# Mechanics and Calculations of Textile Machinery

Mechanics and Calculations of Textile Machinery
by B. Varadarajan, C. B. Senthil Kumar, and N. Gokarneshan

Contents

Preface xiii
1.1 Introduction 3
1.2 Various methods of drive 3
1.3 Applications of belt and rope drives in textile industry 4
1.4 Transmissions of power by belts and ropes 4
1.5 Different methods to adjust the belt tensions 5
1.6 Types of belts 6
1.7 Rope drive 19
1.8 HP transmitted by ropes 21
1.9 Comparison of flat and V-belts 21
1.10 Variable speed drives 22
1.11 Centrifugal tension 24
1.12 Selection of flat belt 27
1.13 Selection of V-belt 29
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2.1 Introduction 43
2.2 Classification of gears 43
2.3 Important terminologies 43
2.4 Simple gears 47
2.5 Compound gears 47
2.6 Compound epicyclic gear train (sun and planet wheels) 48
2.7 Epicyclic gear train with bevel wheels 53
2.8 PIV gears 54
2.9 Worm and worm wheel 55
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3.1 Introduction 57
3.2 Design of cone pulleys for piano feed regulation of web in 57
3.3 Design of cone pulleys for speed frame 59
3.4 The profile of the cone drums 62
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4.1 Introduction 66
4.2 Methods of driving cams 66
4.3 Cam followers 67
4.4 Types of cams 68
4.5 Types of followers 69
4.6 Limits imposed on the shape of the cam working surface by 70
the choice of follower type
4.7 The cam profile for a given motion of the follower 70
4.8 The motion of the follower for a given cam profile 70
4.9 The equivalent mechanism for a cam and follower 70
4.10 Negative cams and positive cams 71
4.11 Lift of tappet 73
4.12 Eccentric movement of healds 77
4.13 Construction of twill tappet 77
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5.1 Introduction 81
5.2 Definitions 81
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6.1 Introduction 89
6.2 Deriving the expressions for potential and kinetic energy 90
6.3 Worked examples 91
6.4 Principle of moment 96
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7.1 Introduction 98
7.2 Coefficient of friction 98
7.3 Static friction 98
7.4 Dynamic or kinetic friction 99
7.5 Friction b/w two surfaces depends upon 99
7.6 Coil friction 99
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8.1 Introduction 112
8.2 Clutches 112
8.3 Jaw/toothed clutches 113
8.4 Friction clutches 114
8.5 Materials for friction lining 116
8.6 Cone clutches 116
8.7 Centrifugal clutches 117
8.8 Brakes 118
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9.1 Introduction 123
9.2 Sley displacement or motion 123
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10.1 Introduction 135
10.2 Calculation of depth of shed 135
10.3 Heald movement 137
10.4 Geometry of warp shed 138
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11.1 Introduction 145
11.2 Different types of drives 145
11.3 Drive without idler wheels 147
11.4 Movement of hooks, knives and warp threads in jacquard 149
shedding
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12.1 Introduction 152
12.2 Shuttle traverse 152
12.3 Control of shuttle during weaving 153
12.4 Shuttle flight and its timing 155
12.5 Weft insertion rate 157
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13.1 Introduction 159
13.2 Shuttle acceleration 159
13.3 Elastic properties of picking mechanism 162
13.4 Initial and average shuttle speed during traverse 164
13.5 Factors affecting initial shuttle speed 165
13.6 Shuttle checking 168
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14.1 Introduction 179
14.2 Basic definitions 179
14.3 Equations of motion 186
14.4 Vibratory motions 188
14.5 Impulse and impulsive force 196
14.6 Collision of bodies 196
14.7 Friction 197
14.8 Belt and gear drives 199
14.9 Gears 206
14.10 Some important quantitative definitions 218
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15.1 Introduction 220
15.2 Basic definitions 220
15.3 Various other formulae 221
15.4 Key definitions in mechanical properties of fibres 225
15.5 Formulae relating to pressley strength tester 227
15.6 Other formulae 228
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16.1 Introduction 229
16.2 Basic terminologies 229
16.3 Blow room 230
16.4 Carding 242
16.5 Draw frames 247
16.6 Sliver lap machine 252
16.7 Ribbon lap machine 255
16.8 Comber 257
16.9 Fly frame 260
16.10 Ring frame 264
16.11 Basic requirements for a standard spinning mill 269
16.12 Conversion cost per spindle shift 270
16.13 General causes for end breakages in ring spinning 270
16.14 Reasons for high end breakage rates 271
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17.1 Introduction 272
17.2 Miscellaneous formulae 272
17.3 Basic definitions 275
17.4 Yarn numbering systems 275
17.5 Universal system of yarn numbering 276
17.6 Practical significance of yarn count 276
17.7 Indirect system of yarn numbering 276
17.8 Direct system of yarn numbering 278
17.9 Conversion from one system to another in the in direct system 278
17.10 Conversion factors for the indirect system 279
17.11 Conversion factors for the direct system 280
17.12 Conversion from the indirect system to the direct system and vice versa 281
17.13 Calculations pertaining to ply or folded yarns in the indirect system 283
17.14 Conversion of worsted and rayon yarn count into cotton counts 287
17.15 Formula to predict spinning value from fibre properties 288
17.16 Miscellaneous formulae 289
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18.1 Introduction 292
18.2 Winding 292
18.3 Important formulae in pirn winding 294
18.4 Warping 297
18.5 Sizing 302
18.6 Drawing in 305
18.7 Silk reeling and throwing 306
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19.1 Introduction 311
19.2 Speed and pick calculations 311
19.3 Take up motion 311
19.4 Take up calculations 314
19.5 Production and related calculations 315
19.6 Production planning 318
19.7 Factors affecting the production of looms 320
19.8 Loom and weaving shed efficiency 320
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20.1 Introduction 321
20.2 Warp knitting 321
20.3 Weft knitting 321
20.4 Basic terminologies 322
20.5 Calculations pertaining to weft knitting 329
20.6 Fabric calculations 330
20.7 Calculations pertaining to warp knitting 332
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21.1 Introduction 334
21.2 Useful definitions 334
21.3 Miscellaneous formulae 335
21.4 Calculations for cloth 337
21.5 Other miscellaneous formulae 341
21.6 Warp calculations 341
21.7 Weft calculations 343
21.8 Quantity of material in a piece 344
21.9 Calculations related to cloth sett 344
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22.1 Basic statistics 347
22.2 Key definitions 347
22.3 Importance of SD 351
22.4 Practical importance of CV% 351
22.5 Average range method for calculating SD 351
22.6 Variation analysis 352
22.7 Process to process variation analysis 353
22.8 Sample size 354
22.9 Test of significant variance 355
22.10 Control chart 355
22.11 Methods of computing ‘average’ and ‘range’ charts 355