Master's Thesis in Mechanical Engineering Experimental Dynamic Substructuring of an Ampair 600 Wind Turbine Hub together with Two Blades - A Study of the Transmission Simulator Method Authors: Magdalena Cwenarkiewicz Tim Johansson Supervisor, LNU: Andreas Linderholt Examiner, LNU: Andreas Linderholt Course Code: 4MT31E Semester: Spring 2016, 15 credits Linnaeus University, Faculty of Technology Abstract In this work, the feasibility to perform substructuring technique with experimental data is demonstrated. This investigation examines two structures with different additional mass-loads, i.e. transmission simulators (TSs). The two structures are a single blade and the hub together with two blades from an Ampair 600 wind turbine. Simulation data from finite element models of the TSs are numerically decoupled from each of the two structures. The resulting two structures are coupled to each other. The calculations are made exclusively in the frequency domain. A comparison between the predicted behavior from this assembled structure and measurements on the full hub with all three blades is carried out. The result is discouraging for the implemented method. It shows major problems, even though the measurements were performed in a laboratory environment. Key words: Experimental dynamics, FBS Frequency Based Substructuring, FRF Frequency Response Function, Coupling, Decoupling, Transmission simulator method, Ampair 600, A600 I Acknowledgements During the spring of 2016 we had the opportunity to explore the world of substructuring. The journey has taught us to respect the errors that may arise when theory is applied in practice. We have also learned to be doubtful, rather than making improvident assumptions. Besides all the education, we have once more experienced how rapidly the time passes. We would like to reflect on the people who supported and helped us throughout the period of this thesis. First of all, we would like to express our deepest sense of gratitude to our supervisor Andreas Linderholt, Head of the Mechanical Engineering Department at Linnaeus University. His expertise, guidance and continuous advice have contributed considerably to our work. This thesis would not exist without his ideas. We would like to express the profound gratitude to Mats Almström, technician at the Mechanical Department, Linnaeus University, who has contributed with technical support. We are indebted for the precision of the masses he manufactured, and the work time he invested in our project. We would also like to thank Yousheng Chen, doctoral student at the Mechanical Department, Linnaeus University, for her support and encouragement. We appreciate her valuable help with the laboratory proceedings and openness to share her special command of measurement data analysis. Very special thanks go to our colleagues and friends Judas Tadeu dos Santos and Nidaa Al-Mahdi, who worked in parallel with a similar thesis topic. The mutual exchange of knowledge and all the discussions we had were essential for both of our theses. Magdalena Cwenarkiewicz and Tim Johansson Växjö 15th of June 2016 II Contents 1. INTRODUCTION ............................................................................................ 1 1.1 BACKGROUND....................................................................................................................... 2 1.2 PURPOSE ............................................................................................................................... 3 1.3 AIM ....................................................................................................................................... 3 1.4 HYPOTHESIS AND LIMITATIONS ............................................................................................ 3 1.5 RELIABILITY, VALIDITY AND OBJECTIVITY .......................................................................... 4 1.6 NOMENCLATURE ................................................................................................................... 5 2. THEORY AND LITERATURE REVIEW ................................................... 7 2.1 AMPAIR 600 .......................................................................................................................... 9 2.2 ERRORS IN EXPERIMENTAL MEASUREMENTS ..................................................................... 10 2.3 COUPLING ........................................................................................................................... 12 2.3.1 Physical model - Coupling ......................................................................................... 12 2.3.2 Primal Assembly – Physical Domain ......................................................................... 13 2.3.3 Dual Assembly – Physical Domain ............................................................................ 14 2.4 COUPLING –FREQUENCY DOMAIN ...................................................................................... 14 2.4.1 Primal Assembly – Frequency Domain ...................................................................... 15 2.4.2 Dual Assembly – Frequency Domain ......................................................................... 15 2.4.3 Experimental Formulation of the Dual Assembly ...................................................... 16 2.5 REDUCTION AND COMPONENT MODE SYNTHESIS ............................................................... 16 2.5.1 Primal Formulation - Reduction ................................................................................ 18 2.5.2 Dual Formulation - Reduction ................................................................................... 18 2.6 A SIMPLE EXAMPLE OF SUBSTRUCTURING ......................................................................... 19 2.7 TRANSMISSION SIMULATOR ................................................................................................ 21 3. METHOD ....................................................................................................... 22 3.1 PROCEDURE OVERVIEW ...................................................................................................... 22 3.2 THE SUBSTRUCTURING CONFIGURATIONS .......................................................................... 25 3.3 EXPERIMENTAL SETUPS ...................................................................................................... 26 3.3.1 Accelerometers (Sensors) ........................................................................................... 29 3.3.2 Transmission Simulators (Masses)............................................................................. 29 3.3.3 Coordinate System and Numbering of Nodes and Blades .......................................... 31 3.4 SIMULATIONS IN SIMXPERT AND MSC NASTRAN ........................................................... 33 3.5 CALCULATIONS IN MATLAB ............................................................................................. 37 3.5.1 Overview .................................................................................................................... 38 3.5.2 Data Extraction .......................................................................................................... 38 3.5.3 Accelerances for Excitations in the Coupling Point................................................... 39 3.5.4 Accelerances for Excitations on the Blades ............................................................... 41 3.5.5 Decoupling of the Transmission Simulator from the 2-Bladed Hub .......................... 41 3.5.6 Coupling of the 2-Bladed Hub with the Single Blade ................................................. 42 4. RESULTS AND ANALYSIS ........................................................................ 43 4.1 MEASUREMENTS OF THE 3-BLADED HUB ........................................................................... 43 4.2 MEASUREMENTS OF THE 2-BLADED HUB WITH A TRANSMISSION SIMULATOR MASS ......... 49 4.3 SIMULATIONS OF TRANSMISSION SIMULATORS .................................................................. 50 4.4 COUPLING OF DATA FROM THE 2-BLADED HUB AND THE SINGLE BLADE .......................... 52 5. DISCUSSION ................................................................................................. 55 6. CONCLUSION .............................................................................................. 57 7. REFERENCES ............................................................................................... 58 8. APPENDICES ................................................................................................ 61 III IV 1. Introduction Dynamic substructuring constitutes a significant aspect of the structural dynamics research area. Experimental works depend both on the possibility to measure required properties and on the methods of data analysis. In the age of computers, numerical methods have been empowered. Moreover, digitalized test equipment allows implementation of ameliorated and advanced measurements. The substructuring techniques originate from the domain decomposition which is the field of study well-developed by Schwarz [1, pp. 133-134]. The work provided a foundation for new discretization and approximation techniques, such as the Rayleigh-Ritz model, the boundary element approach and the finite element method (FEM). Exploring different computation techniques, FEM emerged to be the most favorable for effective calculations of the decomposed domains. The next milestones for the substructuring techniques were