I STEADY STATE MECHANICS OF THE FALSE TWIST YARN TEXTURING PROCESS by RAYMOND Z. NAAR Ing. A.I.V., Ecole Superieure des Textiles de Verviers (1955) S.M., Massachusetts Institute of Technology (1958) SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF SCIENCE at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY FEBRUARY 1975 Signature of Author_ Department of Mechanica4 Engineering, December 5, 1974 Certified by - - -- -Nw, V II ThesiA Supervisor Accepted by Chairman, Department Committee on Graduate Students AfAR 3 1975 LOR 1ctS _ STEADY STATE MECHANICS OF THE FALSE TWIST YARN TEXTURING PROCESS by RAYMOND Z. NAAR Submitted to the Department of Mechanical Engineering on December 5, 1974 in partial fulfillment of the requirements for the Degree of Doctor of Science ABSTRACT In the false twist texturing process a moving threadline is subjected to temporary twist while heat is applied to part of the twist zone. The purpose of the process is to heat set the twist deformation so that after cooling and twist removal, the filaments will seek to return to their set helically crimped paths. This crimping action leads to bulk and/or stretch development such as is encountered in double knit suitings and/or stretch hosiery. During processing, the entire twisted threadline is under constant tension and torque, but is not at constant temperature, since part of it is intentionally heated to effect the setting process. The threadline is thus divided into three contiguous zones, all under the same stress field but each with different mechanical properties. The threadline tension is a result of filament strain which arises from the difference between the denier of the exiting yarn (imposed by the feed and exit roll velocities) and the equilibrium denier for the unrestrained yarn at the heater temperature, while the torque is due to the twist imparted by the spindle. In the portion of the thread- line before the heater, the torque is supported by components of the bending and torsional moments acting on the individual filaments, as well as the moment due to the tension of the filaments. At the heater, the bending and torsional moments become insignificant, and the torque is supported by tension components only; the twist, therefore, increases to maintain torque equilibrium. This uptwisting is assumed to occur with- out filament migration. As the properties of the filament change along the threadline due to temperature changes, so does the mechanism by which the yarn is deformed. The pertinent filament properties and yarn twisting mechanism have been analyzed. Values of tension and torque have been calculated for a wide range of temperatures and over- feeds and are in agreement with experiment. Thesis Supervisor: Professor Stanley Backer Title: Professor of Mechanical Engineering 3 ACKNOWLEDGEMENTS The author is indebted to the Phillips Petroleum Company and to the WESTVACO Corporation for their fellowship support in the early stages of his graduate program. Thanks are due also to Burlington Industries, Inc. and to the E. I. du Pont de Nemours & Company for fellowship and research assistantship support during the latter part of his doctoral research. With- out this generous industrial backing and encouragement the completion of this program would not have been realized. The author wishes to thank Professor S. Backer, Professor M. B. Bever, Professor E. Orowan and Professor I. V. Yannas who served on his Doctoral Committee. He greatly profited by con- tact and discussions with them on scientific and other topics. He also profited by discussions and collaboration with a number of classmates and office mates, among them A. Crugnola, D. Brookstein, A. Tayebi, S. Arghyros, B.Y. Lee, C. Brogna. He also greatly profited from contact, discussions and friendship with Drs. S. Batra and W. L. Yang, staff members of the Fibers and Polymers Laboratories. The support of Professor Yannas, who was always ready to help, listen and make suggestions is most gratefully acknowledged. Professor J. J. Thwaites was most helpful and gave unstintingly of his time. The writer greatly profited from discussions with a person of such critical and creative wit and is sincerely grateful to him. The author wishes to acknowledge the moral support he received from his colleagues in the Department of Chemical Engineering at Tufts University, Professors van Wormer, Botsaris and Sussman. He is also grateful to Professor Gyftopoulos who never ceased to encourage him towards completion. Among others, the writer wishes to thank his wife and his mother for their encouragement. Many thanks to Dorothy Eastman who typed many of the progress reports connected with the manuscript; to Joanna Larsen for typing the manuscript, and to Guddi Wassermann for her accurate drawings. 