Kinematics and Dynamics of Multibody Systems with Imperfect Joints

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Kinematics and Dynamics of Multibody Systems with Imperfect Joints
Lecture Notes in Applied and Computational Mechanics Edited by f. Pfeifer and P. Riggers Furthervolumesofthisseriesfoundonourhomepagespringer.com Vol. 34: Flores P: Ambrosio J. Pimenta Claro, J C Vol. 21: Hinkelmann R Lankarani hamid M Efficient Numerical Methods and Information-Processing Kinematics and Dynamics of Multibody Systems Techniques for Modeling Hydro- and Environmental with Imperfect Joints: Models and Case Studies 186p.2008[978-3-540-743590 305p.2005[978-3-540-24146-1 Vol. 33: Nieshony, A. Macha, E Vol. 20: Zohdi Tl, Riggers P. Spectral Method in Multiaxial Random Fatigue Introduction to Computational Micromechanics 46p.2007[978-3-540-73822-0] 196p.2005[978-3-540-22820-2 Vol. 32: Bardzokas, D L. Filshtinsky, M L Filshtinsky, LA(Eds) Vol. 19: McCallen R, Browand F, Ross J. 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Civil Engineering Deformation and failure in metallic materials 400p.2005978-3-540-25567-3] 409p.2003[978-3540-008484] Vol. 22: Chang Ch Vol. 9: Skrzypek J, Ganczarski A W.(Eds Mechanics of elastic structures with inclined members. Anisotropic Behaviour of Damaged Materials Analysis of Vibration, Buckling and Bending of X-Braced 366p.2003978-3-540-00437-0 Frames and Conical shells 90p.2004[978-3540-243847] Vol. 8: Kowalski. SJ Thermomechanics of Drying Processe 365p.20039783-540-004127] Kinematics and dynamics of multibody systems with Imperfect Joints Models and case studies Paulo Flores Jorge Ambrosio J C Pimenta Claro Hamid m. Lankarani With 127 Figures and 14 Tables S pringer P F J. Ambrosio Department of Mechanical Engineering Department of Mechanical Engineering University of minho Instituto Superior tecnico Campus azure Technical University of Lisbon 4800-058 Guimaraes Av. Rovisco pais 1 Portugal 1049-001 Lisboa Portugal J.C. Pimenta Claro Hamid m. lankaran Department of Mechanical Engineering Department of Mechanical Engineering University of minho Wichita State University Campus azure Wichita, KS 67260-133 4800-058 Guimaraes USA Portugal ISBN978-3-540-74359-0 e-ISBN978-3-540-74361-3 ISSN1613-7736 Library of Congress Control Number: 2007933833 o 2008 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broad casting, reproduction on microfilm or in any other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable for prosecution under the German Copyright Law The use of general descriptive names, registered names, trademarkS, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Cover design: WMX Design GmbH, Heidelberg Printed on acid-free paper 98786543210 springer. com Preface The primary goal of this book is to present suitable methodologies for dynamic analysis of multibody mechanical systems with imperfect or real joints, that is considering clearances, including their tribological characteristics and surface com pliance properties. Two-and three-dimensional methodologies for imperfect kine matic joints with and without lubrication are presented In the process, different contact-impact force models are revised in the face of their suitability to represent collision between the bodies connected by imperfect joints. The incorporation of friction forces, based on the Coulomb friction law, is also discussed together with an effective computational strategy. Further a general methodology which accounts for squeeze-film and wedge-film actions, including the cavitation effect, for modelin dynamically loaded journal-bearings is also presented The equations that govern the dynamical behavior of the general multibody me chanical systems incorporate the contact-impact forces due to collision between the bodies that constitute the imperfect joints, as well as the hydrodynamic forces owing to the lubrication effect The Newton-Euler's equations of motion and the general- ized Cartesian coordinates are used here. Elementary multibody mechanical systems are used to discuss the assumptions and procedures adopted. The main results ob tained from this research work show that the effect of imperfect joints, namely joints with clearance, can have a predictable nonlinear dynamic response This book is written for academics, students and practitioners in mechanical er gineering, design, researchers in the field and teaching staff. This book can also be used by students in the final year of MSc or in the beginning of Phd in mechanics and computation sciences Motivation and Contributions for this book Computer-aided multibody mechanical systems emerged over the last three decades as an important scientific part of Applied and Computational Mechanics, with sig nificant applications in several branches of engineering. This has been made possi ble not only thanks to the impressive improvement of the computer hardware and ftware but also due to the development of robust and accurate computational tools Preface which in turn generated a demand for the analysis of more complex mechanical systems. Not long ago, the design of machines and components was based on trial and error and knowledgeable craftsmanship. Later, algebraic methods for analy sis eliminated part of the limitations of the trial and error and led to documented methods used in the design of mechanical components In todays industry there is little room for error and a great need for optimized and cost-effective production of components and machines with high reliability and durability. still, all areas of research require the construction of models and. therefore the use of assumptions and approximations. The analysis of complex mechanical systems is an area where in the past few decades, faster data processing has lead to an increased research effort This includes kinematic and dynamic analyses synthesis and optimization of the motion of mechanical systems. The main objective of this book is to contribute to the improvement of the methodologies dealing with the analysis of realistic me chanical systems, which include imperfect or real joints, 1. e, joints in which the effects of clearance, misalignment, friction and lubrication are taken into account by employing the multibody systems formulation. In line with the multibody systems formulation, such systems can include several rigid and deformable bodies intercon nected to each other by different types of kinematic joints and being acted upon by forces and moments. These systems are characterized by large displacements and rotations having, generally, a nonlinear behavior None of the real mechanical systems have perfect mechanical joints because of the functional tolerances required between adjacent moving segments. Due to either the loads carried by the mechanical devices or the misalignments that are required for their operation, real joints must be lubricated or must include bushings, generally made with metals and polymers. By using rubber bushings a conventional mechan ical joint is transformed into a joint with clearance allowing for the mobility of the over-constrained system