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Linkping Studies in Science and Technology Dissertation No. 1009 Contributions to the Modeling and Simulation of Mechanical Systems with Detailed Contact Analyses by Iakov Nakhimovski Department of Computer and Information Science Linkpings universitet SE-581 83 Linkping, Sweden Linkping 2006 AbstractThe motivation for this thesis was the need for further development of multibodydynamics simulation packages focused on detailed contact analysis. The three partsof the thesis make contributions in three different directions:Part I summarizes the equations, algorithms and design decisions necessary fordynamics simulation of exible bodies with moving contacts. The assumed gen-eral shape function approach is presented. It is expected to be computationally lessexpensive than FEM approaches and easier to use than other reduction techniques.Additionally, the described technique enables studies of the residual stress releaseduring grinding of exible bodies. The proposed set of mode shapes was also suc-cessfully applied for modeling of heat ow.The overall software system design for a exible multibody simulation systemSKF BEAST (Bearing Simulation Tool) is presented and the specics of the exiblemodeling are specially addressed.An industrial application example is described. It presents results from a casewhere the developed system is used for simulation of exible ring grinding withmaterial removal.Part II is motivated by the need to reduce the computation time. The availabilityof the new cost-efcient multiprocessor computers triggered the development of thepresented hybrid parallelization framework.The framework includes a multilevel scheduler implementing work-stealing strat-egy and two feedback based loop schedulers. The framework is designed to be easilyportable and can be implemented without any system level coding or compiler mod-ications.Part III is motivated by the need for inter-operation with other simulation tools.A co-simulation framework based on the Transmission Line Modeling (TLM) tech-nology was developed. The main contribution here is the framework design. Thisincludes a communication protocol specially developed to support coupling of vari-able time step differential equations solvers.The framework enables integration of several different simulation componentsinto a single time-domain simulation with minimal effort from the simulationcomponents developers. The framework was successfully used for connectingMSC.ADAMS and SKF BEAST simulation models. Some of the test runs arepresented in the text.Throughout the thesis the approach was to present a practitioners road-map. Thedetailed description of the theoretical results relevant for a real software implemen-tation is put in focus. The software design decisions are discussed and the results ofreal industrial simulations are presented.iiiAcknowledgmentsMany people contributed and rendered possible the work presented in this thesis.First, I would like to thank my supervisor Dag Fritzson at SKF who suggestedmany of the ideas realized in this work, encouraged me to tackle the problems duringthe whole period of studies, and gave many important comments on the text of thethesis.Many thanks to the co-authors of the papers that were presented over the yearsof studies: Alexander Siemers, Lars-Erik Stacke, Mikael Holgerson, Jonas St ahl,Stathis Ioannides and Dag Fritzson.I also want to express my gratitude to all the other members of the Analytics teamat SKF and my colleagues at PELAB, Link oping University who have created a greatworking atmosphere and provided a lot of useful feedback.Special thanks to Bodil Mattsson-Kihlstr om for handling all the administrativework caused by my frequent travels to G oteborg. Furthermore, I am grateful to allthe administrative staff at IDA for providing the necessary support.I would like to thank SKF, ECSEL (Excellence Center for Computer Science andSystems Engineering in Link oping), The Knowledge Foundation (KK-stiftelsen),and The Foundation for Strategic Research (SSF/ProViking) for the nancial sup-port.Finally, I would like to thank my wife Olga, my parents in Russia, and my rela-tives and friends in different countries around the world for constant moral supportand belief in my ability to do the work and write this thesis.Iakov NakhimovskiG oteborg, January 2006iiiivContents1 Thesis Overview 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Work not Published in Papers . . . . . . . . . . . . . . . . . . . . . 51.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.6 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Introduction Bibliography 8Appendix: The BEAST Toolbox 9I Modeling and Simulation of Flexible Bodies for DetailedContact Analysis in Multibody Systems 13Notation 142 Introduction 182.1 Simulation of Flexible Mechanical Components . . . . . . . . . . . 182.2 Model Requirements . . . . . . . . . . . . . . . . . . . . . . . . . 192.3 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.4 Part I Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Key Equations in Flexible Body Dynamics 243.1 Flexible Body Motion and Shape Functions . . . . . . . . . . . . . 253.2 Rotation of a Material Particle due to Deformation . . . . . . . . . 263.3 Using Intermediate Coordinate System . . . . . . . . . . . . . . . . 263.4 Generalized Newton-Euler Equation . . . . . . . . . . . . . . . . . 283.5 Mass Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.6 Quadratic Velocity Vector . . . . . . . . . . . . . . . . . . . . . . . 313.7 Generalized Forces . . . . . . . . . . . . . . . . . . . . . . . . . . 323.7.1 Generalized Elastic Forces . . . . . . . . . . . . . . . . . . 323.7.2 Generalized Viscosity Forces . . . . . . . . . . . . . . . . . 34v3.7.3 Generalized External Forces . . . . . . . . . . . . . . . . . 363.7.4 External Point Force . . . . . . . . . . . . . . . . . . . . . 373.7.5 External Point Moment . . . . . . . . . . . . . . . . . . . . 383.7.6 External Volume Load . . . . . . . . . . . . . . . . . . . . 383.7.7 Generalized Forces from the Internal Stress Release duringGrinding . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.7.8 An Interpolation Method for Forces with Discontinuities . . 413.8 Calculating Jacobian . . . . . . . . . . . . . . . . . . . . . . . . . 434 Static, Eigenmode and Quasi-static Single Body Analysis 484.1 Static Loading Cases . . . . . . . . . . . . . . . . . . . . . . . . . 494.2 Eigenmode Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 494.3 Quasi-static Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 505 Generation of Mode Shapes from Finite Element Analysis 526 Flexible Body Exchange Formats for Systems Engineering 546.1 Different Formats for Mode Data . . . . . . . . . . . . . . . . . . . 546.2 Generating MNF . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.3 BEAST-MNF Interface . . . . . . . . . . . . . . . . . . . . . . . . 566.4 Model Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.5 Simulation example . . . . . . . . . . . . . . . . . . . . . . . . . . 576.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597 General Shape Functions 607.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607.2 Choice of Shape Functions . . . . . . . . . . . . . . . . . . . . . . 617.3 Special Shape Functions for Solid Bodies in Cylindrical Coordinates 627.4 Volume Integration . . . . . . . . . . . . . . . . . . . . . . . . . . 637.5 Reducing the Number of Flexible States . . . . . . . . . . . . . . . 658 Mean-Axis Conditions on the Reference Frame 688.1 Separation of Elastic and Rig