Journal ArticleDOI
Multiple Impacts of a Ball Between Two Plates—Part 2: Mathematical Modelling
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In this article, a mathematical model is developed to portray the vibroimpacts of a steel sphere which is trapped between two flat steel plates with clearance, while the plates are oscillated by an electromagnetic shaker.Abstract:
A mathematical model is developed to portray the vibroimpacts of a steel sphere which is trapped between two flat steel plates with clearance, while the plates are oscillated by an electromagnetic shaker. Data from a long series of experimental observations are reported in Part 1 of this paper [53]. The aim is to determine a law of motion by which a computer simulation can satisfactorily reproduce the major characteristics of the observed movement. During each impact the motion of the ball is taken to be a brief half wave, due to the highly nonlinear forces of surface compliance and surface damping. Modelling is by analog simulation. It was found first that linearization of the surface stiffness does not reproduce the observed phenomena. The mathematical model formulated is that the motion of the ball during contact is governed by the equation mx + cx1.5 x + kx1.5 = 0, where x is the penetration, c is a damping constant, and kx1.5 is the Hertzian force of compliance. The results of experiments can be corroborated only on the basis of a variable damping coefficient cxn with n = 3/2.read more
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Journal ArticleDOI
Impact behaviour of an oscillator with limiting stops, part I: A parametric study
TL;DR: In this article, the impact of a periodically forced oscillator with limiting stops on the frequency and intensity of contacts with the stops is investigated. Butler et al. examined the influence of the various excitation and physical variables of the system on the frequencies and intensities of contact with stops.
Journal ArticleDOI
Effect of nonlinear impact damping on the frequency response of a torsional system with clearance
TL;DR: In this paper, the impact damping model with a linear spring was examined along with the clearance nonlinearity including the backlash problem, and three semi-analytical methods, namely, Describing Function Method, Multi-term Harmonic Balance Method and Stochastic Linearization Method, were used to investigate the effect of impact damp.
Journal ArticleDOI
The experimental response of an impacting pendulum system
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Proceedings ArticleDOI
An impact model of mechanical backlash for control system analysis
J.C. Gerdes,Vijay Kumar +1 more
TL;DR: In this article, the authors present a model of mechanical backlash which incorporates viscoelastic contact forces between the two masses and show that low amplitude motions are dominated by stable impact patterns, or contact regimes, which differ greatly from the predictions of simple backlash models.
Journal ArticleDOI
On Crossley's contribution to the development of graph based algorithms for the analysis of mechanisms and gear trains
TL;DR: This paper celebrates a particular branch of Crossley's early work dedicated to Mechanism Science, which deals with a rigorous introduction of Graph Theory to the study of some fundamental and intrinsic properties of kinematic chains and mechanisms.
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