Assignment

on

Cloth Geometry

Submitted to: Kazi Sirajul Islam

Lecturer,

Dept. of Textile Engineering

Southeast University

Submitted By: A.H.M. Shamsuddin(Muttaki)

ID: 2008200400019

Batch: 9th-1(Retake)

Date of Submission: 18.12.2011

Southeast University Dept. of Textile Engineering

Contents 1. Introduction

2. Cloth Geometry Models

1. Pierce’s Model

2. Modified Pierce’s Model

3. Kemp’s racetrack Model

4. Hearle’s Lenticular Model

3. Mathematical descriptions of each model

4. Limitations on Cloth geometry

Introduction The objectives of cloth geometry (math models for fabric) is to:

1. Prediction of the maximum sett (density) of fabric and fabric

dimensions;

2. Find out relationship between geometrical parameters (picks and

ends);

3. Prediction of mechanical properties by combining fabric and yarn

properties;

4. Understanding fabric performance (handle and surface effect).

Geometry Theories Approach 1. In conventional approaches, the general character of fabrics was

idealized into simple geometrical forms (circle, ellipse, rectangle)

2. They treated the micro-mechanics of fabrics on the basis of the unit-cell approach, ie fabrics are considered as a repeating network of identical unit cells in the form of crimp weaves and constant yarn cross-section in the woven structure.

3. By combining this kind of geometry with or without physical parameters (material), mathematical deductions could be obtained.

Four Fabric Models (geometry models)

By using circle, ellipse, rack-track approaches, four fabric geometrical models are formed

1. Pierce model 2. Modified model (ellipse) 3. Kemp’s race track model (rectangle & circle) 4. Hearle’s lenticular model

Mathematical Notation for each model

Pierce’s Model (Classical Model)

Pierce’s Model (1) In this model, a two-dimensional unit cell of fabric was built by superimposing linear and circular yarn segments to produce the desired shaped.

The yarns were assumed to be circular in cross-section and highly incompressible, but perfectly flexible so that each set of yarns had a uniform curvature imposed by the circular cross-sectional shape of interlacing yarns.

Geometrical parameters such as thread spacing (p), weave crimp, weave angle and fabric thickness (h) can be found.

Pierce’s Model (2) Results

Pick spacing (p1) and end spacing (p2), warp thickness (h1), weft thickness (h2) can be found from this model

Pierce’s Model Limitations

• In this model, a two-dimensional unit cell of fabric was built by superimposing linear and circular yarn segments to produce the desired shaped.

• The yarns were assumed to be circular in cross-section and highly incompressible, but perfectly flexible so that each set of yarns had a uniform curvature imposed by the circular cross-sectional shape of interlacing yarns.

• Geometrical parameters such as thread spacing (p), weave crimp, weave angle and fabric thickness (h) can be found.

Pierce’s Elliptic Model

• In more tightly woven fabrics, however, the inter-thread pressures setup during weaving cause considerable thread flattening normal to the plane of cloth. • Pierce recognized this and proposed an elliptic section theory as shown in Fig 3.2 • Because such model would be too complex and laborious in operation, he adopted an approximate treatment, which involved merely replacing the circular thread diameter in his circular-thread geometry with minor diameter as shown in Fig 3.2 • This modified model is good for reasonable open fabric but cannot be applied for very closed jammed fabric.

Kemp Model (Race-track section)

To overcome the jammed structure, Kemp proposed a racetrack section to modified cross-section shape.

The model consisted of a rectangle enclosed by two semi-circular ends and had the advantage that it allowed the relatively simple relations of circular-thread geometry, already worked out by Pierce, to be applied to a flatted threads.

A rectangle and semi-circular cross section of Kemp Model

Kemp Model Results

Hearle’s Model

Using energy method for calculations in fabric mechanics, a lenticular

geometry was proposed by Hearle as shown in Fig 3.5

Energy approach for Hearle’s model

Hearle’s Model Results

Limitations Cloth Geometry Models

1. Firstly, fabrics are complicated materials that do not conform even approximately to any of the ideal features suggested by these four fabric models.

2. Secondly, the measurement of geometrical parameters is not easy in practice.

3. Thirdly, the relationship between fabric mechanic (tensile, elongation, bending) to fabric geometry is not fully explored.

Conclusion:

Although the world market of Textile products continuously grows, it faces the structural readjustment followed by the change of global economic condition, raw material capacity and consumers’ needs and behavior. In addition, new expansionary manufacturers are emerging while the existing Textile producers are concerned by present consumers. This research focuses on the prediction of the future global Textile production by analyzing information about the Cloth Geometry.