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Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach

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Abstract

The main purpose of this paper is to present and discuss a methodology for a dynamic modeling and analysis of rigid multibody systems with translational clearance joints. The methodology is based on the non-smooth dynamics approach, in which the interaction of the elements that constitute a translational clearance joint is modeled with multiple frictional unilateral constraints. In the following, the most fundamental issues of the non-smooth dynamics theory are revised. The dynamics of rigid multibody systems are stated as an equality of measures, which are formulated at the velocity-impulse level. The equations of motion are complemented with constitutive laws for the normal and tangential directions. In this work, the unilateral constraints are described by a set-valued force law of the type of Signorini’s condition, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb’s law for dry friction. The resulting contact-impact problem is formulated and solved as a linear complementarity problem, which is embedded in the Moreau time-stepping method. Finally, the classical slider-crank mechanism is considered as a demonstrative application example and numerical results are presented. The results obtained show that the existence of clearance joints in the modeling of multibody systems influences their dynamics response.

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Authors and Affiliations

  1. Mechanical Engineering Department, University of Minho, Campus de Azurém, 4800-058, Guimarães, Portugal

    Paulo Flores

  2. Department of Mechanical and Process Engineering, Center of Mechanics, IMES – Institute of Mechanical Systems, 8092, Zurich, Switzerland

    Remco Leine & Christoph Glocker

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  1. Paulo Flores
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  2. Remco Leine
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  3. Christoph Glocker
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Correspondence to Paulo Flores.

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Flores, P., Leine, R. & Glocker, C. Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach. Multibody Syst Dyn 23, 165–190 (2010). https://doi.org/10.1007/s11044-009-9178-y

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