ETH Library Vibration assisted guillotining of stacked thin material Doctoral Thesis Author(s): Deibel, Karl-Robert Publication date: 2014 Permanent link: https://doi.org/10.3929/ethz-a-010099027 Rights / license: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information, please consult the Terms of use. Diss. ETH No. 21667 Vibration Assisted Guillotining of Stacked Thin Material A thesis submitted to the ETH ZURICH to attain the degree of DOCTOR OF SCIENCES of ETH ZURICH (Dr. sc. ETH Zurich) presented by KARL-ROBERT DEIBEL MSc ETH, Zurich born March 2nd 1985 citizen of Germany accepted on the recommendation of Prof. Dr. Konrad Wegener, examiner Prof. Dr. Pavel Hora, co-examiner 2014 Acknowledgments I wish to acknowledge the many following people, who invaluably helped throughout my dissertation at ETH Zurich and at other times. Foremost, I graciously thank my supervisor, Prof. Dr. Konrad Wegener, head of IWF, forofferingmeapositionathisrenownedinstitute,givingmetheopportunitytofurthermy knowledgeandresearchinmanufacturingandproduction. Eventhroughchallengingtimes, his council provided much insight and inspiration in various fields. Our great collaboration since my undergraduate and graduate studies have brought fruitful results in research and in the classroom. My gracious thanks also go to Prof. Dr. Pavel Hora, head of IVP, for his provoking interest in my research, and for his continuous guidance and stimulating suggestions throughout my dissertation. Iamgratefulfortheintriguingworksofmystudents, whoallowedmetosupervisethem for their Bachelor Theses, Semester Projects, and Master Theses: Peter Bolt, Nils Furrer, Fabian Kaiser, Sarah La¨mmlein, Nino Lemann, Linus Meier, Simon Mu¨ller, Christian Raemy, Maria Schneider, Dennis Stone, Raffael W¨aspi, and Remo Zimmermann. Through their invaluable contributions, a profound base for my work and other fields were build. They represent the best mechanical engineers. Many thanks go to my colleagues at the IWF, who contributed to my work by either givingsupportiveadviceortechnicalhelp: Dr. SaschaWeikertforhisknowledgeonmodel- ing and dynamic systems, his insights in design, and the great time as office colleagues; Dr. Wolfgang Knapp for his support in matters of metrology; Dr. Nikolaus Ru¨ttimann for his extraordinary council in simulation, optimization, and material failure; Dr. Bastian Migge for discussion on optimization algorithms and proper research papers; Daniel Spescha for carrying out various experimental modal analyses. Special thanks go the Michael Gebhardt, doctoral student in the field of metrology, for his great companionship throughout the time at the IWF. The joined trip to NAMRC in Madison,Wisconsin,USA,andthefollowingdaysinTroy,Montana,whereanessentialpart of this work was created, were one of the greatest time during my research. Approximately 5640km were driven from Madison, Wisconsin to Troy, Montana to Las Vegas, Nevada to San Francisco, California, USA. Special thanks also go to Dr. Markus Ess for in-depth supportinnumericalsimulation, adviceinperformingresearch, andbeingagreatcolleague since our time as graduate students at ETH Zurich. Many thanks go to Konrad Rudin for the wonderful time as a fellow student during undergraduate, graduate, anddoctoralyears. Theadviceoncontrolsystemwasinvaluable. I would like to place special emphasize on the adventurous scuba diving activities. I owe thanks to Jens Boos, laboratory supervisor, for great help in creating measure- ment setups, data recording, high-speed video recording, and many other experimental works. I am grateful for the sedulous help of Samuel Staub, laboratory supervisor of IVP, in carrying out proper tensile tests, compression tests, and cutting tests. Thanks go to Sandro Wigger and Albert Weber for manufacturing the many tools and unique parts for my measurement setup. Many thanks also go to the Institute of Mechanical Systems