186 195

Woven fabric production Akhtarul Islam Amjad, J.P. Singh and Madan Lal Regar 8.1 Introduction 8.2 Primary motions 8.3 Beat-up mechanism 8.4 Secondary motions 8.5 Auxiliary or stop-motions 8.6 Nonconventional weaving machine 8.7 Conclusion References

197

Woven fabric structure Biswapati Chatterjee 9.1 Introduction References

215

Knitted fabric production Roopam Chauhan and Subrata Ghosh 10.1 Introduction 10.2 Some basic terminologies and their relevant mathematical equations 10.3 Geometry of loop and loop length 10.4 Robbing back 10.5 State of relaxation 10.6 Fabric areal density 10.7 Tightness factor 10.8 Productions calculations 10.9 Warp knitting calculations References

237

Calculations in fabric chemical processing Chet Ram Meena and Janmay Singh Hada 11.1 Introduction 11.2 Calculations at various stage of textiles processing 11.3 Cuprammonium fluidity 11.4 Mercerization 11.5 Barium activity number 11.6 Dyeing

255

197 197 203 207 210 210 214 214

215 236

237 237 240 242 243 244 245 245 246 253

255 255 259 260 260 260

viii

Contents

11.7

12

13

14

15

Conclusion References

273 273

Apparel manufacturing measures and calculations Manoj Tiwari and Prabir Jana 12.1 Introduction 12.2 Plant set-up and facility designerelated measures and calculation 12.3 Manufacturing operationserelated measures and calculations 12.4 Conclusion References

275

Fiber testing Madan Lal Regar, Chet Ram Meena and Janmay Singh Hada 13.1 Introduction 13.2 Standard conditions for yarn testing 13.3 Statistical averages 13.4 Humidity 13.5 Fiber length 13.6 Fiber fineness 13.7 Fiber maturity 13.8 Fiber quality index 13.9 Spinning consistency index 13.10 Tensile property 13.11 Nep count 13.12 Fiber crimp 13.13 Conclusion References

301

Yarn testing Vijay Goud, Apurba Das and Alagirusamy Ramasamy 14.1 Yarn linear density 14.2 Moisture in yarn 14.3 Yarn twist 14.4 Tensile properties of yarns 14.5 Evenness of yarn 14.6 Conclusion Further reading

325

Fabric testing Chet Ram Meena, Janmay Singh Hada, Madan Lal Regar and Akhtarul Islam Amjad 15.1 Introduction 15.2 Major testing standards for textile testing 15.3 Gram per square meter 15.4 4-Point system

349

275 276 284 298 298

301 301 301 305 307 310 316 318 319 320 323 323 324 324

325 328 331 333 339 348 348

349 349 350 351

Contents

15.5 15.6 15.7 15.8 15.9 15.10 15.11 15.12

Index

ix

Strength of the fabric Fabric handle Thickness Clothing science and comfort Flame-retardant Measurement of color strength Dimensional change Conclusion References

352 355 360 361 365 366 367 368 368 369

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List of contributors

Akhtarul Islam Amjad Department of Fashion Technology, National Institute of Fashion Technology Panchkula, Panchkula, Haryana, India Supriyo Chakraborty Pradesh, India

Uttar Pradesh Textile Technology Institute, Kanpur, Uttar

Biswapati Chatterjee Government College of Engineering & Textile Technology, Serampore, West Bengal, India R. Chattopadhyay Department of Textile Technology, Indian Institute of Technology Delhi, New Delhi, Delhi, India; Department of Textile and Fibre Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Roopam Chauhan Punjab, India

Dr. B.R. Ambedkar National Institute of Technology, Jalandhar,

Apurba Das Department of Textile and Fibre Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Subrata Ghosh Punjab, India

Dr. B.R. Ambedkar National Institute of Technology, Jalandhar,

Vijay Goud Department of Textile and Fibre Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Janmay Singh Hada Department of Textile Design, National Institute of Fashion Technology Jodhpur, Ministry of Textiles, Govt. of India, Jodhpur, Rajasthan, India Prabir Jana India

National Institute of Fashion Technology Delhi, New Delhi, Delhi,

Subhankar Maity Pradesh, India

Uttar Pradesh Textile Technology Institute, Kanpur, Uttar

Chet Ram Meena Department of Textile Design, National Institute of Fashion Technology Jodhpur, Ministry of Textiles, Govt. of India, Jodhpur, Rajasthan, India Alagirusamy Ramasamy Department of Textile and Fibre Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Madan Lal Regar Department of Fashion Design, National Institute of Fashion Technology Jodhpur, Jodhpur, Rajasthan, India

xii

List of contributors

J.P. Singh Department of Textile Technology, Uttar Pradesh Textile Technology Institute, Kanpur, Uttar Pradesh, India S.K. Sinha Department of Textile Technology, National Institute of Technology Jalandhar, Jalandhar, Punjab, India Manoj Tiwari India

National Institute of Fashion Technology Kannur, Kannur, Kerala,

Introduction: textile manufacturing process

1

R. Chattopadhyay 1 , S.K. Sinha 2 and Madan Lal Regar 3 1 Department of Textile Technology, Indian Institute of Technology Delhi, New Delhi, Delhi, India; 2Department of Textile Technology, National Institute of Technology Jalandhar, Jalandhar, Punjab, India; 3Department of Fashion Design, National Institute of Fashion Technology Jodhpur, Jodhpur, Rajasthan, India

1.1

Raw material and its characteristics

Both natural and man-made fibers are used for spinning yarns on staple fiber spinning system. The machines have been designed primarily to process cotton fibres. The other fibers processed are viscose rayon, polyester, nylon, acrylic, polypropylene, etc. either in 100% form or in blends with one another. The design of the amchines and the processing parameters to be chosen are dependednt on fibre properties. The fiber properties relevant to spinning are shown in Table 1.1. It is important that fibers should be fine, flexible, and strong enough to withstand the processing stresses and strains.

1.2 1.2.1

Expression of fineness Linear density/count

Linear density is an indirect expression of fineness of fiber/filament or yarn. The fineness is not expressed by diameter due to following reasons: (i) Diameter is not uniform along the length of natural fiber and spun yarn and (ii) Cross-sectional shape may not be circular both for fiber and yarn

Hence, it is indirectly expressed by either measuring the - weight of known length of fiber/yarn or - number of unit length in a known weight of fiber/yarn.

These two basic methods to express linear density of any textile fibre/strand are known as direct or indirect system of expression of fineness. Therefore, by definition, the two systems of expression are: (i) Direct System ¼ weight/length and (ii) Indirect system ¼ length/weight

Textile Calculation. https://doi.org/10.1016/B978-0-323-99041-7.00008-4 Copyright © 2023 Elsevier Ltd. All rights reserved.

2

Textile Calculation

Table 1.1 Properties of fibers suitable for cotton system of spinning.

a

Properties

Cotton

Viscose

Nylon

Polyester

Acrylic

PPa

Staple length (mm) Fineness range (dtex) Tenacity (cN/tex) Breaking ext.% Modulus (cN/tex) Moisture regain (%) Electrical conductivity (log Rs1) Heat resistance ( C)

20e38 1e4 20e50 5 300e500 7 0.14

32e60 1e4 0.20 15 600 12.5 0.10

32e60 1e4 30e60 20 250 4.3 0.13

32e60 1e4 35e60 20 1000 0.4 0.08

32e60 1e4 0.27 30 500 1.3 0.07

32e60 1e4 0.65 15 700 0 0.06

105

105

100

140

120

105

PP ¼ Polypropylene.

Generally, the unit of weight is small and length is large so that reasonable numerical values are obtained in both the systems to indicate fineness or linear density. In direct system, larger the indicated number of fineness, coarser will be the yarn. In indirect system, the fineness is actually expressed as the ratio of number of unit length per unit weight. The following Table 1.2 gives a comprehensive account of the units used in the expression of linear density. The conversion factors from one counting system to the other are stated in Table 1.3.

1.3

Importance of fiber properties

1.3.1

Length characteristics

Staple length diagram of cotton and synthetic fibers are shown in Figs. 1.1 and 1.2. In the case of synthetic fiber, the length parameter is staple length only. But for cotton, the fiber length varies; there are no single length parameters by which one can Table 1.2 Units of linear density. System

Weight unit

Length unit

System unit

Symbol unit

Direct Tex denier Indirect English metric

Gramme (g) Gramme (g) Pound (lb) kilogram Count conversion (kg)

1000 m (m) 9000 m (m) 840 yard (yd) Kilometer (km)

g/1000 m

Tex denier

No. of 840 yds/lb No. of km/kg

Ne Nm

Introduction: textile manufacturing process

3

Table 1.3 Conversion factor. Direct system From

To Tex

To Denier

Tex (Nt) Denier (Nd) English (Ne) Metric (Nm)

1 0.11 Nd 590.5/Ne 1000/Nm

9.0 Nt 1 5315/Ne 9000/Nm

Indirect system To English system (Ne) 590.5/Nt 5315/Nd 1 0.5905/Nm

To Metric system (Nm) 1000/Nt 9000/Nd 1.293/Ne 1

60 mm 45 mm 30 mm

Short fibre

15 mm 0 mm 0

25%

50%

75%

100%

50%

75%

100%

Figure 1.1 Staple diagram of cotton.

60 mm 45 mm 30 mm 15 mm 0 mm 0

25%

Figure 1.2 Staple diagram of synthetic fiber.

4

Textile Calculation

completely describe length characteristics. Thus, cotton fiber is characterized by mean length; upper half mean length; 2.5% span length; 50% span length; short fiber%; and length uniformity (Table 1.4). The span length is the % fibers greater than the stipulated length prescribed. Thus 2.5% span length ¼ 30 mm means 2.5% fibers in the population are 30 mm Uniformity ratio ¼

50% span length ðmmÞ  100 2:5% span length ðmmÞ

Uniformity index ¼

Mean length ðmmÞ  100 Upper half mean length ðmmÞ

The length parameters, i.e., staple length/mean length or 2.5% span length, are used for adjusting machine settings. 50% span length and short fiber % are used for predicting processing behavior and yarn properties. The uniformity ratio or uniformity index express, how uniform the length array is. Longer length means strong yarn, less end breakages during spinning, low twist requirement for maximum strength, and more production speed. Hairiness and yarn evenness are also affected by length. Short fibers are fibers less than 12.5 mm (half an inch). Short fiber % greatly affects fly liberation during spinning and drafting disturbances and therefore yarn evenness and strength. Table 1.4 Cotton fiber characteristics.

Length uniformity Good Average Poor

Uniformity ratio 50 45 43

Fineness Very fine Fine Average Coarse

5 MIC

IFC% ( Imamtured fibre content) Low (very mature) Average (mature) High (immature)

4%e8% 8%e12% 12%e18%

Maturity ratio Immature Mature Very mature

0.7e0.8 0.8e1.0 >1.0

Uniformity index 85 82 80

Introduction: textile manufacturing process

1.3.2

5

Fineness

Fineness of man-made fibers is expressed in dtex or denier, and for cotton, it is micronaire value. Since cotton fibers differ in terms of diameter, cross-sectional shape, and maturity, the fineness is measured indirectly by measuring resistance to air flow at a certain pressure for a given mass of fiber packed in a constant volume chamber. The conversion factor from dtex to micronaire value is dtex ¼ Mi  0:394

½Mi ¼ microniare value of cotton

The minimum mass irregularity (CVlim ) expected in a yarn can be given by following equation: 100 CVlim ¼ pffiffiffi  n

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi 1 þ 0:004 CV2d

where, n ¼ number of fibers in the yarn cross-section and CVd ¼ coefficient of variation of fiber diameter.

1.3.3

Maturity (MIC) of cotton fiber

High MIC (>4.5) fibers lead to - Increase in end breakages due to the presence of a smaller number of fibers in the yarn crosssection - reduces yarn strength and elongation - deteriorates yarn appearance - increases roving twist requirement

Low MIC ( F” less than 0.0500 indicate model terms are significant. In this case, linear mixture components are significant model terms and none of the interaction terms is significant. The value of coefficient of determination (R2) obtained is 0.670 as shown in Fig. 2.17 that implies the goodness of fit of the present model. The coefficients of all main components and their interaction effects

34

Textile Calculation

Table 2.6 The design runs of {3, 3} simplex-lattice design. Components No. of runs

x1

x2

x3

1 2 3 4 5 6 7 8 9 10

0 0 0 0.333 0.333 0.333 0.667 0.667 1 0

0 0.667 1 0 0.333 0.667 0 0.333 0 0.333

1 0.333 0 0.667 0.333 0 0.333 0 0 0.667

Figure 2.21 Simplex-centroid mixture design produced in Design Expert 6.0.8.

Table 2.7 Parameters for mixture design. Components

Symbol

Cotton fiber % Polyester fiber % Viscose fiber %

x1 x2 x3

Uncoded level components %

Coded level

100 50 0

1 0.5 0

Applications of selected response surface design of experiments

35

Figure 2.22 ANOVA output of simplex-centroid design from Design Expert 6.08 software.

are shown in Fig. 2.23. The model equation in terms of coded unit is shown in Fig. 2.24. The contour diagram of the experiment is shown in Fig. 2.25 where one can see the effects of the components on the tenacity of yarn. The contour lines depict that as the proportion of polyester fiber increases, the tenacity value of the yarn increases. Numerical optimization of yarn tenacity is performed by keeping tenacity as maximum and all components in range. The graphical output is shown in Fig. 2.26. It can be observed that the maximum tenacity value of 15.19 nN/Tex can be achieved at (0, 1, 0) levels of the components, i.e., with 100% polyester yarn with a desirability value of 0.96.

2.4

Process control in textiles by advanced control chart

Statistical control charts are very useful for controlling and monitoring the process variations of manufacturing of quality textile product. Textile industry adopted and implemented various conventional control charts like other industries [10,11]. Shewhart control charts for attributes and variables were used by traditional basis [12]. But, there

36

Textile Calculation

Figure 2.23 Output of simplex-centroid design from Design Expert 6.0.8.

are advances in this area of control charts with some new features of detecting the small shift of variability in the process. Brief descriptions about some of these advanced control charts are described in this chapter with some practical illustrations.

2.4.1

Individuals control charts

The individuals control chart is suitable for the situation when there is continuous variation observed in the data during the time period of measurement. Like most of the other variables control charts, it is also a two-chart. One chart is for the individual sample result (xi). The other chart is for the moving range (Ri) between successive individual samples. The individuals chart is very useful for monitoring processes where data are not available on a frequent basis. The individuals control chart examines variation in individual sample results over time. If the process is in statistical control, the average on the individuals chart is our estimate of the population average. The average range will be used to estimate the population standard deviation [13]. Control charts for individual measurements, e.g., the sample size ¼ 1, use the moving range of two successive observations to measure the process variability.

Applications of selected response surface design of experiments

37

Figure 2.24 Model equation of simplex-centroid design from Design Expert 6.0.8.

The moving range is defined by Eq. (2.8). MRi ¼ jxi  xi1 j

(2.8)

which is the absolute value of the first difference (e.g., the difference between two consecutive data points) of the data. Analogous to the Shewhart control chart, one can plot both the data (which are the individuals) and the moving range. For the control chart for individual measurements, the lines plotted are: UCL ¼ x þ 3

MR d2

Centre Line ¼ x LCL ¼ x  3

MR d2

where UCL is Uper Control Limit, LCL is Lower Control Limit, x is the average of all the individuals and MR is the average of all the moving ranges of two observations. d2 is an arbitrary constant used for estimation of population standard deviation from average range. The value of d2 can be obtained from standard statistical table. Here, at n ¼ 2 observations d2 ¼ 1:128. The individual control chart is a method of looking at variation. One source of variation is the variation in the individual sample results. This represents “long-term”

38 Textile Calculation

Figure 2.25 Contour plot of simplex-centroid design.

39

Figure 2.26 Numerical optimization of yarn tenacity.

Applications of selected response surface design of experiments

40

Textile Calculation

variation in the process. The second source of variation is the variation in the ranges between successive samples. This represents “short-term” variation [5e7,13].

2.4.2

Utility and limitations of individual control chart

This chart is useful where automated inspection and measurement technology is used. Every unit manufactured can be analyzed during manufacturing. It is also used where no basis for rational subgrouping is available. But the moving range individual chart cannot really provide useful information about a shift in process variability. However, the ability of the individuals control chart to detect small shifts is very poor [14].

2.4.3

Illustration of individual control chart

The following example illustrates the control chart for individual observations. A converter machine produces wet wipes from spunlace nonwoven. Each pack contains 20 pieces of wet wipes having nominal weight of 50 gm. In order to monitor the mass variation of these packs, an automatic weight measurement system is installed in the machine line which weighs and reports each and every single pack of wet wipes. The weight results of first 10 consecutive packs are shown in Table 2.8. This yields the below parameters for individual values. UCL ¼ x þ 3

MR 1:767 ¼ 49:91 þ 3 ¼ 54:61 1:128 1:128

Centre Line ¼ x ¼ 49:91 LCL ¼ x  3

MR 1:767 ¼ 49:91  3 ¼ 45:21 1:128 1:128

Table 2.8 Result of weight measurement of packs of wet wipes. Batch

Mass (gm)

Moving range

Number 1 2 3 4 5 6 7 8 9 10 Average

xi 48.6 46.6 48.9 50.3 46.8 50.2 51.6 51.4 52.6 52.1 x ¼ 49.91

MR e 2 2.3 1.4 3.5 3.4 1.4 0.2 1.2 1.5 MR ¼ 1.767

Applications of selected response surface design of experiments

41

Fig. 2.27 shows that the process is in control, since none of the plotted points fall outside either the UCL or LCL.

2.4.4

Zone chart

The basic Shewhart control chart is a common tool used in monitoring the mean of a process to ensure that it remains in control. This chart has a center line at the in-control mean value and 3s limits on either side of the center line. The chart signals an out-ofcontrol condition if any one of observed sample mean falls beyond the 3s limits. The concept behind the zone control chart is to allow for automatic signaling of the following out-of-control indicators in the Shewart chart. A zone chart is divided into four zones. Zone 1 is defined as values within 1s of the mean, zone 2 is defined as values between 1s and 2s of the mean, zone 3 is defined as values between 2s and 3s of the mean, and zone 4 as values 3s or more from the mean. Weights are assigned to the four zones. Weights for points on the same side of the center line are added. When a cumulative sum is equal to or greater than the weight assigned to zone 4, this is taken as a signal that the process is out of control. The cumulative sum is set equal to 0 after signaling a process out of control, or when the next plotted point crosses the center line [15].

2.4.5

Interpretation of zone control chart

The process signals out of control when any of the following situations appears. The situations are represented graphically at below in Fig. 2.28:

I-MR Chart of mass of wet wipes (gm)

Individual V alue

55.0

U C L=54.61

52.5 _ X=49.91

50.0 47.5

LC L=45.21

45.0 1

2

3

4

5 6 O bser vation

7

8

9

10

M oving Range

6.0

U C L=5.772

4.5 3.0 __ M R=1.767

1.5

LC L=0

0.0 1

2

3

4

5 6 O bser vation

7

8

9

Figure 2.27 MINITAB output of individual chart of mass of wet wipe packet.

10

42

Textile Calculation

Figure 2.28 Interpretation of zone chart.

1. 2. 3. 4.

A point falling outside the 3s limits, Two of three successive points falling outside the 2s limits on the same side of the center line. Four of five successive points falling outside the 1s limits on one side of the center line, Eight consecutive points falling on the same side of the center line.

2.4.6

Utility and limitations of zone chart

The shift of process mean and variability can be detected more efficiently and categorically. Any trend in the process toward higher shift from central limit can be detected quickly and process can be modified to maintain the quality. Only difficulty of this chart is that it is little complicated to study and interpret the process.

2.4.7

Illustration of zone chart

Test results of average areal density in gram per square meter (GSM) of spunlace nonwoven fabric are shown in Table 2.2. Fabric samples were randomly collected from production line after an interval of 1 h. 10 measurements of GSM were done for each sample and average GSM was calculated. All results of average GSM for two consecutive shifts (16 hours) have been shown in Table 2.2. The nominal GSM

Applications of selected response surface design of experiments

43

was 40. Zone chart of mean has been plotted with MINITAB 15 software as shown in Fig. 2.29. Standard deviation is estimated from mean range as shown in Table 2.9. It can be seen from Fig. 2.29 that though sample no 12 falls outside 2s limits, none of the rules is satisfied for decision of out of control. So, process was within control.

2.4.8

CUSUM control charts

CUSUM chart, i.e., cumulative sum control chart, is not as intuitive and simple to operate as Shewhart charts. However, this chart is more efficient in detecting small shifts from the process mean. CUSUM control chart is demonstrated better than Shewhart control charts when it is desired to detect shifts in the mean that are beyond 2s limit or less. An illustration of the CUSUM chart is as follows. Let us collect m samples, each of size n, and compute the mean of each sample. Then, the cumulative sum (CUSUM) control chart is formed by plotting one of the following quantities as shown in Eq. (2.8). m X

Sm ¼

ðxi  m c0 Þ or S0m ¼

i¼1

m 1X ðxi  m c0 Þ sx i¼1

(2.9)

c0 is the estimate/target where m ¼ sample number, xi is the average of the ith sample, m of the in-control mean, and sx is the known (or estimated) standard deviation of the sample means. The choice of which of these two quantities is plotted is usually determined by the statistical software package. In either case, as long as the process remains in control

Zone Chart of Nonwoven GSM 8 +3 StDev=44.83 4

4

+2 StDev=43.37 2 0

2

2 0

0

0 0

0

2

2

+1 StDev=41.91 _ _ X=40.44

0 0

0

2

-1 StDev=38.98 2

2

2

2

-2 StDev=37.52 4 -3 StDev=36.05 8 1

3

5

7

9 Sample

Figure 2.29 Zone chart of nonwoven GSM.

11

13

15

44

Textile Calculation

Table 2.9 Test results of nonwoven GSM. Sample no.

Average GSM

Grand mean

Standard deviation

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

40.84 39.11 38.69 39.83 40.68 39.66 39.39 39.36 40.14 41.11 41.09 42.51 40.05 39.70 40.35 41.25

40.443

1.466

centered at sx , the CUSUM plot will show variation in a random pattern centered about zero. If the process mean shifts upward, the charted CUSUM points will eventually drift upwards and vice versa if the process mean decreases [16,17].

2.4.9

Illustration of CUSUM control chart

Consistency in GSM of spunlace nonwoven fabric is very important which otherwise affects the quality of end products. Test results of average GSM of spunlace nonwoven fabric are shown in Table 2.10. The fabric samples were collected randomly from production line after each 1 h for GSM measurement. From each fabric sample, 10 measurements were done and average GSM was calculated. The test results of average GSM for 25 samples have been shown in Table 2.10. We need to formulate a CUSUM control chart to detect the small shift of GSM from targeted mean value. The targeted mean value was 40. The graph in Fig. 2.30 is not a control chart because it lacks control limits. There are two general approaches to devising control limits for CUSUM such as V-Mask and tubular CUSUM. The older of these two methods is the V-Mask procedure.

2.4.10

V-mask used to determine if process is out of control

A visual procedure proposed by Barnard in 1959, known as the V-Mask, is sometimes used to determine whether a process is out of control. More often, the tabular form of the V-Mask is preferred. A V-Mask is an overlay shape in the form of a V on its side that is superimposed on the graph of the cumulative sums. The origin point of the V-

Applications of selected response surface design of experiments

45

Table 2.10 CUSUM chart of GSM data of 25 samples of spunlace nonwoven fabric.

Obs no. (i)

Garment GSM (xi)

Target

xi L 40

Cumulative sum Si [ (xi L 40) D SiL1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

40.68 39.66 39.39 39.36 40.14 41.11 41.09 42.51 40.05 39.7 40.35 41.25 39.91 39.54 40.14 39.06 40.36 40.26 39.31 39.6 40.5 39.65 39.05 40.5 41.65 40.8

40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40

0.68 0.34 0.61 0.64 0.14 1.11 1.09 2.51 0.05 0.3 0.35 1.25 0.09 0.46 0.14 0.94 0.36 0.26 0.69 0.4 0.5 0.35 0.95 0.5 1.65 0.8

0.68 0.34 0.27 0.91 0.77 0.34 1.43 3.94 3.99 3.69 4.04 5.29 5.2 4.74 4.88 3.94 4.3 4.56 3.87 3.47 3.97 3.62 2.67 3.17 4.82 5.62

Mask (see Fig. 2.31) is placed on top of the latest cumulative sum point and the past points are examined to see if there is any fall above or below the sides of the V. As long as all the previous points lie between the sides of the V, the process is in control. Otherwise (even if one point lies outside in Fig. 2.31) the process is suspected of being out of control [14,17]. In Fig. 2.31 the V-Mask shows an out-of-control situation because of the point that lies above the upper arm. By sliding the V-Mask backwards so that the origin point covers other cumulative sum data points, we can determine the first point that signaled an outof-control situation. This is useful for diagnosing what might have caused the process to go out of control. From the diagram, it is clear that the behavior of the V-Mask is determined by the distance k (which is the slope of the lower arm) and the rise distance h. These are the design parameters of the V-Mask. Note that we could also specify d and the vertex angle (or, as is more common in the literature, q ¼ 1/2 of the vertex angle) as the design parameters, and we would end up with the same V-Mask.

46

Textile Calculation

6 5

CUSUM (Si)

4 3 2 1 0 -1 -2 0

5

10

15

20

25

Observations (i)

Figure 2.30 CUSUM control chart.

Figure 2.31 Illustration of V-Mask of CUSUM chart.

In practice, designing and manually constructing a V-Mask is a complicated procedure. A CUSUM spreadsheet style procedure shown below is more practical, unless you have statistical software that automates the V-Mask methodology. Before describing the spreadsheet approach, we will look briefly at an example of a V-Mask in graph form.

Applications of selected response surface design of experiments

47

We can design a V-Mask using h and k or we can use an alpha and beta design approach. For the latter approach we must specify • • •

a: the probability of a false alarm, i.e., concluding that a shift in the process has occurred, while in fact it did not, b: the probability of not detecting that a shift in the process mean has, in fact, occurred, and d (delta): the amount of shift in the process mean that we wish to detect, expressed as a multiple of the standard deviation of the data points (which are the sample means).

The values of h and k are related to a, b, and d based on Eqs. (2.10)e(2.12). k¼

dsx 2

(2.10)

d¼

  2 1b ln a d2

(2.11)

h ¼ dk

(2.12)

Generally, we choose a ¼ 0.0027 (equivalent to the 3 sigma criteria used in a standard Shewhart chart) and b ¼ 0.01. Finally, we decide we want to quickly detect a shift as large as 1 sigma, which sets d ¼ 1. A general rule of thumb if one chooses to design with the h and k approach, instead of the a and b method illustrated above, is to choose k to be half the d shift (0.5) and h to be around 4 or 5.

2.4.11 Illustration 1 of CUSUM chart with V-mask Same dataset of Table 2.10 is used here for CUSUM chart with V-mask for target value of mean GSM equal to 40. General h and k approach is adopted here with k equals to half the d shift (0.5) and h equals to 4. The origin point of the V-Mask (see Fig. 2.32) is placed on top of the latest cumulative sum point and past points are examined to see if there is any fall above or below the sides of the V. As all the previous points lie between the sides of the V, the process is in control.

2.4.12 Illustration 2 of CUSUM chart with V-mask Another study of the same nonwoven production is illustrated here. Test result of average GSM of 12 samples has been shown in Table 2.11. 10 observations were made for each case and average GSM was evaluated for each samples. A CUSUM chart has been constructed with V-mask for target value of mean GSM equal to 50. The CUSUM control chart with V-Mask of nonwoven GSM has been constructed by Minitab 15 software as shown in Fig. 2.33. It can be seen that though the process means drift below the target value, the process is in control, as none of points are outside the control limit.

48

Textile Calculation

Vmask Chart of Avg GSM 20

Cumulative Sum

15 10 5 Target=0

0 -5 -10 1

4

7

10

13 16 Sample

19

22

25

Figure 2.32 CUSUM chart with V-mask of nonwoven GSM, process means drift in lower side.

2.4.13

Tabular CUSUM

The other approach to CUSUM control, the tabular CUSUM, is superior. The tabular procedure is particularly attractive when the CUSUM is implemented on a computer [10]. Let SH(i) be an upper one-sided CUSUM for period i and SL(i) be a lower one-sided CUSUM for period i. These quantities are calculated from the following: sH ðiÞ ¼ max½0; xi  ðm0 þ KÞ þ sH ði  1Þ Or sH ðiÞ ¼ max½0; ðm0 KÞ xi þsL ði 1Þ Table 2.11 Nonwoven GSM measurement. Sample no.

Nonwoven GSM

1 2 3 4 5 6 7 8 9 10 11 12

49.42 48.85 49.68 47.74 49.66 50.34 49.51 49.87 49.88 49.46 51.26 51.50

Applications of selected response surface design of experiments

49

Vmask Chart of Avg GSM 5.0

Cumulative Sum

2.5 0.0

Target=0

-2.5 -5.0 -7.5 -10.0 1

2

3

4

5

6 7 Sample

8

9

10

11

12

Figure 2.33 CUSUM chart with V-Mask for nonwoven GSM, process means drift in lower side.

where the starting values sH ð0Þ ¼ sL ð0Þ ¼ 0 K is called the reference value, which is usually chosen about halfway between the b 0 and the value of the mean corresponding to the out-of-control state, m1 [ m b0 target m D D. That is, K is about one-half the magnitude of the shift, D/2.

2.4.14 Illustration of tabular CUSUM The tabular CUSUM is illustrated by applying it to the below data of nonwoven GSM measurement as shown in Table 2.12. The process target is 99, and we will use K ¼ 1 as the reference value and H ¼ 10 as the decision interval. The observations of CUSUM are sH ð1Þ ¼ max½0; xi  100 þ sH ð0Þ ¼ max½0; 102:0  100 þ 0 ¼ 2:0 sL ð1Þ ¼ max½0; 98  x1 þ sL ð0Þ ¼ max½0; 98  102:0 0 ¼ 0 Notice that the CUSUMs in this example never exceed the decision interval H ¼ 10. We would therefore conclude that the process is in control.

2.4.15 Utility and limitations of CUSUM chart CUSUM control charts are better than Shewhart control charts when it is desired to detect shifts in the mean that are 2s or less. Small shifts in the control chart can be detected easily by change in the slope of the V-mask [17].

50

Textile Calculation

Table 2.12 Test result and analysis of tabular CUSUM. Observation (i) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2.5

Xi 102 94.8 98.3 98.4 102 98.5 99 97.7 100 98.1 101.3 98.7 101.1 98.4 97 96.7 100.3 101.4 97.2 101

Upper sum Xi-100 2 5.2 1.7 1.6 2 1.5 1 2.3 0 1.9 1.3 1.3 1.1 1.6 3 3.3 0.3 1.4 2.8 1

SH(i) 2 0 0 0 2 0.5 0 0 0 0 1.3 0 1.1 0 0 0 0.3 1.7 0 1

Lower sum nH 1 0 0 0 1 2 0 0 0 0 1 0 1 0 0 0 1 2 0 0

98-Xi 4 3.2 0.3 0.4 4 0.5 1 0.3 2 0.1 3.3 0.7 3.1 0.4 1 1.3 2.3 3.4 0.8 3

SL(i) 0 3.2 2.9 2.5 0 0 0 0.3 0 0 0 0 0 0 1 2.3 0 0 0.8 0

nL 0 1 2 3 0 0 0 1 0 0 0 0 0 0 1 2 0 0 1 0

EWMA control charts

The Exponentially Weighted Moving Average (EWMA) is a statistic for monitoring the process that averages the data in a way that gives some importance to old data as they are further removed in time. For the Shewhart chart control technique, the decision regarding the state of control of the process at any time, t, depends solely on the most recent measurement from the process and, of course, the degree of “trueness” of the estimates of the control limits from historical data. For the EWMA control technique, the decision depends on the EWMA statistic, which is an exponentially weighted average of all prior data, including the most recent measurement. By the choice of weighting factor, l, the EWMA control procedure can be made sensitive to a small or gradual drift in the process, whereas the Shewhart control procedure can only react when the last data point is outside a control limit. The statistic that is calculated is: EWMAt ¼ lYt þ (l  l) EWMAt1 for t ¼ 1, 2, ., n.

Applications of selected response surface design of experiments

51

where • • •

EWMA0 is the mean of historical data (target) Yt is the observation at time t n is the number of observations to be monitored including EWMA0

0 < l  1 is a constant that determines the depth of memory of the EWMA. The parameter l determines the rate at which “older” data enter into the calculation of the EWMA statistic. A value of l ¼ 1 implies that only the most recent measurement influences the EWMA (degrades to Shewhart chart). Thus, a large value of l ¼ 1 gives more weight to recent data and less weight to older data; a small value of l gives more weight to older data. The value of l is usually set between 0.2 and 0.3 although this choice is somewhat arbitrary. The estimated variance of the EWMA statistic is approximately s2ewma ¼ (l/(2  l)) s2 when t is not small and where s is the standard deviation calculated from the historical data. The center line for the control chart is the target value or EWMA0. The control limits are: UCL ¼ EWMA0 þ ksewma LCL ¼ EWMA 0  ksewma where the factor k can be set equal to 3 for 3s limit. As with all control procedures, the EWMA procedure depends on a database of measurements that are truly representative of the process. Once the mean value and standard deviation have been calculated from this database, the process can enter the monitoring stage, provided the process was in control when the data were collected. If not, then the usual Phase 1 work would have to be completed first.

2.5.1

Utility and limitations of EWMA chart

The EWMA chart is an alternative to the individuals or X-bar chart that provides a quicker response to a shift in the process average. The EWMA chart incorporates information from all previous subgroups, not only the current subgroup. By the choice of weighting factor, l, the EWMA control procedure can be made sensitive to a small or gradual drift in the process, whereas the Shewhart control procedure can only react when the last data point is outside a control limit [17,18].

52

Textile Calculation

2.5.2

Illustration of EWMA control chart

EWMA chart of online GSM measurement data of spunlace nonwoven fabric (Table 2.13) has been shown in Fig. 2.34. To illustrate the construction of an EWMA control chart, consider a process with the following parameters calculated from historical data: EWMA0 ¼ 102 s¼1 with l chosen to be 0.2 so that l/(2  l) ¼ 0.2/1.8 ¼ 0.1111 and the square root ¼ 0.3333. The control limits are given by UCL ¼ 102 þ 3 (0.3333)  1 ¼ 103

Table 2.13 Nonwoven GSM data of 25 samples. Sample no.

GSM

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

100.00 100.75 101.00 102.75 103.50 100.50 100.75 106.25 101.00 100.50 101.25 102.00 101.75 101.50 103.50 102.75 101.50 102.00 101.50 102.00 100.00 102.00 103.75 104.75 102.25

Applications of selected response surface design of experiments

53

EWMA Chart of nonwoven GSM 103.0

UCL=103.000

EWMA

102.5 _ _ X=102

102.0

101.5

LCL=101.000

101.0 1

3

5

7

9

11

13 15 Sample

17

19

21

23

25

Figure 2.34 EWMA chart of nonwoven GSM.

LCL ¼ 102  3 (0.3333)  1 ¼ 101 The chart tells us that the process is in control because all EWMAt lie between the control limits.

2.6

Conclusions

Response surface methodology is a statistical approach and technique which is useful in understanding, developing, and optimizing processes and products. Using this methodology, the responses that are influenced by several variables can be modeled, analyzed, and optimized. It forms relationship between the response (dependent) and factor (independent) variables which is not known. The response surface is analyzed to locate a direction that goes toward the general vicinity of the optimum. In textile engineering, there is a huge scope on the development and application of response surface methodology for optimizing processes and products. This chapter can throw some light on that. Shewhart control charts for attributes and variables which were used by traditional basis are not efficient of detecting small shift of variability in the process. Advanced control charts with some new features are able to detect small shift of variability in the process. The individual control chart is very useful for monitoring processes where data are not available on a frequent basis. This chart examines variation in individual sample results over time. This chart is a method of looking at short-term and long-term variation. This chart is useful where automated inspection and measurement technology is used. Every unit manufactured can be analyzed. It is also used where no basis

54

Textile Calculation

for rational subgrouping is available. The concept behind the zone control chart is to allow for automatic signaling of the following out-of-control indicators in the Shewart chart. The shift of process mean and variability can be detected more efficiently and categorically. This chart is little complicated to study and interpret the process. CUSUM chart is more efficient in detecting small shifts in the mean of a process. They are better than Shewhart control charts when it is desired to detect shifts in the mean that are 2s or less. Small shifts in the control chart can be detected easily by change in the slope of the V-mask. EWMA control chart is a statistic for monitoring the process that averages the data in a way that gives some importance to old data with recent data. This chart is an alternative to the individuals or X-bar chart that provides a quicker response to a shift in the process average. By the choice of weighting factor, l, the EWMA control procedure can be made sensitive to a small or gradual drift in the process, whereas the Shewhart control procedure can only react when the last data point is outside a control limit.

References [1] H.G.J. Pacheco, N.Y.M. Elguera, H.D.Q. Sarka, M. Ancco, K.I.B. Eguiluz, G.R. SalazarBanda, Box-Behnken response surface design for modeling and optimization of electrocoagulation for treating real textile wastewater, Int. J. Environ. Res. 16 (4) (2022) 1e12. [2] M. Demirel, B. Kayan, Application of response surface methodology and central composite design for the optimization of textile dye degradation by wet air oxidation, Int. J. Ind. Chem. 3 (1) (2012) 1e10. [3] S. Ghosh, R. Das, S. Maity, Optimization of material and process parameters of fibrous quilt for comfortable heat loss from human body, J. Text. Inst. 110 (6) (2019). [4] S. Maity, A. Chatterjee, Preparation and characterization of electro-conductive rotor yarn by in situ chemical polymerization of pyrrole, Fibers Polym. 14 (8) (2013). [5] P. Bansal, S. Maity, S.K. Sinha, Effects of process parameters on tensile and recovery behavior of ring-spun cotton/lycra denim yarn, J. Inst. Eng. Ser. E 100 (1) (2019). [6] N. Nasirizadeh, H. Dehghanizadeh, M.E. Yazdanshenas, M.R. Moghadam, A. Karimi, Optimization of wool dyeing with rutin as natural dye by central composite design method, Ind. Crop. Prod. 40 (2012) 361e366. [7] S. Maity, Optimization of processing parameters of in-situ polymerization of pyrrole on woollen textile to improve its thermal conductivity, Prog. Org. Coating 107 (2017). [8] S. Maity, S. Pandey, A. Kumar, Influence of needle-punching parameters for the preparation of polypyrrole-coated non-woven composites for heat generation, Tekstilec 64 (2) (2021). [9] S. Hassanzadeh, H. Hasani, M. Zarrebini, Analysis and prediction of the noise reduction coefficient of lightly-needled Estabragh/polypropylene nonwovens using simplex lattice design, J. Text. Inst. 105 (3) (2014) 256e263. [10] A. Anwar, D.D. Rochman, Implementation X and R control chart at Pt, Grand Text. Ind. (2009). [11] O.P. Beckwith, The quality control chart technique in applied textile research, Text. Res. 14 (10) (1944) 319e325. [12] M.S. Ahmad, M.A. Iqbal Javed, H.M. Naeem, M. Sarwar, Application of statistical quality control in yarn spinning, Pak. J. Agli. Sci. 29 (1) (1992).

Applications of selected response surface design of experiments

55

[13] D.C. Montgomery, Introduction to Statistical Quality Control, John Wiley & Sons, 2020. [14] S. Maity, The application of advanced control charts in textiles, J. Text. Assoc. 74 (3) (2013). [15] R.B. Davis, A. Homer, W.H. Woodall, Performance of the zone control chart, Commun. Stat. Methods 19 (5) (1990) 1581e1587.  € _ ERTUGRUL, [16] I. A. Ozçil, The application of ‘p’ and ‘p-CUSUM’ charts into textile sector in the statistical quality control process, Text. Appar. 24 (1) (2014) 9e14. [17] P.K. Carson, A.B. Yeh, Exponentially weighted moving average (EWMA) control charts for monitoring an analytical process, Ind. Eng. Chem. Res. 47 (2) (2008) 405e411. [18] T. Maros, B. Vladimír, T.M. Caner, Monitoring chenille yarn defects using image processing with control charts, Textil. Res. J. 81 (13) (2011) 1344e1353.

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Man made fiber manufacturing process

3

Supriyo Chakraborty Uttar Pradesh Textile Technology Institute, Kanpur, Uttar Pradesh, India

3.1

Introduction

Since long, synthetic fibers dominate as textile fibers compared to the natural fibers for various purposes. More than half of the quantity of textile fibers consumed globally is captured by the synthetic fibers, which is supposed to continue in future also. The most popular synthetic textile fibers include polyester, acrylic, nylon, viscose rayon, vinyl fibers, and polypropylene which is used in various apparel or some highly technical applications. Synthetic fibers can be organic as well as inorganic composed to polymers and polymer molecules are composed of monomers. Properties of the monomers and the polymer itself can critically influence the properties of the fiber produced. Many textbooks are available those document basic information related to monomer their properties, polymer characteristics, processing related technical facts, their utilization, etc. Each step of production of textile fiber requires a thorough understanding of information related to monomer, polymer, and processing of them to successfully produce a textile fiber. Some quantitative illustrations related to textile fibers and their manufacturing processes have been compiled here. In this chapter, fundamental concepts of polymeric molecules, degree of polymerization, molecular weights, aspect ratio of a polymer macromolecule, denier and diameter relationships, and some examples of fiber production have been covered.

3.2

Degree of polymerization

In general, two kinds of polymerization processes are carried out to produce polymers for producing textile fiber: (1) addition polymerization or free radical polymerization (essential steps initiation / propagation / termination) and (2) step growth polymerization. Condensation polymerization can be conducted using an AB type (Nylon 6), or AABB type (Nylon 66) monomers. Molar mass of a
½ AB]
or
[AABB]
type polymer can simply be calculated by multiplying molar mass of the repeat units by number of such repeating units in the molecule Mpolymer ¼ n  MAB orMAABB

Textile Calculation. https://doi.org/10.1016/B978-0-323-99041-7.00002-3 Copyright © 2023 Elsevier Ltd. All rights reserved.

(3.1)

58

Textile Calculation

Here, n is the number of repeat units in the polymer which is exactly the degree of polymerization. In case of a condensation polymerization reaction of polymers of
[AA]
type, there is a
[BB]
monomers will be used where during condensation reaction for example with dicarboxylic acid and a diol the polymer the molar mass decreases by ð2n
1ÞH2 O in each step, n
½AA
þ n
½BB
/ n
½AABB
þ ð2n
1ÞH2 O

(3.2)

n
½AB
/ n
½AB
þ ðn
1ÞH2 O

(3.3)

whereas in case of
[AB]
type polymer (for example, aminocaproic acid) corresponding polymer molar mass decreases by ðn
1ÞH2 O. For
[AABB]
type polymers, the degree of polymerization, Pn, is same as the number of repetitions n and it can be calculated as follows: Pn ¼

n0 nt

(3.4)

where n0 is initial number of molecules and nt is number of molecules at time t. Or it can also be expressed as the ratio of initial concentration of functional groups to that of time t. If the stoichiometric ratio of monomers is r and P is the extent of reaction, then degree of polymerization is given by Pn ¼

rþ1 ðknown as Carother's eqautionÞ. r
2rp þ 1

(3.5)

what value of the stoichiometric imbalance (r) of hexamethylene diamine (HMDA) and adipic acid (AA) should be employed in order to obtain a polyamide of molecular weight 10,500 at 99.0% conversion? Also identify the end groups of the product (Nylon 66).

Example 3.1.

Solution.

Formula weight of repeating unit e[
HN(CH2)6NHCO(CH2)4CO
]e ¼ 226

M0 ¼ 1=2  226 ¼ 113; X n ¼ Mn =M0 ¼ 10; 500=113 ¼ 92:92; with P ¼ 99.0%, Xn ¼

rþ1 ¼ 92:92 r
2rð0:99Þ þ 1

Man made fiber manufacturing process

59

So, r ¼ 0.9984 implies that stoichiometric imbalance to be kept at a ratio of the value obtained to achieve desired molecular weight, if HMDA is taken in excess end groups obtained in the final product will be basic (
NH2), reverse will happen as eCOOH groups will be end groups if AA is taken in excess [1]. How much degree of polymerization will be required to obtain the polymer molecular weight up to 1,00,000 g mol
1 for polyacrylonitrile (PAN,
[CH2e CH.CN]n
)? (Molar mass of acrylonitrile is 53.06 g mol
1)

Example 3.2.

Approximate degree of polymerization required will be ¼ 1,00,000/ 53.06e1890. To control the degree of polymerization for a [eAAe], [eBBe] type polymerization reaction when we add a small quantity of a mono-functional species, for example, B, in an equimolar polymerization of [eAAe] and [eBBe], the stoichiometric imbalance may be calculated as follows:

Solution.

r¼

NA0 NB0 þ 2NB0 0

(3.6)

NB0 0 is the number of mono-functional B molecule initially present, NA0 ¼ 2NAA0 and NB0 ¼ 2NBB0 . The number of average molecular weight of Nylon 66 is desired to be kept under 15,000 as the extent of reaction p approaches 1. How many moles of acetic acid will be required (used as stabilizer) to keep the required DP under control, so that molecular weight is maintained below the mentioned level?
rþ1 Solution. X n ¼ r
2rðp¼1Þþ1 ¼ 15; 000 113 ¼ 132:74 or r ¼ 0.985, then using Eq. 2 ; then solving for x, we obtain x y 0.0152; hence, (3.6) we write, r ¼ 0:985 ¼ 2þ2x for every mole of adipic acid 0.01522 mol of acetic acid has to be added to control molecular weight of the polymerization. Example 3.3.

3.3

Number average molecular weight, weight average, and viscosity average molecular weight of polymers

The mathematical expressions for various molecular weights defined as number average molar mass (Mn), which is also lightly mentioned as number average molecular weight, mass/weight average molecular weight (Mw), Z-average molecular weight (Mz), where z stands for centrifugation and viscosity average molar mass (Mv). Ni stands for number of polymer molecules for each category (denoted by i) of molecular weights, a is the exponent from MarkeHouwink equation relating to intrinsic viscosity.

60

Textile Calculation

P Mi Ni (a) Mn ¼ P N ; P i2 Mi Ni (b) Mw ¼ P M N P 3i i M i Ni (c) Mz ¼ P M 2 N i i P 1þa 1=a M i Ni (d) Mw ¼ P M i Ni

There are various ways which can be used to determine the average molecular weight of the polymers that can be marked as absolute method, namely end-group analysis to measure number average molecular weight, colligative method, membrane osmometry, vapor pressure osmometry, light scattering methods, etc. Some relative methods include viscometry, size exclusion chromatography, etc. Each method include established scientific facts and methodology by aid of which estimation of molecular weights can be done. In this section, only a few methods have been elucidated with some numerical illustrations.

3.3.1

End-group analysis to measure number average molecular weight

If the polymer has detectable end groups and the amount of such end groups per molecule is known ahead of time, end-group analysis can be used to calculate the number average molecular weight Mn of polymer samples. End-group analysis has primarily been used on condensation polymers, as they used to have reactive functional end groups as terminal groups. The carboxylic groups of polyesters and the amine groups of polyamides, for example, are generally acidic or basic in character; such groups are easily measured by titration. In the following example, determination of number average molecular weight is shown to be determined using end-group analysis technique. Determine the number average molecular weight of carboxyl terminated polybutadiene (CTPB, monomer is bifunctional) from the given experimental information. A small quantity of CTPB (0.8734 g) was dissolved in a mixture of toluene and ethanol (1:3) and titrating against alcoholic KOH (0.125N) using phenolphthalein indicator. During titration, 5.1 mL of alcoholic KOH was consumed. Comment on the limitation of the method adopted.

Example 3.3.1.1.

Development of the theoretical concept; carboxyl value of polymer is determined as the first step based on the following formula. Let the volume of KOH consumed ¼ V ml; normality of KOH ¼ N; gram equivalent of the titrating base or acid; and weight of the sample taken ¼ w g (this can be dealt with the following relationship)

Solution.

Man made fiber manufacturing process

Carboxyl value ¼

V NM w

Carboxyl equivalent=100g ¼ ¼

61

(3.7)

V  N  56:1ðgm equivalent of KOHÞ  100 wð1000Þ  56:1

V N 10w

In the given experimental example, 0.8734 g of the sample has consumed 5.1 mL of 0.125 (N) alcoholic KOH solution; then Carboxyl equivalent=100g ¼

5:1  0:125 ¼ 0:073 10  0:8734

As the functionality of the monomer is 2, then number average molecular weight 100 Mn ¼ ð0:073=2Þ y2739. This chemical analysis method is limited to the insolubility and titration of the polymer in the solvent and also it gives only number average molecular weight [2].

3.3.2

Dilute solution viscometers: determination of number average and viscosity average molecular weight of the polymer

Vinyl polymers such as PAN fiber or polypropylene fiber molecular weight cannot be determined by end-group analysis as they do not have detectable end groups. For such polymers, the dependence of viscosity on size permits estimation of an average molecular weight from solution viscosity (polymer intrinsic viscosity, IV). The average molecular weight that is measured is the viscosity average M v which differs from M n and Mw.

3.3.2.1

Determination of number average molecular weight by intrinsic viscosity method

Intrinsic viscosity of polyethylene was determined in this example as
hsp c has been plotted against concentration (Fig. 3.1); then number averaged molecular weight was determined using the following equation as derived by Harris [3,4] (Eq. 3.8). Example 3.4.

h ¼ 1:35  10
4  Mn0:63

(3.8)

Measured specific viscosities are plotted with decreasing concentration and extrapolated to obtain y-axis intercept. Hence, in this graph, we can locate that at infinite dilution for PE, polymer-specific viscosity is about w0.101, thus using the above

62

Textile Calculation

0.3

0.2

/ 0.1

0 0

5

10 15 20 Concentration (g/lit) 
 Figure 3.1 Specific viscosity/concentration hsp c is plotted against concentration.

empirical equation developed by Harris that was used to determine M n of the polymer which comes to about 36,000 in close with the same value determined by some other methods such as colligative and osmotic pressure methods (32,000).

3.4

Quantitative concepts of polymeric molecules for fibers

Polymeric molecules for fiber formation require the molecules to have large molecular weight and high degree of polymerization. For example, molecular weight of cellulose molecule as per some recent study can be as high as 10,000 g mol
1. One of the requirement of fiber-forming polymer is that it should have minimum or no branching of side chains as well as very high length: diameter ratio; similarly, a textile fiber should have an adequate L:D ratio required for successful processing of the fibers. For example, typical diameter of cotton and wool fiber is 0.000700 and length 100 , 0.00100 and 300 resulting length to diameter ratio greater than 1400e3000. The arrangement of molecules in a crystalline structure, crystallinity, crystallite size, and degree of orientation was all investigated using X-ray diffraction. Researchers such as W. T. Astbury used advanced X-ray diffraction methods, demonstrating that the individual molecules of cotton or wool fiber are extremely long [5]. The overall thin and lengthy shape of the fibers reflects the long shape of the molecules. Length of the cellobiose (constituting element of large cellulose molecule) unit is approximately 10.28Å and width is 7.5 Å. For a cellulose molecule of degree of polymerization 7,000, calculate length/diameter ratio. The L:D ratio can be calculated as follows: 7000/2  10.28Å/7.5 Å ¼ 4797 (reflecting the high L:D ratio of the fiber itself) [4].

Example 3.5.

Man made fiber manufacturing process

...

63

... CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 0.252nm

Polyethylene repeat unit

Figure 3.2 Schematic diagram of polyethylene molecule.

Determine the length of a fully extended polyethylene molecular chain of molecular weight 100,000 g mol
1. Given length of repeat unit (eCH2eCH2e) is 0.252 nm.

Example 3.6.

The first task is to estimate the number of repeat units, n, in the polyethylene chain. Each repeat unit has 2 carbons and 4 hydrogen atoms. The molecular weight of carbon is 12 and that of hydrogen 1. Hence, MW/repeat unit ¼ 2(12) þ 4(1) ¼ 28 (Fig. 3.2). The number of repeat units is computed as n ¼ MW/(MW/repeat unit)

Solution.

n ¼ 100,000/28 ¼ 3571 units, Using the diagram presented in Fig. 3.2, we can now estimate the length of the fully extended molecule using, l ¼ 0.252 nm  (3571) ¼ 890 nm ¼ 0.89 mm. However, in a fibrous polymer, natural or synthetic molecules of different degrees of polymerization exist that form a distribution (molecular weight distribution) characteristic for a particular polymer. Chemically, molecular distribution can be determined by dissolving a polymer in a suitable solvent (for example, cellulose nitrate in acetone or Orlon in DMF) and then precipitating the polymers on different molecular weights, by step by step adding a nonsolvent to reduce the solvating power of the solution, followed by molecular weight determination of each fraction by viscosity measurement method.

3.5

Relation between filament fineness (denier) and it’s diameter

Conceptually when we know the denier of filament, which can be easily determined in a laboratory, and from the knowledge of density of the polymer used, we can establish a relationship between filament diameter, density, and denier. Following example will illustrate this. It will provide an interesting exercise to calculate the diameter of a nylon filament of denier ¼ 3, from a knowledge of the specific gravity, which is 1.14, and the shape of the cross-section, which is circular. Example 3.7. Considering that the filament denier is 3,9000 m of filament weigh 3 g or 3000 m weigh 1 g. But 1 g also, since the specific gravity is 1.14, occupies a volume of 1/1.14 cc. Therefore, 3000 m of yarn occupy a volume of 1/1.14 cc. Considering fila
ment diameter being d, then volume of a length l of a given yarn is d2 4  l. Then, 1 g of filament will be having a volume 1/1.14 cc. and length 3000 m.

64

Textile Calculation

So, it follows that using Eq. (3.9) pd2  3000m ¼ 1=1:14cc ¼ 0:877  10
6 m3 4

(3.9)

Then, carrying out the simplification, it can be obtained that d ¼ 19:3m. Handily, it can be written that 3.0 den nylon fiber will be having diameter, d ¼ 20:0m; hence, for other finenesses diameter (D) of the filament can be obtained from Eq. (3.10) as follows, dy20

pffiffiffiffiffiffiffiffiffiffiffiffiffi Den=3ðmÞ

(3.10)

for example, for a yarn of 7 denier, corresponding filament diameter will be 30.5m. Useful similar relationships can be derived for filaments made of other polymers of known density. If a filament 7 Den is observed under microscope with 500x magnification, its diameter will appear to be 15.2 mm. Knowing the density and denier of a fiber length, diameter ratio can be easily calculated which can be between 1000e4000 which is suitable for textile purposes.

3.6

Tensile strength of a filament

Tenacity of a textile fiber or filament is usually expressed in g den
1. When an applied load of 450 g will just break a 90-denier yarn, the tenacity is said to be 5.0 g per denier. Few fibers such as the regenerated proteins or ordinary viscose rayon may have tenacities as low as 1 g per denier, whereas others like Nylon and Fortisan have 6e7 g per denier. Tensile strength of the textile fiber can be expressed as lb inch
2 or GPa (Giga Pascal) or MPa (Mega Pascal) more conveniently expressed as g den
1; the reason behind this is measuring fiber diameter accurately is practically not easy. However, the tenacity or tensile strength of a filament yarn is occasionally stated in pounds per square inch or in mega Pascal instead of in grams per denier; a relationship can be derived the between the two methods using the following formula (Eq. 3.11): Tensile strength ¼ ½12; 800d ðspecific gravityÞ  gm:=denierlb=in2 .

(3.11)

where d is the specific gravity of the fiber material/polymer. A polypropylene (PP) sample filament is having specific gravity 0.92 and tenacity 2 gpd, what will be its tensile strength in lb/in2?

Example 3.6.1.

The tensile strength will be calculated as per the derived Eq. (3.11), and the resulting tensile strength will be w23,500 l b/in2 (12,800  0.92  2 l b/in2). (Using the conversion relationship stating 1 l b/in2 is approximately equal to 6895 Pa; the value in lb/in2 can be converted to Pa, MPa, or GPa) [4].

Solution.

Man made fiber manufacturing process

65

Both the molecular weight and the molecular weight distribution are of prime importance in (1) controlling and thus conducting the polymerization process; (2) the fiber forming process, because of the strong effects on the rheological properties of the melt of polyamides; and (3) the final product characteristics, particularly in regard to the tensile properties. Therefore, more than the determination of one molecular weight is necessary for adequate polymer characterization and evaluation.

3.7

Temperature dependence of polymer viscosity

During flow of molten polymers, a typical behavior and deformation which depends on both temperature and time (frequency), that is, the viscoelastic response of a polymer, will depend on the shear history. The viscosity is independent of the shear history only in case of Newtonian liquids, or only for low molecular weight polymers. The temperature dependence of the polymer viscosity may be described by a simple Arrhenius equation of the following form: hðTÞ ¼ AeEh =RT

(3.12)

Inorganic glasses and metals show close to Newtonian behavior in the fluid-like state. For these fluids, plots of log hðTÞ against 1/T give a straight line. Activation energy Eh can be easily estimated from this plot. The above equation can be written in the form taking logarithm with base of 10 and Eq. (3.12) becomes logðhÞ ¼ logðAÞ þ E=RT

(3.13)

For most of the polymer melts, a straight line can be found over a relatively small range of temperature, approx. up to 50 C. In case of wider temperature range, the relationship becomes nonlinear; apparent activation energy Eh decreases with increase in temperature. In general, the relationship holds better for lower shear rates. After the work of Dolittle who has given a better and more accurate relationship for entangled polymers, where he hypothesized that viscosity is an exponential function of reciprocal of the free volume fraction, and equation takes the form, hðTÞ ¼ AeB=f ðTÞ

(3.14)

or after taking logarithm of (of base-10) Eq. (3.14), logðhÞ ¼ logðAÞ þ B=f ðTÞ

(3.15)

where A and B are constants and f ¼ ðv
vhc Þ=v, vhc is inaccessible volume, and v is measured molar volume. Fractional free volume can be observed to increase with temperature.

66

Textile Calculation

Taking the free volume fraction at glass transition temperature (fg ) as reference, fractional free volume at other temperatures can be related using Eq. (3.16), where aF is the coefficient of thermal expansion   f ¼ fg þ aF T
Tg

(3.16)

Later in the year 1955, Williams, Landel, and Ferry suggested that viscosity of a polymer may be related to temperature and viscosity at the glass transition temperature hg . The aT , the so-called WLF shift factor, can be obtained from the equations.   logðaT Þ ¼ logðhT Þ
log hg ¼ B

"

1 1
f ðTÞ fg

# (3.17)

Finally, WLF equation of the following form can be obtained [6]: 

log hT =hg



 
17:44 T
Tg   ¼ 51:6 þ T
Tg

(3.18)

A new linear amorphous polymer has a Tg of þ10 C. At 27 C, it has a melt viscosity of 4  108 P. Estimate its viscosity at 50 C.

Example 3.8.

Given: T ¼ 27 C, h ¼ 4  108 P, Tg ¼ 10 C,

Solution.

T
Tg ¼ 17 C Using the WLF equation, "

# 4  108
17:44  17 ¼
4:32 log ¼ 51:6 þ 17 hg Solving for hg, we find, hg ¼ 8.3  1012 P. At 50 C, (T
Tg) ¼ 40 C. Therefore, using Eq. (3.18),  log

 h
17:44  40 ¼
7:61 ¼ 8:3  1012 51:6 þ 40

Again solving the equation, we can find h ¼ 2.0  105 P [1]. The estimated viscosity at 50 C is 2.0  105 P; theoretically, calculated viscosity is decreasing with increase in temperature.

Man made fiber manufacturing process

3.8

67

Melt spinning variables

Ziabicki et al. [7] classified various melt spinning variables primarily into to three groups namely primary, secondary, and resultant variables.

3.8.1 (a) (b) (c) (d) (e) (f) (g) (h)

Independent (or primary) variables of melt spinning (as defined by Ziabicki [7,8])

Polymer material; Extrusion temperature (T0); Spinneret channel dimensions (do, diameter; l, length of the spinneret); Number of filaments in the spinning line (n); Mass output rate (W); Spinning path length (L); Take-up velocity (VL); Cooling conditions (cooling medium, its temperature, and flow rate).

