Journal of The Institution of Engineers (India): Series E

RNI Number: 5041/57

40034

Journal of The Institution of Engineers (India): Series E

ISSN 2250-2483 (print version) ISSN 2250-2491 (electronic version)

Volume 96 · Issue 2 · July–December 2015

Volume 96 · Issue 2 · July–December 2015



Volume 96 · Issue 2 · July–December 2015 · pp 85–180

Chemical Engineering · Textile Engineering

SPECIAL THEME: Modeling and Optimization in Fibrous Materials GUEST EDITORS: Abhijit Majumdar · Yordan Kyosev

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The Institution of Engineers (India)

J. Inst. Eng. India Ser. E (July–December 2015) 96(2):85 DOI 10.1007/s40034-015-0076-y

FOREWORD

Foreword Arcot R. Balakrishnan

Ó The Institution of Engineers (India) 2015

I would like to present, with great pleasure, the current issue of the journal of The Institution of Engineers: Series E on ‘‘Modeling and Optimization in Fibrous Materials’’. This issue is devoted to the gamut of textile engineering topics, from theoretical aspects to applicationdependent studies and the validation of emerging technologies. There are eleven papers which shed light on the contemporary research work in the domain of fibrous materials. I congratulate the Editorial Board and Editorial Advisory Board and particularly Dr. Abhijit Majumdar,

Associate Editor of this Journal and Prof. Yordan Kyosev, Guest Editor of this issue for their sincere effort to bring out this fine collection of papers. In addition, I would like to thank the reviewers of the Journal who have contributed to the making of the issue and whose work has increased the quality of articles even more. I hope, this issue will be a valuable resource for the readers and will stimulate further research in modeling of fibrous materials.

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J. Inst. Eng. India Ser. E (July–December 2015) 96(2):87–88 DOI 10.1007/s40034-015-0067-z

EDITORIAL

Modeling and Optimization in Fibrous Materials Abhijit Majumdar1 • Yordan Kyosev2

Published online: 13 June 2015 Ó The Institution of Engineers (India) 2015

Fibrous materials are increasingly being used in various technical applications including healthcare, protection, sports, industrial and composites. For ages, fibrous materials have been developed based on intuition, thumb rules and trial and error approach. However, in recent years, development of models to understand the manufacturing process and structure–property relationship of fibrous materials has emerged as a challenging area of research. Tensile, impact, bending, compression, shear, heat transfer, moisture-vapour transfer, fluid permeability and UV transmission are some of the properties of fibrous materials which have been modelled extensively by mathematical, analytical, statistical and intelligent techniques. The physical and performance requirements of fibrous materials are dependent on the end use. Sometimes, these requirements are conflicting with each other and thus optimization becomes essential. These models are often used to optimize

This special issue is a modest endeavour to compile some modelling and optimization related research work in the domain of fibrous materials. We hope that this issue will kindle some interest among the textile researchers to take this area forward. & Abhijit Majumdar [email protected] Yordan Kyosev [email protected] 1

Department of Textile Technology, Indian Institute of Technology, Delhi, India

2

Faculty of Textile and Clothing Technology, Hochschule Niederrhein - University of Applied Sciences, Mo¨nchengladbach, Germany

the properties of the final product by varying the materials properties, structural and process parameters. This special issue entitled ‘‘Modeling and Optimization in Fibrous Materials’’ contains 11 papers. These papers encompass the applications of various modeling techniques in fibres, yarns, fabrics and carpets. The first paper is a thematic one which deals with various types of mathematical models and their principles. The second paper presents an insight into the mechanics of 1 9 1 rib loop formation system on dial and cylinder machine. The degree of agreement between predicted and measured values of loop length and cam force justifies the efficacy of the model. The third paper proposes a theoretical model for predicting warp yarn tension during weaving based on the dynamic nature of shed geometry. The study also reveals that the developed yarn tension peak values are different for the extreme positions of a heald. The fourth paper deals with a strain sensitive textile based elastomeric tape sensor development. The weave structure, number of conductive threads and rubber thread tension has been optimized by using the Box–Behnken design of experiment method. The fifth paper describes the optimization of the aqua splicer parameters namely opening time, splicing time, splice length and duration of water joining for lycra-cotton core spun yarn using Taguchi experimental design. The sixth paper presents Eyring’s non-linear viscoelastic model to simulate stress–strain behaviour of polyester and viscose filaments. The complex mathematical equations of Eyring’s model for curve fitting are handled by genetic algorithm. The authors demonstrate that that Eyring’s model can be used to simulate the stress–strain behaviours of polyester and viscose filaments with reasonable accuracy. The seventh paper proposes different

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possibilities of micromagnetic modeling of magnetic fibers or coatings. It presents an overview of calculation times for different dimensions of magnetic materials, indicating the limits due to available computer performance. The eighth to eleventh papers deal with various soft computing methods like Artificial Neural Network (ANN), Adaptive Network based Fuzzy Inference System (ANFIS) and genetic algorithm for textile modeling and optimization. The eighth paper presents an endeavor to predict the percentage yarn strength utilization in cotton woven fabrics using ANN approach. The results indicate that while an increase in the number of load bearing or transverse yarns increases the percentage yarn strength utilization, an increase in the float length and the crimp percentage in the yarns have a detrimental effect. The ninth paper propounds a new approach of fabric engineering using ANN and genetic algorithm. The three ANN models has been developed for the prediction of drape coefficient, air permeability and thermal resistance. The fabric engineering problem has been solved using genetic algorithm. The tenth paper presents prediction of bending rigidity of cotton woven fabrics by ANN and two hybrid soft computing methodologies, namely neuro-genetic modeling (GANN) and ANFIS. The GANN model, in particular, shows better prediction accuracy than the other two models. The last paper presents the application of ANN modeling for the prediction of abrasion resistance of Persian handmade wool carpets.

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J. Inst. Eng. India Ser. E (July–December 2015) 96(2):87–88

Abhijit Majumdar obtained Bachelors Degree from Calcutta University with first class first position in Textile Technology program. Subsequently, he acquired M.Tech. degree in Textile Engineering from IIT Delhi and Ph.D. in Production Engineering from Jadavpur University, Kolkata. He also holds M.B.A. degree from IIT Delhi with specialization in Operations Management. He has worked in industries like Voltas Limited and Vardhman Group. He joined IIT Delhi as Assistant Professor in 2007. Currently he is associate professor in textile engineering group. His research areas include protective textiles, soft computing applications and operations management. He has completed three research projects, as Principal Investigator, funded by DST and CSIR, India. He has published 50 research papers in International refereed Journals. He is the Associate Editor of Journal of the Institution of Engineers (India) Series E (Chemical and Textile Engineering). Yordan Kyosev obtained his Masters in Technique and Technology of Textile and Clothing and Applied Mathematics from Technical University of Sofia, Bulgaria. He completed his Ph.D. in Textile Engineering from the same University. He worked as Assistant Professor until 2005 in Technical University of Sofia, Bulgaria. He received Alexander von Humboldt Fellowship for Postdoctoral study at the Institute of Textile Technology (ITA) [Institut fu¨rTextiltechnik] of the RWTH Aachen University, Germany. Prof. Kyosev joined as Professor in the Textile and Clothing Technology, HochschuleNiederrhein – University of Applied Sciences, Germany in the year 2006. He has published numerous Journal papers, Conference presentations, several Book Chapters about Modeling of Textiles. He has also authored a book on Fuzzy Logic with Prof. K. Peeva. Prof. Kyosev has published a Monograph titled, ‘‘Braiding Technology for Textiles’’, which becomes the main textbook in this area. He has also developed industrial software, which is used in modelling and simulation of textile structures for several companies.

J. Inst. Eng. India Ser. E (July–December 2015) 96(2):89–98 DOI 10.1007/s40034-015-0057-1

ARTICLE OF PROFESSIONAL INTEREST

A Review on Mathematical Modeling for Textile Processes R. Chattopadhyay

Received: 19 November 2014 / Accepted: 14 January 2015 / Published online: 17 February 2015 The Institution of Engineers (India) 2015

Abstract Mathematical model is a powerful tool in engineering for studying variety of problems related to design and development of products and processes, optimization of manufacturing process, understanding a phenomenon and predicting product’s behaviour in actual use. An insight of the process and use of appropriate mathematical tools are necessary for developing models. In the present paper, a review of types of model, procedure followed in developing them and their limitations have been discussed. Modeling techniques being used in few textile processes available in the literature have been cited as examples. Keywords Mathematical model Fibre breakage Texturising Twist density Filament

Introduction Mathematical models are very concise and exact mathematical statements about a process, phenomenon, possibilities of an event or arrangement of elements in a structure. It is way to establish mathematical relationship between dependent and independent variables based on cause effect relationship that helps to better understand the relation between process parameters, material behaviour and product properties. Various mathematical concepts are used to develop these models. Models help us to get an insight about a problem or process and improve our understanding about it. Computer based models are developed with appropriate software for visualization. R. Chattopadhyay (&) Indian Institute of Technology Delhi, New Delhi 110016, India e-mail: [email protected]

Computational modeling can improve quality of work and reduce changes, errors and rework. Models have emerged as a powerful, indispensable tool in engineering for studying a variety of problems related to product, process development and manufacturing.

Definition of Mathematical Model A mathematical model is a triplet (S, Q, M) where S is a system, Q is a question relating to S, and M is a set of mathematical statements M = {1, 2,…, n} which can be used to answer Q. ‘‘Typically, a system is described first followed by a question regarding that system and to seek answer, a mathematical model is developed. Each of the constituents of the triplet (S, Q, M) is an indispensable part of the whole. Without S, there will not be any Q; and without a question Q, M would be no more than a mere mathematical statement. In textile we may be interested to predict the elongation of a fabric subjected to a force [1]. Here fabric becomes the system (S), the question (Q) is the displacement and a mechanistic model (M) needs to be developed to get the answer.

Need for Modeling It is often used in place of performing experiments when experiments are too large, expensive, dangerous, or time consuming. In an industrial process the regular process cannot be disturbed for the sake of carrying out experiments to improve the process or improve quality. A mathematical model can be a handy tool to understand the influence of various process parameters on product quality or process performance.

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Limitations of Models The limitations of a model are stated below: –

– – – – –

Models are never a perfect description of reality as approximations and assumptions are necessary while developing a model. Models are based on current knowledge and there always exists scope for improvement. Resolution in time and space is limited (computing time). Initial and boundary conditions are crucial but often may not available as needed. Enough data may not be available to use the model as exact depiction of the environment. Sometimes we may get good results for the wrong reasons.

Types of Mathematical Model Models can be of different types such as: 1.

2.

3.

Geometrical Model: In geometric model, the spatial arrangement of the basic elements of a structure is modeled by establishing geometrical relationship between various physical/dimensional parameters. The model helps us to understand how various geometrical parameters of a textile structure are interdependent on each other. Examples are helical geometry of twisted yarns, Pierce’s model of woven fabrics, geometrical models of nonwoven and knitted fabrics. Mechanistic and Empirical (Phenomenological) Model: Mechanistic models are based on laws of physics and mechanics and generally describes what happens at one level in the hierarchy by considering processes at lower levels. The system information is necessary to build such models. Phenomenological models are easy to set up but limited in scope whereas mechanistic models gives deeper insights into the system, better predictions and have applicability over a wider data range. However, they need much more resources and time. There could be situations when mechanistic models can not be formulated. As an example the influence of dye concentration, temperature and pH of dye bath on dye exhaustion. Physical laws may not be available and a regression based model could be more appropriate. As a prerequisite, mechanistic models need a priori knowledge of the system. Deterministic and Probabilistic (Stochastic) Model: In deterministic model each set of variable states is uniquely determined by parameters in the model.

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4.

Therefore, deterministic models perform the same way for a given set of initial conditions and gives same outcome. Conversely, in a stochastic model, there exists uncertainty about model’s coefficients or inputs. The variable states are not described by unique values, but rather by probability distributions such as mean and variance and hence it gives distribution of possible outcome. Static and Dynamic Model: A static model does not account for the element of time, while a dynamic model does. Mechanistic model and phenomenological models describe stationary state of system. These model equations represent time –independent (stationary) state. The elongation (y) of high tenacity fibre can be modeled by the equation

y ¼ kx; where k is the modulus of the fibre and x = force applied. This is based on the force equilibrium concept where the external force exactly matches the internal force of the fibre under extended state. One gets equilibrium elongation of the fibre under load x. In static model the coefficients are constant. The output in a static model at any given time depends upon its input at that time. Dynamic model accommodates the possible changes in the variables as a function of time. The steps involved in the development of dynamic model are: (i)

Identification of all process and product variables involved in the process and connected with each other via cause effect relations. (ii) Formulation of all possible differential equations of the system following mass, energy and momentum balances. (iii) Determination of coefficients of differential equation coefficients theoretically and experimentally and finding their solutions. (iv) Performing mathematical simulations in order to answer the technological questions. If we are interested in the time dependent extension of the fibre i.e. y (t), after application of a force x at time t = 0 then, time dependent mathematical equations has to be formulated which will be known as dynamic model. In dynamic models, the present output depends upon not only on the present but also on past inputs. Dynamic models are represented by differential Equation.

5.

Black Box Model: At times, there may not be any prior information available about the functional relationship between the variables. In black-box models one tries to


6.

estimate both the functional form of relations between variables and the value of the coefficients in those functions. Prior information helps us to describe the system adequately. Without any priori information one has to use functions in general. An often used approach for black-box models is neural network which usually do not assume almost anything about the incoming data. Phenomenological models also fit this category. Lumped and Distributed Parameter Models: Many variables in nature are a function of both time and space. If we ignore the spatial dependence and choose a single representative value, it is called lumping. As an example the Relative Humidity (RH) in a loom shed. It is usually an average relative humidity of the shed which is used to express the RH of the shed though we know it may vary from place to place within the shed. In a lumped system the dependent variables of interest are a function of time alone. In general, this will mean solving a set of Ordinary Differential Equations (ODE).

If the spatial dependence is included, spatial co-ordinates as well as time needs to be included in the model which will be known as distributed parameter model. In a distributed system, all dependent variables are functions of time and one or more spatial variables. Distributed parameters are typically represented with partial differential equations. Suppose a rope is made by selective placement of yarns in different layers. The rope as a whole behaves more like a spring. Suppose we are interested to know the equilibrium deformation of the rope under certain constant load. Since the rope for all practical purposes can be approximated to behave like a spring, to predict the equilibrium elongation of the rope, one needs to know the spring constant ‘k’ of the rope and apply the well known equation y ¼ kx In these models, all spatial information is lumped together into the parameter k. Now suppose the rope elongates more than desired at a certain load and it is required to design a stiffer rope. The question arises yarns belonging to which layer are to be made stiffer? Obviously those yarns are to be made stiffer which are subjected to highest mechanical stresses. To identify them, the distribution of stresses inside the rope under load is required to be worked out. Let (x, y, z) denote the mechanical stress distribution inside the rope depending on the spatial coordinates x, y, and z. Then we need a mathematical model with r(x, y, z) as a state variable. The important difference between this model and the previous model is that in this case the state variable depends on the spatial coordinates. On the other hand, if one is looking for

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the internal stress distribution in the rope, a spatially distributed mathematical statement of the stresses inside the rope is needed. A model should be simple and easy to handle. Adding too many parameters increase complexity and inaccuracy in the overall result as inputting estimated value of each parameter may add to the overall uncertainty of the results. In many cases, engineers often can accept some approximations in order to get a more robust and simple model.

Model Building Process The purpose of mathematical model is to build a mathematical structure of the real world situation based on rules and laws of mathematics and physics. A schematic of the steps involved in model building is shown in the diagram below (Fig. 1). Model objective: Understand the phenomenon or process. Decide model objective. Identify and select factors that are relevant for the model. Make simplifying assumptions. Identify model variables. Determine governing principles and inter relationship. Real world data: One has to gather real relevant data based on background research, experimentations in a laboratory or from the field. Mathematical Model: Formulate the model based on physical laws, and mathematical concepts related to algebra, trigonometry, differential equations, probability etc. and finally transform it to simple mathematical relationship. Computational Model: Change Mathematical Model into a form suitable for computational solution. It involves choice of the numerical method, algorithm and software (Matlab, Mathematica, Excel, Java etc.). Results/Conclusions: Computational model are run to obtain results. Graphs, charts, and other visualization tools are used in interpreting results and drawing conclusions.

Developing Model objective

Gather

Real world data

Formulate

Mathematical Model Translate

Interpretation/ explanations

Analysis

Results

Simulate

Computational Model

Fig. 1 Modeling steps

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Model Evaluation A very important part of the modeling process is the evaluation of the model or validation. A common approach is to split the experimental data into two parts; training and verification data. The training data is used for estimating model parameters. The verification data is to be used to evaluate model performance. If the model describes the verification data well, then the model is expected to describe the real system well.

yarns, fabrics (woven or knitted), nonwoven nets, twisted or braided ropes etc. In geometrical model building a geometrical repeat cell of the structure is identified (Fig. 2). The path of the elements which could be fibre, or yarns are described based on geometrical relationships. Such models help us to estimate many other important parameters of the structure by measuring few geometrical parameters. This in turn helps to understand the performance behaviour of the product. Some simple geometrical relationships are shown in Table 1.

Modeling Examples

Modeling of Mechanical System [3]

Geometrical Modeling of Textile Structure [2]

Mechanical systems consists of many mechanical elements which are interconnected to perform some mechanical functions. The motions of the elements could be either translational or rotational. We may need to formulate the

Geometrical modeling is the first step to understand the structure property relationship for any textile structure be it Fig. 2 Unit cell of yarn and fabric

Table 1 Model for geometrical equations

Yarn

Geometrical equations

Parameters

h = 1/T

R = yarn radius

l2 = h2 ? 4p2r2 2

2

2 2

r = radius of cylinder containing helical path of a particular fibre

L = h ? 4p R

T = Yarn twist (tpcm)

tan h = 2 pr/h

h = length of one turn of twist (cm)

tan a = 2p R/h = 2pRT

a = surface angle of twist h = corresponding helical angle at radius r l = length of fibre in one turn of twist at radius r (cm) L = length of fibre in one turn of twist at radius R (cm)

Fabric D = d1 ? d2 = h1 ? h2

d—diameter of thread

C1 ¼ pl12 1

p—thread spacing

p2 = (l1 - Dh1)Cosh1 ? DSinh1 h1 = (l1 - Dh1)Sinh1 ? D(1 Cosh1)

h—maximum displacement of thread axis normal to the plane of cloth (crimp height) h—angle of thread axis to the plane of cloth (weave angle in radians) l—length of thread axis between the planes through the axes of consecutive cross- threads (modular length) c—crimp (fractional) Suffix 1 and 2 to the above parameters represent warp and weft threads respectively

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governing equations to better understand their working. These can be formulated directly or indirectly based on Newton’s law of motion. Translational motion were those motions which occur along a straight line. The variables used to describe the motions are acceleration, velocity and displacement. Table 2 shows few situations where a force or torque acts on a body, spring or dashpot. The corresponding governing equations are stated. Modeling a Gear Train Gear train is very common in many textile machines. A gear train transmits mechanical energy from one part of the system to another in such a way that force torque speed and displacement may be altered. Lets us take the example of two gears coupled together (Fig. 3). Gear A is connected to a motor and gear B to a load. The inertia and friction are neglected. The relationship between the torques s1 and s2, angular displacement h1 and h2 and teeth number N1 and N2 of the gear trains A and B are: The number of teeth on the gear surface is proportional to their radii as pitch remains same. So r1 N2 ¼ r2 N1

ð1Þ

The distance travelled by each gear is same i.e. r 1 h1 ¼ r 2 h2

ð2Þ

The work done by one gear will be equal to that of the other. Work done = Torque 9 Displacement s1 h1 ¼ s 2 h2

ð3Þ

Combining all the three equations s1 h2 r1 N1 ¼ ¼ ¼ s2 h1 r2 N2

ð4Þ

The toque balance equation for the motor is: sM ¼ J 1

d 2 h1 dh1 þ s1 ; þ B1 dt2 dt

ð5Þ

where J1 and B1 are inertia and viscous friction coefficient of bearing of gear A and s1 is the torque transmitted to gear B. The toque balance equation for the load side s2 ¼ J 2

d 2 h2 dh2 þ sL þ B2 dt2 dt

ð6Þ

where J2 and B2 are inertia and viscous friction coefficient of bearing of gear B. sL is coulomb friction torque. Substituting s2 ¼ s1 NN21 N1 d 2 h2 dh2 þ sL s1 ¼ J 2 2 þ B2 N2 dt dt

Through substitution and simplifying it can be shown that motor torque (sM) is: " " 2 # 2 2 # N1 d h1 N1 dh1 sM ¼ J 1 þ J2 þ B1 þ B2 N2 dt2 N2 dt N1 þ sL ð7Þ N2 Modeling of Technological Process In any technological process, the input material is processed and transformed into a product having some desirable characteristics. For a process, the process and product characteristics are: Process characteristics: mechanical, speed, temperature, and pressure related parameters or variables. Product characteristics: quality characteristics or state of input material, intermediate processed material or output materials. Though the input material characteristics and the process variables are supposed to be at their designated mean level but many times, these vary around their operating midpoint. As a result the product characteristics oscillate around the desired set value due to dynamics caused by cause-effect relation. Steady State and Non Steady State Process [4] In a process, the machine and material to be processed constitute a system. When the system begins to run, the process begins and the process and product variables start interacting. The mean values of the variables and their fluctuations can be considered as similar to signals. If the signals miss, the interactions between the variables stop such as process interruptions after a yarn breakage during rotor spinning. The process falls back to its static (unproductive) state. Therefore, process = system ? signal and Scientific analysis of the process = system analysis ? signal analysis. One needs to study the process because: (i) an unstable process leads to product quality attributes going beyond tolerances. The causes have to be investigated and eliminated. (ii) when too many disturbances lead to process interruptions, the causes have to be determined and eliminated (iii) development in machine occurs to improve the process. For all the above mentioned facts, one needs to establish quantitative relationship between process and product variables and their time dependent behaviour. This can be a formula, a graph, regression equation, a differential equation (DEq) or a simulation of the process or part of it. All these representations are model.

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Table 2 Mechanical models System

Model equation

Symbols 2

d yðtÞ f ðtÞ ¼ MaðtÞ ¼ M dvðtÞ M = mass, f(t) = force, dt ¼ M dt2

Force - Mass

y(t) = displacement

y(t) M

f(t)

Linear spring

f ðtÞ ¼ KyðtÞ

K = spring constant

f ðtÞ W ¼ KyðtÞ

W = preload

TðtÞ ¼ KhðtÞ

T(t) = torque,

y(t) f(t)

Preloaded spring

y(t)

W

f(t) Torsion spring

k = torsional spring constant,

Τ(t)

h(t) = angular rotation

θ(t) f ðtÞ ¼ B dyðtÞ dt

Viscous friction

y(t) displacement, f(t) = force,

y(t)

B = viscous frictional coefficient

f(t) 2

d hðtÞ TðtÞ ¼ JaðtÞ ¼ J dxðtÞ dt ¼ J dt2

Rotational motion

T(t)

a(t) = angular acceleration,

J

θ(t)

A steady state model describes the relations between constant mean values of the process and product variables. Where as a dynamic model tries to establish relationship

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J = inertia, h(t) = angular displacement, x(t) = angular velocity

between the changes and fluctuations in the process and product variables. Thus dynamic model represents the time dependence of the cause effect relations.


τ1, θ1

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Dynamic Model [5]

N1

Motor

Twisting is a dynamic process. The dynamic model of false twisting [Fig. 5] is presented below. A false twister placed between two pair of rollers turns at a speed N to insert false twist in the yarn passing through it at a constant speed V m/min. The assumptions are:

A

Load

B N2

τ2, θ2

Fig. 3 Gear train

– –

Model for Steady State Process

–

A steady state model describes the relations between constant mean values of the process and product variables. Let us consider sliver making process being carried out by two pair of rollers where one pair moves faster than the other (Fig. 4). Let, ti, t0, are the mean values of input and output linear density (tex) of sliver (process variable), vi, vo are input and out velocities of rollers (m/min) (i.e. product variables) and n = number of slivers at the input. According to mass balance vi t0 v0 ¼ nti vi ; ) t0 ¼ nti ð8Þ v0 Filament production process: To from filaments the molten polymer is extruded through fine holes and is drawn by a take up unit which applies the necessary force. An analysis of this process can be made by mass balance equation: Q ¼ Tt : v

ð9Þ

where Q is the polymer extrusion rate (g/m), Tt is the filament linear density (denier) and v is the extrusion velocity (m/sec) Steady state static model assumes that material and process variables are held constant at their designated mean level.

At time t = 0, no twist is present in yarn When twist is inserted in each zone, it is uniformly distributed and Twist contraction is negligible

At time t = t1, there are x turns/m in zone AX and y turns/m in zone XB. Let, N is the twist insertion rate (turns/min), V is the yarn speed (m/min), Zone AX is the L (metre), Zone XB is the K (metre) and L = K Twist Density for Zone AX At time t1 ? dt, the number of turns in zone AX will be the sum of the following: Turns already present = xL Turns inserted by twisting device = N. dt Turns lost because of the filament length moving into zone XB = x V dt Thus the twist level (turns/unit length) in AX at t = t1 ? dt = x ? (N - xV) dt/L The change in twist = dx ¼ ðNxVÞdt R Ldx R Rearranging and integrating NxV ¼ L1 dt When t = 0, x = 0, thus the integral gives N t 1 eV L x¼ ð10Þ V Twist Density for Zone BX dt The change in twist in zone XB ¼ dy ¼ ½xVðNþVyÞ ¼ K t 1 V L þ Vy dt K Ne t Multiplying by eV L and integrating,

n

ni

D

D0

ti vi

N

V

t0

vo K

L

l A

Fig. 4 Drawing process

X

B

Fig. 5 False twisting process

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Twist in zone BX ¼ y ¼

NL VðL KÞ

t t eV L eV K

ð11Þ

The Fig. 6 shows the graphs representing the change in twist in the two zones AX and BX. In AX the twist converge towards its equilibrium value N/V and in BX to zero. Statistical Model: Probabilistic Model of Fibre Breakage Fibre breakage is common while processing fibres on blow room, card and comber. As a result of breakage a new length distribution pattern of fibre is generated this is different from bale fibre. It is well known that length distribution pattern that shows high percentage of short fibres can have a damaging consequence on yarn properties and process performance. Fibre breakage process has been investigated by many. The objective of these studies were to develop a mathematical model which can describe the breakage function of a process in order to predict the length distribution in the output material from input length distribution pattern. The work done by John D. Tallant et al. [6] is reported here as an example. Considerations / Assumptions

there are two possibilities when fibres passes through a process i.e. the fibres may either break or not if it breaks, it breaks only once if breakage occurs, it may occur anywhere along the length and after breakage both ends of the fibre remain in the output i.e. daughter population Schematically the process may be represented as shown in Fig. 7. There is an input fibre length distribution which N/V Twist in AX

Twist in BX

Fig. 6 Twist time curve

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Model formulation Let, F(x) is the cumulative parent (input) distribution (normalized), G(x) is the cumulative daughter (output) distribution (normalized), p(x) is the generalized breakage function. Let’s say we are interested to know how many fibres is less than a given length ‘x’ after breakage in the daughter population? Logically, this can be stated as: Proportion of fibres less than length \x after breakage ¼ proportion of fibres originally of length x in parent population þ proportion of broken fibres of length x in parent population þ proportion of broken fibres; originally of length x and becomes \x after breakage Let Py(x) = probability that a fibre of original length y will be less than length x after breakage. Therefore, Py ðxÞ ¼

Before formulation of the model, one has to make certain assumptions to make the formulation relatively easy. In the present case these are:

0

gets changed in the output due to the processing. The input and output length distribution needs to be linked with the unknown breakage function so that knowing any two, explicit solution for the third can be found out.

xpðyÞ if x\ y or 1 if x [ y y

All those fibres having length [ x in the parent population, after breakage may or may not contribute to the daughter population of length \ x. These fibres can be categorized into two groups: x B y B 2 9 and y [ 2x. Fibre Length Lying in Between x and 2x (i.e. x B y B 2x) Let AD represent the fibre (Fig. 8). Segment AC and BD equals to length x. Since break point can be located any where with equal probability, the length of the broken segments to be less than x will depend where the break point occurs. If the break occurs in AB or CD region, one broken segment becomes less than x. However, if it occurs in the region BC, both the segments will be of length less than x. Hence, probability that the break will occur within BC ¼ BC=AD ¼ 2xy that the break will be y . Probability within AB or CD ¼ 1 2xy ¼ 2 1 xy . y

Time ( t ) INPUT

OUTPUT PROCESS

Fig. 7 Breakage process


A

x

B

C

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D

ZGðxÞ ¼ FðxÞ þ

x

Zx

0

pðyÞF ðyÞdy þ 2

þ

y

2x y pðyÞF ðyÞ dy y 0

x

0

Z2x

Z2x

Z1 x 2x pðyÞF 0 ðyÞ2 1 dy þ pðyÞF 0 ðyÞ dy y y

x

2x

0

ð12Þ

Fig. 8 Fibres of length in between x and 2x

B

A

C

On simplification it becomes Z1 Zx x 0 pðyÞF 0 ðyÞdy ZGðxÞ ¼ FðxÞ þ pðyÞF ðyÞdyþ2 y

D

x

0

y-2x 0

y

Fig. 9 Fibres of length greater than 2x

Fibre length [ 2x (i.e. y [ 2 x) In this case (Fig. 9), whether the broken segments will be length less than x or not depends upon where the break actually occurred. If the break occurs either in AB or CD region then only, there is a chance that one broken segment will be of length less than x. However, if it occurs in the region BC, none of the segment will be less than length x. Probability that the break will occur either on AC or BD ¼ 2xy. Therefore, in the daughter population, proportion of fibres less than specified length (x)

ð13Þ

The term Z is a pure number and represents the normalizing factor present in daughter population after breakage. To find out Z, we have to put the limit of x = ? which will make right hand R1 side of the equation equal to 1. When x = ?, Z ¼ 1 þ pð yÞF 0 ð yÞdy. 0 In differential form, the model equation turns into 1 Z pðyÞ 0 F ðyÞdy pðxÞF 0 ðxÞ ZG0 ðxÞ ¼ F 0 ðxÞ þ 2 ð14Þ y x

The first term indicates fibres originally of length \ x, 2nd term fibres of length x gained by breakage of fibres of length [ x, the presence of Z signify retention of both segments originally of length \ x and the last term fibres of length x broken. The equation needs to be solved to find out the breakage function p(x).