in which it is used. a good example of the application of these joints is vehicle dynamics in which the handling response or the vibration characteristics of land vehicles are greatly improved when these elements are used in the suspension system The mechanical joints of any industrial machine are obtained by allowing the relative motion between the components connected by them. Due to the manufac turing tolerances, wear or material deformation, these joints are imperfect and have clearances. These clearances modify the dynamic response of the system, justify the deviations between the numerical predictions and the experimental measurements and eventually lead to important deviations between the projected behavior of the mechanisms and their real outcome The attenuation of the impact response and of the vibration characteristics in industrial machines is obtained by including, in their design, a selection of joint clearances The imperfect joints with direct contact between the parts involved generally use lubrication to minimize the energy dissipation. Therefore appropriate tribological models must be devised in the framework of their application in general multibody systems. The characterization of the normal contact forces in the nonlubricated joints is realized by using the continuous contact force model while their tangential forces are obtained by using appropriate friction force models. The joints, which Preface have rubber bushings, can be described by a linear model that does not include coupling between radial and axial or bending loading or by a more advanced non linear model for rubber bushings The general-purpose computational tools used for the design and analysis of me chanical systems have a wide number of mechanical systems modeling features that require the description of rigid or flexible bodies for which geometry, mass, center of mass, moment of inertia and other relevant properties are defined The compu tational codes also provide a large library of kinematic joints that constrain relative degrees of freedom between connected bodies. The kinematic joints available in the commercial programs are represented as ideal joints that is, there are no clearances or deformations in them Thus modeling the dynamics of multibody mechanical sys tems with clearances and imperfections is a challenging issue in mechanical design and much work still remains to be done to achieve more advanced modeling tools This observation, coupled with the dearth of design guidelines in the field of mechanical systems with real or imperfect joints, and also the importance of such systems have motivated the work reported in this book Organization of the book An introduction and an overview of the book are provided in the first chapter. The remainder of this book consists of five more chapters, dealing with the different aspects involved in the study of imperfect joints in multibody mechanical systems In Chap. 2, the formulation of motions equations of multi-rigid body systems s described. The generalized coordinates are the centroidal Cartesian coordinates and the system configuration is restrained by constraint equations. The dynamic formulation uses the Newton-Euler's equations of motion, which are augmented with the constraint equations that lead to a system of differential algebraic equations Constraint violation stabilization methods and the coordinate partition method are also presented and discussed in this chapter. An elementary four-bar linkage is used as an application example to demonstrate the computational treatment of this type of systems Chapter 3 deals with contact-impact force models for both spherical-and cylindrical-shaped surface collisions in multibody mechanical systems. The inclu sion of friction forces based on Coulomb's friction law is also presented and dis- cussed for effective computational implementation Chapter 4 focuses on the modeling of planar clearance joints without lubricant namely revolute and translational joints with clearance. Kinematic aspects of rev- olute and translational joints with clearance are also presented Results for a basic slider-crank mechanism with a revolute clearance joint and a translational clearance joint are presented and used to discuss the assumptions and procedures adopted The fifth chapter covers the lubricated models for revolute clearance joints in multibody mechanical systems. The squeeze-film and wedge-film actions are con sidered as well as the cavitation effect. First, some techniques for modeling and Preface evaluating the forces in lubricated revolute joints are presented and applied to a simple journal-bearing under a constant and unidirectional external load. Finally,a slider-crank mechanism with a lubricated revolute joint is considered as a numerical example. Both the effect of the clearance size and oil lubricant viscosity effects are studied Chapter 6 describes the modeling of spatial clearance joints, namely spherical and revolute joints. a quick review on the formulation of spatial multibody sys tems is presented. In addition, a simple and brief description of the perfect spherical and revolute joints is done. Three simple multibody systems are used as illustrative examples, namely, the spatial four-bar mechanism, the double pendulum and the slider-crank mechanism Acknowledgments The road to this book has been long but rewarding. It has implied hard work, benefited from exceptional circumstances and fortunate opportunities, hesitated against minor difficulties, but eventually made its way receiving sometimes a stim ulating recognition from the international scientific community. However, that jour ney has certainly not been the result of a solitary commitment. many individuals and institutions have offered their support along the way, making it possible, visible and consequent Certainly we will forever be in debt to them We are grateful to Fundacdo para a Ciencia e a Tecnologia and Fundo comu nitario Europeu FEDER for sponsoring our research work, through project nr 38281 entitled ' Dynamic of Mechanical Systems with Clearances and Imperfections. This work was also supported by PRODEP under the project 5.3/N/189.015/01. This support is thankfully acknowledged We are indebted to Professor Michel fillon, university of poitiers for his stim ulating comments and suggestions on the lubrication issues. We would also like to express our sincere gratitude to Professor Parviz Nikravesh, university of arizona for sharing with us some thoughts, ideas and computational codes on the dynamics of multibody systems. We are also grateful to Professor Werner Schiehlen, Uni versity of Stuttgart, for his feedback on the history of mechanics and multibody dynamics and to Professors Peter Eberhard, University of Stuttgart, and Cristoph Glocker. ETh Zurich. for their comments on the contact mechanics Finally, we would like to thank our families and our friends in different countries around the world for their never-ending encouragement, constant moral support and belief in our ability to do the work

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