These factors as listed out by Ziabicki [7] affect the spinning conditions and resulting fiber properties directly or a combined effect of these factors can be observed. For instance, number of filaments in the spinning line, mass throughput rate, and speed of production together can demand a typical cooling condition or spinning path length for proper formation of fiber structure.

3.8.2

Secondary variables in melt spinning

(a) Average extrusion velocity is given by the following Eq. (3.19):

V0 ¼

4W nr0 pdo 2

(3.19)

where r0 is the density of the melt, calculated from volumetric throughput rate, spinneret hole diameter. To note that equation of continuity of flow is given by AVr ¼ constant; (continuity of mass flow equation), considering change in density is negligible (though at sometimes it may be considerable, in melt or dry spinning), change in cross-sectional area of the filament can be obtained with change in speed in spinline, which results a very useful relationship for further analysis. This can be achieved as follows: W ¼ AVr

(3.20)

vV vA V ¼
vx vx A

(3.21)

68

Textile Calculation

Spinline stress (s) is given by the following equation: s¼

F dV ¼ 3h0 A dx

(3.22)

dV is velocity gradient and the factor 3 comes for the dx incompressible extensional flow. In another way, change in cross-sectional area with respect to distance traveled by a small volume of yarn can be written as

where h0 is shear viscosity and

vA rFA ¼
vx 3Wh0

(3.23)

(b) Equivalent diameter of a single filament at x ¼ L, (c) Denier of the filament ¼ 9000[W(g min
1)/VL(m min
1)]. (d) Deformation ratio or meltedraw ratio, S ¼ Vd/V0 ¼ d20/d2L.

3.8.3 (a) (b) (c) (d)

Resulting variables in melt spinning mentioned as follows

Tensile force at take-up device, Fext . Tensile stress at take-up device, sL ¼ 4Fextrusion/n p d2L; Temperature of filament at x ¼ L, TL; Filament structure (orientation, crystallinity, morphology).

Eqs. (3.20)e(3.23) is solved with the thermal energy balance equation to get the spinning tension, temperature, and velocity profile. Determination of denier of filament from the given information: It is required to produce a yarn of fineness 94.4 dtex, number of filaments 100, polymer (PET) given that the throughput rate: 0.496 g hole
1 min
1, takeup speed: 1400 m min
1; show that as spun individual filament denier is 3.188; Find the Draw ratio required to produce the final dtex of the yarn, if Number of Holes in Spinneret: 100.

Example 3.9.

Solution.

Denier ¼ 9000  [0.496/1400] ¼ 3.188 D

Corresponding fineness (dtex) of the as-spun yarn is ¼ 3.188  1.11  100 ¼ 353.87 Required Draw Ratio ¼ 353.87/94.4 ¼ 3.75 Calculate the volumetric throughput rate and length of melt spun PET fiber per minute with the following technical information given. Draw ratio ¼ 1.5, spinning speed ¼ 3200 m min
1, 50 denier/100 filament (filament cross-section is circular), no of orifices 100, diameter of orifice 0.18 mm, and capillary length 0.50 mm, (assuming the given PET polymer is spinable at 285 C, with density of polymer 1.161 g cm
3) [8].

Example 3.10.

Man made fiber manufacturing process

69

[polymer weight fraction of spin finish/moisture in POY is 0.985]. Length of filament spun/sec ¼ 3200/60 m ¼ 53.33 m (approx.) Final fineness ¼ 50/100 ¼ 0.5 den per filament (dpf). Draw Ratio ¼ 1.5. Then, as-spun fiber fineness is 0.5  1.5 ¼ 0.75 den. Hence, mass through put rate/orifice is given by

Solution.

W¼

0:75  0:985  53:33 ¼ 0:004377gs
1 9000

Volumetric throughput rate is obtained by dividing this value by density 1.161 g cm
3, i.e., 3.7707  10
3 cm
3 s
1 per orifice. Subsequently, the extrusion velocity is calculated from the data given. The volume of polymer flowing out per minute per orifice is 3.7707  10
3  60 cm3. This volume is divided by the cross-sectional area (p  0.009  0.009 cm2) which gives the length in cm coming out every minute from the spinneret orifice and comes out to be 889 cm min
1 or 8.89 m min
1 (extrusion velocity).

Temperature profile of filaments in melt spinning

3.9 3.9.1

Theoretical argument

Temperature of the filament at a distance from the spinneret during melt spinning (Fig. 3.3) or in contrary in a given set of conditions at what distance the temperature of the filament will reach a given value can be estimated from the energy balance equations. In order to obtain the appropriate relationship that can be employed to guess the filament temperature at a given distance, detailed analysis of the molten polymer flow during spinning is necessary. Flow of molten polymer during melt spinning system is schematically demonstrated in Fig. 3.3, where a stream of molten polymer is forced through the spinneret of orifice of diameter D0. Just after fiber extrusion, the velocity of the molten mass, temperature, and force at its exit is denoted by v0, T0, F0 ; at some distance x (arbitrarily taken), diameter of filament, velocity, temperature, and spinline force are all dependent on distance x and on several fundamental and process variables. It is significant to note that at some distance a point x ¼ xs, where the solidification is expected to be complete (Fig. 3.3). Speed of the take-up and mass throughput rate ensures that the final denier of the filament is achieved. Also, the condition of mass continuity should be maintained (Eq. 3.20). A small element of filament (Fig. 3.4) in the production line can be considered in such a way that there is only slight change in filament diameter as it passes through a position from x to x þ dx and for that portion heat balance equation can be written as follows [9]: Q:Cp:T
Q:Cp:ðT þ dTÞ ¼ hðT
Tair ÞpDdx

(3.24)

70

Textile Calculation

Figure 3.3 Schematic representation of melt spinning.

Figure 3.4 A small element in filament with negligible change in filament diameter.

where Q is the mass throughput rate [kg s
1 hole
1], Cp is the specific heat of the polymer melt, h is the heat transfer coefficient, D is the mean diameter of the filament at that point, and Tair is quench air temperature. The equation states that on moving from one point to the other along the spinline by a small distance dx, heat is dissipated from the filament to the surrounding as the quench air flowing to cool and solidify the fiber.

Man made fiber manufacturing process

71

Nusselt number is defined by the ratio of convection heat transfer to fluid conduction heat transfer under the same conditions: Nu ¼ h  kDa where h is the heat transfer coefficient from Newton’s law of cooling, D is the filament diameter, and ka is thermal conductivity of air. Then, Eq. (3.24) is written as follows: dT h  pD ¼
ðT
Tair Þ  dx Q  Cp

(3.25)

dT Nu  ka  p ¼
ðT
Tair Þ  dx Q  Cp

(3.26)

Nu:ka :p has the same dimension as the reciprocal length (Lc, the Q:Cp cooling length), so it can be written as follows [9]: The expression

Nu:ka :p y1=Lc Q:Cp

(3.27)

Eq. (3.24) now can be written as [9] dT 1 ¼
ðT
Tair Þ  dx Lc

(3.28)

Finally, solving the equation expression for the temperature at any point from the orifice can be obtained as follows: Tx ¼ Tair þ ðTm
Tair Þ:expð
x = Lc Þ

(3.29)

where Tm is the temperature of molten polymer at the orifice. To calculate temperature of the filament in steady state at some distance from the orifice, we need to know the value of Lc, for which we need to find out Nusselt number and put it in Eq. (3.24). Necessary relationships for finding out Nu are as follows: Reynold's number Re ¼ DV=y

(3.30)

ReðReynold's number at 20 CÞ ¼ DV =y ¼ 16:40  10
6 

0:5 15:16  10
6

¼ 0:54 Prandtl number Pr ¼ Cpm=ka [use of these relationships can be understood in the following example].

(3.31)

72

Textile Calculation

From the given information, find the temperature of the melt spun filament at a distance 1 m away from the filament. Denier for the polyester filament : 126/48 (arbitrary). Quench air temperature Tair : 20 C. Velocity of air : 0.5 m s
1. Distance from the spinneret : 1 m. Density of PET filament : 1.38 g/cc. Take-up speed : 3200 mpm. Related properties of air (kinematic viscosity, dynamic viscosity, thermal conductivity, specific heat) are to be taken from standard values available. Step 1: Finding filament denier/diameter:

Example 3.10.1.

Fineness of single filament for the yarn of 126/48 denier (arbitrary) ¼ 2.625 dpf Diameter in micron (mm) ¼ 11.89O(d/r) where d is denier of filament (dpf) and r is approx. yarn (polymer) density in gm/cm3. Then, for the above filament, diameter will be ¼ 11.89O(2.625/1.38) ¼ 16.40 micron or equal to 16.40  10
6 m (SI units). Step 2: Finding values of Reynolds number (Re) and Prandtl number (Pr) and subsequently Nusselt number (Nu). Nusselt number is a function of two numbers: Reynolds (Re) and Prandtl number (Pr). Reynolds number Re for quenching air at 20 C for 126/48 polyester yarn is calculated from the formula Re ¼ DV=y, [(diameter of single filament of 2.625 denier) D ¼ 16.40  10
6 m, V (velocity of air) ¼ 0.5 m/s and y (kinematic viscosity of air) ¼ 15.16  10
6 m2/s)] From Eq. 3.31 Prandtl number can be calculated, where Cp ¼ specific heat of air in KJ/kg.  C, m ¼ dynamic viscosity of air kg/m/s, and k ¼ coefficient of thermal conductivity of air watt/m C (values for these were collected from different sources) [10e12]. Prandtl number of airðat 20 CÞðPrÞ ¼ Cpm=ka ¼ 1005:6  1:825  10
5 =0:025 ¼ 0:73 For this range of Reynolds numbers and Prandtl number, we can use the relation given by Nu ¼ hd=k ¼ CRem Pr1=3

(3.32)

where C ¼ 0.99 and m ¼ 0.33 are constants of this equation for circular cylinder in cross-flow condition [13,14]. Nu (of quench air at 20 C) ¼ 0.99  0.541/3  0.731/3 ¼ 0.725 [Note: Similarly for other specified qualities of filaments and spinning parameters, Nusselt number can be determined from the corresponding Reynolds and Prandtl numbers for known diameter of the given filaments.]

Man made fiber manufacturing process

73

Step 3: Calculating for Lc. As per the formula mentioned for Lc, Q:Cp where Q is mass throughput rate, value of Nu is already found, and Cp, Lc ¼ Nu:k a :p ka of air is also known. Mass throughput rate (kg/s/hole) for 126/48 PET yarn can be obtained by calculating as ¼ 126  3200/9000 ¼ 44.8 g/min (with take up speed, 3200 mpm) and finally mass throughput rate (kg/s/hole) is 44.8/48/60  10
3 kg/s/
3 hole ¼ 0.016  10 kg/s/hole (in SI unit). Using all known values and value of Nusselt number, 0.722, we calculate Lc for given throughput for the given yarn of e.g., 126/48 denier as follows. Lc ¼ 0:016  10
3  1005:7=½0:725  3:14  0:025 ¼ 0:283 meterðapprox.Þ Step 4: Calculate temperature of the filament at 1 m distance from the spinneret. Cooling air/surrounding air temperature is 20 C and molten polymer temperature is 285 C. At a distance 1 m, temperature of the filament is obtained from Eq. (3.29) by using value of Lc. T1
meter ¼ 20 þ ð285
20Þ  e
1=0:283 ¼ 27:74 C [Note: Looking in the other way for a given spinning condition, at what distance from the spinneret x a particular temperature (e.g. Tg) of filament may be reached can be calculated using the same procedure.]

3.10

Determination of degree of crystallinity from DSC study

Here, data obtained from the differential scanning calorimeter (DSC)-based thermal analysis of a screw top of polyester bottle have been used for the determination of degree of crystallinity. A differential thermal scan was carried out on DSC on a 2.5 mg polyethylene terephthalate sample as mentioned above from a PET bottle. Heating rate was fixed to 5 m
1 (5 K rise every minute). The resultant DSC scan output is shown in Fig. 3.5. All the required information such as glass transition temperature, melting point, heat of fusion, and specific heat capacity can be determined from the obtained thermal curve. From the obtained information, the degree of crystallinity of the sample polymer can be determined if the hypothetical 100% crystalline PET sample is known (which is 137 kJ kg
1). Using the DSC scan, glass transition temperature w 72 C, crystallization temperature 125 C, and melting point (250 C) can be identified. It is also to be noted that

74

Textile Calculation

Figure 3.5 DSC scan for the polyester as mentioned in the problem [15] (arbitrary diagram).

all the transitions occur not sharply at some temperature but at over a range. Enthalpy of fusion of polymers can be calculated by finding the area under the Q_ versus temperature curve around the melting point, i.e., between 210 degrees and 260 C. To perform the above calculation, temperature scale must be transformed to the time scale in the following way [15]: t¼

T 60s  5K=min 1 min

Hence, 50 C becomes 600 s, 100 C becomes 1,200s, etc. Using software, the above integration gives an amount of heat 37.8 kJ/kg, which is the heat of fusion of the sample during the temperature during heating. Nevertheless, one must consider that this thermal energy of melting includes an extra heat of crystallization which occurs between 108 and 155 C. In this case, the exothermic energy is computed by integrating the curve between those two temperatures in a transformed time scale. The integral equals 22.9 kJ/kg. We can also find the area under the curve by transforming _ to heat capacity, Cp, and integrating using the temperature scale the heat flow, Q, instead of a time scale. Heat capacity of the specific polymer may be computed using Cp ¼

Q_ 60s  5K=min 1 min

Man made fiber manufacturing process

75

and the degree of crystallinity of the initial PET bottle screw-top can now be found computing using c¼

37:87kJ=kg
22:9kJ=kg ¼ 0:109 or 10:9% 137kJ=kg

Using the same procedure, the degree of crystallinity of other processed sample polymers can be determined.

3.11

Determining crystallinity of the spun polymeric fibers

3.11.1 Determination of crystallinity of fibers by density method Estimate the fraction of crystalline material in a sample of polyethylene of density 0.983 g/cm3 (density of amorphous polyethylene ¼ 0.866 g/cm3) (Fig. 3.6).

Example 3.12.

Unit cell dimensions of polyethylene crystal containing four CH2 groups are as follows:

Solution.

a ¼ 7.41 A, b ¼ 4.94 A, c (fiber axis) ¼ 2.55 A, a ¼ b ¼ g ¼ 90 ; Volume of unit cell ¼ 93.34  10
24 cm3 and the cell contains four CH2 groups or 9.3  10
23 g; Density of crystalline material ¼ weight/volume of unit volume ¼ 0.996 g cm
3; % crystallinity ¼ 91% [1].

Figure 3.6 Structure of the ordered region of polyethylene polymer.

76

3.12

Textile Calculation

Conclusion

Some examples of calculations in relation to the Fibre munufacturing has been demostrated here starting from polymers itself. Several other numerical examples may be included as well, such as numerical problems associated to solution and wet spinning, and fibre characterisation techniques. Such problems is dealt in some advanced textbook of Fibre and Polymer science, that a reader can refer for further learning.

References [1] M. Chanda, Introduction to Polymer Science and Chemistry: A Problem-Solving Approach, CRC Press, 2006. [2] V.R. Gowariker, N.V. Viswanathan, J. Sreedhar, Polymer Science, New Age International, 1986. [3] I. Harris, The number-average molecular weight of polythene, J. Polym. Sci. 8 (4) (1952) 353e364. [4] R.W. Moncrieff, Man-made Fibres, 1975. [5] W.T. Astbury, C.E. Dalgliesh, S.E. Darmon, G.B.B.M. Sutherland, Studies of the structure of synthetic polypeptides, Nature 162 (4120) (1948) 596e600. [6] https://polymerdatabase.com/polymer%20physics/WLF.html. [7] A. Ziabicki, H. Kawai (Eds.), High-speed Fiber Spinning: Science and Engineering Aspects, Wiley-interscience, 1985. [8] V.B. Gupta, V.K. Kothari (Eds.), Manufactured Fibre Technology, Springer Science and Business Media, 1997. [9] R. Beyreuther, H. Br€unig, Dynamics of Fibre Formation and Processing: Modelling and Application in Fibre and Textile Industry, Springer Science and Business Media, 2006. [10] engineeringtoolbox.com/air-properties-viscosity-conductivity-heat-capacity-d_1509.html. [11] engineersedge.com/physics/viscosity_of_air_dynamic_and_kinematic_14483.htm. [12] theengineeringmindset.com/properties-of-air-at-atmospheric-pressure/. [13] engineersedge.com/heat_transfer/nusselt_number_13856.htm. [14] F.P. Incropera, D.P. DeWitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer, vol. 6, Wiley, New York, 1996, p. 116 (Page no 420, (Chapter 7)). [15] T.A. Osswald, J.P. Hernandez-Ortiz, Polymer Processing. Modeling and Simulation, Hanser, Munich, 2006, pp. 1e651.

4

Prespinning processes (opening and cleaning, carding and drawing)

R. Chattopadhyay Department of Textile and Fibre Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India

4.1

Introduction

Yarn manufacturing process, involves prespinning, spinning, and postspinning operations. In the prespinning process, the fiber (bale form) is loosened, opened, doubled, drafted, and cleaned. Mainly three types of action occur at the prespinning satge on the fibre tufts, viz action of opposing spikes; action of air current; and action of beaters/pinned rollers. The machines used in prespinning process are blow room; card; and draw frame.

4.2

Opening and cleaning

In blow room the compressed fiber tufts are opened, cleaned, mixed, and evened out first and then passed to the carding machine. The mixing/blending operation in blow room helps in averaging out the variation in fiber properties and minimize cost.

4.2.1

Average fiber parameters in fiber mixture

The following Table 4.1 shows fiber parameters of different components. Table 4.1 Fiber parameter for different components. Fiber parameter Weight of fiber kg Mean fiber length (mm) Fineness ( mg= inch) Fineness (den) Mean trash (%) Strength (g/tex) Proportion

Components C1 w1 l1 m1 den1 T1 s1 p1

C2 w2 l2 m2 den2 T2 s2 p2

C:: .. .. .. .. .. . .. .. .

Textile Calculation. https://doi.org/10.1016/B978-0-323-99041-7.00012-6 Copyright © 2023 Elsevier Ltd. All rights reserved.

Ci wi li mi deni Ti si pi

C:: .. .. . .. .. . .. . .. .

Cn wn ln mn denn Tn sn pn

Average

78

Textile Calculation

Let n ¼ number of fiber components in the mix. w1 , w2 ; w3 , . . . [ weight of fibers of components 1,2,3 . ...n n P

•

Total weight (W) of fibers in the mix: W ¼ w1 þ w2 þ . þ wi þ . þ wn ¼

• •

pi ¼ proportion of ith component, then p1 ¼ ¼ Overall average length of fibers in the mixture: L ¼ pi li .::: ð4:1Þ [li ¼ mean length of component i] P Average strength of fibers in the mixture: Sm ¼ pi si .: ð4:2Þ [si ¼ mean strength of component i] Average fineness of a mixture cannot be the simple arithmetic mean since number of fibers in a given blend component will depend upon its own fineness and weight. It should be based on total weight divided by total length.

• •

w1 W,

Mx ¼

p2 ¼ wW2 ; pi P

wi W

wi

1

Total weight of fibres w1 þ w2 þ ...þwn ¼ w1 w2 wn Total length þ þ ..: þ m1 m2 mn

Dividing by total weight (W) w1 w2 wn P þ þ ...:: þ 1 pi W W W M x ¼ w1 w2 w n ¼ P pi ¼ P pi þ þ ...: þ Wm1 Wm2 Wmn mi mi

(4.3)

If fineness is expressed in denier, then mean denier of the mixture/blend: 1 M den ¼ P pi deni If fineness is expressed in dtex, then M dtex ¼

X

pi dtexi

(4.4)

Relation between ‘dtex’ and ‘denier’: dtex ¼ den  1:11

Two cotton fiber varieties of 4.2 mg/inch and 3.6 mg/inch are mixed together in the proportion of 60:40.

Example 4.1.

(i) Calculate the average fineness of the mixture. (ii) The weight of bales having 4.2 mg/inch fiber and 3.6 mg/inch fiber are 220 kg and is 180 kg, respectively. If 5 ton material is to be processed, how many bales of the two fineness types are to be taken?

Prespinning processes (opening and cleaning, carding and drawing) Solution.

79

(i) Average fineness of the mixture:

1 M x ¼ P pi ¼ mi

1 1 1 ¼ ¼ 3:94 mg=inch ¼ 0:6 0:4 0:1428 þ 0:111 0:2539 þ 4:2 3:6

The average fineness of the mixture is 3:94 mg=inch. (ii) Number of 4.2 mg/inch fiber bales to be taken ¼ 50000:6 ¼ 13:63 z 14 220

Number of 3.6 mg/inch fiber bales to be taken ¼ 50000:4 ¼ 11:11 z 11 180 Total 14 bales of 4.2 mg/inch and 11 bales of 3.6 mg/inch are required for of the 5 ton material. Example 4.2. Three cotton fiber varieties having mean length 28, 34, and 27 mm are mixed in the proportion of 20%, 30%, and 50%. What is the average fiber length of the mixture? Solution.

¼

Average fiber length of the mixture ¼ p1  l1 þ p2  l2 þ p3  l3 20 30 50  28 þ  34 þ  27 100 100 100

¼ 5:6 þ 10:2 þ 13:5 ¼ 29:3 mm Two fibers DCH 32 and MCU5 are to be mixed in the ratio of 60:40. The tenacities of DCH 32 and MCU5 are 26 cN/tex and 24 cN/tex, respectively.

Example 4.3.

(i) What will be the tenacity of the fiber mix? (ii) If 10% variation in the mixing % of individual component is expected, what will be the maximum and minimum tenacity of the mix? 60  26 þ 40  24 ¼ 15:6 þ 9:6 ¼ 25:2 cN=tex (i) Average tenacity ¼ 100 100   10 (ii) Present DCH ¼ 60  1 þ100 ¼ 66%

Solution.

% of MCU5 ¼ 100e66 ¼ 34% 66  26 þ 34  24 Average tenacity due to 10% rise in the % of DCH32 ¼ 100 100 ¼ 0:66  26 þ 0:34  24 ¼ 17:16 þ 8:16 ¼ 25:32 cN=tex Similarly, average tenacity due to 10% decrease in DCH 32 ¼ 0:54  26 þ 0:46  24 ¼ 14:04 þ 11:04 ¼ 25:08 cN=tex

80

Textile Calculation

Therefore, the maximum and minimum tenacities are 25.32 cN/tex and 25.08 cN/ tex, respectively.

4.2.2

Bale lay down

The arrangement of bales in a bales lay down is shown in Table 4.2. In industries, five types of arrangement are possible. Example 4.4. There are 100 bales in a laydown. Each bale is 200 kg. The tuft extractor moves at a velocity of 20 m/min. The lay down length is 50 m. The production of tuft extractor is 600 kg/h. How many cycles will it take to consume all the bales? Solution.

The cycle time for one complete traverse: 50 20  2 ¼ 5 min Material peeled out by tuft extractor in 1 cycle ¼ 60060 5 ¼ 50 kg  200 ¼ 400 Number of cycles required to consume all the material ¼ 100 50 Total time required to consume all the material ¼ 5  400 ¼ 2000 min ¼ 33:33 h

Table 4.2 Bales lay down. Type

Bales lay down variants (top view)

Rows

Description

1

1

2

1.5

3

2

4

3

5

4

one row of bales with broad sides in the direction of detaching One and half rows of bales with long and broad sides in the direction of detaching Two rows of bales with long side in the direction of detaching Three rows of bales with long side in the direction of detaching Four rows of bales with long side in the direction of detaching

Prespinning processes (opening and cleaning, carding and drawing)

81

Example 4.5. From the data given in the previous example, calculate number of tufts removed per half cycle if the average tuft weight is 50 mg.

Material peeled out per half cycle ¼ 50/2 ¼ 25 kg. 25 ¼ 0:25 kg ¼ 250 g Material removed per bale in half cycle ¼ 100 Assume average weight of tuft to be ¼ 50 mg. 250 Number of tufts removed per bale/half cycle ¼ 50=1000 ¼ 5000

Solution.

Example 4.6. Considering bale length and width to be 1.3 and 0.65 m, respectively. How much length of space will be occupied by 90 bales?

If the bale placement is as shown below, then with in 1.3 m length, 3 bales can be accommodated (Fig. 4.1). For 90 bales, the length of space required will be ¼ 1:3 3  90 ¼ 30  1:3 ¼ 39 m

Solution.

4.2.3

Intensity of opening

It is expressed by: (i) Blows/unit length of material fed (ii) Blows per kg of material fed (iii) Mass of material per striking element

Opening Intensity ¼

Speed of beater  number of blades on beater Delivery of feed roller

Opening Intensity ¼

Speed of beater ðnb Þ  number of blades on beaterðNÞ   Circumference of feed roller  speed of feed roller nf

Figure 4.1 Bale arrangement.

82

Textile Calculation

Opening Intensity ¼

nb  N d  nf

(4.5)

where nb ¼ beater speed (rpm), N ¼ number of blades/strikers, d ¼ diameter of feed roller, and nf ¼ feed roller speed.

4.2.4

1Blows/kg

An alternative to tuft size is number of blows per kg of cotton, (Nk) Nk ¼

Blows per hour 1 ¼ ð60nb  NÞ Production per hour ðkgÞ P

(4.6)

In some cases, feeding may not be done by any pair of rollers (axi-flow cleaner, step cleaner). In such cases, the opening intensity is defined as the fiber mass (in mg per striker or needle or saw tooth of the beater at a given production rate and beater speed). Let P ¼ production rate (kg/h), nb ¼ beater speed (rpm), and N ¼ number of strikers or needles on beater/opener. Production rate ðmg = hÞ ¼ P  103  103 Striking per hour ¼ 60  nb  N Intensity of opening ðIÞ ¼

P  106 60  nb  N

(4.7)

The calculation does not take into account of the effect of the setting between beater and feed roller, beater and grid bar, and grid spacing and beater to deflector plate. • • •

It represents the number of strikes by beater, while the sheet of fibers advances one inch. The more is the blows/inch, more waste is generated and more will be the cleaning Excessive beating may cause fiber damage.

4.2.5 4.2.5.1

Force on fiber tufts 1Impulse due to beating action

  Impulse ¼ change in momentum ¼ m vi  vf m ¼ mass of tuft/trash, vi ¼ initial velocity of tuft (feed roller surface speed). vf ¼ final velocity of tuft (surface speed of beater blade).

(4.8)

Prespinning processes (opening and cleaning, carding and drawing)

83

Since vi is practically zero, the change of momentum is primarily dependent on vf . Therefore, higher the surface speed of beater blade, more will be the impulse (Fig. 4.2).

4.2.5.2

Centrifugal force

The centrifugal force acting on a tuft/trash particle while it revolves along with the beater blade is: CF ¼ mru2 ¼ mrð2pnÞ2 ¼ 4mrp2 n2

(4.9)

m ¼ mass of tuft/trash, r ¼ radius of opener. u ¼ rotational speed of opener (rad/min). n ¼ rotational speed of opener (rpm). Sheet of tufts of 1.5 kg/m is being fed to a cleaner at 12 m/min. A threearmed beater is running at 800 rpm. Calculate intensity of opening in g/strike.

Example 4.7.

Mass balance: feed rate ¼ production rate. Feed rate/min ¼ 1:5  12 ¼ 18 kg=min nb ¼ 800 rpm, N ¼ 3

Solution.

Intensity of opening ðIÞ ¼

18000 18000 ¼ ¼ 7:5 g per strike 3  800 2400

The intensity of opening is 7.5 g/strike.

Figure 4.2 Bladed beater.

84

Textile Calculation

In the above example, consider the beater diameter to be 600 mm, and the time required to change the speed of the tuft mass detached per strike from 12 m/min to the surface speed of beater blade is 0.001 s. Calculate the average force acting on the tuft

Example 4.8.

Solution.

Feed rate of tufts ¼

12 ¼ 0:2 m=s 60

Surface speed of beater blade ¼

p  600  800 ¼ 25:13 m=s 1000  60

  7:5 Change of momentum of 7:5 g of tuft ¼ m vf  vi ¼ ð25:13  0:2Þ 1000 7:5  24:93 ¼ ¼ 0:187 kg: m = s 1000 Average force ¼

0:187 ¼ 187 N 0:001

The average force acting on the tuft is 187 N. A Kirschner beater is running at the speed of 800 rpm. A sheet of cotton of 1.2 kg/m is fed by a feed roller (10 cm diameter) running at 10 rpm. Calculate blows /kg oncotton

Example 4.9.

Solution.

Surface speed of feed roller ¼

p  10  10 ¼ 3:14 m=min 100

Material feed rate ¼ 3:14  1:2 ¼ 3:77 kg=min Blows per kg of cotton: Nk ¼

Blows per min 3  800 ¼ ¼ 636:6 Feed per min ðkgÞ 3:77

The blows/kg of cotton is 636.6. A Kirschner beater has a diameter of 44 cm. Its rotational speed is 700 rpm. Calculate its surface speed (km/h) and centrifugal force a tuft of 2 mg will experience

Example 4.10.

Diameter of Kirschner beater ¼ 44 cm. Kirschner beater speed ¼ 700 rpm ¼ 11.66 rev/s

Solution.

Surface speed ðvÞ ¼ pnD ¼ p 

700 44  ¼ 16:12 m=s ¼ 58 km=h 60 100

Prespinning processes (opening and cleaning, carding and drawing)

Centrifugal force ¼

4.2.6 4.2.6.1

85

mv2 2  103  16:122 ¼ ¼ 2:36 N 44 r  100 2

Multimixers Blending delay time

In multitier the material is poured into the vertical compartments by a tuft feeder one after the other. The filling height may remain same or differ from compartment to compartment depending upon the type of feeding. Let us imagine that the compartments are divided into horizontal sections. Now, when the machine delivers the stock of material, the content from the bottom of all the compartments moves out together in the form of a layer for further processing. The material belonging to any delivered layer was actually fed into the mixer at different points of time. Thus, in a continuous flow, an opportunity is created for the material to get mixed not with its immediate neighbor with respect to original flow but with the others arriving at different times. The difference in the filling time of the earliest and latest segment of tufts exiting from the compartments for further processing is defined as the blending delay time.

4.2.6.2

Doubling factor

Multimixer can operate in series or parallel. Series operation is more common. If the number of hoppers/compartment are x and y in two mixers, then • •

Doubling factor: ¼ x þ y ½ parallel configuration Doubling factor: ¼ x  y ½series processing

A multimixer has 8 compartments. Each compartment’s size (H L WÞ is 6 m  2 m  0:5 m. The average density of cotton tuft within the compartment is 12 kg/m3. The mixer is filled up in a staggered fashion. Example 4.11.

(i) What is the capacity of the multimixer? (ii) If time to fill up each box is 5 min, what will be the blending delay time for the first layer of tufts moving out of the machine? Solution.

Volume of each small box ¼ 620:5 ¼ 0:75 m3 8 volume of cotton ¼ 0:75 ½1 þ 2 þ 3 þ 4 þ 5 þ 6 þ 7 þ 8 ¼ 7:5  36

The ¼ 27 m3  Weight of cotton ¼ 27 m3  12 kg m3 ¼ 324 kg Blending delay for first layer ¼145e5 ¼ 140 min (Fig. 4.3).

The density of cotton bale is 0.2 g/cm3. If the tuft density within the multimixer is 0.012 g/cm3, what will be the % change in density due to opening?

Example 4.12.

Solution.

Change in density ¼

0:2  0:012 0:188  100 ¼  100 ¼ 94% 0:2 0:2

The % change in density due to opening is 98.5%

86

Textile Calculation

Compartment 1

2

3

4

5

6

7

8 180

5

140

175

105

135

170

75

100

130

165

50

70

95

125

160

30

45

65

90

120

155

15

25

40

60

85

115

150

10

20

35

55

80

110

145

Figure 4.3 Time of filling up of different segments.

4.2.7

Lap formation

The lap sheet is rolled on a lap spindle under pressure. Once the required length of lap is rolled, the process stops and the lap is taken out. A new spindle is inserted and the rolling continues (Fig. 4.4). The unrolled length and weight of a lap are 40 m and 20 kg, respectively. The rolled lap length and diameter are 1m and 60 cm, respectively. Calculate lap density in g/cm3 and lap linear density in ktex.

Example 4.13.

Solution.

Lap volume ¼ p Lap density ¼

0:62  1 ¼ 0:2827 m3 4

20 70:74  1000 ¼ 70:74 kg=m3 ¼ ¼ 0:07074 g=cm3 0:2827 106

Linear linear density ¼

20 ¼ 0:5 kg=m ¼ 500 g=m ¼ 500 ktex 40

The lap density is 0.07074 g/cm3 and linear density is 500 ktex.

Prespinning processes (opening and cleaning, carding and drawing)

87

Figure 4.4 Lap formation.

4.2.8

Cleaning efficiency

The cleaning efficiency of any cleaner is defined as follows: Cleaning efficiency ðCEÞ ¼

Trash% in feed  trash% in delivery  100 Trash% in feed (4.10)

Example 4.14. The trash % in the feed and delivery of a beater is 5% and 1.5%, respectively. Calculate the cleaning efficiency. Solution.

Cleaning efficiency ðCEÞ ¼

5  4:2  100 ¼ 16% 5

The cleaning efficiency is 16%. The trash content of a cotton as fed to a beater is 3.6%. The waste extraction is 1.5% of which 80% is trash. What is the cleaning efficiency?

Example 4.15.

Trash taken out by the beater ¼ 80/100  1.5% ¼ 1.2% of the input trash Hence, trash remaining in the material delivered from the beater ¼ 3.6e1.2 ¼ 2.4%

Solution.

CE ¼

Trash% in feed  trash% in delivery  100 Trash% in feed

88

Textile Calculation

CE ¼

3:6  2:4  100 ¼ 33:3% 3:6

The cleaning efficiency is 33.3%. Example 4.16. The cleaning efficiencies of axi-flow cleaner and step cleaner are 15% and 12%, respectively. How much will be the combined cleaning efficiency? Solution.

     CE1 CE2 Combined CE% ¼ 1  1   1  100 100 100

where; CE1 and CE2 are cleaning effciencies of two cleaners respectively ¼ ½1  ð1  :15Þ  ð1  :15Þ100 ¼ ½1  :85  :88100 ¼ ½1  :85  :88100 ¼ ð1  :748Þ100 ¼ 25:2% The combined cleaning efficiency is 25.2%.

4.2.9

Production calculation of blow room

The formulae for production calculation are: ProductionðmÞ ¼ delivery speedðm = minÞ  duration of deliveryðminÞ

(4.11)

Production (kg/min) ¼ Delivery speedðm=minÞ  duration of deliveryðminÞ 

1 1000

 lap linear density ðg=mÞ Formulae for production calculation in kg/8h including efficiency: Production ðkg=8hÞ ¼ Delivery speedðm=minÞ  8  60 

Lap linear density ðktexÞ Efficiency%  1000 100

¼ Delivery speedðm = minÞ  480 

Lap linear density ðktexÞ efficiency%  1000 100

Prespinning processes (opening and cleaning, carding and drawing)

89

Or ¼ Delivery speedðm=minÞ  1:09  8  60  

453:6 1  840  1000 Lap hankð Ne Þ

Efficiency% 100

Or ¼ 0:2825 

delivery speed ðm=minÞ Efficiency%  lap hank ð NeÞ 100

(4.12)

A scutcher is producing a lap of 0.0012 Hk. The delivery speed is 10 m/ min. Calculate (i) production/shift at 85% efficiency, (ii) production if the lap hank is made 10% finer, and (iii) % loss in production due to finer lap hank.

Example 4.17.

Solution.

Production calculation formula is the following:

Production=8hðkgÞ ¼ 0:2825   ¼ 0:2825 

delivery speed ðm=minÞ lap hank ð NeÞ

machine effciencyð%Þ 100

10 85  0:0012 100

¼ 2001 kg or 2007:7ðbased on lap hank converted to ktexÞ (ii) Finer lap hank ¼ 0:0012  1:1 ¼ 0:00132 10  85 z 1819 kg Production/8h kg ¼ 0:2825  0:00132 100

(iii) Loss in production ¼ 2001  1819 z 182 kg

Loss in production ¼ ¼ 20011819  100 z 9:1% 2001 Total production/shift at 85% efficiency is 2001 kg. Total production/shift at 85% efficiency for 10% finer lap hank is 1819 kg. Loss in production is 9.1% In an ONeOFF control in blow room, the ON:OFF ratio is 70:30. If average production rate is 350 kg/h, what will be the production rate during ON period?

Example 4.18.

The production is for 70% of time i.e., ¼ 1  0:7 h Production during ON period ¼ ¼ 350 0:7 ¼ 500 kg=h

Solution.

90

Textile Calculation

4.3

Carding

4.3.1

Carding angle

For effective carding, the simple relationship between wire angle and coefficient of friction between fiber and wire point is Cot a > m

(4.14)

Example 4.19. If fiber to metal friction is 0.23, what should be the inclination of front flank of the teeth for effective carding action. Solution.

Coefficient of friction between fiber to metal (mÞ is 0.23

Cot a > 0:23 Or

1 > 0:23 tan a

1 > 0:23 tan a So; tan a
FMU  FMU  FMI

(6.46)

MI ¼

FMA  FMU ½when FMA > FMU  FMU  FMI

(6.47)

164

Textile Calculation

Zone No.

1

2

3

4

5

Total

Fiber A Fiber B

32 6

90 15

144 25

182 38

217 136

665 220

The following table is the frequency distribution of fiber components A and B in five different zones of a blended yarn cross-section. Calculate the migration index (MI) based on moments.

Example 6.24.

First we have to calculate number of fibers in different zones based on three hypothetical distributions, i.e., uniform distribution, maximum inward distribution, and maximum outward distribution. Calculation of fibers considering uniform distribution. 665  38 ¼ 0:75  38 ¼ 29 Number of A type fiber in zone 1 ¼ 885 665 Number of A type fiber in zone 2 ¼  105 z 79 885 665 Number of A type fiber in zone 3 ¼  169 z 127 885 665 Number of A type fiber in zone 4 ¼  220 z 165 885 665 Number of A type fiber in zone 5 ¼  353 z 265 885

Solution.

Number of fibers in different zones Zone weightage Zone No. Fiber A Fiber B Zone total Uniform distribution fiber type A Maximum inward distribution Maximum outward distribution

2

1

0

þ1

þ2

1 32 6 38 29

2 90 15 105 79

3 144 25 169 127

4 182 38 220 165

5 217 136 353 265

Total 665 220 885 665

38

105

169

219

134

665

e

e

92

220

353

665

For maximum inward distribution, the number of sites available in zone 1 will get filled up by A type fibers first, followed by zone 2 sites, and then zone 3 and zone 4 sites and finally whatever will be left will go to the last zone. Similarly, for maximum outward distribution, the number of sites available in zone 5 will get filled up by A type fibers first, followed by zone 4 sites, and then zone 3 and zone 2 sites and finally whatever will be left will go to the first zone.

Yarn structure and mechanics

165

Now the moment FMA ¼ 2ðn5  n1 Þ þ ðn4  n2 Þ ¼ 2ð217  32Þ þ ð182  90Þ ¼ 370 þ 92 ¼ 462 FMU ¼ 29  ð2Þ þ 79  ð1Þ þ 127  0 þ 165  1 þ 265  2 ¼ 58  79 þ 165 þ 530 ¼ 558 FMI ¼ 38  ð2Þ þ 105  ð1Þ þ 169  0 þ 219  1 þ 134  2 ¼ 76  105 þ 219 þ 268 ¼ 306 Since FMA < FMU , MIA ¼

FMA  FMU 462  558 96 ¼ ¼ 38:1% ¼ 558  306 252 FMU  FMI

A type fibers are placed mostly near the center.

6.14.3 Blended yarn strength According to J. W. Hamburger [2], a spun yarn consisting of two types of fibers (A & B) shows two break points when extended till failure. Tenacity at the breaking extension of least extendable fiber (A): S1 ¼

 1  pSA þ qS0B 100

(6.48)

Tenacity at the breaking extension of rest of the fibers (B) second break point S2 ¼

qSB 100

(6.49)

where, SA ¼ tenacity of component A, SB ¼ tenacity of component B; S0B ¼ stress at the breaking extension of least extendable component (A) p ¼ % of fiber component A; q ¼ % of fiber component B

Considering the following three compositions for polyester/cotton blended yarns determine the blend which will have a tenacity more than 100% cotton yarn. The blend compositions are 40% polyester: 60% cotton.; 60% polyester: 40% cotton; and 80% polyester : 20% cotton.

Example 6.25.

166

Textile Calculation

The ultimate tenacity and extension of the fibers are as under: Cotton: 33 g/tex and 7%, Polyester: 45 g/tex and 40%. The fiber densities are: cotton ¼ 1.54 g/cm3, polyester ¼ 1.38 g/cm3. Cotton has higher initial modulus than polyester. Assume catastrophic rupture in all the cases. Solution.

For 40:60 polyester/cotton blended yarn

S1 ¼

 1  aSA þ bS0b 100

S1 ¼

60 40 45  33 þ   7 ¼ 19:8 þ 3:15 ¼ 22:95 g=tex 100 100 40

S2 ¼

bS0B 40  45 ¼ 18 g=tex ¼ 100 100

For 60:40 polyester/cotton blended yarn S1 ¼

40 60 45  33 þ   7 ¼ 13:2 þ 4:725 ¼ 17:92 g=tex 100 100 40

S2 ¼

bS0B 60  45 ¼ 27 g=tex ¼ 100 100

For 80:20 polyester/cotton blended yarn S1 ¼

20 80 45  33 þ   7 ¼ 6:6 þ 6:3 ¼ 12:9 g=tex 100 100 40

S2 ¼

bS0B 80  45 ¼ 36 g=tex ¼ 100 100

Only 80:20 polyester/cotton blended yarn will have higher tenacity than 100% cotton yarn which is 36 g/tex.

6.15

Self-locking structure of spun yarn [3]

In spun yarn tension is transmitted from one fibre to the other. At the tip of a fibre ends , there is no tension and the tension gardually builds up along the fibre length in a coherent yarn till it reaches a level equivalent to what one expects in a similar filament yarn ( Fig. 6.7). The zone indicating gradual increase in tension is known as slip zone (S). Slip factor indicates fractional loss in tension compared to tension without slip.

Yarn structure and mechanics

167

Figure 6.7 Tension build up along fiber length.

Tension

Fibre gripped zone

Slip zone S

L-2S

S

L Let S ¼ slip zone length z ¼ operational factor representing the conversion of yarn tensile stress to transverse stress rf ¼ fiber radius m ¼ coefficient of friction L ¼ fiber length (Fig. 6.7)

Slip factor ðSFÞ ¼

rf mean stress with slip S ¼1 ¼1 stress without slip L 2m zL

(6.50)

z ¼ 0:3  103 to 1:0  103 If, Slip Factor < 0:5, the yarn will not show self-locking structure. Example 6.26. A yarn is made of 40 mm  1:5 den polyester fibers. The coefficient of friction between fibers is 0.4. If the operation factor representing the conversion of tensile stress to transverse stress is 0.8  103, determine whether the yarn will have selflocking structure or not? What is the slip length?sffiffiffiffiffiffiffi fden Solution. Fiber diameter ¼ df ¼ 1:1894  103 cm rf rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1:5 4 ¼12:39  104 cm ¼ 12:4 micron ¼ 11:894  10 1:38

Slip factor SF ¼ 1 

¼1

rf 12:4  104 ¼1 2mTL 2  0:4  0:8  103  4:0

12:4  101 2  0:4  4:0  0:8

168

Textile Calculation

¼ 1  0:484 ¼ 0:516 Since SF is more than 0.5, it will create a self-locking structure. Slip length (S) Slip factor ¼ 1 

S L

S a ¼ L 2mTL S¼

6.16

aL ¼ 0:484  40 ¼ 19:36 mm 2mTL

Core sheath yarn

A core sheath yarn consists of polyester filament in core and FR viscose in sheath. The linear density and packing coefficient of core component are 60 tex and 0.7, respectively. The yarn diameter is 500 mm. The packing coefficient of sheath is 0.5. Calculate the thickness and linear density of sheath. Assume FR viscose density to be 1.52 g/cm3.

Example 6.27.

Solution.

Diameter of polyester yarn:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Cy 60 dy ¼ 2 ¼2 ¼ 0:0281 cm 5 5 p  10  0:7  1:38 p  10  f  rf ¼ 281 mm Diameter with sheath ¼ 500 mm 500  281 ¼ 109:5 mm z 110 mm Thickness of sheath ¼ 2 ! Volume of sheath/cm of yarn ¼ p  diamter ¼

dy2 dC2 4 4

[ dy ¼ yarn diamter; dC ¼ core

 p p 0:05002  0:02812  1 ¼  1:71  103 ¼ 1:34  103 cm3 4 4

Weight/1000m of sheath ¼ 1:34  103  0:5  1:52  105 ¼ 100 g Sheath linear density ¼ 100 tex.

Yarn structure and mechanics

6.17

169

Exercise problems

1. Calculate specific surface area of polyester and polypropylene fibers of 256 militex. The densities are 1.38 g/cc and 0.91 g/cc for polyester and polypropylene, respectively. [12614:3 cm1 and 2115:3 cm 1] 2. A fiber is inclined at an angle of 15 with respect to yarn axis on the surface of the yarn. If the yarn diameter is 200 micron, find out torsion and bending curvature of the fiber. 3. The twist angle in a yarn is 20 . An increase in 10% twist resulted in the specific volume to decrease by 5%. What will be the twist angle now? Assume no change in count due to yarn contraction [21,3 0]. 4. A 30 tex cotton yarn has a tex twist factor of 60. The specific volume of the yarn is 0.5 cm3 = g. You have to produce a yarn with similar twist angle with specific volume 1.0. What will be the twist factor? 5. A multifilament PET yarn (filament density ¼ 1.38 g/cm3) was tested for twist angle and was found to be 27 . The yarn had tex twist factor of 42. Determine yarn packing coefficient. If gravimetric analysis yielded a 25 tex yarn, what would be the yarn diameter in micron? [0.62, 193 micron] 6. The final yarn count required from a ring frame is 36s Ne with twist 28 TPI (twist per inch). The twist contraction during spinning is 3%. If the feed roving count is 2 Ne, how much will be the mechanical draft required in the ring frame? [18.54] 7. A viscose rayon yarn has the following particulars: yarn count ¼ 30 tex fiber fineness ¼ 1.5 denier packing coefficient ¼ 0.45 fiber density ¼ 1.5 g/cm3 (a) If polyester fiber is used to replace viscose rayon keeping all other parameters same, what will be the diameter differences between the two yarns in microns (polyester fiber density ¼ 1.38 g/cm3) (b) Estimate the diameter of the polyester yarn in microns using closed packed hexagonal yarn geometry. Ignore yarn obliquity and contraction due to twist while estimating number of fibers [75.1 micron at the middle of hexagon]. 8. A multifilament polyester yarn is required for industrial use. The yarn contraction due to twist is to be such that the twisted yarn is exactly 1100 denier . A total of 350 monofilaments of 3 denier each are to be used to manufacture the yarn with a tex twist factor of 30. (a) Estimate the yarn packing coefficient. Polyester filament density is 1.38 g/cm3 [0.41] (b) Estimate the diameter of the yarn above by analytical means and not by hexagonal closedpacked geometry [158 micron]. 9. A multifilament yarn is subjected to a tensile test yielded following data: Original yarn diameter ¼ 0.1 cm Gauge length ¼ 20 cm, length at break ¼ 26.5 cm, yarn diameter at break ¼ 0.08 cm. Estimate the % change in packing coefficient of the yarn at the point of rupture. It is assumed that filament density does not change due to strain. 10. A polyester multifilament yarn has 140 filaments of 1.5 denier each. The average diameter of the yarn was found to be 215 microns. (a) Estimate yarn density (Note: ignore any contraction due to twist). (b) What is the estimate of the packing coefficient?

170

11.

12. 13.

14.

15. 16.

Textile Calculation

(c) For the packing coefficient as determined in (b) what is the estimate of yarn diameter (in microns) if all polyester filaments are replaced by polypropylene filaments of same denier? (PP fiber density ¼ 0.9 g/cm3) [0.64 g/cm3; 0.465]. The helix angle of fibers on yarn surface is 20 . Calculate contraction and retraction factors. If the angle is increased by 2 times, what would be the new contraction and retraction factors? If a yarn cross-section is divided into annular rings of equal thickness, what would be the diameter ratios? [1:3:5] 4 Kg (net) of twisted multifilament yarn with packing coefficient of 0.65 comprising of 120 filaments has a twist of 12 turns/cm. User demand is for a twist increase of 35%. The yarn is made from 2 denier monofilament having density 1.31 g/cm3. An increase of 6% in the packing coefficient is expected due to higher twist. Determine the increase in weight of the package of yarn with higher twist if the same length as in the previous (low twist) case is supplied. A viscose yarn of 45 tex has a mean diameter of 220 microns. Determine (i) specific volume of the yarn (ii) the packing coefficient of the yarn (b) If nylon fiber (density 1.14 g/cm3) is used to make the yarn keeping packing coefficient and count similar to the viscose yarn, what would be the yarn diameter in microns? The contraction factor of yarn upon twisting is found to be 1.05. What will be the mean fiber position in it? A filament of 27 denier is wrapped around a 5 mm diameter yarn at a uniform tension of 20cN/tex. At what wrapping angle, the inward radial pressure/unit area on the yarn surface will be 115 cN/cm2?

5 mm

References [1] J.W.S. Hearle, P. Grossberg, S. Backer, Structural Mechanics of Fibres, Yarns and Fabrics, 1, Wiley Interscience, 1969, pp. 62e304. [2] W.J. Hamburger, The industrial applications of the stressestrain relationship, J. Text. Inst. 40 (1949) 700e720. [3] J.W.S. Hearle, J.J. Thwaites, J. Amirbayat, The Mechanics of Dense Fibre assemblies. Mechanics of Flexible Fibre Assemblies, Sijthoff & Noordhoff, Alphen den Rijn, Netherlands, 1980, pp. 51e86.

Fabric preparatory 1

2

7

Akhtarul Islam Amjad and Madan Lal Regar 1 Department of Fashion Technology, National Institute of Fashion Technology Panchkula, Panchkula, Haryana, India; 2Department of Fashion Design, National Institute of Fashion Technology Jodhpur, Jodhpur, Rajasthan, India

7.1

Introduction

Weaving is a process of interlacing at least two sets of yarns (warp and weft) in a regular and recurring pattern. But the yarn from ring spinning is not suitable for direct supply to the looms because of quality, and small size of the package. Such ring spun yarn has to undergo a set of preparatory processes such as winding, warping, sizing, drawing, and denting. In winding operation, objectionable fault-free bigger packages (cheeses or cones) are produced [1]. These packages can be directly used as weft package for nonconventional looms. For conventional loom small packages called pirns are made and the process is known as pirn winding. Warping is done to prepare a warper’s beam or weaver’s beam with many parallel ends in a double-flanged beam to fulfill the warp yarn requirement [2]. A protective coating is applied on the warp yarns with the help of a sizing operation. Drawing-in and tying-in are the processes by which a new warp end is inserted into the weaving elements of the loom, namely drop wires, healds, and reed, while starting up a new fabric. Finally, the fabric is made onlooms by interlacing the warp and weft yarns which leads to continuous fabric formation [3].

7.2

Winding of yarn

Objectionable faults like thick, thin, and slubs, as well as a small cope size cause problems in the succeeding processes and may result in inferior quality of fabric. As a result, it is necessary to transform a small package into a larger package. The winding produces a bigger package that is free from objectionable defects and sufficiently compact for subsequent operations. Two motions are required for smooth transfer of material from smaller package to a bigger package viz; a rotational motion and a traverse. The rotational motion of the output package is required for smooth yarn withdrawal from the supply package. A traverse motion is required to wind the yarn across the entire width of the package. Without the traverse motion, yarns will be laid in the same region and overlap one on exactly top of another coil. The winding operation can be divided into warp and weft winding [1e4]. Warp winding may be precision (spindle driven) or nonprecision (drum-driven or random winders) types. In a drum-driven winder, rotational motion to the package is provided by a drum through surface or frictional contact. In contrast, a yarn traverse Textile Calculation. https://doi.org/10.1016/B978-0-323-99041-7.00005-9 Copyright © 2023 Elsevier Ltd. All rights reserved.

172

Textile Calculation

is provided by grooves cut on the drum or a reciprocating guide. When a noncontact or precision winding drum is not used for rotational motion, the package is mounted on a spindle that is driven positively by a gear system and traversed by a traverse guide. Weft winding, also known as filling or quill winding leads to weft package which is suitable for shuttle looms. The supply package could either be a ring cop or cheese/ cone. Unlike warp winding, weft winding does not remove the yarn faults [3e5].

7.2.1

Drum-driven winding

The frictional contact between the drum and the package rotates the package in the drum-driven winder. Assume that the drum and package rotate at N and n rpm, respectively. The drum is driven directly by the gears, so N is constant. D and d are the diameters of the drum and package, respectively (Fig. 7.1). During winding process, the package diameter (d) increases with time due to continuous laying of yarn. Considering zero slippage between drum and package, it can be said that the surface speed of the drum and the package are always constant [4]. Therefore, pND ¼ pnd..............1 To maintain the constant surface speed, the package speed with respect to time (n) reduces continuously (Fig. 7.1). From Fig. 7.1, different expressions can be derived for wind angle, coil angle, wind, traverse ratio, etc.

7.2.1.1

Angle of wind

The wind angle (a) is defined as the angle formed by the inclined yarn (yarn lay) on the package and a line perpendicular to the package axis [3].

Figure 7.1 Different position of package and drum during winding [3,4].

Fabric preparatory

173

The coil angle is the angle formed by the yarn direction on the package and the traverse length direction. The coil angle and wind angle are complementary angles because they add up to 90 degrees. Therefore, a þ b ¼ 90 degrees.

7.2.1.2

Wind

It is the number of revolutions made by the package (i.e, the number of coils wound on the package) during the time taken by the yarn guide to make a traverse in one direction across the package [3,4].

7.2.1.3

Traverse ratio or wind ratio or wind per double traverse

Number of yarn coils wound per traverse cycle (from one end of the package to the other end and back) or it is the number of revolutions made by the package (i.e, number of coils wound on the package) during the time taken by the yarn guide in making to and fro traverses [3,4]. It is twice the wind. Traverse ratio ¼ 2 Wind. Let L is the length of the drum and package. Distance covered in one complete traverse ¼ 2L Assume the drum made S number of revolutions during the complete traverse So; the time to complete S revolution ¼

Travesrse speedðVtÞ ¼

S minute ðequal to the complete traverseÞ N

Distance covered in one complete traverse 2L 2 LN ¼ ¼ S Time taken for one complete traverse S N

2 LN Vt 2L tan a ¼ ¼ S ¼ Vs pDN pDS So, N, L, D, and S are constants. So in a drum-driven winder, the angle of wind remains constant with the increase in package diameter. Travesrse RatioðTrÞ ¼

WInd per minute n nS DS ¼ ¼ ¼ N Traverse per minute N d S

So, in a drum-driven winder, the traverse ratio reduces with the increase in package diameter.

174

Textile Calculation

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Winding speed ¼ ðDrum surface speedÞ2 þ ðTraverse SpeedÞ2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2ffi 2 LN ¼ ðpDNÞ2 þ S It is evident from the above expression that the winding speed remains constant during package building in case of drum-driven winder.

7.2.2

Spindle-driven winding

A spindle-driven winder is depicted in Fig. 7.2. The package is being carried by a spindle that is rotating at n revolutions per minute. The two gears responsible for transmitting rotational motion from the spindle to the traverse mechanism are A and B (representing the respective tooth number). If these gears (A and B) are not changed, the ratio of spindle speed (r.p.m.) to traverse speed (number of traverses per minute) remains constant and thus the value of the traverse ratio remains constant [3,5,6]. Let R is the number of complete traverse, the traversing device makes per minute. Time required for one complete traverse ¼ R1 Distance covered in one complete traverse ¼ 2L Distance covered in one complete traverse 2L ¼ 1 Time for one complete traverse R ¼ 2LR

Travesrse speed ðVtÞ ¼

Figure 7.2 Spindle-driven winder [3,4].

Fabric preparatory

tan a ¼

175

Vt 2LR ¼ Vs pdn

If a grooved drum causes the traverse, and makes S number of revolutions during the complete traverse; then time to complete the S revolution ¼ S/N minute (equal to the complete traverse). C RPM of grooved drum ¼ N ¼ n A CB Distance covered in one complete traverse ¼ 2L Traverse speed and tangent wind angle are Distance covered in one complete traverse 2L ¼ S Time for one complete traverse N 2L A n ¼ S B

Travesrse speed ðVtÞ ¼

2L A n Vt S B ¼ 2L  A ¼ tan a ¼ Vs pdS B pdn As a result, L, d, S, A, and B remain constant. In a precision winder, the wind angle decreases as d increases with package building. The traverse ratio is Travesrse ratio ðTrÞ ¼

Wind per minute n ¼ ¼ Traverse per minute R

n A C nS  C B

¼

B S A

So, for spindle-driven winders, the traverse ratio remains constant during the package building. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Winding Speed ¼ ðSurface SpeedÞ2 þ ðTraverse SpeedÞ2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðpdnÞ2 þ ð2LRÞ2 Determine the winding speed and angle of wind of a full and empty cylindrical package powered by a spindle. The empty diameter is 5 cm, while the full diameter is 10 cm. The spindle speed is 2000 rpm, and the traverse speed is 100 m/ min.

Example 7.1.

Solution.

Given

176

Textile Calculation

Spindle r.p.m. (n) ¼ 2000, traverse speed (Vt) ¼ 100 m/min, diameter of empty cylindrical package (d) ¼ 5 cm tan a ¼

Vt 100 100 ¼ ¼ ¼ 0:318 Vs pdn 3:14  5  2000

Angle of wind ðaÞat empty ¼ tan1 0:318 ¼ 17:66 Winding speed when the package is empty qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðSurface speedÞ2 þ ðTraverse SpeedÞ2 Winding speed when the package is empty ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3:14  5  2000Þ2 þ ð100Þ2

¼ 329:69 m=min. Diameter of full cylindrical package ¼ 10 cm tan a ¼

Vt 100 100 ¼ ¼ ¼ 0:159 Vs pdn 3:14  10  2000

Angle of wind ðaÞ when the package is full ¼ tan1 0:159 ¼ 9:04 Winding speed when the package is full qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðSurface speedÞ2 þ ðTraverse SpeedÞ2 Winding speed when the package is full ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3:14  10  2000Þ2 þ ð100Þ2

¼ 403:5 m=min Determine the winding drum length if a drum-driven winder’s wind angle is 30 degrees. The diameter of the drum is 5 cm resulting in 5 rotations for one complete traverse. Calculate traverse speed if drum rpm is 500.

Example 7.2.

Here The angle of wind a ¼ 30 degrees; drum diameter (D) ¼ 5 cm; and revolutions for one complete traverse (S) ¼ 5. Let us assume L ¼ the length of the drum, then surface speed of drum (Vs) ¼ pDN ¼ 3:14  5  5 ¼ 78:5 cm=minute

Solution.

tan a ¼

Vt 2L ¼ Vs pDS

Fabric preparatory

tan 30 ¼

177

2L 78:5

Drum length ðLÞ ¼ Traverse speed ¼

7.2.3

78:5  tan 30 ¼ 22:67 cm ¼ 0:227 m 2

2 LN 2  0:227  1000 ¼ ¼ 90:8 m=min S 5

Slippage of the drum

The amount of nontranslation between the drum surface speed and the package surface speed is known as drum slippage. It is calculated with the help of the translation ratio. Translation ratioðxÞ ¼

Surface speed of the package Surface speed of the drum

Winding speed with actual translation ratio qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðSurface speed of drum  xÞ2 þ ðTraverse SpeedÞ2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 LN 2 2 ¼ ðpDNxÞ þ S

A drum comprises of three crossings that rotate at 4000 rpm. The drum diameter and length are 10 cm and 30 cm respectively. If the winding speed is 1200 m/min, calculate the slippage constant.

Example 7.3.

Solution.