Conclusion

¼ Proportion of unbroken fibre of length \x in parent population þ proportion of broken fibre of length \ x in parent population þ proportion of fibre in length group x y 2x in parent population where both the parts becomes\x after breakage þ proportion of fibre in length group x y 2x in parent population where only one

Mathematical models are very concise and exact mathematical statements. The model helps us to get an insight about the process, its input out relationship or about a structure and response of the structure to stresses and strains. Each model has its own merits and limitations. There are various ways to formulate a model. Depending upon the nature of the problem one has to decide what type of model building exercise to be followed. Each developed model needs validation so as to assess its performance and utility.

part becomes\x after breakage þ proportion of broken fibre in length group y [ 2x in parent population where one part becomes\x:

Therefore the basic equation relating cumulative distribution of parent and daughter population can be written as

References 1. K. Velten, Mathematical Modeling and Simulation: Introduction for Scientists and Engineers (WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim, 2009)

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98 2. J.W.S. Hearle, P. Grossberg, S. Backer, Structural Mechanics of Fibres, Yarns and Fabrics (Wiley Interscience, New York, 1969) 3. W.J. Palm III, Control System Engineering (John Wiley & sons Inc, Somerset, 1986), pp. 33–62 4. R. Beyreuther, H. Brunig, Dynamics of Fibre Formation and Processing (Springer, Berlin, 2007), pp. 5–32

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J. Inst. Eng. India Ser. E (July–December 2015) 96(2):89–98 5. C.A. Lawrenc, Fundamentals of Spun Yarn Technology (CRC Press, Boca Raton, 2003), pp. 53–54 6. J.D. Tallant, R.A. Pittman, E.F. Schultz Jr., The changes in fibrenumber length distribution under various breakage models. Text. Res. J. 36, 729–737 (1966)


ORIGINAL CONTRIBUTION

An Insight to the Modeling of 1 3 1 Rib Loop Formation Process on Circular Weft Knitting Machine using Computer Sadhan Chandra Ray

Received: 16 November 2014 / Accepted: 11 February 2015 / Published online: 17 March 2015 The Institution of Engineers (India) 2015

Abstract The mechanics of single jersey loop formation is well-reported is literature. However, as the concept of any model of double jersey loop formation process is not available in accessible international literature. Therefore, it was planned to develop a model of 1 9 1 rib loop formation process on dial and cylinder machine using computer so that the influence of various input variables on the final loop length as well on the profile of tension on the yarn inside Knitting Zone (KZ) can be understood. The model provides an insight into the mechanics of 1 9 1 rib loop formation system on dial and cylinder machine. Besides, the degree of agreement between predicted and measured values of loop length and cam forces as well as theoretical analysis of the model have justified the acceptability of the model. Keywords Cam force Dial Loop length Knitting zone Mechanics Knitting timing

Introduction The length of yarn in a loop, mostly decided on the machine during knitting, is the most important parameter of a knitted fabric which influences the properties of the same. It is obvious that if the variables governing the length of loop as well as the mutual interaction between the variables inside KZ are known it would be possible to produce a fabric with

S. C. Ray (&) Department of Jute and Fibre Technology, Institute of Jute Technology, University of Calcutta, Kolkata, West Bengal, India e-mail: [email protected]

pre-determined loop length. The basic purpose behind the modeling of loop formation is to establish the degree of influence of various input variables on the final loop length as well as on the yarn tension profile inside KZ. This would enable on one hand better prediction of output variables of the loop formation system from the known values of input variables and provide on the other hand a logical basis for modifying the design of knitting elements. The mechanics of single jersey loop formation was explained by the researchers [1] which was based on the concept of Robbing Back (RB). A mathematical model of the single jersey weft knitting process involving flat bottom stitch cam was formulated [2]. A geometrical model of single jersey process was developed envisaging a complex form of yarn movement inside KZ involving leading and trailing arms of a loop [3]. A mathematical model of single jersey loop formation was developed involving non-linear stitch cam and incorporating five different stages of initial geometry of KZ [4]. Previous researchers proposed a model based on the concept of balance of forces acting on a needle that decides the Loop Forming Point (LFP) at which the final length is established [5]. All these models and various knitting tension/force measuring methods [2, 3, 6–10] have contributed significantly towards the understanding of single jersey loop formation. A comprehensive list of factors which are likely to alter loop length of double jersey machine has been proposed in earlier research [11]. Measurement of cam force on double jersey machine was attempted in previous studies to evaluate the performance of needles and cam as well as to find out the ways of increasing the rate of production [12]. However, as neither the concept of any model of loop formation system on double jersey machine nor well defined geometrical expression of length of yarn in a 1 9 1 rib loop at Knitting Point (KP) or at any other point inside

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KZ is available in accessible international literature, it was planned to develop a model of 1 9 1 rib loop (simplest of all double jersey structures) formation process on dial and cylinder machine using computer for establishing the degree of influence of various input variables on the final loop length as well on the profile of tension on the yarn inside KZ under both synchronized (SYN) and delayed [two needle delayed (2ND)] timing [13–15]. So the basic objective of the proposed modeling was to gain an insight into the mechanics of loop formation on double jersey machine. In order to develop the model, different concepts of 1 9 1 rib loop formation process were developed [16, 17].

Preliminary Experiments In order to simulate the knitting process with the help of computer, the action of the knitting elements and the movement of yarn across needles inside KZ were observed. The machine was turned slowly by hand and the instantaneous positions of the needles and extent of yarn movement were recorded by travelling microscope. This microscope permitted following of yarn and Cylinder Needle (CN) in vertical plane (X–Y direction) only, but following of the movement of a yarn segment in the rib knitting machine would involve monitoring it’s co-ordinates in the space, i.e., of X, Y and Z values. Accordingly, to monitor the Z-co-ordinate, a mirror was positioned (Fig. 1) just above the KZ at 45 angle to the horizon. The movement of yarn and Dial Needle (DN) along YZ plane could then be projected and observed through microscope on XY plane. The direction of yarn movement by applying a mark on the yarn was also observed during loop formation. A few fabric samples were also produced under monitored conditions of knitting for studying the effect of delay timing and other process parameters of loop length. The important findings were the guidelines in formulating the model.

Fig. 1 Method of projection of horizontal displacement into vertical displacement

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Concepts of Rib Knitting The different concepts of 1 9 1 rib loop formation process, as stated below, were developed in the beginning through intensive visual observation of the KZ and some experimental findings. Geometry of KZ A dial and cylinder type 1 9 1 rib knitting machine is equipped with two sets of needles, namely CN and DN arranged on cylinder bed (XY-plane) and dial bed (XZplane), respectively which are mutually perpendicular to each other (Fig. 2). There are vertical (VG) and horizontal (HG) gaps between the two beds, the VG is adjustable and known as dial height. There is no sinker in the machine but the extension of CN and DN intersects at a point (S), termed in the study as point of intersection. The line joining the points of intersection of all needles is termed as reference line, equivalent to sinker line in single jersey machine. On account of movement of CN and DN along two mutually perpendicular planes, a complete rib loop is formed in multiple planes and is made up of one cylinder loop, one dial loop and two links. In the course of knitting, the neighbouring needles of both sets may form loop simultaneously by drawing yarn from the supply package and reach their respective KPs—cylinder KP (CKP) and dial KP (DKP)—at the same time, designated as SYN timing, or the DNs may form loop and reach KP with a phase lag to the neighbouring CN, designated as delayed (ND) timing. The extent of phase difference between DKP and CKP is adjustable on the machine and measured in terms of number of needle delay and hence an important

Fig. 2 Side view of knitting zone geometry of 1 9 1 rib loop formation


factor in the understanding of mechanics of loop formation on a double jersey machine. So the geometry of KZ of a circular rib knitting machine is described by the enclosed space generated by the boundary elements, namely CNs and DNs. In between CN and DN, the loop forming yarn comes in contact with Cylinder Bed Verge (CBV) and Dial Bed Verge (DBV). So the geometry of KZ will be influenced by the contour of the stitch cams, stitch cam settings, HG and VGs between the beds, phase difference between CKP and DKP, and the position of the contact points of loop arms with bed verges. The KZ geometry of a circular rib knitting machine can also be illustrated in a simplified form on a two dimensional plane by an imaginary rotation of the dial plane (XZ) through 90 (Fig. 3). Figures 4 and 5 refer to such KZ geometry under SYN timing and 2ND timing of a dial and cylinder type rib knitting machine with flat bottomed cylinder stitch cam and angled bottom cylinder stitch, respectively. The position of any needle inside KZ at any instant can only be determined if the stitch cam profile equations are known. The equations of the stitch cam profiles were obtained from the stitch cam angles, tuck height (YBAR), extent of Needle Delay (ND) between CKP and DKP, half needle spacing (a) and some other parameters of the KZ, like number of steps and their extent in the rising side of the stitch cams.

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needles, needle dimensions, needle spacing and tuck height. The second type of wrap is generated at the points of contact of the newly drawn yarn with CBV and DBV, which is not encountered in single jersey knitting. This wrap angle can be expressed in terms of machine parameters and instantaneous position of the needles inside dynamic KZ. In addition some amount of wrap also takes place at the feed plate which depends on the diameter of the feed hole, thickness of the feed plate and the angles at which the yarn enters and leaves the feed plate. Formulae for Expressing Instantaneous Length of Rib Loop The instantaneous loop length at any point within the KZ would be given by the length of yarn contained between either two neighbouring CN or two neighbouring DN. This length of yarn would keep on changing along the axis of horizontal displacement of needles until a balance between needle forces and yarn tension is achieved at LFP beyond the KPs. Moreover the configuration of the rib loop changes inside the KZ during its formation in multiple planes. Six different combinations of loop arm configuration out of possible nine (Fig. 6a–c) were observed under both SYN and delayed timings. So formulae for theoretical rib loop length were derived segment wise using the KZ geometry. A few assumptions were also made for the purpose.

Wrap Angles Effect of Cast-off Loop Two types of wrap angle are observed in dial and cylinder type machine. The first type of wrap is the wrapping of yarn around the two sets needles (CN and DN). This wrap angle can be expressed in terms of the coordinates of the

As fabric take down is transmitted to the new loop through cast-off loop, effect of cast-off loop on the mechanics of loop formation was also incorporated. However, as the casting-off of dial loop takes place at a later phase of loop formation, the effect of the same was neglected. Yarn Tension and Knitting Force

Fig. 3 Conversion of three dimensional knitting zone geometry into two dimension

The major component of the force acting on the stitch cam is caused by the upward pull of the needle, which, in turn, is caused by the tension on the corresponding loop arms. However, the correspondence between the two would depend on the geometrical configuration of the loop arms. So, the expression of yarn force acting on the needle hook inside KZ varies with the different stages of loop formation. The movement of the needle butt during loop formation is constrained by the descending profile of the stitch up to the KP. But the same, beyond the respective KPs, would be governed by the equilibrium between (i) pull on the needle due to tension (UPT) on the loop arms, and (ii) frictional as well as inertial resistance offered by the needles. Moreover, due to inclination of the loop arms to the needle axis, the axial component of the yarn tension would

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Fig. 4 Knitting zone geometry of 1 9 1 rib loop formation under synchronised timing

Fig. 5 Knitting zone geometry of 1 9 1 rib loop formation under two needle delayed timing

assist upward movement of the needle and the normal component of the yarn tension would resist the movement of the needle by adding frictional resistance to the sliding in the trick. Coordinates of the Needles Inside KZ and Geometric Length of Loop As shown in Figs. 2, 4 and 5, the tuck height is the origin of the X–Y coordinate system. The reference line RR0 is

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described by the equation, Y = YBAR. The CN and DN would follow the descending profile of the respective stitch cams while moving from tuck height to KP. Beyond the respective KPs, the CN and DN would follow either ascending profile of the respective stitch cams or a path governed by the yarn tension and resistance to needle movement in the trick. So, if the X-value of any needle at the tuck height is known, the X-value of the other needles and the Y and Z values of all the needles are calculated using the equations of the cam profiles and other machine


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Fig. 6 a First four different configurations of 1 9 1 rib loop arms after catching of yarn by the cylinder needle during loop formation. b Next three different configurations of 1 9 1 rib loop arms after reaching of cylinder needle at the knitting point during formation. c Last two types of configurations of 1 9 1 rib loop arms after reaching of cylinder needle and neighbouring dial needle to their respective knitting points during loop formation

parameters. From the coordinates of needles and specific configuration of the loop arms, the length of both leading and trailing arms of a loop under the control of any CN or DN can be calculated. After initial contact with yarn, as a particular needle is shifted by a small amount towards the

KP, the new positions of all other needles would be known. As the needles take up new positions, the vertical distances of the needles with respect to the reference line change which would result change in geometric length of loop arms as well as wrap angles.

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Fig. 6 continued

Change in Yarn Tension due to Change in Geometric Length The change in geometric length as a result of displacement of the needles forming the loop inside the KZ is only possible due to either extension of loop arm or flow of extra yarn to the loop under formation. Again the flow of yarn may be of two types—forward flow of yarn from the package or backward flow of yarn from the earlier formed loop. Such possibilities are governed by the tension profile of various loop arms inside KZ which can be tested from the expressions of tensioned and relaxed lengths of loop arms, modulus of yarn, coefficient of friction between yarn and needle as well as wrap angles. If there is no flow of yarn for change in loop length, then the new length would cause change (increase) in yarn tension the extent of which will depend on the modulus of yarn and change in loop length. Condition of Yarn Flow Mathematical relationships have been developed for both forward flow and backward flow across CN and DN before and after casting-off of the old loop with due consideration of the tensions in leading and trailing arms, yarn wrap angles around CN and DN and the force component of the cast-off loop. Final Length of Loop Arm If a state of balance in the two arms of a loop after some amount of flow—forward or backward—is achieved, tension in one arm decreases and in other arm increases and hence the relaxed length of both the arms changes.

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Relationship has been derived to establish the final relaxed length of loop arm as well as magnitude of tension on both the arms after relaxation.

Formulation of the Model The development of the model of 1 9 1 rib loop formation system under SYN and 2ND timings is based on the specific nature of yarn movement inside KZ derived from the knowledge of the preliminary investigation of rib loop formation, the published literature on mechanics of loop formation in single jersey machine and the different concepts developed for rib loop knitting system. The model is designed to indicate the initial contacts of CN and DN with feed yarn, instantaneous configuration and length of loop arms for any needle inside KZ, build-up of yarn tension and final value of loop length going into the fabric for any combination of input variables. The formulation of model is such that the change in yarn tension and yarn length can be calculated for each and every increment of needle movement inside KZ. Out of different delay timings possible, 2ND was chosen due to two reasons—(a) the 2ND timing is a situation where DN catches the feed yarn and deflects the same for dial loop formation after the neighbouring CN has crossed the CKP, and (b) facility for adjusting timing on both the machine available in the laboratory for the purpose of validation of the model. The following assumptions have been considered for the purpose of modeling: (i)

The tension changes in yarn during movement across knitting elements according to Amonton’s law.


(ii) (iii) (iv) (v)

(vi) (vii)

The yarn tension inside KZ is proportional to the yarn extension. The elastic coefficient (relative rigidity) of the yarn is constant. The frictional coefficient of the yarn is constant. The half wrap angles of yarn around CN and DN are 90 when the needles are positioned below their respective bed verges. The CN hook catches feed yarn always ahead of neighbouring DN. The bending stiffness of yarn is negligible.

The First Approximation The knitting process is assumed to be initiated when CN1 just touches the feed yarn under both SYN and 2ND timings. At that instant, one end of the loop under formation is assumed to be fastened to DN1 such that no relative movement between the two can take place. Subsequently minute displacements of needles cause wrap of yarn around CN1 and the length of yarn in between CN1 and DN1, i.e., the leading arm of the new loop under formation decreases until the leading arm becomes parallel to the reference line. Afterward the length of leading arm increases. The change in loop arm length and wrap angle lead to following three possibilities: •

• •

The loop arm segment connecting CN1 and DN1 receives yarn freely from the yarn package to compensate for the new geometric length. The loop arm segment connecting CN1 and DN1 extends and becomes equal to the new geometric length. A combination of extension of loop arm yarn and flow of yarn from the yarn package takes place.

After certain amount of further movement of CN1, the DN2 touches the feed yarn between CN1 and feed plate and hence the leading arm of the loop stats forming. Till CKP the trailing arm is generally shorter than leading arm. In the process the DN1 reaches below the reference line and deflects the leading arm from the vertical plane. The timing of such happening depends on timing of knitting, stitch cam settings and machine parameters. Moreover, casting-off of old loops takes place when the needles reach the respective bed verge levels. So again the following tests are to be done at this stage: • • •

Whether DN1 has reached below the reference line, Whether old cylinder loop has been cast-off, Whether old dial loop has been cast-off.

As during the first cycle of computation, one end of the leading arm is held rigidly by the DN1, flow back of yarn across CN1 and or DN1 cannot occur till CN1 reaches CKP.

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So, the tension on the loop arms is such that yarn can flow in forward direction only. There will be some difference in further computation under SYN and 2ND due to difference in shape of the KZ geometry. Under SYN timing CN1 and DN1 reach the respective KPs at the same time. Upon further movement of needles, CN1 and DN1 may ascend or maintain same level depending on the ascending profile of the stitch cams and the forces acting on the needles. As a result, the length of leading arm of CN1 remains same or decreases but the length of trailing arm goes on increasing as DN2 approaches DKP. The extra length of trailing arm may come either from package or from the leading arm. So the tensions in various arms are tested for forward and backward across any CN and DN inside KZ. When no more flow occurs, the values of relaxed length of loop arms, tensions in the relaxed loop arms and the forces acting on the needles are stored. As the knitting continues, more and more needles enter the KZ and needles CN1 and DN1 move beyond their KPs. Computation of relaxed length of loop arms and tension on them are carried out till the CN1 reaches LFP and the length of the loop arms are stable. Under 2ND timing, DN1 goes below the reference line generally after CN1 crosses CKP. Moreover, the casting-off of the old loops on DN1 and DN2 occur while CN1 in between DN1 and DN2 is positioned at or beyond CKP. So after every minute displacement of CN1 along X-axis, the followings tests are to be done: • • • • • •

Whether Whether Whether Whether Whether Whether

DN1 has moved below the reference line, DN2 has moved below the reference line, CN1 has crossed the extent of flat bottom, DN1 has reached DKP, the old loop of DN1 has been cast-off, the old loop of DN2 has been cast-off.

Iteration for Final Loop Length The values of relaxed length of loop arms, tensions in the relaxed loop arms and the forces acting on the needles obtained under both SYN and 2ND timings for the first needle (CN1) would not be very accurate as initially it was assumed that the feed yarn is rigidly held by DN1. So the process of iteration for calculating relaxed loop length and yarn tensions, etc., for CN1 as described in the foregoing is then continued for CN2, CN3, etc., by initializing them as CN1. It is no more necessary to assume a rigid contact between DN1 and yarn during subsequent iteration cycle. While each needle reaches LFP, the values of loop length, tension in the arms and the coordinates of the needles are stored. This is continued until the difference of the values between the two consecutive needles reaching the LFP is less than an arbitrarily chosen small value (say 0.01 mm for loop length).

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In order to simulate and compute the different desired parameters of the 1 9 1 rib loop forming system the programmes are written in user friendly manner using PROFORT software so that input parameters can be supplied according to requirement. After execution of the programme for any combination of input parameters, the required output parameters are either noted down or printed from the result file. The output parameters are then compared with the output of the real system of loop formation for validation of the model as well as for critical analysis of the modelled system.


cam setting, dial stitch cam setting, resistance to needle movement inside trick, yarn properties, etc., and there is reasonable agreement between the two.

Conclusions •

Validation of the Model • Validation of the developed model is must for evaluating the predictive power of the model in one hand and justifying the acceptability of the same on the other. The two main output parameters of the model are final relaxed loop length and yarn tension profile for a complete loop forming cycle. So in order to validate quantitatively the developed model in terms of actual loop length and yarn tension inside KZ, 66 fabric samples have been experimentally produced with known values of input variables. Length of loop has been measured for the first 50 fabrics in dry relaxed state. The tension generated inside the KZ during loop formation has been measured for 16 fabrics. For the purpose of measuring yarn tension profile for a complete loop forming cycle in side KZ, an experimental knitting force measuring set-up has been installed on the cylinder stitch cam. The analog force signals produced by the piezoelectric transducer (made of M/S. Kisteler A. G., Switzerland) have been recorded and stored in digital form in the computer using analog to digital conversion card and Turbo-Pascal (Version-5) software. These values are then compared with the predicted values of the model, employing the same values of input variables. It has been observed that the percentage error of predicted values of loop length varies in the range of (-) 9.71 to (?) 9.74 with a trend of under estimation in general for both SYN and delayed timings and most of the predicted loop length values are just near the actual loop length values. So far as the knitting tension is concerned, the nature of predicted cam force curve follows the trend of measured cam force and shows two peaks—one at CKP and other at a distance of one needle pitch from the CKP. Out of 32 peak values for 16 fabrics, 14 values are within the confidence interval. The over estimation (6.10–32.39 %) and under estimation (1.88–27.29 %) have taken place in 7 and 11 cases, respectively. It has been also observed that both the model and the real system of loop formation are sensitive to change in input parameters like input tension, cylinder stitch

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• •

The degree of fit between the experimental values of loop length and yarn tension profile within KZ on one hand and their corresponding theoretical values predicted from the programme so developed is a reasonably accurate representation of the 1 9 1 rib loop formation on a dial and cylinder type circular double jersey weft knitting machine. It is possible to identify the key input parameters influencing the ultimate loop length and knitting force from the sensitivity of the double jersey loop forming system, i.e., change in output variables (loop length and cam force) due to change in input variables (input tension, stitch cam settings, yarn quality, resistance to needle movement inside trick, etc.). Mechanics of 1 9 1 rib knitting also stand on the theory of RB which takes place in phases. The developed model can provide necessary information for easy understanding the mechanics of 1 9 1 rib loop formation on a dial and cylinder machine.

References 1. J.J.F. Knapton, D.L. Munden, Text. Res. J. 36, 1072 and 1081 (1966) 2. N. Aisaka, J. Text. Mach. Soc. Jpn 17, 82 (1971) 3. D. Peat, E.R. Spicer, HATRA Research Report, No. 26 (1973) 4. T.W.Y. Lau, J.J.E. Knapton, J. Text. Inst. 69, 169 and 176 (1978) 5. P.K. Banerjee, S. Ghosh, J. Text. Inst. 90, 187 (1999) 6. D.E. Hensaw, Text. Res. J. 38, 592 (1968) 7. D.H. Black, D.L. Munden, J. Text. Inst. 61, 340 (1970) 8. L. Pietikaeine, Melliand Textilber. 10, 603 (1981) 9. L. Pietikaeine, L. Valkama, Melliand Textilber. 12, 187 (1983) 10. G.R. Wray, N.D. Burns, J. Text. Inst. 67, 113, 119, 123, 189, 195, 199, 206 (1976) 11. T.J. Little, Text. Res. J. 48, 361 (1978) 12. M.D.E. Araujo, A.M. Rocha, M. Neves, M. Lima, Melliand Textilber. 68, 406 (1987) 13. A.A.A. Jeddi, A. Zareian, J. Text. Inst. 97(6), 475 (2006) 14. S.C. Ray, P.K. Banerjee, Indian J. Fibre Text. Res. 25(2), 97 (2000) 15. S.C. Ray, P.K. Banerjee, Indian J. Fibre Text. Res. 28(2), 185 (2003) 16. S.C. Ray, P.K. Banerjee, Indian J. Fibre Text. Res. 28(3), 239 (2003) 17. S.C. Ray, P.K. Banerjee, Indian J. Fibre Text. Res. 37(2), 138 (2012)

J. Inst. Eng. India Ser. E (July–December 2015) 96(2):107–124 DOI 10.1007/s40034-014-0044-y


Development of Warp Yarn Tension During Shedding: A Theoretical Approach Subrata Ghosh • Prabhakara Chary Sukumar Roy

•

Received: 20 August 2014 / Accepted: 3 November 2014 / Published online: 11 December 2014 Ó The Institution of Engineers (India) 2014

Abstract Theoretical investigation on the process of development of warp yarn tension during weaving for tappet shedding is carried out, based on the dynamic nature of shed geometry. The path of warp yarn on a weaving machine is divided into four different zones. The tension developed in each zone is estimated for every minute rotation of the bottom shaft. A model has been developed based on the dynamic nature of shed geometry and the possible yarn flow from one zone to another. A computer program, based on the model of shedding process, is developed for predicting the warp yarn tension variation during shedding. The output of the model and the experimental values of yarn tension developed in zone-D i.e. between the back rest and the back lease rod are compared, which shows a good agreement between them. The warp yarn tension values predicted by the model in zone-D are 10–13 % lesser than the experimentally measured values. By analyzing the theoretical data of the peak value of developed yarn tension at four zones i.e. zone-A, zone-B, zone-C and zone-D, it is observed that the peak yarn tension value of A, B, C-zones are much higher than the peak tension near the back rest i.e. at zone-D. It is about twice or more than the yarn tension near the back rest. The study also reveals that the developed yarn tension peak values are different for the extreme positions of a heald. The impact of coefficient of friction on peak value of yarn tension is nominal. Keywords Tappet Heald Shedding Wrap angle Warp tension S. Ghosh (&) P. Chary S. Roy Department of Textile Technology, National Institute of Technology Jalandhar, Jalandhar 144011, Punjab, India e-mail: [email protected]

List of symbols S Lift of the tappet s Displacement of treadle bowl m Slope of the falling/rising angle of the tappet n Number of the heald shaft hw Working angle of cam (rising or falling) hd Dwell angle of cam (top or bottom) d1 Diameter of small reversing roller d2 Diameter of big reversing roller x Distance between fulcrum to treadle bowl y Distance between treadle bowl to front heald connection z Distance between front and back healds (spacing of healds) a Horizontal distance between cloth fell and heald shaft (zone A) b Horizontal distance between heald shaft and front lease rod (zone B) c Horizontal distance between lease rods (zone C) d Horizontal distance between back lease rod and back rest (zone D) a Angle made by the line joining centers of two elements carrying the yarn with the horizontal in different zones. b Angle made by the line parallel to yarn axis in the straight portion with the line joining the centers of two elements carrying the yarn in different zones A, B, C, D Half wrap angles on an element in the respective zones W Total wrap angle on each element followed by subscript indicating the element l Geometrical length of yarn in any zone (straight portion)

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L h h0 hmin hmax t ry rh rl rb lm h fl bl br 1 2


Total geometrical length in any zone (including wrap length) Displacement of heald from the healds level position Relative heights of two yarn carrying surfaces Displacement of heald when it is at its bottom most position Displacement of heald when it is at its top most position Length of heald eye Yarn radius Radius of heald eye surface that carries the yarn Radius of lease rod Radius of back rest Coefficient of yarn–metal friction Heald Front lease rod Back lease rod Back rest First heald or front heald Second heald or back heald

Introduction The performance and the efficiency of a weaving machine depend on several factors. One of the most important factors affecting the efficiency of weaving machine and quality of the fabric is the warp yarn break. Repeated fluctuation of the warp yarn tension during the process of weaving causes a fatigue in the warp yarn which leads to an increase in the warp yarn breakage rate. The degree of warp tensions during weaving also have an appreciable effect on the dimensions of the fabric. Hence, the uniform control of the warp yarn tension in weaving is one of the fundamental requirements for the better performance of weaving machine and production of quality fabric. During the process of weaving an interaction takes place between yarn variables (yarn diameter, yarn rigidity, coefficient of friction etc, machine variables (shedding cam profile, dimensions and position of back rest, lease rod, heald eye etc.) and the process variables (initial yarn tension, the beat up, let off, and take up action etc.), which ultimately contribute to the continuous change of yarn tension during weaving. In order to assist the formation of clear shed, tension is applied to warp yarn during weaving. Warp yarn tension requirements will vary depending on fabric structure and

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density of warp. The initial tension on the warp threads during weaving usually kept at slightly higher level to obtain a clear shed for the passage of weft carrier and to resist the action of the reed as it moves to beat up the weft. However the warp yarn tension is not same throughout the weaving cycle, but will be affected by the different motions of weaving machine. Fluctuation of warp yarn tension is the result of shedding, beat up, takes up and let off motions. The effects of these factors are not simultaneous but vary in duration and magnitude over a pick cycle. Among these, the shedding and the beat up processes are being mainly responsible for considerable rise in yarn tension. Out of that, the impact of shedding motion on yarn tension is of longest duration. This is an area of fabric research yet to be examined in depth and only partially understood. A few research papers are available on the subject mostly dealing with the experimental procedures to measure the cyclic variation of yarn tension. It is observed from the literature that in all the cases of experimental measurement of warp yarn tension, the tension meter was placed somewhat between back rest and the back lease rod [1–6]. This zone is chosen for tension measurement not only for the negligible warp yarn vertical movement but also it is difficult to measure the yarn tension in shedding zone. But the tension indicated in this zone may be much lower than the actual yarn tension developed in the shedding zone because of high level of strain imposed on the yarn at this zone. The present work forms a logical step in which an attempt has been made for predicting the developed yarn tension in shedding zone by formulating a theoretical model and a computer program.

Formulation of Model A model on the development of warp yarn tension during shedding process is formulated based on geometry of shed during weaving (Fig. 1). The shedding mechanism on a plain weaving machine works based on the profile of the cams mounted on the bottom shaft. Hence a model is developed to predict the warp yarn tension during shedding for every minute changes in angular displacement of the bottom shaft. The formulation model is given in the Appendix A. The displacement of heald shafts originates from the shedding tappets, which are normally placed on the bottom shaft and rotates as the bottom shaft rotates. With the rotation of the tappet, the treadle bowls are displaced and the treadle bowl displacement depends on the cam profile.


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Fig. 1 Passage of warp on a plain weaving machine

For this a coordinate system is developed such that the displacement of treadle bowl from the treadles level position based on cam profile is given on Y axis corresponding to the angular displacement of bottom shaft as represented on X axis. As the healds are connected with treadle levers, the treadles motion are transferred to the healds which give the corresponding heald displacements from the healds level position (closed shed position) due to the rotation of cams mounted on the bottom shaft. The magnitude of heald displacement changes with the change of lift of the tappet and settings of shedding elements. So, the displacement of heald shaft can be expressed as a function of bottom shaft rotation and other parameters. As the shed starts opening, the warp yarn is raised or lowered from the closed shed line resulting in the changes in the path of the warp yarn. It can be seen from the path of warp yarn on a weaving machine that the yarn is wrapped on different elements like back rest, lease rod and heald surface etc., by varying amounts. The amount of wrap and the geometrical length of the yarn change continuously in each section of the weaving machine due to the action of shedding cam. The warp yarn path inside the weaving machine is divided into four zones and the tension levels in each zone are estimated based on geometrical length and yarn movement in each zone with the rotation of the bottom shaft.

Assumptions 1. The cam is a rise-dwell-fall type and linear in nature. 2. There are no mechanical losses during the transfer of motion from cam to heald displacement. 3. The movement of treadle lever about its fulcrum is in an arc and hence the displacements of treadle bowl

4. 5. 6. 7. 8. 9. 10.

11.

and heald shafts are also in an arc. But as the radius of arc is too large when compared to its displacement, the displacements are assumed to be linear. The cross section of yarn is circular in nature. Yarn is elastic in nature. The bending stiffness of the yarn is negligible. The surface of heald eye touching the yarn is circular in nature. There is no lateral movement of heald wires in the heald shaft. The shed is symmetric in nature. The fabric under consideration of weaving is very open in nature so that there is no displacement of cloth fell during beat-up. The back rest is fixed and there is no oscillatory motion attached to it.

Treadle Bowl Displacement Equations The treadle bowl displacements are shown on a simple coordinate system (Fig. 2). A line parallel to the bottom shaft is chosen as X axis on which the degrees of rotation of bottom shaft is represented. The treadle bowl displacement is shown on Y axis. The origin of the coordinate system is at the point at which both the treadles come to the same level. The thick lines in the Fig. 2 represent the positive action of cam and the dotted lines indicate the negative action of the cam i.e., indirect displacement of the bowl through top reversing rollers. For linear cam, the equations for displacement of the treadle bowl for a given rotation of the bottom shaft are obtained by the following equations. These equations are developed by considering the Fig. 2.

