A STUDY ON INTERACTIONS OF THIN FLEXIBLE MEDIA WITH GROOVED ROLLERS A Dissertation Presented By Tuğçe Kaşıkcı to The Department of Mechanical and Industrial Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the field of Mechanical Engineering Northeastern University Boston, Massachusetts August 2016 I ABSTRACT Tape to grooved roller interaction is modelled and analyzed by means of numerical and experimental methods. In general, air enters the tape-roller interface as the tape is transported between the reels. This phenomenon, known as air entrainment, causes air lubrication under the tape, and it could eventually lead to reduction of rigid body contact pressure. However, traction in the tape roller interface is critical for the tape to stay on a prescribed path during transport. Contact mechanics in wrapping a thin-shell (tape/web) around a grooved cylindrical surface (roller) under tension is investigated in the slow and operational tape transport speed limits. In the slow tape transport speed limit, the effects of air lubrication in the tape-roller interface can be neglected. In this case the equations of equilibrium lead to analytical solutions, however; the problem is nonlinear due to the unknown nature of the contact area and location. It is shown that in case of no air entrainment, three distinct contact cases describe the interaction of the tape/web with respect to the lands. Non-dimensional analysis shows that contact state depends on the width of the groove and the land, and the non-dimensional belt-wrap pressure only modulates the amplitude of the deflected profile. In the operational tape transport speed limit, the tape deflection, air and contact pressures are coupled to one another. The tape is modeled as a thin, translating, tensioned shell. The effects of air lubrication are modeled by using the Reynolds lubrication equation. The coupled problem, generally known as the foil bearing problem, is solved numerically by using a transient coupling algorithm. The traction characteristics of the tape-roller interface are investigated as functions of tape tension, tape transport speed and groove geometry. It was shown that air lubrication effects reduce the contact force; however the underlying effects of tape mechanics are not entirely eliminated. Unlike the classical foil bearing solution, bending of the tape into the grooves dominates the mechanics of the coupled air-lubrication/tape-deflection problem. Tape clearance over the grooved rollers is measured experimentally by using a modified, commercially available tape transport system. A novel method to measure this clearance over rollers with helical grooves is described. Experiments show that tape-to-roller clearance increases with increasing tension and tape transport velocity. Analysis shows that the air entrainment is responsible for the velocity dependence, whereas the tension dependence is due to II the tape bending into the grooves. Thus, it has been shown that the tape deflection in the lateral direction is critical for thin tapes, in order to accurately assess the contact over grooved rollers. This work contributes to our understanding of traction mechanics of thin webs over grooved rollers, which has been understudied in the past, and helps in selecting design parameters for improved traction. III ACKNOWLEDGMENTS Here I would like to pay my gratitude to all people who have touched my life with their unlimited support. First and foremost, I would like to thank my adviser, Professor Sinan Müftü for his invaluable help, guidance and patience throughout this study. Without his valuable mentoring, ideas, this work would never be possible. His guidance gave me enthusiasm to work more diligently every day. I would like to thank members of my committee, Professors Hamid Nayeb-Hashemi and Carol Livermore, for their insightful comments and valuable feedback and advice on my research. I would like to dedicate this study in the memory of late Professor Yaman Yener for his unconditional support and mentorship. He was like a second ‘father’ to me, as he was to many other students. I miss him every day. In addition, I would like to thank Ms. Demet Yener, Ms. Zeynep Yener for their unconditional support and I would like to thank friends of the Yaman Yener Memorial Fund for their financial support during my studies. I also would like to thank my lab members, and especially Dr. Hankang Yang, for his valuable comments, support, and friendship throughout these years. Moreover, I would like to thank Mr. Soroush Irandoust, Mr. Qiyong Chen, Ms. Ara Kim, Ms. Tinting Zhu and last but not least Mr. Runyang Zhang to carry on this research onto the next step. I gratefully acknowledge the financial support provided in support of my work by the International Storage Industry Consortium and their sponsor companies and the Oracle Corporation; and also the summer internship at Quantum Research. I am grateful for the technical assistance I received from many colleagues at Quantum and Oracle. Especially, I would like to thank Drs. Turguy Goker, Ming Chih-Weng, and Ash Nayak at Quantum Research, Dr. Mark Watson, Clark Jenson, Peter Coburn, and Kathryn Barnes of Oracle Corporation, and Drs. Mark Lantz and Johan Engelen at IBM Zurich, for the research motivation throughout my studies. IV Moreover, I would like to thank my parents, Ayla and Bülent Kaşıkcı for their unconditional love and support during my studies. They always supported and encouraged me to dream big, and achieve even bigger. I would like to thank my friends especially to Tugbay Sahin, Aysun Demircan, Selen Uguroglu, Gonca Aydogdu, Engin Pehlivanoglu, Levent Akkok, Oguz Barin, Emre Guler, Drs. Melda Ulusoy, Alphan Ulusoy, Baran Yıldırım, Onur Arslan and Ozgur Keles for their insightful discussions and support in every part of my life. Last but not least, I would like to thank Mr. Stephen Lafaille, for his unconditional support in all aspects of life from start to finish of this study. If he had been the only person left in my life, I could still achieve a lot of things. The roots of education are bitter, but the fruit is sweet -Aristotle V CONTENTS ABSTRACT ..................................................................................................................................... I ACKNOWLEDGMENTS ............................................................................................................ III CONTENTS ................................................................................................................................... V LIST OF FIGURES ................................................................................................................... VIII LIST OF TABLES ....................................................................................................................... XII 1 Introduction ........................................................................................................................... 13 1.1 Historical Perspective on Data/Information Storage on Flexible Media ....................... 17 1.2 Mechanics of Tape Moving in Contact with a Roller .................................................... 20 1.3 Foil Bearing Literature Survey ....................................................................................... 23 1.4 Traction Literature Survey ............................................................................................. 25 1.5 Traction in Grooved Rollers ........................................................................................... 27 1.6 Research Objective ......................................................................................................... 31 2 Governing Equations ............................................................................................................ 33 2.1 Equation of the Motion of the Tape ............................................................................... 33 2.1.1 Assumptions ............................................................................................................ 33 2.1.2 Force and Moment Resultants ................................................................................ 34 2.2 Boundary Conditions and Initial Conditions .................................................................. 41 2.3 Tape Geometry ............................................................................................................... 43 2.4 Equation of Air Lubrication ........................................................................................... 44 VI 2.5 Contact Models .............................................................................................................. 49 2.6 Tape-Guide Spacing ....................................................................................................... 52 3 Wrap Pressure ....................................................................................................................... 53 3.1 Introduction .................................................................................................................... 53 3.2 Boundary Conditions...................................................................................................... 56 3.3 Solution of Tape Pressure for Contact States ................................................................. 60 3.4 Summary and Conclusion .............................................................................................. 68 4 Mechanics of Tape Grooved Roller Interface