Given N ¼ 400 rpm, winding speed ¼ 1200 m/min, D ¼ 10 cm, L ¼ 30 cm

Winding speed with actual translation ratio qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðSurface speedÞ2 þ ðTraverse SpeedÞ2 ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 LN 2 ðpDNxÞ2 þ S

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2ffi 2  0:30  4000 1200 m=min ¼ ðp  0:10  4000  xÞ2 þ 6 or; 1256:63x ¼ 1131:37 or; Translation constant x ¼ 0:9 or; Slippage constant ¼ 1  :9 ¼ 0:1

178

Textile Calculation

7.2.4

Yarn tensioning

The primary objective of yarn tensioning is to build a package with adequate compactness. There are three types of yarn tensioners, additive type or disc type, multiplicative type, and combined type of tensioner shown in Fig. 7.3. In an additive type or disc type tensioner, yarn is passed through two discs, and a dead weight or spring is used for the force (F) to give an increment of tension to the yarn shown in Tout ¼ Tin þ 2mF

½ m ¼ coeffcient of friction between disc and yarn

In the case of a multiplicative type tensioner, the yarn is passed around a curved or cylindrical element which provides the capstan effect and output tension is expressed as Tout ¼ TIn  ðemƟ Þ

h

Ɵ ¼ angle of wrap

i

A combined system of the tensioner is the combination of additive and multiplicative tensioner systems, and output tension is expressed in the form of Tout ¼ TIn þ 2mF1  emƟ1  emƟ2 þ 2mF2

h

Ɵ1 and Ɵ2 are wrap angles

i

In a winding machine, a combined form of tensioning system is used. The input applied tension is 10 cN. The first and fourth tensioners are additive in nature, whereas the second and third tensioners are multiplicative in nature. The coefficient of friction is 0.3. The wrapped angle in an multiplicative tensioner is 90 . Suppose the force applied to first and last tensioners is the same as 34 cN, determine the system’s output tension.

Example 7.4.

Given Input tension ¼ 10 cN; F1]F2¼34 cN; m ¼ 0.3; Q ¼ 90 degree As this is a combined type of tensioner system, so

Solution.

Output tension ¼ Input tension þ 2mF1  emƟ1  emƟ2 þ 2mF2

Figure 7.3 A) Disc (additive) tensioner (B) Multiplicative type tensioner (C) Combined tensioner.

Fabric preparatory

179

1

0 Output tension ¼ ð10 þ 2  :3  34Þ  @e

20:3p 2

A þ ð2  :3  34Þ

Output tension ¼ 98.22 cN.

7.3

Splicing

Splicing is the technique of joining the two ends of yarn. Pneumatic splicers are utilized in the majority of spun yarn machines. Splicing efficiency, also known as retained splicing strength, is calculated as Splicing efficiencyð%Þ ¼

Spliced yarn strength  100 Strength of parent yarn

The efficiency of splicing is also evaluated by the splice breaking ratio as follows: Splicing breaking ratio ¼

Number of breakages in splicing zoneð10 mmÞ Total number of tests

50 spliced yarn samples are subjected to break and 40 of these samples break from the splicing zone. Calculate the splice breaking ratio.

Example 7.5.

Given that Number of breakages in splicing zone (10 mm) ¼ 40; Total number of tests ¼ 50

Solution.

Number of breakages in splicing zoneð  10 mmÞ Total number of tests 40 ¼ ¼ 0:80 50

Splicing breaking ratio ¼

The splicing breaking ratio is 0.80.

7.4

Production calculation of winding machine Production calculation of winding ðper hourÞ ¼

Surface speed of the winding drum ðm=minÞ60Number of drums EfficiencyYarn count ðTexÞ 10001000

180

Textile Calculation

Time required to wind the yarn ¼ or

Quantity of yarn in kg to be wound Actual production in kg=hr  No: of drums

Total warp length in yards Actual production in yards=hr  No: of drums

Calculate the production of a winding machine with 60 drums ( 8 cm diamter) and drum speed is 2400 r.p.m. The count of the yarn is 20 tex and efficiency is 68%.

Example 7.6.

Solution.

Production calculation of winding ðper hourÞ ¼

p  0:08  2400  60  60  0:68  20 ¼ 295:17 kg=h 1000  1000

The production of 60 drum winding machine is 295.17 kg/h.

How much time will be required to wind 1083.19 kg of 20s Ne cotton yarn on 40 drums winding machine? If the calculated winding speed is 1299 yards per min and the efficiency is 85%.

Example 7.7.

Given that Calculated winding speed in yard/minute ¼ 1299; efficiency ¼ 85% ; quantity of yarn to be wound ¼ 1083.19 kg.

Solution.

Actual production in yards per minute ¼ Calculated yard/minute  no. of drums  efficiency Actual production in yards per minute; ¼ Calculated yards=minute  Number of drums  Efficiency ¼ 1299  40  0:85 ¼ 44166 yards=minute Production ðYards per minuteÞ 840  2:2  CountðNeÞ 44166 ¼ 1:19 kg=min ¼ 840  2:2  20

Actual production in kg per minute ¼

Time required to wind the yarn in hour ¼

Quantity of yarn in kg to be wound Actual production ðin kg=hourÞ  Number of drums

Fabric preparatory

181

Time required to wind the yarn ¼

1083:19 hrs ¼ 15:17 hrs 1:19  60

Time required to wind the yarn is 15.17 h. A precision winder must wind 4 kg of 40 tex yarn. If the machine winds at 800 m per minute without interruption, what is the time in minutes required for winding? Calculate the additional time necessary to accomplish the same work if the machine’s efficiency is 91%.

Example 7.8.

Given Yarn to wind ¼ 4 Kg; yarn count ¼ 40 tex ( 14.76 Ne); winding speed ¼ 800 m/ min

Solution.

Winding speedðmeter=minuteÞ  1:09 kg=min 840  2:2  CountðNeÞ 800  1:09 ¼ 0:032 kg=min ¼ 840  2:2  14:76

Actual production ðin kg=minÞ ¼

Time required to wind the yarn ¼

Quantity of yarn in kg to wind 4 ¼ Actual production in kg=hr 0:032

¼ 125 min If the efficiency of the machine is 91% Time required ¼

Time required at 100% efficiency 125  100 ¼  100 Actual efficiency 91

¼ 137:36 min So additional time required ¼ 137.6 mine125 min ¼ 12.36 min.

7.5

Warping

Warping is the process of gathering individual creel ends and transferring them to a beam. Warping is the parallel winding of warp ends from several winding packages (cone or cheese) onto a standard package (warp beam). The warping procedure aims to turn the yarn packets into a warper’s beam with the necessary width and number of ends. During warping, individual strands are kept at a constant tension. Three alternative warping methods are often used viz; beam, sectional and ball. In the case of beam warping, the yarn is wrapped straight from the cone onto the beam. It’s sometimes referred to as high-speed warping or direct warping. Direct warping generates

182

Textile Calculation

smaller beams called warper’s beams, which are then sent to the sizing process for combination to produce the weaver’s beam [3,5,7]. For a striped look, sectional warping is preferable to beam warping. In this case, warp yarns are wound into yarn bands (sections) of the same warp density as for the weaver’s beam. These bands were moved from the drum to the weaver’s beams once the yarn was completely wound onto the drum [5e8].

7.4.1

Calculation on warping

Warping calculation depends on the fabric particulars such as ends per inch (EPI) the width of the fabric, yarn count, etc. The total number of ends required on the weaver’s beam can be calculated by Number of ends ¼ EPI  Fabric width in inch number of ends In case of direct warping machine-Number of warpers beams ¼ TotalCreel capacity In the case of sectional warping machine

Number of sections on drum ¼

Total number of ends Creel capacity

In the case of patterning Number of patterns per section on drum ¼

Total number of ends Total ends in pattern

A fabric has 200 ends per inch and width of 58 inches. Suppose the weaver’s beam is created from a combination of warper’s beams produced by a direct beam warping machine with a capacity of 602 creels. Calculate (i) the total number of ends in the weavers and warper’s beam and the number of warper’s beams, (ii) the possible practical number of warper’s beam, creel size, weight, and length of warp beam and (iii) number of sections and patterns in each section if this weaver’s beam is manufactured on a sectional warping machine with 58 patterns using the same creel.

Example 7.9.

Solution.

Number of ends in weavers beam ¼ EPI  Fabric width in inches ¼ 200  58 ¼ 11600 Number of warpers beams ¼

Total number of ends 11600 ¼ ¼ 19:26 Creel capacity 602

Fabric preparatory

183

As the number of warper’s beam cannot be in decimal, so corrected creel size will be calculated Creel size ¼

Total number of ends 11600 ¼ ¼ 580 Number of warpers beams 20

The number of ends in the warper’s beam is equal to creel size, so the number of ends per warper’s beam is 580. Number of sections on drum ¼

11600 ¼ 20 580

Number of patterns per section on drum ¼

Creel size 580 ¼ ¼ 10 Number of patterns 58

The width of a weaver’s beam is 140 cm which comprises of 800 ends of 20 tex yarn. The diameter of the empty beam is 30 cm and the yarn depth on the beam is 45 cm. Calculate the length of the warp and its mass in kg if the beam density is 0.4 g/cm3.

Example 7.10.

Given-beam width (L) ¼ 140 cm; number of ends ¼ 800; count of yarn ¼ 20 tex; depth of warp sheet (h) ¼ 22.5 cm; empty beam diameter (d) ¼ 30 cm; density ¼ 0.4 g/cm3;

Solution.

Full beam diameter ðDÞ ¼ Empty diameter þ 2  Depth of the warp sheet ¼ 30 þ 2  22:5 ¼ 75 cm Volume of the yarn ¼ Volume of the full beam  Volume of empty beam p p ¼ D2  d2 Þ  L ¼ 752  302 Þ  140 ¼ 519541 cm 3 4 4 Mass of the yarn ðKgÞ ¼ Volume of the yarn  Density of the beam ¼ 519541  Weight of single end ¼

0:4 ¼ 207:82 Kg 1000

Weight of yarn in the beam 207:82 ¼ ¼ 0:2598 Kg Number of ends 800 Weight of single end ðgÞ 0:2598  1000 ¼ Tex 20 ¼ 12:99 km

Length of the warp in Km ¼

A warper beam contains 1000 ends of 20s Ne yarn of of 4000 m length. Calculate the weight of the beam.

Example 7.11.

184

Textile Calculation

Given that Number of ends ¼ 1000; length of warp is 4000 m; count of yarn ¼ 20Ne

Solution.

The total length of warp yarns ¼ Length of single yarn  Total number of ends ¼ 4000  1000 ¼ 4000000 meter Mass of the yarn ðKgÞ ¼ Total length of the warp yarns ¼ 4000000 

ðmeterÞ Tex  1000 1000

590:5 ¼ 118:1 Kg 20

A patterned warp of 30 tex yarn will be wound onto a sectional warping drum of 1 m diameter and 1.38-meter working width. The drum is set at a 15 degree angle to the axis. The total number of ends for warping is 6480. The material density on the beam is 0.58 g/m3. The whole diameter of the drum is 1.2 m. Determine the warp and traversal lengths for each section.

Example 7.12.

Solution. Given , Yarn count ¼ 20 tex; warp width (L) ¼ 1.38 m; empty beam diameter (d) ¼ 1m; full drum diameter (D) ¼ 1.2 m

Volume of the yarn ¼ Volume of the full drum  Volume of empty drum p p ¼ D2  d2 Þ  L ¼ 1:22  12 Þ  1:38 ¼ 0:477m 3 4 4   Mass of the yarn ðKgÞ ¼ Volume of the yarn m3    Density of the beam g=m3  1000 ¼ 0:477  0:58  1000 Kg ¼ 276:66 Kg Weight of yarn in beamðKgÞ 276:66  1000 ¼ Kg Number of ends 6480 ¼ 42:694 Kg

Weight of single end ¼

Weight of single end ðgÞ 42:694 ¼ Km Tex 30 ¼ 1:42 Km

Length of the warp in Km ¼

Depth of warp sheet ðhÞ ¼ Radius of full drum  Radius of empty drum   1:2 1  m ¼ 0:1m ¼ 2 2

Fabric preparatory

185

If traverse length is x Then x¼

h ¼ tan Ɵ x

h 0:1  100 10 ¼ cm ¼ cm ¼ 46:94 cm tan Ɵ tan 12 0:213

So, the length of warp and traverse length per section is 1.42 km and 46.94 cm respectively. Data of a warping machine are given below. Number of ends ¼ 500; speed in m/min ¼ 400, set length (m) ¼ 20,000, number of ends/beam ¼ 500, end breaks/400 ends/1000 m ¼ 3, time to mend a warp break (seconds) ¼ 30, time to change a beam (seconds) ¼ 600, time to change a creel (seconds) ¼ 3600, time loss due to miscellaneous causes/1000 m (seconds) ¼ 30; by the help of one cone, four beams can be made.

Example 7.13.

(a) Calculate the total stoppage time per 1000 m (sec) (b) Calculate the approximate machine efficiency in making four beams. Solution.

From the above data,

The total length of the warp ¼ Set length  Number of beams ¼ 20000  4 ¼ 80000 m Run time ¼

Total length of warp 80000 ¼ min ¼ 200 min Speed ðm=minÞ 400

So Number of breakages ¼

Number of breakages∕400 ends=1000meter 400  1000  Total number of ends  Total length

¼

3 80000  500  80000 ¼ ¼ 300 400  1000 400

Total mending time ¼ Mending time of a breakage  Number of breakages ¼

30  300 ¼ 150 min 60

186

Textile Calculation

Total stoppage time ¼ Mending time þ Beam change time þ Creel change time þ Miscellaneous time 600 3600 30 80000 30 þ þ  ¼  300 60 60 60 1000 60 ¼ 150 þ 30 þ 60 þ 40 ¼ 280 min ¼ 150 þ 3 

The efficiency of the warping machine ðh%Þ ¼

200  100 ¼ 41:67% 200 þ 280

The efficiency of warping machine is 41.67%.

7.6

Sizing

The object of warp sizing is to increase the weaving ability of yarns by adding a homogeneous coating to the yarn surface and laying down projecting hairs on it. The warp yarns are abraded by different loom components such as the backrest, heald eyes, reed, and front rest throughout the weaving process. Warp yarns rub against one other during the shedding process. The yarn structure is protected from abrasion by a size coating. As a result, the loom’s warp breaking rate decreases [6,8]. Size paste concentration, size pickup, and size add-on are some of the words commonly used in sizing process. They are defined as follows: Size concentration ð%Þ ¼ Size add on ð%Þ ¼

Oven dry weight of size material  100 Weight of size paste

Oven dry weight of size material  100 Oven dry weight of unsized yarns Weight of size paste Oven dry weight of unsized yarns Oven dry weight of size material  100 Size concentration ð%Þ ¼ Oven dry weight of size material  100 Size add on ð%Þ Size add on ð%Þ ¼ Size concentration ð%Þ

Wet pick up ðsize paste pickupÞ ¼

Fabric preparatory

187

The warp sheet is dried by passing through a series of Teflon (poly tetra fluoroethylene)coated drying cylinders in sequential order. Depending on how much water needs to be evaporated in a given length of time, the number of drying cylinders might range from 2 to 30. In general, a faster sizing speed necessitates a greater number of drying cylinders. The following equations can calculate the amount of water that will be evaporated during the drying process [3,4,8]: Mass to be evaporated ¼ Wet pick up  Oven dry weight of sized matetial ¼

Size add on ð%Þ Size add on ð%Þ  Size concentration ð%Þ 100

The preceding calculation assumes that the sized yarn has no left over moisture after drying. However, it is also necessary to calculate the mass of water to be evaporated in unit time (minute) for the machine . This will be determined by the speed of the sizing machine, the total number of yarns, yarn linear density (tex) add-on percent and the size concentration percent [3,4,8]. The weight of yarn that passes through the machine each minute is expressed as: Production ðlbs=minÞ ¼

Speed of sizing machineðm=minÞ  Number of warp yarn in the beam  1:09 840  Ne

The mass of wet pick up per minute can be calculated in the following way: Wet pickup ðlbs=minÞ m Speed of sizing machine  Number of warp yarn in the beam  1:09 min ¼ 840  Ne  Wet pick up m Speed of sizing machine  Number of warp yarn in the beam  1:09 min ¼ 840  Ne 

Size add on ð%Þ Size concentration ð%Þ

So, the following equations may be used to calculate the mass of water that will be evaporated each minute throughout the drying process.

188

Textile Calculation

Mass to be evaporated ðlbsÞ per minute ¼ Wet pick up per minute  Oven dry weight of sized matetial

¼

Speed of sizing machine



m  Number of warp yarn in the beam  1:09 min 840  Ne

Size add on ð%Þ Size add on ð%Þ  Size concentration ð%Þ 100

m  Number of warp yarn in the beam  1:09 min ¼ 840  Ne   Size add on ð%Þ Size concentration ð%Þ  1 Size concentration ð%Þ 100 Speed of sizing machine

Mass to be evaporated ðKgÞper minute ¼

Speed of sizing machineðm=minÞ  Number of warp yarn in the beam  tex 1000  1000   Size add on ð%Þ Size concentration ð%Þ  1 Size concentration ð%Þ 100

Sizing increases not only the weight of warp but also changes the yarn count so the yarn count can be evaluated Count of unsized warp yarn ðNeÞ ¼

Unsized warp length ðyardsÞ  Number of warp yarn in the beam 840  Unsized warp yarns weight ðlbsÞ Count of sized warp yarn ðNeÞ

¼

Sized warp yarn length ðyardsÞ  Number of warp yarn in the beam 840  Sized warp yarns weight ðlbsÞ

The true performance of sized yarn can only be assessed during the weaving operation. However, the performance of sized yarns can be predicted by evaluating the tenacity and breaking elongation of sized yarn, cohesiveness and adhesion of the sized film, abrasion resistance and fatigue resistance [3,6e8]. The following expression can evaluate the adhesive power of sizing paste:

Fabric preparatory

189

Adhesive power Breaking strength of sized roving at the gauge length ðgreater than the staple length of fiber Þ ¼ Breaking strength of sized roving at the zero gauge length

Deterioration in strength due to the abrasion can be evaluated by the following expression: Yarn strength deterioration due to abrasionð%Þ Breaking strength of yarn before abrasion Breaking strength of yarn after abrasion ¼  100 Breaking strength of yarn before abrasion

Calculate the wet pickup if the add-on % is 10 and the concentration of size paste is 15%.

Example 7.14.

Given that Add on % is 10 and the concentration of size paste is 15%.

Solution.

Wet pick up ¼

Size add on ð%Þ 10 ¼ ¼ 0:667 Size concentration ð%Þ 15

The pick up is 0.667.

200 kg oven-dry warp yarns were sized to an add-on of 8% and dried to overall (yarn and dry size) moisture regain of 10%. Calculate the final mass of the sized yarns.

Example 7.15.

Given Oven-dry warp yarn is 200 kg; add on % is 8 and the moisture regain is 10%

Solution.

Oven dry weight of sized material ¼ Size add on ð%Þ  Oven dry weight of unsized yarns  ¼

1 100

8  200 ¼ 16 Kg 100

190

Textile Calculation

Oven dry weight of sized yarns ¼ Oven dry weight of size material þ Oven dry weight of unsized yarn ¼ 200 þ 16 ¼ 216 Kg Moisture regain  Oven dry weight of sized yarn 100 10  216 ¼ 21:6 Kg ¼ 100

Mass of water ¼

Therefore; the final weight of sized yarns ¼ Oven dry weight of size material þ Oven dry weight of unsized yarn þ Mass of water ¼ 200 þ 16 þ 21:6 ¼ 237:6 Kg The final mass of the sized yarns is 237.6 kg. On the 2800 warp yarns of 987 m each, the add-on percent of the size material on the warp yarns is 20%. Calculate the amount of size material in the warp, warp yarn weight and yarn count after sizing if the unsized yarn count is 40s Ne.

Example 7.16.

Given that Number of warp yarn ¼ 2800; add on ¼ 20%; warp yarn length ¼ 987 m; yarn count before applying starch ¼ 40sNe

Solution.

Weight of unsized warp yarns ðlbsÞ ¼

Unsized warp length ðyardsÞ  Number of warp yarn in the beam 840  Count of unsized warp yarn ðNe Þ ¼

987  2800  1:09 lbs ¼ 89:65 lbs 840  40

Oven dry weight of size material ¼

Size add on ð%Þ  Oven dry weight of unsized yarn 100 20  89:65 lbs ¼ 17:93 lbs ¼ 100

Fabric preparatory

191

Oven dry weight of sized yarns ¼ Oven dry weight of size material þ Oven dry weight of unsized yarn ¼ ð89:65 þ 19:93 Þlbs ¼ 107:58 lbs Count of sized warp yarn ðNe Þ ¼

Sized warp length ðyardsÞ  Number of warp yarn in the beam 840  Sized warp yarns weight ðlbsÞ ¼

987  2800  1:09 ¼ 33:33 Ne 840  107:58

The count of sized warp yarn is 33,33 Ne. A 8% add-on is applied to the warp sheet. Determine the oven-dry mass of the size applied per kilogram of the unsized warp yarn if the moisture content of the unsized warp yarn is 10%.

Example 7.17.

Solution.

Given that size add on ¼ 5%; Moisture content ¼ 10%

Mass of water ¼

Total weight of unsized yarn  Moisture content 10 ¼ 100  100 100

¼ 10kg Oven dry weight of unsized yarn ¼ Total weight of unsized yarn  Mass of water ¼ 100  10 ¼ 90 Kg Oven dry weight of sized material ¼

¼

Size add onð%Þ 100  Oven dry weight of unsized yarns 8  90 ¼ 7:2 Kg 100

Oven dry mass of the size added per Kg of warp ¼

Oven dry weight sized material 7:2 ¼ ¼ 0:072 Kg Total weight of the warp 100

A Sized roving with 30 mm staple length of fibers possess breaking strength 170gf, 150gf, and 130 gf at zero gauge, 25 mm gauge, and 32 mm gauge length, respectively. Calculate the adhesive power of sizing paste on the yarns.

Example 7.18.

192

Textile Calculation

Given that Breaking strength at the gauge length (greater than the staple length of fiber) ¼ 130 gf; breaking strength at the zero gauge length ¼ 170 gf Solution.

Adhesive power ¼

Breaking strength of sized roving at the gauge length ðgreater than the staple length of fiberÞ Breaking strength of sized roving at the zero gauge length ¼

130 ¼ 0:764 170

The adhesive power of sizing paste on the yarns is 0.764. Calculate the stretch percentage of a beam whose length is 5020 m before size and 5160 m after sizing.

Example 7.19.

Solution.

Stretch ð%Þ ¼

Beam length after the sizing  Beam length before the sizing Beam length before the sizing

 100 ¼

5160  5020  100 ¼ 2:78% 5020

The stretch percentage is 2.78. Calculate the size concentration measured by the refractometer if the size ingredients are starch 100 kg at 6% moisture content, liquid binder 8 kg at 25% concentration, pure solid binder 7 kg and pure solid softener 2 kg. The amount of water added is 568 litre and steam condensation is 10%. If the add-on is 8%, then calculate the wet pickup.

Example 7.20.

Solution.

Total weight of starch  Moisture content 100 100  6 ¼ 6 Kg ¼ 100

Amount of water in the starch ¼

Oven dry weight of starch ¼ Total weight of starch  Mass of water ¼ 100  5 ¼ 95 Kg Amount of water in the liquid binder ¼

Total weight of liquid binder  Concentration 8  25 ¼ ¼ 2 Kg 100 100

Fabric preparatory

193

Oven dry weight of binder ¼ Total weight of liquid binder  Mass of water ¼ 8  2 ¼ 6 Kg Oven dry weight of size material ¼ Oven dry weight of starch þ Oven dry weight of binder ðsolid and liquidÞ þ Oven dry weight of softner ¼ 94 þ 6 þ 7 þ 2 ¼ 109 kg Add water  Condensation ð%Þ 100 568  10  100 ¼ 56:8 ¼ 100

Condensed water in the paste ¼

Actually added water present in size paste ¼ Added water  Condensed water ¼ 568  56:8 ¼ 624:8 Net water present in size paste ¼ Actual added water present in size paste þ Water present in starch þ Water present in binder ¼ 624:8 þ 6 þ 2 ¼ 632:8 Weight of size paste ¼ Oven dry weight of size material þ Net water present in the paste ¼ 109 þ 632:8 ¼ 741:8 Size concentration ð%Þ ¼

Oven dry weight of size material 109  100 ¼  100 Weight of size paste 741:8

¼ 14:69%

Wet pick up ¼

Size add on ð%Þ 8 ¼ ¼ 0:544 Size concentration ð%Þ 14:69

The wet pickup is 0.544. A sizing machine runs at 140 m/min and has 6428 ends. The add-on need is 12% and the size paste refractometer (Rf %) is 18%. Calculate the number of drying cylinders necessary if the yarn count is 29.5 Ne (without any moisture) and the residual moisture content in the sized yarn and film after drying is 10%. A single drying cylinder can evaporate 4 kg of water per minute.

Example 7.21.

194

Textile Calculation

Given that Speed of sizing machine ¼ 140 m/min, total ends ¼ 6428, add-on % ¼ 12%, count 29.5 Ne, moisture in sized yarn ¼ 10%, concentration or Rf% ¼ 18

Solution.

 Oven dry mass passing through the machine i:e; Production

¼

Speed of sizing machine

Wet pick up ¼

lbs min



m  Number of warp yarn in the beam  1:09 min 840  Count 140  6428  1:09 ¼ 39:58 lbs ¼ 840  29:5

Size add on ð%Þ 12 ¼ ¼ 0:667 Size concentration ð%Þ 18

The total mass of sized paste picked up by the warp yarns ¼ Wet pick up  Oven dry mass of warp ¼ 0:667  39:58 ¼ 26:39 Oven dry weight of size material ¼

Rf %  Total mass of sized paste picked by the yarn 100 18  26:39 ¼ 4:75 lbs ¼ 100

Oven dry mass of sized warp yarns ¼ Oven dry weight of size material þ

Production Time ðminÞ

¼ 4:75 þ 39:85 ¼ 44:60 lbs Total weight of starch  Moisture content 100 44:60  1 ¼ 4:95 lbs ¼ 9

Amount of water in the sized yarn ¼

Amount of water in the picked  up size paste of 26:39 lbs ¼ 26:39 

ð100  concentrationÞ 26:39  ð100  18Þ ¼ ¼ 21:64 lbs 100 100

So water to be evaporated in one minute ¼ 21:64  4:95 ¼ 16:72 lb

Fabric preparatory

Cylinders require to evaporate the 16:72 lbs of water ¼ ¼

195

Water to be evaporated Cylinder drying capacity

16:72 ¼ 1:89 w 2 4  2:2

The required number of drying cylinders is 2.

References [1] A. Majumdar, Principles of Woven Fabric Manufacturing, first ed., CRC Press, 2016 https:// doi.org/10.1201/9781315367729. [2] D.V. Bihola, N.A. Hiren, Classimat yarn faults, Int. J. Adv. Eng. Res. Dev. 2 (2) (2015) 286e295. [3] https://nptel.ac.in/courses/116102005 (Accessed 24 May 2022). [4] https://nptel.ac.in/courses/116102017 (Accessed 15 June 2022). [5] A. Patnaik, S. Patnaik (Eds.), Fibres to Smart Textiles: Advances in Manufacturing, Technologies, and Applications, first ed., CRC Press, 2019 https://doi.org/10.1201/ 9780429446511 10.1016/j.clet.2021.100320. [6] J.Y. Drean, M. Decrette, Weaving preparation, in: Y. Kyosev, F. Boussu (Eds.), Advanced Weaving Technology, Springer, Cham, 2022, https://doi.org/10.1007/978-3-030-91515-5_1. [7] A.M. Seyam, 3. Advances in weaving and weaving preparation, Textil. Prog. 30 (1e2) (2000) 22e40. [8] T. Ahmed, R. Mia, G. Farhan, I. Toki, J. Jahan, Md M. Hasan, Md A. Saleh Tasin, Md Salman Farsee, S. Ahmed, Evaluation of sizing parameters on cotton using the modified sizing agent, Clean. Eng. Technol. 5 (2021) 100320. ISSN 2666-7908.

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Woven fabric production 1

2

3

8

Akhtarul Islam Amjad , J.P. Singh and Madan Lal Regar 1 Department of Fashion Technology, National Institute of Fashion Technology Panchkula, Panchkula, Haryana, India; 2Department of Textile Technology, Uttar Pradesh Textile Technology Institute, Kanpur, Uttar Pradesh, India; 3Department of Fashion Design, National Institute of Fashion Technology Jodhpur, Jodhpur, Rajasthan, India

8.1

Introduction

Weaving is accomplished through the interlacement of warp and weft. Winding, warping, sizing, drawing, and denting are the procedures that precede it. The yarn in the vertical direction is referred to as a warp or end [1]. Weft yarn or a pick is the yarn that runs cross-wise. The cloth can be made on a handloom, a power loom, or a nonconventional loom. To weave a fabric, looms use three basic actions are known as primary motions. The first is shedding, in which the warp sheet is separated into two portions to create a clear passage for the weft thread or weft carrying device. The second step is picking, which involves inserting a weft or weft carrying device (shuttle, projectile, or rapier) through the shed. The third is beating in which the newly inserted weft yarn is pushed up to the fell of the cloth. Secondary motions are also required for continuous fabric manufacturing [2]. There are two types of secondary motions: let-off motion and take-up motion. The fundamental purpose of let-off and take up is to keep the weaving process consistent. After the beat-up, the take-up action winds the newly formed fabric on the cloth roller continuously or intermittently. To compensate, the let-off mechanism rotates the weaver’s beam, releasing some new warp sheet; aside from these motions or mechanisms, auxiliary motions are also used to activate the various stop motions for manufacturing fault-free fabric and reducing waste. These motions are warp stop motion, weft stop motion, and warp protector motion in the event of warp breaking, weft breakage, and shuttle entrapment, respectively. Many calculations are required to ensure the smooth operation of these motions. As a result, this chapter discusses such calculations and numerical issues [3].

8.2

Primary motions

Primary, secondary, and auxiliary motions are used to manufacture fabric on looms. The primary motions are shedding, picking, and beating.

8.2.1

Shedding

Shedding is the primary motion in which whole warp sheet is divided into two sheets in order to make a sufficient spacing for the continuous passage of the weft from one Textile Calculation. https://doi.org/10.1016/B978-0-323-99041-7.00007-2 Copyright © 2023 Elsevier Ltd. All rights reserved.

198

Textile Calculation

side of the loom to the other. The entire warp yarns are divided into two groups by raising and lowering the heald frames with a tappet. Tappet, dobby, and jacquard are well-known shedding devices. Shedding is categorized into four types based on its closing position: bottom close, center close, partly open, and open shed. Tappets and cams are irregular metallic components used in followers and levers to provide an up-and-down motion [4]. The up-and-down motion is obtained by giving rotary motion to these pieces. Tappets contain distinct segments that correlate to “dwell” periods, which are regular intervals of rest in which other major parts involved in the action. When motions coming from the loom drive are used to lift and springs are used to lower the healds, a mechanism of this type is known as negative shedding. If the motions coming from the loom drive are used to lift and lower the healds, it is known as positive shedding. The transmission of motions to the various loom parts is depicted in Fig. 8.1 [5]. The machine pulley receives direct motion from the motor pulley. Because the crankshaft is linked to the machine pulley, the crank shaft’s revolution per minute (r.p.m.) corresponds to the loom speed and, ultimately, to the same number of picks/minute. Sley is also linked to the crankshaft, so one revolution of the crankshaft results in one beat-up. The crankshaft is also linked to the bottom shaft through gears. In the case of shuttle looms, the picking motion is generated from the bottom shaft. On the bottom shaft, two picking cams are installed, one on each side. As a result, one revolution of the bottom shaft results in the insertion of two picks. The shedding device can be connected directly to the bottom shaft or indirectly via the tappet or cam shaft. The number of cams linked to the tappet/cam shaft determines the frequency of shedding [5]. In a loom weaving 4/4 twill, if the rotational speed of the crankshaft is 300 rpm (revolotion per minute), then find the ratios of crankshaft, bottom shaft, and tappet shaft rotational speed.

Example 8.1.

Solution.

R.P.M. of crank shaft ¼ NC ¼ 300.

Figure 8.1 Transmission of motion in the loom.

Woven fabric production

199

Thus, R.P.M. of bottom shaft ¼ NB ¼ 300 2 ¼ 150 Number of cams required ¼ 4 þ 4 ¼ 8. 300 So, R:P:M: of bottom shaft ¼ NT ¼ 4300 þ 4 ¼ 8 ¼ 37:5 Ratio of rpm ¼ NC : NB : NT ¼ 300:

300 300 : ¼ 8: 4: 1 2 8

Calculate the throw (lift) of the cam controlling the back heald from the following particulars: throw (lift) of the cam for the front heald (L1) ¼ 7 cm; the distance between the front and back heald (b) ¼ 4 cm; the distance between the fulcrum and bowl on the treadle (x) ¼ 18 cm; the distance between the bowl and the fastening point of the back heald (y) ¼ 18 cm; diameter of small reversing roller (d1) ¼ 4 cm; and diameter of large reversing roller (d2) ¼ 6 cm.

Example 8.2.

Solution.

dThe expression to be used for calculating the throw or lift of the cam is as

follows: L₂ x þ y þ b a þ b ¼  L1 xþy a Given • • • • • •

Throw (lift) of the cam for the front heald (L1) ¼ 7 cm The distance between the front and back heald (d2) ¼ 4 cm The distance between the fulcrum and bowl on the treadle (x) ¼ 18 cm The distance between the bowl and the fastening point of the back heald (y) ¼ 18 cm Diameter of small reversing roller (d1) ¼ 4 cm Diameter of large reversing roller (d2) ¼ 6 cm

a þ b d2 ¼ 0a ¼ 8 cm a d1 L₂ xþyþb aþb ¼  So, L1 xþy a

Now,

L₂ ¼ 1:66 0L2 ¼ 1:66  7 0L2 ¼ 11:66 cm L1 So, the lift of the cam controlling the back heald is 11.66 cm. A cloth having 15% weft crimp is produced on loom with reed width of 3 meter. Calculate the width of cloth.

Example 8.3.

Solution.

Weft crimp % ¼

ðReed width  Cloth widthÞ  100 Cloth width

200

Textile Calculation

15 ¼

ð3  Cloth widthÞ  100 Cloth Width

15  cloth width ¼ 300e100  cloth width Cloth width ¼ 2.61 m.

8.2.2

Picking mechanism

Picking is the operation of transferring the pick from one side of the loom to the other side of the loom and so on in case of shuttle looms. In a shuttle-less loom, picking is done from only one side of the loom. Several picking systems are available; the most conventional picking mechanism uses the shuttle as a weft carrier. The shuttle transports the weft yarn in a package known as pirn. This system’s primary role is to transport the shuttle along the proper flight path and to project the shuttle at a predetermined velocity. In a nonconventional picking mechanism, the weft yarn is inserted directly or positively into the warp shed by air, water, projectile, needle, or rapier. There is a direct relationship between the loom speed and the shuttle velocity. Let us assume that P ¼ loom speed (picks/min.) or number of revolutions of the crank shaft/ min, R ¼ width of the reed (m), V ¼ average shuttle velocity (m/s), L ¼ effective length of the shuttle (m), q ¼ degree of crank available for the passage of the shuttle through the shed, and T ¼ time required for the shuttle passage through the shed (S), then Average shuttle velocity ðVÞ ¼ or; t ¼

ðR þ LÞ m∕s t

ðR þ LÞ second V

(8.1)

P revolution of the crankshaft is made in 60 seconds. One revolution of the crankshaft is taking place in 60/P seconds. or 360 degrees of crankshaft rotation is taking place in 60/P seconds. or q of crankshaft rotation is taking place in q=6P seconds

(8.2)

From Eqs. (8.1 and 8.2), we have: V¼

6PðR þ LÞ q

(8.3)

From Eq. (8.3), the following interpretation can be made: loom speed can be improved for a given loom width and shuttle length by increasing velocity (V) or q or both. However, an increase in q can be obtained by increasing the sley eccentricity (e), as sley remains in the back center of the loom for a longer period of time when the sley eccentricity is greater. As a result, the shuttle can get more time for its flight

Woven fabric production

201

through the shed. A high sley eccentricity value should be avoided to prevent loom wear and tear. Furthermore, a rise in q poses a challenge for fast reed warp protector motion because the shuttle must reach the swell at the correct time to avoid trapping. Therefore, q cannot be increased. On the other hand, increased V necessitates higher kinetic energy dissipation during shuttle checking, which increases loom frame wear. The loom speed in the shuttle loom is clearly limited based on the preceding logic. Find the loom speed of a loom if the average velocity of the shuttle is 50 km/h. The degree of crankshaft rotation for passage of shuttle is 135 . The length of the shuttle is 40 cm and the reed width is 2 m.

Example 8.4.

Length of shuttle (L) ¼ 40 cm ¼ 0.4 m; Velocity of shuttle (V) ¼ 50 km/h; Reed width (R) ¼ 2 m

Solution.

V¼

6PðR þ LÞ q

V ¼ 50 

1000 6Pð2 þ 0:4Þ m=sec ¼ P ¼ 130:20 60  60 135

P ¼ 130.20 picks per minute or 130.20 rpm. If the reed width is 1.2 m, the shuttle length is 30 cm, the loom speed is 240 pick/min, and the degree of crankshaft rotation for passage of shuttle is 140 . Then calculate shuttle speed.

Example 8.5.

Reed width (R) ¼ 1.2 m; Shuttle length (L) ¼ 30 cm ¼ 0.3 m; Loom speed (P) ¼ 240 picks/min

Solution.

V¼

6PðR þ LÞ q

V¼

6  240  ð1:2 þ 0:3Þ 140

Velocity of shuttle ¼ 15.43 m/s. Example 8.6.

Find the cloth width whose reed width is 3.1 m and weft crimp is given as

12%.

Solution.

Weft crimp % ¼

ðReed width  Cloth widthÞ  100 Cloth Width

202

Textile Calculation

12 ¼

ð3:1  Cloth widthÞ  100 Cloth width

12  cloth width ¼ 310e100  cloth width Cloth width ¼ 2.76 meter. Weft insertion rate: The weft yarn is inserted through the shed after each shed change. These weft yarns can differ in color, count, material, and so on, and a selection mechanism is employed to accomplish this. Weft insertion rate (WIR) refers to the amount of weft yarn placed into the warp sheet per unit time. The following formula is used to calculate it: Weft Insertion Rate ¼ loom speed ðP; picks = minuteÞ X reed width ðRÞ or length of one pick

Calculate the WIR in m/min if the loom speed is 500 pick/min. The weft crimp is 8.5%, and the fabric width is 3 m.

Example 8.7.

Solution.

Loom speed (P) ¼ 500 pick/minute; weft crimp (%) ¼ 8.5

Weft Insertion Rate ¼ loom speed ðPÞ  reed width ðRÞ ¼ 500  ð3 þ f3X8:5%gÞ ¼ 1627.5 m/min. The energy used to accelerate the shuttle is equal to its kinetic energy when it leaves the picker, So, energy pick ¼ 1/2 mv2J where m ¼ mass of the shuttle (kg) and v ¼ shuttle velocity (m/s). Now power required for picking ¼ Work done/s for picking ¼ Energy used to accelerate the shuttle/s. If the loom speed is P picks/min., then the number of picks inserted/seconds ¼ P/60. mv2 1 As power for picking ¼ : kW 60  2 1000 6PðR þ LÞ Now from Eq. (8.3) V ¼ q 3MP3 ðR þ LÞ2 X104 By substituting the expression of V, power for picking ¼ q2 kW. From the above expression, it can be attributed that the power of picking is also influenced as follows: • • •

Increases linearly with the mass of the shuttle. Increases proportionately with the square of loom width. Decreases proportionately with the square of the degree of crankshaft rotation available for the shuttle’s passage through the shed.

Woven fabric production

203

Find the energy of the shuttle whose length is 0.5-meter and the reed width is 2 m. Loom speed is 252 rpm and the shuttle’s mass is 480 g. The degree of crankshaft rotation for passage of shuttle is 130 .

Example 8.8.

Solution.

R ¼ 2 m; L ¼ 0.5 m; M ¼ 480 gm ¼ 0.48 kg; N ¼ 252 rpm; q ¼ 130

Energy ¼

18MN2 ðR þ LÞ2 q2

Energy ¼

180  :48  2522  ð2 þ 0:25Þ2 1302

¼ 202.91. Energy ¼ 0.20 kJ. Calculate the power when the reed width is 1.5 m. Shuttle length is 0.32 m, loom speed is 224 rpm, and shuttle mass is 520 g. The shuttle enters into the shed at 115 , and the shuttle leaves the shed in 248 .

Example 8.9.

Degree of crank shift rotation available (q) ¼ 248 e115 ¼ 133 , loom speed (N) ¼ 224 rpm; mass of shuttle (M) ¼ 500 gm ¼ 0.5 kg, reed width ¼ 1.5 m, shuttle length L ¼ 0.32 m.

Solution.

Power for picking ¼

Power ¼

3MP3 ðR þ LÞ2  104 kW q2

3  0:5  2243  ð1:5 þ 0:32Þ3 10  ð133Þ2

¼ 315.47 Watt ¼ 0.315 kW.

8.3

Beat-up mechanism

The beat-up mechanism (sley mechanism) performs the third primary weaving motion. The objective of the beat-up mechanism is the reciprocating motion of the reed and performs the following functions [2]: 1. It holds the warp ends at given distances, thus determining the warp density and fabric width precisely,

204

Textile Calculation

2. Together with the race board and other guiding elements, it guides the weft carrier across the warp sheet. 3. The reed’s principal and most important function is to beat-up every inserted weft thread up to the fell of the cloth.

Sley approximates simple harmonic motion for good beat-up. Sley should stay as long as feasible near the rear dead center to leave the most angle available for the weft insertion. In order to get the necessary pick density, the weft to the fabric should be vigorously beat-up. Sley eccentricity is represented by e¼

r l

The sley-eccentricity ratio e is the ratio r/L, where r is the radius of the crank circle and l is the length of the crank arm. The greater the deviation from simple harmonic motion, the longer the sley remains in its most backward position, more time is available for shuttle passage, more effective beat-up (beat-up force increases), but more stress on the loom parts and possibly more wear and tear. However, the effects of varying the sley-eccentricity ratio within practical limitations are higher than those achieved by varying the crankshaft height [2]. A high number indicates that the sley beat-up accelerates and decelerates rapidly. It increases the forces operating on the swordpins, crankpins, cranks, crankarms, crankshaft, and their bearings, as well as indirectly on the loom frame. A high sleyeccentricity ratio will consequently necessitate more robust loom parts and a more rigid loom frame to prevent excessive vibration and wear, resulting in a higher loom cost for a given quality of performance. The sley and its accompanying parts, as a whole, have a high moment of inertia. As a result, the reciprocation of this unit generalizes large dynamic forces caused by the acceleration moment and has a significant impact on the machine operation. Long connecting rod length is utilized for highly smooth with low acceleration forces and fine cotton, silk, and continuous filament fabrics. For smooth acceleration force and medium density cotton materials, a medium connecting rod length is employed. Short connecting rod lengths are used for applications with high acceleration forces and are suitable for thick cotton and woolen textiles [3]. For a shuttle loom, if radii of crank and length of connecting rod are 10 and 40 cm, respectively, then find the value of sley-eccentricity ratio, ratio of sley acceleration at the front and back center of the loom, and length eccentricity.

Example 8.10.

Solution.

a. The value of sley-eccentricity ratio.

Sley eccentricity ratio ðeÞ ¼

radius of crank length of connecting rod

Woven fabric production

e¼

r l

e¼

10 ¼ 0:25 40

205

b. Ratio of sley acceleration at the front and back center of the loom. When crank is at front center q ¼ 0 means. F max ¼ mrw2 (1 þ e). When crank is at back center q ¼ 180 means F min ¼ mrw2 (1e). Now, the ratio of acceleration from front center to back center F ðmaxÞ maðmaxÞ aðmaxÞ aðfrontÞ rw2 ð1 þ eÞ ¼ ¼ ¼ ¼ F ðminÞ maðminÞ aðminÞ aðbackÞ rw2 ð1  eÞ a front ð1 þ eÞ 1 þ 0:25 1:25 ¼ ¼ ¼ ¼ 1:67 a back ð1  eÞ 1  0:25 :75 C. Find length eccentricity

We know, length eccentricity ¼

le ¼

ðradius of crankÞ2 length of connecting rod

r2 102 ¼ l 40

le ¼ 2:5

Example 8.11. A loom is running at a speed of 300 picks/minute. Find maximum and minimum acceleration of sley if sley eccentricity is 0.50 and length eccentricity ¼ 1.75.

Solution.

e¼

R ¼ 0:50 l

Le ¼

r2 ¼ 1:75 l

Le ¼r e r¼

1:75 ¼ 3:5 0:50

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Textile Calculation

Loom speed (n) ¼ 300 picks/min ¼ 5pick/second Maximum acceleration ðamax Þ ¼ r  u2  ð1 þ eÞ ¼ r  ð2PnÞ2  ð1 þ eÞ ¼ 3:5  ð2  3:14  5Þ2  ð1 þ 0:5Þ Maximum acceleration ðamax Þ ¼ 5176:29m = sec2 Maximum acceleration ðamin Þ ¼ r  u2  ð1  eÞ ¼ r  ð2PnÞ2  ð1  eÞ ¼ 3:5  ð2  3:14  5Þ2  ð1  0:5Þ amin ¼ 1725.43 m/s2. Reed is a component of the loom’s beat-up mechanism and is chosen based on the number of ends/inch required in the fabric and the width of the cloth. Normally, reed count (stock port system) is defined as the number of dents per 200 . Reed count equals ends/inches in reed with two ends/dent order. Redcliff reed count tells the number of dents per inch; Stockport reed count tells the number of dents per two inches; and Bradford reed count tells the number of groups of 20 dents in 36 inches.

Example 8.12.

Solution.

Calculate the ends per inch of the 3/60s Stockport system

3/60s Stockport means 60 dents per two inches and having three warp in each

dent. So the number of ends per inch is ¼ ¼

Reed count  No: of end per dent 2

60  3 ¼ 90 2

EPI ¼ 90. Calculate the EPI of the 60s Bradford system and convert it into the Redcliff system. One end is passing from each dent.

Example 8.13.

Woven fabric production

Bradford reed count ¼ 60 groups of 20 dents in 36 inch

Solution.

¼

207

Reed count  20 60  20 ¼ ¼ 33:33 dents=inch 36 36

As one end is passing from each dent, so ends per inch also ¼ 33.33. Redcliff reed count means the number of dents per inch ¼ 33.33 w 34 A shuttle loom is producing 3/1 twill fabric running at 180 picks/min. Calculate angular velocity of tappet shaft in radian/sec in two decimal places.

Example 8.14.

Loom speed ¼ 180 picks per minute ¼ 3 picks per second. Rpm of crank shaft ¼ 180. Then rpm of tappet shaft ¼ 180 4 ¼ 45 rpm 45 Rpm ¼ 60 rev/sec (჻rpm/60 ¼ rps)

Solution.

u ¼ 2pn u ¼ 2p 

45 ¼ 4:71 radian=sec 60

Example 8.15. A shuttle loom is running at 250 pick/min. The angular velocity of the bottom shaft in radian/sec is pn. What is the value of n?

Crank shaft speed ¼ 250 rpm. 125 Then bottom shaft speed ¼ n0 ¼ 250 2 ¼ 125 rpm ¼ 60 rps ¼ 2:08rps

Solution.

angular velocity ¼ u ¼ 2pn0 p  n ¼ 2p  2:08 n¼

8.4

2p  2:08 ¼ 4:16 p

Secondary motions

Although main motions are the primary motions of a loom, secondary motions are the important motions after primary motions. These motions aid in the ongoing production of fabric even though the fabric can be knitted without these actions. However, without

208

Textile Calculation

this mechanism, the loom cannot be run continually. The loom’s secondary motions are take-up and let-off.

8.4.1

Take-up motion

The aim of the take-up motion is to draw forward the woven cloth after laying the new pick. With the help of this, constant pick spacing can be maintained. There are two types of take-up motion: negative and positive. The attribute “negative” is justified in that no positive or direct motion is provided to the take-up roller in order to wind up the woven cloth. Motion is sent to the take-up roller directly through the gear train in positive take-up. Another differentiation is intermittent and continuous take-up. Intermittent take-up activates only after the newly inserted pick has been beaten up by the sley. Continuous take-up, on the other hand, draws the woven fabric continually. The inclusion of a ratchet and pawl arrangement in the take-up mechanism makes it intermittent, but the presence of a worm and worm wheel makes it continuous. Five-wheel take-up motion is depicted in Fig. 8.2a. The typical gear size is F ¼ 75, E ¼ 15, D ¼ 120, and A ¼ 50. Normally, circumference of the take-up roller is 15”. Wheel CW denotes the change wheel, which is in the driver position for five-wheel take-up. The ratchet wheel A, having 50 teeth, is turned by one tooth for every pick. So, pick spacing can be calculated as Pick spacing ¼

1 CW 15 CW    15 ¼ inch. 50 120 75 2000

Seven-wheel take-up motion is shown in Fig. 8.2b. It is also a positive intermittent type take-up motion. The typical size of the gear is G ¼ 90, F ¼ 16, E ¼ 89, D ¼ 24,

Figure 8.2 (a) five wheels take-up motion (b) seven wheels take-up motion.

Woven fabric production

209

B ¼ 36, and A ¼ 24. Here, the position of CW is in a driven position. For each pick, the ratchet wheel (A) is turned by one tooth. So pick spacing can be calculated as Pick spacing ¼

1 36 24 16     15:05 ¼ 1:015=CW inch 24 CW 89 19

Finds picks per inch (PPI) in five-wheel take-up motion and seven-wheel take-up motion having 36 teeth in its change wheel?

Example 8.16.

Solution.

In 5-wheel take-up motion,

PPI ¼

2000 2000 ¼ teeth in change wheel 36

PPI ¼ 55:55 In 7-wheel take-up motion, PPI ¼ 1.015  change wheel teeth. PPI ¼ 1  36. PPI ¼ 36.54.

8.4.2

Let-off motion

Let-off motion aims to keep the warp-free length within defined limits and to control warp tension by feeding the warp to the weaving zone at the correct rate. There are two types of let-off motion: negative and positive. A warp is drawn from the warper’s beam by a slipping-friction system in the event of a negative let-off. In a positive let-off system, the warp beam is rotated at a controlled pace through the driving mechanism to maintain continuous warp tension [2]. Example 8.17. What tension should be there if beam height is 20 cm, dead weight hanging on the horizontal lever is 2 kg, and dead weight is 40 cm away from the hook (assume negative let-off)?

Solution.

To maintain tension in negative let-off

Tension  beam height ¼ dead weight  dead weight distance from hook T x 20 ¼ 2  40 T ¼ 4 N.

210

8.5

Textile Calculation

Auxiliary or stop-motions

Auxiliary motions are added to looms to increase production and fabric quality. These motions are beneficial but not required. In the cases of shuttle trapping (warp protective motion), weft break (weft stop-motion), and warp break, these motions are used to stop the loom (warp stop-motion).

8.6

Nonconventional weaving machine

A conventional shuttle serves three purposes: it stores a certain length of weft within its hollow in the shape of a pirn, delivers this package over a warp shed, and allows the appropriate length of pick to be smoothly unwound from the pirn stationed within its hollow. In conventional looms, an over-pick or under-pick shuttle propulsion mechanism propels a shuttle containing a pirn of weft yarn through the warp shed. Such a system has several drawbacks, including a huge shuttle mass, unguided free flight of the shuttle, low efficiency and manufacturing, a high labor and space demand, and so on. Nonconventional fabric manufacturing methods were developed to circumvent these constraints. In this type of loom, the weft yarn package is mounted out from the loom frame, and the weft carrier inserts the pick into the warp shed while also assisting in unwinding the yarn from the supply package. The weft carrier can be either solid or fluid. It might be partially or completely guided. There are four principles of weft insertion into the nonconventional weaving machine, projectile, rapier, air-jet, and water jet [6]. The picking system of the projectile weaving machine works on the torsion bar picking mechanism. The main component is the torsion rod. Every loom cycle causes a specified angular distortion to the torsion rod. If the torsional rigidity of the rod is Kt N.m, and it is twisted through 4 radians, then the torque Mt generated is given by M t ¼ kt  j If the torsion rod diameter is d meter, the length of the torsion rod is l meter, and the shear modulus of the torsion rod is G N/m2, then the torque Mt will be
P  d4  G  j Mt ¼ 32  l Rapier is another weft carrier used in nonconventional weaving machines for weft yarn insertion. Rapier weaving machines are the most adaptable on the market [5]. Projectile and rapier are the solid weft carriers. The weft carrier might be fluid. Fluid carriers, such as water and air, have far lower inertia than solid carriers because the density of pure water at 40 C is 1 g/cc and that of dry air at sea level is 0.001275 g/ cc at 0 C. Just as potential energy may be stored in the gripper loom’s torsion rod, energy can be stored in the fluid by compressing it. Releasing some of this energy at the right time has proven to be an ingenious method of propelling a pick [6]. The air jet loom is incredibly fast. Weft insertion is accomplished with the use of compressed air. The weft yarn passes through the reed profile guide from one selvedge to the

Woven fabric production

211

next. The weft yarn package is placed on the weft creel. The weft yarn is first sent through the weft prewinder. The primary goal of the prewinder is to maintain continuous weft supply at steady tension while also releasing the exact pick length for weft insertion. In the case of water-jet looms, compressed water is employed to propel the weft. Air-jet weaving machines have the highest WIR and are the most productive in the production of light to medium weight fabrics, preferably made of cotton and certain man-made fibers. It should be noted, however, that technically positive results are being attained with high-weight fabrics (denim) and that some manufacturers have machine models for terry production. These machines are suitable for generating large volumes of unique fabric styles. Weaving widths typically range from 190 to 400 cm. Up to eight different wefts can be used with the multicolor weft carrier [2e5]. It should be noted that air-jet weaving machines require a significant amount of energy to prepare compressed air. The energy consumption increases significantly with increasing loom width and running speed [6]. Energy consumption reduction is one of the producer’s primary objectives and is a significant selection criterion for the consumer. These looms are used to produce light and medium weight fabrics with standard properties and in water repellent fiber materials, usually multifilament synthetic yarns. Water jet machines are widely utilized in East Asia but are less common in other countries. They are distinguished by their great insertion performance and low energy usage [7]. A rapier loom having a reed space of 180 cm and running at 225 picks/ min will not have excessive velocities if the rapier can be made to enter the shed at 60 and leave at 300 , then the average velocity will be: Example 8.18.

Reed space ¼ 180 cm ¼ 1.80 m; loom speed ¼ 225 picks/minute, angle available for picking ¼ 300e60 ¼ 240 .

Solution.

180 100  v¼ 60 300  60  215 360 V¼

180 225 360   100 60 240

Average velocity ¼ 10.125 m/s. Plain woven viscose fabric is made from 30s Ne warp and 35s Ne weft yarn. Ends per centimeter and pick per centimeter are 35 and 20, respectively. The crimp % in the warp direction is 6.5% and in the weft direction is 13%. If the cotton fiber density is 1.52 g/cm3, what will be the fabric weight in GSM?

Example 8.19.

Ends per cm ¼ 35, picks per cm ¼ 20, warp crimp ¼ 6.5%, weft crimp ¼ 13%, total warp length of size of 1 square meter fabric ¼

Solution.

212

Textile Calculation

   warp crimp% ¼ Ends per metre  1 þ 1  100    6:5% ¼ 3500  1 þ 1  ¼ 3727:5 m 100 Total weft length of the size of 1 square meter fabric ¼    weft crimp% ¼ Picks per metre  1 þ 1  100    13 ¼ 2000  1 þ 1  ¼ 2260 100 Weight of warp (g) in 1 square meter fabric ¼ Tex  Total warp length in km  ¼

   590:5 3727:5  ¼ 73:36 g 30 1000

Weight of weft (g) 1 square meter fabric ¼ Tex  Total weft length in km  ¼

   590:5 2260  ¼ 38:13 g 35 1000

GSM ¼ Total weight of weft yarn and warp yarn in one square fabric ¼ 73:36 þ 38:13 ¼ 111:49 g

Find the length of fabric in meters produced by loom in 8 h whose loom speed is given as 300 rpm, ends per inch is given as 30, and picks per inch are 30.

Example 8.20.

Solution.

PPI ¼ 30, EPI ¼ 30 loom, rpm ¼ 300.

Length of fabric ¼

Number of picks in 8hrs 300  60  8 ¼ Number of picks in 1 meter 30  39:37

¼ 121:92 meter

Example 8.21. Calculate the length of weft used to make a fabric in 1 h if loom speed is 400 picks/min; cloth width is 2 m, and warp and weft crimp is 10% and 5%, respectively.

Woven fabric production Solution.

213

Reed width ¼ 2.1 m, number of picks per minute ¼ 400

Length of weft yarn ¼ Weft crimp% ¼ 5¼

Number of picks Picks per inch

reed width  cloth width  100 cloth width

reed width e 2  100 2

Reed Width ¼

52 þ 2 ¼ 2:1 m 100

Number of picks inserted in 1 h ¼ 400  60 ¼ 24,000. Length per hour inserted ¼ Number of picks per hr  Reed width ¼ 24,000  2.1 ¼ 50,400 m. The diameter and length of the torsional rod used in a projectile loom are increased by 5% and 20%, respectively. Calculate the relation between the original torque and increased torque.

Example 8.22.

Let us assume that the diameter of the torsional bar is d1 105 5% increase in diameter leads to diameter (d2) ¼ d1100 ¼ d1  1:05 Similarly, if the initial length is l1, then length after increasing 20% (L2) ¼ l1 120 100 ¼ l1  1:20

Solution.

Tf

d4 l

If T1 is the initial torque and T2 is the increased torque, then T1 d41  l2 ¼ T2 l1  d24 T1 d4  l1  1:20 ¼ 1 T2 l1  ðd1  1:05Þ4 T1 1:20 1:20 ¼ ¼ 4 1:215 T2 ð1:05Þ T2 ¼ 1:0125  T1

214

8.7

Textile Calculation

Conclusion

In manufacturing the fabric, there is a requirement for a lot of calculations. There are several different mechanisms and motions. The efficiency of a loom depends on the smooth operation of different mechanisms. This chapter has summarized the various calculations associated with these mechanics.

References [1] S. Adanur, Handbook of Weaving, CRC press, 2020. [2] R. Marks, A.T.C. Robinson, Principles of Weaving, textile Institute, Manchester, UK, 1976, p. 249. [3] M. Decrette, J.Y. Drean, Shedding principles and mechanisms, in: Advanced Weaving Technology, Springer, Cham, 2022, pp. 115e166. [4] A. Majumdar, Principles of Woven Fabric Manufacturing, first ed., CRC Press, 2016 https:// doi.org/10.1201/9781315367729. [5] https://nptel.ac.in/courses/116102005 accessed on 15-06-2022. [6] https://nptel.ac.in/courses/116102017 accessed on 15-06-2022. [7] A. Patnaik, S. Patnaik (Eds.), Fibres to Smart Textiles: Advances in Manufacturing, Technologies, and Applications, first ed., CRC Press, 2019 https://doi.org/10.1201/ 9780429446511.

Woven fabric structure

9

Biswapati Chatterjee Government College of Engineering & Textile Technology, Serampore, West Bengal, India

9.1

Introduction

Woven fabrics are materials made of longitudinal warp yarns and transverse weft yarns that are interlaced to create the desired weave or pattern. The Peirce geometry of the plain weave fabric is based on the following assumption: • •

Yarn is circular in cross-section. Yarn is flexible in nature, i.e., the bending rigidity of the yarn is negligible.