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Fig. 2 Displacement of treadle bowls represented on a co-ordinate system

s ¼ ½ðmÞh þ S=2 for 0 h\hw

ð1Þ

s ¼ ½S =2 for hw h\hw þ hd

ð2Þ

s ¼ ½ðmÞh S ð3=2 þ hd =hw Þ for hw þ hd h \2hw þ hd

ð3Þ

s ¼ ½S=2 for 2hw þ hd h \2ðhw þ hd Þ

ð4Þ

From the Fig. 2 and the Eqs. (1–4) it is clear that in the above equations (?) sign is assigned to the treadle that starts from top to bottom and the (-) sign for the treadle that moves from bottom to top.

Heald Displacement Equations Figure 3 shows how the cam, treadle lever, heald and reversing roller are connected. Any motion of the bottom shaft will be transformed to heald shaft through the connected link. Front heald displacement ¼ Front treadle bowl displacement ðx þ y Þ = x Back heald displacement ¼ Back treadle bowl displacement ðx þ y z Þ = x

For any number of heald shaft the generalized equation for the displacement of heald for a given value of bottom shaft rotation h, is given by hh ¼ sh ½x + y ðn 1Þ z=x

ð5Þ

where z is spacing of heald shafts and displacement indicating for nth heald shaft. By using the Eqs. (1–4) of treadle bowl displacements the displacement of healds can be expressed as a function of bottom shaft rotation. Hence for a given angle of bottom shaft rotation, the displacement of heald is given by

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Fig. 3 Tappet shedding mechanism

h ¼ ½ðmÞh þ S=2 ½x þ y ðn 1Þ z= x for 0 h \hw h ¼ ½S =2 ½x þ y ðn1Þ z=x for hw h\hw þ hd

ð6Þ ð7Þ

h ¼ ½ðmÞh Sð3=2þhd =hw Þ ½x þ y ðn1Þ z=x for hw þ hd h \2hw þ hd ð8Þ h ¼ ½S=2 ½x þ y ðn 1Þ z=x for 2hw þ hd h \2ðhw þ hd Þ

ð9Þ

If n = 1, it indicates the position of first heald and if n = 2, it indicates the position of second or back heald.


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Stages of Heald Shaft Displacement

Warp Yarn Path in the Weaving Machine

The displacement of heald shafts with the warp yarn inside the heald eye pass through different stages as shown in the Fig. 4. The stage I is at which first heald is falling from upper most position and the second heald is raising from the bottom most position (Fig. 4a). This corresponds to the position of the bottom shaft at which raising angle of first tappet and the falling angle of second tappet will be in action. The study of various stages indicates the various positions taken by the yarn during the heald displacement. It also indicates how the wrap angle changes with the heald eye and the first lease rod. There are total five different stages, out of which three (stage II, III and IV) are transitional in nature. After these stages the method of calculating the geometrical parameters changes.

The path of warp yarn on a plain weaving machine is divided into four zones and which is shown in the Fig. 5. It is usual practice to put the first yarn below the second lease rod and above the first lease rod and then to draw through eye of the first heald shaft. Similarly the second yarn is put above the second lease rod and below the first lease rod and then to draw through the eye of second heald shaft. An imaginary line touching the top surfaces of back rest and front rest and passing through the centers of both lease rods is taken as the reference line. It may be assumed that when the centers of both the heald eyes will coincide with the reference line then it can be termed as closed shed position. The path of warp yarn from back rest to cloth fell is divided into four zones, separated by a vertical line passing through the center of different elements.

Stage I (Fig. 4a) The front heald shaft is at upper most position and the back heald is at bottom most position. The front heald yarn is in contact with bottom portion of the heald eye whereas the back heald yarn is in contact with upper surface of the heald. Stage II (Fig. 4b) The front heald moves down and the back heald moves up and reaches in such a position that the yarns are lying parallel to each other between heald eye and front lease rod. Stage III (Fig. 4c) Both the healds take up a position where the yarns between the lease rod and the cloth fell are straight in nature. The yarn is free from any wrap with top and bottom surface of heald eye. Stage IV (Fig. 4d) At this position, the top surface of front heald eye and bottom surface of back heald eye come in line with reference line and the yarns in between cloth fell and heald eye are also placed on the same line. Stage V (Fig. 4e) Both the yarns cross each other and the front heald reaches to the bottom most position and back heald reaches to the top most position. When compared with stage I, yarns undergo maximum wrap on the lease rod surface.

Zone Zone Zone Zone

A between cloth fell and heald shaft B between heald shaft and front lease rod C between front and back lease rods D between back lease rod and back rest

The various geometrical parameters (Fig. 6) like wrap angle, geometrical length of yarn etc., are in Appendix B. Initially the half wrap angle and straight length of the yarn in each zone is calculated for a given shed geometry. The total wrap angle on any element like lease rod, heald are calculated by adding or subtracting two half wrap angles depending on the inclination of the yarn on the surface of the element. The geometrical length of the yarn in a zone consists of two components. One comes from straight length of the yarn and other comes from the length of arc around the weaving element. Calculations of Half Wrap Angle and Geometrical Length of Yarn By thorough analysis of various stages, the half wrap angle is found to be a function of a and b (Appendix B) in such a way that half wrap angle is given by ða bÞ where, a is the angle made by the line joining centers of two elements carrying the yarn with the horizontal, b is the angle made by the line joining the centers of two elements carrying the yarn with a line parallel to yarn axis and passing through center of any element. The positive and negative sign depends on the geometry of yarn and the weaving elements. Calculation of Half Wraps Angle and Geometrical Length of Yarn in Zone A and Zone B at Different Stages The various possibilities of shed geometry resulting due to the displacement of heald from top most position to bottom

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112 Fig. 4 Different stages of heald displacement

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Fig. 5 Geometry of warp yarn on a plain weaving machine

Fig. 6 Representation of various geometrical parameters

most position or vice versa are shown in the Figs. 7 and 8. The half warp angle and geometrical length at various stages for zone A and zone B are given below: Stage I; between Stage I and Stage II At this stage, the yarn from first heald forms the upper shed line and it is in contact with the bottom surface of heald eye. The yarn from second heald forms the bottom shed line and it is in contact with top surface of heald eye. Both the yarns have no contact with the front lease rod in zone B. This type of yarn contact with the heald eye and the lease rod continue till it reaches next stage. Half wrap angle on heald eye in zone A is (Ah) = (aa ? ba) Half wrap angle on heald eye in zone B is (Bh) = (ab - bb) Half wrap angle on front lease rod in zone B (Bfl) is zero.

Stage II The healds are in such a position that the yarn axis in zone B is parallel to the reference line making tangential contact with both lease rod and heald eye surface. The yarn in zone A is having some wrap on heald eye surface. Half wrap angle on heald eye in zone A is (Ah) = (aa ? ba) Half wrap angle on heald eye in zone B (Bh) is zero Half wrap angle on front lease rod in zone B (Bfl) is zero

Between Stage II and Stage III During this period of time the first heald is moving down and second heald is moving up. Both the yarns make contact with lease rod. The yarns do not have contact with

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Fig. 7 Path of warp yarn passing through front heald in zone A and B

Fig. 8 Path of warp yarn passing through back heald in zone A and B

heald eye in zone B. The yarn wrap on heald in zone A is calculated by subtracting an amount of wrap from zone B. Half wrap angle on heald eye in zone A is (Ah) = (aa ? ba) - (bb - ab) Half wrap angle on heald eye in zone B(Bh) is zero Half wrap angle on front lease rod in zone B is (Bfl) = (bb - ab) Stage III At this position both the yarns are between the lease rod and the cloth fell are straight in nature. The yarns are free from any wrap with top and bottom surface of healds. But at this position of the healds, both the yarns are in contact with front lease rod. The wrap angles are given by

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Half wrap angle on heald eye in zone A (Ah) is zero Half wrap angle on heald eye in zone B (Bh) is zero Half wrap angle on front lease rod in zone B is (Bfl) = bb Between Stage III and Stage IV The first heald moves down and second heald moves up. During this period, the yarn in front heald is in contact with top surface of heald eye and the yarn in second heald is in contact with bottom surface of heald eye. During this stage of heald displacement the amount of wrap on heald eye in zone B is to be calculated by subtracting an amount of angle from A zone. Half wrap angle on heald eye in zone A (Ah) is zero Half wrap angle on heald eye in zone B is (Bh) = (bb - ab) - (aa - ba)


Half wrap angle on front lease rod in zone B is (Bfl) = (bb - ab)

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from h to hi, the displacement of heald shaft (hi) at an angle hi, is given by the following equation (refer Eqs. 1 and 5) hi ¼ ½ðm1Þ hi þ S =2 ½x þ y ðn 1Þ z=x

Stage IV The healds are in such a position that the yarn axis in zone A coincides with the reference line. The yarns in zone A make tangential contact with the heald eye. Half wrap angle on heald eye in zone A (Ah) is zero Half wrap angle on heald eye in zone B is (Bh) = (bb - ab) Half wrap angle on front lease rod in zone B is (Bfl) = (bb - ab) Between Stage IV and Stage V; Stage V The yarn from first heald is reached at the bottom shed line and it is in contact with top surface of heald eye. The yarn from second heald is reached at the top shed line and it is in contact with the bottom surface of heald eye. Half wrap angle on heald eye in zone A is (Ah) = (aa ? ba) Half wrap angle on heald eye in zone B is (Bh) = (ab ? bb) Half wrap angle on front lease rod is in zone B (Bfl) = (ab ? bb)

Displacement of Heald as a Function of Bottom Shaft Rotation Shedding process is initiated with the rotation of bottom shaft (h). The arrangement of shedding tappets at the beginning is assumed such that the follower of the front tappet is just to start rising and the follower of the back tappet is just to start falling. This corresponds to fall of front treadle bowl from the top most position and raising of back treadle bowl from the bottom most position as represented in the Fig. 2. One complete rotation of bottom shaft (360°) corresponds to two picks during which the treadles complete one cycle of its movement from top/bottom to bottom/top or to the position from where it is started. During this period each cam completes its full action of raising, top dwell, falling and bottom dwell. The displacement of treadle bowl from the treadles level position is given by Eqs. (1–4), for different ranges of bottom shaft rotation. Starting from the angle at which treadles come to level (which corresponds to the closed shed position) the displacement of heald at each degree of bottom shaft can be estimated by using Eq. (5) for different values of h. When the bottom shaft rotates from h to hi, the heald displaces

As the heald starts displacing from the closed shed position due to the rotation of bottom shaft, the yarn displaces from the closed shed line causing continuous change in geometry of shed. Due to change in shed geometry, various geometrical parameters e.g., geometrical length of yarn, angle of wrap over the weaving element will be changing. Geometrical Length of Yarn at any Angle of Bottom Shaft Rotation The displacement of heald causes the movement of warp yarn and change in shed geometry particularly in zone A and B and to a small extent in zone C. All the geometrical parameters of different zones are estimated based on new position of heald (defined by hi) by using the equations developed zone wise in ‘‘Treadle bowl displacement equations’’ section. The instantaneous values of half wrap angle and geometrical length in these zones are given by Half wrap angle in a zone ¼ ai bi p 0 Geometrical length ðli Þ ¼ hi 2 þ d2x r02 i where ai, bi, r0 i and hi0 will be having different values in each zone which changes with the value of hi and dx (the horizontal distance of any zone). The values of wrap angle and geometrical length 0 zone D are independent of heald displacement (hi) and are obtained from the equations derived in Appendix B. So the values of half wrap angle at different zones for any given time are represented by Ai, Bi, Ci and Di. Similarly the values of geometrical length of yarn are represented by lai, lbi, lci and ldi. As the healds take new position, the new shed geometry will result in change of wrap angle and geometrical length at different zones. The value of wrap angles on different elements at different zones for a given position of bottom shaft rotation (hi) are given by the following equations (refer ‘‘Heald displacement equations’’ section.) ðWh Þi ¼ ðAh Þi þ ðBh Þi ð10Þ ðWfl Þi ¼ ðBfl Þi þ ðCfl Þi ð11Þ ðWbl Þi ¼ ðCbl Þi þ ðDbl Þi ð12Þ ðWbr Þi ¼ ðp=2Þ ðDbr Þi ð13Þ The total geometrical length in any zone consists of geometrical straight length of the yarn and the length of the arc in that zone. The total geometrical length of yarn in different zones at any given position of the of bottom shaft

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rotation (hi) are given by the following equations (refer ‘‘Stages of heald shaft displacement’’section) ð14Þ ðLa Þi ¼ ðla Þi þ ðWh Þi =2 rh ðLb Þi ¼ ðlb Þi þ ðWh Þi =2 rh Þ þ ðWfl Þi =2 rl Þ

The possibility of yarn flow due to tension variation between any two zones in the weaving process can be determined in the same manner.

ð15Þ ðLc Þi ¼ ðlc Þi þ ðrl ½ðWfl Þi þðWbl Þi =2Þ ð16Þ ðLd Þi ¼ ðld Þi þ ðWbl Þi þ2 rl Þ þ ðWbr Þi =2 rb Þ

New Length of the Yarn

ð17Þ Tension due to Change in Geometrical Length Change in geometrical length of yarn in zone A and B by the movement of heald cause to develop strain in yarn which increases tension in the yarn. If there is no yarn flow from one zone to another and then the extension of yarn is only considered for increase of yarn tension. The developed tension in the yarn can be given by Ti ¼ E ð Li Lo Þ = Lo

ð18Þ

where Lo is the length of yarn at zero tension in any zone. Likewise tension values in all the zones due to geometrical length change are obtained by ðTa Þi ¼ E ðLa Þi Loa Loa ð19Þ ðTb Þi ¼ E ðLb Þi Lob Lob ð20Þ ðTc Þi ¼ E ðLc Þi Loc Loc ð21Þ ðTd Þi ¼ E ðLd Þi Lod Lod ð22Þ

Even though it is difficult to know the exact amount of yarn flow at each intermediate step, the flow can be estimated by assuming a small quantity of yarn (Dl) flow from one zone to the other. The amount of flow length (Dl) being deducted from one zone and added to the other zone. Each time the tension equation inequality given in the direction of yarn flow be checked whether the condition for more flow exists or not. If the condition is fulfilled for more flow of yarn, then again (Dl) more amount of length flows from one zone to other till the tension equation is satisfied for no flow at each zone. The total flow can be obtained by adding Dl as many numbers of times as the flow has taken place. The amount of flow is affected with the help of lab VIEW program. The flow of yarn causes change of length at each zone and is given by (Lo)i = Lo ? (Dl)i (when the inflow of yarn takes place) (Lo)i = Lo - (Dl)i (when the outflow of yarn takes place) Tension in the Yarn After Yarn Flow Once the new value of the length of yarn is established and there is no possibility of yarn flow from any zone, then the final yarn tension in each zone can be given by ðTiÞfinal ¼ E ðLi Loi Þ = Loi

ð23Þ

Flow of Yarn due to Yarn Tension The change in warp yarn tension at zone A and B due to heald displacement may cause the flow of yarn from one zone to the other. The possibility of yarn flow and its direction can be calculated by using Amonton’s equation of friction. Direction of Yarn Flow If (Ta)i [ (Tb)i e (lW) the yarn flow will occur from B zone A zone till the tension in A zone is as follows ðTa Þi ðTb Þi eðlWÞ where l is coefficient of friction between yarn-metal surfaces And If (Tb)i [ (Ta)i e (lW)the yarn flow will occur from A zone to B till the tension till B zone is as follows ðTb Þi ðTa Þi eðlWÞ

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Flow Chart for Calculation of Yarn Tension In order to operate this program, input in the form of heald shaft number, lift of the tappet and angle of bottom shaft rotation (h) are fed. The output of the program is warp yarn tension profile at different zones with respect to the bottom shaft rotation. The complete program consists of sub routines and the sequence of executing the programs is described in the Fig. 9. The program ‘h’ gives the values of heald displacement at any angle of bottom shaft rotation based on the Eqs. (6–9). As there are two heald shafts, if the number of the heald shaft and its lift is fed to the program, it gives displacement of respective heald shaft. The program H gives the height at which yarns do not have any contact with the yarn (refer Fig. 4c), which is useful to know the yarn contact with either top or bottom surface of heald eye. The values of heald displacement (h) obtained from program ‘h’ and the value of height of yarn (H) from program H are fed to programs A, B and C where half


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Fig. 9 Simulation of warp yarn tension—a block diagram

wrap angle and geometrical length in A, B and C zones are calculated, as per the equations. Similarly half wrap angle and geometrical length in zone D are calculated in program D. In all these zone wise programs, the necessary parameters like heald eye radius, lease rod radius, yarn radius, horizontal distance of each zone etc., are defined as input variables. The program L gives the total wrap angle on an element and then the total geometrical length of yarn in each zone at any angle of bottom shaft rotation by the values of half wrap angle and geometrical length obtained in the programs A, B, C and D. The program Lo is modification of program L, to get the length of yarn at zero tension. Program T calculates the tension values based on the total geometrical length of yarn and length of yarn at zero tension. In the program T, the obtained values of tension are used to find the flow of yarn by using a while loop to get the new geometrical length of yarn, based on which final values of yarn tension are obtained.

Experimental Set Up Verification of the model is carried out on a CIMCO GWALIOR plain automatic loom. The loom width is 5800 and is fitted with automatic cop change mechanism, and with positive let off motion. For the experiment, the yarn is passed on the loom, through back rest, lease rods and heald eye, and through the reed. The yarn at one end is fixed on the front rest. The yarn at the other end is passed over the back rest and is kept under tension by using dead weights, a case similar to negative let off system. The top surface of back rest and front rest are kept at the same level and the line joining these two points is taken as the reference line. Lease rods are arranged such that center of lease rods coincides with the reference line. The position healds is kept such that when they come to closed shed

position, the center of both the heald eyes coincides with the reference line. The shedding elements are arranged to form symmetric shed. The tension meter is arranged between back rest and back lease rod (nearer to the back rest). The tension meter is held in a special frame. The care has been taken so that no movement or vibration transmits to the tension sensor during experiment. The tension meter is arranged between back rest and back lease rod (nearer to the back rest). The tension meter is held in a special frame. The care has been taken so that no movement or vibration transmits to the tension sensor during experiment. Results and Discussions Figure 10 showed the general profile of warp yarn tension curve, which was obtained during the process of shedding by using the theoretical model developed in the present work. The curve indicated the expected yarn tension values to be developed at the zone D during shedding, where most of the experimental measurements had been carried out by a

Fig. 10 General profile of warp yarn tension during a pick cycle

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Fig. 11 Typical warp yarn tension cycle

Fig. 12 Profile of tension of yarn passing through first heald shaft during two picks of weaving cycles

number of researchers [5–7]. The tension curve was also generated by using a yarn of 74 tex, with relative rigidity 6300 cN and at an initial warp yarn tension of 15 cN to verify the model. The time period of warp yarn tension measurement is over one pick i.e., when the heald shaft was moving down from closed shed position, reaching bottom shed line and again moving back to closed shed position. The nature of curve during shedding over a pick cycle showed that tension started rising with the rotation of bottom shaft from zero value and reaches to maximum value at an angle about 50°–60°. The yarn tension maintained more or less a constant value over next 60° rotation of bottom shaft and after that the tension fell down to minimum value at 180°. The yarn tension was started building due to opening up of the shed and reached the maximum value when the yarn was at the bottom shed line. After that the tension remained same due to the dwell of the cam i.e., no heald movement. As the dwell period of the cam was over, the yarn tension then started falling to the minimum value when shed was closed. The similar trend in yarn tension development was observed for a yarn, when it was moving up from closed shed position, gradually reaching the top shed line and again moving back to the closed shed position. This showed that peak values of tension occurred when shed was fully opened and the average open shed tension was found to be 2–3 times more than the closed shed tension. The duration of peak value of yarn tension and the nature of the yarn tension curve

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(during rising or falling) were dependent on the dwell of the tappet (normally 60° of bottom shaft rotation) and the profile of shedding cams used, respectively. The nature of warp yarn tension curve during weaving was recorded by Greenwood (Part-II), Gu and Weinsdorfer in their experimental work shown on Fig. 11 [4, 6, 8]. It indicated a sharp rise of tension for a short period of time followed by a smooth build-up of yarn tension over a longer duration. The obvious reason was that they had measured the tension values over complete weaving cycle in which a sharp rise of tension was observed at the time of beat up and the rest of the part of yarn tension might be due to shedding. However, in the present theoretical approach for predicting warp yarn tension, the beat up action was not taken into account. The model was based on the tensions developed due to shedding process only, therefore no sharp rise in tension was found in the profile of theoretical tension curve. However, the profile of warp yarn tension was obtained by using the model given in Fig. 10 which was very similar to the works of simulated model developed by Wulfhorst [9] and warp tension profile obtained by controlling the let off through evaluation program, developed by Dayik et al. and the works of Greenwood (Part-II) [4, 10].The average open shed yarn tension value which was reported about 2 times that of closed shed and was at per the work reported by Gu for different types of cam profiles [8]. It was also observed from the experimental measurement that the warp yarn tension remained the same at the peak value during the dwell of the cam.


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Fig. 13 Profile of tension of yarn passing through second heald shaft during two picks of weaving cycle

Fig. 14 Comparison of theoretical model with the experimental

The yarn tension traces obtained from the model were found to be repeated for every two picks (Fig. 12). This corresponds to the one rotation of bottom shaft on weaving machine which completes in two picks. Any warp thread that starts moving from its position will again be back in the same position after an interval of two picks. The two pick cycle yarn tension curve is given in the Figs. 12 and 13 for front and back heald yarns. It was observed from the Figs. 12 and 13 that the peak value of yarn tensions for top andbottom shed lines were differing for both front and back heald, resulting in a ‘two pick cycle’. It was also noted that the front heald tension value was maximum when the yarn was at bottom most position and the back heald tension value was highest when the yarn was at the top most position. This difference in the peak value of tension was because of the difference in the path followed by of the warp when it formed top shed line and bottom shed line. The yarn which passed above the front lease rod (yarn of front heald shaft) had more wrap on the lease rod and heald eye when it was at bottom most position. The opposite was true for back heald. It had higher yarn wrap on heald and front lease rod when the heald was at upper most position. Due to higher wrap, the yarn was supposed to overcome more frictional resistance for the flow of yarn from one zone to other and ultimately from the warp beam, causing in higher value of peak tension. The peak value of yarn tension of back heald yarn

was always higher than the peak value of front heald yarn, probably due to high lift of back heald tappet as compared to front heald tappet. These results were similar to the fundamental works on warp yarn tension carried out by Owen, Holcombe et al. and Wulfhorst [1, 5, 9]. It was noticed that the peak value of yarn tension was repeated over two picks. The differences in the peak tensions occurred between top and bottom sheds was explained as a result of raising the back rest or sinking the closed shed line i.e., formation of asymmetric shed to improve the cover of the fabric [1].

Verification of the Model In order to verify the model, experiments were carried out on a plain automatic weaving machine fitted with tappet shedding mechanism. Two different yarns of 3/14’s (126 tex) and 8’s count (74 tex) with relative rigidities of 17,358 and 6,300 cN respectively are used. The coefficients of yarn-metal friction are 0.33 and 0.37 respectively. The warp yarn tension values were measured by using digital electronic tension meter of AG Instruments Pvt Ltd, model YTEN 201. The tension meter was placed between the back rest and back lease rod. The warp yarn tension is noted for the rotation of bottom shaft. The experimental values of warp yarn tension and theoretical values of warp

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Fig. 15 Comparison of theoretical model with the experimental

Fig. 16 Zone wise tensions for yarn passing through first heald

Fig. 17 Tensions in different zones for yarn passing through second heald

yarn tension calculated from the model are plotted against the rotation of bottom shaft and are given in the Figs. 14 and 15, for two different yarns. Figures show the comparison of tension profile obtained from theoretical model to that of experimental values measured for two different yarns at an initial tension of 15 cN. From the results it is observed that nature of theoretically derived warp yarn tension curve is very similar to that of experimental one. But the theoretically calculated values of yarn tension are always less than the experimental values. It is noted that the calculated values of warp yarn tension are about 11–13 % less than the experimental values of corresponding yarn tension. This result is observed in both the yarns and for first heald. The

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reason for the discrepancies between theoretical and the experimental yarn tension values may be due to simplification in formulating the model as compared to the actual process. The peak tension values are higher in the case of thick yarn because of the higher relative rigidity of 3/14’s yarn.

Tension Developed in Different Zones All the previous works reveal that the warp yarn tension measurements were taken in the zone between back rest and back lease rod. This is due to the difficulties in measuring the warp yarn tension in the actual shedding


zone (between cloth fell and the heald and between heald and front lease rod) where the yarn is always under dynamic condition. So, usually the warp yarn tension measured after back rest which may be much lower than the actual developed tension in yarn during weaving. This model can help us in predicting the warp yarn tension at different zones i.e., between the two lease rods, between front lease rod and heald eye and in between heald eye and cloth fell. So from this theoretical approach, one can have an idea of the expected warp yarn tension values at different zones. The passage of yarn is divided into four zones A, B, C and D and the tension levels developed in these four zones are calculated by using the model for the rotation of the bottom shaft. The tension curve is plotted against bottom shaft rotation and which is shown in (Figs. 16, 17). Figures 16 and 17 show typical profiles of warp yarn tension in different zones for front and back heald shafts of a plain weaving machine. It is observed from the (Fig. 16) that the peak values of warp yarn tension in shedding zone are much higher than the peak values near the back rest i.e., zone D. The peak value of yarn tension at zone A is almost double the value of peak yarn tension of zone D, where usually warp yarn tension is measured on a weaving machine. It is also observed that the yarn tension at zone B and C are also much higher than that of zone D. A similar trend is observed for back heald yarn also (Fig. 17). The reason for this is that the yarn in actual shedding zone is subjected to more strain when compared with other zones. As there is minimum or almost no possibility of yarn flow from the cloth fell, the increased tension values in shedding zone tend to pull the yarn from warp beam by overcoming the frictional resistance of back rest, lease rods and heald eye to achieve the equilibrium. This causes the flow of yarn from zone B to A, zone C to B and zone D to C resulting in increased values of yarn tension in these zones. However the increased value of yarn tension in D zone is much less as compared to the yarn tension in the shedding zone. It is also observed that the peak tensions in zone A are 2.5–3.5 times higher than tension values when shed is closed. Both the peak values of warp yarn tension for the yarn passing through the back heald are higher than the front heald. This may be due to the high lift of the back heald tappet. The results confirm the statement made by Snowden [7] that ‘‘The thread tensions between the heald and cloth fell are possibly greater than tensions measured near the back rest and the measured tensions are of value regarding estimating the peak tensions likely to be imposed on warp threads between cloth fell and healds’’. However they have not predicted quantitative values of tension in the shedding zone. It also confirms with the works of Dolecki [11] that most of the warp breaks that occur due to tension variations are between heald and cloth fell, the reason may

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be due to highest level of yarn tensions developed in this zone during the process of weaving [11].

Conclusions A theoretical model is developed based on the shed geometry to determine the tension developed in the warp yarn during the process of shedding on a plain weaving machine. The change in warp yarn tension values are calculated by using a computer program for the minute rotation of the bottom shaft. The theoretical model of shedding process is formulated based on the knowledge gathered from research reports published in the literature and by observing closely the yarn movement on a weaving machine. The model takes into account the dynamic nature of shed geometry and sequence of yarn flow from one zone to the other. A computer program based on this model has been developed for predicting the warp yarn tension during shedding for every minute rotation of the bottom shaft. The theoretical model is verified qualitatively. It is found that the nature of the theoretically calculated warp yarn tension curve is very similar to that of the experimental tension curve of previous researchers. Tension in the warp yarn increases as the shed opens and reaches to a maximum value when the shed is fully opened. The yarn tension reduces to a minimum value as the shed is closed. The peak yarn tension value remains almost same over the dwell period of the tappet. The yarn tension value obtained from the model when plotted against the rotation of bottom shaft is found to be repeated over two successive picks. The peak value of yarn tension occurs when the heald is either at the top or at the bottom most position. The model is also validated quantitatively by using some data generated on a plain weaving machine which shows a good agreement between the theoretical and the experimental values. The values of warp yarn tension obtained from the model are about 10–13 % less than the experimental values. The peak value of yarn tension is different for the front and the back heald and back heald yarn tension is always higher. This may be due to higher lift of the back heald cam. The path of the warp yarn on a plain weaving machine is divided into four different zones and the tension value developed in each zone is estimated by using the developed computer program. The yarn tension is maximum at the A zone followed by the tension value at B, C and D zone. The predicted yarn tension value in shedding zone (A and B zones) is found to be much higher than the tension near the back rest (D zone). The peak value of warp yarn tension in shedding zone is almost double the value of yarn tension near the back rest.

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Appendix A: The Formulation of Model for Development of Warp Yarn Tension during Shedding Process Developing the mathematical relations for treadle bowl displacement based on cam profile at different angles of bottom shaft rotation

Transforming the treadle bowl displacements into Heald displacement

Path of warp yarn on the weaving Machine for a given position of heald

Calculation of the geometrical length of warp as the shed height changes

Calculation of the tension based on the change in geometrical length for changing shed

Flow of warp yarn from one zone to other due to tension Variation as per Amonton’s equation

The new actual length of warp yarn after flow in different zones

The final tension in warp yarn based on actual length in Different zones

Appendix B r0 r0 is the distance between two lines parallel to the yarn axis and passing through centers of circular surfaces carrying the yarn. This variable changes according to the arrangement of yarn on two surfaces. There are two possibilities arrangements; (i)

When the yarn lies above and below the two surfaces (Fig. 18)

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Fig. 18 Definition variables r0


(ii)

When the yarn lies either above or below both the surfaces where it is the difference between the two radii (Fig. 19).

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a ¼ tan1 ðh0 =dÞ b b is the angle made by the line parallel to yarn axis in the straight portion with the line joining the centers of two circular elements carrying the yarn (Fig. 22).

Fig. 19 Definition of variable r0

h0 h0 is the difference in heights of two yarn carrying surfaces (Fig. 20). Fig. 22 Definition of b

b ¼ tan1 ðPQ = OQÞ ¼ tan1 ðr0 =lÞ Half Wrap Angle on an Element in a Zone (A/B/C/D)

Fig. 20 Definition of variable h0

It is the angle made by a line perpendicular to the yarn axis with the vertical line that divides two zones. For example half wrap angle in zone B is represented in the figure (Fig. 23).

a a is the angle made by the line joining centers of two circular elements carrying the yarn with the horizontal line (Fig. 21).

Fig. 23 Half wrap angle or wrap angle in a zone

Total Wrap Angle on an Element (W)

Fig. 21 Definition of a

Wrap angle on any element that divides into two zones is the sum of the two half warp angles on either side of it (Fig. 24).

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Fig. 26 Total geometrical length of a yarn in a zone

References Fig. 24 Definition of total wrap angle on an element

Geometrical Length of Yarn in a Zone (1) It is the length of straight portion of yarn measured in any zone between two contacting points i.e., excluding the wrap length. It is represented by ‘‘l’’ in the chapters (Fig. 25).

Fig. 25 Geometrical length of yarn

Total Geometrical Length of Yarn in a Zone (L) It is the sum of straight length and wrap length calculated by multiplying warp angle with the radii of respective yarn holding elements. It is represented by ‘‘L’’ in the chapters. Say in zone B (Fig. 26).

