Contents
Preface………………………………………………………………………………………………………..xi
Acknowledgments………………………………………………………………………………….. xiii
About the Author………………………………………………………………………………………xv
1 Rotor Dynamics…………………………………………………………………………………..1
1.1 Introduction………………………………………………………………………………..1
1.2 Rotor Vibrations………………………………………………………………………….3
1.2.1 Rotor’s Critical Speed………………………………………………………3
1.2.2 Influence Coefficients………………………………………………………4
1.2.3 Equivalent Mass………………………………………………………………5
1.2.4 Critical Speed of Non-Conventional Rotor………………………7
1.2.5 Critical Speed of a Traditional Rotor………………………………..9
1.2.6 Amplitude of Vibration…………………………………………………. 11
1.2.7 Dynamic Reactions……………………………………………………….. 11
1.3 Nota Bene…………………………………………………………………………………. 11
1.3.1 Influence Coefficients……………………………………………………. 11
1.3.2 Critical Speeds………………………………………………………………. 11
1.3.3 Naked Spindle………………………………………………………………. 11
1.3.4 Inertia Force………………………………………………………………….. 12
1.3.5 Weightless Shaft……………………………………………………………. 12
1.3.6 Massive Spindle……………………………………………………………. 13
1.3.7 Weightless Shaft……………………………………………………………. 13
1.4 Active Example…………………………………………………………………………. 13
1.5 Summary Points……………………………………………………………………….. 17
Bibliography……………………………………………………………………………………….20
References………………………………………………………………………………………….. 21
2 Rotor Bearings……………………………………………………………………………………23
2.1 Introduction………………………………………………………………………………23
2.2 Ball Bearing……………………………………………………………………………….23
2.2.1 Rigidly Mounted Rotor………………………………………………….23
2.2.2 Elastic Mounting of Rotor………………………………………………25
2.3 Magnum Bearing………………………………………………………………………26
2.4 Cooling of the Rotor’s Ball Bearing……………………………………………27
2.5 Rotor Air Bearing………………………………………………………………………28
2.6 Twin Disc Bearings……………………………………………………………………29
2.7 Thrust Bearing………………………………………………………………………….. 32
2.8 Summary Points………………………………………………………………………..35
2.9 Related Information to Chapter 2………………………………………………36
2.10 Equivalent Dynamic Load Reaction of the Antifriction
Bearing 37
2.11 Equivalent Static Load Rating……………………………………………………38
Bibliography………………………………………………………………………………………. 39
References…………………………………………………………………………………………..40
3 Rotor Drives………………………………………………………………………………………. 41
3.1 Introduction……………………………………………………………………………… 41
3.2 Individual Rotor Drive (Patented)…………………………………………….. 41
3.3 Central Group Drive………………………………………………………………….44
3.4 Indirect Rotor Drive…………………………………………………………………..47
3.5 Summary Points……………………………………………………………………….. 52
Bibliography………………………………………………………………………………………..55
References…………………………………………………………………………………………..56
4 Rotor Power Requirements……………………………………………………………….. 57
4.1 Introduction……………………………………………………………………………… 57
4.2 Methods of Power Calculation………………………………………………….. 59
4.2.1 The Shirley Institute (1968)……………………………………………. 59
4.2.2 Moscow State University of Design & Technology, msta.ac……………….60
4.2.3 Zurich Method (SFIT)…………………………………………………….65
4.3 Summary Points………………………………………………………………………..65
Bibliography………………………………………………………………………………………..73
References…………………………………………………………………………………………..73
5 Power Distribution in the Rotor Spinning Machine………………………..75
5.1 Introduction………………………………………………………………………………75
5.2 Opening Mechanism…………………………………………………………………75
5.2.1 Technological Opening Power……………………………………….75
5.2.2 Combing Roller Opening……………………………………………… 76
5.3 Twisting Mechanism…………………………………………………………………77
5.3.1 Effect of Yarn on Rotor…………………………………………………..77
5.3.2 Rotor with Drive (Equation 4.15)…………………………………… 78
5.4 Rotor-Spun Yarn Withdrawal from the Doffing Tube……………….. 78
5.5 Yarn Winding……………………………………………………………………………79
5.6 Feed, Delivery, and Winding……………………………………………………..80
5.7 Ventilation…………………………………………………………………………………80
5.8 Control Systems………………………………………………………………………… 81
5.9 Specific Energy…………………………………………………………………………. 81
5.10 Summary Points………………………………………………………………………..83
Bibliography………………………………………………………………………………………..88
References…………………………………………………………………………………………..88
6 Air Flow Inside the Rotor Spin Box…………………………………………………..89
6.1 Introduction………………………………………………………………………………89
6.2 Suction Head of the Self-Pumping Rotor…………………………………..89
6.3 Air Flow Rate…………………………………………………………………………….90
6.3.1 Head Loss in Both Fiber and Yarn Tube…………………………90
6.3.2 Head Loss in the Rotor’s Hole……………………………………….. 91
6.4 Summary Points………………………………………………………………………..93