The essential formulas are based on the Peirce cloth geometry as shown in Fig. 9.1. The symbols used here follow the literature subscripts 1 that indicates warp and 2 indicates weft. Here, ed ; pd are the warp and weft threads per cm; Cy1 ; Cy2 are the warp and weft tex 4 pffiffiffiffiffi 4 pffiffiffiffiffi l1 ¼ p2 ð1 þ c1 Þ; l2 ¼ p1 ð1 þ c2 Þ; h1 ¼ p2 c1 ; h2 ¼ p1 c2 ; q1 3 3 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi pffiffiffiffiffi ðweave angle of the warpÞ ¼ 106 ðl1 =p2  1Þ ¼ 106 c1 ; q2 ¼ 106 c2 ; where l1 , c1 , h1 , p1 are the modular length, crimp, crimp height, and ends spacing of the warp yarn. For weft yarn, the parameters can be represented by interchanging the subscripts. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tex of yarn 3 cm; for crimp interdy1 ðdiameter of warp yarnÞ ¼ 4:44  10 fibredensity change to occur when l1 ; l2 ; and D remain invariant, dy1 þ dy2 ¼ D, pffiffiffiffiffi 4 pffiffiffiffiffi 4 pffiffiffiffiffi 4 pffiffiffiffiffi 4 l1 l2 c1 þ  c2 ; h1 þ h 2 ¼ p2 c 1 þ p1 c 2 ¼ D ¼  3 3 3 ð1 þ c1 Þ 3 ð1 þ c2 Þ h1 þ h2 Average degree of flattening of thread ¼ e ¼ ; dy1 þ dy2 l1 ¼ q1 ; then pD1 ¼ sin q2 For warp way jammed cloth D pffiffiffiffiffi pffiffiffiffiffi ðp2 2c1 þp1 2c2 Þ For better accuracy D ¼ 1þ0:2ðc 1 þc2 Þðd1 þd2 Þ where ðd1 þd2 Þ is small correction depending on the values of D D pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi ; ; c1 %; c2 %. Other formulas for bending rigidity, initial modulus, and initial p1 p2 shear modulus are given in the respective problems. In SI units or in tex system, the cover factor K for the warp of a woven fabrics is given by

Textile Calculation. https://doi.org/10.1016/B978-0-323-99041-7.00011-4 Copyright © 2023 Elsevier Ltd. All rights reserved.

216

Textile Calculation

Figure 9.1 Peirce cloth geometry.

K1 ¼ ed 

pffiffiffiffiffiffi Cy  101

where ed and Cy are the threads per cm and tex of threads of the fabric. The Peirce cover factor is equal to 1:045  K ðin tex systemÞ. For both sides jammed plain woven fabrics in tex or SI system sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi 27:8 27:8b 1 þ 1 ¼1 ð1 þ bÞK1 ð1 þ bÞK2 sffiffiffiffiffiffiffi Cy2 where b ¼ and density of the fiber taken is 1.52 gm/cc. Cy1 A tenting canvas has the following structural parameters: threads per cm 123.0tex  134.2tex, 15.51  15.51per cm and crimps 26.4%  1.5%. A cut of the fabric was held at 20% extension along warp direction. Calculate the structural changes of extended fabric (assuming fiber density ¼ 1.52 gm/cm3). Example 9.1.

l1 ; l2 , c1 , c2; h1 ; h2 , p1 ; p2 ; dy1 and dy2 are the modular length, crimp, crimp height, and ends spacing of the warp and weft yarn. As per available data, the first step is to calculate the diameter of yarn and can be calculated by:

Solution.

dy ¼ 4:44  10

3

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tex of yarn ; dy1 ¼ 0:0396 cm; dy2 ¼ 0:0413 cm; fibre density

dy1 þ dy2 ¼ 0:0809 cm before extension; Warp cover factor (in tex system)

Woven fabric structure

K1 ¼ ed

217

pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi Cy1  101 ¼ 15:51  123  101 ¼ 17:2

Weft cover factor ðin tex systemÞ K2 ¼ ed

pffiffiffiffiffiffiffi Cy2  101 ¼ 17:97

sffiffiffiffiffiffiffi Cy2 ¼ 1:09 b¼ Cy1 Cloth cover ðin tex systemÞ kf ¼ K1 þ K2  0:036  K1 K2 ¼ 23:44; 4 pffiffiffiffiffi 4 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð0:264Þ ¼ 0:04420 cm; h1 ¼ p2 c 1 ; h1 ¼  3 3 15:51 4 pffiffiffiffiffi 4 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð0:015Þ; h2 ¼ 0:01041 cm; h2 ¼ p 1 c 2 ; h 2 ¼  3 3 15:51 h1 þ h2 ¼ 0:054 cm ¼ D. Mean ratio of flattening e ¼

h1 þ h2 ¼ 0:64. A considerable flattening of the dy1 þ dy2

threads occurs. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  The relation is expressed by D ¼ 0:00357 Cy1  v1 þ Cy2  v2 where v1 ; v2 are the specific volumes of warp and weft yarn in cm3/gm. If the specific volume of the two threads are the same, then pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi pffiffiffi v ¼ 0.0546/(0.00357  ( 123 þ 134:2) ¼ 0.67; v ¼ 0.46, p1 p2 In the original fabric, ¼ 1.181 and ¼ 1.181. D D l1 l2 l1 ¼ p2 ð1 þc1 Þ ¼ 0.08153 cm; similarly, l2 ¼ 0.0635 cm; D ¼ 1.493; and D ¼ 1.163; for any change of dimensions of the fabric due to crimp interchange, the three l1 p l2 p parameters D, l1 ; l2 are invariants of the structure. From the fact < ; < , it D 2 D 2 means that warp and weft will be jammed before warp and weft become straight individually. When warp way stretch occurs, it continues to decrimp till weft ways are jammed. l2 When weft way reaches a state of just jammed, pD1 ¼ sin q2 ¼ sin D ¼ 0.93. l2 D Thus, crimp c2 ¼ p1 e1 ¼ 0.29, h2 =D ¼ 0.638, and h1 =D ¼ 1  h2=D ¼ 0.362. D From crimp interchange equation, it can be written as pffiffiffiffiffi 4 pffiffiffiffiffi 4 ðh1 þ h2 Þ=D ¼ ðp2 =DÞ c1 þ ðp1 =DÞ c2 3 3 where ðh1 þ h2 Þ ¼ D

218

Textile Calculation

or pffiffiffiffiffiffiffiffiffi pffiffiffiffiffi 4 1 ¼ ð1:493  c1 =ð1 þ c1 Þ þ 0:93  0:29 Þ. 3 pffiffiffiffiffi c1 where ¼ 0.167. Solving this equation, the feasible root is c1 ¼ 0.0296; thus, 1 þ c1 p2 ¼ 0.0792 cm. There is 22.83% extension along warp when weft is jammed. But the fabric does not reach at a state of weft jammed when extended to 20% along warp. At the 20% p2 ¼ 1.4172 and c1 ¼ 0.05348, also from crimp interwarp way extension of fabric D pffiffiffiffiffi c2 ¼ 0.4223 c2 ¼ 0.3025 p1 ¼ 0.04875 cm and there is change equation 1 þ c2 24.39% contraction of the weft direction. It appears the weft way of the structure is not jammed when it is extended to 20% along warp and there is also contraction of 24.39% along weft direction. In the previous example No 9.1, calculate the change in the structure of the original cloth when extended 14% along warp assuming that mean degree flattening of threads falls to the value 0.64 and the warp yarn extends 1%, the weft yarn remaining constant in length.

Example 9.2.

Here, due to extension of warp yarn, the new count of warp ¼ 123 tex before extension/(1þextension%/100)¼(123/(1 þ 1/100) ¼ 121.8 tex. There is no change of weft tex. After the extension of warp and flattening of threads, new sum of diameter D ¼ the flattened minor diameter of warp   b1 þ b2 ¼ e ðaverage flattening coefficientÞ  dy1 þ dy2 ¼0.64  (4.44  103  (O121.8þO134.2)/O1.52) ¼ 0.0521 cm. After extension of 14% along warp direction new p2

Solution.

p2 ¼ original p2  ð1 þ extension% of cloth along warp=100Þ p2 ¼ ð1=15:51Þ  ð1 þ 14=100Þ ¼ 0:0735 cm; p2 ¼ 1.44. D The new warp yarn modular length

Thus, after fabric extension,

l1 ¼ original modular length  ð1 þ extension% of warp thread=100Þ l1 ¼ 0:08153 cm  ð1 þ 1%=100Þ ¼ 0:0823 cm

Woven fabric structure

219

The weft modular length remains same as there is no extension of weft thread i.e., l1 l2 l2 ¼ original weft thread modular length ¼ 0.0655 cm. Thus, ¼ 1.61; ¼ 1.28; D D l1 ¼ p2 ð1 þc1 Þ when c1 ¼ 0.118; 4 pffiffiffiffiffi h1 h2 h1 ¼ 1  ¼ 0.333; by using the h1 ¼ p2 c1 ¼ 0.337 cm, ¼ 0.667; hence, 3 D D D    pffiffiffiffiffi 4 pffiffiffiffiffi 4 1 pffiffiffiffiffi 1 same formula, h2 ¼ p1 c2 ; h2 =D ¼ l2 =D c2 or c2 1þc2 ¼ 0.195. 3 3 1 þ c2 Solving this equation, the feasible root is then c2 ¼ 0.0412; the spacing p1 ¼ 0.0629 cm; Thus, the new structure would have 15.90 ends per cm of 121.8 tex warp yarn and 13.61 picks per cm of 134.2 tex of weft yarn with crimps 11.8% and 4.12%. The warp way strips of extended material were tested 20 cm  5 cm between grips on testing machine and gave a breaking load of 215 kg (2.6 kg per thread), extension of 16.8%. Assuming that extension of warp yarn at break is equal to that found in the single thread test (5.1%) and that of the weft being zero, what are the structural changes at break? The original cloth had figures 125.6 tex  137.3 tex, 16.2/cm  14/cm, and crimp 13.3  5.3%.

Example 9.3.

Solution.

The pick spacing of the cloth at the onset of the breaking extension p2 is

p2 ¼ ð1=14Þ  ð1 þ extension %=100Þ ¼ ð1=14Þ  ð1:168Þ ¼ 0:0833 cm; New warp modular length after extension l1 ¼ ðwarp modular length of the original clothÞ  ð1 þ extension % of the warp threadsÞ l1 ¼ ½ð1=14:0Þ  ð1 þ :133Þ  ð1:051Þ ¼ 0:0849 cm; Weft modular length of the original cloth l2 ¼ ð1=16:2Þ  ð1 þ 0:053Þ ¼ 0:06492 cm; which remains unchanged at the onset of the cloth break. Hence, crimp of the warp at the onset of the cloth break c1 c1 ¼

new warp modular length enew pick spacing new pick spacing

c1 ¼

0:0849  0:0833 ¼ 0:0192 0:0833

c1 ¼ 1:92% ðin percentageÞ

220

Textile Calculation

At the point of onset of the breakage of the cloth with this crimp against warp tension, the weft must be jammed, so there would be two equations to satisfy at the point of break: (1) the warp and weft threads are in contact each other at the point of interlacing: h1 þ h2 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 0:06492 pffiffiffiffiffi 4 pffiffiffiffiffi 4 pffiffiffiffiffi 4 p2 c1 þ p1 c2 ¼ D ¼  0:0833 0:0192 þ   c2 which is the crimp 3 3 3 3 1 þ c2 interchange equation. q2  1. The c2 calculated from the equa(2) As the weft reaches the jammed state, the c2 ¼ sin q2 tion of the jammed structure is substituted in the crimp interchange equation to get the relal2 0:06492 ¼ q2 , is also used to ¼ q2 , i.e., tion between q2 and D; another equation D D calculate to find the q2 dD relation in Excel and shown in Fig. 9.2.

The intersecting point of the two curves in Fig. 9.2 provides a solution of the D (i.e., just at the onset of breakage of cloth) equal to 0.0523 cm at q2 ¼ 1.242 radian. Other structural parameters then calculated just at the break point of the cloth are as pffiffiffiffiffiffiffiffiffiffiffiffiffiffi p2 0:0833 pffiffiffiffiffi ¼1.592, h1 ¼ 43  p2 c1 ¼ 43  0:0833  0:0192 ¼ ¼ follows: 0:0523 D h1 0:0154 0:06492 h2 l2 ¼ 0.294; hD2 ¼ 1  hD1 ¼ 0.706; D ¼ 1.241; 0.0154 cm, ¼ ¼ ¼ 0:0523 D 0:0523 pffiffiffiffiffi D pffiffiffiffiffi c2 c2 4 p1 pffiffiffiffiffi 4 l2 4  c2 ¼   ¼ 0.706 ¼  1:241  ; 3 D 3 D 1 þ c2 3 1 þ c2 p1 Solving this equation, the feasible root of c2 is given by c2 ¼ 0:311 or 31.1%; ¼ D l2 D 1 þ c2 ¼ 1.241/(1 þ0.311) ¼ 0.9466, p1 ¼ 0.0523  0.9466 ¼ 0.0495 cm, i.e., 20 ends per cm. At the point of onset of the break of the cloth, the ends per cm is increased from 16.2/cm to 20/cm.

0.14 0.12

D cm

0.1 D-theta2 from crimp interchange equaon

0.08 0.06

D vs theta2 from l/D theta2

0.04 0.02 0 0

0.5

1

1.5

θ2 in radian

Figure 9.2 Intersecting point of the two curves.

2

Woven fabric structure

221

With the weft crimp of 3.7%, the warp crimp of the cotton cloth is changed from 9.7% to 8.0%. The parameters of the original cloth are as follows: the spacing of warp and weft are 0.0181 cm and 0. 0452 cm, respectively, and the warp and weft count are 11.81 tex and 11.45 tex. Calculate the features of the structure due to changing of the warp crimp.

Example 4.

Solution.

For the original cloth:

the modular length of warp l1 ¼ p2 ð1 þc1 Þ ¼ 0.0496 cm;

l2 ¼ p1 ð1 þ c2 Þ ¼ 0:0187 cm; 4 pffiffiffiffiffi h1 ¼ p2 c1 ¼ 0:0188 cm; 3 4 pffiffiffiffiffi h2 ¼ p1 c2 ¼ 0:00465 cm; 3 h1 þ h2 ¼ 0:0234 cm ¼ D; rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tex ofyarn So, dy1 ¼ 0.0124 cm and dy2 ¼ 0.0122 cm; dy ¼ 4:44  fibre density   average flattening coefficient e ¼ ðh1 þ h2 Þ dy1 þ dy2 ¼ 0.91; there is very low l1 l2 ¼ 2.12, D ¼ 0.799. flattening of the threads in the original cloth. Also for the cloth D Here, the changed values are represented by accent. l1 ¼ 0.0496/(1 þ 0.08) ¼ 0.0459 cm. The changed pick spacing p'2 ¼ ð1 þ c1 Þ When the warp crimp is changed with the invariant l1 =D; l2 =D, the following crimp interchange equation can be written qffiffiffiffiffi qffiffiffiffiffi 4 l1 1 4 l2 1 ' '   c1 þ   c2 ¼ 1. Substituting the values, the e3 D 1 þ c'1 3 D 1 þ c'2 qffiffiffiffiffi pffiffiffiffiffiffiffiffiffi 1 4 1 4  2:12  0:08 þ  0:799  c'2 ¼ 1. quation becomes 3 1 þ 0:08 3 1 þ c'2   Solving the equation, the feasible root, c'2 ¼ 0.0677; p'1 ¼ l2 1 þ c'2 ¼ 0.0176 cm. There is contraction (0.0181e0.0176)/0.0181 ¼ 0.028, i.e., 2.8%, in weft way and extension (0.0459e0.0452)/0.0452 ¼ 0.0153, i.e., 1.53% along warp direction.   l1 dy1 2 l d 2 The weight of the fabric in gm/m2 is W ¼ 7890.42  þ 2 v2y2 = ðp1 p2 Þ. v1 Here, specific volumes v1 ; v2 of the yarn are assumed to be unchanged equal to 1.1cm3/gm. Having substituted all the values in formula W, for the original fabric,   0:0496  0:01242 0:0187  0:01222 þ W ¼ 7890.42 =ð0:0181  0:0452Þ ¼ 1:1 1:1 91.27. 103

222

Textile Calculation

As the warp crimp is changed, with new structural parameters, the fabric GSM (gram per square meter) is changed to W ¼ 7890.42   0:0496  0:01242 0:0187  0:01222 þ =ð0:0176  0:0459Þ ¼ 92.43. 1:1 1:1   The thickness of the fabric max h1 þdy1 ; h2 þdy2 ¼ max [(0.0188 þ 0.0124), (0.00465 þ 0.0122)] ¼ 0.0312 cm. After the warp crimp is changed, the h1 ¼ 43 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffi p2 c1 ¼ 43  0:0459 0:08 ¼ 0.0173 cm; h2 ¼ 43  p1 c2 ¼ 43  0:0176 0:0677 ¼ 0.00610 cm the fabric thickness ¼ max [(0.0173 þ 0.0124), (0.00610 þ 0.0122)] ¼ 0.0297 cm. Plain cotton cloth in the finished state with 36.53/cm ends of 27.6 tex and 16.57/cm picks of 47.6 tex. The observed shrinkages were 8.5% in the warp and 2.4% in the weft. The crimps were 5.3% and 5.3% before shrinking and after shrinking the crimps were 14.8% and 6.9%. Calculate the shrinkage due to yarn length, swelling, and redistribution of crimps in the fabric.

Example 9.5.

Before shrinkage, the structural features are given by the following: p1 ¼ 0.0273 cm p2 ¼ 0.0603 cm, l1 ¼ p2 ð1 þc1 Þ ¼ 0.0632 cm, l2 ¼ p1 ð1 þc2 Þ ¼ 0.0288 cm, dy1 ¼ 0.0197 cm, dy2 ¼ 0.0259 cm, dy1 þ dy2 ¼ 0.0457 cm, h1 ¼ 43 pffiffiffiffiffi p2 c1 ¼ 0.00838 cm h2 ¼ 0.01851 cm, h1 þ h2 ¼ 0.02689 cm,  Mean flattening ratio e ¼ h1 þ h2 Þ=ðdy1 þ dy2 ¼ 0.588;

Solution.

After shrinkage, p1 ¼ 0.0273  ð1 0:024Þ ¼ 0.0266 cm, p2 ¼ 0.0630 cm  (1e0.085) ¼ 0.0552 cm, l1 ¼ p2 ð1 þc1 Þ ¼ 0.0633 cm, l2 ¼ 0.0285 cm. Warp yarn shrinkage ¼ 0.002, i.e., 0.2%, weft yarn shrinkage ¼ 0.009, i.e., 0.9%, pffiffiffiffiffi h1 ¼ 43  p2 c1 ¼ (4/3)  0.0552 O0.148 ¼ 0.0283 cm, h2 ¼ 0.0093 cm, D ¼ h1 þ h2 ¼ 0.0376 cm,  Mean flattening ratio e ¼ h1 þ h2 Þ=ðdy1 þdy2 ¼ 0.823;

Shrinkage due to swelling of yarns:

1 þ c2 of the structure before shrinkage is main1 þ c1 1 þ c2 tained constant during swelling of yarns, i.e., ¼ 1; c2 ¼ c1 . Analytically using crimp 1 þ c1 pffiffiffiffiffi pffiffiffiffiffi c1 c2 4 l1 4 l2 þ   ¼ 1. interchange equation, it can be written as   3 D ð1 þ c1 Þ 3 D ð1 þ c2 Þ l1 =D ¼ 1.68, l2 =D ¼ 0.758. The criterion of

pffiffiffiffiffi pffiffiffiffiffi c1 c1 4 4 þ  0:758  ¼ 1 or Having substituted the values  1:68  ð1 þ c1 Þ 3 ð1 þ c1 Þ 3 pffiffiffiffiffi c1 ¼ 0:311 which is f ðc1 Þ ¼ 0 needs to be solved numerically or by using Excel ð1 þ c1 Þ when c1 ¼ 0.1212, i.e., 12.12%. (¼c2 Þ due to shrinkage from original crimp 5.3%. So, p2 ¼ 0.0633/(1 þ0.1212) ¼ 0.0565 cm, p1 ¼ 0.0254 cm, shrinkage in the warp way 0.0630 or 6.30% and 0.0696 or 6.96% in the weft.     Total cloth shrinkage (sÞ is given by 1 s ¼ ð1 sw Þ 1 sy 1 sr

Woven fabric structure

223

where s ¼ cloth shrinkage, sw ¼ contribution due to swelling of threads, sy ¼ contribution due to shrinkage of the yarn, sr ¼ contribution due to redistribution of crimps. Thus shrinkage due to redistribution of crimp sr ¼ 1-(1e0.085)/[(1e0.002)  (1e0.063)] ¼ 0.021522, i.e., 2.152% in the warp and 1e(1e0.024)/[(1e0.009)  (1e0.0696)] ¼ 0.0585, i.e., 5.85% in the weft. Example 9.6. The following are the data obtained from the poplin cloth after sometime woven in the loom: Count 11.8 tex  11.4 tex spacing of warp and weft 0.0180 cm 0.023 cm, respectively, crimps 25.3%  3.6%. Find the degree of openness relative to the limit of close weaving. Also find the pick spacing which would jam the warp with the following conditions of cloth at the beat-up, width per end ¼ 0.0182 cm, pick length per end ¼ 0.0186 cm, and D ¼ 0.0204 cm. pffiffiffiffiffi Solution. For the loom state cloth structure, h2 ¼ 43  p1 c2 ¼ 0.0045 cm h1 ¼ 0.0159 cm,

l1 ¼ p2 ð1 þc1 Þ ¼ 0.0293 cm, l1 ¼ 1.438; D qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p2  p22 þ h22  D2 From the equation, tanðq1 =2Þ ¼ ¼ 0.444, ðq1 =2Þ ¼ 23:95 ; q1 ¼ D þ h2 47.9 ¼ 0.836 radians. D ¼ ðh1 þh2 Þ ¼ 0.0204 cm; and

l1 Degree of openness along warp ¼ D  q1 ¼ 0. 604. When the warp direction is l1  q1 ¼ 0. jammed and closest cloth in respect of warp D l1 The actual value shows that warp is still not in jammed state, i.e.,  q1 s 0. D From the data given at the beat up: p1 ¼ 0.0182, pick length per end ¼ l2 ¼ l2 l2 0.0186 cm, D ¼ 0.0204 cm. Thus; c2 ¼  1 ¼ 0.0219, i.e., 2.19%, ¼ 0.912, p1 D h2 ¼ ((4/3)  0.0182  O0.0219)/0.0204 ¼ 0.176, D

h1 ¼ 1  h2 =D ¼ 0.824. D

For the jammed structure with the

h1 l1 ¼ 0.824 and the condition [1]  q1 ¼ D D

h1 ¼ 1  cos q1 , the following values are obtained: cos q1 ¼ 1e0.824 ¼ 0.176; D l1 q1 ðradianÞ ¼ cos1 ð0:176Þ ¼ ¼ 1.394 radian ¼ q1 , pD2 ¼ sin q1 ¼0.984, i.e., D p2 ¼ 0.984  0.0204 ¼ 0.0201 cm, i.e., 49.77 number of picks/cm. Thus, 0.0201 cm picks spacing is required at the beat-up of cloth fell to produce the warp jammed structure. 0;

Example 9.7. Calculate the initial Young’s modulus of the plain-woven fabrics along warp and weft direction assuming yarns are incompressible and inextensible with following experimental data:

224

Textile Calculation

p1 ¼ 0.0485 cm, p2 ¼ 0.0588 cm. l1 ¼ 0.0700 cm, l2 ¼ 0.0514 cm, B1 ðwarp yarn bending rigidityÞ ¼5.62 mN mm2, B2 ðweft yarn bending rigidity ¼ 6.06 mN mm2. This model is simple to calculate the initial loadeextension behavior of plain-woven fabrics. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Here, q1 ¼ 106 l1 =p2  1 ¼ 46.2 ; q2 ¼ 106 l2 =p1  1 ¼ 25.9 ( ) B2 l31 cos2 q1 12 B1 p2 Initial Young’s modulus (along warp) [5] Efb1 ¼ 1þ 3 . B1 l2 cos2 q2 p1 l31 sin2 q1 Substituting all the values of the parameters, the Young’s modulus along warp ¼ 13.6 N/cm. By changing subscripts, Young’s modulus along weft Efb2 is equal to ¼ 13.1 N/cm.

Solution.

The particulars of the fabric are given below: cotton casement cloth: 18.5  37 tex; 21.2/cm  25.2/cm; 4%  17%. Find whether it is possible to achieve the conditions of weft spacing which is equal to warp spacing following the crimp redistribution. Example 9.8.

When p1¼ p2¼p (suppose), then crimp interchange equation is modified pffiffiffiffiffi pffiffiffiffiffi c1 þ c2 ¼ 34  D l2  ð1 þc2 Þ,    pffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi or c2 þ ðl1 =l2 Þð1 þ c2 Þ  1 ¼ 34  D l2  ð1 þc2 Þ, or f ðc2 Þ ¼ 0 for a given     pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi value of ll12 ; D ðl1 =l2 Þð1 þ c2 Þ  1  0, or l2 . For real solution of the function Solution.

c2  ll21  1. Thus, all the structures will not satisfy the condition. 4 From the above cloth particulars: p1 ¼ 0.0470 cm, p2 ¼ 0.0396 cm, h1 ¼  p2  3 pffiffiffiffiffi c1 ¼ 0.0105 cm, h2 ¼ 0.0258 cm D ¼ h1 þ h2 ¼ 0:0364 cm; l2 ¼ p1 ð1 þ c2 Þ ¼ 0:05499 cm; l1 ¼ p2 ð1 þ c1 Þ ¼ 0:04118 cm; D l1 ¼ 0:662; ¼ 0:7489. l2 l2 Substituting these values in the modified crimp interchange equation and evaluating the function in Excel for the c2 from 0.05 to 0.5, suitable root of c2 is found to be 0.3422, i.e., 34.22%. The equation can be also solved by numerical methods. The corresponding value of the c1 with the condition of equal spacing is equal to 0.00663, i.e., 0.663%. The spacing of the ends (p1 Þ and picks ðp2 Þ are 0.0411 and 0.04099 cm, respectively, and nearly equal.

Woven fabric structure

225

It implies when the structural condition reaches a state where the warp is almost straight but the weft is bent around warp yarn, both the warp and weft spacing equal. The cloth particulars are 16.4 tex  17.6 tex; 43.4/cm 23.4/cm; and 2.98%  1.61%. If one set of threads spacing is closed by saying p1 ¼ dy1 what are the structural conditions of the cloth?

Example 9.9.

From the values of the cloth particulars, the following structural parameters are obtained:

Solution.

h2 ¼

pffiffiffiffiffi 4  p1 c2 ¼ 0:0039 cm; h1 ¼ 0:0098 cm; D ¼ h1 þ h2 ¼ 0:0137 cm; 3

l2 ¼ p1 ð1 þ c2 Þ ¼ 0:0237 cm; l1 ¼ 0:0433 cm; dy1 ¼ 0:0146 cm; dy2 ¼ 0:0151 cm;   Thickness ¼ max h1 þ dy1 ; h2 þ dy2 ¼ ð0:0190; 0:0244Þ ¼ 0:0244 cm. K1 ¼ ed 

pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi Cy1  101 ¼ 43:4  16:4  101 ¼ 17:58;

K2 ¼ 23:4 

pffiffiffiffiffiffiffiffiffi 17:6  101 ¼ 9:82. dy1 dy2 dy1 dy2 þ  p1 p2 p1 p2 0:0146 0:0151 0:0146 0:0151 þ    ¼ 1 1 1 1 43:4 23:4 43:4 23:4

The total fractional fabric cover ¼

¼ 0:763 i:e; 76:3%. Applying the condition p1 ¼ dy1 , i.e., 0.0146 cm, the crimp interchange equation   pffiffiffiffiffi c1 pffiffiffiffiffi 3 D D l1 c2 ¼    .  4 dy1 dy1 D 1 þ c1 The values of the parameters are substituted in the modified equation and calculated as follows: with c1 ¼ 0.0298 then c2 ¼ 0.184; other parameters are calculated l2 ¼ p1 ð1 þ c2 Þ ¼ 0:0146  ð1 þ 0:184Þ ¼ 0:0173 cm h2 ¼ 0:00835 cm; h1 ¼ D  h2 ¼ 0:00535 cm;  thickness ¼ max (h1 þ dy1 ; h2 þ dy2 ¼ (0.01995,0.02345) ¼ 0.02345 cm. pffiffiffiffiffiffiffi cover factor of warp ¼ K1 ¼ ed  Cy1  101 ¼  pffiffiffiffiffiffiffiffiffi (1/0.0146  16:4  101 ¼ 27.78, K2 ¼ 9.82, i.e., same as the original.

226

Textile Calculation

Total fractional fabric cover ¼

dy1 dy2 dy1 dy2 0:0151 0:0151 1 ¼ þ  ¼1þ 1=43:4 1=43:4 p1 p2 p1 p2

1, i.e., 100%. This change in the structure reduces 3.89% in the fabric thickness. The features of the light weight cotton duck are given as follows: 126/3  126/3 tex cotton 10.6  11.41 per cm; 12.5%  10.5%. Find the maximum thickness and minimum thickness of the cloth. Example 9.10.

Solution.

The structural parameters of the original fabric:

pffiffiffiffiffi 4 h1 ¼  p2 c1 ¼ 0:04131 cm. 3 h2 ¼ 0:04076 cm; h1 þ h2 ¼ D ¼ 0:08207 cm; l1 ¼ p2 ð1 þ c1 Þ ¼ 0:0986 cm; l2 ¼ 0:10425 cm; l1 =D ¼ 1:201;

l2 ¼ 1:2701; D

dy1 ¼ 0:04043 cm; dy2 ¼ 0:04043 cm.   Cloth thickness of the fabric ¼ max h1 þdy1; h2 þdy2 ¼ (0.08174, 0.08118) ¼ 0.08118 cm. In the structure, if the cloth is stretched weft way, the warp will be jammed before l1 p weft becomes straight as < . D 2 Thus, when the warp is just jammed,     l1 h1 l1 h2 l1 ¼ 1  cos ¼ cos q1 ¼ ¼ 1:2013 ðin radianÞ; or when the thickD D D D D l1 ness G ¼ D cos þ dy2 ; thus, G ¼ 0.07006 cm; D If the cloth is stretched warp way, the similar condition will arise with weft direcl2 tion. The thickness G ¼ dy1 þ D cos ¼ 0.0647 cm. Thus, here the minimum thickD ness can be obtained by extending warp jamming the weft. The maximum thickness of the cloth G ¼ D þ dy1 ¼ 0.1225 cm would have been obtained if any of threads is straightened but this is not possible in the present fabric. Thus, maximum thickness is therefore obtained in its original state, i.e., 0.08118 cm. Typical particulars of a cotton poplin are given below: warp and weft thread count 12/2 tex, 55.5  29.9 threads per cm; crimps 14.4%  3.5%. Test which way the cloth can be extended without jamming and which way the cloth will be

Example 9.11.

Woven fabric structure

227

jammed. Also find the structural condition after stretching in warp or weft way following only geometrical change. Solution.

The structural parameters of the original cloth are calculated as follows:

p1 ¼ ð1=55:5Þ ¼ 0:0180 cm; p2 ¼ 0:0334 cm; dy1 ¼ 0:0129 cm ¼ dy2; pffiffiffiffiffi 4  p2 c1 ¼ 0:0169 cm; h2 ¼ 0:00449 cm; h1 þ h2 ¼ 0:02138 cm 3 ¼ D;

h1 ¼

ðh1 þ h2 Þ  ¼ 0:829; The mean flattening of the threadse ¼  dy1 þ dy2 pffiffiffiffiffi Weave angle of warp q1 ¼ 106 c1 ¼ 40:2 deg weave angle of weft q2 ¼ 19.8 deg; l1 ¼ 0:0382 cm; l2 ¼ 0:01863 cm; l1 =D ¼ 1:7867; l2 =D ¼ 0:8714;   thickness ¼ max h1 þdy1 ; h2 þdy2 ¼ 0.0298 cm; When warp is stretched, the weft will be jammed before warp becomes straight as l1 l2 =D p=2; Thus; the warp will be stretched till weft is jammed. Then,   l2 as weft is jammed, new spacing pD1 ¼ sin ¼ 0.7655, p1 ¼ 0.01637 cm; crimp of D weft c2 ¼ 0.1383, i.e., 13.83%. The contraction in width direction is [(original warp spacing-warp spacing after the weft jammed)/original warp spacing]  100 ¼ 9.056%. pffiffiffiffiffiffiffiffiffiffiffiffiffiffi h2 4 p1 pffiffiffiffiffi 4 ¼  c2 ¼  0:7655  0:1383 ¼ 0.3795; 3 D 3 D  pffiffiffiffiffi  c1 h1 h2 h1 4 p2 pffiffiffiffiffi 4 l1 ¼ 1  ¼ 0.620; ¼  c1 ¼  . As the crimp inter3 D 3 D 1 þ c1  D D D pffiffiffiffiffi  c1 l1 change occurs, there is no change of D i:e l1 =D ¼ 1.7867, then ¼ 0.260. 1 þ c1 Solving the equation, the feasible root is c1 ¼ 0.0787 or 7.87%; The weft spacing of jammed cloth pD2 ¼ 1.656 and the same of the original cloth p2 ¼ 1.562; stretch of warp direction of the cloth ¼ [(original weft spacing-weft D spacing after jamming)/original weft spacing]  100 ¼ 6.02%. When cloth is stretched weft way, it is possible to extend weft thread straight without jamming of the warp, i.e.,: h2 ¼ 0; the condition of the structure is a limiting structure of the cross thread straight.

h1 ¼ D or

 pffiffiffiffiffi  c1 h1 4 p2 pffiffiffiffiffi 4 l1 p2 ¼1¼  c1 ¼  ¼ 1.366; ; c1 ¼ 0.308, i.e., 30.8%; 3 D 3 D 1 þ c1 D D

228

Textile Calculation

The contraction in warp way ¼ (original weft spacing-weft spacing after weft straight)/original weft spacing 0.1254 i.e. 12.54%; As the weft is straight, the weft crimp c2 ¼ 0, i.e., warp spacing p1 ¼ l2 so p1 ¼ 0.01863 cm. The extension in weft way ¼ (warp spacing after weft straight - original warp spacing)/original warp spacing ¼ (0.01863e0.0180)/0.0180 ¼ 0.035 or 3.5%.

pffiffiffiffiffi The weave angle of the warp thread when weft thread is straight q1 ¼ 106 c1 ¼ pffiffiffiffiffiffiffiffiffiffiffi 106 0:308 ¼ 58.83deg. The loom state of plain cotton cloth particulars is given below: 29.23tex  32.27tex; 26  26.7 per cm; 7.4%  8.6%. Test whether the fabric on both sides is in jammed state or not. The density of fiber used in the yarn ¼ 1.52 g/cm3.

Example 9.12.

The warp cover factor: pffiffiffiffiffiffiffi K1 ðin tex system or SI unitsÞ ¼ ed  Cy1  101 ¼ 14:11; The weft cover factor: pffiffiffiffiffiffiffi K2 ðin tex system or SI unitsÞ ¼ pd  Cy2  101 ¼ 15.17; qffiffiffiffiffi C b ¼ Cy2y1 ¼ 1:051. These are the data of the loom state cloth.

Solution.

The cover factors of the closest spacing of warp and weft with the given b ¼ 1.051 are plotted by the Excel from the following equation sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi





2ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2ffi 27:77b 1  27:77 þ 1 ¼ 1; 1þb =K2 1þb =K1 For the cloth with the value of b ¼ 1.051, the relation between warp and weft cover factors of the closest cloth with both sides jammed can be written as follows:

30 25

K2

20 15

closest cloth with beta=1.051

10

data for calculation

5 0 0

10

20

30

K1

Figure 9.3 Warp and weft cover factors of the closest cloth with b ¼ 1.051 and the cover factors of the cloth in the example.

Woven fabric structure

229

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1  f13:54=K1 g2 þ 1  f14:23=K2 g2 ¼ 1. The square point indicates the data calculated from this example (i.e, 14.11, 15.17) and the cloth are not on closest curve but nearer to closest one (Fig. 9.3). Calculate the weave angles and average degree of flattening of the yarns from the following cloth particulars: cotton tex 54 of warp and weft, p1 ¼ 0.0528 cm, p2 ¼ 0.0429 cm c1 ¼ 7.01%, c2 ¼ 12.0%. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Solution. The weave angle (in degree) q1 ¼ 106 c1 ðin fractionÞ ; q1 ¼ 28.1 ; q2 ¼ 36.7 ; Example 9.13.

pffiffiffiffiffi 4  p2 c1 ¼ 0:0151 cm; h2 ¼ 0:0244 cm: h1 þ h2 ¼ 0:0395 cm 3 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u tex u 3 t dy ðdiameter of yarnÞ ¼ 4:44  10 fibre cm; dy1 ¼ dy2 ¼ 0:0265 cm; density

h1 ¼

Average degree of flattening ¼ e ¼

h1 þ h2 ¼ 0.745; dy1 þ dy2

cover factor of warp circular pffiffiffiffiffi pffiffiffiffiffiffiffi threads ¼ K1 ðin tex system or SI unitsÞ ¼ ed  Cy1  101 ¼ (1/0.0528)  54 101 ; K1 ðin tex system or SI unitsÞ ¼ 13:92 cover factor of weft circular threads ¼ K2 ðin tex system or SI unitsÞ pffiffiffiffiffiffiffi ¼ pd  Cy2  101 K2 ðin tex system or SI unitsÞ ¼ ð1 = 0:0429Þ 

pffiffiffiffiffi 54  101 ¼ 17:13

cover factor of warp flattened

  pffiffiffiffiffiffiffi ed  Cy1  101 ¼ (1/0.0528)  threads ¼ K1 ðin tex system or SI unitsÞ ¼ e pffiffiffiffiffi 54 101 /0.745 ¼ 18.68; cover factor of weft flattened   pffiffiffiffiffiffiffi threads ¼ K1 ðin tex system or SI unitsÞ ¼ ed  Cy1 101 e ¼ (1/0.0429)  pffiffiffiffiffi 54 101 /0.745 ¼ 22.99. The flattening increases the cover of 34.2% in both the warp and weft threads. In a scoured and bleached cloth, the following data are obtained from the following measurements: 27.7tex  30 tex, 28.1 ends per cm  26.5 picks per cm, warp crimp 6.9%  weft crimp 14.5%, and the horizontal diameters (major dia) of

Example 9.14.

230

Textile Calculation

warp and weft thread are 0.0229 and 0.0225 cm respectively. The vertical diameter (minor dia) of warp and weft thread are 0.0142 and 0.0140 cm, respectively. Find the minimum value of weft spacing (or maximum number of picks per cm) for the cloth having same value of warp spacing. B ¼ sum of minor diameters ¼ b1 þ b2 ¼ 0:0142 þ 0:0140 ¼ 0.0282 cm

Solution.

For the Kemp geometry [4] for the jammed structure, the spacing of thread is given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2  h22 þ ða1  b1 Þ; p1 ¼ 0:0357 cm qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:02822  h22 þ ð0:0229  0:0142Þ

p1 ¼

h2 ¼ 0:0081 cm; h1 ¼ B  h2 ¼ 0:0201 cm; So pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p2 ¼ 0:02822  0:02012 þ ð0:0225 0:0140Þ ¼ 0:0282 cm or 35:3 picks per cm. Calculate theoretical minimum and maximum flexural rigidity of a fabric from the following data in Table 9.2:

Example 9.15.

Solution.

Flexural rigidity of yarn

¼ Gy ¼ GF 

Cy Cf

2:303

½



2

a2 dy2 1 þ

GF sF

 ½



log10

  GF a2 dy2 1 þ sF 1þ 2



The minimum flexural rigidity of a fabric is considered when there is no interaction between the individual fibers [2]. And, it is given by: the minimum fabric flexural

Table 9.2 Property of the fiber/yarn/fabric constituting the fabric. Property

Values

GFmN mm2 (flexural rigidity of single fiber) ГFmN mm2 (torsional rigidity of single fiber) C f (fiber tex) Cy (yarn tex) a radian/cm (¼2p X number of turns per cm of the yarn) Diameter of yarn dy cm ed warp threads/cm pd weft threads/cm Crimp of warp ðc1 Þ Crimp of weft ðc2 Þ

0.0288 0.0110 0.373 23.5 42.8 0.0088 28.0 26.4 0.032 0.096

Woven fabric structure

231

NGy when there is no interaction between fibers and yarns; here c 1þc is fractional crimp and N is the threads per unit width of fabric. Similarly, at the other extreme of the fabric, all the fibers are so bound together that each yarn may be considered as a solid rod. Then, maximum fabric flexural rigidity   2 Gmax ¼ N GF Cy Cf =ð1 þcÞ; from the above data and using the foregoing for-

rigidity ¼ Gmin ¼

mula, yarn flexural rigidity and theoretical minimum and maximum flexural rigidity of fabric can be calculated as follows: Gy ¼ 0.0168 mNcm2; then Gmin ¼ 0.455 mNcm2/cm. Gmax ¼ 31.02 mNcm2/cm. There are two fabrics with the following data: Cotton sheeting GSM ¼ 159.4 g/m2 and its thickness ¼ 0.031 cm; Woolen Tweed plain weave: GSM ¼ 389.9 g/m2 and its thickness ¼ 0.119 cm; Which fabric does contain more air space? Also, what is the porosity of each cloth?

Example 9.16.

The specific volume of cloth would indicate the amount of air space in the fabric with respect to volume of solid material, i.e., fibers in the cloth. Specific volume of the cloth ¼ thickness of the cloth/cloth GSM. For sheeting, nsheeting ¼ 0.031  104/159.4 ¼ 1.94 cm3/gm; For Tweed ntweed ¼ 0.119  104/389.9 ¼ 3.05 cm3/gm. The tweed shows higher value of specific volume and that there is three times air space as fiber in the volume occupied by the cloth but in sheeting fabric about twice air space as fiber in the cloth. So, the tweed contains more air space. The porosity of the cloth P ¼ 100  (rfibre-rcloth)/rfibre where rfibre and rcloth are the densities of fiber and cloth, respectively. For sheeting cloth, rsheeting ¼ 1/nsheeting, and for tweed cloth, rtweed ¼ 1/ntweed. Taking the cotton and wool fiber density as 1.52 gm/cm3 and 1.32 gm/cm3 and substituting theses values in the formula Psheeting ¼ 66.17% and Ptweed ¼ 89.85%.

Solution.

A square plain cloth has the thread spacing equal to 2:5 dy ; the flattening coefficient (i.e., O(minor diameter /major diameter)) 0.866 with elliptical crosssection. Find fabric fractional cover and how much cover is increased from the circular threads due to flattening. Also find the GSM of the fabric in both the cases.

Example 9.17.

For elliptical cross-section of the thread [1] a  b ¼ dy2 and b ¼ e dy where a, b, dy , and e are major axis, minor axis, circular diameter of the yarn and flattening coefficient. qffiffi As e ¼ ba ¼ 0.866 so ba ¼ 0.75, a ¼ 1.15dy ; b ¼ 0.866dy ;

Solution.

the fractional warp ¼ ap ¼ 0.46 as p ¼ 2.5 dy and so also same for weft being the structure square. The fabric fractional cover ¼ warp fractional cover þ weft fractional cover ewarp fractional cover  weft fractional cover, i.e., ¼ 0.46 þ 0.46e0.462 ¼ 0.71.

232

Textile Calculation

If threads are circular in cross-section, the warp fractional cover ¼ weft fractional d d cover ¼ py ¼ 2:5dy y ¼ 0.40; and the fractional cover of fabric ¼ 0.64. The increased

fabric cover with moderate yarn flattening of 0.866 is about 11%. For square fabric, h1 ¼ h2 ¼ h; and b1 ¼ b2 ¼ b; h1 þ h2 ¼ b1 þ b2 or 2h ¼ 2b; pffiffiffi pffiffiffi b ¼ 43 p c i:e 0:866dy ¼ 43 2:5 dy c or c ¼ 0.0675 or 6.75%. pffiffiffi When the threads are circular in cross-sectional, h ¼ dy ¼ 43 2:5dy c; or c ¼ 0:09; or 9%; The fabric areal density is given by the following formula: W ¼ 0:1  Cy1  ed ð1 þ c1 Þ þ Cy2  pd ð1 þ c2 Þ . For square fabric thread count   Cy1 ¼ Cy2 ¼ Cy ; ed ¼ pd ¼ n; c1 ¼ c2 ¼ c; then W ¼ 0:2 Cy n ð1 þcÞ ;   Due to flattening of threads, the areal density ¼ W ¼ 0.21 Cy n as c ¼ 0.0675;   Without flattening W ¼ 0.22 Cy n as c ¼ 0.09 for the cotton fabric. Wcircular 0:22 ¼ 1:048, i.e., areal density with the circular thread is ¼ It shows 0:21 Wflattening about 4.8% higher than that of with the flattened threads. A 2/2 twill gabardine cloth on which measurements gave the figures: R 14.8 tex/2  R 14.8 tex /2; 77.1  38.6 threads per cm; crimps 7%  5%. Now the cloth shrinks warp way by 2%. How will the width, the crimps, and thickness change?

Example 9.18.

p1 ¼ 0.0130 cm; p2 ¼ 0.026 cm; l1 ¼ p2 ð1 þc1 Þ ¼ 0.0277 cm; l2 ¼ 0.0137 cm. As it is 2/2 twill cloth, along warp and weft way, the thread has two portions: one under intersection and other in float region. All the parameters are therefore designated by single prime for the intersection region and for full repeat unit without prime. As there is float and intersection length here D is essentially determined by the intersection zone of repeat unit. pffiffiffiffiffiffiffi In that case, c'1 ¼ 2 c1 ; c'2 ¼ 2 c2 ; h1 ¼ 43  p2 2c1 ¼ 0.0131 cm, h2 ¼ 0.0055 cm. pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi Then, D ¼ h1 þ h2 ¼ 43  p2 2c1 þ 43  p1 2c2 ¼ 0.0187 cm; dy1 þ dy2 ¼ 2dy1 ¼ 2 0.0139 cm ¼ 0.0276 cm.   Average degree of flattening e ¼ D dy1 þdy2 ¼ 0.676; For warp, modular length under intersection l' 1 l'1 ¼ p2 ð1 þ 2  c1 Þ ¼ 0:0296 cm; l'2 ¼ p1 ð1 þ 2  c2 Þ ¼ 0.0143 cm, ¼ 1.583, D ' l2 ¼ 0.765; D When the cloth shrinks warp way by 2%, the new p2 ¼ 0.0255 cm; p2/D¼ 0.0255/ 0.0187 ¼ 1.364; now, following the crimp interchange in the structure,    pffiffiffiffiffiffiffi c1 ¼ l' 1  p2 p2 2 ¼ 0.0816; h'1 ¼ 43  p2 2c1 ¼ 0.0141 cm h2 ¼ D h1 ¼ pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi 4 2c2 l2 pffiffiffiffiffiffiffi 4 2c2 , or ¼ 0.248; solving the equa0.0047 cm ¼ 3  p1 2c2 ¼ 3  1 þ c2 1 þ c2 tion, the crimp can be found out: c2 ¼ 0.0328. Solution.

Woven fabric structure

233

l2 Hence, new p1 ¼ 1þc ¼ 0.0132 cm, i.e., there is extension of cloth weft way by 2 (0.0132e0.0130)/0.0130 ¼ 0.0193, i.e., about extension of 1.93%.  The thickness of the cloth before shrinkage is max (h1 þdy1 ; h2 þdy2 ¼ max (0.0270, 0.0174) ¼ 0.0270 cm, and after shrinkage, the thickness is max  (h' 1 þ dy1 ; h'2 þ dy2 ¼ max (0.028, 0.0185) ¼ 0.028 cm resulting in an increase of thickness 3.7% of the cloth.

A voile fabric has the following particulars: tex 19.7/20.3; threads per cm 19.0/21.6; crimps 4.5%/9.5%. Test whether both sides of the fabric are jammed, and if not, determine sffiffiffiffiffiffiffi onerpossible ffiffiffiffiffiffiffiffiffi way to make it both sides jammed. Cy2 20:3 ¼ Solution. b ¼ ¼ 1:030; 19:7 Cy1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi K1 ¼ ed  Cy1  101 ¼ 19:0 threads per cm  19:7 tex  101 ¼ 8:43; Example 9.19.

K2 ¼ pd 

pffiffiffiffiffiffiffi Cy2  101 ¼ 9:73;

The relation between cover factor of warp and weft for the cloth of both sides jammed sides sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi 27:7 27:7b can be written as follows: 1  þ 1 ¼ 1; here b ¼ ð1 þ bÞK1 ð1 þ bÞK2 1:030; the plots of warp and weft cover with both sides jammed and cover of the voile fabric as shown in Fig. 9.4.

In Fig. 9.4, it is evident from the equation as well as from the graph, the nearest point on the both sides jamming would occur when given K1 ¼ 17.0 K2 ¼ 15.5 (as obtained from Excel graph), i.e., if the ed ¼ 17.0 10/O(19.7) ¼ 38/cm, pd ¼ 34/

Weft cover factor(in tex)K2

30

both side jammed cloth with β=1.030 voile cloth in the example

25 20 15 10 5 0 0

10 20 30 Warp cover factor (in tex) K1

40

Figure 9.4 Warp and weft cover of the closest plain fabric with b ¼ 1:030 and cover factors of the fabric in the example.

234

Textile Calculation

cm. The cloth would be jammed if ends and picks per cm increase to 38 and 34 keeping the threads count same. Thus, more 19 warp and 12.4 weft threads per cm are required to be added in the cloth to reach a limit of the fabric both sides jammed. By using Hamilton system [4]: dy1 ¼ 4:44  10

3

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tex ¼ 0:0160 cm; dy2 ¼ 0:0163 cm; fibre density

p1 ¼ 0:0529 cm; p2 ¼ 0:0462 cm dy1 dy2 dy2 K1 ¼ 0.302; K2 ¼ ¼ 0.353 a ¼ ¼ 0.856; b ¼ ¼ 1.018; from the graph [4] p1 p2 K2 dy1 ðK1 þ K2 Þactual  100 ¼ ðK1 þ K2 Þlimit ¼ 1:15; ðK1 þ K2 Þactual ¼ 0.655; tightness factor ðK1 þ K2 Þlimit 56.96% which indicates the degree of firmness of the structure. K1 ¼

Example 9.20. A plain woven fabric has the following values of the structural parameters: modular length of warp l1 ¼ 0.07 cm; warp thread spacing, p1 ¼ 0.0485 cm; weft thread spacing p2 ¼ 0.0588 cm; yarn bending rigidity b1 ¼ 5.62 mNmm2; sum of the crimp amplitudes D ¼ 0.05 cm; weave angle q1 ¼ 0.821radians; fabric warp way bending rigidity B1 ¼ 19.6 mNmm2/mm; k1 ¼ 0.8; Calculate how much change in the ends spacing is required to vary bending rigidity 19.6 mNmm2/mm to 19.0 mNmm2/ mm. b1  p2 ; Solution. B1(bending rigidity of fabric in the warp direction)[6] ¼ p1 ðl1  k1 D q1 Þ differentiating this equation with respect to p1 , it can be written as dB1 ¼  b1  p2 dp1 . 2 p1 ðl1  k1 D q1 Þ Substituting the values of the parameters from the example dB1 ¼ 37:8  dp1 , now dB1 ¼-0.6 mNmm2/mm then,

dp1 ¼ 0.6/37.8 ¼ 0.0158 cm.

New spacing p1 ¼ 0.0485 þ 0.0158 ¼ 0.0643 cm; i.e., number of warp threads ¼ 15.5 ends per cm but in original fabric ends per cm ¼ 20.6 ends per cm. About 5.11 ends per cm needs to be decreased to reduce the bending rigidity. A plain woven cotton fabric has the following parametric values: tex 36.9  59.0; spacing 0.0498  0.0646 cm; crimp (fraction) 0.100619  0.034137; flexural rigidity of the yarn 2.82  4.54 mNmm2. Calculate the shear modulus of the fabrics. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi Solution. Weave angle (radians) q1 ¼ 1.88 c1 ¼ 1.88 0:100619 ¼ 0.596, Example 9.21.

pffiffiffiffiffi q2 ¼ 1:88 c2 ¼ 0:347;

Woven fabric structure

235

dy1 ðdiameter of threadÞ ¼ 4:44  10

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u tex  gm ¼ 0:0219cm; t fibre density cm3

3 u

dy2 ¼ 0:0277 cm; D ¼ dy1 þ dy2 ¼ 0.496 mm; yarn flexural rigidity b1 ¼ 2.82 mNmm2, b2 ¼ 4.54 mNmm2; substituting all these values in the following formula for shear modulus GðmN=mmÞ: ( )1 p1 ½p2 ð1 þ c1 Þ  0:8 D q1 3 p2 ½p1 ð1 þ c2 Þ  0:8 D q2 3 þ ¼ G ¼ 12 b1 p2 b2 p1 269.14 mN/mm.

Calculate the warp way initial tensile modulus of the plain-woven cotton fabric from the following data: ends spacing p1 ¼ 0.485 mm, picks spacing p2 ¼ 0.588 mm, modular length of warp l1 ¼ 0.700 mm, modular length of weft l2 ¼ 0.514 mm, bending rigidity of warp B1 ¼ 5.62 mNmm2; and bending rigidity of warp B2 ¼ 6.06 mNmm2.

Example 9.22.

The warp " way fabric # 12B1 p2 B2 l31 cos2 q1 ¼ 3 2 1 þ B l3 cos2 q 1 2 2 p1 l1 sin q1

Solution.

Efb1

initial

modulus [3] can be written as



Here, weave angle of the warp in (degrees) q1 ¼ 106

l1 p2

1=2 1

¼ 46.3o.

By changing the subscript 1 to 2 in the equation, the weft way initial modulus can also be obtained. By substituting all the values of the parameters in the equation, Efb1 ¼ 11.93 N/cm. The following are the parameters of a polyester plain woven fabric: tex 19.7  19.7; spacing: 0.365  0.578 mm; crimp (fraction): 0.0536  0.0356; flexural rigidity ðbÞ: 1.97  1.97 mNmm2. Calculate the bending moduli along warp and weft. Example 9.23.

Solution.

Bending modulus of fabric along warp   mm2 b1 p2 mN B1 ¼ mm p1 ½p2 ð1 þ c1 Þ  0:8758Dq1 

The weave angle (radians) q1 ¼ 1.88

pffiffiffiffiffi pffiffiffiffiffi c1 ¼ 0.4354, q2 ¼ 1.88 c2 ¼ 0.3548; dy1

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u tex  gm ¼ 0:0167cm; dy2 ¼ 0:0167cm; ðdiameter of threadÞ ¼ 4:44  103 u t fibre density cm3

D ¼ dy1 þ dy2 ¼ 0:0335 cm; yarn flexural rigidity b1 ¼ 1:97; b2 ¼ 1:97;

236

Textile Calculation

  2 B1 ¼ 5:211. Then substituting all the values in Bending modulii mN mm mm

Similarly,

  2 mm Bending modulii mN mm B2 ¼

b2 p1 ¼ 4:544. p2 ½p1 ð1 þ c2 Þ  1:0778Dq2 

Example 9.24. A cotton plain woven fabric is with the following particulars: warp 2/24 Ne, 23.6 ends/cm weft 12Ne, 15.74 picks/cm, thickness 0.72 mm, GSM ¼ 222.85 g/m2. Calculate porosity of the fabric. 2

3   2 W areal density in gm=m 6 7  Fabric Porosity ¼ 4fb ¼ 100  41  gm 5 1000  t ðthickness of fabric in mmÞ  r density of the fibre in 3 cm

Solution.

3

2 6 Thus Porosity ¼ 4fb ¼ 100  41 

222:85gm=m2

7 gm 5 ¼ 79:6%; 1000  0:72mm  1:52 3 cm

The apparent specific volume of the cloth n ¼ 103  cloth thickness (mm)/ GSM ¼ 3.23 cm3/gm. The following are the data for terry pile fabrics: Counts of the ground warp (N1 Þ, weft thread ðN2 Þ, and pile thread (N1 Þ are 20/2 Ne, 16/1Ne, and 20/2Ne, respectively. The crimp of ground warp  ðc1 Þ and weft thread ðc2 Þ are 9.8% and 8.1%, respectively. The pile length hp is 9.3 mm, ground warp ðn1 Þ and weft yarn ðn2 Þ densities are 10ends/cm and 16.0 picks/cm, respectively. Calculate the GSM (W) of the terry pile fabric. Example 9.25.

The weight per square meter of the terry pile fabric (in gram) is given by the formula [5]   c  c c2 1 2 n2 100 1þ n1 100 1þ n2 =3100n1 100 1þ 100 100 100 W ¼ þ þ hp . 1:69N2 1:69N1 1:69N2 Having substituted the values of the parameters in the question W ¼ 422.43 g/m2.

Solution.

References [1] F.T. Pierce, The geometry of cloth structure, J. Text. Inst. (1937). March, T45-T96. [2] R.G. Livesey and J.D. Owen, Cloth stiffness and hysteresis in bending, J. Textil. Inst., 55, T516-T530. [3] G.A.V. Leaf, K.H. Kandil, J. Text. Inst. 71 (1) (1980) 1e6. [4] J.B. Hamilton, A general system of woven-fabric geometry, J. Text. Inst. Trans. 55 (1) (1964) T66eT82. [5] M. Karahan, RecepEren, HalilRifatAlpay, an investigation into the parameters of terry fabrics regarding the production, Fibres Text. East. Eur. 13 (April/June 2005). No. 2 (50).

Knitted fabric production Roopam Chauhan and Subrata Ghosh Dr. B.R. Ambedkar National Institute of Technology, Jalandhar, Punjab, India

10.1

10

Introduction

Knitting is a fabric manufacturing technique which converts thread or yarn directly into fabric by intermeshing of loops of yarns. When one loop is drawn through another, loops are formed in horizontal or vertical direction. Knitting is classified on the basis of the direction of yarn path. There are two broad categories of knitting, viz. weft knitting and warp knitting. a. Weft knitting: Weft knitting is the process of fabric formation where loops are made and intermeshed in a horizontal way across the width of fabric from a single yarn as shown in Fig. 10.1. In weft knitting, one single yarn is used continuously to form courses or wales across a fabric and is fed to one or more needles at a time. Weft knitting machines can produce both flat and circular fabric. Weft knitting includes knit structures like plain knit, rib knit, purl knit, interlock knit structures, and their derivatives. b. Warp knitting: Warp knitting is the process of fabric formation where loops are made and intermeshed in a vertical way from the yarn supplied from warp beam as shown in Fig. 10.2. In warp knitting, each needle loop has its own thread and produces parallel rows of loops simultaneously interlocked in a zigzag pattern. Warp knitting produces fabric in flat form. Two common types of warp knitting machines are the Tricot and Raschel machines.

10.2

Some basic terminologies and their relevant mathematical equations

Some of the basic terminologies involved in knitted structure are defined as below ([6],Ray, S.C.): a. Loop- Loop is the smallest building block of knitted fabric which is intermeshed in horizontal and vertical directions to form a fabric as shown in Fig. 10.3. The length of yarn required to produce a complete knitted loop (i.e., needle loop and sinker loop) is known as stitch length or loop length and is given by Eq. (10.1) as:

Loop length ¼

Course length Total number of loops

Textile Calculation. https://doi.org/10.1016/B978-0-323-99041-7.00004-7 Copyright © 2023 Elsevier Ltd. All rights reserved.

(10.1)

238

Textile Calculation

Figure 10.1 Weft knitted structure.

Figure 10.2 Warp knitted structure. b. Wale spacing- The column of loops in vertical direction is called a “wale” as shown in Fig. 10.4. The number of wales determines the width of the fabric and is measured as the number of wales per centimeter which is also termed as wale density. The distance between the wales of two successive loops is known as wale spacing and is given by Eq. (10.2) as:

Wale spacingðcmÞ ¼

1 wpcm

(10.2)

c. Course spacing- The row of loops in horizontal direction across the width of the fabric is called “a course” as shown in Fig. 10.4. The number of courses determines the length of the fabric and is measured as number of courses per centimeter which is also termed as course

Knitted fabric production

239

Figure 10.3 Loop.

Figure 10.4 Wales and courses in knitted structure. density. The distance between the courses of two successive needle loops is known as course spacing and is given by Eq. (10.3).