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1. A.E. Owen, The Tension in a single warp thread during plain weaving. J. Text. Inst. (Trans.) 19, 365–388 (1928) 2. N.H. Chamberlain, D.C. Snowden, Variations in individual warp thread tension during weaving cycle. J. Text. Inst. (Trans.) 39(2), 23–43 (1948) 3. K. Greenwood, W.T. Cowhig, The position of cloth fell in power looms, part I: stable weaving conditions. J. Text. Inst. 47, T241 (1956) 4. K. Greenwood, W.T. Cowhig, The position of Cloth fell in power looms, part II: disturbed weaving conditions. J. Text. Inst. 47, T255 (1956) 5. B.V. Holcombe, R.E. Griffith, R. Postle, A study of weaving systems by means of dynamic warp and weft tension measurement. J. Text. Inst. 71, 1–5 (1980) 6. H. Weindorfer, Effects of shed formation on the loading of warp yarn. Indian J. Fiber Text. Res. 19(9), 139–146 (1994) 7. D.C. Snowden, Some factors influencing the number of warp breakages in woolen and worsted weaving. J. Text. Inst. 40, 317–329 (1949) 8. H. Gu, Reduction of warp tension fluctuation and beat up strip width in weaving. Text. Res. J. 54(3), 143–148 (1984) 9. B. Wulfhorst, Simulation calculations as a development tool in weaving. Int. Text. Bull. 47(2), 54–58 (2001) 10. M. Dayik, M.C. Kayacan, H. Calis, E. Cakmak, Control of warp tension during weaving procedure using evaluation programming. J. Text. Inst. 97(4), 313–324 (2006) 11. S.K. Dolecki, The causes of warp yarn breaks in the weaving of spun yarns. J. Text. Inst. 65, 68–74 (1974)



Experimental Investigations of Woven Textile Tape as Strain Sensor T. Kannaian • V. S. Naveen • N. Muthukumar G. Thilagavathi

•

Received: 2 September 2014 / Accepted: 20 January 2015 / Published online: 18 February 2015 Ó The Institution of Engineers (India) 2015

Abstract In this article, a strain sensitive textile based elastomeric tape sensor has been developed and process parameters for sensor development are optimized. Polyester yarns are used as base threads and rubber threads are used as elastomer for the sensor development. The sensor has been developed with the help of narrow width tape loom by introducing the silver coated nylon yarn in the middle of the tape structure. The influence of weave structure, number of conductive threads and rubber thread tension on sensor development has been optimized by using the Box–Behnken method and the results are analyzed using the Design expert software. From the results, it is found that six numbers of conductive threads in a plain weave structure with rubber thread tension of 750 g is suitable for the sensor to give high gauge factor of 1.626. Keywords Elastomeric tape Electrical resistance Gauge factor Hysteresis Strain sensor

Introduction Electro-textiles can be defined as textiles with unobtrusively built-in electronic and photonic functions. They are mostly used for electromagnetic shielding, anti-static and heating purposes, and also for soft circuits: electric circuits

T. Kannaian Department of Electronics, PSG College of Arts and Science, Coimbatore 641014, India V. S. Naveen N. Muthukumar (&) G. Thilagavathi Department of Textile Technology, PSG College of Technology, Coimbatore 641014, India e-mail: [email protected]

or sensors made out of a combination of special fabrics, threads, yarns and electronic components. Electrical functions can be embedded in textiles by using weaving, knitting and embroidery or nonwoven production techniques. The integration of electronic properties directly into the clothing environment carries some advantages such as increased comfort, mobility, usability and aesthetic properties. However, there are some challenges to be addressed. Yarns that are used for making cloth should be fine and elastic in order to ensure the wearer’s comfort. The fibers have to be able to withstand handling and fabrics should have low mechanical resistance to bending and shearing which means they can be easily deformed and draped. The creation of textile-based strain sensors has attracted researchers attention, so many investigators have studied this area and different kinds of technique have been used in order to create strain sensing structures. These sensors have been used to measure human body movements or respiratory activity [1, 2]. Earlier researchers created knitted strain sensors by using stainless steel yarns and carbon yarns and identified that the contacting electrical resistance between overlapped fibers is the primary factor in the sensing mechanism [3, 4]. They also considered electrically conductive fabrics as pure resistive networks and found a solution for the plain fabric circuit network. Yang et al. modeled 1 9 1 conductive rib fabrics as resistive networks and found a relationship between extension and the equivalent resistance, both experimentally and theoretically [5]. Li et al. also investigated the relationship between the electrical resistance and textile force which includes the length related resistance of conductive yarns and the contact resistance of two overlapped yarns [6]. However, the effects of processing parameters of sensor development on the electrical resistance were not studied in the earlier research.

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The primary objective of this work is to develop elastomeric strain sensing tape sensor using narrow width tape loom by introducing the silver coated nylon yarn in the middle of the tape structure. For sensor development, number of conductive threads, tension weight and weave structures are taken as independent variables and gauge factor is taken as dependent variable. These variables are optimized using Box–Behnken method and the data are analyzed using design expert software.

Table 2 Box–Behnken design for process optimization No. of warp upper repeat

Gauge factor

750

2

0.68

750

2

1.03

2 6

1,250 1,250

2 2

0.64 1.05

Sample—5

2

1,000

1

0.89

Sample—6

6

1,000

1

1.54

Materials and Methods

Sample—7

2

1,000

3

0.18

Sample—8

6

1,000

3

0.28

Polyester high bulk yarn (70/2 denier) was used in both warp and weft and rubber threads of 40 gauge having thickness of 0.64 mm was used in warp as elastomer. The silver coated polyamide yarn of 235 9 2 DTex having resistance \50 X/m from M/s Statex Gmbh, Germany was used as conductive threads. Jakob Muller narrow width tape loom was used for elastomeric tape sensor weaving. The elastomeric tape sensor design was optimized with Box and Behnken 3-variable and 3-level experimental design. The independent variables are the number of conductive threads (X1) (2, 4 and 6), tension weight (X2) (750, 1,000 and 1,250 g), weave structures (X3) (plain weave, warp rib and 3/1 twill weave). In order to optimize the design the weave structure was converted into the numerical format, and the number of warp up per repeat was chosen as numbers. The dependent variable was the sensitivity factor or gauge factor, i.e. ratio of change in resistance for a small change in length. Response surface equation was formed with the help of design expert software. The coded levels of Box and Behnken 3-variable 3-level experimental design are shown in Table 1. The other variables like Ends per inch (EPI), Picks per inch (PPI), width and thickness were kept as a constant. The sample specifications of 15 experiments are shown in Table 2.

Sample—9

4

750

1

1.27

Sample—10

4

1,250

1

1.16

Sample—11

4

750

3

0.22

Sample—12

4

1,250

3

0.34

Sample—13

4

1,000

2

0.69

Sample—14

4

1,000

2

0.79

Sample—15

4

1,000

2

0.74

Resistance and Gauge Factor Measurement The elastomeric tape sensors were extended with the help of fabric extension meter from an initial length of 25 cm. They were extended up to 40 % with an interval of 1 cm. The resistance change (linear resistance) thus caused due to the extension was noted down using Agilent 34401A 6

No. of conductive threads (X1) Tension weight (X2) (g) No. of warp upper repeat (X3)

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Low

No. of conductive threads

Sample—1

2

Sample—2

6

Sample—3 Sample—4

Tension weight

digital multimeter. The gauge factor was calculated by the slope of the curve for resistance with extension, as shown below: Gauge factor ðSensitivity factorÞ ¼ Dr=Dx

ð1Þ

where Dr is the change in resistance for a change in distance Dx, for which the curve was linear [7].

Results and Discussion The samples were developed as per the Box–Behnken design and the gauge factor was calculated for each samples from zero to 40 % extension and listed in the Table 2. Table 3 showed ANOVA for response reduced quadratic model. The model F-value of 309.60 implies the model was significant. There was only a 0.01 % chance that an F-value of this large could occur due to noise. Values of ‘‘Prob [ F’’ less than 0.0500 indicate model terms are significant. In this case X1, X3, X1 X3, X2 X3, X21, X22, X32 are significant model terms. The following equation was obtained with gauge factor value (Y) as dependent variable and number of conductive threads (X1), tension weight (X2) and weave structure (X3) as independent variables with the help of Design Expert software package. Y ¼ 0:74 þ 0:19X1 0:48X3 0:14X1 X3 þ 0:058X2 X3

Table 1 Variables and their coded levels Variables

Sample no.

Medium

High

2

4

6

750

1,000

1,250

1

2

3

þ 0:043X21 þ 0:068X22 0:060X23

ð2Þ

R2 ¼ 0:9968 The negative coefficient of all variables such as weave structure and the interaction between the conductive


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Table 3 Analysis of variance (Partial sum of squares—Type III) Source

Sum of squares

Degree of freedom

Mean square

F value

p value Prob [ F

309.60

\0.0001

Model

2.26

7

0.32

X1 (no. of conductive threads)

0.29

1

0.29

273.77

\0.0001

X3 (warp float)

1.84

1

1.84

1770.48

\0.0001

X1 X3

0.076

1

0.076

72.64

\0.0001

X2 X3

0.013

1

0.013

12.70

0.0092

X21

6.669E-003

1

6.669E-003

X22

0.017

1

6.41

0.0392

0.017

16.16

0.0051

12.77

0.0091

0.18

0.9448

X23

0.013

1

0.013

Residual

7.288E-003

7

1.041E-003

Lack of fit

2.288E-003

5

4.575E-004

Pure error Cor total

5.000E-003 2.26

2 14

2.500E-003

threads and weave structures in the response surface equations indicated that the increase in their values decrease the gauge factor. The higher R2 value of 0.9968 indicated their significant relation. Among the three variables the weave structure strongly influenced the gauge factor. Effect of Number of Conductive Threads on Gauge Factor It has been observed from Fig. 1 that the gauge factor increases with the increase in the number of conductive threads in a dent. It is due to the fact that, when the number of conductive threads increased, the possibility of interaction between the conductive threads also increased and as a result it increased the change in resistance and thus the gauge factor increased.

Significant

Not significant

according to the weave structure. Tension weight applied on the rubber threads determines the crimp introduced in the structure. When the weight increases, the crimp also increases and at higher levels of crimp the adjacent yarns come closer to reduce the initial resistance. Thus the gauge factor is reduced. At lower weights, the crimp are reduced and the change in resistance are also less. The weight has been kept in such a range that the yarns can not act as a strand. Effect of Weave Structure on Gauge Factor It is observed from Fig. 3 that as the interlacement increases, the gauge factor increases. Increase in warp float minimizes the interaction between the warp threads and the gauge factor reduces with the increase in warp float.

Effect of Tension Weight on Gauge Factor

Optimization of Variables for Elastomeric Tape Sensor Design

It has been observed from Fig. 2 that the tension weight should be in an optimum level and the level changes

Figure 4 shows the influence of the number of conductive threads (X1) and the tension weight (X2) on gauge factor of

Fig. 1 Effect of number of conductive threads on gauge factor

Fig. 2 Effect of tension weight on gauge factor

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Fig. 3 Effect of weave structure on gauge factor

Fig. 4 3D surface plot for the variables tension weight and number of conductive threads

Fig. 5 3D surface plot for the variables warp float and no. of conductive threads

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the tape sensor. It has been observed from the graph that the gauge factor of the developed tape sensor increases with increase in the number of conductive threads. As the number of conductive threads increase, the contact area also increases and hence increase the electrical conductivity. Figure 4 depicts that the influence of tension weight on gauge factor of the tape sensor is very low. The interaction of X1 X2 is negligible (Eq. 2) and hence removed. Figure 5 shows the influence of the number of conductive threads (X1) and the warp float (X3) on gauge factor. The graph shows that the highest gauge factor is observed at reduced warp float length. The increased length of float increases the path of current flow, which in turn increases


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Fig. 6 3D surface plot for the variables tension weight and warp float

the resistance of the yarn and reduces the gauge factor. Figure 6 shows the effect of length of warp float and tension weight on the gauge factor. The variable X3 (warp float) significantly influences the gauge factor as shown in Eq. 2. As per experimental data, the optimized results for the chosen variables are as follows: number of conductive threads: 6, tension weight: 764, warp float: 1, for the gauge factor of 1.64.

Electrical Resistivity for Linear Extension The sample has been developed with six conductive threads, 750 g tension weight and in a plain weave pattern. It has been tested for its gauge factor. The developed elastomeric tape sensor is shown in Fig. 7. Table 4 shows the change in resistance at different levels of stretching. It is observed from Table 4, that the developed strain sensor has achieved the suggested gauge factor as per the Box– Behnken design.

The test has been carried out for five times in order to find out the repeatability. The gauge factor obtained for the five repeatability trials, as shown in the Table 5. It has been observed from the Table 5 that the gauge factor goes on increasing as the increase in number of trials. It is due to the fact that the coated yarns which loses few silver particles in the surface so the probability for change in resisTable 4 Change in resistance for change in strain of the developed sensor Strain (%)

Length (mm)

Loading

Unloading

0

250

55.8

56.3

4

260

59.7

59.7

8

270

63.8

62.5

12

280

68.2

66.5

16

290

72.9

70.3

20

300

77.2

74.1

24 28

310 320

81.0 84.5

78.0 81.6

32

330

87.2

85.0

36

340

89.2

88.1

40

350

92.1

92.1

Gauge factor

1.626

1.59

Table 5 Gauge factor for five trials Sample

Fig. 7 Elastomeric tape sensor

Gauge factor Loading

Unloading

Trial—1

1.626

1.575

Trial—2

1.629

1.578

Trial—3

1.637

1.593

Trial—4

1.638

1.624

Trial—5

1.640

1.625

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130


elastomeric tape sensor developed with six numbers of conductive threads, in a plain weave structure with rubber thread tension of 750 g has high gauge factor of 1.626. The samples have been tested for change in resistance with linear extension for strain sensor application and it is observed that the resistance changes up to 40 % extension. The elastomeric tape sensor prepared in this work is expected to find applications in sensing garment, wearable hardware and rehabilitation. Acknowledgments We wish to thank DST-IDP, New Delhi, for sponsoring the project and for the financial assistance.

References Fig. 8 Repeatability trends of five cycles

tance becomes higher which increases the gauge factor. It may be also due to the conditioning of base yarns which can nullify the problem of cold start. It can be confirmed by observing the last three trials, which does not have larger change in gauge factor than that of previous two trials. The trend of change in resistance has been analyzed in order to find out the repeatability of the developed elastomeric tape sensor. A hysteresis between the loading and unloading curves has been observed in Fig. 8 and the trend has followed the same path.

Conclusions In this work, Elastomeric tape sensor fabrics have been developed using silver coated polyamide yarn along with polyester and rubber threads. The process variables for sensor design have been optimized using Box and Behnken experimental design. It has been found that the

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1. D. De Rossi, F. Carpi, F. Lorussi, A. Mazzoldi, R. Paradiso, E.P. Scilingo, A. Tognetti, Electro active fabrics and wearable biomonitoring devices. AUTEX Res. J. 3, 4 (2003) 2. L. Van Langehove, Smart textiles for medicine and healthcare: Materials, systems and applications (Wood head publishing, Cambridge, 2007) 3. H. Zhang, X. Tao, S. Wang, T. Yu, Electro-mechanical properties of knitted fabric made from conductive multi-filament yarn under unidirectional extension. Text. Res. J. 75, 598–606 (2005) 4. H. Zhang, X. Tao, T. Yu, S. Wang, Conductive knitted fabric as large-strain gauge under high temperature. Sens. Actuat. A: Phys. 126, 129–140 (2006) 5. Y. Kun, S. Guang-li, Z. Liang, L. Li-wen, Modeling the electrical property of 1 9 1 rib knitted fabrics made from conductive yarns, Proceedings of the Second International Conference on Information and Computing Science (ICIC’09), pp. 382–385 (2009) 6. L. Li, W.M. Au, Y. Li, K.M. Wan, S.H. Wan and K.S. Wong. Electromechanical Analysis of Conductive Yarn Knitted in Plain Knitting Stitch under Unidirectional Extension, Proceedings of Textile Bioengineering and Informatics Symposium (TBIS 2008), pp. 793–797 (2008) 7. O. Atalay, W.R. Kennon, M.D. Husain, Textile-based weft knitted strain sensors: effect of fabric parameters on sensor properties. Sensors 13, 11114–11127 (2013)

J. Inst. Eng. India Ser. E (July–December 2015) 96(2):131–138 DOI 10.1007/s40034-014-0043-z


Optimizing Aqua Splicer Parameters for Lycra2Cotton Core Spun Yarn Using Taguchi Method Vinay Kumar Midha • ShivKumar Hiremath Vaibhav Gupta

•

Received: 30 August 2014 / Accepted: 15 October 2014 / Published online: 8 November 2014 Ó The Institution of Engineers (India) 2014

Abstract In this paper, optimization of the aqua splicer parameters viz opening time, splicing time, feed arm code (i.e. splice length) and duration of water joining was carried out for 37 tex lycra-cotton core spun yarn for better retained splice strength (RSS%), splice abrasion resistance (RYAR%) and splice appearance (RYA%) using Taguchi experimental design. It is observed that as opening time, splicing time and duration of water joining increase, the RSS% and RYAR% increases, whereas increase in feed arm code leads to decrease in both. The opening time and feed arm code do not have significant effect on RYA%. The optimum RSS% of 92.02 % was obtained at splicing parameters of 350 ms opening time, 180 ms splicing time, 65 feed arm code and 600 ms duration of water joining. Keywords Aqua splicer Lycra-cotton core spun yarn Splice abrasion resistance Splice appearance Taguchi experimental design

Introduction The state of the art weaving machines, which work with high weft insertion rates, put stringent demands on the yarn joints. Traditional method of joining yarn ends like fisherman’s knot or weaver’s knot are highly objectionable and lead to expensive stoppages and weaving faults. The fisherman’s knot is more durable but is thicker than the weaver’s knot. To overcome this, splicing was introduced, which is most commonly used method of joining yarn ends V. K. Midha (&) S. Hiremath V. Gupta Department of Textile Technology, Dr B R Ambedkar National Institute of Technology, Jalandhar 144011, India e-mail: [email protected]

for ring spun yarns, worsted and semi-worsted yarns, woolen spun yarns of cotton, wool, synthetic and blends. Even yarn which could hardly be joined with a fisherman’s knot can be spliced effectively. Many techniques for splicing have been developed such as electrostatic splicing, mechanical splicing and pneumatic splicing. Among them, pneumatic splicing is the most popular. Splicing proceeds in two stages with two different air blasts of different intensity. The first air blast untwists and causes opening of the free ends. The untwisted fibres are then intermingled and twisted in the same direction as that of parent yarn by another air blast [1]. Kaushik et al. [2], reported that the splice structure comprises of three distinct regions: wrapping at the two ends, twisting, and tucking/intermingling in the middle of splice. The primary contribution to the strength of the splice is due to tucking and intermingling of fibres between the strands being joined. Wrapping provides binding of fibres in the splice. Twisting generates transverse forces that are beneficial in reducing inter-fibre slippage. The quality of splice is affected by the type of splicer, i.e. mechanical, pneumatic, wet and thermal, and the splicing parameters like splicing chamber, opening pressure, splicing duration and splice length [3–9]. Mashly et al. [10] reported that opening of fibres prior to twisting and/or wrapping them to form yarn splice was of paramount importance in obtaining good splice strength. Unal et al. [11, 12] reported that the fibre diameter, fibre length, yarn count, yarn twist and opening air pressure affect the spliced yarn tenacity and yarn appearance. Over the years, wet/aqua splicing was introduced, in which an additional water jet nozzle is provided to impart little amount of water on the splice point while twisting the fibres during splicing operation. The improvement in splice strength has been observed due to better mingling of fibres inside the splicing chamber. Jaouachi et al. [13] reported that increase in

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splice length and duration of water injection improves the splice’s mechanical behavior. Hassen et al. [14] reported that increase of water duration affects yarn appearance but it has no significant effect on mechanical properties of the splice. The water has a lubricating effect that reduces the splice diameter and increases the chance that elastane will be placed at the centre of the yarn. Various researchers have studied the effect of different process parameters on pneumatic splicer and the effect of water joining on the aqua splicer for ring spun yarns. However, the optimization of these process parameters on aqua splicer for lycracotton core spun yarn has not been done. Moreover, all the researchers studied the effect of these parameters on retained spliced strength and yarn appearance. None of the researchers studied the effect of these process parameters on splice abrasion resistance. In this paper, optimization of the aqua splicer parameters viz opening time, splicing time, feed arm code (i.e. splice length) and duration of water joining was carried out for 37 tex lycra-cotton core spun yarn for better retained splice strength, splice abrasion resistance and splice appearance using Taguchi Experimental Design.

Materials and Methods Ring spun lycra-cotton core spun yarn of 37 tex (16 Ne) with 5 % lycra content was used in the study. Taguchi orthogonal L9 array was used to optimize the splicing parameters viz opening time, splicing time, feed arm code (splice length) and duration of water joining for better spliced yarn strength, abrasion resistance and appearance (Table 1). The yarns were spliced by wet splicer on Oerlikon Schlafhorst Autoconer-X-5 winding machine at optimum opening and splicing pressure. In total, twenty seven experimental combinations were analyzed using three repeat observations. Opening time indicates the time duration for opening of yarn ends, whereas splicing time is the twisting time available for splicing of yarn. Splice length is adjusted by the change in feeder arm code, which indicates the

Table 1 Splicing parameters Level

Opening time (ms) [A]

Splicing time (ms) [B]

Feed arm code* [C]

Duration of water joining (ms) [D]

1

300

140

65

500

2

350

160

70

550

3

400

180

75

600

* Feed arm code C1, C2 and C3 corresponds to splice length of 30, 25 and 20 mm respectively, as measured on Leica image analyser

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overlapping distance of yarn ends at splicing chamber. Feed arm code setting does not indicate the value of splice length on the machine. Therefore, the splice lengths were checked on Leica Image Analyser and it was found that 65, 70 and 75 feed arm codes indicate the 30, 25 and 20 mm splice length respectively. The time for which water nozzle is switched on is represented by duration of water joining. Signal to Noise ratio (S/N) was calculated for all responses at ‘larger the better’ because the output response required was to acquire the maximum splice characteristics, using Eq. 1. ! S 1X 1 2 ðlarger the betterÞ ¼ 10 log ð1Þ N n Yi Analysis of variance was conducted and for each significant factor, the level corresponding to the highest S/N ratio is chosen as its optimum level. A confirmatory run was then conducted using the optimum parameters to verify the compromised optimum splicing parameter giving maximum RSS% with greatest robustness (i.e. minimum variation). Tensile strength of the parent yarn and spliced yarns were tested according to ASTM D2256 at a gauge length of 250 mm on AIMIL Tensile Tester. Retained Splice Strength (RSS) was calculated using Eq. 2: RSS% ¼

Breaking strength of spliced yarn 100 Breaking strength of parent yarn

ð2Þ

Abrasion resistance of the parent and spliced yarns was tested according to ASTM D2258 on MAG SITRA Abra Tester by measuring Retained Yarn Abrasion Resistance (RYAR) using Eq. 4: RYAR% ¼

RRIspliced yarn 100 RRIparent yarn

ð3Þ

where, RRI spliced yarn and RRI parent yarn are the mean Relative Resistance Index of spliced and parent yarn respectively. RRI was calculated using Eq. 4 RRI ¼

No of strokes Pretension in gms: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Yarn linear density ðin texÞ

ð4Þ

Splice appearance is a subjective measure of change in diameter and filamentation expressed as splice appearance grade. In the main section of the splice, there is an increase in the yarn diameter, since the two yarns occupy the space normally occupied by one and in certain circumstances, it may demonstrate filamentation [8]. However in this study splice appearance was measured on Leica Image Analyzer by its Retained Yarn Appearance (RYA) from the diameter of parent yarn and the spliced yarn using Eq. 5: RYA% ¼

Dparent yarn 100: Dspliced yarn

ð5Þ


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Table 2 RSS%, RYAR% and RYA% for aqua spliced core spun yarn Sr.

A

B

C

D

RSS%

RYAR%

RYA%

Mean

S/N

Mean

S/N

Mean

S/N

1

1

1

1

1

72.21

37.17

81.23

38.19

77.68

37.81

2

1

1

1

1

74.59

37.45

82.33

38.31

77.23

37.76

3

1

1

1

1

76.21

37.64

82.32

38.31

74.32

37.42

4

1

2

2

2

73.68

37.35

79.72

38.03

84.11

38.50

5

1

2

2

2

75.64

37.58

83.20

38.40

72.84

37.25

6

1

2

2

2

74.51

37.44

82.33

38.31

79.42

38.00

7 8

1 1

3 3

3 3

3 3

77.62 76.25

37.80 37.64

81.09 84.12

38.18 38.50

91.61 87.70

39.24 38.86

9

1

3

3

3

74.52

37.45

82.24

38.30

80.26

38.09

10

2

1

2

3

78.21

37.87

86.31

38.72

82.37

38.32

11

2

1

2

3

80.30

38.09

86.23

38.71

86.42

38.73

12

2

1

2

3

71.69

37.11

83.21

38.40

79.58

38.02

13

2

2

3

1

76.77

37.70

84.24

38.51

81.31

38.20

14

2

2

3

1

73.43

37.32

79.22

37.98

74.34

37.42

15

2

2

3

1

77.14

37.75

83.58

38.44

83.70

38.45

16

2

3

1

2

77.92

37.83

86.31

38.72

80.32

38.10

17

2

3

1

2

80.33

38.10

86.24

38.71

83.25

38.41

18

2

3

1

2

78.66

37.92

84.94

38.58

80.54

38.12

19

3

1

3

2

74.35

37.43

79.21

37.98

80.62

38.13

20

3

1

3

2

78.29

37.87

80.34

38.10

71.78

37.12

21

3

1

3

2

76.31

37.65

81.09

38.18

77.55

37.79

22 23

3 3

2 2

1 1

3 3

79.21 81.64

37.98 38.24

86.24 84.16

38.71 38.50

82.90 79.10

38.37 37.96

24

3

2

1

3

81.65

38.24

86.93

38.78

79.94

38.05

25

3

3

2

1

79.21

37.98

86.23

38.71

78.25

37.87

26

3

3

2

1

77.87

37.83

88.12

38.90

84.37

38.52

27

3

3

2

1

76.96

37.72

84.24

38.51

82.34

38.31

where, Dspliced yarn and Dparent yarn are the mean diameters of spliced and parent yarns in mm respectively.

Results and Discussion Parent yarn and spliced yarns were tested for breaking force, abrasion cycles and diameter to optimize the spliced yarn breaking force, spliced yarn abrasion resistance and spliced yarn appearance. The parent yarn characteristics were: breaking force—570 cN, abrasion cycles—62 and yarn diameter—0.35 mm. RSS%, RYAR% and RYA% were calculated using Eqs. 2–5 and optimized using Taguchi experiments conducted at different splicing parameters. After optimizing RSS%, RYAR% and RYA% individually, overall optimum splicing parameters were obtained for highest RSS% and RYA% by compromising on RYAR%, and neglecting the insignificant splicing parameters.

Effect of Splicing Parameters on Retained Splice Strength (RSS%) Table 2 shows the RSS%, RYAR% and RYA% at different levels of splicing parameters. Figure 1 shows the main effects of splicing parameters on retained splice strength. It is observed that as opening time, splicing time and duration of water joining increase, the RSS% increases, whereas increase in feed arm code leads to decrease in RSS%. As opening time increases the RSS% increases due to higher opening of the fibres under constant air pressure, which increases the uniformity of splice wrapping. Higher intermingling of the fibres under constant air pressure and twisting for longer duration increase the compactness of spliced yarn, and results in higher RSS%. Increasing the duration of water joining at higher duration of water joining results in higher splice strength; because the water dosage at the time of intermingling and twisting of fibres provides lubricating effect

123

134


Fig. 1 Effect of splicing parameters on RSS%

that improves inter fibre and fibre-elastane cohesion. With the increase in feed arm code, the overlapping distance of the joining ends decreases and the splice length decreases, which is responsible for the reduced RSS%. Higher overlapping distance and splice length at lower feed arm code provides better binding action to the fibres in the yarn and result in higher splice length and strength, which is in agreement to earlier finding [3, 4]. Analysis of variance (Table 3) shows that among all the parameters, opening time has highest contribution of 27.72 % whereas duration of water joining has least contribution of 8.3 %. There is a strong interaction between the splicing time and duration of water joining with a contribution of 37.88 % (Fig. 2). The S/N values of RSS% at different interaction levels is shown in Table 4. It is observed that at lower level of splicing time/duration of water joining, increasing duration of water joining/splicing time results in significant increase in RSS% because of the lubricating effect and better intermingling of fibres during splicing. Table 5 illustrates the marginal means (S/N value) and optimum expected RSS% at different levels of splicing parameters. The expected mean value for RSS% at optimum levels of splicing parameters was obtained from expected S/N value. The confirmation of the same was carried out on the basis of level of significance of factor and percentage contribution indicated by ANOVA analysis. The optimum RSS% of 81.36 % was obtained at A3, B3, C1, D3 splicing parameters. Effect of Splicing Parameters on Retained Yarn Abrasion Resistance (RYAR%) Figure 3 shows the main effects of splicing parameters on retained splice abrasion resistance. It is observed that as

123

opening time, splicing time and duration of water joining increase, there is increase in the retained abrasion resistance of the splice, whereas it decreases with increase in feed arm code. As opening time increases, there is increase in the abrasion resistance of the spliced yarn due to better opening and uniform wrapping of the fibres. Further increase in the opening time leads to marginal decrease in abrasion resistance, which is not statistically significant. As splicing time increases, there is increase in abrasion resistance of the spliced yarn due to better intermingling and twisting of fibres. As the feed arm code increases abrasion resistance decreases due to lower overlapping distance and less number of intermingled fibres in splice cross section. As the duration of water joining increases, abrasion resistance slightly decreases and then increases. Higher water joining duration provides lubrication to the intermingling and twisting of fibres which leads to better compactness of the spliced yarn and is responsible for better abrasion resistance. Analysis of variance (Table 4) shows that feed arm code has highest contribution of 28.17 % followed by opening time with 17.67 % along with an interaction effect with 25.41 % contribution (Fig. 4). The interaction marginal means are shown in Table 4. It is observed that at lower level of feed arm code, as opening time increases the yarn abrasion resistance increases, whereas at higher value of feed arm code, as opening time increases, the yarn abrasion resistance decreases. At lower value of feed arm code, splice overlapping distance and number of fibres in the splice are higher, which give better intermingling of fibres as opening time increases. At lower overlapping distance, lower number of fibres in the splice may get disturbed and hinder uniform twisting as opening time increases. Similar trend is observed when feed arm code is increased at higher opening time.