for iii allowing me to use the Laser-Vibrometers. All the people at and related to IWF provided a comfortable working environment I wish to return to. I extend my thanks to Claus Dold, Marcel Henerichs, Michal Kuffa, Dr. Fredy Kuster, Umang Maradia, Raoul Roth, Nicolas Schaal, Josef Stirnimann, Stefan Thoma, Robert Transchel, Robert Voss, Christian Walter, Dr. Eduardo Weing¨artner, and Lukas Weiss for all the work and non-work related discussions over the years and the fun times. I appreciate the supportive insights of Dr. Anna Kubik throughout the beginning of my thesis. I graciously thank Prof. Dr. Thomas Ro¨sgen for the inspiring council and guidance at ETH Zurich. My thanks go to the Jiu-Jitsukas of Ju-Jitsu at ASVZ and their contribution to an exceptional atmosphere outside of work. My grateful thanks go to Moya Mu¨ller, who supported me through the ups and downs during writing and long hours at the office. I dedicate this work to my brothers and my parents, who have always encouraged me to do what it takes. Karl-R. Deibel, February 2014 iv To my brothers and parents Contents List of Symbols x Abstract xvii Kurzfassung xviii 1 Introduction 1 1.1 Ultrasonic Applications in Manufacturing . . . . . . . . . . . . . . . . . . . 1 1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 State of the Art and Scope 3 2.1 Definition of Cutting and Guillotining . . . . . . . . . . . . . . . . . . . . . 3 2.2 Cutting and Guillotining of stacked thin Material . . . . . . . . . . . . . . 4 2.2.1 Overall process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 Essential material parameters of paper . . . . . . . . . . . . . . . . 8 2.3 Modeling of Cutting and Guillotining . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 General Cutting Model . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.2 General Guillotining Friction Model . . . . . . . . . . . . . . . . . . 13 2.4 Fracture Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.5 Vibration Assisted Cutting and Guillotining . . . . . . . . . . . . . . . . . 17 2.5.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.5.2 Influences of Ultrasonics on Forces . . . . . . . . . . . . . . . . . . 19 2.5.3 Application of Vibration Assisted Cutting . . . . . . . . . . . . . . 20 2.6 Structural Optimization of Ultrasonic Devices . . . . . . . . . . . . . . . . 22 2.7 Scope of this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3 Cutting Knife Design with Optimization Methodology 24 3.1 Manual Multi-Step Design using FEM - Intuitive Design Process . . . . . . 24 3.2 Introduction to Structural Optimization . . . . . . . . . . . . . . . . . . . 24 3.2.1 Objective Function (Fitness Function) . . . . . . . . . . . . . . . . 26 3.2.2 Constraining Functions . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.3 Formulation the Optimization Problem . . . . . . . . . . . . . . . . 27 3.2.4 Eschenauer’s Three-Columns Concept . . . . . . . . . . . . . . . . . 27 3.2.5 Stochastic Search Methods . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.6 Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2.7 Simplex Search Method . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3 Structural Optimization of Ultrasonic Cutting Knives . . . . . . . . . . . . 31 3.3.1 Starting Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3.2 Parameterization of Device Shape (Genotype) . . . . . . . . . . . . 34 3.3.3 Material Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 36 vii Contents 3.3.4 Fitness Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3.5 Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 38 3.3.6 Genetic Algorithm and Simplex Search Settings . . . . . . . . . . . 39 3.3.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4 Models of Vibration Assisted Guillotining of Stacks 44 4.1 Observed Cutting Forces for Longitudinal Vibration Assisted Cutting . . . 