Course spacing ðcmÞ ¼

1 cpcm

(10.3)

d. Machine gauge- It is defined as the number of needles per inch in a knitting machine. In flat bed knitting machine, gauge of the machine lies in the range of 5e14 needles per inch and in circular machines, gauge lies in the range of 5e40 needles per inch. e. Needle pitch- Needle pitch is the distance between two neighboring needles and is given by Eq. (10.4) as:

Needle pitch ¼

1 Machine gauge

(10.4)

240

Textile Calculation

f. Course length- The length of yarn required to produce a complete knitted course is known as course length and can be evaluated from Eqs. (10.5)e(10.7) as given below:

Course length ¼ Number of loops per course  Stitch length

(10.5)

Course lengh ¼ Number of needles  Stitch length

(10.6)

Course length ðcmÞ ¼ pDGl

(10.7)

where D is the diameter of the machine (inches), G is machine gauge (number of needles/inch), l is the loop length (cm) g. Stitch density-It refers to the total number of loops in a measured area of fabric and is calculated from Eq. (10.8):

Stitch density ¼ Wales per cmðwpcmÞ  Courses per cmðcpcmÞ

(10.8)

h. Relation between count and gauge - The count of the yarn to be used in knitting machines depends on the gauge of the machine and needle specifications. The dimensions or size of the needle changes with the change in the machine gauge. So, high variation in yarn count is required for machines with different gauges. The relation between yarn count and machine gauge for different types of fabric constructions in different machines is given below: i. Circular knitting machine Yarn count in English system ¼ G2/20 (for plain knitting machine) Yarn count in English system ¼ G2/6 (for rib knitting machine) Yarn count in English system ¼ G2/9.6 (for interlock knitting machine) ii. Flat bed machine Yarn count in English system ¼ G2/15 (for plain knitting machine) Yarn count in English system ¼ G2/12.5 (for rib knitting machine) i. Feeder density- It is defined as the number of feeders per inch machine diameter and is given by Eq. (10.9) as:

Feeder density ðDÞ ¼

10.3

Number of feeders Machine diameter in inches

(10.9)

Geometry of loop and loop length

The shape of knitted loop and its length affect the properties of knitted fabric. Loop length is the fundamental unit of weft knitted structure and is the length of yarn contained in a loop. The geometry of a knitted loop in jammed condition is shown in Fig. 10.5. From Fig. 10.5,

Knitted fabric production

241

Figure 10.5 Geometry of loop.

Wale spacing w ¼ 4d, Course spacing c ¼ 3.4643d, where ‘d’ is the yarn diameter. Loop shape factor ¼ w=c ¼ 1:17 where, ‘c’ and ‘w’ are courses per cm and wales per cm, respectively. This leads to the expression of the loop length in jammed structure as given by Eq. (10.10): Loop length; l ¼ 16:6 d

(10.10)

10.3.1 Theoretical loop length [3], suggested a model by considering the depth of needle at knitting point inside the knitting zone as shown in Fig. 10.6 and developed an equation for the calculation of theoretical loop length as given by Eq. (10.11): Theoretical loop length; lt ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4h2 þ a2

(10.11)

where a is the sinker spacing and h is the depth of stitch cam at knitting point, i.e., cam setting [3].

242

Textile Calculation

Figure 10.6 Calculation of loop length [2].

[1], proposed more appropriate method of calculating theoretical loop length considering the value of needle depth, dimensions of yarn, and knitting elements as shown in Fig. 10.7. For a sinker top machine, the equation was: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   lt ¼ 2 kq þ h2 þ s2  k 2

(10.12)

where k ¼ sr þ 2yr þ nr sr is the effective sinker radius, yr is the effective yarn radius, nr is the radius of needle crown, and s is half the sinker spacing and 1

q ¼ tan

    h k 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ tan s h2 þ s 2  k 2

(10.13)

Neglecting yarn, needle, and sinker dimensions, Eq. (10.12) reduces to Eq. (10.11) lt ¼ 2

10.4

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h2 þ s 2

(10.14)

Robbing back

Robbing back (RB) is the phenomenon or tendency of the yarn to rob-back or flow back from the already-formed loops inside the knitting zone. It occurs when the

Knitted fabric production

243

Figure 10.7 Geometry of a loop inside knitting zone: sinker body [2].

yarn tension is lower on the already formed loop and higher on the yarn package side. It is commonly experienced that the theoretical length of loop (lt) is always higher than the actual loop length (lu). This difference in loop lengths is explained by this phenomenon of RB and is given by the difference between the theoretical and unroved loop lengths, neglecting the yarn extension properties as shown by Eq. (10.15). R:B:% ¼

lt  lu  100% lt

(10.15)

where lt and lu denote theoretical and unroved loop length, respectively [3].

10.5

State of relaxation

Knitted fabric attains three main relaxed states as given below [5]: A) Dry-relaxed state- Fabrics knitted in tubular form were laid free from constraints for 24 h on a flat surface to facilitate recovery from the stresses imposed during knitting in standard atmospheric conditions (65%  2% RH and 27 C  2 C). B) Wet-relaxed state- Fabric samples were put into a large stainless steel tub containing water and 0.1% wetting agent maintained at a constant temperature of 40 C. The samples remained in this container for 24 h before being lifted out and then allowed to dry naturally for at least 3 days. After drying, the fabrics were brought back to the standard conditions (65%  2% RH and 27 C  2 C).

244

Textile Calculation

C) Finished relaxed state- Fabric samples were put into a large stainless steel tub containing water and 0.1% wetting agent maintained at a constant temperature of 40 C. The samples were wetted thoroughly for 24 h, washed thoroughly, and then briefly hydroextracted and tumble dried for 1 1 2 hours at 70 C. The samples were laid flat for 24 h in standard conditions (65%  2% RH and 27 C  2 C). =

The dimensions of knitted fabric change with relaxation treatments until stable values are obtained in fully relaxed condition. The relationships are given below: Courses per cm (cpcm) f1l cpcm ¼

kc l

So; Course constant; kc ¼ cpcm  l

(10.16)

Wales per cm (wpcm) f1l wpcm ¼

kw l

So; Wale constant; kw ¼ wpcm  l

(10.17)

Stitch density (S) fl12 Stitch density constant; S ¼ Loop shape factor; R ¼

10.6

Ks l2

Kc Kw

(10.18)

(10.19)

Fabric areal density

Fabric areal density (GSM) is the weight per unit area of fabric. GSM of weft knitted fabric is given by Eq. (10.20) as: Areal density ¼

S  l  T Ks  T ¼ 100 100l

(10.20)

where T ¼ Yarn tex, S ¼ stitch density (loops/square cm), and l ¼ loop length in mm.

Knitted fabric production

10.7

245

Tightness factor

Tightness factor (TF) is a number that indicates the extent to which the area of a knitted fabric is covered by the yarn. It is a similar kind of expression to that of cover factor of a woven fabric which indicates the relative openness or closeness of a knitted fabric. It is the ratio of the area covered by the yarn in a loop to the area occupied by the loop. TF for plain weft knitting fabric is expressed by Eq. (10.21) as: TF ¼

pffiffiffiffiffiffi tex l

(10.21)

where l is loop length (mm). TF for nonplain weft knitted structure is expressed by Eq. (10.22) as: TFN ¼

pffiffiffiffiffiffi tex  n lu

(10.22)

where n is the number of needles participated in producing a unit cell of nonplain structures and lu is the unroved loop length of a unit cell of nonplain structure.

10.8

Productions calculations

10.8.1 Circular knitting machine For calculating the production of circular weft knitting machine, the following parameters are to be considered: N- Machine rpm F- Total number of feeders C- Courses per cm G- Machine gauge T- Yarn count in Tex system h- machine efficiency l- loop length (cm) x- the weight of yarn package in Kg

Using these particulars, production can be evaluated in different forms by using Eqs. (10.23)e(10.26). Production of circular knitting machine in meters per hour ¼

N  F  60  h C  100 (10.23)

246

Textile Calculation

Width of the fabric in tubular form in cm ¼

Total number of wales pDG ¼ Wales per cm wpcm (10.24)

Production of plain circular knitting machine in Kg per hour ¼

pDGl  F  N  60  h  T 100  1000  1000

Total number of conical packages needed per hour ¼

10.8.2

(10.25)

Production in kg=hr x (10.26)

V-bed knitting machine

Total number of needles in a bed ¼ w  G

(10.27)

where w is the active width of the bed in inch. Length of a rib course ¼ w  G  l  FðcmÞ

(10.28)

where l is the length of yarn in cm in a unit cell of rib fabric Carriage speed ¼ n traverse=minute

(10.29)

Total course length introduced in a minute ¼ w  G  l  F  nðcmÞ

(10.30)

Production in Kg=hr of V  bed knitting machine ¼

w  G  l  F  n  T  h  60 100  1000  1000

Production of V  bed knitting machine in m=hr ¼

10.9

(10.31) F  n  h  60 c  100

(10.32)

Warp knitting calculations

The main parameter controlling the quality and properties of a warp knitted structure is the “run-in” per rack or the amount of yarn fed into the loop. Run-in per rack is defined as the length of warp fed into fabric over 480 courses (1 rack ¼ 480 courses). In two guide bar fabrics, the run-in per rack for each guide bar may be same or different depending upon fabric structure. For example, in full Tricot structure (front guide bar: 1e2, 1e0//and back guide bar: 1e0/1e2//), the run-in per

Knitted fabric production

247

rack for both beams is the same, i.e., 1:1. The three needle shark skin fabric (front guide bar: 1e2, 1e0//and back guide bar: 1e0, 3e4//) run-in per rack required from the back beam would be more than from the front beam (1:1.66). The change in run-in may be altered by the number of courses/inch, weight of fabric, and cover of the fabric [4]. Some of the important parameters to be considered in warp knitting are given below: a) Loop length: It is the length of yarn consumed in an over lap and under lap and is given by Eq. (10.33) as:

Loop length in cm; l ¼ lo þ lu

(10.33)

where lo is the length of yarn in an overlap and lu is the length of yarn in under lap b) Tightness factor: TF of warp knitted fabric may be calculated by adding the tightness of front guide bar yarn and back guide bar yarn as given by Eq. (10.34).

Tightness factor ¼

pffiffiffiffiffi pffiffiffiffiffi T1 T2 þ lf lb

(10.34)

where T1 and T2 are the tex values of yarn for front and back guide bar; lf and lb are the loop length of front and back guide bar thread (cm). c) Fabric weight: The fabric weight in g/m2 of warp knitted fabric with two guide bars with fully threaded is given by Eqs. (10.35) and (10.36).

    Fabric weight g = m2 ¼ c  w  T  lf þ lb  101

(10.35)

where c and w are the courses and wales per cm, T is the tex value of yarn   Fabric weight g = m2 ¼ c  w  T  Rt  2:08  104

(10.36)

where Rt is the total run-in per rack d) Total run-in per rack in cm is given by Eq. (10.37):

Rt ¼ Rf þ Rb

(10.37)

where Rf and Rb are the run-in rack in cm for front and back guide bar, respectively.

248

Textile Calculation

e) Loop length for front and back guide bar is given by Eqs. (10.38) and (10.39) as:

lf ¼

Rf 480

(10.38)

lb ¼

Rb 480

(10.39)

10.9.1

Solved problems

1. Find out the gauge of a 30-inch diameter circular knitting machine if the total number of wales in the fabric is 1320.

Solution- Total number of wales ¼ 1320. By definition, gauge ¼ number of needles per inch So; gauge of the machine ¼

¼

Total number of needlesði:e: total number of walesÞ circumference of the machine in inch 1320 ¼ 14 3:14  30

2. Calculate the total number or needles in a double jersey knitting machine having 24 inch diameter and 30 gauge?

Solution- Number of needles in each bed ¼ pDG ¼ 3.14  24  30 ¼ 2260.8 ¼ 2261 needles. Total number of needles in double jersey knitting machine ¼ 22261 ¼ 4522 needles 3. A circular plain knitting machine with 26-inch diameter is producing a fabric using 20 tex yarn. If the unroved loop length is 2.6 mm, what will be the course length? 2

g Solution- Yarn count (Ne) ¼ 20

590:5 ¼ 29:5 20 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Gauge; g ¼ 29:5  20 ¼ 24 Ne ¼

Total number of needles ¼ pdg. ¼ 3.14  26  24 ¼ 1960 needles

Course lengthðmÞ ¼

Number of needles  loop length 100

Knitted fabric production

¼

249

1960  2:6 ¼ 51 cm 100

4. In a single jersey knitted fabric, number of courses introduced by the machine per hour are 5000 and number of wales are 900. If cpcm and wpcm is 20 and 15, respectively, calculate the length of the fabric produced in 1 hour and width of the fabric in cm?

Solution- Number of courses per cm ¼ 20. Total number of courses per hour ¼ 5000 Length of the fabric produced in one hour ¼ ¼

total number ofcourses per hour courses per cm 5000 ¼ 250 cm 20

Number of wales per cm ¼ 15. Total number of wales ¼ 900 Fabric width ¼

total number of wales 950 ¼ ¼ 60 cm wales per cm 15

5. Calculate the stitch density in terms of stitches/cm2 of a single jersey knitted fabric using the same data as given in Example 3

Solution- Courses per cm ¼ 20. Wales per cm ¼ 15. Stitch density ¼ cpcm  wpcm ¼ 2015. ¼ 300 loops/cm.2 6. Calculate wpcm and yarn tex of a circular rib knitting machine with 18 gauge?

Solution- Gauge ¼ number of needles/inch ¼ 18. As the number of wales per inch ¼ number of needles per inch ¼ 18. So, wpcm ¼ wales=inch 2:54 ¼ 7.08. For rib knitting machine, yarn count (Ne) ¼ G2/6 ¼ 182/6 ¼ 54 Ne. Yarn tex ¼ 590.5/54. ¼ 10.93 x 11 tex 7. Calculate the total length of yarn consumed in one rotation of a circular knitting machine having machine diameter 26 inch, gauge ¼ 20, number of feeders ¼ 90, and loop length is 2 mm

Solutione Length of yarn in one course ¼ p26  20  2 mm ¼ 3265 mm ¼ 3.265 m. Total length of yarn consumed in one rotation ¼ Number of feeders  3.265 ¼ 90  3.265 ¼ 293.85 m.

250

Textile Calculation

8. Calculate the theoretical loop length in mm of 12-gauge machine having stitch cam setting of 2.5 mm

Solution- Sinker spacing (a) ¼ 25:4 2.11 mm 12p¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Using Eq. (10.11), loop length ¼ 4h2 þ a2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 4ð2:5Þ2 þ ð2:11Þ2 ¼ 5:42 mm 9. Calculate the amount of yarn robbed back if theoretical loop length is as calculated in example 7 and unroved loop length is 4.21 mm

Solution- Using Eq. (10.15), RB ¼ 5:424:21 ¼ 0.223 and RB% ¼ 22.3% 5:42 10. Calculate the loop density per cm2 and loop shape factor of a wet relaxed knitted fabric having loop length is 0.5 cm

Solution- From Table 10.1, for wet relaxed fabric, Kc ¼ 5.3 and Kw ¼ 4.1. Ks ¼ Kc  Kw ¼ 5.3  4.1 ¼ 21.73. From Eq. (10.18), stitch density or loop density ¼ 21.73/0.52 ¼ 86.92. Loop shape factor ¼ 5.3/4.1 ¼ 1.29 11. A fully relaxed plain-knitted fabric is made from 45 tex yarn and has a stitch length of 4 mm. Estimate the areal density of the fabric.

Solution- T ¼ 45, l ¼ 4 mm. For fully relaxed fabric, Ks ¼ 2310. Using Eq. (10.20), GSM ¼ 231045 1004 ¼ 259.87 12. Calculate the areal density of a single jersey knitted fabric made of 24s cotton yarn having 35 courses per inch, 30 wales per inch and there are 50 loops in 7 inches yarn.

Solution- Ne ¼ 24, Tex ¼ 590.56/24 ¼ 24.6 tex cpcm ¼ 35/2.54 ¼ 13.78 wpcm ¼ 30/2.54 ¼ 11.81 Loop length ¼ 7/50 ¼ 0.14 inch ¼ 3.556 mm

Table 10.1 Knitting constants of single Jersey cotton fabrics, loop length in cm.

*

Knitting constant

Dry relaxed

Wet relaxed

Fully relaxed

kc kw ks

5.0 (50*) 3.8 (38*) 19.0 (1900*)

5.3 (53*) 4.1 (41*) 21.6 (2160*)

5.5 (55*) 4.2 (42*) 23.1 (2310*)

loop length in mm.

Knitted fabric production

251

Stich density, S ¼ cpcm  wpcm ¼ 13.78  11.81 ¼ 162.74

Areal density ¼

S  l  T 162:74  3:556  24:6 ¼ ¼ 142:52g=m2 100 100

13. Find out the tightness factor of a fully relaxed knitted fabric made of 36s cotton yarn if the loop length is 0.12 inch.

Solution- Ne ¼ 36, Tex ¼ 590.56/36 ¼ 16.4 tex. Loop length ¼ 0.12 inch ¼ 0.1225.4 ¼ 3.048 mm. pffiffiffiffiffiffiffi 16:4 Using Eq. (10.21), TF ¼ 3:05 ¼ 1.32 tex1/2mm1 14. Calculate the fabric weight in ozs/square yard from the data given:

Total weight of the fabric ¼ 15 Kg, Length of the fabric ¼ 35 m, Width of the fabric in open form ¼ 60 inches. Solution- Length of fabric ¼ 35 m, width of fabric ¼ 60 inches ¼ 1.524 m. Area of the fabric ¼ 351.524 ¼ 53.34 m2 Weight of the fabric ¼ 15 Kg ¼ 15,000 gm Fabric weight in gram per meter square (GSM) ¼ 15,000/53.34 ¼ 281.21 g/m.2 Fabric weight in ozs/square yard ¼ 281:210:035 1:091:09 ¼ 8.28 ozs/sq.yd 15. A knitted fabric produced from 42 tex yarn has 10 cpcm when it is in wet relaxed state. If another knitted fabric is produced from 35 tex yarn with same TF, calculate the cpcm and wpcm of the fabric produced in same relaxed state.

Solution- For wet relaxed fabric, kc ¼ 5.3, kw ¼ 4.1 when loop length is in cm kc cpcm ¼ klc and l ¼ cpcm ¼ 5:3 10 ¼ 0.53 cm ¼ 5.3 mm pffiffiffiffi 42 TF of first fabric ¼ 5:3 ¼ 1.22 pffiffiffiffi TF of second fabric ¼ l35 ¼ 1.22 From here, loop length of second fabric ¼ 4.85 mm ¼ 0.485 cm cpcm ¼ kc=l ¼ 5:3=0:485 ¼ 10:93x11 wpcm ¼ kw=l ¼ 4:1=0:485 ¼ 8:45x8 16. Calculate the machine production of a single jersey knitting machine in Kg/hr with following particulars: machine gauged24, machine diameterd30 inch, number of feedersd90, machine rpmd26, yarn countd24 Ne, loop lengthd4 mm and efficiencyd85%. If there are 20 courses per cm in the knitted fabric, what will be the production in m/hour?

Solution- G ¼ 24, d ¼ 30 inch, F ¼ 90, N ¼ 26, Ne ¼ 24, l ¼ 4 mm ¼ 0.4 cm, h ¼ 85%

252

Textile Calculation

Yarn tex, T ¼ 590.56/24 ¼ 24.61 Production in Kg=hr ¼

3:14  30  24  0:4  90  26  60  0:85  24:61 100  1000  1000

¼ 26:45Kg=hr Production in m=hour ¼

26  90  60  0:85 ¼ 59:67 m 20  100

17. Calculate the production in Kg/hour of a flat bed knitting machine with following particulars: gauge ¼ 10, number of feeders ¼ 2, loop length ¼ 1.2 cm, traverse speed ¼ 200 m/ min, yarn tex value ¼ 110. 2  1:2  200  110  60 ¼ 12:67 Solution- Production in kg/hr ¼ Kg40  10 1000  1000  100

18. A sharkskin warp knitted fabric is produced with 15 wales/cm and 20 courses/cm. The runin is 160 and 100 cm for back and front bar, respectively. Both the bars are being fed by 15 tex yarn. Calculate the areal density of the fabric in g/m2.

Solution- wpcm ¼ 15, cpcm ¼ 20, Rb ¼ 160 cm, Rf ¼ 100 cm, Tex ¼ 15. Loop length for front guide bar, lf ¼ 100/480 ¼ 0.2083 cm Loop length for back guide bar, lb ¼ 160/480 ¼ 0.333 cm Areal density (GSM) ¼ 20  15  15  (0.208 þ 0.333) 101 ¼ 243.45 g/m.2

10.9.2

Unsolved problems

1. Estimate the fabric width in flat form after full relaxation produced on a circular knitting machine of 50 cm diameter with 6 needles/cm and stitch length of 3 mm. 2. Estimate the number of courses/cm and wales/cm if stitch density of a dry-relaxed knitted fabric is 75 stitches per cm2 3. A circular knitting machine having machine diameter ¼ 26 inch, machine gauge ¼ 24, number of feeders ¼ 50 is running at 40 rpm with 80% efficiency. Find the machine production per day in kg if yarn count ¼ 35 Ne and stitch length ¼ 2.5 mm. 4. A plain-knitted fabric having stitch density of 68 stitches per cm2 is made from 42 tex yarn. Determine the TF of the fabric if Ks value is 2160. 5. Calculate the areal density in g/m2 of a single jersey knitted fabric made of 25 tex cotton with 42 courses per inch, 38 wales per inch, and 15 inch length of a course having 100 loops. 6. Find out the production per shift of 8 h in both length and weight of a circular plain weft knitting machine from the following particulars: RPM-30, number of feederse40, diametere26 inch, gaugee24, loop lengthe0.12 inch, cpie4,5 and machine efficiencye85% 7. Find out the number of knitting machines required to convert 1000 Kg of 20s cotton yarn in fabric in one shift from the following particulars: machine diametere26 inch, number of

Knitted fabric production

8. 9. 10. 11.

12.

13. 14.

15.

16.

253

feederse60, RPMe40, gaugee20, course lengthe4.0 m, fiber fly generation during conversione2%, and efficiencye90%. Also find the loop length in mm. If linear density (tex) of a yarn is doubled, then what will be the percentage increase in TF of single jersey knitted fabric? If wale constant and course constant of knitted fabric are 4.2 and 5.46, respectively, then what will be the value of loop shape factor? What will be the fabric width (cm) in finished relaxed form of a fabric produced on 50 cm diameter circular knitting machine having 15 gauge and stitch length of 2.5 mm. A 18 gauge knitting machine is set at 2.2 mm stitch cam setting, what will be the theoretical loop length as per Knapton and Munden model and Ghosh and Banerjee model (considering same dimensions of yarn, needle, and sinker)? If the unroved loop length is 3.8 mm, what will be the RB value? In a circular knitting machine producing commercial knitted fabric with 24 gauge, 30 inch diameter, 96 feeders working at 35 rpm with 90% efficiency, calculated(a) the optimum yarn tex, (b) loop length, c) course length, (d) cpcm and wpcm in relaxed state, (e) fabric width, (f) fabric length per hour, and (g) GSM of the fabric? Calculate the width of the flat fabric in fully relaxed state produced on a 20 inch flat knitting machine of 10 gauge having 6 mm stitch length. What will be GSM and TF of the fabric? A plain weft knitted fabric has 26 courses per inch and 20 wales per inch. Find the number of loops in the fabric if its length and width are 100 and 50 cm, respectively. Also calculate its course length in cm. A single jersey fabric having 10 courses/inch is produced on a flat bed knitting machine having 30 inch width and 10 gauge. The carrier is running on a machine with an average speed of 6 inches/s. (a) Find the time taken (in min) to make one course, (b) What is the total number of wales? and (c) What is the production in m/hr? A warp knitted fabric is having 9.5 wales/cm and 25.5 courses/cm. The run-in ratio is 170.5 cm for back bar and 100 cm for front bar, and both the bars are threaded with 6 tex filament yarn. Calculate the front and back guide bar stitch length, GSM value of the fabric, and TF of the fabric?

10.9.3 Answers of unsolved problems (1) 33.64 cm; (2) 10 cpcm, 8 wpcm; (3) 190.39 Kg/day; (4) 1.15 tex1/2mm1; (5) 235.68 g/m2, (6) 276.29 m/8 h, 59.98 kg/8hr; (7) 8, 2.45 mm; (8) 41.4%; (9) 1.3; (10) 55.17 cm; (11) 4.62 mm, 4.73 mm, 17.75%, 19.66%; 12) 20.5, 0.312 cm, 705.36 cm, 17.62 cpcm, 13.46 wpcm, 1.68 m, 102.97 m/h, 151.69 g/m2; (13) 89.71 cm, 341 g/m2, 15.71; (14) 393, 208 cm; (15) 5 s, 300, 3.04 m/h; (16) 2.08 mm, 3.55 mm, 81.83 g/m2, 1.85 tex1/2mm1.

References [1] S. Ghosh, P.K. Banerjee, Mechanics of the single-Jersey weft knitting process, Textil. Res. J. 60 (1990) 203e211.

254

Textile Calculation

[2] S. Ghosh, R. Chauhan, S. Roy, Mechanics of loop formation in plain weft knitting machinery, in: R. Maity, S. Rana, P. Pandit, K. Singha (Eds.), Advanced Knitting Technology, Elsevier Ltd, 2021, pp. 67e92, 2021. [3] J.J.F. Knapton, D.L. Munden, A study of the mechanism of loop formation on weft knitting machinery. Part I: the effect of input tension and cam setting on loop formation, Textil. Res. J. 36 (1966) 1072e1080. [4] S.C. Ray, in: Fundamental and Advances in Knitting Technology, Woodhead Publishing India Pvt.Ltd, 2011. [5] I.C. Sharma, S. Ghosh, N.K. Gupta, Dimensional and physical characteristics of single Jersey fabrics, Textil. Res. J. 55 (3) (1985) 149e156. [6] Spencer, D.J. In Knitting Technology. Woodhead Publishing Limited, Cambridge, (Pergamon Press).

Calculations in fabric chemical processing

11

Chet Ram Meena and Janmay Singh Hada Department of Textile Design, National Institute of Fashion Technology Jodhpur, Ministry of Textiles, Govt. of India, Jodhpur, Rajasthan, India

11.1

Introduction

This chapter focuses on calculations related to pretreatment, dyeing, printing and finishing processes with examples. A flow chart of textile chemical process is shown in Fig. 11.1 for better understanding and comprehension.

11.2

Calculations at various stage of textiles processing

11.2.1 Moisture regain and moisture content Moisture regain is defined as the weight of water in a textile material expressed as a percentage of its oven-dry weight. Moisture content is the weight of water in a material expressed as a percentage of the total weight of textile material and moisture. All

Figure 11.1 Flow chart for textile chemical processing. Textile Calculation. https://doi.org/10.1016/B978-0-323-99041-7.00009-6 Copyright © 2023 Elsevier Ltd. All rights reserved.

256

Textile Calculation

materials generate heat when absorb moisture and absorb heat when releasing moisture. Let the oven-dry weight of a textile material is D & the weight of moisture be W then the moisture regain (R) and moisture content (C) can be expressed by the following formulae : Moisture RegainðRÞ% ¼

Weight of moistureðWÞ  100 Oven dry weight of textile materialðDÞ

Moisture Content ðCÞ% ¼

Weight of moistureðWÞ  100 Weight of moistureðWÞ þ Oven dry weight of textile materialðDÞ

The standard atmospheric condition for conditioning any sample in tropical country like India is: relative humidity (RH) 65  2% and temperature 27  2 C. 10 tons of 30s Ne 70/30 polyester/cotton yarn is shipped at 6% moisture content. What will be the correct invoice weight when moisture regains of polyester and cotton fiber are 0.4% and 8.5%, respectively?

Example 11.1.

Solution.

Weight (kg) ¼ Weight of moisture (W) þ Oven dry weight (D)

10000 kg ¼ Weight of moisture (W) þ Dry weight of fibre (D) at 6% moisture content Regain ¼ 0.7  0.4 þ 0.3  8.5 ¼ 2.83% Moisture ContentðCÞ% ¼

Weight of moistureðWÞ Weight of moistureðWÞ þ Oven dry weightðDÞ  100

6% ¼

W W  100% ¼  100 WþD 10; 000

W ¼ 600 kg; so dry mass of the yarn is 10,000e600 ¼ 9400 kg, where total water allowed is 2:83 ¼

Weight of invoice  100 9; 400

Weight invoice ¼

2:83  9; 400 ¼ 266:02 kg 100

Total invoice weight ¼ 9400 þ 266.02 ¼ 9666.02 kg

Calculations in fabric chemical processing

257

11.2.2 Pretreatment All fabrics contain impurities that have to be removed prior to dyeing or printing. These impurities may be those present in natural fibers e.g., cotton waxes and natural coloring matter or those added to facilitate spinning, weaving or knitting i.e., warp sizes or lubricants. Synthetic fibers contain less impurity than natural fibers [1]. Some processes are used to remove the impurities from fibers to make it dyeable or printable. Natural and synthetic fibers contain primary impurities that are contained naturally and secondary impurities that are added during spinning, knitting and weaving process. The textile pretreatment is the series of cleaning operations of all impurities which cause adverse effect during dyeing and printing that is removed in the pretreatment process.

11.2.3 Desizing Desizing is the process of removal of the size material applied on warp threads of a fabric to facilitate weaving. It can be classified as hydrolytic and oxidative desizing. The efficiency of desizing is defined by the % starch removed after desizing process with respect tp present earlier. The weight of poplin after sizing is 10 g. The same poplin fabric is desized by the enzyme process and its weight decreases up to 9.2 g. Determine the weight loss %?

Example 11.2.

Solution.

The weight loss in poplin sample is determined by

Weight Loss ð%Þ ¼

ðInitial weight  Final weightÞ  100 Initial weight

Weight Loss ð%Þ ¼

10  9:2  100 10

¼ 8% The efficient desizing process gives a weight loss of around 8%.

11.2.4 Scouring Scouring is a process to remove the hydrophobic agents (oil, fat and wax etc) from fabric and to make them more absorbent. Scouring is probably the most important process in the wet processing of textile materials. Effective scouring is essential for the subsequent processing of any textile substrate, regardless of type [2] (Table 11.1). If the weight of the fabric is 10 g, the calculation for required amount of chemicals is according to the below mentioned formula

258

Textile Calculation

Table 11.1 A typical recipe for scouring process (Cotton fabric). S.No.

Name of chemicals

Quantity (gpl)

1. 2. 3. 4. 5. 6. 7. 8.

NaOH Na2CO3 Detergent Wetting agent Sequestering agent ML ratio Temperature Time

6 4 0.5 1 1 1:20 100 C 90 minutes

Amount of Chemical ¼

Total liquor  Recipe amount of chemical ðgplÞ Stock solution %  1000

Let us assume that stock solution (%) ¼ 1% Total liquor ¼ 10  20 ¼ 200 mL Amount of NaOH according to the above formula ¼ 200  6 / 1  1000 ¼ 1.2 mL Na2CO3 ¼ 200  4 / 1  1000 ¼ 0.8 mL Detergent ¼ 200  0.5 / 1  1000 ¼ 0.1 mL Wetting Agent ¼ 200  1 / 1  1000 ¼ 0.2 mL

11.2.5

Assessment of scouring efficiency

Weight loss method is an indirect method to test the scouring efficiency, i.e., amount of impurities removed. The weight loss % is: Weight Loss % ¼

Weight before scouring  Weight after scouring  100 Weight before scouring

After desizing the weight of cotton fabric is 1000 kg. After NaOH scouring, the fabric weight decreases by 950 kg. What is % weight loss in scoured fabric?

Example 11.3.

Solution.

Weight Loss % ¼

Weight before scouring  Weight after scouring  100 Weight before scouring

Weight Loss % ¼ 1000e950/1000  100 ¼ 5%

Calculations in fabric chemical processing

11.3

259

Cuprammonium fluidity

It is the measurement of chemical degradation of cotton cellulose during pretreatment process. It works on cellulose damage due to less degree of polymerization. The solution of cellulose (damaged) will be less viscous and have more fluidity as compared to its initial viscosity. The cotton sample is exactly weighed and dissolved in cuprammonium hydroxide solution. The flow time of this solution between two fixed marks on a calibrated viscometer (fluidity tube) is measured at a specific temperature. Fluidity ValueðFÞ ¼ C=t where “C” is viscometer constant and “t” is flow time. The results are expressed as Rhe (poise-1), which is reciprocal of unit of viscosity. Fluidity value of 5e8 is considered satisfactory for normal bleached cotton fabric.

11.3.1 Bleaching Bleaching is a process to remove the natural colors from the textiles material and impart the whiteness to the textiles.

11.3.2 Available chlorine (active chlorine) One gram of 100% active chlorine bleach has the same bleaching power as 1 g of chlorine. It is based on the assumption that hypochlorite ions can liberate an equivalent amount of iodine by oxidation from a potassium iodide solution. The amount of iodine released is measured indirectly by titration. In that sense, available chlorine measures active oxidizing matter in the bleach solution. It is vital to determine active or available chlorine in a bleach solution since it may also contain some fraction of chloride ions (a by-product of bleach decomposition) with no bleaching power. Only hypochlorite ions have bleaching (and oxidizing power to liberate Cl2 and cause bleaching). Calculate the active oxygen, in terms of percent and grams, if solution contains the 30 % hydrogen peroxide (H2O2)?

Example 11.4.

Solution.

Active Oxygen% ¼ 47:05  CO100 where C is the concentration (w/w%) of the hydrogen peroxide solution Active Oxygen % ¼ 47:05  30O100 ¼ 14:115 Hence, expressed on the weight basis, 1000 g of H2O2 (30%) contains 14.115 g active oxygen.

260

Textile Calculation

11.4

Mercerization

It is a process to improve dye pick up, luster, and absorbency in cellulosic materials. It is a pretreatment as well as finishing treatment of cotton with a strong caustic alkaline solution.

11.4.1

Determination of degree of mercerization

Mercerized sample absorbs barium hydroxide (alkali) to a greater degree than sodium hydroxide and from practical point of view, barium hydroxide is easier to estimate. The ratio of uptake for this reagent has been referred to barium activity number [3].

11.5

Barium activity number

The barium activity number is the ratio of the amount of barium hydroxide absorbed by mercerized cotton to that absorbed by unmercerized cotton under the same conditions. Mercerized cotton can absorb more barium hydroxide than unmercerized cotton and this is the basis for this test. The amount of Ba(OH)2 is more in mercerized fabric than in unmercerized fabrics. Ideally, barium activity number activity number should be 115e160 for mercerized fabrics (Table 11.2). Barium Activity Number ðBANÞ ¼

BM  100 BC

whereas B ¼ Quantity, in mL, of hydrochloric acid (HCL) required for the blank M ¼ Quantity in mL, of HCL required lor the mercerized cotton C ¼ Quantity, in mL, of HCL required for the unmercerized cotton

11.6

Dyeing

Dyeing is the process to apply colors on the fabric by dyestuffs or pigments. Dyestuffs give color to the material onto which they have been anchored by selectively retaining some wavelength out of light falling from the surface [5e7]. Table 11.2 BAN number of mercerized and semi-mercerized cotton. Types of cotton

BAN number

Mercerized cotton Semimercerized cotton

150e160 115e130

Calculations in fabric chemical processing

261

For any textile chemical process, the objective is maximum output with minimum cost. The exhaust or batch dyeing is normally used to dye the textile materials. The dye particles slowly move or migrate or exhaust from a dye bath to the textile material (any substrate like fiber, yarn, fabric, or garment). In dyeing either the fabric is circulated, or dye liquor is circulated (fabric is stationery), or both material and dye liquor are circulated (Fig. 11.2) (Table 11.3).

Figure 11.2 Flow chart for coloring material for dyeing of the textile material.

Table 11.3 Batch dyeing machines with material and liquor mechanism. S.No.

Type of batch dyeing machines

Process

1. 2. 3. 4. 5.

Winch Jigger Cabinet dyeing Jet dyeing Soft flow dyeing machine

Only material is agitated, liquor stationery Only material is agitated, liquor stationery Only material is agitated, liquor stationery The material and liquor both agitated The material and liquor both agitated

262

Textile Calculation

11.6.1

Weight of fabric

All calculations in dyeing are based on the weight of material to be dyed. It gives a convenient way to state how much dyestuff is needed for a given shade, regardless of whether the dyer wants to color yarns or fabric. The weight of dyestuff is expressed as a percentage of weight of material. Example 11.5.

To dye a medium-red with madder (50% wof) if the weight of cotton is

one pound. Solution.

Weight of fiberðDryÞ  %WOF ¼ Weight of Dyestuff ðdryÞ 50% WOF madderd(metric) 450g x 0.5 ¼ 225g. Use 225g of dyestuff to dye 450g of fiber. 50% WOF madderd(imperial) 1lb x 0.5 ¼ 0.5lb. Use half a pound of dyestuff to dye a pound of fiber. Alternatively, cochineal bugs only require 5% WOF for a deep shade. Hence, to dye the same amount of fiber, 5% WOF cochineald(metric) 450g  0.05 ¼ 22.5g. Use 22.5g of dyestuff to dye 450g of fiber. 5% WOF cochineald(imperial) 1lb x 0.05 ¼ 0.05lb. Use 0.05lb of dyestuff to dye a pound of fiber.

11.6.2

Shade percentage (%)

The amount of dye “present” on the textile material (fiber, yarn, fabric) after dyeing is expressed as “percent shade.” The shade depth in textile material is normally calculated as weight of material (textiles). This is divided qualitatively in light, medium, dark, and deep shade as per hue of dye. 1% depth shade means 1 gram dye on 100 g of textiles. The strength of color does vary with different types of dyestuffs. Normally the shades are classified as shown in Table 11.4. The % may vary as per fiber, chemicals, and types of dyestuffs. Normally, to calculate the dyeing quantities, metric system is used. Calculate the reactive dye required to dye the light shade up to 0.5%, medium shade of 1%, and dark shade of 3% for 100-g poplin fabric.

Example 11.6.

Solution.

Material weight (Poplin): 100 g, light Shade %: 0.5

Calculations in fabric chemical processing

263

Table 11.4 Dyeing recipe with chemicals percent. Auxiliaries

Types of shade

% Concentration*

Acids (acetic)*

Salt (glauber)*

Wetting agents*

Light shade Medium shade

Up to 0.5% 0.5%e1%

2% 5%

0.5% Up to 1%

Dark shade Heavy dark shades

2%e4% >4%

0.5% Up to 1%e2% 2% 2%e2.5%

10% 10%e20%

2% 2%e2.5%

Dyes Amount ¼ Material weight  ð% of shadeÞ Dye amount ¼ 100  0:5 Dye amount ¼ 0:5 g Medium Shade %: 1 Dye amount ðgÞ ¼ 100  1 Dye amount ¼ 1 g Dark Shade %: 3 Dye amount ðgÞ ¼ 100  3 Dye amount ¼ 3 g of reactive dye

11.6.3 Stock solution It is a solution containing predetermined amount of dyestuff dissolved in prescribed quantity of water. The stock solution is prepared by adding small amount of dyestuff (as per the required % shade) in water. The advantage of making stock solution is accuracy and convenience in dyeing different % of shades. To make 1% stock solution, 1 g dye is to be dissolved in 100 g of water. The stock solution required can be calculated as stated below: Amount of stock solution required inðmLÞ ¼

Weight of fabricðgÞ  Shade % stock solution%

264

Textile Calculation

Amount of water required ¼ Weight of fabricðgÞ  M : L Ratio  Amount of stock solution required

Example 11.7. Solution.

Calculate 1% stock solution for 1 kg (1000 g) of fiber.

Consider 1000 g as equivaent to 1000 mL.

Amount of dye ¼ Liquor volume ðmLÞ  ð% of ShadeÞ Amount of dye ðgÞ ¼ 1000  1 Amount of dye ¼ 10 g In a factory to dye 100 kg muslin fabric by Vat Yellow 5G in medium shades of 1.5%, one percent (1%) stock solution is prepared. Calculate the amount of Vat Yellow 5 G required to dye the muslin fabrics.

Example 11.8.

Solution.

Requires dye amount of Vat Yellow 5 G is:

Dyes Amount ¼ Liquor  ð% of ShadeÞ Dyes Amount ¼ 100 Kg  1:5% of shade Dyes Amount ¼ 1:5 kg Amount of dye calculation formula: Required amount of dye ¼

Weight of fabric ðgÞ  % of shade 1% stock solution

Or, the required amount of solution, Amount of solution ¼

Wt:  Sp Cs

where Wt. indicates the weight of yarn, or fiber, or fabric. Sp indicates the shade percentage; Cs indicates the concentration of the stock solution.

11.6.4

Material to liquor ratio

Dyeing is done normally in an aqueous medium. In common, the total amount of water used in dyeing is calculated from the material to liquor ratio or MLR ratio. When it is 1: 10, it means 10 L of water is required for 1 kilogram (kg) fabric.

Calculations in fabric chemical processing

265

The initial concentration of dye bath works out to be 100 g/100 L or 1 g/L. If at the end of the dyeing the dye bath concentration drops put 0.1 g/L, it means under the condition, 90% dye exhausted. Dye bath exhaustion can be calculated by a simple formula. Where the x g l is the initial concentration of dye, y g l is the final concentration of dye. So, the percent exhaustion is =

 x  y x

=

¼

 100

Calculate dye bath concentraion when 2% shade is required in 100 Kg of fabric. Also find out dye bath concentarion for MLR 1:5 and 1:10.

Example 11.9.

For 2% shade and 100 kg fabric, the requirement of dyestuff is 2 Kg. For MLR 1:5 and 1:10, 2 Kg dyestuff has to be added to 500 L and 1000 L of water. In 1:5 MLR dye concentration ¼ (21000)/500 ¼ 4 gpl and for 1:10 MLR the dye concentarion ¼ (21000)/1000 ¼2 gpl. Solution.

11.6.5 Auxiliaries or chemicals calculation formula The following formula has to be used to calculate the required quantity of auxiliaries or chemicals. Required amount of solution ðmLÞ ¼

Weight of fabricðgÞ  gram per litre  liquor ratio %concentration of stock solution  10

11.6.6 Additional auxiliaries calculation formula The formula for the addition of auxiliaries in solid forms such as salt and soda is as follows: Salt ðgplÞ ¼ sample weight ðgÞ  liquor ratio  salt ð%Þ required =1000

11.6.7 Percentage to gram conversion formula The conversion formula from percentage to gram/litre is shown below: Gram per litre ¼ Required amount in percentage  10 If alkali concentration is given, then the following formula is to be used for calculating this in gram per liquor (gpl):

266

Textile Calculation

Required amount of solution ðmLÞ ¼

Weight of Fabric ðgÞ  gram per litre  liquor ratio %concentration of stock solution  10

Or Required amount of solution ðmLÞ ¼

Weight of fabric ðgÞ  Required amount %  Liquor ratio %concentration of stock solution

Calculations in lab dip dyeing process. Recipe: Dyes

Example 11.10.

Rema Blue RR ¼ 1.122% React Red KHW ¼ 2.014% React Yellow KHW ¼ 1.486% Chemicals Soda Ash (concentration 20%) ¼ 5 g/L Sample Weight ¼ 5 g Caustic Soda ¼ 1.32% Salt ¼ 70% Stock Solution (%) ¼ 1, M:L ¼ 1:8. Now, calculate the required recipe for dyes and auxiliaries or chemicals in gram per liter. Solution.

In the case of dyes,

Required amount of dye ðmLÞ ¼ Weight of Fabric ðgÞ  % of shade∕% stock solution Calculation of dyestuff for Rema Blue RR will be ¼ (1.122  5)/1 ¼ 5.61 g/L React Yellow KHW ¼ (1.486  5)/1 ¼ 7.43 g/L, React Red KHW ¼ (2.014  5)/ 1 ¼ 10.07 g/L In the case of auxiliaries or chemicals, SaltðgplÞ ¼ sample weightðgÞ  liquor ratio  required amountð%Þ=1000

Calculations in fabric chemical processing

Salt ðgplÞ ¼

267

5  8  70 1000

¼ 2.8 So, the required amount of salt is 2.8 gpl In the case of Soda Ash (concentration 20%): Required amount of solution ðmLÞ ¼

Weight of fabric ðgÞ  Gram per litre  Liquor ratio  10 %Concentration of stock solution

Required amount of solutionðmLÞ ¼

558 ¼ 1 mL 20  10

Required amount of solution ¼ 1 mL Extra amount of water required ¼ Total liquor required e(Required amount of water to make a solution of auxiliaries and dyes) ¼ [(5  8)e{(5.61 þ 10.07þ7.43) þ (1.0 þ 0.12)}] ¼ 40e24.112 ¼ 15.77 mL. So, 15.77 amount of salt is added in solid form. Example 11.11. Calculate total liquor required for 8 g of material if M: L ratio is 1:15. For material weight “x” (g) and M: L (Material: Liquor) is 1: N the total amount of liquor will be: Solution.

Total amount of liquor ¼ x  N ¼ mL or cc Material weight ¼ 8 g, M: L ¼ 1:15 Total liquor ¼ 8  15 ¼ 120 mL If the amount of chemical in the recipe is expressed in percentage (%), then calculate the required amount of chemical for 10 g of fabric.

Example 11.12.

268

Textile Calculation

Solution.

Required amount of chemicalðmLÞ ¼ Weight of FabricðgÞ  chemical amount in recipe∕% stock solution Fabric weight ¼ 10 g salt required ¼ 1% Stock solution ¼ 1% Required amount of chemical ¼ (101%)/1% ¼ 10 mL Example 11.13.

Calculate the required amount of chemical in g/L for 10 g of fabric.

Solution.

Required amount of chemicalðmLÞ ¼ total liquor  chemical required in

g = ð%stock solution  1000Þ litre

Fabric or material weight ¼ 10 g M: L ¼ 1:10 Soda-lime ¼ 25 g/L Stock solution ¼ 1% Total liquor required 10  10 ¼ 100 mL Soda lime required ¼ (100  25) / (1000  1%) ¼ 250 mL Example 11.14.

Calculate the initial water for dyeing the 5 g of fabric.

Solution.

Required amount of intial water ¼ amount of total liquor  ðchemical 1 þ chmical 2 þ .Þ Fabric/material weight ¼ 5 g M: L ratio ¼ 1:20

Calculations in fabric chemical processing

269

Total liquor ¼ 5  20 ¼ 100 mL Chemical-1 ¼ 10 mL Chemical-2 ¼ 5 mL Initial water ¼ 100-(10 þ 5) ¼ 85 mL For the preparation of “x%” stock solution of a solid chemical compound, take 100 mL of distilled water and then add “x” g of that chemical to make 100 mL. To make 5% stock solution of sodium chloride (NaCl), dissolve 5 g of NaCl in 100 mL of distilled water. For the preparation of the “y%” stock solution of a liquid chemical compound, take (100-y) mL distilled water and then add “y” mL of that liquid chemical to make a 100mL stock solution. To make a 4% stock solution of HCL, take 100e4 ¼ 96 mL of distilled water and to it add 4 mL HCL to 96 mL of water.

11.6.8 Printing Printing is localized dyeing and the main ingredients are dyestuffs and thickener. These ingredients provide color and proper viscosity to the printing paste. Printing paste contains ingredients which are used as essential chemicals as well as auxiliaries. In printing, the printing paste is applied using a block or engraved roller or using a partially marked flat or rotary screen followed by squeezing system to get the desired effect on textiles [8] (Table 11.5). In textile printing, printing paste is prepared in parts. Solid and liquor chemicals are measured in parts. 1 part equals to 1 mL and 1 g as well. Total printing paste is prepared in 1000 parts as mentioned in the above. Example 11.15.

Calculate the percentage shade if 40 parts dyes are used with 1000 parts

printing paste. Table 11.5 Printing ingredients for color discharge print on silk. Name of printing ingredients

Quantity (parts)

Nondischargeable acid dye Diethylene glycol Urea Zinc dust Sodium bisulfate British gum Water Total

40 parts 30 parts 20 parts 120 parts 60 parts 600 parts 130 parts 1000 parts

270

Textile Calculation

Solution.

As mentioned above

40 Parts-1000 Parts 4 Parts-100 Parts 1 Part ¼ 1 g/1 mL. Hence, printing paste percent shade is 4%.

11.6.8.1 Printing cost in textile industry Calculating printing cost formula: Printing Cost per kg ¼

D:M þ D:L þ D:E þ O:H Total print production

where D.M - direct material cost, D. Lddirect labor cost, D. Eddirect expense cost, O. Hdoverhead cost. Example 11.16. To print the 500 kg knitted fabric on rotatory printing machine, tentative cost of printing for 500 kg fabric is Rs. 25000, labor charges is 5000, direct expenses (fixation, washing off, etc.) is Rs. 1000, and overhead charges is Rs. 10000, calculate the cost of 1 kg fabric printing? Solution.

If given fabric weight ¼ 500 kg

Printing Cost per kg ¼ D:M þ D:L þ D:E þ O:HOTotal print production Printing cost per kg ¼

25000 þ 5000 þ 1000 þ 10000 500

Print cost per kg ¼ Rs. 82

11.6.9

Finishing

Finishing processes are carried out to improve the natural properties or aesthetic value of the fabric and to improve its serviceability. Textile finishing, in a restricted sense, is the term used for a series of processes to which all bleached, dyed, printed, and gray fabrics are subjected before they are put on the market. The purpose of textile finishing is to improve the unique properties that they must possess to meet appropriate in-service requirements and secure customer satisfaction. Apparel and leisurewear must have an acceptable handle, should not crease in wear, and should display good easy-care properties. Workwear must resist hazards encountered by the wearer, e.g., boiler suits worn by garage mechanics must have adequate oil and stain repellency, firemen’s uniforms must be flame-retardant, and outdoor workwear must be water-repellent. However, many chemical finishes can also be successfully applied to textiles at the yarns, fabrics, or garments stage [9].

Calculations in fabric chemical processing

271

Chemical finishing can be defined as the application of chemicals to produce a desired fabric characteristic. Chemical finishing, commonly known as “wet” finishing, refers to procedures that alter the chemical make-up of the materials to which they are applied. In other words, a cloth treated with a chemical finish will have a different elemental composition than a fabric that has not been finished. Finishing agents performed their performance according to the selection of appropriate finishing agent for required finish [10].

11.6.10 Wet pick up The quantity of dye, size, or other fluid that the fibre, yarn, or fabric absorbs as a percentage of its weight during an application process. % Wet pick up ¼

Weight of solution absorbed  100 Weight of dry fabric

Add on: Amount of chemical added to the fabric % conc

wt % addon  %wet pick up ¼ wt 100

Gram per litre (gpl) to weight per cent concentration wt Concentration in g % conc in solution ¼ wt 10  densityðg=lÞ

A cotton fabric is to be treated with 10% on the weight of fabric (owf) with a chemical finish in a wet on dry padding process. If the wet pick is 80%, what concentration of chemical is required?

Example 11.17.

% conc

wt % add on  % wet pick up ¼ wt 100

% conc

wt 10  80 ¼ wt 100

% conc

wt wt ¼8 wt wt

Solution.

If the cotton fabric has a linear density of 0.3 kg m1 and speed is 50 m min , solution density is 1.10 g mL1, and wet pick up is 80% with linear density of 0.3 kg m1, what is the flow rate of solution to maintain a constant level in pad?
Fabric mass flowðkg min1 Þ% wet pick up Solution. Flow rate 1 min1 ¼ , Solution density100 Example 11.18. 1

272

Textile Calculation

Where

Fabric mass flow ¼ fabric speed m min1  fabric linear density kg min1 Fabric mass flow ¼ 50  0:3 ¼ 15 kg min1




Therefore,


Solution flow rate 1 min1 ¼ 15  80 O 1:10  100 ¼ 10:99 min1 A cotton fabric is to be treated with 4% owf of the chemical finish in a wet on wet pad application with entry wet pick up of 80%, exit wet pick up of 95%, and interchange factor of 0.5 and solution density is 1.10 g mL1, what are the effective wet pick up and necessary pad concentration?

Example 11.19.

Solution.

Wet pick up efficiency ¼ ðWet pick upout  Wet pick upin Þ þ Wet pick upin f Wet pick up efficiency ¼ ð95  80Þ þ 80  0:5 ¼ 55%
Pad conc gL1 ¼ ð% addon  1000  solution densityÞOWet pick up efficiency
Pad conc gL1 ¼ 4  1000  1:10O55 ¼ 80 gL1 Determine the required feed solution concentration and flow rate using the parameters from the preceding example.

Example 11.20.

Solution.

For the above example



Feed Conc gL1 ¼ ðpad conc  WPU effÞOðWPUo  WPUi
Feed Conc gL1 ¼ 80  50O95  80 ¼ 266:67gL1
Feed flow rate 1 min1 ¼ Fabric Mass flow ðkg=minÞ  ðWPUo  WPUi ÞOfeed solution density ðg=LÞ  100 Feed flow rate ð1=minÞ ¼ 15  ð95  80ÞO1:10  100 ¼ 2:05 ðL=minÞ To calculate the finishing bath concentration: ¼ PA  1000OLA ¼ g=L

Calculations in fabric chemical processing

273

PA ¼ chemical amount (expressed as a percentage on the weight of the fabric) which should be retained by the fabrics after immersion and hydro extraction. LA ¼ Liquor pick up after the immersion and hydroextraction

11.6.11 Curing of chemical finishes Curing is a treatment carried out after the application of a finishing chemical to a textile substrate in which appropriate conditions are used to affect a chemical reaction. Generally, the fabric is heat treated for defined duration according to the process. It may be subject to higher temperatures for short times (flash curing) or to low temperatures for longer periods and at higher regain (moist curing). Curing time ¼ Amount of fabric in machine OSpeed of the fabric through the machine

If the fabric content of the machine is 30m and fabric speed is 50 m/min what will be the curing time?

Example 11.21.

Curing time ¼ 30/50 ¼ 0.6 min Stone washing: Stone ratio to fabric weight would vary from 0.5 to 3.1

Solution.

Stone ratio ¼ Stone WeightOFabric Weight

11.7

Conclusion

It is an integrated approach to cover all processes with suitable examples. The approach is example-based, i.e., the readers are required to gain knowledge by solving these examples. Solved examples are provided, wherever felt necessary, to elucidate the concept. Approriate calculations for various chemical processing are also helpful for optimizing the use of natural resources such as chemicals, water and energy.

References [1] G. Madaras, G. Parish, J. Shore, Batchwise Dyeing of Woven Cellulose Fabrics, Technology of Fabric preparation, 1993, p. 3. [2] C. Carr, Chemistry of the Textiles Industry. S.L, Balckie Academic and professional, 1995. [3] S. Karmakar, Chemical Technology: The Pre-treatment Process of Textiles. S.L, Elsevier, 1999.

274

Textile Calculation

[4] E. Trotman, Dyeing and Chemical Technology of Textile Fibers, B.I.Publications pvt. Ltd, New Delhi, 1994. [5] R. Welham, Early History of the Synthetic Dye Industry. S.L, J.S.D.C, 1963. [6] E. Mairet, A Book on Vegetable Dyes. E-Book 50079 Ed. S.L, Douglas Pepler, 2015. [7] D. Broadbent, Basic Principles of Textils Colouration, in: ed. s.lSociety of Dyers and Colourists, 2001. ISBN 0901956. [8] L.H. Needles, Textiles Fibers, Dyes, Finishes And Processes. S.L, Noyes Publication, 1986. [9] G. Madaras, G. Parish, J. Shore, Technology of Fanric Preparation. Batchwise Dyeing of Woven Cellulose Fabrics, 1993, p. 109. [10] W. Schindler, P. Hauser, Chemical Finishing of Textiles. S.L, Woodhead Publishing Limited, 2004.

Apparel manufacturing measures and calculations

12

Manoj Tiwari 1 and Prabir Jana 2 1 National Institute of Fashion Technology Kannur, Kannur, Kerala, India; 2National Institute of Fashion Technology Delhi, New Delhi, Delhi, India

If you cannot measure it, you cannot improve it. - Lord Kelvin.

12.1

Introduction

Measurement quantifies the attributes of an object or event, which can be used to compare it with other objects or events. The scope and application of measurement are dependent on the context and discipline. Measures are a general name for measurements, metrics, or facts that interest the data analysis. Measures are mostly numerical [1]. Measures can be defined as the dimensions, capacity, or amount of something ascertained by measuring or estimating what is expected (as of a person or situation) [2]. While measuring any attribute, it is essential that the measurement process may involve some mathematical calculations. In this chapter, we will discuss different measures and their calculations. Apparel manufacturing activities can be broadly classified into three categories: (1). Preproduction, (2). Production, and (3). Postproduction. Preproduction activities primarily involve product costing, material consumption estimations, material procurement, storage and inventory management, product development, capacity booking, process planning, pilot runs, spreading and cutting processes, etc. The next category is production, which mainly includes sewing-related processes involving a significant share of resources. Sewing of the garments is considered the focal point of producing the products. The third category is postproduction which covers the processes after the garments are stitched. It includes several processes such as dry process, wet process, finishing and packing, and dispatch of the garments. Apart from these three broad categories, several support activities or processes also work as allied to the production process. Such activities include plant set-up, process planning and control, industrial engineering, quality assurance or quality control, maintenance management, etc. In addition to the basic calculations that reveal the necessary information about the progress (against target), some other indicators or indices are also practiced to measure the process’s effectiveness. These indicators can reveal vital insights into the organization’s health. With the advent of Industry 4.0 solutions, the availability of information Textile Calculation. https://doi.org/10.1016/B978-0-323-99041-7.00014-X Copyright © 2023 Elsevier Ltd. All rights reserved.

276

Textile Calculation

(right from the source of origin) has made it possible to visually monitor the progress in a real-time manner and make necessary informed decisions at the right time. The range of activities (main and allied) varies from organization to organization, depending on the product-specific requirements. The most commonly observed activities and processes are considered here to discuss various calculations involved. This chapter is structured in two sections: (1). plant set-up and facility designe related measures and calculations, and (2). manufacturing operationserelated measures and calculations.

12.2 12.2.1

Plant set-up and facility designerelated measures and calculation Manufacturing plant set-up

The plant set-up of an apparel manufacturing facility is an important strategic step. Planning and implementing plant set-up is a strategic move that must align with the organization’s mission and vision. The setting of various infrastructure, departments, and facilities is decided according to the product chosen and the targeted production capacity. Development of layout by ensuring sufficient area allocation to the departments or processes is one of the critical activities in any plant set-up. This section discusses the calculations in determining the area in a layout design using a practical example. A plant with a targeted capacity to produce 10,000 garments per day (in a shift of 8.0 Hrs.) is to be set up. The product is 5-pocket jeans with a standard minute value (SMV) of 13.0 min. The average fabric inventory is maintained for 2 weeks (12 working days) before the start of bulk cutting. We need to calculate the area for different departments and processes to develop the layout.

12.2.2

Fabric store

Let’s assume that the average consumption per garment is 1.2 m. Further, an extra 3% quantity is produced to be considered to offset the wastage/rejections (the most common practice in apparel manufacturing is that buyers generally have an agreement with vendors to accept a deviation of
3% in the order quantity while shipping the goods). Hence, the quantity to be produced per day shall be 10,300 units consuming 12,360 m (10,300  1.2 m) of fabric. Considering an average 100-meter quantity in a fabric roll, the average consumption of fabric roles shall be 123.6 (w124) rolls/day. As the inventory is maintained for 12 working days, the fabric store should be able to store a quantity of 1488 rolls. To be safer, let us consider 1500 rolls in this example.

12.2.2.1 Fabric rack capacity calculation We must calculate the area required to store this fabric quantity of 1500 rolls. On average, a denim fabric (as required for this product) is 60 inches in width. Hence,

Apparel manufacturing measures and calculations

277

the fabric roll package length shall be 60 inches with an average diameter of 12 inches, excluding the central rod, which is generally 2e3 inches larger than the fabric width. Considering these dimensions as a reference for the fabric roll, the rack to keep the fabric may be designed. Assuming four rolls in a layer, the inner dimensions of a rack shall be 48 inches (4 feet). Similarly, assuming four such rows of fabric rolls are to be kept in a rack (refer to Fig. 12.1), the height of the rack may also be 48 inches (4 feet). The side angles of 3 inches width on each side and an additional 6 inches allowance for roll movement may be kept. Further, the base with 9 inches thickness and a 3 inches allowance on the vertical side to keep roll movement is kept. Hence, the final outer dimensions of a rack shall remain as 60 inches (5.0 feet in width) and 60 inches (5.0 feet in height). The depth of the rack can be as per the fabric roll package length, which is considered 66 inches (5.5 feet in depth) in this case. Assuming a rack can store 14e15 such rolls, there shall be approximately 100 racks required to store these 1500 fabric rolls. Finally, 2.54 square meters per rack shall be enough to store 15 rolls.

