Dynamic Analysis of Mechanical Systems With Clearances—Part 1: Formation of Dynamic Model
01 Feb 1971-Journal of Engineering for Industry (American Society of Mechanical Engineers)-Vol. 93, Iss: 1, pp 305-309
TL;DR: A mathematical model of an elastic mechanical joint with clearances has been formulated and the dynamical equations of motion derived (Part I). The model, which we have called an Impact Pair, is basic to the determination of the dynamic response of mechanical and electromechanical systems as mentioned in this paper, including determination of dynamic force amplification, frequency response, time displacement characteristics, and other dynamic characteristics.
Abstract: A mathematical model of an elastic mechanical joint with clearances has been formulated and the dynamical equations of motion derived (Part I). The model, which we have called an Impact Pair, is basic to the determination of the dynamical response of mechanical and electromechanical systems with clearances, including determination of dynamic force amplification, frequency response, time-displacement characteristics, and other dynamic characteristics. Whenever possible, the results for the impact pair under various operating conditions are illustrated by graphs, which may also offer some insight into the behavior of clearance-coupled systems.
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TL;DR: In this paper, the Kelvin-Voigt model is shown to be logically untenable, for it indicates that the bodies must exert tension on one another just before separating, and it denotes that the damping energy loss is proportional to the square of the impacting velocity, instead of to its cube.
Abstract: During impact the relative motion of two bodies is often taken to be simply represented as half of a damped sine wave, according to the Kelvin-Voigt model. This is shown to be logically untenable, for it indicates that the bodies must exert tension on one another just before separating. Furthermore, it denotes that the damping energy loss is proportional to the square of the impacting velocity, instead of to its cube, as can be deduced from Goldsmith's work. A damping term $\lambda x^n \dot{x} $ is here introduced; for a sphere impacting a plate Hertz gives $n = 3/2$. The Kelvin-Voigt model is shown to be approximated as a special case deducible from this law, and applicable when impacts are absent. Physical experiments have confirmed this postulate.
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TL;DR: An overview of the state of the art on impact and contact modelling methodologies, taking into account their different aspects, specifically, the energy loss, the influence of the friction model, solution approaches, the multi-contact problem and the experimental verification is provided.
690 citations
TL;DR: In this paper, the main issues associated with the most common compliant contact force models of this type are analyzed in terms of the dynamic simulations of multibody systems, which allow for the comparison of the similarities and differences among the models considered.
474 citations
TL;DR: The status and some recent developments in computational modeling of flexible multibody systems are summarized in this article, where a number of aspects of flexible multi-body dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies.
Abstract: The status and some recent developments in computational modeling of flexible multibody systems are summarized. Discussion focuses on a number of aspects of flexible multibody dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies. The characteristics of the three types of reference frames used in modeling flexible multibody systems, namely, floating frame, corotational frame, and inertial frame, are compared. Future directions of research are identified. These include new applications such as micro- and nano-mechanical systems; techniques and strategies for increasing the fidelity and computational efficiency of the models; and tools that can improve the design process of flexible multibody systems. This review article cites 877 references. @DOI: 10.1115/1.1590354#
360 citations
TL;DR: In this paper, a computational methodology for dynamic analysis of multibody mechanical systems with joint clearance is presented, based on a thorough geometric description of contact conditions and on a continuous contact force model, which represents the impact forces.
287 citations