135

Table 3 Analysis of variance for RSS%, RYAR% and RYA% Source

SS

DF

MS

RSS%

F

Contribution (%)

R2 = 0.93

R2ADj = 0.88

Opening time

0.661

2

0.33

29.79*

27.72

Splicing time

0.225

2

0.11

10.12*

09.44

Feed arm code

0.242

2

0.12

10.88*

10.15

Duration of water joining

0.198

2

0.10

8.92*

08.30

Splicing time 9 duration of water joining

0.903

4

0.23

20.34*

37.88

Residual

0.155

14

0.01

Total

2.384

26

6.50 100

RYAR%

R2 = 0.96

R2ADj = 0.94

Opening time

0.32

2

0.16

36.29*

17.67

Splicing time Feed arm code

0.28 0.51

2 2

0.14 0.25

32.08* 57.69*

15.46 28.17


0.18

2

0.09

20.55*

09.94

Opening time 9 Feed arm code

0.46

4

0.12

26.31*

25.41

Residual

0.06

14

0.00

Total

1.81

26

3.31 100

RYA%

R2 = 0.85

R2ADj = 0.72

Opening time

0.15

2

0.07

1.15

02.50

Splicing time

1.18

2

0.59

9.13*

19.66

Feed arm code

0.15

2

0.08

1.16

02.50


1.22

2

0.61

9.48*

20.33

Opening time 9 feed arm code

2.40

4

0.60

9.30*

40.00

Residual

0.90

14

0.06

Total

6.00

26

15.00 100

* Indicates that the parameter is significant at 99 % confidence level ** Indicates that the parameter is significant at 95 % confidence level Table 4 S/N value of interacting parameters Parameter

RSS%

Parameter

RYAR%

Parameter

RYA%

Fig. 2 Effect of splicing time and duration of water joining on RSS%

Splicing time (ms)

Duration of water joining (ms) 500

550

600

140

37.42

37.65

37.68

160

37.58

37.45

38.15

180

37.84

37.94

37.62

Opening time (ms)

Feed arm code 65

70

75

300

38.27

38.24

38.32

350

38.67

38.61

38.30

400

38.66

38.70

38.08

Opening time (ms)

Feed arm code 65

70

75

300

37.66

37.91

38.72

350

38.20

38.35

38.02

400

38.12

38.23

37.68

123

136


Table 5 shows that optimum RYAR% of 88.25 % is obtained at A2, B3, C1 and D3 splicing parameters. Effect of Splicing Parameters on Retained Yarn Appearance (RYA%) Figure 5 shows the main effects of splicing parameters on retained splice appearance. It is observed that as splicing time and duration of water joining increase, retained yarn appearance increases due to better intermingling of fibres. Water provides a lubricating effect and helps elastane take a place in the centre of the yarn. Both parameters have around 20 % contribution in RYA%. The effect of opening

Table 5 Optimum splicing parameters Parameter

Level

RSS% S/N

RYAR% S/N

RYA% S/N

A

1

37.50

38.28

38.10

2

37.74

38.53*

38.19*

3

37.88*

38.48

38.01

B

C

D

1

37.58

38.32

37.89

2

37.73

38.40

38.02

3

37.80*

38.56*

38.39*

1 2

37.84* 37.66

38.53* 38.52

37.99 38.16*

3

37.62

38.24

38.14

1

37.61

38.43

37.97

2

37.68

38.33

37.93

3

37.82*

38.53*

38.40*

81.36

88.85

87

Optimum value * Optimum splicing parameter

Fig. 3 Effect of splicing parameters on RYAR%

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time and feed arm code are not statistically significant, but have an interaction effect with 40 % contribution (Table 3; Fig. 6). At lower value of feed arm code, overlapping distance and number of fibres is higher and increasing opening time provides better intermingling and compact yarn leading to better appearance, whereas at lower overlapping distance, higher opening time may disturb the fibres and therefore hinder uniform twisting of fibres, which is responsible for poor yarn appearance. Similarly at higher opening time, as the feed arm code increases there is decrease in appearance of the spliced yarn. The splice appearance was better at higher level of opening time and lower level of feed arm code. The combined interaction mean S/N values are shown in Table 4. The optimum RYA% of 87 % was observed at optimum splicing parameters of A2, B3, C2, D3 (Table 5). Trial Run on Compromised Setting It was found that each response shows different optimum splicing parameters (Table 5). It is very interesting to decide which splicing parameters can serve the purpose altogether for better spliced yarn. The percentage contribution of each factor helps to neglect insignificant optimum levels while at same time it is necessary to prioritize the crucial responses like RSS and RYA. Parameters B and D are optimum at level 3 for all the responses. Therefore level 3 is selected for parameters B and D for the trial run. Parameter A is optimum at level 3 for RSS%, at level 2 for RYAR% and RYA%. However, S/N values of parameter A, for RSS% at level 2 and 3 are insignificantly different. So, level 2 is chosen for parameter A. Similarly, Parameter


137

C is optimums at level 1 for RSS% and RYAR% and at level 2 for RYA%, but S/N value of factor C, for RYA% is insignificantly different level 1 and level 2. So, level 1 is chosen for factor C. Hence the trial run was taken at A2, B3, C1 and D3. The trail run has been carried out on the compromised setting and Table 6 shows the mean response value at compromised optimum splicing parameters. The value obtained for RSS% is 92.02 with standard deviation of 0.963, which was expected to be 81.36. A

13 % increase in RSS% at compromised optimum splicing parameters was observed. 9.92 and 12.87 % reduction in RYAR% and RYA% respectively was also observed at compromised splicing parameters. This reduction may be because of dropped optimum settings at trial run. Lowest splice thickness percentage necessarily won’t give better yarn tenacity, so a compromise on RYA% was made, which is well justifiable because obtained optimum splice diameter offers maximum breaking strength.

Fig. 4 Effect of feed arm code and opening time on RYAR%

Fig. 6 Effect of opening time and feed arm code on RYA%

Fig. 5 Effect of splicing parameters on RYA%

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138


Table 6 RSS%, RYAR% and RYA% at compromised splicing parameters Response

Initial level

At compromised settings

Change (%)

RSS%

81.36

92.02

(?) 13.00

RYAR%

88.85

80.03

(-) 09.92

RYA%

87.00

75.80

(-) 12.87

Conclusion Taguchi experimental design method were successfully applied to optimize splicing parameters viz. opening time, splicing time, feed arm code (i.e. splice length) and duration of water joining for better RSS%, RYAR% and RYA%. It is observed that as opening time, splicing time and duration of water joining increase, the RSS% and RYAR% increases, whereas increase in feed arm code leads to decrease in both. The opening time and feed arm code do not have significant effect on RYA%. The optimum RSS% of 92.02 % was obtained at splicing parameters of 350 ms opening time, 180 ms splicing time, 65 feed arm code (i.e. 30 mm splice length) and 600 ms duration of water joining. Acknowledgments The authors are grateful to the management of Aarti International Limited Ludhiana, India for providing the facilities to prepare splice samples.

References 1. R.B. Pordenone, L.B. Salo, C.S. Pordenone, Splicer device for the mechanical splicing of textile yarns. US Patent 4637205 (1987)

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2. R.C.D. Kaushik, P.K. Hari, I.C. Sharma, Mechanism of the splice. Text. Res. J. 58(5), 263–268 (1988) 3. K.P.S. Cheng, H.L.I. Lam, Physical properties of pneumatically spliced cotton ring spun yarns. Text. Res. J. 70(12), 1053–1057 (2000) 4. K.P.S. Cheng, H.L.I. Lam, Strength of pneumatic spliced polyester/cotton ring spun yarns. Text. Res. J. 70(3), 243–246 (2000) 5. H.L.I. Lam, K.P.S. Cheng, Pneumatic splicing. Text. Asia. 7, 66–69 (1997) 6. I. Khaled, R. Gru¨tz, New technique for optimizing yarn-end preparation on splicer, and a method for rating the quality of yarn end. Autex Res. J. 5(1), 1–19 (2005) 7. C.J. Webb, G.T. Waters, A.J. Thomas, G.P. Liu, C. Thomas, The use of the Taguchi design of experiment method in optimizing splicing condition for a nylon 66 yarn. J. Text. Inst. 98(4), 327–336 (2007) 8. C.J. Webb, G.T. Waters, A.J. Thomas, G.P. Liu, C. Thomas, Optimizing splicing parameters for splice aesthetics for a continuous filament synthetic yarn. J. Text. Inst. 100(2), 141–151 (2009) 9. C.J. Webb, G.T. Waters, A.J. Thomas, G.P. Liu, C. Thomas, The influence of yarn count on the splicing of simple continuous filament synthetic yarns. Text. Res. J. 79(3), 195–204 (2009) 10. R. Mashaly, E.El Helw, K. Akl, Factors affecting spliced yarn quality. Ind. Text. J. 100, 60–64 (1990) 11. P.G. Unal, N. Ozdil, C. Taskin, The effect of fibre properties on the characteristics of spliced yarns part-I: prediction of spliced yarns tensile properties. Text. Res. J. 80(5), 429–438 (2010) 12. P.G. Unal, N. Ozdil, C. Taskin, The effect of fibre properties on the characteristics of spliced yarns part-II: prediction of retained spliced diameter. Text. Res. J. 80(17), 1751–1758 (2010) 13. B. Jaouachi, M. Sahnoun, Impact of the splicer parameters on the spliced open-end denim spun-yarns physic-mechanical performances. Autex Res. J. 9(3), 66–69 (2009) 14. M.B. Hassen, B. Jaouachi, M. Sahnoun, F. Sakli, Mechanical properties and appearance of wet spliced cotton/elastane yarns. J. Text. Inst. 99(2), 119–123 (2008)



Simulation of Stress–Strain Curves of Polyester and Viscose Filaments Anindya Ghosh • Subhasis Das • Bapi Saha

Received: 20 August 2014 / Accepted: 13 October 2014 / Published online: 8 November 2014 Ó The Institution of Engineers (India) 2014

Abstract Eyring’s non-linear visco-elastic model has been used to simulate stress–strain behaviours of polyester and viscose filaments. The complex mathematical equations of Eyring’s model for curve fitting are handled by non-traditional optimization methods such as genetic algorithm. The findings show that Eyring’s model can be used to simulate the stress–strain behaviours of the polyester and viscose filaments with reasonable degree of accuracy. It can also decipher the underlying molecular mechanism of the stress–strain behaviours. Keywords Curve fitting Eyring’s model Genetic algorithm Stress–strain curve Visco-elastic

Introduction The tenacity and breaking strain of fibrous materials are two very important mechanical properties. Yet, the values of tenacity and breaking strain represent only about the peak point in a stress–strain curve. In many situations, knowledge of the full course of the stress–strain curves is more desirable, since it provides the complete information about the behaviour of stresses under various levels of strains [1]. The behaviour of the stress–strain curve is largely dependent on the chemical nature and morphological structure of the constituent fibres. One way of analysing the mechanical behaviour of fibrous materials is to use the linear visco-elastic models composed of one or several elements such as ideal viscous A. Ghosh S. Das (&) B. Saha Government College of Engineering and Textile Technology, Berhampore 742 101, West Bengal, India e-mail: [email protected]

dashpots obeying Newton’s law of viscosity and ideal elastic springs obeying Hook’s law. Maxwell and Voigt– Kelvin models are such types of models which consist of a single spring and a single dashpot in series and parallel, respectively [2, 3]. However, neither of these models is adequate in explaining the stress–strain behaviour of a fibrous material. Vangheluwe and Ghosh et al. studied the stress–strain curves of spun yarns with a model based on the modification of Maxwell element [1, 4]. Nevertheless, the linear visco-elastic models are restricted to a linear dependence of stress i.e. if all the stress values of a given sequence are doubled; all the strain values will also be doubled [3]. However, a textile material usually shows linear visco-elastic behaviour at a low level of stress, but its behaviour becomes markedly non-linear for larger values of stresses [2]. Hence, nonlinear visco-elastic model would be more appropriate in explaining the stress–strain behaviours of fibrous materials. A non-linear visco-elastic model developed by Eyring and co-workers was based on the assumption that the deformation of a polymer involves the motion of chain molecules or parts of a chain molecule over potential energy barriers [5]. The most attractive feature of this model is that it offers the possible identification of molecular mechanism and hence helps in unravelling some aspects of structure-dependence of mechanical behaviour. In addition, it provides a common basis to explain stress– strain curve, stress relaxation and creep behaviours of fibrous materials. Although the Eyring’s model was developed way back in 1940s decade of the last century, its applications have been limited to the textile materials due to the mathematical rigors involved in the computational works. In few reported works many assumptions are made to simplify the equations derived from Eyring’s model [6]. With the advent of very high computational speed and

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140


mathematical techniques it has now been possible to solve this problem using the original equations. Recently, Ghosh et al. studied the stress relaxation and creep behaviours of the core-spun worsted yarns using Eyring’s model with the aid of non-traditional optimization technique [7]. In this study, an attempt has been made to explain the stress–strain curves of polyester and viscose filaments using Eyring’s model with the help of Genetic Algorithm (GA).

of the flow respectively. As the spring and dashpot are in series, the total strain of the right arm is given by: e ¼ e1 þ e2 : By differentiating Eq. (4) we have de de1 de2 ¼ þ : dt dt dt

Eyring’s three elements non-linear visco-elastic model is shown in Fig. 1 [5]. For the spring in the right hand arm of the model, the stress–strain relationship is given by: r1 e1 ¼ ð1Þ E1 where e1, r1 and E1 are the strain, stress and the modulus of the spring respectively. By differentiating Eq. (1) with respect to time, t we get

where e, r2 and E2 are the strain, stress and the modulus respectfully of the left hand spring respectively. By differentiating Eq. (7) we have de 1 dr2 ¼ : dt E2 dt

ð8Þ

As the right and left arms of model are in parallel, the total stress r can be expressed as: r ¼ r1 þ r2 :

de2 ¼ A sinh ar1 dt

dr dr1 dr2 ¼ þ : dt dt dt

where e2 and r1 are the strain and stress of the dashpot respectively; A and a, are the two constants of the nonNewtonian fluid. Constants A and a are the indirect measures of activation free energy and activation volume

ð6Þ

For the spring in the left hand arm of the model, the stress–strain relationship is given by: r2 e¼ ð7Þ E2

de1 1 dr1 ¼ : ð2Þ E1 dt dt For the dashpot, the strain rate of the non-Newtonian fluid is represented by the hyperbolic-sine law of viscous flow, as shown below ð3Þ

ð5Þ

Substituting the relations from Eqs. (2) and (3), Eq. (5) becomes de 1 dr1 ¼ þ A sinh ar1 : dt E1 dt

Stress–Strain Relationship on Eyring’s Non-linear Visco-Elastic Model

ð4Þ

ð9Þ

By differentiating Eq. (9) we have ð10Þ

Eliminating the relations from Eqs. (6)–(9), Eq. (10) becomes dr de ¼ ðE1 þ E2 Þ E1 A sinhðr E2 eÞa: dt dt

ð11Þ

For a constant rate of strain, ds dt ¼ r, where r = constant. At t = 0, e = 0, hence, e = rt. In order to solve the Eq. (11), we put z ¼ sin hðr E2 eÞa:

ð12Þ

By differentiating Eq. (12), we get dz d ¼ cosh aðr eE2 Þ aðr eE2 Þ: dt dt After further simplification, Eq. (13) becomes pffiffiffiffiffiffiffiffiffiffiffiffi dz ¼ E1 a 1 þ z2 ðr AzÞ: dt The solution of the Eq. (14) is found to be h pffiffiffiffiffiffiffiffiffi p ri 2 2 z ¼ tan 2 tan1 e r þA ðE1 atþcÞ cot1 2 A Fig. 1 Eyring’s three elements non-linear visco-elastic model

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where

ð13Þ

ð14Þ

ð15Þ


1 p 1 r þ c ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lntan cot1 : 4 2 A r 2 þ A2

141 Table 1 Constants of the Eyring’s model for polyester and viscose yarns

Substituting, z ¼ sin haðr eE2 Þ and t ¼ re. Equation (15), we get the stress–strain relation as pffiffiffiffiffiffiffiffiffi p n h 1 r io 2 2 E1 ae r ¼ sinh1 tan 2 tan1 e r þA ð r þcÞ cot1 a 2 A þ eE2 :

Constants

Polyester

Viscose

E1 (gpd)

106.01

75.73

E2 (gpd)

45.74

5.07

A (s-1)

5.28 9 10-4

6.19 9 10-6

a (gpd-1)

5.19

17.90

ð16Þ Materials and Methods High tenacity polyester multifilament yarn of 210 denier consisting of 72 mono-filaments and viscose multifilament yarn of 150 denier consisting of 40 monofilaments were considered in this study. The yarn samples were conditioned for 24 h at the standard atmospheric condition of 65 % RH and 27 °C before the experiments. To study the stress–strain curves of yarns, tensile tests were performed in an Instron tensile tester at a strain rate of 1 min-1 and gauge length of 500 mm. For each type of yarns, 50 tests were conducted. A typical stress–strain curve having tenacity and breaking strain close to the average values was selected for curve fitting.

The sum of squares of the distances from the theoretical points obtained with Eq. (16) to the experimental points of stress–strain data for both polyester and viscose yarns were minimized using GA. The GA coding is done using MATLAB (version 7.7) software on a 2.6 GHz PC to determine the optimum values of E1, E2, A and a. Table 1 shows the optimum values of these constants for the two yarns. The optimum solution of GA is obtained with the values of 0.7 and 0.001 for crossover probability (pc) and mutation probability (pm), respectively. Roulette wheel selection scheme is applied for reproduction operation and uniform cross-over method has been applied. Maximum number of generation was set to 2,000. The optimization process has been detailed in the flowchart shown in Fig. 2.

Curve Fitting Using Genetic Algorithm Results and Discussion The nature of Eq. (16) makes it difficult to obtain the best fitted curve on the experimental stress–strain data by means of classical optimization method. Non-traditional search based optimization technique such as GA is an appropriate method to solve such type of complex problems [8, 9]. GA mimics nature’s evolutionary principles to drive its search towards an optimal solution. GA proceeds by randomly generating an initial population of individuals, which should ideally cover the domain to explore. Each individual is represented by a binary coded string or chromosome encoding a possible solution in the data space. At every iteration step or generation, the individuals in the current population are tested according to the fitness function. To form a new population (the next generation), good individuals are selected according to their fitness, which is termed as reproduction. New individuals in the search space are generated by two operations, namely crossover and mutation. Crossover concerns two selected individuals (parents) that exchange parts of their chromosome to form two new individuals (offsprings). The mutation operation is used as a means to achieve a local change around the current solution, i.e. if a solution gets stuck at the local minimum, mutation may help it to come out of this situation and consequently, it may jump to the global basin.

The experimental and fitted stress–strain curves obtained with Eq. (16) for stress–strain curves of polyester and viscose yarns are depicted in Fig. 3. The experimental curves are shown by the solid lines and the corresponding fitted curves are shown by the dotted line. Invariably for both yarns, a high degree of coefficient of determination (R2) justifies a good fit to the experimental data. It is evident from Table 1 that the values of E1, E2 and A are higher for polyester yarn than those of viscose yarn, whereas it shows a opposite trend for a. The higher values of E1 and E2 for polyester yarn can be attributed to its higher crystallinity, modulus and elasticity compared to the viscose yarn. Constants A and a correspond to the activation free energy and activation volume of the flow respectively for the non-Newtonian dashpot of Eyring’s model. A stiff dashpot shows higher value of A and lower value of a in comparison to a slack dashpot. As the viscous part dominates in viscose yarn, it shows lower value of A and higher value of a in comparison to the polyester yarn. Higher activation volume of flow for viscose yarn is accountable to the greater plastic flow in its stress–strain curve than that of polyester yarn. As a consequence of that viscose has low modulus compared to polyester.

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142 Fig. 2 Flowchart of GA process


Start

Evaluate, r =

Set, max no. of generations, population size, pc, pm

Evaluate fitness function i.e. sum of squares of the distances from the calculated points (using Eq. 16) to the experimental points of stress-strain data

Average fitness Maximum fitness

Check whether, r ≥ 0.95?

Generate random population for E1, E2, A and α.

No

Reproduction

Crossover Yes Mutation

End

No

Yes

Is generation –< Maximum number of generation?

Set, generation = generation + 1

Evaluate, fitness function for whole population and compute r

model. The advent of non-traditional search based optimization technique GA makes it easy to solve the complex curve fitting problem with the Eyring’s equations. Eyring’s model can be used to simulate the stress–strain behaviours of both polyester and viscose filaments with reasonable degree of accuracy. Further, it can decipher the underlying molecular mechanism of stress–strain behaviours from its parameters.

References

Fig. 3 Experimental and fitted stress–strain curves for polyester and viscose yarns

Conclusions The stress–strain curves of polyester and viscose filaments have been described using Eyring’s nonlinear visco-elastic

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1. A. Ghosh, S.M. Ishtiaque, R.S. Rengasamy, Stress–strain characteristics of different spun yarns as a function of strain rate and gauge length. J. Text. Inst. 96, 99 (2005) 2. I.M. Ward, Mechanical Properties of Solid Polymers, 2nd edn. (Wiley, New York, 1983) 3. W.E. Morton, J.S.W. Hearle, Physical Properties of Textile Fibress, 3rd edn. (The Textile Institute, Manchester, 1993) 4. L. Vangheluwe, Influence of strain rate and yarn number on tensile test results. Text. Res. J. 62, 586 (1992) 5. G. Halsey, H.J. White, H. Eyring, Mechanical properties of textiles, Part I. Text. Res. J. 15, 295 (1945) 6. C.H. Reichardt, H. Eyring, Mechanical properties of textiles, Part XI: application of the theory of the three-element model to stress–

J. Inst. Eng. India Ser. E (July–December 2015) 96(2):139–143 strain experiments on cellulose acetate filaments. Text. Res. J. 16, 635 (1946) 7. A. Ghosh, S. Das, D. Banerjee, Simulation of yarn stress relaxation and creep behaviours using genetic algorithm. Indian J. Fibres Text. Res. 38, 375 (2013)

143 8. D.E. Goldberg, Genetic Algorithms in Search, Optimization & Machine Learning, 1st edn. (Addison-Wesley, New York, 1989) 9. J.H. Holland, Adaptation in Natural and Artificial System (The University of Michigan Press, Ann Arbor, 1975)

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Micromagnetic Simulation of Fibers and Coatings on Textiles Andrea Ehrmann • Tomasz Blachowicz

Received: 31 August 2014 / Accepted: 11 December 2014 / Published online: 7 January 2015 Ó The Institution of Engineers (India) 2015

Abstract Simulations of mechanical or comfort properties of fibers, yarns and textile fabrics have been developed for a long time. In the course of increasing interest in smart textiles, models for conductive fabrics have also been developed. The magnetic properties of fibers or magnetic coatings, however, are almost exclusively being examined experimentally. This article thus describes different possibilities of micromagnetically modeling magnetic fibers or coatings. It gives an overview of calculation times for different dimensions of magnetic materials, indicating the limits due to available computer performance and shows the influence of these dimensions on the simulated magnetic properties for magnetic coatings on fibers and fabrics. Keywords Micromagnetic simulation Magnetic fiber Magnetic coating Magpar OOMMF

Introduction Several parameters of fibers, yarns and textile fabrics can be simulated in order to predict and adjust the desired material properties. Micro-mechanical models can be used to describe woven fabrics used for ballistic protection [1], while other models have been developed long before to understand drape shapes of woven fabrics [2] or stiffness and strength of woven fabric composites [3]. Similarly, the A. Ehrmann (&) Faculty of Textile and Clothing Technology, Niederrhein University of Applied Sciences, Mo¨nchengladbach, Germany e-mail: [email protected] T. Blachowicz Institute of Physics – Center for Science and Education, Silesian University of Technology, 44-100 Gliwice, Poland

mechanical properties of knitted fabrics have been modeled for pure [4] and reinforced textiles [5, 6]. Besides these mechanical properties, other parameters have been calculated, such as heat and moisture transfer [7–9] or the bagging behavior of wool fabrics [10]. However, technical textiles and smart clothes are not only used due to their mechanical or comfort properties. Nowadays, conductive textiles or yarns are often integrated, e.g., as ECG sensors, for energy and data transmission etc. [11]. The resistances of such conductive yarns or fabrics has accordingly often been simulated [12–16]. Magnetic textiles also have interesting properties which can be used, e.g., for magnetic heating under an alternating current magnetic field, especially useful in localized hyperthermia cancer therapy [17], in textile magnetic coils or magnetic sensors used in smart textiles [18, 19] or for magnetic shielding [20]. Simulations of the magnetic properties of such fibers, yarns or fabrics are scarce. Only a few articles report about modeling of magnetic microfibers [21] or of the magnetic core of a textile coil [22]. This article thus aims at giving an overview of the possibilities and borders of modeling magnetic fibers as well as magnetic coatings on fibers and textile fabrics. A comparison with experimental results is not yet given due to the strong dependence of the magnetic properties on the coating dimensions, which will be discussed in this article and the respective necessity to examine the coating thickness etc. exactly to allow for quantitative conformity. Since the mechanical properties of the base textile materials—such as tensile strength, bursting strength etc.— are not influenced by such nano-coatings, they are not taken into consideration in this article. The optical properties, however, will naturally be altered by a metallic coating [23], as well as the electrical properties can be changed in case of conductive coatings, the hydrophophic/

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146

hydrophilic, antibacterial properties etc. Thus, this article aims at examining the magnetic properties of these coatings, thus neglecting these possible side effects.

Effects of Magnetic Coatings/Fibers on Physical Properties of Textiles Magnetic coatings on textiles or magnetic fibers, included in textile materials, can be used for different applications, depending on their magnetic properties. Firstly, the coercive field and remanence depend strongly on the material used. Permalloy is well-known to have a very small coercive field which can be used for shielding of small magnetic fields in the same order of magnitude as the coercive field. Permalloy shields are often used to prevent laboratory equipment from the very small magnetic field of the earth—a textile shield could be used as a simple curtain, being more flexible, lightweight and less space-consuming than fixed walls from permalloy. Shielding from larger magnetic fields is possible by coatings from materials with higher coercivity, such as iron, cobalt or stainless steel; however, it should be mentioned that the shielding effect of thin coated layers is limited to relatively small magnetic field intensities, far below the requirements for the walls around a Magnetic Resonance Tomography (MRT) scanner. Secondly, the layer geometry has also a significant influence on coercive field and remanence. The thickness of the magnetic layer/fiber determines possible magnetization reversal processes. If there is an additional nano- or micro-structure—which can be assumed for a coating on a rough textile surface. This will also influence magnetization reversal, leading to strong modifications of the magnetic hysteresis loop compared with bulk material. These effects are based on the so-called shape anisotropy of small magnetic particles and often results in an in-plane orientation of the magnetization vector in thin magnetic layers. Due to the significant differences of the exchange lengths, anisotropy constants, domain wall widths etc. in different magnetic materials. However, it is not possible to give universal rules in which dimensions these effects play a role. Due to the combined influence of material and geometry on the magnetic properties of a magnetic coating/fiber, simulations or experimental tests are necessary for each combination. Thus, only approximate design rules can be given for a coating/fiber meeting the demands of a special application. If a magnet shall be used to attract the single textile fibers due to their ferromagnetic properties, resulting in an altered local hydrophobicity, their magnetic coating should have a large in-plane magnetization component (given e.g. for thin iron or stainless steel coatings), while a

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coating which is used to handle large textile layers by electro-magnets should have a large out-of-plane magnetization component (which can be created, e.g., by cobalt/ platinum multi-layers).

Micromagnetic Simulations Fibers as well as coatings can have thicknesses up to several ten micrometers, but can also be in the submicrometer range. Such a scale is on the one hand large enough to ignore the atomic structure of the material, but on the other hand small enough for magnetic structures like domain walls being important. Thus, for these fine structures, it is necessary to switch from macroscale calculations to micromagnetic simulations. Several commercial and freely available micromagnetic simulators can be used to model round or flat structures. One of the most well-known free programs is OOMMF, the Object Oriented MicroMagnetic Framework [24], which works with so-called finite differences, is based on small cuboids filling the space of the magnetic object. Due to this geometrical restriction, OOMMF can compute demagnetization fields quite fast, but is less accurate for magnetic objects with round shapes which can only be approximated by the small cuboids. For round or other irregularly formed magnetic objects, a hybrid finite element/boundary element method is preferable, as it is used in the free micromagnetic solver Magpar, the Parallel Finite Element Micromagnetics Package [25], which can accurately resolve curved objects, but needs more calculation time for thin films than OOMMF. Thus, in the following parts of this article, the simulations of magnetic fibers and magnetic coatings on fibers will be performed by Magpar, while simulations of thin films on textile fabrics are computed with OOMMF. Both programs do not take into account any mechanical forces between fibers or other magnetic systems, contact points are assigned by the geometrical descriptions. Periodic boundary conditions are not available in both programs, thus the dimensions of the system under examination influence the results.

Simulation of Magnetic Fibers Several yarns contain metallic fibers, e.g. can be produced from stainless steel, with diameters of about 10 lm. The magnetic properties of such macroscopic fibers can be approximated by common models without taking into account nanoscale effects. On the other hand, magnetic nanofibers, with diameters of *100 nm or less, show


interesting magnetic properties [26, 27] and should thus also be simulated. Here, we concentrate on such nanofibers which can be modeled with micromagnetic simulations. Figure 1 shows two neighboring iron (Fe) nano-fibers of diameter 10 nm and length 70 nm in two different situations, with both fibers completely in contact (left panel) or not touching (right panel), leading to different hysteresis loops. In both cases, the 0° orientation (parallel to the fiber axis) shows a typical ‘‘easy axis’’ loop, nearly rectangularshaped, indicating that the magnetization reversal process occurs quite fast and in a small field range. For a vanishing external magnetic field Hext (i.e. along the y-axis), the relative magnetization M/MS is nearly 1, showing that the magnetization is almost saturated—the magnetic moments are oriented almost perfectly parallel to the fiber axis. This behavior changes completely for the external magnetic field aligned perpendicular to the fibers (90°). Here, a completely closed hysteresis loop can be seen, with the remanent magnetization for vanishing external magnetic field identical to zero. For the diagonal orientation (45°), the hysteresis loop is ‘‘open’’, but significantly changed in comparison with 0°, indicating a much ‘‘harder’’ direction with a broader field range in which the magnetization reversal process occurs. Comparing both coupled and non-coupled fibers, it can be recognized that coupling reduces the coercive fields (switching fields) of the systems. This happens due to the form anisotropy, forcing the magnetic moments in a direction along the fibers, being reduced by the coupling in larger systems.