Figure 12.1 Fabric rolls in a storage rack. (Image Courtesy: XYX Metal Co. Ltd. China, https://xyxmetal.en.made-in-china.com/)

278

Textile Calculation

12.2.2.2 Area calculation for fabric storage Assuming an arrangement for fabric storage in the apparel manufacturing set-ups, there can be two racks (one over the other) utilizing the vertical space. This way, in the 2.54 square meter area, 30 rolls may be stored. For 1500 rolls, the area requirement shall be 127 square meters. Further, there shall be a requirement for passage and aisle (for fabric movement) and some free space for activities like fabric inspection and office space. For this purpose, an additional space (approximately 2.5 times the storage area) may be considered. This makes the total space requirement for the fabric store approximately 317 square meters. The layout of the fabrics store may be developed accordingly.

12.2.3

Spreading and cutting

Spreading and cutting are an integral part of apparel manufacturing. In the example being discussed here, the sewing capacity of 10,000 units per day is considered. The availability of cut panels is to be ensured for the sewing process. The cutting capacity is generally kept 10% higher than the sewing capacity to prevent the sewing lines from drying out (due to the unavailability of cut panels). Hence, we need to have the spreading and cutting department space with 11,000 units per day.

12.2.3.1 The calculation for spreading and cutting table dimensions 12.2.3.1.1

Spreading and cutting table length

Fabric required for 11,000 units: 13,200 m (fabric consumption per garment is 1.2 meters). Assumptions: The number of plies in a lay: 100 plies. Average way marker (number of garments in a layer or plie): 6-way marker. Average market length: 7.2 m. Space required for spreading head (in case of automatic/semiautomatic spreading) or keeping fabric roll (in case of manual spreading) at the starting end: 1.0 m. Space required to hold the fabric rolls and to keep weights, etc., at the other end: 0.80 cm. Total length required to spread one lay: 9.0 m. It is recommended that once lay is spread, the same should be transferred to another place using clamps. This practice saves time and increases workforce utilization. As it is easy to slide the lay rather than lift it, the spreading table can be extended to multiple spreading lengths. Hence, the table length may be kept as 18.0 m. In the industry, tables of 2.5e3.0 m are used, and based on the requirements, such tables are clubbed to achieve the desired spreading table length.

12.2.3.1.2

Spreading and cutting table width

The spreading and cutting table width is generally kept 1200 more than that of the fabric width. This additional width is required to keep tools and equipment (such as straight knife cutter, fabric weights, clams, etc.) required while spreading and cutting. In the example taken, fabric width for 5-pocket jeans is kept as 60 inches, hence the table width may be 72 inches.

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12.2.3.2 Requirement for the number of spreading and cutting tables The spreading and cutting capacity is discussed in detail in the next sections. Here, we need to consider some parameters (in the context of example taken for 5-pocket jeans) as follows: Spreading time per lay: approximately 2.0 Hrs. Cutting, and number, and bundling time per lay: approximately 0.5 Hrs. (with 4e5 cutters). Total time required for spreading and cutting a lay (approximately 600 garments): 2.5 Hrs. The working hours per shift are considered as 8.0 Hrs. There shall be spreading and cutting of three lays in a shift making cutting production as 1800 garments/shift. To achieve the cutting capacity of 11,000 garments (as taken in this example), there will be six such tables required. Keeping six tables may require a large area, hence this cutting capacity may be achieved by working in two shifts of each 8.0 Hrs.

12.2.3.3 Area calculation for spreading and cutting department Considering requirement of three spreading and cutting tables with dimensions as 18.0 m (length)  1.83 m (width). This makes the area requirement of a table as 32.94 square meters per table. For three tables, an area of 99e100 square meters shall be required. Further, additional space shall be required for purposes including passage and aisle to transport fabric rolls, temporary storage for fabric, area for storing ready cut panels, area for band knife machine, area for fusing machine, and office space. It is recommended to have at least 250% additional area (to the area consumed in the spreading and cutting tables). Hence, the spreading and cutting department area requirement shall be approximately 350 square meters in the example taken. Here, it is to be noted that the spreading and cutting department area requirement may vary with the type of product. Kids garments (which have smaller parts and need shorter cutting tables) may need a smaller spreading and cutting area. The large size products (such as home textile items) may require a larger space for spreading and cutting and other material handling; hence, the spreading and cutting area requirement for such products shall be relatively more.

12.2.4 Sewing Sewing is the heart of apparel manufacturing. The stitching process involves the maximum amount of human intervention, as well as the material movement. For the requirement of sewing machines, we need to have some considerations as follows: SMV for 5-pocket jeans: 13.0 min. Average factory efficiency: 65% Standard allowed min: 20.0 min (13.0 Minutes/0.65). Garments production per machine per shift: 24.0 garments/machine/shift. Number of machines required to produce 10,000 garments: 417 machines. Spare sewing machines (approximately 10% of the number of machines): 42. Total number of sewing machines required on the floor: 459 machines (460 machines as round off).

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12.2.4.1 Sewing workstation area calculation The most common dimensions of a basic sewing machine are 1.1 meter (length)  0.50 meter (width). Further, approximately the same amount of area is required for the sitting arrangement of the operator for this work station. This makes dimensions of a basic sewing machine workstation as 1.1 meters  1.0 meter (1.10 square meters). There shall be a requirement of additional space for various other purposes including placing center table (0.70 meter width), main passage (approximately 2.5 meters), aisles (minimum 1.5 meters width), space between the workstation and the yellow line of the aisle and passages (0.30 meter or 1 foot, enabling a person to stand or keeping a stool or trolley inside the yellow line if require), temporary storage area in the beginning of the lines, material loading area, material unloading area at the end of the lines, area for quality checks and inspections, etc. The area required for all these activities is generally 2.5 times of the basic sewing machine area. Hence, the total average area requirement for one workstation shall be 3.85 square meters (1.1 square meter þ 2.5  1.1 square meter). It is recommended to allocate a horizontal space of around 4 square meters including a free-floor area of minimum 2 square meters per person as recommended by Kanawaty [3] to a sewing workstation [4]. It is recommended that for stitching of the products which consume more space (for example, home textile products such as curtains, bed sheets, etc.), relatively larger area of 6e8 square meter should be allocated [5].

12.2.4.2 Sewing line dimensions’ calculation In this example of 5-pocket jeans, there is generally a layout of 48e50 sewing workstations in the assembly line set-up. Each line (with 48e50 machines) is capable of producing approximately 1200 garments per shift (at 13.0 min as SMV and working efficiency as 65%). To produce 10,000 garments, there shall be a requirement of such 8 sewing lines. The most common workstation arrangement practiced in the apparel manufacturing set-ups is with two parallel sewing workstations with a center table in between (refer to Fig. 12.2). The total width of the sewing line in such fashion shall be approximately 3.5 meters including the space between workstation and the yellow lines of the passages on both the sides (refer to Fig. 12.3). The details of this calculation are as follows: Width of the workstations: 2.2 meters (1.1 meters  2). Width of the center table: 0.70 meter. Additional space between workstation and the yellow lines: 0.6 meter (0.3 meter at each side). Total width of a sewing line: 3.5 meters. The length of a one workstation is approximately 1.0 m (0.5 m for sewing machine and 0.5 m for operator sitting arrangement). As the workstations are arranged in a parallel manner, there shall be total 25 workstations in the length wise set-up. This arrangement shall require a length of approximately 25 m. Hence, the final dimensions

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Figure 12.2 Sewing line dimensions. (Image courtesy: Apparel Resources Pvt. Ltd., India, https://apparelresources.com/businessnews/manufacturing/basics-of-machine-layout-in-sewing-line/)

Figure 12.3 Sewing line set-up with parallel workstations and center table. (Image courtesy: Apparel Resources Pvt. Ltd., India, https://apparelresources.com/businessnews/manufacturing/basics-of-machine-layout-in-sewing-line/)

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of the sewing line shall be approximately 3.5 m (width)  25 Meters (length). The area consumed by a sewing line shall be 87.5 square meters. Total area requirement for eight such sewing lines shall be 875 square meters. The additional area requirement for other activities (as indicated in the previous section) is generally double (2 times) of the sewing line area. Hence, the total area requirement for the sewing section shall be approximately 1750 square meter. This area requirement can be reconfirmed by using the logic as explained in the previous section, where the area requirement of single work station was 3.85 square meters. The total area requirement to accommodate 460 sewing workstations shall be approximately 1771 square meters. The outcome from both the logics is more or less same and in conformance to the area recommendation by the International Labour Organization (ILO).

12.2.5

Finishing and packing

Finishing and packing is the last step of the apparel manufacturing process. It involves handling of stitched garments. The garments are checked for measurements, uncut threads, size segregation, shade segregation, assortment (maybe based on size and/ or color), attaching different packing trims, quality check, poly-bagging, and finally packing of the finished garments. Most of the workstations in the finishing and packing section are standing workstations as there is relatively high human movement than other processes. Here also, we need to consider some basic assumptions to determine the area requirement. Standard time for finishing and packing may be taken as 2.0 min for the 5-pocket jeans. This makes on an average 240 garments to be packed per person in a shift of 8.0 h. A total of 42 workers shall be required to achieve the packing target of 10,000 garments per shift.

12.2.5.1 Finishing workstation dimensions There are several types of workstations in a finishing room; however, for calculation point of view, we may consider a slanted table of 3 feet as length and 2.5 feet as width. Assuming a space of 2 feet is required for standing and movement while working, the space required for one workstation shall be 13.5 square feet (3  4.5 feet) or 1.25 square meter.

12.2.5.2 Area requirement for finishing and packing section With one workstation needing 1.25 square meter area, the area requirement to work for 42 workers shall be 52.5 square meter. Here, it is to be noted that as per the specific process requirements, some activities may be done collectively (such as thread trimming, shade segregation, attaching packing trims, etc.) using a single large table. The finishing and packing sections require relatively larger space for keeping inventories (the sewn products as input and the finished goods as output). Apart from it, a sufficient space is required to keep prepared cartons (which consumes a significant space), designated area for final quality check, and the buyer QA inspections.

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Considering all these requirements, the finishing and packing section needs area around 6 to 7 times of the area of the workstations used in this section. Hence, to achieve the target of finish and pack 10,000 garments, the total area requirement shall be approximately 367.5 square meters (52.5 Square meter  7). This area requirement is in the specific context of 5-pocket jeans, and it may vary depending on the product and the volumes to handle.

12.2.6 Relationship between area requirement of different manufacturing processes In this example of 5-pocket jeans, the distribution of area requirement to produce 10,000 garments is as indicated in Table 12.1. The area distribution for different activities or processes may vary and can be adjusted as required. Based on the experience of several apparel manufacturing setups for different products, the area requirements can be roughly determined. The recommended percentage area distribution (accommodating the product-specific requirements) is indicated in Table 12.2. The values mentioned in the tables are just indicative and for reference only. At the time of plant set-up, one must consider the practical realities and constraints. Also, the factors such as product type, level of automation, type of material movement mechanism, type of manufacturing system (such as assembly line or modular or group system), inventory levels in different processes, and input and output patterns of material play a crucial role in determining the area requirements.

Table 12.1 Relationship of area requirement for different apparel manufacturing processes. Activity or process

Area

Percentage area share

Fabric stores Spreading and cutting Sewing Finishing and packing Total area

317 square meter 350 square meter 1771 square meter 367.5 square meter 2805.5 square meter

11.30% 12.48% 63.13% 13.10%

Table 12.2 Recommended Percentage Area Share for different apparel manufacturing processes. Activity or process

Recommended percentage area share

Fabric stores Spreading and cutting Sewing Finishing and packing

10%e15% 10%e15% 55%e65% 10%e15%

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12.3 12.3.1

Textile Calculation

Manufacturing operationserelated measures and calculations Fabric defects and defective panels

Fabric quality is generally evaluated by 4-point inspection system and popularly expressed as points per 100 square yards (PPHSY). The 4-point system assigns 1, 2, 3, and 4 penalty points according to the size, quality, and significance of the defect as indicated in Table 12.3. No more than four penalty points are assigned for any single flaw [6]. Upon the number and the size of the imperfections in the given yard, a maximum of four points can be given to one linear yard. Four points can be given for each linear yard when a defect is running continuously along the length of the fabric. So, the maximum point that can be assigned to any fabric is 400 PPHSY. Generally, there are no benchmarks for acceptable standards; however, less than 40 PPHSY is considered good fabric. In a contract manufacturing scenario (especially CM) where the garment manufacturer procures fabric from nominated fabric supplier, the buyer/ retailer/brand decides the benchmark PPHSY that can be accepted. After the fabric is spread and cut, the garment manufacturer replaces the defective panels with defect-free panels, cut from the end-bits of each roll. For example, a fabric roll of 120 m length and 45 inches width is inspected and the following defects are found as indicated in Table 12.4.

Table 12.3 Penalty points in 4-Point System. Defect size in inches

Defect size in millimeter

Points

From 0 > 300 length/width From 3.1” > 600 length/width From 6.1” > 900 length/width More than 900 length/width

Up to 75 mm 76 mm > 150 mm 151 mm > 230 mm More than 230 mm

1 point 2 points 3 points 4 points

Table 12.4 Assigning penalty using 4-Point System. No. of defects

Defect sizes

Points

5 3 1 2 Total defect points

6.0 inches 6.1 > 9.0 inches More than 900

5 defects  1 point ¼ 5 points 3 defects  2 points ¼ 6 points 1 defect  3 points ¼ 3 points 2 defects  4 points ¼ 8 points 22 points

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Total defect points per 100 square yards of fabric ¼ (Total defect points in the roll  36 inches per yard 100 yards) / (Fabric width in inches  fabric length in yards) ¼ (22  36  100) / (45  120) ¼ 14.66 defect points per 100 square yards Now the 120 m of roll has: • • •

Total numbers of defects ¼ 11 (sum of first column) Total defect points ¼ 22 (as per four-point inspection) PPHSY ¼ 14.66

After the fabric is spread and cut, the garment manufacturer replaces the defective panels with defect-free panels, cut from the end-bits of each roll. Suppose this fabric roll is spread in 12 layers of 10 m lay. Inspection is done to find out the defective cut panels after the cutting is over. The following are the theoretical possibilities: • • •

There are a total of 11 defects in the roll, so a maximum 11 cut panels should be defective, assuming one defect is restricted within one panel. The number of defective panels can be less than 11 if some defects will fall in the dead area of the marker or more than one defects appears in one panel The number of defective panels can be more than 11 if any single defect spreads across more than one panel (specially for the larger size of defects).

There also exists a practice of benchmark panel rejection %. Panel rejection % ¼ (number of panels rejected in a lay) / (number of panels per garment  number of garments in the marker  no of layers’ fabric) Suppose a lay of 100 layers is for a style that has 14 panels and the marker is having three garments (S-M-L). After the lay is cut, during panel inspection total 36 panels were found to be defective and need replacement. So, the panel rejection % ¼ 36/ (14  3  100) ¼ 0.8% When panel rejection exceeds 1% for fabric faults, usually the garment manufacturers claim for additional fabrics free of charge. However, panel size may contradict such practices if the benchmark is not factored style wise. For example, a lower panel rejection % in a trouser marker may be more damaging than higher panel rejection % in a brassiere marker.

12.3.2 Fabric requirement 12.3.2.1 Consumption calculation Fabric requirement for mass manufacturing can be defined as weighted average of (marker length þ wastage)  No. of plies. In order to increase fabric utilization, all three parameters, i.e., marker length, end loss, and plies for the overall order, need to be minimized. Two popular measures used in factories are marked consumption and lay consumption. While marked consumption only tells about the quality of

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markers and ignores their impact on the order, lay consumption is a practical and better indicator of overall consumption for the order as it takes into account the influence of all the markers over the order in terms of plies [7].

12.3.2.2 Marker efficiency Marker can be defined as the arrangement of all the pattern components of one or more sizes and/or styles in a given equivalent of fabric width. Fabric is generally traded in linear length of a given width; therefore, a fabric layer forms a rectangular shape while spreading. Therefore, when all the pattern components of one garment are arranged, the total area consumed by all the pattern components may not be exactly rectangular, resulting in wastage of fabric. The percentage of area covered by patterns as a ratio of the rectangular fabric area is called ’marker efficiency’ Manually, this can be calculated by weighing the cut components and equivalent fabric meterage; however, Computer-aided Design (CAD) marker mentions the marker efficiency % in every marker (refer to Fig. 12.4 for a schematic view of a marker generated by CAD showing marker efficiency of 93.45%). Total area of marker: This is simple multiplication of length  width. Marker efficiency ¼ (Area of Marker used by garments  100)/(Marker Length  Marker Width) Marked consumption of a style is calculated as per the markers made by the CAD department. The following steps have to be followed to calculate this metric: [a] Make cut order plan stating markers and no. of plies for each lay. [b] Make all the markers. [c] Calculate total length of fabric being used on the lays. [d] Divide this by total garments to be produced. [e] This value does not include wastages such as end loss or end bits. Marked consumption ¼ S Marker length/Total bodies marked

Figure 12.4 Schematic view of a marker generated by CAD. Image courtsey: Bennell, J. A., & Oliveira, J. F. (2008). The geometry of nesting problems: A tutorial. European Journal of Operational Research, 184(2), 397-415. https://doi.org/10.1016/j. ejor.2006.11.038

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Lay consumption is calculated exactly the same way as marked consumption by taking end loss also into account. The following steps have to be followed to calculate this metric: [a] Cut order plan is created stating markers and no of plies for each lay. [b] Make all markers. [c] Add end loss to the length of each marker. [d] Calculate total length of fabric being used in lay [e] Divide this by total garments to be produced Lay consumption ¼ S (Marker length  Plies)/Total pieces cut Example: An order ABC has the following quantity as indicated in Table 12.5. The cut plan of the above order was made as indicated in Table 12.6. Marked consumption ¼ 9.59/8 ¼ 1.198. Lay consumption ¼ 46.69/38 ¼ 1.223. The actual usage of fabric will happen based on lay consumption numbers. Therefore, this number should be used for calculation purposes for fabric requirement.

12.3.2.3 Wastage calculation In order to eliminate this fabric waste, it is essential to first identify the different types of wastes, secondly, segregate them into essential (unavoidable) and nonessential (avoidable), and then finally, develop ways to minimize or eliminate the wastes. The types of wastes are as follows: End Loss: It is an unavoidable loss and a function of the factory process. It is an allowance left at the ends of a ply to facilitate cutting. P End Loss Wastage ¼ [(Lay LengtheMarker Length)  Actual Number of Plies] Table 12.5 Size-wise order quantity distribution. Size

XS

S

M

L

XL

Total

Quantity

4

6

10

15

3

38

Table 12.6 Cut plan for an order.

Lay number

Plies

Lay 1 Lay 2 Lay 3 Lay 4 Lay 5 Total

10 5 1 3 1 20

XS

S

M 1

1

L 1 1

1 1 4

XL

1 1 6

10

15

3

Marker length (meter)

End loss (2 cm each side)

Marker length X plies

2.4 2.35 1.09 2.55 1.2 9.59

0.04 0.04 0.04 0.04 0.04

24.4 11.95 1.13 7.77 1.24 46.49

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Fabric Joint Loss: Fabric rolls are stitched together when undergoing manufacturing processes for the sake of uniformity. This results in fabric wastage of the areas having stitch holes or marks. This is fabric joint loss. It is an unavoidable loss for the factory. Edge Loss: The width of the marker is a few centimeters less than the edge-to-edge width of the fabric. It is an unavoidable loss and done to accommodate the selvedge of fabric. Splicing Overlap Loss: Splicing is a process of cutting fabric across its width and overlapping layers in between the two ends of a lay. Splicing process used for joining fabric roll ends in the middle of the marker either during defect rejection or between two rolls. This is an avoidable loss and a trade-off between higher end bits. Stickering loss: Several times, the patterns are cut a little extra tab outside the seam allowance. This area is used for ticketing and has to be cut off during sewing. This is the stickering loss. A superior marking technique can be used to combat this wastage.

12.3.2.4 Weighted efficiency While the marker efficiency is an important indicator for the quality of markers, to estimate the quality of markers across the order, weighted efficiency metric should be used. This tells us the efficiency of the markers over the whole order weighed according to its number of plies. P Weighted efficiency ¼ (Plies  Marker Efficiency)/ Total plies The marker efficiency for the ABC order can be calculated accordingly, as indicated in Table 12.7. The average marked efficiency ¼ 77.308% The weighted efficiency ¼ 1564.7/20 ¼ 78.235%

12.3.2.5 Material productivity This is an indicator of the output or value generated per unit of material used. This is a fundamental reexamination of how, when, and why materials are used. This measure shows how effectively material is used throughout the system. Any material left in the Table 12.7 Marker efficiency for an order. Lay number

Plies

Lay 1 Lay 2 Lay 3 Lay 4 Lay 5 Total

10 5 1 3 1 20

XS

S

M 1

1

L 1 1

1 1 4

XL

1 1 6

10

15

3

Marked efficiency

Marker efficiency X plies

79.28 76.91 76.05 78.5 75.8 77.308

792.8 384.55 76.05 235.5 75.8 1564.7

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fabric store is also a waste as it will be disposed of at a much cheaper rate. This is not a very common metric in the garment industry but has been extensively used in the textile industry. Material Productivity ¼ [Output (value or unit or value added)]/(Value of material used)

12.3.2.6 Fabric utilization (by weight and by length) This is the ratio of fabric used on garments to fabric available to be used. This metric tells us the fabric utilization status of the entire order. Fabric utilization ¼ (Fabric Used in Garments)/(Total Fabric Available) Total fabric available ¼ Fabric allocated or bought for the order; fabric used on garment ¼ This can be calculated in the following ways. By weight: Weigh one garment of each size (garment should be weighed before sewing). Multiply weight with a number of garments cut in each size. Divide total weight by Grams per Square Meter (GSM) and fabric width to get total meters used in garments. By length: multiple marker length with its marker efficiency and number of plies laid in the marker. The above calculation is done for each marker in the order and then the sum of all gives the total meters used in garments. The above will give fabric utilization for the order. The formula can be extended to calculate overall fabric utilization for the factory in a month. Fabric Utilization % ¼ (Fabric used in Garments  100) Actual Fabric Received

12.3.3 Capacity calculations and cycle time Although commonly capacity of any department is expressed as a number of garments per hour or per day, technically this expression is incomplete and is misleading. Capacity of any resource should be expressed in human minutes per hour or any similar unit. A cutting room activity basically consists of fabric checking, spreading, cutting, bundling and ticketing, fusing, and embroidery, if any. While calculating capacity, two things need to be checked: whether activities are parallel (simultaneous) or sequential. In case of sequential activities, the bottleneck activities will determine the whole department capacity. The capacity of parallel activities can be independently calculated and will not influence the departmental capacity unless the capacity of parallel activity is lesser than the lowest capacity of any sequential activity. The activities in presewing include fabric inspection, spreading, cutting, ticketing and bundling, and fusing, to name a few. As most of these activities are humandriven, the capacity will depend on a number of human beings available to run the

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machine. The cycle time of operations is generally calculated per unit although presewing activities convert the material from a unit measurement of meter (for woven fabric) or kg (for knitted fabric) to number of cut pieces. As the standard unit of product in apparel manufacturing is a piece of a garment, the cycle time will be calculated for processing material equivalent per unit garment.

12.3.3.1 Fabric inspection Fabric Inspection cycle time per garment ¼ (1/Fabric inspection speed in linear meter per minute)  (Average consumption in meter per garment) Let us say the manual fabric inspection speed in 15 linear meter per minute and average consumption for the style is 2.15 m, then the fabric inspection cycle time per garment ¼ (1/15)  2.14 min ¼ 0.14 min. If in a factory there are five human beings available to do the fabric inspection, then fabric inspection capacity is 5  60 ¼ 300 human-minutes per hour; therefore, approximately 2142 (300/0.14) garment equivalent fabric can be inspected per hour.

12.3.3.2 Fabric spreading Spreading cycle time per garment ¼ (Spreading time per meter)  (marker length in meter)/(Number of garments per marker) Let us say the factory has a total of four spreading operators each, who as a team of two spreaders can spread fabric at 5 m per minute. Capacity for the factory is 2  60 ¼ 120 min per hour or 600 m of fabric per hour (5 m per min  2 teams  60 min per hour ¼ 600) per shift. The average consumption for the style is 2.15 m and a three-garment marker length is 6.45 m. Spreading cycle time per garment ¼ [(1/5)  (6.45)]/3 ¼ 0.43 min. The output can be calculated by dividing the capacity (i.e. 120 min per hour) by the cycle time (i.e. 0.43 min), the output ¼ (120/0.43) ¼ 279.06 pieces per hour. Similarly, the garment output rate can be calculated by dividing the fabric output rate (i.e. 600 m of fabric per hour) by average consumption (i.e., 2.15 m), garment output ¼ (600/ 2.15) ¼ 279.06 pieces per hour.

12.3.3.3 Fabric cutting Cutting time depends on marker length and number of pattern components in the marker; a number of layers have negligible influence on cutting time. Again, cutting capacity is 60 min per hour per CAM. Suppose a typical 5 m marker cutting time is 15 min by CAM, then cutting capacity will be 4 markers (60/15 ¼ 4) per hour, i.e., Four lays per hour. If there are 50 layers spread and cut per lay and four garments per marker, then (4  50  4 ¼ 800) 800 garments per hour can be cut.

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Cutting cycle time per garment ¼ (Cutting time per marker in minutes)/(Number of garments per marker  number of layers per lay) Therefore, cutting cycle time per garment ¼ (15)/(4  50) ¼ 0.075 min.

12.3.3.4 Ticketing and bundling Ticketing of cut components is done to avoid mix up of panels of different layers during assembling resulting in possible shade variation between panels of same garment. Bundling of panels is done after ticketing; bundling makes counting and transfer of WIP (work in process) between sewing workstation easy. Ticketing and bundling cycle time may be calculated as under: Ticketing cycle time per garment ¼ (Time of ticketing one ply)  (Number of components in the garment) ¼ (1/ plies per minute)  (No. of components in the garment) Bundling cycle time per garment ¼ (1/Bundles per minute)  (1/Number of plies/pieces per bundle)  (Number of components in the garment)

12.3.3.5 Fusing In a continuous fusing machine, capacity of fusing is expressed in square meter per minute and mainly depends on working width of belt and speed of belt. If belt speed is 5 m per minute and working width of belt is 600 mm, then fusing capacity of that machine is 3.0 square meter per minute (0.6  5 ¼ 3.0). Suppose collar and cuff of a shirt requires to be fused and total area of collar and cuff pattern components is 0.20 square meter, it may be noted that 100% belt area of continuous fusing machine cannot be utilized when parts are loaded by human operator in a moving belt. Assuming 33% area utilization (i.e., 1.0 square meter per minute), collar and cuffs of five shirts (1.0/0.2 ¼ 5) can be fused per minute. It has been observed that belt area utilization in best case scenario ranges between 20% and 35% only.

12.3.4 Sewing production Sewing production is the term used for the core manufacturing activities where raw materials (such as cut panels, sewing trims, etc.) are joined together to form a semifinished or finished garment. In the industrial apparel manufacturing, sewing production is referred to the stitching department where assembly of parts or panels takes place. Sewing department is unarguably the most important department as it involves a high level of human intervention, maximum number of machines, and of course the most complex process that is stitching the garments. Due to such a high importance of sewing production, parameters such as factory capacity and factory efficiency are also communicated in the context of sewing process only. Further, as this is the place where the actual conversion of fabric into garments takes place, a key focus in apparel

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manufacturing remains on the sewing department only. There are several parameters and calculations that are involved in sewing, and some important parameters shall be discussed in this section.

12.3.4.1 Capacity The capacity of a production unit or sewing section is generally referred to the number of garments produced in a given time (maybe as in hours, shifts, or in months). However, this is not a rational way of communicating capacity, as the work content of the products is not the same; hence, the production output (with keeping input resources as constant) may vary depending on the complexity of the product. This can be understood with below example: Assuming the sewing output of an apparel manufacturing unit “A” is 5000 trousers per day and the output of an another manufacturing set-up “B” is 6000 shirts per day. With this information, it cannot be said that which setup has higher sewing capacity. Work content of the product is required to determine the capacity. The logical way to communicate the capacity is based on the number of minutes available. Each of the sewing operator has 60 min available in 1 hour to work on the sewing machine. This can also be considered as the available capacity per hour is 60 min. For example, there are 50 machines in a set-up and work is done in a shift of 8 hours. In this case, total 24,000 (50  8  60) minutes will be available to work, and this shall be the capacity of the plant. Now, based on the work content of the product, the output from the same machines in a given time may vary. If the garment is complex (more work content), the output in a given time from a same number of machines may be lesser compared to the output of relatively simple (less work content) product. There are several other factors affecting the capacity of a plant. Such factors should be taken into consideration while determining the actual or realistic capacity. Such factors may include average operator efficiency, absenteeism, utilization, etc. If the average efficiency, absenteeism, and utilization of operators are 85%, 10%, and 90%, respectively, the actual capacity of the plant would be 16,524 (24,000  85%  90%  90%) minutes per day.

12.3.4.2 Production The term production is referred primarily in two contexts. Production may be considered as a manufacturing process as well as an output of a process. Here we shall refer to production in the context of output of a process where it indicates the quantum. For example, 5000 shirts produced in a shift of 8.0 Hours. As the production is just a number, it has some limitations as it does not indicate the input resources (such as man, machine, material, space, etc.) consumed to achieve this output.

12.3.4.3 Productivity Productivity may be treated as an extension of the production, where production is just a mathematical value; productivity provides insights about the input resources utilized

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to achieve production. Productivity is referred to as a ratio of output to input. Bheda (2003) discusses types of productivity as partial productivity and overall productivity. Partial productivity can have different measures such as manpower or labor productivity (output per worker), Machine productivity (output per machine), material productivity (output per unit material), etc. The output may be considered in terms of value (like revenue generated) as well, the productivity may be measured as output (in value terms) per worker or machine or material, etc. This kind of productivity is classified as partial productivity. Further, both output and input may be treated in value terms, and such a ratio of output and input shall indicate how much value is created by investing per unit value [8]. Assuming an output of 1000 shirts per shift is achieved with 100 machines and 120 workers. The value of one shirt is USD 10, while the cost of inputs is USD 8. Here, the machine productivity shall be 10 shirts/machine (1000 shirts/100 machines), manpower productivity shall be 8.33 shirts/worker (1000 Shirts/120 machines). Overall productivity (in terms of value productivity) shall be 1.25 USD per USD. Means average 1.25 USD revenue is created on investment of 1 USD as input cost.

12.3.4.4 Efficiency Efficiency is one of the most common measures of effectiveness of a process or department or workforce (generally for a group of workers). It is an important measure used for determining the actual capacity of a facility. Efficiency is the ratio of standard minutes earned against the attended time as: Efficiency ¼ (Standard minutes earned on-standard/attended time)  100 Efficient values are expressed in percentage (%) terms, hence it does not have any unit of measurement. Assuming in a factory with 100 machines, the standard time to produce a garment is 10 min, and the output per shift (8.0 Hours) is 4000 garments. Here 8.0 h is considered as attended time, when the operators are supports to work in the factory. The break times during the work (such as lunch break, tea breaks, etc.) are not included in this. As during breaks, the operators are not supposed to work. The total standard minutes earned may be determined by multiplying the output to the standard time of a garment, that is 40,000 min. The attended time shall be 48,000 min (100 machines  480 min). The efficiency of the plant shall be 83.33%.

12.3.4.5 Performance The attended time has two components as on-standard time and off-standard time. Onstandard time is the time operator spends on productive work (to do such work the operator possesses necessary skills) for which the performance of an operator is measured. The off-standard work is for which the standard time is not allocated, and it is not counted in calculating the performance. The time spent in off-standard activities are hurdles to achieve higher productivity and efficiency. Such activities may

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include waiting time, machine breakdowns, quality issues, reworks and rejects, power failures, work imbalance in the lines, etc. Attended time ¼ On-Standard time þ Off-Standard time Unlike the efficiency that is a group measure, the performance is generally calculated for individual operators. Many a times, the time spent on off-standard activities is beyond the control of the operators. Despite being available to work on-standard, the operator is unable to produce any output in such situations; hence, his/her efficiency is affected. Hence, the performance is calculated as a ratio of standard minutes produced on-standard and the on-standard attended time. Efficiency ¼ (Standard minutes earned on-standard/on-standard attended time)  100 Let us assume an operator has produced 30 garments (standard time as 10 min per garment) in 8.0 hours against the target of 48 garments. A power failure for 30 min and an unplanned machine breakdown for 1.0 h were reported. In such case, the offstandard time shall be 90 min. The performance of the operator may be calculated as follows: Standard minutes earned on-standard ¼ 300 min (30 garments  10 min) Attended time on-standard

¼ 390 min (480e90 min)

Performance

¼ 76.92% (300 min/390 min)

12.3.4.6 Utilization Logically, utilization is same as efficiency, as both the measures are ratio of onstandard time to the attended time. Utilization ¼ (Standard minutes earned on-standard/attended time)  100 However, both the terms are used in different contexts. Utilization is generally referred in the context of management to see how well the operations or processes are being done. This is possible when we take out the best from the available resources or how well we are utilizing the available resources. Utilization is referred to the time spent on productive time (on-standard time) out of total attended time. It is usually calculated for a line (or a production section or production floor) as it is a measure of how well the supervisor is running the operations.

12.3.4.7 SAM and SMV SAM (Standard Allowed Minute) and SMV are interchangeably used terms in the apparel manufacturing. There is no clear difference recorded so far, and most of the

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experts have mixed opinions on whether these two terms are the same or not. The authors are in the opinion (which is also the most acceptable among the apparel industry in Asian countries) that SMV is the time value derived from PMTS (Predetermined Motion and Time Systems) at a standard performance. The SAM is generally determined based on the shop-floor time study based observations. In such cases, the time is normalized by incorporating the operator rating into the observed time. Further, necessary allowances such as personal, fatigue and delay, and contingency allowances are added [4]. Cycle time is the time required to complete the task (may be a part of a single piece involving multiple operations). Cycle time of an operation may be determined by observing the time required to complete the operation. The cycle time depends on the work content of the operation of the activity, and the same may vary based on the complexity involved in the task. For example, in a T-shirt with standard time as 10 min shall be having multiple operations as shoulder attaching, sleeve attaching, side seaming, bottom hemming, etc., and each of the operation may have different cycle times. In most of the cases, while line balancing, the cycle time works as a base to determine the hourly output and daily output targets. Further, the requirements of workstations and operators to meet the production targets are calculated accordingly. Determination of standard time from the cycle time may be done as follows: Observed time (OT) ¼ Sum of the Cycle times as observed in the time study/ number of cycles observed Basic time (BT) ¼ Observed time (OT)  Rating of the Operator Standard time (ST) ¼ Basic time (BT) þ Personal, Fatigue and Delay Allowances Assuming observed time (average cycle time) for an operation is 0.75 min and the operator rating is 80%. The various allowances to be considered are 15%. The standard time can be calculated as follows: Basic time

¼ 0.75  (80/100) ¼ 0.6 minutes (or 36 seconds)

Standard time ¼ 0.6 þ 0.6  (15/100) ¼ 0.6  (1.15) ¼ 0.69 minutes (or 41.4 seconds)

12.3.4.8 Lead time Lead time is referred to the time required to complete a process or a series of processes. It is essential to know the starting point and the endpoint of a process to determine the lead time. For example, where we refer to the production lead time, it may be in the context of the sewing process, where the start point may be loading of the pieces on the very first sewing workstation. The production lead time may be in the context of the entire apparel manufacturing process as well, when the start point may be initiation of the bulk cutting in the spreading and cutting room.

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Textile Calculation

12.3.4.9 Throughput time Throughput time in sewing is referred to the elapse time between the material (cut panels) loaded on the very first sewing workstation and the exit time from the last sewing workstation. Throughput is a rate at which the goods are produced, and it may be expressed as a number of goods produced per unit time. The throughput time of a product depends on the WIP (work-in-process) or inventory and the material flow time [9]. The same can be understood with the Little’s law, as: Inventory ¼ Throughput  Material Flow time According to Little’s law, at every WIP level, WIP is equal to the product of throughput and cycle time [10]. The same may be expressed as WIP ¼ Throughput  Cycle Time Assuming the cycle time of a process is 5 min, and throughput is 1 piece in every 5 min, then WIP in the process shall be 1. With increase of WIP, the throughput shall be reduced. The throughput time for a garment in a sewing line may be calculated as follows: Throughput time ¼ Standard time of the garment [1 þ (average WIP between each sewing operation)] Assuming the standard time of a garment is 10 min and the manufacturing system used is unit production system with an average WIP of 10 garments before each operation. Then the throughput time for one garment shall be 110 min (10  (10 þ 1)). Here it is important to note that, if the same garment is produced using progressive bundle system with only one bundle (of 10 pieces) before each operation, the throughput time should not be calculated on the standard time of 10 min. In such cases, throughput time should be determined based on the critical path in the process.

12.3.4.10 Pitch time Pitch time is an average time consumed or spent by an individual operator on the product. The pitch time has significance in balancing the manufacturing processes and helps in improving the manpower utilization by an efficient work allocation. Assuming the standard time of a garment is 12 min, it involves eight operators (sewing and nonsewing) to meet the production target. Here, the pitch time can be referred as average 1.5 min work-content should be contributed by an individual operator. The cycle time of a process may vary depending on the work content of the operation; it may result into requirement of a varied number of workstations to meet the production targets. In such cases, there may be instances when the required number of the machines or the operators are in decimals, i.e., 3.67 machines to meet the target. Here, pitch timeebased balancing helps. In such cases, the clubbing and splitting of operations may be done to bring the cycle time equal or near to the pitch time (1.5 min in this case). The cycle time of individual operations may also be in the multiples of the pitch time to achieve an effective and efficient line balance.

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12.3.4.11 Takt time The term takt has its roots in German, where it is referred to as the rhythm or beats of a drum. In the context of manufacturing, Takt indicates the rate of output from the last workstation. This term is popularly used in the lean manufacturing based production facilities. In the recent years, many of the apparel manufacturing set-ups have started using process balancing based on takt time. The processes are arranged to meet the demand rate (Takt rate) to meet the delivery deadlines. Assuming there is an order of 10,000 garments to be completed in 25 days, and the production facility is working for 8.0 h shift per day, to meet the delivery deadline, on an average 400 garments to be produced per day, the takt time may be calculated as: Demand rate per day: 400 garments per shift (8.0 h) or 50 garments per hour or 0.833 garments per minute. This can also be treated as the output of one garment after every 1.2 min. Hence, the takt time in this example shall be 1.2 min and the manufacturing processes shall be balanced accordingly to meet this rate of output.

12.3.4.12 Factory minute-cost calculation Factory minute-cost or cost per machine-minute is an important term in the apparel manufacturing operations. This works as a base to determine the manufacturing cost of a product and quoting the price of the garment to the buyers. According to Ref. [11], the factory minute cost is determined by calculating the total running cost or operational cost incurred by the factory (in a unit time), and dividing the same with the total number of sewing machines [11]. Here, the cost of capital expenses and material costs are not considered in the operational cost of the factory. The logic of considering sewing machine to calculate the factory minute-cost is that the actual conversion of raw material into the garment takes place in the sewing department only. Hence, a sewing machine may be treated as a source of production of goods which eventually earns the revenue to the organization. The factory minute-cost calculation is explained with an example as below: Assuming an apparel manufacturing set-up has 100 sewing machines. The factory is working for one shift (8.0 h) per day with 25 working days per month. The total operational cost of the factory per month is USD 50,000. Factory Machine-Cost per Shift ¼ (Total Operational cost per month)/(working days per month  number of sewing machines) Factory machine-cost per shift ¼ USD 50,000 /(25  100) ¼ USD 20 Factory machine-cost per hour ¼ (Total Operational cost per month) / (working days per month  number of sewing machines  hours per shift) Factory machine-cost per hour ¼ USD 50,000 /(25  100  8) ¼ USD 2.5 Factory machine-cost per minute ¼ (Total running cost per month)/(working days per month  number of sewing machines  hours per shift  minutes per hour)

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Textile Calculation

Factory machine-cost per minute ¼ USD 50,000 /(25  100  8  60) ¼ USD 0.04167 Suppose the factory company is manufacturing a 5-pocket jean with standard time as 20 min. The manufacturing cost of a 5-pocket jean shall be USD 0.833 (factory minute-cost per Machine  Standard time of the product). If the factory wants to work at a profit of 20%, then the quoted CM price (cut-make price) to the buyer for a 5-pocket jean shall be USD 1.00. If the standard time of a particular operation in this garment is 1.5 min, then this operation shall cost USD 0.0625 (factory minute-cost per Machine  standard time of the operation). With this standard time of 1.5 min of the given operation, the hourly Target at 100% shall be 40 Pcs./Hour. In such case, the operator should get USD 2.5 per hour on achieving the target in all aspects.

12.4

Conclusion

Numbers, measures, and calculations play a vital role in apparel manufacturing. It is essential to have the correct calculations while manufacturing plant and facility setup as well as during the routine manufacturing operation. There have been several calculations involved which help in determining the right requirement of infrastructure and resources; however only a few important ones have been discussed in this chapter, as the scope of this chapter has been restricted to the manufacturing operations only. There may be some other measures and calculations related to the processes including merchandizing, product development or sampling, production planning and control, quality management, dry process, washing, and final shipments.

References [1] TIBCO, What Are Measures? TIBCO Software Inc., August 22, 2018. Retrieved November 2021, from TIBCO: https://docs.tibco.com/pub/sfire-analyst/7.14.0/doc/html/ en-US/TIB_sfire-analyst_CubesInSpotfire/GUID-0ACFC7FF-9EB6-43F7-9A88225134369AE0.html. [2] Merriam-Webster, Measure, Merriam-Webster, Inc., April 5, 2022. Retrieved April 2022, from Merriam-Webster: https://www.merriam-webster.com/dictionary/measure. [3] G. Kanawaty, Introduction to Work Study, International Labour Office, Geneva, Switzerland, 1992. [4] P. Jana, M. Tiwari, Industrial Engineering in Apparel Manufacturing, Apparel Resources Pvt. Ltd, New Delhi, India, 2018. [5] J.C. Hiba, Improving Working Conditions and Productivity in the Garment Industry: Practical Ideasfor Owners and Managers of Small and Medium-Sized Enterprises, International Labour Office, Geneva, Switzerland, 1998. [6] N. Hassan, P. Jana, Fabric Defects, 4-Point Inspection and Defective Panels: The Unsolved Puzzle. Apparel Resources, January 22, 2022, p. 1. Retrieved June 10, 2022, from, https:// in.apparelresources.com/business-news/manufacturing/fabric-defects-4-point-inspectiondefective-panels-unsolved-puzzle/.

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[7] M. Ambastha, P. Jana, Cut oder planning, in: P. Jana (Ed.), Cutting Room Management in Apparel Manufacturing, Apparel Resources Publishing, New Delhi, 2020, p. 52. [8] R. Bheda, Managing Productivity in Apparel Industry, CBS Publishers and Distributors, New Delhi, New Delhi, India, 2006. [9] P. Jana, M. Tiwari, Lean terms in apparel manufacturing, in: P. Jana, M. Tiwari, P. Jana, M. Tiwari (Eds.), Lean Tools in Apparel Manufacturing, Elsevier Ltd, Cambridge, Massachusetts, United States of America, 2021. [10] W.J. Hopp, M.L. Spearman, Basic factory dynamics, in: W.J. Hopp, M.L. Spearman (Eds.), Factory Physics, Waveland Press, Inc, Long Grove, Illinois, United States of America, 2008. [11] P. Jana, Y.P. Garg, Cost of Manufacturing: Are We Still Competitive? StitchWorld, June 1, 2007.

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Fiber testing 1

2

2

13

Madan Lal Regar , Chet Ram Meena and Janmay Singh Hada 1 Department of Fashion Design, National Institute of Fashion Technology Jodhpur, Jodhpur, Rajasthan, India; 2Department of Textile Design, National Institute of Fashion Technology Jodhpur, Ministry of Textiles, Govt. of India, Jodhpur, Rajasthan, India

13.1

Introduction

Textile fibers are long and fine, and categorized as either natural or manufactured (regenerated and synthetic). Natural fibers are obtained from plants, animals and minerals in nature. Man-made fibers are manufactured from petro chemicals, wood pulp and do not exist in fiber form, initially.

13.2

Standard conditions for yarn testing

Textile fibers can be either hydrophilic or hydrophobic. The properties of hydrophilic fibres change with absorption of moisture. Presence of moisture is particularly critical with respect to its processability and properties viz; tensile, thermal and electrical. Therefore, prior to testing, conditioning must be carried out under constant standard atmospheric condition. The standard atmosphere for textile testing is: temperature of 20
2 C, and relative humidity of 65
2%. In tropical regions, maintaining a temperature of 27
2 C, 65
2% RH is appropriate. Prior to testing, the samples must be conditioned for 24 h under standard atmospheric condition[1,2].

13.3

Statistical averages

The measures of central tendency, the three most important ones, are the arithmetic average or mean, median, and mode.

13.3.1 Mean The mean (also known as average) is obtained by dividing the sum of observed values by the number of observations, n. Mean ¼

Sum of number ðX1 þ X2 þ X3 þ X4 .... þ Xn Þ Number of observation ðnÞ

Textile Calculation. https://doi.org/10.1016/B978-0-323-99041-7.00013-8 Copyright © 2023 Elsevier Ltd. All rights reserved.

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X¼

Pi¼n

i¼1 Xi

n

Mean deviation is the distance between each value and the mean. Mean deviation ¼

Mod of Sum of the deviation from the mean Total number of observations ðnÞ P

Mean Deviation ¼

jxi  xj n

Percentage mean deviation ðPMDÞ ¼

13.3.2

Mean deviation  100 Mean

Median

The median is the middle value of a set of data containing an odd number of values, or the average of the two middle values of a set of data with an even number of values. The median is especially helpful when separating data into two equal sized parts.

13.3.3

Mode

The mode of a set of data is the value which occurs most frequently.

13.3.4

Standard deviation

The standard deviation gives an idea of how close the entire set of data is to the average value. Data sets with a small standard deviation have tightly grouped, precise data. Data sets with large standard deviations have data spread out over a wide range of values. To measure dispersion, variance and its square root i.e. the standard deviation-are the most often used. The standard deviation of a sample data can be calculated using following formula: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u i¼n  u1 X  2 s¼t Xi  X n i¼1

where; Xi are values of any parameter



and X is its mean and n ¼ number of observations: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u i¼n  u 1 X 2 s¼t Xi  X n  1 i¼1

13.3.5

Variance and coefficient of variation

Variance is the square of the standard deviation. The variance measures the distance of each number is in the set from the mean.

Fiber testing

303 iP ¼n 

Sample variance ¼

i¼1

  2 Xi  X

n1

The denominator should be n for the population data and n1 is for sample. The coefficient of variation is used when one needs to comapre between differnt data set varying in units or mean. It is expressed in percentage. The formula for Coefficient of variation (CV%) is given below: Coefficient of variation ¼

Standard deviation s  100 ¼  100 x Mean

Standard error of mean is a measure of reliability of the mean obtained from sample data. It is standard deviations of means obtained by drawing repeated sample of same size from a population. The standard error of mean is : s Standrad error of mean ¼ pffiffiffi n

13.3.6 Sample size Sample size is the number of observations or replicates to be included in a statistical sample. The sample size depends upon [3]: • • •

The level of precision required by users The confidence level desired Degree of variability

Assuming the sample is from a normally distributed population, the following formula can be used to calculate the sample size: Sample size ðnÞ ¼

  Uf s 2 E

where Uf ¼ 1.96 for confidence limit 95% Uf ¼ 2.58 for confidence limit 99% s ¼ Standard deviation of the population E ¼ Tolerance. Example 13.1. The 95% confidence limit of average fiber strength (cN/tex) based on 50 test is 10
1.0. Determine the required sample size to obtain the 99% confidence limit of 10
0.2.

The known sample size n1 ¼ 50, Uf ¼ 2:58, E for known sample size is 1 and for unknown sample size E is 0.2.

Solution.

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Since, Sample size ðnÞ ¼

  Uf s 2 E 

Substituing known values we get; 50 ¼

 2:58 s 2 1

pffiffiffiffiffi 1  50 Therefore; s ¼ 2:58 For unknown sample size 0 B n¼B @

2:58

pffiffiffiffiffi 12  1  50 C 2:58 C A 0:2

Unknown sample size ðnÞ ¼ 1250 The required sample size (n) is 1250. Example 13.2. If 95% confidence range of the mean based on 36 test sample is
5, determine the required number of test samples to obtain 95% confidence range of
3.

The known sample size n1 ¼ 36, Uf ¼ 1:96, E for known sample size is 5 and for unknown sample size is 3. For known sample size:

Solution.

Sample size ðnÞ ¼  36 ¼

1:96 s 5

  Uf s 2 E

2

pffiffiffiffiffi 5  36 ¼ 15:31 s¼ 1:96 For unknown sample size Unknown sample sizeðnÞ ¼

  1:96  15:31 2 3

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Unknown sample sizeðnÞ ¼ 100 The required sample size is 100.

13.4

Humidity

Humidity is the amount of water vapor present in the air. Water vapor is the gaseous state of water and is invisible. Humidity indicates the likelihood of precipitation, dew, or fog. Higher humidity reduces the effectiveness of sweating in cooling the body by reducing the rate of evaporation of moisture from the skin [4,5]. Humidity can be classified into the following: • •

Absolute humidity: Absolute humidity is the water content of the mixture of water vapour and other elements found in the air. Relative humidity: Relative humidity is the percentage of water vapour in the air at a given temperature.

RH ð%Þ ¼

Mass of water vapour in given volume of air  100 Mass of water vapour required to saturate

RH ð%Þ ¼

Actual vapour pressure  100 Saturated vapour pressure

13.4.1 Wet and dry bulb thermometer The dry bulb, wet bulb and dew point temperature are important to determine the state of humid air. Wet and dry bulb thermometer consist of two thermometers used in industry to measure the relative humidity, one that is kept moist with distilled water on a sock or wick. •

•

Dry-bulb temperature: The dry-bulb temperature is the temperature indicated by a thermometer exposed to the air in a placed sheltered from direct solar radiation. The term dry-bulb is customarily added to the temperature to distinguish it from wet-bulb and dew-point temperature. Wet-bulb temperature: The thermodynamic wet-bulb is a thermodynamic property of mixture of air and water vapor. The value indicated by a wet-bulb thermometer often provides an adequate approximation of the thermo-dynamic wet-bulb temperature (Table 13.1).

RH ð%Þ ¼ 98:2 

Dry o F  Wet o F  300 Dry o F

Moisture regain ð%Þ ¼

Weight of moisture ðwaterÞ  100 Oven dry weight of specimen

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Table 13.1 Standard moisture regain for natural and man-made fiber at standard atmosphere [1,2]. Fiber type

Regain (%)

Acetate Acrylic Nylon 6, 6 and 6 Polyester Polypropylene Triacetate Viscose rayon

6.5 1.5 4.5 0.4 0.04 3.5 11e12

Cotton Linen Silk Wool

8.5 12 11 16e18

Man-made fibers 1 2 3 4 5 6 7

Natural fibers 1 2 4 5

Moisture content ð%Þ ¼

Weight of moisture ðwaterÞ  100 Total weight of specimen

Calculate the relative humidity, if the dry bulb temperature is 86 F and wet bulb temperature is 75 F, respectively.

Example 13.3.

Dry bulb temperature: 86 F; Wet bulb temperature: 75 F

Solution.

Relative humdity ¼ 98:2 

86  75  300 86

Relative humdity ¼ 59.8% Calculate the moisture content and moisture regain of 70/30 (cotton/ viscose blend) yarn. (Consider the standard moisture regain for cotton to be 8.5% and moisture regain for viscose 11%)

Example 13.4.

As per standard formula for the moisture regain, the following can be used to calculate the moisture regain (MR) for blended composition:

Solution.

Moisture regain ð%Þ blend ¼

MRð AÞ  Fibre compositionð AÞ þ MRðBÞ  Fibre compositionðBÞ Fibre compositionð AÞ þ Fibre compositionðBÞ

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Moisture regain ð%Þfor blend ¼

8:5  70 þ 11  30 70 þ 30

Moisture regain ð%Þfor blend ¼

925 ¼ 9:25 % 100

The moisture regain of cotton viscose blend is 9.25%; further the moisture content of same yarn can be calculated by following formula: Moisture content ð%Þ for blend ¼

MR MR 1þ 100

Moisture content ð%Þ for blend ¼

9:25 9:25 1þ 100

Moisture content ð%Þ for blend ¼ 8:47 % The moisture content of cotton viscose blend is 8.47%. Example 13.5. An unknown fiber sample weighing 80 gm at standard condition and oven dry weight is 76.9 gm. Calculate the moisture regain and identify the unknown fiber. Solution.

Moisture regain ¼

80  76:9  100 76:9

Moisture regain ¼ 4:03 As per standard condition, nylon is having 4.0% moisture regain so the unknown fiber is nylon.

13.5

Fiber length

Fibre length is one of the important properties of a fibre. For cotton, the Baer sorter method is used where fibers are arranged in the form of the array in descending order of length. A tracing of this array is taken for determing, mean length, % of short fibers and dispersion etc.

13.5.1 Baer sorter The pattern of fiber array is drawn on transparent scale, with 1/8 inch lines placed over the pattern. The drawn pattern is known as “sorter diagram”. The diagram is used to

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Textile Calculation

Figure 13.1 Cotton fibre bear sorter diagram. OA¼ maximum fibre length, LL ¼ effective length.

find out the effective length, mean length, % of short fibers and dispersion of fibres (Fig. 13.1).

13.5.2

Fibrograph

It is an optical instrument which scans a randomly aligned tufts of the fibers (beard) simulating fibre arrangement during yarn production process and the light intensity that passes through the beard is used to produce a diagram as shown in Fig. 13.2 called Fibrogram. The X axis indicates length and the Y axis % of fibres. Various legth parameters are calculated based on this diagram. In the fibrogram, there are two interpretation systems: Span length (SL) or mean length (ML): Span length of fibre is the distance exceeded by a stated percentage of fibers from a random catch point in drafting zone of fibrograph. In commercial, 50% SL (an approximation of the average length of the scanned fibers) and the 2.5% SL (suitable for the spinning process and used as commercial length) are use to evaluating the cotton fibre. As per ICCS (International Standard Calibration Cotton) gave the lengths according to fibrogram. The “Mean length” is graphically equivalent to the tracing of the tangent of the fibrogram tuft at characteristic points. It is obtained by drawing the tangent from 100% (fiber point) to the length axis. Uniformity ratio ðUR%Þ ¼

50% Span length  100 2:5% Span length

It gives an idea about length variability of the cotton. Uniformity index ðUI%Þ ¼

Mean length  100 Upper half mean length

Cotton fiber length variation can be expressed by uniformity index.

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Figure 13.2 Cotton fibro graph diagram [2].

Uniformity Index (UI) ¼ 1.8  U.R. For normal cotton U.R. U.I.

For polyester having same length 40%e50% 75%e80%

U.R. U.I.

51% 100%

Uniformity Index (UI%) ¼ 75e80% The 2.5% span length and uniformity ratio of a particular variety of cotton fiber are 30 mm and 45%, respectively. Calculate the span length (mm) of the fiber (rounded of 1 decimal place).

Example 13.6.

2.5% SL ¼ 30 mm; UR% ¼ 45%; 50% SL ¼ ?

Solution.

Uniformity ratio ðUR%Þ ¼

50% Span length  100 2:5% Span length

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Textile Calculation

45 % ¼

50% Span length  100 30

50% Span length ¼

45  30 100

The 50% span length is 13.5. The 50% span length and uniformity ratio of H-4 cotton fiber are 13.5 mm and 45%, respectively. Calculate the 2.5% span length (mm) of the fiber.

Example 13.7.

Solution.

50% SL ¼ 13.5 mm; UR% ¼ 45%

Uniformity ratio ðUR%Þ ¼ 45 ¼

50% Span length  100 2:5% Span length

13:5  100 2:5% Span length

2:5% Span length ¼

13:5  100 ¼ 30 45

2.5% span length is 30.

13.6

Fiber fineness

Fineness is one of the most important properties of fibers. The fineness is usually expressed by weight of a known length of fiber. It is also termed as linear density. Fiber fineness plays a significant role in the end product performance as well as intermediate processes. The fiber fineness can be also be characterized by perimeter, diameter, area of crosssection, and specific surface area. Some of these measures are interrelated. For cotton, maturity is used to express degree of cell wall thickening [6]. Fiber fineness is expressed in micrograms per inch (106 g/inch) or in millitex which is weight in milligrams of 1 kilometer length of fiber. This is identical to the unit of 106 gm/cm.

13.6.1

Solid fibers of circular cross-section

Cross sectional area A is related to the diameter D and radius r by the following equations: A ¼ Pr 2 ¼ P D2 ∕4

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The perimeter (circumference) P is given by P ¼ 2Pr ¼ P D It is also valid with P, r and D in mm (Table 13.2). For length L, surface area ¼ PL and volume ¼ AL. Hence, on a volume basis, specific surface Sv is given by Sv ¼

P 2 ¼ ¼ 4=D A r

It is valid with Sv in (mm)1, r, and D in mm. The quality of cotton fiber depends on a large set of features which includes length, maturity, fineness, strength, colour, and trash. Image analysis is an attractive alternative to existing systems for investigating some quantitative fiber features. It is a quick, reliable, and unbiased technique which is used to evaluate fiber maturity and fineness [7]. The weight of 30000 yards polyester filament is 500 g. Calculate the fineness of polyester filament in tex (1 yard ¼ 0.9144 m).

Example-13.8.

The length of 30000 yard polyester filament in meter is ¼ 27432 m (1 yard ¼ 0.9144 m)

Solution.

FinnessðtexÞ ¼ Fineness ¼

Weight in grams  1000 Length in meters

500  1000 tex 27432

Fineness ¼ 18:22 tex The resultant fineness of polyester filament is 18.22 tex. The 8000 meter length of the polypropylene filament weighing is 70 g. Calculate the denier of the polypropylene filament.

Example-13.9.

Solution.

The weight of 8000 m of polypropylene filament is 70 g.

Table 13.2 Units are widely used for fiber fineness [5]. Sr. No.

Units

Description

1.

Micronaire

Microgram/inch

2.

Denier

Weight in grams of 9000 m

3. 4.

Tex Decitex

Weight in grams of 1000 m Weight in grams of 10,000 m

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Textile Calculation

Denier ¼

Weight in grams  9000 Length in meters

Denier ¼

70  9000 8000

Denier ¼ 78:75 The resultant fineness of polypropylene filament is 78.75 denier.

13.6.2

Fiber fineness measurement methods

13.6.2.1 Gravimetric method The basic principle of this method is to count the number of fibers in a given bunch, measure the length, and weigh them. It is classified for wool and cotton individually. It is also known as the direct fiber fineness measurement method. By using the gravimetric approach, 100 cotton fibres from each comb sorter group may be extracted, weighed, and the weight per unit length can be calculated to determine the cotton fibre fineness.

13.6.2.2 Gravimetric method (wool) Wool has an almost circular cross-section, and the fineness of wool can be calculated by following equation: X Total weight of all classes ¼ W∕ hn Total length in all classes where, h ¼ the class length (cm). n ¼ number of fibers in each class. W ¼ total weight of all the classes (mg). The gravimetric diamter of wool in micron is given in the following equation dgrav ðmicronsÞ ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi  X  97190  W∕ hn

If 3 km wool fiber weighs is 900 mg, calculate the gravimetric diameter of wool in micron.

Example 13.10.

Solution.

Specific gravity of wool ¼ 1.31 g/cc

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi  X  dgrav ðmicronsÞ ¼ 97190  W∕ hn

Fiber testing

dgrav ðmicronsÞ ¼

313

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð97190  900∕300000Þ

dgrav ðmicronsÞ ¼ 17:08 mm

13.6.2.3 Airflow method In airflow method, fibers of constant weight are filled-in a fixed volume, and air is allowed to pass through. The flow of air is affected by the surface area of the fibers. The variation in air flow is directly translated into the values of linear density. Airflow method comes under indirect method and it is easy and less time consuming. Therefore, indirect method of the measurement of fineness is more popular (Fig. 13.3). Let the volume of the chamber ¼ V V ¼ Crossectional Area A  Length L  2 d ¼p L 2 Where d ¼ diameter of the cylinder. The surface area ¼ pdL Therefore, specific surface (S)

Figure 13.3 Air flow and fiber fineness [2].

