Journal ArticleDOI

# Multiple Impacts of a Ball Between Two Plates—Part 2: Mathematical Modelling

01 Aug 1975-Journal of Engineering for Industry (American Society of Mechanical Engineers)-Vol. 97, Iss: 3, pp 828-835
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.

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Journal ArticleDOI
Gabriele Gilardi1, Inna Sharf1Institutions (1)
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.

Abstract: Impact is a complex phenomenon that occurs when two or more bodies undergo a collision. This phenomenon is important in many different areas––machine design, robotics, multi-body analysis are just a few examples. The purpose of this manuscript is to provide 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. The paper is intended to provide a review of results presented in literature and some additional insights into existing models, their interrelationship and the use of these models for impact/contact scenarios encountered in space robotic applications.

644 citations

### Cites background from "Multiple Impacts of a Ball Between ..."

• ...Other researchers have measured e for specific contact situations, such as the collision of steel bars with external surfaces [56], impact of an unconstrained slender bar with a massive surface [43], impacts of a steel sphere moving between two plates [61], and the oblique impact between a sphere and a plate [62]....

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Journal ArticleDOI
Jianjun Wang1, Runfang Li2, Xianghe Peng2Institutions (2)

173 citations

Journal ArticleDOI
TL;DR: A comprehensive survey of the literature of the most relevant analytical, numerical, and experimental approaches for the kinematic and dynamic analyses of multibody mechanical systems with clearance joints is presented in this review.

Abstract: A comprehensive survey of the literature of the most relevant analytical, numerical, and experimental approaches for the kinematic and dynamic analyses of multibody mechanical systems with clearance joints is presented in this review. Both dry and lubricated clearance joints are addressed here, and an effort is made to include a large number of research works in this particular field, which have been published since the 1960′s. First, the most frequently utilized methods for modeling planar and spatial multibody mechanical systems with clearance joints are analyzed, and compared. Other important phenomena commonly associated with clearance joint models, such as wear, non-smooth behavior, optimization and control, chaos, and uncertainty and links’ flexibility, are then discussed. The main assumptions procedures and conclusions for the different methodologies are also examined and compared. Finally, future developments and new applications of clearance joint modeling and analysis are highlighted.

171 citations

45

Journal ArticleDOI
R.S Haines1Institutions (1)
Abstract: The survey is confined to plain unlubricated revolute joints in which the relative motion is sensibly 2-dimensional, a topic shown to give rise to certain distinctive problems Emphasis is placed on motion in continuous contact, but relative motion across the clearance, impact and rebound, and restoration of continuous contact are also covered The relevant published work is subjected to critical review, and some outstanding uncertainties are highlighted

66 citations

Journal ArticleDOI
C.N. Bapat1, N. Popplewell1, K. McLachlan1Institutions (1)
Abstract: The asymptotically stable motion of two rigid masses separated by a clearance is formulated most generally when the masses collide periodically. Predictions are shown to agree satisfactorily with comprehensive experimental results. Difficulties encountered in the practical application of this and similar stability theories are discussed with the help of empirical data. A technique is proposed for determining a clearance's dimensions in situ which could provide a basis for detecting progressive wear in mechanisms like gear trains.

65 citations

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