Simulation of Magnetic Coatings on Fibers As an example for coated fibers, nanofibers of diameter 10/100 nm and length 100 nm/1 lm have been simulated. The coating has been modeled in the form of a uniform Fe

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layer with thickness 5 nm. Figure 2 shows the results of simulations along the fiber axis, perpendicular and diagonal to the fiber. While for an external magnetic field parallel to the fiber direction the magnetization reversal occurs fast and at relatively small external field values (‘‘easy axis’’), the form of the hysteresis loop changes significantly for the ‘‘hard axis’’ perpendicular to the fiber, where the hysteresis loop is almost completely closed; similar to the magnetic fibers depicted in Fig. 1. The finding that the magnetization, perpendicular to the fiber is again almost zero, for a vanishing external field, i.e. that all magnetic moments are aligned parallel to the fiber, means that there is no remanent magnetization perpendicular to the fiber. For a woven fabric or a non-woven, in which the fibers are oriented relatively parallel to the plane, it can be concluded that there is nearly no magnetization detectable and usable along the perpendicular to the fabric. Comparing the results of these simulations for fine fibers, the significant quantitative and qualitative changes in the hysteresis loops are also visible. This indicates that it is not possible to simulate a very thin fiber, in order to save calculation time and to trust on up-scaling the results to thicker and longer magnetically coated fibers afterwards. Another problem which has to be taken into account in a simulation of magnetic coatings on fibers can be recognized in Fig. 3. Here, bundles of 7 parallel fibers have been simulated, with the lengths and the aspect ratio identical to the values in Fig. 2. Nevertheless, the hysteresis loops have changed qualitatively and quantitatively. On the one hand, their forms change significantly, with one or more steps visible, which can be attributed to the magnetization reversal of one or more fibers at the same time, while other fibers still remain in their original magnetization state and switch only at larger external magnetic fields. On the other hand, the coercive fields are significantly decreased. These examples show that magnetic fiber coatings need to be modeled with parameters very similar to the

Fig. 1 Simulation of a coupled (left panel, upper inset) and a non-coupled (right panel, lower inset) pair of magnetic Fe fibers, calculated along the fiber (0°), perpendicular (90°) and diagonal to it. From Ref. [28], modified

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Fig. 2 Fe coated fiber, simulated along the fiber (0°), perpendicular (90°) and diagonal to it, for fiber lengths of 100 nm (left panel) and 1 lm (right panel) with aspect ratios of 1:10

Fig. 3 Fe coated bundles of 7 fiber each, simulated along the fiber (0°), perpendicular (90°) and diagonal to it, for fiber lengths of 100 nm (left panel) and 1 lm (right panel) with aspect ratios of 1:10

experimental ones to gain a sufficient validity. Nevertheless, this necessity can lead to strongly increased calculation times in the order of magnitude of days to weeks, depending on the available computer power. Thus, future simulations have to show how the models can be reduced in order to combine acceptable calculation times with satisfying simulation accuracy.

Simulation of Magnetic Coatings on Fabrics Similar to fine fibers, complete textile fabrics can be coated with magnetic materials, e.g. by sputtering. Such fine layers can, as a first approximation, be regarded as flat, even planes with constant thickness. Figure 4 shows such fine layers (thickness 5 nm) for the magnetic materials iron (Fe), cobalt (Co) and nickel (Ni), simulated for relatively small squares of edge lengths 500 nm (left panel) or 1,000 nm (right panel) respectively. These three materials have been chosen for first tests since they are typical elementary ferromagnets and already give

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an overview of possible implications of the material choice. Further materials can be tested in future simulations, adapted to available textile coatings. Firstly, it can be recognized that the hysteresis loops differ significantly for the three materials. In both cases, the Ni layer shows a much narrower loop, without the noticeable steps of the Fe and Co loops. Both Co hysteresis loops contain several prominent steps, a behavior which cannot necessarily be recognized in experimental examinations of similar coatings. Secondly, comparing both panels shows that in spite of the large aspect ratio between lateral dimensions and layer thickness, the different edge lengths lead to significantly different results for all materials. While the coercive fields become smaller for Fe and Ni with enhanced lateral dimensions, the loop shape changes completely for Co, without a significant alteration of the coercive field. Figure 5 shows a comparison of hysteresis loops simulated for different layer thicknesses (left panel) and different lateral dimensions (right panel) respectively. It is clearly visible that increasing the layer thickness strongly


149

Fig. 4 Comparison of different magnetic coatings of dimensions 500 nm 9 500 nm (left panel) and 1,000 nm 9 1,000 nm (right panel), respectively, for a layer thickness of 5 nm

Fig. 5 Thin Fe layers, simulated for different thicknesses (left panel) and different lateral dimensions (right panel) Table 1 Comparison of calculation times for different materials, dimensions and numbers of threads calculated parallel Material Edge length (nm)

Thickness (nm)

No. of threads

Calculation time

Fe

500

5

1

2 h 12 min

Co

500

5

1

4 h 40 min

Ni Fe

500 1,000

5 5

1 1

6 h 42 min 14 h 3 min

Co

1,000

5

1

19 h 3 min

Ni

1,000

5

1

23 h 24 min

Fe

500

10

4

24 h 10 min

Fe

500

15

4

37 h 38 min

Fe

500

20

4

48 h 9 min

Fe

5000

5

20

140 h 48 min

changes the form of the hysteresis loops and the coercive fields as well as the remanent magnetization for vanishing external magnetic field. Obviously, the results presented here can only be transferred to the experiment for very thin magnetic layers of well-defined thickness, e.g., prepared by

sputtering, and not to coated magnetic films of several micrometer thickness. Similarly, the hysteresis loops depend significantly on the different lateral dimensions (Fig. 5, right panel). Even the largest area of (5 lm)2, showing a relatively even hysteresis loop, opposite to the nanostructure loops with their usual steps, cannot be regarded as typical large-area loop. Instead, even larger structures have to be modeled in order to identify the lateral dimensions which can be considered as sufficient for simulation of magnetic coatings with macroscopic lateral dimensions and nano-scale thickness.

Possibilities and Limits of Micromagnetic Simulations As described before, nanoscale magnetic fibers as well as coatings on textile fabrics or fibers cannot be calculated by common macroscale calculations. On the other hand, micromagnetic simulations have the disadvantage of significantly increased calculation times for larger models. An overview of the calculation times of the models depicted in

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the article is given in Table 1. It can be recognized that an increase in the layer thickness leads to an almost linear increase in the calculation time for thicknesses starting from 10 nm, while an increase in the layer area results in a relatively stronger increase in the calculation time.

Conclusion Micromagnetic simulations are necessary to model magnetic layers or fibers on the nanometer scale. However, simulations of larger areas are restricted by the necessary calculation times. Simulations of magnetic nano-fibers as well as magnetic coatings on fibers and textile fabrics have shown significantly different hysteresis loop shapes and coercive fields, dependent on the coating material (Fe, Co or Ni) and the dimension of the magnetic component. Even the largest area of (5 lm)2 still resulted in a hysteresis loop with typical features of nanosystems, such as abrupt jumps due to coherent reversal processes. On the other hand, this strong dependence of the magnetic properties of such coatings on the dimensions allow for tailoring the desired magnetic behavior by using pointlike application of magnetic material, e.g., by printing, screen printing, or spraying through a defined mask. In the future, it will be tested which compromises between calculation times on common computers and the necessary dimensions model the experimental results best. Additionally, more advanced hardware solutions, based on multicore graphic card technology (CUDA), will be used for simulations of larger magnetic areas.

References 1. A. Tabiei, I. Ivanov, Computational micro-mechanical model of flexible woven fabric for finite element impact simulation. Int. J. Numer. Method Eng. 53, 1259–1276 (2001) 2. T.J. Kan, W.R. Yu, Drape simulation of woven fabric by using the finite-element method. J. Text. Inst. 86, 635–648 (1995) 3. T. Ishikawa, T.W. Chou, Stiffness and strength behaviour of woven fabric composites. J. Mater. Sci. 17, 3211–3220 (1982) 4. M. de Arau´jo, R. Fangueiro, H. Hong, Modelling and simulation of the mechanical behavior of weft-knitted fabrics for technical applications—Part 2: 3D model based on the elastica theory. AUTEX Res. J. 3, 166–172 (2004) 5. N. Takano, Y. Ohnishi, M. Zako, K. Nishiyabu, Microstructurebased deep-drawing simulation of knitted fabric reinforced thermoplastics by homogenization theory. Int. J. Solids Struct. 38, 6333–6356 (2001) 6. M. Duhovic, D. Bhattacharyya, Simulating the deformation mechanisms of knitted fabric composites. Compos. A Appl. Sci. Manuf. 37, 1897–1915 (2006) 7. Y. Li, Z. Luo, An improved mathematical simulation of the coupled diffusion of moisture and heat in wool fabric. Text. Res. J. 69, 760–768 (1999)

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J. Inst. Eng. India Ser. E (July–December 2015) 96(2):145–150 8. J. Fan, Z. Luo, Y. Li, Heat and moisture transfer with sorption and condensation in porous clothing assemblies and numerical simulation. Int. J. Heat Mass Transf. 43, 2989–3000 (2000) 9. Y. Du, J. Li, Dynamic moisture absorption behavior of polyestercotton fabric and mathematical model. Text. Res. J. 80, 1793–1802 (2010) 10. X. Zhang, Y. Li, K.W. Yeung, M. Yao, Mathematical simulation of fabric bagging. Text. Res. J. 70, 18–28 (2000) 11. S. Aumann, S. Trummer, A. Bru¨cken, A. Ehrmann, A. Bu¨sgen, Conceptual design of a sensory shirt for fire-fighters. Text. Res. J. 84, 1661–1665 (2014) 12. J. Wang, H. Long, S. Soltanian, P. Servati, F. Ko, Electromechanical properties of knitted wearable sensors: part I—theory. Text. Res. J. 84, 3–15 (2014) 13. J. Wang, H. Long, S. Soltanian, P. Servati, F. Ko, Electromechanical properties of knitted wearable sensors: part 2— parametric study and experimental verification. Text. Res. J. 84, 200–213 (2014) 14. H. Zhang, X. Tao, S. Wang, T. Yu, Electro-mechanical properties of knitted fabric made from conductive multi-filament yarn under unidirectional extension. Text. Res. J. 75, 598–606 (2005) 15. H. Zhang, X. Tao, S. Wang, Modeling of electro-mechanical properties of conductive knitted fabrics under large uniaxial deformation. Qual. Text. Qual. Life 1–4, 1109–1112 (2004) 16. Y. Kun, S. Guang-li, Z. Liang, L. Li-wen (2009) Modelling the electrical property of 1 9 1 rib knitted fabrics made from conductive yarns, in Proceedings of the ICIC 2009: Second International Conference on Information and Computing Science, vol. 4, pp. 382–385 17. A. Amarjargal, L.D. Tijing, C.H. P, I.T. Im, C.S. Kim, Controlled assembly of super paramagnetic iron oxide nanoparticles on electrospun PU nanofibrous membrane: a novel heat-generating substrate for magnetic hyperthermia application. Eur. Polym. J. 49, 3796–3805 (2013) 18. M. Rubacha, J. Zieba, Magnetic textile elements. Fibres Text. East. Eur. 14, 49–53 (2006) 19. P. Ciureanu, G. Rudkowska, P. Rudkowski, J.O. Stro¨m-Olsen, Magnetoresistive sensors with rapidly solidified permalloy fibers. IEEE Trans. Magn. 29, 2251–2257 (1993) 20. M. Rubacha, J. Zieba, Magnetic cellulose fibres and their application in textronics. Fibres Text. East. Eur. 15, 101–104 (2007) 21. S. Wiak, A. Firych-Nowacka, K. Smo´lka, Computer models of 3D magnetic microfibres used in textile actuators. COMPEL Int. J. Comput. Math. Electr. Electron. Eng. 29, 1159–1171 (2010) 22. J. Zieba, M. Frydrysiak, Modeling of textile magnetic core. Smartex Res. J. 1, 102–110 (2012) 23. M. Grecka, A. Rizvi, A. Ehrmann, J. Blums (2013) Influence of abrasion and soaking on reflective properties of Cu and Al coated textiles. in Proceedings of Aachen-Dresden International Textile Conference, Aachen/Germany, 28–29.11.2014 24. M. J. Donahue, D. G. Porter (1999) OOMMF User’s Guide, Version 1.0. Interagency Report NISTIR 6376, National Institute of Standards and Technology, Gaithersburg, MD 25. W. Scholz, J. Fidler, T. Schrefl, D. Suess, R. Dittrich, H. Forster, V. Tsiantos, Scalable parallel micromagnetic solvers for magnetic nanostructures. Comput. Mater. Sci. 28, 366–383 (2003) 26. N.A.M. Barakat, B. Kim, H.Y. Kim, Production of smooth and pure nickel metal nanofibers by the electrospinning technique: nanofibers possess splendid magnetic properties. J. Phys. Chem. C 113, 531–536 (2009) 27. T. Blachowicz, A. Ehrmann, Fourfold nanosystems for quaternary storage devices. J. Appl. Phys. 110, 073911 (2011) 28. Ehrmann A (2014) Examination and simulation of new magnetic materials for the possible application in memory cells. Dissertation thesis, Silesian University of Technology, Gliwice/Poland



Prediction of Yarn Strength Utilization in Cotton Woven Fabrics using Artificial Neural Network Swapna Mishra

Received: 12 August 2014 / Accepted: 14 November 2014 / Published online: 4 December 2014 Ó The Institution of Engineers (India) 2014

Abstract The paper presents an endeavor to predict the percentage yarn strength utilization (% SU) in cotton woven fabrics using artificial neural network approach. Fabrics in plain, 2/2 twill, 3/1 twill and 4-end broken twill weaves having three pick densities and three weft counts in each weave have been considered. Different artificial neural network models, with different set of input parameters, have been explored. It has been found that % SU can be predicted fairly accurately by only five fabric parameters, namely the number of load bearing and transverse yarns per unit length, the yarn crimp % in the load bearing and transverse directions and the float length of the weave. Trend analysis of the artificial neural network model has also been carried out to see how the various parameters affect the % SU. The results indicate that while an increase in the number of load bearing or transverse yarns increases the % SU, an increase in the float length and the crimp % in the yarns have a detrimental effect. Keywords Tensile strength Woven fabrics Artificial neural networks Structure–property relationship Percentage yarn strength utilization List of symbols % SU Percentage strength utilization ANN Artificial neural network Ne English count of the yarn

S. Mishra (&) Guru Nanak Dev University, Amritsar 143005, Punjab, India e-mail: [email protected]

NL and NT L and T MAPE MSE SL, ST CL, CT FL pL VT

Number of load bearing and transverse yarns per 2.5 cm in a sample Load bearing and transverse yarns Mean Absolute Percentage Error Mean Squared Error Single yarn strength of load bearing and transverse yarns Crimp % in load bearing and transverse yarns Float length of the weave Spacing between load bearing yarns Binding force of transverse yarns on the load bearing yarn

Introduction Fabrics may be classified broadly into wovens, knits and non-wovens. Out of these, woven fabrics offer the best combination of tensile strength and dimensional stability. A wide range of fabric strength can be obtained by altering the material and construction related parameters in woven fabrics. The tensile behavior of woven fabrics has therefore, captured the interest of textile researchers since long. The initial attempts at understanding structure–property relationships in woven textiles started with geometrical models. Peirce’s [1] work is considered pioneering in calculating the characteristics of plain woven fabrics from the geometrical model. Kemp [2] considered race-track cross section of the yarns in the fabric and proposed a model to predict the tensile behavior of plain woven fabrics. Hamilton [3] extended Peirce’s and Kemp’s model to give a model applicable to all types of

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152

woven fabrics. Olofsson [4] considered the fabric geometry to be a consequence of forces acting on the yarns. Unlike Peirce’s model which was restricted to plain weave only, Olofsson’s model was applicable to twill weaves also and considered crimp as primary geometrical parameter while yarn diameters were considered secondary. Leaf and Anandjiwala [5] gave a generalized model for the geometry of plain weave considering the bending behavior of the constituent yarns. The work included formulae for calculating weave angle and crimp height to yarn spacing ratio in the fabric. The endeavors to model the fabric geometry were followed by efforts to predict tensile strength of woven fabrics based on their structural parameters. Anandjiwala and Leaf [6, 7] worked on the theoretical aspects and experimental results of plain woven fabrics for uniaxial tensile loading and unloading in both the principle directions. Disagreements between the experimental results and values obtained from the theoretical model were observed, especially during recovery. The authors assigned it to high yarn curvature bending during tensile deformation of fabric and suggested a modified yarn bending rule. Kawabata, Niwa and Kawai [8, 9] proposed finite-deformation theory for uniaxial and biaxial deformation of plain woven fabrics while Sagar and Potluri [10] developed energy based models for predicting tensile behavior of woven fabrics. Shahpurwala and Shwartz [11] utilized statistical Weibull distribution to model the tensile strength of plain, twill and satin fabrics while Chen and Ding [12] used the Monte Carlo simulation to simulate the failure and to predict the tensile strength of plain woven fabrics under uniaxial tensile loading. Artificial Neural Network (ANN) is a computational tool proven to be effective in predicting the outputs from a given number of inputs when the exact relationship between the inputs and outputs is not known. Recently ANN has been used successfully in the field of textiles to predict various fabric properties. Fan and Hunter [13] proved ANN to be a useful tool for predicting nine properties of worsted fabrics from 30 fiber, yarn and fabric properties as input parameters. The thermal resistance of fabrics has been predicted fairly accurately by Bhattacharjee and Kothari [14] using ANN. Behera and Mishra [15] predicted the handle and comfort properties of worsted fabrics from its structural parameters using ANN based on radial basis function. Zeydan [16] used ANN and Taguchi design of experiments methods to predict the warp wise strength of polyester and cotton fabrics. The ANN method was found to give lower root mean squared error of prediction. Behera and Guruprasad [17] successfully predicted the bending rigidities of cotton plain and broken twill fabrics using ANN with a mean prediction error of 7.8 %

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and a high correlation between actual and predicted values (0.99). The yarn count, yarns per unit length, yarn twist and weave were used as inputs to predict the bending property in both warp and weft directions. Majumdar et al. [18] compared multiple linear regression and ANN approaches for predicting tensile strength of plain woven fabrics and found the latter to have higher accuracy of prediction. They also concluded that the number of load bearing yarns and their single yarn strength were instrumental in deciding the tensile strength for plain fabrics. Dobnik and Brezocnik [19] utilized ANN technique to predict the UV protection of dyed cotton fabrics. Though application of ANN has been explored extensively in the field of textiles, there has been no reported work to predict % yarn strength utilization in woven fabrics. The present work aims at developing a model based on ANN to predict the % yarn strength utilization (% SU) obtained in a fabric. The numbers of yarns per unit length, the initial crimps, yarn counts and single yarn strengths in the load bearing and transverse directions along with the float length of the weave have been taken as input parameters. The trend analysis has also been carried out to understand how various input parameters individually affect the % SU. The scope of this work is limited to fabrics made of 100 % cotton yarns.

Materials 100 % cotton fabrics woven in the four weaves (plain, 2/2 twill, 3/1 twill and 4-end broken twill) were used for this investigation. Three levels of weft counts (30, 40 and 50 Ne) and three levels of pick densities (23, 25 and 27 picks per cm) were used for each of the four weaves making a total of 36 samples.

Methods Fabric Characterization The fabrics were desized and scoured in relaxed state to remove the size and stresses due to weaving. They were then ironed flat and relaxed in standard testing atmosphere (temperature = 27 °C and RH = 65 %). The fabrics were tested for single yarn strength, yarn density per 2.5 cm, yarn crimp and breaking load and elongation of woven fabrics in both warp and weft directions according to standard ASTM methods D2256, D3775, D3883 and D5035 RT-2 respectively. The % SU was calculated according to Eq. 1.


% SU ¼

153

Fabric breaking strength ðNÞ 100 Number of load bearing yarns in the sample Single yarn breaking strength ðNÞ

ð1Þ

Artificial Neural Network Model

Processing of Data using Artificial Neural Networks

ANN is a very powerful tool that is able to model the functional relationship between inputs and outputs using experimental data. A typical ANN possesses one or more hidden layers between the input and output layers. Each layer is composed of a large number of nodes or artificial neurons which are actually the processing elements for mathematical operations. The number of hidden layers and the number of nodes per layer vary depending on the intricacy of the problem. Each node in the hidden layer receives a signal from the nodes of the input layer and these signals are multiplied by separate synaptic weights. The weighted inputs are then summed up and passed through a transfer function (usually a sigmoid), which converts the output to a fixed range of values. The output of the transfer function is then transmitted to the nodes of next layer and finally the output is estimated at the output layer. Backpropagation algorithm is the most popular among the existing neural network algorithms [20]. According to this algorithm, training occurs in two phases, namely a forward pass and a backward pass. In the forward pass, a set of experimental data is presented to the ANN as input and its effect is propagated, in stages, through different layers of the network. Finally, a set of outputs is produced. The calculation of error vector is done from the difference between actual and predicted outputs. In the backward pass, this error signal is propagated backwards to the ANN and the synaptic weights are adjusted in such a manner that the error signal decreases with each iterative step. Thus, the ANN model approaches closer and closer to producing the desired output. Details of ANN architecture and training algorithm are available in standard literature [21–24].

The data consisted of 72 sets of results obtained from testing 36 fabrics in the two principle directions (warp and weft). The number of load bearing and transverse yarns per 2.5 cm in a sample were labeled as NL and NT respectively. Using similar notations, the crimps in the two directions were designated as % CL and % CT; the yarn counts in Ne were marked as NeL and NeT while the single yarn strengths in Kgf were labeled as SL and ST respectively for load bearing and transverse directions. The float length for a weave was labeled as FL. In order to rule out any bias, seven sets of data were randomly selected for testing of ANN while the remaining 65 sets of data were used for ANN training purpose. Table 1 presents the summary statistics of input and output parameters. ANN, having only one hidden layer, was trained using back propagation feed forward training algorithm. The learning rate and momentum parameters were optimized at 0.3 and 0.2 respectively. Various ANN models with different nodes in the hidden layer were used for predicting % SU of yarns in woven fabrics.

Results and Discussion Selection of Best Neural Network Model Table 2 shows the comparison of prediction performance between various ANN models explored in this research. MAPE and MSE were calculated according to Eqs. 2 and 3 respectively for comparing the prediction performance of the ANN models.

Table 1 Summary statistics of input and output parameters Level

Input parameters NL

Minimum

NT

Output NeL

NeT

SL

ST

FL

% CL

% CT

% SU

60

60

30

30

0.2

0.2

1

2.6

2.6

72.36

Average

100

100

40

40

0.24

0.24

2

9.07

9.07

104.52

Maximum

133

133

50

50

0.35

0.35

3

20.79

20.79

135.75

123

154


Table 2 Comparison of prediction performance of various ANN models in testing data sets Model

No. of inputs

ANN parameters

Performance parameters

Inputs

Nodes

Cycles

Coefficient of determination (R2)

MAPE

MSE

I

3

SL, FL, CL

8

10,000

0.80

5.94

46.09

II

4

SL, FL, CL, CT

3

10,000

0.80

5.78

45.78

III

4

NL, FL, CL, CT

3

10,000

0.90

2.92

23.61

IV

5

NL, NT, FL, CL, CT

6

4,000

0.92

2.58

17.91

V

9

NL, NT, NeL, NeT, SL, ST, CL, CT, FL

8

8,000

0.97

2.60

13.39

Pr MAPE ¼

YiðactualÞ

ð2Þ

r

Pr MSE ¼

jðYiðactualÞ YiðpredictedÞ Þj100

i¼1

i¼1

ðYiðactualÞ YiðpredictedÞ Þ r

2

ð3Þ

where ‘Y’ is the property predicted or measured, which is % SU in this case, ‘i’ is the iteration and ‘r’ is the total number of data sets, as mentioned in Eqs. 2 and 3. Three input parameters namely SL, FL and % CL, which were expected to be critical in deciding the % SU, were used in Model I as shown in Table 2. All the three parameters are related to the load bearing yarns. However, the R2 value was not very high (0.80) and MAPE and MSE were relatively large (5.94 and 46.09 respectively). Assuming that the crimp in the transverse yarns (% CT) can be a decisive factor influencing crimp interchange and hence can be instrumental in deciding the % SU, % CT was also introduced as an input parameter along with SL, FL and % CL in Model II. However, the results improved only marginally (R2 = 0.80, MAPE = 5.78 and MSE = 45.78). The strength of load bearing yarn (SL) in Model II was replaced by the number of load bearing yarns per 2.5 cm (NL) in Model III and the ANN model was trained. A substantial improvement in the results (R2 = 0.90, MAPE = 2.92 and MSE = 23.61) followed indicating that NL is definitely contributing considerably to the % SU. Model IV included the number of transverse yarns (NT) along with NL, FL, % CL and % CT and the resulting prediction performance was very encouraging (R2 = 0.92, MAPE = 2.58 and MSE = 17.91). When NL and NT were not used as inputs parameters (Models I and II), the MAPE and MSE were very high and the coefficient of determination (R2) between actual and predicted values was also low. This implies that NL and NT are very important parameters affecting % SU. As expected, Model V which includes all the nine parameters as inputs gave the best results (R2 = 0.97 and MAPE = 2.60) in terms of coefficient of determination as well as MSE (13.39). Compared to Model IV, four more factors (count of yarns (NeL and NeT) and strength of yarns

123

(SL and ST)) were introduced in Model V. If anyone of them had significant influence on the % SU, the results for Model V would have significantly improved with respect to that of Model IV. Comparing the results obtained from Models IV and V in Table 2, it can be seen that the change is only marginal. Moreover, the % SU has been normalized against the single strand strength of load bearing yarns and hence a change in it is not expected to change % SU much. The fabric strength is, however, expected to change with a change in single strand strength of load bearing yarns. The transverse yarns strength is not expected to contribute much to fabric strength. Therefore, it can be inferred that count of yarns (NeL and NeT) and strength of yarns (SL and ST) individually, or collectively, do not have dominant influence in determining the % SU in woven fabrics. Therefore, Model IV was considered to be optimum model as it is simpler (lower number of input parameters and hidden nodes) and yields prediction performance which is comparable to nine input parameter system Model V. Hence, Model IV has been used subsequently for trend analysis. Trend Analysis In order to explore the manner in which % SU changes with the change in the input parameters, a trend analysis was carried out. For this, nine equally spaced values, including the minimum and maximum were calculated for each of the input parameters. The value of one input parameter was varied from the minimum to the maximum, in steps, keeping the rest of the input parameters at their respective average values. The predicted % SU was plotted against the parameter varied and the trend line was generated. The process was repeated by varying each of the parameters one by one, keeping the other four parameters at their average level. Figure 1 depicts the change in % SU with the change in the number of load bearing yarns per 2.5 cm (NL). It can be seen that % SU in woven fabrics increases with increase in NL for some time before stabilizing. It is worth noting that NL affects % SU even though the latter has been normalized with respect to the former.

155

140

140

120

120

% SU

% SU


100

80

80

60

60 24

27

31

34

38

42

45

49

24

52

This may be explained by Grossberg’s work [25] which computes the force v at the interlacement points (Fig. 2a) responsible for yarn curvature in the woven fabric (Eq. 4). ð4Þ

where m is the bending modulus of the yarn, h is weave angle and p is the inter yarn spacing in the transverse direction.The spacing between load bearing yarns (pL) decreases with an increase in their number per 2.5 cm (NL). This results in increasing the binding force of transverse yarns on the load bearing yarn at each interlacement point as shown in Eq. 5. The parameters in load bearing and transverse directions are represented by the subscript L and T respectively in the equation. 8 mT sin hT p2L

ð5Þ

The crimp in the transverse yarns increases as pL goes down (Fig. 2b).

(a) pL VT VT

Transverse yarn

(b)

V’T V’T

p’L

31

34

38

42

45

49

52

Fig. 3 % SU against number of transverse yarns per 2.5 cm

Fig. 1 % SU against number of load bearing yarns per 2.5 cm

1 2 vp ¼ m sin h 8

27

Number of transverse yarns per 2.5 cm (NT)

Number of load bearing yarns per 2.5 cm (NL)

vT ¼

100

Transverse yarn

Fig. 2 a Forces acting on yarns at crossover points, b Change in forces acting on yarns at crossover points with a change in yarn spacing

Hence a larger section of the surface of load bearing yarn is gripped with higher forces at the interlacement point. Therefore, an increase in NL increases % SU in spite of the fact that the latter is normalized with respect to the former. Figure 3 shows change in % SU with that in the number of transverse yarns per 2.5 cm (NT). It is evident that the % SU initially increases with an increase in NT and then starts decreasing. The following things are associated with an increase in NT: (a)

Number of pin-joints or interlacement points where the load bearing yarn is gripped by the transverse yarns increases (b) The length of load bearing yarn gripped between two successive pin-joints decreases and (c) The crimp in the load bearing yarn increases Initially, when the NT is low, the first two factors contribute towards increasing % SU with an increase in NT. However, as the magnitude of NT increases, the crimp % in the load bearing yarn (% CL) becomes too high to be de-crimped completely before the failure occurs. The crimped yarns would be able to contribute lesser to the fabric strength as compared to straight yarns due to obliquity effect and hence the % SU would decline at higher level of NT. The change in % SU with a change in % CL is shown in Fig. 4. It is apparent that an increase in crimp in load bearing yarns decreases the % SU. As explained before, too high a crimp in the load bearing yarn would mean higher residual crimp near failure and hence lower % SU. Figure 5 shows the plot of % SU against crimp in transverse yarns (% CT). It is observed that an increase in % CT lowers the % SU to some extent. This may be attributed to the fact that straightening or decrimping of load bearing yarns is difficult when initial values of crimp % in the transverse yarns is high.

123

156


parameter on % yarn strength utilization which was found to be rational.

140

% SU

120

Acknowledgments The author is thankful to Vardhaman Textiles Ltd., India for manufacturing of fabrics at C.P.D.C., Mahavir Spinning Mills—Textile Division Textiles, Baddi, H.P., India and Shahi Exports Pvt. Ltd. (Unit of Sarla Fabrics Ltd. Ghaziabad, U.P.), India for desizing and scouring of the fabrics in relaxed form.

100

80

References

60 2.60

4.87

7.15

9.42

11.69

13.97

16.24

18.51

20.79

Crimp % in load bearing yarns (% CL) Fig. 4 % SU against crimp % in the load bearing direction 140

% SU

120

100

80

60 2.60

4.87

7.15

9.42

11.69

13.97

16.24

18.51

20.79

Crimp % in transverse yarns (% CT ) Fig. 5 % SU against crimp % in the transverse yarn

A comparison between Figs. 4 and 5 reveals that the deterioration in % SU with the increase in yarn crimp % is lower in case of transverse yarns. A high crimp in the transverse yarn is also accompanied by an increase in the binding force it offers on the load bearing yarn as explained in Eq. 5. This has a positive influence on % SU. Therefore, the decrease in % SU due to an increase in % CT is lower than that due to an equivalent increase in % CL.