314

Textile Calculation

S ¼ pdL O P

 2 d L¼4=d 2

This ratio also equals the ratio Perimeter of cross sectionOArea of cross section ¼ pdOp

 2 d ¼ 4=d 2

Thus, Sf1=d

13.6.2.4 Optical method The natural fiber shape and diameter of the cross-section are subjected to a greater degree of variation than those of man-made fiber. To obtain reliable results, it is therefore necessary to measure a large number of fibers. The more variable the measured dimension the higher the number will have to be too, for desired accuracy. Fineness in decitex can be obtained using following expression: Decitex ¼ 7:85  103  r  d 2



r ¼ fibre density; d ¼ fibre diameter



where d ¼ diameter of fibers in micrometers. Similar for finensess in denier Denier ¼ 7:07  103  r  d2

Example 13.11.

A diameter of given cotton fiber is 40 mm, Calculate the fineness in

decitex. Solution.

As per given diameter of cotton fiber ¼ 40 mm

Decitex ¼ 7:85  103  r  d 2 ¼ 7:85  103  1:52  402 ¼ 19:09 decitex

13.6.2.5 Vibroscope method It is based on the vibrating string method. For a perfectly flexible string, the natural frequency of transverse vibration f is given by f ¼ l=2lOðT = MÞ

Fiber testing

315

where M ¼ the mass per unit length of a perfectly flexible string. l ¼ the length f ¼ the natural fundamental frequency of vibration (c/s). T ¼ the tension in the string. To express M in terms of denier, it can be written as follows:   M ¼ wg = l2 f 2  9  105

Example 13.12. A cotton fiber of 6 micronaire is examined in a vibroscope instrument with the free distance between the clamp and the support being 1 inch. Calculate the mass of the weighing clip (in mg) to have a natural fundamental frequency of vibration of the fiber sample of 3 kHz?

Natural fundamental frequency of vibration of the fiber sample is 3 kHz. Substituting values in the following equation:

Solution.

  M ¼ wg = l2 f 2  9  105   6 ¼ Wg=2:542  30002  9  105   Wg ¼ 6  2:542  30002  9  105 ¼ 387:096 dynes or 394:73mg The mass of the weighing clip is 394.73 mg. A 4.8 micronaire cotton fiber is tested on a vibroscope with the free distance between the clamp and the support being 1 inch. Calculate the mass of the weighing clip (in dynes) to have a natural fundamental frequency of vibration of the fiber sample of 2.9 kHz?

Example 13.13.

Natural fundamental frequency of vibration of the fiber sample is 2.9 kHz. We know

Solution.

  M ¼ wg = l2 f 2  9  105   4:8 ¼ wg=2:542  29002  9  105 wg ¼

4:8  ð2:54Þ2  ð2900Þ2 9  105

wg ¼

4:8  ð2:54Þ2  ð2900Þ2 9  105

316

Textile Calculation

wg ¼

4:8  ð6:45Þ  ð8410000Þ 900000

wg ¼ 289 dynes The mass of the weighing clip is 289 dynes.

13.7

Fiber maturity

Fiber maturity is an index to express the extent of development of cell wall in cotton fibers. The maturity of cotton fiber varies not only between fibers of different samples but also between fibers on the same seed. Thus, a ripened full mature cotton ball contains both mature and immature fibres [2]. Category ¼

Lumen width ðLÞ Wall thickness ðWÞ

Mature when;

Lumen width ðLÞ < 1 Wall thickness ðWÞ

Half mature when; 1
2 Wall thickness ðWÞ

From the total number of fibers and number of mature fibers, the percentage of the mature fibres (Pm) is calculated. Pm ¼ Mature Fibers/ Total Fibers 100 • • •

Normal fibers (N): mature fibers with a well-developed cell wall, cotton fiber becomes rodlike after swelling. These fibers are classed as normal. Thin-walled fibers: this category of fibers lie between the other two classes. Dead fibers (D): if the wall is less than one-fifth of the total width, the fiber is classed as dead.

A combined index known as ‘maturity ratio’ is used to express the results. Maturity ratio is calculated by using the following equation: Maturity ratio ¼

ND þ 0:70 200

where N ¼ percentage of normal fibers and D ¼ percentage of dead fibers.

Fiber testing

317

The theoretical range for the value of M will be from 0.2 for all dead to 1.2 for all matured or normal fibres. The results are also expressed in terms of ‘maturity coefficient’ which is a unitary expression signifying the multiple character of fiber maturity usually represented by the percentage of mature, half-mature, and immature fibers, calculated from the following formula: Maturity coefficient ¼

ðM þ 0:6H þ 0:4IÞ 100

M, H, and I are the percentages of mature, half-mature, and immature fibers, respectively, in the sample. • • •

Maturity affects the quality of the yarn and its processing behaviour. The effect of immature fibers are seen especially in the spinning process. The large number of ends down in a ring frame is due to the immature fibers. The loss in yarn strength and the dyeing troubles are all due to the presence of immature fibers (Table 13.3).

The three commonly used measures of maturity are maturity ratio (Mr.), percentage of mature fiber (Pm), and maturity coefficient (Mc). These formulae are useful for predicting one measure from another. Pm¼ (Mce 0.394) (3.434e1.783 Mc) Pm¼ (Mre 0.2) (1.5652e0.471 Mr) Mr¼ (Mce 0.301) (2.252e0.526 Mc)

A sample of cotton fibers was tested for maturity. The number of normal (N) and thin-walled (T) fibers were found to be 66 and 14, respectively. Calculate the maturity ratio of cotton fiber.

Example 13.14.

Solution.

Maturity Ratio ¼

66  20 þ 0:7 200

Table 13.3 Classification of the cotton fiber on the basis of maturity. Category

Range of maturity coefficient

Very immature Immature Average maturity Good maturity Very high maturity

Below 0.60 0.60 to 0.70 0.71 to 0.80 0.81 to 0.90 Above 0.90

318

Textile Calculation

Maturity Ratio ¼ 0:93 Example 13.15. A sample of 200 cotton fibers was tested for maturity. 120 normal, 60 semi-mature, and 20 dead were observed. Find out the maturity ratio of tested cotton fiber.

Total fiber: 200, Normal fiber:120 ¼ 60%, Semimature or thin-walled fibers: 60 ¼ 30%, Dead fibers: 20 ¼ 10%

Solution.

Maturity Ratio ¼

ND þ 0:70 200

Maturity Ratio ¼

60  10 þ 0:70 200

Maturity Ratio ¼ 0:95 Maturity ratio for tested cotton fiber is 0.95.

13.8

Fiber quality index

The most popular method for estimating cotton fiber’s technological value is the fiber quality index. Its widespread use can primarily be attributed to the equation’s ease of use. The fiber quality index proposed by the South Indian Textile Research Association is the following [8]: Fibre quality index ðFQIÞ ¼

LSm f

Fibre quality index ðFQIÞ ¼

L  UR  S  m f

where L ¼ 50% span length, S ¼ the fiber bundle strength, m is maturity coefficient, f ¼ fiber fineness (mic), and UR ¼ the uniformity ratio. If the HVI mode of fiber testing is used, then the above expression is changed as follows: Fibre quality index ðFQIÞHVI ¼

UHML  UI  S f

where FQIHVI is the HVI quality index, UHML is the upper half mean length, and UI is the uniformity index.

Fiber testing

319

13.8.1 Fiber quality index and lea CSP Predication of lea CSP (Strength of yarn in pound  Count in English system) based on fiber parameters is obtained from high volume instrument (HVI) and Shirley maturity by following equation [8e10]: For carded counts: Lea CSP ¼ 280 OFQI þ 700e13C For combed counts: Lea CSP ¼ {280 OFQI þ 700e13C} {l þ W/100} where C ¼ Yarn count (Ne) ; W ¼ % Comber Noil; If maturity ratio values are not readily available then, as an approximation, the lea CSP values may be arrived at from the following expression: Lea CSP ¼ 250 (OLS/f) þ 590e13C Predication of lea CSP based on fiber parameters obtained from HVI test system (HVI mode): For carded counts: Lea CSP ¼ 165 (OFQI) þ 590 e (13C) For combed counts: Lea CSP ¼ {165 (OFQI) þ 590 e (13C)} {l þ W/100}

13.9

Spinning consistency index

Spinning consistency index (SCI) is used to predict the cotton fiber’s general quality and spinnability. The regression equation of SCI uses most of the individual HVI measurements. The regression equation used to calculate SCI is as follows: SCI ¼  414:67 þ 2:9 S þ 49:17UHML þ 4:74UI  9:32f þ 0:65Rd þ 0:36ðþ bÞ where, S ¼ the fiber bundle strength, UHML ¼ the upper half mean length, UI ¼ the uniformity index, f ¼ fiber fineness (mic), and Rd ¼ the reflectance degree and þb ¼ the yellowness of cotton fiber [8e10]. Calculate the lea CSP using the fiber properties, measured by HVI test system (HVI mode) with following data: yarn count 30 Ne; noil: 18%; mean length (L): 28 mm; bundle strength (s): 8 gm/tex and fineness: 4.2 micrograms/ inch.

Example 13.16.

320

Textile Calculation

Solution.

As per the following equation,

FQI ¼

Ls f

FQI ¼

28  8 4:2

Lea CSP ¼ {165 (OFQI) þ 590 e (13C)} {l þ W/100} (for combed counts) Lea CSP ¼ {165 (O53.33 þ 590 e (13* 30)} {l þ 18/100} Lea CSP ¼ 1657.31 The predicated lea CSP is 1657.31.

13.10

Tensile property

Tensile properties of the fibers are considered as an important benchmark for yarn quality. It denotes the maximum tension the fiber is able to sustain before breaking. The tenacity is expressed as breaking load for unit fineness of the fibers. Elongation denotes elongation percentage of fiber at break [1e4]. Major factors responsible for fiber strength are its molecular structure, relative humidity, number and intensity of weak places.

13.10.1 Tensile strength/stress The “tensile” term has been derived from the word “tension”. Tensile stress is a very important property of textile materials, which represents the ratio between force required to break a specimen and cross-sectional area of that specimen. Tensile Stress ¼

Force required to break a specimen Cross  sectional area

13.10.2 Strain When a load is applied to a specimen, a certain amount of stretching takes place. The elongation that a specimen undergoes is proportional to its initial length. Strain expresses the elongation as a fraction of the original length. Strain ¼

Elongation Initial length

Fiber testing

321

13.10.3 Tenacity or specific strength The tenacity of material is the stress at break. Tenacity is defined as the ratio between breaking load and linear density of a specimen. Tenacity is expressed in g/tex, g/denier, Newton/tex, etc. Tenacity ¼

Breaking load Linear density

13.10.4 Breaking extension The load required to break a specimen is a useful quantity. Breaking extension of a specimen is defined as the actual, percentage increase in length up to breaking. It is expressed in percentage (%). Breaking extension ð%Þ ¼

Elongation at break  100 % Original length of specimen

13.10.5 Work of rupture The energy required to break a specimen or total work done for breaking a specimen is termed as work of rupture and is expressed by the units of joule, calorie, etc. If applied force ‘f’ increases the length of a specimen in small amount by ‘dl,’ then Z Work done ¼

f dl

13.10.6 Initial modulus The tangent of the angle between initial part of the stress - strain curve and the horizontal axis is initial modulus. It equals to the ratio of stress and strain in the intial region. Initial modulus of textile materials depends on molecular structure, (crystallinity, orientation, amorphous region of fiber). Initial modulus; tan q ¼

Stress Strain

tan q [Y / extension Y[ A textile filament records at tensile stress of 0.3 GPa at a tensile strain of 0.04. Calculate the tensile modulus (GPa) of the filament.

Example 13.17.

Tensile stress ¼ 0.3 GPa, Tensile strain ¼ 0.04

Solution.

Tensile modulus ¼

Tensile stress Tensile strain

322

Textile Calculation

Tensile modulus ¼

0:3 GPa ¼ 7:5 GPa 0:04

The tensile modulus is 7.5 GPa. The fiber tensile testing machine can be categorized in to three types like constant rate of load (CRL), constant rate of extension (CRE), and constant rate of traverse (CRT) according to their working principle. Individual fibers or groups of fibers are tested to assess the fiber strength. Manmade fibers have relatively little variation in length and fineness, hence, their single fiber strength testing is performed. The great degree of length and fineness variation in natural fibers necessitates testing of their bundle strength.

13.10.7 Single fiber strength Single fibers strength test can be carried out on a universal tensile tester, if a suitable load cell is available. Also required are lightweight clamps that are delicate enough to hold fibers whose diameters may be as low as 10e20 mm.

13.10.8 Fiber bundle fiber strength The Pressley tester is an instrument for measuring the strength of a bundle of cotton fibers. Pressley fiber strength tester works on pivoted beam balance principle. A bundle of natural fibers are gripped by two jaws. The jaws are moved until the breaking of the fibres. The breaking load and elongation at break of bundle of fiber are noted. At the end of the test, the two halves of the bundle are weighed, and as the total length of the bundle is fixed of merit known as the Pressley index can be calculated. PI ¼ force ðlbfÞ=mass ðmgÞ The stelometer is a bundle testing instrument which is capable for measuring elongation as well as strength. The instrument uses the same type of jaws as the Pressley instrument, but they have a separation of 3.2 mm (1/8in) as distinct from zero separation of the Pressley instrument. The stelometer works on pendulum lever principle. Tenacity ðgf=texÞ ¼ Breaking force in kgf  15= sample mass ðmgÞ The effective total length of the sample is 15 mm (0.590in) for a 1/8 in (3.2 mm) gauge length and 11.81 mm (0.465 in) for a zero-gauge length so that 11.8 should be used in the formula, if a zero-gauge length is used. In a stelometer, 0.23 mg of fibers were broken at a force of 6 kgf; calculate the fiber bundle tenacity when gauge length is zero.

Example 13.18.

Fiber testing

323

Solution.

Tenacity value at zero gauge ðgf =texÞ ¼

Bundle tenacity ðgf =texÞ ¼

Breaking strength of bundle in kg  11:81 Weight of bundle in mg

6  11:81 0:23

Bundle tenacity ðgf =texÞ ¼ 308 In a stelometer, 4.2 mg of fibers were broken at a force of 5 kgf; calculate the fiber bundle tenacity if the gauge length is kept at 15 mm.

Example 13.19.

Solution.

Tenacity at zero gauge ðgf =texÞ ¼ Bundle tenacity ðgf =texÞ ¼

Breaking strength of bundle in kg  15 Weight of bundle in mg

5  15 4:2

Bundle tenacity ðgf =texÞ ¼ 17:86

13.11

Nep count

Neps are small entanglement of textile fibers in the form of tiny ball. Presence of neps, on the surface of the fabric, causes undyed or unprinted spots after dyeing or printing. Nep count is the number of neps per 100 square inches of card web forming a standard hank of sliver of 0.12 Ne on a 40-inch-wide card. First a web is collected from the card and placed on a 10  10 inch black board. Then, the neps are counted and the number of neps found is corrected from any difference in hank or card width. Mathematically, Nep count, n ¼ m  100 [m ¼ number of neps per inch square card web.] For cotton fiber; there are five types of neps. These are as follows: • • • • •

Process neps: Commonly produced by faulty carding or up to spinning yarn. Mixed neps: Fibers tangle around a foreign material. Immature neps: Generally formed by processing immature fiber. Homogeneous dead neps: A tangle of nearly all dead fibers. Fuzz neps: A fault of short fuzz fibers.

13.12

Fiber crimp

The crimp is the most important property of natural and man-made fibers. The fiber crimp influences the end properties of the products. It can be measured by crimp

324

Textile Calculation

length, crimp frequency, crimp amplitude, angle, degree, and index. Its degree of deviation is from linearity of a nonstraight fiber. Natural fibers like cotton have a natural crimp, but for man-made fibers, artificial waviness should be introduced to obtain better cohesion and friction [11]. Crimp is defined as the mean difference between the straightened fiber length and curved/curl fiber and is expressed as percentage. Crimp % ¼

Uncrimped length  Crimped length  100 Crimped length

Crimp % ¼

ðl  pÞ  100 P

where, C ¼ crimp, l ¼ straightened fiber length, p ¼ the length of crimped fiber, crimped length

13.13

Conclusion

This chapter dealt with calculations of important fiber properties viz; fineness, length, strength, fineness, and maturity.

References [1] B.P. Saville, Physical Testing of Textiles, Woodhead Publishing Ltd., U. K, 1999. [2] J.E. Booth, Principles of Textile Testing, Heywood Books, London, 1961. [3] H. Sarmah, B. Hazarika, Importance of the Size of Sample and its Determination in the Context of Data Related to the Schools of Greater Guwahati, vol 12, Bulletin of the Gauhati University Mathematics Association, 2012, pp. 55e76. ISSN 0975-4148. [4] Testing and Quality Management e Edited by V. K. Kothari, IAFL Publications, New Delhi. [5] Handbook of Textile Testing and Quality Control by E. B. Grover and D. S. Hamb. [6] The Characteristics of Raw Cotton, in: E. Lord (Ed.), Manual of Cotton Spinning, Vol. II Part 1, The Textile Institute and Butterworths, London, 1961, p. 103. [7] A. Ghith, F. Fayala, R. Abdeljelil, Assessing cotton fiber maturity and fineness by image, Anal. J. Eng. Fibers Fabr. 6 (2 - 2011) (2011). [8] Norms for the Spinning Mills, the South Indian Textile Research Association, 1995, pp. 1e17. [9] Y.E. El Mogazhy, R. Broughton, W.K. Lynch, A statistical approach for determining the technological value of cotton using HVI fibre properties, Text, Res. J. 60 (9) (1990) 495e500. [10] A. Majumdar, P.K. Majumdar, B. Sarkar, Determination of technological value of cotton fibre: a comparative study between traditional and multiple criteria decision making approach, Autex Res. J. 5 (2) (2005). [11] S. Maity, Characteristics and effects of fibre crimp in nonwoven structure, J. Textil. Assoc. 76 (2014) 360e366.

Yarn testing

14

Vijay Goud, Apurba Das and Alagirusamy Ramasamy Department of Textile and Fibre Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India

14.1

Yarn linear density

14.1.1 Introduction One of the utmost vital property for a yarn is its “diameter.” However, as a result of its compressible nature, it is difficult to measure the diameter of a yarn with instruments used for metals. Thus, a system has been developed which defines the fineness of a yarn by weighing a known length. This system is known as the linear density. It can be determined precisely if an adequate length of yarn is used. There are two systems of linear density in use. They are as follows: U Direct system U Indirect system

14.1.1.1 Important terminologies and formulae Direct system The direct system defines linear density of a yarn in terms of mass per unit length. It is fixed length system. In direct system, finer the linear density of yarn, lower is its yarn number. The widely used direct systems for measurement of linear density are as follows: U TexdMass in grams of 1000 m U DenierdMass in grams of 9000 m U DecitexdMass in grams of 10,000 m

The general formula for direct system: Let N ¼ the yarn number or count; L ¼ the length of the sample; M ¼ the mass of the sample at the official regain in the units of the system; l ¼ the unit length of the system,

Then, N ¼ (M  l)/L

Textile Calculation. https://doi.org/10.1016/B978-0-323-99041-7.00010-2 Copyright © 2023 Elsevier Ltd. All rights reserved.

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Textile Calculation

Indirect system The indirect system defines linear density of a yarn in terms of length per unit mass and is usually known as count. It is fixed mass system. In indirect system, finer the linear density of yarn, higher is its yarn number. The main systems in use are as follows: U Worsted count (Nw) ¼ number of hanks of 560 yards long in 1 pound U Cotton count (Ne) ¼ number of hanks of 840 yards long in 1 pound U Metric count (Nm) ¼ number of kilometer lengths per kilogram

The general formula for indirect system: Let N ¼ the yarn number or count; L ¼ the length of the sample; M ¼ the mass of the sample at the official regain in the units of the system; l ¼ the unit length of the system, m ¼ the unit mass of the system

Then, N ¼ (m  L)/(M  l). Yarn count conversion chart. Conversion

Tex

Decitex (dtex)

Denier (den)

Tex Decitex (dtex) Denier (den) Metric No. (Nm) English cotton No. (Ne)

e dtex/10 den/9 1000/Nm 591/Ne

10  tex e den/0.9 10,000/Nm 5910/Ne

9  tex 0.9  dtex e 9000/Nm 5314/Ne

Yarn count conversion chart. Conversion

Metric No. (Nm)

English cotton No. (Ne)

Tex Decitex (dtex) Denier (den) Metric No. (Nm) English cotton No. (Ne)

1000/tex 10,000/dtex 9000/den e Ne  1.69

591/tex 5910/dtex 5314/den 0.59  Nm e

14.1.1.2 Numericals Problem.

Mass of 2500 m (L) yarn is 25 g (M). What is the count of yarn in tex?

Solution.

Count of yarn (tex) ¼ 25  1000/2500 ¼ 10

Problem.

Mass of 120 yard (L) yarn lea is 3 g (M). What is the cotton count of yarn

(Ne)? Cotton count (Ne) ¼ number of hanks of 840 yards long in 1 pound (453.6 g)

Solution.

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327

Cotton Count, Ne ¼ (453.6  120)/(3  840) ¼ 21.6 ¼ 0.54  (Length in yard/Mass in g) Problem.

Length of 20 tex polyester/cotton yarn in km on a 6 kg cone will be how

much? Solution.

Tex ¼ 20; i.e., Mass of 1000 m yarn is 20 g

Length of 1 g yarn 1000 /20 ¼ 50 m Length of 6 kg yarn is 6  1000  50 m ¼ 300 km Problem.

Calculate length of 2 kg of 180 denier polyester yarn.

Denier ¼ 180 i.e., mass of 9000 m polyester yarn ¼ 180 g. So, length of 2 kg yarn ¼ (9000  2  1000)/(180 1000) km ¼ 100 km.

Solution.

14.1.1.3 Count of folded/plied yarn The count of individual threads (singles) that have been plied together to form the final yarn is called the folding count. If there is only one, then the yarn itself is often referred to as a “singles yarn.” However, depending on the counts system being applied, the folding number appears differently in the yarn count. Using any of the cotton, woolen or worsted systems, a twofold 30 Ne cotton would be written as “2/30” with the 1st digit signifying the folding number, and the 2nd the count of each single yarn. In the spun silk system, a twofold of 30 Ne cotton would be written as “2/15” because officially, the count of spun silk is the total yarn count (i.e., 15 Ne) with the folding number placed in front. The direct system is almost always simpler, and generally to be preferred. The tex is regarded as SI unit.

In indirect system Resultant countdNR Component yarn countdN1, N2, N3, N4, . . . . . . . . So, 1/NR ¼ 1/N1 þ 1/N2 þ 1/N3 þ 1/N4 þ . . . . .

In direct system Resultant countdNRD Component yarn countdN1D, N2D, N3D, N4D, . . . . . . . .

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Textile Calculation

So, NRD ¼ N1D þ N2D þ N3D þ N4D þ . . . . .

14.1.1.4 Numericals Problem.

Calculate resultant count of 3/50s Ne 3-ply folded yarn in tex?

Solution.

Resultant English count in Ne is NeR

1/NeR ¼ 1/N1 þ 1/N2 þ 1/N3 ¼ 1/50 þ 1/50 þ 1/50 NeR ¼ 16.66 NT  NeR ¼ 590.1 NT ¼ 590.1/16.66 ¼ 35.42 What is the count of multifilament yarn in tex with 36 filaments of 3 denier monofilaments?

Problem.

Solution.

Resultant denier of multifilament is NDR

NDR ¼ N1 þ N2 þ . . . .. þ N36 ¼ 36  3 ¼ 108 NT ¼ ND/9 ¼ 108/9 ¼ 12 tex What is the resultant count of 3-ply yarn in tex made from 50 Nm worsted yarn; 100 denier polyester filament; and 60 Ne cotton yarn?

Problem.

Solution.

Let, the resultant count in tex ¼ NTR

(i) Wool yarn count in tex (N1T) ¼ 1000/50 ¼ 20 (ii) Polyester filament count in tex (N2T) ¼ 100/9 ¼ 11.11 (iii) Cotton yarn count in tex (N3T) ¼ 590.1/60 ¼ 9.83

NTR ¼ N1T þ N2T þ N3T ¼ 20 þ 11.11 þ 9.83 ¼ 40.94

14.2 14.2.1

Moisture in yarn Introduction

Buyer pays for material, not for moisture and water. So a “Correct Invoice Weight” is to be determined. When consignment is to be delivered and weighed, a sample is taken and tested for moisture present in it and then necessary correction for moisture is made.

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329

14.2.1.1 Important terminologies and formulae Moisture regain It is the ratio of weight of water present in a material to the oven dry weight of textile material. It is given by MR ¼

W  100% D

Moisture content It is the ratio of weight of water present in a textile material to the sum of weights of water present and oven dry weight of a textile material. MC ¼

W  100% W þD

where, Weight of water present in a textile material ¼ W. Oven dry weight of textile material ¼ D. The relationship between moisture content and regain is shown below: MC ¼

MR MR 1þ 100

MR ¼

MC MC 1 100

and

Correct invoice weight The aforementioned scenario in Section 14.2, can be described as follows: U U U U U

Total weight of consignment is takendW At that point sample is taken from consignment (mass of sample with moisture)dS The sample is then oven dried and its weight is d Calculated oven dry weight (D) of consignment ¼ [W  d]/S ¼ D Thus, correct invoice weight (WC),   U Wc ¼ D 100þR , 100 U U U U

Where “R” is officially allowed regain % For cotton, R ¼ 8.5% Polyester, R ¼ 0.4% Nylon, R ¼ 4%

330

Textile Calculation

14.2.1.2 Numericals 20,000 km of 150 denier yarn at 8.5% moisture content is shipped. What should be the correct invoice weight if the official moisture regain is 6.0%.

Problem.

Length of yarn ¼ 20,000 km; denier of yarn ¼ 150 denier. M.C. ¼ 8.5%; official moisture regain (MR) ¼ 6.0%. Correct invoice weight ¼ ?

Solution.

Mass of 20,000 km yarn shipped with 8.5% MC ¼ (150  20,000)/9 g ¼ 333.33 kg W þ D ¼ 333.33 kg MC ¼

W  100% W þD

Mass of water (W) ¼ 0.085  333.33 ¼ 28.33 kg. Oven dry mass (D) ¼ 305 kg. Correct invoice weight,   100 þ R Wc ¼ D 100 “R” is officially allowed regain % ¼ 6.0% Correct invoice weight ¼ 305  (106/100) ¼ 323.3 kg. 50,000 km of 40 Ne 80/20 polyester/cotton yarn at 4% moisture content is shipped. What will be the correct invoice weight? [The official moisture regain of polyester and moisture regain of cotton are 0.4% and 8.5%, respectively]

Problem.

Length of yarn ¼ 50,000 km; Cotton count ¼ 40 Ne (i.e., 14.7625 tex) Moisture content (M.C.) ¼ 4% Official moisture regain of blended yarn (Rb) ¼ ? Correct invoice weight ¼ ?

Solution.

Rb ¼ ð0:4  0:8 þ 8:5  0:2Þ ¼ 2:02% Mass of 50,000 km yarn with 4% MC ¼ 14.7625  50,000 g ¼ 14.7625  50 kg ¼ 738.125 kg

Yarn testing

331

W þ D ¼ 738.125 kg MC ¼

W  100% W þD

Mass of water (W) ¼ 0.04  738.125 ¼ 29.525 kg. Oven dry mass (D) ¼ 708.6 kg. Correct invoice weight,   100 þ Rb Wc ¼ D 100 “Rb” is officially allowed regain % ¼ 2.02% Correct invoice weight ¼ 708.6  (102.02/100) ¼ 722.9 kg

14.3

Yarn twist

14.3.1 Introduction Twist is the measure of the spiral turns given to yarn in order to hold the fibers or threads together. Twist is primarily imparted in to a staple yarn in order to hold the constituent fibers together, thus giving strength to the yarndduring spinning in R/F or any other spinning process. Twist level is usually expressed as the number of turns per unit length, e.g., twist per metre (TPM) or twist per inch (TPI). However, the ideal amount of twist varies with the yarn diameter, i.e., the thinner the yarn, the greater is the amount of twist that has to be inserted to give the same effect. The factor that determines the effectiveness of the twist is the angle that the fibers make with the yarn axis. d

Ɋ‹ ɂ

1/T

1/T ɂ

A fiber taking one full turn of twist in a length of yarn L (L ¼ 1/T); fiber makes an angle q with the yarn axis.

332

Textile Calculation

14.3.1.1 Important formulae As, tan q ¼ п d/L. The greater the diameter of the yarn, the greater the angle of twist (for same TPI or TPM) tan q N d  turns/unit length In the indirect system for measuring linear density, the yarn diameter dN1/Ocount So, tan q N (turns/unit length)/O count tan q ¼ pdT qfT qfd where, T ¼ twist per unit length q ¼ twist angle. and, d ¼ yarn diameter ¼ 1/[CONe] Thus, T ¼ tan q/pd ¼ [C tan q/p]  ONe ¼ K  ONe Where C.tan q/p ¼ Twist multiplier (K) Value of K differs with each count system. (a) In tex (direct system): K (twist factor) ¼ TPM  OTex (b) Indirect system: K (twist multiplier) ¼ TPI/OCotton count

14.3.1.2 Numericals 20, 30, 40, and 50s Ne cotton yarns have the same twist per inch, say 20. The yarn having maximum fiber obliquity is

Problem.

Solution.

Twist ¼ TM  ONe; i.e., TM ¼ TPI/ ONe

Twist multiplier Twist multiplier Twist multiplier Twist multiplier

(TM) (TM) (TM) (TM)

for for for for

20s 30s 40s 20s

yarn ¼ 20/O20 ¼ 4.47. yarn ¼ 20/O30 ¼ 3.65. yarn ¼ 20/O40 ¼ 3.16. yarn ¼ 20/O50 ¼ 2.82.

Yarn testing

333

For same twist level, higher twist multiplier (TM) is for coarser count (i.e., 20s yarn will have highest TM). C.tan q/p ¼ twist multiplier (TM) TM a tan q 20s Ne yarn has maximum twist angle, i.e., maximum fiber obliquity. The direct twist factor of 35 Nm yarn is 36 tpcm$tex1/2. (i) What is the approximate twist (in Twist per inch)? (ii) If the diameter of the yarn is 0.28 mm, what will be the approximate twist angle?

Problem.

Solution.

(i) Given data  yarn linear density ¼ 35 Nm

Yarn tex (Nt) ¼ 1000/35 tex ¼ 28.57 tex Twist factor (K) ¼ 36 tpcm$tex1/2 Twist in yarn (twist/cm) ¼ twist factor/ONt ¼ 36/O28.57 ¼ 6.73 tpcm ¼ 17.1 twist/inch (ii) Given data  yarn diameter ¼ 0.28 mm ¼ 0.028 cm

Twist in yarn (Twist/cm) ¼ 6.73 tan q ¼ pdT tan q ¼ p  0.028  6.63 ¼ 0.5832 q ¼ tan1 0.5832 ¼ 30.25

14.4

Tensile properties of yarns

14.4.1 Introduction Tensile testing of yarns is necessary to know the level of strength provided by materials. For house hold, apparel use as well as industrial and technical products, it is equally vital to have an accurate determination of tensile properties of yarns.

14.4.1.1 Important formulae • • •

Stress: Force/cross-sectional area Specific stress ¼ Force/linear density (initial) Strain ¼ Elongation/initial length

334

Textile Calculation

•

Extension % or elongation% ¼ (elongation/initial length)  100 • Specimen length and irregularity: Pierce’s empirical equation

Sl  Srl ¼ 4.2 (1  r1/5) sl 1  Srl/Sl ¼ 4.2 (1  r1/5) V/100 V ¼ sl/Si  100 where sl ¼ Standard deviation of strength result at gauge length “l” Sl ¼ Mean strength measured at length “l” (higher Sl is at lower length) Srl ¼ Mean strength measured at length “rl” V ¼ CV% of strength •

Rate of loading and time to break

FT ¼ F10 (1.1  0.1 log T), if T > 10, FT < F10 FT ¼ The breaking load for a time to break of T sec. F10 ¼ The breaking load for a time to break of 10 s FT/F10 ¼ 1 þ 0.1  0.1 log T ¼ 1 þ 0.1 (log 10  log T) (FT  F10)/F10 ¼ 0.1 log (10/T) If some other standard time other than 10 s is chosen, s sec, then, (FT  FS)/FS ¼ 0.1 log (S/T) •

Pendulum lever principle

Yarn testing

Tensile testing machine working on pendulum lever principle.

M ¼ Mass of pendulum. Its C.G. is at R distance from the pivot. For extensible material, v > u. Assuming the specimen is inextensible, Taking moments about pivot, F.r ¼ Mg.x ¼ Mg.R sin q, R, M, g, r, are constants. F f sin q, F is tension in the specimen.

335

336

Textile Calculation

Machine rate of loading (m): Increase in the load per unit results in increase in the displacement of upper jaw (J1) The displacement of upper jaw (J1) ¼ rdq dF/dq ¼ (MgR/r)cos q, dF/rdq ¼ m ¼ (MgR/r2)cos q MgR/r2 is constant for a particular m/c and known as “standard machine rate of loading” or m0 Ratio of m at start and at 45 is (1:0.707), i.e., cos 0 : cos 45 Time rate of loading (L): Rate at which the load on the specimen increases with respect to time vdt ¼ rdq (for inextensible specimen) dq/dt ¼ v/r L ¼ df/dt ¼ (dF/dq)  (dq/dt) ¼ (MgR cos q/r)  (v/r) ¼ (MgRv/r2)  cos q ¼ m.v L f cos q L changes throughout the test, maximum at q ¼ 0 (at start) and minimum (i.e., 0) at q ¼ 90 .

14.4.1.2 Numericals A yarn specimen of 200 mm extends by 10% when loaded with 500 cN force. The length of the specimen after removal of load was found to be 202 mm. Calculate percentage elastic recovery of yarn.

Problem.

Given data: Original length of specimen ¼ 200 mm; extension% ¼ 10% Loaded force ¼ 500 cN; final length ¼ 202 mm. Percentage elastic recovery of yarn ¼ ?

Solution.

Extended length ¼ Original length  [(1 þ (10/100)] ¼ 200  110/100 ¼ 220 mm Total extension ¼ 220  20 ¼ 20 mm Elastic extension ¼ Extended length  final length ¼ 220  202 ¼ 18 mm

Yarn testing

337

So, percentage elastic recovery of yarn ¼ (Elastic extension/total extension) * 100 ¼ (18/20)  100 ¼ 90% If a yarn shows strength of 400 cN when the time taken to break is 10 s, calculate the breaking load if the rate of loading is increased to cause the yarn to break in 1 s.

Problem.

Solution.

Given data:

F10 ¼ 400 cN FT ¼ F10 (1.1  0.1 log T) F1 ¼ F10 [1.1  (0.1  log 1.0)] ¼ 400 [1.1  (0.1  0.0)] ¼ 400  1.1 ¼ 440 cN If the rate of extension of a yarn is doubled, what will be the % increase in measured yarn strength for same gauge length? Consider the breaking elongation remains unchanged.

Problem.

1st stage time to break ¼ S 2nd stage time to break (T) ¼ S/2

Solution.

(FT  FS)/FS ¼ 0.1 log (S/T) So, % change in breaking strength ¼ (FT  FS)  100/Fs ¼ 0.1  log (S/T)  100 ¼ 0.1  log (2)  100 ¼ 3.01% A 40 Ne 67/33 polyester/cotton blended yarn showed a breaking load of 300 g when tested on a constant rate of extension (CRE) tester with 100 mm gauge length and at 100 mm/min traverse rate. What is the expected percentage change in the observed tenacity of the yarn if (i) the traverse rate is increased to 500 mm/min (keeping the gauge length constant) and (ii) the gauge length is increased to 500 mm (keeping the traverse rate constant). [Assume a constant breaking extension of 25% and single yarn strength CV% of 10% for all the above conditions.]

Problem.

As the traverse rate is increased by 5 times, the time required to break is reduced by 5 times.

Solution.

S ¼ 5  T; S/T ¼ 5 (FT  FS)/FS ¼ 0.1 log (S/T)

338

Textile Calculation

(i) The % change (increase) in the observed tenacity

¼ (FT  FS) 100/Fs ¼ 0.1  log (S/T)  100 ¼ 0.1  log (5) 100 ¼ 6.99% w 7% (ii) As the gauge length is increased by 5 times, i.e., r ¼ 5

and CV% ¼ 10%, i.e., V ¼ 10 1  Srl/Sl ¼ 4.2 (1  r1/5) V/100 The % change (decrease) in the observed tenacity (Sl  Srl)100/Sl ¼ 4.2  (1  51/5)  10 ¼ 11.56% The following are the tensile test data of a 30 Ne single yarn while testing on a tensile tester and works on pendulum lever principle with Standard machine rate of loading (mo) 440 cN/cm. Tenacity-11 cN/tex; breaking extension-7% Gauge length-20 cm; traverse rate-57 mm/min. Calculate the time to break.

Problem.

Solution.

30 Ne ¼ 19.68 tex

Pmax ¼ 11  19.68 ¼ 216.5 cN mo ¼ 440 cN/cm, i.e., 1/mo ¼ m ¼ 1/440 cm/cN m  Pmax ¼ Total movement of upper jaw (J1) Velocity of lower jaw (J2) ¼ V ¼ 57 mm/min m  Pmax ¼ Total movement of upper jaw (J1) ¼ 216.5/440 cm e ¼ extension of yarn (cm) ¼ (7/100)  20 ¼ 1.4 cm Total movement of lower jaw (J2) ¼ m  Pmax þ e Velocity of lower jaw (J2) ¼ V ¼ 5.7 cm/min Time to break ¼ (m  Pmax þ e)/V ¼ (216.5/440 þ 1.4)/5.7 min ¼ 0.3319 min ¼ 19.92 s w 20 s

Yarn testing

14.5

339

Evenness of yarn

14.5.1 Introduction Variability in properties, i.e., mass/length, diameter, twist, thickness, strength, etc., is the measure of evenness of the yarn. Two expressions for variation measurement are: CV% ¼ SD/mean  100 U% ¼ PMD ¼ Mean deviation/mean 100 ¼ [{(SIx  xI)/n}/x]  100 When the distribution is normal distribution about the mean, the two values are related by the following equation: CV ¼ 1.25  PMD

14.5.1.1 Important terminologies and formulae Limit irregularity Most uniform strand of material which our present machines can produce is one in which the fiber ends are laid in a random order in the sliver, roving, or yarn. For such a strand of material, the irregularity is given by the following formula: Vr2 ¼ [(100)2/N] þ (Vm2/N) where Vr ¼ limit CV % of mass per unit length; N ¼ the average number of fibers in a cross-section of the strand, and Vm ¼ Actual CV% of the fiber mass per unit length e For man-made fiber, Vm w 0, Vr2 ¼ (100)2/N e For cotton fibers, Vr2 ¼ [(100)2/N] þ (Vm2c /N), (Vmc ¼ 35.16%) ¼ (106)2/N e For wool fibers, Vr2 ¼ [(100)2/N] þ (Vm2w/N), (Vmw ¼ 50.44%) ¼ (112)2/N e For blend of cotton with other fiber

Vr2 ¼ (118.8)2/N

Index of irregularity Vr ¼ the calculated limit irregularity and V ¼ the actual irregularity, Then, the index of irregularity (I) is: I ¼ V/Vr

340

Textile Calculation

Hence, a value of unity for this ratio corresponds to the limit irregularity, i.e., best possible yarn evenness. The higher the value of “I,” the more irregular the yarn and poor performance of spinning m/c. In the formula given in limit irregularity, the square of the coefficient of variation is used; in this form, it is known as the ‘relative variance’ often abbreviated to “variance” By using the squares of the coefficients of variation, it becomes possible to add and subtract the irregularities produced at various stages in yarn preparation and spinning.

Addition of irregularity Suppose the CV% of a sliver is V1 and it is fed to a machine which adds irregularity V2 to its during processing. Let V be the coefficient of variation of the processed sliver. Using the squares of the coefficients, V2 ¼ V21 þ V22

Reduction of irregularity by doubling One of the objectives of doubling is to reduce the irregularity. If “n” strands of material, each having the same coefficient of variation, are doubled, then the coefficient of variation of the combined strands is given by: C.V. of doubled strands ¼ C.V. of individual strands/On

14.5.1.2 Spectrogram Amplitude of periodic mass variation is plotted against the wavelength in a spectrogram. Amplitude is a measure of the number of times a fault of that repeat length occurs not the extent of irregularity. From the speed at which the yarn is running (through capacitance type sensor), the frequencies are converted to wavelengths and plotted into a finite number of discrete wavelength steps. Histogram is then plotted automatically. Spectrogram helps in locating the following: U The generating point of a periodic fault. U Spreading of humps is due to periodic faults generated due to “drafting waves” U The wavelength due to drafting wave will be around 2.5e3.0 inch for cotton

14.5.1.3 Variance-length curves Between length Mass of each length (l) is measured and CV % is calculated [l varies subsequently] This CV% is the CV% of between l yds lengths and is given by symbol CB(l) The corresponding square, i.e., the variance, has the symbol B(l).

Yarn testing

341

Between length curve.

Within length U CV% of each individual length (l) is determined U And mean of CV% is calculated as CV% within l yds length. U The symbols are CV(L) and V(L), respectively.

Within length curve.

C. Total Variance: V(T) ¼ B(L) þ V(L)

14.5.1.4 Numericals If the most uniform 24 tex polyester staple fiber yarn has a CV of 20%, (i) what is the lowest CV one would expect for a 12 tex yarn produced from the same fiber? (ii) What would be the CV of a 4-ply yarn produced from 12 tex yarn?

Problem.

Solution.

Given: Yarn count ¼ 24 tex; CVlim % ¼ 20%

342

Textile Calculation

CVlim ¼ 100/ON1 ¼ 20 N1 ¼ Number of fibers in cross-section of 24 tex yarn ¼ 25 Fiber tex ¼ 24/25 ¼ 0.96 tex N2 ¼ Number of fibers in cross-section of 12 tex yarn ¼ 12/0.96 ¼ 12.5 (i) So, limiting CV% of 12 tex yarn-

CVlim12tex ¼ 100/ON2 ¼ 100/O12.5 ¼ 28.28% (ii) For the CV of a 4-ply yarn produced from 12 tex yarn

CV4-Ply ¼ CV12tex/O4 ¼ 28.28/O4 ¼ 28.28/2 ¼ 14.14% Two rovings with a CV of 8% each are fed into a spinning zone, and if the spinning unit adds 8% CV, what will be the CV% of output yarn approximately?

Problem.

Coefficient of variation (CV) of roving ¼ 8% q Two rovings are fed, r CVFEED % of doubled roving ¼ 8/O2

Solution.

CVADD ¼ 8% CVOUTPUT ¼ O(CVFEED)2 þ (CVADD)2 ¼ O(8/O2)2 þ (8)2 ¼ 9.8% The CV% of 3-ply yarn produced using these single yarns will be approximately.

Problem.

Solution.

CV% of 3-ply yarn is ¼ 9.8/O3 ¼ 5.66%

Eight ends of slivers, each having a CV of 6%, are doubled and drawn to produce the resultant sliver of same hank. If the draw-frame introduces 2.12% CV, what will be the CV% of resultant sliver approximately?

Problem.

Coefficient of variation of individual sliver (CV) ¼ 6% q 8 slivers are fed, r CV% of D/F input material (CVinput) ¼ 6/O8 ¼ 2.121

Solution.

CVADD ¼ 2.12% CVOUTPUT ¼ O(CV

input)

2

þ (CVADD)2

¼ O(2.121)2 þ (2.12)2 ¼ 2.998% w 3%

Yarn testing

343

Consider the following particulars for a spinning line producing 30 tex yarn from 150 militex polyester fiber: Mass CV of card sliver: 3% Mass CV added at draw-frame: 2% Mass CV added at speed-frame: 3% Mass CV added at ring-frame: 7% Number of doubling at draw-frame: 6 Number of draw-frame passage: 1

Problem.

(i) Find the mass CV% of roving (ii) Calculate Index of irregularity of yarn

Mass CV input at draw-frame ¼ 3/O6 ¼ 1.225% For mass CV output at draw-frame:

Solution.

CVOut-D/F ¼ O[(CVinput-D/F)2þ(CVAdd-D/F)2] ¼ O[(1.225)2þ(2)2] ¼ 2.345% For mass CV output at speed-frame: Mass CVAdd-S/F at speed-frame: 3% Mass Cvinput-S/F at speed-frame ¼ 2.345% CVOut-S/F ¼ O[(CVinput-S/F)2 þ (CVAdd-S/F)2] ¼ O[(2.345)2 þ (3)2] ¼ O14.499 ¼ 3.808% (ii) Calculate index of irregularity of yarn

For mass CV output at ring-frame: qMass CV added at ring-frame: 7% And mass CV input at ring-frame ¼ 3.808% CVOut-R/F ¼ O[(CVinput-R/F)2 þ (CVAdd-R/F)2] ¼ O(3.808)2 þ (7)2 ¼ 7.969 CVOut-R/F ¼ 7.969 Index of irregularity of yarn ¼ CVOut-R/F/CVLIM CVLIM ¼ 100/ON N ¼ Number of fiber Number of fiber (N) ¼ Yarn tex/fiber tex ¼ 30/0.150 ¼ 200 So, CVLIM ¼ 100/ON ¼ 100/O200 ¼ 7.07.

344

Textile Calculation

So, index of irregularity of yarn ¼ CVOut-R/F/CVLIM ¼ 7.969/7.07 ¼ 1.127 The R/F-I is producing 30 tex polyester with CV% of 10%, from 1.5 denier fiber. And the R/F-II is producing 30 tex polyester with CV% of 8.5%, from 1.0 denier fiber. Which R/F is performing better?

Problem.

R/F-I: Actual irregularity (V1) ¼ 10% Number of fibers in yarn cross-section ¼ N1

Solution.

¼ 30  9/1.5 ¼ 180 Limit irregularity (V1r) ¼ 100/ON1 ¼ 100/13.4 ¼ 7.46 Index of irregularity ¼ V1/V1r ¼ 10/7.46 ¼ 1.34 R/F-2: Actual irregularity (V2) ¼ 8.5% Number of fibers in yarn cross-section ¼ N2 ¼ 30  9/1.0 ¼ 270 Limit irregularity (V1r) ¼ 100/ON2 ¼ 100/16.4 ¼ 6.1 Index of irregularity ¼ V1/V1r ¼ 8.5/6.1 ¼ 1.39 The higher value of “I” in R/F-2 shows that it has poor spinning performance. The following table gives the relevant processing details used in the production of a 32-tex yarn spun from 152 mm, 0.5 tex man-made fiber on a semiworsted system, together with the CV% of each product

Problem.

Process

Draft

Doublings

CV%

1st drawing 2nd drawing 3rd drawing Roving Spinning

8.0 9.37 5.7 10.0 14.1

8 6 2 1 1

3.4 2.8 5.5 7.5 14.9

Calculate the index of irregularity and addition of irregularity at each stage. Given: Yarn count  32 tex; fiber linear density  0.5 tex; type of fiber  man-made fiber.

Solution.

Yarn testing

345

(i) Yarn:

No. of fibers in yarn cross-section ¼ 32/0.5 ¼ 64. Limit irregularity (Vry) ¼ 100/O64 ¼ 12.5. Index of irregularity (Iy) ¼ 14.9/12.5 ¼ 1.19. CV% of input material (roving) ¼ 7.5. CV% of output material (yarn) ¼ 14.9. Addition of irregularity ¼ O[(14.9)2  (7.5)2] ¼ 12.87% Process

Draft

Doub

1st 2nd 3rd Rov Spg

8.0 9.37 5.7 10.0 14.1

8 6 2 1 1

Tex

CV%

Add

I

32

3.4 2.8 5.5 7.5 14.9

12.87

1.19

Given: Roving count 32  14.1 ¼ 451.2 tex; fiber linear density  0.5 tex; type of Fiber  man-made fiber. (i) Roving:

No. of fibers in roving cross-section ¼ 451.2/0.5 ¼ 902. Limit irregularity (Vry) ¼ 100/O902 ¼ 3.33. Index of irregularity (Iy) ¼ 7.5/3.3 ¼ 2.27. CV% of input material ¼ 5.5. CV% of output material ¼ 7.5. Addition of irregularity ¼ O[(7.5)2  (5.5)2] ¼ 5.1% Process

Draft

Doub

1st 2nd 3rd Rov Spg

8.0 9.37 5.7 10.0 14.1

8 6 2 1 1

Tex

CV%

Add

I

450 32

3.4 2.8 5.5 7.5 14.9

5.1 12.84

2.27 1.19

Given: 3rd D/F sliver count  451.210 ¼ 4512 tex; fiber linear density  0.5 tex; type of fiber  man-made fiber. (i) 3rd D/F:

No. of fibers in 3rd D/F sliver cross-section ¼ 4512/0.5 ¼ 9024

346

Textile Calculation

Limit irregularity (Vry) ¼ 100/O9024 ¼ 1.05. Index of irregularity (Iy) ¼ 5.5/1.05 ¼ 5.23. CV% of input material ¼ 2.8/O2 ¼ 1.98. CV% of output material ¼ 5.5. Addition of irregularity ¼ O[(5.5)2d(1.98)2] ¼ 5.13% Process

Draft

Doub

1st 2nd 3rd Rov Spg

8.0 9.37 5.7 10.0 14.1

8 6 2 1 1

Tex

CV%

Add

I

4512 451.2 32

3.4 2.8 5.5 7.5 14.9

5.13 5.1 12.84

5.23 2.27 1.19

Figure below shows a 3/3 drafting arrangement of a ring-frame producing 40 Ne cotton yarn from 1.212 Ne roving with break draft of 1.115. Identify the positions of the peaks in the spectrogram of the yarn if (i) Pinion D and (ii) Pinion F are defective. Consider that in case of pinion the defect is due to broken single teeth and in case of drafting roller the defect is due to roller eccentricity. The values in the parentheses are number of teeth in case of pinions and diameters in mm in case of rollers.

Problem.

Solution.

(i) Pinion D, defective:

For 1 revolution of D, the front roller (FR) will rotate e (90  121)/(30 11) ¼ 33 revolution i.e., FR Delivery ¼ (p  25.4  33)/1000 ¼ 2.63 m. (ii) Pinion F: For 1 revolution of F, the MR will rotate e

26/26 ¼ 1 revolution i.e., MR Delivery per revolution ¼ (p  23  1)/1000 ¼ 7.23 cm. Front zone draft ¼ (40)/(1.212  1.115) ¼ 29.6. FR Delivery ¼ (7.23  29.6) ¼ 214 cm ¼ 2.14 m.

Yarn testing

347

A 14.7 tex ring spun yarn was tested and found to have a periodicity with a long wave length of 57.7 m. The total drafts at the draw-frame, roving frame, and the ring-frame were 6.0, 10.5, and 25.0, respectively. The roll sizes and draft distribution of the drawing frame used are as follows:

Problem.

Roller

Draft

Back roll (28 mm) to 3rd roll 3rd roll (25 mm) to 2nd roll 2nd roll (25 mm) to front roll Front roll (32 mm) to calendar roll (50 mm)

1.15 1.86 Main draft zone (maximum draft) 1.02

Find the faulty/eccentric roller.

Periodic wave length of yarn ¼ 57.7 m; Total draft in R/F ¼ 25; Periodic wave length of roving ¼ 57.7/25 ¼ 2.308 m; Total draft roving frame ¼ 10.5; Periodic wave length of D/F sliver ¼ 57.7/(25  10.5) m;

Solution.

¼ 0.2198 m ¼ 219.8 mm Periodic wavelength of D/F sliver ¼ 219.8 mm. Diameter of calendar roll ¼ 50 mm. Circumference of calendar roll ¼ p  50 ¼ 157.07 mm. Not matching with wavelength of sliver, i.e., wave length is more. Draft between F and calendar roll ¼ 1.02. Periodic wavelength after F ¼ 219.8/1.02 ¼ 215.5 mm. Periodic wavelength after F ¼ 219.8/1.02 ¼ 215.5 mm. Diameter of F ¼ 32 mm. Circumference of F ¼ p  32 ¼ 100.53 mm. Not matching with wavelength of after front roll, i.e., wavelength is more Draft between 2nd roll and F (main zone draft) ¼ Total D/F draft, i.e., 6/(1.02  1.86  1.15) ¼ 2.75 Periodic wave length after 2nd roll ¼ 215.5/2.75 ¼ 78.4 mm

348

Textile Calculation

Periodic wavelength after 2nd roll ¼ 78.4 mm. Diameter of 2nd roll ¼ 25 mm. Circumference of 2nd roll ¼ p  25 ¼ 78.5 mm. Matching with wavelength of after 2nd roller. Conclusion: The 2nd roll is faulty, i.e., there is eccentricity in 2nd roll. The nature of B(l) curve is Y ¼ mX þ C [Y is Variance (i.e., square of CV%) and X is log10 (cut length in cm)]. The variances with 10 cm and 1 m cut lengths are 49 and 36, respectively. What will be the approximate U% of that yarn when tested in Evenness tester?

Problem.

Solution.

From the B(l) curve,

Variance (V) ¼ m  log10 (cut length in cm) þ C V ¼ CV2 From given conditions, 49 ¼ m  log1010 þ C ¼ m þ C 36 ¼ m  log10100 þ C ¼ 2m þ C By solving the above equations, m ¼ 13 and C ¼ 62. In Uster evenness tester, the cut length is 1 cm V ¼ CV2 ¼ 13  log101 þ 62 ¼ 62 So, CV% ¼ O62 ¼ 7.87% U% ¼ PMD ¼ CV%/1.25 ¼ 6.23%

14.6

Conclusion

This chapter dealt with calculations of important yarn properties of count, moisture, twist, tensile strength, and evenness.

Further reading [1] [2] [3] [4]

B.P. Saville, Physical Testing of Textiles, Woodhead Publishing Ltd., UK, 1999. J.E. Booth, Principles of Textile Testing, Heywood Books, London, 1961. V.K. Kothari (Ed.), Testing and Quality Management, IAFL Publications, New Delhi. E.B. Grover, D.S. Hamb, Handbook of Textile Testing and Quality Control.

Fabric testing 1

1

2

15

Chet Ram Meena , Janmay Singh Hada , Madan Lal Regar and Akhtarul Islam Amjad 3 1 Department of Textile Design, National Institute of Fashion Technology Jodhpur, Ministry of Textiles, Govt. of India, Jodhpur, Rajasthan, India; 2Department of Fashion Design, National Institute of Fashion Technology Jodhpur, Jodhpur, Rajasthan, India; 3Department of Fashion Technology, National Institute of Fashion Technology Panchkula, Panchkula, Haryana, India

15.1

Introduction

Testing is an important segment of the textile industry. Textile products are tested at various stages of production to assure quality processing and products. The testing provides the physical, chemical and performance properties of the textile products to predict their end use performance [1]. The practice of measuring and evaluating the physical properties and attributes of fabrics and textiles using various standardised procedures and equipment is referred to as physical textile testing. These tests are performed to establish a fabric’s fitness for its intended function, as well as to evaluate its durability, strength, comfort, look, and other relevant characteristics. There are the physical tests for the fabrics such as tensile strength test, tearing strength test, bursting strength test, pilling resistance test, abrasion resistance test, seam slippage, and functionality test for fabrics such as Kawabata, air permeability, flame resistance, wicking, etc.

15.2 • • • • • • • • •

Major testing standards for textile testing

American Association for Textile Chemists and Colorists (AATCC): It is used for testing dyed and chemically treated fibers and fabrics. American Society for Testing and Materials (ASTM): ASTM is applicable for technical standards for materials, products, systems, and services. American National Standard Institute (ANSI): ANSI organization supports the development of technology standards in the United States. British Standard Institute (BSI): It produces standards and information for products that promote and share best practice. International Organization for Standardization (ISO): To develop technical and economical standards. Bureau of Indian Standards (BIS): It is used for the standardization, quality control, quality management system, environmental management system, laboratory management, etc. Japanese Industrial Standard (JIN): It is used for textile engineering activities in Japan. Canada Standard Association (CSA): CSA standards are safety standards in Canada for electrical appliances, medical devices, machinery, equipment etc. German Standards Institute - Deutsches Institut fuer Normung (DIN): It is used for stakeholders to develop consensus-based standards that meet market requirements (Tabel 15.1).

Textile Calculation. https://doi.org/10.1016/B978-0-323-99041-7.00006-0 Copyright © 2023 Elsevier Ltd. All rights reserved.

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Textile Calculation

Table 15.1 Testing quality parameters for woven, knitted and Nonwoven fabrics. Testing parameters

Woven

Knitted

Nonwoven

Dimensional characteristics

Length Width Thickness Weight per unit area Weight per unit length Ends per inch (EPI) Picks per inch (PPI) Warp crimp Weft crimp Tensile Tearing Bursting Stiffness Drape Abrasion Pilling Water Crease Crease Elastic Shrinkages Air permeability Water vapor permeability

Length Width Thickness Weight per unit area

Length Width Thickness Weight per unit area

Wales per inch (WPI) Course per inch (CPI)

Needle penetrations per unit area

Bursting

Bursting

Abrasion Pilling Water Crease Crease Elastic Shrinkages Air permeability Water vapor permeability

Water Crease

Weight of fabric

Threads per inch of fabric

Crimp Fabric strength and extensibility Handle Resistance

Recovery

Permeability

15.3

Crease Elastic Shrinkages Air permeability Water vapor permeability

Gram per square meter

GSM is basically weight of the fabric in gram per one square meter. It may be expressed as weight per unit length (GLM). The template area is 1/100 square yard of which each arm is 1/10 yards in length. For measuring GSM, a cutter is used to cut the fabric and weight is taken in balance. It is a metric measurement unit of surface or areal density which is used to measure the thickness of sheet material [2]. The twill weave fabric (end per inch: 130, pick per inch 70) warp count is 30 Ne and weft count is 20 Ne. Calculate the gram per square meter (GSM) and grams per linear meter (GLM) of the fabric?

Example 15.1.

The GSM of the fabric will
 be calculatedbythe following  formula: EPI PPI  25.64 Gram per square meter (GSM) ¼ Warp Count þ Weft Count

Solution.

Fabric testing

351

EPI-130, PPI-70, warp  count-30  Ne, weft count- 20 Ne 70 So, GSM will be ¼ 130 30 þ20  25.64 ¼ 89.74 GSM Gram per linear metre ðGLMÞ ¼ Gram linear metre ðGLMÞ ¼

89:74  Fabric width 39:37

89:74  60 ¼ 1:36 39:37

So, 500meter fabric total weight ¼ GLM  fabric quantity Total weight ¼ 136.76  500 ¼ 68,380 g ¼ 68.38 kg

15.4

4-Point system

This system, also called the American Apparel Manufacturers Association point grading system for determining fabric quality, is widely used by the producers of apparel fabrics and by the Department of Defense in the United States and is endorsed acceptability criteria for defects: Normally, fabrics containing up to 40 points per 100 sq yds. are acceptable. A 50 m fabric roll is tested with 4-point system; if the penalty points are 15 and width of fabric roll is 1.5 m, find out the maximum acceptable points on a 100 m’ basis

Example 15.2.

Given: linear points ¼ 15, length of the roll ¼ 50 m, and width of the roll ¼ 1.5 m

Solution.

Points=100 sq:yard ¼ Points=100 sq: m ¼

3600  Total points assigned Fabric length in yards  Fabric width in inches

100  Total points assigned Fabric length in meters  Fabric width in mm

Area ¼ Length  Width Area ¼ 50  1:5 ¼ 75 m2 So, 75 square meter has total linear points ¼ 15 1 square meter has total linear points ¼ 15/75 Points per 100 square meter ¼ (15/75)  100 ¼ 20 points/m2. The maximum acceptable point is 20 points/m2.

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Textile Calculation

15.5

Strength of the fabric

Tensile, tear, and bursting strength are important parameters for determining a fabric’s level of strength. Tear resistance (or tear strength) measures how well a material can withstand tearing effects, whereas tensile strength measures the force required to pull something to the point where it breaks. Another important criterion for evaluating the strength of nonwoven and knitted fabrics is bursting strength. During bursting strength testing, a uniformly distributed force is applied to the fabric surface, and the breaking load is measured.