Bibliography………………………………………………………………………………………..97
References…………………………………………………………………………………………..97
7 Rotor-Spun Yarn’s Dynamic Tension………………………………………………..99
7.1 Introduction………………………………………………………………………………99
7.2 Theoretical Dynamic Yarn Tension Calculations……………………….99
7.2.1 First Technique………………………………………………………………99
7.2.2 Second Technique……………………………………………………….. 104
7.2.3 Additional Approaches……………………………………………….. 106
7.3 Relationship between [_/_ ] and VC ……………………………………….. 107
7.4 Dynamic Yarn’s Tension Measurement…………………………………… 108
7.5 Summary Points……………………………………………………………………… 109
Bibliography……………………………………………………………………………………… 114
References………………………………………………………………………………………… 114
8 Some Mathematics in Rotor Spinning……………………………………………. 115
8.1 Introduction……………………………………………………………………………. 115
8.2 Basic Equations for Rotor-Spun Yarn Production on Rotor
Spinning Machines 115
8.2.1 The Draft (Attenuation)……………………………………………….. 115
8.2.2 The Twist…………………………………………………………………….. 120
8.3 Summary Points……………………………………………………………………… 131
8.4 Back Doubling………………………………………………………………………… 139
8.4.1 Definitions………………………………………………………………….. 140
8.4.2 Back Doubling and Harmonic Waves in the Fed Sliver…..145
8.4 Summary Points……………………………………………………………………… 151
Bibliography …………………………………………………………………………………….. 158
References………………………………………………………………………………………… 158
Appendix I……………………………………………………………………………………………… 159
Appendix II: Constructional Aspects of Different Rotor Sets and
Their Resonances Curves………………………………………………… 179
Appendix III: An Experimental Determination of the Mass
Moments of Inertia of the Rotor Spinning
Machine’s Rotor……………………………………………………………… 183
Appendix IV: Dynamic Balancing of Rotors………………………………………… 191
Appendix V: Noise Level of the Rotor Spinning Machine…………………… 199
Appendix VI: Mechanical Vibrations…………………………………………………… 207
Appendix VII: Lubrication……………………………………………………………………. 217
Appendix VIII: Systems of Maintenance……………………………………………… 231
Appendix IX: Spike Energy…………………………………………………………………… 237
Appendix X: G1……………………………………………………………………………………… 245
Appendix X: G2………………………………………………………………………………………253
Appendix X: G3……………………………………………………………………………………… 259
Index……………………………………………………………………………………………………….263
Preface
There is a familiar statement made by both textile technologists and designers of textile machines: “The textile technological requirements are the basic resources for the textile machine designer.” For example, the rotor spinning machine has three technological functions: (1) the sliver opening; (2) twisting, that is, inserting a twist in the strand of fibers that collect on the rotor’s collecting surface during their withdrawal via the doffing tube; and (3) packaging, that is, winding the yarn on a spool at the top of the machine. Therefore, the designer has established three mechanical items: the opening device (feed roll and opening roll), the twisting mechanism (rotor), and the winding head. The running mechanical performance of these mechanisms will reflect the quality of the produced rotor-spun yarn, and maintaining the optimum mechanical conditions of the working element of the mechanism via various types of maintenance will be an additional factor for achieving a competitive yarn quality/price ratio in the global market. Knowledge of the previously mentioned terms and systems can be attained through the study of the mechanics—kinematic or dynamic—of the rotor spinning machine’s elements or mechanisms. This textbook will help students of engineering institutions, engineering graduates, and the textile industry. Also, this textbook will help in prolonging a spinning machine’s lifespan and improving the production of quality rotor-spun yarn.
The interaction between the machine and the processed material is responsible for 40% of product quality. We will produce a series of handbooks and textbooks on topics in the field of textile machine mechanics such as rotor dynamics (rotor spinning machines), ring-spindle vibrations (ring spinning machines), the vibrations of rotors, spindles and drafting systems, stresses in textile rotating masses, and so on. It must be highlighted that the student, engineer, and reader of such a series must have a good general background in mechanical engineering and mechanical vibrations especially.