MODELING AND CONTROL OF TRANSPORT BEHAVIOR OF MOVING WEBS THROUGH HEAT TRANSFER PROCESSES By YOUWEI LU Bachelor of Science in Mechanical Engineering Huazhong University of Science and Technology Wuhan, China 2007 Master of Science in Mechatronic Engineering Harbin Institute of Technology Harbin, China 2009 Submitted to the Faculty of the Graduate College of the Oklahoma State University, in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY July, 2015 MODELING AND CONTROL OF TRANSPORT BEHAVIOR OF MOVING WEBS THROUGH HEAT TRANSFER PROCESSES Dissertation Approved: Dr. Prabhakar R. Pagilla Dissertation Adviser Dr. Karl N. Reid Dr. Xiaoliang Jin Dr. Martin T. Hagan ii ACKNOWLEDGMENTS I wish to express my sincerest appreciation to my advisor, Dr. Prabhakar R. Pagilla for his valuable guidance, inspiration, intelligent supervision, and friendship during my doctoral program. I am forever indebt to him for his motivation and technical insights. I would like to extend my warmest thanks to my committee members: Dr. Karl N. Reid, Dr. Xiaoliang Jin, Dr. Martin T. Hagan, and former committee member Dr. Gary E. Young for their support and guidance in completion of this research. I thank the engineers from the Armstrong World Industries, Tim Gottlob and Jamie Lynch, and the engineer from the Pohang Iron and Steel Company in South Korea, Changwoon Jee, for their help in the collection of measured data. I would also like to thank my research colleagues at Oklahoma State Univer- sity: Aravind Seshadri, Carlo Branca, Pramod Raul, Mauro Cimino, Kadhim Jabbar, Shyam Konduri, Orlando Cobos, Ben Pacini, Muthappa Ponjanda-Madappa, Supraj Paleti, Austin Elledge, Theo Ramseyer, Maya Wulandari, Emilio Gabino, Andrew Burnap, Matt Hollen, and Rushd Julfiker, for their friendship and technical support. Finally and most deeply, I would like to express my appreciation to my parents, wife, parents-in-law, son, and family for their love and support throughout my life. This work was supported by the National Science Foundation under Grant 1246854. Acknowledgements reflect the views of the author and are not endorsed by committee members or Oklahoma State University. iii Name: YOUWEI LU Date of Degree: JULY, 2015 Title of Study: MODELING AND CONTROL OF TRANSPORT BEHAVIOR OF MOVING WEBS THROUGH HEAT TRANSFER PROCESSES Major Field: MECHANICAL AND AEROSPACE ENGINEERING Abstract: Heat transfer processes are widely employed in Roll-to-Roll (R2R) process machines to heat/cool moving webs. The general goal is to efficiently transport webs over heating/cooling rollers and ovens while achieving the specified web temperature at different locations of the R2R machine. One of the key controlled variables is web tension. When webs are heated or cooled during transport, the temperature distri- bution in the web causes changes in the mechanical and physical material properties and induces thermal strain. Because web strain and elastic modulus are functions of temperature distribution in the web, web tension resulting from mechanical strain is affected by heating/cooling of the web. A multi-layer heat transfer model for composite webs is developed. Based on this model, temperature distribution in moving webs is obtained for webs transported on a heat transfer roller and in web spans between two adjacent rollers. Model simu- lations are conducted for a section of a production R2R coating and fusion process line, and temperature data from these simulations are compared with measured data obtained at key locations within the process line. In addition to determining thermal strain in moving webs, the model can be employed to design heating/cooling equip- ment that is required to obtain a certain desired temperature at a specific location within the process line. The governing equations for web strain and tension are then obtained by considering the temperature effects. Based on the web tension governing equation that includes both mechanical and thermal effects, a nonlinear adaptive ten- sion control scheme is developed for control of tension in each tension zone of an R2R system. The control scheme is implemented on a modular R2R experimental platform containing two heat transfer rollers. Experimental results indicate that better tension regulation is obtained in the heated tension zone. Further, the temperature distri- bution model and the governing equations for web dynamics are utilized to design a tension observer for heating/cooling spans of a continuous strip annealing line where tension measurement is not available. iv TABLE OF CONTENTS Chapter Page 1 INTRODUCTION 1 1.1 HeatTransferProcess .......................... 2 1.2 WebTensionControl ........................... 5 1.3 Contributions ............................... 9 1.4 OrganizationoftheDissertation . 