Conclusions ANN model can predict the % yarn strength utilization in woven fabrics very accurately using the fabric constructional parameters as inputs. It was found that the five most important parameters affecting the % yarn strength utilization in woven fabrics are the number of load bearing and transverse yarns per 2.5 cm, initial % crimp in load bearing and transverse directions and the weave or float length. The first two factors have an enhancing effect on % yarn strength utilization while the remaining three have detrimental effect on the % yarn strength utilization when their values are incremented. Trend analyses of artificial neural network model revealed the influence of individual input

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1. F.T. Pierce, The geometry of cloth structure. J. Text. Inst. 28(3), T45–T96 (1937) 2. A. Kemp, An extension of Peirce’s cloth geometry to the treatment of non-circular threads. J. Text. Inst. 49(1), T44–T48 (1958) 3. J.B. Hamilton, A general system of woven fabric geometry. J. Text. Inst. 55, 66 (1964) 4. B. Olofsson, A general model of a fabric as a geometric mechanical structure. J. Text. Inst. 55(11), T541 (1964) 5. G.A.V. Leaf, R.D. Anandjiwala, A generalized model of plain woven fabrics. Text. Res. J. 55, 92 (1985) 6. R.D. Anandjiwala, G.A.V. Leaf, Large scale extension and recovery of plain woven fabrics, part-I: theoretical. Text. Res. J. 61, 619 (1991) 7. R.D. Anandjiwala, G.A.V. Leaf, Large scale extension and recovery of plain woven fabrics. Part-II: experimental and discussion. Text. Res. J. 61(12), 743–755 (1991) 8. S. Kawabata, M. Niwa, H. Kawai, The finite-deformation theory of plain weaves. Part II: the uniaxial-deformation theory. J. Text. Inst. 64(2), 47 (1973) 9. S. Kawabata, M. Niwa, H. Kawai, The finite-deformation theory of plain weaves. Part I: the biaxial-deformation theory. J. Text. Inst. 64(2), 21 (1973) 10. T.V. Sagar, P. Potluri, J.W.S. Hearle, Mesoscale modelling of interlaced fibre assemblies using energy method. Comput. Mater. Sci. 28, 49 (2003) 11. A.A. Shahpurwala, P. Schwartz, Modeling woven fabric tensile strength using statistical bundle theory. Text. Res. J. 59, 26 (1989) 12. G. Chen, X. Ding, Breaking progress simulation and strength prediction of woven fabric under uni-axial tensile loading. Text. Res. J. 76, 875 (2006) 13. J. Fan, L.A. Hunter, Worsted fabric expert system. Part II: an artificial neural network model for predicting the properties of worsted fabrics. Text. Res. J. 68, 763 (1998) 14. D. Bhattacharjee, V.K. Kothari, A neural network system for prediction of thermal resistance of textile fabrics. Text. Res. J. 77, 4 (2007) 15. B.K. Behera, R. Mishra, Artificial neural network-based prediction of aesthetic and functional properties of worsted suiting fabrics. Int. J. Cloth. Sci. Technol. 19(5), 259 (2007) 16. M. Zeydan, Modelling the woven fabric strength using artificial neural network and Taguchi methodologies. Int. J. Cloth. Sci. Technol. 20(2), 104 (2008) 17. B.K. Behera, R. Guruprasad, Predicting bending rigidity of woven fabrics using artificial neural networks. Fibers Polymers 11(8), 1187 (2010) 18. A. Majumdar, A. Ghosh, S.S. Saha, A. Roy, S. Barman, D. Panigrahi, A. Biswas, Empirical modelling of tensile strength of woven fabrics. Fibers Polymers 9(2), 240 (2008) 19. D.P. Dobnik, M. Brezocnik, Prediction of the ultraviolet protection of cotton woven fabrics dyed with reactive dystuffs. Fibers Text. East. Eur. 17(72), 55 (2009)

J. Inst. Eng. India Ser. E (July–December 2015) 96(2):151–157 20. D.E. Rumelhart, G. Hinton, R.J. Williams, Learning Internal representations by error propagation, in Parallel Distributed Processing, vol 1, ed. by D.E. Rumelhart, J.L. McClelland (MIT Press, Cambridge, MA, 1986), p. 318 21. S. Haykin, Neural networks: a comprehensive foundation, 2nd edn. (Pearson Education, Singapore, 2004), p. 161 22. A. Majumdar, Soft computing in fibrous materials engineering. Text. Progress 43(1), 1 (2011) 23. S. Rajasekaran, G.A.V. Pai, Neural networks, fuzzy logic and genetic algorithms: synthesis and applications (Prentice-Hall of India Pvt. Ltd, New Delhi, 2003), p. 42

157 24. J.M. Zurada, Introduction to artificial neural systems (Jaico Publishing House, Mumbai, 2003), p. 175 25. P. Grosberg, The geometrical properties of plain cloths, in Structural Mechanics of Fibers, Yarns and Fabrics, vol. 1, ed. by J.W.S Hearle, P. Grosberg, S. Backer (Wiley Interscience, New York, 1969) p. 325

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Production of Engineered Fabrics Using Artificial Neural Network–Genetic Algorithm Hybrid Model Ashis Mitra • Prabal Kumar Majumdar Debamalya Banerjee

•

Received: 1 August 2014 / Accepted: 13 November 2014 / Published online: 28 November 2014 Ó The Institution of Engineers (India) 2014

Abstract The process of fabric engineering which is generally practised in most of the textile mills is very complicated, repetitive, tedious and time consuming. To eliminate this trial and error approach, a new approach of fabric engineering has been attempted in this work. Data sets of construction parameters [comprising of ends per inch, picks per inch, warp count and weft count] and three fabric properties (namely drape coefficient, air permeability and thermal resistance) of 25 handloom cotton fabrics have been used. The weights and biases of three artificial neural network (ANN) models developed for the prediction of drape coefficient, air permeability and thermal resistance were used to formulate the fitness or objective function and constraints of the optimization problem. The optimization problem was solved using genetic algorithm (GA). In both the fabrics which were attempted for engineering, the target and simulated fabric properties were very close. The GA was able to search the optimum set of fabric construction parameters with reasonably good accuracy except in case of EPI. However, the overall result is encouraging and can be improved further by using larger data sets of handloom fabrics by hybrid ANN–GA model.

A. Mitra (&) Department of Silpa-Sadana, Visva-Bharati University, Sriniketan, Birbhum, West Bengal 731236, India e-mail: [email protected] P. K. Majumdar Government College of Engineering & Textile Technology, Serampore, Hooghly, West Bengal 712201, India D. Banerjee Department of Production Engineering, Jadavpur University, Kolkata, West Bengal 700032, India

Keywords Fabric engineering Artificial neural network Genetic algorithm Objective function Fitness function

Introduction The important wearing performance and qualities of apparel fabrics are comfort, handle, drape and appearance. The analysis of fabric behavior is of great importance to know how the fabric is going to behave during actual use. Fabric testing has been an effective means of choosing suitable fabrics for a particular application. However, it would be much better if one knew how the fabric should be made to meet specific property requirements. This aspiration has led to the domain of ‘fabric engineering’, which implies designing the fabrics based on end-use requirements. The process of fabric engineering or fabric development, which is generally practiced in most of the R&D section of textile mills, is a very complicated but crude one. It is repetitive in nature and hence, tedious and time consuming. The desired set of fabric properties are attained by trial and error approach which involves modifying the fabric design and construction parameters (yarn count and spacings) in iterative steps. A general fabric engineering process may be illustrated as in Fig. 1 [1]. To eliminate this trial and error approach, a new approach of fabric engineering has been attempted in this research. Previously three artificial neural network (ANN) models have been developed to predict three fabric comfort properties namely drape coefficient, air permeability and thermal resistance with sufficient accuracy using ends per inch (EPI), picks per inch (PPI), warp count and weft count as inputs. These are essentially forward prediction models where fabric construction parameters and fabric properties

123

160 Fig. 1 A generalized cycle of fabric engineering


Market Survey

End-use Requirements

Modification

Comparison

Sample Evaluation

Fabric Design Composition Weave Sett, Yarn Count Finishing Routine etc.

Sample Trials

Volume Production

are inputs and outputs respectively. However, for fabric engineering, a reverse system is required which will be able to predict the values of fabric construction parameters when the desired or target values of fabric properties are known. The relationship between fabric construction parameters and fabric properties, as captured by the optimized ANN models, is the key in this fabric engineering approach. The powerful searching capability of genetic algorithm has been used here to elicit the optimum set of fabric construction parameters which will fulfill the desired fabric properties. During the last thirty years, there has been a rapidly growing interest in the domain of GAs. With their great robustness, GAs have proven to be a promising technique for many optimization, design control, and machine learning applications. GA approach has seen widespread acceptance in various engineering fields [2]. However, there are only a few research efforts in the domain of textile engineering where the GA has been used [3–10]. Amin et al. [3] demonstrated a new technique for detecting the source of fault in spinning mills from spectrograms by using genetic algorithm. Lin et al. [4] proposed a method for searching weaving parameters for woven fabrics within controlled costs based on a genetic algorithm approach. Dubrovski and Brezocnik [5] attempted to predict the macroporosity of woven cotton fabrics using genetic programming. Lv et al. [6] attempted to apply genetic algorithm–support vector machine for prediction of spinning quality of yarn. The applications of ANN–GA hybrid model in the domain of textile engineering are still very much limited. Admuthe and Apte [7] has developed a hybrid neuro-genetic and genetic algorithm techniques to model, to simulate and to predict ring yarn spinning process and cost optimization. They reported that the performance of hybrid model was superior compared to current manual machine

123

intervention. Huang and Tang [8] proposed a systematic approach, which is the application of Taguchi method, neural network and genetic algorithm, for determining parameter values in melt spinning processes to yield optimal qualities of denier and tenacity in as-spun fibres. The results showed that the ANN–GA approach could yield better qualities of denier and tenacity in PP as-spun fibres than the Taguchi method. In another similar work, Huang and Tang [9] proposed a quantitative procedure for determining the values of critical process parameters in melt spinning to optimize denier, tenacity, breaking elongation, and denier variance in as-spun PP yarn. Das et al. [10] attempted to engineer cotton yarns with requisite quality by selecting suitable raw materials for a given spinning system. A hybrid model based on ANN and GA was used to engineer a yarn having predefined level of tenacity and evenness from a set of given fibre properties like strength, elongation, upper half mean length, length uniformity index, fineness and short fibre content. GA was used to solve the optimization problem searching the best combination of fibre properties to produce a yarn having desired qualities. The model was capable in identifying the set of fibre properties for requisite yarn quality with reasonable degree of accuracy.

Experimental Methods Sample Preparation Test samples for this study, was consisted of 25 plain woven cotton handloom fabrics, which had been manufactured using semi-automatic handloom by a skilled weaver. During manufacturing of the samples, fabric constructional parameters were varied as much as possible so that the samples cover a wide range of variability.


161

Testing Before testing, all the fabric samples were subjected to one hot wash (at 60 °C) and one cold wash followed by light ironing. The purpose of these treatments was to remove excess size applied before weaving, and to remove undue creases. The fabric samples were conditioned for at least 24 h under standard testing conditions prior to testing. Thread density (i.e. EPI and PPI) was measured by using a pick glass. Yarn count (Ne) was determined on a direct yarn count balance. The Cusick drape tester was used to measure fabric drape coefficient according to ISO 9073-9 standard. Air permeability tests were conducted according to American Standard for Testing and Materials (ASTM standard) D737-96 on SDL Air Permeability Tester under a pressure head of 10 mm of water level in the manometer. Thermal resistance of fabric was measured according to ASTM standard D1518 using computer-controlled semiautomatic instrument Alambeta at a pressure of 200 Pa. Optimized ANN Models The ANN models for the prediction of drape coefficient, air permeability and thermal resistance developed

2 6 6 6 6 6 6 6 W1D ¼ 6 6 6 6 6 6 4

1:329234

3:849645

12:651904

3:036826

1:769182

0:401916

1:547405 0:475855 6:437420 6:104938

0:914915 10:110906

0:562286 0:571874 1:786432 0:872555

0:161070 1:185579

0:185547

11:526627

0:180514

3:869055

0:754594

1:062127

W2D ¼ ½ 10:10859 2:77949 3 2 7:98451 6 0:91038 7 7 6 7 6 6 1:56812 7 7 6 6 0:57941 7 7 6 B1D ¼ 6 7 6 1:21329 7 7 6 6 1:32263 7 7 6 7 6 4 11:88351 5

0:28987

previously have been used here. Data sets of construction parameters and properties of 25 handloom cotton fabrics, as shown in Table 1, were used. The fabric construction parameters comprised of EPI, PPI, warp count and weft count were the inputs to the ANN model. The training and testing of the ANN model were done with randomly partitioned data sets of 20 and 5, respectively. Only one hidden layer was used in all the three ANN models. The log-sigmoid transfer functions were used as the activation functions for the hidden and output layers. The optimum number of neurons in the hidden layers was adjusted by trial and error method. It was found that for drape coefficient, air permeability and thermal resistance, optimized ANN models had 8, 10 and 7 nodes in the hidden layer. The back-propagation algorithm was used in each case to train the ANN model. The training parameters like learning rate and momentum were kept as 0.5 and 0.2 respectively for drape and air permeability prediction, and 0.3 and 0.2 respectively for thermal resistance prediction. The trained or optimized networks formulated the equations for prediction of the three fabric properties from the given fabric construction parameters. The weights and biases of optimized ANN model for drape were as follows:

22:330160

3

1:945636 7 7 7 0:404418 7 7 5:007566 7 7 7 1:773994 7 7 0:244275 7 7 7 26:234380 5 8:122076

7:20593

0:94907

0:04352

9:04399

5:20601

0:93265 B2D ¼ ½7:954706

123

162


Table 1 Data sets of construction parameters and properties of handloom fabrics Sample no.

EPI

PPI

Warp count (Ne)

Weft count (Ne)

Drape coefficient (%)

Air permeability (cm3 s-1 cm-2)

Thermal resistance (m2 K W-1 9 10-3)

1

69.20

68.90

34.10

36.70

65.90

243.42

11.00

2

77.00

56.70

30.80

32.70

67.62

217.92

11.13

3

69.30

57.20

33.10

43.20

68.28

244.14

12.01

4

67.20

59.60

30.30

35.20

63.69

216.45

11.68

5

67.40

63.90

28.55

24.30

66.00

218.24

12.67

6

69.60

51.40

33.60

38.10

80.09

241.52

12.05

7 8

87.60 68.80

78.30 48.40

33.10 26.30

36.40 42.50

75.76 63.34

224.44 214.23

14.17 13.16 15.98

9

67.00

67.00

34.30

36.00

64.94

253.97

10

101.50

105.20

85.20

90.30

76.73

241.38

7.97

11

65.90

55.60

31.40

38.05

79.53

246.62

13.66

12

71.20

55.80

15.60

18.50

78.43

214.45

10.90

13

68.80

73.50

36.40

33.40

64.81

242.45

12.24

14

66.60

103.00

49.80

43.95

68.76

238.67

12.04

15

69.50

66.10

32.30

35.40

67.07

241.26

12.44

16

31.20

24.40

5.60

6.10

65.08

246.72

24.65

17

64.50

96.70

39.10

35.60

67.01

236.61

12.01

18

66.90

65.70

35.70

35.40

70.97

258.50

13.27

19

70.60

66.20

33.70

36.60

66.65

258.50

13.69

20

70.00

95.30

25.50

56.00

68.09

214.69

13.62

21

69.40

53.40

25.70

39.10

61.41

215.00

12.54

22 23

64.20 68.60

42.50 62.40

25.00 34.70

13.30 38.20

68.31 80.00

217.62 244.50

12.22 14.22

24

67.30

115.50

35.40

50.60

65.48

236.54

13.85

25

82.20

112.00

51.70

51.60

77.94

239.28

12.08

Min.

31.20

24.40

5.60

6.10

61.41

214.23

7.97

Max.

101.50

115.50

85.20

90.30

80.09

258.50

24.65

Mean

69.66

69.79

33.88

37.89

69.68

234.68

13.01

SD

11.44

22.85

14.01

15.50

5.91

14.71

2.85

CV %

16.43

32.74

41.36

40.92

8.48

6.27

21.91

where W1, W2, are the weight matrices connecting input to hidden layer, and hidden to output layers respectively; B1 and B2 are the bias weight matrices for input and hidden layers respectively. Similar matrices were developed for air permeability and thermal resistance also.

The following optimization problem was developed in order to engineer the handloom fabrics with desired qualities and performance: Objective function: Minimize f ðXÞ ¼ ðT1 P1 Þ2

ð1Þ

Subject to the constraints Designing a Hybrid ANN–GA Model The weights and biases of the three optimized ANN models for prediction of drape coefficient, air permeability and thermal resistance were used to optimize the fabric construction parameters like EPI, PPI, warp count and weft count by GA in order to achieve the target fabric properties.

123

5\ T2 P2 \0

ð2Þ

0 \ T3 P3 \ 5

ð3Þ

where P1, P2 and P3 are ANN predicted values and T1, T2 and T3 are the target values of fabric thermal resistance, air permeability and drape coefficient respectively. The foremost objective of this fabric engineering endeavour was to design a handloom fabric suitable as


163

PðX; RÞ ¼ f ðXÞ þ XðR; g1 ðXÞ; g2 ðXÞÞ

ð4Þ

where R indicates a set of penalty parameters, X indicates the penalty operator and g1(X) and g2(X), which are expressed as in Eqs. 5 and 6 respectively, are the inequality constraint functions: g1 ðXÞ ¼ T2 P2

ð5Þ

g2 ðXÞ ¼ T3 P3

ð6Þ

Here a Bracket operator penalty term has been used which is defined as X ¼ Rhg1 ðXÞ þ g2 ðXÞi2

ð7Þ

where a bracket operator hai is defined as hai = a, when a is negative and zero, otherwise. Since the bracket operator assigns a positive value to the infeasible points, this is an exterior penalty term. The first sequence begins with a small value of the penalty parameter R and is increased in subsequent sequences. This operator is mostly used in handling inequality constraints. In the case of exterior penalty term, a small initial value of R results in an optimum solution close to the unconstrained optimum point. As R is increased in successive sequences, the solution improves and finally approaches the true constrained optimum point [2]. As GA is basically a maximization procedure, the following fitness function is developed from the penalty function of Eq. 4: FðX; RÞ ¼

1 1 þ PðX; RÞ

ð8Þ

Genetic Algorithm Parameters Initially, a population size of 1,000 was generated. Each individual of the population consisted of a set of four randomly generated elements (i.e., parts of chromosome) representing the four fabric construction parameters within the specified boundary. Each individual was used as inputs

No. of Generation vs. Fitness Ratio

1 0.9 0.8 0.7

Fitness Ratio

summer clothing material. Therefore, the target and predicted values of thermal resistance were used to formulate the objective function. As higher air permeability is desirable in summer clothing, penalty was imposed when the predicted value was either lower than the target value or exceeds the target value by 5. As lower drape (i.e. more flexible fabric) is desirable in summer clothing, penalty was imposed when the predicted value was either lower than the target value by more than 5 or higher than the target value. Two handloom fabrics, namely original fabric samples 19 and 22 were attempted for engineering. A penalty function method was employed to manage the inequality constraint of Eqs. 2 and 3. By incorporating the constraints, the objective function of Eq. 1 was converted to the following penalty function:

0.6 0.5 0.4 0.3 0.2 0.1 0

50

100

150

200

250

300

350

400

Generation No.

Fig. 2 Change in fitness ratio with respect to no. of generation

to the optimized neural network for getting the predicted outputs such as fabric drape coefficient, air permeability and thermal resistance. For the whole population, the fitness function of Eq. 8 was evaluated, and the fitness ratio, r, which is defined as the ratio of the mean fitness value to the maximum fitness value was determined. The population of the input elements were then modified to create a new modified population of fabric construction parameters by using three primary operators of GA like reproduction, cross-over and mutation. This new modified population of fabric construction parameters was again used as the inputs to the optimized ANN models to generate the predicted fabric properties. Re-evaluation of the fitness value and recalculation of fitness ratio, r, were done to complete the first generation of GA which was run for generation after generation till the termination criteria was achieved. The termination criteria were either r reached a desired value which was chosen as 0.99, or the number of generations reached to the maximum value which was 400 in this work. The desired value of r = 0.99 implied that mean fitness value is 99 % of the maximum fitness value. Figure 2 depicts the change of fitness ratio with respect to the number of generations. The parameters of GA were kept as follows to get the optimum solution: the cross-over probability, Pc = 0.7, mutation probability, Pm = 0.001, and the no. of bits = 14, 14, 12 and 12 (for EPI, PPI, warp count and weft count, respectively). The Roulette wheel selection scheme was used during the reproduction operation for the selection of the good individuals from the population of four fabric construction parameters based on their fitness information. Uniform cross-over method was adopted to generate new individuals representing fabric construction parameters. Since it was basically a constrained optimization, the penalty

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164


Use training dataset like EPI, PPI, Warp count and we count as inputs, and fabric drape coefficient, air permeability and thermal resistance as output

Start

Training of ANN

Set, maximum no. of generaons, populaon size, pc, pm

Generate random populaon for fabric construcon parameters (EPI, PPI, warp count and we count) Input

Trained ANN Output Evaluate, r = (average fitness/ maximum fitness)

Check whether, r≥0.99

Evaluate fitness funcon for whole populaon

Get fabric drape coefficient, air permeability and thermal resistance using trained ANN

No Go for Reproducon, Crossover, Mutaon

Create modified populaon of fabric construcon parameters

Yes

Input End

Trained ANN Output

No Get drape coefficient, air permeability and thermal resistance from modified populaon using trained ANN

Yes Check whether, generation ≤ max no. of generation

Set, generaon = generaon + 1

Evaluate, fitness funcon (for whole populaon) and compute r

Fig. 3 Flow-chart of ANN–GA program

constant was kept as 100,000 for all the constraints during optimization. The flow-chart of the ANN–GA program is shown in Fig. 3. The program algorithm was developed using MATLAB 7.0.1 programming environment and run on an Intel Core i5 3rd generation processor based PC.

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Results and Discussion After the termination of genetic algorithm program, the optimized set of fabric parameters were fed to the ANN models to obtain the simulated values of fabric drape, air


165

Table 2 Target and simulated properties of engineered fabric-1

values. The high error in case of EPI may be attributed to the inherent irregularity of handloom fabrics. However, the overall result is encouraging and it can be improved further by using large data sets of handloom fabrics.

Fabric properties

Target value

Simulated value

Drape coefficient

66.7

70.0

Air permeability

258.5

259.1

13.7

13.1

Thermal resistance

Conclusion Table 3 Target and simulated properties of engineered fabric-2 Fabric properties

Target value

Simulated value

Drape coefficient

68.3

68.9

Air permeability

217.6

220.4

12.2

12.2

Thermal resistance

Table 4 Actual and optimum fabric construction parameters for engineered fabric-1 Fabric construction parameters

Actual value

Optimum value (searched by GA)

EPI

70.6

82.5

PPI

66.2

68.7

Warp count

33.7

33.8

Weft count

36.6

36.6

The fabric engineering has been attempted using hybrid ANN–GA approach. Three fabric properties, namely drape coefficient, air permeability and thermal resistance were attempted for engineering by searching the optimum set of fabric construction parameters using genetic algorithm. The weights and biases of three optimized ANN models were used to formulate the fitness function of genetic algorithm. In both the fabrics, which were attempted for engineering, the target and the simulated fabric properties were very close. The genetic algorithm was able to search the optimum set of fabric construction parameters with reasonably good accuracy except in case of EPI. Use of more number of data sets can further improve the accuracy of fabric engineering by hybrid ANN–GA model.

References Table 5 Actual and optimum fabric construction parameters for engineered fabric-2 Fabric construction parameters

Actual value

Optimum value (searched by GA)

EPI

64.2

91.2

PPI

42.5

41.5

Warp count Weft count

25.0 13.3

22.3 12.5

permeability and thermal resistance. Then the target and the simulated values of fabric properties were compared to appraise the accuracy of fabric engineering attempt. The target and simulated values of the three fabric properties are given in Tables 2 and 3 for fabric samples 19 and 22 respectively. The actual and optimum set of fabric construction parameters as given by GA for fabric samples 19 and 22 are given in Tables 4 and 5 respectively. From Tables 2 and 3, it is observed that all the simulated fabric properties are very close to the respective target values. This bolsters the perception that ANN–GA is a very potent tool for fabric engineering research. From Tables 4 and 5, it is noted that all the fabric construction parameters, except EPI, are reasonably close to the respective actual

1. J. Fan, L. Hunter, A worsted fabric expert system: part I: system development. Text. Res. J. 68(9), 680–686 (1998) 2. K. Deb, Optimization for Engineering Design—Algorithms and Examples (Prentice Hall of India Pvt. Ltd., New Delhi, 2005) 3. A.E. Amin, A.S. El-Geheni, I.A. El-Hawary, R.A. El-Beali, Detecting the fault from spectrograms by using genetic algorithm techniques. AUTEX Res. J. 7(2), 80–88 (2007) 4. J.J. Lin, A genetic algorithm for searching the weaving parameters of Woven fabrics. Text. Res. J. 73(2), 105–112 (2003) 5. P.D. Dubrovski, M. Brezoenik, Using genetic programming to predict the macroporosity of Woven cotton fabrics. Text. Res. J. 72(12), 187–194 (2002) 6. Z.J. Lv, Q. Xiang, J.G. Yang, Application of genetic algorithmsupport vector machine for prediction of spinning quality, In Proceedings of the World Congress on Engineering, Vol II, London July 6–8, (2011) 7. L.S. Admuthe, S.D. Apte, Neuro-genetic cost optimization model: application of textile spinning process. Int. J. Comput. Theory Eng. 1(4), 441–444 (2009) 8. C.C. Huang, T.T. Tang, Parameter optimization in melt spinning by neural networks and genetic algorithms. Int. J. Adv. Manuf. Technol. 27, 1113–1118 (2006) 9. C.C. Huang, T.T. Tang, Optimizing multiple qualities in as-spun polypropylene yarn by neural networks and genetic algorithms. J. Appl. Polym. Sci. 100, 2532–2541 (2006) 10. S. Das, A. Ghosh, A. Majumdar, D. Banerjee, Yarn engineering using hybrid artificial neural network-genetic algorithm model. Fibres Polym. 14(7), 1220–1226 (2013)

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Comparative Analysis of Soft Computing Models in Prediction of Bending Rigidity of Cotton Woven Fabrics R. Guruprasad • B. K. Behera

Received: 6 September 2014 / Accepted: 12 November 2014 / Published online: 11 December 2014 Ó The Institution of Engineers (India) 2014

Abstract Quantitative prediction of fabric mechanical properties is an essential requirement for design engineering of textile and apparel products. In this work, the possibility of prediction of bending rigidity of cotton woven fabrics has been explored with the application of Artificial Neural Network (ANN) and two hybrid methodologies, namely Neuro-genetic modeling and Adaptive NeuroFuzzy Inference System (ANFIS) modeling. For this purpose, a set of cotton woven grey fabrics was desized, scoured and relaxed. The fabrics were then conditioned and tested for bending properties. With the database thus created, a neural network model was first developed using back propagation as the learning algorithm. The second model was developed by applying a hybrid learning strategy, in which genetic algorithm was first used as a learning algorithm to optimize the number of neurons and connection weights of the neural network. The Genetic algorithm optimized network structure was further allowed to learn using back propagation algorithm. In the third model, an ANFIS modeling approach was attempted to map the input–output data. The prediction performances of the models were compared and a sensitivity analysis was reported. The results show that the prediction by neurogenetic and ANFIS models were better in comparison with that of back propagation neural network model.

R. Guruprasad (&) Mechanical Processing Division, Central Institute for Research on Cotton Technology, Matunga, Mumbai 400019, India e-mail: [email protected] B. K. Behera Department of Textile Technology, Indian Institute of Technology Delhi, New Delhi 110016, India

Keywords GANN

ANN ANFIS Bending rigidity BPNN

Introduction Woven fabrics are widely used for domestic and industrial applications. As domestic products, e.g., fabrics for clothing and bedding, properties relating to particular uses such as fabric cover, strength, and drape are consciously sought by customers. The majority of textiles made today are produced by non-specific, ad hoc specifications, sometimes with trial and error regimes [1, 2]. In most current cases, there is insufficient knowledge about fabric properties during manufacturing, and there is obviously an absence of knowledge about how fabrics should be made to meet specific requirements. The change from empirical to engineering based design of structures basically involves the ability to quantitatively predict the mechanical properties of a material [3]. One such mechanical property, which has the maximum influence on textile structure formation and end use performance of textile material, is that of bending rigidity. An accurate modeling of the bending behavior of fabric using the conventional analytical solutions requires rigorous mathematical procedures that are difficult to achieve from the pragmatic point of view. Moreover, a closed form solution is very difficult to obtain as many structural variables are involved in predicting the bending behavior of fabrics. It is an established fact that macroscopic structural factors like fabric weight, fabric thickness and fabric cover affect the bending rigidity of fabrics to a greater extent, but the relationships are nonlinear in nature and difficult to quantify. In this respect, soft computing techniques like ANNs, Fuzzy Logic (FL) and Genetic Algorithms (GAs), which do not need

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168


incorporation of any assumptions or simplifications, are more efficient. These methods offer great flexibility with respect to the ability to approximate a wide variety of functions [4, 5]. The prediction of bending rigidity of plain and satin fabrics from independent fabric constructional variables using ANN has been reported in earlier studies [6]. The same authors have also modeled bending rigidity of woven fabrics from fabric macroscopic factors using ANFIS and Neuro-genetic modeling [7, 8]. In this article, a comparative analysis on the prediction potential of neural network, ANFIS and neuro-genetic models has been made in predicting the Overall Bending Rigidity (OBR) of cotton woven fabrics. The fabric structural parameters, namely fabric thickness, fabric weight and fabric cover were used as input parameters for the model.

Table 1 Summary of fabric data used for model development

Materials and Methods

where B1 and B2 are warp way and weft way bending rigidities respectively.

Fiber material

100 % Cotton

Yarn type in warp

Ring spun

Yarn type in weft

Ring spun

Weave design

Plain

Fabric treatments

Desizing, scouring and wet relaxing Min

Max

Thread density in warp (threads/cm) 24

57

Thread density in weft (threads/cm) 22

60

Linear density of warp (tex)

5.9

29.5

Linear density of weft (tex)

5.9

29.5

Mass/area (g/m2) Thickness (mm)

51 0.10

232 0.26

Fabric cover (%)

52

93

Material Selection and Preparation Data Division and Preprocessing For this study, a set of fifty grey cotton fabrics meant for apparel end use were procured. The fabrics were of plain weave design with different construction parameters (thread density and yarn counts). The grey woven fabrics were desized using enzyme, scoured using alkali and wet relaxed. The fabrics were then kept in standard conditioning atmosphere for 6 h before testing [9].

Firstly, the fifty sets of data were randomly partitioned into a training set of 42 samples and a test set of 8 samples. The input and output variables were preprocessed by scaling them between 0 and 1.0, to eliminate their dimension and to ensure that all variables receive equal attention during training.

Input–Output Parameters and Testing

Back propagation Neural Network Modeling (BPNN)

The fabric weight (mass/unit area), fabric thickness, and fabric cover were considered as input parameters for development of models. The fabric weight (g/m2) was measured by cutting and weighing specimens whereas fabric thickness was measured at a pressure of 50 gf/cm2 using Kawabata Evaluation System (KES)-FB3 tester. The cover of fabric (K) was calculated using the expression,

The BPNN generally consists of three layers of neurons: an input layer, hidden layer, and output layer (Fig. 1). The number of hidden layers was set to unity. It has been reported that the BPNN with a single hidden layer can encode any arbitrary complex input–output relationship [12]. For the hidden layer, tan-sigmoid transfer activation function was used and for the output layer, linear transfer function was used. This combination of activation functions for the hidden layer and output layer was arrived after trying out all other combinations. Gradient descent with momentum and adaptive learning rate back propagation was employed as learning algorithm to train the network. The training performance of the network is given by Mean Square Error (MSE) which is defined as:

K ð%Þ ¼ ðK1 þ K2 K1 K2 Þ 100

ð1Þ

where warp cover, K1 = d1/p1; weft cover, K2 = d2/p2; d is yarn diameter and p is thread spacing. The summary of fabric details is given in Table 1. The fabrics were tested for their bending property using KESFB 2 tester. The bending rigidity was measured as the average of slopes of the linear regions of the bendinghysteresis curve when fabric is bent on its face and back between the curvatures of ±0.5 and 1.5 cm-1 [10]. Each sample was tested both in warp and weft way and the average of four readings was taken. From these values, the output parameter, OBR was calculated as [11], p p OBR ¼ B1 B2 ð2Þ

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1X 1X eðkÞ2 ¼ ðtðkÞ aðkÞÞ2 Q k¼1 Q k¼1 Q

MSE ¼

Q

ð3Þ

where t is the target output; a is the predicted output from neural network; Q is the number of input vectors. With an adaptive learning rate, the learning rate is increased or decreased during training based on the performance [13].