4 Finally, it would be unfitting to conclude without stressing the writer's deep indebtedness to Professor Stanley Backer, the Chairman of his Doctoral Committee, who helped, advised and encouraged the writer throughout his work. The writer considers himself lucky to have been associated with a person of Professor Backer's stature; he enjoyed and greatly profited from the experience of working under a man of uncompromising standards of quality and capability of seeing through complex situations to the simple physical essence of a problem. 5 TABLE OF CONTENTS Abstract Acknowledgements List of Tables 9 List of Figures 10 Chapter I. Introduction 12 Chapter II. Plan of Work 14 Chapter III. The False-Twist Process 15 (a) Description of the Process 15 (b) Twist Development in the Machine 18 (c) Controllable Machine Variables 20 (d) The False-Twisted Yarn 21 (e) Machine-Yarn Interaction 22 Chapter IV. Yarn Geometry 26 (a) Model for Yarn Geometry 26 (b) Yarn Contraction 30 Chapter V. Yarn Mechanics 31 (a) Classical Mechanics 31 1. Stress-Strain Curves of Yarns 31 2. Average Filament Strain 34 3. Yarn Torque 35 Bending Moment Contribution to Yarn Torque Fiber Torsional Moment Contribution to Yarn Torque Torque due to Tension (b) Tension and Torque for the Case of Equal Tension on all Filaments 40 1. Tension: Stress-Strain Curve 41 2. Torque 41 (c) Overtwisting 42 1. Stress-Strain Curve 42 6 2. Torque in Overtwisted Yarn 46 3. Overtwisting from Zero Twist 47 4. Average Filament Strain on Overtwisting 48 5. Average Filament Strain on Overtwisting in Various Zones of the Yarn 49 6. Torque on Overtwisting in Various Zones of the Yarn 50 Chapter VI. Experimental Apparatus and Materials 51 (a) Apparatus 51 1. Texturing Machine 51 2. Torque Measuring Apparatus 54 3. Tensile Testing Machine 54 (b) Material Properties 58 1. Stress-Strain Curve of Feed Yarns 59 2. Stress-Strain Curve of Yarns Processed through the False-Twister without Twist 60 3. Stress-Strain Curve of Freshly Textured Yarns 60 4. Stress-Strain Curve of Yarns at Elevated Temperatures--The Contractile Stress 69 Chapter VII. Experimental Results: Twist and Tension 76 (a) Introduction 76 (b) Experimental Procedure 78 (c) Experimental Results 82 1. Twist in Exit Zone 82 2. Twist in Entrance Zone 85 3. Tension 85 4. Denier 90 5. Analysis of the Data and Implications for the Process 90 (d) Experimental Results: The Effect of Twist 92 (e) Experimental Data: The Effect of Draw Ratio 92 (f) Qualitative Model for the Process 92 Chapter VIII. Calculation of Tension 100 (a) False-Twister Operating, but Spindle Stationary 100 1. Analysis 100 7 2. Experimental Verification 102 (b) Determination of the Tension during False- Twisting 104 1. Analysis 104 2. Experimental Verification 109 3. Discussion 110 4. Example of Tension Calculation 120 Chapter IX. Measurement and Calculation of Torques 126 (a) Introduction 126 (b) Torque in the Entrance Zone 127 1. Torque due to Filament Bending 127 2. Torque due to Filament Torsion 127 3. Torque due to Filament Tension 130 4. Comparison of Calculated and Experimental Data for the Case of the Entrance Zone 131 (c) Torque in the Heater Zone 133 1. Material Properties 133 2. Torque from Classical Yarn Mechanics and from Equal Filament Tension Contributions 137 3. Overtwisting 137 4. Discussion of the Data 140 (d) Example of Calculation of Torque 148 1. Entrance Zone 148 (i) Torque due to Tension (ii) Torque due to Bending (iii)Torque due to Torsion 2. Heater Zone 151 (i) Torque due to Tension (ii) Torque due to Bending (iii)Torque due to Tension-Overtwisting Chapter X. Discussions, Conclusions and Recommendations (a) Discussion 158 (b) Conclusions 161 (c) Recommendations 164 8 APPENDICES Appendix I. Additional Yarn Mechanics Derivations 161 (a) Stress-Strain and Torque-Strain Expressions for Yarns; Twist Varies with Extension 161 (b) Stress-Strain Curves of Yarns Assuming the Twist to Vary with Extension and the Fila- ments to Extend at Constant Volume 169 (c) Stress-Strain and Torque-Strain Curves of Yarns Assuming the Twist to Vary with Ex- tension and the Filaments to Extend at Constant Volume (Alternate Derivation) 171 (d) Overtwisting at Constant Radius 173 (e) Mechanics of Yarn Shrinkage due to Fiber Shrinkage 175 (f) Shearing Strains on Fiber due to Torsion and Bending 179 1. Differential Geometry of Yarns 179 2. Local Shear Strain on Fibers as they lie in the Yarn 182 3. Local Shear Strain on Untwisted, False- Twist Fibers 186 Appendix II. Literature Review 191 (a) Interaction between Machine Variables 191 (b) Heating and Thermal Plasticization 198 (c) Crimp Rigidity 215 (d) Effect of Machine Settings on Yarn Quality 230 References 240 Biographical Sketch 243 9 LIST OF TABLES TABLE I: YOUNGS MODULUS OF YARNS PROCESSED