11 2 MODELING OF TEMPERATURE DISTRIBUTION IN MOVING WEBS 13 2.1 Multi-layerWebHeatTransferModel . 16 2.1.1 Web in a Span Between Consecutive Rollers (Convection+ConvectionCondition). 20 2.1.2 Web Wrapped on a Heat Transfer Roller (Conduction+ConvectionCondition) . 21 2.1.3 Web Between Two Nipped Rollers (Conduction+ConductionCondition) . 23 2.1.4 Model with Thermal Contact Resistance . 24 2.2 SpecialCasesofSingleLayerWebModel . 25 2.2.1 Temperature Distribution in a Single Layer Web Span Between TwoConsecutiveRollers . 26 v 2.2.2 Temperature Distribution in the Region of Single Layer Web WrappedonaHeatTransferRoller . 26 2.3 DeterminationofEigenvalues . 29 2.4 DeterminationofHeatTransferPeriod . 30 2.5 The Coefficient of Heat Transmission of a Web Span Surrounded by SteadyAir................................. 34 2.5.1 The Coefficient of Heat Transmission of a Web Span Surrounded byForcedAir ........................... 36 2.5.2 The Coefficient of Heat Transmission of a Web Heated by Ra- diation............................... 38 2.5.3 Viscosity and Thermal Conductivity of Air . 39 2.6 Summary ................................. 41 3 APPLICATIONS OF TEMPERATURE DISTRIBUTION MODEL 42 3.1 CoatingandFusionProcessLine . 42 3.1.1 HeatTransferRoller ....................... 43 3.1.2 EmbossingSection ........................ 46 3.2 Roll-to-Roll Machine for Atomic/Molecular Layer Deposition . 50 3.3 Summary ................................. 52 4 STRAIN AND TENSION GOVERNING EQUATIONS AND CON- TROL 55 4.1 Governing Equations for Web Strain and Tension Considering Tem- peratureEffects.............................. 56 4.1.1 Governing Equation for Web Strain and Tension . 57 4.1.2 Governing Equation for Roller Speed . 61 4.2 AdaptiveNonlinearControlDesign . 62 vi 4.3 Experiments on a Modular Roll-to-Roll Machine . 66 4.3.1 PureSpeedControlExperiments . 69 4.3.2 TensionControlExperiments . 71 4.4 Summary ................................. 74 5 TENSION OBSERVER DESIGN AND MODELING OF ROLL TO ROLL LAMINATION PROCESS 81 5.1 Tension Observer Design for Steel Strip Processing Line . .. 81 5.1.1 Analysis of Continuous Galvanizing/Annealing Lines Furnace 83 5.1.2 Tension Observer Design for Strip in a Single Span . 86 5.1.3 Tension Observer Design for Multiple Spans . 91 5.1.4 Model Simulations of Continuous Annealing Line . 94 5.2 Modeling and Control of Roll-to-Roll Lamination Process . 98 5.2.1 Lamination Process and Governing Equations for Single Layer Webs................................ 99 5.2.2 Mechanical and Physical Properties of Web Laminates . 100 5.2.3 GoverningEquationsforLaminatedWeb . 101 5.2.4 Control Algorithm of Lamination Process . 104 5.2.5 Model Simulations off Lamination Process . 106 5.3 Summary ................................. 107 6 SUMMARY AND FUTURE WORK 110 BIBLIOGRAPHY 113 vii LIST OF TABLES Table Page 2.1 Criterion of eigenfunction cross zeros point between β and β + ∆β . 30 2.2 Coefficients of the collision integral equation (2.55) . 40 2.3 Coefficients and exponents of the residual air viscosity equation (2.56) 40 2.4 Coefficients and exponents of the residual air thermal conductivity equation(2.59) .............................. 41 3.1 Properties of each layer of web and oil drum outer shell . 43 3.2 Parameters of a heat transfer section of the embossing line . ... 49 3.3 PropertiesofeachlayerinR2RALD/MLDmachine. 52 4.1 Diameters and wrap angles of driven rollers . 69 5.1 Simulationparameters .......................... 96 5.2 Propertiesandparametersofwebs . 106 viii LIST OF FIGURES Figure Page 1.1 Web free span and web wrapped on a heat transfer roller . 4 1.2 ControlstrategywithtwoPIcontrollers . 9 2.1 Webspanandwebwrappedonaheattransferroller . 14 2.2 Pictureofaheattransferroller . 15 2.3 Multi-layerwebsketch .......................... 16 2.4 Convectiveheattransferinwebspan . 20 2.5 Web wrapped and transported on a heated/chilled roller . 22 2.6 Web nipped between two heat transfer rollers . 23 2.7 Web and roller surface contact: (a) Imperfect contact model, (b) Equiv- alentmodel ................................ 25 2γkλ 2.8 Graphs of tan(λl) and . The Abscissas of intersection are k2λ2 γ2 − the solutions of λ ............................. 27 β kr κw 2.9 Graphs of tan lr and G(β). The abscissas of intersec- √κ k κ r w r r tion are the solutions of β, and G(β) is defined in (2.35) . 28 2.10 Sketch of intersections of eigenfunction f(β) = 0 and the β axis . 30 2.11 Graphs of τ(x, t), td is the abscissa of intersection of τ = t and τ = g(x, t) ................................... 32 2.12 Illustration of numerical method to determine τ ............ 33 2.13 Webspansurroundedinsteadyair . 34 2.14 Configurationofjetimpingement . 36 ix 2.15 Slotjetarrayconfiguration. 37 3.1 Schematic of a coating and fusion process