15.5.1

Tensile strength

Tensile strength is the capacity of a textile material to withstand a force. It is one of the most important mechanical properties for woven fabrics. Tensile strength of fabric is mostly tested by grab and strip test method. Generally, grab test method is used for routine and strip test method is used for research purpose. Testing instruments are based on constant rate of elongation (CRE), constant rate of loading (CRL) and constant rate of traverse (CRT) testing principles. It is used for determining the breaking strength and elongation of most textile fabric and expressed in units of force per cross-sectional area. Tenacity of the fabric ðcN = texÞ ¼

Breaking forece ðcNÞ g per linear 1000 meter

or Tenacity of the fabric ðg = texÞ ¼

Breaking load in kgf linear density in tex

A 100 gsm woven fabric is tested for tensile strength. If the 40 mm width is utilized during the testing and the load applied for a break is 0.4 KN, then calculate the tenacity in cN/tex.

Example 15.3.

GSM of fabric ¼ 100 g/m2; breaking force ¼ 0.4 KN ¼ 400 N, sample width ¼ 40 mm ¼ 0.04 m

Solution.

Tenacity of the fabric ¼

Breaking forece ðcNÞ g per linear 1000 meter

Tenacity of the fabric ¼

Breaking forece ðcNÞ g GSM 2  WidthðmÞ  1000 m

Tenacity of the fabric ¼

40; 000 ¼ 10 cN=Tex 100  0:04  1000

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353

A 250 gsm woven fabric is tested for strip tensile strength. The sample specimen size is 5 cm wide and 20 cm gauge length. The average breaking load for tested fabric specimen is found 51.5 kgf. Calculate the tenacity of fabric in g/tex.

Example 15.4.

The mass of fabric test specimen ¼ 250  0.01 ¼ 2.5 g The actual area of fabric test specimen ¼ 20  5 ¼ 100 cm2 ¼ 0.01 m2 Length of strip ¼ 20 cm ¼ 0.2 m, Linear density of fabric strip (tex) ¼ (2.5  1000)/0.2 ¼ 12,500 tex

Solution.

Tenacity of the fabric ðg = texÞ ¼

Breaking load in kgf linear density in tex

Tenacity of the fabric ðg = texÞ ¼

51; 500 12; 500

Tenacity of the fabric ðg = texÞ ¼ 4:12 g=tex A woven fabric with area density of 300 g/m2 is tested by strip tensile test method. The sample specimen size is 5 cm wide and 25 cm gauge length. The average breaking load for tested fabric specimen is found 900 N. Calculate the tenacity of fabric in cN/tex.

Example 15.5.

The mass of fabric test specimen ¼ 300  0.0125 ¼ 3.75 g The actual area of fabric test specimen ¼ 25  5 ¼ 125 cm2 ¼ 0.0125 m2 Length of strip ¼ 25 cm ¼ 0.25 m Linear density of fabric strip (tex) ¼ (3.75  1000)/0.25 ¼ 15,000 tex

Solution.

Tenacity of the fabric ðcN = texÞ ¼

Breaking load ðcNÞ linear density in tex

Tenacity of the fabric ðcN = texÞ ¼

90; 000 15; 000

Tenacity of the fabric ðcN = texÞ ¼ 6 cN=tex The tenacity of fabric is 6 cN/tex. The relationship between load (y) in N and elongation (x) in mm of cotpffiffiffi ton fabric is y ¼ x. Find out the work of rupture in N mm, if the breaking elongation of the fabric is 9 mm.

Example 15.6.

Solution.

From the equation Z

Work of rupture ¼

y dx Z

Work of rupture ¼ 0

$ %9 x3=2 x dx ¼ 3=2

9 pffiffiffi

0

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Textile Calculation

2 Work of rupture ¼ ð9Þ3=2 3 Work of rupture ¼ 18 N:mm

15.5.2

Tearing strength

Tearing strength is an important mechanical property of woven fabrics. The amount of force necessary to rip the fabric depends on its tearing strength. •

Tear Strength: Tear strength is the force required either to start or to continue the tear in a fabric under specific condition.

Tearing strength ¼ Tearing force ðNÞ  Tearing distance ðmÞ • •

Tearing Force: Tearing force is the average force required to continue a tear previously started in a fabric. Tearing Resistance: Tearing resistance is one of the important properties of a textile fabric. The tear resistance of a fabric indicates its resistance to tearing force.

A fabric is subjected to the tearing force on the pendulum-type ballistic tester; the tearing direction is perpendicular to the acting force 100 N, and the tearing distance is 40 mm. Calculate the energy loss.

Example 15.7.

Solution.

Tearing force ¼ 100 N; tearing distance ¼ 40 mm ¼ 0.04 m

Tearing strength ¼ Tearing force ðNÞ  Distance ðmÞ ¼ 100  0:04 ¼ 4 Nm The energy loss is 4 Nm.

15.5.3

Bursting strength

Knits offer comfort to consumer because of built-in stretch, and are preferred by consumers worldwide. All knits have stretch that alleviates several fitting problems more than the woven fabrics. Strength of knitted fabrics measured by bursting strength tester and expressed in terms of bursting index [3]. In addition to bursting strength, one frequently reports the burst factor and/or the burst index.   gf Burst strength cm2 g Bursting factor ¼ GSM 2 m Bursting index ¼

Burst strengthðKPaÞ KSMðkg=m2 Þ

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355

Note that 1 kPa ¼ 1 kN/m2, where kPa stands for kilopascal and kN for kilonewton. Grammage is the basis weight in units of gf/m2. Example 15.8. Calculate the bursting factor and burst index if the bursting strength of a single jersey knitted fabric is 316 Kpa. GSM of the fabric is 210. Solution.

Bursting strength ¼ 316 KPa ¼ 316  10:197 ¼ 3222:252 gf/cm2; 

 gf Burst strength 3222:252 cm2 g ¼ 15:34 ¼ Bursting factor ¼ 210 GSM 2 m Bursting index ¼

Burst strengthðKPaÞ 316  1000 ¼ 1504:76 ¼ KSMðkg=m2 Þ 210

The bursting factor is 15.34 and index is 1504.76.

15.5.4 Abrasion resistance It is the ability of a fabric to resist surface wear caused by flat rubbing contact with another material. Abrasion is one aspect of wear and is the rubbing away of the component fibers and yarns of the fabric. Abrasion may be classified as follows: • • •

Plane or flat abrasiondA flat area of material is abraded. Edge abrasiondThis kind of abrasion occurs at collars and folds. Flex abrasiondIn this case, rubbing is accompanied by flexing and bending.

Generally, the abrasion is measure in the terms of % weight loss or grading.

15.6

Fabric handle

Fabric handle is very important for apparel application. The fabric handle, as its name suggests, is focused on how the material feels and hence relies on touch. Fabric handle can be measured in terms of stiffness, hardness, or softness, roughness or smoothness. Different types of material will have varying degrees of smoothness or roughness.

15.6.1 Bending length Measurement of bending length is based on cantilever principle, where the horizontal strip of fabric is allowed to bend like cantilever under its own weight. High bending length fabrics are stiffer, have poor drape, and are less flexible. The bending length is related to the angle that the fabric makes to the horizontal by the following equation (Fig. 15.1):

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Textile Calculation

Figure 15.1 Bending length measurement.

11=3 1 cos q B 2 C Bending Length ðCÞ ¼ L@ A mm 8 tan q 0

3 q 6 27 Flexural rigidity ðGÞ ¼ M L3 4 5mN m 8 tan q 2

cos

Flexural rigidity ðGÞ ¼ 9:81 M C 3  106 ðmN mÞ Bending modulus ðqÞ ¼

12 G  103 N = m3 3 t

where M: mass per unit area (g/m2); L: overhanging length; and t: cloth thickness in mm. When the tip of the fabric strip reaches a plane inclined at 41.5 below the horizontal, the overhanging length is then twice the bending length. This angle is used in bending length tester. • • •

Ring loop: l0 ¼ L/p ¼ 0.3183 L Bending length (C) ¼ L 0.133  f(q), q ¼ 157  d/l0, Pear loop: l0 ¼ 0.4243 L, Bending length (C) ¼ L  0.133  f(q)/cos (0.87) q ¼ 504.5  d/l0, Heart loop: l0 ¼ 0.1337 L, Bending length (C) ¼ L  0.1337  f(q) q ¼ 32.85  d/l0,   cos q 1=3 where, f ðqÞ ¼ tan q

Fabric testing

357

A 250 GSM cotton fabric is having flexural rigidity of 230 mNm. Calculate the overhanging length, if the tip of the fabric specimen has to reach a plane inclined at 10 below the horizontal?

Example 15.9.

Solution.

Flexural rigidity equation:

Flexural rigidity ðGÞ ¼ 9:81 M C3  106 ðmN mÞ 230 ¼ 9:8  250  C3  106 C3 ¼

230  106 9:81  250

Bending Length ðCÞ ¼ 45:43 mm 11=3 1 q B 2 C Bending Length ðCÞ ¼ L@ A 8 tan q 0

cos

1 10 1=3 B 2 C 45:43 ¼ L@ A 8 tan 10 0

cos

45:43 ¼ L  0:89 Overhanging length ðLÞ ¼

45:43 0:89

The overhanging length (L) is 51.04 mm. A fabric, with mass per unit area of 250 g/m2, has flexural rigidity 275 mNm. What will be the overhanging length, if the tip of the specimen has to reach a plane inclined at 14.2 below the horizontal plane? [5]

Example 15.10.

Given data: Fabric mass per unit area (M) ¼ 250 g/m2 Flexural rigidity (G) ¼ 275 mNm q ¼ 14.2

Solution.

Flexural rigidity ðGÞ ¼ 9:81 M C3  106 ðmN mÞ 275 ¼ 9:81  250  C3  106

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Textile Calculation

C3 ¼

275  106 9:81  250

Bending Length ðCÞ ¼ 48:22 mm 11=3 1 q B 2 C Bending Length ðCÞ ¼ L@ A 8 tan q 0

cos

1 14:2 1=3 B 2 C 48:22 ¼ L@ A 8 tan 14:2 0

cos



cos 7:1 48:22 ¼ L 8 tan 14:2

1=3

48:22 ¼ L  0:79 Overhanging length ðLÞ ¼

48:22 0:79

The overhanging length (L) is 61.04 mm. If the fabric is of 150 g/m2, and its bending length in the warp direction is 3 cm, calculate the flexural rigidity in g cm.

Example 15.11.

Given data: Fabric mass per unit area (M) ¼ 150 g/m2 ¼ 0.015 g/cm2 Bending length (C) ¼ 3 cm

Solution.

Flexural rigidity ðGÞ ¼ M C 3 ðg cmÞ Flexural rigidity ðGÞ ¼ 0:015  33 Flexural rigidity ðGÞ ¼ 0:405 g cm The flexural rigidity for fabric is 0.405 g cm.

15.6.2

Drape

Drape is a fabric’s propensity to take on an elegant aspect when worn. It is a vital feature of textile materials that permits cloth to be formed into elegant folds or pleats.

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359

The drape ability of a cloth can be measured with a drape meter and is stated in terms of drape coefficient. Drape Coefficient ðDÞ ¼

A3  A2 1 A1  A2

where A1: total area of the sample; A2: area of the supporting platform; A3: area of the shadow; The CUSICK drape tester consists of light source, circular disk, and paper ring. In test, the light beam casts a shadow of the draped fabric onto a ring of highly uniform translucent paper supported on a glass screen. The surface drape pattern area on the paper ring is directly proportional to the mass of that area. So, the drape coefficient (D) can be calculated in a simple way (Fig. 15.2): Drape Coefficient ðDÞ ¼

Mass of shaded area  100% total mass of paper ring

A plain weave cotton fabric sample is tested on drape meter. Projected area of a 30-cm diameter fabric specimen placed on 20 cm diameter support plate of drape tester is 302 cm2. Calculate the drape coefficient of the fabric.

Example 15.12.

Projected area (A3  A2) ¼ 302 cm2 Area of specimen (A1) ¼ p/4  302 ¼ p/4  900 cm2 Area of supported disk (A2) ¼ p/4  202 ¼ p/4  400 cm2

Solution.

Drape Coefficient ðDÞ ¼

A3  A2 A1  A2

Drape Coefficient ðDÞ ¼

302 ðp =4  900Þ  ðp =4  400Þ

Figure 15.2 CUSICK drape tester.

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Textile Calculation

Drape Coefficient ðDÞ ¼

302 ðp =4  ð900  400Þ

Drape Coefficient ðDÞ ¼ 0:769 The draping coefficient of fabric is 0.769. A plain weave cotton fabric sample is tested on drape meter. The area of projected image of draped fabric of 30-cm diameter fabric specimen kept on an anvil of 18 cm diameter was measured as 362 cm2. Calculate the drape coefficient of the fabric.

Example 15.13.

Projected area (A3  A2) ¼ 362 cm2 Area of specimen (A1) ¼ p/4  302 ¼ p/4  900 cm2 Area of supported disk (A2) ¼ p/4  182 ¼ p/4  324 cm2

Solution.

Drape Coefficient ðDÞ ¼

A3  A2 A1  A2

Drape Coefficient ðDÞ ¼

362 ðp =4  900Þ  ðp =4  324Þ

Drape Coefficient ðDÞ ¼

362 ðp =4  ð900  324Þ

Drape Coefficient ðDÞ ¼ 0:801 The draping coefficient of fabric is 0.801.

15.7

Thickness

Fabric thickness is defined as the distance between the top and bottom surfaces of a fabric under standard pressure. Normally, it is measured in millimeters. Various studies have discovered that fabric thickness affects the comfort, thermal, and handle characteristics of the fabric. Thickness testing of woven fabric is carried out under a pressure of 20 gf/cm2. Determine the pressure on fabric during the thickness testing.

Example 15.14.

Solution.

As per standard:

100 gf ¼ 1 N 20 gf ¼

20 N 100

Fabric testing

361

1 m2 1002

1cm2 ¼

20 gf=cm2 ¼

20=100 N=m2 1=1002

Pressure during testing ¼ 2000 N=m2 or Pa

15.8

Clothing science and comfort

Human expectations nowadays go far beyond the basic need for clothing. Clothing comfort is one of the most important criteria for clothing selection. As a result, the wearer and textile technocrat must have a basic understanding of comfort aspects. Physiological reactions and regulation of body temperature influence comfort. In other terms, “Comfort is the state of pleasantness in which there is psychological, physiological, and physical harmony between the human being and the environment” [4]. Body thermoregulation is the interaction of core and surface temperature. In the case of normal thermal regulation in the human body, there is a constant core temperature near 37 C; it varies slightly among different body organs. The weighted mean method may calculate average skin temperature [5]. Mean skin temperature can be calculated as ¼ Tskin ¼ 0:12 ðTback þ Tchest þTabdomen Þ þ 0:14Tarm þ0:19Tthigh þ 0:13Tleg þ0:07Thead þ 0:05Thand þ0:06Tfoot Mean body core temperature can be calculated by deriving the weighted mean between the core and skin temperature. Tbody ¼ 0:67 Trectal þ 0:33Tskin

Calculate the mean body temperature if the rectal temperature is 37 C and the skin temperature is 36.6 C.

Example 15.15.

Solution.

Given: Trectal ¼ 37 C; Tskin ¼ 36:6 C

Tbody ¼ 0:67 Trectal þ Tskin Tbody ¼ 0:67  37 þ 0:33  36:9 ¼ 36:96 C The mean body temperature is 36.96 C.

362

Textile Calculation

15.8.1

Thermal properties

Without cloth, a human can be comfortable between a temperature of 26e30 C. But the earth’s temperature varies so high that clothing is needed. With the cloth, a human can comfortably survive at 40 to 40 C. For different ambient conditions, different clothing is required based on thermal conductivity and resistivity of the cloth [4,8]. 1  dQ. Heat transfer coefficient (W/m2 K) ¼ h ¼ SDT dt Where dQ/dt is the heat transfer rate (W); S is the area of the fabric (m2); and DT is the difference between the average temperature of the system and the ambient temperature (K). If R is the thermal resistance, then thermal conductivity is expressed as l ðW =mKÞ ¼ R1  dS. R is the clothing’s thermal resistance (K/W), and d is the fabric’s thickness in meters. Example 15.16. A wearer is wearing a cloth made from the fabric thickness of 0.1 cm, and the total surface area of the fabric is 1.1 m2. The heat transfer rate from the human body to the outer ambient is 0.2 W. Mean skin and ambient temperatures are 310 and 313 K, respectively. If the heat transfer mode is convection only, calculate the heat transfer coefficient.

Given: T1 ¼ 310 K; T2 ¼ 313 K; d ¼ 0.1 cm ¼ 0.001 m;

Solution.

S ¼ 1.1 m2;

dQ dt

¼ 0:2 W;

and

 Heat transfer coefficient

 W 1 dQ 1  ¼  0:2 ¼ m2 K SDT dt 1:1  ð313  310Þ



Heat transfer coefficient W = m2 K ¼

0:2 ¼ 0:06 W = m2 K 1:1  3

In a system of thermoregulation, fabric thickness is 0.1 cm, and the total surface area of fabric is 0.5 m2. The heat transfer rate from the system to the outer atmosphere is 0.5 W, and the temperature difference is 2 K. If the mode of heat transfer is conduction only, then calculate the fabric’s thermal conductivity and thermal resistance.

Example 15.17.

Given: DT ¼ 2; S ¼ 0.5 m2; dQ/dt ¼ 0.5 W; d ¼ 0.1 cm ¼ 0.001 m; Thermal conductivity is expressed as d  dQ ¼ 0:5  0:01 ¼ 0.005 W/mK. l ðW =mKÞ ¼ SDT dt 2 0:5 1  0:01  ¼ 4 K/W Thermal resistance R ðK =WÞ ¼ 1l  dS ¼ 0:005 0:5 The fabric’s thermal conductivity is 0.005 W/mK and thermal resistance is 4 K/W.

Solution.

15.8.2

Moisture transmission

Moisture transmission is also important for comfortable clothing. Sweat (moisture) from the human body is transmitted as liquid and vapor. The sweating rate for any

Fabric testing

363

activity is the amount of sweat produced per unit of time. It can range from 100 to 8000 mL per day. As a result, managing sweat transmission is critical for comfortable clothing. Wetting and wicking mechanisms are used for liquid transmission, while absorptionedesorption, adsorption, and forced convection mechanisms are used for vapor transmission [6]. The forces in equilibrium at a solideliquid boundary are commonly described by Young’s equation [5]. gsv  gsl ¼ gsl cos q where gSV shows surface tension at the solid vapor interface, gSL shows surface tension at the solideliquid interface, and gLV shows surface tension at the liquidevapor interface. q is a contact angle between a solid surface and a liquid drop. Wicking can be defined as the spontaneous transport of liquid into the porous system of textile material driven by the capillary forces. The liquid rise in a capillary is attributed to capillary pressure (P), which is equal to internal wetting force (Fw) per unit area and is given by the following Laplace equation [4] capillary pressure ðPÞ ¼

2glv cos q r

attainable capillary height ðhÞ ¼

2glv cos q rgr

where glv is interfacial tension between liquid and vapor (air), q is the equilibrium contact angle, and r is the radius of the capillary, liquid of density is r. A yarn is hung, and one end is in contact with water. Calculate the height of water achieved by the yarn due to capillary pressure if the tension between liquid and vapor (air) is 0.0728 N/m and the contact angle is 80 , the radius of capillary ¼ 0.2 mm, and the density of water is 1000 kg/m3. Assume all capillaries are perfectly cylindrical and possess the same radius.

Example 15.18.

Solution.

Given: q ¼ 80 ; glv ¼ 72.86 N/m

Attainable capillary height ðhÞ ¼ Capillary pressure ðPÞ ¼

2glv cos q rgr

2  0:0728  cos 80 0:0002  1000  9:8

Capillary pressure ðPÞ ¼ 0:0129 m The capillary pressure is 0.0129 m. Synthetic sweat rises to a height of 4.5 cm in a yarn hanged vertically. Calculate the capillary radius if all the capillaries are of the same radius. Synthetic

Example 15.19.

364

Textile Calculation

sweat’s density and surface tension are 1000 kg/m3 and 0.072 N/m, respectively. The contact angle is 15 . Assume suitable data. Solution.

Given: h ¼ 4.5 cm ¼ 0.045 m, q ¼ 15 ; and glv ¼ 0.072 N/m

attainable capillary height ðhÞ ¼

2glv cos q rgr

capillary radius ðrÞ ¼

2glv cos q rgh

capillary radius ðrÞ ¼

2  0:072  cos 15 0:045  1000  9:8

capillary radius ðrÞ ¼ 0:000315 m ¼ 0:315 mm The capillary radius is 0.315 mm.

15.8.3

Water vapor transmission

Apart from the liquid transmission of sweat, vapor transmission also takes place. It is measured in terms of the fabric’s water vapor permeability index or water vapor transmission (WVT). The testing is done by BS 7209 and BS 3424 standards. The water vapor transmission or WVT in g/m2/day is WVT ¼

24M A:T

M(g) is the loss in mass of the assembly over the period T. T is the time between successive weighing of the assembly in hours, A is the exposed area of fabric to the water vapor transmission. Calculate the fabric’s water vapor transmission if measured by the upright cup method under standard conditions. Change in the mass of the cup is 3 g mass after 8 h due to evaporation from the cup through the fabric. The open area of the cup covered by the fabric is 0.004534 m2.

Example 15.20.

Solution.

Given: M ¼ 30 g, T ¼ 8 h, and exposed area ¼ 0.4534 m2.

Water Vapour Transmission ¼

24M 24  3 ¼ A:T 0:04534  8

Water Vapour Transmission ¼ 19:85 g=m2 =day The water vapor transmission is 19.85 g/m2/day.

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365

15.8.4 Air permeability The measurement of the air permeability covers the rate of air flow passing perpendicularly through a known area under a prescribed air pressure differential between the two surfaces of a material of textile fabrics. This can be measured for woven, knitted and nonwoven fabrics. It is generally expressed in SI units as cm3/s/cm2 and in inchpound units as ft3/min/ft2. Air permeability is an important factor in the performance of such textile materials as gas filter, fabrics for air bags, clothing, mosquito netting, parachutes, sails, tents, mask, vacuum cleaners etc. It can also be used to provide an indication of the breathability of weather-resistant and rainproof fabrics. Permeability of a fabric depends on the degree of openness in fabric. The air permeability is expressed by the following relationship: Air permeability ¼ p

V dm3 m2 s1 A:s:ðDpÞ

Where, V is the capacity of the flowing medium, A is the area through which the medium is flowing, s is the time of flow and Dp is the drop in pressure of the medium. [4] A Needle punched nonwoven fabric has 3 mm thickness and 450 g/m2 aerial density. If the fiber density is 0.9 g/cm3 then calculate the volume porosity of fabric Example 15.21.

Porosity ¼ 1  Packing factor. Specefic voilume of fibre Packing factor of fabric will be ¼ Specefic volume of fabric.

Solution.

Specific volume of fabric ¼ density 1of fabric. Mass . Density of fabric (gram/CC) ¼ Volume

Aerial density ðGSMÞ

Density of fabric (gram/CC) ¼ . thickness 450 Density of fabric (gram/CC) ¼ 10;000 cm ¼ 0.15 2 0:3 cm 1 ¼ 6.66 Specific volume of fabric ¼ 0:15

g cm3 .

cm3 . g

1  1 ¼ 0.167. Packing factor ¼ 0:9 6:66 Porosity ¼ 1  0.167 ¼ 0.833. Porosity of the fabric is 83.3%.

15.9

Flame-retardant

The flameproof fabrics are required for protective clothing in industrial textile as well domestic purpose. General terminology used in regard to the flammability are as follows: • • •

Flammable: The fabric which propagates the flame or continues burn after the flame has been removed. Flameproof: The fabric which does not propagate the flame. Flame-resistant: The fabric whose resistance rating is high, i.e., above 150.

366

• •

Textile Calculation

Flame-resistant rating: A figure derived from the flammability of fabrics. Inherent flameproof: The material not submitting to flame.

The factors which are responsible to flame resistance are mainly the type of fibers and weight of the fabrics. The yarn structure and manufacturing process like knitting or weaving are not the deciding factors for fabrics flammability. In heavier fabric, flame resistance is higher compare to lightweight fabrics. Normally, two tests are performed like visual timing test (the flame rate of vertically suspended fabric is determined), 45 test (the fabric is suspended at 45 and time is determined for 5-inch fabric) and hoop test (fabric mounted on semicircular frame and flame rate is determined). These tests are valid for only some specific types of fabrics because some fabrics burn very quickly. All cellulosic materials propagate the flame which is inversely proportional to their weight [7]. The essential safety tools in a variety of industrial, commercial, and municipal applications are flame-resistant and fire-retardant fabrics. Flame resistance properties of fabrics depend on the thermal or burning behavior of textile fibers, fabric structure and garment shape, type of finishes, the intensity of the flame, presence of oxygen amount, etc. [8].

15.9.1

Limiting oxygen index

The purpose of limiting oxygen index (LOI) test is to measure the relative flammability of textiles, polymers, and composite materials by burning them in controlled atmosphere of mixture of oxygen and nitrogen. The LOI represents the minimum level of oxygen in the atmosphere that can sustain flame on thermoplastic materials. The higher the LOI value, the lower the flammability. The LOI testing tool is used as quality control, to indicate the flammability. The following formula is used to calculate the LOI by following expression: Limiting Oxygen Index ðLOIÞ ¼

O2  100 ðO2 þ N2 Þ

Here, O2 and N2 are the minimum (oxygen and nitrogen) concentrations in the inflow gases to pass the minimum length creation. The air contains 21% oxygen and therefore any material with an LOI less than 21% will probably support the burning of textile material in open air. This specifies the minimum concentration of oxygen in medium that will support combustion of small vertical specimens under specified test conditions like IS No. 6359:1971 (method of conditioning the textiles) and 11871: 1986 (methods of determination of flammability and flame resistance in textile fabrics) [9].

15.10

Measurement of color strength

The color yield of both dyed and mordant is normally measured by light reflectance measurements. The color strength (K/S value) is evaluated by the KubelkaeMunk equation: K∕S ¼

ð1  RÞ2 2R

Fabric testing

367

where K is the sorption coefficient, R is the reflectance of the dyed fabric, and S is the scattering coefficient. Example 15.22. Cotton sample dye with reactive dye in jade green and peacock blue color at wavelength (600 WL) with reflectance % 1.85 and 2.10, respectively, by spectrophotometer. Calculate the K/S value of the fabric for individual dyestuff. Solution.

The color strength (K/S value) Reflectance (R) ¼ 0.0185 & 0.021

K∕S ¼

ð1  RÞ2 2R

For jade green XBN: K∕S ¼

ð1  RÞ2 2R

K∕S ¼

ð1  0:0185Þ2 2  0:0185

¼ 26:04 For peacock blue: K=S ¼

ð1  0:021Þ2 2  0:021

K=S ¼

0:958441 0:042

¼ 22:82

15.11

Dimensional change

Dimensional change in the length and width of a fabric called growth or shrinkage, respectively. Dimensional Change ð%Þ ¼

Dimension after Laundering ðBÞ  Original Dimension ðAÞ Original Dimension ðAÞ  100

Shrinkage is denoted as “,” which is decrease in dimensions. Growth/elongation is denoted as “þ,” which is increase in dimensions.

368

Textile Calculation

A cotton fabric length and width are 35 and 35 cm respectively, after washing dimensions became 32 and 34 cm respectively Calculate the dimensional change.

Example 15.23.

Solution.

Dimensional change in length ð%Þ ¼

32  35  100 35

Densional change in length ¼ 8:57% Dimensional change in width ð%Þ ¼

34  35  100 35

Dimensional change in width ¼ 2:86% The dimensional change length wise is 8.57% and width wise is 2.85%.

15.12

Conclusion

This chapter dealt with calculations of important fabric properties, i.e., tensile strength, handling, drape, thickness, comfort, and dimensional properties. The simple calculations provided in this chapter will be equally useful to the academicians as well as to the individuals working in the industry.

References [1] Jinlian, in: Fabric Testing, Introduction of Fabric Testing, W. P. Limited, Ed., 2008. [2] P. Sarkar, what-is-gsm-in-fabric.html, September 06, 2018. Retrieved September 21, 2022, from, https://www.onlineclothingstudy.com. [3] C. Usha, M.M. C, Bursting strength and extension for jersey, interlock and pique knits, Trends Text. Eng. Fashion Technol. 1 (2) (2018, February 07) 19e27. [4] D. Apurba, in: Science in Clothing Comfort, W. P. Limited., Ed., 2010. [5] S.M. Mohsen Gorji, A review on emerging developments in thermal and moisture management by membrane-based clothing systems towards personal comfort, J. Appl. Polym. Sci. (May 11, 2022). [6] G.H. Julia Wilfling, Consumer expectations and perception of clothing comfort in sports and exercise garments, Res. J. Text. Apparel (July 2021). [7] J. Booth, in: C.P. Distributors (Ed.), Principle of Textile Testing, S.K. Jain, 1996. [8] A.R. Horrocks, S. A., Handbook of Technical Textiles, Heat and Flame Protection, Woodhead Publishing Limited, 2000. [9] B.O. Standards, Indian Standard Textiles: Determination of Flammability of Oxygen Index, September 1992. Retrieved September 21, 2022, from, https://law.resource.org/pub/in/bis/ S12/is.13501.1992.pdf.

Index Note: Page numbers followed by f indicate figures and t indicate tables. A Abrasion, 355 resistance, 355 test, 349 Absolute humidity, 305 Acceleration, 204 Acrylic, 57 Active chlorine, 259 Actual draft, 93, 98e99, 117, 133 relation between actual and mechanic draft, 117 Additional auxiliaries calculation formula, 265 Additive type tensioner, 178 Air jet loom, 210 Air permeability, 365 Airflow method, 313e314 Air-jet weaving machines, 210e211 Alpha design approach, 47 American Apparel Manufacturers Association, 351 American Association for textile Chemists and Colorists (AATCC), 349 American National Standard Institute (ASNI), 349 American Society for Testing and Materials (ASTM), 349 Amplitude, 340 Analysis of variance (ANOVA), 19e20 Angle of wind, 172e173 Angular distortion, 210 Apparel manufacturing activities, 275 measures and calculations manufacturing operations, 284e298 plant set-up and facility design, 276e283 Arrhenius equation, 65 Attended time, 293e294 Auxiliaries, 265

Average. See Mean Average extrusion velocity, 67 B Backward feed modes, 114 Bale lay down, 80e81 Barium Activity Number (BAN), 260, 262 Barium hydroxide, 262 Basic time (BT), 295 Beam warping, 181e182 Bear sorter, 307e308 Beating, 197 Beat-up mechanism, 203e207 let-off motion, 208e209 take-up motion, 207e209 Bending length, 355e358 Bending modulii, 236 Bending of fiber within twisted yarn, 143 Betadesign approach, 47 Bleaching, 259 Blended yarn, 162e166 migration index, 163e165 strength, 165e166 strictly similar yarn, 162e163 Blending on draw frame, 103e104 slivers having linear density, 103 two components of different linear densities, 103e104 Blow room, 77e89 average fiber parameters in fiber mixture, 77e80 bale lay down, 80e81 blows/kg, 82 cleaning efficiency, 87e88 force on fiber tufts, 82e85 intensity of opening, 81e82 lap formation, 86 multimixers, 85 production calculation of, 88e89

370

Bobbin rail, traverse rate of, 124e126 Body thermoregulation, 361 Boundary length and noil% in comber, 114 BoxeBehnken design (BBD), 16e17, 22 illustration of, 22e27 Bradford reed count, 207 Break draft, 123 constant, 134 Breaking extension, 321 British Standard Institute (BSI), 349 Bureau of Indian Standards (BIS), 349 Bursting strength, 354e355 test, 349 C Calculations in fabric chemical processing barium activity number, 260 calculations at various stage of textiles processing, 255e258 cuprammonium fluidity, 259 dyeing, 260e273 mercerization, 260 Canada Standard Association (CSA), 349 Capacity calculations, 289e291 Carboxyl terminated polybutadiene (CTPB), 60 Carded yarn production process, 7e8 Carding process, 7, 90e97 carding angle, 90 draft, 93e94 intensity of opening, 90e91 periodic variation, 97 production calculation of carding, 94e95 production constant, 95e96 tooth density, 91e92 Cellulose molecule, 62 Center point, 17 Central composite design (CCD), 16e18 illustration of, 18e20 Centrifugal force, 82e83 Chemical finishes, curing of, 273 Chemical finishing methods, 273 Chemicals calculation formula, 265 Chlorine, 259 Circular knitting machine, 240, 245e246 Cleaning efficiency, 87e88 process, 7

Index

Close pack geometry, yarn structure, 153e155 Clothing science and comfort, 361e365 air permeability, 365 moisture transmission, 362e364 thermal properties, 362 WVT, 364 Coefficient of variance, 302e303 Coil angle, 173 Color strength, measurement of, 366 Comb sorter method, 312 Combed yarn productionprocess, 9 Comber, 9, 111e120 boundary length and noil% in comber, 114 comber production, 115e116 combing efficiency, 119 draft and production calculation of lap former, 111e112 draft in, 117e118 Nep removal efficiency, 119e120 piecing wave length, 114e115 production of lap former, 112e113 Combing efficiency, 119 Comfort, 361e365 Continuous fusing machine, 291 Contraction factor, 143 Control chart CUSUM control charts, 43e44 illustration of CUSUM chart with V-mask, 47 of CUSUM control chart, 44 of individual control chart, 40e41 of tabular CUSUM, 49 of zone chart, 42e43 individuals control charts, 36e40 interpretation of zone control chart, 41e42 process control in textiles by advanced, 35e49 tabular CUSUM, 48e49 utility and limitations of CUSUM chart, 49 of individual control chart, 40 of zone chart, 42 V-mask used to determine process out of control, 44e47 zone chart, 41 Core sheath yarn, 168 exercise problems, 169e170 Correct invoice weight, 328e329

Index

Cost per machine-minute, 297 Cotton bale, 85 fabric, 14 fibers, 2e5 density, 124 length variation, 308 yarn, 148 Count conversion, 139e140 relation between gauge and, 240 Course density, 238e239 Course length, 240 Course spacing, 238e239 Courses per cm (cpcm), 244 Cover factors, 228 Crankshaft, 198 Crimp, 324 interchange equation, 217, 221 redistribution, 222e223 Cumulative sum control chart (CUSUM control chart), 43e44 illustration of, 44 with V-mask, 47 utility and limitations of, 49 Cuprammonium fluidity, 259 available chlorine, 259 bleaching, 259 Curing of chemical finishes, 273 Cycle time, 289e291, 295 of process, 296 D Data, 14 Dead fibers (D fibers), 316 Degree of crystallinity from DSC study, determination of, 73e75 Degree of mercerization, determination of, 260 Degree of polymerization, 57e59 Denier and filament diameter, relation between, 63e64 Density method, determination of crystallinity of fibers by, 75 Density of cotton bale, 85 Design expert 6.0.8 software, 18e19, 25 Design of experiment (DOE), 14e16 Desizing process, 257 Deutsches Institut fuer Normung (DIN), 349

371

Diameter of nylon yarn, 151 Dicarboxylic acid, 58e59 Dilute solution viscometers, 61e62 Dimensional change, 367e368 Direct fiber fineness measurement method, 312 Direct system, 1e2, 142 folded/plied yarn, 327e328 of yarn linear density, 325 Disc type tensioner, 178 Doubling, reduction of irregularity by, 340 Draft, 93e94 in comber, 117e118 draft due to noil extraction, 118 major draft, 117 relation between actual and mechanic draft, 117 tension draft, 117 and draft constant, 99e101 ring spinning, 133e134 roving frame, 122e123 Draft change pinion (DCP), 99 Draft of lap former, 111e112 Drafting irregularity, 132e133 wave, 106 Drape, 358e360 Drape coefficient (D), 359e360 Draw frame, 97e106. See also Roving frame actual draft, 98e99 blending on, 103e104 draft and draft constant, 99e101 drafting wave, 106 efficiency, 105 irregularity due to drafting, 101e103 limit irregularity in sliver, 101 mechanical draft, 97e98 periodic variation, 106 production calculation, 104e105 wave length of periodic mass variation, 103 Drawing process, 8 Drum-driven winding calculation, 172e174 angle of wind, 172e173 different position of package and drum during winding, 172f traverse ratio or wind ratio or wind per double traverse, 173e174 wind, 173

372

Drums lippage, 177 Dry bulb thermometer, 305e307 Dry-bulb temperature, 305 Dry-relaxed state, 243 DSC study, determination of degree of crystallinity from, 73e75 Dyeing, 260e273 additional auxiliaries calculation formula, 265 auxiliaries or chemicals calculation formula, 265 curing of chemical finishes, 273 finishing, 270e271 material to liquor ratio, 264e265 percentage to gram conversion calculation formula, 265e269 printing, 269e270 shade percentage, 262 stock solution, 262e263 weight of fabric, 263e264 wet pick up, 271e273 Dynamic forces, 204 E Edge abrasion, 355 Edge loss, 288 Efficacy of splicing, 179 Efficiency draw frame, 105 sewing production, 293 Efficient values, 293 End loss, 287 End-group analysis to measure number average molecular weight, 60e61 Energy, 202 consumption reduction, 211 Evenness of yarn, 339e348 important terminologies and formulae, 339e340 addition of irregularity, 340 index of irregularity, 339e340 limit irregularity, 339 reduction of irregularity by doubling, 340 numericals, 341e348 spectrogram, 340 variance-length curves, 340e341 Experimental design, 15 Experiments, 15

Index

Exponentially Weighted Moving Average (EWMA), 50 control charts, 50e53 illustration of EWMA control chart, 52e53 utility and limitations of EWMA chart, 51 Extreme low star point, 17 F Fabric areal density, 244 defects and defective panels, 284e285 handle, 355e360 bending length, 355e358 drape, 358e360 inspection, 290 joint loss, 288 manufacturing, 197 preparatory sizing, 186e195 splicing technique, 179 warping, 181e186 winding of yarn, 171e179 quality, 284 requirement for mass manufacturing, 285e286 rolls, 288 store, 276e278 area calculation for, 278 fabric rack capacity calculation, 276e277 strength of, 352e355 thickness, 360e361 utilization, 289 weight, 247, 263e264 Fabric testing. See also Yarn testing; Fiber testing clothing science and comfort, 361e365 dimensional change, 367e368 fabric handle, 355e360 flame-retardant, 365e366 gram per square meter, 350e351 major testing standards for textile testing, 349 measurement of color strength, 366 4-point system, 351 strength of fabric, 352e355 thickness, 360e361

Index

Facility design, 276e283 fabric store, 276e278 finishing and packing, 282e283 area requirement for finishing and packing section, 282e283 finishing workstation dimensions, 282 manufacturing plant set-up, 276 relationship between area requirement of different manufacturing processes, 283 sewing, 279e282 spreading and cutting, 278e279 Factory minute-cost calculation, 297e298 Feeder density, 240 Fiber fineness, 310e316 measurement methods, 312e316 airflow method, 313e314 gravimetric method, 312e313 optical method, 314 vibroscope method, 314e316 solid fibers of circular cross-section, 310e312 Fiber testing. See also Fabric testing; Yarn testing fiber crimp, 323e324 fiber fineness, 310e316 fiber length, 307e310 fiber maturity, 310e312 fiber quality index, 318e319 humidity, 305e307 Nep Count, 323 SCI, 319e320 standard conditions for yarn testing, 301 statistical averages, 301e305 mean, 301e302 median, 302 mode, 302 sample size, 303e305 standard deviation, 302 variance and coefficient of variance, 302e303 tensile strength, 320e323 Fibers, 32, 114, 139, 149, 160, 301 bundle fiber strength, 322e323 crimp, 323e324 estimation of fiber parameters from fiber linear density, 7 fiber diameter, 139 force on fiber tufts, 82e85

373

length, 307e310 bear sorter, 307e308 manufacturing process degree of polymerization, 57e59 determination of degree of crystallinity from DSC study, 73e75 determining crystallinity of spun polymeric fibers, 75 melt spinning variables and calculations, 67e69 number average molecular weight, weight average, and viscosity average molecular weight of polymers, 59e62 quantitative concepts of polymeric molecules for fibers, 62e63 relation between denier and filament diameter, 63e64 temperature dependence of polymer viscosity, 65e66 temperature profile in filaments melt spinning condition, 69e73 tensile strength of filament, 64e65 maturity, 310e312 migration in spun yarn, 155e157 migration parameters, 156te157t number of fibers in yarn cross-section, 141 parameters estimation of fiber parameters from fiber linear density, 7 in fiber mixture, 77e80 properties fiber strength, 5e6 fineness, 5 importance of, 2e6 length characteristics, 2e4 MIC of cotton fiber, 5 quality index, 318e319 and lea CSP, 319 shape factor, 140 properties of few fibers, 140t specific fiber surface area, 139 specific surface area of hollow fiber, 139 torsion and bending of fiber within twisted yarn, 143 values of fiber density, 122 Fibro graph method, 307e310 Filaments example, 73e75

374

Filaments (Continued) relation between denier and filament diameter, 63e64 temperature profile in filaments melt spinning condition, 69e73 tensile strength of, 64e65 theoretical argument, 69e73 Filling of looms, 171e172 Fineness, 5 conversion, 139e140 expression of, 1e2 linear density/count, 1e2 Finished relaxed state, 244 Finishing process, dyeing, 270e271 First-order model, 16 Flameproof fabrics, 365e366 Flame-retardant, 365e366 LOI, 366 Flat abrasion, 355 Flat bed machine, 240 Flex abrasion, 355 Fluid carriers, 210 Folded/plied yarn count of, 327e328 in direct system, 327e328 in indirect system, 327 Folding count, 327 Force on fiber tufts, 82e85 centrifugal force, 82e83 impulse due to beating action, 82e83 Forward feed modes, 114 4-point system, 351 4-point inspection system, 284 Functionality test for fabrics, 349 G Garmenting process flow chart, 11e12 Gauge, relation between count and, 240 Giga Pascal (GPa), 64 Grab test method, 352 Gram conversion calculation formula, percentage to, 265e269 Gram per square meter, 350e351 Gram square meter (GSM), 350e351 Gravimetric method, 312e313 H Harmonic motion, 204 Head comber, 116

Index

Heart loop, 356 Heat capacity of specific polymer, 74e75 Heat transfer coefficient, 362 High volume instrument (HVI), 319 Higher point, 17 Hollow fiber, specific surface area of, 139 Humidity, 305e307 fibro graph, 307e310 wet and dry bulb thermometer, 305e307 Hybrid design, 16e17 I Image analysis, 311e312 Index of irregularity (I), 339e340 Indirect system, 1e2, 142 folded/plied yarn, 327 of yarn linear density, 326 yarn count conversion chart, 326 Individuals control charts, 36e40 illustration of, 40e41 utility and limitations of, 40 Initial modulus, 321e322 Initial Young’s modulus, 224, 321e322 Input sliver linear density, 99 International Organization for Standardization (ISO), 349 International Standard Calibration Cotton (ICCS), 308 Interpretation systems, 308 Intrinsic viscosity method, determination of number average molecular weight by, 61e62 Irregularity addition of, 340 due to drafting, 101e103 reduction of irregularity by doubling, 340 J Jammed plain woven fabrics, 216e224 Japanese Industrial Standard (JIN), 349 K Kinetic energy, 200e201 Kirschner beater, 84 Knitted fabric, 243e244 Knitted fabric production basic terminologies and relevant mathematical equations, 237e240 fabric areal density, 244

Index

geometry of loop and loop length, 240e242 theoretical loop length, 241e242 productions calculations, 245e246 RB, 242e243 state of relaxation, 243e244 TF, 245 warp knitting calculations, 246e253 Knitting, 237 KubelkaeMunk equation, 366e367 L Lap density, 86 Lap formation, 86 Lap former, 9 draft and production calculation of, 111e112 production of, 112e113 Lap sheet, 86 Lay consumption, 287 Lea CSP, 319 Lead time, 295 Length of drum, 176e177 Length parameters, 4 Limit irregularity, 339 in sliver, 101 Limiting oxygen index (LOI), 366 of polymers, 366 Linear density of comber lap, 118 linear density/count, 1e2 of plied yarn, 142 direct system, 142 indirect system, 142 of slivers, 111e112 slivers having, 103 two components of different linear densities, 103e104 Linen fiber, 5 Liquor ratio, material to, 264e265 Little’s law, 296 Loom cycle, 210 Loop, 237 geometry of, 240e242 Loop length, 247 geometry of, 240e242 Low point, 17 M Machine gauge, 239

375

Machine models, 210e211 Man-made fibers, 1, 5 Manufacturing operations, 284e298 capacity calculations and cycle time, 289e291 fabric cutting, 290e291 fabric inspection, 290 fabric spreading, 290 fusing, 291 ticketing and bundling, 291 fabric defects and defective panels, 284e285 fabric requirement, 285e289 consumption calculation, 285e286 fabric utilization, 289 marker efficiency, 286e287 material productivity, 288e289 wastage calculation, 287e288 weighted efficiency, 288 sewing production, 291e298 Manufacturing plant seteup, 276 Manufacturing processes, relationship between area requirement of different, 283 Marker, 286 efficiency, 286e287 MarkeHouwink equation, 59e60 Material productivity, 288e289 Material to liquor ratio (MLR), 264e265 Mathematical equations, basic terminologies and relevant, 237e240 Maturity coefficient (Mc), 317e318 Maturity of cotton fiber (MIC of cotton fiber), 5 Maturity ratio (Mr), 316e318 Maximum fabric flexural rigidity, 231 Mean, 301e302 Mean deviation, 302 Mean length (ML), 308 Measurement, 275 Measures, 275 and calculations manufacturing operations, 284e298 plant set-up and facility design, 276e283 Mechanic draft, relation between actual and, 117 Mechanical draft, 93, 97e99, 117, 133 Median, 302 Mega Pascal (MPa), 64

376

Melt spinning variables and calculations, 67e69 independent variables of, 67 resulting variables in melt spinning, 68e69 secondary variables in, 67e68 Mercerization, 260 determination of degree of mercerization, 260 Mercerized cotton, 262 Migration index, 163e165 Minimum flexural rigidity of fabric, 230e231 Mixture design, 28e32 Mixture experiment, illustration of, 32e35 Mode, 302 Model F-value, 33e35 Modified crimp interchange equation, 224 Moisture content, 301 textiles processing, 255e256 yarn, 329 Moisture in yarn, 328e331 important terminologies and formulae, 329 correct invoice weight, 329 moisture content, 329 moisture regain, 329 numericals, 330e331 Moisture regain textiles processing, 255e256 yarn, 329 Moisture transmission, 362e364 Molar mass, 57 Molecular weights, 59e60 Molten polymer, 69 Molten polymers, 65 Moving range, 37 Multimixers, 85 blending delay time, 85 doubling factor, 85 Multiplicative type tensioner, 178 N Natural fibers, 1, 257 Needle pitch, 239 Nep Count, 323 Nep removal efficiency, 119e120 Newton’s law, 71 Noil extraction, draft due to, 118 Nonlinear model, 33e35 Normal fibers (N fibers), 316

Index

Number average molecular weight of polymers, 59e62 determination of, 61e62 by intrinsic viscosity method, 61e62 end-group analysis to measure number average molecular weight, 60e61 Nusselt number, 71 Nylon, 57 diameter of nylon yarn, 151 O Observational study, 14e15 Observed time (OT), 295 Off-standard time, 293e294 One factor-at-a-time experiments, 15 On-standard time, 293e294 Opening intensity blow room, 81e82 carding, 90e91 Opening process, 7 Optical method, 314 Outputs liver linear density, 99 P Package diameter, 172 Packing coefficient, 149e152 circular fibers in contact, 150f Packing density, values of, 122 Panel rejection%, 285 Pawl arrangement, 208 Pear loop, 356 Peirce cover factor, 216 Pendulum lever principle, 334e335 Percentage Mean deviation (PMD), 302 Percentage of mature fiber (Pm), 317e318 Periodic mass variation back roller eccentric, 103 front bottom roller eccentric, 103 wave length of, 103 Periodic variation carding process, 97 draw frame, 106 Physical tests, 349 for fabrics, 349 Pick spacing, 208 Picking mechanism, 200e203 motion, 198 systems, 200

Index

Picks per inch (PPI), 209 Piecing wave length, 114e115 Pierce formula, yarn diameter by, 145e149 Pilling resistance test, 349 Pirn, 10 winding, 11 Pitch time, 296 Plane abrasion, 355 Plant set-up, 276e283 fabric store, 276e278 finishing and packing, 282e283 area requirement for finishing and packing section, 282e283 finishing workstation dimensions, 282 manufacturing plant set-up, 276 relationship between area requirement of different manufacturing processes, 283 sewing, 279e282 spreading and cutting, 278e279 Plied yarn count of, 327e328 linear density of, 142 Points per 100 square yards (PPHSY), 284 Polyesters, 57, 60e61 bottle, 73 fiber, 169 Polymeric molecules for fibers, quantitative concepts of, 62e63 Polymerization process, degree of, 57e59 Polymers, 58e61 number average molecular weight, weight average, and viscosity average molecular weight of, 59e62 temperature dependence of polymer viscosity, 65e66 Polypropylene (PP), 57, 64 fiber, 169 yarn count, 151 Porosity of cloth, 231 Postproduction (apparel manufacturing activity), 275 Potential energy, 210 Prandtl number, 72 Preproduction activities (apparel manufacturing activity), 275 Prespinning process, 77 blow room, 77e89 carding, 90e97 draw frame, 97e106

377

Pressley index, 322 Pressley tester, 322 Pretreatment process, 259 Printing, 262e263, 269e270 determination of printing cost in textile industry, 270 paste, 271e273 Production (apparel manufacturing activity), 275 calculation, 245e246 of blow room, 88e89 of carding, 94e95 circular knitting machine, 245e246 of draw frame, 104e105 of lap former, 111e112 ring spinning, 136e137 roving frame, 126e127 V-bed knitting machine, 246 of circular weft knitting machine, 245 constant, 95e96 of lap former, 112e113 Productivity, 292e293 Q (q 1) simplex, 31 q-cuboid, 31 R Radial force, 161 Radial pressure in twisted yarn, 160e161 Ranking fiber properties for spinning technologies, 6 Rapier, 210 Raw material and characteristics, 1 Redcliff system, 206 Regression equation of SCI, 319e320 Relative humidity (RH), 256, 305 Relative variance, 340 Response surface design, 16e35 boxeBehnken design, 22 central composite design, 17e18 illustration BoxeBehnken design, 22e27 of central composite design, 18e20 of mixture experiment, 32e35 mixture design, 28e32 Response surface methodology (RSM), 16 Retained splicing strength, 179 Retrospective study, 14e15

378

Reynolds numbers, 72 Ring loop, 356 Ring spinning, 128e137 draft and draft constant, 133e134 drafting irregularity, 132e133 process, 8 production calculation, 136e137 twist constant, 134e136 twist factor, 129e130 winding equation, 128e129 winding tension, 130e132 yarn twist, 129 Robbing back (RB), 242e243 Roving frame, 120e127. See also Draw frame draft and draft constant, 122e123 production calculation, 126e127 roving diameter, 122 roving twist, 120e121 traverse rate of bobbin rail, 124e126 twist factor, 121e122 winding speed, 123e124 Roving making process, 8 S Salt, 267 Scouring efficiency, assessment of, 258 Scouring process, 257e258 Seam slippage, 349 Second-order models, 16e17 Sewing, 279e282 capacity, 292 efficiency, 293 factory minute-cost calculation, 297e298 lead time, 295 line dimensions’ calculation, 280e282 performance, 293e294 pitch time, 296 production, 291e298 production, 292 productivity, 292e293 SAM and SMV, 294e295 Takt time, 297 throughput time, 296 utilization, 294 workstation area calculation, 280 Shade percentage, 262 Shear modulus, 235 of fabrics, 234

Index

Shedding, 197e200 transmission of motion in loom, 198f Shewhart control charts, 35e36, 41 Shirley maturity, 319 Short fibers, 4 Shrinkage, 222e223 Shuttle’s mass, 203 Simplex-lattice design, 31 Single fiber strength, 322 Singles yarn, 327 Sizing process, 11, 186e195 Sley, 198 Sley eccentricity, 200e201 Sley-eccentricity ratio, 204 Slipping-friction system, 209 Sliver limit irregularity in, 101 linear density, 103 to yarn spinning process, 10 Soda, 267 Solid fibers of circular cross-section, 310e312 Sorter diagram, 307e308 South Indian Textile Research Association, 318 Span length (SL), 4, 119, 308 Specific surface, 311 Spectrogram, 340 Speed, 198 Spindle-driven winding, 174e177 Spinning process carded yarn production, 7e8 combed yarn production, 9 flow chart of, 7e10 sliver to yarn spinning, 10 ranking fiber properties for spinning technologies, 6 Spinning consistency index (SCI), 319e320 Splicing overlap loss, 288 technique, 179 zone, 179 Spreading and cutting, 278e279 area calculation for spreading and cutting department, 279 calculation for spreading and cutting table dimensions, 278 table length, 278

Index

table width, 278 requirement for number of spreading and cutting tables, 279 Spun polymeric fibers determination of crystallinity of fibers by density method, 75 determining crystallinity of, 75 Spun yarn fiber migration in, 155e157 self-locking structure of, 166e168 Squares of coefficients, 340 Standard Allowed Minute (SAM), 294e295 Standard deviation, 302 Standard minute value (SMV), 276, 294e295 Standard time (ST), 295 Star point, 17 State of relaxation, 243e244 Statistical control charts, 35e36 Statistical methods, 14 Statistics for textile engineers, role of, 13e15 Stelometer, 322 Stickering loss, 288 Stitch density (S), 240, 244 Stitching process, 279 Stock solution, 262e263 Strain, 320 Strength blended yarn, 165e166 of fabric, 352e355 abrasion resistance, 355 bursting strength, 354e355 tearing strength, 354 tensile strength, 352e354 Strictly similar yarn, 162e163 Surface speed ratio, 94 Synthetic fibers, 2e4, 57, 257 T Tabular CUSUM, 48e49 illustration of, 49 Takt time, 297 Tappets, 197e198 Tear strength, 354 Tearing force, 354 resistance, 354 strength, 354

379

test, 349 Tenacity or specific strength, 321 Tensile properties of fibers, 320 of yarns, 333e338 important formulae, 333e336 numericals, 336e338 Tensile strength, 320e323, 352e354 breaking extension, 321 fiber bundle fiber strength, 322e323 initial modulus, 321e322 single fiber strength, 322 strain, 320 tenacity or specific strength, 321 tensile strength/stress, 320 test, 349 work of rupture, 321 Tensile testing of yarns, 333 Tensioner system, 178e179 Testing, 349 Tex system, 215e216 Textiles calculations at stage of textiles processing, 255e258 assessment of scouring efficiency, 258 desizing, 257 moisture regain and moisture content, 255e256 pretreatment, 257 scouring, 257e258 chemical process, 262e263 determination of printing cost in textile industry, 270 experiments and advanced control charts in textile engineering design of experiment, 15e16 EWMA control charts, 50e53 process control in textiles by advanced control chart, 35e49 response surface design, 16e35 statistics for textile engineers, 13e15 fibers, 57, 301 major testing standards for textile testing, 349 material, 263e264 printing, 271 process estimation of fiber parameters from fiber linear density, 7

380

Textiles (Continued) expression of fineness, 1e2 flow chart of spinning process, 7e10 flow chart of weaving process, 10e11 flow chart of weft knitting process, 11 garmenting process flow chart, 11e12 importance of fiber properties, 2e6 ranking fiber properties for spinning technologies, 6 raw material and characteristics, 1 Theoretical loop length, 241e242 Thermal conductivity, 25 Thermodynamic wet-bulb, 305 Thin-walled fibers, 316 3-D surface plots, 27 3-level factorial design, 16e17 Throughput time, 296 Tightness factor (TF), 245, 247 Tooth density, 91e92 Torsion rod diameter, 210 Torsional rod, 213 Torsionof fiber within twisted yarn, 143 Total cloth shrinkage, 222 Total draft, 98 Traverse rate of bobbin rail, 124e126 Traverse ratio, 173e174 Twist, 331 Twist constant, 134e136 Twist factor (TF), 121e122 Twist multiplier (TM), 332e333 Twist wheel (TW), 135 Twisted filament yarn, tensile behavior of, 157e160 relation between fiber and yarn strain, 158t Twisted yarn, radial pressure in, 160e161 U Uniformity index (UI), 309 Utilization, sewing production, 294 V Variability, 14 Variance, 302e303 Variance-length curves, 340e341 between length, 340e341 within length, 341 V-bed knitting machine, 246

Index

Vibroscope method, 314e316 Vinyl fibers, 57 Vinyl polymers, 61 Viscose rayon, 57 Viscosity average molecular weight of polymers, 59e62 determination of, 61e62 V-mask illustration of CUSUM chart with, 47 used to determine process out of control, 44e47 W Wale spacing, 238 Wales per cm (wpcm), 244 Warp cover factor, 216e217 Warp density, 182 Warp knitting, 237 answers of unsolved problems, 253 calculations, 246e253 solved problems, 248e252 unsolved problems, 252e253 Warp sheet, 187, 197 Warp sizing, 186 Warp winding, 171e172 Warp yarns, 186 Warper’s beams, 181e182 Warping, 171 calculation regarding warping, 182e186 process, 11, 181e186 Wastage calculation, 287e288 Wastes, 287 extraction, 87 Water vapor, 305 Water vapor transmission (WVT), 364 Water-jet looms, 210e211 Wave length of periodic mass variation, 103 Weaving, 171, 197 machine, 171 process, 11, 257 flow chart of, 10e11 Weft carrier, 210 Weft insertion rate (WIR), 202 Weft knitting, 237 flow chart of weft knitting process, 11 Weight average molecular weight of polymers, 59e62

Index

Weight loss method, 258 Weight of fabric, 263e264 Weighted efficiency, 288 Wet bulb thermometer, 305e307 Wet finishing. See Chemical finishing Wet pick up, 271e273 Wet processing, 255 of textile materials, 257 Wet-bulb temperature, 305 Wet-relaxed state, 243 Wind, 173 angle of, 172e173 ratio, 173e174 Wind per double traverse, 173e174 Winding equation, 128e129 operation, 171 process, 8 speed, 123e124, 128 tension, 130e132 of yarn, 171e179 drum-driven winding calculation, 172e174 slippage during drum, 177 spindle-driven winding, 174e177 yarn tensioning, 178e179 Wool, 312e313 fabric, 18e19 thermal conductivity of, 22e25 gravimetric method, 312e313 Work in process (WIP), 291, 296 Work of rupture, 321 Woven fabrics, 215 beat-up mechanism, 203e207 primary motions, 197e203 picking mechanism, 200e203 shedding, 197e200 secondary motions shedding, 207e209 Wrap yarn, 161e162 X X-ray diffraction methods, 62e63 Y Yarn linear density, 325e328 count of folded/plied yarn, 327e328

381

important terminologies and formulae, 325e326 direct system, 325 indirect system, 326 numericals, 326e328 Yarn testing. See also Fabric testing; Fiber testing evenness of yarn, 339e348 moisture in yarn, 328e331 standard conditions for, 301 tensile properties of yarns, 333e338 yarn linear density, 325e328 yarn twist, 331e333 important formulae, 332 numericals, 332e333 Yarns, 139, 171 blended yarn, 162e166 close pack geometry, 153e155 core sheath yarn, 168 diameter, 160 fiber migration in spun yarn, 155e157 fineness/count conversion, 139e140 linear density of plied yarn, 142 manufacturing process, 77 number of fibers in yarn cross-section, 141 packing coefficient, 149e152 radial pressure in twisted yarn, 160e161 radius, 154 relationship between structural parameters, 145e149 in idealized helical yarn geometry, 146te147t idealized helix geometry, 145f yarn diameter by pierce formula, 145e149 self-locking structure of spun yarn, 166e168 structure, 186 tenacity, 35 tensile behavior of twisted filament yarn, 157e160 tensioning, 178e179 torsion and bending of fiber within twisted yarn, 143 twist, 129 winding of, 171e179

382

Yarns (Continued) wrap yarn, 161e162 yarn contraction/extension due to twisting/ untwisting, 143e144 yarn diameter, 140e141 Young’s equation, 363e364

Index

Z Zero slippage, 172 Zone chart, 41 illustration of, 42e43 utility and limitations of, 42 Zone control chart, interpretation of, 41e42