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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
TL;DR: 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.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the impact between two elastic bodies with a liquid lubricant is modeled as a linear combination of the impact load and the coefficient of restitution with reasonable accuracy for a wide range of the problem domain.
Abstract: This paper complements several previous papers on modeling of the impact between two elastic bodies with a liquid lubricant. The main feature of the work is the efficient incorporation of various engineering aspects of the impact process making use of approximations consistent with the physical insights of the problem. The model can very efficiently calculate the impact load and the coefficient of restitution with reasonable accuracy for a wide range of the problem domain. The modeling concepts and methodology may be useful in future research on interdisciplinary analyses of the dynamics of mechanical systems in which the interactions are strong between vibrations of the components and impacts in the lubricated kinematic pairs.

24 citations

Journal ArticleDOI
TL;DR: In this paper, a non-resonant electrostatic energy harvester targeted at the wideband frequency response for micro-system powering is presented, where the vertical gap changing method is adopted to induce variable charges, which generates approximately 17 times of charge change compared with the conventional method of laterally changing overlap area (at 1 mm gap).
Abstract: Presented is a novel non-resonant electrostatic energy harvester targeted at the wideband frequency response for micro-system powering. To boost non-resonance power output under low frequency, the vertical gap changing method is adopted to induce variable charges, which generates approximately 17 times of charge change compared with the conventional method of laterally changing overlap area (at 1 mm gap). Further, to boost the low frequency and non-resonant power generating capability, the differential structure is adopted to achieve doubled output voltages. Testing results reveal that optimal output power occurs when the inner plate is of large effective movement range and large relative displacement with surrounding electrets. Maximally, 3.9–7.0 V voltage and 0.2–0.7 μW power are achieved over the 5–120 Hz frequency range.

18 citations

Journal ArticleDOI
TL;DR: In this article, a new cam-follower system experiment was used to estimate the impact damping model parameters, which was designed to precisely measure the forces and acceleration during impulsive events.

15 citations


Cites result from "Multiple Impacts of a Ball Between ..."

  • ...Some reasons for the difference between the β values are: a) Hunt and Crossley [24] derived the relationship for vibroimpacts under dry conditions assuming pure metal to metal contact, but the experiments were under lubricated condition; b) even a small change in n value affects β significantly; and c) the ξ concept has an inherent drawback [9,23] and hence the experimental estimation of γ might have some inaccuracies....

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Journal ArticleDOI
01 Dec 1994-Chaos
TL;DR: It is shown that the state is always changed into a saddle point after a bifurcation of the vibroimpacting one-degree-of-freedom model, and transversal homoclinic points are found to exist for some of these parameter combinations.
Abstract: The motion of a vibroimpacting one‐degree‐of‐freedom model is analyzed. This model is motivated by the behavior of a shearing granular material, in which a transitional phenomenon is observed as the concentration of the grains decreases. This transition changes the motion of a granular assembly from an orderly shearing between two blocks sandwiching a single layer of grains to a chaotic shear flow of the whole granular mass. The model consists of a mass‐spring‐dashpot assembly that bounces between two rigid walls. The walls are prescribed to move harmonically in opposite phases. For low wall frequencies or small amplitudes, the motion of the mass is damped out, and it approaches a stationary state with zero velocity and displacement. In this paper, the stability of such a state and the transition into chaos are analyzed. It is shown that the state is always changed into a saddle point after a bifurcation. For some parameter combinations, horseshoe‐like structures can be observed in the Poincare sections. Analyzing the stable and unstable manifolds of the saddle point, transversal homoclinic points are found to exist for some of these parameter combinations.

11 citations

Proceedings ArticleDOI
10 Dec 1997
TL;DR: In this paper, a dynamic model of two mating gears is determined in three different cases: in the ideal case, in which the gears are rigid and no backlash is present; when the gears were flexible, in absence of backlash; in a realistic case, both the elasticity of the gears and the presence of backlash are to be taken into account.
Abstract: The paper deals with the problems related to the mechanical gears, which are commonly used for manipulators and servomechanisms, when elasticity and backlash affect their connection. The dynamic model of two mating gears is determined in three different cases: in the ideal case, in which the gears are rigid and no backlash is present; when the gears are flexible, in absence of backlash; in a realistic case, in which both the elasticity of the gears and the presence of backlash are to be taken into account. The same control algorithm, a PD one, is then applied to the three different cases, under the assumption that only the position and the velocity of the driving gear are available for feedback. The properties of the solutions of the closed-loop systems thus obtained are studied and analytically proven in the paper. Some simulation results complete and confirm the analysis.

8 citations