44 4.1.1 Stack and Force Sensor Behavior . . . . . . . . . . . . . . . . . . . 44 4.1.2 Parallel Vertical Cutting with Longitudinal Vibration . . . . . . . . 45 4.2 Dynamic Model - Basic Physical Characterization . . . . . . . . . . . . . . 50 4.2.1 Cutting Knife Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.2 Representation of the Paper Stack . . . . . . . . . . . . . . . . . . . 52 4.2.3 Cutting of Single Paper Sheet . . . . . . . . . . . . . . . . . . . . . 53 4.2.4 Partial Motion of Stack at Detaching . . . . . . . . . . . . . . . . . 54 4.2.5 Material and Model Parameters . . . . . . . . . . . . . . . . . . . . 55 4.2.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.3 Parallel Vertical Cutting with Lateral Vibration . . . . . . . . . . . . . . . 66 5 Fracture Model of Slice-Push Cutting 75 5.1 State of Stress at the Cut Edge . . . . . . . . . . . . . . . . . . . . . . . . 75 5.2 Determination of the Stress Intensity Factors . . . . . . . . . . . . . . . . . 77 5.2.1 Symmetrical Cutting Edge . . . . . . . . . . . . . . . . . . . . . . . 77 5.2.2 Asymmetrical Cutting Edge . . . . . . . . . . . . . . . . . . . . . . 81 5.3 Cutting Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.3.1 Symmetrical Cutting Edge . . . . . . . . . . . . . . . . . . . . . . . 83 5.3.2 Asymmetrical Cutting Edge . . . . . . . . . . . . . . . . . . . . . . 87 6 Vibration Assisted Guillotining of Paper Stacks - Model Verification 89 6.1 Experimental Setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 6.2 Proof of Concept for Structural Optimized Longitudinal Cutting Knife . . 92 6.3 Dynamic Model Verification and Results . . . . . . . . . . . . . . . . . . . 93 6.3.1 Dynamic Model Settings . . . . . . . . . . . . . . . . . . . . . . . . 93 6.3.2 Dynamic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.3.3 Cutting Forces for Longitudinal Vibration Assisted Cutting . . . . . 95 6.4 Friction Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.5 Cutting Forces for Lateral Vibration Assisted Cutting . . . . . . . . . . . . 100 6.6 Verification of Fracture Mechanics Model for Lateral Slice-Push Cutting . . 105 6.6.1 Tensile Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.6.2 DENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.6.3 Cutting Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.6.4 Applying Model to Lateral Cutting of Stack . . . . . . . . . . . . . 112 7 Conclusion and Outlook 113 A Appendix 115 A.1 Alternative Expression of the Transfer Function for 2nd Order System . . . 115 A.2 Fourier Series of Pulse Wave . . . . . . . . . . . . . . . . . . . . . . . . . . 115 viii Contents A.3 UVA Cutting with Rigid Plastic and Ideal Elastic Plastic Material Model . 117 A.4 Calculation of Damping - graphically . . . . . . . . . . . . . . . . . . . . . 118 A.5 Flow diagram for the dynamic model . . . . . . . . . . . . . . . . . . . . . 119 A.6 Integration Steps for F . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Z A.7 Vertical Friction Reduction with respect to ξ . . . . . . . . . . . . . . . . . 122 A.8 J for Nonlinear Elastic Plastic Materials . . . . . . . . . . . . . . . . . . . 123 c A.9 DENT Testing of Paper (illustrating photos) . . . . . . . . . . . . . . . . . 125 A.10 Length of Axially Symmetric Devices . . . . . . . . . . . . . . . . . . . . . 125 A.11 Basic Equations for Dynamic Analysis using FEM . . . . . . . . . . . . . . 127 A.11.1 Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 A.11.2 Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 A.12 Additional Figures of the Optimization Results . . . . . . . . . . . . . . . 128 A.13 Reflection Electron Microscope (REM) Images of the Paper Sheets . . . . . 131 A.14 Sheets scaling off after cutting and self-locking cutting angle . . . . . . . . 131 A.15 Additional Photos of the Guillotining Test Stand . . . . . . . . . . . . . . 133 B List of Publications 134 C List of supervised Theses 135 Bibliography 136 ix