169

search was then performed using back propagation algorithm. The GA was run using the optimization tool box of MATLAB software. The optimal solution search using GA requires the tuning of some features, for example population size, selection and crossover functions, mutation rate, migration, etc. After many number of trials, the parameters were set as follows:

Fig. 1 A three layer feedforward network structure

Fig. 2 Neural network training curve

The optimal number of hidden nodes was obtained by a trial-and-error approach. It should be noted that (2I ? 1) is the upper limit for the number of hidden layer nodes needed to map any continuous function for a network with I inputs, as discussed by Caudill [14]. For training the network, Neural network toolbox of MATLAB software was used. No significant improvement in the error was observed after 1,500 training cycles. The optimal number of neurons in the hidden layer was found to be three. The momentum parameter was optimized at 0.9 after trying out different constant levels, namely 0.1, 0.3, 0.5, 0.7 and 0.9. The MSE and Mean Absolute Percentage Error (MAPE) values of the best-performing model were 0.27 and 5.11 respectively. The learning curve is shown in Fig. 2.

Population type Population size Creation function Population range Fitness scaling function Selection function Elite count Crossover fraction Mutation function Crossover function Migration Migration fraction Stopping criteria

Double vector 20 Uniform [0; 0.2] Rank Roulette wheel 2 0.9 Gaussian Two point Migration direction: Forward 0.2 100 Generations (maximum)

The optimum number of hidden neurons was found to be four. For a four neuron structure, the number of weight values (including biases) to be optimized was 21. The optimization procedure terminated after 59 generations as there is no significant change in the fitness values beyond this. The GA learning curve is shown in Fig. 3. The network weight values obtained from the best of number of candidate trained models were then used as initial weights for back propagation algorithm to learn and reach the global optimum i.e. the minimum value of error on test set. The training was performed for 1,300 cycles. Adaptive Neuro-Fuzzy Inference System (ANFIS) Modeling The ANFIS is a useful neural network approach for the solution of function approximation problems. An ANFIS gives the mapping relation between the input and output data by using hybrid learning method to determine the

Neuro-Genetic Modeling (Genetic Algorithm for Artificial Neural Network or GANN) In the second model, a hybrid modeling approach combining GA and back propagation learning strategies was attempted. The number of hidden neurons and the weight values of network connections were first optimized using a GA. With the optimum number of neurons and by assigning the weight values as initial weights, a local

Fig. 3 GA learning curve

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170

J. Inst. Eng. India Ser. E (July–December 2015) 96(2):167–174 Layer 1

A1 x

A2

Layer 4 Layer 2

Layer 3 x y

∏

ω1

N

ϖ1

Layer 5

ϖ 1 f1 ∑

B1

∏

ω2

y B2

N

f

ϖ 2 f2

ϖ2 x y

Fig. 4 ANFIS architecture

optimal distribution of Membership Functions (MFs) [15]. Both ANN and FL are used in ANFIS architecture. The architecture of ANFIS for a two inputs and one output system is shown in Fig. 4. Structure Identification This is the preparation phase for parameter identification and it primarily involves establishing the inputs for the ANFIS models and generating the initial FIS. The inputs to the model and the number of training and checking data

used were the same as that of previous models. The generation of the initial FIS involves selecting a structure for the ANFIS model by determining the number of MFs per input, type/shape of the MFs for the premise part of the rule and the output MFs for the consequent part of the rule. Grid partitioning was chosen as the method for creation of initial FIS as number of inputs to the model was only three. Once the grid partitioning technique is applied at the beginning of training, a uniformly partitioned grid which is defined by MFs with a random set of parameters is taken as the initial state of ANFIS. During training, this grid evolves as the parameters in the MFs change. In generating the initial FIS by grid partitioning, four different types of MFs were chosen. They were (1) generalized bell-shaped MF (2) Gaussian MF (3) Triangular MF and (4) Trapezoidal MF. A linear function was used as output MF. Different numbers of MF combinations were tried such as [2 2 2], [2 3 2], [3 2 2], [2 2 3], [3 3 3] etc., for the inputs: fabric thickness, fabric weight, and fabric cover respectively. Parameter Identification Parameter Identification is the training of the ANFIS models through the application of an optimization

Fig. 5 a. Initial form of membership functions (MFs) for the inputs b. Final form of membership functions (MFs) after training

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scheme on the generated initial FIS. Training involves tuning the parameters of the ANFIS models, which determine the shape of the MFs and ultimately dictates how the rules for the trained prediction models would behave. The FL toolbox of MATLAB provides two optimization methods: hybrid and back propagation. The hybrid technique was chosen as it is more popularly used with ANFIS than the back propagation [15]. The training was done for 100 epochs (cycles). The results of the best of the models developed using Gaussian, generalized bell-shape, trapezoidal and triangular MFs showed that the bell-shaped MF was appropriate to model the data with the combination of [2 2 2] MFs for the inputs. The training performance of ANFIS was given by Root Mean Squared Error (RMSE). The initial form of MF and the final form after training are given in Fig. 5a and b respectively.

171

Results and Discussion Training Performance of Models The training performance of the models has been evaluated by feeding only the input data to the model and allowing the model to predict the output values. It can be seen from the linear regression graphs shown in Fig. 6a–c, that the learning by all three methods was satisfactory. The correlation values achieved in all three models were around 0.99, which shows that the learning performance was excellent. It should be mentioned here that, utmost care has been taken to avoid network overtraining in all three cases. On observing the graphs, in particular, the learning capability of ANFIS has been found exceptionally good, with almost all predicted data points matching with the training data. However, better learning performance not necessarily

Fig. 6 a BPNN model, b GANN model, c ANFIS model

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172


Table 2 Prediction values for test set fabrics S. no.

Experimental values (mN mm)

Predicted values (mN mm) BPNN

Prediction error % (MAPE)

GANN

ANFIS

BPNN

GANN

ANFIS

S1

8.2611

8.1934

8.0287

7.7227

0.82

2.81

S2

3.4345

3.0853

3.3974

3.3062

10.17

1.08

3.74

S3

7.0462

6.446

6.4720

6.1469

8.52

8.15

12.76

S4

12.375

12.552

12.079

12.848

6.52

1.43

2.39

3.82

S5

6.8508

6.5309

6.5338

6.9908

4.67

4.63

2.04

S6

3.5632

3.2646

3.5825

3.5578

8.38

0.54

0.15

S7 S8

2.2764 4.8676

2.6187 4.6720

2.3488 4.9261

2.2748 5.2274

15.04 4.02

3.18 1.20

0.07 7.39

Table 3 Statistical estimation of results Statistical parameters

BPNN

GANN

ANFIS

Maximum absolute percentage error Minimum absolute percentage error

15.04

8.15

12.76

0.82

0.54

0.07

Mean absolute percentage error (MAPE)

6.63

3.00

4.56

Number of error values [10 %

2

0

1

Mean squared error

0.1081

0.0727

0.1860

Correlation coefficient

0.99

0.99

0.99

ensures better generalization ability. The ability of the models to generalize has been tested using test data and the comparative results are discussed in next section. Generalization Performance The individual prediction values for the test set fabrics are given in Table 2 and the statistical parameter estimates are given in Table 3. From the results, it can be seen that the prediction accuracy of hybrid models are better than that of the standalone BPNN model. The merits of each modeling methodology have been combined in case of hybrid models, which results in better prediction accuracy. In particular, the GANN model shows better prediction accuracy, as the prediction error is only 3 % and also the maximum error and the range of error values are less. The GANN model is closely followed by the ANFIS model in performance.

adopting the approach used by Goh [16], where all input variables, except one, were fixed to the mean values used for training and a set of synthetic data (whose values lie between the minimum and maximum values used for model training) were generated for the single input that was allowed to vary. The synthetic data were generated by increasing their values in increments equal to 10 % of the total range between the minimum and maximum values. These input values were then entered into models and the corresponding outputs obtained. The robustness of the models was determined by examining how well the predictions compare with available structural knowledge. The sensitivity analysis graphs of all three models are shown in Fig. 7 a–c. The trends predicted by models agree well with the existing knowledge on the effect of these input parameters on bending rigidity [17, 18]. All three models exhibit greater sensitiveness to change in fabric weight. ANFIS and GANN models show greater sensitivity for changes in weight, in particular at higher GSM levels.

Sensitivity Analysis To further examine the generalization ability (robustness) of the developed models, sensitivity analysis was carried out that demonstrates the response of model to a set of hypothetical input data that lie within the range of the data used for model training. The results were obtained by

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Conclusions The prediction potential of BPNN, GANN and ANFIS models were analyzed in prediction of OBR of cotton woven fabrics. Although the predictions of all three models


(a) OBR (mN mm)

Fig. 7 a. Fabric thickness versus Overall bending rigidity b. Fabric weight vs. Overall bending rigidity c. Fabric cover versus Overall bending rigidity

173

14.00 12.00 10.00 8.00 6.00

BPNN

4.00

GANN

2.00

ANFIS

0.00

0.10

0.12

0.14

0.15

0.17

0.18

0.20

0.22

0.23

0.25

0.26

Thickness (mm)

OBR (mN mm)

(b)

30.00 25.00 20.00 15.00 10.00

BPNN

5.00

GANN

0.00

ANFIS 51

69

87

105

123

142

160

178

196

214

232

(c)

10.00

OBR (mN mm)

Weight (GSM)

8.00 6.00 4.00

BPNN

2.00 0.00

GANN ANFIS 52

56

60

64

68

73

77

81

85

89

93

Cover (%)

showed acceptable statistical performance, the prediction performance of hybrid models using GA and ANFIS were better than that of standalone back propagation network model. The superior performance of ANFIS in comparison to BPNN model is due to the fact that ANFIS combines the learning capabilities of a neural network and reasoning capabilities of fuzzy logic, thus having an extended prediction capability compared to BPNN. The GANN model, in particular, shows better prediction accuracy than other two models. Such an improvement in prediction results is attributable to the ability of the GA in finding the global optimum region in the search space. BP algorithm complements GA and performs local search efficiently to reach global optimum. The sensitivity analysis confirmed the robustness of the developed models and has predicted an acceptable trend for the effect of fabric structural variables on the bending rigidity. The same hybrid modeling strategy can be extended to prediction of other fabric mechanical properties as well and these models can be grouped into an

expert system for intelligent prediction of fabric mechanical properties.

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

G. Stylios, Int. J. Cloth. Sci. Technol. 10(2), 1 (1998) X. Chen, G.A.V. Leaf, Text. Res. J. 70(5), 437 (2000) J.W.S. Hearle, Int. J. Cloth. Sci. Technol. 16, 141 (2004) J.S.R. Jang, C.T. Sun, E. Mizutani, Neuro-fuzzy and Soft computing (Prentice hall of India Pvt. Ltd., New delhi, 2008) A. Majumdar, Soft Computing in Textile Engineering (Woodhead publishing Ltd., Cambridge, 2011) B.K. Behera, R. Guruprasad, Fibers polym 11(8), 1187 (2010) B.K. Behera, R. Guruprasad, J. Text. Inst. 103(11), 1205 (2012) R. Guruprasad, B.K. Behera, Fibers Polym 15(5), 1099 (2014) The ASTM Standards. ASTM International, U.S.A The Manual for bending tester KES-FB2. Kato Tech Co. Ltd., Kyoto, Japan, 2002 M.H. Mohamed, P.R. Lord, Text. Res. J. 43, 154 (1973) S. Haykin, Neural Networks (Macmillan, New York, 1994)

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174 13. H. Demuth, M. Beale, Neural Network Toolbox for use with Matlab (The Math Works Inc., Natick, 2000) 14. M. Caudill, AI Expert 3, 53 (1988) 15. J.S.R. Jang, IEEE Trans Syst, Man Cybern 23(3), 665 (1993)

123

J. Inst. Eng. India Ser. E (July–December 2015) 96(2):167–174 16. A.T.C. Goh, Artif. Intell. Eng. 9, 143 (1995) 17. F.T. Peirce, J. Text. Inst. 21, T377 (1930) 18. R. Guruprasad, Ph.D. Dissertation, Indian Institute of Technology, New Delhi, 2011



Modeling of Abrasion Resistance Performance of Persian Handmade Wool Carpets Using Artificial Neural Network Shravan Kumar Gupta • Kamal Kanti Goswami

Received: 26 August 2014 / Accepted: 2 December 2014 / Published online: 22 January 2015 Ó The Institution of Engineers (India) 2015

Abstract This paper presents the application of Artificial Neural Network (ANN) modeling for the prediction of abrasion resistance of Persian handmade wool carpets. Four carpet constructional parameters, namely knot density, pile height, number of ply in pile yarn and pile yarn twist have been used as input parameters for ANN model. The prediction performance was judged in terms of statistical parameters like correlation coefficient (R) and Mean Absolute Percentage Error (MAPE). Though the training performance of ANN was very good, the generalization ability was not up to the mark. This implies that large number of training data should be used for the adequate training of ANN models. Keywords Abrasion resistance ANN MAPE Box-Behnken design Persian handmade wool carpet

Introduction Carpet is a three-dimensional textile structure which is generally used as floor coverings. There are two types of carpets based on their manufacturing techniques namely, machine made and handmade carpets. Tufting, weaving, knitting, braiding, needle felting, fusion bonding and flocking are the techniques used for manufacturing of

S. K. Gupta (&) K. K. Goswami Indian Institute of Carpet Technology, Bhadohi 221 401, Uttar Pradesh, India e-mail: [email protected]

machine made carpets. On the other hand, knotting, flat weaving and tufting techniques are popular for producing handmade carpets. Knotting is a very widely used method for handmade carpet manufacturing. The texture of hand knotted carpets is created by the knots such as Persian or Sehna, Tibetan, Turkish or Ghiordes, Spanish, Kiwi etc. Among these, Persian knot is extensively used in handmade carpet sector [1–4]. Carpet durability is of paramount importance for carpet manufacturers to meet the customer satisfaction during actual use. Carpet durability is defined as the wear life of a carpet in a given situation. The durability of these products is an important parameter because these products are costlier than apparel. Compression and recovery characteristics, thickness loss under dynamic loading, thickness loss and recovery after prolonged heavy static loading, surface pile mass density factor, abrasion resistance, tuft bind etc. are some of the measures of carpet durability. Abrasion resistance is one of the most important parameters of carpet durability. WIRA carpet abrasion machine is extensively used to measure the abrasion behavior of carpets. Abrasion resistance of Persian handmade wool carpets is influenced by wool fibre properties, yarn and carpet constructional parameters. The earlier researchers reported the influence of wool fibre diameter and modulation on abrasion behavior of hand-knotted carpets and found that the abrasion loss increases with the increase in fibre diameter and medullated fibre content [5]. The abrasion loss of carpets depends on wool fibre diameter and number of medullated fibres present in the yarn [6]. The previous studies showed that the influence of tuft constitution (the number of threads assembled together to form a tuft whether single or plied) on the abrasion performance of handwoven carpets [7]. Lower abrasion loss was found in carpets having more regular pile surface (when using single

123

176


ply yarn) than in carpets having reduced regularity in pile surface (when using plied yarn). The influence of carpet constructional parameters on the durability properties has been reported by some researchers [6, 8–10]. It has been found that pile density and pile height play important roles in determining carpet durability. Carnaby developed a theoretical model to predict the carper wear performance [11]. ANN is a very useful technique for prediction related problems and it has been used extensively in textiles for fibre, yarn and fabric property prediction as well as for controlling of process parameters in textile chemical processing, garment manufacturing and technical textiles [12–15]. Researchers have already attempted to evaluate carpet wear objectively by using image analysis and ANN [16–18]. However, there is no reported research where the role of yarn and carpet parameters (number of ply in pile yarn, pile twist level, pile height and knot density) on abrasion resistance have been studied comprehensively. Therefore, in this investigation, an attempt has been made to study the abrasion resistance behavior of Persian handmade wool carpets by developing a predictive model using ANN.

Materials and Methods Manufacturing of Handmade Carpet Samples Pile, warp, thick weft and thin weft yarns were used for producing Persian handmade carpet samples. Pile yarns of 3.90 metric counts (Nm) with three different twist levels i.e. 3.5, 4.0 and 4.5 twists per inch (tpi) were spun from 100 % wool fibres by woollen spinning system. The specifications of wool fibres and pile yarns are given in Tables 1 and 2 respectively. The specifications of Warp, thin weft and thick weft yarns are given in Table 3. Carpet samples were manufactured by creation of Persian knots (also called Sehna knot). This knot is an asymmetrical single knot. The Persian knots are created by wrapping the tuft around one warp thread at an angle of 2p radians and then around another adjacent warp thread at an angle of p radians as depicted in Fig. 1. A short piece of yarn is tied by hand around two neighboring warp strands. After each row of knots is completed, two strands of weft are passed through a complete set of warp strands in alternate shedding. Then the knots and the weft threads are

Pile Yarn Table 1 Specifications of wool fibres Fibre properties

Values

Mean fibre diameter (lm)

37.65

Fibre diameter CV (%)

24.4

Mean fibre length (mm)

75.03

Fibre length CV (%)

28.5

Warp Yarn

Fig. 1 Persian knot

Table 2 Pile yarn specifications Sample no.

Nominal metric count

Nominal twist per inch

Actual metric count (CV %)

Actual twist per inch (CV %)

Twist direction

1.

3.90

3.5

3.64 (7.98)

3.63 (9.51)

S

2.

3.90

4.0

3.86 (8.29)

4.02 (9.61)

S

3.

3.90

4.5

3.96 (2.67)

4.62 (6.73)

S

Table 3 Warp, thin weft and thick weft specifications S. no.

Sample

No. of ply

Resultant cotton count (CV %)

Twist per inch (CV %)

Twist direction

1.

Warp

6

0.9 (0.32)

5.5 (2.56)

S

2.

Thin weft

2

1.6 (1.36)

5.1 (2.09)

S

3.

Thick weft

2

0.9 (0.86)

5.1 (1.59)

S

123


177

with coded levels and actual values of variables is given in Table 5.

beaten with a comb for securing the knots in place. The weaving process begins at the bottom of the loom and as the knots and weft yarns are added, the carpet moves upwards until it is finished. A four factor three level Box-Behnken experimental design was used for carpet sample preparation. The variables and their coded levels are given in Table 4. Twenty-seven (27) samples were prepared by using three levels of knot density, pile height, number of ply in pile yarn and pile yarn twist. The experimental design plan

Testing of Carpet Parameters Knot Density Number of knots of Persian handmade wool carpets was determined as per IS: 7877 (Part III)—1976 (Reaffirmed 1997) by using a rule capable of measuring to the nearest

Table 4 Coded and actual levels of Persian handmade carpet variables Variables code

Variables

Levels -1

x1

Knot density (inch-1)

x2

Pile height (mm)

x3 x4

0

?1

5

6

7

10

13

16

Number of ply (Pile Yarn)

2

3

4

Pile yarn twist (tpi)

3.5

4

4.5

Table 5 Box-Behnken experimental design plan Sample no.

Knot density (Knots/inch in each direction)

Pile height (mm)

Number of ply in pile yarn


1.

-1 (5)

-1 (10)

0 (3)

0 (4.0)

2.

-1 (5)

?1 (16)

0 (3)

0 (4.0)

3.

?1 (7)

-1 (10)

0 (3)

0 (4.0)

4.

?1 (7)

?1 (16)

0 (3)

0 (4.0)

5.

-1 (5)

0 (13)

-1 (2)

0 (4.0)

6.

-1 (5)

0 (13)

?1 (4)

0 (4.0)

7.

?1 (7)

0 (13)

-1 (2)

0 (4.0)

8.

?1 (7)

0 (13)

?1 (4)

0 (4.0)

9.

-1 (5)

0 (13)

0 (3)

-1 (3.5)

10.

-1 (5)

0 (13)

0 (3)

?1 (4.5)

11.

?1 (7)

0 (13)

0 (3)

-1 (3.5)

12.

?1 (7)

0 (13)

0 (3)

?1 (4.5)

13.

0 (6)

-1 (10)

-1 (2)

0 (4.0)

14.

0 (6)

-1 (10)

?1 (4)

0 (4.0)

15. 16.

0 (6) 0 (6)

?1 (16) ?1 (16)

-1 (2) ?1 (4)

0 (4.0) 0 (4.0)

17.

0 (6)

-1 (10)

0 (3)

-1 (3.5)

18.

0 (6)

-1 (10)

0 (3)

?1 (4.5)

19.

0 (6)

?1 (16)

0 (3)

-1 (3.5)

20.

0 (6)

?1 (16)

0 (3)

?1 (4.5)

21.

0 (6)

0 (13)

-1 (2)

-1 (3.5)

22.

0 (6)

0 (13)

-1 (2)

?1 (4.5)

23.

0 (6)

0 (13)

?1 (4)

-1 (3.5)

24.

0 (6)

0 (13)

?1 (4)

?1 (4.5)

25.

0 (6)

0 (13)

0 (3)

0 (4.0)

26.

0 (6)

0 (13)

0 (3)

0 (4.0)

27.

0 (6)

0 (13)

0 (3)

0 (4.0)

123

178

millimeter. This parameter was measured at the back of carpet in lengthwise and widthwise direction. Pile Height The pile height of carpets was measured as per IS: 7877 (Part IV)—1976 (Reaffirmed 1997) using flat metal gauges of known height. Abrasion Resistance The abrasion resistance of carpets was evaluated by rubbing the carpet samples against a standard abrading fabric for 5,000 number of rotations. The WIRA abrasion tester was used for conducting this test, based on the Schiefer principle of offset heads rotating in the same direction at the same speed. The rate of weight loss per 1,000 number of rotations was calculated as per IWS/TM—283: 2,000 standards. The images of two samples are shown in Figs. 2 and 3. The Figs. 2a and 3a show images of sample numbers 11 and 17 before abrasion testing. Figures 2b and 3b show the images of same samples after abrasion testing. Artificial Neural Network Modeling ANN are models which imitate the working principles of biological neurons. The goal of ANN is to generate a model that can exactly mimic the functional relationship between inputs and outputs using experimental data. ANN

Fig. 2 Images of sample number 11


has three operational layers. The input layer contains the input variables whereas the output later predicts the output variable. The hidden layer connects the input and output layers by synaptic weights. Each layer comprises computing elements, called nodes. Each node receives a signal from the nodes of the previous layer and these signals are multiplied synaptic weights. The weighted inputs are then summed up and passed through a transfer function which converts the cumulative weighted inputs within a fixed range of values. The output of the transfer function is then transmitted to the nodes of the next layer. Finally, the output is produced at the node(s) of the output layer. Transfer function in the hidden and output layers was logsigmoid, as shown in the following equation: y ¼ f ð xÞ ¼

1 ð1 þ ex Þ

ð1Þ

where y is the transformed output from the node; and x, the weighted sum to the node. Four handmade carpet parameters i.e. knot density, pile height, number of ply in pile yarn and pile yarn twists were chosen as the inputs to the ANN model. Here knot density in terms of knots per inch in each direction has been used as one of the input parameters. However, ANN model is capable to capture any form of functional relationship between inputs and output. Therefore the relationship between the knot density in number of knots per square inch, which is the quadratic term of knots per inch in one direction, and carpet abrasion resistance is expected to be captured by the ANN model. To use knot density outside the range of 5–7 knots per inch would necessitate changes in other specifications of handmade carpet such as count and tpi of warp, thick weft, thin weft as well as pile yarn counts, which are constant parameters in this research. The only output was carpet abrasion resistance. ANN model with only one hidden layer was used in this investigation. As the number of input parameters was four, 3, 4 and 5 numbers of nodes were tried in the hidden layer. Training was stopped after 200 iterations and performance of the ANN model was checked. From the available 27 data sets, 22 data sets were used for the ANN training purpose and the remaining 5 data sets were used for testing or validation of ANN models. Training of ANN was done using the back-propagation algorithm. The schematic representation of the ANN structure is presented in Fig. 4.

Results and Discussion Prediction Performance of ANN Model

Fig. 3 Images of sample number 17

123

The performance of the ANN model was evaluated using statistical parameters such as MAPE and correlation coefficient (R). The MAPE was calculated as follows:


179

MAPE ¼ Knot density

Pile height Abrasion resistance Number of ply

Pile yarn twist

Hidden nodes

Fig. 4 ANN model for abrasion resistance prediction

Table 6 Summary of prediction performance Statistical parameter

Training dataset

Testing dataset

Correlation coefficient (R)

0.99

0.82

Mean absolute percentage error

1.21

13.66

n yactual ypredicted 1X 100 n 1 yactual

ð2Þ

where n is the number of observations. Table 6 shows correlation coefficient (R) and MAPE between the actual and predicted values of for training and testing datasets. It is observed that the R value is higher and MAPE value is lower for training datasets (0.99 and 1.21, respectively) than testing datasets (0.82 and 13.66, respectively). It is also noted from Table 7 that only two training data sets (sample no. 16 and 21) are showing error higher than 5 %. Remaining 20 training data sets are showing very low prediction error. On the other hand, Table 8 reveals that most of the testing data (four out of five) are showing more than 10 % prediction error. This indicates that generalization has not been achieved properly during ANN training which can be attributed to lower number of training data sets (22 only) used in this study. Four input parameters were used in this work and the hidden layer had four nodes. Therefore, considering the bias weights, there were 20 (4 9 4 ? 4) weighs connecting

Table 7 Training datasets of Persian handmade wool carpets Sample no.

Knot density

Pile height (mm)

Number of ply (pile yarn)


Actual abrasion loss (mg)

Predicted abrasion loss (mg)

Error (%)

1.

5

10

3

4

37.33

37.03

0.80

2.

5

16

3

4

59.17

59.13

0.07

3.

7

16

3

4

56.20

56.20

0.00

4.

5

13

2

4

64.52

64.54

0.03

5.

5

13

4

4

68.16

69.00

1.23

6.

7

13

2

4

69.00

68.98

0.03

7. 8.

7 5

13 13

4 3

4 4.5

57.80 51.80

57.80 52.00

0.00 0.39

9.

7

13

3

4.5

56.00

56.00

0.00

10.

6

10

2

4

38.40

38.39

0.03

11.

6

10

4

4

43.20

43.24

0.09

12.

6

16

2

4

67.27

67.84

0.85

13.

6

10

3

3.5

33.70

34.72

3.03

14.

6

10

3

4.5

41.13

41.12

0.02

15.

6

16

3

3.5

56.40

56.39

0.02

16.

6

16

3

4.5

41.00

44.52

8.59

17.

6

13

2

3.5

61.10

61.04

0.10

18.

6

13

2

4.5

61.53

61.52

0.02

19.

6

13

4

3.5

63.60

63.63

0.05

20.

6

13

4

4.5

59.73

59.64

0.15

21.

6

13

3

4

49.07

44.52

9.27

22.

6

13

3

4

43.67

44.52

1.95

123

180


Table 8 Testing datasets of Persian handmade wool carpets Sample no.

Knot density

Pile height (mm)

Number of ply (pile yarn)


Actual carpet pile abrasion loss (mg)

Predicted carpet pile abrasion loss (mg)

Error (%)

1.

7

10

3

4

52.73

65.55

24.31

2.

5

13

3

3.5

48.27

42.56

11.83

3.

7

13

3

3.5

66.09

67.87

2.69

4.

6

16

4

4

56.40

66.54

17.98

5.

6

13

3

4

39.93

44.52

11.50

input and hidden layer. In addition to this, there were five weights connecting the hidden and output layers. Therefore, the number of weights to be optimized was quite high as compared to the training data sets available leading to poor prediction performance in the testing data sets. For comparison, the analysis of all 27 data sets was also done by using Response Surface Methodology (RSM). The coefficient of determination (R2) of this model was 0.913 which is better than ANN results in testing data sets but inferior to ANN results in training data sets.

Conclusions The abrasion resistance of Persian handmade wool carpets has been modeled with the help of ANN by using knot density, pile height, number of ply in pile yarn and pile yarn twist as inputs. The prediction performance was very good for the training datasets. The correlation coefficient was 0.99 and MAPE was 1.21 for the training data sets. However, the prediction performance was not good in the testing datasets which is indicated by relatively low correlation coefficient of 0.82 and relatively high means absolute percentage error of 13.66. This might have happened as limited data sets were used for the training of the ANN model. Therefore, more training data should be included in order to elicit good generalization performance from the ANN.

References 1. K.K. Goswami, Advances in carpet manufacture (Woodhead Publishing Limited, Cambridge, 2009), pp. 171–201 2. G.H. Crawshaw, Carpet manufacture (Wronz Developments, Christchurch, 2002), p. 158

123

3. F. Liu, A.P. Maher, J. Lappage, E.J. Wood, The Measurement of the tuft-withdrawal force in machine-made and hand-knotted carpet. J. Text. Inst. 93, 276 (2002) 4. M. Topalbekiroglu, A. Kireçci, C.L. Du¨lger, Design of a pileyarn manipulating mechanism. Proc. Inst. Mech. Eng. Part B 219, 539 (2005) 5. N.P. Gupta, D.B. Shakyawar, R.D. Sinha, Influence of fibre diameter and medullation on woollen spun yarns and their products. Indian J. Fibre Text. Res. 23, 32 (1998) 6. D.B. Shakyawar, N.P. Gupta, P.C. Patni, R.K. Arora, Computeraided statistical module for hand-knotted carpets. Indian J. Fibre Text. Res. 33(4), 405 (2008) 7. R.K. Arora, P.C. Patni, R.S. Dhillon, D.L. Bapna, Influence of tuft constitution on performance properties of hand-woven carpets. Indian J. Fibre Text. Res. 24, 111 (1999) 8. Schiefer HF and Cleveland RS (1934) Wear of carpets. U. S. Department of Commerce, Bureau of Standards, Research paper RP 640, Part of Bureau of Standards Journal of Research, vol. 12, p.155 ¨ nder, O ¨ .B. Berkalp, Effects of different structural parameters 9. E. O on carpet physical properties. Text. Res. J. 71, 549 (2001) 10. K.K. Noonan, The wear to backing of wool and other carpets in a turning trial. J. Text. Inst. 64, 528 (1973) 11. G.A. Carnaby, The mechanics of carpet wear. Text. Res. J. 51, 514 (1981) 12. R. Chatopadhyay, A. Guha, Artificial neural network: applications to textiles. Text. Prog. 35, 1 (2004) 13. A. Majumdar, Soft computing in fibrous materials engineering. Text. Prog. 43, 1 (2011) 14. R. Guruprasad, B.K. Behera, Soft computing in textiles. Indian J. Fibre Text. Res. 35, 75–84 (2010) 15. A. Majumdar, Soft computing in textile engineering (Woodhead Publishing Limited, Cambridge, 2011), p. 1 16. S. Sette, L. Boullart, P. Kiekens, Self-organizing neural nets: a new approach to quality in textiles. Text. Res. J. 65, 196 (1995) 17. S. Sette, L. Boullart, Fault detection and quality assessment in textiles by means of neural nets. Int. J. Cloth. Sci. Technol. 8, 73 (1996) 18. W.V. Steenlandt, D. Collet, S. Sette, P. Bernard, R. Luning, L. Tezer, K.H. Bohland, H.J. Schulz, Automatic assessment of carpet wear using image analysis and neural networks. Text. Res. J. 66, 555 (1996)